By Dr. Bruno Dorner (auth.)
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Extra info for Coherent inelastic neutron scaterring in lattice dynamics
In perturbation calculation we find (HARRISON, 1966) E(q) ~ IS(q)l 2 v2(g) _ _ ~-T~-Tx(9) The total energy # o f ~n = Ui + E . the crystal (46) is the sum of the ionic and the electronic energy. (47) This energy depends on the positions of the ions 5. At T = 0 the ions are supposed to occupy t h e i r ordered equilibrium positions RO (disregarding the zero point 34 motion). This state, in which no phonons are excited, has the lowerst energy of the crystal ~0" I f we introduce, by a gedcc~kene~eriment, one static plane wave with wavevector 90 and amplitude y(qo) ~(90) = ~O(~o)'sin(90~ ) ' the resulting d i s t o r t i o n of the l a t t i c e will increase the crystal energy to ~n" This change in energy ~n-#O is the phonon energy ~m(90) in case that the d i s t o r t i o n is not s t a t i c but dynamic and i f the amplitude UO(qO) corresponds to one quantum~m(qO (one phonon).
These branches may cross each other i f they belong to d i f f e r e n t i r r e d u c i b l e representations or they avoid each other i f they belong to the same represent a t i o n . In the l a t t e r case i t happens quite often that two branches from the same representation e x h i b i t an anticrossing behaviour in t h e i r dispersion curves connected with an exchange of t h e i r eigenvectors. In these cases one can very often i d e n t i f y branches by a q u a l i t a t i v e analysis of the measured i n t e n s i t y (Sect.
21. 4 THz l i b r a t i o n in naphthalene with increasing volume. The experimental points ~ are obtained at normal pressure with increasing temperature (indicated on the abscissa). The dashed and dotted curves are Calculated at constant temperature and negative hydrostatic pressure using the measured and the calculated mode Gr~neisen parameters, respectively. (SCHMELZERet a l . , 1981) Recently we performed i n e l a s t i c neutron scattering on anthracene (a f l a t molecule of three benzene rings) (DORNERet a l .