Testing interaction models by using x-ray absorption spectroscopy: solid Pb

Abstract

Structural models obtained using classical molecular dynamics (MD) simulations and realistic interatomic potentials for solid metals are tested using experimental results obtained by x-ray absorption spectroscopy (XAS). Accurate L-edge extended x-ray absorption fine-structure (EXAFS) measurements of Pb grains dispersed in BN and graphite matrices have been collected for temperatures up to the melting point. The thermal expansion of the grains was measured by energy-dispersive x-ray diffraction techniques and found to be coincident with that of pure Pb up to the limit of the present measurements. L3-edge EXAFS measurements of solid Pb at various temperatures have been analysed using advanced data-analysis techniques (GNXAS) based on exact spherical-wave multiple-scattering simulation of the absorption cross-section. Realistic structural models for solid Pb were obtained from MD simulations using an empirical pair potential (Dzugutov, Larsson and Ebbsjo (DLE)), a tight-binding (TB) square-root functional, and an embedded-atom (EA) model potential parametrized by us. The short-range pair distribution function g(r) reconstructed by means of EXAFS is compared with those obtained by MD simulations. The empirical DLE potential, originally designed for the liquid state, is too soft, showing too-large values for the average distance R, variance σ2, and skewness β. The TB and EA potentials are both compatible with XAS data as regards the average distance and skewness of the first neighbours. The distance variance, associated with the thermal vibration amplitudes, is underestimated for the TB potential, while the EA model is found to be in agreement with XAS data. The present results are also compared with those from a previous EXAFS study on solid lead, where the cumulant expansion and a simple one-dimensional anharmonic oscillator model were used. The need for realistic interaction models and appropriate simulation schemes for reliable XAS data analysis is emphasized, while differences from and improvements with respect to previous approaches are only briefly discussed.

High‐pressure and high‐temperature study of phase transitions in solid germanium

“…[15]). Structural refinement was aimed only to obtain accurate measurements of the variation of the cell parameters a (Ge I), or a and c (Ge II and III) under high pressure and high temperature conditions, which determine the energy position of the Bragg reflections hkl associated with a given interplanar distance d, for fixed diffraction angle q E ¼ hc 2d sin ðqÞ .…”

The structure of liquid lead: EXAFS and MD studies

“…We have shown in [10] that the DLE interaction model reproduces the structure of solid Pb poorly. At the same time, the EA is a many-body potential designed to reproduce the specific long-range solid state properties of Pb.…”

“…At the same time, the EA is a many-body potential designed to reproduce the specific long-range solid state properties of Pb. It has been shown in [10] to produce structural models excellently compitable with EXAFS-extracted data for solid lead. In the present work we have shown that this EA model is unable to reproduce the shape of g(r) in liquid Pb.…”

“…The MD simulations were performed by ourselves. The simulation method and conditions (other than the temperature) were the same as those described in [10]. All the mentioned RDFs, referred to as ND, XD, MD-DLE and MD-EA, respectively, are shown in Fig.…”

“…In particular, detailed studies of simple solid metals at high temperatures (e.g. Cu [5], Rh [6,9] and Pb [10]) demonstrated that a deep insight into atomic interactions can be gained by looking at the evolution of the first cumulants of the first-shell distribution as a function of temperature. It was shown in [11] that the shape of an effective pair potential describing interatomic interactions in MD simulations of solid Rh can be refined using first-neighbor pair distribution functions determined by XAS at various temperatures.…”