A method for predicting high power factor thermoelectric materials using anisotropy
By selecting the anisotropic principal axis direction in the crystal structure and utilizing the rotational relationship between the Zebeck tensor and the conductivity tensor, a method for predicting high power factor thermoelectric materials has been developed. This method solves the problem of improving the power factor of materials in existing technologies and achieves more efficient material screening and performance enhancement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SHANGHAI UNIV
- Filing Date
- 2023-06-05
- Publication Date
- 2026-05-29
AI Technical Summary
It is difficult to improve the power factor of existing thermoelectric materials, and existing methods have limited room for improvement and are very challenging.
By selecting two principal axis directions with large anisotropy in the crystal structure, and utilizing the rotational relationship between the Seebeck tensor and the conductivity tensor, new directions for high power factors can be predicted, avoiding complex processing techniques.
This enables the application of thermoelectric materials with superior performance through angle adjustment without the need for doping or hot pressing, simplifying the material selection process.
Smart Images
Figure CN119092010B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of thermoelectric material performance prediction technology, specifically a method for predicting high power factor thermoelectric materials using anisotropy. Background Technology
[0002] Human civilization can be viewed as a history of human utilization of energy. The First Industrial Revolution marked the beginning of an era where coal was the primary energy source. Following the Second Industrial Revolution, oil became the second fossil fuel widely used. With the extensive use of fossil fuels such as coal, oil, and natural gas, human civilization experienced a leap forward. However, in the 21st century, the status of fossil fuels faces severe challenges. Issues such as safety, pollution, and renewability have spurred an increasingly urgent need for clean energy research and development. Thermoelectric conversion, as a new type of clean energy conversion method, has attracted widespread attention from researchers.
[0003] Thermoelectricity is a new, clean, and renewable energy conversion method. Its energy conversion principle stems from the potential difference created by the difference in the number of electrons in a solid material at different temperatures. Because its energy conversion does not involve drastic changes in the state of matter like fossil fuels, it is renewable. Furthermore, its characteristic of producing no waste gas or waste materials during energy conversion makes it a member of the clean energy category. The solid materials used in thermoelectric conversion are called thermoelectric materials, which are generally semiconductors. The thermoelectric figure of merit (ZT) is often used to represent the performance of thermoelectric materials, expressed as ZT = S. 2 σT / κ, where S represents the Seebeck coefficient, σ represents electrical conductivity, κ represents thermal conductivity, and T represents temperature. Since both the Seebeck coefficient and electrical conductivity characterize the electrical transport properties of a material, S... 2 σ is called the power factor (PF). Therefore, from the perspective of electrical transport performance, the higher the power factor of a material, the higher its thermoelectric figure of merit.
[0004] The main challenge currently facing the application of thermoelectric materials is their low efficiency, while improving the power factor is an effective means to enhance the thermoelectric figure of merit. Power factor improvement is generally achieved through methods such as optimizing carrier concentration and increasing band degeneracy. However, these methods offer limited improvement potential for specific materials, and even after improvement using these methods, the power factor of the material often fails to meet requirements, posing significant technical challenges in practical application. Summary of the Invention
[0005] To address the problems of existing technologies, the present invention aims to overcome the shortcomings of existing technologies and provide a method for predicting high power factor thermoelectric materials using anisotropy. This method predicts new directions with better power factors by using the Zebeck tensor components and conductivity tensor in the two principal axis directions with greater anisotropy in the crystal.
[0006] To achieve the above objectives, the specific technical solution of the present invention is as follows:
[0007] A method for predicting high power factor thermoelectric materials using anisotropy includes the following steps:
[0008] S1. Determine two directions m and n in the crystal structure, obtain the original Zebeck tensor and original conductivity tensor of the crystal structure in directions m and n, and the components of the original Zebeck tensor and original conductivity tensor in the two directions m and n respectively, wherein direction m and direction n are the first direction and the second direction respectively, and the angle between the first direction and the second direction in the counterclockwise direction is 90°.
[0009] S2. Determine two new directions m' and n' on the plane formed by the two directions m and n after rotating the two directions m and n counterclockwise by an angle θ perpendicular to the plane. Determine the new Zebeck tensor and the new conductivity tensor under the two new directions m' and n', as well as the relationship between the new Zebeck tensor and the new conductivity tensor and the original Zebeck tensor, the original conductivity tensor, and the angle θ.
[0010] S3. Determine the relationship between the new Zebeck coefficient in the new direction m' and the new conductivity and the new power factor in the new direction m'. Further calculate the relationship between the new power factor and the components of the original Zebeck tensor and the original conductivity tensor in the directions m and n, respectively, as well as the angle θ.
[0011] Preferably, an S4 step is added after step S3, specifically: determining the value of angle θ when the new power factor is at its maximum as θ'.
[0012] Preferably, the selection criteria for the two directions m and n are as follows: based on the components of the third-order Zebeck tensor and the third-order conductivity tensor in the directions of principal axis a, principal axis b and principal axis c of the crystal structure, the two principal axes with relatively large anisotropy are selected as the two directions m and n.
[0013] Preferably, the crystal structure is an optimized structure obtained through first-principles calculations, used to determine the third-order Zebeck tensor and the third-order conductivity tensor.
[0014] In a further preferred embodiment, the optimized structure undergoes self-consistent calculations to obtain information on the electronic structure, such as charge density, which is used to determine the third-order Zebeck tensor and the third-order conductivity tensor.
[0015] In a further preferred embodiment, the optimized structure performs transport property calculations to obtain information such as energy within the Brillouin zone, which is used to determine the third-order Zebeck tensor and the third-order conductivity tensor.
[0016] Compared with the prior art, the beneficial effects of the present invention are:
[0017] The present invention provides a method for predicting high power factor thermoelectric materials using anisotropy. By using the material's own characteristics, the method predicts the direction with better performance, so that in practice, thermoelectric materials do not need to be processed by difficult methods such as doping and hot pressing. They can be obtained by simply rotating them along a certain regular angle to obtain the application direction with better performance.
[0018] The present invention provides a method for predicting high power factor thermoelectric materials using anisotropy. When applied to first-principles calculations of thermoelectric materials, the method can relatively easily screen out materials with the potential to achieve high properties from a variety of materials through prediction. Attached Figure Description
[0019] Figure 1 This is a schematic diagram of the relationship between the new direction and the main axis and the selection of the optimal value in this invention. (a) is a schematic diagram of the components of the power factor in the directions m and n, and (b) is a schematic diagram of the magnitude of the power factor in the direction at an angle θ with the direction m.
[0020] Figure 2 This is a schematic diagram of the structure of the Ba3S7Zr2 unit cell and the direction of the maximum power factor in an embodiment of the present invention. Detailed Implementation
[0021] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.
[0022] To facilitate understanding, the abbreviations or names mentioned below will be explained first:
[0023] Principal axes: In a crystal structure, the three mutually orthogonal coordinate axes that reflect the symmetry of the crystal are called principal axes. Parameters such as unit cell units and atomic coordinates are described in the coordinate system formed by the principal axes. In this invention, the transport along the principal axes of the crystal has a diagonalized characteristic (i.e., the transport tensor is 0 in the non-diagonal directions).
[0024] It should be noted that the three principal axes are the a-axis, b-axis, and c-axis, and the third-order Zebeck tensor is denoted as [formula missing]. The third-order conductivity tensor is denoted as... Among them, S aa σ aa These are their respective components in the principal axis a direction, and also represent the Seebeck coefficient and conductivity in the principal axis a direction, and so on.
[0025] This specific embodiment provides a method for predicting high power factor thermoelectric materials using anisotropy. Specifically, it predicts new directions with better power factors by using the Zebeck tensor components and conductivity tensor components along the two principal axes with greater anisotropy in the crystal structure. A schematic diagram of the principle is shown below. Figure 1 As shown, the specific steps are as follows:
[0026] S1. Determine the third-order Zebeck tensor and third-order selection of the crystal, where the Zebeck coefficients and conductivity exhibit significant anisotropy in two directions, m and n, and the Zebeck coefficients in the two directions are S0 and S0, respectively. mm S nn The conductivity is σ mm σ nn The second-order tensor form is denoted as: They are named the original Zebeck tensor S and the original conductivity tensor σ, respectively, where the off-diagonal elements of the second-order tensor are 0 under the principal axis;
[0027] S2. Determine two new directions after rotating directions m and n counterclockwise by an angle θ in the same direction on the mn plane, corresponding to m' and n' respectively. Then, determine the relationship between the Zebeck tensor and conductivity tensor (named the new Zebeck tensor S' and the new conductivity tensor σ' respectively) under these two new directions and S, σ, and the angle θ, specifically expressed as follows:
[0028] After transforming the relationship, it can be represented as:
[0029]
[0030]
[0031] Thus, the new Zebeck coefficient S' of the new direction m' m'm' With the new conductivity σ' m'm' They are respectively:
[0032] S' m'm' =S mm cos 2 θ+S nn sin 2 θ
[0033] σ' m'm' =σ mm cos 2 θ+σ nn sin 2 θ
[0034] S3. Determine the new Seebeck coefficient S' in the new direction m' based on the expression for the power factor. m'm' and the new conductivity σ' m'm' The power factor relative to the new direction m' (named the new power factor PF) m'm' The relationship between these factors was used to further deduce the new power factor PF. m'm' The relationship between the components of the original Zebeck tensor S and the original conductivity tensor σ in directions m and n, respectively, and the angle θ, is specifically expressed as follows:
[0035]
[0036] Furthermore, an S4 step is added after step S3, specifically: based on the expression of the new power factor, the value of angle θ when the new power factor is at its maximum is calculated as θ'.
[0037] Thus, when the angle θ takes the value θ', the new direction m' is represented as m' θ' This direction is the direction with the largest power factor.
[0038] The crystal structure of Ba3S7Zr2 is used as an example for the following introduction:
[0039] To improve the accuracy of the results, the crystal structure of Ba3S7Zr2 was first optimized using VASP. Self-consistent calculations and transport property calculations were then performed on the optimized structure, as detailed below:
[0040] The crystal structure of Ba3S7Zr2 was optimized to obtain the optimized structure. The main parameters in the calculations were set as follows: energy convergence was 10⁻⁶. 4 The optimized flat-wave cutoff energy is 520 eV, and the final lattice constants of the unit cell are as follows: 158.28°, 158.28°, 30.90°, more detailed structural information is listed in Tables 1 and 2;
[0041] Table 1. Primitive cell basis vectors of Ba3S7Zr2
[0042]
[0043] Table 2 Atomic coordinates of Ba3S7Zr2 (coordinates based on unit cell basis vectors)
[0044]
[0045] Self-consistent calculations were performed on the optimized structure to obtain information on electronic structure such as charge density. The main parameters were set as follows: the high symmetry K-point was set to 60 / a+1, 60 / b+1, and 60 / c+1, and the smoothing cutoff energy was 520eV.
[0046] Transport properties of the optimized structure are calculated to obtain the energy ε within the Brillouin zone. nk =ε(n,k) and other information, where n represents the band index and k is the coordinate in the reciprocal space. The main parameters in the calculation are set as follows: the high symmetry K-points in the Brillouin zone are set to 240 / a+1, 240 / b+1, and 240 / c+1; the energy convergence criterion is also set to 10. -4 eV.
[0047] Then, the TransOpt electric transport calculation program was used to calculate the crystal structure information, self-consistent calculations, and transport property calculations obtained after optimization using the constant electro-acoustic coupling approximation. This yielded the complete third-order Zebeck tensor and third-order conductivity tensor, from which the components along each principal axis were extracted. The main parameters for the calculation were set as follows: deformation potential of 3 eV, Young's modulus of 100 GPa, temperature of 300 K, and calculated carrier concentration of 8.36 × 10⁻⁶. 20 cm -3 .
[0048] Calculations revealed that the Seebeck coefficient and conductivity along the principal axis
[100] of the Ba3S7Zr2 crystal structure are -3.97 μV / K and 3.52 × 10⁻⁶, respectively. 6 The S / m, Zebeck coefficient and conductivity in the principal axis
[001] direction are -417.81 μV / K and 6.46 × 10⁻⁶, respectively. 2 S / m is anisotropic, therefore the principal axis
[100] and principal axis
[001] are selected as direction m and direction n, respectively.
[0049] Thus, in this embodiment, S mm = -3.97μV / K, σ mm =3.52×10 6 S / m, S nn = -417.81μV / K, σ nn =6.46×10 2 S / m, therefore
[0050]
[0051] Based on the above function, θ = 35.45° is calculated, which is converted to the crystal orientation
[701] . That is, on the mn plane formed by directions m and n, the direction PF is at an angle of 35.45° counterclockwise to direction m. m'm' The maximum value is PF. m'm' = 919.39 μW / (K 2 cm), such as Figure 2 The diagram shown is a schematic representation of the structure of the Ba3S7Zr2 cell and the direction of the maximum power factor in this embodiment.
[0052] It should be noted that this invention uses VASP 5.4.4 for calculations. Since there are multiple versions of the software, the calculation results of different versions will have certain errors. The purpose of this invention is to provide a method for predicting high power factor thermoelectric materials using anisotropy. It is not limited to this version of the software for calculation. In other versions, the parameters can be appropriately modified according to the rules of first-principles calculation to calculate the required physical quantities. In addition, there are many programs that can be used for first-principles calculations. This invention uses VASP to calculate the crystal structure. Other calculation software, such as Quantum Espresso, can also be used for calculations, which will not be elaborated here.
[0053] It should be noted that the Ba3S7Zr2 example given in this invention is only one example, and this method can also be used to predict other thermoelectric materials.
[0054] In summary, this invention provides a method for finding high power factors in anisotropic thermoelectric materials, which requires achieving anisotropy of the Seebeck coefficient and conductivity in different principal axis directions. Furthermore, this invention also provides a method for finding the direction with the highest power factor, which is simpler to implement for thermoelectric materials that meet the requirements. It only requires adjustments to the appropriate angle and adaptive shape adjustments during application, without the need for complex doping, hot pressing, or other processing techniques, thus achieving a significant improvement in power factor.
[0055] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended embodiments and their equivalents.
Claims
1. A method for predicting high power factor thermoelectric materials using anisotropy, characterized in that, Includes the following steps: S1. Determine two directions m and n in the crystal structure, obtain the original Zebeck tensor and original conductivity tensor of the crystal structure in directions m and n, and the components of the original Zebeck tensor and original conductivity tensor in the two directions m and n respectively, wherein direction m and direction n are the first direction and the second direction respectively, and the angle between the first direction and the second direction in the counterclockwise direction is 90°. S2. Determine two new directions m' and n' on the plane formed by the two directions m and n after rotating the two directions m and n counterclockwise by an angle θ perpendicular to the plane. Determine the new Zebeck tensor and the new conductivity tensor under the two new directions m' and n', as well as the relationship between the new Zebeck tensor and the new conductivity tensor and the original Zebeck tensor, the original conductivity tensor, and the angle θ. S3. Determine the relationship between the new Zebeck coefficient in the new direction m' and the new conductivity and the new power factor in the new direction m'. Further calculate the relationship between the new power factor and the components of the original Zebeck tensor and the original conductivity tensor in the directions m and n, respectively, as well as the angle θ.
2. The method for predicting high power factor thermoelectric materials using anisotropy according to claim 1, characterized in that, Add step S4 after step S3, specifically: determine the value of angle θ when the new power factor is at its maximum as θ'.
3. The method for predicting high power factor thermoelectric materials using anisotropy according to claim 1, characterized in that, The selection criteria for the two directions m and n are as follows: based on the components of the third-order Zebeck tensor and the third-order conductivity tensor in the directions of principal axis a, principal axis b and principal axis c of the crystal structure, the two principal axes with relatively large anisotropy are selected as the two directions m and n.
4. The method for predicting high power factor thermoelectric materials using anisotropy according to claim 1, characterized in that, The crystal structure is an optimized structure obtained through first-principles calculations, used to determine the third-order Zebeck tensor and the third-order conductivity tensor.
5. The method for predicting high power factor thermoelectric materials using anisotropy according to claim 4, characterized in that, The optimized structure is subjected to self-consistent calculations to obtain information on electronic structure such as charge density, which is used to determine the third-order Zebeck tensor and the third-order conductivity tensor.
6. The method for predicting high power factor thermoelectric materials using anisotropy according to claim 4, characterized in that, The optimized structure performs transport property calculations to obtain information such as energy within the Brillouin zone, which is used to determine the third-order Zebeck tensor and the third-order conductivity tensor.