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Subsections

(ii) Inorganic compounds

(a) Silicon carbide and zinc sulphide

SiC has a binary tetrahedral structure in which the Si and C layers are stacked alternately, each carbon layer occupying half the tetrahedral voids between successive close-packed silicon layers. One can regard the structure as consisting of two identical interpenetrating close-packings, one of Si and the other of C, with the one displaced relative to the other along the c -axis through one fourth of the layer spacing. The binding between Si and C atoms in SiC is predominantly covalent. The silicon-carbon bond length of 1.94 Å as calculated from the known covalent tetrahedral radii of C and Si is nearly equal to the observed silicon-carbon bond length of 1.89 Å. The tetrahedral arrangement of Si and C in SiC does not permit either a centre of symmetry ($\overline{1}$) or a plane of symmetry (m ) perpendicular to [00.1]. Silicon carbide can therefore have only four possible space groups -- P 3m 1, R 3m 1, P 63mc and F $\overline{4}$3m.


Figure 11: Tetrahedral arrangement of Si and C atoms in 6H SiC structure.
\begin{figure} \includegraphics {fig11.ps} \end{figure}

Commercial SiC crystals are grown at temperatures above 2000$^{\circ}$ C and are called $\alpha$-SiC crystals. The more common modifications in the $\alpha$-SiC crystals are 6H , 15R and 4H . They have stacking sequences /ABCACB/ (=6H ), /ABCBACABACBCACB/(=15R ) and /ABCB/...(4H ). Figure 11 depicts the structure of the most common $\alpha$-SiC modification 6H with a packing ABCACB. In addition to the common modications (often called the `basic structures` of $\alpha$-SiC) several polytype structures with stacking sequences of larger repeat periods have been discovered. These have either a hexagonal or a rhombohedral lattice2. Table 3 lists the known structures of SiC. In all these structures the h/a ratio is 0.817, which is very close to the value of 0.8165 for an ideal close-packing. The cubic or $\beta$-SiC, with a packing /ABC/ABC/..., is denoted as 3C and normally forms2 at temperatures below 1800$^{\circ}$ C. It is regarded as the low- temperature modification of SiC and undergoes a solid-state transformation to the 6H structure at temperatures above 1800$^{\circ}$ C2,16,17. The wurtzite (2H ) modification of SiC, with a stacking sequence /AB/AB/..., does not occur in commercial SiC and has been synthesized by special methods between the temperatures of 1400 and 1500$^{\circ}$ C18. It is regarded as a metastable modification of SiC and undergoes solid-state transformation to the 3C and 6H structures at temperatures above 1400$^{\circ}$ C17. The h/a ratio in this structure is 0.8205 which differs considerably from the ideal h/a ratio for perfect close-packing.


 
Table 3: List of SiC polytypes with known structures
Polytype Structure (Zhdanov sequence) Polytype Structure (Zhdanov sequence)
2H 11 54H (33)6323334
3C ${\infty}$ 57H (23)93333
4H 22 57R (33)234
6H 33 69R 1 (33)332
8H 44 69R 2 33322334
10H 3322 75R 1 (33)334
14H (22)233 75R 2 (32)3(23)2
15R 23 81H (33)535(33)634
16H 1 (33)222 84R (33)3(32)2
16H 2 332332 87R (33)432
18H (22)333 90R (23)43322
19H (23)322 96R (33)33434
20H (22)344 99R (33)43222
21H 333534 105R (33)532
21R 34 111R (33)534
24R 35 120R (22)523222333
27H (33)2(23)3 123R (33)632
27R 2223 141R (33)732
33R 3332 147R (3332)432
33H 1 (33)2353334 159R (33)832
33H 2 (33)3(23)3 168R (23)1033
36H 1 (33)232(33)234 174R (33)66(33)54
36H 2 (33)43234 189R (34)843
39H (33)232(33)3(32)2 222R (33)634(33)434
39R 3334 267R (23)1722
45R 232332 273R (23)1733
51R 1 (33)232 303R (33)1632
51R 2 (22)323 393R (33)2132

The structure of ZnS is analogous to that of SiC. The bonding in ZnS is known to be partly ionic and partly covalent. The wurtzite and sphalerite modifications of this compound, which occur as minerals, correspond to the /AB/AB/AB/... and /ABC/ABC/,... packings respectively.

The cubic form is known to be the low-temperature modification and undergoes a reversible phase transformation2 to the 2H form around 1020$^{\circ}$ C. In addition to these two common modifications, ZnS is known19 to display a large variety of polytype structure with larger identity periods. As stated earlier, all the polytype modifications of a material have identical a and b lattice parameters and differ only along c . The h/a ratio for the 2H modification of ZnS is 0.818 which is somewhat different from the ideal value 0.8165 for a perfect close-packing.

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Next: Cadmium Iodide Up: Examples of Some Close-Packed Structures Previous: (i) Elements

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