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We have studied the pressure effect on the rattling of tetrahedriteCu$_{10}$Zn$_{2}$Sb$_{4}$S$_{13\,}$(CZSS) and type-I clathrateBa$_{8}$Ga$_{16}$Sn$_{30\,}$(BGS) by specific heat and x-ray diffractionmeasurements. By applying pressure $P$, the rattling energy for CZSS initiallydecreases and steeply increases for $P$ $\textgreater$ $1$ GPa. By contrast,the energy for BGS increases monotonically with $P$ up to 6.5 GPa. An analysisof the pressure dependent specific heat and x-ray diffraction indicates thatthe out-of-plane rattling of the Cu atoms in the S$_{3}$ triangle of CZSSoriginates from the chemical pressure, unlike the rattling of the Ba ions amongoff-center sites in an oversized cage of BGS. The rattling in CZSS ceases uponfurther increasing $P$ above 2 GPa, suggesting that Cu atoms escape away fromthe S$_{3}$ triangle plane.

Pressure induced quenching of planar rattling in Cu$_{10}$Zn$_{2}$Sb$_{4}$S$_{13}$ studied by specific-heat and x-ray diffraction measurements