A method for evaluating the lattice thermal conductivity of a material with high efficiency
By integrating Grüneisen parameters and Debye temperature into a combined testing method, optimizing the Slack model, and combining it with a high-throughput computing platform, the problems of high computational resource consumption and inaccurate results in the evaluation of material lattice thermal conductivity were solved. This enabled rapid and accurate material screening and database construction, improving the efficiency of new material design.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- CHONGQING SCI & INNOVATION CENT OF NORTHWEST POLYTECHNICAL UNIV
- Filing Date
- 2023-04-12
- Publication Date
- 2026-06-19
AI Technical Summary
Existing technologies for evaluating the thermal conductivity of material lattices suffer from high computational resource consumption, long processing time, and insufficient accuracy, which limits their application, especially in the design of new materials. Traditional methods are insufficient for quickly screening materials that meet the required thermal properties.
By integrating Grüneisen parameters and Debye temperature into a combined testing method, the Slack quasi-harmonic Debye model was optimized. Combined with a high-throughput computing platform, the optimal parameters were selected using a phenomenological method to rapidly evaluate the lattice thermal conductivity. Corrections for the effects of actual defects were also added, and a materials thermodynamics database was constructed.
This enables efficient, accurate, and rapid evaluation of material lattice thermal conductivity, reducing design costs and R&D time, improving the efficiency of new material screening, and providing technical support for subsequent thermal property parameter calculations.
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Figure CN116401877B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of high-throughput computational technology and thermodynamic computational technology of materials genome engineering, specifically involving a high-efficiency method for evaluating the lattice thermal conductivity of materials. Background Technology
[0002] In many fields of modern science and mechanical engineering, the lattice thermal conductivity of materials is of paramount importance. It is a core indicator for designing advanced materials in areas such as thermoelectric materials, heat dissipation materials, and thermal protection materials. A reasonable assessment of the lattice thermal conductivity κL of materials is of great significance. In traditional experimental measurements, the accurate measurement of thermal conductivity is affected by thermal contact between the instrument and the material at high temperatures, as well as by convection and heat transfer effects with the external environment. Therefore, the theoretical calculation of material thermal conductivity is receiving increasing attention.
[0003] Current calculations of lattice thermal conductivity require a balance between the accuracy of the results and the complexity of the computation. Commonly used methods for accurate lattice thermal conductivity calculations include solving the Boltzmann transport equation for phonons using first-principles calculations, simulating actual thermal processes using non-equilibrium molecular dynamics, and solving the Green-Kubo equation using equilibrium molecular dynamics. However, these methods consume significant computational resources and time, limiting their application in guiding materials design. In addition, two lower-cost methods exist for rapidly screening materials with suitable thermal properties: the theoretical minimum lattice thermal conductivity prediction model and the Slack quasi-harmonic Debye model. The theoretical minimum lattice thermal conductivity prediction model can predict the thermal conductivity of materials at high-temperature limits using sound velocity, roughly matching experimental values, but it requires elastic properties and is computationally complex. Under the Slack quasi-harmonic Debye model, given temperature, pressure, and other conditions, only energy needs to be calculated to predict the material's thermal conductivity, greatly reducing computational load. However, it is highly dependent on the Debye temperature and Grüneisen parameters. Therefore, developing a suitable lattice thermal conductivity evaluation model is crucial for the design of new materials.
[0004] With the development of computer technology, integrated computational materials design has achieved numerous original results in database establishment, new material design, and key component development through cross-scale and multidisciplinary integration, while also promoting the comprehensive development of computational materials science in basic research. High-throughput computing provides theoretical support for new material design schemes and can significantly shorten research and development costs and cycles. Innovative research based on integrated computational materials engineering and materials genome database technology is an important way to address the demand for advanced materials in my country's thermally related materials field. Therefore, this method aims to develop a more accurate and rapid assessment method for lattice thermal conductivity suitable for high-throughput computing platforms, which is conducive to constructing a database of key thermal properties of corresponding materials, achieving efficient screening of target materials, and thus significantly improving the development of advanced materials. Summary of the Invention
[0005] This invention addresses the need for high-throughput computational platforms and databases for materials in thermal applications. By integrating Grüneisen parameters and Debye temperatures in a combined testing method, it optimizes the accuracy of the Slack quasi-harmonic Debye model. Through phenomenological methods, it rationally selects corresponding parameters to achieve high-throughput, rapid assessment of the lattice thermal conductivity of relevant materials, improving the accuracy of prediction results and reducing material design costs and development time. Furthermore, it provides technical support and relevant data for the efficient calculation of other thermal property parameters.
[0006] To achieve the above-mentioned objectives, the specific technical solution adopted by this invention is as follows:
[0007] A method for efficiently evaluating the lattice thermal conductivity of materials is provided, comprising:
[0008] The structural files and energy information of the relevant materials are obtained through first-principles calculations; wherein, the structural files include the types and numbers of atoms; and the energy information includes energy-volume curves.
[0009] The structure file and energy information are converted using the Helmholtz free energy relation, and their changes with temperature and pressure are analyzed to obtain the relationship between volume and external pressure, Debye temperature, relationship between bulk modulus and temperature, and relationship between isochoric heat capacity and temperature and volume.
[0010] The Grüneisen parameters are obtained based on thermodynamics and the Debye model. The Grüneisen parameters are then simplified to obtain a reduced Grüneisen parameter model.
[0011] Substitute the Grüneisen parametric model and the Debye temperature into the Slack equation to solve for the combined solution of lattice thermal conductivity;
[0012] Based on the combined solution of the lattice thermal conductivity, the optimal combination of Grüneisen parameter and Debye temperature is selected by comparing phenomenological methods with experimental values.
[0013] Based on the optimal combination of Grüneisen parameters and Debye temperature, and with the addition of corrections for the effects of actual defects, the actual lattice thermal conductivity is obtained.
[0014] Based on the correction process of the actual lattice thermal conductivity, high-throughput calculations are performed on materials with different compositions to form a material thermodynamic database, from which thermally relevant materials with the best thermodynamic properties are screened out.
[0015] As a further explanation of the present invention, the specific process of converting the structure file and the energy information using the Helmholtz free energy relation is as follows:
[0016]
[0017]
[0018] Where F(V,T) is the Helmholtz free energy, E0(V) is the ground state energy, and F vib (V, T) is the quasi-harmonic approximate Helmholtz free energy, B0 is the bulk elastic modulus at zero temperature and zero pressure, B′0 is its derivative, V0 and V are the equilibrium volume and the volume under external field, respectively, and Θ D Let be the Debye temperature, n be the number of atoms in the basic unit cell, and D(x) be the Debye integral equation.
[0019] As a further explanation of the present invention, the specific process of obtaining the relationship between volume and external pressure P(V) based on the Helmholtz free energy relation is as follows:
[0020] P(V)=3B0[(V0 / V) 7 / 3 -(V0 / V) 5 / 3 ]{1+3(B′0-4[(V0 / V) 2 / 3 -1]) / 4} / 2 (4)
[0021] The Debye temperature θ is obtained from the Helmholtz free energy relation. D The specific process is as follows:
[0022]
[0023] Where M is the initial unit cell mass, s is the Debye temperature scattering factor representing a value related to the material's Poisson's ratio, A is a constant, and γ is the Grüneisen parameter.
[0024] As a further explanation of the present invention, the method further includes: taking a value for s based on the experimental value and the corresponding experimental value range, and using s(1) s (2) s (3) and s (4) The average, maximum, and minimum values of the experimental measurements, along with the theoretically calculated recommended value, are used to obtain the corresponding Debye temperature: θ. D (s (1) ), θ D (s (2) ), θ D (s (3) ) and θ D (s (4) ).
[0025] As a further explanation of the present invention, the specific process of obtaining the relationship between the bulk modulus B(V) and temperature based on the Helmholtz free energy relation is as follows:
[0026]
[0027] The isochoric heat capacity C is obtained based on the Helmholtz free energy relation. V The specific process involving (V, T) and temperature and volume is as follows:
[0028]
[0029] Where, k B is the Boltzmann constant.
[0030] As a further explanation of the present invention, the specific process of obtaining the Grüneisen parameters based on thermodynamics and the Debye model, and simplifying the Grüneisen parameters to obtain the reduced Grüneisen parameter model is as follows:
[0031] Based on thermodynamic methods, the Grüneisen parameters are rewritten as a thermodynamic model (th):
[0032]
[0033] By introducing the free volume theory and simplifying the thermodynamic model, the Grüneisen parameters are rewritten as the Vaschenko-Zubarev model (VZ):
[0034]
[0035] By modifying the free volume theory, the Grüneisen parameters are rewritten as a modified free volume model (mvf):
[0036]
[0037] According to Debye theory, the modes are reduced, and the Grüneisen parameters are rewritten as a Debye model (D):
[0038]
[0039] Where, ω D The Debye frequency represents the limit of phonon frequencies during lattice vibration;
[0040] Introducing the speed of sound and reducing the Debye frequency, the Grüneisen parameters are rewritten as a Slater model (S):
[0041]
[0042] Dugdale-MacDonald model (DM):
[0043]
[0044] As a further illustration of the present invention, the lattice thermal conductivity κ is solved using the Slack equation. L The specific process of the combined solution is as follows:
[0045] Grüneisen parameter γ th γ VZ γ mvf γ S and γ DM and Debye temperature θ D (s (1) ), θ D (s (2) ), θ D (s (3) ) and θ D (s (4) Substitute the solutions into the Slack equation to find the combined solution of the lattice heat ratio;
[0046] The Slack equation is as follows:
[0047]
[0048] As a further explanation of the present invention, the specific process of obtaining the actual lattice thermal conductivity based on the optimal combination of Grüneisen parameters and Debye temperature, with the addition of corrections for the influence of actual defects, is as follows:
[0049] By considering the effect of porosity on the theoretical lattice thermal conductivity κ L The specific process of the correction is as follows:
[0050]
[0051] Among them, κ L-effφ represents the actual lattice thermal conductivity, and φ represents the porosity, which is obtained through experimental measurement.
[0052] Compared with the prior art, the present invention has the following beneficial technical effects:
[0053] This method aims to replace the traditional trial-and-error method of multiple sequential iterations with a high-throughput parallel method, develop a fast and reliable computational method, establish a bridge from composition and structure to predict macroscopic performance, understand the characteristics of material systems from a wider range of components and more diverse and complex structures, find and identify the "material genes" that affect material properties, and construct a standard thermodynamic database for material gene research to improve the R&D efficiency of new thermal materials.
[0054] This method achieves goal-oriented design based on theoretical models, and leverages high-throughput concurrent materials calculation algorithms to establish a precise database that aids in deepening understanding and ensures performance consistency, providing data support and a theoretical foundation for the development of novel materials. The methods described above not only overcome the shortcomings of traditional trial-and-error methods, saving resources and time, but also provide convenient and rapid access to relevant thermophysical parameters based on first-principles calculations. Furthermore, this method, through theoretical calculations, selects suitable samples for experimental verification, saving experimental time and resources, improving experimental efficiency, providing guidance, and avoiding blind experimentation. Attached Figure Description
[0055] Figure 1 A schematic diagram illustrating the principle of the high-efficiency method for evaluating the lattice thermal conductivity of materials provided by this invention.
[0056] Figure 2 This is a diagram of the thermophysical parameter calculation model in this invention.
[0057] Figure 3 A flowchart illustrating the Grüneisen parameter selection and application combination to the Slack model to obtain the corresponding lattice thermal conductivity. Detailed Implementation
[0058] To better understand the above-mentioned objects, features, and advantages of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted that, unless otherwise specified, the embodiments of the present invention and the features thereof can be combined with each other.
[0059] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. The terminology used herein in the description of the invention is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
[0060] This invention relates to a high-throughput combinatorial calculation method for rapidly evaluating lattice thermal conductivity, such as... Figure 1As shown, the Helmholtz free energy is obtained by reading the structure and energy files calculated using first-principles calculations, and its derivative is used to obtain a series of thermophysical parameters: heat capacity, bulk modulus, etc. Then, according to... Figure 2 and 3 The calculation process shown calculates five Grüneisen parameters for the corresponding material. Simultaneously, four approximate values of Poisson's ratio are selected based on experimental values to correct the Debye model. Finally, the five Grüneisen parameters are substituted into four different Debye model relationships to obtain 20 different combinations of Debye temperatures. By substituting these 20 Debye temperatures and the five Grüneisen parameters into the Slack model to solve for the material's theoretical thermal conductivity, different combinations are screened and judged using existing experimental values to select the optimal combination. Finally, porosity is introduced to correct the theoretical lattice thermal conductivity, resulting in an effective actual lattice thermal conductivity, achieving efficient, accurate, and rapid evaluation of the material's lattice thermal conductivity.
[0061] Specifically, a method for efficiently evaluating the lattice thermal conductivity of a material is provided, comprising the following steps:
[0062] Step 1: Obtain the structural files and energy information of the relevant materials through first-principles calculations;
[0063] The structure file includes the types and number of atoms.
[0064] Energy information includes energy-volume curves.
[0065] Step 2: Analyze the changes in material structure and energy information with temperature and pressure using the Helmholtz free energy F(V,T) relationship;
[0066] The specific process of conversion using the Helmholtz free energy relation is as follows:
[0067] F(V, T) = E0(V) + F vib (V, T) (1)
[0068]
[0069]
[0070] Where E0(V) is the ground state energy, F vib (V, T) is the quasi-harmonic approximate Helmholtz free energy, B0 is the bulk elastic modulus at zero temperature and zero pressure, B′0 is its derivative, V0 and V are the equilibrium volume and the volume under external field, respectively, and Θ D Let be the Debye temperature, n be the number of atoms in the basic unit cell, and D(x) be the Debye integral equation.
[0071] Step 201, the specific process of obtaining the relationship between volume and external pressure based on the Helmholtz free energy relation is as follows:
[0072] P(V)=3B0[(V0 / V) 7 / 3 -(V0 / V) 5 / 3 ]{1+3(B′0-4[(V0 / V) 2 / 3 -1]) / 4} / 2 (4)
[0073] The specific process of obtaining the Debye temperature based on the Helmholtz free energy relation is as follows:
[0074]
[0075] Where M is the initial unit cell mass, s is the Debye temperature scattering factor representing a value related to the material's Poisson's ratio, A is a constant, and γ is the Grüneisen parameter.
[0076] Step 202: Based on the experimental values and the corresponding experimental value ranges, assign values to s, and use s... (1) s (2) s (3) and s (4) The average, maximum, and minimum values of the experimental measurements, along with the theoretically calculated recommended value, are used to obtain the corresponding Debye temperature: θ. D (s (1) ), θ D (s (2) ), θ D (s (3) ) and θ D (s (4) ).
[0077] Step 203, the specific process of obtaining the relationship between the bulk modulus B(V) and temperature based on the Helmholtz free energy relation is as follows:
[0078]
[0079] The isochoric heat capacity C is obtained based on the Helmholtz free energy relation. V The specific process involving (V, T) and temperature and volume is as follows:
[0080]
[0081] Where, k B is the Boltzmann constant.
[0082] Step 3: Obtain the Grüneisen parameters based on thermodynamics and the Debye model, simplify them, and obtain a reduced Grüneisen parameter model to explain the vibrational anharmonicity.
[0083] The specific process of obtaining Grüneisen parameters based on thermodynamics and the Debye model is as follows:
[0084] Step 301: Using thermodynamic methods, rewrite the Grüneisen parameters into a thermodynamic model (th):
[0085]
[0086] Step 302: By introducing the free volume theory and simplifying the thermodynamic model, the Grüneisen parameters are rewritten as the Vaschenko-Zubarev model (VZ):
[0087]
[0088] By modifying the free volume theory, the Grüneisen parameters are rewritten as a modified free volume model (mvf):
[0089]
[0090] According to Debye theory, the modes are reduced, and the Grüneisen parameters are rewritten as a Debye model (D):
[0091]
[0092] Where, ω D The Debye frequency represents the limit of phonon frequencies during lattice vibration;
[0093] Introducing the speed of sound and reducing the Debye frequency, the Grüneisen parameters are rewritten as a Slater model (S):
[0094]
[0095] Dugdale-MacDonald model (DM):
[0096]
[0097] Step 4, take the Grüneisen parameter γ obtained in step 3. th γ VZ γ mvf γ S and γ DM and the Debye temperature θ obtained in step 2 D (s (1) ), θ D (s (2) ), θ D (s (3) ) and θ D (s (4) Substitute the solutions into the Slack equation to find the combined solution of the lattice thermal conductivity.
[0098] The Slack equation is as follows:
[0099]
[0100] Step 5: Based on the multiple solutions of the lattice thermal conductivity calculated in Step 4, select the optimal combination of Grüneisen parameter and Debye temperature by comparing the phenomenological method with the experimental values.
[0101] Step 6: Based on the combination obtained in Step 5, add corrections for the actual defect effects to obtain the actual lattice thermal conductivity κ. L-eff .
[0102] By considering the effect of porosity on the theoretical lattice thermal conductivity κ L The specific process of the correction is as follows:
[0103]
[0104] Among them, κ L-eff φ represents the actual lattice thermal conductivity, and φ represents the porosity, which is obtained through experimental measurement.
[0105] Step 7: Based on the corrected formula obtained in Step 6, perform high-throughput calculations on materials with different compositions to form a material thermodynamics database, and screen out the heat-related materials with the best thermodynamic properties.
[0106] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.
Claims
1. A high-efficiency method for evaluating the lattice thermal conductivity of materials, characterized in that, include: The structural files and energy information of the relevant materials are obtained through first-principles calculations; wherein, the structural files include the types and numbers of atoms; and the energy information includes energy-volume curves. The structure file and energy information are converted using the Helmholtz free energy relation, and their changes with temperature and pressure are analyzed to obtain the relationship between volume and external pressure, Debye temperature, relationship between bulk modulus and temperature, and relationship between isochoric heat capacity and temperature and volume. The Grüneisen parameters are obtained based on thermodynamics and the Debye model. The Grüneisen parameters are then simplified to obtain a reduced Grüneisen parameter model. Substitute the Grüneisen parametric model and the Debye temperature into the Slack equation to solve for the combined solution of lattice thermal conductivity; Based on the combined solution of the lattice thermal conductivity, the optimal combination of Grüneisen parameter and Debye temperature is selected by comparing phenomenological methods with experimental values. Based on the optimal combination of Grüneisen parameters and Debye temperature, and with the addition of corrections for the effects of actual defects, the actual lattice thermal conductivity is obtained. Based on the correction process of the actual lattice thermal conductivity, high-throughput calculations are performed on materials with different compositions to form a material thermodynamic database, from which thermally relevant materials with the best thermodynamic properties are screened out.
2. The method for evaluating the lattice thermal conductivity of materials according to claim 1, characterized in that: The specific process of converting the structure file and the energy information using the Helmholtz free energy relation is as follows: （1）； （2）； （3）； in, For Helmholtz free energy, It is the ground state energy. It is the Helmholtz free energy of the quasi-harmonic approximation vibration. The bulk modulus at zero temperature and zero pressure Let V0 be its derivative, and V0 be the equilibrium volume and the volume under the influence of the external field, respectively. Boltzmann's constant, For Debye temperature, This is the Debye integral equation.
3. The method for evaluating the lattice thermal conductivity of materials according to claim 2, characterized in that: The volume and external pressure are obtained based on the Helmholtz free energy relation. The specific process of the relationship is as follows: （4）； The Debye temperature is obtained based on the Helmholtz free energy relation. The specific process is as follows: （5）； Where M is the mass of the primordial protocell, The Debye temperature scattering factor represents a value related to the material's Poisson's ratio, A is a constant, and γ is a Grüneisen parameter.
4. The method for evaluating the lattice thermal conductivity of materials according to claim 3, characterized in that: The method further includes: based on the experimental values and the corresponding experimental value ranges, To retrieve values, use , , and The average, maximum, and minimum values of the experimental measurements, along with the theoretically calculated recommended value, are used to obtain the corresponding Debye temperature: , , and .
5. The method for evaluating the lattice thermal conductivity of materials according to claim 4, characterized in that: The bulk modulus is obtained from the Helmholtz free energy relation. The specific process relating to temperature is as follows: （6）； The isochoric heat capacity is obtained based on the Helmholtz free energy relation. The specific process relating to temperature and volume is as follows: （7）； Where n is the number of atoms in the basic unit cell.
6. The method for evaluating the lattice thermal conductivity of materials according to claim 4, characterized in that: The specific process of obtaining the Grüneisen parameters based on thermodynamics and the Debye model, and then simplifying these Grüneisen parameters to obtain the reduced Grüneisen parameter model is as follows: Based on thermodynamic methods, the Grüneisen parameters are rewritten as a thermodynamic model (th): （8）； By introducing the free volume theory and simplifying the thermodynamic model, the Grüneisen parameters are rewritten as the Vaschenko-Zubarev model (VZ): （9）； By modifying the free volume theory, the Grüneisen parameters are rewritten as a modified free volume model (mvf): ； Based on Debye theory, the modes are reduced, and the Grüneisen parameters are rewritten as a Debye model (D): （11）； in, The Debye frequency represents the limit of phonon frequencies during lattice vibration; Introducing the speed of sound and reducing the Debye frequency, the Grüneisen parameters are rewritten as a Slater model (S): ； Dugdale-MacDonald model (DM): 。 7. The method for evaluating the lattice thermal conductivity of materials according to claim 6, characterized in that: Solving the lattice thermal conductivity using the Slack equation The specific process of the combined solution is as follows: Grüneisen parameter , and and Debye temperature and Substitute into the Slack equation to solve for the combined solution of the lattice heat ratio; The Slack equation is as follows: （14）。 8. The method for evaluating the lattice thermal conductivity of materials according to claim 1, characterized in that: The specific process for obtaining the actual lattice thermal conductivity based on the optimal combination of Grüneisen parameters and Debye temperature, with corrections for the effects of actual defects, is as follows: By considering the effect of porosity on theoretical lattice thermal conductivity The specific process of the correction is as follows: ； in, The actual lattice thermal conductivity, Porosity is obtained through experimental measurement.