In semiconductors and insulators, the primary heat carriers are quantized lattice vibrations called phonons. By calculating harmonic (i.e., frequency, group velocity) and anharmonic (i.e., lifetime) phonon properties, it is possible to obtain the thermal conductivity of the material. These properties can be found using a technique called lattice dynamics, which uses the force constants between individual atoms as inputs to solve the Boltzmann transport equation.

For molecular crystals with strong bonds, however, the atomic degrees of freedom can be restricted in order to model the system as rigid molecules rather than individual atoms. This choice allows for an examination of the effect of small rotations about equilibrium (i.e., librations) on the thermal properties, as well as the impact of removing the intra-molecular vibrations.  This approach was previously used in molecular dynamics simulations of the C60 molecular crystal in order to explain its trends in thermal conductivity versus temperature.  

An approach already exists to perform harmonic lattice dynamics calculations in the rigid molecule framework. Here, we extended this rigid molecule formulation to anharmonic lattice dynamics calculations, allowing us to examine its full impact on thermal transport properties. In addition, it allows us to closely examine the phonon scattering caused by librations, as well as the effect of removing intra-molecular vibrations and the associated scattering phase space.

We used an in-house lattice dynamics code for our calculations and selected a toy system to benchmark. For ease of calculating the force constants analytically, we chose a Lennard-Jones argon crystal, with the four conventional cell basis atoms connected together into two pairs of diatomic molecules with perpendicular orientations. In addition, using a pair potential allowed us to perform molecular dynamics simulations on the same system and apply the Green Kubo method to predict its thermal conductivity, which can then be compared against the lattice dynamics results. The predicted thermal conductivities are in reasonable agreement, with values of 5.50 W/m-K from lattice dynamics and 5.45 W/m-K from molecular dynamics along the intra molecular bond length directions at a temperature of 5 K. The phonon properties and scattering rates were then examined in order to identify the cause behind the decrease in thermal conductivity compared to a full degrees of freedom system. 

The crystal was then modified by decreasing the intramolecular bond length until free rotation was possible. The resulting change in thermal conductivity was captured using both lattice dynamics and molecular dynamics, with the emergence of imaginary branches in the phonon dispersion indicating a phase transition. With the success of the modified lattice dynamics code in calculating the thermal conductivity of this toy system, it can now be extended to real materials such as sodium superoxide to study the impact of their librational modes.


Predicting Phonon Properties and Thermal Conductivity of Rigid Molecular Crystals Using Rotational Lattice Dynamics

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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