ANRV347-MR38-16 ARI 28 May 2008 10:15

Crystal Chemistry ofComplex Perovskites:New Cation-OrderedDielectric OxidesP.K. Davies,1,∗ H. Wu,2 A.Y. Borisevich,3

I.E. Molodetsky,4 and L. Farber5

1Department of Materials Science and Engineering, University of Pennsylvania, Philadelphia,19104-6272; email: davies@seas.upenn.edu2National Institute of Standards and Technology, Gaithersburg, Maryland 208993Oak Ridge National Laboratory, Oak Ridge, Tennessee 378314Schlumberger, Princeton Junction, New Jersey 085505Merck & Co., Inc., West Point, Pennsylvania 19486

Annu. Rev. Mater. Res. 2008. 38:369–401

First published online as a Review in Advance onApril 9, 2008

The Annual Review of Materials Research is online atmatsci.annualreviews.org

This article’s doi:10.1146/annurev.matsci.37.052506.084356

Copyright c© 2008 by Annual Reviews.All rights reserved

1531-7331/08/0804-0369$20.00

∗To whom all correspondence should be addressed.

Key Words

cation ordering, microwave ceramics, niobates, tantalates, titanates

AbstractThe crystal chemistry of complex perovskite dielectric oxides is reviewed,with an emphasis on structures derived from ordering of the cations on theoctahedral B-sites. New classes of perovskites, designed to exhibit 1:2 or1:3 B-site order for application as low-dielectric-loss microwave ceramics,are identified, and their synthesis, structure, and properties are described.Through the use of B-site chemistries based on Li, Nb, Ta, Ti, and W,members of four new families with 1:2 order, A(βI

1/3βII

2/3)O3, and threenew families with 1:3 order, A(βI

1/4βII

3/4)O3, were successfully prepared.The formation and stability of the new and previously prepared orderedperovskites are rationalized through the use of familiar crystal chemical toolssuch as cation size and charge difference, bond valence, tolerance factor,and new concepts related to the local charge imbalance on the A- and B-sublattices. These tools can be successfully applied to develop stability fieldmaps for each structure and to predict other new ordered systems.

369

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INTRODUCTION

Many classes of electronic oxide ceramics are dominated by ABO3 perovskite and perovskite-related compounds. The unique range of responses, coupled with the flexibility of perovskites inaccommodating a broad spectrum of atomic substitutions, provides a robust platform for probingcorrelations between structure, bulk chemistry, and properties. When the A- or B-sites containmixtures of two (or more) different atoms, control of the positional ordering of the cations ina complex perovskite provides an additional tool for mediating the bulk electronic response.For example, alterations in the B-site order can induce ferroelectric-to-relaxor transitions inPb-based systems (1) or order-of-magnitude changes in the dielectric loss properties of alkalineearth-based microwave dielectrics (see, e.g., Reference 2). This paper reviews the crystal chemistryof ordered complex perovskite dielectric oxides and describes work in which the compositionwas designed to stabilize new systems for potential application as low-dielectric-loss microwaveceramics. The primary focus is on how the stability of the cation order responds to specific changesin bulk chemistry, rather than a review of the properties of ordered complex perovskite dielectricoxides, which can be found in several other literature sources.

Overview of Perovskite Crystal Chemistry

The structural chemistry of ABO3 perovskites can be described in terms of close packing of AO3

layers, where the B-site cations occupy 100% of the resultant BO6 oxygen octahedra. When theAO3 layers are arranged in cubic close packing, the BO6 octahedra are connected exclusivelythrough corner sharing, and the structure is termed a cubic perovskite (Figure 1). In an idealcubic perovskite the A and B cations realize their equilibrium bond distances to oxygen withoutinducing any distortion of the unit cell, and dA-O = √

2(dB-O). The resultant symmetry is cubic(space group Pm-3m), and the so-called Goldschmidt tolerance factor (t), = (rA + rO)/

√2(rB +

rO) = 1. In many perovskites the A-O and B-O bond lengths are geometrically incompatible, andlower symmetry structures are stabilized. When the A cation is undersized, t < 1, the A-O distance

A

B

C

A

B

C

Figure 1Ideal cubic ABO3perovskite structure.(Left) Viewed along(110) to highlight thecubic close packing ofAO3 layers and theresultant cornersharing of the BO6octahedra (A cationsare omitted for clarity).(Right) Perspectiveview highlighting thecorner sharing of theoctahedra.

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can be shortened, and the coordination number of the A cation can be lowered through a corre-lated tilting of the surrounding BO6 octahedra (Supplemental Figure 1; for this and subsequentsupplemental figures, follow the Supplemental Material link from the Annual Reviews homepage at http://www.annualreviews.org). An oxide with one of the smallest tolerance factors isCa4Nb2O9 (3), where t = 0.91 (3). In the seminal studies of Glazer (4) and, more recently, thoseof Woodward (5, 6), the changes in symmetry that result from different types of octahedral tiltinghave been systematized and rationalized for simple (single-ion) and complex perovskites with andwithout cation order. Glazer’s notation specifies the magnitude and phase of the rotation of theoctahedra about the three orthogonal axes of the aristotype cubic unit cell. Letters indicate themagnitude of the rotation about a given axis; e.g., the use of the letters a, b, and c implies unequaltilts about the x, y, and z axes. Superscripts denote the phase of the tilt: A positive superscriptindicates neighboring octahedra tilt in the same direction (in phase), a negative superscript indi-cates the octahedra tilt in opposite directions (out of phase), and a zero superscript signifies notilting about that axis. For example, the tilt system a0a0a0 represents an undistorted perovskite;a−b+a− represents compounds such as CaTiO3 (Supplemental Figure 1) and GdFeO3, with equalout-of-phase tilts along two axes (a and c in this example) and a different, in-phase tilt along thethird axis (b). The reader is also referred to the papers of Levin et al. (3, 7) for treatment of thesymmetries of ordered, tilted mixed-metal systems and to the work of Howard & Stokes (8) for agroup-theory analysis of simple tilt systems. The tilting of the octahedral framework also plays amajor role in determining the dielectric response of oxide perovskites. In Pb-based systems octa-hedral rotation often competes with ferroelectricity (9), and for alkaline earth-based perovskitesthe tilting mediates the temperature dependence of the dielectric permittivity (10).

Deviations from ideal cubic symmetry can also be induced by distortion of the octahedra throughJahn-Teller-type displacements or from the off centering of d 0 cations within the octahedra via asecond-order Jahn-Teller distortion. When the A-site is occupied by a cation that also undergoeslarge off centering, in particular lone-pair ions such as Pb2+ or Bi3+, cooperative displacements onthe A and B sublattices can induce tetragonal distortions from cubic symmetry [e.g., c/a ∼ 1.065in PbTiO3 (11) and ∼1.20 in Bi(Zn1/2Ti1/2)O3 (12–14)] that are often accompanied by a largeferroelectric polarization.

When the tolerance factor is >1, the AO3 layers typically adopt mixed cubic (c) and hexagonal(h), or pure hexagonal, close-packed stacking sequences. The introduction of hexagonal stackingis accompanied by face-sharing of adjacent BO6 octahedra and by the formation of 90◦ BOB bondangles (Figure 2). The stability of hexagonal perovskites is strongly dependent on the compen-sation of the electrostatic repulsion between the highly charged cations occupying neighboringface-shared octahedra. This repulsion can be overcome by the formation of metal-metal bonds,as is found in BaRuO3 (15), or reduced through the occupation of the face-shared octahedraby cations with smaller formal charges [e.g., BaLi1/4(Nb,Ta)3/4O3, Ba(Li2/5W3/5)O3 (16, 17)] orvacancies [e.g., Ba5Ta4O15 (18), Ba8(Ta4Ti3)O24 (19), Ba8(NiTa6)O24 (20)]. Blasse (21) has alsodiscussed the role of the increased anion polarization that accompanies the formation of 90◦ BOBbonds in stabilizing a hexagonal form of perovskite. Many examples of mixed (c) and (h) layers areknown; these include, e.g., ten-layer (hcccc)2 Ba(Li2/5W3/5)O3, eight-layer (hccc)2 Ba(Li1/4Nb3/4)O3

(16, 17), six-layer (hcc)2 BaTiO3 (22, 23), four-layer (chch) SrMnO3, and nine-layer (chh)3 BaRuO3

(15). A unique feature of the hexagonal perovskites is their ability to accommodate significantconcentrations of vacancies on the B-sites, which destabilize their cubic counterparts. The cationvacancies are always located, and typically ordered, in the face-shared octahedra; one example isthe Ba5Nb4O15 structure, in which the vacancies occupy sites in the center of the sequence ofthree face-shared octahedra (Figure 2).

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c

c

c

h

c

c

c

h

h

h

c

c

c

h

h

Figure 2Structures ofhexagonal perovskiteswith a tolerance factorof >1 viewed along(110)c. The cubic(c) and hexagonal(h) layers are indicated.A cations are omittedfor clarity. (Left)Ba4LiNb3O12. (Right)Ba5Nb4O15, where thecentral face-sharedoctahedron is vacant.

Cation Ordering

Cation order-disorder transitions play a major role in adjusting the crystal structure, phase sta-bility, and properties of many complex oxide perovskites. Alterations in the degree of order caninduce substantial changes in magnetic behavior, dielectric/ferroelectric response, and electronicor ionic conductivity (24). The permutations for inducing order include mixed-metal cation or-der on the A- and B-site positions and vacancy/mixed-anion order on the oxygen sublattice. Anordered arrangement is usually stabilized when two cationic species occupying the same site differsufficiently in their coordination preference, valence, or size. Whereas examples of A-site order-ing are quite rare and often involve vacancies as the alternate cation species (see, for example,Reference 25), B-site-ordered perovskites are quite common owing to the increased covalentcharacter of the corner-shared BO3 framework.

In defect perovskites that contain high concentrations of oxygen vacancies, the nature of thecation (and vacancy) order is dictated by the coordination preference of the B-site cations (26). Themost common arrangement has a [100] layering of the differently coordinated BI and BII cations;well-known examples include the brownmillerite family (ordering of tetrahedral- and octahedral-coordinated cations) and the layered order of square planar and square pyramidal Cu cationsin high-Tc superconductors. Because significant concentrations of anion vacancies often have adeleterious effect on the electronic response, most dielectric and ferroelectric perovskites are fullystoichiometric. In these cases the thermodynamic stability of the cation order is determined by thesize and charge difference of the BI and BII cations, although other factors such as the tolerancefactor and the covalency of the cations also play a role. Almost all examples of B-site ordering in

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Figure 31:1-ordereddouble-perovskiteA(βI

1/2βII

1/2)O3structure viewedalong (110)c tohighlight thedoubled 〈111〉 repeatof the βI and βII

cation sites.

stoichiometric A(BIxBII

y)O3 complex perovskites involve a 〈111〉 layering of the different cations.The structures are traditionally categorized according to the crystallographic site stoichiometryx:y in the ordered A(βI

xβII

y)O3 structure (here β represents a crystallographic site; B specifies acation). The known examples have x:y = 1:1, 1:2, or 1:3; other stoichiometric ratios are possible,but none have been reported.

1:1 order: A(βI1/2β

II1/2)O3. The 1:1-ordered A(βI

1/2βII

1/2)O3 (A2(βIβII)O6) systems are themost frequently encountered family of ordered complex perovskites. The different cations oc-cupy alternate B-sites in a NaCl-type arrangement, and in the absence of octahedral tilting, theresultant double-perovskite structure has aord = 2ac and Fm3m symmetry. The order maximizesthe separation of similar ions; each BI cation has 6BII cations as nearest neighbors and vice versa.With this arrangement the intermediate oxygen anions can satisfy the different bond length re-quirements of the two cations by moving toward the smaller ion. This structure is often viewedin terms of an ordered alternation of βI and βII cation layers perpendicular to the [111] directionwith an associated ordering vector = 1/2[111]∗ (Figure 3).

The first oxide perovskite with 1:1 B-site order was described by Steward & Rooksby (27) forthe A(A1/2B1/2)O3 systems (A = alkaline earth ion, B = Mo6+, W6+). The order was analogousto the previously studied (NH4)3FeF6 system. Since its discovery, 1:1 order has been found inhundreds of oxides. After analysis of the structural data for a number of mixed B-site perovskites,Galasso et al. (28) suggested that a large charge and/or size difference between the BI and BII

cations were necessary for ordering. A later study of Ba2+2(B3+Nb5+)O6 systems (29) demonstrated

that for a fixed charge difference of 2, a threshold in ionic radii difference lying between 5%and 17% separated compounds with B-site order from those with a random cation distribution.A subsequent systematization of the data for all known double perovskites (30) provided radiithresholds for charge differences from 1 to 5; examples for a charge difference of 6 also exist inthe Ba(B1/2Os1/2)O3 (B = Li, Na) and corresponding Re7+ systems (31).

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PMN:Pb(Mg1/3Nb2/3)O3

BZT:Ba(Zn1/3Ta2/3)O3

BZN:Ba(Zn1/3Nb2/3)O3

Although size and charge are the primary factors affecting the formation of the B-site or-der, bonding or coordination preferences can also influence the stability. For example, theA2+(B2+

1/2Sb1/2)O3 antimonates always form an ordered structure in which an unstable 180◦

Sr5+-O-Sb5+ linkage can be completely avoided (32). A converse example is the recently reportedBi(Zn1/2Ti1/2)O3 system, which shows no evidence for cation order and adopts an apparently sta-ble disordered arrangement of Zn and Ti (13). Lufaso & Woodward (33) have also discussed theinterplay between Jahn-Teller distortions, octahedral tilting, and cation order. In contrast to allother known 1:1-ordered systems, the ordered form of La2CuSnO6 (34) is notable for its forma-tion of a structure in which the two B cations alternate along 〈100〉 rather than 〈111〉. Additionalexamples of this type of order with A = Pr or Nd and in La2CuZrO6 have been prepared at highpressure (35).

An important characteristic of the 1:1-ordered structure lies in its ability to accommodate sig-nificant deviations from a 1:1 B-cation stoichiometry. The lead-based Pb(B2+

1/3B5+2/3)O3 relaxor

ferroelectrics [e.g., Pb(Mg1/3Nb2/3)O3, or PMN] are a well-known example in which the cationsadopt 1:1 crystallographic order even though the B-sites have a 1:2 chemistry (36). The detailsof the cation distribution in PMN and other related lead-based perovskites were hotly debatedfor more than a decade, until it was established that the cation order could be described by theso-called random-site model (37, 38). In this model for PMN, one of the sites (βII) in the 1:1-ordered Pb(βI

1/2βII

1/2)O3 structure is fully occupied by Nb5+, whereas the other (βI) contains a2:1 random distribution of Mg2+ and Nb5+. The reason that this structure, rather than a stoi-chiometric 1:2-ordered structure (see below), is adopted by the Pb(BI

1/3BII2/3)O3 compounds is

believed to be related to the interaction of the 6s2 lone pair of Pb2+ with the oxygen atoms bondedto the lower-charged B2+ cations (39). The stability of the order and the ferroelectric responseof the 1:1-ordered lead perovskites are remarkably sensitive to the chemistry of the cations onthe mixed βI site; this is discussed in more detail in several references (40, 41). Many examplesof nonstoichiometric, 1:1-ordered, lead-free perovskites are known (see, for example, Reference42), and their stability can also be rationalized in terms of the difference in the average charge andsize of the β sites.

1:2 order: A(βI1/3β

II2/3)O3. Compared with the many examples with 1:1 order, relatively few

families of 1:2-ordered A(BI1/3BII

2/3)O3 [or A3BI1BII

2)O9] complex perovskites have been pre-pared. The first description of 1:2 order was given by Galasso et al. (43) for Ba(Sr1/3Ta2/3)O3,in which a 1:2 layering of Sr and Ta (..SrTaTa..) along the [111] direction (ordering vector1/3[111]∗) yields a hexagonal superstructure with aord = ac

√2 and cord = ac

√3 and P3m1

symmetry (Figure 4). This arrangement was subsequently observed in other niobate and tan-talate members of the A2+(B2+

1/3B5+2/3)O3 family with A2+ = Ca, Sr, Ba; B2+ = Mg, Ca, Sr,

Mn, Fe, Co, Ni, Cu, Zn; and B5+ = Nb, Ta (44–46). Ruthenates such as Sr3(CaRu2)O9 andBa3(CaRu2)O9 have been added to this list (47), and a mixed A-site compound with 1:2 B-siteorder, (Na1/2La1/2)(Mg1/3Nb2/3)O3, is also known (48). In the systems with lower tolerance fac-tors, e.g., Ca(Ca1/3Nb2/3)O3 (Ca4Nb2O9), the presence of octahedral tilting (CaTiO3 type in thisexample) lowers the symmetry to monoclinic (P21/c), where a = √

6ac, b = √2ac, c = 3

√2ac,

β ≈ 125◦ (3; see Supplemental Figure 2).The 1:2-ordered A2+(B2+

1/3B5+2/3)O3 tantalates and niobates, e.g., Ba(Mg1/3Ta2/3)O3,

Ba(Zn1/3Ta2/3)O3 (also known as BZT), and Ba(Zn1/3Nb2/3)O3 (also known as BZN), have beenextensively studied because their very low dielectric losses are ideally suited for application asdielectric resonators in commercial microwave communication devices. Several of these inves-tigations have focused on kinetic aspects of the formation of the layered 1:2 order, which cannucleate and grow along any of the 〈111〉 directions of the parent cubic structure (49). The

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c

Figure 41:2-ordered A(βI

1/3βII

2/3)O3 structure viewed along (110)c to highlight the tripled 〈111〉-layered repeat ofthe βI and βII cation sites.

microstructures are typically composed of nanosized domains of all possible orientational vari-ants of the 1:2 order, and the resultant high volume of disordered and elastically strained domainboundaries can adversely affect the dielectric properties; this has been discussed in Davies et al.(49). Although the niobate and tantalate members of this family exhibit identical ordered struc-tures, the stability of the order responds to the different covalency of Nb and Ta. For a givenstoichiometry the transition to a disordered B-site arrangement in the more ionic tantalates al-ways occurs at a higher temperature compared with their niobate counterparts. The differencein stability has important ramifications for the processing of niobate microwave ceramics such asBa(Zn1/3Nb2/3)O3 for which the transition (∼1375◦C) to the lower-dielectric-loss ordered phaseoccurs during cooling from the sintering temperature (∼1500◦C). Therefore, optimization of thedielectric properties requires the incorporation of a lower temperature anneal or slow coolingtreatment to coarsen the ordered domains (see, for example, References 50 and 51).

Until recently, Ba(Bi3+2/3Te6+

1/3)O3 was the only known example with 1:2 B-site order outsideof the 2+/5+ A2+(B2+

1/3B5+2/3)O3 family (52). All other perovskites with 1:2 chemical stoichiome-

tries, such as Ba(W1/3Sc3+2/3)O3 (53), Ba(M2+

1/3Bi5+2/3)O3 (54), La(Ta1/3Mg2/3)O3 (55), and the

aforementioned PMN-type systems, adopt a 1:1-ordered random-site structure, with one site oc-cupied by the majority cation and the other by a mixture of the remaining cations. Because of theirimportance in microwave communications, our group has focused on preparing new families of1:2-ordered perovskites by exploring a variety of Li-, Ti-, Nb-, Ta-, and W-containing chemistries.These studies, which led to the preparation of several new 1:2-ordered Li-containing compoundssuch as La(Li1/3Ti2/3)O3 (56) and A2.33+(Li1/3Nb/Ta2/3)O3 (57, 58), are described below.

The limited occurrence of 1:2 order is related to the resultant coordination environment ofthe oxygen anions, although as noted above lone-pair interactions can also play a role in Pb-basedsystems. In the ordered A(BI

1/3BII2/3)O3 structure, the different size and charge of the BI/BII

cations are accommodated via a concerted long-range displacement of the intermediate layer of

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O(1)

O(1)

O(2)

Figure 5Schematic view of the off-centered displacement of the cations on the βII sites, which accommodate theunderbonded O(1) and overbonded O(2) anions in the A(βI

1/3βII

2/3)O3 structure.

BVS: bond valencesum

anions toward the 〈111〉 layer containing the smaller, more highly charged B-site ions (typically BII)(49, 59–61). However, this movement leads to an overbonding of the O(2) anions lying betweentwo BII layers and an underbonding of the O(1) anions between the BI and BII layers (Figure 5).For example, in Ba(Zn1/3Ta2/3)O3 or Ba(Zn1/3Nb2/3)O3 the O(2) anion is coordinated by 2B5+

and 4A2+, and for ideal octahedra the resultant bond valence sum (BVS) = 2.33; for the O(1)anion (1B2+, 1B5+, and 4A2+ neighbors) the ideal BVS = 1.833. The order is stabilized only whenthe over- and underbonding can be alleviated through a displacement of the BII cations towardthe face of their octahedra to lengthen the three BII-O(2)-BII bonds and shorten the three BII-O-BI bonds (62). A stable off-centered coordination usually requires a d 0 ion, e.g., Nb5+, Ta5+,Ti4+, which can undergo a second-order Jahn-Teller distortion or a lone-pair cation such as Bi3+

(52). Consequently, 1:2 order is observed in the A2+(B2+1/3B5+

2/3)O3 niobates and tantalates andBa(Te6+

1/3Bi2/3)O3, but not in compounds such as Ba(W1/3Sc3+2/3)O3 or La(Ta1/3Mg2+

2/3)O3, inwhich a distorted octahedral environment for the majority B-site ion (Sc3+, Mg2+ in the examplescited) is not stable. A similar argument can be used to rationalize the absence of 1:2 order in severalother perovskites in which the cations have partially filled d orbitals [e.g., A2+(M6+

1/3M3+2/3)O3

(A = Sr, Ba; M6+ = Mo, W, Te, U; M3+ = Co, Cr, Fe)]; here the change in order can influencethe resultant magnetic exchange interactions (63–67). Antimonates such as Sr(Ni1/3Sb2/3)O3 (32,68) adopt alternate arrangements because of the instability of Sr5+-O-Sb5+ linkages; electroniceffects also destabilize 1:2 ordering in Ba(Cu1/3Nb2/3)O3, which forms a ferroelectric perovskitewith a tetragonally distorted (PbTiO3-type) structure (69).

In contrast to 1:1-ordered perovskites, the reported 1:2-ordered systems are remarkably resis-tant to deviations from their ideal stoichiometry. Isovalent substitutions can be made within theA2+(B2+

1/3B5+2/3)O3 family; the partial replacement of Zn2+ by Ni2+ is particularly important be-

cause it allows the temperature coefficient of the resonant frequency of BZT to be tuned to a zerovalue. However, low concentrations of substituent ions of a different charge [e.g., 3% BaZrO3 inBa(Zn1/3Ta2/3)O3, 0.5% Ba(Zn1/2W1/2O3 in Ba(Zn1/3Nb2/3)O3] destabilize the 1:2 order in favorof 1:1-ordered random-site or completely disordered B-site arrangements (49, 50, 70, 71). Thesensitivity of the order to these additives has been related to the frustration of the long-range

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displacement of the oxygen anion layers (49). Recent studies of Ba(Zn1/3Nb2/3)O3 also revealedthat the 1:2 structure can accommodate only very small (∼0.1 mole%) degrees of nonstoichiom-etry through the formation of A- or B-site vacancies (72, 73). Although the concentrations ofvacancies are exceptionally small, they can accelerate the kinetics of the ordered domain growthand enable the processing of ceramics with enhanced microwave properties (72–75).

1:3 order: A(βI1/4β

II3/4)O3. Following the discovery of 1:1 and 1:2 B-site order, several attempts

were made to stabilize cation order in complex perovskites with other stoichiometric cation ratios,e.g., 1:3 (76, 77). However, A(BI

1/4BII3/4)O3 [or A4(BI

1BII3)O12] systems such as Ba(Na1/4Ta3/4)O3

and Sr(Na1/4Ta3/4)O3 (76, 78) were reported to be disordered, and for a long time perovskites withhexagonal stacking sequences [e.g., Ba(Li1/4Nb3/4)O3 (16, 17, 79), Ba(Re1/4Cr3/4)O3 (80)] werebelieved to be the only examples for which the ordering involved a more complex stoichiometry.The first example of 1:3 order in a cubic perovskite was observed in Ba(BI

0.25BII0.75)O3 (BI = Li+,

Na+, BII = Sb5+, Bi5+) (81, 82), which forms a cubic body-centered superstructure (SupplementalFigure 3) with a maximum separation of the BI cations (

√3ac). Sr(Li0.25Sb0.75)O3 (83) has a

distorted monoclinic version of the same structure. Unlike the 〈111〉-ordered schemes discussedabove, this structure is not layered and contains a three-dimensional distribution of the two cations.

Quite recently, 1:3 〈111〉-layered order was identified in a metastable polymorph of Ca4Nb2O9

(3, 7). In this case the 1:3 (..βIβIIβIIβII..) layering (ordering vector 1/4[111]∗) yields a monoclinicbase-centered supercell with aord = a

√6, bord = a

√2, cord = a2

√2, β = 125.3◦ (Figure 6).

A similar pseudomonoclinic cell with 1:3 order of Ca and Nb had been reported for a reducedniobate, Ca5Nb3O12 (84). Because Ca4Nb2O9 has a very low tolerance factor (0.91), the octahedral

a

c

Figure 61:3, 〈111〉-type A(βI

1/4βII

3/4)O3-ordered structure viewed along (110)c to highlight the quadrupled layeredrepeat of the βI and βII cation sites.

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network shows extensive tilting (CaTiO3 type, b−b−c+), and the actual symmetry is triclinic(P1). Even though the 1:3-ordered form (LT1/4 phase) of Ca4Nb2O9 is a metastable andextended heat treatment results in conversion to a stable 1:2-ordered Ca(Ca1/3Nb2/3)O3 phase(3), the observation of 1:3 order in this system is surprising because the composition is not com-patible with a stoichiometric A(βI

1/4βII

3/4)O3-ordered structure. A subsequent study showed the1:3 phase could be stabilized for compositions with a small excess of Nb2O5 (79% CaO, 21%Nb2O5), although mixed-site occupancies still occur (7). Until recently, this was the only exam-ple of 1:3 〈111〉 B-site layering; several new examples prepared in our laboratory are describedbelow.

NEW 1:2 AND 1:3 B-SITE-ORDERED PEROVSKITES

Over the past few years our research has focused on identifying new types of ordered perovskites,particularly 1:2 and 1:3 chemistries designed for application as potential low-loss microwave dielec-tric materials. Table 1 summarizes all possible 1:1-, 1:2-, and 1:3-ordered B-site stoichiometriesfor a complex oxide perovskite with A-site valences = +1, +2, and +3. Systems in which the va-lence difference of the two B-site cations is <2 are excluded because they typically do not exhibitany cation order. The highlighted compositions represent new potential ordered stoichiometriesthat had not been investigated or prepared in an ordered form.

If the constraint of a single-ion, integer valence A-site is lifted, broader ranges of new orderedcompositions become apparent. In Table 2 the A-site valence required to balance charge for 1:1,1:2, and 1:3 B-site order is calculated for all possible B-cation combinations. Again, entries areincluded only for A-site valences between 1 and 3 and for B-site valence differences ≥2. Thehighlighted entries represent systems in which the B-site chemistry produces a fractional chargeon the A-site. The removal of the requirement for an integer A-site charge, which is realizedthrough the use of a combination of two (or more) aliovalent A-site cations, produces many newpotential classes of ordered B-site perovskites. For example, a 1:3 distribution of B2+ and B5+

yields a fractional charge (1.75+) on the A-site that could be charge balanced through the useof a 1:3 mixture of monovalent and divalent cations. (Ba3/4Na1/4)(Ca1/4Nb3/4)O3 is one exam-ple of a compound with this stoichiometry. Each composition lies in a known or a hypotheticalpseudobinary perovskite solid solution system—the example above occurs in the (1−x)NaNbO3-(x)Ba(Ca1/3Nb2/3)O3 pseudobinary at x = 3/4. A review of the literature revealed that thesecompositions had not been targeted as new ordered perovskites. The following subsections sum-marize investigations of these new 1:2- and 1:3-ordered chemistries; additional detail is providedfor systems that appear here for the first time.

Table 1 Potential ordered B-site stoichiometries in single-A-site complex oxide perovskites

A-sitevalence 1:1 order 1:2 order 2:1a order 1:3 orderA1+ (B4+

1/2B6+1/2)

Not reported(B3+

1/3B6+2/3)

Not reportedNot possible (B2+

1/4B6+3/4)

Not reportedA2+ (B2+

1/2B6+1/2), e.g., Mg1/2W1/2;

(B3+1/2B5+

1/2), e.g., Y1/2Nb1/2

(B2+1/3B5+

2/3),e.g., Zn1/3Ta2/3

(B3+2/3B6+

1/3),e.g., Sc2/3W1/3

(B1+1/4B5+

3/4)Not ordered

A3+ (B2+1/2B4+

1/2), e.g., Mg1/2Ti1/2 (B1+1/3B4+

2/3)Not reported

(B5+2/3B2+

1/3),e.g., Mg2/3Nb1/3

(B6+1/4B2+

3/4)Not reported

aTypically 1:1 ordered (see text).

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Table 2 A-site charge for all possible ordered B-site stoichiometries

B-site cations 1:1 order 1:2 order 1:3 orderB1+B4+ – A3+ A2.75+

e.g., (A3+3/4A2+

1/4)Not reported

B1+B5+ A3+ A2.33+

e.g., (A2+2/3A3+

1/3)Not reported

A2+

B1+B6+ A2.5+

e.g., (A3+1/2A2+

1/2)Known

A1.67+

e.g., (A2+2/3A1+

1/3)Not reported

A1.25+

e.g., (A2+1/4A1+

3/4)Not reported

B2+B4+ A3+ A2.67+

e.g., (A3+2/3A2+

1/3)Not reported

A2.5+

e.g., (A3+1/2A2+

1/2)Not reported

B2+B5+ A2.5+

e.g., (A3+1/2A2+

1/2)Known

A2+ A1.75+

e.g., (A2+3/4A1+

1/4)Not reported

B2+B6+ A2+ A1.33+

e.g., (A2+1/3A1+

2/3)Not reported

A1+

B3+B5+ A2+ A1.67+

e.g., (A2+2/3A1+

1/3)Not reported

A1.5+

e.g., (A2+1/2A1+

1/2)Not reported

B3+B6+ A1.5+

e.g., (A2+1/2A1+

1/2)Not reported

A1+ –

B4+B6+ A1+ – –

1:2 B-Site Order

Single-A-cation systems. The A2+(B2+1/3B5+

2/3)O3 systems are the only known family of 1:2-ordered perovskites; however, new families are feasible for a mono- and trivalent A-site charge(Table 1). Systems based on A3+ have the general formula A3+(B1+

1/3B4+2/3)O3; because Ti4+

readily adopts a stable, off-centered octahedral coordination, the potential formation of orderedcompositions such as La(Li1/3Ti2/3)O3 was explored (56). Below 1185◦C this compound forms atilted (b−b−c+), 1:2-ordered structure, and the X-ray patterns can be indexed via the use of thesame P21/c cell reported for other low-tolerance-factor 1:2 systems such as Ca(Ca1/3Nb2/3)O3 (3,7). This new phase was the first example of a titanate perovskite with a 1:2 ordering of cationson the B-site. Above 1175◦C the ordered form of La(Li1/3Ti2/3)O3 converts to a structure with arandom distribution of the B-site cations; the order-disorder temperature is somewhat lower thanthose reported for A2+(B2+

1/3B5+2/3)O3 systems, with a comparable difference in their B-site radii.

Attempts to prepare other members of this family such as La(Li1/3Zr2/3)O3 were not successful,presumably because of the limited stability of Zr4+ in an off-centered coordination.

1:2 perovskites, ordered or disordered, based on a monovalent A-site ion, i.e.,A1+(B3+

1/3B6+2/3)O3 [e.g., Na(Al3+

1/3W6+2/3)O3], were unstable, even though their tolerance fac-

tors lie in a range in which perovskite formation is reasonable. The instability of this tungstatesystem is related to local imbalances in the formal ionic charge of the structure; this is addressedbelow in a general discussion of W-rich perovskites.

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Noninteger charge A-site systems. From Table 2, five new formulations of 1:2 B-site order arepossible for perovskites with a fractional A-site charge. For (B1+

1/3B5+2/3) the charge (2.33+) can

be balanced by (A2+2/3A3+

1/3), giving target compositions such as (Ba2/3La1/3)(Li1/3Nb2/3)O3.Investigation of several compositions within this family yielded single-phase 1:2 order for(Sr2/3La1/3)(Li1/3Nb2/3)O3, (Sr2/3La1/3)(Li1/3Ta2/3)O3, and (Ca2/3La1/3)(Li1/3Nb2/3)O3 (51, 58,85). In each case the X-ray patterns could be indexed in the ordered and tilted monoclinic cell (spacegroup P21/c) described above for La(Li1/3Ti2/3)O3. The validity of the structural model was con-firmed by Rietveld refinement of data collected via neutron diffraction (Supplemental Figure 4),which showed essentially complete 1:2 order (≤0.1% antisite disorder) of the Li+ and Nb/Ta5+

cations on their respective sites (51). Although the A-site also contains a mixture of cations, no evi-dence was found for any additional order. The B-site order in the (A2+

2/3La3+1/3)(Li1+

1/3B5+2/3)O3

compounds is stable up to their melting/decomposition temperatures; this enhanced stability com-pared with the stability of the A2+(B2+

1/3B5+2/3)O3 family reflects the higher charge difference

(�qβ = 4) of the ions involved in the ordering. For (Ca2/3La1/3)(Li1/3Ta2/3)O3 it proved difficultto prepare impurity-free samples; however, single-phase 1:2 order could be stabilized by the partialsubstitution of W for Nb (see below). Other compositions in the (A2+

2/3RE3+1/3)(B1+

1/3B5+2/3)O3

family were also explored. The X-ray patterns of (Ba2/3La1/3)(Li1/3Nb2/3)O3 consistently containedpeaks from impurity phases, although an untilted 1:2-ordered phase was the major component ofthe resultant mixture. Formulations containing Nd3+ all yielded multiphase products (85).

The stable (A2+2/3La1/3)(Li1/3B5+

2/3)O3 phases accommodate some degree of substitution ofB5+ by W6+ when the replacement is accompanied by a compensatory substitution of La3+ bySr2+, i.e., (A2+

2(1+x)/3La(1−2x)/3)(Li1/3(Nb1−xWx)2/3)O3. These Nb/W solid solutions retain their1:2 order for x ≤ 0.2 when A2+ = Sr, Ca, B5+ = Nb and for x ≤ 0.125 when A2+ = Sr, Ca,B5+ = Ta; neutron structure refinements confirmed they are isostructural with the W-free endmember (51). Because the incorporation of W6+ increases the charge (and size) difference of theordered β-sites and the charge/size mismatch of Nb and W on the βII site is small, the 1:2-ordered solid solutions were expected to be stable up to the highest possible value of x ( = 0.5), i.e.,A2+(Li1/3(Nb1/2W1/2)2/3)O3, where �qβ = 4.5. However, for x > 0.25 (Nb) or x > 0.125 (Ta),the 1:2 order was destabilized in favor of a nonstoichiometric 1:1-ordered structure.

The instability of 1:2 B-site order for compositions rich in W6+ also prevented the preparationof several of the other stoichiometries identified in Table 2. For example, the 1+/6+ family, e.g.,A5/3+(Li1/3W2/3)O3, was explored through the use of several combinations of cations to balance theA-site charge (Sr2/3Na1/3, Ba2/3K1/3, Sr5/6vac1/6, etc.). In all cases the syntheses yielded multiphaseproducts that included nonperovskite phases. Correspondingly, perovskites with a 1:2 mixture of2+ and 6+ cations, A4/3+(B2+

1/3B6+2/3)O3, are also unstable (51).

1:2 mixtures of 2+ and 4+ cations (Table 2) yield a general stoichiometry ofA2.67+(B2+

1/3B4+2/3)O3. (La2/3Ca1/3)(Ca2+

1/3Ti4+2/3)O3, which forms a stable perovskite in the

(1−x)CaTiO3-(x)La2O3 system at x = 0.33 (86, 87), is one possible member of such a family. Areinvestigation of this system revealed no evidence for 1:2 ordering at this composition, which in-stead adopted a nonstoichiometric 1:3-ordered structure that is described below. Studies of otherpotential 2+/4+ stoichiometries, e.g., La2/3Sr1/3(Mg2+

1/3Ti4+2/3)O3, also failed to produce any

new 1:2-ordered perovskites. It was concluded that the charge difference of the cations (�qβ = 2)in this family is too low to stabilize 1:2 order. Although it was not investigated, the charge differ-ence in the remaining stoichiometry in Table 2, A1.67+(B3+

1/3B5+2/3)O3, likely is also too low for

ordered compound formation.

Nonstoichiometry. As noted above, the 1:2 order in the 2+/5+ Ba(Zn1/3Ta2/3)O3 family isrigidly stoichiometric, and trace levels of foreign ions induce a transition to a disordered or

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BLNW:(1−x)Ba(Li1/4Nb3/4)O3-(x)Ba(Li2/5W3/5)O3

a nonstoichiometric double-perovskite arrangement. Because some degree of mixed-site occu-pancy was observed in the W-substituted A2.67+(Li1/3Nb2/3)O3 systems, we explored the potentialformation of nonstoichiometric 1:2 order in other niobate tungstates. An unusual family of solidsolutions was discovered in (1−x)A2+(Li1/4Nb3/4)O3-(x)A2+(Li2/5W3/5)O3 systems with A2+ =Ca, Sr, and Ba (88, 89). In the Ba system [BLNW, or (1−x)Ba(Li1/4Nb3/4)O3-(x)Ba(Li2/5W3/5)O3]neither end member forms a cubic perovskite, and instead both end members crystallize withhexagonal perovskite structures; furthermore, in their solid solution there is no value of x forwhich a 1:2 ratio of cations can be realized. However, 1:2-ordered cubic perovskites were dis-covered for 0.238 ≤ x ≤ 0.385. Refinement of the ordered Ba(βI

1/3βII

2/3)O3 phases revealed thatLi+ and W6+ occupy different cation sites whereas Nb5+ is distributed on both positions with astoichiometry of Ba[(Li3/4+y/2Nb1/4−y/2)1/3(Nb1−yWy)2/3]O3, where y = 0.9x = 0.21–0.35 (88).Similar phases were observed in the corresponding Sr and Ca (SLNW, CLNW) solid solutions,in which the lower tolerance factor and associated tilting reduce the symmetry to P21/c (89). TheCa-based tantalate counterparts of these phases, (1−x)Ca(Li1/4Ta3/4)O3-(x)Ca(Li2/5W3/5)O3, alsoform for 0.111 ≤ x ≤ 0.278 but are not stable in the Sr or Ba systems (51).

The stabilization of nonstoichiometric 1:2 order in the BLNW phases is most likely relatedto the large difference in the charge of the βI and βII positions, which exceeds 3 for y > 0. 1:2order first appears for y = 0.21 when �qβ = 3.61+ and is maintained up to y = 0.35 where�qβ = 4.05+. These site charge differences are significantly higher than for the BZT familyor La(Li1/3Ti2/3)O3 and lie in the same range as the ordered A(Li)1/3(Nb/Ta)2/3O3 systems. Theabsence of 1:2 order for y ≤ 0.21 is presumably associated with the high charge/size mismatchof the Li/Nb ions on the βI-site, which increases as y decreases. However, the destabilizationof the order for 0.35 < y ≤ 0.5, which has the highest charge/size site difference and the loweston-site mismatch, cannot be rationalized by these crystal chemical arguments and provide anotherexample of the instability of ordered W-rich perovskites.

Instability of W-rich systems: local charge imbalances. To rationalize the behavior of theaforementioned 1:2-ordered W-rich phases, it is useful to make reference to other W-containingperovskites in the literature. In all reported tungstate cubic perovskites, e.g., A2+(B2+

1/2W1/2)O3

(A2+ = Ba, Sr, Pb, B2+ = Ca, Mg, Ni, Zn) and A2+(B3+2/3W1/3)O3 (A2+ = Ba, Sr, Pb, B3+ = Sc,

Fe, Bi), the B-site ions adopt 1:1-ordered or -disordered arrangements. Only a few exam-ples with both Li and W on the octahedral positions are known; these include 1:1-ordered(Sr/Ba)1/2La1/2(Li1/2W1/2)O3 and Sr(Li2/5W3/5)O3 (90, 91). No cubic perovskites are known withmore than 60% W on the B-site, and our investigations of 1:2 tungstate stoichiometries [e.g.,A1.67+(Li1/3W2/3)O3] consistently yielded multiphase products. It is possible that the instabilityof these tungstates, and the loss of 1:2 order in the W-rich BLNW solid solutions, is associ-ated with large imbalances in the local anion bond valences. For example, for a 1:2-orderedform of A1.67+(Li1/3W2/3)O3 with ideal polyhedra, the bond valence sums are 2.56 and 1.72 atthe O(2) and O(1) anions, respectively. Because of the higher charge on W, the imbalance islarger than in the BZT-type systems, and larger octahedral displacements would be requiredto produce an ideal BVS. A larger off centering of W6+ may simply be unstable; however, thisconflicts with the large displacements observed in the ordered hexagonal perovskite Ba3W2O9

(92).A more likely explanation for the loss of 1:2 order in W-rich cubic perovskites lies in the in-

compatibility of the distribution of the B-site cations with the local charges on the A-site lattice.In the 1:2 structure the {..βIβIIβII..} layering creates two different A-site environments; these arehighlighted in Figure 7. The A(1) site, located between two βII layers, has 2βI and 6βII nearestneighbors; the two A(2) sites, located between the βI and βII layers, have 3βI and 5βII nearest

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βI

βII

O2–

= A(1):2βI/6βII

= A(2):3βI/5βII

Figure 7Schematic view of the perovskite subcells in the 1:2-ordered A(βI

1/3βII

2/3)O3 structure, highlighting thedifferent coordination environment of the A(1) and A(2) sites.

neighbors. When βI = Li+ and βII = W6+ [A1.67+(Li1/3W2/3)O3], in the A(1) and A(2) subcellsthe formal charge on the octahedral framework = –1.25 and –1.875, respectively. If the A-sitesare occupied by a combination of cations with an average charge of +1.67, the excess formalcharge per subcell (�q) is +0.417 at A(1) position and –0.208 at the A(2) position. This imbalanceis much larger than the values in the stable A2+(B2+

1/3B5+2/3)O3 perovskites, for which �q =

+0.25 and –0.125. Analysis of the local charge imbalance in Ba/Sr[Li1/3(Nb1/2W1/2)2/3]O3 revealsa similar instability. Here a 1:1 mixture of Nb:W with a mean charge of 5.5+ yields average formalframework charges of –1.625 and –2.1875 in the A(1) and A(2) subcells, and resultant �qs =0.375 and –0.1875, respectively. The random occupancy of βII by Nb and W would yield higherlocal imbalances ranging from �q = +0.75 to 0.0 at A(1) and +0.125 to –0.5 at A(2) for en-vironments with Nb:W = 0:6 and 6:0, respectively. These local instabilities have been invokedto explain the destabilization of 1:2 ordering in A-site-substituted (Na1/2La1/2)(Mg1/3Ta2/3)O3

(93), and we believe they are also responsible for the loss of 1:2 order in the W-rich solidsolutions.

Stability fields. Figure 8 maps the known 1:2-ordered perovskites as a function of the charge(�qβ) and size (�rβ) differences of the ordered B-sites. For the BZT-type Ba(B2+

1/3B5+2/3)O3 ox-

ides, �qβ = 3, and �rβ can vary from 0.05 A (Ni) to much higher values in Ba(Sr1/3Ta2/3)O3 (0.54A). The new stoichiometric La(Li1/3Ti2/3)O3 and (Sr2/3La1/3)[Li1/3(Ta, Nb)2/3]O3 phases have�qβ = 3 and 4 and �rβ = 0.155 A and 0.12 A, respectively. The only other known stoichiometric1:2-ordered phase, Ba(Bi2/3Te1/3)O3 (52), also has �qβ = 3 and a large size difference (�rβ = 0.47A). No known 1:2-ordered systems have �qβ < 3.0. Additives that destabilize the 1:2 order in BZT

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BZT type

1:2 order

2.00.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

5.04.84.64.44.24.03.83.6

Charge difference (Δq)

Siz

e d

iffe

ren

ce (Δr,

Å)

3.43.23.02.82.62.42.2

BLNW

A2.33+(Li1/3

Nb2/3

)O3

Li1/3

(Nb1–x

Wx)

2/3

A1.67+(Li1/3

W2/3

)O3

Ba(Zn1/2

W1/2

)O3

La(Mg2/3

Nb1/3

)O3

BaZrO3

La(Li1/3

Ti2/3

)O3

Figure 8Map of the stability of 1:2-ordered A(βI

1/3βII

2/3)O3 perovskites as a function of the size (�r) and charge(�q) difference of the cations on the βI and βII positions. Stable 1:2-ordered compounds are formed in theshaded region of the diagram; unshaded areas with lower or higher �q represent fields of stability foralternate B-site arrangements (1:1 ordered or disordered) or the formation of nonperovskite phases [e.g.,A1.67+(Li1/3W2/3)O3]. Triangles represent compositions in the (1−x)Ba(Li1/4Nb3/4)O3-(x)Ba(Li2/5W3/5)O3 (BLNW) system; circles represent compositions of (Sr2+x/3La1−x/3)[Li1/3(Nb1−xWx)]O3 solid solutions.Black lines represent changes in charge and size for solid solutions of Ba(Zn1/3Ta2/3)O3 (BZT) with theindicated end members.

reduce �qβ to a value below 3 [e.g., (x)BaZrO3-(1−x)BZT, “Ba(Zn1−xZrx)1/3(Ta1−xZrx)2/3O3”;(x)La(Zn2/3Ta1/3)O3-(1−x)BZT, “Ba1−xLax(Zn)1/3(Ta1−x/2Znx/2)2/3O3”] or increase the on-sitesize/charge mismatch without increasing �qβ or �rβ [e.g., (1−x)BZT-(x)BaZn1/2W1/2O3,“Ba(Zn)1/3(Ta1−xW3x/4Znx/4)2/3O3”].

The stable nonstoichiometric 1:2 phases discovered in the (1−x)A2+(Li1/4Nb3/4)O3-(x)A2+(Li2/5W3/5)O3 systems have �qβ > +3.6; this suggests that mixed occupancy on theordered β-sites can be accommodated only when the substituent increases the site chargedifference to a value greater than 3. However, for W-rich compositions with �qβ = 4.5(A[Li1/3(Nb1/2W1/2)2/3]O3) or even higher [A(Li1/3W2/3)O3], the stability of the perovskite ismediated by the local charge imbalances at the A-sites discussed above. The stability field mapimplies that nonstoichiometric 1:2-ordered perovskites should be stable in other systems whenvalues of �qβ ≥ 3.0 can be realized without large on-site mismatches. Consistent with thesepredictions, the partial substitution of W into (Sr2/3La1/3)(Li1/3Nb2/3)O3 and the formation of(Sr2+x/3La1−x/3)[Li1/3(Nb1−xWx)2/3]O3 solid solutions give �qβ > 4.0 and produces stable 1:2order (51). We also found that 1:2 cation order can be retained in the BZT family when the sub-stituent increases �qβ; for example, Ba(Zn1/3Nb2/3)O3 forms a complete range of ordered solidsolutions with BLNW. This additive also reduces the sintering temperature of BZT and may beuseful in developing new microwave ceramics (see below).

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1:3 B-Site Order

Prior to our studies, examples of 1:3 〈111〉-ordered perovskites [A(BI1/4BII

3/4)O3] were lim-ited to the metastable polymorph (LT1/4 phase) of Ca4Nb2O9 (3, 7). Following reports thathigher-tolerance-factor perovskites with 1:3 stoichiometries, e.g., Ba(Na1/4Ta3/4)O3 (t = 0.996),Sr(Li1/4Nb3/4)O3 (t = 0.973), adopt disordered cation arrangements (76, 78), extensive octahe-dral tilting was suggested to be a necessary requirement for stabilizing 1:3 cation order (3). FromTables 1 and 2, it is apparent that several other chemistries may be compatible with the formationof 1:3 order; the results for these systems are reported here for the first time.

Single-A-Cation Systems

A2+(B1+1/4B5+

3/4)O3

Sr(Li1/4Nb3/4)O3 and Sr(Li1/4Ta3/4)O3. A2+(B1+1/4B5+

3/4)O3 perovskites such asSr(Li1/4Nb3/4)O3 and Sr(Li1/4Ta3/4)O3 were reported (78) to have a random B-site distri-bution; in a reinvestigation of their stability we found clear evidence for the formation of orderedstructures. For Sr(Li1/4Nb3/4)O3 the majority of the peaks in the X-ray patterns could be indexedin a disordered cubic perovskite cell (a = 4.003 A); however, a series of additional weak peaks wasapparent at lower angles; the first peak corresponded to d = 4d111 (Figure 9). The entire patterncould not be indexed through the use of any of the 1:3-ordered structures described above, andrequired a primitive cubic cell with a = 4ac ( = 16.014 A) to index all the peak positions. Aseries of quenching experiments revealed two structural transitions (Figure 10). At T ≥ 1400◦Ca disordered cubic perovskite is stable; a low-temperature (LT) form, tentatively indexable inthe a = 16.014 A cubic cell, forms for T ≤ 1300◦C. Between 1300 and 1400◦C a polymorph

10 20 30 40

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Figure 9X-ray patterns collected from the low-temperature (LT) form of Sr(Li1/4Nb3/4)O3. The inset shows possibleindexing for the weaker ordering peaks on the basis of a cubic cell with a = 4ac.

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5

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1325°C

1350°C

1375°C

1400°C

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Figure 10X-ray patterns collected after quenching Sr(Li1/4Nb3/4)O3 from the temperatures indicated.

of intermediate symmetry was identified. The diffraction pattern of this new form (HT) alsocontained a peak at d = 4d111 but was less complex than the LT phase and could be indexed ina C2/m monoclinic structure (a = 9.815 A, b = 5.665 A, c = 11.333 A, β = 125.30◦) with〈111〉 1:3 B-site order. Both transitions (LT→HT, HT→disordered) were reversible; however,the kinetics of the HT→LT transition are very slow, suggesting that the transformation involvessignificant diffusion and redistribution of the B-site ions into the different ordered structure.

Electron diffraction provided additional information on the structure of the two polymorphsof Sr(Li1/4Nb3/4)O3. The patterns for the HT polymorph (Figure 11) are similar to those re-ported for 1:3-ordered Ca4Nb2O9 (3); the highest-order reflections in the [110] diffraction patterncorrespond to a quadrupling of the [111] direction, implying that the structure is based on a 1:3〈111〉 layering of Li and Nb. At the same time, the symmetric character of the pattern along the[111] zone axis suggests that, although octahedral tilting is present, it corresponds to a highersymmetry type, such as a+a+a+ or a−a−a−, as opposed to the b−b−c+ scheme in Ca4Nb2O9. The[110] diffraction patterns of the LT polymorph were more complex and, consistent with the X-raydata, suggest the possibility of simple cubic symmetry (Figure 11). Unlike the HT polymorph, the[111] pattern contains evidence for a fourfold superstructure, implying that the layers stacked inthe [111] direction have a mixed B-site composition and are ordered or that a layered description isnot applicable to this structure. It is likely that the LT polymorph has a previously unreported typeof 1:3 order, whereas the HT polymorph has a combination of layered 1:3 order with a differenttype of octahedral tilt system. In both cases additional studies will be necessary to resolve theseissues.

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Figure 11Electron diffraction patterns collected from high-temperature (HT) (left) and low-temperature (LT) (right)forms of Sr(Li1/4Nb3/4)O3 along [100]c (top), [110]c (middle), and [111]c (bottom).

In agreement with previous reports, as-synthesized samples of Sr(Li1/4Ta3/4)O3 did not showevidence of cation order. However, after slower cooling (1◦C min−1) from 1350◦C, 1:3 〈111〉-typeorder was observed. The positions and intensities of the peaks in the X-ray patterns can be inter-preted with the same structure (C2/m, a = 9.772 A, b = 5.6615 A, c = 11.333 A, β = 125.01◦)used for HT-Sr(Li1/4Nb3/4)O3, although confirmation must await future refinement. No evidencewas found for a different lower-temperature form of the tantalate. Quenching experiments, con-ducted using muffling powders to avoid loss of Li, indicated that the order in Sr(Li1/4Ta3/4)O3

is stable up to at least 1500◦C; at higher temperatures the samples suffered from excessive lossof Li.

Ca(Li1/4Nb3/4)O3 and Ca(Li1/4Ta3/4)O3. Ca(Li1/4Nb3/4)O3 and Ca(Li1/4Ta3/4)O3 have neverbeen reported in the literature. The only reference to a compound of Ca, Li, and Nb with aperovskite structure is an oxygen-deficient composition, Ca(Li1/3Nb2/3)O3−x (94), which was not

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prepared in a single-phase form. We also found, using mixtures of CaCO3, Li2CO3, and Ta2O5, thatconventional solid-state syntheses yield multiphase products; however, a single-phase perovskitecould be obtained through the use of CaC2O4·H2O, LiTaO3, and Nb2O5 as precursors. The X-raydiffraction pattern of Ca(Li1/4Ta3/4)O3 was analogous to the 1:3-ordered polymorph of Ca4Nb2O9

(3) and could be indexed in the same 1:3-ordered, tilted, P1 triclinic cell (a = 9.599 A, b = 5.472 A,c = 11.259 A, α = 89.95◦, β = 125.34◦, γ = 90.55◦). Initial studies suggested that the niobateCa(Li1/4Nb3/4)O3 may exhibit 1:2 order (85); however, subsequent investigation demonstratedthat it also adopts a layered 1:3 ordering of Li and Nb with lattice parameters essentially identicalto the tantalate (51).

Sr(Na1/4Nb3/4)O3. 1:3 〈111〉 B-site order can also be stabilized in Sr(Na1/4Nb3/4)O3, but onlyafter extended annealing at ∼1000◦C. Although the ordering reflections are weak and diffuse, theirpositions are consistent with the structure reported for the 1:3-ordered form of Ca4Nb2O9. Thesynthesis of Sr(Na1/4Nb3/4)O3 is complicated by excessive volatilization of Na at fairly moderatetemperatures; this leads to bulk decomposition at T > ∼1100◦C, even for samples protected withmuffling powders. Although the loss of Na is a potential issue in any Na-based system, perovskitesin which Na occupies the A-site (e.g., NaNbO3) show significant resistance to volatilization. Webelieve that the higher volatility of Na in Sr(Na1/4Nb3/4)O3 compared with other sodium-basedperovskites reflects the relative instability of Na on the B-site lattice.

Noninteger charge A-site systems

A1.75+(B2+1/4B5+

3/4)O3: A2+3Na1+CaNb3O12. The removal of a requirement for an integer

charge on the A-site leads to many new potential classes of 1:3-ordered perovskites (Table 2). A1:3 distribution of B2+ and B5+ yields a fractional charge (1.67+) that can be balanced by a mixture ofmonovalent and divalent cations on the A-site, i.e., (A1+

1/3A2+2/3)(B2+

1/4B5+3/4)O3. Examples in-

clude (Na1/3Ba2/3)(Ca1/4Nb3/4)O3, (Na1/3Sr2/3)(Ca1/4Nb3/4)O3, and (Na1/3Ca2/3)(Ca1/4Nb3/4)O3.These compositions were investigated by reacting pellets muffled in their own powders andwrapped in Pt envelopes to suppress the volatilization of Na. For all three systems a single-phase perovskite was formed after a single firing at 1100◦C. The X-ray patterns contained strongreflections originating from 1:3 〈111〉 cation order; in particular, a strong peak corresponding tod = 4d111 was evident at 2θ ∼ 9.4◦. The X-ray pattern of Ca4NaNb3O12 (Figure 12) is very sim-ilar to the published pattern of the 1:3-ordered form of Ca4Nb2O9 and was successfully indexedin the same P1 cell with a = 9.650 A, b = 5.641 A, c = 11.145 A, α = 90.02◦, β = 123.73◦,γ = 89.99◦. The similarity of the structure to Ca4Nb2O9 was confirmed by TEM, and electrondiffraction patterns collected along [110]c and [101]c (Figure 13) are identical to those reportedby Levin et al. (3).

The patterns of Sr3NaCaNb3O12 [ = (Sr3/4Na1/4)(Ca1/4Nb3/4)O3] and Ba3NaCaNb3O12

(Figure 14) could be indexed via the use of a 1:3-ordered, tilt-free, P2/m structure with a =9.934 A, b = 5.743 A, c = 11.471 A, β = 124.97◦ (Sr) and a = 10.176 A, b = 5.852 A, c =11.729 A, β = 125.59◦ (Ba). Very weak additional reflections in the Sr phase (t = 0.939) mayarise from a small degree of tilting and symmetry reduction; these were absent in the Ba phase,for which t = 0.981. TEM studies confirmed the presence of the 1:3 B-site order in both phases,although the ordering reflections are quite diffuse, and dark-field images revealed a microstructurecomposed of nanosized 1:3-ordered domains (Figure 15).

Although the formation of a 1:3-ordered A(βI1/4β

II3/4)O3 structure is compatible with the

stoichiometry of the A2+3NaCaNb3O12 phases, the B-site order could involve Ca and Nb as written

above, i.e., (Ca3/4Na1/4)(Ca1/4Nb3/4)O3, or Na and Nb [i.e., Ca(Na1/4Nb3/4)O3]. Simulations of

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Figure 12X-ray pattern collected from 1:3-ordered Ca4NaNb3O12.

110c

a b

* *

111c

001c

110c 111c

001c

Figure 13Electron diffraction patterns collected from (Ca3/4Na1/4)(Ca1/4Nb3/4)O3 along (a) [110]c and (b) [101]c.The asterisks indicate nondiffracted (0,0,0) beam, and the white arrow highlights one of the 1/4[111]∗ordering reflections.

the powder patterns, using the atom positions reported for Ca4Nb2O9 for the Ca phase and anontilted P2/m structure for the Ba and Sr polymorphs, provided clear support for the occupancyof βI by Ca and 1:3 ordering of Ca and Nb. Additional, albeit indirect, support for this assignmentcame from the relatively high thermal stability of these phases, which were stable up to ∼1400◦C.

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Ba

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Figure 14X-ray patterns of 1:3-ordered (Ba3/4Na1/4)(Ca1/4Nb3/4)O3 (Ba), (Sra3/4Na1/4)(Ca1/4Nb3/4)O3 (Sr), and(Ca3/4Na1/4)(Ca1/4Nb3/4)O3 (Ca).

100 nm

Figure 15Dark-field image of ordered domains in (Sra3/4Na1/4)(Ca1/4Nb3/4)O3 collected through the use of1/4〈1-11〉c reflection; the corresponding [110]c diffraction pattern is inset.

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This is in sharp contrast to the very high volatility of Na in Sr(Na1/4Nb3/4)O3 described above,for which the chemistry dictates the occupancy of the βI-site by Na.

The formation of these new A(βI1/4β

II3/4)O3 phases demonstrates that extensive tilting is

not a requirement for 1:3 order. However, the tilting is a factor in determining the stability ofthe order: Quenching experiments revealed the Ba polymorph transforms to a disordered B-sitearrangement at ∼1300◦C, whereas the Sr phase retains the 1:3 order up to ∼1350◦C, and thelowest-tolerance-factor Ca phase shows no sign of disordering up to temperatures (1400◦C) atwhich decomposition becomes an issue.

A2.5+(B2+1/4B4+

3/4)O3: (1−x)CaTiO3-(x)La2O3; A-site and B-site order. The utility of simpleperovskites such as SrTiO3 and CaTiO3, which combine a high dielectric constant with a relativelylow dielectric loss, as microwave resonators is severely limited by their very large temperature co-efficient of resonant frequency (τ f ) (95). Many investigations have focused on tuning τ f throughsolid solution with a variety of end members; (1−x)CaTiO3-(x)La2O3 constitutes one such systemfor which τ f = 0 at x ∼ 0.2. Previous studies of the cation distribution in solid solutions of CaTiO3

with La2O3 (86, 87) showed that all the substituted La3+ cations enter the A-site, with Ca2+ par-titioning between the A- and B-site according to the formula (Ca1−2xLa2x)(CaxTi1−x)O3. For thismechanism the limit of substitution is x = 0.5 [La(Ca1/2Ti1/2)O3]. This end member has neverbeen stabilized, presumably owing to the very low resultant tolerance factor (0.886), and the ob-served range of homogeneity extends only to x = 0.4. This range includes a composition (x = 0.25)for which the stoichiometry of the B-site is compatible with the 1:3-ordered A2.5+(B2+

1/4B4+3/4)O3

composition identified in Table 2, i.e., (La0.5Ca0.5)(Ca1/4Ti3/4)O3. Although the difference in thecharge of the cations (�qβ = 2) is less than in other 1:2- or 1:3-ordered systems, we felt that thelarge difference in the octahedral cation radii of Ca2+ and Ti4+ (Ca2+ = 1.0 A, Ti4+ = 0.605 A)might stabilize an ordered arrangement.

Our reinvestigation of (1−x)CaTiO3-(x)La2O3 confirmed that the limit of solid solution liesclose to x = 0.4. The X-ray patterns were similar to those of the orthorhombic (Pnma) CaTiO3 endmember, and the magnitude of the orthorhombic distortion increased with x in accordance withthe lowering of the tolerance factor. At the x = 0.25 composition, (La0.5Ca0.5)(Ca1/4Ti3/4)O3,electron diffraction revealed weak additional reflections at k = 1/4[111]∗, consistent with theformation of 1:3 Ca:Ti order (Figure 16). The symmetry of the patterns was again essentiallyidentical to those reported for the LT1/4 polymorph of Ca4Nb2O9, and a triclinic unit cell (a =9.742 A, b = 5.564 A, c = 11.326 A, α = 89.88◦, β = 125.45◦, γ = 89.97◦) could also indexthe X-ray patterns (Supplemental Figure 5). Because the scattering cross section of Ca and Tiis so similar, it was difficult to detect the additional reflections associated with the cation order,using X-rays, even after annealing the samples for extended periods at temperatures ranging from1100◦C to 1500◦C to strengthen the order.

When the specimens were annealed between 800◦C and 900◦C, an additional phase trans-formation strengthened the ordering reflections. Figure 17 shows the lower-angle regions of theX-ray patterns collected from samples after annealing at 1000–1250◦C to promote the B-site orderand after a subsequent heat at 850◦C for 24–48 h. After the low-temperature anneal, the patternsshow clear evidence for the stronger broad peak at 2θ ∼ 9.4◦ (Figure 17) that corresponds to4d111. An increase in the intensity of the 1/4(111)∗ reflections was also observed in the electrondiffraction patterns of the lower-temperature annealed samples (Figure 16). Dark-field imagesof the 850◦C annealed samples collected using one of the k = 1/4[111]∗ reflections (Figure 18)show direct evidence of the ordering and reveal a structure composed of ∼10–20-nm domains,separated by what appear to be antiphase or orientational domain boundaries. The transformationat 850◦C was fully reversible.

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a b

Figure 16Electron diffraction patterns of 1:3-ordered (Ca1/2La1/2)(Ca1/4Ti3/4)O3 collected along [110]c (a) after a1250◦C anneal and (b) after a subsequent anneal at 850◦C. Examples of reflections associated with the cationorder are indicated by arrows.

10 2015

After 850°C anneal

Before 850°C anneal

2θ (degrees)

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Figure 17Low-angle region of the X-ray patterns of (Ca1/2La1/2)(Ca1/4Ti3/4)O3 before and after annealing at 850◦C.

Although the additional reflections in the X-ray patterns after the 850◦C annealing are broad,their intensity is far greater than expected for 1:3 Ca:Ti order alone. Furthermore, the temperatureof the transition is considerably less than those usually associated with B-site ordering reactions. Wesuspect that this transition arises from an additional ordering reaction involving a 〈111〉 layering ofCa2+ and La3+ on the A-site sublattice. Examples of A-site ordering in stoichiometric perovskitesare quite rare. However, a transition involving the ordering of Na+ and La3+ has been observedin a similar temperature range in Na1/2La1/2(Mg1/3Nb2/3)O3 (48). Although there is a precedent

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30 nm

Figure 18Dark-field image of A-site-ordered domains after annealing (Ca1/2La1/2)(Ca1/4Ti3/4)O3 at 850◦C.

for A-site ordering at these temperatures, every known A-site ordering transition involves a 〈001〉layering of the A-site cations (24, 96). It is interesting, therefore, to understand why this systemshould be the first example of a perovskite with 〈111〉 A-site order.

An explanation for the 〈111〉 layering may lie in the different local formal charges on theA-site sublattice that result from the 1:3 B-site order. This concept was used to rationalizethe instability of the W-rich perovskites described above and has also been invoked to un-derstand ordering reactions in other systems involving A- and B-site-ordered perovskites (93).Figure 19 shows a representation of the 1:3-ordered A(βI

1/4βII

3/4)O3 structure that highlightsthe different B-site arrangements in the constituent perovskite subcells. The B-site order producestwo different A-site environments: One, A(1), has 1βI and 7βII nearest neighbors; the second, A(2),has 3βI and 5βII neighbors. These two A-sites repeat with a layered [..A(1)A(1)A(2)A(2)..] sequencealong the 〈111〉 direction of the parent perovskite. In (Ca1/2La1/2)(Ca1/4Ti3/4)O3, for which βI =Ca2+ and βII = Ti4+, the resultant local lattice charges at the A(1) and A(2) sites are –2.25and –2.75, respectively. A random or (001) layered distribution of Ca2+ and La3+ on the A-sitewould lead to occupancy of the A(1) and A(2) positions by both cations and to a large mismatch( ± 0.75) between their charge and the local potential. The mismatch can be reduced significantly(to ± 0.25) if Ca is ordered on A(1) and La on A(2) (Figure 20). We believe the large reductionin the mismatch is the driving force for the stabilization of a layered (..CaCaLaLa..) 〈111〉 repeatat less than ∼850◦C. Because the ordering temperature is so low, it is not surprising the lengthscale of the order is small and that the samples are composed of nanoscale ordered domains.

Similar A-site transitions should be expected in the 1:3-ordered (A2+3/4Na1/4)(Ca1/4Nb3/4)O3

niobates. In this case the charges on βI and βII are +2 and +5, which again lead to quite differentlocal potentials, –1.375 and –2.125, on the A(1) and A(2) sites. However, in this case the ratio ofthe two A-sites (2:2) is incompatible with the cation stoichiometry (3:1 A2+:Na+), and there wouldno energetic gain in ordering the A cations along 〈111〉. A series of extended lower-temperatureanneals was subsequently conducted on that family of compounds, and no evidence was found

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βI

βII

O2–

= A(1):1βI/7βII

= A(2):3βI/5βII

Figure 19Schematic illustration of the perovskite subcells in the 1:3-ordered A(βI

1/4βII

3/4)O3 structure highlightingthe different coordination environment of the A(1) and A(2) sites.

c

a

Figure 20〈111〉 A-site-ordered structure of the low-temperature form of 1:3-ordered (Ca1/2La1/2)(Ca1/4Ti3/4)O3;Ca = red, La = green.

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for any change in the intensity of the ordering reflections that might indicate an A-site orderingreaction.

As a side note, a perplexing aspect of the (1−x)CaTiO3-(x)La2O3 system is the absence of1:2 order at x = 0.33, which has a 1:2 B-site stoichiometry: (Ca1/3La2/3)(Ca1/3Ti2/3)O3. In fact,we found that this composition also adopts 1:3 B-site order even after extended annealing. It isunclear whether the absence of 1:2 order reflects the intrinsic instability of the stoichiometric 1:2structure versus nonstoichiometric 1:3 order or, more likely, kinetic limitations on the nucleationof the 1:2 order. A similar metastability was reported for Ca4Nb2O9 (3, 7).

Attempts were made to prepare other new phases in the 1:3 A2.5+(B2+1/4B4+

3/4)O3 family, e.g.,(La1/2A2+

1/2)(Mg2+1/4Ti4+

3/4)O3 (A2+ = Ca, Sr, Ba); none of these showed any evidence for B-siteorder. For a valence difference of 2, 1:3 order can be stabilized only when the cations have a verylarge difference in their size, which is the case for Ca2+ and Ti4+.

A1.25+(B1+1/4B6+

3/4)O3 and A1.5+(B3+1/4B5+

3/4)O3. For the remaining potential 1:3-orderedsystems identified in Table 2, the A1.25+(B1+

1/4B6+3/4)O3 family was explored for W6+ and yielded

nonperovskite products, consistent with the results of the W-rich 1:2-ordered chemistries. In lightof the absence of order in systems with a charge difference of 2, except for cations with very largecharge differences, examples in the A1.5+(B3+

1/4B5+3/4)O3 family were not explored.

A2.75+(B+1/4B4+

3/4)O3. Attempts to prepare 1:3-ordered phases with B1+/B4+, e.g.,(Ca1/4La3/4)(Li1/4Ti3/4)O3, were unsuccessful even after slow cooling and prolonged (1 week)annealing at 900–1000◦C. The patterns could be indexed in terms of a disordered, tilted Pbnmorthorhombic cell. The failure to stabilize B-site order for this composition is consistent withthe order-disorder transition temperatures of other related systems. For a given pair of BI, BII

ions the ordering temperature typically decreases on proceeding from a 1:1-, to a 1:2-, to a 1:3-ordered state. The order-disorder temperature in La(Li1/3Ti2/3)O3 is 1180◦C (56). Therefore, a1:3-ordered state in (Ca1/4La3/4)(Li1/4Ti3/4)O3 is likely to be stable only at considerably lowertemperatures, at which the B-site ions are kinetically inactive.

Stability fields. Figure 21 maps the stability of the 1:3-ordered perovskites as a function of thecharge and size differences of the β-sites and delineates phases with and without cation order. Thestability of the W-rich phases with �qβ = 5.0 is again compromised by local charge imbalances.For a given charge difference, the formation of 1:3 order requires a larger size difference comparedwith the 1:2-ordered systems. In addition to these crystal chemical driving forces, for a given familythe order is further stabilized by a reduced tolerance factor. We do not believe that the impact ofthe tolerance factor is associated with a lower free energy for the low-t ordered phases but thatthis impact instead reflects a decrease in the stability of their disordered counterparts, which inturn provides a more negative �G for the ordering reaction.

Dielectric Properties

Table 3 summarizes the dielectric properties of the new ordered perovskites. Compounds notlisted could not be sintered to the high densities required for meaningful measurement of theirmicrowave loss. The quality factors Q ( = 1/tan δ) are comparable or better than many perovskiteoxides but do not approach those of the 1:2-ordered BZT or BZN systems, for which the Q × fproduct can exceed 100,000. However, several of the new oxides can be densified at tempera-tures considerably less than those required to sinter BZN and BZT (typically 1500–1600◦C).

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1:3 order

Ca/Ti

Ca/NbNa/Nb

Li/Nb

Mg/Ti

Mg/Nb

Li/Ti Li/W

Charge difference (∆q)

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45S

ize

dif

fere

nce

(∆r,

Å)

2.01.8 5.04.84.64.44.24.03.83.63.43.23.02.82.62.42.2

Figure 21Map of the stability of 1:3-ordered A(βI

1/4βII

3/4)O3 perovskites as a function of the size (�r) and charge(�q) difference of the cations on the βI and βII positions. 1:3 order is observed in the shaded region. Squaresdenote perovskite-forming compositions: blue, 1:3 ordered; red, disordered. The triangle indicates a systemthat does not form a single-phase perovskite.

Furthermore, the order-disorder transition temperatures for the majority of the new ordered nio-bates are significantly higher than for BZN (Torder = 1375◦C). Therefore, their practical utilitymay be as additives to the known high-Q systems to enhance the stability of the cation order andreduce the sintering temperature. The new systems also have a broad range of negative and pos-itive τ f values that may be useful in providing alternate ways to tune the temperature coefficientof BZN (τ f = +30 ppm/◦C).

Preliminary investigations were made to examine the effectiveness of a composition in theBLNW system, Ba(Li0.3Nb0.5W0.2)O3, in stabilizing the order in BZN (51). The 1:2 order wasstable across the entire solid solution, and the disordering transition increased from 1375◦C forpure BZN to 1420◦C for 15% BLNW and to >1500◦C for 75% BLNW. The substitution alsoreduced the sintering temperature of BZN by as much as 100◦C and enabled the direct sinteringof ordered ceramics. The Q × f (∼40,000) of as-sintered (6 h, 1420◦C), ordered, 75% BZN–25% BLNW was higher than that of as-sintered, disordered pure BZN and could be increasedto ∼70,000 by annealing at lower temperature to coarsen the ordered domains. Although this isstill lower than the Q × f of fully ordered pure BZN, fully ordered pure BZN requires a highersintering temperature. Other additives chosen from the compounds in Table 3 likely will providesimilar enhancements in the ordering and sintering, but perhaps with even higher benefits in thefinal Q × f properties. In related work we found that the most promising Q-enhancing additivesto BZN involve the substitution of small concentrations of W for Nb or the introduction of smallconcentrations of cation vacancies (72–75).

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Table 3 Microwave dielectric properties

Compound εR Q.f ( f, GHz) τ f (ppm/◦C)Sr2/3La1/3(Li1/3Nb2/3)O3 30 5700 (9) –Sr0.8La0.2(Li1/3[Nb0.8W0.2])O3 29 22,300 (9) –68Sr2/3La1/3(Li1/3Ta2/3)O3 25 18,100 (10.2) –Sr0.75La0.25(Li1/3[Ta0.875W0.125]2/3)O3 26 22,800 (9.9) –73Ba(Li0.85Nb0.15)1/3(Nb0.85W0.15)2/3O3 (BLNW; x = 0.33) 32 19,000 (7.8) +18Sr(Li0.85Nb0.15)1/3(Nb0.85W0.15)2/3O3 (SLNW; x = 0.33) 31 27,400 (8.7) –23Ca(Li0.85Nb0.15)1/3(Nb0.85W0.15)2/3O3 (CLNW; x = 0.33) 29 15,690 (9.7) –35Ca(Li0.8Ta0.2)1/3(Ta0.9W0.1)2/3O3 (CLTW; x = 0.111) 24 21,900 (9.4) –42Ca(Li0.86Ta0.14)1/3(Ta0.78W0.22)2/3O3 (CLTW; x = 0.278) 20 22,700 (10) –22(Na1/4Ca3/4)(Ca1/4Nb3/4)O3 34 9462 (8.3) 100(Na1/4Sr3/4)(Ca1/4Nb3/4)O3 46 10,310 (7.2) –60(Na1/4Ba3/4)(Ca1/4Nb3/4)O3 43 <9000 (7.4) –100Ca1/2La1/2(Ca1/4Ti3/4)O3 44 12,600 (7) –8Ca1/2La1/2(Ca1/4Ti3/4)O3 (after 825◦C anneal) 37 14,800 (7) –25Ca(Li1/4Nb3/4)O3 37 22,800 (8.7) –Ca(Li1/4Ta3/4)O3 27 30,000 (9.4) –

SUMMARY/FUTURE ISSUES

The design of new B-site perovskites based on chemistries containing a single A-site cation andnoninteger charge, mixed A-site cations enables the preparation of many new families of 1:2- and1:3-ordered dielectric oxides. The choice of the B-site cations was guided by criteria known tostabilize these two structure types and by the desire to engineer new systems with low dielectriclosses. It is likely that several other members of these new families, perhaps designed for magneticor ferroelectric responses, could be prepared and that their properties could be mediated by thecation order. The stability of the order in these and other perovskites responds to well-knowncrystal chemical factors such as cation charge and size, satisfaction of local bond valence, andtolerance factor. The order also responds to other factors such as covalency (e.g., Nb versus Ta)and ionic displacements [which are critical in ferroelectric and piezoelectric perovskites (14)],which can have important practical ramifications for the processing of dense ceramics. In thesystems involving more highly charged cations, imbalances in the local lattice potential play animportant role; these are responsible for the absence of stability in W-rich perovskites and for theA-site ordering in (Ca1/2La1/2)(Ca1/4Ti3/4)O3, the first example of a perovskite for which the Acations are also layered along 〈111〉.

Many opportunities exist to engineer other perovskites with different types of cation order.Because of the smaller driving force, stabilization of A-site order can require annealing at tem-peratures typically deemed too low for cation activity. However, clear evidence for ordering tran-sitions in the range of 850–900◦C was observed in this and other studies (48). Although A-siteorder is not the primary focus of this review, we note that several new examples have been reportedrecently. Knapp & Woodward (96) have explored how the A-site order is influenced by tilting andby the chemistry and degree of order on the B-site sublattice and used group theoretical treatmentsto elucidate the possible structures of (AIAII)(BIBII)X6 double perovskites. That work providedexplanations for the absence of order in systems such as (Na1/2La1/2)TiO3 and the stabilizationof 〈100〉 Na/La order in B-site-ordered derivatives such as (Na1/2La1/2)(Mg1/2W1/2)O3. Very

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recently, Guiton & Davies (97) described an unusual family of phases in perovskites containingundersized cations such as Li on the A-site [e.g., (Nd2/3−xLi3x)TiO3]. The complex nanostruc-tural modulations in that system result from a periodic separation into domains of two phases withnanometer dimensions, one Li-rich with a composition (Nd1/2Li1/2)TiO3 and the other Li-freewith a composition Nd2/3TiO3. A remarkable feature of this structure is that the phase-separateddomains form a superstructure that extends across the entire crystal, with a periodicity that can betuned by changing the overall composition. These structures offer the potential for new classesof perovskites that may serve as templates for the assembly of nanoscale objects or molecularoverlayers.

DISCLOSURE STATEMENT

The authors are not aware of any biases that might be perceived as affecting the objectivity of thisreview.

ACKNOWLEDGMENTS

We acknowledge the help of several collaborators in these studies, in particular Tyke Negas, SteveBell, and Matjaz Valant; we also thank Igor Levin, Terrell Vanderah, and Robert S. Roth for manyuseful discussions. The work was supported by Ericsson Radio Access AB, the Ceramics Programof the National Science Foundation (most recently through grant DMR 0704255), and by theOffice of Naval Research (grant N00014-01-1-0860). We also acknowledge the MRSEC programat NSF for support of shared facilities (grant DMR 05-20020).

LITERATURE CITED

1. Cross LE. 1994. Relaxor ferroelectrics: an overview. Ferroelectrics 151:305–202. Kawashima S, Nishida M, Ueda I, Ouchi H. 1986. BaZn1/3Ta2/3O3 ceramics with low dielectric loss at

microwave frequencies. J. Am. Ceram. Soc. 66(6):421–233. Levin I, Bendersky LA, Cline JP, Roth RS, Vanderah TA. 2000. Octahedral tilting and cation ordering in

perovskite-like Ca4Nb2O9 = Ca(Ca1/3Nb2/3)O3 polymorphs. J. Solid State Chem. 150:43–614. Glazer AM. 1972. The classification of tilted octahedra in perovskites. Acta Crystallogr. B 28:3384–925. Woodward PM. 1997. Octahedral tilting in perovskites. I. geometrical considerations. Acta Crystallogr. B

53:32–436. Woodward PM. 1997. Octahedral tilting in perovskites. II. structure stabilizing forces. Acta Crystallogr. B

53:44–667. Levin I, Chan JY, Geyer RG, Maslar JE, Vanderah TA. 2001. Cation ordering types and dielectric prop-

erties in the complex perovskite Ca(Ca1/3Nb2/3)O3. J. Solid State Chem. 156:122–348. Howard CJ, Stokes HT. 1998. Group-theoretical analysis of octahedral tilting in perovskites. Acta Crys-

tallogr. B 54:782–899. Fornari M, Singh DJ. 2001. Possible coexistence of rotational and ferroelectric lattice distortions in

rhombohedral PbZrxTi1−xO3. Phys. Rev. B 63:09210110. Reaney IM, Colla EL, Setter N. 1994. Dielectric and structural characteristics of Ba-based and Sr-based

complex perovskites as a function of tolerance factor. Jpn. J. Appl. Phys. 33:3984–9011. Shirane G, Hoshino S, Suzuki K. 1950. X-ray study of the phase transition in lead titanate. Phys. Rev.

80:1105–612. Suchomel MR, Davies PK. 2005. Enhanced tetragonality in (x)PbTiO3—(1−x)Bi(Zn1/2Ti1/2)O3 and

related solid solution systems. Appl. Phys. Lett. 86:262905/1–313. Suchomel MR, Fogg AM, Allix M, Niu H, Claride JB, Rosseinsky MJ. 2006. Bi2ZnTiO6: a lead-free closed-

shell polar perovskite with a calculated ionic polarization of 150μ C cm−2. Chem. Mater. 18(21):4987–89

www.annualreviews.org • Crystal Chemistry of Complex Perovskites 397

Ann

u. R

ev. M

ater

. Res

. 200

8.38

:369

-401

. Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

gby

Uni

vers

ity o

f H

yder

abad

on

10/1

5/12

. For

per

sona

l use

onl

y.

ANRV347-MR38-16 ARI 28 May 2008 10:15

14. Grinberg I, Suchomel MR, Dmowski W, Wu H, Davies PK, Rappe AM. 2007. Structure and polarizationin the high Tc ferroelectric Bi(Zn,Ti)O3-PbTiO3 solid solutions. Phys. Rev. Lett. 98(10):107601

15. Donohue PC, Katz L, Ward R. 1965. The crystal structure of barium ruthenium oxide and relatedcompounds. Inorg. Chem. 4(3):306–10

16. Collins BM, Jacobson AJ, Fender BEF. 1974. Preparation of the ordered perovskite-like compoundsbarium tantalum or niobium lithium oxide (Ba4M3LiO12). Powder neutron diffraction determination ofthe structure of barium tantalum lithium oxide (Ba4Ta3LiO12). J. Solid State Chem. 10:29–35

17. Negas T, Roth RS, Parker HS, Brower WS. 1973. Crystal chemistry of lithium in octahedrally coordinatedstructures. I. Synthesis of Ba8(Me6Li2)O24 (Me = Nb or Ta) and Ba10(W6Li4)O30. J. Solid State Chem.8:1–13

18. Shannon J, Katz L. 1970. A refinement of the structure of barium tantalum oxide, Ba5Ta4O15. ActaCrystallogr. B 26:102–5

19. Shpanchenko RV, Nistor L, Van Tendeloo G, Van Landuyt J, Amelinckx S, et al. 1995. Structural studieson new ternary oxides Ba8Ta4Ti3O24 and Ba10Ta7.04Ti1.2O30. J. Solid State Chem. 114:560–74

20. Abakumov AM, Van Tendeloo G, Scheglov AA, Shpanchenko RV, Antipov EV. 1996. The crystal structureof Ba8Ta6NiO24: cation ordering in hexagonal perovskites. J. Solid State Chem. 125:102–7

21. Blasse G. 1965. New compounds with perovskite-like structures. J. Inorg. Nucl. Chem. 27:993–100322. Akmoto J, Gotoh Y, Oosawa Y. 1994. Refinement of hexagonal BaTiO3. Acta Crystallogr. C 50:160–6123. Burbank RD, Evans HT Jr. 1948. The crystal structure of hexagonal titanate. Acta Crystallogr. 1:330–3624. Davies PK. 1999. Cation ordering in complex oxides. Curr. Opin. Solid State Mater. Sci. 4:467–7225. Alario-Franco MA, Grey IE, Joubert JC, Vincent H, Labeau M. 1982. Structural studies on A-cation

deficient perovskite-related phases. I. ThNb4O12, thorium-vacancy ordering in slow-cooled samples.Acta Crystallogr. A 38:177–86

26. Grenier JC, Darriet J, Pouchard M, Hagenmuller P. 1976. Model of a new family of phases of the orderedvacancy perovskite type with the formula A3M3O8 (AMO2.67). Mater. Res. Bull. 11(10):1219–25

27. Steward SG, Rooksby HP. 1951. Pseudocubic alkaline earth tungstates and molybdates of the R3MX6

type. Acta Crystallogr. 4:503–728. Galasso F, Katz L, Ward R. 1959. Substitution in the octahedrally coordinated cation positions in com-

pounds of the perovskite type. J. Am. Chem. Soc. 81:820–2329. Galasso F, Darby W. 1962. Ordering of the octahedrally coordinated cation position in the perovskite

structure. J. Phys. Chem. 66:131–3230. Anderson MT, Greenwood KB, Taylor GA, Poeppelmeier KR. 1993. B-cation arrangement in double

perovskites. Prog. Solid State Chem. 22:197–23331. Sleight AW, Longo J, Ward R. 1962. Compounds of Os and Re with ordered perovskite structure. Inorg.

Chem. 1:245–5032. Blasse G. 1964. Qualitative approach to the strucutral differences between some mixed metal oxides

containing Sb5+, Nb5+ and Ta5+. J. Inorg. Nucl. Chem. 26:1191–9933. Lufaso MW, Woodward PM. 2004. Jahn-Teller distortions, cation ordering and octahedral tilting in

perovskites. Acta Crystallogr. B 60:10–2034. Anderson MT, Poeppelmeier KR. 1991. Lanthanum copper tin oxide (La2CuSnO6): a new perovskite-

related compound with an unusual arrangement of B cations. Chem. Mater. 3:476–8235. Azuma M, Kaimori S, Takano M. 1998. High-pressure synthesis and magnetic properties of layered double

perovskites Ln2CuMO6 (Ln = La, Pr, Nd, and Sm; M = Sn and Zr). Chem. Mater. 10:3124–3036. Krause HB, Gibbon DL. 1971. Ordering of magnesium and niobium in the octahedral positions of the

“cubic” perovskite structure of Pb3MgNb2O9. Z. Kristallogr. 134(1–2):44–5337. Akbas M, Davies PK. 1997. Domain growth in Pb(Mg1/3Ta2/3)O3 perovskite relaxor ferroelectric oxides.

J. Am. Ceram. Soc. 80(11):2933–3638. Yan Y, Pennycook SJ, Xu Z, Viehland D. 1998. Determination of the ordered structures of

Pb(Mg1/3Nb2/3)O3 and Ba(Mg1/3Nb2/3)O3 by atomic-resolution Z-contrast imaging. Appl. Phys. Lett.72(24):3145–47

39. Burton BP. 2000. Long-range vs short-range interactions and the configurational energies of Ba(B,B′)O3

and Pb(B,B′)O3 perovskites. Model. Simul. Mater. Sci. Eng. 8:211–19

398 Davies et al.

Ann

u. R

ev. M

ater

. Res

. 200

8.38

:369

-401

. Dow

nloa

ded

from

ww

w.a

nnua

lrev

iew

s.or

gby

Uni

vers

ity o

f H

yder

abad

on

10/1

5/12

. For

per

sona

l use

onl

y.

ANRV347-MR38-16 ARI 28 May 2008 10:15

40. Akbas MA, Davies PK. 2001. Structure, stability, and dielectric properties of chemically ordered relaxorsin the Pb(Mg1/3Ta2/3)O3-PbZrO3 system. Int. J. Inorg. Mater. 3:123–34

41. Juhas P, Davies PK, Akbas MA. 2004. Structure and dielectric properties of the Pb(Sc2/3W1/3)O3-PbMO3

systems (M = Zr, Ti). J. Am. Ceram. Soc. 87(11):2086–9242. Akbas MA, Chai L, Davies PK, Parise J. 1997. Cation ordering transformations in Ba(Mg1/3Ta2/3)O3-

BaZrO3 solid solutions. Mater. Res. Bull. 32(9):1261–6943. Galasso F, Barrante JR, Katz L. 1961. Alkaline earth-tantalum-oxygen phases including the crystal struc-

ture of an ordered perovskite compound, Ba3SrTa2O9. J. Am. Chem. Soc. 83:2830–3244. Galasso F, Pyle J. 1963. Ba(Ca0.33Ta0.67)O3, an ordered perovskite of the Ba(Sr0.33Ta0.67)O3 type. J. Phys.

Chem. 67:533–3445. Galasso F, Pyle J. 1963. Ordering in compounds of the A(B′

0.33Ta0.67)O3 type. Inorg. Chem. 2:482–8446. Galasso F, Pyle J. 1963. Preparation and study of ordering in A(B′

0.33Nb0.67)O3 perovskite-type com-pounds. J. Phys. Chem. 67(7):1561–62

47. Rijssenbeek JT, Saito T, Malo S, Azuma M, Takano M, Poeppelmeier KR. 2005. Effect of explicit cationicsize and valence constraints on the phase stability of 1:2 B-site-ordered perovskite ruthenates. J. Am. Chem.Soc. 127(2):675–81

48. Tarvin R, Davies PK. 2004. A- and B-site order in (Na1/2La1/2)(Mg1/3Nb2/3)O3 perovskites. J. Am.Ceram. Soc. 87(5):859–64

49. Davies PK, Tong J, Negas T. 1997. Effect of ordering-induced domain boundaries on low-lossBa(Zn1/3Ta2/3)O3-BaZrO3 perovskite microwave dielectrics. J. Am. Ceram. Soc. 80(7):1727–40

50. Molodetsky I, Davies PK. 2001. Effect of Ba(Y1/2Nb1/2)O3 and BaZrO3 on the cation order and propertiesof Ba(Co1/3Nb2/3)O3 microwave ceramics. J. Eur. Ceram. Soc. 21:2587–91

51. Hui W. 2005. Investigation of nonstoichiometric ordered niobate perovskites for microwave applications. PhDdissertation. Univ. Penn.

52. Park J-H, Woodward PM. 2000. Synthesis, structure and optical properties of two new perovskites:BaBi2/3TeO6 and Ba3Bi2TeO9. Int. J. Inorg. Mater. 2(1):153–66

53. Fresia EJ, Katz L, Ward R. 1959. Cation substitution in perovskite-like phases. J. Am. Chem. Soc. 81:4783–85

54. Subramanian MA. 1994. Ordered perovskites containing pentavalent bismuth: Ba(Bi0.75M0.25)O3 andBa(Bi0.67M0.33)O3. J. Solid State Chem. 111:134–40

55. Youn HJ, Kim IT, Hong KS, Kim H. 1997. Crystal structure and microwave dielectric properties ofLa(Mg2/3Ta1/3)O3 ceramics. Ferroelectrics 193(1–4):167–74

56. Borisevich AY, Davies PK. 2003. La(Li1/3Ti2/3)O3: a new 1:2 ordered perovskite. J. Solid State Chem.170(1):198–201

57. Davies PK, Borisevich AY, Thirumal M. 2003. Communicating with wireless perovskites: cation orderand zinc volatilization. J. Eur. Ceram. Soc. 23(14):2461–66

58. Borisevich AY, Davies PK. 2004. 1:2 cation order in A(Li1/3(Nb,Ta)2/3)O3 microwave perovskites. Appl.Phys. Lett. 84(8):1347–49

59. Katz L, Ward R. 1964. Structure relations in mixed metal oxides. Inorg. Chem. 3(2):205–1160. Akbas M, Davies PK. 1998. Cation ordering transformations in the Ba(Zn1/3Nb2/3)O3—

La(Zn2/3Nb1/3)O3 system. J. Am. Ceram. Soc. 81(4):1061–6461. Akbas M, Davies PK. 1998. Structure and dielectric properties of the Ba(Mg1/3Nb2/3)O3—

La(Mg2/3Nb1/3)O3 system. J. Am. Ceram. Soc. 81(8):2205–862. Jacobson AJ, Collins BM, Fender BEF. 1976. A powder neutron and X-ray diffraction determination of

the structure of Ba3Ta2ZnO9: an investigation of perovskite phases in the system Ba-Ta-Zn-O and thepreparation of Ba2TaCdO5.5 and Ba2CeInO5.5. Acta Crystallogr. B 32(4):1083–87

63. Harari D, Poix P, Bernier JC. 1974. Structural study of four new cobalt perovskites. J. Solid State Chem.11:330–39

64. Harari D, Poix P. 1973. Preparation and study of the properties of the mixed oxide with perovskitestructure Sr3Cr2WO9. Comptes Rendus Seances C 276:265–68

65. Ropars C, Berthon J, Bernier JC, Poix P. 1966. Crystallographic study of Ba3UFe2O9 and Sr3UFe2O9.Ann. Chem. (Paris) 1:377–82

www.annualreviews.org • Crystal Chemistry of Complex Perovskites 399

Ann

u. R

ev. M

ater

. Res

. 200

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yder

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10/1

5/12

. For

per

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ANRV347-MR38-16 ARI 28 May 2008 10:15

66. Berthon J, Grenet JC, Poix P. 1979. Structural properties of Ba3Fe2−xMxUO9 solid solutions where Mis a trivalent element. Ann. Chem. (Paris) 4:609–21

67. Viola MC, Augsburger MS, Pinacca RM, Pedregosa JC, Carbonio RE, Mercader RC. 2003. Order-disorder at FE sites in SrFe2/3

′ ′1/3O3 (B′ ′ = Mo, W, Te, U) tetragonal double perovskites. J. Solid State

Chem. 175:252–5768. James M, Attfield JP, Roriguez-Cavajal J. 1995. Synthesis, crystal structure and magnetism of

Sr3Sb2NiO9—a ferrimagnetic perovskite. J. Phys. Chem. Solids 56:1331–3769. Zhang W, Kumada N, Yonesaki Y, Takei T, Kinomura N, et al. 2006. Ferroelectric perovskite-type barium

copper niobate: BaCu1/3Nb2/3O3. J. Solid State Chem. 179:4052–5570. Jancar B, Davies PK, Suvorov D, Valant M. 2002 . Cation arrangement and microstructure of dielectric

ceramics based on the system Ba(Zn1/3Nb2/3)O3-Ba(Zn1/2W1/2)O3. Zb. Ref. Posvetovanja Slov. Kem. Dnevi,Maribor, Slov., Sept. 26–27, ed. P Glavic, D Brodnjak-Voncina, pp. 808–13. Maribor, Slov.: Univ. Mariboru,Fak. Kem. Kemijsko Tehnol.

71. Chai L, Davies PK. 1997. Formation and structural characterization of 1:1 ordered perovskites in theBa(Zn1/3Ta2/3)O3-BaZrO3 system. J. Am. Ceram. Soc. 80(12):3193–98

72. Wu H, Davies PK. 2006. Influence of nonstoichiometry on the structure and properties ofBa(Zn1/3Nb2/3)O3 microwave dielectrics: I. Substitution of Ba3W2O9. J. Am. Ceram. Soc. 89(7):2239–49

73. Wu H, Davies PK. 2006. Influence of nonstoichiometry on the structure and properties ofBa(Zn1/3Nb2/3)O3 microwave dielectrics: II. Compositional variations in pure BZN. J. Am. Ceram. Soc.89(7):2250–63

74. Wu H, Davies PK. 2006. Influence of nonstoichiometry on the structure and properties ofBa(Zn1/3Nb2/3)O3 microwave dielectrics: III. Effect of the muffling environment. J. Am. Ceram. Soc.89(7):2264–70

75. Wu H, Davies PK. 2006. Influence of nonstoichiometry on the structure and properties ofBa(Zn1/3Nb2/3)O3 microwave dielectrics: IV. Tuning τ f and the part size dependence of Q × f. J. Am.Ceram. Soc. 89(7):2271–78

76. Galasso F, Pinto J. 1965. Preparation of Ba(Na0.25Ta0.75)O3 and Sr(Na0.25Ta0.75)O3 with the perovskitestructure. Inorg. Chem. 4(2):235–36

77. Kapyshev AG, Ivanova VV, Venevtsev YN. 1966. New perovskites. Sov. Phys. Doklady 11(3):195–9678. Hikichi Y, Chen Z, Newnham RE, Cross LE. 1982. Preparation, thermal change and dielectric properties

of cubic perovskites A(B1/4Nb3/4)O3 (A = Ba or Sr, B = Na or Li). Mater. Res. Bull. 17:1371–7779. Jendrek EF Jr, Potoff AD, Katz AD. 1974. A single-crystal study of eight-layer barium niobium lithium

oxide, Ba4Nb3LiO12. J. Solid State Chem. 9:375–7980. Baud G, Picaud B, Besse JP. 1975. New series of rhenium perovskite compounds of Ba4M3ReO12 type.

J. Am. Ceram. Soc. 58(5–6):25981. Alonso A, Mzayek E, Rasines I. 1987. A new kind of 1:3 ordering in cubic perovskites: the oxides

BaM0.25Sb0.75O3 (M = Li, Na). Mater. Res. Bull. 22:69–7482. Subramanian MA. 1994. Ordered perovskites containing pentavalent bismuth: Ba(Bi0.75M0.25)O3 and

Ba(Bi0.67M0.33)O3. J. Solid State Chem. 111:134–4083. Alonso JA, Mzayek E, Rasines I. 1990. The distorted perovskite Sr(Na1/4Sb1/4)O3: a novel example of

1:3 B-cation ordering. J. Solid State Chem. 84:16–2284. Hervieu M, Studer F, Raveau B. 1977. Perovskite oxides in the Ca-Nb-O system. J. Solid State Chem.

22:273–8985. Borisevich AY. 2002. Investigation of Li-containing dielectric oxides for microwave applications. PhD dissertation.

Univ. Penn.86. Saltykova VA, Melnikova OV, Fedorov NF, Polevaya IA. 1989. A study of phase equilibria in the CaTiO3-

La2O3 system. Russ. J. Inorg. Chem. 34(10):1520–2287. Pivovarova AP. 2002. Synthesis of complex lanthanum and calcium titanates with a perovskite structure

and their electric properties studied at high temperature. Refract. Indust. Ceram. 43(11–12):329–3188. Wu H, Davies PK. 2004. Non-stoichiometric 1:2 ordered perovskites in the Ba(Li1/4Nb3/4)O3-

Ba(Li2/5W3/5)O3 system. J. Solid State Chem. 177:3469–7889. Wu H, Davies PK. 2004. Ordered perovskites in the A2+(Li1/4Nb3/4)O3-A2+(Li2/5W3/5)O3 (A2+ = Sr,

Ca) systems. J. Solid State Chem. 177:4305–15

400 Davies et al.

Ann

u. R

ev. M

ater

. Res

. 200

8.38

:369

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. Dow

nloa

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yder

abad

on

10/1

5/12

. For

per

sona

l use

onl

y.

ANRV347-MR38-16 ARI 28 May 2008 10:15

90. Brixner LH. 1974. New ordered perovskites. Mater. Res. Bull. 9:1041–4391. Hikichi Y, Suzuki S. 1987. Preparation of cubic perovskites A(B2/5W3/5)O3 (A = Ba or Sr, B = Na or

Li). J. Am. Ceram. Soc. 70(5):C99–10092. Poeppelmeier KR, Jacobson AJ, Longo JM. 1980. The structure of Ba3W2O9: an example of face-shared

octahedra with tungsten (VI). Mater. Res. Bull. 15:339–4593. Dupont L, Chai L, Davies PK. 1999. A- and B-site order in (Na1/2La1/2)(Mg1/3Ta2/3)O3 perovskites.

Mater. Res. Soc. Symp. Proc. Solid State Chem. Inorg. Mater. II, 547:93–98. Pittsburgh, PA: Mater. Res. Soc.94. Choi J-W, Kang C-Y, Yoon S-J, Kim H-J, Jung H-J. 1999. Microwave dielectric properties of

Ca[(Li1/3Nb2/3)1−xMx]O3−d (M = Sn, Ti) ceramics. J. Mater. Res. 14(9):3567–7095. Ouchi H, Kawashima S. 1985. Dielectric ceramics for microwave application. Jpn. J. Appl. Phys. 24:60–6496. Knapp MC, Woodward PM. 2006. A-site cation ordering in AA′BB′O6 perovskites. J. Solid State Chem.

179:1076–8597. Guiton BS, Davies PK. 2007. Nano-chessboard superlattices formed by spontaneous phase separation in

oxides. Nat. Mater. 6:586–91

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Annual Review ofMaterials Research

Volume 38, 2008Contents

Low- and High-Temperature Wetting: State of the Art

Wetting and Molecular Dynamics Simulations of Simple LiquidsJ. De Coninck and T.D. Blake � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 1

Dynamics of Wetting from an Experimental Point of ViewJohn Ralston, Mihail Popescu, and Rossen Sedev � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �23

Anisotropy of WettingDominique Chatain � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �45

Wetting and RoughnessDavid Quere � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � �71

Wetting and Dewetting of Complex Surface GeometriesStephan Herminghaus, Martin Brinkmann, and Ralf Seemann � � � � � � � � � � � � � � � � � � � � � � � � � 101

Modeling of Wetting in Restricted GeometriesKurt Binder � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 123

Wetting Phenomena in NanofluidicsM. Rauscher and S. Dietrich � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 143

Interfacial Segregation Effects in Wetting PhenomenaPaul Wynblatt � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 173

High-Temperature Wetting and the Work of Adhesionin Metal/Oxide SystemsEduardo Saiz, Rowland M. Cannon, and Antoni P. Tomsia � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 197

Wetting and Prewetting on Ceramic SurfacesJian Luo and Yet-Ming Chiang � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 227

Wetting in Soldering and MicroelectronicsT. Matsumoto and K. Nogi � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 251

Segregation Phenomena at Thermally Grown Al2O3/Alloy InterfacesP.Y. Hou � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 275

ix

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Current Interest

Combinatorial Materials Sciences: Experimental Strategiesfor Accelerated Knowledge DiscoveryKrishna Rajan � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 299

Bamboo and Wood in Musical InstrumentsUlrike G.K. Wegst � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 323

Controlled Patterning of Ferroelectric Domains: FundamentalConcepts and ApplicationsDongbo Li and Dawn A. Bonnell � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 351

Crystal Chemistry of Complex Perovskites: New Cation-OrderedDielectric OxidesP.K. Davies, H. Wu, A.Y. Borisevich, I.E. Molodetsky, and L. Farber � � � � � � � � � � � � � � � � � � � 369

Formation and Properties of QuasicrystalsD.V. Louzguine-Luzgin and A. Inoue � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 403

Integral Textile Ceramic StructuresDavid B. Marshall and Brian N. Cox � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 425

Mechanical Behavior of Metallic Glasses: Microscopic Understandingof Strength and DuctilityMingwei Chen � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 445

Recent Developments in Irradiation-Resistant SteelsG.R. Odette, M.J. Alinger, and B.D. Wirth � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 471

Trends in the Development of New Mg AlloysM. Bamberger and G. Dehm � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 505

The Theory and Interpretation of Electron Energy Loss Near-EdgeFine StructurePeter Rez and David A. Muller � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 535

Transmission Electron Microscopy of Multilayer Thin FilmsAmanda K. Petford-Long and Ann N. Chiaramonti � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � � 559

Index

Cumulative Index of Contributing Authors, Volumes 34–38 � � � � � � � � � � � � � � � � � � � � � � � � � � � 585

Errata

An online log of corrections to Annual Review of Materials Research articles may befound at http://matsci.annualreviews.org/errata.shtml

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