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Acta Materialia 59 (2011) 5440–5450

Oxygen permeability in cation-doped polycrystalline aluminaunder oxygen potential gradients at high temperatures

Tsuneaki Matsudaira ⇑, Masashi Wada, Tomohiro Saitoh, Satoshi Kitaoka

Japan Fine Ceramics Center, 2-4-1 Mutsuno, Atsuta-ku, Nagoya 456-8587, Japan

Received 9 July 2010; received in revised form 31 March 2011; accepted 7 May 2011Available online 7 June 2011

Abstract

The oxygen permeability through the grain boundaries of Hf- and/or Lu-doped polycrystalline alumina wafers that were exposed tooxygen potential gradients generated by combinations of different oxygen partial pressures (P O2

) was investigated at temperatures up to1923 K. Hf doping decreased the mobility of Al grain-boundary diffusion from the lower P O2

surface side to the higher P O2surface side to

half that of undoped samples, but did not influence oxygen diffusion through the grain boundaries. Lu doping had the opposite effect. Itis thought that the ability of a dopant to inhibit the mobility of either Al or oxygen would strongly depend on the atomic structuralenvironment in the vicinity of dopant segregated at the grain boundaries. However, the oxygen permeability was increased by co-dopingwith Lu and Hf under all the oxygen potential gradients investigated, although the corresponding power constants were maintained.� 2011 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Alumina; Oxygen permeation; Oxygen potential gradient; Diffusion; Grain boundary

1. Introduction

Alumina-forming alloys are widely used in hot-sectioncomponents such as thermal-barrier coating systems [1].The durability of these components is generally controlledby the barrier’s performance with respect to oxygen perme-ation through the grain boundaries in the polycrystallinealumina scale formed on the alloy surfaces, which areexposed to steep oxygen potential gradients. These alloystypically contain small quantities of oxygen-reactive ele-ments (REs) (e.g., Y, La, and Zr) to improve their oxidationresistance. These REs segregate to grain boundaries ingrowing alumina scales during oxidation of the alloys,which are thought to suppress both inward diffusion of oxy-gen and outward diffusion of Al [2,3]. The obvious difficultyis that it is not known what the diffusing species along thegrain boundaries in the scales might be. Nevertheless, theREs are believed to inhibit scale growth by effectively block-

1359-6454/$36.00 � 2011 Acta Materialia Inc. Published by Elsevier Ltd. All

doi:10.1016/j.actamat.2011.05.018

⇑ Corresponding author. Tel.: +81 52 871 3500; fax: +81 52 871 3599.E-mail address: matsudaira@jfcc.or.jp (T. Matsudaira).

ing the outward grain-boundary diffusion of Al due to anionic-size mismatch, since the ionic sizes of the REs are lar-ger than that of Al3+ [3]. However, it was found that duringlong-duration, high-temperature oxidation, REs that segre-gated to grain boundaries diffused toward the scale surfacestogether with Al, resulting in the precipitation of RE-richparticles on the surfaces [3]. This casts doubt on the conjec-ture that REs will always be able to control the movementof Al. The coexistence of various REs further complicatesthe interpretation of experimental results.

On the other hand, it is well known that the segregationof rare-earth (e.g., Y, Lu, Tm, and Eu) and group IV (Zr,Hf) elements at the grain boundaries of alumina can signif-icantly retard oxygen grain-boundary diffusivity, resultingin suppression of creep deformation, and final-stage sinter-ing under homogeneous environments without any oxygenpotential gradients [4–9]. The retardation of these masstransfers is thought to be related to (i) ionic size of the dop-ing elements, (ii) bond strength between cation and oxygen,(iii) oxygen coordination number of the dopants segregatedat grain boundaries.

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T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450 5441

It has been suggested that in the ionic size effect, thegrain-boundary environment is changed by “site-blocking”

critical oxygen diffusion pathways due to the ionic size mis-match of the large dopants segregated at the grain bound-aries [10–15]. For example, the ionic radii of rare-earth andgroup IV elements with the corresponding ionic valence foran oxygen coordination number of 6 are, respectively, 0.90,0.86, 0.72, and 0.71 A for Y3+, Lu3+, Zr4+, and Hf4+, allmuch larger than the 0.51 A reported in the literature forAl3+ [16]. Therefore, the ionic size effect for rare-earth ele-ments is speculated to be larger than that for group IV ele-ments. Cho et al. [12] have investigated the steady-statecreep rate of various singly doped aluminas from 1473 to1623 K, where larger dopants such as Y, Nd, and La effec-tively decreased the creep rate compared with the smallerdopant, Zr.

With respect to the bond strength effect, Yoshida et al.[5] demonstrated that the creep resistance of polycrystallinealumina can be improved by doping elements that increasethe bonding strength between Al and oxygen near a dopantsubstituted for Al in Al2O3, for which the product of the Aland oxygen net charges decreased in the order Lu- or Y-doped > Zr-doped > undoped alumina, as determined byfirst-principles molecular orbital calculations. On the otherhand, Buban et al. [17] reported for Y as a dopant segre-gated at the R31 grain boundary of an alumina bicrystalthat the increase in the bond strength between Y and oxy-gen toward a more covalent bond was responsible for theimprovement in creep resistance, according to Z-contrastimages obtained by scanning transmission electron micros-copy (STEM) of the bicrystal and charge density maps gen-erated by first-principles ab initio calculations using theVienna Ab Initio Simulation Package (VASP).

Buban et al. [17] pointed out that, in addition to theincrease in bonding strength, the improvement in creepresistance was presumably also related to the increase ofthe oxygen coordination number for Y segregated at thegrain boundaries [17]. In theoretical modeling and STEMenergy-loss near-edge structure (ELNES) studies of a nearR11 grain boundary in a non-doped polycrystalline alu-mina, the oxygen coordination number of some Al wasreported to be reduced to four, compared with six in per-fect Al2O3 [18–20]. This reduction is likely to distort cationarrangements in the grain boundaries. The atomic struc-tural environment of grain boundaries in Y- or Zr-dopedpolycrystalline alumina was investigated through extendedX-ray absorption fine structure (EXAFS) measurements,where the oxygen coordination numbers for Y and Zr seg-regated at the grain boundaries were 4.2 and 5.0, respec-tively [11]. The oxygen coordination numbers for thedopants were evidently higher than that for Al in non-doped alumina. An increase in the oxygen coordinationnumbers of the dopants, namely an increase in the bondnumbers at the grain boundaries, likely retards the masstransfer through the grain boundaries. However, despitethese vigorous investigations, it has remained unclearwhich inhibition parameters, viz., the ionic-size mismatch,

bonding strength and oxygen coordination number, effec-tively controlled the diffusion of Al, oxygen, or both.

We have evaluated the oxygen permeability of undopedand Lu-doped polycrystalline alumina wafers, which wereexposed to oxygen potential gradients (DP O2

) at high tem-peratures, with each surface of the wafer deliberately sub-jected to different oxygen partial pressures (P O2

) [21–24].The main diffusion species during oxygen permeationthrough the alumina grain boundaries were found todepend on the P O2

that created the oxygen potential gradi-ents. Under a DP O2

generated by low P O2values, where

oxygen permeation occurred by oxygen diffusion fromregions of higher to lower P O2

, segregated Lu at the grainboundaries suppressed only the mobility of oxygen in thewafers, owing to a reduction in the effective area of grainboundary diffusion, without affecting the oxygen perme-ation mechanism. By contrast, under oxygen potential gra-dients generated by high P O2

values, where oxygenpermeation proceeded by Al diffusion from regions oflower to higher P O2

, Lu had little effect on Al diffusionand migrated with Al, resulting in precipitation and growthof Al5Lu3O12 particles on the higher P O2

surface [24]. Theeffective retardation of the oxygen grain boundary diffusiv-ity by Lu-doping is thought to be caused by grain-bound-ary strengthening due to the bonding strength between Aland oxygen and by site-blocking due to the ionic-size mis-match. The influence of Lu-doping on the diffusion of Alalong the grain boundaries was small, presumably becauseof the generation of a large number of Al vacancies at thegrain boundaries under DP O2

, which may reduce such inhi-bition parameter effects. Furthermore, because Al vacancyformation decreases the oxygen coordination number of Alnear the grain boundaries, the Al grain boundary diffusiv-ity is thought to be strongly affected by the change in theoxygen coordination number of Al. To date, there havebeen no theoretical or experimental reports on the oxygencoordination number of Lu segregated at the grain bound-aries. However, Lu belongs to the same homologous seriesin the periodic table as Y. The core levels of Lu3+ are com-pletely filled with electrons like those of Y3+, and their cat-ionic radii are comparable. The excess doping of thesecations into alumina leads to the precipitation of complexoxides with a garnet structure at high temperatures. Thus,it is believed that the characteristics of grain boundarieswith segregated Lu would be similar to those of grainboundaries with segregated Y, and the oxygen coordina-tion number of Lu at the grain boundaries may be slightlylarger than those of Al.

The mass transfer behavior through grain boundaries inalumina was systematically investigated using four types ofalumina bicrystal wafers at high temperatures [25]. In thebicrystal wafers, which were exposed to a constant DP O2

,Al mainly diffused through the single grain boundary,resulting in the growth of a grain boundary ridge on thesurface exposed at the higher P O2

side due to alumina for-mation. The grain boundary diffusion coefficients of Alestimated from the volume of the grain boundary ridges

5442 T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450

showed a clear correlation to the local bonding environ-ments of grain boundary cores estimated from the staticlattice calculations reported previously. The Al grainboundary diffusion coefficients tended to be proportionalto the mean bond lengths between Al and oxygen nearthe grain boundary. The decrease in the mean bond lengthseems to be related to the increase in the oxygen coordina-tion number of Al in the grain boundary core region.Therefore, the grain boundary segregation of dopants thathave obviously larger oxygen coordination numbers at thegrain boundaries than that of Al may effectively retard theAl grain boundary diffusivity.

There has been no investigation into the oxygen coordi-nation number of Hf, which belongs to the same period asLu, segregated at the grain boundaries. But it is well knownthat the ionic radius of Hf and its chemical properties arevery similar to those of Zr, in the same homologous series,so that their bonding strengths and oxygen coordinationnumbers are thought to be the same. Thus if, as speculated,the oxygen coordination number of Hf at the grain bound-aries is larger than that of Lu, Hf-doping may inhibit theAl grain boundary diffusion.

In this study, the effects of Hf doping or co-doping of Luand Hf on oxygen permeability in polycrystalline aluminawafers exposed to steep DP O2

were evaluated at high tem-peratures to investigate the mass transfer behavior throughthe wafers, in comparison with data for non-doped [23] andLu-doped polycrystalline alumina wafers [24]. The role ofdopants in suppressing the grain-boundary diffusion ofAl and oxygen in polycrystalline alumina was elucidatedwith respect to grain-boundary strengthening due to theincrease in bonding strength and oxygen coordinationnumber and site blocking due to the ionic-size mismatch.

2. Experimental

2.1. Materials

Commercial, high-purity alumina powder (TM-DAR,Taimei Chemicals Co. Ltd., Nagano, Japan, purity>99.99 wt.%) was used as non-doped alumina. Hf-dopedpowders were prepared by mixing the alumina powder withan aqueous solution of hafnium oxychloride(Hf(OCl)2xH2O (>99.99 wt.%), Sigma–Aldrich Co., MO,USA) containing 0.2 mol.% HfO2 per AlO1.5, and subse-quent drying to remove the water. In addition, Co-dopedpowders were prepared that contained 0.1 mol.% LuO1.5–0.1 mol.% HfO2 per AlO1.5. Lutetium nitrate hydrate(Lu(NO)3xH2O (>99.999 wt.%), Sigma–Aldrich Co., MO,USA) was used as a Lu source. Each powder was moldedin a uniaxial press at 20 MPa, and then subjected to coldisostatic pressing at 600 MPa. The green compacts werepressureless sintered in air at 1773 K for 5 h. Wafers23.5 mm in diameter � 0.25 mm in thickness were cut fromthe sintered bodies, and their surfaces polished to a mirror-like finish. The relative density of the wafers was 99.5% ofthe theoretical density. The average grain sizes of all the

alumina wafers except the co-doped wafer were about10 lm; that of the co-doped wafer was slightly larger(12 lm).

2.2. Oxygen permeability constants

The method used to measure the oxygen permeabilityconstants has been described in detail elsewhere [23]. Eachwafer was placed between two alumina tubes in a furnace,using Pt gaskets to create a seal between the wafer and thetubes. The P O2

, included as an impurity in the Ar gas, wasmonitored at the outlets of the upper and lower chambersthat enclosed the wafer and the alumina tubes, using a zir-conia oxygen sensor at 973 K. The partial pressures ofwater vapor (P H2O) and H2 (P H2

), which were also impuri-ties in the Ar gas, were measured at room temperatureusing an optical dew point sensor and gas chromatography,respectively. A gas-tight seal was achieved in both cham-bers by heating to 1893–1923 K. Subsequently, the mea-sured P O2

, P H2O, and P H2were regarded as backgrounds.

Pure O2 gas or Ar gas containing either 1–10 vol.% O2 or0.01–1 vol.% H2 was introduced into the upper chamberat a flow rate of 1.67 � 10�6 m3 s�1. A constant flux of oxy-gen permeation was judged to be achieved when the mon-itored values of P O2

, P H2O, and P H2at the outlets became

constant. The P O2in each chamber at high testing temper-

ature, with the wafer exposed to an oxygen potential gradi-ent DP O2

, was calculated thermodynamically from the P O2

measured at 973 K, or from the P H2O and P H2measured

at room temperature. The oxygen permeation of the waferswas evaluated at temperatures up to 1923 K. Since oxygenpermeation was detected for all polycrystalline wafers butnot for a single-crystal wafer [21–24], it was considered tooccur preferentially along the grain boundaries. Thus, theoxygen permeation strongly depended on the grain-bound-ary density Sgb (hence, on the grain size) of the wafers.Therefore, oxygen permeability constants normalized bySgb were calculated using the equation

PLSgb

¼ Cp � Q � LV st � S � Sgb

ð1Þ

where P is the oxygen permeability, L is the wafer thick-ness, Cp is the concentration of permeated oxygen (P O2

/PT, where PT = total pressure), Q is the flow rate of the testgases, Vst is the standard molar volume of an ideal gas, andS is the permeation area of the wafer. Sgb values weredetermined by image analysis of scanning electron micros-copy (SEM) microstructures on the wafer surfaces after theoxygen permeation tests. The wafer samples that were ex-posed to Ar at 1923 K for 3 h, namely, just before beingsubjected to DP O2

, were examined by X-ray diffraction(XRD), SEM, and STEM combined with energy dispersivespectroscopy (EDS).

The grain-boundary diffusion coefficients of Al andoxygen in the doped wafers were calculated from the rela-tionship between oxygen permeability constants deter-mined experimentally and the corresponding flux, using

(a) 0.2%LuO1.5

10μmμ

(b) 0.2%HfO2

10μm10μm

(c) 0.1%LuO1.5 0.1%HfO2

T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450 5443

calculation procedures that have been described elsewhere[21–24].

3. Results and discussion

3.1. Oxygen permeation

Fig. 1 shows XRD patterns of the surfaces of the dopedwafer samples exposed to 1923 K for 3 h in Ar, just beforebeing subjected to DP O2

. There is the alpha-Al2O3 phase aswell as crystalline phases containing the dopants, identifiedas Al5Lu3O12 (LAG), monoclinic-HfO2 (m-HfO2), andcubic-HfO2 (c-HfO2) and LAG for the Lu-doped, Hf-doped, and co-doped samples, respectively.

Fig. 2 shows SEM micrographs of the surfaces of thedoped wafer samples exposed to 1923 K for 3 h under Aratmosphere. The average grain sizes of the Lu-doped andHf-doped samples were about 10 lm, whereas that of theco-doped sample was slightly larger. In the Lu-doped sam-ples shown in Fig. 2a, there are white particles almost seg-regated at the grain boundaries. In the case of the Hf-doped samples in Fig. 2b, there are white particles smallerthan those in Fig. 2a, mainly at the grain boundaries, butto some extent also in the alumina grains. In accordancewith the XRD patterns in Fig. 1a and b, the particles inFig. 2a and b are identified as LAG and m-HfO2, respec-tively. For the co-doped samples in Fig. 2c, the white par-

Al O m HfO(a) 0.2%LuO1.5

α-Al2O3Al5Lu3O12

m-HfO2c-HfO25 3 12

(b) 0 2%HfO(b) 0.2%HfO2

(c) 0.1%LuO1 5 - 0.1%HfO2( ) 1.5 2

20 30 40 50 6 0

2θ (deg.)

Fig. 1. XRD patterns of polycrystalline alumina doped with (a) 0.2%LuO1.5, (b) 0.2% HfO2, and (c) 0.1% LuO1.5–0.1% HfO2, exposed to1923 K for 3 h in Ar.

10μm10μm

Fig. 2. SEM micrographs of the surfaces of polycrystalline alumina dopedwith (a) 0.2% LuO1.5, (b) 0.2% HfO2, and (c) 0.1% LuO1.5–0.1% HfO2,exposed to 1923 K for 3 h in Ar.

ticles that are mainly segregated at the grain boundaries arelarger than those observed in the single-element-dopedsamples.

Fig. 3 shows the STEM image and corresponding EDSmaps for Lu and Hf around the segregated particles inthe co-doped sample, pertaining to the magnified imagein Fig. 2c. The large particle with a size of a few lm is iden-tified as LAG because the only signal detected from it isattributed to Lu. By contrast, the submicron-sized particlesdispersed at the grain boundaries and in the grain interiorsare attributed to c-HfO2, where strong signals due to Hf aredetected in addition to the weak Lu signal. The chemicalcomposition of the c-HfO2 particles, as determined bySTEM-EDS, revealed that the particles contained about30 mol.% LuO1.5, which would have resulted in the forma-tion of a large amount of oxygen vacancies. The brightness

(a)(a)Al5Lu3O12

c-HfO2

1μm

1μm

1μm

Lu(b)(b)

Hf(c)

Fig. 3. STEM image and EDS maps of polycrystalline alumina dopedwith 0.1% LuO1.5–0.1% HfO2, exposed to 1923 K for 3 h in Ar: (a) STEMimage, (b) Lu map, and (c) Hf map.

5444 T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450

of the EDS maps shown in Fig. 3b and c were adjusted toenhance the difference in chemical composition of the par-ticles in Fig. 3a, and so it is difficult to show simultaneouslythe tiny amount of dopant segregated at the grain bound-aries. Fig. 4 shows the STEM image and EDS maps nearthe alumina grain boundaries of the doped samples, corre-sponding to the magnified images in Figs. 2 and 3. Thedoping elements are also segregated along the grain bound-aries of all the samples without an amorphous layer.

Fig. 5 shows the effect of the steady-state P O2in the

upper chamber on the oxygen permeability constants ofpolycrystalline alumina (Hf-doped and co-doped with Luand Hf) at 1923 K, compared with non-doped [23] andLu-doped [24] alumina containing the same molar ratioof Lu as in the Hf-doped sample. P O2

in the lower chamberwas held constant, at approximately 1 Pa. Error bars wereomitted because the standard deviations were smaller thanthe symbol size.

When DP O2is formed by combinations of a P O2

valuebelow 10�3 Pa and a P O2

value of about 1 Pa, the oxygenpermeability constants decrease with increasing P O2

forall alumina wafers. The oxygen permeability constantsfor Hf-doped alumina are comparable to those for thenon-doped wafer, but those for Lu-doped alumina areabout three times lower than those for the other aluminawafers. However, co-doping with Lu and Hf increases theconstants, compared with those of non-doped and Hf-doped alumina. Under DP O2

values below 10�3 Pa, allcurve slopes correspond to similar values to a power con-stant of n = �1/6, which is applicable to the defect reactiongiven in Eq. (2) on the higher-P O2

(P O2(II)) surface; and the

reverse reaction proceeds on the opposite, lower-P O2

(P O2(I)) surface (P O2

(II)� P O2(I)).

1=2O2 þ V��O þ 2e0 ! OXO ð2Þ

Oxygen permeation is thought to occur mainly by grain-boundary diffusion of oxygen from the P O2

(II) surface sideto the P O2

(I) surface side through oxygen vacancies [22–24],which are thought to be induced as new defects in the vicin-ity of the grain boundaries by subjecting the wafer to DP O2

.Under DP O2

generated by combinations of a high P O2

(>103 Pa) and a P O2of about 1 Pa, the oxygen permeability

constants increase with increasing P O2for all wafers.

Although Hf doping halves the oxygen permeability con-stants relative to the non-doped and Lu-doped cases, co-doping with Lu and Hf increases them. All the slopes underhigh P O2

values (>103 Pa) are comparable to each otherand correspond to a power constant of n = 3/16, suggestingthat the defect reaction given in Eq. (3) progresses on thehigher-P O2

(II) surface side, while the reverse reactionoccurs on the lower-P O2

(I) surface side.

1=2O2 ! OXO þ 2=3V000Al þ 2h� ð3Þ

O2 molecules seem to permeate mainly by grain-bound-ary diffusion of Al from the P O2

(I) to the P O2(II) surface

side through Al vacancies, which are also believed to beproduced preferentially in the vicinity of grain boundariesby DP O2

[22–24].Thus, Hf doping does not influence oxygen diffusion

along grain boundaries, but does decrease Al grain-bound-ary diffusion. Lu doping has the opposite effect [24]. Thissuggests that the mass transfer suppressing mechanismsin polycrystalline alumina wafers are completely differentfor Hf doping than for Lu doping. However, co-dopingwith Lu and Hf accelerates grain-boundary diffusion ofboth oxygen and Al.

Fig. 6 shows surface and cross-sectional SEM micro-graphs of polycrystalline alumina subjected to 1923 K for4 h under a DP O2

with P O2(II)/P O2

(I) = 1 Pa/10�8 Pa.Fig. 7 shows top-view SEM images of the surfaces corre-sponding to Fig. 6. Shallow grain-boundary grooves, simi-lar to those produced by conventional thermal etching, areobserved on both surfaces of all the wafers.

There are, as seen in Fig. 7, dopant-containing particles,such as LAG, m-HfO2 and c-HfO2, dispersed on both

0.2%LuO1 5 0.2%HfO2 0.1%LuO1 5 21.5 2 1.5 2

500nm 500nm 500nm

Lu Hf Lu HfLu Lu

500nm 500nm 500nm 500nm

Fig. 4. STEM image and EDS maps from near the alumina grain boundaries of the samples doped with 0.2% LuO1.5, 0.2% HfO2, and 0.1% LuO1.5–0.1%HfO2, exposed to 1923 K for 3 h in Ar.

Additives, Non-doped [23], 0.2%LuO1.5 [24] , 0.2%HfO2

, 0.1%LuO1.5 -0.1%HfO2

n = 3/16

n = -1/6

10 -14

10 -17

10 -16

10 -15

10 -5 10 -3 10 -1 101 103 10710-7 10510-9

P in the upper chamber (Pa)O2

/s)

mol

S gb

(L

/ SPL

Fig. 5. Effect of P O2in the upper chamber on the oxygen permeability

constants of polycrystalline alumina (non-doped, doped with 0.2% LuO1.5,0.2% HfO2, and 0.1% LuO1.5–0.1% HfO2) at 1923 K.

T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450 5445

surfaces in the same manner as those present just beforeexposure to DP O2

(see Fig. 2). Thus, the degree of disper-

Cross-section

Surface

Cross-section

Surface

Surface

Cross-section Cross-section

Surface

P (

II)

side

O2

P (

I) si

deO

2

0.2%LuO1.5 0.2%

Fig. 6. SEM micrographs of the two surfaces and cross-sections of polycrystalHfO2, exposed to 1923 K for 4 h under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa.

sion was maintained during exposure of the wafers.Because oxygen molecules permeate mainly by grain-boundary diffusion of oxygen in wafers under DP O2

withlow P O2

values from the higher- to lower-P O2surface side,

and not by participation of grain-boundary migration ofAl in the opposite direction, doped cations composed ofthose particles and segregated at the grain boundaries arethought to be as unlikely to migrate toward the higher-P O2

surface side as the Al in all the samples.Under DP O2

values below 10�3 Pa, because the powerconstants of all samples corresponded to n = �1/6 asshown in Fig. 5, doping with Hf and/or Lu did not affectthe oxygen permeation mechanism. Lu-doping could onlysuppress the oxygen diffusivity at the grain boundaries,whereas Hf-doping had no effect at all. Thus, the oxygendiffusivity would be effectively inhibited by the grain-boundary strengthening due to the bonding strengthbetween Al and oxygen and by site-blocking due to theionic-size mismatch [4–15,17] rather than the oxygen coor-

Cross-section

Surface

Al5Lu3O12

c-HfO2

Cross-section

Surface

5μm

Al5Lu3O12

c-HfO2

HfO2 0.1%LuO1.5 - 0.1%HfO2

line alumina doped with 0.2% LuO1.5, 0.2% HfO2, and 0.1% LuO1.5–0.1%

Al5Lu3O12 m-HfO2 Al5Lu3O12

c-HfO2

Al5Lu3O12

Al5Lu3O12

c-HfO2

10μm

m-HfO2

P (

II)

side

O2

P (

I ) si

deO

2

0.2%LuO1.5 0.2%HfO2 0.1%LuO1.5 - 0.1%HfO2

Fig. 7. SEM micrographs of the two surfaces of polycrystalline alumina, doped with 0.2% LuO1.5, 0.2% HfO2, and 0.1% LuO1.5–0.1% HfO2, exposed to1923 K for 4 h under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa.

5446 T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450

dination number of the dopants segregated at the grainboundaries. The reduction in the effective area for oxygengrain-boundary diffusion due to these factors, namely thedecrease in the number of diffusion paths that maintaineda length corresponding to the wafer thickness, is thoughtto be responsible for the retardation of oxygen diffusivity.

By contrast, far from inhibiting the oxygen permeation,co-doping with Lu and Hf accelerated it. As mentionedabove, the c-HfO2 particles at the grain boundaries in theco-doped sample contained about 30 mol.% of LuO1.5, sothat the amount of the remaining LuO1.5 was�0.07 mol.%, a part of which was segregated at the grainboundaries whereas the remainder was incorporated intoLAG particles. The residue was approximately0.05 mol.% LuO1.5, where the oxygen permeation couldnot be inhibited [24]. Since DP O2

through the wafer seemsto result in the formation of new defects such as oxygenvacancies for lower P O2

values near the grain boundaries,the retardation under DP O2

was presumably small com-pared to that for creep deformation and final-stage sinter-ing under uniform environments [24]. Therefore, thedecrease in the effective amount of Lu due to the formationof a solid solution in the HfO2 particles segregated at thegrain boundaries is thought to make it difficult to suppressoxygen permeation by co-doping.

Because a large number of oxygen vacancies was pro-duced in c-HfO2 by the solid solution of Lu, the oxygenshould readily diffuse through the vacancies in the c-HfO2 particles. For example, it was reported that the oxy-gen permeability constant of cubic-ZrO2 (c-ZrO2) with17 mol.% YO1.5 at 1873 K was 104 times larger than thatof non-doped polycrystalline alumina [21,26]. The oxygenpermeability of c-HfO2 is likely to be very large, as in thecase of c-ZrO2, given their similar ionic radii and chemicalproperties. Thus, the oxygen diffusivity in the c-HfO2 par-ticles segregated at the grain boundaries is thought to be alot higher than that through the alumina grain boundaries.In other words, the total distance of oxygen diffusionthrough the grain boundaries in the alumina wafer is

believed to be decreased by the sum of sections correspond-ing to the c-HfO2 particles segregated at the grain bound-aries. As shown in Fig. 5, the oxygen permeabilityconstant of the co-doped sample under 1 Pa/10�8 Pa at1923 K was 1.5 � 10�15 mol s�1, which was 1.5 times largerthan that of the non-doped sample under the same condi-tions. When it is assumed that all the Hf dopant of0.1 mol.% exists as spherical particles of c-HfO2 with thesame diameter only at the grain boundaries in the co-dopedsample and the diffusion distance of oxygen is shortened bythe sum of the diameters of the particles, the diameter ofthe c-HfO2 particles corresponding to the increase in oxy-gen permeability constant can be estimated. This calculateddiameter is about 0.8 lm. When half (0.05 mol.%) of the c-HfO2 particles are segregated at the grain boundaries, thecorresponding diameter is about 0.6 lm. These diameterestimates are comparable to that of the c-HfO2 particlesobserved in Figs. 2c and 3. This suggests the validity ofthe above model where the oxygen diffusivity is increasedby the grain boundary segregation of c-HfO2 particles.

Fig. 8 shows surface and cross-sectional SEM micro-graphs of non-doped polycrystalline alumina exposed to1923 K for 4 h under a DP O2

with P O2(II)/P O2

(I) = 105 Pa/1 Pa, where oxygen permeability was governed by grain-boundary diffusion of Al. In the Lu-doped sample, grain-boundary ridges are clearly visible on the P O2

(II) surface,while deep crevices were formed along the grain boundarieson the P O2

(I) surface, similar to those formed in non-dopedsamples [23,24]. There are fewer ridges and crevices in theHf-doped and co-doped samples than in the Lu-dopedsample.

Fig. 9 shows top-view SEM images of the surfaces cor-responding to Fig. 8. In the case of the Lu-doped sample,there are LAG particles on the P O2

(II) surface and the par-ticles are clearly larger than those observed on the surfaceexposed under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa shown in

Fig. 7. These particles are completely dispersed on theP O2

(I) surface. Thus, Lu must migrate with Al from theP O2

(I) to the P O2(II) surface side, resulting in the formation

Cross-section

Surface

Al5Lu3O12

c-HfO2

Surface

Cross-section

Surface

Cross-section 5μm

Surface

Cross-section

Surface

Cross-section

Surface

Cross-section

Al5Lu3O12

P (

II)

side

O2

P (

I) si

deO

2

0.2%LuO1.5 0.2%HfO2 0.1%LuO1.5 - 0.1%HfO2

Fig. 8. SEM micrographs of the two surfaces and cross-sections of polycrystalline alumina, doped with 0.2% LuO1.5, 0.2% HfO2, and 0.1% LuO1.5–0.1%HfO2, exposed to 1923 K for 4 h under P O2

(II)/P O2(I) = 105 Pa/1 Pa.

Al5Lu3O12 m-HfO2

Al5Lu3O12

c-HfO2

m-HfO2

P (

II)

side

O2

P (

I) si

deO

2

10μm

0.2%LuO1.5 0.2%HfO2 0.1%LuO1.5 - 0.1%HfO2

Fig. 9. SEM micrographs of the two surfaces of polycrystalline alumina, doped with 0.2% LuO1.5, 0.2% HfO2 and 0.1% LuO1.5–0.1% HfO2, exposed to1923 K for 4 h under P O2

(II)/P O2(I) = 105 Pa/1 Pa.

T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450 5447

of grain-boundary ridges and precipitation and growth ofparticles on the P O2

(II) surface side. By contrast, in the caseof Hf-doped alumina, there are m-HfO2 particles dispersedon both surfaces, and the degree of dispersion is main-tained during exposure under DP O2

. Therefore, doped Hfclearly migrated much less than doped Lu. For the co-doped sample, there are many more LAG and c-HfO2 par-ticles at the grain boundaries on the P O2

(II) surface than onthe surface exposed under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa,

as shown in Fig. 7, while no particles are found on theopposite surface. Co-doping accelerates the grain-bound-ary diffusion of Hf in addition to Lu.

Under DP O2values above 103 Pa, where Al mainly dif-

fused at the grain boundaries, because the power constantsof the all samples corresponded to n = 3/16 as shown inFig. 5, doping with Hf and/or Lu did not affect the oxygenpermeation mechanism similarly to the case of lower P O2

,where oxygen mainly diffused at the grain boundaries.The Al diffusivity was not affected by Lu-doping, andwas retarded only by Hf-doping. Thus, the Al diffusivitywould be effectively suppressed by increasing oxygen coor-

dination number of the dopants segregated at the grainboundaries, rather than the bonding strength between Aland oxygen and by site-blocking due to ionic-size mismatch[4–15,17].

However, oxygen permeation was accelerated by co-doping with Lu and Hf. As shown in Fig. 4, both Lu andHf were segregated at the same grain boundaries, whosecharacteristics were presumably significantly different fromthose induced by each dopant alone. The contiguity withLu and Hf through oxygen at the grain boundaries mightdecrease the oxygen coordination number of the cations,resulting in the precipitation and growth of many LAGand c-HfO2 particles owing to the increase in diffusivityof both Al and the dopants, as shown in Fig. 9.

The grain boundary ridges formed on the P O2(II) surface

of the co-doped sample were not clear compared with thoseof the Lu-doped sample (see Fig. 8) despite the increase inoxygen permeation. Because the oxygen diffusivity in thec-HfO2 particles segregated at the grain boundaries ispresumably very much higher than that through the grainboundaries, the oxygen permeability data may contain

5448 T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450

the contribution of oxygen diffusion in addition to the cat-ion diffusion.

3.2. Grain-boundary diffusion of oxygen and Al

The grain-boundary diffusion coefficients of oxygen andAl (Dgbd) were estimated from the oxygen permeabilityconstants shown in Fig. 5, assuming that the flux of oxygenpermeating through the wafer was due to a single species(oxygen or Al), using the procedure described in Refs.[19,20]. Because the oxygen vacancies, which are intro-duced by the formation of c-HfO2 particles segregated atthe grain boundaries, will affect, but not predominate thepermeation behavior in co-doped alumina, calculations ofDgbd for co-doped alumina are omitted to reveal the effecton grain-boundary diffusion of oxygen and Al of newdefects induced solely by DP O2

.Fig. 10 shows the Dgbd for oxygen and Al in Hf-doped

polycrystalline alumina as a function of the equilibriumpartial pressure of oxygen in the upper chamber at1923 K in comparison with non-doped [23] and Lu-dopedsamples [24]. Fig. 6 also shows data on oxygen diffusioncoefficients taken from the literature [6,7,27]. These weredetermined by using either secondary ion mass spectros-copy (SIMS) [6,7] or nuclear reaction analysis (NRA) [27]to obtain 18O isotopic tracer depth profiles for bicrystalline(R31) or polycrystalline alumina annealed in homogeneousenvironments containing 18O-enriched oxygen, in theabsence of any DP O2

. Actual grain boundaries in polycrys-talline alumina can be classified as being general bound-aries with high R values, as in the case of a bicrystal,according to coincidence site lattice theory.

The data for Refs. [6,7,27] are estimated by extrapolat-ing to 1923 K and the P O2

values in the abscissa correspondto the data in the annealing environments. The Dgbd valuefor oxygen decreased with increasing P O2

, whereas the

10-19

10-20

)

10 -21 s-1m

3

10

δδ(

-22

Dgb

δ

Additive Diffusion speciesO Al

10-23 O Al

Non-doped [23]

0.2%LuO1.5 [24]

0 2%HfO

10-24 0.2%HfO2

10-5 10-3 10-1 10 1 10 3 10 710-7 10 510-9

P in the upper chamber (Pa)O2

Non-doped polycrystal [6]

Non-dopedbicrystal [7]

Non-doped polycrystal [27]

Y-doped polycrystal [6] Y-doped

bicrystal [7]

Fig. 10. Dgbd of oxygen and Al in polycrystalline alumina (non-doped,doped with 0.2% LuO1.5, and 0.2% HfO2) as a function of the equilibriumpartial pressure of oxygen in the upper chamber at 1923 K. The solid andopen symbols indicate the Dgbd of oxygen and Al, respectively. Theliterature data obtained by isotopic tracer profiling are shown as well[6,7,24].

value for Al increased for both non-doped and doped alu-mina. For the Hf-doped sample, under the DP O2

generatedby combinations of P O2

(I) values below 10�3 Pa and P O2(II)

values of about 1 Pa, the Dgbd and the corresponding slopefor oxygen are comparable to those for the non-dopedsample. But, under DP O2

conditions induced by combina-tions of P O2

(II) values below 105 Pa and P O2(I) values of

about 1 Pa, the Dgbd of Al are one-half of those of thenon-doped case and their slopes are almost constant. Thus,Hf retards the mobility of Al, but hardly affects the masstransfer of oxygen. Lu doping has the opposite effect, asshown in Fig. 10 and reported in the literature [24]. It isnoteworthy that the role of Hf as dopant on the grain-boundary diffusion of oxygen and Al is distinct from thatof Lu.

Therefore, the mobility of oxygen is considered to beeffectively reduced by grain-boundary strengthening dueto the bonding strength between Al and oxygen and bysite-blocking due to the ionic-size mismatch [4–15,17],rather than grain-boundary strengthening due to theincrease in oxygen coordination number of cations segre-gated at the grain boundaries. By contrast, the mobilityof Al is believed to be retarded by the latter factor.

For non-doped alumina, the line extrapolated to higherP O2

for the Dgbd of oxygen is consistent with previouslyreported data determined using SIMS [6,7], but deviateswidely from using NRA. As discussed in Refs. [23,24], ther-mal equilibrium amounts of defects such as Schottky pairs[28] or Frenkel pairs [27] are expected to be preferentiallyinduced in the vicinity of the grain boundaries in aluminaheld in uniform environments at high temperatures. TheDP O2

through the wafer appears to result in the formationof new defects such as oxygen vacancies for lower P O2

ranges and Al vacancies for higher P O2ranges, in addition

to the thermally-induced defects. Because diffusion coeffi-cients of elements constituting the oxide medium are gener-ally proportional to the concentration of their respectivevacancies, the extrapolated line for the Dgbd of oxygen inFig. 10 may correspond to the SIMS data [6,7], wherethe concentration of oxygen vacancies induced by the oxy-gen potential gradient at higher P O2

values is asymptotic totheir concentration under thermal equilibrium. Neverthe-less, the reason why the NRA result deviates so signifi-cantly cannot be ascertained on the basis of thedescriptions given in Ref. [27].

Fig. 11 shows Arrhenius plots of Dgbd for oxygen inpolycrystalline alumina, where the Dgbd data were deter-mined from the temperature dependence of oxygen perme-ability constants under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa and

1 Pa/10�4 Pa, together with data from the literature[6,7,27,29]. Previously obtained data for oxygen [6,7,27],with the exception of those in Ref. [29], were determinedfor non-doped and Y-doped alumina annealed in homoge-neous, high-P O2

environments without DP O2values. The

data from Ref. [29] were obtained from polycrystallinealumina scales formed during oxidation of Fe–Cr–Al alloysin an O2 atmosphere, where Imphy and ODS-MA956 in

Temperature (K)1800 1700 1600 1500 1400 130019002000

10-19 O OP (II) / P (I) (Pa/Pa)

)

O2 O2AdditiveP (II) / P (I) (Pa/Pa)10 0 / 10 – 8 10 0 / 10 – 4

N d d [23]10-21

s–

1 Non-doped [23]

0.2%LuO1.5 [24]

m3 0.2%HfO2

10-23 n (

Non-doped yge

Polycrystal [27]

S l (I h10-25 ox

Non-dopedNon-doped polycrystal [6]

Scale (Imphy, Zr-doped) [29]δ

of

Non dopedBicrystal [7]

polycrystal [6]

10 -27 Dgb

δD

Y-doped Bicrystal [7]Y-doped

l t l [6] Scale (ODS-MA956,Y-doped) [29]

10-29

polycrystal [6]

5.0 5.5 6.0 6.5 7.0 7.5 8.0

T 1 (10 4 K 1)

Fig. 11. Arrhenius plots of Dgbd for oxygen in polycrystalline alumina,where the Dgbd data were determined from the temperature dependence ofthe oxygen permeability constants under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa

and 1 Pa/10�4 Pa, together with data from the literature [6,7,24,26].

T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450 5449

Fig. 11 were Fe–Cr–Al alloys doped with Zr and Y, respec-tively. Therefore, these alumina scales were subjected tosteep DP O2

conditions, and the dopant ions were presum-ably segregated at the grain boundaries in the scales [3].Table 1 summarizes the Arrhenius parameters D0 and Qfor grain-boundary diffusion in alumina.

The Dgbd values of oxygen determined from oxygen per-meation through alumina wafers increase with increasingtemperature, such that they are proportional to T�1. TheDgbd values for the Hf-doped alumina are almost the sameas those for non-doped alumina and can be decreased onlyby Lu single doping. The Dgbd values of oxygen calculatedfrom the oxygen permeability constants tend to be largerthan those given in other reports, including the extrapolateddata. The larger the DP O2

value induced by a combinationof P O2

(II) and P O2(I) through the wafer is, the smaller the

Table 1Arrhenius parameters, D0 and Q, for grain-boundary diffusion in polycrystalli

Diffusional species Sample Method

Oxygen

Kitaoka et al. [23] Non-doped polycrystal OxygenMatsudaira et al. [24] 0.2%LuO1.5 doped polycrystalThis work 0.2%HfO2 doped polycrystalThis work Non-doped polycrystal Oxygen

0.2%LuO1.5 doped polycrystal0.2%HfO2 doped polycrystal

Plot et al. [6] Non-doped polycrystal IsotopicY-doped polycrystal

Heuer [27] Non-doped polycrystal IsotopicNakagawa et al. [7] Non-doped bicrystal Isotopic

Y-doped bicrystalMessaoudi et al. [29] Oxide scale of ODS-MA956 (Zr-doped) Isotopic

Oxide scale of Imphy (Y-doped)

Aluminum

Kitaoka et al. [23] Non-doped polycrystal OxygenMatsudaira et al. [24] 0.2%LuO1.5 doped polycrystalThis work 0.2%HfO2 doped polycrystal

corresponding activation energy is, smaller even than thepreviously obtained values for annealing in homogeneous,high-P O2

environments [6,7,27], as listed in Table 1. Rather,the activation energies determined from oxygen permeationare comparable to those for the scales. Because the increaseof DP O2

should accelerate the formation of oxygen vacan-cies near the grain boundaries, the barrier to the grain-boundary diffusion of oxygen may decrease, resulting inlower activation energies, as shown in Fig. 10. The extrap-olated lines of Dgbd under P O2

(II)/P O2(I) = 1 Pa/10�8 Pa

are much higher than those for the scales [29]. The Dgbd val-ues for the scales were determined from 18O depth profilesfrom the scale surface to a depth of about 250 nm in alu-mina scales with a thickness of a few lm, and likely corre-spond to the data for small DP O2

consisting of high P O2

values, where there is a small number of oxygen vacancies.On the other hand, since the extrapolated lines correspondto those for large DP O2

produced by low P O2values, these

lines might be higher than the scale data in accordance withthe relationship shown in Fig. 10.

The line for oxygen Dgbd in ODS-MA956 (Y-doped) rep-resents lower values than Imphy (Zr-doped). Although careshould be taken in comparing Dgbd values for two kinds ofscales formed on Fe–Cr–Al alloys of different compositions,Y doping tends to retard oxygen grain-boundary diffusionmore effectively than does Zr doping. In this study, it wasfound that Lu doping effectively suppressed the mobility ofoxygen grain-boundary diffusion, while Hf doping had noeffect on oxygen diffusion. As mentioned, Lu and Hf proba-bly have similar characteristics to Y and Zr, respectively.Thus, the retardation effects of Lu doping and Hf dopingon oxygen diffusion in alumina wafers may correspond tothose obtained from the scales formed on the alloys.

Fig. 12 shows Arrhenius plots of Dgbd for Al in poly-crystalline alumina, where the Dgbd data were determinedfrom the temperature dependence of the oxygen permeabil-ity constants under P O2

(II)/P O2(I) = 105 Pa/1 Pa. The Dgbd

ne alumina (Dgbd = D0exp(�Q/RT)).

D0 (m3 s�1) Q (kJ mol�1)

permeation P O2(II)/P O2

(I) = 1 Pa/10�8 Pa 4.0 � 10�10 3953.9 � 10�11 3721.2 � 10�10 380

permeation P O2(II)/P O2

(I) = 1 Pa/10�4 Pa 1.5 � 10�7 5062.2 � 10�7 5262.1 � 10�7 515

tracer (SIMS) 1.6 � 103 9217.0 � 10�3 800

tracer (NRA) 5.5 � 101 825tracer (SIMS) 8.4 � 10�6 627

6.5 � 10�4 729tracer (SIMS) 2.1 � 10�13 391

5.3 � 10�7 505

permeation P O2(II)/P O2

(I) = 105 Pa/1 Pa 2.8 � 10�4 6116.9 � 10�5 5901.2 � 10�5 601

Temperature (K)

10-192000 1950 1900 1850 1800 1750

-1)

O2 O2Additive P (II) / P (I) (Pa/Pa)10 5 / 10 0

3s

10 / 10Non-doped [23]0 2%L O [24]

(m3

0.2%LuO1.5 [24]0.2%HfO2

10-20

um

min

ual

um

10-21 of

bδδ

Dg

10-22

5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8

T -1 (10- 4 K-1)

Fig. 12. Arrhenius plots of Dgbd for Al in polycrystalline alumina, wherethe Dgbd data were determined from the temperature dependence of theoxygen permeability constants under P O2

(II)/P O2(I) = 105 Pa/1 Pa.

5450 T. Matsudaira et al. / Acta Materialia 59 (2011) 5440–5450

of Al increase proportional to T�1. The Dgbd values fornon-doped and Lu-doped alumina are almost the same;only Hf doping can decrease them. The corresponding acti-vation energies for Dgbd of Al are comparable for all sam-ples, as shown in Fig. 12 and Table 1. The activationenergies for Dgbd of Al should also depend strongly onthe degree of DP O2

and differences in the diffusion species,similarly to those of oxygen.

4. Conclusions

The oxygen permeability constants of polycrystallinealumina wafers with 0.2 mol.% of dopants such as HfO2

and/or LuO1.5 were evaluated at temperatures up to1923 K under various DP O2

generated by combinations ofdifferent P O2

values (P O2(II)� P O2

(I)). When oxygen per-meation occurred mainly by grain-boundary diffusion ofAl from the P O2

(I) to the P O2(II) surface side, the mobility

of Al diffusion was retarded only by Hf doping, but not byLu doping. When oxygen permeation was controlledmainly by grain-boundary diffusion of oxygen from theP O2

(II) to the P O2(I) surface side, the mobility of oxygen

diffusion was effectively suppressed only by Lu doping,and not by Hf doping. The ability of a dopant to inhibitthe mobility of either Al or oxygen is presumably relatedto grain-boundary strengthening due to the oxygen coordi-nation number or bonding strength and to site blockingdue to the ionic-size mismatch. Co-doping with both Luand Hf increased the oxygen permeation under all DP O2

conditions, although the corresponding power constantswere maintained.

Acknowledgments

This work was supported in part by a Grant-in-Aid forScientific Research in the Priority Area “Nano MaterialsScience for Atomic Scale Modification 474” from the Min-istry of Education, Culture, Sports, Science, and Technol-ogy (MEXT) of Japan. The authors are grateful to Prof.Y. Ikuhara and Dr. N. Shibata of the University of Tokyo,and Dr. H. Yoshida and Dr. T. Nakagawa of the NationalInstitute for Materials Science for valuable discussions andadvice during the course of this research.

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