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On the X-ray diffraction spikes of diamond 169 jihis is a conclusion which we shall not accept unless more familiar and comprehen- dble concepts are incapable of explaining the result. In reaching the conclusion cloerni & Wooster dismiss the possibility of an explanation in terms of atomic displacements rather sooner than the logic of their argument demands, and then nurn to deriving the required modification of atomic form factor. This turns out i;o correspond to, in their words, ‘a transfer of peripheral electrons from one side >f the atom to the other, just in the range of the valence electrons ’. Now, since the atomic nucleus is invisible to X-rays, there is really no observable distinction between this process and an atomic displacement; but it is easier to conduct the analysis in terms of displacements, and leave the atomic form factor out of it. We shall see presently that displacements can fully account for the results.
F. C. Frank 170 in the case of growth ‘ghosts’, we should indeed look for six distinct domains of this kind the six pyramidal sectors from the centre to each cube face, and should be able to select a piece of crystal with its spikes all in one direction by sawing it through the centre on (110) planes. This is a matter which could be put to the test, but the indicated near-uniformity of the displacement strongly favours the alternative hypothesis of segregation from solid solution.
On the X-ray diffraction spikes of diamond 171 mik' both contribute to steepening the fall). This is in entire agreement with Hoerni rfc Wooster’s observation of a spike intensity proportional to p being pro portional to k'. The strength of this spike is also correlated, through the factor sin kS, tfcvith the order of diffraction k, in very nearly, though not precisely, the required inanner. We shall return to this point. The relative magnitude of the third term of |5) to the fourth, for small k',is — (e/k') cot and it is therefore negligible except Ivhen sin kd is very small. In any case it is very weak in the region ' > e, and unlikely po1 be observable. In the special case h — 0, that is close to the origin of reciprocal icpace, we have for small k (but still > e) A = B - l + 2ejk'2-2 (6) IThat is, apart from the small term just referred to, a spike of amplitude — 1 — 28) independent of distance from the origin of reciprocal space. This vanishes if B = 1 + 2$, the value required to give a uniform scattering density averaged over idistances exceeding an interatomic spacing.
On the X-ray diffraction spikes of diamond 173 Ilf these, silicon is very much the most acceptable on all grounds. Helium and «eon can be clearly rejected; it is difficult to see how the other elements, replacing ^arbon atoms one for one, could satisfy the valency requirements; and the associated displacements required for elements beyond calcium are excessively large. The anomalous plane might of course consist of more than one kind of atom, but no assortment which could satisfy the requirements seems to offer itself (except, Conceivably, aluminium plus hydrogen).