Thermodynamics of volume collapse transitions in cerium and related compounds

TL;DR

This paper introduces a non-linear elastic model explaining the thermodynamics and phase transition features of cerium and similar compounds, including hysteresis, critical behavior, and bulk modulus softening.

Contribution

The model uniquely captures the coherent volume collapse transition with a solvable statistical mechanics framework, linking elastic properties to phase behavior.

Findings

Reproduces hysteresis and negative bulk modulus in volume collapse.

Predicts critical point where hysteresis loop vanishes.

Explains phase diagram features of cerium and related materials.

Abstract

We present a non-linear elastic model of a coherent transition with discontinuous volume change in an isotropic solid. The model reproduces the anomalous thermodynamics typical of coherent equilibrium including intrinsic hysteresis (for a pressure driven experiment) and a negative bulk modulus. The novelty of the model is that the statistical mechanics solution can be easily worked out. We find that coherency leads to an infinite-range density--density interaction, which drives classical critical behavior. The pressure width of the hysteresis loop shrinks with increasing temperature, ending at a critical point at a temperature related to the shear modulus. The bulk modulus softens with a 1/2 exponent at the transition even far from the critical point. Many well known features of the phase diagram of Ce and related systems are explained by the model.