Thermal Expansion and the Grueneisen Relation

Abstract

The linear thermal expansion coefficient a is defined by the relative length change per temperature variation

$$ \alpha = \frac{{dL}}{{dT}}\frac{1}{L} ; {K^{ - 1}} $$

(4.1a)

For an isotropic solid the volume expansion coefficient β is given by

$$ \beta = \frac{{dV}}{{dT}}\frac{1}{V} = 3\alpha ; {K^{ - 1}} $$

(4.1b)

The experimentally measured quantity is the integral thermal expansion

$$ \frac{{\Delta L}}{{{L_0}}} = \int_{293}^T {\alpha (T)dT} $$

(4.2)

where the reference temperature is 293K and L₀ =L(293K). In this definition, for a positive a, the quantity ΔL/L₀ becomes negative for cooling. For many technical purposes the integral thermal expansion is more directly applicable, but for physical interpretations the differential quantity a is of more significance. Thermal expansion is one of the thermodynamic properties which has been investigated for three centuries. Nevertheless, theoretical explanations are still difficult, since several types of binding potentials and vibrational modes are involved and influences from the glass transitions are superimposed.