Directionally solidified eutectic ceramic oxides

Progress in Materials Science 51 (2006) 711–809

www.elsevier.com/locate/pmatsci

Directionally solidified eutectic ceramic oxides

Javier LLorca a,*, Victor M. Orera b

a Departamento de Ciencia de Materiales, Universidad Politecnica de Madrid, E.T.S. de Ingenieros de Caminos,

28040 Madrid, Spainb Instituto de Ciencia de Materiales de Aragon, CSIC/Universidad de Zaragoza, 50009 Zaragoza, Spain

Received 2 August 2005; accepted 17 October 2005

Abstract

The processing, structure and properties (mechanical and functional) of directionally solidifiedeutectic ceramic oxides are reviewed with particular attention to the developments in the last 15years. The article analyzes in detail the control of the microstructure from the processing variables,the recently gained knowledge on their microstructure (crystallographic orientation, interface struc-ture, residual stresses, etc.), the microstructural and chemical stability at high temperature, the rela-tionship between the eutectic microstructure and the mechanical properties, and the potential ofthese materials as patterning substrates for thin films, templates to manufacture new compositematerials, photonic materials and electroceramics. The review highlights the achievements obtainedto date, the current limitations and the necessary breakthroughs.� 2005 Elsevier Ltd. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7122. Eutectic oxide systems and processing techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714

0079-6

doi:10

* CoE-m

2.1. Oxide eutectic systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7142.2. Coupled eutectic growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7152.3. Eutectic range . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7222.4. Preparation techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

425/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

.1016/j.pmatsci.2005.10.002

rresponding author. Tel.: +34 91 336 5375; fax: +34 91 543 7845.ail address: [email protected] (J. LLorca).

mailto:[email protected]

712 J. LLorca, V.M. Orera / Progress in Materials Science 51 (2006) 711–809

3. Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 731
3.1. DSE oxides microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7323.2. Crystallography and interfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736
4. Microstructural and chemical stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741
4.1. Microstructural stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7414.2. Oxidation and chemical resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 746
5. Residual stresses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747
5.1. Origins . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7475.2. Measurement techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7485.3. Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7505.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753
5.4.1. Al2O3–YSZ system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7545.4.2. Al2O3–YAG system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7605.4.3. NiO–ZrO2 and Co1�xNixO–ZrO2 systems . . . . . . . . . . . . . . . . . . . . . . . 7605.4.4. Al2O3–YAG–YSZ ternary eutectic system . . . . . . . . . . . . . . . . . . . . . . . 762

6. Mechanical behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 762
6.1. Elastic modulus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7636.2. Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 764
6.2.1. Ambient temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7646.2.2. High temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7696.2.3. Anisotropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 775

6.3. Hardness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7756.4. Fracture toughness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7756.5. Creep deformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7786.6. Subcritical crack growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 782

7. Functional properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783
7.1. Substrates for thin film deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783
7.1.1. YBCO in CaSZ/CaZrO3 (CZO) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7857.1.2. LCMO in CaSZ/CZO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7877.1.3. YBCO in MgSZ/MgO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

7.2. Structured Ni/YSZ and Co/YSZ composites . . . . . . . . . . . . . . . . . . . . . . . . . . 7877.3. Photonic materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 791

7.3.1. Optical waveguides . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7937.3.2. Effect of microstructure size on luminescence. . . . . . . . . . . . . . . . . . . . . 795

7.4. Electroceramics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7987.5. Bioeutectics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 800

8. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 801Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 804

1. Introduction

Eutectics are a paradigm of composite materials with a fine microstructure on the lmscale whose characteristics are controlled by the solidification conditions. These in situcomposites have been studied for decades because of their excellent mechanical propertiesinherent to the reduced interphase spacing, homogeneous microstructure and large surfacearea of clean, strong interfaces. Attention in the past was mainly focused on metalliceutectics, and most of the advances in the comprehension of eutectic growth and micro-structure were achieved in these materials [1]. Less effort was devoted to ceramic eutectics,

J. LLorca, V.M. Orera / Progress in Materials Science 51 (2006) 711–809 713

notwithstanding the pioneer work on some oxide–oxide systems (such as Al2O3–ZrO2 orZrO2–CaZrO3 [2]). These early studies demonstrated the outstanding mechanical proper-ties and the thermal and microstructural stability of directionally solidified eutectic (DSE)ceramic oxides, as compared with conventional composites and monolithic ceramics [3].

Recently, interest in DSE ceramic oxides has been renewed by the synergistic effect of newdevelopments in the processing and characterization techniques. From the point of view ofprocessing, the key to obtaining a homogeneous microstructure is to keep flat solid–liquidinterfaces during growth at microscopic and macroscopic level, and this requires large ther-mal gradients in the solidification direction. The Bridgman method used in the 1970s togrow DSE is limited to thermal gradients below 102 K/cm but new processing techniquesdeveloped recently can reach thermal gradients in the range 103–104 K/cm, providing moredegrees of freedom to control the microstructure through changes in processing variables.This led to a better understanding of the physical mechanisms which control the microstruc-tural development upon directional solidification [4]. In addition, the knowledge of the rela-tionship between the eutectic microstructure and the properties has profited from thewidespread use of better techniques of microstructural characterization. This includeshigh-resolution transmission electron microscopy of the interfaces, the determination ofthe orientation relationship between the eutectic phases [5], and the precise evaluation ofresidual stresses by X-ray diffraction [6] and piezospectroscopic techniques [21].

As a result of the advances in processing and characterization, DSE ceramic oxides withnovel microstructures have been developed in the last 15 years. Al2O3-based DSE withminimum interphase spacing and free of large defects showed excellent mechanical prop-erties up to temperatures very close to the melting point [7,8], as well as outstanding micro-structural stability and corrosion resistance. This new generation of DSE ceramic oxidespresents important advantages over conventional structural ceramics for high temperaturestructural applications. In addition, Galasso [9] showed nearly four decades ago the poten-tial of some DSE for optical, electronic or magnetic applications. Regular eutectics withordered microstructures of either single crystal rods embedded in a single crystal matrixor alternating lamellae behave as planar optical waveguides, as reported in ZrO2–CaOeutectics [10], while CaF2/MgO fibrous eutectics can be viewed as an array of micron-sizedsingle crystalline optical fibers with a density of 40,000 fibers/mm2 [11]. From the point ofview of optical spectroscopy, eutectics made from large optical band gap materials, such asinsulator compounds, present the unusual characteristic of being at the same time a mono-lith and a multiphase material, and the optically active ions can be placed in different crys-tal field environments in the same material, as reported in ZrO2–CaO eutectics activatedwith Er3+ ions [12]. Finally, new applications have appeared recently in the areas of electro-ceramic and biomaterial engineering.

These recent developments in processing, microstructural characterization and mechan-ical and functional properties of DSE ceramics oxides are reviewed in this paper, which isstructured as follows. After the introduction, the Section 2 describes briefly the mostimportant DSE ceramic oxide systems and analyzes in detail the mechanisms of coupledeutectic growth, necessary to understand the relationship between processing and micro-structure. Section 3 shows the rich variety of eutectic microstructures found in these mate-rials, and special attention is paid to the crystallographic orientation of the phases andinterfaces. Section 4 analyzes the kinetics of phase coarsening in DSE ceramic oxides athigh temperature and their chemical and oxidation resistance, while thermo-elastic resid-ual stresses in DSE are studied in Section 5, which covers the origin, experimental


techniques, and models to determine their magnitude. The main mechanical properties ofthese materials (elastic modulus, strength, hardness, toughness, creep resistance) and theirrelationship to the eutectic microstructure and composition are summed up in Section 6,while Section 7 explores new functional applications of DSE ceramic oxides as patterningsubstrates for thin films, templates to manufacture for new composite materials, photonicmaterials and electroceramics. The review ends with Section 8, where the achievementsobtained to date, the current limitations and the necessary breakthroughs are considered.

2. Eutectic oxide systems and processing techniques

DSE may be defined as composite materials with a complex and homogeneous micro-structure which controls their properties. Hence, most of the research has been aimed atunderstanding the relationship between microstructure and properties, and at controllingthe growth processes to obtain the desired microstructure for specific applications. In thisframework, the first question to answer is how the properties of the eutectic depend uponthose of their components. Broadly speaking, composite properties can be divided in twocategories, namely additive and product properties [13]. The former depend only on thevolume fraction and spatial distribution of the phases and their magnitude is limited bythe maximum and minimum values of the composite phases. Examples of additive prop-erties are elastic stiffness, electrical conductivity and mass density. Product properties arethose that depend on the interaction between the composite phases and thus are controlledby structural factors such as periodicity or phase size. Of course, product properties arenot bounded by the phase properties and may exist in the composite but not in the indi-vidual phases. Examples of product properties in DSE oxides are optical interference orhardness. Finally, it should be noted that the eutectic phases are usually solid solutionswhose characteristics depart from those of the pure phases. In summary, the mechanicaland functional properties of DSE are strongly dependent on the characteristics of themicrostructure (morphology, phase shape and size), which can be controlled to someextent during the solidification process. This section describes the process of eutectic solid-ification from the melt after a brief description of the main DSE ceramic oxides systemswhich present interesting properties for engineering applications.

2.1. Oxide eutectic systems

Several eutectic oxide systems have been studied in the past. The reviews from Minfordet al. [3], Ashbrook [14] and Revcolevschi et al. [5] describe the investigations carried out until1990 in DSE ceramic oxides. More recent efforts have been focused on Al2O3-based eutecticsbecause the outstanding creep resistance of sapphire along the c-axis was combined with otheroxide properties to create new families of compounds with exceptional thermo-mechanicalproperties. In particular, binary and pseudo-binary eutectics, ternary eutectics and even someoff-eutectic compositions of the ternary system Al2O3–ZrO2–Y2O3 were explored in detailfollowing the phase diagram for this system presented by Lakiza and Lopato [15]. Thisincludes the Al2O3/Y3Al5O12 (YAG) system, extensively studied because of its exceptionalcreep resistance [16–19], and the Al2O3/ZrO2 system. The addition of Y2O3 to Al2O3/ZrO2

led to the pseudo-binary Al2O3/ZrO2(Y2O3) eutectic in which different zirconia polymorphs(monoclinic, tetragonal or cubic zirconia) could be obtained just by changing the yttria con-tent. The presence of the zirconia polymorphs gave rise to a rich variety of microstructural


morphologies and residual stress states, which controlled the mechanical properties [20,21].More recently, attention has been paid to the oxide ternary compounds, such as Al2O3/YAG/YSZ (yttria-stabilized zirconia), to further improve the excellent mechanical propertiesof their binary counterparts [22,23]. In addition, rare-earth aluminates–sapphire of theAl2O3/(RE)AlO3 (RE = rare earth) families are eutectic composites made up by sapphirein combination with either perovskite (in the case of the larger rare-earth ions as Sm, Eu,Gd) or garnet phases (in the case of the smaller rare-earth ions Sm, Lu, Y) [7,24].

Magnesium spinel (MgAl2O4) is another well-known oxide material with excellent ther-mal and chemical resistance and two different spinel-based eutectics were grown. MgO/MgAl2O4 eutectic consisted of thin MgO crystalline fibers embedded into the spinel matrix[25]. Conversely, the fosterite-spinel eutectic is composed of MgAl2O4 fibers within aMg2SiO4 matrix. Interestingly, it was reported that the silicate matrix could be removedin this eutectic to obtain isolated spinel fibers of 50 lm in length [26].

ZrO2-based eutectics make up a family of eutectic oxides, which is of interest because oftheir functional applications. For example, the microstructure of the NiAl2O4/YSZ eutec-tic is of highly ordered colonies of YSZ fibers in a hexagonal arrangement embedded in aNiAl2O4 single crystal matrix, and Ni nanoparticles were produced by chemical reductionof the Ni-spinel matrix [27]. The reduction from NiAl2O4to Ni took place throughout thesample as the YSZ fibers acted as channels for oxygen ion transportation from the externalsurface, thus producing a homogeneous reduction of the spinel domains. The same prin-ciple was used to produce very stable Ni (or Co) porous cermets from lamellar NiO/CaSZ(CaO stabilized-zirconia) or NiO/YSZ eutectics, which were envisaged as potential mate-rials for fuel cell anodes or as catalysts [28]. In addition, CaSZ/CaZrO3 eutectics presentedrelatively large (several mm3) regions of well-aligned lamellae, which led to anisotropicionic conductivity and light waveguide effects [27].

Fibrous MgO–MgSZ (MgO-stabilized ZrO2) eutectics present a structure formed by analmost hexagonal array of MgO fibers of �1 lm diameter embedded within a MgSZ singlecrystal matrix, and interesting optical effects were reported in CaF2/MgO and MgF2/MgOeutectics with a similar structure in which the light is transmitted through the MgO singlecrystalline fibers with a higher refractive index [29,11]. Moreover, Revcolevschi et al. [5]have reviewed in detail other eutectic oxide families of either MO (M = 3d ions) and/orRE2O3 (RE = rare-earth ions) oxides. These systems comprised lamellar NiO/CaO [30],NiO/Y2O3 [31] and NiO/Gd2O3 [32], and fibrous NiO in NiAl2O4 (Ni-spinel) [33].

The composition and the eutectic temperature of the most relevant DSE ceramic oxidesystems is given in Table 2.1. Of course, there are other DSE oxide systems with potentialinterest for engineering applications but they are not addressed in this review because ofthe lack of information available. The only exception will be the CaSiO3/Ca3(PO4)2 eutec-tic composite, which presents two unconventional and interesting properties: firstly, thedegenerated lamellar structure of the system favored the biological transformation ofthe tricalcium phosphate phase into hydroxiapatite, giving rise to a biological materialwith a microstructure similar to that of human bone [34]. Secondly, it is possible to forma eutectic glass of this composition with excellent optical properties [35].

2.2. Coupled eutectic growth

A crucial aspect of the study of eutectic systems is the understanding of the dynamics ofeutectic growth. Since the pioneering ideas of Zener [36] and Tiller [37], a lot of excellent

Table 2.1Eutectic phases, eutectic temperature, TE, composition, and vk2 (v growth rate, k interphase spacing) of someoxide eutectics

Eutectic phases TE (K) Composition(wt%)

% Volume(minor phase)

vk2 (lm3/s) Reference

Al2O3/YSZa 2135 42YSZ + 58Al2O3 32.7ZrO2 11 [62]Al2O3/Y3Al5O12 2100 33.5Y2O3 + 66.5Al2O3 45Al2O3 100 [16]Al2O3/Er3Al5O12 2075 52.5Al2O3 + 47.5Er2O3 42.5Al2O3 �60 [59]Al2O3/EuAlO3 1985 46.5Al2O3 + 53.5Eu2O3 45Al2O3 – [24]Al2O3/GdAlO3 2015 47Al2O3 + 53Gd2O3 48Al2O3 6.3 [233]Al2O3/Y3Al5O12/YSZ 1990 54Al2O3 + 27Y2O3 + 19ZrO2 18YSZ 70 [22]Ca0.25Zr0.75O1.75/CaZrO3 2525 23.5CaO + 76.5ZrO2 41CaSZ 400 [3]Mg0.2Zr0.8O1.8/MgO 2445 27MgO + 73ZrO2 28MgO 50 [3]YSZ/NiAl2O4 2270 54NiAl2O4 + 46Zr0.85Y0.15O1.92 39YSZ 8 [27]CaSZ/NiO 2115 61NiO + 39Zr0.85Ca0.15O1.85 44CaSZ 32.5 [234]CaSZ/CoO 2025 64CoO + 36Zr0.89Ca0.11O1.89 38.5CaSZ 25 [235]MgAl2O4/MgO 2270 45MgO + 55Al2O3 23.5MgO 150 [25]CaF2/MgO 1625 90CaF2 + 10MgO 9MgO 68 [11]

a Tetragonal or cubic yttria-stabilized zirconia.


work has been published on this topic. For instance, Hecht et al. [38] have recentlyreviewed the experimental and theoretical aspects of the solidification of multiphase mate-rials, including the advances in phase field modeling. Kurz and Fisher [39] described thefundamentals of solidification including eutectic growth and rapid solidification from avery tutorial point of view, while Hunt and Lu [40] and Magnin and Trivedi [41] appliedthe current solidification theories to eutectic growth. Finally, Hogan et al. [42] focused onmodels to explain the development of eutectic microstructures.

A characteristic of eutectic structures is the simultaneous growth of two or more phasesfrom the melt, and a summary of the theoretical bases of coupled eutectic growth is pre-sented in this section, as they elucidate the microstructural features found in DSE ceramicoxides. Regular lamellar growth is assumed for the sake of simplicity and a typical phasediagram is shown in Fig. 2.1(a) for a binary eutectic a/b with lamellar structure and lamel-lar spacing k. The relevant magnitudes of this diagram are the eutectic temperature, TE,the growth temperature T0, the eutectic composition CE (wt%), and the slopes of the liq-uidus lines ma and mb for the a and b phases, respectively. When T0 < TE (under-cooling),the reduction in the free energy of the liquid at CE is the driving force behind the growth ofboth a and b phases while the solid phases of compositions Cs

a and Csb are in equilibrium

with the liquid at the growth temperature T0. The segregation phenomenon can bedescribed by the partition coefficient defined as ka ¼ Cs

a=Cla in equilibrium. A solute redis-

tribution takes place because each solid phase rejects the other solute component and theconcentration profile in the liquid ahead of the lamella tips is no longer a flat surface (seeFig. 2.1(b)). Extensive lateral mixing takes place as a consequence of this concentrationgradient at the a–b interface, and a diffusion flux parallel to the solid–liquid interfacereduces the concentration oscillation to values between Cl

a and Clb, as depicted in

Fig. 2.1(b). The concentration gradients across the solid–liquid interface, which aredefined by DCC = C(z) � CE (both a and b phases), decrease exponentially with z in thegrowth direction along a boundary layer given by dC = 2D/v, D being the diffusion coef-ficient in the liquid and v the growth rate. The compensation between the lateral flux, scale

Fig. 2.1. (a). Schema of a typical temperature–composition phase diagram of a binary eutectic with lamellarstructure. The liquidus and solidus lines are assumed to be straight and thus the partition coefficients ka and kb areindependent of the concentration. The tie line between the a and b solid solution fields at the eutectic temperatureTE gives the equilibrium concentrations of the eutectic phases. (b) Concentration profile in the liquid ahead of thelamella tips, which determines the boundary layer.


length k, and the flux perpendicular to the growth front, scale length dC, produces theeutectic-coupled growth. The concentration gradient is equivalent to a temperature gradi-ent according to the phase diagram, which is given for the phase i (=a,b) as

DT C ¼ �miDCC ð2:1Þin which mi is the liquidus slope (Fig. 2.2). The temperature at the interface also dependson other factors such as the interface curvature (also called capillarity effect), DTr and thekinetic under-cooling DTK.

The curvature under-cooling is taken into account by the Gibbs–Thomson equation,and is given by

Fig. 2.2. Contributions of solute under-cooling, DTC, and curvature under-cooling, DTr, to the total under-cooling DT0. DTC is proportional to DC ¼ Cl

a � Clb.


DT r ¼2c

rDSm

ð2:2Þ

for a sphere of radius r in which c is the solid–liquid surface energy and DSm the fusionentropy per unit volume. A positive under-cooling (decrease in melting point) producesa surface convex towards the liquid phase. The Gibbs–Thomson principle states thatthe higher the curvature radius of the solid–liquid interface the lower the solute concentra-tion in the liquid phase in equilibrium. This contribution to the under-cooling is importantfor radii equal to or lower than 10 lm.

The kinetic under-cooling increases with growth rate and is generally negligible in com-parison with the other contributions in most metals but it can be large in systems with highentropy of melting, such as ceramic oxides, even at low growth rates.

Hence the overall under-cooling, DT0, is obtained by adding the three contributions

DT 0 ¼ T E � T 0 ¼ DT C þ DT r þ DT K ð2:3Þand it can be nearly constant along the solid–liquid interface if the curvature of the solid–liquid interfaces in each phase varies along the interface to compensate for constitutionalunder-cooling (Fig. 2.2).

Solidification is a surface reaction whose rate depends upon the degree of under-coolingthat drives it. Steady-state solidification produces regular lamellar or fibrous eutectic struc-tures where the flat interface moves at uniform and constant speed v. In a reference framemoving with the interface, z! z � vt, the diffusion field equations are

r2T ¼ �KoToz; ð2:4Þ

r2C ¼ � vD

oCoz; ð2:5Þ

K being the thermal diffusion coefficient and C ¼ Cli (i = a,b). As explained by Davis [43],

if solute diffusion in the solid phase is negligible (one sided model) and D� K (frozen tem-perature approximation, FTA), the temperature in both solid and liquid phase can be de-fined by a constant thermal gradient GT,

T ¼ T E þ GTz. ð2:6Þ


If the densities of the a and b phases are equal, and the regular microstructure inter-spacing is given by k = ta + tb, the solution to Eq. (2.5) is [44,45]

C ¼ CE þX1n¼0

Bn exp �xnz cos2npx

k

� �� ; ð2:7Þ

in which

xn ¼v

2Dþ v

2D

� �2

þ 2npk

� �2" #1=2

. ð2:8Þ

It is worth noting in Eq. (2.7) the exponential decay along the z (growth) direction andthe periodic fluctuation of the concentration in x. The coefficients Bn are determined byimposing the mass conservation law at the interface in Eq. (2.7). If the eutectic interfaceis assumed to be planar to simplify the problem, the average concentration Ci and theaverage constitutional under-cooling DT C ¼ miðCE � CiÞ can be easily evaluated [45].

The second source of under-cooling is the curvature of the a � l and b � l interfaces(Fig. 2.3), which changes the equilibrium temperature. An average change in the liquidustemperature can be estimated from the average curvature, and the capillarity effect can bedescribed from Eq. (2.2) as

DT r;i ¼2ai

tiwith i ¼ a; b; ð2:9Þ

in which ti is the thickness of the lamella of phase i and ai = Ci sinhi, where Ci = (TE/Li)ci isthe Gibbs–Thomson coefficient, Li the heat of fusion per unit volume and ci the interfacialsolid–liquid energy of phase i. The contact angle, hi, at the three contact points (Fig. 2.3)obeys the equilibrium relationships

ca cos ha ¼ cb cos hb and ca sin ha þ cb sin hb ¼ cab; ð2:10Þ

cabbeing the solid–solid interfacial energy. Curvature under-cooling is clearly caused bythe increase of interface energy. An insight into the physical meaning of this term canbe obtained from energy arguments, considering that the energy necessary to create thesolid–solid interface in the eutectic system is provided by the decrease in the Gibbs energy.

Fig. 2.3. Liquidus–solid interfaces in the lamellar eutectic. The mechanical equilibrium at the three-phase jointpoint is also shown.


In particular, if ta = tb (50% in volume lamellar eutectic), the curvature under-cooling isclearly related to the interface solid–solid energy. In fact, the a–b interfacial area per unitvolume is 2/k and the net Gibbs free energy change during the solidification process is gi-ven by

�DG ¼ LDT r

T E

�2cab

k. ð2:11Þ

Obviously, the minimum under-cooling that leads to zero free energy change for a givenspacing k is given by,

DT r ¼2cabT E

Lk; ð2:12Þ

which is similar to expression (2.9).Coming back to Eq. (2.9) and neglecting the kinetic contribution, the average under-

cooling can be obtained by the addition of constitutional and curvature under-cooling as

DT i ¼ miðCE � CiÞ þ2ai

ti. ð2:13Þ

During coupled growth, the average under-cooling in front of each phase has to beabout the same, DTa � DTb = DT, and the relationship between under-cooling DT andspacing k is given by [45]

DT�m¼ kv

DC0Pðk; kiÞ

fafbþ a

k. ð2:14Þ

It is easily recognized that the first term on the right-hand side of Eq. (2.14) correspondsto the constitutional under-cooling DTC, and the second one to the capillarity effect DTr.C0 is the concentration difference, which can be obtained from the tie-line of the eutecticphase diagram, and P(k,ki) is a structure function defined in [45] which depends on theeutectic Peclet number Pe = k/dC = kv/2D, the volume fraction of the phases, and the seg-regation coefficients, ki. �m and a are defined as a function of the liquidus slopes mi andvolume fractions fi as

�m ¼ jmajjmbjma þ mb

and a ¼ 2aa

fajmajþ ab

fbjmbj

� �. ð2:15Þ

Similar expressions were obtained for fibrous structures [45]. Fig. 2.4 represents theunder-cooling given by Eq. (2.14) as a function of the lamellar spacing k. The diffusion-driven term DTC increases while the capillarity term DTr decreases with spacing, givingrise to a minimum for the total under-cooling DT. At large values of the spacing, the lim-iting growth process is diffusion, while at lower ones it is capillarity. Zener [36], Tiller [37]and Jackson and Hunt (JH) [1] proposed that the eutectic grows precisely at this minimuminterface under-cooling (growth at extremum).

If it is assumed that P and C0 are independent of k, the relationships between spacing,thermal under-cooling and growth rate are given by

vk2 ¼ aDf afb

PC0

¼ K1; ð2:16aÞ

kDT ¼ 2ma ¼ K2; ð2:16bÞ

Interlamellar spacing λ

0

Δ

TE

Tem

pera

ture

ΔT

T

C

σ

ΔT

ΔT

Fig. 2.4. Solute under-cooling DTC and curvature under-cooling DTr contributions vs. interlamellar spacing k atconstant growth rate v. The sum of the contributions gives a minimum total under-cooling.


and the parameters and coefficients in Eq. (2.16) can be found in Table 1 of Ref. [45] forboth lamellar and fibrous eutectic structures. Eq. (2.16a) is the well-known law which re-lates the interphase spacing to the solidification rate for coupled eutectic growth condi-tions. However, this equation implies the JH condition: the diffusion distance in theliquid is larger than the spacing in the eutectic, which is only valid at low growth rates.In principle, the structure function P(k,ki), C0 and even m and D depend on the growthrate. Moreover, at high growth rates there will not be enough time for the solute to under-go lateral diffusion before being trapped at the solid surface. Trivedi et al. (TMK theory)[46] studied eutectic growth at high solidification rates and established that coupledgrowth is unstable above a certain value of the solidification rate. In other words, the rela-tion k2v = constant is only valid if the eutectic Peclet number Pe < 1.

Experimental values of the phase interspacing, k, are plotted in Fig. 2.5 as a function ofgrowth rate v for two important DSE ceramic oxides, Al2O3/YSZ and Al2O3/YAG. Typ-ical spacings in both systems are in the range 0.2–10 lm, corresponding to growth rates

10 100 1000

0.1

1

10

Al2O3 / YSZ

Al2O3 / YAG

λ (μ

m)

v (mm/h)

Fig. 2.5. Log–log representation of the microstructural interspacing vs. growth rate for two irregular eutecticsAl2O3/YSZ and Al2O3/YAG. The straight lines correspond to expression k2v = constant.


between 1 mm/h and 1500 mm/h [22]. It is worth to noting that the k2v = constant lawholds for binary oxide eutectics with different microstructures and also for ternary eutec-tics with few exceptions limited to the regions of extreme low or high growth rates (seeTable 2.1).

Eq. (2.16a) can also be used to estimate the interfacial surface energy and the diffusioncoefficient of solute in the liquid. Bourban et al. [47] compared the measured eutecticspacing in Al2O3/ZrO2 eutectic laser remelted surfaces with values calculated by Eq.(2.16a) but with thermo-physical constants obtained from literature. The growth ratewas quite high in this case (up to 10,000 mm/h) and the observed spacing was four timeslarger than calculated. The discrepancy was attributed to the inaccuracy in the estimationof D. Conversely, they obtained a diffusion coefficient of D � 5.0 · 10�10 m2/s using k asa data. Minford et al. [3] also used Eq. (2.16a) and parameters taken from literature,including a value of D � 2.0 · 10�9 m2/s, to obtain an interfacial energy of8.5 · 10�1 J/m2 for the MgO/MgAl2O4 system from v–k experimental data, which wasin good agreement with other independent estimations. It is interesting that in both casesthe eutectic Peclet number was low, which assures the validity of the analysis. Thegrowth of DSE oxides usually takes place with a low Peclet number, and in principle,the coupled regime could be attained even at very fast growth rates. Then, fast solidifi-cation could be used to produce nanometric sized ordered microstructures but, as will beshown below, a new effect hinders the production of very fine microstructures in thisregime.

2.3. Eutectic range

Coupled growth produces regular eutectics growing near the extremum conditions.The structure can self-adapt to local growth instabilities by branching, which is a mech-anism in which lamellae or rods can change the growth direction or branch to recover theminimum under-cooling conditions and coupled growth dynamics. Two material charac-teristics hinder this adaptation. The first one occurs when one or both phases show amarked tendency to grow in preferred directions, which makes changes in growth direc-tion very difficult and impedes the soft microstructure adaptation to front instabilities,leading to irregular spacing. This is fairly common in DSE oxides. A second difficultyarises when the material composition departs from the exact eutectic composition, whichproduces the growth of single-phase dendrites or cells. The presence of dendrites or cellsdepends strongly on the growth rate, the solidification thermal gradient, and the concen-tration gradient. In fact v, GT, and DC are the three parameters that control planargrowth. It has been found that for a given GT and DC, the planar front is stable upto a certain critical growth rate v = vC, where shallow cells start to appear as a secondaryphase. If v keeps increasing one-phase dendrites appear. Dendrites become deep cells andeventually a planar front is established again at higher v values. This evolution is illus-trated in Fig. 2.6 with several scanning electron microscope (SEM) images of anAl2O3/YSZ eutectic grown at increasing rate [48]. The transition from coupled to cellularand then to shallow cells with increasing growth rate is evident. One simple way tounderstand this behavior uses the concept of ‘‘competitive growth’’. Dendrites insteadof coupled eutectics grow when the temperature at the dendrite tip is above the eutecticgrowth temperature [49]. Burden and Hunt [50] proposed the following phenomenolog-ical equation for the under-cooling at the b-dendrite tip

Fig. 2.6. SEM micrographs showing the microstructure of an Al2O3/YSZ DSE grown by the laser-heatedfloating-zone method at different growth rates: (a) 10 mm/h, (b) 100 mm/h, (c) 300 mm/h, and (d) 1500 mm/h.(Reprinted by permission of Elsevier from [48].)


DT D ¼ T l � T D ¼GTD

vþ K3v1=2 ð2:17Þ

where Tl is the liquidus temperature, TD the dendrite tip temperature, and K3 is a constantgiven by (for the b phase)

K3 ¼ 22=3 �maCLð1� kbÞCb

D

� �1=2

;

where CL is shown in Fig. 2.7, and the under-cooling for coupled growth is obtained fromEq. (2.16) as

DT E ¼ T E � T 0 ¼K2ffiffiffiffiffiffiK1

p v1=2 ð2:18Þ

TD and T0 are plotted in Fig. 2.7 as a function of the growth rate according to Eqs. (2.17)and (2.18) for an irregular eutectic with different growth kinetics of the a and b primaryphases. Dendrites grow if TD > TE, which can occur at intermediate v values. The resultsare superimposed into the eutectic phase diagram in order to show the skewed region ofcoupled eutectic growth for irregular eutectics, while the coupled eutectic growth regionin the case of a regular eutectic is shown in Fig. 2.8. The coupled-growth region extends

Fig. 2.7. The skewed coupled eutectic growth zone associated with irregular eutectics. The plot at the right-handside shows the under-cooling as a function of the growth rate; b-dendrites grow at higher temperatures than a-dendrites. TDb and TDa stand for the temperatures at the tip of the dendrites of phases b and a, respectively (Eq.(2.17)).

CE C

0

Torv1/2

TEPlanar Eutectic

-dendrites + Coupled Eutectic

-dendrites + Coupled Eutectic

Cells coupledeutectic

Faceted eutectic dendrites

CE C

0

ΔTorv1/2

TEPlanar Eutectic

α-dendrites + Coupled Eutectic

β-dendrites + Coupled Eutectic

Cells coupledeutectic

Faceted eutectic dendrites

Fig. 2.8. The symmetric eutectic-coupled zone projected over the phase diagram for a regular binary eutectic.


towards compositions departing from the true CE eutectic composition at low growthrates. The mixed primary dendrite–eutectic zone is attained even for small departures fromeutectic compositions at high growth rates.

Thermal gradient and growth rate are entangled magnitudes. In fact, the thermal gra-dient term dominates in the low growth rate region and Eqs. (2.17) and (2.18) can be com-bined to give the following constitutional under-cooling:

miDC ¼ T l � T E ¼GTD

vþ ðT D � T 0Þ; ð2:19Þ

mi being the liquidus slope of the phase in excess. Dendrites could be avoided if

miDCD� GT

v. ð2:20Þ


Coupled-growth implies either low growth rates or high growth gradients. For instance,thermal gradients above 105 K/m are needed to obtain a planar front at v > 20 mm/h foreutectic oxides with m � 10 K/%, D � 10�10 m2/s and DC > 0.1%. Trivedi and Kurz [51]extended the TMK theory to the case of cellular growth during fast solidification andobtained qualitatively similar results except that their theory predicted a critical growthrate above which coupled growth is not possible. This implies that the second planargrowth regime at very high growth rates may not always be attainable even if the coupledeutectic zone is symmetric (see Fig. 2.8), and eutectic glass can be formed at very highgrowth rates.

2.4. Preparation techniques

As shown in the previous section, the key rule for regular homogeneous growth is tokeep micro- and macroscopically flat solid–liquid interfaces during growth, thus prevent-ing constitutional under-cooling and cellular growth. This in turn requires large thermalgradients. These conditions are essentially the same as those required for the growth ofsingle crystals from the melt, and consequently similar directional solidification proceduresare used to grow ceramic eutectics. The growth methods can be classified in two groups, (i)unidirectional solidification in a container, (ii) pulling of a solid from a melt meniscus.

Among the former methods, the Bridgman–Stockbarger technique is suitable for grow-ing bulk samples of large size, the ingot volume being limited only by crucible size. Meltoxide eutectics are usually contained in molybdenum, tungsten or iridium crucibles heatedby resistance heaters or more frequently, by radio frequency (RF) induction through agraphite susceptor. Unidirectional solidification is achieved by slowly pulling the crucibleoff the hot region [25]. Schmid and Viechniki used this procedure to grow Al2O3/ZrO2

DSE [52,53] and Echigoya et al. [54] produced various DSE oxides and reported melt tem-peratures up to 2600 �C. The apparent thermal gradients in the Bridgman method are gen-erally below 102 K/cm and consequently the growth rates have to be relatively low toavoid cellular growth, usually v < 100 mm/h, and interphase spacing is large accordingto Eq. (2.16a), usually k > 10 lm. In the Czochralski method, a container for the melt isalso needed but direct contact between crucible and grown material is avoided since theeutectic is pulled out from the melt pool. Thick rods of about 6 cm diameter can be grownby this method. For the high melting point oxide eutectics the melt is heated by RF in aself-container ‘‘skull’’ of the same material [55]. The oxide powder has to be preheated tocouple with the RF radiation, so heating is initiated by introducing some chips of metal orgraphite into the oxide powders.

Larger thermal gradients, and consequently faster growth rates, can be attained in themelt zone methods. Rudolph and Fukuda [56] published an excellent review in which thefundamentals of fiber crystal growth from free melt meniscus, i.e., the melt zone, are welldescribed. Fig. 2.9 shows three diagrams illustrating the most commonly used melt zonemethods. The processing techniques based on floating zone (FZ) or on pedestal growth(PG) are crucibleless methods in which a relatively small amount of sample volume ismelted by the action of lasers, radiofrequency or lamp mirror furnaces (Fig. 2.9(a)).Growth thermal gradients of up to 104 K/cm can be obtained, and Al2O3/YSZ andAl2O3/YAG DSE oxides grown by laser-heated floating-zone method (LFZ) presentedinterphase spacings that could be smaller than 1 lm [57–60,48]. Other growth-from-menis-cus methods are based on solid pulling from a wetting shaper as in the Stepanov or

Fig. 2.9. Solid–melt interfaces during directional solidification from meniscus showing the growth angle at theinterface /. (a) Floating zone method, (b) edge-defined film-growth method, (c) micropulling down method. Thearrows indicate the growth direction. The eutectic rod diameter is R, and the feeding rod diameter in (a) orthe wetting shaper diameter in (b) and (c) is R0. The liquid region is marked by horizontal broken lines.


edge-defined film-growth (EFG) and micro-pulling down (l-PD) methods (Fig. 2.9(b) and(c)). These methods can give thermal gradients of the order of 103 K/cm and the solidifiedsample is obtained by pulling out at high growth rates (up to m/h) from a liquid pool feedby capillaries through the shaping dies. Sample width is limited by meniscus stability andcan vary from several microns to several centimeters. l-PD methods have been used inten-sively by the Fukuda group to grow sapphire-based DSE oxides [56,61,62] while Borodinet al. produced cylinders of Al2O3/YSZ DSE up to 12 mm diameter using the Stepanovmethod and molybdenum dies [63].

Establishing capillary stable growth conditions is a crucial issue in the growth-from-meniscus methods. For a uniform rod cross section, the growth angle at the solidus-meltinterface / (Fig. 2.9) has to be kept constant and equal to a certain angle /0 determinednot from growth conditions such as growth rate, diameter or zone length, but from ther-modynamic equilibrium conditions at the liquid–solid–vapor three phase interface [64]. /0

has been experimentally determined for some simple materials such as YAG {10 0} (8�)


and Al2O3 {1000} (17�). There is also a limit to the melt zone length lm for stable growth,lm = 2pR for floating zone and lm = 3(R + R0)/3 for pedestal growth. Similar simple rela-tionships between the fiber diameter and the melt zone length are found in the case ofgrowth from dies [56]. The rod radii and the pulling rate are also related by the mass con-servation law (qS = qL),

R2v ¼ R20v0; ð2:21Þ

where R, v and R0, v0 stand, respectively, for the radius and velocities of the grown fiberand the feeding rod or shaper.

It should be borne in mind that there is a maximum attainable DSE rod diameter due tothe heat transfer through the section. For example, since the absorption coefficient of mol-ten oxides for CO2 laser radiation is high [65], most of the energy is absorbed within thefirst 0.1 mm near the exposed surface. Heating of the internal volume takes place via ther-mal diffusion, which competes with radiation losses. Consequently, the melt zone is limitedto a few cubic millimeters and the feed rod to less than 2 mm in diameter with a CW-laserof about 100 W. With RF heating, the radiation is absorbed in the bulk rather than at thesurface and the melting of large sample volumes is not a problem. However, the large ther-mal stresses generated during growth as a consequence of the high axial thermal gradientsat the liquid–solid interface often lead to fracture in thick samples. During eutectic growththe thermal gradients can be directly measured in situ using non-contact optical methods[66] but this gives only the surface temperature given the high absorption of molten oxides.Thus, the growth thermal gradient along a growing rod of radius R has to be calculatedfrom, for example, the following expression proposed by Brice [67].

T ðr; zÞ ¼ T ext þ ðT E � T extÞ1� hr2

2R

1� hR2

exp � 2hR

� �1=2

z

" #; ð2:22Þ

where the origin of the cylindrical reference frame is taken at the rotation axis in the li-quid–solid interface. h is a cooling constant, given by the ratio between thermal lossesby radiation to the ambient and by conductivity along the rod (equal to 1.1 cm�1 forYSZ and 0.65 cm�1 for sapphire [68]), and Text is the ambient temperature. Pena et al.[48] measured the surface temperature profile during solidification of an Al2O3/YSZ eutec-tic rod grown by the LFZ method and obtained a cooling constant of h = 0.5 cm�1 and anaxial gradient dT/dz = GT = 6.0 · 105 K/m by fitting the experimental data to Eq. (2.22).

Due to the heating constraint discussed above, the rod diameter is relatively small,R < 0.1 cm and hR� 1. Then, the axial gradient is

GTðz ¼ 0Þ � 2hR

� �1=2

ðT E � T 0Þ; ð2:23Þ

which is essentially independent of r and decreases as the rod diameter increases. The ra-dial thermal gradient is related to the axial thermal gradient by

dTdr

� �z¼0

� rh

2R

� �1=2

GT ð2:24Þ

which is linearly dependent on r. The through-the-thickness thermal gradients lead to ther-mal stresses and limit the axial gradient to avoid sample failure. According to the Bricemodel [67], GT is limited to


GT <4e

ah1=2R3=2; ð2:25Þ

where a stands in Eq. (2.25) for the thermal expansion coefficient and e is the failure strain.In conclusion, thermal stresses associated with large axial thermal gradients limit thesample diameter in the meniscus-driven eutectic growth methods, although eutectic rodsthicker than single crystal rods can be processed thanks to the good thermo-mechanicalproperties of DSE. For instance, the maximum rod diameter in the Al2O3/YSZ eutecticsis about 2 mm, assuming a failure strain of 10�3 and using the values of h and GT givenabove, and this value is in agreement with the experiments.

It should be noted, however, that the Brice theory, originally developed for Czochralskigrowth, does not predict correctly the liquid–solid profiles observed in the LFZ experi-ments although it gives a reasonable picture of the temperature gradient in the solidand a good estimation of the maximum radius. The solid–liquid interface in a transparentmelt is shown in Fig. 2.10: the front is convex towards the melt. The melt is highly absor-bent in most DSE oxides, which impedes visualization of the growth front. However, theprofile of the solid–liquid interface is shown in Fig. 2.11 in the longitudinal section of aAl2O3/YAG/YSZ ternary eutectic grown by the LFZ method. The rod was obtained byswitching off the laser, and the differences in the microstructure between the quenchedregion (top) and the grown rod (bottom) delineate the solidification front. The isothermsas a function of z (calculated from Eq. (2.22)) are plotted in the same figure. Those pre-dicted by the Brice model in the solid are concave towards the melt while the solidificationfront presents the opposite curvature. Basically, the heat distribution in the melt is not uni-form, not only because of the absorption of the heating source but also due to the conven-tion and thermal flow in the molten liquid. As a consequence, the equations governingcrystal growth are complex and the solution has to be approached by numerical simula-tions. Equations and solution methods, as well as some simulations illustrating the detailsof crystal growth from melt, are found in the book of Kou [69].

Fig. 2.10. Solid–liquid interface of a CaSiO3/Ca3(PO4)2 (wollastonite-three calcium phosphate) glass growth bythe LFZ method. The solid phase is transparent and the solidification front can be observed.

Fig. 2.11. Longitudinal section of an Al2O3/YAG/YSZ ternary eutectic in which the solidification front is clearlyobserved. The rod was obtained by switching off the laser and the differences in the microstructure between thequenched region (top) and the grown rod (bottom) delineate the solidification front. The 50 �C isothermscalculated from Eq. (2.22) are superimposed.


Recently, two interesting variations of the FZ method have been applied to DSE oxidegrowth. One is rapid solidification, which was applied to Al2O3/YAG/YSZ ternary sys-tems melted in an arc-image furnace. Of course, the enormous thermal stresses inducedby quenching limited the sample size to a few mm3 so the interphase spacing was extremelysmall, about 50 nm [70]. Balasubramaniam et al. [71] also produced powders with nano-meter interphase spacing of Al2O3/ZrO2(Y2O3) eutectics by arc plasma spraying followedby rapid quenching. Subsequent hot-forging of the powders yielded dense ceramics ofnanometric microstructural size. Interestingly, the densification of these nanosize powderswas controlled by the microstructural dimensions rather than by the particle size. Rapidsolidification of some eutectic systems also opens up the possibility of fabricating glass.In fact, glass is formed if the kinetic under-cooling brings the system below the glass tran-sition temperature Tg (Fig. 2.1(a)). In addition, the low melting point of the eutectic com-position helps glass formation and minimizes evaporation from the melt at the same time[72,35]. The CaSiO3/Ca3(PO4)2 eutectic is a good example of a binary glass made fromeutectic composition with excellent optical properties and resistance to corrosion [35].

The second variation exploited the favorable geometry of the narrow line laser spots orof diode laser arrays to solidify the surface of an eutectic ceramic oxide plate directionally.Surface melting was very useful for DSE cladding on metals [73] and in DSE surface


processing [74]. Fig. 2.12 shows the experimental set-up. The spot line sweeps over the pre-cursor eutectic ceramic and a melt pool is created when the laser fluence exceeds a certainthreshold determined by radiation thermal losses, heat of fusion and diffusion according tothe principles of laser surface melting, which are given elsewhere [75]. Basically, the meltpool depth depends on laser power, sweep speed, optical properties and thermal diffusiv-ity, and hence on the substrate properties. The melt pool section is symmetric at lowgrowth rates but becomes asymmetric at high growth rates. Of course, thermal stressesthrough the thickness are also a problem during surface melting and sample failure areavoided by using porous ceramic substrates and/or preheating the system. The transversesection of an NiO/YSZ DSE oxide processed by this method is shown in Fig. 2.13. The

Fig. 2.12. Schema of the experimental set-up for laser surface melting used to process in-plane Al2O3/YSZeutectics. The CO2 laser beam is transformed into a line beam and sweeps over the precursor ceramic surface asshown. (Reprinted by permission of Elsevier from [74].)

Fig. 2.13. SEM micrograph of the transverse cross section of a NiO/YSZ eutectic ceramic processed by surfacemelting. The successive melt front lines and growth directions are indicated. The inset shows a photograph of theupper surface after laser treatment.


microstructure of the DSE plate depended on the melt front geometry. The phases grewwith a depth-dependent orientation, and the growth rate v varied from the sweep speedv0 at the surface to 0 at the bottom of the melt pool. Then, the relationship k2v0 sina = constant (where a is the angle between the normals to the solidification front and tothe plate surface) was found in all surface melt eutectics following Eq. (2.16a) [74]. Thistechnique efficiently produces large surfaces of DSE oxides with improved wear and ero-sion resistance.

In conclusion, several useful methods are available for growing DSE oxides with ahomogeneous microstructure, although the relationships between thermal gradient,growth rate and microstructure size established in Sections 2.2 and 2.3 impose some limitsto the sample dimension and/or microstructural characteristics, and different growthmethods have to be found for each need. For example, Bridgman methods are optimumif large volume samples are desired, although the relatively modest thermal gradientsinherent to this method imply low growth rates and consequently large interface spacing,which may not be the best in terms of strength and hardness. On the contrary, the growth-from-meniscus methods induce large thermal gradients and admit high growth rates, lead-ing to eutectics of small interphase dimensions, but the large thermal stresses associatedwith steep thermal gradients impose a limit to the macroscopic sample size. In practice,a compromise between processing method and microstructure variables must be estab-lished for each requirement.

3. Microstructure

Eutectic solids show not only a lower melting temperature than their constituent phasesbut also a very fine microstructure with clean interface and a rich variety of microstructuremorphologies that control their structural and functional properties. Much has been doneto study their microstructure by the latest methods of structural analysis: X-ray or electrondiffraction, image analysis, synchrotron radiation, high-resolution electron microscopy,and spectroscopic techniques (Raman and electron probe microanalysis) in conjunctionwith recent improvements in theoretical modeling to provide an ever more precise charac-terization of DSE microstructures and interfaces.

In a multiphase eutectic material, it is especially interesting to evaluate the homogeneityof the microstructure. Homogeneous microstructures are produced in coupled eutecticgrowth conditions (as discussed in Section 2.2) while uncoupled growth leads to the devel-opment of colonies or dendrites. Other important aspects are the grain size, the size andshape of the eutectic domains, and the relative crystallographic orientation, as well asthe morphology and nature of the interfaces between the eutectic domains. The presenceof eutectic grains is ubiquitous in regular eutectic structures, as illustrated in Fig. 3.1.These grains are a consequence of the adaptation of the eutectic structure to small insta-bilities in the solidification front, and the grain size is governed by both the growth con-ditions and the eutectic ability to accommodate growth fluctuations. Although directionalsolidification imposes an orientation of the grains preferably in the growth direction, thelateral dimensions can be rather small. Larger grain sizes can be obtained by using singlecrystals as growth seeds, but even then the longitudinal dimension rarely exceeds 0.5 mmand the lateral one 100 lm in most eutectic oxides. The small size of the eutectic grainsimposes limits in applications that need phase continuity extended in space, such as thoseinvolving light or electrical transport. Interestingly, eutectic grains seem to be absent in

Fig. 3.1. SEM micrograph of the transverse section of a lamellar NiO/YSZ DSE grown by the LFZ, showing thedistribution of eutectic grains.


irregular eutectic structures. The problem of the small dimensions of the grains in regulareutectics has not yet been solved satisfactorily.

3.1. DSE oxides microstructure

The microstructure and crystallography of some oxide eutectics was reviewed by Min-ford et al. [3], Stubican and Bradt [76], Revcolevschi et al. [5] and Ashbrook [14]. This pre-vious work is taken into account here, but the discussion is focused on more recent results.The microstructure morphology of some DSE oxides grown with different solidificationmethods is summarized in Table 3.1. Regular structures which consist of non-facetedphases, either single crystal rods or lamellae, embedded in a single crystal matrix are foundin some DSE oxides. In the simplest case of isotropic surface energy, rods are predictedwhen the volume fraction of the minority phase is lower than 28% and lamellae when itis above 28%. This crossover between lamellar and fibrous microstructures can beexplained using interfacial energy arguments similar to those described in Section 2.3.The interfacial energy in isotropic media is proportional to the interface surface per vol-ume unit, which is equal to 2/k for lamellae and to 2(2pf)1/2/1.31k for a hexagonal distri-bution of rods (Fig. 3.2) where f is the volume fraction of the rods. This rule is nearlyalways followed by regular oxide eutectics, as shown in Table 3.1.

However, simple regular microstructures are the exception rather than the rule in DSEoxides due to the strong tendency of most oxide crystals to grow along certain crystallo-graphic planes, for example to faceting. This highly anisotropic growth behavior wasquantified by the Jackson interface roughness parameter defined as a � DSf/R whereDSf is the entropy of fusion and R the gas constant. According to Jackson’s criterion, ifa > 2 for one of the phases, its growth is limited by the rate of nucleation and facets areeasily produced. As a rule of thumb, the growth is coupled if phases possess low meltingentropy but the microstructure is irregular when the fusion entropy of one or both com-ponents is high because the growth interface cannot easily deviate from certain crystal ori-entations and faceted phases are produced [1]. Although the Jackson parameter is notknown for many of the oxide systems discussed in this review, oxide phases have in general

Table 3.1Microstructure and crystallography of DSE oxides

Eutectic Microstructure Growth direction Orientation relationships or interface planes References

YSZ/Al2O3 TDI ð�110�2ÞAl2O3kð�110ÞYSZ ð�110�2ÞAl2O3k � ð�110ÞYSZ [74]½02�21�Al2O3k � ½111�YSZ

YSZ/Al2O3 CR, YSZ fibers [0001]Al2O3k [001]YSZ½01�10�Al2O3k½001�YSZ ð2�1�10ÞAl2O3kð100ÞYSZ [5,81][0001]Al2O3kh011iYSZ ð2�1�10ÞAl2O3kð100ÞYSZ [59]

Al2O3/Y3Al5O12 TDI ½1�100�Al2O3k½�111�YAG ð0001ÞAl2O3kð1�12ÞYAG [236]½�1100�Al2O3k½�111�YAG ½1�100�Al2O3k½�111�YAG

½�1100�Al2O3k½�111�YAG

CaZrO3/CaSZ R, Lamellar �[112]CaSZk�[101]CaZO �(100)CaSZk (011)CaZO [86]�(010)CaSZk (100)CaZO

[110]CaSZk [011]CaZO ð1�10ÞCaSZkð100ÞCaZO [81][110]CaSZk [011]CaZO (100)CaSZk (100)CaZO [76][112]CaSZk [100]CaZO (111)CaSZk (100)CaZO [76]

MgO/MgSZ R, MgO fibers [111]MgOk [111]MgSZ (hkl)MgOk (hkl)MgSZ [76]½1�10�MgOk½1�10�MgSZ (111)MgOk (111)MgSZ [80]½1�10�MgOk½010�MgSZ (111)MgOk (100)MgSZ [80]

Al2O3/GdAlO3 TDI ½01�10�Al2O3k½0�10�GdAlO3 ½2�1�10�Al2O3k½112�GdAlO3 [81]� h10�14iAl2O3k � h111iGdAlO3 – [237]

MgAl2O4/MgO R, MgO fibers [111]MgOk [111]MgAl2O4 (hkl)MgOk (hkl)Spinel [76]

YSZ/NiO (or CoO) R, lamellar ½100�YSZk � ½1�10�NiO (002)YSZk (111)NiO [238]½110�YSZk � ½1�10�NiO (002)YSZk (111)NiO [85]

Abbreviations describing microstructure are: R, regular; CR, complex regular; TDI, irregular three-dimensional interpenetrating network.

J.

LL

orca

,V

.M.

Orera

/P

rog

ressin

Ma

terials

Scien

ce5

1(

20

06

)7

11

–8

09

733

λ λ

(a) (b)

Fig. 3.2. Schema of the two simplest regular microstructures found in DSE oxides.


a high fusion entropy and a strong tendency to faceting (see Table 3.2). The tendency of agiven phase to develop facets can be experimentally established by looking at the morphol-ogy of the primary phases in off-eutectic compositions. In particular, primary oxide phasesof Al2O3, YAG, and RE-aluminates always show facets, an indication of their highentropy of fusion. The strong tendency of these oxides to develop facets generally leadsto irregular eutectic structures. A special case of irregular microstructure was found inDSE oxides where the phases were continuously entangled in a three-dimensional inter-penetrating network (TDI), like the one shown in Fig. 3.3 in a transverse section of anAl2O3/YAG DSE. A TDI microstructure is a homogeneous and fine dispersion of phases,free of grain boundaries, that appears under eutectic coupled-growth conditions. Theabsence of grains and other larger scale irregularities, together with excellent bondingbetween phases, leads to structures with extraordinary mechanical properties [20] as wellas high temperature stability and corrosion resistance [17]. In contrast to metallic eutectics,where this microstructure is observed only in non-faceted/non-faceted composites, TDImicrostructures are also found in faceted/non-faceted Al2O3/YSZ DSE grown at verylow growth rates, and in faceted/faceted Al2O3/YAG DSE over a wide range of growthrates. The domains exhibit sharp angle facets in the latter, and this morphology is referredto in the literature as Chinese Script (CS) microstructure. Recently, three-dimensionalobservations of eutectic structures in Al2O3/YAG DSE using high resolution X-raytomography revealed their truly entangled morphology [77]. In spite of their obvious prac-tical interest, theoretical models of the generation of these irregular eutectic structures arestill embryonic. Kaiden et al. [78] worked out a simple model for irregular CS microstruc-tures based on a cellular automata representation of the growth interface, which took intoaccount the state of the neighboring cells and the anisotropic growth rates. Although thefoundations of the model are not sufficiently clear, it apparently reproduces quite well themicrostructural features of some Al2O3/RE2O3 eutectics (RE = rare earth ions).

Table 3.2Melting entropy of some ceramic oxides

Compound DHm/RTm

Al2O3 5.74ZrO2 3.55MgO 3.01NiO 2.94CoO 3.15MgAl2O4 9.82CaF2 2.11

Fig. 3.3. SEM micrograph of the transverse section of an Al2O3/YAG DSE grown by the LFZ method showingthe continuous three-dimensional interpenetrating (TDI) microstructure, also known as Chinese Script.


As stated in previous sections (see Fig. 2.5), the interphase spacing of DSE oxides withthe irregular TDI microstructure is growth-rate dependent, generally following Eq.(2.16a). The accurate evaluation of the interphase spacing in the case of irregular micro-structures was solved by Mizutami et al. [79] using the relationship between the interfaciallength per unit area, S, in the CS microstructure and the spacing for the equivalent lamel-lar microstructure k (S = 2/k). The interfacial length was estimated numerically from SEMmicrographs of transverse sections in Al2O3/YAG DSE and the corresponding effectivelamellar spacing was compatible with that predicted by different methods.

As in most oxide eutectics, the compositional range for eutectic coupled growth in bothAl2O3/YAG and Al2O3/YSZ DSE oxides was narrow, and small deviations from eutecticcomposition promoted precipitation of the primary phase in excess [77]. However, therewere some interesting differences in the growth behavior of these two DSE oxides withTDI microstructure. Firstly, Al2O3/YSZ eutectics presented curved smooth interfacesrather than the planar sharp interfaces of Al2O3/YAG. Secondly, the TDI structure inAl2O3/YAG eutectic survived even up to quite high growth rates while the TDI micro-structure of Al2O3/YSZ persisted only up to relatively low growth rates before enteringinto the cellular growth regime (Fig. 2.6). In fact, the Al2O3/YSZ eutectic underwent atransition on increasing the growth rate from the planar to the cellular growth regimeand then to faceted cells consisting of a triangular dispersion of embedded, orderly zirco-nia fibers of about 0.3 lm diameter in the Al2O3 matrix (named complex-regular micro-structure). At the highest growth rates the colony structure merged into a nearlyhomogeneous cell structure with lamellae, which resembles that obtained at low growthrates. This behavior is in close agreement with the theoretical predictions for eutectic cou-pled growth, and the different growth regimes follow those depicted in Fig. 2.8. However,the actual growth rates for the transition from a growth regime to the next one dependon the growth procedure. This is illustrated by Fig. 3.4 where the evolution of the

R (mm)0.1 1 10 100

10

100

1000

3

2

v(m

m/h

)

GT

λ

Planar growth Cells Dendrites

Cells

Fig. 3.4. Evolution of the microstructure as a function of the growth rate v and sample radius R for Al2O3/YSZDSE grown by different methods (see text for details).


microstructure with growth rate is presented in log–log plot of the growth rate vs. the sam-ple radius R for Al2O3/YSZ DSE grown under different methods (thermal gradient GT andsample radius R). The experimental data in Fig. 3.4 correspond (in order of increasingsample size) to Al2O3/YSZ grown by the l-PD [62], FZ [54], LFZ [48], Bridgman [53]and EFG [63] methods, respectively. The growth thermal gradients decrease from the leftto the right and the broken lines which delimit the different growth regimes follow theinequality:

R3=2v 6 constant, ð3:1Þwhich derives from the relationship between thermal gradient and growth rate for eutecticplanar growth in Eq. (2.20) and between the maximum sample radius and the thermal gra-dient in Eq. (2.25). The plot in Fig. 3.4 indicates that a similar inequality could hold for thetransition from cellular to dendrite growth regime.

It was demonstrated in the previous section that the relationships between growthparameters and microstructure size imposed limits to the eutectic growth. In addition,these results show that not only the microstructure size but also the microstructure mor-phology strongly depend on the growth procedure in DSE oxides. However, comprehen-sive models to simulate and control the development of the different eutectic morphologiesare not available for these materials and the search for a given microstructure in a partic-ular sample has to rely on experimental expertise.

3.2. Crystallography and interfaces

The single crystal phases in eutectics often grow preferentially along well-defined crys-tallographic directions that are not necessarily the directions of easy growth of the com-ponents but which correspond to structures with minimum interfacial energy (see Eq.(2.11)). In fact, eutectic stability and most of the properties of the structures depend onthe interface properties since the interfacial surface is very large. A complete characteriza-


tion of DSE oxides clearly needs a deep knowledge of the orientation relationshipsbetween the phases and the characteristics and quality of their interfaces. Interfaces aredetermined by two crystallographic relations: the interfacial plane defined as parallel tothe (hkl)A and (hkl)B planes, and the growth direction defined as in the [hkl]A and [hkl]Bdirections. The preferred growth direction and orientation relationships between phasescan be obtained by X-ray or transmission electron microscopy diffraction. The interfacescan also be observed on an atomic scale using high resolution electron microscopy(HREM) in the most favorable cases of perfect orientation between eutectic phases withwell-defined atomic lines [5,55,80].

The solidification directions and orientation relationships in most of the DSE oxideswere measured years ago [3,5]. Mazerolles et al. [81] have recently performed a detailedstudy of the orientation relationships, interface planes and interface structure usingHREM methods in some eutectic oxides; some of these results are presented in Table3.1. As indicated by Stubican and Bradt [76], the orientation relationships of oxide eutec-tics should follow the general rules of metallic systems where the interface is determined bythe minimization of lattice misfit between the component phases and the balance of theionic charge, or better charge neutrality at the interface. These conditions can usuallybe handled by the near coincidence site lattice (NCLS) model as described by Bonnetand Cousineau [82], the atomic misfit and the charge density on the two planes beingthe parameters defining the interface. The following rules are of general application inmost of the DSE oxides studied so far [5,81]:

• Eutectic growth axes correspond to well-defined crystallographic directions and crystal-lographic relations between phases, which are unique in most systems.

• Perfectly aligned lattices produce well-defined interface planes. Interfaces usually corre-spond to dense atomic arrangements in the component phases.

• Growth habit is generally imposed by the major phase.

However, a mistilt between the growth directions and the orientation relationships ofthe component phases is observed in most eutectic oxides. In addition, spatial variationsof these magnitudes along the sample transverse sections are frequently found [236,87]because the surface energy, which determines interface morphology, has to compete withthe growth anisotropy in order to stabilize the optimum structural configuration. Curvedand planar interfaces coexist in some cases, such as the CaF2/MgO fibrous eutectic [11].The fibers are semifaceted, with exact epitaxial relationships between both phases, whichbuild two orientation relationships in two growth directions OR1 [10 0]CaF2k [211]MgOand OR2 [001]CaF2k [110]MgO, the planar interface (100)CaF2k (111)MgO and twocurved ones ½100�CaF2k½01�1�MgO and ½100�CaF2k½�11�2�MgO, as shown in Fig. 3.5.The coincidence of the cation sublattices is plotted in Fig. 3.6 and is characterized bythe parameters RCaF2

¼ 2 and RMgO = 4 with misfits of 5.7% for OR1 and 8.7% forOR2. The charge densities were +0.135 A�2 for {100}CaF2 and �0.126 A�2 for{11 1}MgO and the curved interfaces correspond to a much worse mismatch and chargebalance. A related case is that of the MgO/MgSZ fibrous eutectic. The MgO fibers are gen-erally well-aligned with growth directions [hkl]MgOk [hkl]MgSZ and show well definedfacets corresponding to several sets of planar interfaces. As established by HREM, thepoor lattice mismatch is accommodated by an array of periodic misfit dislocations, leadingto semicoherent interfaces [5,80].

Fig. 3.5. (a) Transmission electron micrograph of a MgO fiber into the CaF2 matrix. (b) Diagram of theorientation relationships found in the CaF2/MgO eutectic grown by Bridgman method. (Reprinted by permissionof the Materials Research Society from [11].)


These examples show the rich variety of phenomena encountered in the DSE oxideinterfaces. Nevertheless, it should be noted that the observed crystallographic orientationrelationships do not correspond to surfaces of minimum interfacial energy in some DSEoxides. As explained above, it could be argued that growth kinetics also play an importantrole in the control of the interface formation due to the large fusion entropy and growthanisotropy of some oxides, such as Al2O3. With strong growth anisotropy, interfacesshould minimize not only the contribution to the surface energy but also that of the solid-ification process, and the interface orientation has to be compatible with the directions offavorable growth. In favor of this interpretation is the fact that multiple orientation rela-tionships have been reported for some of these systems, which can be modified to some

Fig. 3.6. Coincidence of the cationic sublattices at the (010)CaF2k (111)MgO interface. (Reprinted bypermission of the Materials Research Society from [11].)


extent by appropriate changes of the growth parameters. This is the case of Al2O3/YAGwhere the corundum-garnet structures grow with different interface orientations (see Table3.1). The same is true for Al2O3/YSZ where at least two different interface orientation sets,the (00 01)Al2O3k (01 0)YSZ and the [0001]Al2O3k [010]YSZ interfaces [5] were observedby HREM. Recently, Mazerolles et al. [81] performed new HREM studies on these inter-faces and proved that the residual lattice mismatch is accommodated by misfit dislocationsor steps, as shown in Fig. 3.7. In both Al2O3/YAG and Al2O3/YSZ eutectics, it is evidentthat growth parameters play an important role in determining not only the microstructuremorphology but also the crystallography. Another example is given in Fig. 3.8 for anAl2O3/YSZ DSE grown by LFZ at high rates. The microstructure is complex regularand consists of elongated Al2O3 cells growing along the c-axis with three-fold symmetricsets of ZrO2 fibers [48]. The orientation relationships and growth habits found in this caseare found neither in TDI microstructures nor in colonies by other authors (see Table 3.1).

Some lamellar DSE oxides such as (CaSZ or YSZ)/NiO, (CaSZ or YSZ)/CoO andCaSZ/CaZrO3 were able to adapt to growth fluctuations by smoothly changing the inter-phase spacing leading to relatively large, well-aligned eutectic grains (Fig. 3.9). Addition-ally, the fluorite–rocksalt coupled structures in CaSZ/NiO and CaSZ/CoO eutecticspresent perfect planar interfaces, and this allows the detailed study of the interface byHREM [83]. It was found that the phases are well bonded by low energy interface planesin both YSZ/NiO and YSZ/CoO: (111)NiO or CoOk (002)YSZ with periodic steps forthe accommodation of the near coincidence. This interface is that of the lowest energystudied up to now in DSE oxides [84]. However, at least two different growth directionshave also been found in this case: [100]YSZk [110]NiO and [11 0]YSZk [110]NiO [85],

Fig. 3.7. HREM micrograph of the transverse section of an [0001]Al2O3k [010]YSZ interface. The arrowsindicate the phase steps. (Reprinted by permission of Elsevier from [81].)

Fig. 3.8. Transverse and longitudinal sections and orientation relationships in an Al2O3/YSZ DSE grown at300 mm/h by the LFZ. The transverse cross-section is the sapphire c-plane. (Reprinted by permission of Elsevierfrom [48].)


and the zone axes of these phases are not exactly parallel. There was a typical misorienta-tion angle in the range 2� and 12� between adjacent lamellae. This lack of an exact orien-tation relationship pattern also occurs in the CaSZ/CaZrO3 lamellar eutectic. In LFZ

Fig. 3.9. Optical transmission microscope micrograph of a CaSZ/CaZrO3 lamellar DSE. The light is guided bythe CaSZ phase, which is the highest refractive index phase.


grown CaSZ/CaZrO3 samples, X-ray diffraction pole figures point to the following orien-tation relationships: (100)CaSZ approx.k (01 1) pseudocubic CaZrO3 and (010)CaSZapprox.k (100) pseudocubic CaZrO3 [86], while diffraction experiments in the TEMshowed that there is a misorientation of up to 12� between adjacent lamellae [87]. Theseobservations support the hypothesis that in some DSE oxides competition between inter-face energy and growth anisotropy break down the uniqueness of the crystallographic rela-tion between phases, and several sets of crystallographic orientations at the interface canbe found in the same eutectic system.

4. Microstructural and chemical stability

Oxide-based materials are always attractive because of their inherent thermochemicalstability in oxidizing environments at high temperature, so the development of DSE oxideshas been partially driven by the need of new structural materials which have to withstandhigh temperatures for long periods of time [88,89]. This is the case, for instance, of gas tur-bine components which operate at temperatures above 1000 �C for thousands of hours inan oxidizing environment which contains significant amounts of water vapor. Si-basedceramics deteriorate rapidly in moisture-rich atmosphere above 1200 �C [90–92] and can-not be used without expensive protective coatings. Oxides present better environmentalresistance and, for instance, hot-pressed polycrystalline Al2O3 shows good corrosion resis-tance up to 1600 �C even in wet Ar atmosphere [93]. However, samples tested in watervapor above 1600 �C showed evidence of grain boundary etching, weight gains and graingrowth, which affected the mechanical properties. Moreover, subcritical crack growth—which has been detected in single crystal Al2O3 [94] and tetragonal ZrO2 [95] in air attemperatures above 600 �C—rules out their application as structural materials. Theseprecedents have motivated the study of the microstructural stability of DSE oxides afterlong-term exposure at high temperature as well as their resistance to oxidation and chem-ical attack. The main conclusions of these investigations are presented below.

4.1. Microstructural stability

Eutectic microstructures present a large area of interfaces and tend to release the excessof surface energy by coarsening when the temperature is high enough to allow the diffusion


of atoms. The microstructural stability of eutectic microstructures has been analyzed pri-marily in metallic systems, where it was found that the mechanisms controlling the homo-geneous coarsening depended on the eutectic morphology [96,97]. In fibrous eutectics,thicker fibers can grow at the expense of thinner ones by a process similar to the Ostwaldripening of precipitates in matrix where the ‘‘concentration gradient’’ for diffusion betweenfibers arises from the different fiber radii. However, this mechanism is normally hinderedby the uniform fiber diameter distribution produced by eutectic growth, and coarsening isnormally controlled by fault migration [98]. Faults are instabilities that develop duringeutectic growth in both fibrous and lamellar microstructures; they consist of one pair ofa termination and a branch (Fig. 4.1(a)). Branches are expected to fill in, and the termina-tion to shrink backwards as shown in Fig. 4.1(b) since the curvature is maximum at thetermination and minimum (negative) at the branch, leading to the formation of a thickerbulge (Fig. 4.1(c)). The thickening of lamellae at the expense of thin ones cannot operate inlamellar eutectics where both phases form alternating sheets, because the chemical poten-tial at the interface is constant in the absence of any curvature. Graham and Kraft [99]showed that coarsening in lamellar eutectics was due to fault migration and involvedthe diffusive transport of matter from the curved edge of a lamellar termination to acurved bulge in an adjacent lamella. However, the interpretation of the coarsening mech-anisms in eutectics is often more difficult as they cannot be always classified as perfectfibrous or lamellar eutectics. TDI microstructures (also named CS) made up of a three-dimensional interpenetrating network of irregular lamellae are found in many direction-ally solidified eutectics and no coherent theory to explain coarsening in these systemshas been developed. Experimental results on metallic eutectics with this microstructure

Fig. 4.1. Schema of microstructure coarsening by fault migration in rod eutectics. (a) Initial fault geometry, (b)progressive termination shrinkage and branch growth, (c) bulge formed by fault migration.


are consistent with an Ostwald ripening mechanism but no definitive conclusions can bedrawn from the limited amount of data [100].

The investigations of the microstructural evolution at high temperature of DSE oxidesare limited although the experimental data show that these materials present an excellentstability even at temperatures approaching the eutectic point. For instance, Waku et al.[18,101] did not find any coarsening after 100 h at 1700 �C in Al2O3–YAG and Al2O3–GAP DSE manufactured by the Bridgman method. Both materials presented a CS micro-structure with the average domain thickness t, as measured in 2D cross-sections, of�30 lm, and the only change detected was a rounding of the sharp domain corners.Al2O3–YSZ eutectics with a cellular microstructure showed coarsening of the submicronfiber [48] or lamellar [102] structures within the cells after a few hundred hours at1500 �C. Coarsening was, however, limited: the rod and lamella dimensions remained inthe micron range (Fig. 4.2) and the cell size did not change with the heat treatment.

Fig. 4.2. Coarsening of YSZ rods in a cell of an Al2O3–ZrO2 (9 mol% Y2O3) eutectic grown at 300 mm/h by thelaser-heated floating zone method. (a) SEM of the as-received material, (b) Idem after 100 h at 1500 �C in air, (c)Idem after 300 h at 1500 �C in air. YSZ stands as the white phase. (Reprinted by permission of Elsevier from [48].)


The homogeneous degradation of the ordered trigonal fiber structure within the cell iscompatible with a fiber thickening induced by Ostwald ripening and this would explainthe excellent microstructural stability as the initial fiber distribution is very uniform indiameter (Fig. 4.2).

The most comprehensive study of the microstructural stability of DSE oxides was car-ried out by Park et al. [103] in Al2O3–YAG fibers manufactured by the EFG technique.The fibers presented a CS microstructure and were heat treated in air at 1360 �C,1410 �C, and 1460 �C (0.8Tm) for 50–200 h. The evolution of k (average interphase spac-ing) and S (interface length per unit area)1 as a function of time and temperature was mea-sured using an image analysis program on SEM micrographs formed with back-scatteredelectrons. The as-received microstructure was homogeneous and k was between 0.4 and0.5 lm throughout the fiber. Coarsening was more pronounced at the fiber surfaces andk reached 2.5 lm and 1.2 lm at the fiber surface and center, respectively, after 200 h at1460 �C. The kinetics of the microstructural change was modeled following the Grahamand Kraft model [99] for lamellar eutectics under the assumptions that the geometry ofthe lamella does not change (except in size), leading to

1

S� 1

S0

¼ K0 exp�QRT

� �tT; ð4:1Þ

where S0 stands for the initial interface length per unit area, t the time, T the absolute tem-perature, K0 a proportionality constant and Q the activation energy of the process. Theexperimental results were in excellent agreement with the model predictions, as shownin Fig. 4.3(a), which indicates that the homogeneous coarsening of pseudo-lamellarDSE follows the same mechanisms as those discovered in metallic eutectics. Moreover,the activation energy for the diffusion process was estimated from Arrhenius-type plotsof the logarithm of (1/S � 1/S0) vs. the reciprocal of the absolute temperature(Fig. 4.3(b)). The lower activation energy of the surface data (262 ± 42 kJ/mol) wasresponsible for the higher coarsening rate at the surface and indicated that surface diffu-sion dominated over interface and volume diffusion. The activation energy at the bulk(308 ± 103 kJ/mol) suggested that the rate-controlling processes for the coarsening ofthe Al2O3–YAG fibers were the diffusion of O2� ions through the YAG phase and ofY3+ ions through the Al2O3 phase.

These results show that the resistance of DSE oxides to homogeneous coarsening is verygood, but other investigations have detected heterogeneous or localized coarsening at thesurface of Al2O3–YAG [104–106] and Al2O3–YSZ [107] fibers. They appear as largeblotches on the fiber surface, and fiber fracture was nucleated very often at these surfacedefects, which were responsible for the degradation of the mechanical properties after longterm annealing. Discontinuous coarsening in eutectic fibers was normally associated withthe presence of impurities in the coarsened region [105,107] and Matson and Hecht [106]developed a model to explain this phenomenon by the reaction of the eutectic fiber con-stituents with silicates deposited on the fiber surface from dust and dirt.

1 The product kS is constant for a given microstructure and was approximately equal to 3.6 for the CSmorphology of the Al2O3–YAG fibers.

0

0.02

0.04

0.06

0.08

0.1

0.12

1460°C

1410°C

1360°C

0 50 100 150 200 250

1/S

- 1

/S0

(μm

)

Time (hours)

(a)

0.02

0.03

0.04

0.05

0.06

0.070.080.09

0.1

0.2

Bulk, Q = 308 ± 103 kJ/mol

Surface, Q = 262 ± 42 kJ/mol

0.56 0.58 0.6 0.62 0.64

1/S

- 1

/S0

(μm

)

1000 / T (1/K)

(b)

Fig. 4.3. Coarsening kinetics of Al2O3–YAG fibers during high temperature exposure in air. (a) Evolution of theinterface length per unit area, S, and fitting to the predictions of the Graham and Kraft model. (b) Arrhenius plotof log(1/S � 1/S0) vs. (1/T) to estimate the activation energy of diffusion at the surface and in the bulk.(Reprinted by permission of the American Ceramic Society from [103].)


Discontinuous coarsening in the absence of impurities has been reported in metalliceutectics with a lamellar microstructure. Instead of a continuous increase in the thicknessor spacing of the lamellae with high temperature exposure, discontinuous coarseningoccurs by the consumption of the original fine lamellae by cells of new lamellae with spac-ings several times larger than the original ones [100]. This phenomenon is associated withthe presence of high angle grain boundaries and it was reported by Jenecek and Pletka in adirectionally solidified, polycrystalline NiO–CaO lamellar eutectic heat treated at 1422 �C[108]. The coarsening reaction is initiated at the grain boundaries and proceeds by bound-ary migration into the adjacent eutectic grain whose lamellae are oriented most nearly nor-mal to the boundary. The coarsened lamellar interfaces are also oriented normal to the


advancing grain boundary and Livingston and Cahn [109] developed a theory to computethe speed of the advancing grain boundary v as a function of the original (k1) and coars-ened (k2) interphase spacings by assuming that the discontinuous coarsening movementwas controlled by the diffusion along the grain boundary. The theory predicted that v

was proportional to ðk2 � k1Þ=k1k32 and the experimental data of Jenecek and Pletka as

well as data from metallic eutectics followed this trend but quantitative comparisonsbetween theory and experiments are not yet possible as v and k2/k1 cannot be predictedindependently [109].

4.2. Oxidation and chemical resistance

DSE oxides present an excellent resistance to oxidation at elevated temperature owingto the inherent stability of the eutectic oxides and to the absence of impurities at the inter-faces. For instance, no change in weight or in volume was detected in 6 · 6 · 6 mm3 pris-matic bars of Al2O3–YAG after 1000 h at 1700 �C in laboratory atmosphere, whereas theshape of Si3N4 and SiC specimens collapsed after 10–20 h under the same conditions dueto oxidation [110]. Further studies in the Al2O3–YAG system did not measure any varia-tion in weight or volume after 20 h at 1800 �C in Ar or dry air, even though the eutectictemperature was 1826 �C, and these results agree with fundamental studies on the stabilityof the compounds in the Al2O3–Y2O3 binary system, which showed that they are intrinsi-cally stable in oxygen atmosphere up to very high temperature [111].

The most common corroding species is water vapor, and the effect of moisture on thehigh temperature stability was studied in Al2O3–YAG, Al2O3–GAP, and Al2O3–YAG–YSZ DSE [112,113]. The changes in weight at 1500 �C in humid Ar atmosphere (totalpressure 0.6 MPa, partial pressure of water vapor 0.15 MPa) are plotted as function of

-1

-0.8

-0.6

-0.4

-0.2

0

Al2O3 - YAG - YSZ

Al2O3 - YAG

Al2O3 - GAP

0 50 100 150 200 250 300 350

Wei

ght

chan

ge (

mg/

cm2 )

Time (hours)

Si3N

4

SiC

YAG

Al2O3

Fig. 4.4. Weight change as function of time exposure at 1500 �C in a humid Ar atmosphere (partial pressure ofwater 0.15 MPa). The weight changes in Si3N4 and SiC in a similar environment are shown for comparison.(Reprinted by permission of the American Ceramic Society from [113].)


exposure time in Fig. 4.4. The results obtained on single-crystal Al2O3 and YAG are alsoplotted for comparison, and they show that the eutectic weight reduction occurredbetween those of the single-crystals. Other DSE oxides presented slightly greater weightchanges during high temperature exposure, but these variations are negligible when com-pared with those of Si3N4 and SiC in a similar environment (1500 �C and 33 kPa of watervapor partial pressure) reported in [114]. In the three DSE oxides tested, corrosion inhumid environments at high temperature produced localized thermal grooving at the inter-face between Al2O3 and the other phase (YAG, YSZ or GdAlO3). Moreover, roughness ofthe surface increased due to the recession of the Al2O3 domains by approximately 2 lmafter 300 h of thermal exposure, and the new Al2O3 surfaces were faceted. These resultscan be explained by the decomposition of Al2O3 into Al(OH)3(g), particularly at thehigher-energy phase boundaries. Nevertheless, the chemical attack did not progress intothe specimens and the materials retained most of the flexure strength [112]; both facts dem-onstrate their excellent corrosion resistance in the presence of water.

The chemical resistance of DSE oxides at high temperature in environments containingother chemical species has not been studied in detail, to the authors’ knowledge. However,Mah et al. [111] showed that compounds in the Al2O3–Y2O3 system suffered a severe deg-radation at 1500 �C in air containing CO or in the vicinity of SiC under vacuum due thecarbothermal reduction of Al2O3 and Y2O3 and the loss of Al-containing gaseous speciesinto the atmosphere. However, Al2O3–Y2O3 DSE exposed to combustion gases in a bur-ner-rig test did not undergo any chemical degradation and X-ray photoelectron spectros-copy revealed that Y and Al atoms were bonded to oxygen without traces of otherbondings [115], and it was concluded that this eutectic is stable even in fuel-rich combus-tion gas at 1500 �C. No degradation was observed when single crystal YAG specimenswere placed in close proximity, but not in contact, with SiO2 powders at 1650 �C. Finally,the reactivity of DSE oxides with metals was studied by Farmer et al. [107] to asses thepotential of these materials as reinforcement of metallic matrices. They manufactured acomposite made up of Al2O3–YAG eutectic fibers in a FeCrAlY high temperature metallicmatrix, and the fibers were removed from the composite by etching the matrix with a mix-ture of equal parts of H2O, HNO3 and HCl. The fibers extracted from the compositeshowed a 50% reduction in strength, and extensive depletion of YAG from the fiber sur-face was produced during composite fabrication. They concluded that protective coatingswere necessary when using DSE oxides as reinforcements of metallic matrices.

5. Residual stresses

5.1. Origins

DSE oxides are grown directly from the melt at very high temperature, and the eutecticreaction leads to the nucleation of two phases with strong interfacial bonding and differentthermal expansion coefficients. The thermal expansion mismatch between the phasesinduces thermal strains as the material cools down, which cannot be relaxed because plas-tic deformation in ceramics is limited, giving rise to large thermal residual stresses. Theaccurate estimation of the thermal residual stresses is a complex (and important) problem,which depends not only on the thermal expansion mismatch but on the cooling rate fromthe eutectic temperature, the morphology of the eutectic microstructure and the develop-ment of stress relaxation mechanisms. Tensile residual stresses can induce microcracking


throughout the material upon cooling, as it was shown in MgO–MgAl2O4 [157] and Mg–CSZ [116] DSE, but their effects are not always undesirable and, for instance, controlledresidual stresses in laminated materials can be used to increase the toughness by enhancingcrack deflection at the interface. In ZrO2-containing DSE, residual stresses are also influ-enced by tetragonal to monoclinic martensitic phase transformation (which occurs at�900 �C) which is associated with a volume increase of 4.67%. In fact, the magnitudeof the residual stresses in each phase can be tailored to some extent by controlling carefullythe amount of transformed ZrO2, which depends on the dopant content and its nature [21].Similar control was reported in Co1�xNixO/ZrO2(CaO) DSE where Co1�xNixO is a solidsolution of CoO and NiO whose thermal expansion coefficient changes with the Co/Niratio [117].

5.2. Measurement techniques

Residual stresses in DSE oxides have been measured using X-ray diffraction [117,118,6],neutron diffraction [117], and piezospectroscopy techniques [21,119–122]. X-ray and neu-tron diffraction are well-established methods based on the fact that residual stresses mod-ify the interplanar spacings in the crystalline lattice. The actual spacing can be determinedfrom the angular position of the diffraction peaks, and the lattice strains can be computedfrom the strain-free lattice parameter. This latter parameter is not necessary in the study ofmonolithic materials by X-ray diffraction because it can be assumed that the normal stres-ses at the surface vanish. This hypothesis is not valid in neutron diffraction (which mea-sures stresses within the bulk of the sample) and it cannot be applied in either case toDSE because they are made up of two (or more) phases and the normal residual stressesin each phase do not converge to zero at the surface: only the integral over both phases hasto be zero. Moreover, DSE are usually single crystals (or coarse-grained materials) andstrain measurements have to be carried out with a goniometer diffractometer. A given fam-ily of planes (hkl) is selected to measure the strains in each phase taking into account that itis interesting to have as many reflecting planes as possible (although only six are strictlynecessary) and that high angular positions for diffraction increase the strain sensitivity.The sample is rotated to bring into the diffraction plane a particular diffraction vector cor-responding to one plane of the (hkl) family, and the interplanar lattice spacing dhkl is deter-mined from the angular position of the diffraction peaks. The corresponding normal strainehkl can be computed as

ehkl ¼dhkl � d0

d0

; ð5:1Þ

where d0 is the unstressed lattice spacing. This normal strain is related to the strain tensoreij by

ehkl ¼ aiajeij; ð5:2Þwhere ai and aj stand for the direction cosines between the diffraction plane and the bicrys-tal coordinate system which defines the orientation of the strain tensor eij for the phaseconsidered. Although only six measurements are necessary to compute the six independentcomponents of the symmetric strain tensor e, the accuracy is improved if the system ofequations resulting from (5.2) is overdetermined and the eij components are normally com-puted by fitting the tensor components to as many data as possible using the generalized


least squares method. Once the strain tensor is known, the actual stress tensor r can becomputed as2

r ¼ C : e; ð5:3Þwhere C is the crystal stiffness tensor of the phase considered.

The most critical source of error in these measurements comes from the determinationof the unstressed lattice spacing in each phase because small errors in d0 can greatly affectthe accuracy of the strain measurement. In the measurements of residual stresses in DSEoxides reported in the literature [117,118], d0 was determined from crushed powders of theeutectic material. Crushing the material to powder reduces most of the interfacial con-straint and relaxes the residual stresses but it cannot ensure that they have been completelyremoved and the error in d0 introduces an uncertainty in the absolute magnitude of thestresses in each phase. However, if the stresses measured in each phase verify the equilib-rium force equation, it is likely that the independently measured d0, and hence the calcu-lated strains and stresses, are reasonably accurate.

Information about the stresses and strains can also be obtained through the shift ofsome spectroscopic bands (emission or Raman lines) due to the action of stress, the so-called piezo-spectroscopic effect [123]. Among the different piezospectrocopic effects, thefluorescence of Cr-doped sapphire has been extensively used to measure residual stressesin DSE oxides using an optical microprobe [21,119–122]. This non-contacting techniqueis very simple, does not require any specimen preparation, has an excellent lateral spatialresolution (of up to a few microns) and provides good precision in the stress measurement.As is well known, the majority of ceramics are optically transparent because of their largeband gaps but the presence of impurities (mainly transition metal and rare earth ions) cancause intense fluorescence resulting from the electronic transitions of the dopant ions. Forinstance, the O2� ions in sapphire are arranged in a hexagonal closed-packed lattice struc-ture, with the Al3+ ions occupying 2/3 of the octahedral sites. Small amounts of Cr3+

impurities are currently present in the sapphire, and they substitute the Al3+ ions in theoctahedral sites leading to a small trigonal distortion of the lattice. The resulting sequenceof the electronic Cr3+ levels is characterized by two states, whose energy differences withthe ground state are 14,403 cm�1 and 14,433 cm�1 at ambient temperature for small Cr3+

concentrations and in absence of stress. This leads to the presence of two very narrow radi-ative emission bands in the optical spectrum of ruby (Cr-doped sapphire) denominated R1and R2 at the 14,403 cm�1 and 14,433 cm�1 wavenumbers, respectively. These character-istic lines are extremely sensitive to the local ionic environment, as described by the ligandfield theory, and externally applied strains change the Cr3+ ion position within the octa-hedron of O2� ions, modifying the energy differences with the ground state of the twoenergy levels. This is the piezospectroscopic effect which results in the shift of the positionof R1 and R2 lines in the spectra. Forman et al. [124] suggested the use of the R1 line shiftto monitor pressure in diamond anvil cells, and subsequent developments by Clarke et al.[125,126] have taken advantage of this phenomenon to measure residual stresses in poly-crystalline and single crystal alumina and alumina-containing ceramics.

2 Throughout this section, bold lowercase roman and Greek letters stand for second rank tensors, and boldcapital letters for fourth rank tensors. In addition, the different products are expressed as (A : a)ij = Aijklakl, andb : a = bklakl. Finally, �a represents the volumetric average of a.


A phenomenological relationship between the line shift and the applied stress was firstpresented by Grabner [127], where the frequency shift of a fluorescence line, Dm, could beexpressed as a linear function of the stress state given by

Dm ¼ p : r; ð5:4Þwhere r is the applied stress tensor and p is second rank piezospectroscopic tensor. Grab-ner proposed that this latter tensor is symmetric, following the symmetry of the stress ten-sor. Hence the piezospectroscopic tensor for spectra of single, isolated dopant ions, such asCr3+ R lines, should follow the instantaneous point symmetry of the dopant ion in thecrystalline lattice during deformation, and this assumption implies that the piezospectro-scopic tensor is diagonal (pij = 0 if i 5 j) if the reference frame for the piezospectroscopictensor is defined by the three crystallographic a, m and c axes of hexagonal lattice. Follow-ing these hypotheses, He and Clarke [128] determined experimentally the three piezospec-troscopic constants for the R1 and R2 fluorescence lines of ruby (0.05 wt% of Cr3+) at20 �C from uniaxial compression tests, which are given by

Dm1 ¼ 2:56r11 þ 3:50r22 þ 1:53r33;

Dm2 ¼ 2:65r11 þ 2:80r22 þ 2:16r33;ð5:5Þ

where the shift is expressed in cm�1 and the stresses in GPa. Moreover, the results of sheartests showed that the off-diagonal components of pij, if non-zero, are less than 10% of thediagonal components. These piezospectrocopic coefficients are rather insensitive to theCr3+ content and thus can be used to measure stresses in all kind of alumina-containingmaterials. In addition, extrapolation of these coefficients to the tensile range is sensibleif the elastic strains are moderate, and they have been used to monitor the tensile stressesin bundles of alumina fibers [126].

The details of the experimental set-up to measure accurately residual stresses in DSEusing this technique can be found in Refs. [21,119–122] and are not repeated here. The vol-ume of material analyzed was �1 lm in diameter and �4 lm in depth, and luminescencewas measured with a spectral resolution of 0.15 cm�1, while R-line positions and widthwere obtained by fitting the spectra to a pseudo-Voigt function. It should be mentionedthat besides the shift in the peak, the R lines in DSE oxides were broader than inunstressed ruby due to inhomogeneous distribution of residual stresses among the aluminadomains in the eutectic microstructure. This inhomogeneity in the stress distributionwithin the sapphire phase was clearly detected in measurements at 77 K, where the thermalbroadening of R lines is minimum [120].

5.3. Modeling

The experimental measurement of the residual stresses has to be accompanied by themicromechanical modeling of their development upon cooling to ascertain the actualmechanisms (thermal expansion mismatch, stress-free temperature, phase transformation,microcracking, etc.) controlling the residual stresses, and the influence of the microstruc-tural factors (volume fraction, shape and spatial distribution of each phase) on their mag-nitude. Moreover, accurate micromechanical models can supply guidelines for the designof eutectic structures with optimized residual stress fields for specific applications.

The classical micromechanical models provide the thermo-mechanical response (alsodenominated effective) of a representative volume element of the material which is much


larger than the heterogeneities in the microstructure from the rigorous description of thevolume fraction, shape and spatial distribution of the various phases in the material and oftheir corresponding constitutive equations. Detailed descriptions of these techniques arebeyond the scope of this review and can be found in the literature [129,130]. DSE oxidesare formed by a dispersion of two ceramic phases whose deformation is well representedby a thermo-elastic solid; the following discussion will be focused on the two approxima-tions widely used to describe the behavior of two-phase thermo-elastic solids with perfectlybonded interfaces: the Mori–Tanaka [131,132] and the self-consistent models [133]. Exten-sions of these models to three-phase materials (which may be of interest in the case, forinstance, of Al2O3–YSZ–YAG ternary eutectics) are straightforward and can be foundin [134,23].

The thermo-elastic response of a representative volume element of the eutectic two-phase material subjected to a uniform overall stress and strain, expressed by the corre-sponding tensors r and e, and to a uniform change in temperature h is given by

r ¼ C : eþ lh and e ¼ S : rþmh; ð5:6Þwhere C and S, are the effective stiffness and compliance tensors of the eutectic compositeand l and m stand for the corresponding second rank thermal strain and stress tensors. Forconsistency, they must satisfy C = S�1 and l = �C : m. Mean-field approximations (suchas the Mori–Tanaka and the self-consistent method) assume that the stress and strainfields in each phase i (=1,2) are well represented by the volume-averaged values, �ri and�ei, which can be computed by integration over the representative volume element V as

�ri ¼1

V i

ZV i

ri dV and �ei ¼1

V i

ZV i

ei dV ; ð5:7Þ

where Vi is the volume of phase i and V1 + V2 = V. In turn, the composite stress and strainare obtained by integration of the corresponding stresses and strains in each phase withinV. This operation, called homogenization, is expressed as

r ¼X

i

fi�ri and e ¼X

i

fi�ei; ð5:8Þ

where fi stands for the volume fraction of phase i. The effective stress and strain in thecomposite eutectic are related to the average stress and strain in each phase through therespective mechanical and thermal stress and strain concentration tensors,

�ri ¼ Bi : rþ bih and �ei ¼ Ai : eþ aih ð5:9Þwhich clearly satisfy the following relationshipsX

i

fiAi ¼ I ;X

i

fiBi ¼ I ;X

i

fiai ¼ 0;X

i

fibi ¼ 0; ð5:10Þ

where I is the unit tensor of fourth rank. To determine the average stresses induced inphase i by an external stress r and/or by a temperature change h, it is only necessary toknow the expressions for the mechanical (Bi) and thermal (bi) stress concentration factors.They are given by [134]

Bi ¼ ðC i : AiÞ : C�1;

bi ¼ ðI � BiÞ : ðC�11 � C�1

2 Þ�1 : ðm2 �m1Þ

h i;

ð5:11Þ


and depend on the elastic stiffness tensors (C1 and C2) and thermal stress tensors (m1 andm2) of each phase and on the elastic stiffness C of the two-phase eutectic composite, whichcan be obtained easily from (5.6)–(5.10) as

C ¼X

i

fiC i : Ai ¼ C1 þ f2ðC2 � C1Þ : A2. ð5:12Þ

Obviously, the effective composite stiffness depends on the elastic properties and volumefraction of both phases as well as on the strain concentration tensors which, in turn,depend on the volume fraction, shape, and constitutive equation of each phase. Their sim-plest form is given by A1 = A2 = I, the well-known isostrain model, which leads to a verypoor approximation in most microstructures.

More realistic values of the strain concentration tensors can be obtained following var-ious methods. The simplest one, within the framework of linear elasticity, is based on thepioneer work of Eshelby [135] who analyzed the stress distribution in an elastic and iso-tropic ellipsoidal inclusion embedded in an elastic, isotropic and infinite matrix which issubjected to a remote strain e. Eshelby showed that the strain field within the inclusion,ein, was constant and was expressed by [133,135]

ein ¼ Adil : e where Adil ¼ I þ ðEin : C�1m Þ : ðC in � CmÞ

�1; ð5:13Þ

where Cm and Cin stand for matrix and inclusion stiffness tensors, respectively, and Ein isthe Eshelby’s tensor for the inclusion, whose components depend on the inclusion shape aswell as on the matrix elastic constants. The superscript dil indicates that this expression isonly valid when the volume fraction occupied by the inclusion is very small (for practicalpurposes, below 10%).

There are many extensions of Eshelby’s method to account for a higher volume fractionof inclusions and the most popular are the Mori–Tanaka and the self-consistent model.The Mori–Tanaka approximation is better suited to heterogeneous materials with a topol-ogy characterized by inclusions dispersed in a continuous matrix, which is found in fibrouseutectics as well as in degenerated lamellar microstructures formed by the dispersion ofirregular platelets of one eutectic phase into the higher volume fraction phase. Under theseconditions, the connected phase acts as the matrix and the strain concentration tensor ofphase 2 (the dispersed one) is given by [131,132]

A2 ¼ Adil : ½ð1� f2ÞI þ f2Adil��1. ð5:14Þ

The self-consistent method, which was developed to compute the effective elastic prop-erties of polycrystalline solids, is particularly appropriate when the various phases are dis-tributed forming an interpenetrating network, as found in many DSE oxides with CSmicrostructure. Both phases in the composite are assumed to be embedded in an effectivemedium, whose properties are precisely those of the composite, which are sought. The cor-responding strain concentration tensor for each phase, Asc

i , is obtained from Eshelby’sdilute solution (Eq. (5.12)) substituting the matrix elastic constants by those of the effectivemedium, C. Mathematically [133]

Asci ¼ I þ ðE i : C�1Þ : ðC i � CÞ

�1. ð5:15Þ


Introducing Eq. (5.15) in (5.12), it leads to

C ¼ C1 þ f2ðC2 � C1Þ : ½I þ ðE2 : C�1Þ : ðC2 � CÞ��1; ð5:16Þ

where Eq. (5.15) stands for a non-linear set of equations for the components of C whichcan be solved numerically to obtain the elastic constants of the heterogeneous solid. Itshould be noted that Eshelby’s tensor depends on the inclusion shape as well as on theelastic constants of the effective medium given by C.

Both Mori–Tanaka and the self-consistent model can be used to determine the residualstresses generated upon cooling in DSE from the elastic constants of each crystal, theirvolume fraction and the shape of the eutectic domains. In addition, it is necessary to knowthe ‘‘stress-free’’ temperature, at which the build-up of elastic stresses begins. The elasticstrains generated by the thermal expansion mismatch above this temperature aresmoothed out by the plastic deformation of one (or both) phases. An approximate valueof this temperature can be estimated from the minimum temperature necessary to activatethe slip systems in the eutectic crystals, or from experimental data of the residual stressesalong one direction in one phase. Finally, it should be noted that this methodology canalso include the residual stresses induced by phase transformations upon cooling or heat-ing [21,119]. The volumetric strain in one phase due the phase transformation is mathe-matically equivalent to a thermal strain and can be added to the thermal strains in Eq.(5.9).

The mean-field models described above provide very powerful tools to compute theresidual stresses in DSE with a complex microstructure formed by fibers, colonies ordegenerated lamellae. However, the residual stresses in perfect lamellar eutectics can becomputed more easily due to the symmetries of the problem and even analytical expres-sions can be obtained. In a first approximation, lamellar eutectics can be viewed as astack of isotropic, elastic slabs of phases A and B perfectly bonded at the interface.The deformation perpendicular to the lamella is not constrained and the thermal residualstresses along this axis are zero. The in-plane stresses in both phases are isotropic andcan be computed imposing the isostrain and the force equilibrium conditions. This leadsto

rA ¼ DaE�Ah 1þ tA

tB

E�AE�B

� ��1

and rB ¼ �tA

tB

rA ð5:17Þ

where rA and rB are the in-plane residual stresses in the lamellae of phase A and B, tA andtB stand for the corresponding lamella thicknesses, E�A and E�B are the elastic lamella con-stants expressed in terms of the elastic modulus and the Poisson’s coefficient of each phaseas E/(1 � v), and Da is the average mismatch in the thermal expansion coefficient of bothphases. More complex expressions can be obtained from the same hypotheses if the eutec-tic lamellae are orthotropic in the lamella plane (as it is often the case because the eutecticdomains are single crystals which grow in well defined crystallographic directions) andthey can be found in laminate theory textbooks [136].

5.4. Results

The development of residual stresses has been studied in a number of eutectic systemsusing the experimental and analytical tools described above, and the main results are

Table 5.1Elastic constants and thermal expansion coefficients of single crystal Al2O3 [137,138], ZrO2 [139], NiO [117,140],and YAG [23]

Constanta

C11

(GPa)C12

(GPa)C13

(GPa)C33

(GPa)C44

(GPa)m1

b (�C�1 · 10�6) m3b (�C�1 · 10�6)

Al2O3 495 160 115 497 146 8.0 9.2YSZ (tetragonal/cubic)c 288 85.3 12.65 12.65ZrO2 (monoclinic)c 288 85.3 7.5 7.5NiO 270 125 125 270 105 16.7 16.7Y3Al5O12 334 111.2 111.2 334 115.1 8.0 8.0

a The Al2O3 single crystal is transversally isotropic in the basal x1–x2 plane and the c-axis corresponds todirection x3.

b Average values between 1150 �C and 25 �C.c All the ZrO2 polymorphs are assumed to be elastically isotropic to compute the thermal residual stresses and

only two elastic constants are given.


presented in the following sections. The corresponding thermo-elastic constants of theeutectic phases can be found in Table 5.1 [119,137–140].

5.4.1. Al2O3–YSZ system

Al2O3–YSZ DSE oxides are formed by dispersion of YSZ domains within a continuoussingle crystal Al2O3 matrix with the c-axis parallel to the solidification direction. Therespective volume fractions of YSZ and Al2O3 are 30% and 70%, and Y2O3 is alwaysfound in solid solution within the ZrO2. The residual stresses in this system have been mea-sured at ambient temperature [21,119–122] and down to �196 �C [120] using the shift inthe R1 and R2 lines of the fluorescence spectrum of sapphire, which contained smallamounts of Cr3+ impurities, and these analyses were completed with simulations usingthe self-consistent model [21,119]. These detailed investigations have shown that the resid-ual stresses depend on three factors: the nucleation (or not) of the tetragonal to monoclinicmartensitic transformation in the ZrO2 domains upon cooling, the mismatch in the ther-mal expansion coefficients between Al2O3 and the various ZrO2 polymorphs (either mono-clinic, tetragonal or cubic) which may coexist in the eutectic, and the morphology andspatial distribution of the ZrO2 domains within the Al2O3 matrix. This latter factordepends on the solidification rate, which may lead to very different microstructures, asshown in Section 2.

The influence of the martensitic transformation on the residual stresses was carefullyanalyzed by Harlan et al. [21], who grew Al2O3–ZrO2 eutectic rods containing 0–12.2 mol% of Y2O3 (in relation to ZrO2) using the LFZ method. Processing conditionswere chosen to achieve a homogeneous CS microstructure in all the rods. The resultingmaterials were formed by a dispersion of irregular, elongated ZrO2 platelets of �2 lmin thickness and oriented along the solidification axis, with an aspect ratio of �3. The pro-portion of monoclinic ZrO2 in the rods with low yttria content (<3.5 mol%) was deter-mined from the relative intensity of the 177 cm�1 and 260 cm�1 peaks in the Ramanspectra of ZrO2, which are shown in Fig. 5.1(a), according to the expression [141]

xt

xm

¼ I260

1:8I177

and xm þ xt ¼ 1 ð5:18Þ

100 200 300 400 500 600 700

Ram

an i

nten

sity

Wavenumber (cm-1

)

Y (%)

0

0.44

0.9

1.5

2.0

3.3

5.2

7.5

8.6

12.2

m

t

a(a)

0

20

40

60

80

100

xm

xt

+ xc

0 2 4 6 8 10 12

Vol

ume

frac

tion

(%)

Y (%)

(b)

Fig. 5.1. (a) Ambient temperature Raman spectra of Al2O3–ZrO2(Y2O3) DSE as a function of the yttria content(Y) expressed by the mol% of Y2O3 dissolved into the ZrO2. The alumina peaks are marked with an ‘‘a’’, thetetragonal and monoclinic zirconia peaks used to quantify the volume fraction of each phase are marked with ‘‘t’’and ‘‘m’’. (b) Volume fraction of monoclinic (xm) and tetragonal plus cubic (xt + xc) phases in the ZrO2 as afunction of the yttria content Y. (Reprinted by permission of the American Ceramic Society from [21].)


where xt and xm stand for the volume fraction of tetragonal and monoclinic ZrO2 in theeutectic (Fig. 5.1(b)). The spectrum shows that Raman peaks of monoclinic ZrO2 are notpresent when the yttria content is above 3.3 mol% and that tetragonal ZrO2 is progres-sively substituted by the cubic phase as the yttria content increases. However, this latter


fact is not important in our case because both cubic and tetragonal ZrO2 contributeequally to the residual stresses as they have very similar elastic constants and thermalexpansion coefficients.

The average residual stresses in alumina, parallel (rk, along the solidification direction)and perpendicular (r?) to the rod axis, were determined assuming that the residual stressstate was transversally isotropic, a sensible hypothesis taking into account that the Al2O3

continuous phase kept this symmetry and that the contribution of the ZrO2 crystals wasisotropic as they were oriented in various directions. They are plotted as a function ofthe yttria content in Fig. 5.2, and were compressive, composition independent and isotro-pic in the absence of monoclinic ZrO2 (Y > 3.5%). The presence of monoclinic ZrO2 chan-ged the sign of the residual stresses in Al2O3 from compressive to tensile, and induced amarked anisotropy with longitudinal stresses much higher than the transverse ones. More-over, the variability in the residual stresses increased as the yttria content decreased, asshown by the error bars in Fig. 5.2, and this reflects the variability of the stress valuesin different regions of the sample. Finally, there was a marked relaxation of the longitudi-nal residual stresses in the sample without yttria.

Simulations using the self-consistent scheme were fundamental to understanding thecomplex behavior depicted in Fig. 5.2. The eutectic microstructure was represented by adispersion of ZrO2 ellipsoids with an aspect ratio of 3 oriented along the solidification axis.The Al2O3 matrix was modeled as a transversally isotropic thermoelastic solid around thec-axis and their five independent elastic constants as well as the two average thermalexpansion coefficients (parallel and perpendicular to the c-axis) are shown in Table 5.1.The contribution of the ZrO2 crystals was assumed to be isotropic in the absence of awell-defined growth habit and the elastic constants and thermal expansion coefficientsof monoclinic, tetragonal and cubic ZrO2 are also given in Table 5.2. The elastic constantsof monoclinic ZrO2 were taken as equal to those of the tetragonal polymorph due to the

-800

-400

0

400

800

1200

1600

2000 σII

σ⊥

0 2 4 6 8 10 12

Res

idua

l st

ress

(M

Pa)

Y (%)

Fig. 5.2. Residual stresses in Al2O3 parallel (rk, along the solidification direction) and perpendicular (r?) to therod axis as a function of the yttria content Y in Al2O3–ZrO2(Y2O3) DSE. (Reprinted by permission of theAmerican Ceramic Society from [21].)


lack of experimental data. The model also included the effect of the volumetric strain of4.67% associated with the martensitic transformation in the samples with low yttria con-tent, and the amount of transformed material was given by the data in Fig. 5.1(b). Finally,the stress-free temperature of the eutectic composite was taken as 1150 �C, which is inagreement with the minimum temperature necessary to activate plastic deformation inYSZ (�1200 �C [142]), while slip in single crystal Al2O3 occurs at 900 �C in the basal planeand at 1150 �C in prismatic and pyramidal planes [143].

The model predictions for the residual stresses in Al2O3 at ambient temperature areplotted in Fig. 5.3(a). They show that, in the absence of the martensitic transformation

-800

-400

0

400

800

1200

1600

2000σ

II

σ⊥

0 2 4 6 8 10 12

Res

idua

l st

ress

(M

Pa)

Y (%)

(a)

no relaxation by basal slip

-800

-400

0

400

800

1200

1600

2000 σII

σ⊥

0 2 4 6 8 10 12

Res

idua

l st

ress

(M

Pa)

Y (%)

(b)

relaxation by basal slip

Fig. 5.3. Self-consistent simulations of the residual stresses in Al2O3 in the parallel and perpendicular directionsas a function of the yttria content Y in Al2O3–ZrO2(Y2O3) DSE. (a) Without relaxation in the alumina basalplane, (b) with relaxation in the alumina basal plane. (Reprinted by permission of the American Ceramic Societyfrom [21].)


(Y > 3%), the residual stresses are controlled by the thermal expansion mismatch betweenAl2O3 and YSZ, which led to the development of compressive stresses in the former andtensile (�0.9 GPa) in the latter. The longitudinal stresses were slightly higher due to theanisotropy in the thermal expansion coefficients of Al2O3 but the stress state was predom-inantly hydrostatic. The residual stresses changed from compressive to tensile as thevolume fraction of transformed ZrO2 increased, indicating that they were controlled bythe volumetric strain associated with the martensitic transformation. Although the parallelstresses in Al2O3 were similar to the experimental results in the range 0.45% < Y < 3.3%,the computed transversal component was significantly higher. A very likely explanation ofthis behavior was the relaxation of volumetric strains resulting from the martensitictransformation along the perpendicular direction by basal slip in ZrO2 because the temper-ature at which the martensitic transformation occurs (950 �C) is very close to that neces-sary to activate dislocation motion in the Al2O3 basal planes. This mechanism wasaccounted for in the second simulations, which assumed that the volumetric strainsgenerated by the martensitic transformation did not contribute to the generation of resid-ual stresses in the transversal direction. The results are plotted in Fig. 5.3(b), andthe agreement with the experimental data in the transverse direction is much betterthan in Fig. 5.3(a). In fact, the results in Fig. 5.2 fall between those plotted inFig. 5.3(a) and (b) in the range 0.45% < Y < 3.3%, and the actual mechanisms of deforma-tion in the eutectic should involve some degree of stress relaxation by basal slip uponcooling.

The biggest discrepancy between the self-consistent simulations and the experimentaldata was found in the eutectic without yttria. While the model predicted tensile residualstress in Al2O3 in the range 1.2–1.6 GPa along the rod axis, the experimental data onlyreached 0.4 GPa. This difference was due to the development of microcracking in theeutectic, as shown in Fig. 5.4. These defects were nucleated at the Al2O3–ZrO2 interfaceto accommodate the twinning of the ZrO2 grains resulting from the tetragonal-to-mono-clinic martensitic transformation (Fig. 5.5) and they grew driven by high tensile residualstresses induced in the Al2O3 phase by the volumetric change associated with the martens-itic transformation to form the defects in Fig. 5.4. These defects appeared in all the sam-ples with Y < 3% and were responsible for the large variability in the residual stressesindicated by the large error bars in Fig. 5.2. Moreover, they were nor present in the mate-rials with Y > 3% because no microcracks were nucleated at the ZrO2/Al2O3 interface inthe absence of the martensitic transformation and the propagation of interface cracks gen-erated by any other cause was impeded by the compressive residual stresses in the contin-uous Al2O3 phase.

The influence of the morphology and spatial distribution of the ZrO2 domains on theresidual stresses was studied in [119,121] in eutectics with Y = 0% and 9%. Residual stres-ses in the Al2O3 phase were measured in Al2O3–ZrO2 eutectics with three different micro-structures: a regular dispersion of monoclinic ZrO2 fibers of �0.3 lm in diameter and>60 lm in length, and two materials formed by a homogeneous dispersion of degeneratedlamellae (as in Fig. 5.4) of different thicknesses. The experimental values of the residualstresses are presented in Table 5.2 together with the average lamella (or fiber) spacing t.They show that anisotropy between rk and r? (which appears as a result of the martensitictransformation and the stress relaxation by basal slip) is enhanced if the ZrO2 domainshave the shape of elongated fibers. In addition, the residual stresses in microstructuresformed by a dispersion of disordered lamellae decreased rapidly as the lamellae size

Fig. 5.4. Secondary-electron micrograph of the Al2O3–ZrO2 DSE showing microcracking. (a) General view, (b)detail showing cracks and defects at the interface. Monoclinic ZrO2 stands as the white phase. Growth axis isvertical. (Reprinted by permission of the American Ceramic Society from [21].)


(and the spacing) increased. Analysis of the microstructures in the SEM showed residualstress relaxation by microcracking in the material with t � 1.8 lm but not in the other two,and points to a size effect induced by the ability of very fine microstructures to withstandlarge tensile residual stresses without damage.

The effect of the microstructure on the residual stresses was not important, however, inthe case of Al2O3–ZrO2 eutectics with Y = 9% [119]. The residual stresses were very similarin the parallel and perpendicular directions regardless of whether the cubic or tetragonalZrO2 domains were elongated fibers or irregular lamellae, and the experimental resultswere confirmed by self-consistent simulations. While in the absence of yttria the residualstresses are mainly controlled by the martensitic transformation, the anisotropy in theresidual stresses comes from two sources in materials with YSZ: the elongated shape ofthe ZrO2 domains (either lamellae or fibers) and the anisotropy in the Al2O3 thermalexpansion coefficients. These two factors operate in opposite directions and lead to ahydrostatic residual stress state. Moreover, the nucleation and growth of defects isimpeded in these materials by the compressive residual stresses in the continuous Al2O3

Fig. 5.5. TEM micrograph of a monoclinic ZrO2 lamella within the Al2O3 in an Al2O3–ZrO2 DSE showing thenucleation of interfacial cracks as a result of twinning associated with the martensitic transformation in ZrO2.(Reprinted by permission of Elsevier from [74].)

Table 5.2Residual stresses at ambient temperature in the longitudinal (growth) and perpendicular directions in the Al2O3

phase of Al2O3–ZrO2 eutectics with different microstructure

Shape of the ZrO2 domains t (lm) rk (GPa) r? (GPa)

Ordered rods 0.6 2.0 ± 0.4 0.7 ± 0.2Disordered lamellae 0.75 1.1 ± 0.4 0.5 ± 0.2Disordered lamellae 1.8 0.5 ± 0.15 0.19 ± 0.03


phase and the effect of lamella size on the residual stresses observed in materials withoutyttria was not present.

5.4.2. Al2O3–YAG system

Al2O3–YAG DSE present a microstructure formed by an interpenetrating network ofAl2O3 and YAG in the proportion 55/45. The residual stresses in this system were expectedto be low because the thermal expansion coefficient of YAG (8 · 10�6 �C�1) is very closeto that of the Al2O3 (see Table 5.1). This hypothesis was confirmed by Dickey et al. [6],who measured residual stresses in both phases by X-ray diffraction in eutectic crystals pro-cessed by the LFZ method and found values below 100 MPa in both phases, in agreementwith the predictions provided by the self-consistent simulations.

5.4.3. NiO–ZrO2 and Co1�xNixO–ZrO2 systems

NiO–ZrO2 DSE present a regular lamellar microstructure made up of cubic NiO (56%)and cubic ZrO2 (44%) crystals which grow with specific crystallographic orientations½�110�NiOk½010�ZrO2

and ð111ÞNiOkð100ÞZrO2[144]. Cubic ZrO2 was obtained by adding


9 mol% of Y2O3 as stabilizer to the eutectic powders and the resulting material presented astrong, clean, abrupt interface between the two phases, which was able to withstand thelarge thermal residual stresses generated upon cooling from the eutectic temperature(�1700 �C) owing to the strong interfacial bonding which stems from the electrostaticbonding between the polar cation sheets (Ni2+ in the {11 1} plane and Zr4+ in the{10 0} plane) by an interfacial sheet of O2�. Residual stresses at ambient temperature weremeasured in each phase by X-ray diffraction [118] and the results are shown in Table 5.3,where directions 1 and 2 are parallel to the interfaces and direction 3 is perpendicular tothe lamellae. The stresses perpendicular to the lamellae should be zero in a perfect bicrystaland the reduced values measured by X-ray (as compared to the in-plane stresses) could beattributed to surface effects and irregularities in the microstructure (faults and curvedlamellae). The in-plane stresses were very similar in directions 1 and 2 and they fulfilledthe force balance condition (Eq. (5.17)) along each axis with r33(NiO) � �0.79r33(ZrO2). However, the actual prediction of the residual stresses in both phases usingEq. (5.17) and the elastic constants and thermal expansion coefficients in Table 5.1 is hin-dered because the stress free temperature is not known and may be influenced up to a largeextent by the onset of plastic deformation in NiO at intermediate temperatures (Guiber-teau et al. [145] have reported the activation of the {10 0}h110i slip system in NiO at500 �C), which in turn depends on the residual stresses themselves and on the plastic con-straint induced by the small lamella thickness.

An interesting study of the effect the thermal expansion coefficient mismatch on theresidual stresses was carried out by Brewer et al. [117], who measured the residual stressesby X-ray and neutron diffraction in Co1�xNixO–ZrO2(CaO) DSE with x = 0.5, 0.6 andcompared the results with those measured in NiO–ZrO2(CaO). Co1�xNixO–ZrO2(CaO)is a solid-solution DSE which is isostructural with NiO–ZrO2(CaO) possessing a lamellarmorphology and the same interfacial stacking sequence involving the {111} planes ofCo1�xNixO and the {100} planes of cubic ZrO2. The thermal expansion coefficient ofCo1�xNixO at high temperature (1300–1400 �C) is �20.4 · 10�6 �C for 0.3 < x < 0.6, sig-nificantly higher than that of CoO and NiO [146], and this enhances the generation of ther-mal residual stresses upon cooling. The experimental values of the residual stresses in bothphases are presented in Table 5.4 for materials with x = 0.5, 0.66 and 1. They are in agree-ment with those measured by neutron diffraction in the Co1�xNixO phase, and this showsthat surface relaxation of stresses does not influence significantly the residual stresses mea-sured by either X-ray diffraction or piezospectroscopic techniques. As expected, the resid-ual stresses in Co1�xNixO–ZrO2 eutectics were enhanced, as compared to NiO–ZrO2, dueto the higher thermal expansion mismatch. However, they should be much larger accord-ing to Eq. (5.17), which predicted values around 1.7 GPa in each phase assuming a stress

Table 5.3Residual stresses at ambient temperature in the NiO–cubic YSZ eutectics with lamellar microstructure [118]

Phase r11 (GPa)a r22 (GPa)b r33 (GPa)c

NiO 0.91 ± 0.02 0.88 ± 0.02 �0.21 ± 0.02Cubic YSZ �1.1 ± 0.1 �1.1 ± 0.1 �0.16 ± 0.10

a Direction 1 corresponds to the ½�1�12� in NiO and [001] in ZrO2.b Direction 2 corresponds to the ½�110� in NiO and [010] in ZrO2.c Direction 3 corresponds to the [111] in NiO and [100] in ZrO2.

Table 5.4In-plane residual stresses at ambient temperature in the Co1�xNixO–cubic ZrO2(CaO) eutectics with lamellarmicrostructure [117]

Composition x = 0.5 x = 0.66 x = 1

Phase Co1�xNixO ZrO2 Co1�xNixO ZrO2 NiO ZrO2

r11 (GPa)a 1.0 ± 0.09 �0.93 ± 0.08 1.4 ± 0.1 �1.70 ± 0.04 0.93 ± 0.02 �1.05 ± 0.06r22 (GPa)b 1.1 ± 0.13 �1.6 ± 0.1 1.4 ± 0.1 �1.34 ± 0.05 0.93 ± 0.02 �0.84 ± 0.05

a Direction 1 corresponds to the ½�1�12� in Co1�xNixO and [001] in ZrO2.b Direction 2 corresponds to the ½�110� in Co1�xNixO and [010] in ZrO2.


free temperature of �1200 �C. This demonstrates the important role played by the stressrelaxation mechanisms upon cooling. In particular, the stress necessary to promote plasticslip decreases as the Co content increases in this material [147], and this phenomenon wasresponsible for the difference in the residual stresses of the eutectics with x = 0.5 andx = 0.66.

5.4.4. Al2O3–YAG–YSZ ternary eutectic system

More recently, the residual stresses have been measured in ternary Al2O3–Y2O3–ZrO2

[23] eutectic rods grown by the LFZ method. They presented a CS microstructure formedby an interpenetrating network of Al2O3 and YAG domains with respective volume frac-tions of 40% and 42%. The remainder (18%) was formed by smaller cubic YSZ domains,normally located at the Al2O3/YAG interfaces. Compressive residual stresses were mea-sured in Al2O3 by piezospectrosocopy, and their absolute value increased from 160 MPain the rods grown at 1000 mm/h to 300 MPa in those grown at 10 mm/h. Self-consistentsimulations carried out with the thermo-elastic constants and stress-free temperatures ofAl2O3–YSZ and Al2O3–YAG eutectics predicted compressive residual stresses in Al2O3

of 200 MPa, in excellent agreement with the experimental results and a confirmation ofthe thermo-elastic origin of these residual stresses in this ternary eutectic. The self-consis-tent results also showed that YAG and YSZ were subjected to tensile residual stresses of295 MPa and 1130 MPa, respectively. It is worth noting that no interface cracks wereobserved in the microstructure, an indication of the excellent interfacial strength in theseeutectics.

6. Mechanical behavior

The mechanical properties of DSE oxides are dictated by the ionic bonding between theatoms and by the peculiar characteristics of the eutectic microstructure, which sharesmany similarities with single-crystal oxides and ceramic composites. Ionic bonding leadsto hard and brittle materials with high elastic modulus and high melting point, and whereplastic deformation is impeded up to very high temperature. DSE oxides have well definedcrystallographic orientations and do not present grain boundaries (or are coarse-grained,as compared with sintered counterparts), and hence their creep resistance is comparable tothat of single-crystal oxides. In addition, their microstructure is formed by the dispersionof two (or more) phases and presents a large surface fraction of clean, strong interfacesbetween the eutectic domains. The size of the defects which control the strength is relatedto the morphology of the phases in the microstructure and the thermo-elastic residual


stresses and domain interfaces interact with propagating cracks leading sometimes tocrack arrest and deflection, as in ceramic composites. In the following sections, the rela-tionship between the mechanical properties of DSE oxides and their composition andmicrostructure is analyzed, with results up to very high temperatures where DSE oxidespresent a unique behavior.

6.1. Elastic modulus

Ceramic oxides are always very stiff as a result of the strong ionic bonding betweenanions and cations. The mismatch in the elastic modulus between the phases in the eutecticis always limited and never above a factor of two or three. Under these circumstances, themicromechanical models for the thermo-elastic behavior of heterogeneous materials (seeSection 5.3) predict that the elastic constants are a function of the elastic properties of eachphase and their respective volume fractions, while the effect of the spatial distribution of thephases is negligible. For instance, self-consistent estimations (Eq. (5.15)) of the longitudinalmodulus of Al2O3–YSZ eutectics predicted a difference of just 5% if the cubic ZrO2 phasewas dispersed in the form of spheres or long fibers oriented in the solidification direction.Hence theoretical predictions for the elastic modulus can be made for each DSE from theelastic constants of each phase as the phase volume fraction is fixed for each eutectic com-position (Table 5.1) assuming perfect bonding between the phases. Representative resultsobtained with the self-consistent approximation are presented in Table 6.1 for the elasticmodulus in the longitudinal (growth) direction of Al2O3–YSZ and Al2O3–YAG.

Experimental data on the elastic modulus of DSE oxides are scarce due to the limitedavailability of samples large enough to carry out the measurement and to the high stiffnessof the material, which requires non-standard techniques to measure the strain. Pastor et al.[20,148] determined the dynamic longitudinal modulus of Al2O3–YSZ and Al2O3–YAGsamples from the resonance frequency of simple supported beams excited in bending,and the results are shown in Table 6.1. They are in perfect agreement with the theoreticalpredictions in the case of Al2O3–YAG, and slightly below in that of Al2O3–YSZ. This dis-crepancy may be attributed to irregularities in the diameter of the small rods along theirlength and to the presence of internal pores or cracks in the microstructure. Ochiai et al.[149] studied the elastic anisotropy of Al2O3–YAG eutectics using the wave pulse echomethod along the longitudinal and transverse directions and found differences of around1%. In addition, Farmer ad Sayir [57] measured the elastic modulus with an optical exten-someter in hypoeutectic Al2O3–ZrO2 fibers which contained 77 vol.% of Al2O3 (7% abovethe eutectic composition). The modulus of the fibers containing tetragonal YSZ was370 GPa and decreased to 310 GPa as the yttria content increased due to the formationof crack-like shrinkage cavities. The modulus of Al2O3–ZrO2(m) fibers was only270 GPa due to microcracking induced by the martensitic transformation upon cooling.

Table 6.1Self-consistent estimates and experimental results for the longitudinal elastic modulus of DSE at ambienttemperature

DSE oxide Theoretical (GPa) Experimental results (GPa)

Al2O3–YSZ 370 343 ± 7 [20]Al2O3–YAG 340 340 ± 3 [148]

0

0.2

0.4

0.6

0.8

1

Load-deflection curves

Wave pulse echo

0 300 600 900 1200 1500 1800

E /

E25

°C

Temperature (°C)

Tm

Fig. 6.1. Evolution of the longitudinal elastic modulus of Al2O3–YAG DSE as a function of temperature. Datafrom load–displacement curves [148] and from wave pulse echo method [149].


Pastor and LLorca [148] determined the evolution of the elastic modulus with temper-ature in Al2O3–YAG eutectics processed by the Bridgman method. Parallelepipedic beamswere loaded in three-point bending and the modulus was obtained from the slope of theload-midspan deflection register in several loading and unloading cycles at each tempera-ture, where accurate values of the midspan deflection were obtained with a laser extensom-eter. The results are plotted in Fig. 6.1 and show that the elastic modulus remainedpractically constant up to 1300 �C, and then started to decrease as the eutectic temperatureof 1826 �C was approached. These results are in reasonable agreement with those obtainedby Ochiai et al. [149] with the wave pulse echo method from 25 �C up to 1500 �C. Theymeasured a constant reduction in modulus with temperature rather than from 1300 �C.Nevertheless, the moduli determined by both techniques at 1500 �C were very similar.

6.2. Strength

6.2.1. Ambient temperature

The mechanical strength of DSE oxides follows the behavior expected for stiff and brit-tle materials with low fracture toughness and is controlled by the defects in the material,which act as stress concentrators and lead to the nucleation of cracks. This has been dem-onstrated by fractographic studies in DSE oxides tested in tension and bending, whichidentified the critical surface defects by the convergence of the river line patterns foundon the fracture surface (Fig. 6.2) [104,105,107,20,57,150,4,151]. The size and shape of theseflaws depends mainly on the processing conditions and inhomogeneities, banding, and thegeneration of pores and shrinkage cavities3 reduces significantly the strength and increases

3 Shrinkage cavities appear when there is not enough liquid to flow into the intercellular regions, which are thelast to solidify, because they are too far away from the solidification front. The volumetric shrinkage on coolingleads to the development of shrinkage cavities with a crack-like morphology.

Fig. 6.2. SEM micrograph showing the fracture nucleation defect on Al2O3–YAG rods broken in three-pointbending at ambient temperature. (Reprinted by permission of the American Ceramic Society from [150].)


the scatter [151]. However, if these defects are removed by careful processing conditions,the critical flaws which control the strength are a function of the eutectic microstructure,which can be modified by the growth rate.

The effect of growth rate on the strength is evident in the Al2O3–YAG system. Themicrostructure of this eutectic is always formed by an interpenetrating network of bothphases in a proportion 55/45, and higher growth rates only reduce the average domainthickness without modifying the shape of the domains (Figs. 2.5 and 6.3). Several studies[106,150,152] have measured the ambient temperature strength of Al2O3–YAG eutecticsgrown at different rates whose domain thicknesses, t, were in the range 0.2–25 lm; theirresults are compiled in Fig. 6.4. Small diameter monofilaments were tested in tension whilerods and bulk specimens were fractured in three-point bending. The figure also includesone result corresponding to an Al2O3–Er3Al5O12 (EAG) eutectic, whose microstructureis equivalent to that of Al2O3–YAG. The eutectic strength was proportional to 1=

ffiffitp

, indi-cating that the critical defects responsible for brittle fracture depend on the size of theeutectic domains. In fact, if the critical flaws are approximated by semicircular surfacecracks with a radius equal to t, the eutectic strength, ru, is given (according to fracturemechanics) by

ru ¼ffiffiffipp

2

KCffiffitp ; ð6:1Þ

where KC stands for the fracture toughness. The linear fit to the experimental results inFig. 6.4 is obtained with KC = 1.6 MPa

pm. This value is only marginally lower than

the ambient temperature fracture toughness of Al2O3–YAG, �2 MPap

m, which is inde-pendent of the orientation and domain size [148,153]. More recent tests on Al2O3–YAGfibers of 130 lm in diameter grown between 150 mm/h and 1500 mm/h by the EFG meth-od have shown the same linear dependence of the tensile strength with t�0.5 [154].

Reduction in the domain thickness can also be achieved by adding a third phase to forma ternary eutectic composite, Al2O3–YAG–YSZ [22,23,155]. The resulting microstructureis comprised by an interpenetrating network of Al2O3 and YAG domains (40% and 42% involume, respectively) while cubic YSZ (18%) is found as small rounded domains mainly at

Fig. 6.3. Back-scattered SEM micrograph of the transverse section of the Al2O3–YAG rods showing theinterpenetrating network of Al2O3 (black) and YAG (white) domains. (a) Growth rate of 25 mm/h, (b) growthrate of 750 mm/h. (Reprinted by permission of the American Ceramic Society from [150].)


the Al2O3/YAG interfaces. Ternary eutectics showed higher room temperature strengththan binary ones grown at the same rate [22,156] and their flexure strength followed thetrend dictated by Eq. (6.1), as shown in Fig. 6.4, although this ternary eutectic exhibitedhigher toughness and was not free from residual stresses (see [23]). This indicates that as inthe Al2O3–YAG binary eutectics with CS microstructure, the defect size was controlled bythe lamella thickness.

The growth rate controls the strength of the Al2O3–YAG through the domain size butthis conclusion is not applicable to other DSE oxides. For instance, the flexure strength ofMgO–MgAl2O4 [157], ZrO2–MgO [158] and ZrO2–CaZrO3 [2] eutectics was independentof the solidification rate, while several studies in Al2O3–YSZ eutectics found the higheststrength at intermediate growth rates [107,8,159]. The complex effect of the solidificationrate on the strength in this latter system was systematically studied by Pastor et al. [151],who measured the flexure strength of Al2O3–YSZ rods grown from 20 mm/h up to1000 mm/h by the LFZ method. The microstructure of the rods grown at lower rateswas formed by a homogeneous dispersion of micron-sized irregular YSZ platelets withinthe Al2O3 matrix. At intermediate growth rates this microstructure was substituted by

0

0.5

1.0

1.5

2.0

2.5

3.0

Bending Al2O

3-YAG

Tension Al2O

3-YAG

Bending Al2O

3-EAG

Bending Al2O

3-YAG-YSZ

0 0.5 1 1.5 2 2.5

Str

engt

h (G

Pa)

1/¦t (μm-0.5)

Fig. 6.4. Ambient temperature strength of Al2O3–YAG [106,150,152], Al2O3–EAG [152] and Al2O3–YAG–YSZ[23,156] DSE as a function of the average thickness of eutectic domains, t. Rods and bulk specimens were tested inthree-point bending, while monofilaments were broken in tension.


colonies oriented perpendicularly to the solidification front. The colony core (formed by adispersion of submicron YSZ platelets embedded in the Al2O3 matrix) was surrounded bya thick intercolony region containing coarse YSZ particles of irregular shape. The rodsgrown at 1000 mm/h presented very long cells oriented along the growth axis. The cellswere formed by a dispersion of very fine YSZ lamellae and were separated by thin inter-cellular boundaries with coarser microstructure. The flexure strength of the rods is plottedin Fig. 6.5 as a function of a characteristic length of each microstructure, which was takenas the average dimension of the feature which defined the morphology of the microstruc-ture perpendicularly to the tensile stress. This length was the colony or cell diameterperpendicular to the growth axis in rods with cellular and colony microstructure. Theselection of the characteristic length of the rods formed by a homogeneous distributionof YSZ platelets was not so obvious, and various candidates (platelet width or separation)could be chosen. Both were of the order of 1 lm, and selecting one instead of the otherdoes not change the plot significantly.

The data in Fig. 6.5 showed that the highest strength was found in the eutectics formedby a homogeneous dispersion of small YSZ platelets, which were grown at the lowest rate.Moreover, the strength of eutectics with colony and cell microstructure tended to increaseas the colony or cell diameter decreased. This trend follows the behavior found in metalliceutectics and it is supported by the flexure strengths measured by Bates [160] on Al2O3–YSZ eutectic fibers prepared by the edge defined-film fed-growth method. Moreover, Ken-nard et al. fabricated MgO–MgAl2O4 [157] and MgO–CSZ [116] DSE of constant colonysize but with different spacing (by a factor of 4) between the MgO fibers within the coloniesby changing the growth rate. The flexure strength of these eutectics was independent of thegrowth rate and it was concluded that the colony size controlled the eutectic strength.However, as suggested in several publications [107,146,8], this relation holds good so longas the thickness of the intercolony/intercell region is below a critical value. Above this, the

0.6

0.8

1

1.2

1.4

1.6

1.8

PlateletsCellsColonies

0 5 10 15 20 25 30 35

Fle

xure

str

engt

h (G

Pa)

Characteristic length (μm)

Y = 3%

Y = 12%Al2O

3-YSZ

Fig. 6.5. Flexure strength of Al2O3–YSZ eutectic rods as a function of the average characteristic length of eachmicrostructure. Data from [151,159]. See text for details.


weak intercolony regions, which contain pores and microcracks, act as the stress concen-trators which nucleate the crack. An example is found in the two materials with similarcolony diameter (�18–19 lm) and different yttria content (Y = 3% and 12%), whosestrength is plotted in Fig. 6.5. Because of yttria segregation during solidification [161],the intercolony region was thicker in the eutectic with Y = 12%, and the flexure strengthof this latter material was dictated by the coalescence of pores and microcracks at theintercolony region (Fig. 6.6), leading to a much larger critical defect and thus reducingthe flexure strength by a factor of 2. This mechanism explains why the highest strengthhas been found at intermediate growth rates in eutectics with cellular microstructure[8,107,159]: increasing the growth rate reduces the colony size but also increases the thick-ness of the intercolony region, and this latter parameter (and not the colony diameter) con-trols the strength above a critical solidification rate.

An important issue in the strength of brittle materials is the variability, which is nor-mally characterized through the Weibull modulus. This parameter was measured by anumber of investigators in Al2O3–YAG [58] and Al2O3–YSZ [57,102,150] eutectics. HighWeibull moduli in the range 13–15 were measured in materials with a homogeneous micro-structure throughout the sample in both types of eutectics, but processing-related defects(such as shrinkage cavities [105,150] or banding [57]) led to a marked reduction of up to 3–6. Moreover, localized surface coarsening during a high temperature annealing due to con-tact with impurities (see Section 4.1) reduced significantly the Weibull modulus in fibers,which have a high specific surface and are very susceptible to the nucleation of thesedefects [104,105].

Finally, the sign and distribution of residual stresses is also an important factor and thishas been systematically studied in the Al2O3–ZrO2(Y2O3) system, where the presence ofyttria controls the residual stress distribution, as explained in Section 5. This effect wasanalyzed in [122,57] in fiber and rods and the strength (in bending for rods and in tensionfor fibers) is plotted in Fig. 6.7 as a function of the yttria content in the ZrO2 phase, given

Fig. 6.6. Fracture surface of Al2O3–YSZ eutectic rod (Y = 12%) broken at 0.52 GPa. (a) Low magnification, (b)high magnification, showing the surface defect formed by the coalescence of pores and cavities at the intercolonyregion, which nucleated the fracture. (Reprinted by permission of Elsevier from [151].)


by Y. The lowest strength was always found in the yttria-free samples, where zirconia hastransformed from tetragonal to monoclinic upon cooling from the processing temperature.The transformation nucleates microcracks at the interface (Fig. 5.4) and large tensile resid-ual stresses in the Al2O3 continuous phase, which facilitated the propagation of the cracksand impaired the eutectic strength. Tetragonal ZrO2 was found in the eutectics withY � 3% as the tetragonal to monoclinic transformation was completely suppressed byyttria. As a result, the thermo-elastic residual stresses were compressive in the Al2O3 phaseand the strength was almost twice that of the yttria-free materials. Further increase in theyttria content leads to the stabilization of the cubic ZrO2 phase in the eutectic, withoutsignificant changes in the residual stresses. However, higher yttria contents favor the for-mation or cracks and cavities at the intercolony regions and lead to a slight reduction instrength, which is consistent with the results reported by other investigators [161].

6.2.2. High temperature

The outstanding strength retention of DSE oxides at high temperature was reported inthe first investigations [4,2,146,157,159] and follows the microstructural characteristics of

0

300

600

900

1200

1500

Rods, flexure strength

Fibers, tensile strength

0 5 10 15 20 25

Str

engt

h (M

Pa)

Yttria content, Y (mol %)

ZrO2(t)

ZrO2(c)

ZrO

2(m

)

Fig. 6.7. Ambient temperature strength of Al2O3–ZrO2(Y2O3) eutectic fibers [57] and rods [122] as a function ofthe Y2O3 content, expressed by Y = mol% Y2O3/(mol% Y2O3 + mol% ZrO2).


these materials. In addition to the microstructural stability and oxidation resistance (seeSection 4), which limits the development of surface defects, the high temperature strengthof DSE oxides benefits from the clean and strong interfaces between the eutectic domains.Conventionally sintered oxide and non-oxide polycrystalline ceramics always present aglassy phase at the grain boundaries, and high temperature deformation occurs by grainboundary sliding, as opposed to the dislocation motion in DSE. The effect of bothmechanisms on the strength is shown in Fig. 6.8(a), where the flexure strength in Ar upto 1700 �C is plotted for Al2O3–YAG eutectics processed by conventional hot-press sinter-ing and directional solidification. The strength of the polycrystalline material obtained bysintering drops very quickly above 800–1000 �C due to the flow of the glassy phase at thegrain boundaries (Fig. 6.8(b)). On the contrary, the DSE oxides retained the ambient tem-perature strength up to 1700 �C because the domain boundaries were free of amorphousphases, Fig. 6.8(c), and the resistance to deformation was controlled by the activation ofplastic slip, as has been shown in a number of DSE such as Al2O3–YAG, Al2O3–EAG andAl2O3–GAP [152,162,7].

Single crystal oxides normally present higher ambient temperature strength than theDSE owing to smaller defect sizes but their high strength retention is poorer. In somecases, the strength of single crystal oxides, such as sapphire [94,107,8] and ZrO2(Er2O3)[95], experiences a noticeable reduction at intermediate and high temperatures due tothe thermally activated slow crack growth or stress corrosion cracking whereas DSE oxi-des do not undergo this degradation. Moreover, the domain boundaries in the eutectics actas barriers to dislocation motion at high temperature and can improve the resistance toplastic deformation.

The best high temperature strength among DSE oxides has been found in the Al2O3–YAG system. Due to the interpenetrated structure of both phases in the eutectic micro-structure and to the excellent resistance to dislocation motion of YAG, the strength ofthese materials remains constant up to 1400 �C and very little degradation is observed

Fig. 6.8. (a) High temperature flexure strength (in Ar) of Al2O3–YAG eutectics processed by directionalsolidification or sintered by hot pressing. (b) Transmission electron micrograph showing the presence of anamorphous phase at the grain boundary in the sintered Al2O3–YAG eutectic. (c) Transmission electronmicrograph showing the clean interface between Al2O3 and YAG domains of the directionally solidified material.(Reprinted by permission of Elsevier from [162] and of Springer [152].)


up to 1600 �C, Fig. 6.9(a) and only in the materials with smaller domain thickness. Theanalysis of the fracture surfaces of the specimens of t 6 1 lm broken at 1627 �C showedthat the faceted interfaces between Al2O3 and YAG had become rounded and the averagedomain thickness had increased, Fig. 6.9(b), and the reduction in strength was attributedto the homogeneous coarsening of the microstructure [150]. Al2O3–YAG eutectics testedin tension or bending showed a brittle/ductile transition in the fracture mode around

Fig. 6.9. (a) Effect of the temperature on the flexure strength of Al2O3–YAG eutectics with different domainthickness (t) tested in Ar [152] and air [150]. (b) Secondary electron micrograph of the fracture surface of theAl2O3–YAG eutectics with t = 0.6 lm broken at 1627 �C showing the homogeneous coarsening of themicrostructure after short term exposure to high temperature. (Reprinted by permission of the American CeramicSociety from [150].)


1600 �C, which was attributed to the different deformation mechanisms in Al2O3 andYAG. Elastic deformation is dominant in both phases up to 1200 �C but above this tem-perature plastic deformation begins to occur in Al2O3 while YAG remains elastic up to�1550 �C. As a result of the interpenetrating nature of the microstructure, the plasticdeformation of Al2O3 is constrained by the elastic deformation of YAG in the range1100–1550 �C and the overall eutectic behavior is elastic although the crack path tendsto follow the brittle YAG phase and the fraction of YAG in the fracture surface is higher[153]. Above 1550 �C, both phases can deform plastically and the behavior shows a non-linear stress–strain curve, although the overall strength is maintained or even improved asa result of the increase in toughness associated with the plastic deformation around


notches and defects. Of course, the amount of plastic deformation in this regime is verysensitive to the strain rate and to the domain size, and the ductile/brittle transition temper-ature depends on both factors [153,163]. Similar behavior in terms of the plastic deforma-tion and strength retention (or even improvement) has been reported in Al2O3–GAP DSE[101,7] but it is worth noting that polycrystalline Al2O3–YAG eutectics which were notprocessed by directional solidification suffered a marked reduction in strength above1000 �C [164].

Good strength retention at high temperature was also reported in the 1970s in theAl2O3–YSZ eutectic system [2] but more systematic studies to ascertain the effect of yttriacontent and microstructure on the high temperature strength were carried out morerecently [107,122,20,8]. The results of these investigations are plotted in Fig. 6.10, wherethe flexure strength of Al2O3–ZrO2(Y2O3) DSE with an yttria content in the range0.5% < Y < 9% is plotted between ambient temperature and 1427 �C. Eutectics with eithercubic or tetragonal YSZ showed a mild reduction in strength up to 1427 �C and no evi-dence of macroscopic plastic deformation was observed in the load–displacement curves,which were linear until failure. In addition, the fracture surfaces created at elevated tem-perature could not be distinguished from those of the ambient temperature tests: fracturewas nucleated at surface defects which were also found in the specimens broken at 25 �C.Thus, the short term exposure to elevated temperature did not introduce new defects intheir microstructure, in agreement with the investigations on the microstructural stabilityof these eutectics up to 1500 �C [48]. The reduction in strength with temperature wasattributed to two causes: the release of the thermal residual stresses in the microstructureat high temperature, which could reduce the fracture toughness of the material (see Sec-tion 6.4), and the activation of plastic deformation mechanisms at the microscopic levelin the ZrO2 phase above 1200 �C. Similar arguments can be used to explain the limited

0

200

400

600

800

1000

1200

Y = 9%

Y = 3%

Y= 0.5%

0 300 600 900 1200 1500

Fle

xure

str

engt

h (M

Pa)

Temperature (˚C)

Fig. 6.10. Influence of the temperature on the flexure strength of Al2O3–ZrO2(Y2O3) eutectic rods processed bythe laser-heated floating-zone technique with different yttria content, as indicated by Y = mol% Y2O3/(mol%Y2O3 + mol% ZrO2). Data compiled from [122,20].


degradation (�30%) in the flexure strength of MgO–MgAl2O4 DSE between 25 �C and1500 �C [157].

The eutectics containing monoclinic ZrO2 (Y = 0.5% in Fig. 6.10) showed a much moremarked reduction in strength with temperature, which dropped below 200 MPa at 727 �C,and then remained practically constant. The analysis of the fracture surfaces of rods testedat high temperature showed extensive microcracking caused by the propagation of theinterfacial microcracks present in the material (Figs. 5.4 and 5.5). The inversion of themartensitic transformation of ZrO2 at temperatures in the range 700–900 �C (now frommonoclinic to tetragonal) was accompanied by a volume reduction of �4%, which gener-ated large tensile stresses in the ZrO2 and drove the propagation of the cracks.

The high temperature strength retention was also studied in ternary Al2O3–YAG–YSZeutectics [22,23], which showed better ambient temperature strength than did the binarycounterparts, as explained above. The results of flexure tests on rods and of tensile testson fibers are plotted in Fig. 6.11. Although the absolute values are very different (owingto the differences in test and specimen geometry), both investigations showed that the ter-nary eutectics presented good strength retention up to 1200 �C. However, the strengthdropped very rapidly above this temperature: for instance, the flexure strength at1427 �C was only one half of that at ambient temperature. This sudden degradation instrength was attributed to several factors, including the release of residual stresses, theplastic deformation of cubic ZrO2 and the proximity of the eutectic temperature(1715 �C), which may activate diffusion-assisted plastic deformation in these eutecticswhose average domain thickness was just �0.3–0.4 lm. The two former factors werealso operating in Al2O3–YSZ eutectics which presented, however, higher melting temper-ature (1860 �C) and thicker domains and thus the strength degradation at 1427 �C waslimited.

0

500

1000

1500

2000

2500

Rods tested in bending

Fibers tested in tension

0 300 600 900 1200 1500 1800

Str

engt

h (M

Pa)

Temperature (˚C)

Tm = 1715˚C

Fig. 6.11. Effect of the temperature on the flexure strength of Al2O3–YAG–YSZ ternary eutectics. Rodsprocessed by the LFZ method were tested in three-point bending [23] while fibers manufactured by the l-PDtechnique were broken in tension [22].


6.2.3. Anisotropy

Directionally solidified materials tend to present anisotropic properties. Kennard et al.[157], Ochiai et al. [153] and Nakagawa et al. [101] studied the effect of orientation on theflexure strength of MgO–MgAl2O4, Al2O3–YAG and Al2O3–GAP bulk eutectics, respec-tively, manufactured by the Bridgman method. The bending strength parallel to thegrowth axis was slightly higher than in the perpendicular direction from ambient temper-ature up to 1600–1750 �C but the differences were not significant, and indicated that thestrength of bulk DSE oxides is fairly isotropic. Studies on rods and fibers grown at higherrates were only carried out by Pastor et al. [20,150] using the diametral compression test(also known as the Brazilian test). Circular disks sliced from the rods were subjected todiametral compression between two rigid ceramic plates. Although the compressive stres-ses in the load direction are much higher than the transverse tensile stresses, the disk failsby splitting across the compressed diameter in ceramic materials, in which the compressivestrength is significantly higher than the tensile one. The transverse tensile strength of therods was approximately one order of magnitude lower than the longitudinal one measuredis three-point bending. The differences were attributed to the presence of elongated voidsoriented along the growth axis in the rods. These defects, which did not affect significantlythe longitudinal strength, were responsible for the reduced transversal strength.

6.3. Hardness

The hardness of DSE oxides is primarily a function of the hardness of the single crystaloxides in the eutectic, and the highest values reported in the literature were measured inthe Al2O3–YSZ, which reached 18–20 GPa [122,161]. Al2O3–ZrO2 eutectics without yttria[122,62,165] presented much lower hardness (around 11–14 GPa) and this reduction wasmainly attributed to the presence of microcracks in the material, which were nucleatedat the domain interfaces during the martensitic transformation and grew driven by the ten-sile residual stresses in the Al2O3 matrix, as detailed in Section 5.4.1. Al2O3–YAG eutecticspresented hardness in the range 13–16 GPa [150,166], while ternary Al2O3–YAG–YSZ[22,23] eutectics showed intermediate values between Al2O3–YAG and Al2O3–YSZ.

It is worth noting that the hardness of DSE is often higher than that of single crystaloxides in the eutectic. This was first reported in MgO–MgAl2O4 eutectics [157], and ithas been normally found in the systems mentioned the previous paragraph. Moreover,the microhardness of Al2O3–YAG [150,166], Al2O3–YSZ [62] and Al2O3–YAG–YSZ[22,23] DSE with a lamellar microstructure increased with growth rate, or in other words,as the domain size decreased, and this effect was attributed to the strengthening induced bythe presence of interface domains, which act as dislocation barriers. The relationshipbetween the microstructure and the hardness in eutectics with colony microstructure ismore difficult to assess, but higher growth rates, which decreased the size of the fibersor lamellae within the colonies, improved the microhardness [151,157,161].

6.4. Fracture toughness

Ceramics are brittle materials and this characteristic imposes serious limitations ontheir application as structural materials. Hence, toughening of ceramics has been an activeresearch area in recent decades and, as the resistance to crack initiation was very difficultto improve significantly, the strategy was focused in increasing the resistance to crack


propagation. This was achieved in transformation-toughened ceramics [167], fiber-rein-forced ceramics [168,169], particle-reinforced ceramics [170,171], and laminates [172] bydesigning microstructures in which the crack propagation is hindered by obstacles. Themicrostructure of DSE oxides, as opposed to that of single crystal oxides, is likely to pres-ent these mechanisms on account of the large area fraction of interfaces, the presence offluctuating residual stress fields and the elastic mismatch between the eutectic phases; sig-nificant improvements in toughness in relation to the single crystal oxides were found inCaF2–MgO [11], PbO–Nb2O5 [2] and CoO–YSZ [147] DSE in which crack deflection atthe interface (rather than crack penetration) was the main fracture mechanism(Fig. 6.12). The behavior of a crack impinging on an interface between dissimilar elasticmaterials was studied by He and Hutchinson [173], who provided a criterion for crackdeflection in the worst scenario of a crack growing perpendicular to the interface. Undersuch conditions, crack deflection will occur if the ratio between the interface fractureenergy Ci and the fracture energy of the phase which has to be penetrated by the crack,C2, is below a critical value which depends on the elastic mismatch between both phases.The critical ratio Ci/C2 is of the order 0.2–0.4 for the typical elastic mismatch between thephases in DSE oxides and this condition was fulfilled in CaF2–MgO [11] and PbO–Nb2O5

[2]. It should be noted, however, that this behavior is unusual in DSE due to the excellentinterfacial bonding between the phases and they rarely show extended delamination dur-ing crack propagation [105,150,153,23,163,174–178].

The fracture mechanisms of DSE oxides with the best mechanical properties (Al2O3–YSZ, Al2O3–YAG) have received particular attention in the literature. Several studiesof the fracture toughness of Al2O3–YAG [105,150,153,163,176] have reported similar val-ues at ambient temperature (�2 MPa

pm), and this brittle behavior is in agreement with

the fracture micromechanisms observed experimentally (Fig. 6.13(a)). The crack propa-gated through the Al2O3 and YAG eutectic domains and the crack path was straight,not deflected at the interface. Hence, the crack did not interact with the microstructureand the crack propagation resistance was independent of the domain size [150] and orien-tation (perpendicular or transverse to the growth direction) [153]. This was the result of the

Fig. 6.12. Back-scattered scanning electron micrograph showing crack deflection at the CaF2–MgO interface.(Reprinted by permission of the Materials Research Society from [11].)

Fig. 6.13. Back-scattered electron micrograph showing the propagation of a crack through the microstructure.(a) Al2O3–YAG eutectic rod. The Al2O3 phase is dark and the YAG phase white. (Reprinted by permission of theAmerican Ceramic Society from [150].) (b) Al2O3–YSZ eutectic rod. The Al2O3 phase is dark and the YSZ phasewhite. (Reprinted by permission of Elsevier from [20].)


brittle nature of both Al2O3 and YAG, the strong interfacial bonding between them, andthe absence of thermal residual stresses which could promote crack deflection at the inter-face or crack arrest in one phase. Slightly higher toughness was obtained in Al2O3–YAGeutectics doped with CeO2 [175] and it was suggested that it was due to the deflection ofthe cracks along the Al2O3–CeAlO3 interfaces, but no definitive conclusions could beobtained from observation of the crack path.

The fracture toughness of Al2O3–YSZ at ambient temperature was 4–5 MPap

m[75,20,165,176], more than twice that of Al2O3–YAG, and this difference was echoed inthe crack propagation pattern. Several cracks often emerged from the corner of the Vick-ers indentations (Fig. 6.13(b)) and propagated in parallel for a certain distance until one ofthem became dominant and the others were arrested. In general, crack arrest followed bythe development of another parallel crack a few microns above or below the first crack tipwas observed throughout the crack path. This led sometimes to the development of elasticbridges behind the main crack tip during crack propagation, which increased the tough-ness. These fracture mechanisms, not found in Al2O3–YAG, cannot be attributed to


transformation toughening. No traces of monoclinic ZrO2 were found in the broken sam-ples, and in addition, any transformable tetragonal ZrO2 in the eutectics rods shouldundergo a spontaneous transformation into the monoclinic phase prior to the applicationof any load, given the large tensile residual stresses which develop upon cooling. This phe-nomenon was observed in Al2O3–ZrO2 eutectics with low yttria content and led to themicrocracking of the microstructure [122].

The higher toughness of Al2O3–YSZ was attributed to the presence of thermo-elasticresidual stresses. The crack front will prefer to arrest in regions of compressive stress dur-ing crack propagation through a fluctuating residual stress field, and the applied stressintensity factor will have to be increased by an amount equal to the shielding effectinduced by the compressive residual stresses at the crack tip to resume the crack propa-gation. A first order estimation of the effect of the residual stresses on the toughness canbe obtained from the model developed by Taya et al. [171] by ignoring the contributionof all residual stresses other than those around the crack tip. The microstructure of theeutectic composite is idealized as a two-dimensional sandwich of alternative layers ofAl2O3 and YSZ perfectly bonded. The crack propagates perpendicularly to the layers,and lies at the end of an Al2O3 layer. Assuming that the total crack length is much longerthat the Al2O3 layer thickness, tA, the increase in fracture toughness, DKC, can be com-puted as [171]

DKC ¼ 2rr

ffiffiffiffiffiffiffi2tA

p

r; ð6:2Þ

which leads to DKC = 2 MPap

m for tA = 10 lm, and rr = 400 MPa, the average compres-sive residual stress along the rod axis in Al2O3.

These findings of the effect of residual stresses on the toughness of DSE oxides are inagreement with more recent data on ternary Al2O3–YSZ–YAG eutectics [23,177,89].The toughness of Al2O3–YSZ–YAG was found to vary between 4.2 and 2.7 MPa

pm

[23], and the samples with higher toughness presented higher compressive residual stressesin Al2O3 and domain thicknesses (300 MPa and 5–10 lm). The minimum toughness wasfound in rods grown at higher rates where the domain thickness was �0.3 lm and thecompressive residual stresses in Al2O3 only reached 180 MPa.

Finally, it should be noted that the high temperature toughness of Al2O3–YAG eutec-tics was measured by Ochiai et al. [153] up to 1750 �C. The ambient temperature valueswere maintained up to 1500 �C and reached up to 4 MPa

pm above this temperature in

samples tested at low rates due to the plastic deformation at the notch tip. This behavioris superior to that of sapphire along the (000 1) planes, whose toughness decreased from4 MPa

pm to 5 MPa

pm at ambient temperature to �1 MPa

pm at 1000 �C [89].

6.5. Creep deformation

The creep resistance of DSE oxides is superior to that of the sintered counterparts dueto the absence of glassy phases at the interfaces, and the strain has to be accommodated byplastic deformation within the domains rather than by interfacial sliding. The interfacialbonding of DSE oxides is further increased in many oxide eutectic systems by the presenceof homopolar surfaces, where they share a common oxygen plane. This leads to electro-static bonding across the boundary, which retains the strength even at very high temper-ature. In the absence of relative sliding at the domain boundaries, compatibility of


deformation between the eutectic phases is compulsory, and the overall strain rate is con-trolled by the eutectic morphology and the creep resistance of both phases.

The creep resistance of DSE oxides has been studied mainly in two systems: Al2O3–YSZand Al2O3–YAG. The first one is made up by a continuous creep resistant phase (Al2O3),which covers �70% of the eutectic volume and grows with the c-axis parallel to the solid-ification direction. This phase embeds a fine dispersion of a YSZ, an oxide with poor creepresistance. The creep behavior of the eutectic is controlled by that of the continuous Al2O3

phase, whose resistance to creep deformation is highly anisotropic, being maximum alongthe c-axis and decreasing by orders of magnitude as it is loaded just 15� from this axis [8].Hence, creep resistance of Al2O3–YSZ DSE is one order of magnitude above that of Al2O3

single crystals oriented 45� off the c-axis, and of single crystal YSZ of equivalent compo-sition [8,59] but it is inferior to that of c-oriented single crystal Al2O3 because the align-ment of the Al2O3 domains within the eutectic is not perfect. The steady-state creeprates in this eutectic were measured between 1200 �C and 1520 �C at stresses ranging from60 to 300 MPa [59,179] and the minimum creep rate, _e, followed a power-law relationshipas

_e ¼ Arn exp � QRT

� �; ð6:3Þ

where the stress exponent n was in the range 4–6, and the activation energy Q = 300 kJ/mol. These results are compatible with a creep deformation controlled by the climb ofpyramidal dislocations in Al2O3 with the O diffusion in Al2O3 as the rate controlling mech-anism, where the somewhat low value of Q could be explained by the limited number ofexperimental data available.

The role played by the YSZ domains during creep deformation was assumed to be sec-ondary, as they merely remained dormant or underwent stress-relaxation while the topo-logically continuous Al2O3 phase deformed. Moreover, the global back stress in Al2O3

induced by the stress relaxation of YSZ is not important as the creep ductility of DSEoxides is low [179]. However, it should be noted that YSZ fibers and lamella found atthe colony and cell center in eutectics with a cellular microstructure have dimensions inthe submicron range and the mean spacing between them is of a few hundred nm. Thesesubmicron domains present a much higher resistance to plastic deformation on account oftheir small size, and in addition, they act as obstacles to the motion of dislocations in thecontinuous Al2O3 phase. As homogeneous phase coarsening is limited in DSE, they effec-tively strengthen the DSE oxide as compared to single crystal Al2O3, and creep deforma-tion tends to localize in Al2O3–YSZ with cellular microstructure along the cell boundaries,where the size of the YSZ domains is larger (Fig. 6.14). This can offset the beneficial effectsof the dispersed submicron YSZ domains, particularly in tension, because voids are nucle-ated in the intercolony regions, enhancing the creep rate and limiting the tensile creep duc-tility of cellular eutectics [76].

The creep deformation of Al2O3–YAG DSE oxide presents different characteristicsfrom those of Al2O3–YSZ as its microstructure is made up of an interpenetrating networkof both phases. This imposes an isostrain condition on the deformation of Al2O and YAGas strain accommodation by interface sliding is inhibited by the strong bonding at theinterface domains. As YAG stands among oxides with highest creep resistance and itsbehavior is fairly isotropic [180,181], the creep resistance of Al2O3–YAG DSE oxides issuperior to that of most single crystal oxides. Moreover, plastic deformation by basal,

Fig. 6.14. Microstructure of Al2O3–YSZ eutectics after tensile creep deformation at 1400 �C, showing thenucleation and growth of cavities at the intercolony regions. (Courtesy of A.R. Pinto Gomez, A.R. de Arellanoand J. Martınez-Fernandez, University of Seville.)


prismatic and pyramidal slip in single crystal Al2O3 can start at 1000–1200 �C while YAGremains elastic up to 1400–1500 �C. This leads to two different creep regimes depending onthe main deformation mechanism in YAG.

The creep resistance in the high temperature regime (P1600 �C) was measured in sev-eral investigations [110,162,182,183] along the solidification direction in air. The minimumcreep rate, _e, is plotted in Fig. 6.15 as a function of the applied stress, r, for Al2O3–YAGDSE with single crystal [182] and coarse-grained [183] microstructure. The behavior ofboth materials follows the typical power-law relationship given by Eq. (6.3) with a stressexponent of 5, which was normally found in these eutectics above 1600 �C. The activation

CG, 1650˚CCG, 1600˚CSC, 1650˚CSC, 1600˚C

10-8

10-7

10-6

10-5

10-4

100 200 300 400 500

Str

ain

rate

(s-1

)

Stress (MPa)

1

5

Temperature

Fig. 6.15. Minimum creep rate as a function of the applied stress for Al2O3–YAG DSECO manufactured by theBridgman technique and tested at 1600 �C and 1650 �C. The open symbols correspond to single-crystallinematerials [182] and the full symbols to coarse-grained (2–3 mm wide and several cm long) materials [183]. All thesamples were tested in compression in the solidification direction.


energies were 650–800 kJ/mol in the coarse grained material and slightly higher (800–1000 kJ/mol) in the single crystal eutectic. These results are compatible with creep defor-mation controlled by dislocation motion in each phase induced by lattice diffusion in thesingle crystal eutectic, and this assumption was supported by transmission electron micros-copy studies that showed evidence of dislocation activity in both phases, particularly inAl2O3 (Fig. 6.16). Final fracture of the eutectic materials under creep was dictated bythe nucleation of damage at the domain interfaces as a result of the differences in creeprate between the phases and the lack of stress relaxation by interfacial sliding, which ledto the progressive build up of stresses during deformation.

The creep resistance of the directionally solidified Al2O3–YAG eutectics at 1600 �C wasseveral orders of magnitude higher than that of polycrystalline sintered materials with thesame eutectic composition [110,162]. The creep exponent of the latter was very close to 1and the analysis of the deformed specimens by transmission electron microscopy did notshow any evidence of dislocation motion in either phase, Fig. 6.16(c), because inelasticdeformation was controlled by grain boundary sliding rather than by plastic slip. In fact,the resistance to creep deformation of single crystal Al2O3–YAG DSE oxide at 1600 �Calong the solidification was in between that of YAG and c-axis sapphire, and was signif-icantly better than a-oriented sapphire [182,183]. Moreover, a first-order approximation ofthe creep rates in the eutectics could be obtained from the creep rates of both phasesassuming an isostrain approach, which is supported by the interpenetrated microstructureand the strong interfacial bonding. This simple isostrain model successfully explained theanisotropy in the creep rates between the specimens tested at 0� and 90� from the solidi-fication axis, which came about as a result of the anisotropy in the creep deformation ofthe Al2O3 single crystal within the eutectic [182,184].

The creep curves of Al2O3–YAG [106,154,182,183] and Al2O3–Er3Al5O12 (EAG) [185]in the low temperature regime (1400–1600 �C) did not always reach the steady-state sec-ondary creep region because of premature failure triggered by the defects in the micro-structure [106] or because the creep rate decreased below the detection limit and it was

Fig. 6.16. Transmission electron microscopy micrographs showing the dislocation structure in (a) Al2O3 phaseand (b) YAG phase of a directionally solidified Al2O3–YAG eutectic, and (c) Al2O3 and YAG phases of a sinteredAl2O3–YAG eutectic. The specimens were plastically deformed up to 14% in compression at 1600 �C and theinitial strain rate was 10�5 s�1. (Reprinted by permission of Elsevier from [162].)


necessary to increase the stress [183]. The minimum creep rate in the samples whichreached stationary conditions followed the power-law relationship of Eq. (6.3), althoughthe stress exponents were very high (in the range 5–10) and dislocation activity in the YAGdomains was very weak [106,154] or not found [185]. Hence, the high stress exponentscould be explained by the development of a backstress as a result of the formation of dis-location pile-ups in the sapphire in presence of the more creep resistant single crystal YAGdomains. Following this argument, Matson and Hetch [106] recovered the stress exponentof 5 by introducing a threshold stress for creep in Eq. (6.3). They found that the thresholdstress decreased with temperature and increased with the thickness tA of the Al2O3

domains in the eutectic microstructure [106,154], and these experimental results couldbe rationalized with an extremely simple model. If the far field backstress is generatedby a mechanism similar to that of the Orowan bowing mechanism during creep of metals,the threshold stress, rth, can be roughly estimated as

rth ¼ aGbtA

; ð6:4Þ

where a = 0.5 is a geometrical factor, G is the shear modulus of Al2O3 at the test temper-ature and b the burgers vector. Eq. (6.4) predicts that the threshold stress should approachto zero and provide no strengthening at 1500 �C for tA = 5 lm, in agreement withthe experimental data in [183]. Moreover, the threshold stress tended to zero above1550–1660 �C [154], a temperature at which dislocation motion occurs readily in YAG.The progressive build-up of elastic stresses in YAG during deformation at 1400 �C wasalso supported by the evidence of elastic strain recovery in specimens deformed by creepafter unloading [185].

Structural components for gas-turbines are one of the potential applications of DSEoxides, and Harada et al. [186,187] measured the creep rates in Al2O3–YAG andAl2O3–GAP DSE in moist environments at 1400 �C, 1500 �C and 1600 �C as combustiongases may contain as much as 10% water vapor. They found that the presence of watervapor increased the steady state creep rates by a factor of 1.4–4 for H2O vapor partialpressures of 0.06 MPa and by a factor of 5–7 for partial pressures of 0.4–0.6 MPa, as com-pared with specimens tested in air. The stress exponents were consistent with those mea-sured in air at the same temperature but the activation energy was lower (500–650 kJ/mol)and independent of the water vapor partial pressure. Analysis of the deformation mecha-nisms by transmission electron microscopy suggested that the higher creep rates in moistenvironments could be due to the enhanced dislocation mobility induced by the absorptionof protons, but more work is necessary to find out the actual physical mechanisms.

6.6. Subcritical crack growth

Subcritical crack growth has been found responsible for the degradation of the mechan-ical properties of several single-crystal oxides, such as sapphire [94] and tetragonal ZrO2

[95], in air at temperatures above 600 �C. As they are constituents of important DSE oxi-des, evidence of subcritical crack growth was studied by Sayir [188]. The tensile strength ofAl2O3–YAG monofilaments at 1100 �C at strain rates spanning four orders of magnitudewas constant, while sapphire monofilaments oriented along the c-axis showed a markeddependence of strength on strain rate (Fig. 6.17). The reduction of strength in sapphireat lower strain rates has been well correlated to the slow propagation of a crack, although

Sapphire (c axis)Al

2O

3/YAG eutectic

0

500

1000

1500

2000

10-6 10-5 10-4 10-3 10-2

Ten

sile

str

engt

h (M

Pa)

Strain rate (s-1)

Fig. 6.17. Influence of the strain rate on the tensile strength of Al2O3–YAG DSE and c-axis oriented sapphire at1100 �C in air [188].


there is discussion on the actual mechanisms of crack propagation. On the contrary, DSEoxides did not present any fractographic evidence of crack propagation at high tempera-ture [150] and their strength was independent of the loading rate, an indication that sub-critical crack growth was not present in these materials.

7. Functional properties

The outstanding mechanical performance and chemical stability of DSE oxide has beenthe main driving force for the recent developments in this area. However, DSE oxides alsopresent an interesting role as functional materials. At first glance, the mere enhancement inmechanical properties, corrosion resistance and thermal stability, as compared with singlecrystals and conventional ceramics, supports their application as functional materials indevices. Additionally, their multi-component character is a stimulus to search for synergis-tic effects resulting from the combination of complementary functional properties into asingle material. This would be the case of materials with mixed properties such as ferro-magnetic and insulator, conductor and insulator, etc. Moreover, the unique microstruc-ture of regular eutectics made up of ordered arrays of alternating lamellae or fibers withsharp and clean interfaces induces interesting functional properties, such as directionaltransport of light and electricity. The recent research efforts in DSE oxides from the pointof view of the functional applications are summarized below, including the attempts to useDSE oxides as structured substrates for patterned thin films, ionic conductor composites,structured porous cermets, and optical waveguides [27,189].

7.1. Substrates for thin film deposition

The deposition of high-quality patterned epitaxial oxide thin films is noteworthy amonga number of nanotechnologies. The periodic microstructure arrangement found in DSE


can be used as a template to manufacture highly structured substrates for patterned oxidethin films [190]. Many of the applications envisaged for high-TC superconductors (HTSC)or ferromagnetic metals showing a colossal magnetoresistance (CMR) are based on thepreparation of artificial grain boundary junctions (GBJ). For example, weak-link andJosephson effects shown by high-angle grain boundaries could be used to produce super-conducting quantum interference devices (SQUID) with YBa2Cu3O7 (YBCO) films [191].The most reproducible GBJ have been obtained so far in films epitaxially grown on bicrys-tal substrates in which the artificial GBJ is directly induced by the substrate biorientationand the film is obtained in a single deposition step [192]. The main limitation of this tech-nology for practical applications is the small number of active junctions achievable along asingle grain boundary and the difficulties of producing bicrystals of good quality [193].

Regular binary DSE are monolithic two-phase composites structured either in the formof alternating parallel lamellae or of cylinders of one phase embedded in a crystallinematrix of the other phase. They could be considered similar to bicrystal substrates butpresent thousands of grain boundaries per linear cm instead of just one. DSE oxides alsoshow very sharp, atomic-scale interfaces which separate phases with different relative ori-entations, and substrate surfaces with the desired phase orientation relationships can beobtained by cutting the bulk eutectic along the appropriate crystallographic planes.

The only attempt so far to grow thin films on DSE oxide substrates has led to the pro-duction in a single deposition step of biepitaxial films of YBCO and La2/3Ca1/3MnO3

(LCMO) with a regular array of GBJ [190,86]. The films deposited on these substratesreproduced the pattern of the eutectic surface, and hence films with different arrangementsof two well-defined orientations could be prepared. The best result was obtained in specialsurface substrates cut from well-ordered lamellar CaSZ/CaZrO3 and fibrous MgSZ/MgODSE oxides. CaSZ and MgO are among the best substrates for both YBCO and LCMOfilm deposition because of their chemical inertness and good lattice matching [194]. Inaddition, CaZrO3 presents a very stable orthorhombic perovskite with a pseudocubic cellparameter (�4.005 A) close to that of YBCO and LCMO (see Table 7.1). The substratesurfaces were prepared from CaSZ/CaZrO3 and MgSZ/MgO DSE rods of 2 mm in diam-eter grown by the LFZ technique [195]. The former presented relatively large areas (severalmm2 size) of a well-ordered structure consisting of non-faceted alternating CaSZ(Ca0.25Zr0.75O1.75) and CaZrO3 (CZO) single crystal lamellae with a thickness of a fewmicrons. The lamellae showed the orientation relationships described in Section 3.1.Two different types of substrate plates with different relative phase orientations, namelyA and B, were cut longitudinally to the rod axis. The plates were approximately alignedwith (200)CSZk (200), (121), (002)CZO in substrate A and (200)CSZk (202),(040)CZO in substrate B. In the fibrous MgSZ/MgO DSE, the substrate surface was

Table 7.1Crystal structure and lattice parameters of some ceramic oxides

Compound Crystal structure Cell parameters (A)

CaSZ, MgSZ Fluorite (Fm3m) 5.15CZO Orthorhombic (Pnma) 5.756, 8.010, 5.593MgO Cubic (Fm3m) 4.213YBCO Orthorhombic (Pnma) 3.825, 3.886, 11.660LCMO [239] Orthorhombic (Pbnm) 5.472, 5.457, 7.711


aligned with (200)MgSZk (200)MgO [190]. YBCO and LCMO films about 400 nm thickwere deposited on these substrates by different techniques, such as metal-organic chemicalvapor deposition, pulsed-laser deposition, and sputtering [86,190].

7.1.1. YBCO in CaSZ/CaZrO3 (CZO)The parallel strip pattern of biepitaxial YBCO in CaSZ/CZO on substrate A is shown

in Fig. 7.1 together with the X-ray diffraction (XRD) pole figures corresponding to differ-ent reflections of the film and the substrate [86]. The film surface was smooth and uniformon the CaSZ domains (dark strips). Pole diagrams (Fig. 7.1(b)) indicated that the YBCO

Fig. 7.1. (a) SEM image of a YBCO film deposited on the surface of a well-aligned CZO/CaSZ DSE (substrateA). (b) XRD pole figures showing the different reflections of the phases in the film and the substrate. (Reprintedby permission of Wiley-VCH [86].)


film grew epitaxially with c-axis orientation following the so-called cube-on-cube or 0� epi-taxy. The film also grew epitaxially on the CZO domains (bright strips in Fig. 7.1(a)) witha (103) orientation, and presented a rough surface consisting of aligned triangular-shapedcrystallites, typical of (103)-oriented films. The relative orientations of both c-axis and(103)-oriented strips in the YBCO film defined a single and unique type of grain boundarywhere the CuO2 planes of the YBCO structure meet together with a 45� rotation aroundtheir common b-axis parallel to the surface (Fig. 7.2(a)). The YBCO films deposited onsubstrate B showed two YBCO domains with a flat morphology, typical of c-axis orientedgrowth. The texture analysis confirmed the c-axis orientation of both film phases but witha 45� in-plane rotation, as depicted in Fig. 7.2(b).

Electrical resistance measurements along (k) or perpendicular (?) to the strips were per-formed on the YBCO films grown on substrate A using the direct current four-contactmethod [86]. The temperature dependence of the electrical resistance is shown inFig. 7.3. The resistive transition temperature (TC) and transition width (DTC) were 88 Kand 2 K, respectively, along the strips, and 85 K and 5 K, respectively, perpendicularto the strips. The resistivity of the normal state was anisotropic, q?(300 K)/qk(300 K) = 2.4, and the anisotropy was stronger of the critical current density,jCk ð77 KÞ=jC

?ð77 KÞ ¼ 13 with jCk ¼ 4 kA=cm2 [86]. The high sensitivity to the magnetic

field, which produced a shift to lower temperatures of the low TC in the transversemeasurements, proves the weak-link nature of these GBJ. The low values of the criticalcurrents and the high resistance at 0 K were possibly a consequence of the discontinuitiesin the films caused by defects in the substrate.

Fig. 7.2. Schemes of the orientation relationships between films and substrates. (a) YBCO film in substrate A: c-axis oriented YBCO on CaSZ and (103)-oriented YBCO on CZO. (b) YBCO film in substrate B: both c-axisoriented but 0� and 45� in plane alignment on CaSZ and CZO strip phases, respectively. (c) LCMO film onsubstrate B showing epitaxial growth on CZO but polycrystalline growth on CaSZ. (d) YBCO film on MgO/MgSZ substrates with c-orientation on the MgSZ matrix and polycrystalline dots on MgO fibers. (Reprinted bypermission of Elsevier [190].)

Fig. 7.3. Normalized resistance superconducting transitions along (k) or perpendicular (?) to the YBCO strips ofFig. 7.1 for different applied magnetic fields of 0, 10, 25, 50, 75, and 100 mT. Arrow indicates the region whereweak-linked GBJ manifest. Inset shows the measured resistivity curves [240].


7.1.2. LCMO in CaSZ/CZOThe surface morphology of the LCMO films was smooth in both substrates. The pole

figures showed that the film grew epitaxially on the CZO domains, with a high (100)-ori-entation. LCMO grew in the form of a randomly oriented polycrystalline material [190] onthe CaSZ phase, as depicted in Fig. 7.2(c). This difference could be explained by the lowermismatch in LCMO/CZO (�4%) than in LCMO/CaSZ (�11%) (see Table 7.1).

7.1.3. YBCO in MgSZ/MgO

The YBCO films deposited on transverse sections of the MgSZ/MgO eutectic alsoreproduced the fibrous pattern of the substrate. The growth habit depicted inFig. 7.2(d) could be explained by the lattice mismatch between YBCO with MgO, higherthan that between YBCO and MgSZ. An array of micron-sized polycrystalline YBCOislands grew on the MgO substrate phase. The islands were regularly distributed in asmooth YBCO film grown on the MgSZ substrate phase with a c-axis orientation and a45� in-plane rotation [190].

In conclusion, the preliminary findings presented in the previous paragraphs show thatDSE oxides can be used as substrates for patterned oxide thin films growth, and exotic filmconfigurations can be produced in one preparation step by choosing the proper substrateorientation. It should be noted, however, that the small size of the eutectic grains makesit difficult to obtain large areas (above several mm2) of perfectly and continuously orderedlamellae. Moreover, the choice of possible substrates is limited to the eutectic compositionsavailable because off-eutectic compositions tend to develop disordered microstructures.

7.2. Structured Ni/YSZ and Co/YSZ composites

DSE oxides can be used as precursor materials to obtain new composites, which mayfind applications in the fields of heterogeneous catalysis and in fuel cell technology. Fuel


cells are envisaged as a clean, efficient alternative energy source to fossil fuel combustion,and porous cermets of Ni/YSZ are commonly used as anodes [196,197] in solid oxide fuelcells (SOFC). The durability and efficiency of the materials and the manufacturing costsstand among the most important factors in this technology [198], and it is well establishedthat both improve if the cell operation temperature is below 700 �C. However, the poorionic conductivity of most common electrolyte materials at low temperatures limits theelectrolyte thickness, while keeping at the same time the gas tightness across it. Moreover,the efficiency of the anodes is strongly dependent on their microstructure. In particular, thelength and number of triple phase boundaries (TPB) where fuel, ions and electrons meetplays a crucial role in the anode performance, and new anode technologies tend to increasethe number of pores and Ni particles while keeping the good connectivity necessary for gasand charge flow. Another matter of concern arises from the strong tendency of the Ni par-ticles to agglomerate into larger particles at the operating temperatures, the effect beingaccelerated by the poor wetability between metallic Ni and YSZ ceramics [199]. Ni coars-ening decreases the number of TPB and the electrical conductivity of the anodes, deterio-rating the long-term stability of the SOFC under operation.

An alternative to the conventional processes to manufacture of SOFC anodes hasrecently been proposed. The initial step is the growth of NiO/YSZ DSE oxides[200,201], which present a well-ordered lamellar microstructure with strongly bondedinterfaces between the phases [202]. A subsequent reduction treatment produces thedesired porous Ni/YSZ cermet where the metallic Ni remains well-aligned crystallograph-ically with the YSZ phase [84]. The formation of these low energy interfaces prevents thecoarsening of the Ni particles during cell operation. Additionally, the lamellar structure isappropriate for easy gas flow and ionic and electronic transport. The porous cermet alsopresents a thermal expansion coefficient very similar to that of the YSZ phase, whichfavors electrolyte thermo-mechanical integration.

The half-cell preparation steps using this new concept are sketched in Fig. 7.4. Themethod starts with a precursor pellet of NiO/YSZ with the eutectic composition (70mol%NiO–30mol%YSZ) manufactured by standard ceramic procedures, but highly porous(around 65%). The ceramic pellets are processed by directional laser-surface melting, amethod that achieves a good homogenization, densification and texturing of a surface layerwithout modification of the rest of the piece [87]. The thickness of the melt layer can bevaried from 50 to 500 lm (see Fig. 2.13) and the lamellar morphology (Fig. 7.5) is similarto that obtained in rods grown by LFZ [189,234] but—as stated in Section 2.4—the inter-phase spacing changes from the surface to the substrate as a result the gradient in the solid-ification rate. For instance, the interphase spacing varied from 0.4 lm at the surface to1.6 lm near to the unmelted substrate at a typical growth speed of 500 mm/h [74].

The porous Ni/YSZ cermet is subsequently prepared by reduction of the precursoroxide eutectic in a reducing atmosphere. The volume fraction of the YSZ phase is 43and 33.5 vol.% of Ni and 23.5 vol.% of porosity is expected after reduction of NiO tometallic Ni. Due to the lamellar microstructure, the cermet can be visualized as alternatingchannels for oxygen ion diffusion (YSZ) and porous metallic Ni with a pore concentrationof �40%, large enough for gas permeation and Ni content for electronic conduction(Fig. 7.5(b)). Percolation requirements are now restricted to a two phase material (porousNi-channels) instead of three (Ni, pores and YSZ) as in conventional ceramics and this iswhy better connectivity between the Ni particles, pores and YSZ, and an improved anodeyield, are expected.

Fig. 7.4. Scheme illustrating the production of a SOFC half-cell from NiO/YSZ DSE.


The reduction kinetics in NiO/YSZ as well as in CoO/YSZ was studied in rod samplesprepared by the LFZ method by gravimetric methods and the progression of the reductionfront indicated that reduction took place via a diffusion-limited process [201,28]. It is inter-esting to notice that the cermets produced from the reduction of perfectly ordered lamellarprecursors cannot sustain the enormous stresses derived from the �40% volume shrinkageassociated with NiO and CoO reduction, and the lamellae tend to collapse in well-orderedsamples [203]. On the contrary, the small size of the eutectic domains improved themechanical properties and helped the stabilization of the pores, which leads to a bettermaterial for anodes provided there is good macroscopic connectivity between the compo-nent phases. The electrical conductivity of these channeled cermets has been determined tobe around 9000 S/cm, which is twice as high as that of other ceramic cermets [28,204,205].

It was reported in Section 3.2 that the phases in DSE NiO/YSZ presented well-definedorientation relationships with an interface (111)NiOk (00 2)YSZ. The crystallographicorientation of NiO is maintained during reduction, i.e., {hkl}NiOk{hkl}Ni, and(111)Nik (002)YSZ interfaces are established. These are presumably low-energy inter-faces, which determine the good microstructure stability during cell operation. In fact,it was shown that the microstructure, conductivity, and open pore distribution remainedconstant after 300 h at 900 �C in a reducing atmosphere [85]. The coefficients of thermalexpansion of Ni/YSZ and Co/YSZ porous cermets produced from NiO or CoO/YSZDSE were 10.8 · 10�6 K�1, equal to that of YSZ [28]. Consequently, a tight thin layerof YSZ deposited at 800 �C presents a good thermo-mechanical integration with the cer-met [206]. The excellent cermet–electrolyte integration is shown in the fracture cross-sec-tion depicted in Fig. 7.5(a). Thus Ni and Co/YSZ channeled cermets produced from DSEprecursors are very promising electrochemical materials owing to their microstructuralstability and good electrochemical performance.

Fig. 7.5. (a) SEM micrograph of the fracture cross-section of a SOFC showing the anode–electrolyte system.A thin film of YSZ of 3 lm was deposited on top of the anode–electrolyte system to ensure gas tightness [201].(b) Channeled Ni/YSZ anodes for SOFC produced by reduction of NiO/YSZ DSE.


In addition to porous cermets, porous ceramics with applications in filters, gas burners,bio-ceramics, membranes, etc. can be produced by acid leaching of the reduced NiO andCoO/YSZ eutectics [207] (Fig. 7.6). Porous YSZ (with 57% porosity) produced from DSEare made up of tangled single crystal lamellae and its mechanical strength is enough forhandling and processing [208]. It is also worth noting that the existence of oxygen diffusionpaths through the YSZ phases is very convenient for attaining the desired in-depth homo-geneous oxidation–reduction process in the materials. This avoids, for example, the usu-ally deleterious layer-by-layer process in most oxidation–reduction experiments. Thepotential of these porous ceramics manufactured from DSE oxide structures is depictedin Fig. 7.7, which shows a NiAl2O4/YSZ fibrous eutectic in which the Ni-spinel has been

Fig. 7.7. SEM micrograph of a NiAl2O4/YSZ DSE after thermo-reduction at 900 �C. The Ni spinel has beenpartially reduced to Ni, and the Ni nanoparticles can be seen between the YSZ fibers [27].

Fig. 7.6. Optical microscope image of a porous lamellar YSZ obtained by leaching of a Ni/YSZ porous cermet.


partially reduced to Ni nanoparticles by the transport of oxygen through the YSZ fibers ofthe eutectic structure.

7.3. Photonic materials

Although eutectic structures have been known for nearly a century, very few studies oftheir optical properties can be found in the literature. However, the structure of alternatelamellae or cylinders embedded in a matrix and the good bonding between the constituentphases is very interesting for the development of optical devices. In fact, the step indexprofiles and the absence of lattice mismatch defects—both characteristic of eutectic sys-tems—are favorable to a decreasing light losses when they are used as optical waveguidesand an ordered eutectic system is essentially a monolith of planar or fiber waveguides.Additionally, optically active ions (rare-earth or transition metal ions), needed for activeoptical operation, can be easily introduced into the eutectic materials by addition to the


precursor powders before crystal growth. Impurities are expected to be homogeneouslydistributed in each phase during the solidification process owing to their respective parti-tion coefficients.

Preliminary studies on optical properties were performed several decades ago in someregular fibrous fluoride eutectics. These materials were proposed for fiber optic faceplateor microchannel plate components [29]. In fact, a fiber eutectic composed of a high refrac-tive index dielectric compound embedded in a dielectric matrix of lower refractive indexacts as a monolithic bundle of optical fibers. Another option is to etch out one of thephases, leaving a microchanneled matrix that can be filled up with a liquid or solid phase.Alternatively, the matrix can be chemically removed leaving behind a bundle of long singlecrystal fibers of micron section, as was done in the LiF/NaCl eutectics (Fig. 7.8) [209]. Asimilar technique was used several years ago to obtain single crystal spinel fibers from theMgAl2O4/Mg2SiO4 DSE but the colony structure of the eutectic impeded the growth oflong fibers [26]. In addition, the favorable conditions of eutectic mixtures to produceglasses with a low number of components are also remarkable from the point of view

Fig. 7.8. NaCl/LiF DSE. (a) SEM image of the transverse section. The LiF single crystal fibers (black circles) areembedded in the NaCl matrix. (b) Optical microscope image of a single crystal LiF fiber obtained by removing theNaCl matrix.


of the photonic applications of the eutectics. A good optical quality glass can be producedby fast directional solidification of the CaSiO3/Ca3(PO4)2 binary eutectic system [35](Fig. 7.9).

Most of the DSE oxides considered in this paper are formed by phases transparent inthe 0.2–10 lm optical spectral intervals and therefore suitable for optical applications. Therelatively large (several mm long) ordered regions that can be found in most regular oxideeutectics, such as the lamellar CaSZ/CZO or the fibrous MgO/CaF2, can be used as singlecrystalline stacks of planar optical waveguides or optical fibers, respectively. In othercases, a phase dimension of the order of light wavelength adds to the refractive index con-trast between phases to produce diffraction, interference, polarization effects, etc., whichcan be used in optical systems [210,211].

7.3.1. Optical waveguidesResearch into active optical waveguides gained attention in the past because of the

enormous success of the erbium-doped fiber amplifier. Optical gain with relatively lowpump powers can be achieved with optical waveguides [212]. Furthermore, efforts weremade to look for crystalline materials, instead of glassy, for waveguides. Compared withthe glass fibers currently used in optical technologies [213], single crystal fibers offer somepotential advantages: a wider transparency window, greater resistance to radiation dam-age, better mechanical, chemical and thermal stability, non-linear effects, and narroweremission bands. Crystalline composites are also suitable for integration of active and pas-sive media, which can increase the potential applications of the guides [214]. A wide vari-ety of fabrication and processing techniques and host materials are being investigated. Theoptical active ions and the required refractive index profiles are usually implemented byion implantation, ion in-diffusion, co-deposition and ion exchange techniques, and severalwave-guide lasers and amplifiers have been demonstrated in oxide materials such as YAG,LiNbO3, BGO, Al2O3, etc.

In optical waveguides, light is guided by transparent phases, which are surrounded by aphase of lower refractive index. The effect is governed by the waveguide parameter Vdefined as [215]

Fig. 7.9. Wollastonite/TCP eutectic glass rod of 2 mm in diameter grown downwards at high rate by the LFZmethod.


V ¼ 2pk

d n2i � n2

o

�1=2; ð7:1Þ

where k is the light wavelength in vacuum, d the guide size parameter (the fiber radius forcylindrical fibers and one half of the lamella thickness for planar waveguides), and ni andno stand for the refractive indexes of the waveguide and the surrounding medium, respec-tively. The number of modes propagating in the guide also depends on V. The most favor-able situation in terms of light propagation is obtained when V < p/2 for planar guides andV < 2.405 for fibers in the single-mode operation. For a given waveguide (characterized byd, ni and no), the cut-off wavelength kc, the most energetic light propagating in single-modeform, can be defined as

k P kc ¼ 4d n2i � n2

o

�1=2for lamellae, ð7:2aÞ

k P kc ¼2pd

2:405n2

i � n2o

�1=2for fibers. ð7:2bÞ

Table 7.2 compiles the waveguide parameter in some DSE oxides. Light guiding effectsare expected in the CaSZ lamellae of the CaSZ/CaZrO3 eutectic, in the ZrO2 fibers of theZrO2/Al2O3 system and in the MgO fibers of the CaF2/MgO eutectic. It can be concludedthat single-mode operation in the second optical window is predicted for CaZrO3/CaSZand CaF2/MgO eutectics. For the ZrO2/Al2O3 system, the cut-off wavelength decreasesdown to the visible optical range.

Preparation of active planar waveguides using the CaZrO3/CaSZ lamellar eutectic hasrecently been demonstrated [10]. The CaZrO3/CaSZ DSE samples consist of alternatelamella of �2 lm in thickness of cubic CaSZ and orthorhombic perovskite CaZrO3 singlecrystals [195]. Ordered grains extending over several mm in length and up to 100 lm inwidth were produced by the LFZ growth method. The component crystals are transparentfrom 0.3 lm to 15 lm and the refractive index contrast in this composite is 2.5%, enoughto allow visible light guiding. The most refractive material, CaSZ, accommodates largeamounts of rare-earth doping. In particular, Er3+ active ions can be easily introduced inboth phases but at a higher concentration in the most refractive CaSZ phase. Merinoet al. [12] studied the absorption and emission spectra and the corresponding oscillatorstrengths, radiative transition probabilities and emission lifetimes of the electronic transi-tions of Er3+ ions in this eutectic. Another interesting feature of the CaZrO3/CaSZ:Ermaterial is the two photon green emission from the Er3+ ion 4S3/2 level at 545 nm, underexcitation with a diode laser in the 4I15/2! 4I11/2 absorption band at 980 nm. This up-con-version was used to study the wave-guide effect in this material. As shown in the imagesequence of Fig. 7.10, light from a 980 nm laser diode is focused on one polished trans-verse face of a 1.1 mm thick disk of the eutectic crystal whereas the other surface of thedisk is focused by a 40· microscope objective into a charge coupled device (CCD) detec-

Table 7.2Waveguide parameter V (calculated for light of wavelength k = 0.5 lm) and cut-off wavelength kc of some DSEoxides

DSE Guiding phase Shape Phase thickness (lm) V kc (lm)

CaZrO3/CaSZ Ca0.25Zr0.75O1.75 Planar 2 5.2 1.7Al2O3/ZrO2 ZrO2 Fiber 0.3 2.45 0.5CaF2/MgO MgO Fiber 1.2 7.5 1.6

Fig. 7.10. CCD images obtained using the up-conversion effect demonstrating light guiding by CaSZ lamellae.Excitation on the opposite face of a CaZrO3/CaSZ: Er lamellar DSE with a k = 980 nm diode laser and end-firedetection at k = 545 nm. (a, b) Excitation spot of 1.8 lm centered in a CaSZ and a CaZrO3 lamellae, respectively,(c) spot of 3.2 lm, (d) excitation spot of 7.6 lm. (Reprinted by permission of the American Institute of Physics[10].)


tor, which detects the green light. Fig. 7.10(a) and (b) correspond to images taken by excit-ing the sample with a spot centered at a CaSZ and a CaZrO3 lamella, respectively. Theplanar waveguide effect is clearly demonstrated because the light emission is only detectedat the CaSZ lamellae. This wave-guide effect is corroborated by Fig. 7.10(c) and (d)obtained by defocusing the exciting beam. Light guiding has also been demonstrated inthe CaF2/MgO fibrous eutectics [11]. An optical micrograph taken in the transmissionmode through a slab of 300 lm cut with the MgO fibers perpendicular to the film surfaceis shown in Fig. 7.11. Light is guided by the highest refractive index MgO fibers giving adensity of about 40,000 pixels/mm2.

A complete characterization of the optical properties of these eutectic materials is stilllacking but it is advanced that large benefits can be obtained from the extraordinary sta-bility, good crystalline and monolithic characteristics of DSE of wide electronic gap mate-rials. The main constraint for optical applications is the difficulty of growing materialswith large grains for phase continuity through the sample and phase alignment, and thepresent application of these materials in waveguides should be restricted to submillimetersize devices.

7.3.2. Effect of microstructure size on luminescence

Periodic dielectric structures with interphase spacings of the order of the visible andnear-infrared light wavelength, named photonic crystals, have experienced significantdevelopment in the last decade [216]. An important property of these structures is the

Fig. 7.11. Optical transmission micrograph of a [001]kCaF2 plate of 300 lm thickness from an MgO/CaF2 DSEgrown by the Bridgman method. (Reprinted by permission of the Materials Research Society [11].)


modification of the luminescence efficiency of atoms or molecules in strong or weak con-fining structures [217]. The luminescence at certain wavelengths can either be suppressedor forced to radiate in definite directions of the periodic structure in photonic crystals.The usual technique to manufacture photonic crystals is based on the packing of uni-form-size particles from a colloidal suspension of SiO2 or polystyrene (3D) or in the stack-ing of alternating layers of Si and SiO2 (2D), and the main concern is the mechanicalstability of these structures. The periodic microstructures found in regular DSE oxideswith lamellar or fibrous phase arrangement present excellent structural integrity and couldbehave as 1D and 2D photonic crystals, but these latter effects have not yet been defini-tively proved.

An effect which is related to photonic crystals has been recently reported on DSE oxi-des. The radiative lifetime of the 4I13/2 level of Er3+ was modified up to 15% by changingthe microstructure size of the Al2O3/ZrO2 DSE [218]. Erbium in this system only enters inthe higher-refractive-index ZrO2 phase, whose volume fraction is 30%. As shown above,the refractive index contrast produces efficient light guiding but it is not enough to producea full band gap in terms of the photonic crystal theory. Consequently, the weak confine-ment or weak coupling range of the luminescent ion to the electromagnetic field leads toonly feeble effects on the luminescence properties. The lifetimes of the 4S3/2 (545 nm) and4I13/2 (1520 nm) Er3+ levels were measured in Al2O3/ZrO2 DSE samples grown by LFZmethod at various rates, which presented large differences in the microstructure(Fig. 7.12). The sample in Fig. 7.12(a) shows an interpenetrating degenerate lamellae struc-ture where the average thickness of the ZrO2 degenerate lamellae was 0.6 lm. The samplein Fig. 7.12(b) presents a colony structure with a triangular arrangement of ZrO2 cylinderswith average diameter 0.36 lm embedded in the Al2O3 matrix. The sample in Fig. 7.12(c)also presents a colony structure but the ZrO2 phase within the colonies is arranged in theform of lamellae of 0.05 lm in thickness. The luminescence lifetime varied from one

Fig. 7.12. SEM micrographs of transverse sections of Al2O3/YSZ DSE grown by LFZ method at (a) 10 mm/h,(b) 150 mm/h, (c) frozen by switching off the laser [218].


sample to another as depicted in Table 7.3. It is clear that the 4S3/2 (545 nm) lifetimeremains unchanged, whereas that of the 4I13/2 (1520 nm) level increases by about 15% atambient temperature and 10 K as the ZrO2 phase size decreased. This weak but meaning-ful effect was explained as a result of the change in the density of states (DOS) of the elec-tromagnetic radiation at the luminescent wavelength taking place near to the interfaces[219,220]. In a homogeneous dielectric medium, the electric dipole radiative deexcitationprobability varies linearly with the refractive index n (apart from local field corrections).The small size of the ZrO2 phase (either lamellae or cylinders), which is comparable tothe wavelength of the emitted radiation, makes the DOS a function of the distance tothe boundary between the different dielectrics. According to the calculations of Snoekset al. [221], the average DOS is proportional to the refractive index of the hosting dielectric

Table 7.3Lifetime of the 4I13/2 Er3+ emission as a function of the ZrO2 phase size

Al2O3/ZrO2:Er Sample ZrO2 particle size (nm) Lifetime (300 K) ±0.1 ms Lifetime (10 K) ±0.1 ms

Fig. 7.12(a) 600 3.4 4.8Fig. 7.12(b) 360 3.6 5.2Fig. 7.12(c) 50 4.0 5.4


at a distance far away from the interface, and the local DOS decreases down to values thatare proportional to the refractive index of the surrounding medium near to the interfaceand at distances below 0.7k/2p (k being the wavelength in vacuum). Consequently, moreEr3+ ions will perceive a lowered density of states in the thinner phases than in the thickerones, and the lifetime will be longer, as experimentally observed. Hence the variation ofthe luminescence lifetime with the interphase spacing is due to the change of the availableelectromagnetic modes at 1520 nm, which is observable in the fine microstructure obtainedin DSE oxides grown at high rates.

The main limitation of DSE oxides as photonic crystals is the small-refractive-indexcontrast. This handicap might be eliminated in the near future by the selective dissolutionof one phase, to be replaced with a different phase of higher refractive index. In short,although still in their infancy, the photonic DSE materials constitute an alternative forthe fabrication of periodic dielectric structures and they deserve an in-depth study.

7.4. Electroceramics

Most of the research on the electric properties of DSE oxides has been carried outin ZrO2-based eutectics. Cubic zirconia is the oxygen electrolyte most widely used as anoxygen sensor (k-probe) [222] and in high temperature furnaces [223] because of its excel-lent chemical stability and oxygen-ion conductivity at high temperatures. However, thethermo-mechanical stresses associated with high temperature operation as well as the envi-ronmental degradation are limiting factors in terms of durability, which can be overcometo some extent by using DSE oxides if the overall eutectic conductivity is not drasticallyreduced by the presence of phases with lower conductivity than ZrO2. This latter propertydepends on the morphology of the eutectic microstructure, as was shown by Merino et al.[224] and by Cicka et al. [225], who measured the ionic conductivity in CaZrO3/CaSZ andMgO/MgSZ DSE, respectively. The domain size did not modify the eutectic conductivitybut the effect of microstructure was clearly revealed by the strong anisotropy observed insome well-aligned DSE oxides. For instance, the ionic conductivities at 1000 K of lamellarCaZrO3/CaSZ and fibrous MgO/MgSZ eutectics are presented in Table 7.4 in the lamellaor fiber direction (rk) or perpendicular to them (r?). The ionic conductivity along thelamellae plane of the CaZrO3/CaSZ DSE was higher than that of a CaZrO3/CaSZ eutecticmanufactured by conventional sintering which presented a granular microstructure,whereas the conductivity perpendicular to the lamellae was significantly lower.

The differences in conductivity between granular and lamellar CaZrO3/CaSZ eutecticsand the anisotropy of the latter could be easily understood from the predictions of mean-

Table 7.4Experimental and theoretical predictions of DC conductivity at 1000 K of some DSE oxides containingstabilized-zirconia phase

Material Processing E (eV) rk (X�1 cm�1) r? (X�1 cm�1)

Experiment Theory Experiment Theory

Al2O3/YSZ DSE 1.04 2.0 · 10�3 4.0 · 10�3 2.0 · 10�3 4.0 · 10�3

MgO/MgSZ DSE 1.5 1.5 · 10�3 2.8 · 10�3 1.5 · 10�3 3.5 · 10�3

CaZrO3/CaSZ DSE 1.3 1.5 · 10�4 1.45 · 10�4 2.0 · 10�5 0CaZrO3/CaSZ Sintered 1.3 5.0 · 10�5 4.1 · 10�5 5.0 · 10�5 4.1 · 10�5

rT activation energies E in the low temperature range are also shown.


field approximations, whose foundations are similar to those presented in Section 5.3. Theconductivities of the CaZrO3/CaSZ eutectic produced by directional-solidification fol-lowed the predictions for a simple microstructure consisting of an ordered stacking of oxy-gen-conducting (cubic CaSZ) whose conductivity at 1000 K is 3.5 · 10�4 X�1 cm�1 at1000 K [224] and non-conducting (CaZrO3 with a conductivity of 1.7 · 10�9 X�1 cm�1

at 1000 K [226]) phases. This representation leads to predictions of effective conductivityfor the aligned eutectic given by the direct and inverse ‘‘rule of mixtures’’ when the electricfield is parallel or perpendicular to the lamellae, respectively, which stand in good agree-ment with the experimental results parallel to the lamella (Table 7.4). The differencesbetween the model and the experimental data in the perpendicular direction were attrib-uted to some misorientation in the lamellae, as discussed in [224]. The conductivity ofthe sintered eutectic with a granular microstructure computed with the effective mediumapproximation [227] was very close to the experimental one (Table 7.4) although the modelassumed a simple microstructure formed by a 41 vol.% random dispersion of conductingspherical particles of CaSZ embedded in a continuous insulating CaZrO3 matrix. Predic-tions based in the effective medium approximation for fibrous MgO/MgSZ eutecticsshowed a weak anisotropy [228,229], but this was not found experimentally (Table 7.4),and these differences were again explain by the microstructural disorder associated withthe eutectic grains.

Some potential applications of DSE as a result of the good thermo-mechanical pro-perties, corrosion resistance and ionic conductivity are micron-size thin electrolytes forintermediate temperature SOFC, Nerst glower elements, and high temperature heating ele-ments [27,225,230]. YSZ Nerst lamps are stable to very high temperatures (incandescencetemperatures) in air but porous ceramics have to be used due to the poor thermal shockresistance of ZrO2. However, dense rods of YSZ/Al2O3 DSE fabricated by the LFZmethod have been proved to glow at 1600 �C for long periods without any deteriorationof their conductivity or mechanical properties. Microstructural coarsening was observedafter 160 h of operation but the rods retained their structural integrity [27]. The bettermechanical and thermal shock resistance of DSE oxides may compensate for the loweroperation temperature of the eutectics.

Ionic conductivity was measured in Al2O3/YSZ DSE rods with TDI microstructureover the temperature range of 300–1650 �C [27]. The results are given in Fig. 7.13, whichshows the typical behavior of conducting YSZ with lower activation energy (0.8 eV) above900 �C and higher activation energy (1.04 eV) at lower temperatures (see also Table 7.4). Itis important to realize that the conductivity of Al2O3/YSZ DSE is only one order of mag-nitude lower than that of YSZ and that it could be improved by a factor of two (reachingthe theoretical values of the mean-field approximation) if the connectivity between theYSZ domains were improved.

In conclusion, the conductivity of some directionally solidified eutectics based on YSZ,which possess excellent mechanical properties and corrosion resistance, has been charac-terized in recent years. Unfortunately, an improvement in conductivity associated withsmall size effects has not yet been found in these composites whose conducting propertiescan be explained by a mean-field approximation. A highly anisotropic DC conductivityhas been reported for the lamellar CaZrO3/CaSZ eutectic, but the high stabiliser contentin the zirconia phase and its low volume fraction leads to ionic conductivity along thegrowth axis which is about two orders of magnitude lower than the best YSZ ceramics.The fibrous MgO/MgSZ eutectic shows better electrical conduction but it has yet to be

Fig. 7.13. Ionic conductivity of YSZ/Al2O3 DSE in the as-grown condition and after a thermal treatment at1600 �C [27].


proven that the improvement in mechanical strength introduced by the MgO fibers leadsto a material suitable for thin film electrolyte production. Best achievements were obtainedin the Al2O3/YSZ eutectics with TDI microstructure grown by LFZ methods. The ionicconductivity of these compounds was good enough to consider applications such as elec-trolytes for SOFC. For example, the maximum required area specific resistance for elec-trolytes of 0.15 X cm2 for these devices could be achievable with electrolyte layers ofabout 5 lm, a goal that seems not too difficult to reach.

7.5. Bioeutectics

A new procedure was developed to obtain strong macroporous bioactive ceramics forhuman bone replacement. The material (Bioeutectic�) was prepared by slow solidification

Fig. 7.14. SEM micrograph showing the colony microstructure of the wollastonite–tricalcium phosphate eutectic.(Reprinted by permission of Elsevier [232].)


of the wollastonite–tricalcium phosphate eutectic system [231] and is composed of twophases, the pseudowollastonite and the a-tricalcium phosphate, which presents a morphol-ogy of eutectic colonies, as depicted in Fig. 7.14. This compound is reactive in simulatedbody fluid [34] and in human parotid saliva [232] and transforms into apatite and carbon-ate-hydroxiapatite-like phases, respectively. The transformed material is a macroporousbioactive material, which is expected to promote new bone ingrowth.

8. Concluding remarks

The comprehensive review of the recent developments in DSE ceramic oxides presentedin these pages has shown that they are highly structured composite materials with a denseand homogeneous microstructure, which determines the mechanical and functional prop-erties. Several areas of remarkable successes were achieved, particularly in the last 15years, and a number of key issues remain open. Both the achievements and the shortcom-ings are briefly discussed in the last section of the review, and the necessary breakthroughsas well as the emerging areas of research are noted.

Until the late 1970s, most DSE oxides were grown by the Bridgman method, which isstill optimum for large volume samples. The modest thermal gradients inherent in thismethod limited, however, the growth rate and the types of microstructure, which couldbe achieved with a given eutectic composition. Since the early 1990s, axial thermal gradi-ents several orders of magnitude higher were obtained with new processing techniquesbased on the growth-from-meniscus methods (such as LFZ, EFG, and l-pD) where eitherlamps, lasers of RF were used as heating sources. These methods are nowadays readilyavailable for growing DSE oxides whose microstructures have been tailored for specificapplications by controlling the growth rate. However, the relationships between thermalgradients, growth rate and phase size imposed some limitations on sample processingand different growth methods have to be found for each particular need. Moreover, recentdevelopments in processing have opened new possibilities for DSE oxides. They includethe use of fast quenching methods to manufacture nanoeutectic oxides, i.e., eutectics withphase dimensions in the nm range, and the application of diode-laser technologies to thesurface processing of large plates at high growth rates.

The manufacturing of new microstructures was coupled with the detailed characteriza-tion of the growth habits of each eutectic phase and the nature of the interfaces, whichplay a dominant role in the eutectic properties as a result of their large area fraction.The crystallographic directions of eutectic growth and the crystallographic relationsbetween phases are nowadays well established in most of the eutectic systems (and micro-structures) of interest. In addition, the thermo-elastic residual stresses which develop uponcooling after solidification were determined by sophisticated measurement techniques (X-ray, neutron diffraction and piezospectroscopy) and by simulation tools based on mean-field methods, which provided a complete picture of their origin and development.

New developments in processing and microstructural characterization have led to adeeper knowledge of the relationship between the microstructure and the mechanicalbehavior and, as a result, DSE oxides with optimized microstructures for structural appli-cations have been manufactured. In particular, the strength Al2O3–YAG DSE withsubmicron interphase spacing can reach 2 GPa at ambient temperature, and most of thestrength is retained up to 1900 K, while Al2O3–YAG and Al2O3–EAG DSE with largeinterphase spacing made up of a single-crystal network of both eutectic phases stand


among the oxides with best creep resistance at 1900 K. More modest (although still out-standing) ambient temperature strength, creep resistance and strength retention at hightemperature were reported for Al2O3–YSZ DSE, whose toughness was approximatelytwice that of Al2O3–YAG. In addition, these eutectic microstructures showed very limitedhomogeneous phase coarsening even at temperatures approaching the eutectic point,excellent resistance to chemical attack in moist environments, and their mechanicalstrength was not impaired by subcritical crack growth at high temperature, as observed,for instance, in single-crystal Al2O3. As a result of this combination of properties, DSEoxides stand as the best available structural materials for applications at very high temper-ature (>1400 �C), and feasibility investigations are under way to use these materials in anew generation of gas turbines which operate at 1700 �C [89]. Examples of combustor lin-ers and hollow turbine nozzles machined from directionally solidified ingots are shown inFig. 8.1.

Fig. 8.1. Al2O3–YAG components for gas turbines mechanized from a directionally solidified ingot. (a)combustor liners, (b) hollow turbine nozzle. (Courtesy of Prof. Y. Waku.)


Of course, there are still important restrictions on the widespread application of DSEoxides as structural materials. From the processing viewpoint, the relationships betweenthermal gradient, growth rate and microstructure size impose limitations of the sampledimension and/or microstructural characteristics. Bridgman methods are optimum if largevolume samples are desired although the relatively modest thermal gradients inherent inthis method imply low growth rates and consequently large interface spacing, whichmay not be the best in terms of strength and hardness. On the contrary, the growth-from-meniscus methods induce large thermal gradients and admit high growth rates, lead-ing to eutectics with small interphase dimensions, but the large thermal stresses associatedwith steep thermal gradients limit the specimen thickness to a few mm. In addition, theAchilles heel of DSE oxides for structural applications is their low toughness. DSE oxidesare prone to catastrophic failure and their strength is very sensitive to the nucleation ofdefects (for instance, by localized coarsening of the microstructure at high temperatureas a result of the reaction with Si-containing species in the environment). Increasing thetoughness of DSE can only be attained by engineering the interface between domains topromote crack arrest and deflection as the eutectic components are brittle oxides withlow toughness. However, any reduction of the interface strength will compromise theiroutstanding strength and microstructural stability at high temperature. Another optionfor DSE in structural applications is in coatings. DSE coatings may provide their excellentcorrosion and abrasion resistance as well as strength, while the ductile substrate impartsthe structural integrity. The deposition of DSE oxide coatings by laser surface meltingon ceramic and metallic substrates has been demonstrated recently, and this technologyis a promising research line.

Functional applications of DSE oxides are still in the infancy in comparison with struc-tural ones, and research efforts in this area are still very recent. The excellent chemical andthermal stability of DSE oxides, together with the good mechanical properties describedabove, are very important for many functional applications and they are added to theadvantages provided by the synergistic combination of different phases within the samematerial. For instance, channeled Ni–YSZ and Co–YSZ cermets produced from DSEoxide precursors have been proposed for use in SOFC. The lamellar microstructure andthe strong bonding between the YSZ and the metal prevent the coarsening of the metalparticles in working conditions, and improve the efficiency and long-term stability ofSOFC under operation. Promising attempts at using DSE oxides as structured substratesfor patterned thin films, ionic conductor composites, and optical waveguides have beenreported but comprehensives studies of the feasibility of these developments is lacking.In particular, applications, which need phase continuity extended in space, such as thoseinvolving light or electrical transport, are limited by the small grain size in DSE oxideswith regular microstructure to applications in microdevices. However, the problem ofthe small grain size of regular eutectics, induced by eutectic ability to accommodategrowth fluctuations, has not yet been solved satisfactorily. Although the basic principlescontrolling directional solidification of eutectic structures are well known, furtherimprovements should be guided by numerical simulations of the eutectic growth process.This complex task, which requires the coupling of different physical phenomena (solid andfluid mechanics, heat conduction and radiation, phase change), is essential to produceeventually large samples at high growth rates (and hence with small domain size) and reg-ular microstructures without grain boundaries, where phase continuity can be ensuredthroughout the eutectic samples.


Many other functional applications of DSE oxides are being explored. For instance,soft magnetic materials with high initial permeability, low coercive field and high electricalresistance can be produced from lamellar ferromagnetic and insulating eutectic compositeswith possible applications as magnetic flux concentrators in transformers, generators,motors, dynamos and switches and microwave technology. Another area of research isthe manufacture of pseudoeutectic materials by removing one of the eutectic phases inTDI microstructures. This leads to a single crystalline microstructure of one eutectic phasewith interconnected porosity, which can be infiltrated with another phase with differentproperties to create new materials with an eutectic microstructure.

Acknowledgements

The authors are indebted to their colleagues of the Departamento de Ciencia de Mate-riales (Universidad Politecnica de Madrid) and of the Instituto de Ciencia de Materiales deAragon (CSIC-Universidad de Zaragoza) for their help during this work. The usefuldiscussions with J.Y. Pastor, C. Gonzalez, A. Martın, J. Segurado from the PolytechnicUniversity of Madrid and with R.I. Merino, J.I. Pena and A. Larrea from the ICMA inthe course of this work are especially appreciated. Some of the results reported in thispaper were obtained in research projects financed by the Spanish Government undergrants MAT1997-673, MAT2000-1533, MAT2003-6085, and MAT2003-1182, andby the Comunidad de Madrid through the grant GR/MAT/357/2004. Their support isgratefully acknowledged.

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