Minimum thermal conductivity in the context of diffuson-mediated thermal transport

A model for the thermal conductivity of bulk solids is proposed in the limit of diffusive transport mediated by diffusons as opposed to phonons. This diffusive thermal conductivity, kappa(diff), is determined by the average energy of the vibrational density of states, (h) over bar omega(avg), and the number density of atoms, n. Furthermore, kdiff is suggested as an appropriate estimate of the minimum thermal conductivity for complex materials, such that (at high temperatures): kappa(diff) = n1/3k(B)/pi omega(avg) approximate to kappa(min). A heuristic finding of this study is that the experimental oavg is highly correlated with the Debye temperature, allowing kappa(diff) to be estimated from the longitudinal and transverse speeds of sound: kappa(diff) approximate to 0.76n2/3kB1/3(2v(T) + v(L)) thorn vLthorn. Using this equation to estimate kappa(min) gives values 37% lower than the widely-used Cahill result and 18% lower than the Clarke model for kappa(min), on average. This model of diffuson-mediated thermal conductivity may thus help explain experimental results of ultralow thermal conductivity.