Isothermal and Adiabatic Elastic Tensors

TL;DR

This paper derives the relationship between adiabatic and isothermal elastic tensors using thermodynamics, aiding understanding of high-frequency material responses where direct measurement of the adiabatic modulus is challenging.

Contribution

It provides a theoretical derivation linking adiabatic and isothermal elastic tensors from first principles, facilitating better interpretation of high-frequency elastic behavior.

Findings

Derived the relationship between adiabatic and isothermal elastic tensors.

Clarified the thermodynamic basis for elastic tensor differences.

Enhanced understanding of elastic response in high-frequency regimes.

Abstract

The adiabatic elastic modulus is often useful in the high frequency response of materials. Unfortunately, it can be much more difficult to directly measure the adiabatic elastic modulus of material than the isothermal elastic modulus. We derive the relationship between the adiabatic and isothermal elastic tensors from the first law of thermodynamics.