The majority of matters increase their volumes with increasing *T*, which is called thermal expansion [Wiki]. The thermal expansivity
(or thermal expansion coefficient), *α*, which describes the degree of thermal expansion of a matter for a given *T* increase, is defined by the
following equation:

(1)

Although increase in *P* always decreases *V*, as Le Chatelier's principle [Wiki] suggests, there is no such necessity for thermal expansion. One of well-known phenomena against thermal
expansion is water at *T* between 273 and 277 K, where *V* of water decreases with *T*.

Thermal expansion is caused by asymmetry of an atomic potential as shown in Fig. 1. What the blue curve means is that, if an atom approaches to a neighboring atom, it receives a strong repulsion force, whereas it receives relatively weak attractive force even if the distance between these two atoms increases. To the first approximation, a symmetric atomic potential can be approximated by a quadratic function, which is called the harmonic potential. On the other hand, an asymmetric potential is called the anharmonic potential [Wiki].

Fig. 1. Explanation of thermal expansion in view of the anharmonic atomic potential.

At nearly zero temperature (*T*0 in Fig. 1), an atom is located at the bottom of the atomic potential (“Zero position” in Fig. 1). With increasing *T* from *T*0 to
*T*1, *T*2, …, the kinetic energy of atomic motion increases with increasing from *E*0 to *E*1, *E*2, … . Because of the asymmetric potential, the average
atomic position is shifted to the direction of a longer atomic distance at high *T*, which is thermal expansion. Because of the atomic potential contain higher terms, the rate of the
atomic distance increase with *T* increases with increasing *T*.

As in discussed in a separate page, lattice thermal resistance, which is inversely proportional to thermal conductivity [Wiki] or thermal diffusivity [Wiki], is also caused by anharmonicity of an atomic potential. For this reason, a matter with larger thermal expansivity has smaller lattice thermal conductivity and diffusivity.

Let us discuss *P* dependence of *α* (Fig. 2). By pressurizing, the atomic potential is distorted so that the potential minimum is located at a shorter atomic distance (blue curve).
Because of the narrowing of the atomic potential, the rate of the atomic distance increase with *T* decreases by compression. Namely, *α* decreases with increasing *P*. The
decrease in *α* with pressure is expressed by the Anderson Grüneisen parameter, *δ*_{T}. In the case of mantle
minerals, *α* decreases in proportion to 5.5 ± 0.5 power of *V*.

Fig. 2. Explanation of decrease in *α* with *P*.