The Effect of Pressure on the Negative Thermal Expansion of Solid Methane

The effect of pressure on the thermal expansion of solid CH$_4$ is calculated for the low temperature region where the contributions from phonons and librons can be neglected and only the rotational tunnelling modes are essential. The effect of pressure is shown to increase the magnitude of the peaks of the negative thermal expansion and shifts the positions of the peaks to the low-temperature region, which goes asymptotically to zero temperature with increasing pressure. The Gruneisen thermodynamical parameter for the rotational tunnelling modes is calculated. It is large, negative, and increases in magnitude with rising pressure.