high thermal conductivity are widely used in heat dissipating applications, [3][4][5][6] while the materials with low thermal conductivity [7][8][9][10] are used as thermal insulation. In particular, thermal conductivity is one of the key parameters in thermoelectric materials and also plays an important role in other energy materials such as solar cells and battery materials. Therefore, evaluation of thermal conductivity is very fundamental and important, but the measurement could sometimes be a great challenge. The understanding and measurement of thermal conductivity are especially questionable for materials with phase transitions while these materials exist extensively and have been exploited for different fields including thermoelectrics, [11][12][13][14] solid state memory, [15] and switches. [16] The energy exchange during phase transitions gives rise to a few fundamental questions on thermal conductivity measurement. Transient measurement methods such as laser flash method (LFA) are commonly used to measure thermal diffusivity λ and the thermal conductivity κ is calculated using the equation of κ = C P × d × λ (d is the density and C P is the heat capacity), due to the significant advantages of transient methods over the steady-state measurements. [17] It is well known that the heat capacity (C P ) can be significantly increased during phase transition because the extra energy is required to transit a low temperature structure to a high temperature structure in materials (see Figure 1a). Recent study also shows that the thermal diffusivity (λ) can be lowered in some phase transition materials such as Cu 2 Se, Cu 2 S, and Ag 2 S, but is almost unaffected by phase transition in Ag 2 Se (see Figure 1b). The understanding on thermal conductivity during phase transitions is not established yet. This leads to the thermal conductivity calculated with different heat capacity values highly deviated, although the measured heat capacity and thermal diffusivity are quite close or similar. For example, a dramatic decrease in κ in Cu 2 Se second-order phase transition is reported by Liu et al. [11] when using the Dulong-Petit value for heat capacity, while an increased κ is reported by Brown et al. [18] after adding the contribution of phase transition to heat capacity (Figure 1c). Such different κ values change the thermoelectric figure of merit (zT) from a moderate value of 0.6 to an extremely high value of 2.3 (which can be considered as a breakthrough in thermoelectrics) in Cu 2 Se during its second-order phase transition. More confusingly, the heat capacity ( Figure 1a) and electrical transport measurements ( Figure S6, Supporting Information) clearly show that Cu 2 S and Ag 2 S have first-order phase transitions with Thermal conductivity is a very basic property that determines how fast a material conducts heat, which plays an important and sometimes a dominant role in many fields. However, because materials with phase transitions have been widely used recently, understanding and measuring temperature-dependent t...

With the increasingly serious environmental pollution and intensified energy crisis, exploitation and utilization of new kinds of clean energy resources are imperative. Among them, thermoelectric (TE) conversion technology based on highperformance TE materials enables direct energy conversion between heat and electricity through the movement of internal phonons and charge carriers. [1][2][3][4] It has shown extensive and important prospects in power generation using industrial waste heat and electronic refrigeration. [5] The energy conversion efficiency of a TE material is mainly determined by its dimensionless figure of merit, defined as zT = σS 2 T/(κ L + κ e ), where σ, S, T, κ L , and κ e are the electrical conductivity, Seebeck coefficient, absolute temperature, lattice thermal conductivity, and electronic thermal conductivity, respectively. The general criteria for high zTs require high crystal symmetry for materials, many valleys (carrier pockets) near the Fermi level, heavy elements with small electronegativity differences between the constituent elements, or complex crystal structure, etc. [6][7][8][9][10] For the constituent elements in the same group such as S, Se, and Te, the heavy one (Te and Se) always has large atomic mass for low κ L and more covalent bonding character for large carrier mobility (µ H ) and thus outstanding electrical transports. [10] Therefore, the zTs are usually high in tellurides and selenides, but they are low in sulfides. This is the general phenomenon that has been observed in those well-known TE materials such as Bi 2 X 3 -, SnX-, and PbX-based compounds (X = S, Se, and Te). As shown in Figure 1, the zT values gradually improve as the anion element change from S to Se and then to Te. However, the case is different in Cu 2 X-based liquidlike TE materials that are among the hottest materials in recent TE study. They possess exceptionally low thermal conductivity and excellent zTs with the values of 1.7-1.9 for Cu 2 S, 1.5-2.3 for Cu 2 Se, and 0.4-1.1 for Cu 2 Te (see Figure 1). [48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] It is quite abnormal and interesting that the zT in Cu 2 Te is lower than those in Cu 2 S and Cu 2 Se. As we known, tellurium is less electronegative, thus the chemical bonds between Cu and Te should be less ionic as compared with those in Cu 2 S and Cu 2 Se, which is beneficial for large µ H and electrical transports. Besides, the κ L in Cu 2 Te is expected lower than or similar to those in Cu 2 S and Cu 2 Se because tellurium is much heavier than sulfur and Most of the state-of-the-art thermoelectric (TE) materials exhibit high crystal symmetry, multiple valleys near the Fermi level, heavy constituent elements with small electronegativity differences, or complex crystal structure. Typically, such general features have been well observed in those well-known TE materials such as Bi 2 X 3 -, SnX-, and PbX-based compounds (X = S, Se, and Te). The performance is usually high in the materials with heavy constituent elements such as Te and Se, bu...