Implications of cross-species interactions on the temperature dependence of Kapitza conductance

We investigate the behavior of Kapitza conductance at interfaces between two Lennard-Jones fcc solids as a function of the range and strength of cross-species interactions via molecular dynamics simulations. It is found that decreasing either of these quantities leads to a reduction in the slope of linear temperature dependence of Kapitza conductance, suggesting a corresponding decrease in the probability of inelastic phonon-phonon interactions. To further explore the mechanisms responsible for such behavior, we calculate the phonon density of states and spectral temperature of each of the monolayers adjacent to the interface. It is found that the reduction of the range and strength of cross-species interactions leads to a softening of the density of states near the interface, while the spectral temperature calculations provide further evidence that such reductions decrease the probability of inelastic phonon scattering. These findings help explain varying accounts of the temperature dependence of Kapitza conductance observed in previous works.

Figure 1

Temperature-dependent $h_{\mathrm{K}}$ data from NEMD simulations for samples I, V, and VII. Each data point is the average over three to five independent simulations and error bars represent the standard deviation, i.e., repeatability. Solid and dashed lines are linear fits of the data. While the slopes of these linear fits exhibit strong dependence on cross-species interaction parameters, the $y$ intercepts do not.

Figure 2

Phonon density of states curves at 12 K calculated via Eq. (1) within the monolayers adjacent to the interface (heavy lines) compared to bulk (light lines). A reduction in either $r_{c,\mathrm{AB}}$ or ${\varepsilon }_{\mathrm{AB}}$ causes a softening of modes on both sides of the interface.

Figure 3

Spectral temperature of the monolayer within material A adjacent to the interface for two different cross-species interactions at average interface temperatures of (a) 12 K and (b) 33 K. The “flatness” of these curves is indicative of the means of energy transfer across the interface, i.e., elastic only or elastic and inelastic. At 12 K, the spectral-temperature dependence suggests elastic scattering dominates at both interfaces. At 33 K, only the weakly bonded interface exhibits spectral-temperature dependence, suggesting that inelastic channels are inhibited in systems where the interface is poorly bonded. The absolute values of $T\left(\omega \right)$ are not indicative of the strength of coupling, as the average interface temperature varied slightly from simulation to simulation.