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Ca8-χLiχAl3: defects and substitution in the Fe3Al structure type
Journal of Alloys and Compounds, 185 (1992) 221-234 JALCOM 106
221
Cas_xLixA13: defects and substitution in the Fe3A1 structure
type Gordon J. Miller* and Reinhard Nesper** Max-Planck-Institut ffir FestkS"rperfovschung, Heisenbergstrasse 1, 7000 Stuttgart 80 (Germany) (Received November 26, 1991)
Abstract Cas_xiixA13 was obtained in crystalline form during investigations of the Ca-Li-AI ternary phase diagram. The structure is isotypic to Cabin3 (space group P i ; a = 9 4 7 . 0 pro, b = 9 6 0 . 2 pm, c = 9 6 4 . 6 pro, affi99.17 °, fl=101.08 °, T=119.51°), which is an ordered defect structure of the Fe3A1 or the Li3Bi type. Vacancies occur exclusively at pseudotetrahedral sites and lithium substitutes for calcium in the pseudo-octahedral sites when compared with the cubic FeaAl structure (space group F m 3 m ) of a hypothetical "Ca~AI". Madelung and extended Hiickel calculations are utilized to discuss the observed defect and substitutional pattern.
I. Introduction In the Ca-AI binary system, only two phases have been characterized: CaA12 (cubic MgCu2-type) [1, 2] and CaA14 (tetragonal BaA14 type) [3]. No calcium-rich phases are yet known. With gallium and indium, Fornasini and Pani have reported two calcium-rich compounds: CaesGau [4] and CaBin3 [5], the second of which is the so called "Ca3In" phase in the Ca-In system. During efforts to examine the Ca-Li-A1 ternary diagram, we discovered crystals which, after an X-ray structure determination, exhibit geometrical characteristics of the CaBin3 structure, but are deficient in calcium. In this contribution we shall present the structure determination of Cas_~Li~Ala, a comparison with related compounds, and comments regarding the importance of lithium in this material.
2. Experimental details The sample was prepared by melting (T= 1180 K) a mixture of calcium (99.5 at.%, Fluka), lithium (99 at.%, Merck), and aluminium (99.9 at.%, *Present address: Department of Chemistry, Iowa State Umver~ity,Ames, L~ 50011, USA. **Present address: Laboratorium fiir Anorganische Chemie, ETH Zentrum, CH-8092 Ziirich, Switzerland.
0925-8388/92/$5.00
© 1 9 9 2 - Elsevier Sequoia~ All rights reserved
222
Merck) in the ratio 4:1:1 in a molybdenum crucible, which was sealed in a niobium ampoule under an argon atmosphere. The reaction container was placed in an argon-filled quartz Schlenk tube. After 2 h the melt was slowly cooled to room temperature over a 2 day period. Attempts to prepare a pure binary CasAl~ phase failed under similar conditions. A crystal suitable for data collection (checked with Buerger precession photographs) was mounted in an argon-filled capillary and measured on a single-crystal diffractometer. Solution of the structure proceeded with direct methods in space group P1. Table 1 contains all crystal data and refinement parameters. Atomic coordinates and anisotropic temperature factors are listed in Table 2, and significant bond distances are given in Table 3.
TABLE 1 Crystallographic data for Cas_xLi~A13 ( x = 0 . 1 6 ) Empirical formula Crystal size (mm 3) Crystal system Space group a, b, c (pm) a, fl, T (deg) Volume (pro 3) Z Formula weight (Da) Density (calculated) (Mg m -1) Absorption coefficient (mm -1) F(000) Diffractometer; radiation Temperature (K) Monochromator 2e range (deg) Scan type; speed; range Standard reflections Index ranges Reflections collected Independent reflections Observed reflections Absorption correction System used; solution Refinement method Quantity minimized Extinction correction
Ca15.68Lio.32Ale 0.06 x 0.03 × 0.05 Triclimc
Pi 947.0(2), 960.2(2), 964.6(2) 99.17(2), 101.08(2), 119.50(2) 715.2(3) x 108 1 79O.4 1.835 3.021 391.63 Siemens R3m/V; Mo Ka ( A = 0 . 7 1 0 7 3 / ~ ) 298 Highly oriented graphite crystal 4.0-55.0 eo; variable; 0.50-19.50 ° min -1 in w; 2.00 ° 2 measured every 98 reflections
-12~ 3.0~(F)) N/A
SHELXTL; direct methods Full matrix, least squares ~,w(Fo - F c ) 2 X ffi - 0.00021(12) where F * • F[ 1 + O.O02xF2/sin(2e) ] -114
Weighting scheme Number of parameters refined Final R indices (observed data) R indices (all data) Goodness of fit Largest difference peak
w- ' = o2(F)
106 R ffi 5.3296, w R ffi4.00% R = 5.32%, w R ffi4.00% 1.15 1.17 e / ~ - 3
0.47062(7) -0.07839(7) 0.12117(7) 0.66387(7) 0.04373(7) 0.29947(6) 0.22446(7) 0.45202(9) 0 0.5 0.82818(9) 0.32348(9)
Cal Ca2 Ca3 Ca4 Ca5 Ca6 Ca7 Ca8 All Al2 Al3 Al4
0.30106(7) -0.22839(7) -0.40216(7) 0.12081(6) 0.93931(7) -0.50006(6) -0.15364(9) 0.28515(9) 0.5 0 0.66380(9) 0.15872(9)
y
SOFb
0.35035(7) 1 0.89231(7) 1 0.35219(7) 1 0.89032(7) 1 0.33076(7) 1 0.89163(7) 1 0.69921(7) 0.903(4) 0.69999(8) 0.938(4) 0 1 0.5 1 0.49990(10) 1 -0.02741(9) 1
z
217(2) 194(2) 235(2) 211(2) 233(2) 208(2) 263(3) 270(4) 176(5) 195(5) 176(3) 177(3)
Ueq
168(2) 193(2) 259(3) 187(2) 254(3) 144(2) 139(3) 373(4) 156(5) 222(5) 130(3) 158(3)
UII
182(2) 225(3) 213(3) 167(2) 158(2) 183(2) 289(4) 375(4) 174(5) 155(5) 149(3) 159(3)
U22
228(3) 222(3) 230(3) 245(3) 260(3) 250(3) 227(4) 241(4) 210(6) 207(6) 214(4) 206(4)
U~3
61(2) 101(2) 87(2) 70(2) 80(2) 40(2) - 12(3) 156(3) 77(4) 60(4) 66(3) 62(3)
U23
44(2) 93(2) 52(2) 37(2) 106(2) 80(2) 59(3) 147(3) 79(4) 99(5) 32(3) 73(3)
U13
51(2) 134(2) 129(2) 81(2) 80(2) 57(2) 48(3) 292(3) 86(4) 90(4) 54(3) 73(3)
Ul2
~rhe U~j parameters are expressed in the form e x p [ - 2 . z 2 ( U , , h 2 a * 2 + ... + 2 U , ahka*b*] and given in units of square picometres. Standard deviations are given in parentheses. bSite Occupation Factor.
x
Atom
Positional parameters and thermal parameters U~= for Caa_xLi~A13
TABLE 2
bO
Al2 Al3 Al3' Al4 Ca2' Ca3' Ca4' a5 Ca6' Ca7' Ca8 CaB'
All Al3 Al4 Al4' Cal' Ca2' Ca3' Ca4' Ca5 Ca5' Ca6' Ca7
Cal
Ca2
(cominued)
Atom 2
Atom 1
330.2 357.0 359.4 315.4 365.3 390.6 372.3 376.9 399.2 370.4 368.2 355.8
353.3 325.3 354.4 341.7 365.3 390.8 376.9 375.7 362.2 386.1 343.4 380.1
Distance
Ca5
Ca4
Atom 1
Important bond distances (pm) in Cas_~Li~Ala
TABLE 3
Al3 Al3' Al4' Cal Ca2 Ca2' Ca3 Ca4' Ca5' Ca6' Ca7' Ca8'
All Al2 Al4 Al4' Ca1' Ca2' Ca3' Ca5' Ca6' Ca7 Ca7' Ca8
Atom 2
334.1 337.1 367.8 375.7 399.2 370.4 372.2 400.0 367.2 372.7 397.8 400.9
325.1 353.8 363.3 321.8 376.9 360.9 391.7 400.0 372.0 351.6 381.6 353.7
Distance
Ca8
Ca7
Atom 1
Al2 A13' A14 Cal Cal' Ca3' Ca4 Ca5 Ca5' Ca6 Ca6' Ca7'
Al2 Al3 Al4 Ca1' Ca2 Ca3 Ca3' Ca4 Ca4' Ca5 Ca5' Ca8
Atom 2
336.3 325.8 326.5 343.4 380.1 378.7 353.7 411.8 400.9 353.6 379.2 366.6
342.3 324.4 325.4 386.1 355.7 342.8 375.6 351.6 381.6 406.6 397.8 366.6
Distance
Al3
Al2
Atom 1
Cal Cal ' Ca2 Ca3 Ca3' Ca5 Ca5' Ca6' Ca7 Ca8'
Cal Ca1' Ca3 Ca3' Ca4 Ca4' Ca5 CaS* Ca7 Ca7' Ca8 CaB'
Atom 2
325.3 354.4 357.0 361.8 326.2 334.1 337.1 356.1 324.4 325.8
353.3 353.3 352.9 352.9 353.8 353.8 402.2 402.2 342.3 342.3 336.2 336.2
Distance
t~
Atom 2
All Al2 Al3 Al3' CA1 Ca2' Ca4' Ca5 Ca6' Ca7 Ca7' Ca8'
Atom 1
Ca3
TABLE 3 (continued)
318.8 352.9 361.8 326.2 390.8 372.3 391.7 372.2 378.1 342.8 375.6 378.7
Distance
Ca6
Atom 1 All A13' A14 A14' Cal' Ca2' Ca3' Ca4' Ca5' Ca6' Ca8 Ca8'
Atom 2 320.6 356.1 358.8 324.2 362.2 368.2 378.1 372.4 372.7 396.7 353.6 379.2
Distance All
Atom 1 Ca2 Ca2' Ca3 Ca3' Ca4 Ca4' Ca6 Ca6'
Atom 2 330.2 330.2 318.8 318.8 325.1 325.1 320.6 320.6
Distance A14
Atom 1 CA1 Ca2 Ca2' Ca4 Ca4' Ca5' Ca6 Ca6' Ca7 Ca8
Atom 2
341.7 359.4 315.4 363.3 321.8 367.8 358.8 324.3 325.4 326.5
Distance
t~ O1
226 Refinement of site occupation factors for the single crystal that was analysed revealed calcium deficiency. According to the data in Table 2, the resulting stoichiometry is CaT.s4Lio.leA13.
3. A n a l y s i s o f t h e c r y s t a l s t r u c t u r e
The structure of Cas_~Li~Als, which is illustrated in Fig. 1, is quite complicated and seemingly _unusual for an intermetallic compound. It adopts the triclinic space group, P 1 , is isotypic to the reported structure of CaBin3, and, as pointed out by Fornasini, is related to the f.c.c. FeaA1 structure type (also known as Li3Bi or BiFa type) [5]. It should be emphasized that we could only obtain this phase as a ternary compound. The close relationship between the CaB_~Li~A13 structure and the Li3Bi type is clearly evident from the arrangement of aluminium atoms, which forms a slightly distorted f.c.c. framework where the coordination number of aluminium is 12 with distances 5.30 /~
0 CO
0 CO
0
0
CD_
CO_
Uco g~ eco Uco ~
0 o 00o 00o 00o 00o 00o 0
0
0
o00 o00 o00 o00 o00 o 0
o oeOOoo~::~ogOo ~:)Oo ~ooo" o o o o o / o ~ ooo/ooo/ooo o o 0 o 00o 00o 00o 00o 00o 0 0
0
o00 o(30 o00 o00 o00 o 0 CO_ CD~ QO~ CO-- (D-- Q~, gCO U ~ gCO U ~ U~, 0
0
0
0
0
Fig. 1. The crystal structure of Cas_=Li=A13 in a (010) projection: O, aluminium atom positions;
o, Ca atoms originating from the tetrahedral holes of the Li3Bi structure type; O, calcium or lithium sites originating from the octahedral holes in the LisBi type.
227
by introducing higher valent species at the tetrahedral positions as in BiO~F3_z~. A competing solution is the Na~As structure with an h.c.p, array of arsenic atoms. Two-thirds of the sodium atoms occupy all tetrahedral holes, but the octahedral sites are vacant. The residual one-third of the sodium atoms are located halfway between the other sodium atoms to gain three near arsenic neighbours. The transition from the cubic LiaBi type to the hexagonal NasAs type can be tuned experimentally in the series of phases Liz~Mg2-xX ( X - S i , Ge) with increasing lithium content [6, 7]. Consequently, at the border between cubic and hexagonal structures, a regime of superstructures is observed. Driven by fulfilment of the octet rule and according to the Zintl-Klemm concept (for fundamental work, see ref. 8; about the 8N rule see ref. 9), an increasing ratio of lithium with respect to magnesium i n Ll2~Mg2_~S1 -+ 2+ . 4 - results in an increasing population of the unfavourable octahedral sites. Contrary to these silicides and germanides, the El3 compounds CasIna, Ca8_~LixA]3 and Ca2aGa,1 belong to a class of intermetallic phases which do not obey strict valence rules. Applying the Zint]-Klemm concept, however, raises the question whether these compounds tend to follow the octet rule at all. The E13 elements, as they are the most electronegative species in the structures, have the role ofthe formal anions. Theydo not have homonuclear contacts E 1 3 - E 1 3 and thus may be assumed to represent isolated ( E l 3 ) 5octet systems. (The application of formal charges does not imply that these charges really exist. They are used to calculate the occupied orbitals which have their main contributions from the atomic orbitals of the most electronegative atoms. For semiconductors (Zintl phases) the orbitals are not different in number from the sum of orbitals of the free electronegative atoms [6, 8-111.) The valence electron sums of the formal cations Ca 2+ and Li ÷ and the formal charge acquisition sums of the E l 3 elements are collected in Table 4. It is interesting to note that the compound with gallium, which has the largest electronegativity in the series aluminium, gallium and indium, has the smallest number of excess electrons A needed to fulfil the octet rule. In other words, the gallium compound is closest to a Zintl phase or a semiconductor-like composition. A comparison of the structures MaXa, LiaBi and CaeaGal, is given in Fig. 2. The MsXa structure is clearly related to the Li3Bi type, while the TABLE 4 Application of the Zinfl-Klemm concept to the i a X 3 and the Ca2sGan structures Compound
Normal composition
~q(Ca, IA)
q(E13)
A
CaaIna Cas_xLi~Ala Ca2sGall
Ca2.oTIn Ca2.elLio.orrM Ca~.55Ga
5.33 5.27 5.1 0
-- 5 --5 - 5
0.33 0.27 0.1 0
228
Li3Bi
MsX3 • o
o
0
•
•
•
•
•
•
o
o
o
o
o
oo
0
o
0
0
0 0
o
0
o 0
0
o
o
0
o
o
o
o
o
o
o
o
o
o
o
o o
o o
o o
o CO o o
•
•
•
~
o
o
o o
•
•
•
c b
[0011
e
o°°
~
¢0
~
©
69
~o (~9
co
o
o
o ~ oC D
oo o
~
o
~O
(O
•
c
\
X
~
o
b
a •
Ca28Ga11
= a
/ [112]
a
,,[111]"
Fig. 2. Comparison of the structures of (a) Cas_=LixA13 (MsX3), (b) Li3Bi and (e) Ca28Gan in different projections to show the common building principle.
Ca2sGa,1 arrangement is a fairly distorted variant, although the general formation of X layers ( X - I n , Ga, A1, Bi) is obeyed in all three cases. Even the cation framework in Cas_=Li=Al3 (where calcium and lithium are represented by open circles) seems to be just slightly deformed from that of the cubic aristotype Li3Bi in this projection. The space near the unfavourable octahedral holes is no longer directly occupied, but the entire cationic network has rearranged in such a way that 23 cations per anion become acceptably coordinated by anions instead of just 2 in the case of Li3Bi (note: one-third of the cations in Li3Bi have eight close cation neighbours) (see Table 3). The coordination polyhedron of bismuth in the cubic structure is LiB cubes. One-sixth of the X atoms in CasIn3 and Cas_=Li~A13 still has this coordination (All). The environment of Al2 is an elongated icosahedron, while the other two aluminium sites have an irregular tenfold coordination with a cube-like appearance on one side and an icosahedral shape on the other. This figure is called the cubicosahedron [5]. These coordination polyhedra are shown in Fig. 3. From inspection of Table 3, it becomes clear that the coordination of the calcium atoms by aluminium and other calcium atoms is different with either three or four close aluminium neighbours and eight or nine close calcium atoms. However, comparison of the individual atomic volumes by construction of Wirkungsbereiche (Dirichlet domains) [ 12-14 ] reveals strong similarities between the various calcium sites in this structure. (The volumes have been calculated by a FORTRAN 77 program [15] which uses a potential
229
(a)
(b)
(d)
Fig. 3. The four differentcoordinationpolyhedraaround each symmetry-inequivalentaluminium atom in Cas_zLi~A13:(a) cube; (b) icosahedron; (c), (d) cubicosahedra.
plane construction for the generation of the domain boundary [14]. For the chosen atomic radii, a uniform value oft--- 1.0/~ for all calcium and aluminium atoms was chosen.) Although a common construction was applied for all atoms, calcium and aluminium atoms split into two separate volume regions. The differences for each of these is relatively small and varies between 33.1 and 35.7 /~8 for calcium and between 29.0 and 31.1/~3 for aluminium (see Table 5). Similar results are also revealed by differences in other geometrical parameters, e.g. their mean effective "ionic" radii (MEFIR) and effective coordination numbers (ECON) [16], which are also tabulated in Table 5. In addition to this geometrical analysis, local electrostatic potentials at the atomic sites in Cas_~LixA13 were evaluated using the Ewald method [17, 18] with formal charges of - 2 . 6 7 and + 1.00 assigned to aluminium and calcium or lithium respectively. The relative magnitudes of these site potentials v (for cations v < 0 ; for anions v > 0) indicate the relative coordination of ions of one type (aluminium) by ions of the other type (calcium, lithium). Comparison of these results with the bond distances in Table 3 corroborates three close aluminium neighbours for Ca5, Ca7 and Ca8, and four close aluminium neighbours (all distorted tetrahedra) for Cal, Ca2, Ca3, Ca4 and Ca6 sites. The crystal structure analysis indicated exclusive substitution by
230 TABLE 5 Site potentials v a, partial atomic volume V, MEFIR [17] and ECON for Cas_~Li~Al3 ( x = 0.16) Atom
vb
V (/~3)
MEFIR
ECON
Coordination polyhedron
Cal Ca2 Ca3 Ca4 Ca5 Ca6 Ca7 Ca8 All A12 Al3 Al4
- 0.500 - 0.524 - 0.532 -0.515 - 0.483 - 0.527 - 0.489 - 0.498 1.290 1.256 1.272 1.281
33.4 33.3 33.2 33.1 35.7 33.4 33.2 33.2 29.0 31.1 29.5 29.4
1.79 1.77 1.77 1.77 1.86 1.77 1.75 1.75 1.62 1.75 1.68 1.67
11.3 10.6 10.6 10.8 13.0 10.7 10.1 10.1 8.0 10.8 9.37 8.90
Irregular Irregular Irregular Irregular Irregular Irregular Irregular Irregular
Cube Pentagonal antiprism Cubicosahedron Cubicosahedron
aFrom MAPLE calculations. bCalculated with q(A1)= - 2 . 6 7 and q(Ca, Li)= + 1.00.
o
(a) o
o @
o
o
o @
o
o °
o @
o
o
o
@
o
@ o
o
o o
@
o
o
o
@ 0
@
o 0
o
@
o
o
o
@
o o 0
o
o U
a o
o
o o
o
o
I
o
D
o
o
a
o
o o
~
o
o
@ o
o
8
o
o
9
o
o •
o
U
o
o
a
o
o
6
o
9
o
o
a
o
•
o
o 0
o 9
• o
o
@ 0
o o
•
o @
0 •
•
o
@
o •
o o
o
@ 0
0
o @
o
@
o
o
o @
o
o
o
@
o •
o
o o
o o
@
o
o
o
o
@ o
@ o
o
o
@
(b) °
@
o
o
@
o
@
o
o @
o
o o
o o
@
o
o
o
o
@
o
o °
@
o
o
o @
o
D
•
o
• 0
o o
o
o U
a o
• 0
0
o
o •
0
0
0
Fig. 4. (001) projections of the Cas_xLi~A13 structure with only aluminium sites (@) and occupied Ca cl~ sites (o) shown: (a) layer centred at z = 0 ; (b) layer centred at z=½.
lithium a t the C a 7 a n d Ca8 sites, w h i c h w e w o u l d e x p e c t o n t h e b a s i s o f t h e i r s m a l l e r site p o t e n t i a l values, a l t h o u g h Ca5 sites s h o w n o lithium substitution. P l o t s o f a l u m i n i u m p o l y h e d r a a r o u n d the Ca5, C a 7 a n d Ca8 sites at d i s t a n c e s o u t t o 6 0 0 p m r e v e a l t h a t t h e s e t h r e e p o s i t i o n s h a v e shifted a w a y f r o m the c e n t r e s o f a l u m i n i u m o c t a h e d r a . T h e r e f o r e w e c a n f o r m u l a t e Cas_~Li~Al3 as (Ca, Li)8(°)(Ca)sCr)Als with r e s p e c t to t h e Li3Bi s t r u c t u r e t y p e , a n d r e c o g n i z e t h a t lithium s u b s t i t u t e s at t h e o c t a h e d r a l s i t e s a n d t h e v a c a n c i e s o c c u r at the t e t r a h e d r a l sites. T h e a r r a n g e m e n t o f v a c a n c i e s is readily o b s e r v e d b y c o n s i d e r i n g t h e t w o l a y e r s of A1 a t o m s c e n t r e d at z = 0 a n d z = ½ a n d t h e i r Ca cr) n e i g h b o u r s . F i g u r e 4 illustrates t h e s e t w o s h e e t s in a ( 0 0 1 ) p r o j e c t i o n , w h i c h s h o w p a i r s o f v a c a n c i e s in the z = t layer. This c o n f i g u r a t i o n o f v a c a n c i e s r e s u l t s in all
231 a l u m i n i u m a t o m s in this sheet b e i n g six c o o r d i n a t e to Ca (T) r a t h e r t h a n eight c o o r d i n a t e (as in LiaBi): one-third o f the a l u m i n i u m a t o m s with v a c a n c i e s diagonally o p p o s i t e (A12) and two-thirds of t h e aluminium a t o m s with v a c a n c i e s o n an edge o f the cube (A13). This a r r a n g e m e n t o f d e f e c t s also effects c o o r d i n a t i o n v a c a n c i e s for aluminium a t o m s in the z = 0 layer: one-third o f t h e m r e m a i n i n g e i g h t - c o o r d i n a t e cubic, but two-thirds having a single vac a n c y - s e v e n c o o r d i n a t e by Ca cr). Madelung calculations on different d e f e c t a r r a n g e m e n t s in the Li3Bi-type f r a m e w o r k indicated t h a t the o b s e r v e d v a c a n c y o r d e r i n g in Cas_xLixAla is o n e o f the least f a v o u r e d configurations -- the m o s t f a v o u r a b l e energies o c c u r r e d f o r t h o s e p a t t e r n s in w h i c h the v a c a n c i e s w e r e isolated f r o m e a c h o t h e r as far as possible, a l t h o u g h the calculated e n e r g y differences w e r e no larger t h a n a b o u t 1.5 eV. U p o n distortion to the actual g e o m e t r y o f t h e s e MaXa c o m p o u n d s , the Madelung t e r m d r o p p e d b y several electronvolts. Structurally, the M (°) sites c o n t r a c t a r o u n d the v a c a n c y pairs, which results in a m o r e u n i f o r m l y distributed cationic c o o r d i n a t i o n e n v i r o n m e n t a r o u n d e a c h X c e n t r e (see Table 5).
4. E x t e n d e d Hiickel i n v e s t i g a t i o n s E l e c t r o n i c s t r u c t u r e calculations using the e x t e n d e d Htickel ansatz [19] w e r e carried out on an Li3Bi-type "CaaAl", a d e f e c t "CaeAd", Ca3_xA1-CasAl3, a n d the actual CasA13 s t r u c t u r e in o r d e r to e x a m i n e the deviations f r o m the Z i n t l - K l e m m ideas p r e s e n t e d in Table 4. That is, w h a t is the n a t u r e o f the additional electrons b e y o n d the formal o c t e t at the E l 3 e l e m e n t ? T h e s e calculations utilized the tight-binding m e t h o d with a special points set of k p o i n t s in the irreducible w e d g e of the first Brillouin zone ( b e t w e e n 150 and 4 0 0 points). The structural p a r a m e t e r s f r o m CaT.s4Lio.le,A13 w e r e u s e d for CasA13, and cell p a r a m e t e r s for the o t h e r two s t r u c t u r e s w e r e d e t e r m i n e d to maintain equal cell v o l u m e s p e r n u m b e r of aluminium atoms. Atomic p a r a m e t e r s are listed in Table 6. F i g u r e 5 shows the density of states (DOS) c u r v e s for the t h r e e s t r u c t u r e s and highlights the c o n t r i b u t i o n f r o m the Ca (°) orbitals to the total DOS. Clearly, the distribution of d e f e c t s d o e s not e n h a n c e the e l e c t r o n i c stability of a fictitious "Ca~Al", but the final r e l a x a t i o n o f the Ca (°) a t o m s a r o u n d
TABLE 6 Atomic parameters used in the extended Hiickel calculations Atom
Orbital
Energy (eV)
Exponent
A1
3s 3p 4s 4p
- 12.30 - 6.50 - 7.00 -4.00
1.37 1.36 1.10 1.10
Ca
232
°°LIL
-1.5
-3.5
-5.5 -7.5
-9.5 -11.5 -13.5 -15.5
iV" (a)
Ca~hl
7 (b) Ca3-xhl
(c) Caahl3
Fig. 5. Total DOS for "CaaAl" in (a) the LiaBi structure, Co) the "Ca~_xAl" structure undistorted, and (c) CaeAl3 in the observed CaT.s4Lio.lsA1a s t r u c t u r e : . , projected DOS from the Ca (°) sites; , respective Fermi levels determined for 8.33 electrons p e r aluminium atom. Energies are in units of electronvolts.
the vacancies produces significant stability -- the calculated Fermi levels (noted by the broken lines for 8.33 electrons per aluminium atom) differ by nearly 0.75 eV. Evaluation of overlap populations between various sets of Ca-A1 and Ca-Ca pairs indicates that the occupied part of the conduction band in the CasAla structure is Ca-A1 nonbonding and Ca-Ca bonding. As the figure shows, most of the DOS in this energy region is centred on the Ca (°) atoms. Although there are no definitive clusters of calcium and lithium in Cae_~LixAla, this result is consistent with earlier investigations on the lithium-rich silicides Li21Si5 [20] and Li12Si7 [21]. Furthermore, a Mulliken population analysis supports the conclusions from the Madelung calculations. In "CaaAl", the total charges on the two different metal sites were 1.25 and 1.02 for Ca (T) and Ca (°) respectively, whereas in CasAla, the corresponding populations varied between 1.24 and 1.28 for Ca c~ and between 1.17 and 1.30 for Ca (°).
5. C o n c l u s i o n s
The structure of Cas_xLi~Ala (x = 0.16) was determined to be isostructural with an analogous binary compound CasIn3, although no corresponding binary Ca-A1 phase could be isolated. The structure is a defect variation of the cubic LiaBi structure type with lithium substituting for calcium at the octahedral sites (4b in F m 3 m ) and vacancies occurring in the tetrahedral sites (8c in F m 3 m ) . Due to the lower site potentials at the 4b sites, we rationalize the lithium substitution, but the defect pattern arises for stxuctural and electronic reasons. The relaxation of the 4b atoms around the vacancies effects a uniform charge distribution surrounding each aluminium atom as well as stabilizing the bottom of the conduction band by introducing occupied Ca-Ca bonding orbitals.
233 This class of compounds comes close to following the Zintl-Klemm concepts with the additional electrons involved in cation--cation bonding s t a t e s . R e p o r t s o f L i M g 2 G a a n d L i 2 M g G e w h i c h a d o p t t h e Li3Bi s t r u c t u r e with an ordering of cations [22] are also consistent with our observation t h a t t h e g a l l i d e s c o m e c l o s e s t t o f u l f i l l i n g t h e o c t e t r u l e , in a c c o r d a n c e w i t h e l e c t r o n e g a t i v i t y t r e n d s o f t h e g r o u p 13 e l e m e n t s .
Acknowledgments W e t h a n k P r o f e s s o r H. G. v o n S c h n e r i n g f o r h i s c o n t i n u e d s u p p o r t a n d enthusiasm, and Jan Curda for synthesis and initial identification of this phase.
References 1 R. Nesper and G. J. Miller, in preparation. P. Villars and L. D. Calvert, Pearson's Handbook ofCrystaUograpic Data f o r IntermetaUic Phases, Vol. 2, American Society for Metals, Metals Park, OH, 1989, p. 914, and references cited therein. 2 J. B. Friauf, J. Am. Chem. Soc., 40 (1927) 3107. 3 H. Nowotny, E. Wormnes and A. Mornhein, Z. Metallkde., 32 (1940) 39. 4 M. L. Fornasini and M. Pani, Acta Crystallogr. C, 42 (1986) 394. 5 M. L. Fornasini, Acta CrytaUogr. C, 43 (1987) 613. 6 R. Nesper, Habilitationschrifl, Universit~t Stuttgart, 1988. 7 R. Nesper and J. Curda, Diskussionstagung der Arbeitsgemeinschafl KristaUographie, Konstanz, 1988, p. 196; Z. KristaUogr., 182 (1988) 196. 8 E. Zintl and G. Brauer, Z. Phys. Chem., Abt. B, 20 (1933) 245. E. Zintl, Angew. Chem., 52 (1939) 1. W. Klemm, FIAT-review of German science, Naturforschung und Medizin in Deutschland 1939-1946, Anorg. Chem., Teil IV, 26 (1949) 103. 9 W. Klemm, Trab. Reur~ Int. React. SSlidos, 1 (1956) 447; Proc. Chem. Soc. London, (1956) 329; Festkdrperprobleme Vieweg, Braunschweig, 1963. E. Mooser and W. B. Pearson, Phys. Rev., 101 (1956) 1608; Prog. Semicond., (1960) 103. E. Busmann, Z. Anorg. AUg. Chem., 313 (1961) 90. 10 R. Nesper, Prog. Solid State Chem., 20 (1990) 1. 11 R. Nesper, Angew. Chem., 103 (1991) 805; Angew. Chem. Int. Edn` EngL, 30 (1991) 789. 12 P. Niggli, Z. Kristallogr., 68 (1928) 404. 13 F. Laves, Z. KristaUogr., 78 (1931) 208. 14 W. Fischer, E. Koch and E. HeUner, Neues Jahrb. Mineral., Monatsh., (1971) 227. 15 K. Wohlfart, B. Neul~ter and H. G. von Schnering, Programme zur Berechnung konvexer Polyeder, Universit~t Miinster, Miinster, 1967. R. Nesper and U. Hiiussermann, Verbesserte Programmversion) Eidgen6ssirche Technische Hochschule, Ziirich, 1991. 16 R. Hoppe, Angew. Chem., 82 (1970) 7; Angew. Chem. Int. Edn. Engl., 9 (1970) 25; Z. KristaUogr., 150 (1979) 23. 17 P. P. Ewald, Ann, Phys., 64 (1921) 253. 18 R. Hoppe, Angew. Chem., 78 (1966) 52; in O. C. J. M. Rooymans and A. Rabenau (eds.), Crystal Structure and Chemical Bonding in Inorganic Chemistry, North-Holland, Amsterdam, 1975.
234
19
20 21 22
G. Roch, W. Neukiiter and H. G. yon Schnering, Programm z u r Berechnung von Gitterpotentialen und Madelunflfaktoren, Universit~t Mfinster, Miinster, 1962. R. Nesper, M o d ~ z i e r u n g e n z u r Berechnung van Potentialdichten, Max-Planck-Institut ftir Festk6rperforschung, Stuttgart, 1984. R. Nesper and H. Meyer, Verbesserte Programmversion, Eidgen6ssirche Technische Hochschule, Ztirich, 1991. R. Hoffmann, J. Chem. Phys., 39 (1963) 1397. J. Ammeter, H.-B. Btirgi, J. C. Thibeault and R. Hoffmann, J. Am. Chem. Soc., 100 (1978) 3686. R. Nesper and H. G. yon Schnering, J. Solid State Chem., 70 (1987) 48. R. Nesper, H. G. von Schnering and J. Curda, Chem. Ber., 119 (1986) 3576. H. Pauly, A. Weiss and H. Witte, Z. MetaUkde., 59 (1968) 414.
221
Cas_xLixA13: defects and substitution in the Fe3A1 structure
type Gordon J. Miller* and Reinhard Nesper** Max-Planck-Institut ffir FestkS"rperfovschung, Heisenbergstrasse 1, 7000 Stuttgart 80 (Germany) (Received November 26, 1991)
Abstract Cas_xiixA13 was obtained in crystalline form during investigations of the Ca-Li-AI ternary phase diagram. The structure is isotypic to Cabin3 (space group P i ; a = 9 4 7 . 0 pro, b = 9 6 0 . 2 pm, c = 9 6 4 . 6 pro, affi99.17 °, fl=101.08 °, T=119.51°), which is an ordered defect structure of the Fe3A1 or the Li3Bi type. Vacancies occur exclusively at pseudotetrahedral sites and lithium substitutes for calcium in the pseudo-octahedral sites when compared with the cubic FeaAl structure (space group F m 3 m ) of a hypothetical "Ca~AI". Madelung and extended Hiickel calculations are utilized to discuss the observed defect and substitutional pattern.
I. Introduction In the Ca-AI binary system, only two phases have been characterized: CaA12 (cubic MgCu2-type) [1, 2] and CaA14 (tetragonal BaA14 type) [3]. No calcium-rich phases are yet known. With gallium and indium, Fornasini and Pani have reported two calcium-rich compounds: CaesGau [4] and CaBin3 [5], the second of which is the so called "Ca3In" phase in the Ca-In system. During efforts to examine the Ca-Li-A1 ternary diagram, we discovered crystals which, after an X-ray structure determination, exhibit geometrical characteristics of the CaBin3 structure, but are deficient in calcium. In this contribution we shall present the structure determination of Cas_~Li~Ala, a comparison with related compounds, and comments regarding the importance of lithium in this material.
2. Experimental details The sample was prepared by melting (T= 1180 K) a mixture of calcium (99.5 at.%, Fluka), lithium (99 at.%, Merck), and aluminium (99.9 at.%, *Present address: Department of Chemistry, Iowa State Umver~ity,Ames, L~ 50011, USA. **Present address: Laboratorium fiir Anorganische Chemie, ETH Zentrum, CH-8092 Ziirich, Switzerland.
0925-8388/92/$5.00
© 1 9 9 2 - Elsevier Sequoia~ All rights reserved
222
Merck) in the ratio 4:1:1 in a molybdenum crucible, which was sealed in a niobium ampoule under an argon atmosphere. The reaction container was placed in an argon-filled quartz Schlenk tube. After 2 h the melt was slowly cooled to room temperature over a 2 day period. Attempts to prepare a pure binary CasAl~ phase failed under similar conditions. A crystal suitable for data collection (checked with Buerger precession photographs) was mounted in an argon-filled capillary and measured on a single-crystal diffractometer. Solution of the structure proceeded with direct methods in space group P1. Table 1 contains all crystal data and refinement parameters. Atomic coordinates and anisotropic temperature factors are listed in Table 2, and significant bond distances are given in Table 3.
TABLE 1 Crystallographic data for Cas_xLi~A13 ( x = 0 . 1 6 ) Empirical formula Crystal size (mm 3) Crystal system Space group a, b, c (pm) a, fl, T (deg) Volume (pro 3) Z Formula weight (Da) Density (calculated) (Mg m -1) Absorption coefficient (mm -1) F(000) Diffractometer; radiation Temperature (K) Monochromator 2e range (deg) Scan type; speed; range Standard reflections Index ranges Reflections collected Independent reflections Observed reflections Absorption correction System used; solution Refinement method Quantity minimized Extinction correction
Ca15.68Lio.32Ale 0.06 x 0.03 × 0.05 Triclimc
Pi 947.0(2), 960.2(2), 964.6(2) 99.17(2), 101.08(2), 119.50(2) 715.2(3) x 108 1 79O.4 1.835 3.021 391.63 Siemens R3m/V; Mo Ka ( A = 0 . 7 1 0 7 3 / ~ ) 298 Highly oriented graphite crystal 4.0-55.0 eo; variable; 0.50-19.50 ° min -1 in w; 2.00 ° 2 measured every 98 reflections
-12
SHELXTL; direct methods Full matrix, least squares ~,w(Fo - F c ) 2 X ffi - 0.00021(12) where F * • F[ 1 + O.O02xF2/sin(2e) ] -114
Weighting scheme Number of parameters refined Final R indices (observed data) R indices (all data) Goodness of fit Largest difference peak
w- ' = o2(F)
106 R ffi 5.3296, w R ffi4.00% R = 5.32%, w R ffi4.00% 1.15 1.17 e / ~ - 3
0.47062(7) -0.07839(7) 0.12117(7) 0.66387(7) 0.04373(7) 0.29947(6) 0.22446(7) 0.45202(9) 0 0.5 0.82818(9) 0.32348(9)
Cal Ca2 Ca3 Ca4 Ca5 Ca6 Ca7 Ca8 All Al2 Al3 Al4
0.30106(7) -0.22839(7) -0.40216(7) 0.12081(6) 0.93931(7) -0.50006(6) -0.15364(9) 0.28515(9) 0.5 0 0.66380(9) 0.15872(9)
y
SOFb
0.35035(7) 1 0.89231(7) 1 0.35219(7) 1 0.89032(7) 1 0.33076(7) 1 0.89163(7) 1 0.69921(7) 0.903(4) 0.69999(8) 0.938(4) 0 1 0.5 1 0.49990(10) 1 -0.02741(9) 1
z
217(2) 194(2) 235(2) 211(2) 233(2) 208(2) 263(3) 270(4) 176(5) 195(5) 176(3) 177(3)
Ueq
168(2) 193(2) 259(3) 187(2) 254(3) 144(2) 139(3) 373(4) 156(5) 222(5) 130(3) 158(3)
UII
182(2) 225(3) 213(3) 167(2) 158(2) 183(2) 289(4) 375(4) 174(5) 155(5) 149(3) 159(3)
U22
228(3) 222(3) 230(3) 245(3) 260(3) 250(3) 227(4) 241(4) 210(6) 207(6) 214(4) 206(4)
U~3
61(2) 101(2) 87(2) 70(2) 80(2) 40(2) - 12(3) 156(3) 77(4) 60(4) 66(3) 62(3)
U23
44(2) 93(2) 52(2) 37(2) 106(2) 80(2) 59(3) 147(3) 79(4) 99(5) 32(3) 73(3)
U13
51(2) 134(2) 129(2) 81(2) 80(2) 57(2) 48(3) 292(3) 86(4) 90(4) 54(3) 73(3)
Ul2
~rhe U~j parameters are expressed in the form e x p [ - 2 . z 2 ( U , , h 2 a * 2 + ... + 2 U , ahka*b*] and given in units of square picometres. Standard deviations are given in parentheses. bSite Occupation Factor.
x
Atom
Positional parameters and thermal parameters U~= for Caa_xLi~A13
TABLE 2
bO
Al2 Al3 Al3' Al4 Ca2' Ca3' Ca4' a5 Ca6' Ca7' Ca8 CaB'
All Al3 Al4 Al4' Cal' Ca2' Ca3' Ca4' Ca5 Ca5' Ca6' Ca7
Cal
Ca2
(cominued)
Atom 2
Atom 1
330.2 357.0 359.4 315.4 365.3 390.6 372.3 376.9 399.2 370.4 368.2 355.8
353.3 325.3 354.4 341.7 365.3 390.8 376.9 375.7 362.2 386.1 343.4 380.1
Distance
Ca5
Ca4
Atom 1
Important bond distances (pm) in Cas_~Li~Ala
TABLE 3
Al3 Al3' Al4' Cal Ca2 Ca2' Ca3 Ca4' Ca5' Ca6' Ca7' Ca8'
All Al2 Al4 Al4' Ca1' Ca2' Ca3' Ca5' Ca6' Ca7 Ca7' Ca8
Atom 2
334.1 337.1 367.8 375.7 399.2 370.4 372.2 400.0 367.2 372.7 397.8 400.9
325.1 353.8 363.3 321.8 376.9 360.9 391.7 400.0 372.0 351.6 381.6 353.7
Distance
Ca8
Ca7
Atom 1
Al2 A13' A14 Cal Cal' Ca3' Ca4 Ca5 Ca5' Ca6 Ca6' Ca7'
Al2 Al3 Al4 Ca1' Ca2 Ca3 Ca3' Ca4 Ca4' Ca5 Ca5' Ca8
Atom 2
336.3 325.8 326.5 343.4 380.1 378.7 353.7 411.8 400.9 353.6 379.2 366.6
342.3 324.4 325.4 386.1 355.7 342.8 375.6 351.6 381.6 406.6 397.8 366.6
Distance
Al3
Al2
Atom 1
Cal Cal ' Ca2 Ca3 Ca3' Ca5 Ca5' Ca6' Ca7 Ca8'
Cal Ca1' Ca3 Ca3' Ca4 Ca4' Ca5 CaS* Ca7 Ca7' Ca8 CaB'
Atom 2
325.3 354.4 357.0 361.8 326.2 334.1 337.1 356.1 324.4 325.8
353.3 353.3 352.9 352.9 353.8 353.8 402.2 402.2 342.3 342.3 336.2 336.2
Distance
t~
Atom 2
All Al2 Al3 Al3' CA1 Ca2' Ca4' Ca5 Ca6' Ca7 Ca7' Ca8'
Atom 1
Ca3
TABLE 3 (continued)
318.8 352.9 361.8 326.2 390.8 372.3 391.7 372.2 378.1 342.8 375.6 378.7
Distance
Ca6
Atom 1 All A13' A14 A14' Cal' Ca2' Ca3' Ca4' Ca5' Ca6' Ca8 Ca8'
Atom 2 320.6 356.1 358.8 324.2 362.2 368.2 378.1 372.4 372.7 396.7 353.6 379.2
Distance All
Atom 1 Ca2 Ca2' Ca3 Ca3' Ca4 Ca4' Ca6 Ca6'
Atom 2 330.2 330.2 318.8 318.8 325.1 325.1 320.6 320.6
Distance A14
Atom 1 CA1 Ca2 Ca2' Ca4 Ca4' Ca5' Ca6 Ca6' Ca7 Ca8
Atom 2
341.7 359.4 315.4 363.3 321.8 367.8 358.8 324.3 325.4 326.5
Distance
t~ O1
226 Refinement of site occupation factors for the single crystal that was analysed revealed calcium deficiency. According to the data in Table 2, the resulting stoichiometry is CaT.s4Lio.leA13.
3. A n a l y s i s o f t h e c r y s t a l s t r u c t u r e
The structure of Cas_~Li~Als, which is illustrated in Fig. 1, is quite complicated and seemingly _unusual for an intermetallic compound. It adopts the triclinic space group, P 1 , is isotypic to the reported structure of CaBin3, and, as pointed out by Fornasini, is related to the f.c.c. FeaA1 structure type (also known as Li3Bi or BiFa type) [5]. It should be emphasized that we could only obtain this phase as a ternary compound. The close relationship between the CaB_~Li~A13 structure and the Li3Bi type is clearly evident from the arrangement of aluminium atoms, which forms a slightly distorted f.c.c. framework where the coordination number of aluminium is 12 with distances 5.30 /~
0 CO
0 CO
0
0
CD_
CO_
Uco g~ eco Uco ~
0 o 00o 00o 00o 00o 00o 0
0
0
o00 o00 o00 o00 o00 o 0
o oeOOoo~::~ogOo ~:)Oo ~ooo" o o o o o / o ~ ooo/ooo/ooo o o 0 o 00o 00o 00o 00o 00o 0 0
0
o00 o(30 o00 o00 o00 o 0 CO_ CD~ QO~ CO-- (D-- Q~, gCO U ~ gCO U ~ U~, 0
0
0
0
0
Fig. 1. The crystal structure of Cas_=Li=A13 in a (010) projection: O, aluminium atom positions;
o, Ca atoms originating from the tetrahedral holes of the Li3Bi structure type; O, calcium or lithium sites originating from the octahedral holes in the LisBi type.
227
by introducing higher valent species at the tetrahedral positions as in BiO~F3_z~. A competing solution is the Na~As structure with an h.c.p, array of arsenic atoms. Two-thirds of the sodium atoms occupy all tetrahedral holes, but the octahedral sites are vacant. The residual one-third of the sodium atoms are located halfway between the other sodium atoms to gain three near arsenic neighbours. The transition from the cubic LiaBi type to the hexagonal NasAs type can be tuned experimentally in the series of phases Liz~Mg2-xX ( X - S i , Ge) with increasing lithium content [6, 7]. Consequently, at the border between cubic and hexagonal structures, a regime of superstructures is observed. Driven by fulfilment of the octet rule and according to the Zintl-Klemm concept (for fundamental work, see ref. 8; about the 8N rule see ref. 9), an increasing ratio of lithium with respect to magnesium i n Ll2~Mg2_~S1 -+ 2+ . 4 - results in an increasing population of the unfavourable octahedral sites. Contrary to these silicides and germanides, the El3 compounds CasIna, Ca8_~LixA]3 and Ca2aGa,1 belong to a class of intermetallic phases which do not obey strict valence rules. Applying the Zint]-Klemm concept, however, raises the question whether these compounds tend to follow the octet rule at all. The E13 elements, as they are the most electronegative species in the structures, have the role ofthe formal anions. Theydo not have homonuclear contacts E 1 3 - E 1 3 and thus may be assumed to represent isolated ( E l 3 ) 5octet systems. (The application of formal charges does not imply that these charges really exist. They are used to calculate the occupied orbitals which have their main contributions from the atomic orbitals of the most electronegative atoms. For semiconductors (Zintl phases) the orbitals are not different in number from the sum of orbitals of the free electronegative atoms [6, 8-111.) The valence electron sums of the formal cations Ca 2+ and Li ÷ and the formal charge acquisition sums of the E l 3 elements are collected in Table 4. It is interesting to note that the compound with gallium, which has the largest electronegativity in the series aluminium, gallium and indium, has the smallest number of excess electrons A needed to fulfil the octet rule. In other words, the gallium compound is closest to a Zintl phase or a semiconductor-like composition. A comparison of the structures MaXa, LiaBi and CaeaGal, is given in Fig. 2. The MsXa structure is clearly related to the Li3Bi type, while the TABLE 4 Application of the Zinfl-Klemm concept to the i a X 3 and the Ca2sGan structures Compound
Normal composition
~q(Ca, IA)
q(E13)
A
CaaIna Cas_xLi~Ala Ca2sGall
Ca2.oTIn Ca2.elLio.orrM Ca~.55Ga
5.33 5.27 5.1 0
-- 5 --5 - 5
0.33 0.27 0.1 0
228
Li3Bi
MsX3 • o
o
0
•
•
•
•
•
•
o
o
o
o
o
oo
0
o
0
0
0 0
o
0
o 0
0
o
o
0
o
o
o
o
o
o
o
o
o
o
o
o o
o o
o o
o CO o o
•
•
•
~
o
o
o o
•
•
•
c b
[0011
e
o°°
~
¢0
~
©
69
~o (~9
co
o
o
o ~ oC D
oo o
~
o
~O
(O
•
c
\
X
~
o
b
a •
Ca28Ga11
= a
/ [112]
a
,,[111]"
Fig. 2. Comparison of the structures of (a) Cas_=LixA13 (MsX3), (b) Li3Bi and (e) Ca28Gan in different projections to show the common building principle.
Ca2sGa,1 arrangement is a fairly distorted variant, although the general formation of X layers ( X - I n , Ga, A1, Bi) is obeyed in all three cases. Even the cation framework in Cas_=Li=Al3 (where calcium and lithium are represented by open circles) seems to be just slightly deformed from that of the cubic aristotype Li3Bi in this projection. The space near the unfavourable octahedral holes is no longer directly occupied, but the entire cationic network has rearranged in such a way that 23 cations per anion become acceptably coordinated by anions instead of just 2 in the case of Li3Bi (note: one-third of the cations in Li3Bi have eight close cation neighbours) (see Table 3). The coordination polyhedron of bismuth in the cubic structure is LiB cubes. One-sixth of the X atoms in CasIn3 and Cas_=Li~A13 still has this coordination (All). The environment of Al2 is an elongated icosahedron, while the other two aluminium sites have an irregular tenfold coordination with a cube-like appearance on one side and an icosahedral shape on the other. This figure is called the cubicosahedron [5]. These coordination polyhedra are shown in Fig. 3. From inspection of Table 3, it becomes clear that the coordination of the calcium atoms by aluminium and other calcium atoms is different with either three or four close aluminium neighbours and eight or nine close calcium atoms. However, comparison of the individual atomic volumes by construction of Wirkungsbereiche (Dirichlet domains) [ 12-14 ] reveals strong similarities between the various calcium sites in this structure. (The volumes have been calculated by a FORTRAN 77 program [15] which uses a potential
229
(a)
(b)
(d)
Fig. 3. The four differentcoordinationpolyhedraaround each symmetry-inequivalentaluminium atom in Cas_zLi~A13:(a) cube; (b) icosahedron; (c), (d) cubicosahedra.
plane construction for the generation of the domain boundary [14]. For the chosen atomic radii, a uniform value oft--- 1.0/~ for all calcium and aluminium atoms was chosen.) Although a common construction was applied for all atoms, calcium and aluminium atoms split into two separate volume regions. The differences for each of these is relatively small and varies between 33.1 and 35.7 /~8 for calcium and between 29.0 and 31.1/~3 for aluminium (see Table 5). Similar results are also revealed by differences in other geometrical parameters, e.g. their mean effective "ionic" radii (MEFIR) and effective coordination numbers (ECON) [16], which are also tabulated in Table 5. In addition to this geometrical analysis, local electrostatic potentials at the atomic sites in Cas_~LixA13 were evaluated using the Ewald method [17, 18] with formal charges of - 2 . 6 7 and + 1.00 assigned to aluminium and calcium or lithium respectively. The relative magnitudes of these site potentials v (for cations v < 0 ; for anions v > 0) indicate the relative coordination of ions of one type (aluminium) by ions of the other type (calcium, lithium). Comparison of these results with the bond distances in Table 3 corroborates three close aluminium neighbours for Ca5, Ca7 and Ca8, and four close aluminium neighbours (all distorted tetrahedra) for Cal, Ca2, Ca3, Ca4 and Ca6 sites. The crystal structure analysis indicated exclusive substitution by
230 TABLE 5 Site potentials v a, partial atomic volume V, MEFIR [17] and ECON for Cas_~Li~Al3 ( x = 0.16) Atom
vb
V (/~3)
MEFIR
ECON
Coordination polyhedron
Cal Ca2 Ca3 Ca4 Ca5 Ca6 Ca7 Ca8 All A12 Al3 Al4
- 0.500 - 0.524 - 0.532 -0.515 - 0.483 - 0.527 - 0.489 - 0.498 1.290 1.256 1.272 1.281
33.4 33.3 33.2 33.1 35.7 33.4 33.2 33.2 29.0 31.1 29.5 29.4
1.79 1.77 1.77 1.77 1.86 1.77 1.75 1.75 1.62 1.75 1.68 1.67
11.3 10.6 10.6 10.8 13.0 10.7 10.1 10.1 8.0 10.8 9.37 8.90
Irregular Irregular Irregular Irregular Irregular Irregular Irregular Irregular
Cube Pentagonal antiprism Cubicosahedron Cubicosahedron
aFrom MAPLE calculations. bCalculated with q(A1)= - 2 . 6 7 and q(Ca, Li)= + 1.00.
o
(a) o
o @
o
o
o @
o
o °
o @
o
o
o
@
o
@ o
o
o o
@
o
o
o
@ 0
@
o 0
o
@
o
o
o
@
o o 0
o
o U
a o
o
o o
o
o
I
o
D
o
o
a
o
o o
~
o
o
@ o
o
8
o
o
9
o
o •
o
U
o
o
a
o
o
6
o
9
o
o
a
o
•
o
o 0
o 9
• o
o
@ 0
o o
•
o @
0 •
•
o
@
o •
o o
o
@ 0
0
o @
o
@
o
o
o @
o
o
o
@
o •
o
o o
o o
@
o
o
o
o
@ o
@ o
o
o
@
(b) °
@
o
o
@
o
@
o
o @
o
o o
o o
@
o
o
o
o
@
o
o °
@
o
o
o @
o
D
•
o
• 0
o o
o
o U
a o
• 0
0
o
o •
0
0
0
Fig. 4. (001) projections of the Cas_xLi~A13 structure with only aluminium sites (@) and occupied Ca cl~ sites (o) shown: (a) layer centred at z = 0 ; (b) layer centred at z=½.
lithium a t the C a 7 a n d Ca8 sites, w h i c h w e w o u l d e x p e c t o n t h e b a s i s o f t h e i r s m a l l e r site p o t e n t i a l values, a l t h o u g h Ca5 sites s h o w n o lithium substitution. P l o t s o f a l u m i n i u m p o l y h e d r a a r o u n d the Ca5, C a 7 a n d Ca8 sites at d i s t a n c e s o u t t o 6 0 0 p m r e v e a l t h a t t h e s e t h r e e p o s i t i o n s h a v e shifted a w a y f r o m the c e n t r e s o f a l u m i n i u m o c t a h e d r a . T h e r e f o r e w e c a n f o r m u l a t e Cas_~Li~Al3 as (Ca, Li)8(°)(Ca)sCr)Als with r e s p e c t to t h e Li3Bi s t r u c t u r e t y p e , a n d r e c o g n i z e t h a t lithium s u b s t i t u t e s at t h e o c t a h e d r a l s i t e s a n d t h e v a c a n c i e s o c c u r at the t e t r a h e d r a l sites. T h e a r r a n g e m e n t o f v a c a n c i e s is readily o b s e r v e d b y c o n s i d e r i n g t h e t w o l a y e r s of A1 a t o m s c e n t r e d at z = 0 a n d z = ½ a n d t h e i r Ca cr) n e i g h b o u r s . F i g u r e 4 illustrates t h e s e t w o s h e e t s in a ( 0 0 1 ) p r o j e c t i o n , w h i c h s h o w p a i r s o f v a c a n c i e s in the z = t layer. This c o n f i g u r a t i o n o f v a c a n c i e s r e s u l t s in all
231 a l u m i n i u m a t o m s in this sheet b e i n g six c o o r d i n a t e to Ca (T) r a t h e r t h a n eight c o o r d i n a t e (as in LiaBi): one-third o f the a l u m i n i u m a t o m s with v a c a n c i e s diagonally o p p o s i t e (A12) and two-thirds of t h e aluminium a t o m s with v a c a n c i e s o n an edge o f the cube (A13). This a r r a n g e m e n t o f d e f e c t s also effects c o o r d i n a t i o n v a c a n c i e s for aluminium a t o m s in the z = 0 layer: one-third o f t h e m r e m a i n i n g e i g h t - c o o r d i n a t e cubic, but two-thirds having a single vac a n c y - s e v e n c o o r d i n a t e by Ca cr). Madelung calculations on different d e f e c t a r r a n g e m e n t s in the Li3Bi-type f r a m e w o r k indicated t h a t the o b s e r v e d v a c a n c y o r d e r i n g in Cas_xLixAla is o n e o f the least f a v o u r e d configurations -- the m o s t f a v o u r a b l e energies o c c u r r e d f o r t h o s e p a t t e r n s in w h i c h the v a c a n c i e s w e r e isolated f r o m e a c h o t h e r as far as possible, a l t h o u g h the calculated e n e r g y differences w e r e no larger t h a n a b o u t 1.5 eV. U p o n distortion to the actual g e o m e t r y o f t h e s e MaXa c o m p o u n d s , the Madelung t e r m d r o p p e d b y several electronvolts. Structurally, the M (°) sites c o n t r a c t a r o u n d the v a c a n c y pairs, which results in a m o r e u n i f o r m l y distributed cationic c o o r d i n a t i o n e n v i r o n m e n t a r o u n d e a c h X c e n t r e (see Table 5).
4. E x t e n d e d Hiickel i n v e s t i g a t i o n s E l e c t r o n i c s t r u c t u r e calculations using the e x t e n d e d Htickel ansatz [19] w e r e carried out on an Li3Bi-type "CaaAl", a d e f e c t "CaeAd", Ca3_xA1-CasAl3, a n d the actual CasA13 s t r u c t u r e in o r d e r to e x a m i n e the deviations f r o m the Z i n t l - K l e m m ideas p r e s e n t e d in Table 4. That is, w h a t is the n a t u r e o f the additional electrons b e y o n d the formal o c t e t at the E l 3 e l e m e n t ? T h e s e calculations utilized the tight-binding m e t h o d with a special points set of k p o i n t s in the irreducible w e d g e of the first Brillouin zone ( b e t w e e n 150 and 4 0 0 points). The structural p a r a m e t e r s f r o m CaT.s4Lio.le,A13 w e r e u s e d for CasA13, and cell p a r a m e t e r s for the o t h e r two s t r u c t u r e s w e r e d e t e r m i n e d to maintain equal cell v o l u m e s p e r n u m b e r of aluminium atoms. Atomic p a r a m e t e r s are listed in Table 6. F i g u r e 5 shows the density of states (DOS) c u r v e s for the t h r e e s t r u c t u r e s and highlights the c o n t r i b u t i o n f r o m the Ca (°) orbitals to the total DOS. Clearly, the distribution of d e f e c t s d o e s not e n h a n c e the e l e c t r o n i c stability of a fictitious "Ca~Al", but the final r e l a x a t i o n o f the Ca (°) a t o m s a r o u n d
TABLE 6 Atomic parameters used in the extended Hiickel calculations Atom
Orbital
Energy (eV)
Exponent
A1
3s 3p 4s 4p
- 12.30 - 6.50 - 7.00 -4.00
1.37 1.36 1.10 1.10
Ca
232
°°LIL
-1.5
-3.5
-5.5 -7.5
-9.5 -11.5 -13.5 -15.5
iV" (a)
Ca~hl
7 (b) Ca3-xhl
(c) Caahl3
Fig. 5. Total DOS for "CaaAl" in (a) the LiaBi structure, Co) the "Ca~_xAl" structure undistorted, and (c) CaeAl3 in the observed CaT.s4Lio.lsA1a s t r u c t u r e : . , projected DOS from the Ca (°) sites; , respective Fermi levels determined for 8.33 electrons p e r aluminium atom. Energies are in units of electronvolts.
the vacancies produces significant stability -- the calculated Fermi levels (noted by the broken lines for 8.33 electrons per aluminium atom) differ by nearly 0.75 eV. Evaluation of overlap populations between various sets of Ca-A1 and Ca-Ca pairs indicates that the occupied part of the conduction band in the CasAla structure is Ca-A1 nonbonding and Ca-Ca bonding. As the figure shows, most of the DOS in this energy region is centred on the Ca (°) atoms. Although there are no definitive clusters of calcium and lithium in Cae_~LixAla, this result is consistent with earlier investigations on the lithium-rich silicides Li21Si5 [20] and Li12Si7 [21]. Furthermore, a Mulliken population analysis supports the conclusions from the Madelung calculations. In "CaaAl", the total charges on the two different metal sites were 1.25 and 1.02 for Ca (T) and Ca (°) respectively, whereas in CasAla, the corresponding populations varied between 1.24 and 1.28 for Ca c~ and between 1.17 and 1.30 for Ca (°).
5. C o n c l u s i o n s
The structure of Cas_xLi~Ala (x = 0.16) was determined to be isostructural with an analogous binary compound CasIn3, although no corresponding binary Ca-A1 phase could be isolated. The structure is a defect variation of the cubic LiaBi structure type with lithium substituting for calcium at the octahedral sites (4b in F m 3 m ) and vacancies occurring in the tetrahedral sites (8c in F m 3 m ) . Due to the lower site potentials at the 4b sites, we rationalize the lithium substitution, but the defect pattern arises for stxuctural and electronic reasons. The relaxation of the 4b atoms around the vacancies effects a uniform charge distribution surrounding each aluminium atom as well as stabilizing the bottom of the conduction band by introducing occupied Ca-Ca bonding orbitals.
233 This class of compounds comes close to following the Zintl-Klemm concepts with the additional electrons involved in cation--cation bonding s t a t e s . R e p o r t s o f L i M g 2 G a a n d L i 2 M g G e w h i c h a d o p t t h e Li3Bi s t r u c t u r e with an ordering of cations [22] are also consistent with our observation t h a t t h e g a l l i d e s c o m e c l o s e s t t o f u l f i l l i n g t h e o c t e t r u l e , in a c c o r d a n c e w i t h e l e c t r o n e g a t i v i t y t r e n d s o f t h e g r o u p 13 e l e m e n t s .
Acknowledgments W e t h a n k P r o f e s s o r H. G. v o n S c h n e r i n g f o r h i s c o n t i n u e d s u p p o r t a n d enthusiasm, and Jan Curda for synthesis and initial identification of this phase.
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19
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