By Dr. Bruno Dorner (auth.)
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Extra info for Coherent inelastic neutron scaterring in lattice dynamics
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).
The local v i r t u a l excit a t i o n of a 4d electron on the s i l v e r ion into an excited s state leads to a quadrupolar compressibility on the Ag ion. A nearest neighbour d-p hybridization leads to a quadrupolar rotatory term. The phonon dispersion curves have been measured by DORNERet a l . (1976), (Fig. I0). The drawn curves are the r e s u l t of shell model calculations including quadrupolar 29 terms as introduced by FISCHER e t a ! (1972). The parameters of the model were f i t t e d to the experimental data by minimizing the X2 function: •2 : ~ i i 2 Z (~ obs ~ Vcalcl i ~ J (37) where N and K are the number of phonons and parameters, respectively, and ~i is the experimental error of the i th phonon.
3. 4. Lattice Dynamical Models The oldest idea to produce a l a t t i c e dynamical model is the BORN-Von KARMAN (1912) method using central forces between the atoms. There is always a lowest number of forces necessary to s t a b i l i z e the structure. To describe phonon dispersion curves usually the number of forces (parameters) had to be increased including interactions between more distant atoms. This increase of the number of parameters was often f e l t to be unsatisfying because a better f i t to the experimental data did not provide a more profound understanding of the basic physics.
Coherent inelastic neutron scaterring in lattice dynamics by Dr. Bruno Dorner (auth.)