A study of the boron-rich corner of the ErAlB system

Journal of Alloys and Compounds, 210 (1994) 191-196 JALCOM 1129

191

A study of the boron-rich corner of the Er-A1-B system Y. Y u a n d T. L u n d s t r 6 m * Institute of Chemistry, Box 531, S-751 21 Uppsala (Sweden)

(Received January 3, 1994)

Abstract The ternary phase equilibria of the Er-AI-B system have been investigated and determined at 1600 °C. The ternary phase Erl-~dl_yBa4 forms equilibria with ErB4, ErBa2, ErB66, a-AIBa2 and ErAIB4. X-Ray diffraction technique, electron microprobe analysis and X-ray powder Rietveld refinements were used to study the phase equilibria. The presence of the ternary phase Era_xAla_yB14 with a homogeneity range around the composition Ero.57Alo.62B14 has been established.

1. Introduction

More than a dozen ternary borides are presently known to crystallize in the MgA1B14-type structure [1-3]. Most of these borides contain rare-earth (RE) and aluminium metals. In addition, the binary borides Mg2B14 [4], NaBB~4 [5] and related defective sodium borides [6] have been characterized. The early structure determinations of NaBB~4 [5] and MgAIB14 [7] did not reveal any significant concentration of vacancies at the metal positions. Later structural investigations have, however, shown that partial occupancy of both metal positions (50-75%) is common among the ternary compounds. This has been shown, for example, for MgAIB14

cupancy of the metal positions in the crystal structure. Here it is represented by REAIB14, just to simplify the formula. These crystals were obtained by high-temperature solution growth in aluminium flux. Details of crystal structure studies have been reported for these crystals [1-3, 9]. Information on equilibria between these ternary phases and neighbouring phases has not been reported. In view of these facts and the defective nature of the MgA1B14-type structures, it was found interesting to study the phase equilibria between ErA1B14 and the neighbouring binary and ternary phases of the Er-A1-B system. The results are presented as a partial ternary section of the Er-A1-B system at 1600 °C.

[8], HoA1B~4 [9] and ErA1B~4 [2].

Early studies of the RE-A1-B ( R E = r a r e earth) systems can be divided into two parts: polycrystalline and single-crystal studies. Polycrystalline phase mixtures in the Ce-AI-B, La-A1-B and Y-AI-B systems [10] were obtained by arc melting the mixed elemental powders. This procedure was followed by heat treatment at temperatures between 500 and 600 °C. No ternary phases were obtained and no information on phase equilibria for the boron-rich corner was reported in these studies. Single-crystal growth studies were performed mainly on ternary phases of these systems. The crystals were reported to crystallize in three structure types, namely the YCrB4 type (LuAIB4, YbA1B4) [11], the YzReB6 type (Yb2AIB6) [11] and the MgA1B14 type (REA1B~4 with R E = T b , Dy, Ho, Er, Tm) [1-3]. The real composition of the REAIBa, group should be denoted as RE~_~AIa_yB14 due to the partial oc*Author to whom correspondence should be addressed.

2. Experimental details

2.1. Alloy preparation The syntheses were initially performed using crystalline boron (from H.C. Starck, Goslar, Germany; claimed purity 99.6% boron), ErB4 powder (from Cerac, Milwaukee, WI, USA; claimed purity 99.9%) and otA1B12 powder (from Cerac; claimed purity 99%). Although the tetraboride was claimed to be very pure, our electron microprobe analysis showed that it contained considerable amounts of cerium as an impurity. Therefore we prepared master alloys of ErB4 and ErB2 by arc-melting erbium metal (from Cerac; claimed purity 99.4%) and the above-mentioned boron. The initial steps of the arc-melting (filing, weighing, mixing, and pressing of pellets) were performed under an argon atmosphere to prevent direct contact between erbium and air. X-Ray diffraction and electron microprobe

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Y. Yu, T. Lundstrdm / Boron-rich comer of the Er-AI-B system

192

analyses of the alloys obtained did not display significant impurities, and these alloys were used in the subsequent syntheses of samples for phase analysis. Dry mixed powders of the starting materials were pressed into pellets and then arc-melted. The melted and solidified samples were subsequently heat-treated in a resistance furnace at temperatures between 1300 °C and 1600 °C under an argon atmosphere. To prevent chemical reaction between the samples and the AI203 crucible used during heat treatment, ZrB2 pellets were placed between them. Two samples (nos. 13 and 14) were synthesized by reaction sintering in a high-frequency furnace at 1600 °C and 1750 °C, respectively. After phase analysis, some samples were crushed, mixed and used as the starting material for other samples. Sample preparation data are listed in Table 1.

2.2. Phase analysis and composition determination Phase analysis of all samples was performed with a Guinier-H~igg focusing camera using Cu Ks1 radiation and ultra-pure silicon (a =5.43106/~) as internal calibration standard [12]. The unit cell parameters were refined by the least-squares method using the local program UNITCELL [13]. The results of phase analysis and the unit cell dimensions in the representative samples are listed in Table 2. Electron microprobe analysis was performed on a scanning electron microscope equipped with an energy-dispersive detector to perform elemental analysis on the final samples. Three or four samples were prepared with different compositions within each phase region (Fig. 1) and one of

them was used as the representative in the phase analysis. Some representative samples (nos. 1-6 and 8) which contain the ternary phase ErA1B14 were selected for powder profile structure refinements. Data for X-ray powder profile refinements were collected from Guinier-H~igg films with a computer-controlled microdensitometer [14]. A local modification of the Rietveld program LHPM1 b y Wiles and Young [15] and Hill and Howard [16] was used for the profile refinement employing the pseudo-Voigt function to describe the peak shape. The initial values of both positional parameters and occupancy factors were taken from the single-crystal study of ErA1B14 [2]. The Bragg R values (RB) of the Rietveld refinements of different samples are listed in Table 3. The results of partial atomic occupancy of the metal atoms from the profile refinements were used to calculate the compositions of the ternary Erl _~AI~_yBl4 phase in different samples, which are listed in Table 3. As most of the samples contain two or three phases, the weight fraction of each phase can be calculated from its refined scale factor using eqn. (1) [17].

w,= S(MeZ), ES,(MVZ),

(1)

i

where W~ is the weight fraction of phase i, S~ is the scale factor of phase i, M~ is the formula weight of phase i, V~ is the unit cell volume of phase i, Zi is the number of formula units per unit cell of phase i and

T A B L E 1. Preparation data Sample

Approx. weight

Nominal composition

Method

Temperature (°C)

Time (h)

Heating rate (deg rain -1)

Cooling rate (deg min -1)

Er4A14.3B91.7 Er3.aAls.2Ba8 Era.7AI9.3Bs7 b c d * Ers.2AI3.gBgo.9 Er2oAIsB75 Er4.gAl3.sB9L3 Er3.sAls.2Bss f Er3.sAh.sBgt.7 Er3.sAI4.sB91.7

AM + HT a AM + HT AM + HT AM + HT AM + HT AM + HT AM+HT AM + HT AM + HT AM + HT AM + HT AM Sintering Sintering

1600 1600 1600 1600 1600 1600 1600 1600 1600 1300 1450

72 72 72 72 72 72 172 72 72 50 72

9 9 9 9 9 9 9 9 9 9 9

20 20 20 20 20 20 20 20 30 20 20

1600 1750

72 72

(g) 1 2 3 4 5 6 7 8 9 10 11 12 13 14

2 2 2 1.5 1.265 1.235 2.175 2 1 2 2 2 0.5 0.5

SAM, arc-melting; HT, heat treatment. bUsing sample no. 1(1.0 g) and AIB12(0.5 g) as the starting materials. q/sing sample no. 2(1.0 g) and A1Bn(0.265 g) as the starting materials. dUsing sample no. 7(1.0 g) and AIBn(0.235 g) as the starting materials. cUsing sample no. 3(0.83 g) and B(1.345 g) as the starting materials. fSample no. 5 is a part of sample no. 11.

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Y. Yu, 7". LundstrOm / Boron-rich corner o f the Er-AI-B system

[3-rh.B

TABLE 2. Occurrence of phases and their cell dimensions of the representative samples Sample Phase

1 2

3 4

5 6

ErAIB14 ErB4 ErAIB1, ErB4 ErA1B4 ErA1BI 4 ErAIB4 ErAIB14 ErAIB4 a-A1B~2 ErA1B14 a-AIB~2 ErA1B~4 a-A1B12 ErB66

a ~ (/~)

ba (/k)

c" (/~)

5.8138(3) 7.0726(4) 5.8131(3) 7.0709(3) 6.0062(6) 5.8145(2) 6.0150(9) 5.8165(3) 5.922(1) 10.1617(7) 5.8157(4) 10.1547(8) 5.8151(3) 10.1521(5) 23.5482(12)

10.3885(5) 8.1830(4) 3.9975(3) 10.3935(5) 8.1830(3) 3.9982(3) 11.3897(12) 3.4944(4) 10.3954(4) 8.1828(3) 11.3895(9) 3.4953(3) 10.3947(4) 8.1835(4) 11.392(1) 3.5005(6) 14.227(1) 10.3950(4) 8.1820(4) 14.2876(17) 10.3901(5) 8.1838(4) 14.3260(10)

o~-A1

~ / : / ° 4 ~ ~ x ~ ' ~ ErA1B14

~ A1B12 E , rA1B4 ÷liq./

rB2

~ErA1B4 +ErB2÷ liq.

Traces of ErB12

7

ErB12 ErB66 ErAIB~4

7.4849(2) 23.6183(7) 5.8126(14) 10.3912(12) 8.1849(18)

Traces of/3-rh.B

8

9

10

11

12

13

14

ErA1B14 ErB4 ErBz2 ErB4 ErB2 ErA1B4 ErB12 ErB4 ErB6 ErA1B~4 ErB4 ErA1B4 a-A1B~2 ErA1Bx4 ErAIBx4 ErB4 a-AIB~2 ErA1B4 ErB4 ErBI2 ErAIB,4 ErB12 ot-AIB12

Fig. 1. A partial isothermal section of the Er-A1-B system (B/ M>2) at 1600 °C. Atomic percentages are indicated.

3. Discussion 5.8134(3) 10.3895(5) 8.1851(4) 7.0729(5) 3.9984(4) 7.4800(20) 7.0708(3) 3.9937(3) 3.2673(5) 3.7791(9) 5.9213(5) 11,4314(12) 3.5070(6) 7.4854(2) 7.0746(6) 4.1165(4) 5.8186(6) 7.0710(4) 5.9848(8) 10.2215(7) 5.8187(3) 5.8179(3) 7.0699(8) 10.1544(5) 5.8739(7) 7.0736(2) 7.4826(6) 5.806(1) 7.4839(4) 16.513(2)

3.9991(3) 10,3972(10) 8.1893(9) 3.9994(4) 11.4257(20) 3.4816(3) 14.0795(12) 10.3925(4) 8.1861(4) 10.3920(5) 8.1863(4) 3.9995(4) 14.2640(12) 11.4243(15) 3.5025(4) 3.9985(2) 10.378(1)

8.193(2)

17.594(2) 10.025(1)

aEstimated standard deviations are given in parentheses.

N is the number of phases in the mixture. From this weight fraction, the total compositions of the phase mixtures in different samples were calculated, and are also listed in Table 3. The calculated compositions in different phase regions give good information on the homogeneity range of the ternary EI_~11_yBa4.

3.1. Some characteristics of RE-AI-B system In an experimental study of a ternary section of an RE-A1-B system, there are several problems to be solved successfully. Due to the high vapour pressure of aluminium and low vapour pressures of the other elements, considerable losses of aluminium were always observed during arc-melting, heat treatment and sintering reactions, in particular when the elements were used in the starting mixture. The use of AIBa2 as aluminium source led to much lower aluminium losses during the preparation procedure. The determination of the composition of the ternary phase Erl _~AI1-yB14 presents problems for the following reasons. It is often desirable to determine the composition in two- or three-phase samples and in such a case the most attractive method would be to use an electron microprobe equipped with an energy-dispersive detector. However, in the present case there is a considerable overlap between the aluminium K-radiation peak (1.44-1.57 keV for the half-width energy range) and the erbium M-radiation peak (1.38-1.52 keV for the half-width energy range), which leads to a low accuracy. Furthermore, the cell dimension vs. composition method is not anticipated to be profitable, since the cell dimensions are mainly determined by the very rigid icosahedral boron network with a very small influence from the concentration of the metal atoms. In view of these facts, the compositions of Erl_~All _yn14 were obtained from refined atomic occupancy factors by Rietveld X-ray powder diffraction analysis, assuming

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Y. Yu, T. LundstrOrn / Boron-rich comer of the Er--AI-B system

TABLE 3. Results of Rietveld structure refinements and calculated compositions of samples nos. 1-6 and 8 Sample

Phase

R8

IVi

Total composition

(%) 1 2

3 4

5 6

8

aa

ba

ca

(A)

(A)

(A)

Ero.56Alo.59B14 ErB 4

3.04 3.67

91.95 8.05

5.8138(3) 7.0726(4)

10.3885(5)

Er6'aA13sB9°2

8.1830(4) 3.9975(3)

Ero.56AIo.62B~4 ErAIB4 ErB,

3.33 3.32 1.89

89.24 6.53 4.23

Er4.sAI4.4BgLx

5.8131(3) 6.0062(6) 7.0709(3)

10.3935(5) 11.3897(12)

8.1830(3) 3.4944(3) 3.9982(3)

Ero.56Alo.63B~4 ErAIB4

5.90 5.08

97.44 2.56

5.8145(2) 6.0150(9)

10.3954(4) 11.3895(9)

8.1828(3) 3.4953(3)

Ero.ssAlo.64B~4 a-AlB12 ErAIB4

5.19 7.27 5.43

82.65 14.78 2.57

5.8165(3) 10.1617(7) 5.9215(10)

10.3947(4)

Er2.gA14.gB92.2

8.1835(4) 14.2267(11) 3.5005(6)

Ero.57Alo.62B~4 a-A1B12

6.91 8.46

54.75 45.25

10.3950(4)

Ert'7AIs'7B926

5.8157(4) 10.1547(8)

8.1820(4) 14.2876(17)

Ero.57Alo.56B~4 a-AIB12 ErB66

4.89 6.32 6.93

62.34 28.45 9.21

5.8151(3) 10.1521(5) 23.5482(12)

10.3901(5)

Er2.2AI1.6B96.2

8.1838(4) 14.3260(10)

Ero.ssAlo.ssB~4 ErB12 ErB,

3.85 9.11 4.40

79.41 12.24 8.35

Er4.TAI3.aB92

Er3sAI4'aBaL9

5.8134(3) 7.4800(4) 7.0729(5)

11.3921(14)

10.3895(5)

8.1851(4) 3.9984(4)

aEstimated standard deviations are given in parentheses.

full occupancy of all boron positions. This assumption is strongly supported by the powder refinements in this work and also by a recent single-crystal study of ErA1B14 [21.

3.2. Phase analyses The nominal compositions listed in Table 1 are weighed-in compositions. The mass loss during arcmelting and during the subsequent heat treatment was 5-10% and 3-7%, respectively. It was assumed that most of the mass loss was caused by evaporation of aluminium. Traces of ErB12 were observed in sample no. 6 and traces of/3-rh, boron in sample no. 7. After these two samples were heat-treated at 1600 °C for another 100 h, the traces of ErBIE disappeared in sample no. 6 but the traces of/3-rh, boron still occurred in sample no. 7, although a decreased concentration of about 20% was obtained from intensity measurements. Since the Rietveld refinement program used can only refine a maximum of three phases simultaneously and since too many/3-rh, boron diffraction lines overlapped with those of other phases, a refinement of the phases of sample no. 7 was not attempted. Sample no. 11 was mainly composed of erbium borides with traces of ErA1B14. In this sample an erbium hexaboride phase was found. Such a phase is, however, stable only at high temperatures in the Er-B system, according to Mar [18]. Microprobe EDS measurements showed that this phase contained a small amount of

cerium, which can be assumed to stabilize the hexaboride of erbium at low temperature. Phase analysis of sample no. 12 was carried out directly on the arc-melted sample without subsequent heat treatment. Phase equilibria could not be established for either of these two samples (nos. 11 and 12). In the high-# region, a significant number of ErAIB14 reflections overlap with those of other phases. A small variation is observed in the cell parameters of ErAIB14 among the samples (nos. 1--8, 10 and 11) obtained by arc-melting and subsequent heat treatment, as shown in Table 2. No sample was obtained in the two-phase region ErB~E+ ErA1B14. This may be explained by the fact that ErB4 has a much higher stability than ErB~z and that this region is too small. The difference between the sample preparation by arc-melting plus subsequent heat treatment and by reaction sintering can be seen by comparing the results of phase analysis of samples no. 8 and no. 13. These two samples contain the same phases, but with different phase ratios (Table 2). By arc-melting plus subsequent heat treatment, a larger amount of ErA1B~4 was obtained than by reaction sintering. This may be explained by the fact that the diffusion process takes longer to form the ternary phase ErA1B14 during reaction sintering than during heat treatment of the arc-melted sample. In order to increase the diffusion rate during the reaction sintering, a higher temperature of sintering was used (sample no. 14). The result is discussed in Sect. 3.3.

Y. Yu, T. Lundstr6m / Boron-rich comer of the Er-Al-B system

3.3. Influence of temperature on heat treatment and sintering From Tables 1 and 2, it can be seen that after the heat treatment at 1300 °C only a trace of ErA1B~4 was obtained and no equilibrium was established (sample no. 10). The results were similar when the heat treatment temperature was 1450 °C (sample no. 11). No ternary phase was obtained when the sintering temperature was about 1750 °C (sample no. 14), which means that the ternary phase is not stable at or above that temperature. At 1600 °C most samples are in equilibria, with the ternary phase ErAIB14 as the majority phase in the mixtures. This is why we choose 1600 °C to set up the equilibrium of the system. 3.4. Accuracy of the compositions calculated from the powder method In order to compare the methods of the powder Rietveld refinement with the single-crystal refinement of ErA1B14, single crystals from the same batch [2] were collected and crushed into powder, which was then used for a powder Rietveld refinement. It was found that certain differences occurred in the refined occupational parameters for the two methods [19]. The atomic contents of erbium and aluminium as obtained by the powder method are 16% and 19% lower, respectively, than as obtained by the single-crystal method. Considering the levels of the estimated standard deviations and the systematic errors in both methods, it is suggested that values from the single-crystal method are closer to the "true values". The main reason for the above differences in the metal atomic contents is supposed to be that the powder method has a higher systematic error than the single-crystal method. There also exist considerable random errors in the powder method with different Rietveld refinement programs, or even the same program with different users, as stated by Hill [20]. In the present work, only the compositions calculated directly from the Rietveld refinement results are used. 3.5. Phase equilibria of Er-Al-B system in the boronrich comer and the homogeneity range of the ternary ErAlB14 The boron-rich corner of the ternary section of the Er-A1-B system at 1600 °C is displayed in Fig. 1. The tie-lines in the two-phase regions a-AIB12+liq, and ErB2 + liq. are only tentative (indicated by dashed lines) as well as the three-phase triangles ErAIB4 + ErB2 + liq. and a-AIB~2+ErAIB4+liq. The digits in Fig. 1 agree with the same numbers given in Table 2, which displays phases present and their unit cell dimensions. Many more samples were prepared but in the end found to be of less importance. The indicated solid solubility of aluminium in /3-rh. boron is taken from ref. 21 and

195

consequently no significant change of the solubility limit of aluminium in/3-rh, boron in the temperature range around 1600 °C has been assumed. In the partial regions with boron/metal ratio more than or equal to 2 (B/ M > 2) in Fig. 1, there are eight three-phase regions (ErA1B14 + ErB4 + ErA1B4, ErA1B14+ ErB12 + ErB4, ErAIB14 + ErB66 + ErBlz, ErA1B14+ a-A1BIE + ErB66, ErA1B14 + ErA1B4 + a-A1Blu, a-A1BIE+ 13-rh.B + ErB66, ErB4 + ErB= + ErAIB4 and a-mlBlz + ErA1B4 + liq.), seven two-phase regions (a-A1Blz+/3-rh.B, ErB66+ /3-rh.B, ErA1B~4+ ErB~:, ErAIB14 + ErB4, ErA1B14+ ErA1B4, ErA1B~4+ a-A1B12 and a-A1B~2+ liq.) and two one-phase regions (ErA1B~4 and solid solution of /3rh.B), as shown in Fig. 1. ErBz was found to be in equilibrium with ErB4 and ErA1B4 in the present study of the Er-A1-B system. Traces of ErB~E in sample no. 6 disappeared and traces of/3-rh, boron in sample no. 7 decreased in amount as the heat treatment time was prolonged for another 100 h. This means that equilibrium is approached very slowly by heat treatment at 1600 °C and that the heat treatment periods of 170-200 h would have been preferable for most samples. Also, it was found that the most boron-rich samples approached equilibrium very slowly. We never succeeded in preparing a three-phase sample in the ternary triangle a-AIB~2+ ErB66 +/3-rh. boron. But since the triangle a-A1B~2+ ErB66 + ErA1B14 is relatively well established, the existence of the former triangle seems to be reliable. The occurrence of traces of a fourth phase (/3-rh.B) in sample no. 7 is probably due to a non-equilibrium situation, since the amount of /3-rh. boron decreases with prolonged heat treatment. The homogeneity range of ErA1B14 has been obtained from the composition variation of this phase in different samples, as determined by Rietveld refinements (Table 3). It was found that only partial occupancy occurs for the erbium and aluminium positions in Er, _xml I _yB14. The erbium content ranges from 0.55 to 0.58, which is about 5% of the total erbium content, while aluminium ranges from 0.58 to 0.64, which is about 9% of the total aluminium content. For the ternary phase in different samples, it was observed that as the erbium content increases, the aluminium content decreases, and as the erbium content decreases, the aluminium content increases. For most of the samples (nos. 2-5), the sum of the metal content varies only slightly (1.19-1.20). The ternary phase of sample no. 6 contains the smallest number of metal atoms (0.57 + 0.56= 1.14) per formula unit, which means that there exists a boronrich corner in the homogeneity range of the ternary ErAIB14, as shown in Fig. 1. Sample no. 8 contains the largest erbium content and sample no. 4 the largest aluminium content, which form the other two vertices of a triangle. This triangle approximates the homogeneity range of ternary ErA1B~4.

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Y. Yu, T. Lundstr6m / Boron-rich comer of the Er-Al-B system

To sum up the present studies, it has been shown that the ternary Erl_~AIl_yB14 forms two- and threephase equilibria with ErB4, ErB12, ErB66, ct-AIB12 and ErA1B4. In addition to these phase equilibria it was also found that the composition range of Er~ _~AI~_yB14 is very close to x=0.43 and y=0.38 and that the composition range is very small. The melting/decomposition temperature of ErA1B14 lies above 1600 °C and below 1750 °C. The ternary compound ErA1B14 can not be prepared with stoichiometric composition.

Acknowledgments The authors are indebted to Dr. Lars-Erik Tergenius for valuable discussions. Thanks are also given to Mr. Anders Lund for his kind help during the experiments. Financial support from the Swedish Natural Science Research Council and the Research Council for Engineering Sciences is gratefully acknowledged.

References 1 M.M. Korsukova, in D, Emin, T. Aselage, A.C. Switendick, B. Morosin and C.L. Beckel (eds.), Boron-Rich Solids, Am. Inst. Phys. Conf. Proc. 1'4o.231, American Institute of Physics, New York, 1991, p. 232. 2 M.M. Korsukova, T. Lundstr6m, L.-E. Tergenius and V.N. Gurin, Z Alloys Comp., 187 (1992) 39.

3 M.M. Korsukova, V.N. Gurin, Y. Yu, L.-E. Tergenius and T. Lundstr6m, J. Alloys Comp., 190 (1993) 185. 4 A. Guette, M. Barret, R. Naslain, P. Hagenmuller, L.-E. Tergenius and T. Lundstr6m, J. Less-Common Met., 82 (1981) 325. 5 R. Naslain and J.S. Kasper, J. Solid State Chem., 1 (1970) 150. 6 R. Naslain, in Boron and Refractory Borides, V.I. Mathovich (ed.), Springer-Verlag, Berlin, 1977, p. 139. 7 V.I. Matkovich and J. Economy, Acta CrystaUogr., B26 (1970) 616. 8 I. Higashi, J. Less-Common Met., 82 (1981) 317. 9 Yu B. Kuz'ma, V.N. Gurin, M.M. Korsukova, N.F. Chaban and S.I. Chikhrii, lnorg. Mater. (Engl. Transl. of Izv. Akad. Nauk SSSR, Neorg. Mater.), 24 (1988) 1705. 10 N.F. Chaban and Yu. B. Kuz'ma, Dopov Akad. Nauk Ukr. RSR, Set. A, 11 (1971) 1048. 11 S.I. Mikhalenko, Yu. B. Kuz'ma, M.M. Korsukova and V.N. Gurin, Inorg. Mater. (Engl. Transl. of lzv. Akad. Nauk SSSR, Neorg. Mater.), 16 (1980) 1325. 12 R.D. Deslattes and A. Henins, Phys. Rev. Lett., 31 (1973) 972. 13 B.I. NoiSing,Institute of Chemistry, Box 531, S-75121Uppsala, personal communication, 1989. 14 K.E. Johansson, T. Palm and P.E. Werner, J. Phys. E: Sci. Instrum., 13 (1980) 1289. 15 D.B. Wiles and R.A. Young, J. Appl. Crystallogr., 14 (1981) 149. 16 R.J. Hill and C.J. Howard, Australian Atomic Energy Commission, Program No. Ml12 (1986). 17 I.C. Madsn and R.J. Hill, Powder Diffraction, 5 (1990) 195. 18 R.W. Mar, J. Am. Ceram. Soc., 56 (1973) 275. 19 Y. Yu, personal communication, 1993. 20 R.J. Hill, J. AppL Crystallogr., 25 (1992) 589. 21 I. Higashi, H. Iwasaki, T. Ito, T. Lundstr6m, S. Okada and L.-E. Tergenius, J. Solid State Chem., 82 (1989) 230.