Role of high-order lattice anharmonicity in the phonon thermal transport of silver halide $\mathrm{Ag}X (X=\mathrm{Cl},\mathrm{Br},\mathrm{I})$

The phonon transport mechanisms and ultralow lattice thermal conductivities (${\kappa }_{\mathrm{L}}$) in silver halide $\mathrm{Ag}X$ ($X=\mathrm{Cl},\mathrm{Br},\mathrm{I}$) compounds are not yet well understood. Herein, we study the lattice dynamics and thermal property of $\mathrm{Ag}X$ under the framework of perturbation theory and the two-channel Wigner thermal transport model based on accurate machine learning potentials. We find that an accurate extraction of the third-order atomic force constants from largely displaced configurations is significant for the calculation of the ${\kappa }_{\mathrm{L}}$ of $\mathrm{Ag}X$, and the coherence thermal transport is also non-negligible. In AgI, however, the calculated ${\kappa }_{\mathrm{L}}$ still considerably overestimates the experimental values even including four-phonon scatterings. Molecular dynamics (MD) simulations using machine learning potential suggest an important role of the higher-than-fourth-order lattice anharmonicity in the low-frequency phonon linewidths of AgI at room temperature, which can be related to the simultaneous restrictions of the three- and four-phonon phase spaces. The ${\kappa }_{\mathrm{L}}$ of AgI calculated using MD phonon lifetimes including full-order lattice anharmonicity shows a better agreement with experiments.

Figure 1

(a,b) Temperature-dependent ${\kappa }_{\mathrm{L}}$ of AgCl calculated using different sets of IFCs with PBE and PBEsol functionals under the UT [6]. IFCs2, IFCs3, and IFCs4 stand for the second-, third-, and fourth-order IFCs, respectively. Configurations used for fitting the IFCs are generated by performing MD simulations [32] based on our NEP, and via the RDM from a normal distribution with a standard deviation of 0.025 Å. IFCs2_FDM and IFCs2_TDEP are extracted using the FDM and TDEP methods, respectively. The black solid symbols represent the experimental results taken from Refs. [37, 38, 39]. The purple square symbols stand for the theoretical data reported in Ref. [4].

Figure 2

(a) Temperature-dependent ${\kappa }_{\mathrm{L}}^{\mathrm{p}+\mathrm{c}}$ of AgBr calculated using different sets of IFCs under the UT [6]. The black solid symbols represent the experimental results from Refs. [7, 43, 44, 45]. The mallow purple hollow symbols stand for the theoretical data reported in Ref. [4]. (b) ${\kappa }_{\mathrm{L}}^{\mathrm{p}+\mathrm{c}}$ of AgI computed using the different sets of IFCs. ${\kappa }_{\mathrm{L}}$ calculated using the phonon lifetimes (${\tau }_{\mathrm{MD}}$) extracted from MD simulations and that from HNEMD simulations [35, 46] based on NEP are also shown for comparisons. The black solid symbols represent the experimental results from Ref. [8].

Figure 3

Phonon linewidths of AgCl (a) and AgI (b) calculated from PT and MD simulations at 300 K. PT_3ph and PT_($3+4$)ph represent the phonon linewidths computed using only the third-order and both of the third- and fourth-order IFCs, respectively. MD_NEP denotes the phonon linewidths calculated from MD simulations using our NEP.

Figure 4

Three- (a) and four-phonon (b) WPS of AgCl and AgI at 300 K. Mode-resolved three- (c) and four-phonon (d) WPS of AgI calculated at 300 K. Restricted phase space is observed inside the circled areas.