A method for rapidly calculating the lattice thermal conductivity of materials

Abstract

This invention discloses a method for rapidly calculating the lattice thermal conductivity of materials, relating to the field of materials design technology. First, the crystal structure and second-order force constants are obtained through theoretical calculations. Then, a dynamic matrix is ​​constructed, and phonon data is obtained through gridded sampling operations. The point lattice thermal conductivity of each acoustic mode is obtained accordingly. Finally, calculations are performed to obtain the lattice thermal conductivity of the material system. This method can rapidly obtain the lattice thermal conductivity of the material system while ensuring good accuracy.

Description

Technical Field

[0001] This invention relates to the field of materials design technology, specifically a method for rapidly calculating the lattice thermal conductivity of materials. Background Technology

[0002] Thermal conductivity is one of the fundamental physical properties of materials, representing their ability to conduct heat. Higher thermal conductivity indicates a stronger ability to conduct heat, while lower thermal conductivity indicates a weaker ability. Both high and low thermal conductivity materials have important applications in their respective fields. This invention focuses on the application of materials with low thermal conductivity. Low thermal conductivity materials have two important applications. The first and most direct application is thermal barrier coatings. Thermal barrier coatings are an effective means of thermal protection, effectively reducing the waste of unused heat energy by reducing heat transfer. They are mainly used in aerospace and manufacturing industries to improve system performance and lifespan. Examples include turbine engines, gas turbines, brakes, and axles. The second application is in the fields of new energy and refrigeration and temperature control—thermoelectric materials. Thermoelectric materials are functional materials that utilize the movement of charge carriers (electrons and holes) in a solid to convert heat energy into electrical energy. Both thermal barrier coatings and thermoelectric materials require low thermal conductivity. Therefore, research on low thermal conductivity materials has broad research value. The thermal conductivity of a material consists of electronic thermal conductivity and lattice thermal conductivity (κ). L The composition of thermal barrier coatings and thermoelectric materials is primarily based on semiconductors and insulators. Therefore, lattice vibrations / phonons are the main heat transport carriers, and electronic thermal conductivity is negligible. This invention develops a method for rapidly obtaining the lattice thermal conductivity of materials, thereby enabling faster design of high-performance thermal barrier coatings and thermoelectric materials.

[0003] The microscopic formula for lattice thermal conductivity is as follows:

[0004]

[0005] Where C v It is the phonon heat capacity, and its expression is as follows:

[0006]

[0007] Where n is the phonon number, T is the temperature, and k is the phonon number. B It is the Boltzmann constant 1.38 × 10 -23 J / K, It is the reduced Planck constant, ω qλτ is the frequency of the phonon in the λ mode at point q, where q is the wave vector, v is the phonon group velocity, and τ is the phonon relaxation time. The phonon heat capacity and phonon group velocity can be obtained by solving the dynamic matrix using the second-order force constants used to describe harmonics. To obtain the precise relaxation time τ, the phonon Boltzmann transport equations need to be solved, for example, by the method described in Computer Physics Communications, 2014, 185(6):1747-1758. However, solving this equation requires considering a large number of linear equations, whose linear coefficients depend on the interactions between atoms, such as the second- and third-order force constants.

[0008] Currently, there are two main methods for calculating lattice thermal conductivity: one is the first-principles calculation based on density functional theory, which accurately describes the interatomic interactions in many materials. However, obtaining the third-order force constants used to describe anharmonicity is very time-consuming, as exemplified by the method described in Computer Physics Communications, 2014, 185(6):1747-1758, which uses a lengthy third-order force constant method. The other method uses the Slack model for fast calculation, as exemplified by the method described in Materials Research Letters, 2019, 7(4):145-151. While fast, this method is not very accurate. Therefore, there is an urgent need for a calculation method that offers both speed and accuracy to meet the requirements of theoretical prediction. Summary of the Invention

[0009] To address the problems of existing technologies, the present invention aims to overcome the shortcomings of existing technologies and provide a method for rapidly calculating the lattice thermal conductivity of materials. By changing the sampling method and the calculation method of lattice thermal conductivity, a faster and more accurate method for predicting the lattice thermal conductivity of materials is proposed.

[0010] To achieve the above objectives, the specific technical solution of the present invention is as follows:

[0011] A method for rapidly calculating the lattice thermal conductivity of a material includes the following steps:

[0012] S1. Determine the crystal structure file and second-order force constant file of the material system, and extract the initial crystal structure data and second-order force constant data;

[0013] S2. Solve the dynamic matrix for the initial crystal structure data and the second-order force constant data. Use a gridded sampling method to sample the wave vector of the initial crystal structure data to determine the phonon data of the material system. The phonon data includes three acoustic branches and includes the phonon frequency and phonon group velocity in each of the acoustic branches. Obtain the Debye temperature corresponding to each of the three acoustic branches based on the phonon data.

[0014] S3. Based on the phonon data, the Debye temperature, and the Green's Eisen constant in each acoustic mode, the point lattice thermal conductivity in each acoustic mode is obtained using the Debye-Callaway model.

[0015] S4. The lattice thermal conductivity of the material system is obtained by calculating the point lattice thermal conductivity and the number of grid points corresponding to the gridded sampling method.

[0016] Preferably, the initial crystal structure data and the second-order force constant data are determined by searching data from an existing materials database platform.

[0017] Preferably, the material system is structurally optimized based on density functional theory to obtain the initial crystal structure, and the second-order force constants of the optimized crystal structure are calculated by the frozen phonon method or the perturbation method, thereby obtaining the crystal structure data and the second-order force constant data.

[0018] Preferably, the gridded sampling method is as follows: the density of states data is calculated using the phonopy program, and the configuration parameters of the initial crystal structure data include chemical formula, cell expansion parameters and sampling density, wherein the sampling density is the value of 180 / cell edge length rounded up.

[0019] Preferably, the three acoustic branches are: one longitudinal acoustic branch and two transverse acoustic branches.

[0020] Preferably, the highest frequency of each acoustic branch is determined based on the phonon frequency information to obtain the Debye temperature of the three acoustic branches.

[0021] Preferably, the Green-Eisen constant for each of the acoustic support modes is 1.

[0022] Preferably, the value of the Green's constant γ for each acoustic mode is obtained by the following method: expanding or shrinking the initial crystal structure to obtain an expanded crystal structure or a shrunken crystal structure; recalculating the phonon data for the expanded crystal structure or the shrunken crystal structure; and then calculating the Green's constant γ for each acoustic mode based on the phonon data under the two sets of different crystal structures. i The determination.

[0023] Compared with the prior art, the beneficial effects of the present invention are:

[0024] This invention provides a method for rapidly calculating the lattice thermal conductivity of a material. Based on the crystal structure of the material system and the second-order force constant obtained through first-principles calculations, the lattice thermal conductivity of the material system is predicted. This method can quickly obtain the lattice thermal conductivity while ensuring good accuracy. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0026] Figure 2 A comparison graph showing the lattice thermal conductivity of Cu3SbSe3 material at different temperatures predicted using the method provided in this invention, and the experimental values.

[0027] Figure 3 A comparison graph showing the lattice thermal conductivity of Mg2Si material at different temperatures predicted using the method provided in this invention, and the experimental values.

[0028] Figure 4 A comparison graph showing the lattice thermal conductivity of NbFeSb material at different temperatures predicted using the method provided in this invention, and the experimental values.

[0029] Figure 5 This is a comparison chart of the predicted lattice thermal conductivity of Si material at different temperatures using the method provided in this invention, and the experimental values. Detailed Implementation

[0030] 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.

[0031] It should be noted that, in this specific embodiment, the software calculation part is based on density functional theory and uses the commonly used VASP and phonopy programs in combination to perform calculations in order to obtain the data in each step of the present invention.

[0032] This invention provides the following technical solution: a method for rapidly calculating the lattice thermal conductivity of materials, such as... Figure 1 As shown, it includes the following steps:

[0033] S1. Determine the crystal structure file and second-order force constant file of the material system to obtain the initial crystal structure data and second-order force constant data;

[0034] S2. Solve the dynamic matrix from the initial crystal structure data and second-order force constant data. Use a gridded sampling method to sample the wave vector of the initial crystal structure to determine the phonon data of the material system. The phonon data includes three acoustic branches, as well as the phonon frequency and phonon group velocity in each acoustic branch mode. Based on the phonon data, obtain the Debye temperature corresponding to each of the three acoustic branches.

[0035] S3. Based on phonon data, Debye temperature, and Greenessen constant for each acoustic mode, the point lattice thermal conductivity (i.e., the sum of lattice thermal conductivity for each acoustic mode) is obtained using the Debye-Callaway model.

[0036] S4. Calculate the lattice thermal conductivity of the material system using the point lattice thermal conductivity obtained in step S3 and the number of grid points in the gridded sampling method.

[0037] Furthermore, there are two ways to determine the initial crystal structure and second-order force constants. One is to search through existing materials database platforms, such as the phonondb database (http: / / phonondb.mtl.kyoto-u.ac.jp / ), which contains tens of thousands of crystal structures and second-order force constants. The other is to calculate the second-order force constants of the corresponding structure using the frozen phonon method or perturbation method after obtaining the optimized crystal structure (i.e., the initial crystal structure) based on density functional theory.

[0038] Furthermore, the sampling method used in step S2 to calculate the phonon frequency and phonon group velocity is as follows: the wave vector is sampled using a gridded sampling method. Specifically, the density of states data is calculated using the phonopy program. The sampling density value in the mesh.conf configuration file is related to the cell edge length, and the sampling density is the value of 180 / cell edge length rounded up.

[0039] In this embodiment, the setting of sampling density is illustrated using the mesh.conf file as an example, as follows:

[0040] ATOM_NAME = K Cu Sb

[0041] DIM=222

[0042] MESH=181818

[0043] GROUP_VELOCITY = .TRUE.

[0044] The first line contains the name of the chemical formula, the second line contains the cell size (or cell expansion parameter) of the initial crystal structure, the third line contains the sampling density used to calculate the phonon frequency and phonon group velocity, and the fourth line sets GROUP_VELOCITY to TRUE. The crystal structure after cell expansion is called a supercell.

[0045] After running the phonopy mesh.conf command, you will obtain the mesh.yaml file, which contains phonon frequency and phonon group velocity information for each phonon mode in the initial crystal structure.

[0046] Furthermore, the three acoustic branches are: one longitudinal acoustic branch (LA) and two transverse acoustic branches (TA and TA').

[0047] Furthermore, step S2 specifically involves determining the highest frequency ω of each acoustic branch i based on the phonon frequency information. i And according to the formula Obtain the Debye temperature θ of these three acoustic branches TA ,θ TA' and θ LA .

[0048] Furthermore, the Greenessen constant is set to 1 for each acoustic mode in step S3.

[0049] Furthermore, to further improve the calculation accuracy of the material's lattice thermal conductivity, the Green's constant γ for each acoustic mode is obtained using the following method: the initial crystal structure is expanded or reduced to obtain an expanded or reduced crystal structure. Then, using the aforementioned phonon data calculation method, the data of the expanded or reduced crystal structure is used to replace the data of the initial crystal structure, and the phonon data of the expanded or reduced crystal structure is calculated again. Thus, the Green's constant γ for each acoustic mode is calculated based on the phonon data under two different crystal structures (e.g., the initial crystal structure and the expanded crystal structure, or the initial crystal structure and the reduced crystal structure, or the expanded crystal structure and the reduced crystal structure). i The determination is specifically as follows: the highest frequency ω of each acoustic branch i in the two sets of phonon data. i The negative of the ratio of the difference of the natural logarithms of the two sets of phonon data to the difference of the natural logarithms of the crystal structure volumes in each set of phonon data is as follows:

[0050] It should be noted that the expansion or contraction ratio of the initial crystal structure must meet the elasticity requirements under Hooke's Law.

[0051] Specifically, the formula for calculating the point lattice thermal conductivity in step S3 is as follows:

[0052] In the Debye-Callaway model, neglecting the contribution of optical phonon modes, the point lattice thermal conductivity κ is a longitudinal acoustic branch (κ... LA The lattice thermal conductivity and two transverse acoustic branches (κ) TA and κ TA' The sum of the lattice thermal conductivity of )

[0053] κ=κ LA +κ TA +κ TA' Lattice thermal conductivity κ contributed by the three acoustic branches LA, TA, and TA', respectively i The calculation formula is as follows:

[0054]

[0055] Relaxation time τ c The reciprocal of is the scattering rate. For the scattering rate (1 / τ) c The calculations of the Debye-Callaway model consider two main mechanisms that affect lattice thermal conductivity: the phonon scattering rate (1 / τ) during the Umklapp process. u Phonon scattering rate (1 / τ) and normal process N ),Right now, Specifically as follows:

[0056] Phonon scattering rate of the flip process corresponding to the three acoustic modes Phonon scattering rate in normal processes It can be written as the following formula:

[0057] i = TA, TA', or LA;

[0058]

[0059]

[0060]

[0061] Thus, by summing the phonon scattering rates of the flip process and the normal process for each acoustic mode, the scattering rate of the corresponding acoustic mode can be obtained.

[0062]

[0063]

[0064]

[0065] In step S4, the lattice thermal conductivity of the material system is the ratio between the point lattice thermal conductivity κ and the number of grid points N in the gridded sampling method, specifically expressed as:

[0066] Here, the main parameters involved in the above calculation process are explained:

[0067] in, It is Planck's constant, k B It is the Boltzmann constant, i corresponds to TA, TA', or LA, ω i Let θ be the phonon frequency corresponding to acoustic branch i, V be the volume of the expanded crystal structure, and θ be the frequency of the phonon. i Represents the Debye temperature corresponding to acoustic branch i. T is the temperature set when calculating the density of states data. v i It is the phonon group velocity corresponding to acoustic branch i. To calculate the total relaxation time corresponding to acoustic support i at temperature T, To calculate the relaxation time of the acoustic branch i in the normal process at temperature T. To calculate the relaxation time of the flip process corresponding to acoustic branch i at temperature T, ω is the frequency of the density of states data, M is the average atomic mass, and γ is the Green's constant. LA γ TA γ TA' These correspond to the Green's Eisen constants of the acoustic branches LA, TA, or TA', respectively.

[0068] It should be noted that the method for rapidly calculating the lattice thermal conductivity of a material provided above is for a calculation result set at a temperature T during the calculation process. In application, the lattice thermal conductivity of the material can be predicted at different temperatures by calculating the lattice thermal conductivity of the material at several temperatures.

[0069] Using the aforementioned method for rapidly calculating the lattice thermal conductivity of materials, calculations were performed on Cu3SbSe3, Mg2Si, NbFeSb, and Si. The theoretical predictions were compared with experimental values. In this process, the Green's Eisen constant for the acoustic branch was set to 1 for theoretical calculations. Figures 2 to 5 As shown, the theoretical predictions calculated by this method are consistent with the experimental values ​​on the same order of magnitude. In particular, the lattice thermal conductivity obtained by this rapid calculation is very close to the experimental value at high temperatures. For example, the error of the lattice thermal conductivity in the NbFeSb system at 800K is only 6%.

[0070] 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 rapidly calculating the lattice thermal conductivity of a material, characterized in that, Includes the following steps: S1. Determine the initial crystal structure file and second-order force constant file of the material system, and extract the initial crystal structure data and second-order force constant data; S2. Solve the dynamic matrix for the initial crystal structure data and the second-order force constant data. Use a gridded sampling method to sample the wave vector of the initial crystal structure data to determine the phonon data of the material system. The phonon data includes three acoustic branches and includes the phonon frequency and phonon group velocity in each of the acoustic branches. Obtain the Debye temperature corresponding to each of the three acoustic branches based on the phonon data. S3. Based on the phonon data, the Debye temperature, and the Green's Eisen constant in each acoustic mode, the point lattice thermal conductivity in each acoustic mode is obtained using the Debye-Callaway model. S4. The lattice thermal conductivity of the material system is obtained by calculating the point lattice thermal conductivity and the number of grid points corresponding to the gridded sampling method.

2. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 1, characterized in that, The initial crystal structure data and the second-order force constant data are determined by searching data from existing materials database platforms.

3. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 1, characterized in that, Based on density functional theory, the material system is structurally optimized to obtain the initial crystal structure. The second-order force constants of the optimized crystal structure are calculated by the frozen phonon method or the perturbation method, thereby obtaining the initial crystal structure data and the second-order force constant data.

4. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 1, characterized in that, The gridded sampling method is as follows: the phonon density of states data is calculated using the phonopy program, and the chemical formula, cell expansion parameters, and sampling density parameters are configured. The value of the sampling density is the integer part of 180 / the edge length of the unit cell.

5. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 1, characterized in that, The three acoustic branches are: one longitudinal acoustic branch and two transverse acoustic branches.

6. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 1, characterized in that, Based on the phonon frequency information, the highest frequency of each acoustic branch is determined to obtain the Debye temperature of the three acoustic branches.

7. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 1, characterized in that, The Greenessen constant for each of the acoustic submodes is 1.

8. The method for rapidly calculating the lattice thermal conductivity of a material according to claim 4, characterized in that, The Green's constant for each acoustic mode is obtained as follows: the initial crystal structure is expanded or reduced to obtain an expanded or reduced crystal structure; the phonon data for the expanded or reduced crystal structure are calculated again; and the Green's constant for each acoustic mode is then determined based on the phonon data under the two different crystal structures. The determination.

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