Spectral shapes of solid neon

Abstract

We present a Path Integral Monte Carlo calculation of the first three moments of the displacementdisplacement correlation functions of solid neon at different temperatures for longitudinal and transverse phonon modes. The Lennard-Jones potential is considered. The relevance of the quantum effects on the frequency position of the peak and principally on the line-width of the spectral shape is clearly pointed out. The spectrum is reconstructed via a continued fraction expansion; the approximations introduced using the effective potential quantum molecular dynamics are discussed.Rare gas solids (RGS) are the simplest real systems in which we can study lattice vibrations. Argon and the heavier RGS can be well approximated as a set of harmonic oscillators at lowest temperatures, while the classical behaviour is reached before the melting point. Quantum corrections on the thermodynamic quantities, like kinetic energy and specific heat, can be taken into account by means of the effective potential approach (EP) 1 only for small quantum coupling g, (g < 0.25) defined as the ratio between the characteristic frequency and the strength of the binding potential. For neon (g = 0.694) anharmonic effects are present even for determining the ground state 2,3 . Indeed, precise calculations of kinetic energy, to be compared with accurate experiments done by Deep Inelastic Neutron Scattering (DINS) 4 , needed a rather sophisticated Path Integral Monte Carlo (PIMC) computation, being the EP approach inadequate. These results show that quantum effects are very important also at rather high temperatures 2 . Information about phonon dynamics is given by spectral shape, namely the space and time Fourier transform of the (symmetrized) displacement-displacement correlation function:withx α i is α-th component of the displacement of the i-th atom from its equilibrium position. Even though this quantity has been investigated since long time 5 , complete information is not available for various rare gas solids and in particular for neon. The perturbative many-body approach can give frequency and lifetime of phonons only at low temperatures. Classical molecular dynamics (CMD) can describe the behaviour of argon and krypton at highest temperatures, but it is no more valid for lower temperatures or stronger coupling. As shown in the following, the spectra of neon present significant quantum effects up to the melting point and the high quantum coupling prevents us to use the EP method in the entire temperature range.We approach the calculation of the spectra of neon as given in equation (1), by PIMC, evaluating the first three even frequency moments, ω 2n αβ k

Anharmonic phonon energies in rare-gas solids derived by path-integral simulations

“…The anharmonic effect predicted by the LR approximation is realistic when compared to available inelastic neutron-scattering data of solid Ne at temperatures of 4.7 and 6.5 K. 23,24 A previously reported PIMC estimation of the energy of the XL and XT phonons at 10 and 20 K, based on the calculation of the first three moments of the displacement-displacement correlation function, is shown by open triangles. 12 The Lennard-Jones parameters employed in this study ͑⑀ = 3.161 meV and = 2.787 Å͒ are only slightly different from ours. Therefore, the difference with the LR estimation of one-phonon energies is likely a consequence of the different methods used to study anharmonic effects in this rare-gas solid.…”

“…The longitudinal and transverse phonon energies of solid Ne at the boundary of the Brillouin zone ͑BZ͒ have been estimated at two temperatures from the simulation of spectral line shapes. 12 This was achieved by evaluation of moments of the position-position correlation functions from PIMC simulations. Also, two methods have recently been proposed to evaluate the second-order elastic constants of solids, on the basis of path-integral simulations.…”

Effective potential and quantum dynamical correlators

“…The range is dependent, firstly on the smallness of the parameter f , because we have neglected the gaussian quantum spread of the fluctuating forces, secondly on the inverse of the quantum coupling g. Indeed, only the normalized second moment δ 1 is rather well reproduced. All effects related to line shape, like finite lifetimes of the elementary excitations are considered at classical level so that there is a shift of the peak of the lineshape, without any substantial modification of the linewidth, [17].…”