Theoretical studies of heat transfer across interfaces

Abstract

We have performed two intimately related studies of interfacial heat transfer. The first is a study of the Kapitza conductance for one-dimensional systems; the second is a study of three-dimensional interfacial three-phonon processes. When quantum materials are present, the values of the Kapitza conductance predicted by the Khalatnikov acoustic mismatch theory are smaller than experimental values by an order of magnitude or more. In order to test the validity of the fundamental assumptions of the Khalatnikov theory, we have performed the first computer experiments to evaluate the Kapitza conductance of "perfectly clean" systems. We first employ the approach used by Khalatnikov to derive an expression for the Kapitza conductance o f a harmonic, one-dimensional system. We also modify this theory to account for the presence of the bulk heat current. We then "measure" the Kapitza conductance for harmonic lattices with various mass ratios (across the interface) by performing molecular dynamics computer experiments. We find that the Khalatnikov and modified Khalatnikov theories agree with the results of the computer experiments only to within an order of magnitude. This leads us to believe that the Khalatnikov theory is incomplete. We also find that anharmonicity increases the Kapitza conductance of these lattices. An alternate expression for the Kapitza conductance which is derived using linear response theory is discussed and comments on computational difficulties which arise in its application are presented. ...