Tetrahedrite Cu₁₂Sb₄S₁₃ is the mother compound of high-performance thermoelectric materials with very low thermal conductivity [1]. The Cu(2) ions are vibrating perpendicular to the S₃ triangle plane with an anharmonic large amplitude (rattles) at temperatures above 85 K, where a structural phase transition occurs [1]. The characteristic energy of the rattling is reduced by decreasing the area of the S₃ triangle with the substitution of As for Sb [2]. This result implies that the rattling stems from the chemical pressure inherent in the triangle to squeeze Cu(2) out of the plane. The phase transition is quenched by the partial substitution of Zn for Cu in Cu₁₀Zn₂Sb₄S₁₃ [1].

To reveal the relation between the ratting and the area of S₃ triangle, we have measured the specific heat C from 0.5 to 10 K under pressures P. We used an AC calorimetry which enables us to measure the absolute value of C even under high P [3]. We employed the sample of Cu₁₀Zn₂Sb₄S₁₃ without showing the structural phase transition. The pressure dependent crystal structure up to 3.5 GPa was examined by synchrotron powder x-ray diffraction at the SPring-8, BL02B1 beamline using a diamond anvil cell. Figure shows the low-T data of C/T³ under various P up to 3.1 GPa. For P = 0, a broad maximum of C/T³ at 4 K is caused by the rattling. This maximum shifts to low temperatures with increasing P to 1 GPa. This means the reduction of the rattling energy in accordance with the effect caused by the substitution of As for Sb [2]. With further increasing P, the value of C/T³ is decreased and the additional contribution over the Debye specific heat disappears for P > 2.4 GPa. The results indicate the complete suppression of rattling of Cu ions, which will be discussed with the pressure dependent structural parameters.

Fig. Temperature dependence of C/T³ of Cu₁₀Zn₂Sb₄S₁₃ under various pressures up to 3.1 GPa.
The dashed line represents the Debye contribution for Debye temperature of 239 K [4].

References

[1] K. Suekuni et al., Appl. Phys. Express 5, 051201 (2012).

[2] K. Suekuni et al., Adv. Energy Mater. 30, 1706230 (2018).

[3] K. Umeo, Rev. Sci. Instrum., 87, 063901 (2016).

[4] K. Suekuni et al., J. Appl. Phys. 113, 043712 (2013).