Date of Award


Degree Type


Degree Name

Master of Science (MS)


Mechanical and Aerospace Engineering

Committee Chair(s)

Nicholas Roberts


Nicholas Roberts


Heng Ban


Ryan Berke


Phonon dispersion branches are used to obtain an effective relaxation time to calculate thermal conductivity of Uranium Dioxide (UO2). The method presented closely follows that of Deskins’ phonon-phonon interaction that uses a three-phonon process which satisfies momentum and energy conservation. All phonon branches including longitudinal acoustic, transverse acoustic, longitudinal optical and transverse optical are considered in the calculation of the relaxation time.

After one phonon is identified, a scan is initiated to test all phonon combinations that will satisfy the conservation equations. When the scan identifies a valid three-phonon combination a relaxation time is calculated for that combination. All the relaxation times from the possible combinations are summed using Mathias’ rule to obtain a total approximate relaxation time for that phonon.

Thermal conductivity at equilibrium can be calculated at a specific temperature using the relaxation time approximation of the Boltzmann equation. This approximation uses specific heat, relaxation time, group velocity and the Bose-Einstein distribution.

Eventually, the goal of this work is to apply the routine for calculating relaxation time from this work to a Monte Carlo simulation that will treat systems not in equilibrium.