The method of determination of elastic moduli under pressure allows to inel vestigate the Debye temperature eD and the root-mean-square displacements of atoms from the equilibrium position < u ) as a function of pressure.volume elasticity moduli, anisotropic factor A, Debye temperature e : , rootmean-square dynamic displacement of atoms , and lattice parameter a versus pressure are presented, the characteristics being determined from our propagation velocity values f o r elastic longitudinal v1 and shear vq and v waves. The measurements have been made on single crystal niobium at hydrostatic pressure up to 1 GPa. 2 T In this note data on elastic moduli c.. adiabatic BS and isothermal B 1J' 2 1 %2The ultrasonic pulse superposition method has been used to determine elastic moduli / l / . It allows one to measure wave propagation velocities to high precision using the relation v = 2 1 f, where 1 is the specimen length, f is the pulsed frequency.For the experiments single crystal cubic-shaped Nb specimens were taken, 3 having the dimensions lOXtOxl0 mm and the crystallographic planes (100) and{IIO} as crystal faces. Such specimens made it possible to determine propagation velocities of five waves. The accuracy of orientation was checked by X-rays and equalled +_Is', while the deviation from 'plane-parallelism was 20'. The mechanically ruptured surface layer was cleaned and then the specimen was heat treated for removing hydrogen /2/. The density Q = 8544.7 kg/m , calculated from the atomic weight and the X-ray lattice parameter, agrees well with Q found by hydrostatic weighting. 3 ~~ 1 ) Podlesnaya 17, Minsk, USSR.
A method for electron-phonon matrix element calculations based on a Fourier representation of the crystal potential is presented. This method is free from a number of drawbacks inherent to the rigid muffin-tin approximation. At the same time it is much easier realizable as compared with the first-principle frozen-phonon technique. The long-range interactions, the collective character of ion displacements in phonon modes, and effects due to in-sphere electron-ion potential anisotropy can be easily taken into account. Non-muffin-tin corrections are shown to cause electron-ion scattering selection rule variations. Interband transitions due to absorption or emission of optical phonons with q = 0 (e.g. Raman-active A, modes) require the inclusion of nonlinear ion displacement contributions to the matrix elements.
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