Classical infrared spectra of ionic crystals and their relevance for statistical mechanics

TL;DR

This paper investigates the classical infrared spectra of ionic crystals, particularly LiF, revealing a deep analogy with the Fermi--Pasta--Ulam model and suggesting modifications to classical statistical mechanics at low temperatures.

Contribution

It demonstrates the temperature dependence of ionic crystal spectra and proposes a temperature rescaling approach, challenging the traditional Boltzmann--Gibbs framework at low temperatures.

Findings

Classical models accurately reproduce room temperature spectra.

Spectral discrepancies at low temperatures are resolved by temperature rescaling.

Analogies with the Fermi--Pasta--Ulam model suggest modifications to statistical mechanics.

Abstract

It was recently shown that the experimental infrared spectra of ionic crystals at room temperature are very well reproduced by classical realistic models, and here new results are reported on the temperature dependence of the spectra, for the LiF crystal. The principal aim of the present work is however to highlight the deep analogy existing between the problem of spectra in ionic crystal models on the one hand, and that of energy equipartition in the Fermi--Pasta--Ulam model, on the other. Indeed at low temperatures the computations of the spectra show that the dynamics of the considered system is not completely chaotic, so that the use of the Boltzmann--Gibbs statistics is put in question, as in the Fermi--Pasta--Ulam case. Here, however, at variance with the equipartition problem, a first positive indication is given on the modifications that should be introduced in a classical statistical treatment: the new results at low temperatures show that it is indeed the Clausius identification of temperature that has to be modified. In fact, at very low temperatures the theoretical spectra fail to reproduce the experimental ones, if the temperature is taken as proportional to mean kinetic energy, but agreement is recovered through the only expedient of introducing a suitable temperature rescaling. Analogous results are also found in connection with thermal expansion.