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Ab initio computational study on the lattice thermal conductivity of Zintl clathrates [Si$_{19}$P$_{4}$]Cl$_{4}$ and Na$_{4}$[Al$_{4}$Si$_{19}$]

The lattice thermal conductivity of silicon clathrate framework Si$_{23}$ and two Zintl clathrates, [Si$_{19}$P$_{4}$]Cl$_{4}$ and Na$_{4}$[Al$_{4}$Si$_{19}$], is investigated by using an iterative solution of the linearized Boltzmann transport equation (BTE) in conjuntion with ab initio lattice dynamical techniques. At 300 K, the lattice thermal conductivities for Si$_{23}$, [Si$_{19}$P$_{4}$]Cl$_{4}$, and Na$_{4}$[Al$_{4}$Si$_{19}$] were found to be 43 W/(m K), 25 W/(m K), and 2 W/(m K), respectively. In the case of Na$_{4}$[Al$_{4}$Si$_{19}$], the order-of-magnitude reduction in the lattice thermal conductivity was found to be mostly due to relaxation times and group velocities differing from Si$_{23}$ and [Si$_{19}$P$_{4}$]Cl$_{4}$. The difference in the relaxation times and group velocities arises primarily due to the phonon spectrum at low frequencies, resulting eventually from the differences in the second-order interatomic force constants (IFCs). The obtained third-order IFCs were rather similar for all materials considered here.