Neutron scattering in impure anharmonic solids

Debye-Waller Factor in an Isotopically Disordered Semiconductor Crystal

“…The theory of DWF 2W can be achieved for semiconductor crystals by taking the following expression as [12,13,38,39]:…”

“…(1), n (ε), G kk (ε) represent the Planck distribution function and the Fourier transformed double time temperature dependent phonon Green function, respectively [12,13,38,39]. Thus, it is clear that the evaluation of imaginary part of the phonon Green function is the main focus to achieve our goal.…”

“…Let us use equation of motion technique of quantum dynamics and the Dyson equation approach, Fourier transformed phonon Green function is obtained as [13,34,47,48,50]:…”

“…It is known that like X-rays, thermal neutrons have a de Broglie wavelength of the order of the interatomic spacings in crystals so that they can be used in diffraction studies [12]. The Debye-Waller factor (DWF) is used to find the differential scattering cross-section through dynamical structure factor in neutron scattering in impure anharmonic solids [13]. The Debye-Waller factor is one of the dynamical properties of the crystals, and its pressure dependence is found in silicon and germanium by using statistical moment method [14].…”

“…A double time temperature dependent phonon Green function is taken to solve the present problem with the help of Hamiltonian contributed by harmonic part, electron part, electronphonon interaction part, and defect part. The work has been done on neutron scattering in impure anharmonic solids [13], but in present case electron-phonon interaction is taken in semiconductor crystals with isotopic impurity in low concentration in low temperature limit to develop the theory of DWF. The present work differs from previous work that they have not taken the electron-phonon interaction using equation of motion technique of quantum dynamics, and the Dyson equation approach in their studies.…”