Fundamentals on Dependence of Volume on Pressure and Temperature

TL;DR

This paper analyzes how volume depends on pressure and temperature using Hillert thermodynamics, clarifying the conditions under which volume decreases with pressure and temperature, and explaining negative thermal expansion through statistical configuration competition.

Contribution

It provides a thermodynamic analysis of volume dependence on pressure and temperature, and introduces zentropy theory for predicting negative thermal expansion without fitting parameters.

Findings

Volume decreases with pressure in stable systems.

Negative thermal expansion arises from statistical competition of configurations.

Zentropy theory accurately predicts NTE based on density functional theory.

Abstract

The common wisdom that volume decreases with pressure and increases with temperature is analyzed in terms of Hillert nonequilibrium thermodynamics in the present work. It is shown that the derivative of volume to pressure in a stable system is always negative, i.e., volume decreases with the increase of pressure, when all other natural variables of the system are kept constant. This originates from the stability requirement that the conjugate variables, such as volume and negative pressure, must change in the same direction in a stable system. Consequently, since volume and temperature are not conjugate variables, they do not have to change in the same direction and thus do change in opposite directions in both natural and man-made systems. It is shown that the decrease of volume with the increase of temperature, commonly referred as negative thermal expansion (NTE) in the literature, originates from the statistical competitions of configurations in the system when the volumes of metastable configurations are smaller than that of the ground-state configuration. It is demonstrated that the zentropy theory can concisely explain and accurately predict NTE based on the density functional theory without fitting parameters.