Coherent inelastic neutron scattering in lattice dynamics by B. Dorner

Coherent inelastic neutron scattering in lattice dynamics by B. Dorner

By B. Dorner

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The atomic displacements y are considered to be so small that the above series expansion may be broken o f f a f t e r the quadratic term. c) The requirement of periodic boundary conditions. This is equivalent to replacing the f i n i t e specimen by an i n f i n i t e medium without boundary effects. The zeroth term in the Taylor expansion gives the l a t t i c e energy in equilibrium. The f i r s t term has to vanish to garanty equilibrium. Let us call the second term (BILZ and KRESS, 1979) 1 ~2 = ~ ~ y(L) ~ ( k , k ' ) u ( k ' ) (29) where L = (~,d) denotes the d th p a r t i c l e in the ~th c e l l .

In other words, the offset of the second atom in the hexagonal plane does not come into play for q = [00~]. In the case of a monatomic substance in hcp structure, the extended zone scheme - plotting the acoustic and the optic mode side by side and not on top of each other - is very appropriate as the dispersion curves become smooth curves without any i r r e g u l a r i t y at the zone boundary (but a f i n i t e slope), and most important as the observable intensity follows the extended zone scheme.

1965) metals is now well established. 47 BROVMAN and KAGAN (1974) in t h e i r treatment of n o n - t r a n s i t i o n metals have predicted a hierarchy of phonon anomalies related to the i n d i r e c t i n t e r i o n i c i n t e r action mediated by the conduction electrons. In addition to the Kohn anomalies which appear when t h i s i n t e r a c t i o n is central, Brovman and Kagan f i n d f u r t h e r anomalies which r e f l e c t the non-central character of the i n t e r i o n i c forces.

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