High-Throughput Screening of High-Performance Thermoelectric Materials with Gibbs Free Energy and Electronegativity

Abstract

Thermoelectric (TE) materials are an important class of energy materials that can directly convert thermal energy into electrical energy. Screening high-performance thermoelectric materials and improving their TE properties are important goals of TE materials research. Based on the objective relationship among the molar Gibbs free energy (G_m), the chemical potential, the Fermi level, the electronegativity (X) and the TE property of a material, a new method for screening TE materials with high throughput is proposed. This method requires no experiments and no first principle or Ab initio calculation. It only needs to find or calculate the molar Gibbs free energy and electronegativity of the material. Here, by calculating a variety of typical and atypical TE materials, it is found that the molar Gibbs free energy of Bi₂Te₃ and Sb₂Te₃ from 298 to 600 K (G_m = −130.20~−248.82 kJ/mol) and the electronegativity of Bi₂Te₃ and Sb₂Te₃ and PbTe (X = 1.80~2.21) can be used as criteria to judge the potential of materials to become high-performance TE materials. For good TE compounds, G_m and X are required to meet the corresponding standards at the same time. By taking G_m = −130.20~−248.82 kJ/mol and X = 1.80~2.21 as screening criteria for high performance TE materials, it is found that the G_m and X of all 15 typical TE materials and 9 widely studied TE materials meet the requirement very well, except for the X of Mg₂Si, and 64 pure substances are screened as potential TE materials from 102 atypical TE materials. In addition, with reference to their electronegativity, 44 pure substances are selected directly from a thermochemical data book as potential high-performance TE materials. A particular finding is that several carbides, such as Be₂C, CaC₂, BaC₂, SmC₂, TaC and NbC, may have certain TE properties. Because the G_m and X of pure substances can be easily found in thermochemical data books and calculated using the X of pure elements, respectively, the G_m and X of materials can be used as good high-throughput screening criteria for predicting TE properties.

1. Introduction

Thermoelectric (TE) materials have received widespread attention around the world due to their ability to convert heat and electricity directly to each other. Improving their thermoelectric conversion efficiency or finding materials with high thermoelectric properties is a very important goal of thermoelectric material research. In principle, the thermoelectric figure of merit Z = ɑ²σ/K or ZT = ɑ²σT/K (ɑ, σ, K and T are the Seebeck coefficient, electrical conductivity, thermal conductivity and absolute temperature of the material, respectively) is not only a parameter used to evaluate the performance of a TE material but also a theoretical basis for exploring high-performance TE materials. However, since the ZT of thermoelectric materials usually varies significantly with carrier concentration and temperature, thermoelectric materials with an unknown optimum doping concentration and the maximum figure of merit can only be evaluated by preparing numerous samples with different doping concentrations to measure and analyze the parameters over a wide temperature range. Obviously, the time from material composition design, weighing, synthesis and sintering to thermoelectric property testing and a performance analysis will take as little as three months or as much as one year. Therefore, it is difficult to use Z or ZT values to quickly analyze and judge a large number of unknown materials one by one. With the implementation of genetic engineering projects in recent years, the screening of thermoelectric materials using high-throughput calculations has received widespread attention worldwide. The mainstream high-throughput screening methods are theoretical calculations based on density functional theory and the Boltzmann equation, which establishes the relationship between the lattice structure and the thermoelectric transport coefficient of a material, and uses descriptors such as low thermal conductivity, thermoelectric superiority or the power factor to characterize the thermoelectric properties of the material. For example, elastic properties are used to efficiently evaluate the intensity of anharmonicity and lattice thermal conductivity for the high-throughput and efficient screening of thermoelectric materials with low lattice thermal conductivity [1]. But the high-throughput calculations and screening of high-performance thermoelectric materials also face two important difficulties: (1) precise calculations of the electrical and thermal properties of the materials are difficult and time-consuming, and (2) the existing high-throughput methods for evaluating the electrical and thermal properties of the materials have limitations.

Therefore, there is an urgent need for a simple and effective method to make a preliminary determination of the level of thermoelectric properties of a material or a criterion to determine its potential to become a high-performance thermoelectric material. Earlier, based on the thermoelectric figure of merit (Z) proportional to the previously derived material parameter β (see Equations (1) and (2)), Ioffe proposed a method for finding high-performance TE materials using the β value [2].

$$\mathrm{ZT}=\frac{{[\mathsf{\xi }-(\mathrm{s}+\frac{5}{2})]}^2}{{(\mathsf{\beta }\exp \mathsf{\xi })}^{-1}+(\mathrm{s}+\frac{5}{2})}$$

(1)

$$\mathsf{\beta }=5.745\times {10}^{-6}{\displaystyle \frac{{\mathsf{\mu }}_{\mathrm{c}}}{{\mathrm{K}}_{\mathrm{L}}}}{\left(\frac{{\mathrm{m}}^{*}}{\mathrm{m}}\right)}^{3/2}{\mathrm{T}}^{5/2}$$

(2)

where ξ, s, μ_c, K_L, m*, and m are the reduced Fermi level, scattering factor, carrier mobility, lattice thermal conductivity, effective mass, and the mass of the free electron, respectively. In Formula (2), the effective mass m*, lattice thermal conductivity K_L and carrier mobility μ_c are generally weakly dependent on the carrier concentration, so the β parameter can be used to initially determine the thermoelectric properties of a material, even for samples that are not optimally doped. Accordingly, Ioffe believes that an effective way to find thermoelectric materials is to first screen the materials for lattice thermal conductivity and then make a further determination by measuring the (m*)^3/2μ_c value of the materials. It is clear that this method avoids the requirement of the optimal doping of the sample, and it is much simpler than the method that uses the original formula of the thermoelectric figure of merit Z or ZT. Nevertheless, the determination of the β parameter involves the measurement of carrier mobility (μ_c) and effective mass (m*), both of which are more complex to measure than the Seebeck coefficient (ɑ) and electrical conductivity (σ), thus limiting the practical application of this approach. It is also essential to note that, while the variation in the β parameter with carrier concentration is much less pronounced than the thermoelectric figure of merit, it is not a constant.

Based on many years of practice, a number of useful laws, for example, heavy atomic mass [3], a large Fermi surface complexity factor [4], multiple energy valley degeneracies [5,6] or a complex Fermi surface structure [7], the appropriate carrier concentration [8], resonance energy levels [9,10], the energy-filtering effect [11], strong phonon scattering [12], strong anharmonic effects [13] and Phonon Glass–Electron Crystal (PGEC) properties [14], have been gradually obtained that summarize the physical properties of a good thermoelectric material. Among them, the use of materials with a high average relative atomic mass to improve m*/K_L and, thus, thermoelectric properties as criteria for selecting thermoelectric materials was first proposed by Goldsmid [15]. This rule was supplemented in 1995 by Slack et al., who noted the relationship of the electronegativity (X) of compounds with mobility, the effective mass and the forbidden band width, and they proposed the use of the electronegativity of compounds as a metric for the first screening of thermoelectric materials. This law can be briefly stated as follows: (1) The greater the sum of the atomic numbers of a compound, the larger the cell size, and the lower the thermal conductivity in general. (2) The smaller the electronegativity of a compound, the larger the product of the effective mass and mobility generally [16]. While the laws summarized by Goldsmid and Slack are useful for a preliminary judgment of element choices for thermoelectric materials, they do not provide sufficient insight into the effects of the elements in the periodic table on the thermoelectric properties of materials. The other parameters listed above suffer from similar problems as β. They all require extensive experimental measurements or calculations to be obtained. They cannot be used as simple, fast and effective criteria to judge whether a compound or alloy has a high thermoelectric performance or thermoelectric figure of merit.

Obviously, the ideal way to find promising thermoelectric materials in a wide variety of materials is to make preliminary judgments based on the periodic table of the elements and the known basic physical properties of the elements. Moreover, it is a fact that there is a wealth of molar Gibbs free energy (G_m) data or thermochemical data of pure substances and convenient calculation methods for molar Gibbs free energy. In this paper, firstly, the rationality of using molar Gibbs free energy to evaluate the thermoelectric properties of materials is described. Then, the molar Gibbs free energy of a series of typical and atypical pure compound thermoelectric semiconductor materials is shown, the electronegativity (X) of the corresponding materials is calculated, and the change rule is analyzed. A new method using the molar Gibbs free energy and electronegativity of pure compounds as a fast and high-throughput preliminary screening method for thermoelectric materials is discussed.

2. Basal Principle

2.1. Fermi Level as a Criterion for High-Performance Thermoelectric Materials

This paper assumes that there is only one type of carrier that obeys the Fermi–Dirac statistical distribution, the isoenergy surface is spherical, the energy band is parabolic, the relaxation time approximation can be used to describe the scattering process in the crystal, and the contribution of the drag effect can be neglected; furthermore, the Fermi level E_F is considered an independent variable. The relationship between the reduced Fermi level ξ (ξ = E_F/k_BT), the Seebeck coefficient (ɑ) and the conductivity (σ) of a material under different degenerate conditions can be seen in

Table 1. The Seebeck coefficients and electrical conductivities under different ξ values.

ξ	Seebeck Coefficient (ɑ)	Electrical Conductivity (σ)
Any ξ	${\mathsf{\alpha }}_{\mathrm{p},\mathrm{n}}=\pm \frac{{\mathrm{k}}_{\mathrm{B}}}{\mathrm{e}}\left(\frac{(\mathrm{s}+\frac{5}{2}{)\mathrm{F}}_{\mathrm{s}+\frac{3}{2}}(\mathsf{\xi })}{(\mathrm{s}+\frac{3}{2}{)\mathrm{F}}_{\mathrm{s}+\frac{1}{2}}(\mathsf{\xi })}-\mathsf{\xi }\right)$	$\mathsf{\sigma }=\frac{{16\mathsf{\pi }\mathrm{e}}^2{\mathsf{\tau }}_0{{(2\mathrm{m}}^{*}{)}^{1/2}({\mathrm{k}}_{\mathrm{B}}\mathrm{T})}^{3/2+\mathrm{s}}}{{3\mathrm{h}}^3}(\mathrm{s}+\frac{3}{2}{)\mathrm{F}}_{\mathrm{s}+1/2}\left(\mathsf{\xi }\right)$
ξ << 1	$\mathsf{\alpha }=\pm \frac{{\mathrm{k}}_{\mathrm{B}}}{\mathrm{e}}\left[\right(\mathrm{s}+\frac{5}{2})-\mathsf{\xi }]$	$\mathsf{\sigma }=\frac{{16\mathsf{\pi }\mathrm{e}}^2{\mathsf{\tau }}_0{{(2\mathrm{m}}^{*})}^{1/2}{{(\mathrm{k}}_{\mathrm{B}}\mathrm{T})}^{3/2+\mathrm{s}}}{{3\mathrm{h}}^3}\mathsf{\Gamma }(\mathrm{s}+\frac{5}{2}\left)\exp \right(\mathsf{\xi })$
ξ > 4	$\mathsf{\alpha }=\pm \frac{{\mathsf{\pi }}^2}{3}\frac{{\mathrm{k}}_{\mathrm{B}}}{\mathrm{e}}\frac{(\mathrm{s}+\frac{3}{2})}{\mathsf{\xi }}$	$\mathsf{\sigma }=\frac{{16\mathsf{\pi }\mathrm{e}}^2{\mathsf{\tau }}_0{{(2\mathrm{m}}^{*})}^{1/2}}{{3\mathrm{h}}^3}{\mathrm{E}}_{\mathrm{F}}^{\mathrm{s}+3/2}$

.

As mentioned above, in order to obtain a high thermoelectric figure of merit, Ioffe proposed [15] the use of the β factor to predict the thermoelectric performance of a material. It is believed that the greater the β value, the higher the thermoelectric performance of the material. On this basis, in 1959, Chasmar and Stratton used the Fermi–Dirac statistic to rigorously calculate the dependence of the dimensionless value ZT_max on the reduced Fermi level ξ (ξ = E_F/k_BT), the β factor and the scattering factor (s). The results are shown in

Table 2. Correspondence amongst the optimal reduced Fermi level (ξ_opt), the scattering factor (s), the material parameter (β) and the figure of merit (ZT_max).

S	β	0.1	0.2	0.5	1.0	2.0	5.0
−1/2	ZTmax	0.4	0.6	1	1.8	2.9	4.6
	ξopt	−0.1	−0.1	−0.8	−1.0	−1.7	−2.4
1/2	ZTmax	0.8	1.1	2.0	2.8	3.8	5.6
	ξopt	0.8	0.35	−0.4	−0.9	−1.6	−2.3
3/2	ZTmax	1.4	2.0	2.8	3.8	5.0	6.6
	ξopt	1.2	0.5	−0.3	−0.8	−1.5	−2.2

[17,18].

It can be found that the ZT_max value increases with an increase in the scattering factor (s) and the β value, but it increases with a decreasing optimal reduced Fermi level (ξ_opt). In addition, in correspondence to the different scattering mechanisms, the optimal reduced Fermi level (ξ_opt) also has a certain range of variation. When s = −1/2 and 1 ≤ β ≤ 5, the ZT_max is between 1.8 and 4.6, and the ξ_opt is between −1.0 and −2.4. An inverse relationship can also be seen between ZT_max and ξ_opt.

Furthermore, in 1972, Ure [18,19] used a two-band model and disregarded the effects of multi-valley and non-spherical isoenergetic surfaces to avoid excessive complexity. In the study, Ure considered the effects of lattice thermal conductivity and bipolar diffusion and adopted the elastic constant (1.7 × 10¹¹ Nm⁻²), the deformation potential constant D (7 eV) and the effective mass m* (0.014 m) of silicon. For the case where acoustic phonon scattering predominates, Ure used this method to estimate the actual optimal values of thermoelectric materials. The results indicated that the dimensionless optimal upper limit was ZT_max ≈ 8, corresponding to the optimal reduced Fermi level ξ_opt ≈ −3.0.

As explained in the previous paragraph, it should be emphasized that, although the formulas in Table 1 are based on the above assumptions, the conclusion that the Fermi level and the scattering factor have a decisive effect on the thermoelectric properties of a material is universal. Based on the research results of the related literature on the effects of two kinds of carriers (including holes and electrons), an asymmetric band structure and a dual-band structure (considering a conduction band and a valence band) on thermoelectric properties, it can be confirmed that the Fermi level and scattering factor have a decisive influence on the thermoelectric properties of materials [20,21,22,23]. In addition, the typical high-performance thermoelectric materials known to us, such as bismuth telluride, antimony telluride and lead telluride, have more energy valleys. Therefore, the conclusion that Fermi levels and scattering factors have a decisive effect on the thermoelectric properties of materials is universal.

Summarizing the research results reported above, it should be possible to give a preliminary judgment on the thermoelectric performance of a material based on the Fermi level (E_F) or reduced Fermi level (ξ). Therefore, the relationship between the Gibbs free energy and the Fermi level (E_F) of materials is discussed.

2.2. The Relationship between Molar Gibbs Free Energy and Fermi Level

According to thermodynamics theory, the Gibbs free energy G(T, P, N) of a material system has an extensive property, where T, P and N are the absolute temperature, pressure and moles of a pure substance. The G(T, P, N) of the system is equal to the product of the number of moles of the substance (N), and the molar Gibbs free energy G_m(T, P) is equal to the chemical potential (μ) of that substance. This can be expressed as [24,25]

$$\mathsf{\mu }={\mathrm{G}}_{\mathrm{m}}(\mathrm{T},\mathrm{P})=\frac{\mathrm{G}(\mathrm{T},\mathrm{P},\mathrm{N})}{\mathrm{N}}=\mathrm{H}-\mathrm{TS}$$

(3)

where G_m(T, P) (G_m for short), H and S are the Gibbs free energy, enthalpy and entropy per mole of a pure substance.

At 0 K, the Fermi level (E_F) of a pure substance is equal to its chemical potential μ [24], namely,

E_F = μ

(4)

By substituting Formula (3) into Formula (4), we can obtain the following formula:

$${\mathrm{E}}_{\mathrm{F}}{ =\mathsf{\mu }=\mathrm{G}}_{\mathrm{m}}(\mathrm{T},\mathrm{P})=\mathrm{H}-\mathrm{TS}$$

(5)

In Formula (5), it appears that the Fermi level can be solved using the molar Gibbs free energy of the material. However, in addition to the fact that the two are equal at absolute temperatures and not necessarily exactly equal at other temperatures, the ground states calculated for the two are also different. E_F has a ground state temperature of 0 K. That is, the Fermi energy is defined as the energy of the topmost filled level in the ground state of the N electron system. The ground state is the state of the N electron system at absolute zero. However, by definition, for a homogeneous crystal with a uniform temperature, S is calculated as [26]

$$\mathrm{S}\left(\mathrm{T}\right)={\mathrm{kln}\mathsf{\Omega }}_{\mathrm{C}}(\mathrm{T}=0)+{\displaystyle \underset{0}{\overset{\mathrm{T}}{\int }}{(\mathrm{C}}_{\mathrm{p}}/\mathrm{T}})\mathrm{dT}$$

(6)

where C_p(T) and Ω_c are the isobaric heat capacity and the thermodynamic probability of the material, respectively. For a perfect crystal, Ω_c(T = 0) = 1; that is, S(T = 0) = 0.

The enthalpy H(T, P) (H for short) of a pure substance is described entirely by independent internal variables T and P. The state function H(T, P) is determined when the pressure P is constant, except for additional uncertain and arbitrarily selected constants. In other words, for any system, the absolute value of enthalpy (H) cannot be determine. For this reason, different books use different conventions for the zero of H, such as the data cited here stating that the standard enthalpy H of all pure elements in its reference phase is zero at P = 1 bar and T = 298.15 K. Therefore, when using enthalpy values from different sources, we must pay attention to the standard state of the reference phase. For pure material enthalpy, its calculation formula can be expressed as [26]

$$\mathrm{H}\left(\mathrm{T}\right)=\mathrm{H}(298.15)+{\displaystyle \underset{0}{\overset{{\mathrm{T}}_{\mathrm{t}1}}{\int }}{\mathrm{C}}_{\mathrm{p}}}\left(\mathrm{T}\right)\mathrm{dT}+{\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}1}+{\displaystyle \underset{{\mathrm{T}}_{\mathrm{t}1}}{\overset{{\mathrm{T}}_{\mathrm{t}2}}{\int }}{\mathrm{C}}_{\mathrm{p}}}\left(\mathrm{T}\right)\mathrm{dT}+{\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}2}+\cdot \cdot \cdot$$

(7)

where H(298.15) is the enthalpy of the formation of pure matter at 1 bar and 298.15 K, C_p(T) is the temperature function of the heat capacity, and ΔH_t1 is the enthalpy of the phase transition at temperature T = T_t1. The corresponding entropy calculation Formula (6) can also be expressed as follows:

$$\mathrm{S}\left(\mathrm{T}\right)=\mathrm{S}(298.15)+{\displaystyle \underset{0}{\overset{{\mathrm{T}}_{\mathrm{t}1}}{\int }}\frac{{\mathrm{C}}_{\mathrm{p}}\left(\mathrm{T}\right)}{\mathrm{T}}}\mathrm{dT}+\frac{{\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}1}}{{\mathrm{T}}_{\mathrm{t}1}}+{\displaystyle \underset{{\mathrm{T}}_{\mathrm{t}1}}{\overset{{\mathrm{T}}_{\mathrm{t}2}}{\int }}\frac{{\mathrm{C}}_{\mathrm{p}}\left(\mathrm{T}\right)}{\mathrm{T}}}\mathrm{dT}+\frac{{\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}2}}{{\mathrm{T}}_{\mathrm{t}2}}+\cdot \cdot \cdot$$

(8)

$$\mathrm{S}(298.15)=\mathrm{S}(\mathrm{T}=0)+{\displaystyle \underset{0}{\overset{298.15}{\int }}\mathrm{dH}/\mathrm{T}}$$

(9)

$${\mathrm{S}=\mathrm{kln}\mathsf{\Omega }}_{\mathrm{C}}(\mathrm{T}=0)+{\displaystyle \underset{0}{\overset{\mathrm{T}}{\int }}{(\mathrm{C}}_{\mathrm{p}}/\mathrm{T}})\mathrm{dT}$$

(10)

For a complete crystal, at T = 0 K, S = 0, which is Ω = 1.

$$\mathrm{S}(298.15)={\displaystyle \underset{0}{\overset{298.15}{\int }}\mathrm{dH}/\mathrm{T}}$$

(11)

Then, the molar Gibbs free energy of a pure substance at 1 bar can be calculated as follows:

$${\mathrm{G}}_{\mathrm{m}}{\left(\mathrm{T}\right)=\mathrm{G}}_{\mathrm{m}}(298.15)+{\displaystyle \underset{0}{\overset{{\mathrm{T}}_{\mathrm{t}1}}{\int }}{\mathrm{C}}_{\mathrm{p}}}{\left(\mathrm{T}\right)\mathrm{dT}+\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}1}+{\displaystyle \underset{{\mathrm{T}}_{\mathrm{t}1}}{\overset{{\mathrm{T}}_{\mathrm{t}2}}{\int }}{\mathrm{C}}_{\mathrm{p}}}{\left(\mathrm{T}\right)\mathrm{dT}+\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}2}-\mathrm{T}({\displaystyle \underset{0}{\overset{{\mathrm{T}}_{\mathrm{t}1}}{\int }}\frac{{\mathrm{C}}_{\mathrm{p}}\left(\mathrm{T}\right)}{\mathrm{T}}}\mathrm{dT}+\frac{{\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}1}}{{\mathrm{T}}_{\mathrm{t}1}}+{\displaystyle \underset{{\mathrm{T}}_{\mathrm{t}1}}{\overset{{\mathrm{T}}_{\mathrm{t}2}}{\int }}\frac{{\mathrm{C}}_{\mathrm{p}}\left(\mathrm{T}\right)}{\mathrm{T}}}\mathrm{dT}+\frac{{\mathsf{\Delta }\mathrm{H}}_{\mathrm{t}2}}{{\mathrm{T}}_{\mathrm{t}2}}+)\cdot \cdot \cdot$$

(12)

$${\mathrm{G}}_{\mathrm{m}}(298.15)=\mathrm{H}(298.15)-\mathrm{TS}(298.15)$$

(13)

In Equation (13), H(298.15) and S(298.15) are the standard enthalpy and the standard entropy of the pure substance, respectively. Therefore, G(T) function values are also involved in the H(T) convention. Thus, the molar Gibbs free energy of the reference phase of an element E at 198.15 K and 1 bar is given by using the following formula:

$${\mathrm{G}}_{\mathrm{m}}(298.15)=-\mathrm{TS}(298.15)$$

(14)

If there is no phase transition, Equation (12) can be simplified as follows:

$${\mathrm{G}}_{\mathrm{m}}\left(\mathrm{T}\right)={\mathrm{G}}_{\mathrm{m}}(298.15)+{\displaystyle \underset{0}{\overset{\mathrm{T}}{\int }}{\mathrm{C}}_{\mathrm{p}}}\left(\mathrm{T}\right)\mathrm{dT}-\mathrm{T}{\displaystyle \underset{0}{\overset{\mathrm{T}}{\int }}\frac{{\mathrm{C}}_{\mathrm{p}}\left(\mathrm{T}\right)}{\mathrm{T}}}\mathrm{dT}$$

(15)

Therefore, the chemical potential (μ) or Fermi level (E_F) cannot be calculated simply from the data of the molar Gibbs free energy. However, because of the inevitable relationship between the two, we can still summarize the inevitable relationship between the change law of the molar Gibbs free energy data of thermoelectric materials and the thermoelectric properties of materials and use it as one of the methods for the high-throughput screening of thermoelectric materials.

In addition, as mentioned above, Slack et al. noted the relationship between the electronegativity and mobility, effective mass and band gap width in compounds, and they proposed using the electronegativity of a compound as a metric for a preliminary screening of thermoelectric materials [16]. To this end, following the example of Bulter and Ginley et al., the electronegativity X of the semiconductor compound A_nB_m is calculated using the geometric mean value of Mulliken electronegativity [27,28]:

$$\mathrm{X}={{(\mathrm{X}}_{\mathrm{A}}^{\mathrm{n}}{\mathrm{X}}_{\mathrm{B}}^{\mathrm{m}})}^{1/(\mathrm{n}+\mathrm{m})}$$

(16)

where X_A and X_B are the electronegativity of pure elements A and B, respectively.

3. Results and Discussion

Except for special emphasis, the molar Gibbs free energy (G_m) data are selected from Ihsan Barin’s Thermochemical Data of Pure Substances [26] or the Handbook of Inorganic Thermodynamics Data [29].

3.1. Molar Gibbs Free Energy (G_m) of Pure Elements Listed in the Seebeck and Meissner Sequences

The G_ms of the substances listed in the Seebeck and Meissner sequences [30] are shown in

Table 3. Temperature dependence of the G_m of elementary substances listed in Seebeck and Meissner sequences.

Seebeck Sequence	Meissner Sequence	α/ (μV/K)	Gm/kJ/mol
			298 K	300 K	400 K	500 K	600 K	700 K	800 K	900 K	1000 K
Bi	Bi	−70	−16.916	−17.021	−23.098	−29.848	−38.325	−48.221	−58.528	−69.185	−80.151
Co	Co	−17.5	−8.957	−9.012	−12.414	−16.483	−21.119	−26.25	−31.888	−37.932	−44.361
Ni	Ni	−18	−8.907	−8.962	−12.371	−16.496	−21.243	−26.557	−32.322	−38.478	−44.99
	K	−12	−19.281	−19.401	−26.798	−35.244	−44.309	−53.879	−63.876	−74.247	−84.952
Pd	Pd	−6	−11.277	−11.347	−15.541	−20.408	−25.824	−31.704	−37.99	−47.973	−51.611
	Na	−4.4	−15.341	−15.437	−21.246	−28.337	−36.044	−44.251	−52.878	−61.867	−71.178
Pt	Pt	−3.3	−12.412	−12.489	−17.061	−22.3	−28.083	−34.326	−40.97	−38.836	−55.299
U			−14.994	−15.088	−20.561	−26.783	−33.648	−41.095	−49.086	−57.601	−66.792
	Hg	−3.4	−22.629	−22.770	−30.795	−39.514	−48.780	−51.584
	Al	−0.6	−8.430	−8.483	−11.699	−15.565	−19.973	−24.852	−30.150	−35.835	−42.645
	Mg	−0.4	−9.743	−9.803	−13.468	−17.790	−22.661	−28.008	−33.780	−39.937	−47.208
	Pb	−0.1	−19.316	−19.436	−26.340	−33.944	−42.122	−51.588	−61.494	−71.776	−82.389
	Sn	0.1	−15.264	−15.359	−20.911	−27.190	−35.389	−44.143	−53.304	−62.823	−72.658
	Cs	0.2	−25.387	−25.544	−35.244	−45.751	−56.887	−68.542	−80.641	−93.127	−99.241
	Y	2.2	−13.248	−13.330	−18.193	−23.742	−29.851	−36.437	−43.442	−50.824	−58.549
Rh	Rh	2.5	−9.393	−9.452	−13	−17.206	−21.958	−27.18	−32.82	−9.393	−45.199
Zn	Zn	2.9	−12.412	−12.489	−17.055	−22.283	−28.061	−34.393	−42.14	−50.28	−67.574
C			−1.712	−1.722	−2.449	−3.473	−4.789	−6.386	−8.248	−10.358	−12.7
Ag	Ag	1.5/2.4	−12.724	−12.803	−17.471	−22.79	−28.639	−34.939	−41.635	−48.684	−56.057
Au	Au	1.5/2.7	−14.161	−14.249	−19.398	−25.198	−31.525	−38.297	−45.457	−52.962	−60.779
Cu	Cu	2.0/2.6	−9.888	−9.949	−13.654	−17.998	−22.862	−28.17	−33.865	−39.904	−46.255
	W	2.5/1.5	−9.738	−9.798	−13.449	−17.729	−22.519	−27.742	−33.339	−39.271	−45.505
Cd	Cd	2.8	−15.444	−15.54	−21.132	−27.41	−34.322	−42.706	−51.516	−60.698	−70.211
	Mo	5.9	−8.525	−8.578	−11.819	−15.692	−20.084	−24.920	−30.142	−35.707	−41.583
Fe	Fe	16	−8.133	−8.184	−11.317	−15.14	−19.559	−24.513	−29.946	−35.891	−42.302
As			−10.646	−10.712	−14.674	−19.276	−24.4	−29.968	−35.924	−42.225	−48.837
Sb	Sb	35	−13.572	−13.657	−18.609	−24.216	−30.355	−36.949	−43.946	−51.31	−61.128
	Se	1000	−12.599	−12.678	−17.314	−22.738	−29.920	−37.691	−45.966	−54.682	−63.789

. The elements with high Seebeck coefficients listed in both sequences are Bi and Sb. Their G_m values are between −13.572 and −38.325 kJ/mol. Moreover, it is found that their G_m values decrease with an increase in the temperature (the absolute value increases). If G_m = −13.572 and −38.325 kJ/mol are taken as screening criteria, all elements in Table 3, except for element C, may have certain TE properties in the appropriate temperature range, of which the difference is that their optimal working temperature zones are different. At room temperature, only the G_m values of Na, U, Sn, Cd and Au meet the requirements. Although the G_m values of K, Hg, Pb and Cs at 298.15 K are within the above range, their absolute G_m values are larger or comparable to the G_m values of Bi or Sb at higher temperatures, so it is judged that these four elements may have better thermoelectric properties at slightly higher temperatures.

3.2. Molar Gibbs Free Energy and Electronegativity of 15 Typical TE Materials

Table 4. Temperature dependence of the G_m of typical high-performance thermoelectric materials.

Compounds	Gm/kJ/mol
	298 K	300 K	400 K	500 K	600 K	700 K	800 K	900 K	1000 K
Bi2Se3	−211.206	−212.171	−238.210	−267.142	−298.968	−332.723	−368.406	−406.018	−445.559
Bi2Te3	−155.271	−155.271	−184.203	−215.064	−248.819	−285.466	−324.043
Sb2Se3	−190.954	−190.954	−214.100	−241.103	−270.036	−300.897	−333.687	−369.370	−411.804
Sb2Te3	−130.196	−130.196	−157.199	−187.096	−219.886	−255.569	−293.182
GeTe	−75.354	−75.521	−85.337	−96.494	−108.745	−121.928	−135.925	−150.652
PbTe	−101.263	−101.263	−113.801	−126.338	−140.804	−156.235	−171.666	−188.061	−205.420
MnTe	−135.982	−136.947	−146.591	−158.164	−171.666	−185.167	−200.598	−216.029	−231.459
SnSe	−115.730	−115.730	−125.374	−135.982	−148.520	−161.057	−175.523	−189.989	−205.420
CoSb3	−110.908	−110.908	−129.231	−149.484	−171.666	−196.740	−222.779	−250.747	−279.680
Cu2Se	−104.157	−104.157	−118.623	−136.947	−156.235	−177.452	−200.598	−223.744	−247.854
Mg2Si	−102.228	−102.228	−110.908	−121.516	−133.089	−146.591	−161.057	−176.488	−193.847
MnSi	−91.619	−91.619	−97.406	−104.157	−111.872	−120.552	−130.196	−140.804	−151.413
MnSi1.7	−282.573	−281.609	−224.708	−193.847	−174.559	−162.986	−154.306	−149.484	−145.626
Mn5Si3	−284.502	−283.537	−228.566	−198.669	−180.345	−168.772	−161.057	−156.235	−152.377
FeSi2	−97.406	−97.406	−104.157	−112.836	−122.480	−133.089	−145.626	−158.164

shows the G_m and X of 15 typical TE materials [31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51]. It can be seen that, in the range of 298.15~600 K, the optimal operating temperature range of Bi₂Te₃ and Sb₂Te₃, their G_m values are between −130.196 and −248.819 kJ/mol. If these data, or G_m = −130.196~−248.819 kJ/mol, are used as the screening criteria, it can be seen that all the above typical materials have good thermoelectric properties in a certain temperature range, indicating that the G_m of Bi₂Te₃ and Sb₂Te₃ at 298.15~600 K is feasible as the basic standard for a preliminary screening of high-thermal-power-factor thermoelectric materials.

Table 5. The electronegativity of 15 typical thermoelectric materials.

Element	XA	XB	A	B	X	Element	XA	XB	A	B	X
Bi2Se3	1.67	2.4	2	3	2.08	Mg2Si	1.2	1.9	2	1	1.4
Bi2Te3	1.67	2.1	2	3	1.92		1.2	1.74	2	1	1.36
	1.8	2.1	2	3	1.97		1.2	1.8	2	1	1.37
	2.02	2.1	2	3	2.07		1.2	2.44	2	1	1.52
Sb2Se3	1.65	2.4	2	3	2.07		1.32	2.44	2	1	1.62
	1.8	2.4	2	3	2.14	MnSi	1.6	1.9	1	1	1.74
	1.82	2.4	2	3	2.15		1.6	1.74	1	1	1.67
	2.05	2.4	2	3	2.25		1.6	1.8	1	1	1.7
Sb2Te3	1.65	2.1	2	3	1.91		1.6	2.44	1	1	1.98
	1.8	2.1	2	3	1.97	MnSi1.7	1.6	1.9	1	1.7	1.78
	1.82	2.1	2	3	1.98		1.6	1.74	1	1.7	1.69
	2.05	2.1	2	3	2.08		1.6	1.8	1	1.7	1.72
GeTe	1.8	2.1	1	1	1.94		1.6	2.44	1	1.7	2.09
	2.01	2.1	1	1	2.05	Mn5Si3	1.6	1.9	5	3	1.71
	2.02	2.1	1	1	2.06		1.6	1.74	5	3	1.65
PbTe	1.55	2.1	1	1	1.8		1.6	1.8	5	3	1.67
	1.6	2.1	1	1	1.83		1.6	2.44	5	3	1.87
	1.8	2.1	1	1	1.94	FeSi2	1.64	1.74	1	2	1.71
	2.33	2.1	1	1	2.21		1.64	1.8	1	2	1.75
MnTe	1.4	2.1	1	1	1.71		1.64	1.9	1	2	1.81
	1.55	2.1	1	1	1.8		1.64	2.44	1	2	2.14
	1.6	2.1	1	1	1.83		1.8	1.74	1	2	1.76
SnSe	1.7	2.4	1	1	2.02		1.8	1.8	1	2	1.8
CoSb3	1.7	2.05	1	3	1.96		1.8	1.9	1	2	1.87
Cu2Se	1.8	2.4	2	1	1.98		1.8	2.44	1	2	2.2
FeSi2	1.83	1.9	1	2	1.88		1.83	1.74	1	2	1.77
	1.83	2.44	1	2	2.22		1.83	1.8	1	2	1.81

lists the electronegativity of 15 typical thermoelectric compounds calculated using Equation (16) and the electronegativity data of the elements [52,53,54]. It can be seen that, since the same element has different electronegativity values, the electronegativity of the corresponding compound is not unique. In addition, the electronegativity of Bi₂Te₃ and Sb₂Te₃ are very close. Considering that PbTe is a typical medium-temperature thermoelectric material, the electronegativity values of Bi₂Te₃, Sb₂Te₃ and PbTe, that is, X = 1.80~2.21, are used as the criteria for screening thermoelectric materials. It can be seen that all other materials, except for Mg₂Si, have electronegativity values that meet this requirement, indicating that X = 1.80–2.21 is a suitable criterion.

3.3. Molar Gibbs Free Energy and Electronegativity of 102 Atypical TE Materials

The temperature dependences of the G_m of 102 atypical pure compounds are obtained from References [26,29]. The electronegativity X of the 102 pure atypical compounds are calculated using Equation (16). They are shown in

Table 6. The X and the temperature dependence of the G_m of atypical thermoelectric compounds.

Compounds	X	Gm/kJ/mol
		298 K	300 K	400 K	500 K	600 K	700 K	800 K	900 K	1000 K
Bi2S3	2.19	−202.527	−203.491	−225.673	−250.747	−277.751	−308.612	−340.438	−374.192	−409.876
Sb2S3	2.19	−195.776	−196.740	−216.993	−240.139	−265.214	−293.182	−324.043	−359.726	−398.303
Mn3Si	1.78	−241.103	−240.139	−193.847	−168.772	−154.306	−145.626	−139.840	−124.409	−135.018
CoSb2	1.93	−85.833	−85.833	−99.335	−114.765	−131.160	−149.484	−169.737	−189.989	−211.206
Mg3Sb2	1.49	−737.776	−732.954	−574.790	−484.135	−427.235	−387.694	−360.691	−340.438
MgSe	1.70	−1517.022	−1507.378	−1156.331	−948.983	−813.965	−718.488	−649.050	−595.043	−553.573
MgTe	1.59	−1126.435	−1119.684	−868.936	−722.345	−625.904	−558.395	−509.210	−472.562	−443.630
TiS	2.00	−288.360	−289.324	−295.110	−302.826	−311.505	−321.150	−331.758	−342.367	−353.940
TiS2	2.15	−430.128	−431.093	−439.772	−450.381	−462.918	−476.420	−490.886	−507.281	−523.676
ZrS2	2.11	−600.829	−600.829	−609.509	−620.118	−632.655	−646.157	−660.623	−676.054	−692.449
ZrTe2	1.88	−330.794		−345.260		−378.050		−415.662		−458.096
TaS2	2.03	−376.121	−376.121	−395.409	−395.409	−407.947	−421.449	−435.915	−451.345	−467.740
MoS2	2.15	−295.110	−295.110	−301.861	−311.505	−322.114	−333.687	−346.224	−359.726	−374.192
MoSi2	2.12	−137.911	−137.911	−145.626	−155.271	−165.879	−177.452	−190.954	−205.420	−219.886
WS2	2.15	−278.715	−278.715	−286.431	−296.075	−306.683	−318.256
MnS	1.87	−214.100	−214.100	−216.029	−217.957	−219.886	−220.851	−222.779	−276.787	−278.715
MnS2	2.15	−253.641	−253.641	−265.214	−277.751	−292.217	−308.612
MnSe	1.83	−198.669	−198.669	−208.313	−219.886	−232.424	−244.961	−259.427	−273.893	−289.324
MnTe2	1.92	−168.772	−168.772	−185.167	−202.527	−221.815	−242.068
FeS	2.20	−119.587	−119.587	−126.338	−135.982	−146.591	−158.164	−170.701	−184.203	−198.669
FeS2	2.17	−187.096	−187.096	−193.847	−201.562	−211.206	−221.815	−233.388	−246.890	−260.392
FeSe0.96	2.01	−87.762	−87.762	−95.477	−105.121	−115.730	−127.303	−140.804	−155.271	−170.701
FeTe0.9	1.88	−47.256	−47.256	−55.936	−66.545	−77.153	−89.690	−102.228	−115.730	−130.196
FeTe2	1.93	−102.228	−102.228	−113.801	−126.338	−141.769	−158.164	−175.523	−193.847	−199.634
CoS0.89	2.04	−109.943	−109.943	−115.730	−123.445	−131.160	−139.840	−149.484	−160.093	−170.701
CoS2	2.20	−173.594	−173.594	−182.274	−191.918	−202.527	−215.064	−228.566	−243.997	−259.427
CoP3	1.99	−309.577	−309.577	−321.150	−335.616	−351.046	−369.370	−388.659	−409.876	−432.057
NiS	2.12	−103.192	−104.157	109.943	−116.694	−125.374	−135.018	−146.591	−158.164	−170.701
NiSe1.05	2.09	−97.406	−97.406	−106.085	−115.730	−126.338	−137.911	−151.413	−164.915	−179.381
NiSe1.143	2.10	−102.228	−103.192	−111.872	−121.516	−133.089	−145.626	−159.128	−173.594	−188.061
NiSe1.25	2.11	−107.050	−107.050	−115.730	−126.338	−137.911	−151.413	−164.915	−180.345	−195.776
NiTe	1.94	−59.794		−68.473		−89.690		−115.730
NiTe1.1	1.95	−82.940	−82.940	−92.584	−103.192	−115.730	−128.267	−141.769	−156.235	−171.666
NiS2	2.24	−152.377	−153.342	−161.057	−171.666	−183.238	−195.776	−210.242	−225.673	−241.103
NiSe2	2.18	−139.840	−139.840	−151.413	−164.915	−180.345	−196.740	−215.064	−233.388	−253.641
CuS	2.18	−73.295	−73.295	−80.046	−88.726	−98.370	−108.979	−120.552	−132.125	−144.662
Cu2S	2.01	−115.730	−115.730	−129.231	−145.626	−162.986	−183.238	−204.456	−226.637	−248.819
Cu2Te	1.89	−81.975	−81.975	−97.406	−113.801	−133.089	−154.306	−176.488	−201.562	−226.637
Ag2S	2.01	−75.224	−76.189	−91.619	−109.943	−130.196	−151.413	−174.559	−197.705	−222.779
Ag2Se	1.98	−82.940	−82.940	−99.335	−120.552	−142.733	−166.843	−191.918	−217.957	−244.961
Ag2Te	1.89	−81.975	−81.975	−98.370	−118.623	−141.769	−164.915	−189.989
ZnSb	1.84	−43.399	−43.399	−53.043	−63.651	−75.224	−86.797	−100.299
InSb	1.91	−55.936	−55.936	−65.580	−76.189	−88.726	−101.263	−114.765	−135.018	−156.235
GeS	2.12	−95.477	−95.477	−103.192	−111.872	−121.516	−132.125	−143.698	−155.271	−169.737
GeSe	2.08	−92.584	−92.584	−101.263	−110.908	−122.480	−134.053	−146.591	−160.093	−175.523
PbS	2.00	−126.338	−126.338	−135.982	−140.804	−159.128	−172.630	−186.132	−200.598	−216.029
PbSe	1.90	−130.196	−131.160	−141.769	−154.306	−167.808	−182.274	−196.740	−212.171	−228.566
SnS	2.06	−131.160	−131.160	−139.840	−149.484	−160.093	−171.666	−184.203	−197.705	−212.171
SnTe	1.89	−91.619	−91.619	−103.192	−114.765	−128.267	−142.733	−157.199	−172.630	−189.025
AgP2	1.99	−69.438	−69.438	−80.046	−91.619	−105.121	−119.587	−135.018	−152.377
AgP3	2.02	−101.263	−101.263	−113.801	−128.267	−145.626	−163.950	−185.167	−207.349
BeS	1.94	−244.961	−244.961	−249.783	−254.605	−261.356	−268.107	−276.787	−285.466	−294.146
Be2C	1.83	−121.516	−121.516	−124.409	−127.303	−132.125	−136.947	−143.698	−150.448	−157.199
BaC2	2.11	−101.263	−101.263	−110.908	−122.480	−135.982	−149.484	−164.915	−181.310	−198.669
AlAs	1.82	−134.053	−134.053	−140.804	−149.484	−158.164	−167.808	−178.416	−189.025	−200.598
AlI3	2.20	−359.726	−359.726	−380.943	−395.409
AlP	1.84	−178.416	−758.993	−184.203	−190.954	−197.705	−205.420	−215.064	−223.744	−233.388
Al2S3	2.04	−758.993	−758.993	−772.495	−788.890	−808.178	−828.431	−851.577	−875.687	−901.726
Al2Se3	1.99	−613.367	−613.367	−630.726	−650.979	−674.125	−699.200	−726.203	−755.136	−785.032
AlSb	1.82	−69.438	−69.438	−77.153	−85.833	−94.512	−105.121	−115.730	−127.303	−139.840
BaS	1.50	−483.171	−484.135	−491.851	−502.459	−513.068	−524.641	−537.178	−550.680	−564.182
CaC2	1.84	−81.011	−81.011	−88.726	−98.370	−109.943	−122.480	−135.982	−151.413	−166.843
CaH2	1.64	−189.025	−189.025	−193.847	−200.598	−207.349	−215.064	−223.744	−232.424	−243.032
CaPb	1.53	−144.662	−145.626	−154.306	−163.950	−175.523	−188.061	−200.598	−215.064	−229.530
Ca2Pb	1.33	−243.997	−244.961	−256.534	−270.036	−284.502	−300.897	−318.256	−336.580	−355.868
CaS	1.58	−489.922	−489.922	−496.673	−504.388	−513.068	−522.712	−532.356	−543.929	−555.502
CaSi	1.56	−164.915	−164.915	−169.737	−176.488	−183.238	−191.918	−200.598	−210.242	−220.851
CaSe	1.55	−387.694	−388.659	−395.409	−404.089	−413.733	−424.342	−435.915	−447.488	−460.025
NaTe	1.46	−199.634	−199.634	−208.313	−218.922	−230.495
NaTe3	1.75	−165.879	−165.879	−181.310	−198.669	−218.922	−240.139
NbC	2.06	−149.484	−149.484	−153.342	−159.128	−164.915	−171.666	−179.381	−188.061	−196.740
NbSi2	2.16	−146.591	−146.591	−154.306	−163.950	−175.523	−188.061	−200.598	−215.064	−230.495
InSe	1.90	−142.733	−142.733	−151.413	−162.021	−172.630	−185.167	−198.669	−212.171
CaSi2	1.81	−165.879	−165.879	−172.630	−180.345	−189.989	−200.598	−212.171	−224.708	−238.210
Ca2Si	1.35	−233.388	−233.388	−243.032	−253.641	−266.178	−280.644	−295.110	−311.505	−328.865
CaSn	1.40	−180.345	−180.345	−188.061	−196.740	−207.349	−217.957	−230.495	−242.068	−255.569
CaTe	1.45	−315.363	−316.328	−324.043	−333.687	−344.295	−354.904	−366.477	−379.014	−391.552
CaZn	1.28	−92.584	−93.548	−100.299	−108.979	−119.587	−130.196
CaZn2	1.40	−124.409	−124.409	−135.982	−149.484	−163.950	−180.345	−197.705	−216.993
CrS	1.87	−174.559	−174.559	−182.274	−190.954	−199.634	−210.242	−221.815	−234.352	−246.890
CrSi2	2.12	−116.694	−116.694	−123.445	−131.160	−140.804	−151.413	−162.986	−175.523	−189.025
GaP	1.95	−115.730	−115.730	−121.516	−128.267	−136.947	−145.626	−155.271	−164.915	−176.488
GaSb	1.93	−64.616	−64.616	−72.331	−81.011	−89.690	−99.335	−109.943	−119.587
GaSe	2.08	−180.345	−180.345	−188.061	−196.740	−207.349	−217.957	−229.530	−242.068	−255.569
GaTe	1.95	−148.520	−149.484	−158.164	−168.772	−180.345	−192.883	−206.384	−220.851	−235.317
InP	1.93	−106.085	−107.050	−113.801	−121.516	−130.196	−139.840	−150.448	−161.057	−172.630
InS	2.11	−154.306	−154.306	−162.021	−171.666	−181.310	−191.918	−203.491	−216.029	−230.495
Ag2O	2.25	−67.509	−67.509	−81.011	−95.477
MgFe2O4	2.48	−1474.588		−1490.018		−1528.595		−1577.780		−1635.645
CaTiO3	2.33	−1688.687	−1688.687	−1699.296	−1713.762	−1729.193	−1747.517	−1767.769	−1789.951	−1813.097
CaZrO3	2.30	−1796.702	−1796.702	−1808.275	−1822.741	−1839.136	−1858.424	−1878.677	−1900.858	−1924.004
SrTiO3	2.33	−1705.082	−1705.082	−1717.620	−1733.050	−1750.410	−1770.663	−1791.880	−1815.026	−1839.136
Mn2O3	2.49	−992.381	−992.381	−1004.919	−1020.349	−1037.709	−1057.961	−1079.178	−1102.324	−1127.399
FeO	2.40	−290.288	−290.288	−297.039	−305.719	−314.399	−325.007	−335.616	−347.189	−359.726
Fe3O4	2.53	−1162.118	−1162.118	−1179.477	−1200.694	−1226.734	−1255.666	−1287.492	−1323.175	−1360.787
Fe2O3	2.58	−850.612	−850.612	−861.221	−874.723	−890.153	−909.442	−929.694	−951.876	−976.951
CuO	2.47	−168.772	−168.772	−173.594	−180.345	−187.096	−194.811	−203.491	−213.135	−222.779
Cu2O	2.20	−198.669	−198.669	−208.313	−220.851	−234.352	−248.819	−264.249	−280.644	−298.004
NiO	2.47	−250.747	−250.747	−255.569	−263.285	−268.107	−276.787	−285.466	−295.110	−304.755
ZnO	2.29	−363.584	−363.584	−368.406	−375.157	−381.908	−389.623	−398.303	−407.947	−417.591
CdO	2.29	−274.858	−275.822	−281.609	−289.324	−297.039	−306.683	−316.328	−326.936	−338.509
SnO	2.44	−302.826	−302.826	−309.577	−317.292	−325.972	−335.616	−346.224	−356.833	−368.406

. If G_m = −130.196~−248.819 kJ/mol is used as the screening criterion for good TE materials, 67 compounds are screened. It can be found that, in addition to Cu₂S, Cu₂Te, Ag₂S, Ag₂Se, Ag₂Te, SnTe and PbSe, which have been widely investigated as high-performance TE materials [55,56,57,58,59,60,61,62], Bi₂S₃, Sb₂S₂, Mn₃Si, CoSb₂, MoSi₂, MnS, MnSe, MnTe₂, FeS, FeS₂, FeSe_0.96, FeTe_0.9, FeTe₂, CoS_0.89, CoS₂, NiSe_1.05, NiSe_1.143, NiSe_1.25, NiSe₂, NiTe, NiTe_1.1, NiS₂, NiSe₂, CuS, InSb, GeS, GeSe, SnS, PbS, AgP₂, AgP₃, BeS, Be₂C, Ba₂C, AlAs, AlP, AlSb, CaC₂, CaH₂, CaPb, Ca₂Pb, CaSi, NaTe, NaTe₃, NbC, NbSi₂, InSe, CaSi₂, Ca₂Si, CaSn, CaZn, CaZn₂, CrS, CrSi₂, GaP, GaSb, GaSe, GaTe, InP, InS, CuO and Cu₂O may be good TE materials at suitable temperature ranges. If the G_m of Bi₂Te₃ at a temperature of 298–800 K, or G_m = −1.61~−3.36 eV, is used as the standard, it can be found that the other 10 compounds, namely, TiS, MoS₂, WS₂, MnS₂, CoP₃, CaTe, FeO, NiO, CdO and SnO, may be TE materials.

If X = 1.80~2.21 is used as the screening criterion of high-performance TE materials, 67 compounds are screened out. A comparison of the screening results of the two methods shows that their results are not completely consistent, although most of them are. For compounds that meet the G_m screening criteria, the main difference is reflected in alkali metal and alkaline earth metal compounds. These compounds, such as the alkali metal compounds NaTe and NaTe₂ and the alkaline earth metal compounds CaH₂, CaPb, Ca₂Pb, CaSi, Ca₂Si, CaSn, CaTe, CaZn and CaZn₂, are less electronegative than the screening criteria. The X value of some transition metal compounds, such as Mn₃Si, is also lower than the screening criterion. Transition metal oxides or sulfides, such as FeO, CuO, NiO, CdO, SnO and NiS₂, have a larger X value than the screening criteria due to the high electronegativity of O or S. Therefore, although they have TE properties, they are not very good TE materials. So, a bigger X is not better. If both G_m and X are met as screening criteria, a total of 60 pure compounds have the potential to become high-quality TE materials. They are Cu₂S, Cu₂Te, Ag₂S, Ag₂Se, Ag₂Te, SnTe, Bi₂S₃, Sb₂S₂, CoSb₂, TiS, MoS₂, MoSi₂, WS₂, MnS, MnSe, MnTe₂, FeS, FeS₂, FeSe_0.96, FeTe_0.9, FeTe₂, CoS_0.89, CoS₂, CoP3, NiS, NiSe_1.05, NiSe_1.143, NiSe_1.25, NiSe₂, NiTe_1.1, NiS₂, NiSe₂, CuS, InSb, GeS, GeSe, SnS, PbS, AgP₂, AgP₃, BeS, Be₂C, Ba₂C, AlAs, AlP, AlSb, CaC₂, NbC, NbSi₂, InSe, CaSi₂, CrS, CrSi₂, GaP, GaSe, GaTe, InP, InS and Cu₂O.

3.4. Molar Gibbs Free Energy (G_m) and Electronegativity of Some Potential TE Materials

Based on the above G_m and X criteria, 44 possible high-performance thermoelectric compounds are screened directly from the pure substance thermochemical data book [29]. Their electronegativity values are calculated according to Formula (16). The results are presented in

Table 7. The X and the temperature dependence of the G_m of some potential TE compounds.

Compounds	X	Gm/kJ/mol
		298	300	400	500	600	700	800	900	1000
GeS2	2.24	−182.972	−183.134	−192.925	−204.453	−217.428	−231.658	−247.008	−263.375	−280.682
GeSe	2.08	−92.363	−92.509	−101.125	−111.046	−122.039	−133.951	−146.673	−160.125
GeSe2	2.18	−146.525	−146.733	−159.119	−173.371	−189.166	−206.292	−224.597	−243.967	−264.315
InTe	1.94	−103.476	−103.672	−114.999	−127.581	−141.202	−155.719	−171.031	−187.063
In2Te	1.94	−125.861	−126.148	−142.706	−161.059	−180.918	−202.091
IrS2	2.13	−153.634	−153.762	−161.728	−171.474	−182.705	−195.21	−208.836	−223.457	−239.01
MgB4	1.62	−120.499	−120.595	−126.939	−135.278	−145.367	−157.024	−170.113	−184.525	−200.173
Mn7C3	1.83	−180.432	−180.875	−208.533	−242.455	−281.592	−325.235	−372.878	−424.138	−478.719
Mn4N	1.81	−171.263	−171.528	−187.866	−207.711	−230.506
MnP	1.83	−132.428	−132.549	−139.843	−148.441	158.131	−168.751	−180.179	−192.23	−205.1
MnTe2	1.92	−168.757	−169.026	−184.752	−202.457	−221.747	−242.362
Mo2N	1.97	−100.425	−100.524	−107.912	−117.106	−127.873	−140.024	−153.411	−167.92	−183.458
MoSi2	2.12	−138.21	−138.331	−145.876	−155.167	−165.905	−177.882	−190.944	−204.972	−219.876
Mo3Si	1.78	−133.356	−133.554	−145.65	−160.148	−176.604	−194.726	−214.306	−235.189	−257.255
NbC0.702	1.99	−126.67	−126.729	−130.466	−135.13	−140.577	−146.704	−153.431	−160.699	−168.459
NbC0.825	2.02	−134.083	−134.144	−138.012	−142.865	−148.549	−154.954	−161.993	−169.602	−177.729
NbSi2	2.16	−146.353	−146.482	−154.5	−164.221	−175.344	−187.665	−201.037	−215.349	−230.514
Ni3Sn	1.84	−132.871	−133.115	−147.837	−165.181	−184.701	−206.103	−229.177	−253.766
Ni3Sn2	1.86	−208.67	−208.991	−228.08	−250.01	−274.284	−300.573	−328.641	−358.316	−389.461
OsP2	2.07	−176.748	−176.9	−186.225	−197.386	−210.04	−223.964	−238.996	−255.017	−271.933
OsSe2	2.26	−144.406	−144.558	−153.754	−164.629	−176.842	−190.157	−204.405	−219.456	−235.21
PdI2	2.04	−116.886	−117.219	−136.408	−157.551	−180.296	−204.414	−229.74
PdS2	2.04	−104.438	−104.601	−114.449	−126.078	−139.192	−153.58	−169.089	−185.602	−203.028
Pd4S	2.09	−122.901	−123.236	−143.131	−166.052	−191.482	−219.081	−248.607	−279.88	−312.759
PtBr2	2.24	−116.346	−116.445	−122.991	−131.511	−141.651	−153.177	−165.924
PtI4	2.24	−126.692	−127.027	−147.125	−170.65	−197.119	−226.212
PtS2	2.08	−132.725	−132.864	−141.394	−151.706	−163.501	−176.571	−190.762	−205.958	−222.065
ReS2	2.24	−196.745	−196.858	−203.987	−212.896	−223.29	−234.958	−247.748	−261.542	−276.248
ReSi2	2.20	−112.454	−112.591	−121.029	−131.188	−142.771	−155.57	−169.433	−184.245	−199.912
Re2Te5	2.01	−169.237	−169.704	−197.679	−230.246	−266.6	−306.209	−348.694	−393.774	−441.228
RuSe2	2.01	−185.827	−185.979	−195.29	−206.502	−219.273	−233.369	−248.618	−264.893	−282.093
Ta2Si	1.92	−156.956	−157.151	−168.802	−182.292	−197.3	−213.601	−231.031	−249.465	−268.806
TaSi2	2.16	−135.905	−136.01	−142.703	−151.174	−161.121	−172.329	−184.638	−197.924	−212.09
TiSi	2.04	−144.299	−144.39	−150.02	−156.89	−164.797	−173.598	−183.187	−193.483	−204.421
TiSi2	2.16	−152.519	−152.632	−159.805	−168.782	−179.278	−191.085	−204.051	−218.057	−233.01
USi2	2.02	−154.154	−154.306	−163.677	−175.054	−188.12	−202.635	−218.415	−235.315	−253.222
VSi2	2.13	−168.213	−168.323	−175.267	−183.976	−194.162	−205.616	−218.183	−231.744	−246.204
WSi2	2.12	−112.088	−112.207	−119.641	−128.798	−139.381	−151.181	−164.054	−177.858	−192.528
ZrSi	1.91	−172.148	−172.256	−178.783	−186.49	−195.17	−204.68	−214.918	−225.803	−237.276
ZrSi2	2.07	−180.742	−180.874	−189.059	−198.947	−210.238	−222.727	−236.266	−250.746	−266.078
SmC2	1.94	−122.441	−122.604	−132.522	−144.333	−157.717	−172.445	−188.346	−205.292	−223.18
TaC	2.06	−156.734	−156.812	−161.656	−167.544	−174.326	−181.884	−190.128	−198.986	−208.402
ZnSe	2.00	−179.949	−180.08	−187.926	−197.097	−207.337	−218.474	−230.388	−242.988	−256.205
ZnTe	1.87	−142.447	−142.591	−151.162	−161.036	−171.984	−183.858	−196.552	−209.987	−224.099

. There are several compounds, such as GeS₂, MgB₄, Mo₃Si, OsSe₂, Pd₄S, PtBr₂, PtI₄ and ReS₂, whose electronegativity values deviate from the screening criteria.

3.5. The Procedure for the High-Throughput Screening of TE Materials with Gibbs Free Energy and Electronegativity

Because the molar Gibbs free energy of a compound is easily found in the thermochemical data book or calculated, and its electronegativity is easily calculated using the geometric mean value of Mulliken electronegativity, the potential of a material as a high-performance thermoelectric material can be easily and quickly determined. In order to facilitate the screening of TE materials using molar Gibbs free energy (G_m) and electronegativity (X), a schematic diagram of the screening process is shown in Figure 1.

Additionally, one problem should be discussed. From the results of the analysis of the whole paper, the only typical TE compound that cannot meet the requirements of G_m = −130.20~−248.82 kJ/mol and X = 1.80~2.21 at the same time is Mg₂Si. That is, its X does not meet the requirements because the electronegativity of the element Mg is too low. But why can Mg₂Si become a typical thermoelectric material? The first reason is that the G_m of Mg₂Si meets the requirements. The second reason is that X can meet the requirements by changing its composition, which is also the strategy adopted in the research process of Mg₂Si TE materials. Therefore, when screening thermoelectric materials, G_m data can be used as the main data, supplemented by X data. It is a reasonable improvement strategy to adjust the composition of a TE material so that its X value meets the requirements.

4. Conclusions

Screening high-performance thermoelectric materials and improving their thermoelectric properties are important goals of thermoelectric materials research. Based on the objective relationship among the molar Gibbs free energy (G_m), the chemical potential, the Fermi level, the electronegativity (X) and the TE property of a material, a new method using molar Gibbs free energy (G_m) and electronegativity (X) for the high-throughput screening of thermoelectric materials is proposed. The molar Gibbs free energy of 15 typical TE materials, 9 widely studied thermoelectric materials and 93 atypical thermoelectric materials were obtained from a thermochemical data book. The electronegativities of the materials above were calculated using the geometric mean value of Mulliken electronegativity. The feasibility of using G_m and X as high-throughput screening thermoelectric materials is discussed in detail. The results are described below.

1. Because it is universal that Fermi levels and scattering factors have a decisive effect on the thermoelectric properties of materials, taking the molar Gibbs free energy Gm and electronegativity X as screening criteria for high-performance TE materials is reasonable.

2. The molar Gibbs free energy G_ms of typical TE materials Bi₂Te₃ and Sb₂Te₃ range from −130.196 to −248.819 kJ/mol. The electronegativity Xs of Bi₂Te₃, Sb₂Te₃ and PbTe range from 1.80 to 2.21. If G_m = −130.20~−248.82 kJ/mol and X = 1.80~2.21 are used as screening criteria for high-performance TE materials, the G_m and X of all of 15 typical TE materials and 9 widely studied thermoelectric materials meet the requirements very well, except for the X of Mg₂Si. It is indicated that G_m = −130.20~−248.82 kJ/mol and X = 1.80~2.21 are suitable criteria for screening high-performance TE materials.

3. For TE materials, such as Mg₂Si, due to the extremely low electronegativity of the component elements, its X value cannot meet the requirements, but its G_m can meet the requirements very well. G_m data can be used as the main data, supplemented by X data. It is a reasonable improvement strategy to adjust the composition of a TE material so that its X value meets the requirements.

4. For good TE compounds, if G_m and X are required to meet the corresponding standards at the same time, and G_m = −130.196~−248.819 kJ/mol and X = 1.80~2.21 are used as screening criteria, 60 pure substances, including 9 widely studied TE materials, are screened as potential TE materials from 102 atypical TE materials.

5. With reference to their electronegativity, 44 pure substances are selected directly from the thermochemical data book as potential high-performance thermoelectric materials. A particular finding is that several carbides, such as Be₂C, CaC₂, BaC₂ and NbC, may have certain TE properties.

6. Compared with G_m = −130.196~−248.819 kJ/mol, the elemental elements in the Seebeck or Meissner sequence are not good thermoelectric materials. This is consistent with the actual results.

7. The G_m of pure substances can be easily found in thermochemical data books, and the X of compounds can be calculated easily from the X of pure elements, so using G_m and X as high-throughput screening criteria for predicting thermoelectric properties is much more convenient than using the TE figure of merit Z or ZT or the Ab initio calculation method. This method requires no experiments and no first principle or Ab initio calculation.