- Email: [email protected]
Correlation between atom distribution and the mixed alkali effect in (Na, K)-β-gallate
Sofid State Ionics 5 (1981) 219-222
North-Holland PublishingCompany
CORRELATION BETWEEN ATOM DISTRIBUTION AND THE MIXED ALKALI EFFECT IN (Na,K)-8-GALLATE M. P. AndersOn* Exxon Research and Engineering Company Box 45, Linden, NJ 07036 L. 11. Foster Thomas J. Watson Research Center, IB~I Box 218, Yorktown Heights, NY 10598 N a - ~ - g a l l a t e is an a l k a l i f a s t ion conductor which is i s o s t r u c t u r a l w i t h 8-A1203. Previous work had shown t h a t the c o n d u c t i v i t y o f c r y s t a l s having mixed (Na,K) compositions is g r e a t l y reduced over t h a t o f the pure sodium and potassium compounds. The anomaly is s i m i l a r to the "mixed a l k a l i e f f e c t " observed in glasses and amorphous m a t e r i a l s . C r y s t a l l o g r a p h i c i n v e s t i g a t i o n o f the pure compounds and a c r y s t a l in the v i c i n i t y o f the c o n d u c t i v i t y minimum has revealed t h a t the drop in c o n d u c t i v i t y is accom~nied by s i t e preferences o f Na+ and K+. The conduction plane is c h a r a c t e r i z e d by three d i s t i n c t s i t e s f o r the a l k a l i ions, a normal Beevers-Ross l a t t i c e s i t e and two i n t e r s t i t i a l sites. K+ is present on the normal l a t t i c e s i t e s o n l y . Na+ is e x c l u s i v e l y present on the i n t e r s t i t i a l sites. I.
INTRODUCTION
Na-8-Ga203, l i k e i t s aluminum isomorph, ~-A1203, e x h i b i t s h i g h t w o dimensional a l k a l i ion cond u c t i v i t y as a consequence o f d i s o r d e r . The ideal composition is NaGallOl7, but the real c r y s t a l contains about 60% excess sodium. Part o f t h i s is i n c o r p o r a t e d s u b s t i t u t i o n a l l y in the s t r u c t u r e , where i t replaces Ga3+ on t e t r a h e d r a l sites [1,2]. However, there is s t i l l about 46% excess mobile Na+ (compared to about 22% in 8A1203) which is accommodated in i n t e r s t i t i a l sites. Previous work had shown t h a t the cond u c t i v i t y o f c r y s t a l s having mixed (Na,K) comp o s i t i o n s , obtained by s u b s t i t u t i n g K+ f o r p a r t o f the mobile Na+ by ion exchange, was g r e a t l y reduced over t h a t o f the pure sodium and potassium compounds [ 3 ] . This e f f e c t is l i k e n e d to the well-known mixed a l k a l i e f f e c t in glasses and amorphous m a t e r i a l s [ 4 ] . The low conductiv i t y , which a t about 0.67 atom f r a c t i o n K+ is about 8 0 - f o l d below t h a t obtained by l i n e a r e x t r a p o l a t i o n between the c o n d u c t i v i t i e s o f the two end compounds, r e s u l t s from a pronounced increase in the a c t i v a t i o n energy f o r conduction. A s i m i l a r c o n d u c t i v i t y anomaly is observed in 8A1203 [ 5 , 6 ] , but a comprehensive e x p l a n a t i o n f o r the e f f e c t is not y e t a v a i l a b l e . Crystallographic i n v e s t i g a t i o n o f the s e r i e s o f c r y s t a l s Na-8-Ga203, mixed (Na,K)-~-Ga203 near the cond u c t i v i t y minimum, and Na-~-Ga203 with the mobile sodium completely replaced by potassium has been c a r r i e d out in order to e l u c i d a t e the a l k a l i d i s t r i b u t i o n s present. 2.
EXPERIMENTAL
The monocrystals used in t h i s study were grown by slow v a p o r i z a t i o n o f Na20 from a Na20-Ga203 melt [ 7 ] . Mixed (Na,K)-~-Ga203 compositions were prepared by ion exchange in molten s a l t s . The c r y s t a l parameters are given in Table I . The sodium concentrations were measured via radiochemical methods. The second c r y s t a l ( a b b r e v i a t e d Na~ + mixed ion) is somewhat more
sodium-rich than the composition corresponding to the minimum o f the c o n d u c t i v i t y curve (Fig. 3, Ref. 3). The t h i r d c r y s t a l ( a b b r e v i a t e d NaB + K) contains 10% residual sodium, but t h i s is the immobile sodium which has replaced Ga3+ on t e t r a h e d r a l s i t e s [ 1 , 2 ] . X-ray samples cons i s t e d o f small spheres ground to a p p r o x i m a t e l y 150 micron diameter. Measurements were c a r r i e d out in dry n i t r o g e n because o f the moisture sens i t i v i t y o f some o f the B - g a l l a t e samples in t h i s size range. Further d e t a i l s o f data c o l l e c t i o n and a n a l y s i s are discussed in Ref. 8. Table 1 a c Composition parameter parameter Na-B Na-8 ÷ mixed ion NaB ÷ K 3.
Na20-6.8Ga203 (Na20).5(K20).56.8Ga203 (Na20).I(K20).96.8Ga203
5.84 5.83
23.13 23.17
5.84
23.40
RESULTS
The 8 s t r u c t u r e consists o f a layered arrangement o f s p i n e l - l i k e oxide blocks a l t e r n a t i n g w i t h planes c o n t a i n i n g the a l k a l i ions. The a l k a l i planes are c a l l e d conduction planes because o f the ease o f 2-D a l k a l i motion. In Na-8-Ga203 the spinel blocks are d e f e c t i v e , and n e g a t i v e l y charged centers are present which are compensated by excess a l k a l i in the conduction plane [ 2 ] . The conduction plane is c h a r a c t e r i z e d by four d i f f e r e n t types o f s i t e s (Figure I ) . The Bridging Oxygen (BO) is occupied by a "spacer" oxygen i o n , which serves to separate neighboring spinel blocks above and below the plane. The Beevers-Ross s i t e (BR) is occupied by the a l k a l i ion in the ideal s t r u c t u r e , and is coordinated by s i x 02- ions ( t h r e e above and three below). The mid-Oxygen s i t e (mO) and anti-Beevers-Ross s i t e (aBR) are both i n t e r s t i t i a l s i t e s , and are coordinated by s i x 02- ions ( t h r e e above and three below), and two 02- ions (one above and one below) r e s p e c t i v e l y .
0 167 2738/81/0000-0000/$02.75 © North-Holland Publishing Company
220
M.P. Anderson, L.M. Foster / Atom distribution and the mixed alkali effect in (Na, K)-~-gallate
® ® Fig. 1 Sites in conduction plane.
X \ ,~ -112112
® 0
MO
MID-OXYGEN SITE
BR
BEEVERS-ROSS SITE
BO
BRIDGING OXYGEN SITE
1/2
Conduction plane of N a - ~ a i x e d i o n . Contoured every 2.00 e/A 3.
ABR ANTI-BEEVERS-ROSS SITE
Conduction plane o f Na-B. 0.25 e/A3.
Contoured every
The detected electron density in the a v a i l a b l e cation s i t e s o f the conduction plane are given in Table 2. The corresponding e l e c t r o n density maps for the three c r y s t a l s are given in Figure 2, Figure 3, and Figure 4. The data may be characterized as showing t h a t the electron density in the BR s i t e o f NaB ÷ mixed ion is approximately equal to t h a t o f NaB + K, but t h a t the e l e c t r o n density in the mO and aBR s i t e s of NaB -~ mixed ion is approximately equal to t h a t of NaB. Moreover, the e l e c t r o n density detected at the aBR s i t e in NaB and NaB + mixed ion peaks well above background, while the e l e c t r o n density in the aBR s i t e o f NaB ÷ K is not s i g n i f i c a n t . These observations suggest two conclusions. F i r s t , sodium is present in the aBR s i t e of NaB and NaB ÷ mixed ion, but potassium is not present in the aBR s i t e of NaB ÷ K. Second, potassium has replaced sodium p r i m a r i l y on the BR s i t e in NaB ÷ mixed ion. This conclusion is made because the BR density in the Na-B c r y s t a l c o n s t i t u t e s 0.48 o f the t o t a l sodium d e n s i t y in the plane (6.7 e/A 3 out of 14.1 e/A 3 f o r the BR, three mO, and aBR). At 0.55 atom f r a c t i o n potassium, the density in the mO and aBR s i t e s has remained v i r t u a l l y unchanged, but the density in the BR s i t e has increased more than three f o l d to approximately the value in the Na~ ÷ K crystal. The BR density in NaB ÷ K c o n s t i t u t e s 0.50 o f the t o t a l potassium d e n s i t y .
Conduction plane o f NaB~K. Contoured every 2.00 e/A 3 . Table 2 Measured Electron Density (Electrons per A3) Na-B Na-B + mixed ion Na-~ ÷ K
BR s i t e
mO s i t e
aBR s i t e
6.7 23.8
1.8 3.5
2.0 3.0
27.l
9.2
0.7
All values have an e r r o r ,~,0.5 e/A 3 Site occupation numbers for the three c r y s t a l s are given in Table 3. In the case o f Na-~Ga203 only sodium is assumed to be present. For NaB ÷ mixed ion, potassium s c a t t e r i n g factors were used in f i t t i n g the density o f the BR s i t e , and sodium were used in f i t t i n g the density of the mO and aBR. F i n a l l y , only potassium is assumed to be present in NaB ÷ K. The r e s u l t s show t h a t the occupation o f the BR s i t e in NaB ~ mixed ion is in good agreement with Na~ K, while the occupations o f the mO and aBR sites are in good agreement with NaB. The distances o f the a l k a l i ions from the c o o r d i n a t i n g oxygens for the three c r y s t a l s are given in Ref. 8. In general, a l l of the s i t e s are characterized by average bond distances which are l a r g e r than the expected values of 2.42 A for Na-O and 2.78 for K-O. However, the potassium in the BR s i t e of NaB ÷ mixed ion is an exception to t h i s trend. The average bond
M.P. Anderson, L.M. Foster / A torn distribution and the mixed alkali effect in (Na, K)-~-gallate
distance observed (2.858 A) is close to the ideal value,
ABR
Table 3 S i t e Occupation Numbers (Normalized to One Conduction Plane) NaB NaB ÷ mixed ion NaB + K
BR s i t e
mO s i t e s
aBR s i t e
0.81(4)* 0.64(3)**
0.66(8)* 0.69(7)*
0.09(5)* 0.08(3)*
0.67(2)**
0.78(3)**
0.0"*
221
ABR
BR
MO ABR
ABR
BRIDGING OXYGEN (B INTERSTITIAL OXYGEN •
SODIUM
* sodium **potassium 4.
DISCUSSION
The c o n d u c t i v i t y anomaly in mixed (Na,K)-B-Ga203 is associated with the s e p a r a t i o n o f sodium and potassium i n t o d i f f e r e n t s i t e s . Potassium in the presence o f sodium prefers the Beevers-Ross s i t e . This behavior had been p r e d i c t e d by Wang et a l . f o r the system (Na,K)-~-AI203 [ 9 ] , but t h i s is the f i r s t d i r e c t s t r u c t u r a l o b s e r v a t i o n in the knowledge o f the authors. The mixed a l k a l i e f f e c t is also accompanied by a n e g a t i v e d e v i a t i o n from Vegard's law in these crystals. The expected z l a t t i c e parameter f o r (Na,K)-~-Ga203 a t a potassium atom f r a c t i o n o f 0.55 is 23.28, but the observed value is 23.17 ( a p p r o x i m a t e l y the same f o r Na-~). This r e f l e c t s the f a c t t h a t the width o f the conduction plane ( s l o t w i d t h ) in Na-~ ÷ mixed ion is the same as f o r Na-~, but s i g n i f i c a n t l y increased in Na-~ K. The s l o t width o n l y increases in size when sodium is replaced by potassium in the i n t e r s t i tial sites [8]. An understanding o f the circumstances t h a t lead to the p r e f e r e n t i a l bonding o f K+ ions in the BR s i t e requires modeling o f the type done by Wang et a l . [ g ] . However, c a r e f u l examination o f the change in s t r u c t u r a l parameters o f the c r y s t a l s suggest a physical p i c t u r e o f the o r i g i n o f s i t e preference [ 8 ] . F i r s t , the K+-O2" distance is c l o s e r to the normal value f o r 6 - f o l d c o o r d i n a t i o n than the Na+-O2-. Second, the width o f the conduction s l o t is smaller and, hence, provides f o r more normal a l k a l i - o x y g e n s e p a r a t i o n , when the s m a l l e r Na+ is in the i n t e r s t i t i a l sites. Models f o r s h o r t range order in the c r y s t a l s are given in Table 4. These models are based upon the t r i p l e t c l u s t e r as described in Refs. 2 and 8. Figure 5 depicts the conduction plane o f Na~. Triangles are used to d e l i n e a t e the Na-O-Na c l u s t e r and the Na-Na-Na c l u s t e r , w h i l e c i r c l e s i d e n t i f y m i g r a t i n g sodium in the aBR s i t e s . Figure 6 shows the conduction plane at the mixed (Na,K) composition. Potassium has replaced sodium in the BR s i t e s , l e a v i n g o n l y sodium present in the i n t e r s t i t i a l c l u s t e r s ( i t has been assumed t h a t f o r some o f the t r i p l e t c l u s t e r s , sodium is present in an aBR-mO-mO c o n f i g u r a t i o n as opposed to a mO-mO-mO c o n f i g u r a t i o n ) . Two factors may be suggested t h a t c o n t r i b u t e to
Conduction plane o f Na-B. Triangles d e l i n e a t e Na-O-Na and Na-Na-Na i n t e r s t i t i a l clusters, while c i r c l e s i d e n t i f y m i g r a t i n g sodium in the aBR sites. The Na-Na-Na c l u s t e r s may be bound to s u b s t i t u t i o n a l sodium present in g a l l i u m t e t r a hedral s i t e s below the BR s i t e s o f the conduction plane.
Table 4 Short Range Order Models NaB BR mO triplet observed
0.75 0.81(4)
0.68 0.66(8)
aBR 0.08 0.09(5)
Na~ ÷ mixed ion triplet* observed
BR
mO
0.69 0.64(3)
0.74 0.69(7)
aBR 0.08 0.08(3)
NaB + K triplet observed
BR
mO
0.69 0.67(2)
0.82 0.78(3)
aBR 0.0 0.0
*Computed f o r potassium atom f r a c t i o n 0.46. the decrease in c o n d u c t i v i t y : ( I ) There is an increase in the a c t i v a t i o n energy required to remove sodium from the i n t e r stitial clusters. This is because K+ in the BR s i t e is more s t r o n g l y bound than Na+, so t h a t more energy is required to remove K+ and replace i t by Na+ than i f j u s t Na+ were present. (2) There is an increase in the a c t i v a t i o n energy required f o r l a t t i c e m i g r a t i o n . This is because any Na+ which escapes from the defect complex and migrates via an i n t e r s t i t i a l c y mechanism w i l l e v e n t u a l l y encounter o t h e r K+
2..
M.P. Anderson, L.M, Foster / A t o m distribution and the mLYed alkali e lfect in (Na, K)-13-gullate
M• 0
BR
/
REFERENCES
ABR
1.
L. M. Foster, D. R. Campbell, and G. V. Chandrashekhar, J. Electrochem. Soc., 125, 1689 (1978).
2.
M. P. Anderson, L. M. Foster, and S. J. LaPlaca, paper presented at this conference.
3.
G. V. Chandrashekhar and L. M. Foster, Solid State Comm., 2__77,269 (1978).
4.
D. E. Day, J. Non-Crystalline Solids, 21, 343 (1976).
5.
R. N. Radzilowski, Y. F. Yao and J. T. Kummer, J. Appl. Phys., 40, 4716 (1969).
6.
L. M. Foster, in Fast lon Transport in Solids, eds. P. Vashishta, J. N. Mundy, and G. K. Shenoy, 249, North Holland (1979).
7.
L. 1.1. Foster, G. V. Chandrashekhar, J. E. S c a r d e f i e l d , and R. B. Bradford, J. Amer. Cer. Soc., 63, 9-10, 509 (1980).
8.
11. P. Anderson, D. E. Sc. Thesis, School of Engineering and Applied Science, Columbia U n i v e r s i t y (1981).
9.
J. C. Wang, J. B. Bates, T. Kaneda, and Herbert Engstrom, in Fast lon Transport in S o l i d s , eds. P. Vashishta, J . N. Mundy, and G. K. Shenoy, 379, North Holland (1979).
MO
ABR
ABR
• O O (]~
SODIUM POTASSIUM OXYGEN INTERSTITIAL
OXYGEN
/
/f
Conduction plane o f Na-~ at the mixed (Na, K) composition. Triangles d e l i n e a t e Na-O-Na and Na-Na-Na i n t e r s t i t i a l c l u s t e r s .
ions in the BR s i t e . More energy w i l l again be required to remove K+ from the s i t e and replace i t by Na+ than i f j u s t Na+ were present. 5.
CONCLUSION
The drop in c o n d u c t i v i t y due to the presence o f mixed (Na,K) ions in Na-~-Ga203 is accompanied by the separation of the ions into d i f f e r e n t s i t e s . Near the minimum in c o n d u c t i v i t y , sodium is observed in the mO and aBR s i t e s while potassium shows a preference for the BR s i t e . The s i t e separation implies that the m a j o r i t y of i n t e r s t i t i a l c l u s t e r s consist o f sodium. The decrease in c o n d u c t i v i t y is a t t r i b u t e d to the increase in the a c t i v a t i o n energy required to break up sodium c l u s t e r s and the increase in the a c t i v a t i o n energy for motion of the c a r r i e r s .
*Part of t h i s work was c a r r i e d out at the IBM T.J. Watson Research Center
North-Holland PublishingCompany
CORRELATION BETWEEN ATOM DISTRIBUTION AND THE MIXED ALKALI EFFECT IN (Na,K)-8-GALLATE M. P. AndersOn* Exxon Research and Engineering Company Box 45, Linden, NJ 07036 L. 11. Foster Thomas J. Watson Research Center, IB~I Box 218, Yorktown Heights, NY 10598 N a - ~ - g a l l a t e is an a l k a l i f a s t ion conductor which is i s o s t r u c t u r a l w i t h 8-A1203. Previous work had shown t h a t the c o n d u c t i v i t y o f c r y s t a l s having mixed (Na,K) compositions is g r e a t l y reduced over t h a t o f the pure sodium and potassium compounds. The anomaly is s i m i l a r to the "mixed a l k a l i e f f e c t " observed in glasses and amorphous m a t e r i a l s . C r y s t a l l o g r a p h i c i n v e s t i g a t i o n o f the pure compounds and a c r y s t a l in the v i c i n i t y o f the c o n d u c t i v i t y minimum has revealed t h a t the drop in c o n d u c t i v i t y is accom~nied by s i t e preferences o f Na+ and K+. The conduction plane is c h a r a c t e r i z e d by three d i s t i n c t s i t e s f o r the a l k a l i ions, a normal Beevers-Ross l a t t i c e s i t e and two i n t e r s t i t i a l sites. K+ is present on the normal l a t t i c e s i t e s o n l y . Na+ is e x c l u s i v e l y present on the i n t e r s t i t i a l sites. I.
INTRODUCTION
Na-8-Ga203, l i k e i t s aluminum isomorph, ~-A1203, e x h i b i t s h i g h t w o dimensional a l k a l i ion cond u c t i v i t y as a consequence o f d i s o r d e r . The ideal composition is NaGallOl7, but the real c r y s t a l contains about 60% excess sodium. Part o f t h i s is i n c o r p o r a t e d s u b s t i t u t i o n a l l y in the s t r u c t u r e , where i t replaces Ga3+ on t e t r a h e d r a l sites [1,2]. However, there is s t i l l about 46% excess mobile Na+ (compared to about 22% in 8A1203) which is accommodated in i n t e r s t i t i a l sites. Previous work had shown t h a t the cond u c t i v i t y o f c r y s t a l s having mixed (Na,K) comp o s i t i o n s , obtained by s u b s t i t u t i n g K+ f o r p a r t o f the mobile Na+ by ion exchange, was g r e a t l y reduced over t h a t o f the pure sodium and potassium compounds [ 3 ] . This e f f e c t is l i k e n e d to the well-known mixed a l k a l i e f f e c t in glasses and amorphous m a t e r i a l s [ 4 ] . The low conductiv i t y , which a t about 0.67 atom f r a c t i o n K+ is about 8 0 - f o l d below t h a t obtained by l i n e a r e x t r a p o l a t i o n between the c o n d u c t i v i t i e s o f the two end compounds, r e s u l t s from a pronounced increase in the a c t i v a t i o n energy f o r conduction. A s i m i l a r c o n d u c t i v i t y anomaly is observed in 8A1203 [ 5 , 6 ] , but a comprehensive e x p l a n a t i o n f o r the e f f e c t is not y e t a v a i l a b l e . Crystallographic i n v e s t i g a t i o n o f the s e r i e s o f c r y s t a l s Na-8-Ga203, mixed (Na,K)-~-Ga203 near the cond u c t i v i t y minimum, and Na-~-Ga203 with the mobile sodium completely replaced by potassium has been c a r r i e d out in order to e l u c i d a t e the a l k a l i d i s t r i b u t i o n s present. 2.
EXPERIMENTAL
The monocrystals used in t h i s study were grown by slow v a p o r i z a t i o n o f Na20 from a Na20-Ga203 melt [ 7 ] . Mixed (Na,K)-~-Ga203 compositions were prepared by ion exchange in molten s a l t s . The c r y s t a l parameters are given in Table I . The sodium concentrations were measured via radiochemical methods. The second c r y s t a l ( a b b r e v i a t e d Na~ + mixed ion) is somewhat more
sodium-rich than the composition corresponding to the minimum o f the c o n d u c t i v i t y curve (Fig. 3, Ref. 3). The t h i r d c r y s t a l ( a b b r e v i a t e d NaB + K) contains 10% residual sodium, but t h i s is the immobile sodium which has replaced Ga3+ on t e t r a h e d r a l s i t e s [ 1 , 2 ] . X-ray samples cons i s t e d o f small spheres ground to a p p r o x i m a t e l y 150 micron diameter. Measurements were c a r r i e d out in dry n i t r o g e n because o f the moisture sens i t i v i t y o f some o f the B - g a l l a t e samples in t h i s size range. Further d e t a i l s o f data c o l l e c t i o n and a n a l y s i s are discussed in Ref. 8. Table 1 a c Composition parameter parameter Na-B Na-8 ÷ mixed ion NaB ÷ K 3.
Na20-6.8Ga203 (Na20).5(K20).56.8Ga203 (Na20).I(K20).96.8Ga203
5.84 5.83
23.13 23.17
5.84
23.40
RESULTS
The 8 s t r u c t u r e consists o f a layered arrangement o f s p i n e l - l i k e oxide blocks a l t e r n a t i n g w i t h planes c o n t a i n i n g the a l k a l i ions. The a l k a l i planes are c a l l e d conduction planes because o f the ease o f 2-D a l k a l i motion. In Na-8-Ga203 the spinel blocks are d e f e c t i v e , and n e g a t i v e l y charged centers are present which are compensated by excess a l k a l i in the conduction plane [ 2 ] . The conduction plane is c h a r a c t e r i z e d by four d i f f e r e n t types o f s i t e s (Figure I ) . The Bridging Oxygen (BO) is occupied by a "spacer" oxygen i o n , which serves to separate neighboring spinel blocks above and below the plane. The Beevers-Ross s i t e (BR) is occupied by the a l k a l i ion in the ideal s t r u c t u r e , and is coordinated by s i x 02- ions ( t h r e e above and three below). The mid-Oxygen s i t e (mO) and anti-Beevers-Ross s i t e (aBR) are both i n t e r s t i t i a l s i t e s , and are coordinated by s i x 02- ions ( t h r e e above and three below), and two 02- ions (one above and one below) r e s p e c t i v e l y .
0 167 2738/81/0000-0000/$02.75 © North-Holland Publishing Company
220
M.P. Anderson, L.M. Foster / Atom distribution and the mixed alkali effect in (Na, K)-~-gallate
® ® Fig. 1 Sites in conduction plane.
X \ ,~ -112112
® 0
MO
MID-OXYGEN SITE
BR
BEEVERS-ROSS SITE
BO
BRIDGING OXYGEN SITE
1/2
Conduction plane of N a - ~ a i x e d i o n . Contoured every 2.00 e/A 3.
ABR ANTI-BEEVERS-ROSS SITE
Conduction plane o f Na-B. 0.25 e/A3.
Contoured every
The detected electron density in the a v a i l a b l e cation s i t e s o f the conduction plane are given in Table 2. The corresponding e l e c t r o n density maps for the three c r y s t a l s are given in Figure 2, Figure 3, and Figure 4. The data may be characterized as showing t h a t the electron density in the BR s i t e o f NaB ÷ mixed ion is approximately equal to t h a t o f NaB + K, but t h a t the e l e c t r o n density in the mO and aBR s i t e s of NaB -~ mixed ion is approximately equal to t h a t of NaB. Moreover, the e l e c t r o n density detected at the aBR s i t e in NaB and NaB + mixed ion peaks well above background, while the e l e c t r o n density in the aBR s i t e o f NaB ÷ K is not s i g n i f i c a n t . These observations suggest two conclusions. F i r s t , sodium is present in the aBR s i t e of NaB and NaB ÷ mixed ion, but potassium is not present in the aBR s i t e of NaB ÷ K. Second, potassium has replaced sodium p r i m a r i l y on the BR s i t e in NaB ÷ mixed ion. This conclusion is made because the BR density in the Na-B c r y s t a l c o n s t i t u t e s 0.48 o f the t o t a l sodium d e n s i t y in the plane (6.7 e/A 3 out of 14.1 e/A 3 f o r the BR, three mO, and aBR). At 0.55 atom f r a c t i o n potassium, the density in the mO and aBR s i t e s has remained v i r t u a l l y unchanged, but the density in the BR s i t e has increased more than three f o l d to approximately the value in the Na~ ÷ K crystal. The BR density in NaB ÷ K c o n s t i t u t e s 0.50 o f the t o t a l potassium d e n s i t y .
Conduction plane o f NaB~K. Contoured every 2.00 e/A 3 . Table 2 Measured Electron Density (Electrons per A3) Na-B Na-B + mixed ion Na-~ ÷ K
BR s i t e
mO s i t e
aBR s i t e
6.7 23.8
1.8 3.5
2.0 3.0
27.l
9.2
0.7
All values have an e r r o r ,~,0.5 e/A 3 Site occupation numbers for the three c r y s t a l s are given in Table 3. In the case o f Na-~Ga203 only sodium is assumed to be present. For NaB ÷ mixed ion, potassium s c a t t e r i n g factors were used in f i t t i n g the density o f the BR s i t e , and sodium were used in f i t t i n g the density of the mO and aBR. F i n a l l y , only potassium is assumed to be present in NaB ÷ K. The r e s u l t s show t h a t the occupation o f the BR s i t e in NaB ~ mixed ion is in good agreement with Na~ K, while the occupations o f the mO and aBR sites are in good agreement with NaB. The distances o f the a l k a l i ions from the c o o r d i n a t i n g oxygens for the three c r y s t a l s are given in Ref. 8. In general, a l l of the s i t e s are characterized by average bond distances which are l a r g e r than the expected values of 2.42 A for Na-O and 2.78 for K-O. However, the potassium in the BR s i t e of NaB ÷ mixed ion is an exception to t h i s trend. The average bond
M.P. Anderson, L.M. Foster / A torn distribution and the mixed alkali effect in (Na, K)-~-gallate
distance observed (2.858 A) is close to the ideal value,
ABR
Table 3 S i t e Occupation Numbers (Normalized to One Conduction Plane) NaB NaB ÷ mixed ion NaB + K
BR s i t e
mO s i t e s
aBR s i t e
0.81(4)* 0.64(3)**
0.66(8)* 0.69(7)*
0.09(5)* 0.08(3)*
0.67(2)**
0.78(3)**
0.0"*
221
ABR
BR
MO ABR
ABR
BRIDGING OXYGEN (B INTERSTITIAL OXYGEN •
SODIUM
* sodium **potassium 4.
DISCUSSION
The c o n d u c t i v i t y anomaly in mixed (Na,K)-B-Ga203 is associated with the s e p a r a t i o n o f sodium and potassium i n t o d i f f e r e n t s i t e s . Potassium in the presence o f sodium prefers the Beevers-Ross s i t e . This behavior had been p r e d i c t e d by Wang et a l . f o r the system (Na,K)-~-AI203 [ 9 ] , but t h i s is the f i r s t d i r e c t s t r u c t u r a l o b s e r v a t i o n in the knowledge o f the authors. The mixed a l k a l i e f f e c t is also accompanied by a n e g a t i v e d e v i a t i o n from Vegard's law in these crystals. The expected z l a t t i c e parameter f o r (Na,K)-~-Ga203 a t a potassium atom f r a c t i o n o f 0.55 is 23.28, but the observed value is 23.17 ( a p p r o x i m a t e l y the same f o r Na-~). This r e f l e c t s the f a c t t h a t the width o f the conduction plane ( s l o t w i d t h ) in Na-~ ÷ mixed ion is the same as f o r Na-~, but s i g n i f i c a n t l y increased in Na-~ K. The s l o t width o n l y increases in size when sodium is replaced by potassium in the i n t e r s t i tial sites [8]. An understanding o f the circumstances t h a t lead to the p r e f e r e n t i a l bonding o f K+ ions in the BR s i t e requires modeling o f the type done by Wang et a l . [ g ] . However, c a r e f u l examination o f the change in s t r u c t u r a l parameters o f the c r y s t a l s suggest a physical p i c t u r e o f the o r i g i n o f s i t e preference [ 8 ] . F i r s t , the K+-O2" distance is c l o s e r to the normal value f o r 6 - f o l d c o o r d i n a t i o n than the Na+-O2-. Second, the width o f the conduction s l o t is smaller and, hence, provides f o r more normal a l k a l i - o x y g e n s e p a r a t i o n , when the s m a l l e r Na+ is in the i n t e r s t i t i a l sites. Models f o r s h o r t range order in the c r y s t a l s are given in Table 4. These models are based upon the t r i p l e t c l u s t e r as described in Refs. 2 and 8. Figure 5 depicts the conduction plane o f Na~. Triangles are used to d e l i n e a t e the Na-O-Na c l u s t e r and the Na-Na-Na c l u s t e r , w h i l e c i r c l e s i d e n t i f y m i g r a t i n g sodium in the aBR s i t e s . Figure 6 shows the conduction plane at the mixed (Na,K) composition. Potassium has replaced sodium in the BR s i t e s , l e a v i n g o n l y sodium present in the i n t e r s t i t i a l c l u s t e r s ( i t has been assumed t h a t f o r some o f the t r i p l e t c l u s t e r s , sodium is present in an aBR-mO-mO c o n f i g u r a t i o n as opposed to a mO-mO-mO c o n f i g u r a t i o n ) . Two factors may be suggested t h a t c o n t r i b u t e to
Conduction plane o f Na-B. Triangles d e l i n e a t e Na-O-Na and Na-Na-Na i n t e r s t i t i a l clusters, while c i r c l e s i d e n t i f y m i g r a t i n g sodium in the aBR sites. The Na-Na-Na c l u s t e r s may be bound to s u b s t i t u t i o n a l sodium present in g a l l i u m t e t r a hedral s i t e s below the BR s i t e s o f the conduction plane.
Table 4 Short Range Order Models NaB BR mO triplet observed
0.75 0.81(4)
0.68 0.66(8)
aBR 0.08 0.09(5)
Na~ ÷ mixed ion triplet* observed
BR
mO
0.69 0.64(3)
0.74 0.69(7)
aBR 0.08 0.08(3)
NaB + K triplet observed
BR
mO
0.69 0.67(2)
0.82 0.78(3)
aBR 0.0 0.0
*Computed f o r potassium atom f r a c t i o n 0.46. the decrease in c o n d u c t i v i t y : ( I ) There is an increase in the a c t i v a t i o n energy required to remove sodium from the i n t e r stitial clusters. This is because K+ in the BR s i t e is more s t r o n g l y bound than Na+, so t h a t more energy is required to remove K+ and replace i t by Na+ than i f j u s t Na+ were present. (2) There is an increase in the a c t i v a t i o n energy required f o r l a t t i c e m i g r a t i o n . This is because any Na+ which escapes from the defect complex and migrates via an i n t e r s t i t i a l c y mechanism w i l l e v e n t u a l l y encounter o t h e r K+
2..
M.P. Anderson, L.M, Foster / A t o m distribution and the mLYed alkali e lfect in (Na, K)-13-gullate
M• 0
BR
/
REFERENCES
ABR
1.
L. M. Foster, D. R. Campbell, and G. V. Chandrashekhar, J. Electrochem. Soc., 125, 1689 (1978).
2.
M. P. Anderson, L. M. Foster, and S. J. LaPlaca, paper presented at this conference.
3.
G. V. Chandrashekhar and L. M. Foster, Solid State Comm., 2__77,269 (1978).
4.
D. E. Day, J. Non-Crystalline Solids, 21, 343 (1976).
5.
R. N. Radzilowski, Y. F. Yao and J. T. Kummer, J. Appl. Phys., 40, 4716 (1969).
6.
L. M. Foster, in Fast lon Transport in Solids, eds. P. Vashishta, J. N. Mundy, and G. K. Shenoy, 249, North Holland (1979).
7.
L. 1.1. Foster, G. V. Chandrashekhar, J. E. S c a r d e f i e l d , and R. B. Bradford, J. Amer. Cer. Soc., 63, 9-10, 509 (1980).
8.
11. P. Anderson, D. E. Sc. Thesis, School of Engineering and Applied Science, Columbia U n i v e r s i t y (1981).
9.
J. C. Wang, J. B. Bates, T. Kaneda, and Herbert Engstrom, in Fast lon Transport in S o l i d s , eds. P. Vashishta, J . N. Mundy, and G. K. Shenoy, 379, North Holland (1979).
MO
ABR
ABR
• O O (]~
SODIUM POTASSIUM OXYGEN INTERSTITIAL
OXYGEN
/
/f
Conduction plane o f Na-~ at the mixed (Na, K) composition. Triangles d e l i n e a t e Na-O-Na and Na-Na-Na i n t e r s t i t i a l c l u s t e r s .
ions in the BR s i t e . More energy w i l l again be required to remove K+ from the s i t e and replace i t by Na+ than i f j u s t Na+ were present. 5.
CONCLUSION
The drop in c o n d u c t i v i t y due to the presence o f mixed (Na,K) ions in Na-~-Ga203 is accompanied by the separation of the ions into d i f f e r e n t s i t e s . Near the minimum in c o n d u c t i v i t y , sodium is observed in the mO and aBR s i t e s while potassium shows a preference for the BR s i t e . The s i t e separation implies that the m a j o r i t y of i n t e r s t i t i a l c l u s t e r s consist o f sodium. The decrease in c o n d u c t i v i t y is a t t r i b u t e d to the increase in the a c t i v a t i o n energy required to break up sodium c l u s t e r s and the increase in the a c t i v a t i o n energy for motion of the c a r r i e r s .
*Part of t h i s work was c a r r i e d out at the IBM T.J. Watson Research Center