Cubic halide perovskites as potential low thermal conductivity materials: A combined approach of machine learning and first-principles calculations

Thermal conductivity is the key factor affecting thermoelectric properties of materials. Here, machine-learning techniques combined with first-principles calculations are used to identify the cubic halide perovskites ${\text{Cs}B\text{Br}}_3$ (B = Ca, Cd, and Sn) with ultralow thermal conductivity. Based on the Boltzmann transport equation within the relaxation time approximation, we demonstrate this type of perovskites have remarkably low lattice thermal conductivities ${\kappa }_L\sim 0.4-1$ W/mK at 300 K. We employ the self-consistent phonon theory incorporating both cubic and quartic anharmonicity, which is considered from the bubble and loop self-energy diagrams rather than many-body perturbation theory. We show that the approach yields a cubic-tetragonal phase transition of ${\mathrm{CsCaBr}}_3$ at temperature $T_c=226-265\mathrm{K}$, in good agreement with the experimental value of 239 K. An anomalously temperature dependence of ${\kappa }_L$ is observed in ${\mathrm{CsCdBr}}_3$, where the coherent term account for 26% of the total lattice thermal conductivity. We also demonstrate that the hardening of vibrations in low-lying phonon modes offset the phonon population effect as temperature increases by reducing the available phase space.

Figure 1

Receiver operating characteristic curves for the classification models. The low ${\kappa }_L$ model is classified based on the (a) threshold 1.0, (b) threshold 1.5, (c) threshold 2.0, and (d) threshold 2.5.

Figure 2

The periodic table trends of compounds with low thermal conductivity values. It shows the likelihood to search the low ${\kappa }_L$ materials with a given element. The elements in the periodic table are colored by the probability percentage, where the materials with the ${\kappa }_L<$ 1.5 W/mK are counted for a given element.

Figure 3

Anharmonic temperature-dependent phonon dispersions from 300 to 600 K, and atom-decomposed phonon density of states at $T=300$ and 500 K for ($\mathrm{a}){\mathrm{CsCaBr}}_3$, ($\mathrm{b}){\mathrm{CsCdBr}}_3$, and ($\mathrm{c}){\mathrm{CsSnBr}}_3$. (d) Harmonic phonon dispersion at 300 K colored according to the atomic participation ratio of the Cs atom for ${\mathrm{CsCdBr}}_3$.

Figure 4

(a) The ideal cubic structure of ${\mathrm{CsSnBr}}_3$, where Cs and Br are represented by cyan and brown balls. One can observe the atomic environment around the Br atom, where it reflects the anisotropic thermal displacement patterns in the plane and perpendicular to the plane. (b) Theoretical (lines) and experimental (filled shapes) [49] atomic temperature-dependent mean-square displacements for Br (orange and gray) and Cs (blue) atoms in ${\mathrm{CsSnBr}}_3$ materials. The dashed lines are calculated from the self-consistent phonon approximation, while the solid lines are from the harmonic approximation.

Figure 5

Phonon spectral function $S(\mathbf{q},\mathrm{\Omega })$ of (a) ${\mathrm{CsSnBr}}_3$ and (b) ${\mathrm{CsCdBr}}_3$ at 500 K, calculated using TDEP method.

Figure 6

(a) Calculated temperature-dependent squared frequency of soft modes at M and R points. The empty shapes are based on the self-consistent phonon theory with first-order loop diagram theory (SC1) theory and the solid shapes are based on the self-consistent phonon theory incorporating both bubble and loop diagram contributions (SCP). (b) Temperature dependence of the anharmonic phonon frequencies of two $T_{1u}$ modes calculated using SCP with polarization mixing (PM), SC1 with PM, and the TDEP approach.

Figure 7

Calculated temperature-dependent lattice thermal conductivity ${\kappa }_L$ of three cubic perovskites using different theoretical methods.

Figure 8

(a) Comparison of the 3ph scattering rates at $T=300\mathrm{K}$ (blue dots), $T=500\mathrm{K}$ (red dots), and $T=700\mathrm{K}$ (purple dots), respectively (left). (b) The 3ph scattering phase space under different temperatures. (c) Comparison of the 3ph scattering rates based on harmonic approximation (blue dots), SC1 theory (red dots), and SCP theory (purple dots). (d) The 3ph scattering phase space under different methods. The solid black lines indicate the scattering rate equals twice the phonon frequency.

Figure 9

Thermal conductivity spectra ${\kappa }_L\left(\omega \right)$ (the area below curves are filled with colors) and corresponding cumulative values (dotted lines). (a) The results of $\mathrm{SCP}+\mathrm{BTE}$ for ${\mathrm{CsCaBr}}_3$ at 300 K and 500 K. (b) Comparison of the HP $+$ BTE and SCP $+$ BTE results for the ${\mathrm{CsSnBr}}_3$. (c) The $\mathrm{SCP}+\mathrm{BTE}$ results for ${\mathrm{CsCdBr}}_3$ at 300 K and 500 K.