Crystal state prediction method and device based on corrected state equation, terminal equipment and storage medium

Abstract

The invention discloses a crystal state prediction method and device based on a corrected state equation, terminal equipment and a storage medium, and belongs to the technical field of thermodynamic research, the method comprises the following steps: obtaining preset initial unit cell structure parameters of a to-be-detected metal crystal under different densities, carrying out DFT optimization on the to-be-detected metal crystal to obtain target unit cell structure data, a dynamic force constant matrix is constructed, phonon spectrum data under different densities are calculated, and Debye temperature values, Green Eschson coefficient values and melting temperature values under different densities are further calculated; fitting the numerical values to obtain a corrected state equation; and finally, predicting the crystal state of the metal crystal to be measured according to the corrected state equation. By implementing the method, the problem that the prediction accuracy of the thermodynamic behavior of the metal crystal is low due to the fact that the Green Aesson coefficient cannot accurately reflect the real behavior of the metal ions in the complex crystal environment in the prior art can be solved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of thermodynamic research, and particularly relates to a crystal state prediction method and device based on a modified equation of state, a terminal device and a storage medium. BACKGROUND

[0002] In the research and application of metal materials, accurately describing the thermodynamic properties and mechanical behavior of metals under different environmental conditions is crucial for material design and optimization. Especially under extreme temperatures, high pressures and other non-standard conditions, the phase transition, melting, mechanical properties of metals often change significantly, and the prediction and accurate calculation of these changes are of great significance to engineering applications. In order to effectively simulate under these extreme conditions, the equation of state (EOS) of metals is widely used to describe the thermodynamic behavior and physical properties of metals. The equation of state not only determines the basic physical quantities such as volume, density, melting temperature and Debye temperature of metals, but also has important application value in many fields such as physics, chemistry and materials science.

[0003] In the prior art, the traditional equation of state based on empirical relations is usually used to predict the thermodynamic state (such as pressure) of metal crystals under different temperature environments, and the Grüneisen coefficient in the traditional equation of state is usually obtained by simplifying the microstructure and interatomic interaction of the crystal using the Debye model and other approximation methods, ignoring the anharmonicity of atomic vibrations in the crystal and the coupling between different vibration modes. Therefore, the Grüneisen coefficient cannot accurately reflect the real behavior of metal ions in a complex crystal environment, resulting in a decrease in the prediction accuracy of the entire equation of state containing the Grüneisen coefficient for the thermodynamic behavior of metal crystals. SUMMARY

[0004] The present application provides a crystal state prediction method and device based on a modified equation of state, a terminal device and a storage medium, which can solve the problem of decreased prediction accuracy of the entire equation of state containing the Grüneisen coefficient for the thermodynamic behavior of metal crystals due to the inability of the Grüneisen coefficient to accurately reflect the real behavior of metal ions in a complex crystal environment.

[0005] An embodiment of the present application provides a crystal state prediction method based on a modified equation of state, comprising:

[0006] Obtaining preset initial unit cell structure parameters of a metal crystal to be measured under different densities;

[0007] For each density, the DFT optimization is performed on the metal crystal under test according to the preset initial unit cell structure parameters, to obtain target unit cell structure data of each density at the minimum crystal energy;

[0008] Each dynamic force constant matrix is constructed according to the target unit cell structure data, and the phonon spectrum data of the metal crystal under test at different densities is calculated according to the dynamic force constant matrices;

[0009] According to the phonon spectrum data, the different densities, and a preset Debye model, the Debye temperature value and the Grüneisen coefficient value of the metal crystal under test at different densities are calculated;

[0010] According to the Grüneisen coefficient values at different densities, the melting temperature values of the metal crystal under test at different densities are calculated;

[0011] According to the Debye temperature value, the Grüneisen coefficient value, and the melting temperature value, a corrected equation of state is fitted;

[0012] According to the corrected equation of state and the different densities, the crystal state of the metal crystal under test is predicted.

[0013] Further, the Debye temperature value and the Grüneisen coefficient value of the metal crystal under test at different densities are calculated according to the phonon spectrum data, the different densities, and a preset Debye model, including:

[0014] The crystal volume, the number of atoms, and the first Debye frequency of the metal crystal under test at the different densities are obtained;

[0015] According to the phonon spectrum data, the crystal volume, and the number of atoms, a first change curve of the free energy with respect to temperature at different densities is calculated;

[0016] According to the preset Debye model, the phonon spectrum data, and the first Debye frequency, a second change curve of the free energy of the metal crystal under test with respect to temperature and the first Debye frequency at different densities is calculated;

[0017] According to the first change curve and the second change curve, the Debye temperature value of the metal crystal under test at the different densities is calculated;

[0018] According to the Debye temperature value and the corresponding density, the Grüneisen coefficient value at different densities is calculated.

[0019] Further, the Debye temperature value of the metal crystal under the different densities is calculated according to the first change curve and the second change curve, comprising:

[0020] For each density, a difference function of the difference between the second change curve and the first change curve is constructed;

[0021] The difference function is solved by using the least square method to obtain the first Debye frequency at the minimum difference of free energy, and then the Debye frequency value under the different densities is obtained according to the first Debye frequency.

[0022] The product of the Debye frequency value and the preset Planck constant is calculated to obtain the Debye temperature value under the different densities.

[0023] Further, the modified equation of state is fitted according to the Debye temperature value, the Grüneisen coefficient value and the melting temperature value, comprising:

[0024] A preset Debye temperature calculation formula to be fitted, a preset Grüneisen coefficient calculation formula to be fitted and a preset melting temperature calculation formula to be fitted are obtained;

[0025] The Debye temperature value under the different densities is substituted into the Debye temperature calculation formula for fitting, the Grüneisen coefficient value under the different densities is substituted into the Grüneisen coefficient calculation formula for fitting, and the melting temperature value under the different densities is substituted into the melting temperature calculation formula for fitting, to determine the fitting parameter value in the Debye temperature calculation formula, the Grüneisen coefficient calculation formula and the melting temperature calculation formula;

[0026] According to the fitting parameter value, the Debye temperature calculation formula, the Grüneisen coefficient calculation formula and the melting temperature calculation formula, a modified Debye temperature calculation formula, a modified Grüneisen coefficient calculation formula and a modified melting temperature calculation formula are generated;

[0027] According to the modified Debye temperature calculation formula, the Debye temperature calculation formula in the preset traditional equation of state is replaced, according to the modified Grüneisen coefficient calculation formula, the Grüneisen coefficient calculation formula in the preset traditional equation of state is replaced, and according to the modified melting temperature calculation formula, the melting temperature calculation formula in the preset traditional equation of state is replaced, to obtain the modified equation of state.

[0028] Further, the crystal state of the metal crystal is predicted according to the modified equation of state and the different densities, comprising:

[0029] According to the modified equation of state and the different densities, the free energy of the metal crystal to be measured under different densities is calculated.

[0030] According to the free energy, the crystal state of the metal crystal to be measured under different densities is calculated.

[0031] On the basis of the above-mentioned method embodiment, the present application correspondingly provides a device embodiment;

[0032] The present application provides a crystal state prediction device based on a modified equation of state, comprising:

[0033] The cell structure parameter acquisition module, the target cell structure data determination module, the phonon spectrum data calculation module, the Debye temperature value and the Green-Eisen coefficient value calculation module, the melting temperature value calculation module, the equation of state modification module, and the crystal state prediction module;

[0034] The cell structure parameter acquisition module is configured to acquire preset initial cell structure parameters of a metal crystal to be measured under different densities.

[0035] The target cell structure data determination module is configured to perform DFT optimization on the metal crystal to be measured according to the preset initial cell structure parameters for each density, so as to obtain target cell structure data of each density under the minimum crystal energy.

[0036] The phonon spectrum data calculation module is configured to construct a dynamic force constant matrix according to each target cell structure data, and calculate phonon spectrum data of the metal crystal to be measured under different densities according to the dynamic force constant matrix.

[0037] The Debye temperature value and the Green-Eisen coefficient value calculation module is configured to calculate the Debye temperature value and the Green-Eisen coefficient value of the metal crystal to be measured under different densities according to the phonon spectrum data, the different densities, and a preset Debye model.

[0038] The melting temperature value calculation module is configured to calculate the melting temperature value of the metal crystal to be measured under different densities according to the Green-Eisen coefficient value under the different densities.

[0039] The equation of state modification module is configured to fit a modified equation of state according to the Debye temperature value, the Green-Eisen coefficient value, and the melting temperature value.

[0040] The crystal state prediction module is configured to predict the crystal state of the metal crystal to be measured according to the modified equation of state and the different densities.

[0041] Further, the Debye temperature value and Gruneisen coefficient value calculation module comprises:

[0042] The crystal data acquisition unit, the first change curve calculation unit, the second change curve calculation unit, the Debye temperature value determination unit, and the Gruneisen coefficient value determination unit;

[0043] The crystal data acquisition unit is configured to acquire the crystal volume, the number of atoms, and the first Debye frequency under the different densities of the metal crystal to be measured.

[0044] The first change curve calculation unit is configured to calculate, according to the phonon spectrum data, the crystal volume, and the number of atoms, a first change curve of the free energy changing with temperature under different densities.

[0045] The second change curve calculation unit is configured to calculate, according to the preset Debye model, the phonon spectrum data, and the first Debye frequency, a second change curve of the free energy of the metal crystal to be measured changing with temperature and the first Debye frequency under different densities.

[0046] The Debye temperature value determination unit is configured to calculate, according to the first change curves and the second change curves, the Debye temperature values of the metal crystal to be measured under the different densities.

[0047] The Gruneisen coefficient value determination unit is configured to calculate, according to the Debye temperature values and the corresponding densities, the Gruneisen coefficient values under different densities.

[0048] Further, the Debye temperature value determination unit comprises:

[0049] The difference function construction subunit, the difference function solving subunit, and the Debye frequency value calculation subunit;

[0050] The difference function construction subunit is configured to, for each density, construct a difference function of the difference between the free energies of the second change curve and the first change curve.

[0051] The difference function solving subunit is configured to solve the difference function by using the least square method to obtain the first Debye frequency at which the difference between the free energies is smallest, and then obtain the Debye frequency values under the different densities according to the first Debye frequencies.

[0052] The Debye frequency value calculation subunit is configured to calculate the product of the Debye frequency value and a preset Planck constant to obtain the Debye temperature values under the different densities.

[0053] On the basis of the above-mentioned method embodiment, the application provides a terminal device embodiment.

[0054] The application provides a terminal device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, and the processor executes the computer program to realize the method for predicting crystal state based on a modified state equation.

[0055] On the basis of the method embodiment, the application provides a storage medium embodiment.

[0056] The application provides a storage medium, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, and the processor executes the computer program to realize the method for predicting crystal state based on a modified state equation.

[0057] The embodiments of the application have the following beneficial effects:

[0058] This invention provides a method, apparatus, terminal device, and storage medium for predicting the state of a crystal based on a modified equation of state. The method includes: acquiring preset initial unit cell structure parameters of a metal crystal under test at different densities; then, for each density, performing DFT optimization on the metal crystal under test according to the preset initial unit cell structure parameters to obtain target unit cell structure data at the minimum crystal energy for each density; then, constructing dynamic force constant matrices based on the target unit cell structure data, and calculating phonon spectrum data of the metal crystal under test at different densities based on the dynamic force constant matrices; then, calculating the Debye temperature and Green's Eisen coefficient of the metal crystal under test at different densities based on the phonon spectrum data, the different densities, and a preset Debye model; then, calculating the melting temperature of the metal crystal under test at different densities based on the Green's Eisen coefficient; then, fitting a modified equation of state based on the Debye temperature, Green's Eisen coefficient, and melting temperature; and finally, predicting the crystal state of the metal crystal under test based on the modified equation of state and the different densities. Therefore, this invention utilizes DFT (Density Functional Theory) optimization to determine the target unit cell structure data, and then constructs a dynamic force constant matrix based on this target unit cell structure data to calculate phonon spectrum data. Since phonons are a quantized description of atomic vibrations in metallic crystals, phonon spectrum data contains rich information about atomic vibrations in metallic crystals, directly reflecting the vibrational characteristics and interactions of metal ions in the crystal. Furthermore, the optimization principle of DFT is based on quantum mechanics, which can accurately handle the wave and particle properties of electrons, thus accurately describing the motion state and interactions of electrons in the crystal. Subsequently, the Green's Eisen coefficient values ​​determined using this phonon spectrum data are used to correct the equation of state and predict the crystal state, improving the accuracy of the final prediction results. Attached Figure Description

[0059] To more clearly illustrate the technical solution of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0060] Figure 1 This is a schematic flowchart of a crystal state prediction method based on a modified equation of state provided in an embodiment of the present invention.

[0061] Figure 2 This is a schematic diagram of the pressure versus density curve at 8000K, obtained based on the modified state equation of the present invention, according to an embodiment of the present invention.

[0062] Figure 3 is a schematic diagram of a pressure-density curve at 8000K obtained based on a preset conventional equation of state according to an embodiment of the present application.

[0063] Figure 4 is a schematic diagram of a pressure-density curve at different temperatures according to an embodiment of the present application.

[0064] Figure 5 is a schematic diagram of a crystal state prediction device based on a modified equation of state according to an embodiment of the present application. DETAILED DESCRIPTION

[0065] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, but not all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the scope of protection of the present application.

[0066] 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 the present application belongs; the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit the present application; the terms "include" and "have" and any variations thereof in the specification and claims of the present application and the above description of drawings are intended to cover non-exclusive inclusion.

[0067] In the description of the embodiments of the present application, the technical terms "first", "second", etc. are only used to distinguish different objects, and cannot be understood as indicating or implying relative importance or implicitly indicating the number, specific order or primary and secondary relationship of the indicated technical features. In the description of the embodiments of the present application, the meaning of "a plurality of" is two or more, unless otherwise explicitly and specifically limited.

[0068] Reference herein to "an embodiment" means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one embodiment of the present application. The appearance of the phrase in various places in the specification does not necessarily all refer to the same embodiment, nor is it necessarily independent or alternative embodiments to other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0069] In the description of the embodiments of the present application, the term "and / or" is merely to describe an association relationship of associated objects, and can represent three relationships, for example, A and / or B, which can represent three cases of A existing alone, A and B existing simultaneously, and B existing alone. In addition, the character " / " in the present application generally represents an "or" relationship between the front and rear associated objects.

[0070] In the description of the embodiments of the present application, the term "a plurality of" refers to two or more (including two), and similarly, "a plurality of groups" refers to two or more groups (including two groups), and "a plurality of pieces" refers to two or more pieces (including two pieces).

[0071] In the description of the embodiments of the present application, unless otherwise explicitly specified and limited, the technical terms "mounting", "connection", "connection", "fixing" and the like should be understood in a broad sense, for example, can be fixedly connected, or can be detachably connected, or can be integrated; can be mechanically connected, or can be electrically connected; can be directly connected, or can be indirectly connected through an intermediate medium; can be the internal communication of two elements or the interaction relationship between two elements. For those skilled in the art, the specific meaning of the above terms in the embodiments of the present application can be understood according to the specific circumstances.

[0072] Reference is made to Figure 1 To solve the problem in the prior art that the Grüneisen coefficient cannot accurately reflect the real behavior of metal ions in a complex crystal environment, resulting in reduced prediction accuracy of the entire state equation containing the Grüneisen coefficient for the thermodynamic behavior of metal crystals, an embodiment of the present application provides a crystal state prediction method based on a modified state equation, comprising:

[0073] Step S101: obtaining preset initial unit cell structure parameters of a metal crystal to be measured at different densities;

[0074] Specifically, the preset initial unit cell structure parameters include lattice constants and atomic coordinate information.

[0075] Step S102: for each density, performing DFT optimization on the metal crystal to be measured according to the preset initial unit cell structure parameters to obtain target unit cell structure data at the minimum crystal energy of each density;

[0076] Specifically, selecting appropriate exchange-correlation functionals and initial unit cell structure parameters for DFT optimization to obtain an equilibrium state of the metal crystal reaching the lowest point of the crystal energy, and target unit cell structure data.

[0077] Step S103: constructing each dynamic force constant matrix according to each target unit cell structure data, and calculating the phonon spectrum data of the metal crystal to be measured at different densities according to each dynamic force constant matrix;

[0078] Specifically, the phonon spectrum data includes phonon frequency data and corresponding vibration modes. The phonon spectrum of the metal crystal is calculated by using VASP (Vienna Ab-initio Simulation Package) software. After obtaining the target crystal cell structure data, the phonon calculation is performed by taking the target crystal cell structure data as the input data of the VASP software, so as to construct the dynamic force constant matrix of the metal crystal. The phonon frequency and vibration mode are extracted from the dynamic force constant matrix calculated by the VASP software by using the Phonopy tool. Then, the above calculation is repeated under different density conditions to generate a series of phonon spectrum data.

[0079] Preferably, by comparing the changes of the phonon spectrum data under different densities, the density dependence of the phonon characteristic frequency can be preliminarily judged, and reliable data basis is provided for the calculation of the Debye frequency and the Debye temperature.

[0080] Step S104: calculating the Debye temperature value and the Gruneisen coefficient value of the metal crystal to be measured under different densities according to the phonon spectrum data, the different densities and a preset Debye model.

[0081] Specifically, the preset Debye model is as follows:

[0082]

[0083] In the formula, g(ω) represents the phonon state density function, V represents the crystal volume of the metal crystal to be measured, ω represents the phonon frequency, and v represents the average propagation speed of the sound wave in the metal crystal to be measured.

[0084] In a preferred embodiment, the calculation of the Debye temperature value and the Gruneisen coefficient value of the metal crystal to be measured under different densities according to the phonon spectrum data, the different densities and a preset Debye model includes:

[0085] obtaining the crystal volume, the number of atoms and the first Debye frequency under the different densities of the metal crystal to be measured;

[0086] calculating a first change curve of the free energy with respect to the temperature under different densities according to the phonon spectrum data, the crystal volume and the number of atoms;

[0087] Specifically, in the first change curve, the free energy is the y-axis and the temperature is the x-axis. The value of the free energy in the first change curve is calculated by the following formula:

[0088]

[0089] In the formula, F(T;V) represents the free energy under the temperature T and the crystal volume V, T represents the temperature, g(v) represents the phonon state density function, h represents the Planck constant, k represents the Boltzmann constant, and v represents the average propagation speed of the sound wave in the metal crystal to be measured.B This represents the Boltzmann constant.

[0090] Based on the preset Debye model, the phonon spectrum data, and the first Debye frequency, several second variation curves of the free energy of the metal crystal under test as a function of temperature and the first Debye frequency are calculated at different densities.

[0091] Based on several first variation curves and several second variation curves, the Debye temperature values ​​of the metal crystal under test at different densities are calculated.

[0092] Based on the Debye temperature value and the corresponding density, the Green's Eisen coefficient values ​​for different densities were calculated.

[0093] Specifically, after obtaining the Debye temperature values ​​at different densities, the Green's coefficient value can be calculated by mathematically differentiating the derivative of the Debye temperature with respect to density using the definition formula of the Green's coefficient.

[0094]

[0095] In the formula, γ s This represents the Green's coefficient value. Let θ represent the differential operator, Θ represent the Debye temperature, and ρ represent the density.

[0096] Preferably, after calculating the Green's Eisen coefficient values ​​at different densities, the relationship curve between the Green's Eisen coefficient and density can be derived. Then, a quadratic function is used for fitting to obtain an analytical expression for the Green's Eisen coefficient and density. During the fitting process, known boundary conditions are used for parameter calibration, such as the constant term at zero density and the first derivative value at the reference density point. Furthermore, the parameters of the fitting function are optimized to ensure that the function accurately describes the variation of the Green's Eisen coefficient within the actual physical range. After fitting, the results can be visualized for subsequent use.

[0097] In this preferred embodiment, the Debye temperature and Green's coefficient at different densities are calculated based on phonon spectrum data, density, and a preset Debye model.

[0098] In another preferred embodiment, calculating the Debye temperature values ​​of the metal crystal under test at different densities based on a plurality of first variation curves and a plurality of second variation curves includes:

[0099] For each density, construct a difference function for the difference in free energy between the second variation curve and the first variation curve;

[0100] Specifically, the difference function is shown in the following formula:

[0101]

[0102] In the formula, F D (T;V) represents the free energy corresponding to the second change curve, F ph (T;V) represents the free energy corresponding to the first change curve.

[0103] The difference function is solved by using the least square method to obtain the first Debye frequency at which the difference in free energy is the smallest, and then the Debye frequency values at different densities are obtained according to a plurality of the first Debye frequencies.

[0104] Specifically, the least square method is used to minimize the difference between the free energy calculated by the Debye model and the free energy obtained from the first change curve, that is, the first Debye frequency at which the value of the second norm of the difference function is the smallest is taken as the Debye frequency value. Then, the least square method is used to associate the phonon spectrum data with the density to obtain a relationship between the Debye frequency and the density, and finally the Debye temperature curve with the density is further calculated according to the Debye temperature formula.

[0105] The product of the Debye frequency value and the preset Planck constant is calculated to obtain the Debye temperature value at the different densities.

[0106] Specifically, the Debye temperature value corresponding to each density point is calculated by the Debye temperature formula, and a complete curve is arranged. The Debye temperature value is calculated by the following Debye temperature formula:

[0107] Θ = hv Θ

[0108] In the formula, Θ represents the Debye temperature value, h represents the Planck constant, and v Θ represents the Debye frequency value.

[0109] Preferably, the calculation result of the Debye temperature value is visualized to verify its physical reasonableness. In order to improve the accuracy of the curve, the known experimental data can be combined for calibration, and finally a high-precision curve of the Debye temperature value changing with the density is obtained.

[0110] In this preferred embodiment, the Debye temperature values of the metal crystal to be measured at different densities are calculated by the first change curve and the second change curve.

[0111] Step S105: According to the different density values of the Green-Eisen coefficient, the melting temperature values of the metal crystal to be measured at different densities are calculated.

[0112] Specifically, after obtaining the relationship between the Gruneisen coefficient and the density, the Lindemann melting law is used to derive the curve of the melting temperature changing with the density. First, the Gruneisen coefficient curve is substituted into the Lindemann melting formula, and the elastic modulus and vibration frequency parameters of the material are combined to derive the relationship between the melting temperature and the density. After sorting the Gruneisen coefficient values using the Lindemann melting law, the following can be obtained:

[0113] 1+γ F =3γ s

[0114] In the formula, γ F is a parameter representing the sensitivity of the melting temperature to the density (or volume), which is very important in constructing high-temperature and high-pressure equations of state, simulating material phase transitions, and estimating liquid thermodynamic properties. γ s represents the Gruneisen coefficient.

[0115] Specifically, the Lindemann melting formula derived using the Lindemann melting law is as follows:

[0116] T m (ρ) / Θ(ρ)=α / ρ 2 / 3

[0117] In the formula, T m (ρ) represents the melting temperature value corresponding to the density ρ, Θ(ρ) represents the Debye temperature value corresponding to the density ρ, and α represents a parameter related to the metal crystal material, including the elastic modulus and vibration frequency parameters.

[0118] Specifically, the constant term in the formula is calculated by numerical integration, and these integral constants are provided by the reference melting temperature calculated by DFT. The melting temperature formula is sorted, and the numerical value of the melting temperature at different densities is calculated. The melting temperature value is calculated by the following formula:

[0119]

[0120] Preferably, after obtaining the melting temperature values at different densities, the complete melting temperature curve can be sorted. By comparing with the experimental measurement values, the melting temperature formula is adjusted and corrected to ensure that the calculation results are consistent with the actual situation. The sorted melting temperature curve provides key input parameters for subsequent correction of the equation of state.

[0121] Step S106: fitting a corrected equation of state according to the Debye temperature value, the Gruneisen coefficient value, and the melting temperature value;

[0122] In a preferred embodiment, the fitting of the corrected equation of state according to the Debye temperature value, the Gruneisen coefficient value, and the melting temperature value comprises:

[0123] obtaining a preset to-be-fitted Debye temperature calculation formula, a preset to-be-fitted Grüneisen coefficient calculation formula, and a preset to-be-fitted melting temperature calculation formula;

[0124] Specifically, the preset to-be-fitted Debye temperature calculation formula is:

[0125]

[0126] In the formula, Θ s represents a reference Debye temperature under a preset reference density, x represents a ratio of density to the preset reference density, and ρ s represents the preset reference density, and A, B, C, D, E, and F are all to-be-fitted fitting parameter values.

[0127] Specifically, the preset to-be-fitted Grüneisen coefficient calculation formula is:

[0128]

[0129] Specifically, the preset to-be-fitted melting temperature calculation formula is:

[0130]

[0131] Specifically, the preset to-be-fitted Grüneisen coefficient calculation formula can be constructed based on experimental data. After the preset to-be-fitted Grüneisen coefficient calculation formula is determined, the preset to-be-fitted Debye temperature calculation formula and the preset to-be-fitted melting temperature calculation formula can be constructed based on the relationship among the three, on the basis of the preset to-be-fitted Grüneisen coefficient calculation formula. When fitting and solving, γ s determines the constant term of the quadratic function, and γ s determines the constant term of the quadratic function, and γ s determines the constant term of the quadratic function, and γ

[0132] The Debye temperature values under the different densities are substituted into the Debye temperature calculation formula for fitting, the Grüneisen coefficient values under the different densities are substituted into the Grüneisen coefficient calculation formula for fitting, and the melting temperature values under the different densities are substituted into the melting temperature calculation formula for fitting, to determine the fitting parameter values in the Debye temperature calculation formula, the Grüneisen coefficient calculation formula, and the melting temperature calculation formula.

[0133] According to the fitting parameter value, the Debye temperature calculation formula, the Gruneisen coefficient calculation formula, and the melting temperature calculation formula, a corrected Debye temperature calculation formula, a corrected Gruneisen coefficient calculation formula, and a corrected melting temperature calculation formula are generated.

[0134] According to the corrected Debye temperature calculation formula, the Debye temperature calculation formula in the preset traditional equation of state is replaced, according to the corrected Gruneisen coefficient calculation formula, the Gruneisen coefficient calculation formula in the preset traditional equation of state is replaced, and according to the corrected melting temperature calculation formula, the melting temperature calculation formula in the preset traditional equation of state is replaced, to obtain a corrected equation of state.

[0135] Specifically, the preset traditional equation of state is a state equation in the prior art, and the Debye temperature calculation formula in the preset traditional equation of state is:

[0136]

[0137] In the formula, Z represents a fitting parameter in the Debye temperature calculation formula in the preset traditional equation of state, and b is an intermediate quantity.

[0138] Specifically, the Gruneisen coefficient calculation formula in the preset traditional equation of state is:

[0139]

[0140] Specifically, the melting temperature calculation formula in the preset traditional equation of state is:

[0141]

[0142] Preferably, the preset traditional equation of state often relies on empirical formulas and simplified physical assumptions, and is prone to produce large prediction errors, especially under high temperature and high pressure conditions. However, the present application combines density functional theory (DFT) with the equation of state, and uses the first-principles calculation in the DFT optimization to obtain the phonon spectrum data of the metal crystal, and then obtains the Gruneisen coefficient and the Debye temperature, so as to accurately describe the thermodynamic behavior of the metal. Unlike the limitations of traditional methods relying on experimental data, the present application is based on the relationship between the phonon spectrum data and the Debye temperature obtained by DFT calculation and the change of density, which can provide more accurate theoretical basis for thermodynamic parameters such as melting temperature and thermal expansion behavior. Especially in the calculation of the Gruneisen coefficient, the present application innovatively uses the least square method to fit the curve of the change of the Gruneisen coefficient with the density, thereby avoiding the error of the traditional empirical method under extreme conditions. This first-principles-based calculation method makes the corrected equation of state not only have high physical rationality, but also can provide more accurate prediction under high temperature and high pressure conditions.

[0143] In this preferred embodiment, the preset correlation calculation formula to be fitted is fitted and corrected according to the Debye temperature value, the Gruneisen coefficient value and the melting temperature value under different densities, and the relevant calculation formula in the state equation is replaced according to the corrected calculation formula, so as to obtain the corrected state equation.

[0144] Step S107: predicting the crystal state of the metal crystal to be measured according to the corrected state equation and the different densities.

[0145] Specifically, the crystal state includes pressure.

[0146] In a preferred embodiment, the predicting the crystal state of the metal crystal to be measured according to the corrected state equation and the different densities comprises:

[0147] calculating the free energy of the metal crystal to be measured under different densities according to the corrected state equation and the different densities;

[0148] Specifically, for the corrected state equation, except for the calculation formula replaced in the present application, it is the same as the state equation in the prior art.

[0149] calculating the crystal state of the metal crystal to be measured under different densities according to the free energy.

[0150] Specifically, the pressure of the metal crystal to be measured under different densities is calculated by the following formula:

[0151]

[0152] In the formula, P(V, T) represents the pressure under temperature T and crystal volume V, and F represents the free energy.

[0153] Specifically, based on the corrected state equation of the present application, the schematic diagram of the pressure-density curve at a temperature of 8000K is as shown in Figure 2 In Figure 2 , the horizontal axis is density, and the vertical axis is pressure. Based on the preset conventional state equation, the schematic diagram of the pressure-density curve at a temperature of 8000K is as shown in Figure 3 In Figure 3 , the horizontal axis is density, and the vertical axis is pressure. By consulting the literature, it can be known that when the temperature is 8000K and the density is 10(g / cm 3 ), the actual pressure should be 61.64GPA. By comparing Figure 2 and Figure 3 , it can be found that when the temperature is 8000K and the density is 10(g / cm 3) is 53.12 GPA, while the pressure obtained based on the modified state equation of the application is 58.31 GPA under the same temperature and density, which is closer to the actual pressure recorded in the literature, and the accuracy of the pressure is improved. The schematic diagram of the actual pressure recorded in the literature as a function of density at different temperatures is shown in Figure 4 , Figure 4 The horizontal axis in the figure is density, with a unit of g / cm 3 , and the vertical axis is pressure, with a unit of GPa.

[0154] Preferably, the prediction of the crystal state by the modified state equation seamlessly connects the theoretical calculation and numerical simulation, ensuring the high reliability and accuracy of the results. The prediction results can also be used to draw and optimize the metal phase diagram, improving the accuracy of the metal phase diagram and enhancing the prediction of material performance under extreme conditions, providing a more reliable theoretical basis for material design. At the same time, the crystal state prediction method of the application can be widely applied in the fields of material science, energy engineering, aerospace, etc., promoting the development and optimization of new metal materials.

[0155] Preferably, in actual calculation, the calculation process in the application can be converted into program code to automate the calculation and data processing process, making the application of the method more efficient and operable. Specifically, first, a script is designed to read the output file of the phonon spectrum data calculated by the VASP software, automatically extracting the phonon spectrum data and dynamic force constant matrix. Second, numerical fitting algorithm is used to calculate the Debye frequency, Debye temperature and Gruneisen coefficient, and the calculation results are saved as visual charts and data files. Third, the code is designed to automatically input these data into the module for modifying the state equation, and the related formula for the free energy contribution of ions in the state equation is modified.

[0156] Preferably, in the modification of the preset conventional state equation, the Gruneisen coefficient and melting temperature data obtained based on DFT are used to significantly improve the accuracy of the free energy contribution of ions, and thus improve the prediction ability of the metal state equation. Compared with the preset conventional state equation, the modified state equation can more accurately simulate the thermodynamic properties of metals under extreme conditions, especially the performance under high pressure and high temperature environment. In summary, the method of the application overcomes the limitations of traditional methods by introducing more accurate calculation models and automation tools, providing a more reliable and effective improvement scheme for metal state equation, which has wide application prospects and far-reaching technical significance.

[0157] Preferably, the modified equation of state can also be used to further determine the stable phase of the metal crystal at different temperatures and pressures, the phase transition pressure, the melting point curve, and the three-phase point and other key thermodynamic parameters, and thus the further material science and basic physics research on various known or unknown metal crystals can be better performed to explain the physical behavior of the metal under extreme environments.

[0158] In this preferred embodiment, the pressure in the crystal state of the metal crystal to be measured is predicted by the modified equation of state and different densities.

[0159] On the basis of the above-mentioned method embodiment, the application correspondingly provides a device embodiment.

[0160] As Figure 5 shown, on the basis of the above-mentioned method embodiment, a corresponding device embodiment is provided;

[0161] The cell structure parameter acquisition module, the target cell structure data determination module, the phonon spectrum data calculation module, the Debye temperature value and the Grüneisen coefficient value calculation module, the melting temperature value calculation module, the equation of state correction module, and the crystal state prediction module are provided.

[0162] The cell structure parameter acquisition module is configured to acquire preset initial cell structure parameters of the metal crystal to be measured at different densities.

[0163] The target cell structure data determination module is configured to perform DFT optimization on the metal crystal to be measured according to the preset initial cell structure parameters for each density to obtain target cell structure data of each density at a minimum crystal energy.

[0164] The phonon spectrum data calculation module is configured to construct a dynamic force constant matrix according to each target cell structure data, and calculate phonon spectrum data of the metal crystal to be measured at different densities according to the dynamic force constant matrix.

[0165] The Debye temperature value and the Grüneisen coefficient value calculation module is configured to calculate the Debye temperature value and the Grüneisen coefficient value of the metal crystal to be measured at different densities according to the phonon spectrum data, the different densities, and a preset Debye model.

[0166] The melting temperature value calculation module is configured to calculate the melting temperature value of the metal crystal to be measured at different densities according to the Grüneisen coefficient value at the different densities.

[0167] The equation of state correction module is configured to fit a modified equation of state according to the Debye temperature value, the Grüneisen coefficient value, and the melting temperature value.

[0168] The crystal state prediction module is configured to predict a crystal state of the metal crystal under test according to the modified equation of state and the different densities.

[0169] Further, the Debye temperature value and Grüneisen coefficient value calculation module comprises:

[0170] a crystal data acquisition unit, a first change curve calculation unit, a second change curve calculation unit, a Debye temperature value determination unit, and a Grüneisen coefficient value determination unit.

[0171] The crystal data acquisition unit is configured to acquire a crystal volume, an atomic number, and a first Debye frequency at the different densities of the metal crystal under test.

[0172] The first change curve calculation unit is configured to calculate a first change curve of free energy change with temperature at different densities according to the phonon spectrum data, the crystal volume, and the atomic number.

[0173] The second change curve calculation unit is configured to calculate a second change curve of free energy of the metal crystal under test with temperature and the first Debye frequency at different densities according to the preset Debye model, the phonon spectrum data, and the first Debye frequency.

[0174] The Debye temperature value determination unit is configured to calculate the Debye temperature value of the metal crystal under test at the different densities according to the first change curves and the second change curves.

[0175] The Grüneisen coefficient value determination unit is configured to calculate the Grüneisen coefficient value at different densities according to the Debye temperature value and the corresponding density.

[0176] Further, the Debye temperature value determination unit comprises:

[0177] a difference function construction subunit, a difference function solving subunit, and a Debye frequency value calculation subunit.

[0178] The difference function construction subunit is configured to construct, for each density, a difference function of the difference between the free energy of the second change curve and the first change curve.

[0179] The difference function solving subunit is configured to solve the difference function by using a least square method to obtain the first Debye frequency at the minimum difference of free energy, and then obtain the Debye frequency value at the different densities according to the first Debye frequencies.

[0180] The Debye frequency value calculation subunit is configured to calculate the product of the Debye frequency value and a preset Planck constant to obtain a Debye temperature value at the different densities.

[0181] It should be noted that the apparatus embodiments described above are merely illustrative, and the modules described above as separate components can or can not be physically separated, and the components shown as modules can or can not be physical modules, i.e., can be located in one place or distributed on multiple network units. Part or all of the modules can be selected to achieve the purpose of the embodiment according to actual needs. In addition, the connection relationship between the modules in the apparatus embodiments provided by the present application indicates that there is a communication connection between them, which can be implemented as one or more communication buses or signal lines. Those skilled in the art can understand and implement it without creative labor. The above schematic diagram is only an example of a crystal state prediction device based on a modified state equation, and does not constitute a limitation on a crystal state prediction device based on a modified state equation, and can include more or fewer components than the diagram, or combine certain components, or different components.

[0182] On the basis of the above-mentioned method embodiment, the present application correspondingly provides a terminal device embodiment.

[0183] Another embodiment of the present application provides a terminal device, comprising a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor executes the computer program to realize the method for predicting the crystal state based on the modified state equation according to any one of the embodiments of the present application.

[0184] For example, in this embodiment, the computer program can be divided into one or more modules, and the one or more modules are stored in the memory and executed by the processor to complete the present application. The one or more modules can be a series of computer program instruction segments capable of completing a specific function, which are used to describe the execution process of the computer program in the device.

[0185] The terminal device can be a desktop computer, a notebook computer, a palm computer, a cloud server, and other computing devices. The device can include, but is not limited to, a processor and a memory.

[0186] The processor can be a central processing module (CPU), and can also be other general-purpose processors, digital signal processors (DSP), application specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or can also be any conventional processor, etc. The processor is a control center of the device, and is connected with various parts of the device through various interfaces and lines.

[0187] The memory can be used to store the computer program and / or the module, and the processor realizes various functions of the device by running or executing the computer program and / or the module stored in the memory and calling the data stored in the memory. The memory can mainly include a program storage area and a data storage area, wherein the program storage area can store an operating system, at least one application required by a function, etc.; in addition, the memory can include a high-speed random access memory, and can also include a nonvolatile memory, for example, a hard disk, a memory, a plug-in hard disk, a smart media card (SMC), a secure digital (SD) card, a flash card, at least one disk storage device, a flash memory device, or other volatile solid-state memory devices.

[0188] On the basis of the method embodiment, the application provides a storage medium embodiment.

[0189] Another embodiment of the application provides a storage medium, which includes a stored computer program, wherein the computer program controls a device where the storage medium is located to execute the crystal state prediction method based on a modified equation of state according to any one of the embodiments of the application when the computer program is running.

[0190] In this embodiment, the storage medium is a computer-readable storage medium, and the computer program includes computer program code, which may be in the form of source code, object code, executable file, or some intermediate form. The computer-readable medium may include any entity or device capable of carrying the computer program code, recording media, USB flash drive, portable hard drive, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc.

[0191] The above are preferred embodiments of the present invention. It should be noted that, for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A method for predicting the state of a crystal based on a modified equation of state, characterized in that, include: Obtain the preset initial unit cell structure parameters of the metal crystal under test at different densities; For each density, the DFT optimization is performed on the metal crystal under test according to the preset initial unit cell structure parameters to obtain the target unit cell structure data of each density at the minimum crystal energy. Based on the target cell structure data, each dynamic force constant matrix is ​​constructed, and based on the dynamic force constant matrix, the phonon spectrum data of the metal crystal under test at different densities is calculated. Based on the phonon spectrum data, the different densities, and the preset Debye model, the Debye temperature and Green's coefficient of the metal crystal under test are calculated at different densities. Based on the Green's coefficient values ​​at different densities, the melting temperatures of the metal crystal under test at different densities are calculated. Based on the Debye temperature value, the Green's coefficient value, and the melting temperature value, the corrected equation of state is fitted. Based on the corrected equation of state and the different densities, the crystal state of the metal crystal under test is predicted.

2. The crystal state prediction method based on a modified equation of state according to claim 1, characterized in that, The calculation of the Debye temperature and Green's coefficient of the tested metal crystal at different densities, based on the phonon spectrum data, the different densities, and the preset Debye model, includes: The crystal volume, number of atoms, and first Debye frequency at different densities of the metal crystal under test are obtained. Based on the phonon spectrum data, the crystal volume, and the number of atoms, the first variation curve of several free energies with temperature under different densities is calculated. Based on the preset Debye model, the phonon spectrum data, and the first Debye frequency, several second variation curves of the free energy of the metal crystal under test as a function of temperature and the first Debye frequency are calculated at different densities. Based on several first variation curves and several second variation curves, the Debye temperature values ​​of the metal crystal under test at different densities are calculated. Based on the Debye temperature value and the corresponding density, the Green's Eisen coefficient values ​​for different densities were calculated.

3. The crystal state prediction method based on a modified equation of state according to claim 2, characterized in that, The step of calculating the Debye temperature values ​​of the metal crystal under test at different densities based on a plurality of first variation curves and a plurality of second variation curves includes: For each density, construct a difference function for the difference in free energy between the second variation curve and the first variation curve; The difference function is solved using the least squares method to obtain the first Debye frequency when the difference in free energy is minimized. Then, based on several first Debye frequencies, the Debye frequency values ​​under different densities are obtained. The Debye temperature values ​​at different densities are obtained by calculating the product of the Debye frequency value and the preset Planck constant.

4. The crystal state prediction method based on the modified equation of state according to claim 3, characterized in that, The process of fitting the corrected equation of state based on the Debye temperature, the Green's coefficient, and the melting temperature includes: Obtain the preset formulas for calculating the Debye temperature, the Green's Eisen coefficient, and the melting temperature; The Debye temperature values ​​at different densities are substituted into the Debye temperature calculation formula for fitting, the Greenessen coefficient values ​​at different densities are substituted into the Greenessen coefficient calculation formula for fitting, and the melting temperature values ​​at different densities are substituted into the melting temperature calculation formula for fitting, thereby determining the Debye temperature calculation formula, the Greenessen coefficient calculation formula, and the fitting parameter values ​​in the melting temperature calculation formula. Based on the fitted parameter values, the Debye temperature calculation formula, the Greenessen coefficient calculation formula, and the melting temperature calculation formula, a modified Debye temperature calculation formula, a modified Greenessen coefficient calculation formula, and a modified melting temperature calculation formula are generated. Based on the modified Debye temperature calculation formula, the Debye temperature calculation formula in the preset traditional equation of state is replaced; based on the modified Greenessen coefficient calculation formula, the Greenessen coefficient calculation formula in the preset traditional equation of state is replaced; based on the modified melting temperature calculation formula, the melting temperature calculation formula in the preset traditional equation of state is replaced, thus obtaining the modified equation of state.

5. The crystal state prediction method based on the modified equation of state according to claim 4, characterized in that, The step of predicting the crystal state of the metal crystal under test based on the corrected equation of state and the different densities includes: Based on the corrected equation of state and the different densities, the free energy of the metal crystal under test at different densities was calculated. Based on the free energy, the crystal state of the metal crystal under different densities can be calculated.

6. A crystal state prediction device based on a modified equation of state, characterized in that, include: The module includes a cell structure parameter acquisition module, a target cell structure data determination module, a phonon spectrum data calculation module, a Debye temperature and Greensson coefficient calculation module, a melting temperature calculation module, a state equation correction module, and a crystal state prediction module. The cell structure parameter acquisition module is used to acquire the preset initial cell structure parameters of the metal crystal under test at different densities. The target cell structure data determination module is used to perform DFT optimization on the metal crystal under test for each density according to the preset initial cell structure parameters, so as to obtain the target cell structure data of each density at the minimum crystal energy. The phonon spectrum data calculation module is used to construct each dynamic force constant matrix based on the target cell structure data, and to calculate the phonon spectrum data of the metal crystal under test at different densities based on the dynamic force constant matrix. The Debye temperature and Green's coefficient calculation module is used to calculate the Debye temperature and Green's coefficient of the metal crystal under test at different densities based on the phonon spectrum data, the different densities, and the preset Debye model. The melting temperature calculation module is used to calculate the melting temperature of the metal crystal under test at different densities based on the Green's coefficient values ​​at different densities. The equation of state correction module is used to fit the corrected equation of state based on the Debye temperature value, the Green's coefficient value and the melting temperature value. The crystal state prediction module is used to predict the crystal state of the metal crystal under test based on the corrected state equation and the different densities.

7. A crystal state prediction device based on a modified equation of state according to claim 6, characterized in that, The module for calculating the Debye temperature and Green's coefficient includes: The system includes a crystal data acquisition unit, a first variation curve calculation unit, a second variation curve calculation unit, a Debye temperature value determination unit, and a Greenessen coefficient value determination unit. The crystal data acquisition unit is used to acquire the crystal volume, number of atoms, and first Debye frequency of the metal crystal under test at different densities; The first variation curve calculation unit is used to calculate, based on the phonon spectrum data, the crystal volume, and the number of atoms, a first variation curve of several free energies changing with temperature at different densities; The second variation curve calculation unit is used to calculate, based on the preset Debye model, the phonon spectrum data and the first Debye frequency, several second variation curves of the free energy of the metal crystal under test as a function of temperature and the first Debye frequency at different densities. The Debye temperature value determination unit is used to calculate the Debye temperature value of the metal crystal under test at different densities based on a plurality of first variation curves and a plurality of second variation curves. The Green's Eisen coefficient value determination unit is used to calculate the Green's Eisen coefficient value at different densities based on the Debye temperature value and the corresponding density.

8. A crystal state prediction device based on a modified equation of state according to claim 7, characterized in that, The Debye temperature value determination unit includes: Sub-units for constructing sub-units using difference functions, sub-units for solving difference functions, and sub-units for calculating Debye frequency values; The difference function construction sub-unit is used to construct a difference function for the difference between the free energy of the second variation curve and the first variation curve for each density. The difference function solving sub-unit is used to solve the difference function using the least squares method to obtain the first Debye frequency when the difference in free energy is minimized, and then, based on several first Debye frequencies, the Debye frequency values ​​under different densities are obtained. The Debye frequency calculation subunit is used to calculate the product of the Debye frequency value and the preset Planck constant to obtain the Debye temperature value at the different densities.

9. A terminal device, characterized in that, The system includes a processor, a memory, and a computer program stored in the memory and configured to be executed by the processor, wherein the processor, when executing the computer program, implements a crystal state prediction method based on a modified state equation as described in any one of claims 1 to 5.

10. A storage medium, characterized in that, The storage medium includes a stored computer program, wherein, when the computer program is executed, it controls the device where the storage medium is located to perform a crystal state prediction method based on a modified state equation as described in any one of claims 1 to 5.

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