Pressure-dependent thermal conductivity in Al, W, and Pt: Role of electrons and phonons

Understanding the pressure dependence on thermal transport of metals is crucial for high-pressure applications and fundamental research in earth science. As high-pressure thermal measurements are challenging, the theoretical approach and first-principles methods are widely adopted to investigate the pressure-dependent thermal transport in metals. However, these approaches are generally limited to the free-electron metals and the phonon contributions are neglected. The mechanisms behind the pressure effect on thermal transport of metals are not fully addressed. In this work, we implement rigorous mode-level first-principles calculations to reveal different mechanisms behind the pressure-dependent electronic and phonon thermal conductivity in aluminum (Al), tungsten (W), and platinum (Pt). While the overall thermal conductivity values of the three metals all increase with pressure, the mechanisms are different. For the electronic thermal conductivity part, the main contribution for the positive pressure effect on free-electron metal Al is the decrease of the electron-phonon scattering rate, while the dominant contribution in Pt and W, whose $d$ state electrons are abundant around the Fermi energy, is the increase of electron group velocity. Phonon thermal conductivity of Pt and Al is found to increase with pressure, but the rates of increase are different. In contrast, phonon thermal conductivity of W is nearly independent with pressure. Such pressure invariance is due to the competing effect between phonon lifetime decrease and phonon group velocity increase under pressure.

Figure 1

The temperature-dependent (a) electrical conductivity ($\sigma$) and (b) thermal conductivity ($\kappa$) of Al, Pt, and W at 0 GPa. The experiment data are taken from Refs. [61, 62, 63, 64, 65, 66], while the dashed line in (b) shows the simulation results from the literature [41].

Figure 2

Normalized unit cell volume $V$ as a function of pressure from first-principles calculation and the comparison with experiment data of Al [70], Pt [71], and W [72]. The volume is normalized by unit cell volume $V_0$ at 0 GPa.

Figure 3

Electron density of states of Al, Pt, and W at 0 and 80 GPa.

Figure 4

Thermal conductivity of Al, Pt, and W at 300 K as a function of pressure (a) and (b) normalized volume reduction. Our simulation results are compared with the theoretical model which is shown by dot-dash lines.

Figure 5

Normalized electronic thermal conductivity (${\kappa }_{el}/{\kappa }_{el,0}$), averaged square velocity ($\langle v^2\rangle /\langle v_0^2\rangle$), relaxation time ($\langle {\tau }^{\kappa }\rangle /\langle {\tau }_0^{\kappa }\rangle$), and total electron specific heat ($C_{el}/C_{el,0}$) of (a) Al, (b) Pt, and (c) W as a function of pressure.

Figure 6

Variations of ${\alpha }^{2}F\left(\omega \right)$ and phonon density of states of (a) Al, (b) Pt, and (c) W as a function of phonon frequency.

Figure 7

(a) Phonon thermal conductivity and (b) its ratio in total thermal conductivity of Al, Pt, and W under different pressures.

Figure 8

Normalized phonon thermal conductivity (${\kappa }_{\mathrm{ph}}/{\kappa }_{\mathrm{ph},0}$), averaged square of phonon velocity ($\langle v_{\mathrm{ph}}^2\rangle /\langle v_{\mathrm{ph},0}^2\rangle$), relaxation time due to phonon-electron scattering ($\langle {\tau }_{\mathrm{ph}-el}\rangle /\langle {\tau }_{\mathrm{ph}-el,0}\rangle$) and phonon-phonon scattering ($\langle {\tau }_{\mathrm{ph}-ph}\rangle /\langle {\tau }_{\mathrm{ph}-ph,0}\rangle$) and phonon specific heat ($C_{\mathrm{ph}}/C_{\mathrm{ph},0}$) of (a) Al, (b) Pt, and (c) W as a function of pressure.

Figure 9

Lorenz ratio of Al, Pt, and W under different pressure.

Figure 10

Comparison between the phonon dispersion relations of Pt with SOC and without SOC.