Thermal Conductivity during Phase Transitions

Abstract

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...

Promising and Eco‐Friendly Cu2X‐Based Thermoelectric Materials: Progress and Applications

“…Under the conditions of weak or no phase transitions, B/D 0 and C pt /C p0 ratios are small, leading to the D m /D 0 ratio close to 1 which indicates high accuracy of D measurement. However, under strong phase transitions, the B/D 0 and C pt /C p0 ratios are large, leading to reduced D m /D 0 ratio which indicates significant underestimation of D when employing the measured value . In addition, it is of interest to note that the phase transition speeds of Cu 2 Se ( β–α phase transition) and Cu 2 S (cha‐rt to cha‐ht) are different, as shown in Figure e.…”

“…This is possibly related with different level of superionicity between these phases. Due to continuous second‐order phase transition of Cu 2 Se and subsequently wider phase‐transition temperature range, the contribution of phase transition on D ‐measurement at ≈400 K has more influence on Cu 2 Se . After subtracting the contribution of phase transition on D m of Cu 2 Se, D 0 is shown in Figure f in comparison with D m , indicating that D is significantly underestimated at the phase transition point, leading to overestimated zT (Figure c).…”

“…f) Comparison of D m and D 0 of Cu 2 Se . d) Reproduced with permission . Copyright 2018, Wiley‐VCH.…”

“…The phase transition influences not only C p , but also the thermal diffusivity ( D ) . Chen et al built up a model to understand the influence of phase transition on D , where the relationship between measured thermal diffusivity ( D m ) and true thermal diffusivity ( D 0 ) can be expressed as where C pt is the equivalent heat capacity due to the phase transition, C p0 is the normal heat capacity from phonons and electrons, B refers to the phase‐transition speed, and H is the material thickness. Figure d shows the corresponding relationship between these factors, in which the ratio between D m and D 0 is strongly influenced by the B/D 0 and C pt /C p0 ratios.…”

Recent Advances in Liquid‐Like Thermoelectric Materials

“…Via removing the contributions from both altered heat capacity and thermal diffusivity, the true κ data during phase transition were given, agreeing well with those measured by the 3 ω and TPS methods. Accordingly, the true zT value is corrected to be 0.86 at the critical point of Cu 2 Se …”