Anharmonicity in Thermal Insulators: An Analysis from First Principles

The anharmonicity of atomic motion limits the thermal conductivity in crystalline solids. However, a microscopic understanding of the mechanisms active in strong thermal insulators is lacking. In this Letter, we classify 465 experimentally known materials with respect to their anharmonicity and perform fully anharmonic ab initio Green-Kubo calculations for 58 of them, finding 28 thermal insulators with $\kappa <10\mathrm{W}/\mathrm{mK}$ including 6 with ultralow $\kappa \lesssim 1\mathrm{W}/\mathrm{mK}$. Our analysis reveals that the underlying strong anharmonic dynamics is driven by the exploration of metastable intrinsic defect geometries. This is at variance with the frequently applied perturbative approach, in which the dynamics is assumed to evolve around a single stable geometry.

Figure 1

Correlation between measured (circles: single-crystals; stars: polycrystals, [7, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53]) and computed (aiGK) thermal conductivities at room temperature on a log-log scale. The gray area indicates 50% deviation in terms of $\kappa$ from experiment and the error bars denote the standard error between trajectories. Where multiple experimental references were available, the average was taken.

Figure 2

Anharmonicity measure ${\sigma }^{\mathrm{A}}(t)$ for ${\text{KCaF}}_3$ evaluated at each time step during one aiMD trajectory. The upper row shows averaged positions in $(10\overline{1})$ direction for time periods with ${\sigma }^{\mathrm{A}}(t)\approx 0.5$ (blue), and increased ${\sigma }^{\mathrm{A}}(t)\approx 1.2$ (red), in which one Cu cation moves to an interstitial site along $(\overline{1}11)$.

Figure 3

Thermal conductivity $\kappa$ vs anharmonicity at 300 K, ${\sigma }_{300\mathrm{K}}^{\mathrm{A}}$ (tabulated data given in the SM [30]). The dashed trend line and gray areas are shown to guide the eye. (a) The qualitative scaling of $\kappa$ with ${\sigma }_{300\mathrm{K}}^{\mathrm{A}}$ suggested in Ref. [61] and used to disregard good thermal conductors during screening is showcased uusing experimental measurements (black circles) as well as our aiGK calculations for the benchmark materials from Fig. 1 (black squares) and predictions from subplot (b) (red stars). (b) Thermal conductivity aiGK predictions for materials with ${\sigma }_{300\mathrm{K}}^{\mathrm{A}}>0.2$. The symbol and color code indicate the lattice type.

Figure 4

Anharmonicity measure ${\sigma }^{\mathrm{A}}(t)$ for ${\mathrm{KCaF}}_3$ evaluated at each time step during one aiMD trajectory. The upper row shows time-averaged positions in (100) direction for the periods with (a) ${\sigma }^{\mathrm{A}}(t)\approx 0.4$ (blue), and (b) ${\sigma }^{\mathrm{A}}(t)\approx 1.1$ (red). Note the rearrangement of Ca-F bonds from zigzag to straight shape when comparing (a) and (b). See Supplemental Material for a video of the tilt rearrangement around 18 ps.