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

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