Grüneisen parameter

In condensed matter, Grüneisen parameter $γ$ is a dimensionless thermodynamic parameter named after German physicist Eduard Grüneisen, whose original definition was formulated in terms of the phonon nonlinearities.

Because of the equivalences of many properties and derivatives within thermodynamics (e.g. see Maxwell relations), there are many formulations of the Grüneisen parameter which are equally valid, leading to numerous interpretations of its meaning. Some formulations for the Grüneisen parameter include:

\gamma =V\left({\frac {dP}{dE}}\right)_{V}={\frac {\alpha K_{T}}{C_{V}\rho }}={\frac {\alpha K_{S}}{C_{P}\rho }}={\frac {\alpha v_{s}^{2}}{C_{P}}}=-\left({\frac {\partial \ln T}{\partial \ln V}}\right)_{S}

where $V$ is volume, $C_{P}$ and $C_{V}$ are the principal (i.e. per-mass) heat capacities at constant pressure and volume, $E$ is energy, $S$ is entropy, $α$ is the volume thermal expansion coefficient, $K_{S}$ and $K_{T}$ are the adiabatic and isothermal bulk moduli, $v_{s}$ is the speed of sound in the medium, and $ρ$ is density. The Grüneisen parameter is dimensionless.

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