Example of a simple system—lithium hydride

Lithium hydride, LiH, is a rather simple solid there are two atoms in the primitive cell and four electrons. It has the rock salt structure and its primitive cell contains one lithium and one hydrogen atom. Fig. 4.14. There are six dispersion curves of which three are acoustic and three optical. We can compare our calculations with the measured dispersion curves from LiD (rather than LiH because the deuterium coherent scattering cross section is required to measure the relative displacements of pairs of atoms ( 2.1). 

A triple axis spectrometer ( 3.4.1) was employed in these measurements [10,11,12,13]. The vibrational calculations were performed on the primitive cell once its calculated Helmholtz free energy, F, had been minimised using the quasi-harmonic approximation. Quantum effects are present due to the lightness of both atoms [14,15]. 

This is an example of LO-TO splitting of the vibrational modes according to their direction of motion at the gamma point ( 2.6.1.3, 4.2.6). For any general direction the polarisation of the waves is not strictly longitudinal or transverse and the polarisation vectors are dependent on k as well as k. Similarly, the acoustic modes split into a longitudinal and two transverse modes. These modes vary in frequency along different directions in the unit cell [16]. 

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