Atomic Dynamics in Solids and Liquids from Inelastic Neutron Scattering

Citation

Bernal-Choban, Camille Marie (2024) Atomic Dynamics in Solids and Liquids from Inelastic Neutron Scattering. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/3nv3-g144. https://resolver.caltech.edu/CaltechTHESIS:09222023-185858765

Abstract

As temperature increases, atomic scale disorder, or entropy, drives the thermophysical properties of materials. One way it does this is by passing heat through materials in the form of vibrations. In solids, vibrational motions are called phonons, and their behaviors are used to predict macroscopic properties such as thermal expansion and thermal conductivity. Vibrational dynamics also exist in liquids but are traditionally less studied. Other forms of entropy include configurational and electronic entropy, which also evolve with temperature. Configurational changes in solids are often small, but in liquids, the prominence of diffusion makes this contribution significant. This dissertation addresses these atomistic components of entropy in two studies, one on bcc chromium and the other on the melting of monatomic systems.

In the first study, phonon densities of states (DOS) of body-centered cubic chromium were measured by time-of-flight inelastic neutron scattering (INS) at temperatures up to 1493 K. Density functional theory calculations with both quasi-harmonic (QH) and anharmonic (AH) methods were performed at temperatures above the Neel temperature. Features in the phonon DOS decrease in energy (soften) substantially with temperature. A Born-von Karman analysis using fits to the experimental DOS reveals a softening of almost 17% of the high transverse phonon branch between 330 and 1493 K. The low transverse branch changes by approximately half this amount. The AH calculations capture the observed behavior of the two transverse phonon branches, but the QH calculations give some inverted trends. Vibrational entropies from phonons and electrons are obtained, and their sum is in excellent agreement with the entropy of chromium obtained by calorimetry, indicating that above 330 K, no explicit temperature-dependent magnetic contributions are necessary.

The second investigation delves into the latent heat of melting, defined as T_mΔS_fus where T_m is the melting temperature and ΔS_fus is the entropy of fusion. At the scale of atoms and electrons, ΔS_fus has components from changes of atom configurations, atom vibrations, and thermal excitations of electrons. New data analyses were developed for inelastic neutron scattering to obtain changes in vibrational spectra upon melting. Combining these INS experiments with computational work using thermodynamic integration and molecular dynamics, components of ΔS_fus were obtained for a total of six elements, Ge, Si, Bi, Sn, Pb, Li. Upon melting, there is always a positive change of configurational entropy, ΔS_config. A baseline value of ΔS_config=1.2k_B/atom, approximately the value for Richard's rule, corresponds to zero change in the vibrational part of the entropy of fusion, ΔS_vib. Elements having values of ΔS_fus that depart from this value of Richard's rule have both an additional ΔS_vib and an additional ΔS_config. Surprisingly, the extra ΔS_config is close to 77% of ΔS_vib, for both positive and negative deviations from Richard's rule. This implies a correlation between the change in the number of basins in a potential energy landscape and the change in the inverse of their curvature upon melting.