The importance of optical non-propagating modes on thermal conductivity of disordered solids

Current understanding of phonons is based on the phonon gas model (PGM), which is best rationalized for crystalline materials. However, most of the phonons/modes in disordered materials have a different character and thus may contribute to heat conduction in a fundamentally different way than is described by PGM. For the modes in crystals, which have sinusoidal character, one can separate the modes into two primary categories, namely acoustic and optical modes. However, for the modes in disordered materials, such designations may no longer rigorously apply. Nonetheless, the phase quotient (PQ) is a quantity that can be used to evaluate whether a mode more so shares a distinguishing property of acoustic vibrations manifested as a positive PQ, or a distinguishing property of an optical vibration manifested as negative PQ. In thinking about this characteristic, there is essentially no intuition regarding the role of positive vs. negative PQ vibrational modes in disordered solids. Given this gap in understanding, herein we studied the respective contributions to thermal conductivity for several disordered solids as a function of PQ. The analysis sheds light on the importance of optical like/negative PQ modes in structurally/compositionally disordered solids, whereas, in crystalline materials, the contributions of optical modes are usually small.

FIG. 1. Phase Quotient (PQ) and participation ratio for various disordered solids

Fig 2. Thermal conductivity accumulation and density of states verses PQ for a-C, a-SiO2, and In0.53Ga0.47As alloy.

FIG. 3. The ratio of the percentage of thermal conductivity to the percentage of heat capacity associated with positive and negative PQ.