The effect of compression on the thermal conductivity of CuGaS2, CuInS2, CuInTe2, and AgInTe2 chalcopyrites (space group I-42d) was studied at 300 K using phonon calculations. The lattice thermal conductivity (κph) was evaluated by solving the Boltzmann transport equation with harmonic and third-order force constants.
Striking differences are obtained between the κph behavior of CuGaS2, CuInS2, CuInTe2, and AgInTe2 under compression. The κph value of CuGaS2 always increases with pressure up to 9.5 GPa. A drastically different functional dependence is obtained as soon as heavier In is considered instead of Ga (BIII in AIBIIICVI2). Under pressure up to 6 GPa, κph of CuInTe2 decreases from 7.6 to 4.1 W m-1 K-1, which is anomalous. This is consistent with the experimental data [1,2], implying that important physics is captured within the methodology employed herein and structural modulations are not indispensable to drive the anomaly. By exchanging Te with lighter S (CVI in AIBIIICVI2) and hence forming CuInS2, κph increases up to 2 GPa, which is again a common behavior and equivalent to that of CuGaS2. Upon a further pressure increase, κph begins to decrease and reaches a slightly lower value at 8 GPa than that at 0 GPa. To account for the effect of the transition metal constituent (AI in AIBIIICVI2), Cu in CuInTe2 is exchanged with heavier Ag. AgInTe2 exhibits a significantly lower κph value and a steeper decrease in κph under pressure, reaching 0.2 W m-1 K-1 at 2.6 GPa.
Using the Slack model, Gui et al.  have showed that the Thermoelectric Figure of Merit for CuInCVI2 (CVI = S, Se, and Te) uniformly increases at elevated temperatures up to 850 K. However, the effect of pressure on κ has not thoroughly been studied. Using the quasi-harmonic Debye model, Sharma et al. have evaluated electronic, thermal, and mechanical properties of AgInCVI2 (CVI = S, Se, and Te) under pressure and reported a noticeable reduction in the Grüneisen parameter and volumetric thermal expansion coefficient as well as bulk modulus . Since the Grüneisen parameter and volumetric thermal expansion coefficient can be related to κ , it appears that pressure effects on κ are considerable. This is consistent with an experimental study reporting a decrease in κ by 30% for CuInTe2 under pressure up to 2.3 GPa . Generally, κ should increase under compression . This implies that the behavior of CuInTe2 is anomalous. Two possible mechanism have been proposed based on experiments: (i) anharmonic behavior of lattice vibrations  and (ii) structural modifications under high pressure (e.g. stacking faults) .The underlying physics of the κ reduction under compression of CuInTe2 and possibly other AIBIIICVI2 compounds is not fully understood.
This can be understood based on the phonon dispersion curves. Softening of the acoustic phonon modes occurs for these anomalous chalcopyrites. This leads to the negative Grüneisen parameter and negative volumetric thermal expansion coefficient. The decrease in phonon frequency upon compression is suggested to be due to the phonon oscillations in the form of a rotational motion rather than compressive waves. The physical origin of the anomalous thermal conductivity is thus identified in this work and AgInTe2 with a very low thermal conductivity of 0.2 W m-1 K-1 at 2.6 GPa is proposed to be a promising thermoelectric compound.
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