Effect of anharmonicity on the thermal conductivity of amorphous silica

Proper consideration of anharmonicity is important for the calculation of thermal conductivity. However, how the anharmonicity influences the thermal conduction in amorphous materials is still an open question. In this work, we uncover the role of anharmonicity on the thermal conductivity of amorphous silica ($a\text{−}{\mathrm{SiO}}_2$) by comparing the thermal conductivity predicted from the harmonic theory and the anharmonic theory. Moreover, we explore the effect of anharmonicity-induced frequency shift on the prediction of thermal conductivity. It is found that the thermal conductivity calculated by the recently developed anharmonic theory (quasi-harmonic Green-Kubo approximation) is higher than that calculated by the harmonic theory developed by Allen and Feldman. The use of anharmonic vibrational frequencies also leads to a higher thermal conductivity compared with that calculated using harmonic vibrational frequencies. The anharmonicity-induced frequency shift is a mechanism for the positive temperature dependence of the thermal conductivity of $a\text{−}{\mathrm{SiO}}_2$ at higher temperatures. Further investigation on the mode diffusivity suggests that although anharmonicity has a larger influence on locons than diffusons, the increase in thermal conductivity due to anharmonicity is mainly contributed by the anharmonicity-induced increase of the diffusivity of diffusons. Finally, it is found that the cross-correlations between diffusons and diffusons contribute most to the thermal conductivity of $a\text{−}{\mathrm{SiO}}_2$, and the locons contribute to the thermal conductivity mainly through collaboration with diffusons. These results offer new insights into the nature of the thermal conduction in $a\text{−}{\mathrm{SiO}}_2$.

Figure 1

Radial distribution function $g$($r$) of $a\text{−}{\mathrm{SiO}}_2$ of all atom pairs at 300 K from this work, MD simulations of Larkin and McGaughey [22], and experimental measurement [24].

Figure 2

The inverse participation ratio and density of states of vibrational modes in $a\text{−}{\mathrm{SiO}}_2$ at 300 K.

Figure 3

(a) The DOS of anharmonic vibrational modes at different temperatures. (b) Frequency shifts at different temperatures.

Figure 4

The vibrational mode lifetimes of $a\text{−}{\mathrm{SiO}}_2$ at different temperatures.

Figure 5

The thermal conductivities calculated by AF theory [6], QHGK [12], and the theory of Simoncelli et al. [11] using harmonic vibrational frequencies. η is the broadening parameter in the AF theory.

Figure 6

The difference between the thermal conductivities calculated by different methods. $k_{\mathrm{harmo}}^{\mathrm{QHGK}}$ is the thermal conductivity calculated by QHGK using harmonic vibrational frequencies. $k_{\mathrm{harmo}}^{\mathrm{AF}}$ is the thermal conductivity calculated by AF theory using harmonic vibrational frequencies. $k_{\mathrm{anharmo}}^{\mathrm{QHGK}}$ is the thermal conductivity calculated by QHGK using anharmonic vibrational frequencies.

Figure 7

(a) The diffusivities of vibrational modes in $a\text{−}{\mathrm{SiO}}_2$ at 1900 K calculated by AF theory [Eq. (16)] and QHGK [Eq. (17)]. (b) The absolute (left) and relative (right) differences between the diffusivities calculated by QHGK and AF theory.

Figure 8

The temperature dependence of the relative contributions of diffusons (left) and locons (right) to the total diffusivity difference between QHGK and AF theory.

Figure 9

The thermal conductivities calculated by QHGK using harmonic or anharmonic vibrational frequencies and classical or quantum specific heat, and their comparisons with the results of the Green-Kubo formula based on MD simulations and experimental data [27, 28].

Figure 10

The absolute (a) and relative (b) changes in the thermal conductivity of different modes induced by frequency shifts.

Figure 11

(a) The diffusivities of vibrational modes in $a\text{−}{\mathrm{SiO}}_2$ at 1900 K calculated by QHGK [Eq. (17)] using harmonic and anharmonic vibrational frequencies, respectively. (b) The absolute (left) and relative (right) differences between diffusivities calcualted using anharmonic and harmonic vibrational frequencies.

Figure 12

The temperature dependence of the relative contributions of diffusons (left) and locons (right) to the total difference between the diffusivities calculated by anharmonic and harmonic vibrational frequencies.

Figure 13

The contributions of cross-correlations between diffusons and diffusons, between diffusons and locons, and between locons and locons to the total thermal conductivity.

Figure 14

Thermal conductivity of $a\text{−}{\mathrm{SiO}}_2$ at 1900 K computed by AF theory and QHGK, and a comparison with experimental data [27]. The symbol a represents the results calculated using harmonic vibrational frequencies, while b represents the results calculated using anharmonic vibrational frequencies.