Anomalous pressure dependence of thermal conductivities of large mass ratio compounds

The lattice thermal conductivities (κ) of binary compound materials are examined as a function of hydrostatic pressure $P$ using a first-principles approach. Compounds with relatively small mass ratios, such as MgO, show an increase in κ with $P$, consistent with measurements. Conversely, compounds with large mass ratios that create significant frequency gaps between acoustic and optic phonons (e.g., BSb, BAs, BeTe, BeSe) exhibit decreasing κ with increasing $P$, a behavior that cannot be understood using simple theories of κ. This anomalous $P$ dependence of κ arises from the fundamentally different nature of the intrinsic scattering processes for heat-carrying acoustic phonons in large mass ratio compounds compared to those with small mass ratios. This work demonstrates the power of first-principles methods for thermal properties and advances a broad paradigm for understanding thermal transport in nonmetals.

Figure 1

Calculated phonon dispersions for MgO at $P=0$ (solid black curves) and $P=35\mathrm{GPa}$ (dashed red curves). Black circles give measured data from Refs. [41, 42], and red circles give measured data from Ref. [43]. Note the upward frequency shifts of phonons with $P$.

Figure 2

Left panel: Calculated κ (dashed red line) and that including isotopes, impurities, and sample boundaries (solid red line), along with measured thermal conductivity (red circles), vs $P$ for MgO [9]. Right panel: $\kappa /{\kappa }_0$ for BSb (dotted black), BAs (solid orange), BeTe (dashed green), and BeSe (short dashed blue). BeSe has a relatively large contribution to the three-phonon scattering phase space from processes involving one acoustic phonon and two optic phonons. The decrease in this contribution as $P$ increases from zero gives the initial increase in κ seen here in this figure.

Figure 3

Calculated κ vs mass ratio ($m_2/m_1$) for a hypothetical BAs material for which $m_1$ (light mass) and $m_2$ (heavy mass) are varied, but $m_1+m_2$ stays fixed at $m_1+m_2=m_{\mathrm{B}}+m_{\mathrm{As}}$. Solid black and dashed red curves give κ using the BAs IFCs for $P=0$ and $P=16\mathrm{GPa}$, respectively. The square symbols on each curve give the calculated κ for the actual BAs mass ratio, $m_{\mathrm{As}}/m_{\mathrm{B}}=7$, which occurs near the freeze-out condition ${\varphi }_{aao}^{3-\mathrm{ph}}=0$. The inset gives the phase space for aaa scattering, ${\varphi }_{aaa}^{3-\mathrm{ph}}$ (red curve), and aao scattering, ${\varphi }_{aao}^{3-\mathrm{ph}}$ (black curve), vs $m_2/m_1$ for the hypothetical material for $P=0$.