Phase transformations of (Ca, Ti)-partially stabilized zirconia

Materials Science and Engineering, A 131 ( 1991 ) 273-280

273

Phase Transformations of (Ca, Ti)-Partially Stabilized Zirconia YUNGSHON HON and POUYAN SHEN Institute of Materials Science and Engineering, National Sun Yat-Sen University, Kaohsiung (Taiwan) (Received October 3, 1989; in revised form July 17, 1990)

Abstract

The results of phase transformation and microstructural investigation of the ZrOe-rich corner of the CaO- TiO2-Zr02 system are reported. Samples of Ca-PSZ powder (where PSZ is partially stabilized zirconia) containing 10.8 mol.% CaO, had added to them 0-14 mol. % TiO2 (designated specimens OT to 14T). The samples were sintered at 1600 °C for 6 h and studied by X-ray diffraction and electron microscopy. Saturation of Ti02 in the cubic (c) zirconia was reached at a total Ti02 addition of about 4 mol. % at 1600 °C, whereas the solubility limit in tetragonal (t) zirconia was not reached in the composition range studied. The t-zirconia precipitates remained tweed in the cubic matrix for specimens 2T and 4T, but became lenticular with the {101} habit plane for specimens having a larger TiO2 content (e.g. 8T). The amount of t-zirconia increased with increasing TiO2 content at 1600°C. The addition of TiO, also enhanced the eutectoid decomposition of Ca-PSZ to form the (~fphase (CaZr409). Calzirtite (Ca2Zr~ Ti,_01~) was precipitated from the shell of the zirconia grains in specimen 8T.

1. Introduction

Ternary oxides in the system CaO-ZrO2-TiO2 have attracted interest as high-level radioactive waste immobilizers [1-3] and as potential solid electrolytes when anion deficient [4]. Phase equilibria at 1300°C of the perovskite and fluoriterelated ternary phases in this system were recently reported [5]. Attention has also been focused on the ZrO2-rich comer of this system to discover the effects of T i O 2 addition on the phase transformations and physical properties of CaO with partially stabilized zirconia (Ca-PSZ) [6-9]. For example, the addition of TiO2 to Ca-PSZ reduces the stability of the cubic (c) ZrO 2 phase 0921-5093/91/$3.50

[6], promotes sintering at 1460 °C owing to the formation of a liquid phase [7], increases thermal shock resistance [8], and causes contraction and destabilization of the cubic lattice [9]. However, detailed microstructural featurs of PSZ in this ternary system have not been reported. The morphology of PSZs has been extensively studied [10-16]. In PSZ stabilized by MgO (Mg-PSZ), the tetragonal (t) ZrO 2 precipitates have a lenticular shape with a {100} habit plane (indexed as a slightly distorted version of the c-fluorite unit cell)[10]. In PSZ stabilized by TiO (Ti-PSZ, prepared under a vacuum of 13-1.3 Pa) the t-ZrO2 also has a lenticular shape with a {100} habit plane [11]. In PSZ stabilized by CaO (Ca-PSZ) the t-ZrO2 is equiaxed with a {101] habit plane [12]. In the early stage of precipitation in PSZ stabilized by Y203 (Y-PSZ) the t - Z r O 2 also has a {101} habit plane, but it commonly develops "colonies" of twin-related variants which do not readily transform into monoclinic (m) ZrO2 even when they become quite large [13]. Morphology features of t-ZrO2 in ternary systems of (Mg, Ca)-PSZ [14], (Mg, Y)-PSZ [15] and in Y-PSZ-Ni2A1Ti cermet [16] have also been reported. Differences in the morphology and the habit plane behavior of the t-ZrO2 precipitate in these systems have been attributed to the misfit in lattice parameters and interfacial energy between the t-ZrO2 precipitates and the c - Z r O 2 matrix [15-17] following Khachaturyan's theory [18]. The morphology of t-ZrO 2 precipitates in ternary (Ca, Ti)-PSZ was not reported. Reported here are results of our observations for (Ti, Ca)-PSZ sintered at 1600 °C using scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction. The morphology and habit plane of t-ZrO2, the formation of the ternary phase, and the decomposition reaction of Ca-PSZ [19] due to the effect of T i O 2 dissolution were studied. © Elsevier Sequoia/Printed in The Netherlands

274

2. Experimental details The Ca-PSZ powder (5.04 wt.%, i.e. 10.8 mol.% CaO, NGK, Japan) with 0-14 mol.% additions of TiO2 (MERCK, 99.9% pure) (in 1% increments, designated as 0T, 1T . . . . . 14T respectively) were ball milled for 4 h, dry pressed at 50 MPa, then sintered at 1600 °C for 6 h in an alumina crucible and cooled in an open air furnace. It took about 10 rain for cooling from 1600 °C to 1200 °C, then 4 h to room temperature. In general, the sintered pellets suffered less than 0.5 wt.% loss and were yellowish. The polished (with diamond paste, 1/~m in size) surface of the sintered specimens were analyzed by X-ray diffractometry (Cu Ka, 35 kV, 25 mA) for phase identification. The {111} diffraction peaks were used to estimate qualitatively the amount of m-ZrO 2 phase relative to the c-ZrO 2 and t-ZrO 2 phases, the zirconia phases being indexed as a slightly distorted version of the c-fluorite unit cell. The identification of the c-ZrO 2 and t-ZrO2 phases in the {400} region of ZrO2 was carried out with a step-scanning method (step size 0.02 °, fixed count time 90 s, divergence and scatter slit 1°, receiving slit 0.2 mm). The {400} peaks were deconvoluted assuming individual gaussian peaks for the t and c phases. The lattice parameters of the c phase were determined by selecting the (440), (531), (600) and (620) peaks and extrapolating the calculated parameters of these peaks against cos 2 0 to 0 = 9 0 ° [20]. The lattice mismatch between c-ZrO2 and t-ZrO2 was then estimated from the d spacings of the {400} peaks diffracted from the polished surface. The polished specimens were HF etched at room temperature for approximately 3-4 min and coated with gold for SEM (JEOL JSM-35CF operating at 25 kV) observations. The backscattered electron image (BEI) and energy dispersive X-ray (EDX) analysis were used to study the distribution of the alloying elements in the sintered specimens. Thin foils were prepared from dimple-ground thin sections by ion-milling and studied in a transmission electron microscope (JEOL-200CX at 200 kV).

the c phase decreases with increasing T i O 2 c o n t e n t (Fig. 1). This is due to the substitution of smaller Ti 4÷ (or a minor amount of titanium cations of other valencies) for Zr 4÷ and C a 2+ [21, 22]. The ionic radii of T i 4+, Zr 4+ and Ca 2÷ are 0.074, 0.084 and 0.112 nm respectively, according to ref. 21 if the coordination number is assumed to be 8. A constant lattice parameter is obtained for specimens containing more than 4 mol.% T i O 2 (Fig. 1), indicating that the solubility limit of TiO2 in the c phase is reached at a total addition of about 4 mol.%. In contrast, the t phase is not saturated with T i O 2 up to additions of 12 mol.%, as indicated by the continuous decrease in the lattice parameter along the c axis, i.e. ct of the t phase with increasing TiO2 content (Fig. 2). The lattice parameter along the a axis, designated a t of the t phase, decreases slightly with TiO 2 content (Table 1). It should be 'noted that the lattice misfit strain e33 (along ct) increases, whereas ell (along a,) decreases with TiO2 content (Table 1 ). According to the ratio of {111 } counts, the amount of m phase increases with T i O 2 c o n t e n t (Fig. 3). This result indicates that the amount of t phase increases with increasing TiO2 content at 1600 °C.

o0.5120

6 0.5110 ~ 0.5100 0.5090 0.508O

2

4 6 8 TiO2 (mo~%)

10

Fig. 1. Room temperature X-ray lattice parameter of the c-phase in Ca-PSZ sintered (1600 °C, 6 h) with TiO2.

o~ 0.5179 ~ 0.5175

O

D

"~ 0.5171 v

3. Results

3.1. X-ray diffraction For specimens containing less than 4 mol.% TiO2, the room temperature lattice parameter of

0.5167

2

4 6 8 10 12 TiO2 (rnol%)

Fig. 2. R o o m temperature lattice parameter along the c axis of the t-phase, same specimens as in Fig. 1.

275

TABLE 1

R o o m temperature lattice parameters and habit planes for partially stabilized zirconia Mg-PSZ

Ca-PSZ

(Ca, T i ) - P S Z 2T

a~ (nm) a, (nm) q (nm) q/a, ~'ll

87

4T

0.5080 0.5(}77 0.5183 1.021

0.5132 (}.5094 0.5180 1.017

0.5119 0.5(}74 0.5178 1.020

().5107 0.5073 (}.5177 1.021

(}.5083 0.5072 ().5171 1.020

z'~

0.0006 0.0203

0.0074 0.0093

0.0088 0.0115

0.0067 0.0137

0.0022 0.0173

(a, - a~)/( c, - a,.) Habit plane observed

0.029 { 100}

- 0.792 {101 }

- (}.763 ND

- 0.486 ND

- 0.125 {101 }

(Ca, T i ) - P S Z , present work, Z r O z with 1(}.8 mol.% C a O and 2, 4, 8 mol.% TiO+ for s p e c i m e n s 2T, 4T, 8T respectively, sintered at 16()0 °C for 6 h; other PSZs refer to refs. 15, 17 and 23. ~', , = Q2 = ] ( a , - a ~)/ a ~], c> = I( c, - a~)/ a~.]. ND. not d e t e r m i n e d because the individual t precipitate in tweed array is small and probably equiaxed.

0.8-,2 0.6

½

o,~

~Z o.2 i

0

0

, © v 2

4

6

8

,

10

Ii0 2 (tool°/o) Fig. 3. R o o m t e m p e r a t u r e I l l l/ X-ray counts ratio diffracted from polished (Ca Ti)-PSZ.

3.2. Scanning electron microscopy observations The non-faceting grains shown representatively in Fig. 4 indicate that liquid phase sintering occurred for the specimens with TiO2 additive. BEI and EDX analyses (Fig. 4) indicate the enrichment of calcium in the grain boundary phase (dark areas on the BEI). For specimens 4T-14T, pores and a titanium-rich phase, which was identified as ZrTiO 4 by X-ray and electron diffractions, were observed [24]. In general, the grain size of zirconia increases with increasing TiO+ content. However, the grain growth rate was suppressed in specimens 4T-14T [24]. This could be due to the presence of the additional ZrTiO4 phase. 3.3. 7?ansmission electron microscopy observations The t-ZrO2 precipitates, about 20 nm and 35 nm in size, were formed in the c - Z r O 2 matrix of the specimens 2T (Fig. 5(a)) and 4T (Fig. 5(b)) respectively. The selected area diffraction (SAD) pattern of zirconia grains in specimens of 2T, 4T and 8T (Fig. 6) shows diffraction spots of the ~bI

phase (CaZr4Og) which also forms by eutectoid decomposition in Ca-PSZ [19, 25]. Similar to that in the system CaO-ZrO+ [19], the ~bl phase forms precipitate variants which complicate the strain and tweed contrast in (c + t)-ZrO2 grains. The zirconia grain of specimen 8T (Fig. 7(a)) commonly has a coarse-tweed core ( c + t + m+~bl) and a finely tweed shell (c+ t+Ca2ZrsTi2Ot6), and the grain boundary is corrugated (Fig. 7(b)). The ternary phase (Ca 2ZrsTi20~+,) is known as calzirtite with space group 14~/acd and the unit cell of calzirtite is a 3 x 3 x 2 array of subcells of f.c.c, fluorite type [26, 27]. Because of the orientation relationship and the symmetry of the phases, three calzirtite variants can precipitate in the cubic matrix. Since systematically absent reflections in the electron and X-ray diffraction patterns of calzirtite were hkl with h + k + l ¢ 2 n , hkO with h(k)#2n, hOl with / # 2 n and hhl with 2 h + l ¢ 4 n [27], the calzirtite spots are only allowed along one of the three {220]* when viewed along (111). The SAD pattern of the shell region (Fig. 8) shows diffraction spots (arrows) of calzirtite at n/3(220)* of c-ZrO 2, those along (202)* and (022)* belong to other variants. The complexity of the SAD pattern of the shell region is also due to spots of t-ZrO2 variants and double diffraction spots. The formation of a shell region is probably due to the chemical inhomogeneity caused by a liquid phase analog [28] of diffusion-induced grain-boundary migration (DIGM) [29] as indicated by the corrugated grain boundary (Fig. 7(b)). The calzirtite precipitates appear equiaxed in specimen 8T, but further study is required to determine the composition or aging dependence of the precipitate morphology.

276

Fig. 4. Representative backscattered electron image (a) and X-ray mappings of calcium (b), zirconium (c) and titanium (d) of (Ca, Ti)-PSZ (specimen 2T ).

Bright field image (BFI) (Fig. 9(a)) and DFI using {112} spot (Fig. 9(b)) indicate that t-ZrO 2 of the core region is about 50 nm in size and lenticular in shape. Trace analysis indicates that the habit plane of these t precipitates is {101 }, the same as for the Ca-PSZ system. It should be noted that the t precipitate has significant strain contrast within the c matrix of the core region (Fig. 9(b)). Occasionally, transformation of t-ZrO 2 into orthorhombic (o) and m-ZrO 2 was observed during TEM. A grain boundary liquid phase, which shows diffuse electron diffraction, was identified in all the sintered (Ca, Ti)-PSZ specimens. A Z r T i O 4 grain about 2 ktm in size was identified in the 4T specimen by SAD [24].

4. Discussions

4.1. Solubility Eutectic melting is allowed below 1600 °C for the binary system CaO-TiO2 (eutectic point, 1460 °C, CaO with 81.5 wt.% TiO2) [30]. This implies the formation of liquid at 1600 °C in the ternary system CaO-ZrO2-TiO 2. Since liquid facilitates diffusion, dissolution of TiO2 in c-ZrO2 is affected by the quantities of liquid in the specimens 0T-14T. In order to confirm the solubility limit of TiO2 in c-ZrO2, firing of the pellets 0T, 1T and 10T was conducted at 1600 °C for 6, 50 and 70 h [24]. The lattice parameters of c-ZrO 2 of specimens 0T and 1T decrease with annealing time, then reach constant values (0.5130 and

277

fl

I1- "~11

Fig. 5. TEM of tweed grains showing t-ZrOz precipitates in the c-ZrO~ matrix: (a) 2T, (b) 4T, ( 111 zone axis).

Fig. 7. DFIs showing (a) core and shell structure and (b) corrugated boundary of zirconia grain in specimen ST.

Fig. 6. Representative SAD pattern of zirconia grain showing ¢1 phase spots (arrows) (ST, Z = [i 11]).

0.5110 + 0.0003 nm for 0T and 1T respectively) from 50 to 70 h. However, a constant lattice parameter (0.5083 nm) of c-ZrO, was obtained for specimen 10T fired between 6 and 70 h, indicating that 6 h sintering is adequate to saturate the TiO~ content in the c lattice. A lattice parameter of 0.5083 nm is also obtained for c-ZrO2 in specimens 4T-8T which were sintered at 1600 °C for 6 h (Fig. 1). This further justifies the saturation of TiO~ in the c-ZrO, lattice of specimens 4T-10T. Titanium cations of multiple valency, e.g. Ti 4 +, Ti 3÷ and Ti 2+, are possibly dissolved in the zirconia lattice owing to non-stoichiometry of the titanium oxides. However, the system ZrO2-TiO2 [31] contains one binary compound (ZrTiO4) and extensive solid solubility based on the tetragonal

278

t-Z~2

••NN•202 •

calzirtite

hkl

0

c-fluorite

hkl

Fig. 8. SAD pattern (Z = [i 11] of zirconia)of shell region of Fig. 7, showing diffraction spots of calzirtite (arrows) at n/3(220)* of c-ZrO2, {112} t variants spots and double diffraction spots and schematic indexing shows one of the three calzirtite variants.

form of each oxide at 1600°C, indicating that Ti 4 + is the most likely valency of titanium cations if sintering is conducted in open air. Sintering of Ti-PSZ under a vacuum of 13 to 1.3 Pa is known to stabilize TiO, indicating that Ti 2+ is dissolved in the zirconia lattice [11, 32]. 4.2. Habit plane and morphology of t-Zr02 The tweed morphology of t-ZrO 2 in specimens 2T and 4T is similar to those equiaxed in Ca-PSZ [12], but lenticular t-ZrO 2 observed in specimen 8T is significantly different in morphology. This result could be due to the modification of energy terms of the t-m transformation caused by TiO 2 dissolution. It should be noted that the lattice misfit strain e ~1 decreases, whereas e33 increases as the T i O 2 c o n t e n t in (Ca, Ti)-PSZ

Fig. 9. (a) BFI showing lenticular t precipitates in the c matrix of specimen 8T. Note variants of t-ZrO z have {101} habit plane, Z=[010]; (b) DFI of t precipitates in the core region of Fig. 7 showing strain contrast, g = {112 }.

increases (Table 1) and approaches the values of Mg-PSZ. However, instead of forming the {100} habit plane, the habit plane of t precipitates in specimen 8T remains as {101}, the same as in Ca-PSZ. It is likely that the morphology of t-ZrO2 in (Ca, Ti)-PSZ is significantly affected by the interfacial energy. 4.3. Effect of TiO e dissolution on M s of the t - m transformation TiO 2 dissolution in ZrO 2 is known to reduce the value of M s of the t-m transformation [33]; however, this effect is not clear in the (Ca, Ti)PSZ system. According to the {111} counts ratio, the content of m-ZrO2 increases slightly with the increase in the TiO2 content in (Ca, Ti)-PSZ. This could be due to the combined effects of (1)

279

poor matrix constraint by pores which are present in much greater quantities in TiO2-rich specimens; (2) coarsening of the t precipitate to overcome the matrix constraint; (3) thermal mismatch caused by ZrTiO4; (4) alteration of the energy terms of t-m transformation, e.g. the chemical free energy, the interfacial energy, and the strain energy as indicated by the composition dependence of lattice misfit (Table 1 ). 4. 4. Eutectoid decomposition and ternary phase Eutectoid decomposition has been observed in the binary system ZrO2-CaO [19, 25, 34] and the eutectoid decomposition of the c solid solution was found to occur at 1140_+40°C and 17.0 +- 0.5 tool.% CaO [19]. The decomposition results in the formation of two ordered phases, ~b (CaZr4Og) and ~b2 (Ca6ZrlgO44), which have their upper limits of stability at 1235+_15 and 1355_+ 15°C respectively [19]. The occurrence of the ~ phase rather than the 42 phase in (Ca, Ti)-PSZ specimens indicates that hypereutectoid decomposition probably occurs. However, it is not known if the decomposition follows metastable extension of boundary line as in the CaO-ZrO2 system [19]. In contrast to the aging required of days to months for the formation of sharp ~bl spots in Ca-PSZ [19], the sharp and discrete reflections of #~ were observed in (Ca, Ti)-PSZ specimens which were furnace cooled without further aging. This result indicates that the addition of TiO2 facilitates long-range ordering. In the CaO-TiO 2 system, the precipitate morphology of the ~bl phase varies with aging time [25]. For short aging times, the ~b~ precipitates are striated, but appear equiaxed when fully coarsened [25]. Further study is required to clarify the composition or aging dependence of the precipitate morphology of the ~bI phase in (Ca, Ti)-PSZ. The occurrence of calzirtite at the shell of the zirconia grain indicates that the ternary eutectic point is probably calcium and titanium rich. At grain boundaries of ZrO2-CaO-TiO 2 ceramics [9], a CaO and TiO2-rich continuous c phase was observed, which was derived from a liquid phase at a sintering temperature of 1800°C. It is possible that partitioning of cations between the grain-boundary liquid and the zirconia phases also occurred when the (Ca, Ti)-PSZ specimen was sintered at 1600°C. The formation of ZrTiO 4 at grain boundaries could be due to this liquid phase or caused by reactions of the con-

stituent oxides. The corrugated grain boundary indicates chemical inhomogeneity was also caused by DIGM [29] at 1600 °C. In conclusion, the ~l-bearing core and the calzirtite-rich shell were probably derived respectively from a c phase and a grain-boundary liquid phase at 1600°C followed by decomposition upon cooling. This argument is a distinct possibility in view of the stability of ~ phase in the system CaOZrO2 at 1235_+15°C [19] and the formation of the calzirtite phase in the ternary system at 1300 °c [53. 5. Conclusions The following conclusions were drawn from X-ray diffraction and electron microscopy observations of (Ca, Ti)-PSZ specimens sintered at 1600 °C for 6 h. ( 1 ) The solubility limit of TiO2 in c-zirconia is 4 mol.% and the amount of t-zirconia increases as TiO2 addition increases. (2) Tweed t precipitates were found in specimens with TiO 2 contents less than 4 tool.% , but lenticular t precipitates having the {101} habit plane were found in specimens containing 8 mol.% TiO2. (3) TiO2 addition enhanced the eutectoid decomposition of Ca-PSZ and the precipitation of a ternary phase, calzirtite, in the shell of the zirconia grain. Acknowledgments Thanks are due to Mr. W. H. Deng for preparing the ion-milled samples and Mr. S. Chen for helpful discussions. This work was supported by National Science Council of Taiwan. References 1 A. E. Ringwood, S. E. Kesson, N. G. Ware, W. Hibberson and A. Major, Nature, 278 (1979) 219. 2 W.J. Buykx, D. J. Cassidy, C. E. Webb and J. L. Woolfrey, Ceram. BulL, 60(1981) 1284. 3 R. A. Penneman and P. G. Eller, Radiochim. Acta, 32 (1983)81.

4 J. M. Reau, J. Portier, A. Levasseur, G. ViUeneuveand M. Pouchard, Mater. Res. BulL, 13 (1978) 1415. 5 M. O. Figueiredo and A. C. D. Santos, in S. Meriani and C. Palmonari (eds.), Zirconia '88: Advances in Zirconia Science and Technology, Elsevier Applied Science. London, 1989, p. 81. 6 L. W. Coughanour, R. S. Roth, S. Marzullo and E E. Sennett, J. Res. Natl. Bur. Stand. (U.S.), 54 (4) (1955) 191.

280 7 K. C. Radford and R. J. Bratton, J. Mater Sci., 14 (1) (1979) 59. 8 N. C. Biswas and D. Chakravorty, Z Mater Sci. Lett., l (1982) 119. 9 D.C. Agrawal, R. Gopalakrishnan and D. Chakravorty, J. Am. Ceram. Soc., 72 (6)(1989) 912. 10 D. L. Porter and A. H. Heuer, J. Am. Ceram. Soc., 60 (3-4)(1977) 183. 11 C. L. Lin, P. Shen and D. Gan, J. Mater. Sci. Lett., 8 (1989) 395. 12 R. H. J. Hannink, K. A. Johnston, R. T. Pascoe and R. C. Garvie, in A. H. Heuer and L. W. Hobbs (eds.), Advances in Ceramics, Vol. 3, Science and Technology of Zirconia, The American Ceramic Society, Columbus, OH, 1981, p. 116. 13 V. Lanteri, A. H. Heuer and T. E. Mitchell, in N. Clausen, M. Ruhle and A. H. Heuer (eds.), Advances in Ceramics, Vol. 12, Science and Technology of Zirconia I1, The American Ceramic Society, Columbus, OH, 1984, p. l18. 14 L. K. Lenz, M.S. Thesis, Case Western Reserve University, Cleveland, OH, 1982. 15 V. Lanteri, T. E. Mitchell and A. H. Heuer, J. Am. Ceram. Soc., 69(7)(1986)564. 16 P. T. Chao and P. Shen, Mater. Sci. Eng., A l 1 7 (1989) 191. 17 R. R. Lee and A. H. Heuer, J. Am. Ceram. Soc., 70 (4) (1987) 208. 18 A. G. Khachaturyan, Theory of Structural Transformation in Solids, Wiley, New York, 1983. 19 J.R. Hellmann and V. S. Stubican, J. Am. Ceram. Soc., 66 (4)(1983) 260, and references cited therein.

20 B. D. Cullity, Elements of X-ray Diffraction, Addison Wesley, Reading, MA, 1978, p. 359, 2nd edn. 21 R.D. Shannon, A cta Crystallogr. A, 32 ( 1976 ) 751. 22 B. K. Vainshtein, V. M. Fridkin and V. Lindenbom, Modern Crystallography 11, Structure of Crystals, Springer, Berlin, 1982, p. 77. 23 R.H.J. Hannink, J. Mater. Sci., 13 (1978) 2487. 24 Y. Hon, M.S. Thesis, National Sun Yat-Sen University, Taiwan, 1989. 25 J. Hangas, T. E. Mitchell and A. H. Heuer, in A. H. Heuer, N. Claussen and M. Ruhle (eds.), Advances in Ceramics, Vol. 12, Science and Technology of Zirconia, American Ceramic Society, Columbus, OH, 1984, pp. 107, and references cited therein. 26 Y. A. Pyatenko and Z. V. Pudovkina, Kristallografiya, 6 (1961) 196. 27 H.J. Rossell, Acta Crystallogr. B, 38 (1982) 593. 28 E. E Butler and A. H. Heuer, J. Am. Ceram. Soc., 68 (4) (1985) 197. 29 R. W. Balluffi and J. W. Cahn, Acta MetaU., 29 (1981) 493, and references cited therein. 30 A. Jongejan and A. L. Wilkins, J. Less-Common Met., 20 (4) (1970)275. 31 E. M. Levin and H. E McMurdie, Phase Diagrams for Ceramicists, Suppl., American Ceramic Society, Columbus, OH, 1975, p. 169. 32 C.L. Lin, D. Gan and E Shen, J. Am. Ceram. Soc., 71 (8) (1988) 624, and references cited therein. 33 E H. Brown and E Duwez, Z Am. Ceram. Soc., 37 (3) (1954) 132. 34 J. M. Marder, T. E. Mitchell and A. H. Heuer, Acta Metall., 31 (3)(1983) 387.