(a) Schematic of a nanobulk composite material made of randomly oriented superlattice grains, and the global coordinate system , which is aligned to the macroscopic temperature gradient. (b) A single superlattice grain with its local coordinate system , which is aligned to the superlattice planes.
Averaging rules for the effective thermal conductivity of polycrystalline thin films (red squares), wires (blue circles), and nanobulk materials (green triangles). Points: FEM simulations of Table I. Lines: analytical results from Eqs. (11), (15), and (18). Inset: typical FEM simulation of a nanobulk configuration.
Theoretical thermal conductivity of PbTe using only the high-temperature Umklapp expression of Eq. (32) (blue solid line), as compared to experimental data from Greig in Ref. 35 and Devyatkova in Ref. 36 (red squares). Above 80 K, the data and model follow a relation almost perfectly (dashed green line). Inset: experimental data (Ref. 37) (points) for the thermal conductivity of in both -axis and -plane directions also follows a relation around room temperature.
Thermal conductivity as a function of period for four different values of the specularity parameter , for a nanobulk system at with thickness ratio . Solid lines: and are the in-plane and cross-plane values for a single superlattice grain, while is the value for a bulk polycrystal with randomly oriented grains. Dashed lines: and are the classical Fourier-law values for a single superlattice grain, neglecting phonon size effects.
Bulk effective thermal conductivity as a function of specularity for four different periods , for a nanobulk system at with thickness ratio .
Bulk effective thermal conductivity as a function of temperature for four different values of the specularity , for a system with thickness ratio and fixed period . The black dotted line is the bulk classical Fourier law value.
Comparison of present frequency-dependent model (solid lines) and traditional gray media model (dashed lines) for the period-dependence of the cross-plane superlattice thermal conductivity . The calculations are for a superlattice system at with thickness ratio .
Comparison of normalized theoretical (lines) and measured (points) thermal conductivity at . The theoretical results are normalized as and the experimental results as .
Temperature dependence of normalized effective lattice thermal conductivities for periods of 287, 577, and 1590 nm. All thermal conductivities are normalized as .
Parameters used in FEM simulations.
Properties for PbTe and at 300 K. The adjustable parameters for were fitted using the room temperature bulk phonon thermal conductivities in Ref. 39. Densities of primitive unit cells are calculated using the lattice constant and crystal structure. The sound velocities of are estimated from those of using the scaling arguments explained in Appendix B.
Fraction transformed and interlamellar spacing of the samples used for lattice thermal conductivity measurements.
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