Nuclear quantum effects in thermal conductivity

The goal of this project is to develop a general and robust anharmonic phonon theory based on a modern implementation of centroid molecular dynamics (CMD), to combine it with the Wigner transport equation (WTE) for heat transport, and to use the resulting combination to explore the role of nuclear quantum effects (NQEs) in the thermal conductivities of solids and gasses made from electrical insulators and semiconductors.

Since CMD is capable of capturing anharmonic shifts in phonon frequencies, the NQEs considered will go beyond the simple thermal effects that are captured by using harmonic quantum mechanical phonon occupations in WTE.

Since the phonon linewidths will be obtained from CMD phonon velocity autocorrelation functions rather than perturbation theory, there will be no restriction to weak anharmonicity or to few-phonon scattering contributions to linewidth.

Umklapp processes, in which there is a change in the reciprocal lattice vector during the phonon scattering, will also be included automatically.

And since both CMD and WTE can be applied to solids with arbitrarily large unit cells, the combined theory will be applicable to glasses and amorphous solids as well as crystals.

There is as yet no other method we are aware of for calculating thermal conductivities that shares all of these desirable features.

Furthermore, and perhaps even more importantly, CMD is based on the imaginary time path integral expression for the quantum mechanical partition function.

It is therefore consistent with an exact quantum mechanical description of the structural and thermodynamic properties of the system under investigation at the state point of interest. (This is especially true in the case of solids and glasses, the atoms in which are at distinguishable lattice sites and therefore satisfy the distinguishable-particle (Boltzmann) statistics.) This implies, among other things, that the use of CMD to calculate phonon properties will be consistent with an exact quantum mechanical treatment of the thermal expansion coefficient of the material, which is another key observable that depends on anharmonicity.

Thermal conductivity is an important material property in many emerging technologies because of the need (for example) for effective heat dissipation in electronics, thermal insulation in energy storage, and efficient heat transfer in thermoelectric materials for energy conversion.

It would therefore be useful to be able to reliably predict the thermal conductivities of a wide range of materials across a wide range of temperatures, including temperatures below the Debye temperature. The hope is that this project will help us to do that.

At the end of this project, we plan to incorporate our methodology in the freely available iPI software so that others can use it.

This choice is motivated by the fact that iPI already contains much of the requested path integral infrastructure along with well-tested interfaces to empirical, ab initio, and machine learned force fields.

So, if our methodological developments are successful, their incorporation in this package will provide an ideal way to make them available to the broader simulation community. This project falls within the EPSRC Computational and Theoretical Chemistry research area.