Crystal structures of adamantine compounds

J. Phys. Chem.Solids Pergamon Press 1963. Vol. 24, pp. 45-50.

Printed in Great Britain.

CRYSTAL STRUCTURES OF ADAMANTINE

COMPOUNDS

P. C. NEWMAN

Mullard Research Laboratories, Redhill, Surrey (Received 26 July 1962)

method is given for deriving the crystal structures of adamantine compounds by the stacking of hexagonal nets. This leads to a series of structures for compounds of the formulae ABC2;AaBCs, and AsBC4, many of which have been observed in actual compounds. This method of deriving structures is also useful in the case where only part of the crystallographic informa..,crvstal < Abstract-A

tion has been obtained from X-rays.

1. INTRODUCTION

elements and many compounds crystallize with a fourfold tetrahedral co-ordination of atoms. These are generally known as adamantine materials; typical compounds are GaAs, ZnO, SIC. The crystal structures of adamantine materials may be depicted by two interlocking sublattices, with equal numbers of sites on each sublattice. In GaAs, these sub-lattices are geometrically similar to cubic close-packed atoms of one element only, in ZnO to hexagonal close-packed atoms, and in Sic to a mixed close-packing. However, adamantine materials also exist with unequal distributions of atoms on each sub-lattice, and the structure of these compounds will be considered in this paper. When the structures of adamantine compounds are considered in the form of two sub-lattices, it is found that each lattice site is surrounded by four sites on the other sub-lattice. However, it is also possible to consider the structures to be built up from nearly plane nets with hexagonal symmetry. Three of the bonds from one atom to its neighbours lie in the net, while the fourth is perpendicular to the mean plane of the net. The structure of such a net is shown in Fig. 1. The different crystal structures can then be built up by the stacking of such nets, each net being itself stoichiometric. It must be assumed that the stacking is arranged so that consecutive nets are connected by bonds between atoms of the two different types. Then the zincblende structure will SEVERAL

be built up by consistent cubic stacking, the wurtzite structure by consistent hexagonal stacking and the various polytypes of Sic by a mixed, but repetitive, stacking. All these stacking sequences obey the conditions that each atom on the A sub-lattice is surrounded by 4 nearest neighbours on the B sub-lattice and 12 next-nearest neighbours on the A sub-lattice.

l -A

0-s

FIG. 1. Hexagonal net, AB compounds. 2. HEXAGONAL NETS AND NEIGHBOURS

SETS

OF

The compounds to be considered in this papeo have the formulae A3BC3, ABC2, or AsBC4. These are the three simplest deviations from the typical formula AB. The hexagonal nets for these compounds are shown in Figs. 2-4. It is also quite easy to calculate the simplest arrangement of neighbours and next-nearest neighbours for all 45

P.

46

C. NEWMAN

types of atoms in the compounds (see Ref. (1) for the case of A&Ca compounds). The arrangements of neighbours will control the possible stacking sequences for the nets, and also the structure of the nets themselves. For the compounds of the type A&C’s, the table of neighbours is shown in Table 1.

A

B C(X) C(Y)

Neighbours 1 C(X) and 3 C(Y) 2 C(X) and 2 C(Y) 2 A and 2 B 3Aandi B

Next-nearest

Atom

A B C

Neighbours 4c 4c 2 A and 2

Next-nearest

neighboura

4 A and 8 8 A and 4 12 c

B

B B

Here, it is only necessary to use one type of C atom.

Table 1. A2BC3 compounds Atom

Table 2. ABC2 compounds

neighbours

7 A and 5 B 10 A and 2 I3 2 C(X) and 10 C(Y) 5 C(X) and 7 C(Y)

*-A

0-b

@s-c

3a

a-*

0-B

FIG. 2. Hexagonal net,

@-C(Y) AaBCs compounds.

It can be seen that there must be two types of C atom, which are defined by their nearest neighhours.(l) The hexagonal net for A&K’3 compounds is shown in Fig. 2; this contains a unique direction, shown by the arrow B + C(X). The B atoms (and also the C(X) atoms) are arranged in a hexagonal pattern in the net. It is possible to construct other nets, but these do not appear to lead to any fresh structures. For compounds of the type ABC’s, the table of neighbours is shown in Table 2.

3b

Fro. 3. Hexagonal nets, ABCa compounds.

CRYSTAL

STRUCTURES

OF

The hexagonal nets for ABC’2 compounds must contain alternate lines of A and B atoms. The two simplest cases are shown in Fig. 3 ; in Fig. 3a, the lines are straight, but in Fig. 3b the lines are zig-zag (with the shortest possible repeat distances). More complicated zig-zags are, of course, possible, but will not be considered here. For compounds of the type AsBC4, the table of neighbours is shown in Table 3.

ADAMANTINE

Table 3. AsBC4 compounds Next-nearest

Neighbours

Atom A B c

w 0-A

w 0-s

w @-c

4a

neighbours

8 A and 4 B 12 A 12 c

4c 4c 3 A and 1 B

There are only two possible types of hexagonal That shown in Fig. 4a net for AsBC4 compounds. has a rectangular pattern of B atoms with a unique direction B -+ C while that in Fig. 4b has a hexagonal pattern of B atoms, but with no unique direction. There do not appear to be any other forms of net, which will allow stacking. 3. CRYSTAL

w

47

COMPOUNDS

STRUCTURES

3.1 AzBC’s compounds These are built up by stacking the nets shown in Fig. 2 one above the other. Because of the conditions laid down by the neighbours, they must be stacked with a B in one net above a C(X) in the net below. When this is done, there are six ways of setting the unique direction in the upper net relative to that in the lower net. If this setting is maintained for all layers, the six structures shown in Table 4 are obtained. These structures have been deduced previously(l) by a less rigorous method. However, it is always possible to have a mixed form of stacking, as will be discussed below. Several of these crystal structures have been observed in III-VI compounds, where the B atom represents a vacant site. The structure I has been found for InsTea and the structures II and VI (an enantiomorphous pair) for GaaSs,(s) /I-InsSes.@) Table 4. A2BC3 structures Unit cell dimensions no for disordered zincblende

Type

Space Group

2

I

20 Ceo-Imm2

2

ao/2/2

C:-P65

6

2/+.ao

22/3 .a0 ~‘3

II

+A

0-B

a-c

4b FIG. 4. Hexagonal nets, AaBC4 compounds.

III

&P3

2

3

1/*.as

IV

c

b

a

3ao/1/2

2/*.

as

a0

. a0

C&%c21

4

3ao/2/2

V

&P31

3

&.a0

2aoW3 1/3 . a0

VI

C:-P61

6

z/t.ao

2d3.

(2 = number of formula units in unit cell.)

as

48

P. C. NEWMAN

The case of Gas& is of particular interest. HAHN and FRANK@ originally obtained a unit cell for GasSs consisting of types II or VI stacking. Recently, GOODYEARet u1.W have published results giving a monoclinic unit cell for Gas& and proposing one of the space groups C2, C2/m, or Cm. If the a and c axes of this unit cell are transformed as shown in Fig. 5 then the close-packed S planes become (001) planes. The only way of obtaining this unit cell from the hexagonal net of Fig. 2 is by the stacking sequence -II-VI-II-VI-.

3.2 ABC2 compounds Taking the two hexagonal nets shown in Fig. 3, four crystal structures may be built, by using either cubic or hexagonal stacking consistently with each net. It is not possible to mix the types of net, or have more than the two ways of stacking. The structures obtained are detailed in Table 5. Table 5. ABC’2 structures Type

Net

Space Group

2

Unit cell dimensions ao for disordered zincblende

------

a (G000’1~14

---

a (NEWMAN)

tt

I

A

II

A

CkPmc21

2

a01112

III

B

4

ar,

IV

B

D;:-I42d 9

4

2/z.

D&P4m2

1

Cm-Pna21

c

b

a aold

a0

212. ao 2ao/x/3

2ao a0

%/2. a0

2a0/1/3

21.)

c (COlQlONj

FIG. 5. Relation between a, c in the two monoclinic unit

cells for GasSs.

This would give a side-centred monoclinic cell with the space group Cf-Cc. The shape of this cell agrees well with the experimental result of Goodyear et al. as shown below and GOODYEAR has more recently confirmed(s) that the space group Cc is indeed consistent with his results. Gas& a: b Calc. Obs.

1.732 1.738

Unit cell b:c 0.9045 0.9109

B 121.48” 121.85”

The two structures are compared in Figs. 6 and 7. It seems likely that the crystal structures of AlsSa(7* 8) and TlsTes,(s) which are not yet completely resolved, may be determined by thinking along the same lines.

FIG. 6. Crystal structure of Gas% according to and FRANK.(~)

J~AHN

FIG. 7. Crystal structure

of CanSa from data of GOODYEARet uZ.(~)

Structure III is the well known structure of chafcopyrite, CuFeSs.(l*) Recently, many other compounds have been found to have the same structure.ol* 1s) However, HAHN et aE.@) found that ABCz compounds containing either Cu and Ga together or Ag and In together couid not be indexed very convincingly on the basis of the chalcopyrite structure. All the lines found in the powder patterns can however be indexed on the basis of the structure I (but with the condition h+K+Z = 2n). Because of the very similar scattering factors for the Cu and Ga atoms (or the Ag and In atoms) in their surroundings in these crystals, it is extremely difficult to distinguish by X-rays between this structure and the statistically distributed arrangement of metal atoms suggested by HAHN et al. Structure I, however, should give rise to some very weak extra lines with h +k+ I # 2n. It also seems more likely that the structure wili be distorted from exact tetrahedral bonding when the two types of metal atom are arranged in alternate layers than when they are randomly mixed. 3.3 AsBC4 compounds There are four types of crystal structures which may be built by consistent cubic or hexagonal stacking with the two hexagonal nets shown in D

Fig. 4. It is not possible to mix the two types of net or have more than the two ways of stacking. The four structures are shown in Table 6. Table 6. A3BC4 structures Type

Net

Space Group

2

Unit cell dimensions ao for disordered zincblende -

b

a I

II

A

D&$-I42m

2

2ao

a0

A

C&-Ptnn21

2

~‘2.

III

B

8

2ao

IV

B

T:-F+3c 4 CW-Pbamc

2

d2 . ao

___I____--

c

ao

t/*.

ao 2ao/d3

2ao/1/3

Structure I is the structure of the LuzoniteFamatinite series CusAs,Sbr_,S~,(1s) and also of the compound CusSbSe4.(fQ) Structure II is the structure of Enargite CusAsS~(ls) and of the compound CusPS4.(1s) It is interesting to see that the compound CusAsS4 which occurs in two forms contains the same type of hexagonal net in both forms. Recently, a new compound InsTed has been

50

P.

C. NEWMAN

proposed in the In-Te system,(lv) and it seems likely that this compound has tetrahedral bonding. If the existence of InsTed is confirmed, it may be expected to have a structure based on those detailed in Table 6. 4. CONCLUSIONS

A range of possible crystal structures has been derived for admantine compounds containing more than two differently situated atoms. These crystal structures are obtained by varying the stacking of hexagonal nets of atoms, which are themselves stoichiometric. Only very simple arrangements within the net have been considered. Many of the crystal structures so derived have been found to occur in actual compounds. Moreover, this recipe for the building up of crystal structures is very helpful in situations where insufficient X-ray data are available for a complete structure determination (for instance, only the unit cell may be known). However, it can not claim to be entirely exhaustive, without extension to more complicated hexagonal nets.

REFERENCES 1. NEWMANP. C., J. Phys. Chem. Solids 23, 19 (1962). 2. WOOLLEYT. C.. PAMPLINB. R. and HOLMESP. T., J. Less-?cnnkon Metals 1, 362 (1959). 3. HAHN H. and FRANKG., Z. anorg. Chem. 278, 333 (1955). 5, 673 4. SEMILETOVS. A., Sov. Phys. Crystallogr. (1961); Krystallogr. 5, 704 (1960). J., DUFFINW. J. and STEIGMANNG. A., 5. GOODYEAR Acta Cryst. 14, 1168 (1961). 6. GOODYEARJ., unpublished. 7. FLAHAUTJ., Ann. Chim. 7, 632 (1952). K. and GALSTERH., Angew Chem. 8. GEIER~BERGER 64, 81 (1952). 9. RABENAUA., Z. Metal&., 51, 295 (1960). 10. PAULINGL. and BROCKWAYL. O., Z. Kristallogr. 82, 188 (1932). 11. HAHN H. et al., Z. anorg. Chem. 271, 153 (1953). V. M. and SHTRUME. L., 12. ZHUZEV. M., SERGEEVA J. Tech. Phys. MOSCOW 28, 2093 (1958). SOO. Phvs. Tech. Phvs. 3. 1925 (1958). kin. 3?, 291’(1952). 13. GAINESR. V., A&. 14. WERNICKJ. H. and BENSONK. E., J. Phys. Chem. Solids 3, 157 (1957). 88, 15. PAULINGL., and WEINBAUMS., Z. Kristallogr. 48 (1934): A. and CAVALCAL., Gazz. Chim. Italia 78, 16. FERRARI 783 (1948). 17. MASON D. R., unpublished.