Comprehensive first-principles analysis of phonon thermal conductivity and electron-phonon coupling in different metals

Separating electron and phonon components in thermal conductivity is imperative for understanding thermal transport in metals and highly desirable in many applications. In this work, we predict the mode-dependent electron and phonon thermal conductivities of 18 different metals at room temperature from first principles. Our first-principles predictions, in general, agree well with those available experimental data. For phonon thermal conductivity, we find that it is in the range of 2–18 W/mK, which accounts for 1%–40% of the total thermal conductivity. It is also found that the phonon thermal conductivities in transition metals and transition-intermetallic compounds (TICs) are non-negligible compared to noble metals due to the high phonon group velocities of the former. We further show that the electron-phonon coupling effect on phonon thermal conductivity in transition metals and intermetallic compounds is stronger than that of nobles, which is attributed to the larger electron-phonon coupling constant with a high electron density of states within the Fermi window and high phonon frequency in the former. For electron thermal conductivity, we observe that the transition metals and TICs have lower electron thermal conductivities compared to noble metals, which is mainly due to the weak electron-phonon coupling in noble metals. It is found that the Lorenz number of transition metals and TICs hold larger deviations from the Sommerfeld value $L_0=2.44\times {10}^{-8}\mathrm{W}\mathrm{\Omega }{\mathrm{K}}^{-2}$. We also find the mean free paths extracted at 50% accumulation function for phonons (within 10 nm) are generally smaller than those of electrons (5–25 nm).

Figure 1

Phonon thermal conductivity ${\kappa }_p$ predictions at a temperature of 300 K from first-principles calculations and the Klemens model [10], which include both $p\text{−}p$ and $p\text{−}e$ scattering. The dashed line represents ±30% error.

Figure 2

Phonon thermal conductivity ${\kappa }_p^{pp}$ of noble, alkali earth, transition, TICs, and NICs at 300 K. Here, only $p\text{−}p$ scattering is considered in the calculation of phonon thermal conductivity.

Figure 3

(a) Phonon-phonon scattering rate and (b) phonon group velocity for Ag (noble), Mg (alkali earth), Ni (transition), TiAl (TICs), CuAu (NICs), and Si (semiconductor) at 300 K.

Figure 4

The phonon thermal conductivity ${\kappa }_p^{pp}$ variation with (a) Debye temperature ${\theta }_D$ and (b) Grüneisen parameter ${\gamma }_G$ at 300 K.

Figure 5

Phonon thermal conductivity predictions at a temperature of 300 K from first-principles calculations and theoretical calculations using the Klemens [10] and Slack models [26], which only consider the $p\text{−}p$ scattering. The dashed line represents ±30% error.

Figure 6

(a) Percentage of the reduction of phonon thermal conductivity ${\kappa }_p^{pp}$ induced by electron-phonon coupling effect. (b) Electron-phonon coupling constant ${\lambda }_{ep}$.

Figure 7

Electron-phonon coupling matrix of NiAl and CuAu.

Figure 8

Variation of Eliashberg spectral function ${\alpha }^{2}F\left(\omega \right)$ with phonon frequency for CuAu and $\mathrm{C}{\mathrm{u}}_3\mathrm{Au}$. The gray region represents the phonon frequency for acoustic phonons and the blue region for optical phonons. It should be stated that the separating point of the acoustic and optical phonon is at about 3 THz for both CuAu and $\mathrm{C}{\mathrm{u}}_3\mathrm{Au}$, which is shown in the SM, Sec. S7 [48].

Figure 9

The percentage of phonon and electron thermal conductivity contributing to total thermal conductivity for these 18 metals.

Figure 10

Average phonon and electron mean free path of 18 metals at 300 K. The inset plot is the comparison of electron MFP between our calculated values and reference data [27, 67].

Figure 11

Variation of electrical conductivity with electron MFPs for 18 metals at 300 K.