Resistivity, Seebeck coefficient, and thermal conductivity of platinum at high pressure and temperature

Platinum (Pt) is one of the most widely used functional materials for high-pressure and high-temperature experiments. Despite the crucial importance of its transport properties, both experimental and theoretical studies are very limited. In this study, we conducted density functional theory calculations on the electrical resistivity, the Seebeck coefficient, and the thermal conductivity of solid face-centered cubic Pt at pressures up to 200 GPa and temperatures up to 4800 K by using the Kubo-Greenwood formula. The thermal lattice displacements were treated within the alloy analogy, which is represented by means of the Korringa-Kohn-Rostoker method with the coherent potential approximation. The electrical resistivity decreases with pressure and increases with temperature. These two conflicting effects yield a constant resistivity of $\sim 70\mu \mathrm{\Omega }\mathrm{cm}$ along the melting curve. Both pressure and temperature effects enhance the thermal conductivity at low temperatures, but the temperature effect becomes weaker at high temperatures. Although the pressure dependence of the Seebeck coefficient is negligibly small at temperatures below $\sim 1500\mathrm{K}$, it becomes larger at higher temperatures. It requires a calibration of a thermocouple such as Pt-Rh in high-pressure and -temperature experiments.

Figure 1

(a) Electrical resistivity, (b) Seebeck coefficient, (c) thermal conductivity, and (d) Lorenz number of Pt as function of temperature at 0 GPa. Colored symbols are present calculations with $N_{\mathrm{v}}=4$ (*), 6 (▲), 8 (▼), 12 (■), 14 (•), and 20 (♦). These symbols are largely overlapped in (a), (c), whereas they are somewhat scattered in (b), (d). Gray broken lines indicate the literature data of the electrical resistivity [10], the Seebeck coefficient [11], the thermal conductivity [12], and the Lorenz number [10, 12]. Cross symbols are previous experiments of resistivity [13, 14, 16, 17, 18, 19], Seebeck coefficient [15, 16, 17, 20, 21], and thermal conductivity measurements [14, 18, 22, 23]. Open gray circles indicate the previous calculation [33]. Note that the results are almost independent of the $N_{\mathrm{v}}$ except for the Seebeck coefficient, and consistent with the literature.

Figure 2

Pressure and temperature dependence of (a) the electrical resistivity, (b) the Seebeck coefficient, (c) the thermal conductivity, and (d) the Lorenz number of solid fcc Pt up to 100 GPa. The gray region represents the liquid stability field [43]. All the source data are in Tables 1, 2, 3, 4.

Figure 3

Pressure and temperature dependence of (a) the electrical resistivity, (b) the Seebeck coefficient, (c) the thermal conductivity, and (d) the Lorenz number of solid fcc Pt up to 200 GPa. Pressure conditions are 0 (purple), 50 (green), 100 (cyan), 150 (orange), and 200 GPa (yellow). Previous studies at ambient pressure are also plotted for comparison. Gray broken lines indicate the literature data of the electrical resistivity [10], the Seebeck coefficient [11], the thermal conductivity [12], and the Lorenz number [10, 12]. Cross symbols are previous experiments of resistivity [13, 14, 16, 17, 18, 19], Seebeck coefficient [15, 16, 17, 20, 21], and thermal conductivity measurements [14, 18, 22, 23]. Open gray circles indicate the previous calculation [33]. Gray squares represent the previous thermal conductivity measurements at high pressures between 35 and 55 GPa [25].

Figure 4

Electrical resistivity of Pt as function of pressure at 300 K. Solid line with filled square symbols represents the present calculation and open circles indicate the previous measurements [24].

Figure 5

Thermal conductivity of Pt at high pressure as a function of temperature. Square symbols are present calculations at 0 (purple), 50 (green), and 100 GPa (cyan). Gray broken line indicates the literature data at ambient pressure [12]. Gray circles represent the previous measurements at high pressures between 35 and 55 GPa [25].