CN118113969B

CN118113969B - Rapid calculation method of metal liquid phase state equation and electronic equipment

Info

Publication number: CN118113969B
Application number: CN202311834302.4A
Authority: CN
Inventors: 宋海峰; 方俊; 高兴誉; 咸家伟; 陈欣; 刘瑜; 刘海风; 赵艳红; 宋红州
Original assignee: INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS
Current assignee: INSTITUTE OF APPLIED PHYSICS AND COMPUTATIONAL MATHEMATICS
Priority date: 2023-12-28
Filing date: 2023-12-28
Publication date: 2024-10-18
Anticipated expiration: 2043-12-28
Also published as: CN118113969A

Abstract

The invention provides a rapid calculation method of a metal liquid phase physical equation and electronic equipment; wherein the method comprises the following steps: the melting equation is established based on the solid structure of the metal and the free energy of the solid phase Helmholtz, and the established melting equation considers the influence of different solid structures of the metal and different Groneisen coefficient theoretical models on a high-pressure melting line, so that the estimated confidence of the melting line is improved; in addition, carrying out self-consistent field iterative solution on the target equation to obtain a liquid-phase cold energy function to be quantified; in the self-consistent field iteration solution, a multi-step mixed scheme is adopted to realize the correction of the liquid-phase cold energy function, and compared with the single-step scheme adopted in the prior art, the self-consistent field iteration convergence is accelerated; and fitting the correction by adopting a specific cold energy object state equation model to obtain a new liquid phase cold energy function, so that the liquid phase cold energy function is prevented from generating non-physical behaviors in self-consistent field iteration, and the calculation precision and efficiency of the metal liquid phase object state equation are improved.

Description

Rapid calculation method of metal liquid phase state equation and electronic equipment

Technical Field

The invention relates to the technical field of state equations, in particular to a rapid calculation method of a metal liquid phase state equation and electronic equipment.

Background

The object state equation refers to the F (V, T) relation of a substance, namely the functional relation between the free energy F of Helmholtz and the volume V and the temperature T. Currently, there are two general methods for obtaining a metal liquid phase state equation: (1) The first method uses melting points (melting lines) under a plurality of pressures as constraint conditions, simulates a plurality of temperature and pressure states of a metal liquid phase through experimental measurement or first principle molecular dynamics, and then fits the state points under the constraint conditions to determine the parameters of an object state equation. Such methods face mainly the following challenges: the experimental cost of the metal liquid phase state under high pressure is higher; the first principle molecular dynamics simulation of the metal liquid phase needs to adopt a larger supercell to represent the liquid phase configuration, and the calculation cost is high; melting line constraints may make fitting of the object state equation parameters difficult, etc.; (2) The second method is based on melting line and solid free energy, and according to phase balance condition and liquid free energy model, an equation to be solved is established, and the unknown quantity (liquid phase static interaction, liquid phase cold energy for short) in the equation is directly calculated, so as to determine the liquid phase state equation. The method does not need to measure or simulate the thermodynamic state of the metal liquid phase, does not need to carry out the parameter fitting of an equation of the object state, and has the characteristics of low cost/expenditure and no fitting parameter; but face challenges including how to construct a suitable solid/liquid free energy model and how to effectively solve the nonlinear equations satisfied by liquid cold energy on a model-given basis. Therefore, how to calculate the metal liquid phase state equation rapidly is a problem to be solved.

Disclosure of Invention

In view of the above, the present invention aims to provide a method and an electronic device for rapidly calculating a metal liquid phase state equation, so as to alleviate the above problems and improve the calculation accuracy and efficiency of the metal liquid phase state equation.

In a first aspect, an embodiment of the present invention provides a method for rapidly calculating a metal liquid phase state equation, where the liquid phase state equation is:

Wherein the superscript l denotes the liquid phase, F ^l (V, T) is the free energy of the liquid phase Helmholtz in dependence on the volume V and the temperature T, Is a function of the cold energy of the liquid phase,In the case of an ion item,Is an electron term, -0.8k _B T is the melting entropy, and k _B is the boltzmann constant;

The liquid-phase cold energy function is used as a quantity to be quantified, and the determining step comprises the following steps:

Establishing a melting equation based on the known solid phase Helmholtz free energy of the metal and the solid structure of the metal, solving the melting equation to determine a melting line, and calculating the solid phase Gibbs free energy on the melting line;

establishing a target equation to be solved based on the conditions that solid phase and liquid phase Gibbs free energies are equal and the relation G (P, T) =f (V, T) +pv of Gibbs free energy G (P, T) and Helmholtz free energy F (V, T) on the melting line; the target equation is used for representing the corresponding relation between the free energy difference value between the solid-phase Gibbs free energy and the liquid-phase cold energy function, and P is pressure;

Carrying out self-consistent field iterative solution on the target equation to obtain the liquid-phase cold energy function to be quantified; wherein, in each iteration step, starting from the current liquid-phase cold energy function obtained in the current iteration step, calculating the current liquid-phase melting volume and the current liquid-phase Gibbs free energy at any melting point on the melting line, thereby obtaining a current Gibbs free energy difference value delta G (P, T _m(P))＝G^s(P,T_m(P))－G^l(P,T_m (P)) on the melting line, wherein the superscript s represents a solid phase, and T _m (P) is a melting temperature depending on the pressure P; and carrying out correction limited in a solid-phase melting volume interval on the current liquid-phase cold energy function based on the current delta G and the history information of the previous iteration step, obtaining the liquid-phase cold energy function for the new iteration step based on the correction, and entering the next iteration step; judging that when the modulus of the delta G is smaller than a preset convergence threshold, ending iteration and outputting a liquid-phase cold energy function at the moment as the liquid-phase cold energy function to be quantified;

In the correction of the self-consistent field iteration solution, a first updated liquid-phase cold energy function is obtained by adopting a mode of mixing input and output of the existing iteration step; further fitting the first updated liquid phase cold energy function to obtain a second updated liquid phase cold energy function, and taking the second updated liquid phase cold energy function as the liquid phase cold energy function for the new iteration step;

The method comprises the steps of obtaining a first updated liquid-phase cold energy function by adopting a mode of mixing a plurality of input and output of the existing iteration steps; and/or fitting the first updated liquid-phase cold energy function corresponding to the local correction in the solid-phase melting volume interval to obtain the second updated liquid-phase cold energy function.

Preferably, the method of mixing the input and output of a plurality of existing iteration steps is adopted to obtain the first updated liquid-phase cold energy function; and/or fitting the first updated liquid phase cold energy function corresponding to the local correction in the solid-phase melting volume interval to obtain the second updated liquid phase cold energy function, including:

Mixing the input and output of a plurality of existing iteration steps in the solid-phase melting volume interval by adopting an Anderson algorithm to obtain the first updated liquid-phase cold energy function;

and/or fitting the first updated liquid-phase cold energy function in the solid-phase melting volume interval by adopting a 4-order Poirier-Tarantola cold energy object state equation to obtain the second updated liquid-phase cold energy function.

Preferably, said establishing a melting equation based on the known solid phase Helmholtz free energy of the metal and the solid structure of the metal, solving said melting equation to determine a melting line, comprises:

And respectively establishing corresponding melting equations according to the high symmetrical structure or the low symmetrical structure of the solid structure of the metal, and solving the corresponding melting equations to determine melting lines.

Preferably, the solid structure according to the metal is a high symmetrical structure or a low symmetrical structure, and the corresponding melting equation is respectively established, which includes:

if the solid structure of the metal is a high symmetry structure, establishing a melting equation:

if the solid structure of the metal is a low symmetry structure, establishing a melting equation:

Wherein T _m denotes the melting temperature, C denotes the constant, V denotes the volume, R denotes the nearest neighbor atom distance corresponding to said volume V, F ^s(V,T_m) denotes the solid phase Helmholtz free energy in dependence of volume V and melting temperature T _m, η denotes the structural parameter, λ denotes the identification parameter, for characterizing the type of Groneisen coefficient theoretical model used for calculating the Groneisen coefficient.

Preferably, the value of λ includes: -1, 0 and 2, respectively representing the calculation of said gruneisen coefficients using a slave model, a DM model, a free volume model.

Preferably, before the steps of input and output of the existing iteration steps in the solid-phase melting volume interval are mixed by adopting the Anderson algorithm, if the current iteration step is not the 1 st iteration step, the step of converting the current Gibbs free energy difference Δg to a fixed volume point is firstly implemented, and includes:

taking the fixed volume point as the solid phase melting volume corresponding to each melting point on the melting line Wherein, A solid phase melting volume corresponding to a melting temperature T _m (P) dependent on a pressure P;

based on the current Gibbs free energy difference value delta G and the current liquid phase cold energy function, calculating Wherein, A liquid phase melting volume corresponding to a melting temperature T _m (P) depending on the pressure P;

Fitting data points using Birch-Murnaghan or Poirier-Tarantola model To determine a fitting functionThen calculateTo obtain a fixed volume pointThe Gibbs free energy difference of (c) to complete the conversion.

Preferably, the mixing the input and output of the plurality of existing iteration steps in the solid-phase melting volume interval by adopting the Anderson algorithm comprises:

setting the current iteration step as an nth step, wherein n is an integer more than or equal to 1; s is a preset step number, and an integer more than 1 is taken;

If n is more than or equal to s, mixing the liquid-phase cold energy from the current iteration step to the previous step and the value of delta G on the solid-phase melting volume according to an Anderson algorithm to obtain the first updated liquid-phase cold energy function;

If n < s, mixing the liquid phase cold energy of the previous n steps from the current iteration step and the value of delta G on the solid phase melting volume according to the Anderson algorithm to obtain the first updated liquid phase cold energy function.

Preferably, said mixing of the liquid phase cold energy and the value of Δg over the solid phase melt volume from the current iteration step to the preceding s steps according to the Anderson algorithm to obtain said first updated liquid phase cold energy function comprises:

the value of the liquid-phase cold energy in the solid-phase melting volume from the current iteration step to the previous step is denoted as x _n,x_n-1,…,x_n-s+1, the value of the delta G in the solid-phase melting volume from the current iteration step to the previous step is denoted as F _n,F_n-1,…,F_n-s+1, and the first updated liquid-phase cold energy function is denoted as x _n+1;

x _n+1 is denoted as Wherein alpha represents a mixing coefficient,AndExpressed as:

And

Wherein, the combination coefficient β _i is determined by solving the equation set aβ=b, the matrix element of a is a _ij＝(F_n-F_n-i,F_n-F_n-j), and the component of the vector b is b _i＝(F_n-F_n-i,F_n); i, j=1, …, s-1.

Preferably, the fitting the first updated liquid-phase cold energy function in the solid-phase melting volume interval by using a 4-order Poirier-Tarantola cold energy state equation to obtain the second updated liquid-phase cold energy function includes:

taking as a fitting input data points mixed by the Anderson algorithm and limited to the solid phase melting volume interval, the data points being expressed as Wherein, A solid phase melting volume corresponding to a melting temperature T _m (P) dependent on a pressure P;

Using a 4-order Poirier-Tarantola cold energy object state equation as a fitting function to fit and output the second updated liquid-phase cold energy function, and using the second updated liquid-phase cold energy function as the liquid-phase cold energy function for the new iteration step; and the value interval of the liquid-phase cold energy function for the new iteration step is a cold energy volume interval required by constructing an average field potential model.

In a second aspect, an embodiment of the present invention provides an electronic device, including a memory, a processor, and a computer program stored in the memory and capable of running on the processor, where the processor implements the steps of the method for quickly calculating a metal liquid phase state equation of the first aspect when the processor executes the computer program.

The embodiment of the invention has the following beneficial effects:

The embodiment of the invention provides a rapid calculation method of a metal liquid phase state equation and electronic equipment, wherein firstly, a melting equation is established based on solid phase Helmholtz free energy and a solid structure of metal, a melting equation is solved to determine a melting line, and solid phase Gibbs free energy on the melting line is calculated; then, establishing a target equation to be solved based on the conditions that the solid phase and the liquid phase on the melting line are equal in Gibbs free energy and the relation between the Gibbs free energy and Helmholtz free energy; and finally, carrying out self-consistent field iterative solution on the target equation to obtain a liquid-phase cold energy function to be quantified, carrying out correction limited in a solid-phase melting volume interval on the current liquid-phase cold energy function based on the current delta G and the history information of the previous iteration step in each iteration step, obtaining the liquid-phase cold energy function for a new iteration step based on the correction, and entering the next iteration step until the modulus of the delta G is smaller than a preset convergence threshold. In the calculation method, the established melting equation considers the influence of different metal solid structures and different Groneisen coefficient theoretical models on the high-pressure melting line, and compared with the prior art, the confidence coefficient of the melting line estimation is improved; compared with a single-step scheme adopted in the prior art, the method adopts a multi-step mixed scheme to realize the correction of the liquid-phase cold energy function, and accelerates the iterative convergence of the self-consistent field; and adopting a specific cold energy object state equation model to fit the correction to obtain a new liquid phase cold energy function, compared with the prior art that the liquid phase cold energy function outside the melting volume interval is updated by adopting Gibbs free energy difference values at two ends of the melting line, the non-physical behavior of the liquid phase cold energy function in self-consistent field iteration is avoided, and therefore the calculation precision and efficiency of the metal liquid phase object state equation are improved.

Additional features and advantages of the invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. The objectives and other advantages of the invention will be realized and attained by the structure particularly pointed out in the written description and drawings.

In order to make the above objects, features and advantages of the present invention more comprehensible, preferred embodiments accompanied with figures are described in detail below.

Drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will briefly explain the drawings needed in the embodiments or the prior art, and it is obvious that the drawings in the following description are some embodiments of the present invention and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.

FIG. 1 is a flow chart of a self-consistent solution of the present liquid phase cold energy provided by an embodiment of the present invention;

FIG. 2 is a flow chart of a method for fast calculation of a metal liquid phase object state equation according to an embodiment of the present invention;

FIG. 3 is a flowchart of another method for fast calculation of a metal liquid phase object state equation according to an embodiment of the present invention;

FIG. 4 is a schematic diagram showing the result of predicting the high pressure melting line of metal aluminum in a face-centered cubic structure according to an embodiment of the present invention;

FIG. 5 is a schematic diagram of the results of a high pressure melting line for predicting closely packed hexagonal metallic beryllium according to an embodiment of the present invention;

FIG. 6 is a schematic diagram of self-consistent convergence of liquid phase cold energy for solving face-centered cubic structured metallic aluminum according to an embodiment of the present invention;

FIG. 7 is a schematic diagram of a result of solving the cold energy of a face-centered cubic structure of a liquid phase of metallic aluminum according to an embodiment of the present invention;

fig. 8 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.

Detailed Description

For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.

Aiming at a metal liquid phase state equation, the process of obtaining according to the second type of method is as follows:

(A1) Solid phase Helmholtz free energy model: without consideration of electroacoustic interactions or magnetic disorder, the Helmholtz free energy of the solid phase can be written in the form of three decompositions:

Wherein s represents a solid phase (solid), V represents a volume, T represents a temperature, Representing the cold energy term, i.e. the static interaction potential (ions are at lattice equilibrium),Representing the ion term, i.e., the contribution of the thermal motion of the ions (ions vibrating with respect to lattice position),Represents the contribution of an electron term, i.e., thermal excitation of an electron (ion is immobilized at a lattice equilibrium location).

The cold energy itemThe acquisition mode of (2) can be measured through static high-pressure experiments or calculated through a first principle. Ion itemCan be obtained using models, including but not limited to, a quasi-simple harmonic approximation, an average field potential (MFP) model, etc.; an average field potential model is used, for example, in which case the ion termThe expression of (2) is as follows:

Wherein k _B represents a Boltzmann constant, Representing the Planckian constant, T representing the temperature, m representing the ion mass, g (R, V) representing the average field potential, R representing the distance that a single atom deviates from the equilibrium position, and R representing the nearest neighbor atom distance corresponding to the volume V.

Further, the calculation formula of the average field potential g (r, V) is as follows:

Wherein R represents the distance of a single atom from the equilibrium position, E _c (R+r) represents the corresponding cold energy when the nearest neighbor atom distance is R+r, E _c (R-R) represents the corresponding cold energy when the nearest neighbor atom distance is R-R, and E _c (R) represents the corresponding cold energy when the nearest neighbor atom distance is R.

Electronic itemThe specific calculation formula of the integral function which can be expressed as the electron state density is as follows:

Where n ^s (e, V) represents the electron state density of the solid phase, k _B represents the boltzmann constant, f represents the Fermi-Dirac distribution function, and e _F represents the Fermi energy of the solid phase. In practice, the electron density and fermi energy of the solid phase can be calculated from the first principle.

(A2) Melting line estimation: if the first principle molecular dynamics method is adopted to calculate the high-pressure melting point, the calculation cost is high. The prior art scheme mainly establishes the following melting equation based on a solid phase Helmholtz free energy model:

wherein T _m represents the melting temperature, the constant C is determined according to the known melting point, and R represents the nearest neighbor atomic distance corresponding to the volume V.

In practical application, the step of solving the above melting equation (6) to obtain a melting line is as follows: for any given melting temperature T _m, solid-phase cold energy, electron state density and Fermi energy calculated based on a first principle are utilized to obtain solid-phase free energy F ^s(V,T_m) and partial derivatives thereof about R by utilizing a solid-phase Helmholtz free energy model of (A1), and a melting equation is solved on the basis to obtain a solid-phase melting volume corresponding to the melting temperature T _m Then, calculating the melting pressure P _m corresponding to the melting temperature T _m by using the following formula (7);

thus, one melting point (T _m,P_m) can be obtained, and a plurality of different melting points constitute a melting line.

(A3) Liquid phase Helmholtz free energy model: under certain assumptions, the Helmholtz free energy of the liquid phase can be written as a form of decomposition similar to that of the solid phase:

wherein l represents a liquid phase (liquid), The term-k _B Tlnw, which represents the static interaction potential of the liquid phase (abbreviated as liquid phase cold energy) and is more than the solid-phase decomposition form, is the melting entropy.

It should be noted that the existing studies show that the ionic and electronic items of the free energy of the liquid phase Helmholtz can take the same form as the solid phase, respectively. In particular, the ion term still employs an improved average field potential model. In the actual calculation of the liquid phase electronic term, the electron density and fermi energy of the solid phase can be directly used. The melting entropy is determined by taking lnw. Apprxeq.0.8. Thus, the only unknown in the liquid phase Helmholtz free energy resolved form is the liquid phase cold energy function.

(A4) The solution method of the liquid-phase cold energy function comprises the following steps: in the case of known melting lines, the liquid phase cold energy function can be solved according to the conditions that the solid phase and the liquid phase Gibbs free energy on the melting line are equal.

Specifically, gibbs free energy G (P, T) is a function of pressure P, temperature T, and Helmholtz free energy F (V, T) is related as follows:

G(P,T)＝F(V,T)+PV (9)

wherein, for the solid phase Gibbs free energy G ^s(P_m,T_m at any melting point (P _m,T_m) on the melting line, it can be calculated by the following steps:

① Based on solid-phase cold energy, electron state density and fermi energy, using the solid-phase Helmholtz free energy model in (A1) to obtain solid-phase Helmholtz free energy F ^s(V,T_m under temperature T _m;

② The solid phase Helmholtz free energy F ^s(V,T_m) under T _m is derived from the volume V to obtain the pressure-volume relationship under T _m, thereby determining the corresponding volume of P _m, namely the solid phase melting volume corresponding to the melting point (P _m,T_m)

③ Melting point (P _m,T_m) corresponding to the solid phase melting volumeAfter determination, the solid phase Gibbs free energy at the melting point (P _m,T_m) was calculated according to the following formula:

The conditions that the free energy of the solid phase and the free energy of the liquid phase on the melting line are equal establish a nonlinear equation about the cold energy function of the liquid phase, and the solving method is as follows: from an estimated liquid phase cold energy, a liquid phase melting volume at any melting point (P _m,T_m) on the melting line is calculated by adopting a similar step to a solid phase And a liquid phase Gibbs free energy G ^l(P_m,T_m), thereby obtaining a difference in solid and liquid phase Gibbs free energies on the melt line; wherein, the calculation formula of the difference between Gibbs free energy is as follows:

ΔG(P_m,T_m)＝G^s(P_m,T_m)－G^l(P_m,T_m) (11)

Wherein (P _m,T_m) represents any melting point.

And finally, carrying out local correction on the liquid-phase cold energy function based on the information (local meaning that the correction is limited to a melting volume interval), obtaining a new liquid-phase cold energy function based on the local correction, carrying out next iteration, and finally gradually obtaining the liquid-phase cold energy with a sufficiently small delta G module. This process is called self-consistent field (SCF) iterative solution of liquid phase cold energy.

It should be noted that the free energy of the solid phase Gibbs and the solid phase melt volume on the melt line remain unchanged throughout the self-consistent iterative solution.

(A5) Liquid phase cold energy calculation flow: specifically, as shown in fig. 1, the self-consistent solution flow of the existing liquid phase cooling energy includes the following steps:

Step S102, inputting solid-phase cold energy, electron state density and Fermi energy;

Step S104, estimating a melting line, and calculating solid-phase Gibbs free energy on the melting line;

Specifically, based on the input data and the average field potential model, solving a melting equation to obtain a melting line, and calculating solid-phase Gibbs free energy on the melting line; wherein, the estimation of the melting line is shown in the above (A2), and the calculation of the free energy of the solid Gibbs on the melting line is shown in the above (A4).

Step S106, initializing the difference delta G between the liquid-phase cold energy and the solid-liquid-phase Gibbs free energy on the melting line; wherein the liquid phase cooling energy is initialized to the solid phase cooling energy, the difference between the solid and liquid phase Gibbs free energies on the melting line is initialized to Δg (P _m,T_m)＝k_BT_m lnw, where (P _m,T_m) represents any melting point on the melting line, k _B represents boltzmann constant;

It should be noted that, since the initial liquid phase cooling energy is equal to the solid phase cooling energy, only the difference between the initial solid and liquid phase Helmholtz free energies F (V, T) remains in the melting entropy. The melting entropy is irrelevant to the volume V, so that the initial solid-liquid phase Helmholtz free energy F (V, T) is deflected to the volume V, the obtained pressure-volume relationship (P-V relationship) is the same, and the initial liquid phase melting volume is the same as the solid phase melting volume. In summary, initializing Δg leaves only the negative melting entropy term, i.e., initializing Δg (P _m,T_m)＝k_BT_m lnw.

Step S108, updating liquid phase cooling energy in a liquid phase melting volume interval by adopting a single-step mixing algorithm;

Specifically, the liquid phase cooling energy function within the liquid phase melting volume interval is updated as:

x_n+1＝x_n+α*F_n (12)

wherein x _n+1 represents the updated liquid phase cold energy function in the liquid phase melting volume interval, and x _n represents the liquid phase cold energy function of the nth step at the liquid phase melting volume point The vector composed of the values of the two phases F _n represents the vector composed of the difference delta G between the free energy of the solid phase Gibbs and the free energy of the liquid phase Gibbs at each melting point of the n step, alpha represents the preset mixing coefficient, and the value interval is (0, 1).

Step S110, updating liquid phase cold energy outside the liquid phase melting volume interval and on the cold energy volume interval based on delta G at two ends of the melting line; the self-consistent iteration step count n: =n+1.

The necessity of this step is that the cold energy value interval required for constructing the average field potential g (r, V) is larger than the melting volume interval, and the cold energy volume interval required for constructing the average field potential is referred to herein as [ V _min,V_max ], and is collectively referred to as the cold energy volume interval.

Therefore, in the prior art, Δg data at two ends of the nth melting line are respectively accumulated on the liquid-phase cold energy functions at the volumes of the two sides beyond the liquid-phase melting volume interval, so as to update the liquid-phase cold energy functions outside the liquid-phase melting volume interval and on the cold energy volume interval.

Step S112, updating the free energy of the liquid phase Gibbs on the melting line based on the average field potential model;

Specifically, based on the average field potential model and the updated liquid phase cold energy function, the liquid phase Gibbs free energy on the melting line is calculated, and then the difference delta G between the solid and liquid phase Gibbs free energy on the melting line is obtained.

Step S114, judging whether the mode of the delta G on the melting line is sufficiently small; specifically, whether the modulus of Δg is smaller than a preset convergence threshold is determined, if yes, step S116 is executed; if not, returning to the step S108;

step S116, outputting the current liquid-phase cold energy; and ending the self-consistent solving process.

The above-mentioned existing scheme can realize liquid phase cold energy calculation, but has the following problems:

(1) The existing scheme can realize the efficient calculation of the melting line, but has two problems in the confidence level; first, the influence of different Gruneisen coefficient theoretical models is not considered; the Gruneisen coefficient directly influences the slope of the melting line, and the prior art scheme uses the model of the Gruneisen coefficient (hereinafter referred to as the DM model) proposed by Dugdale and MacDonald, without taking into account the Slater model and the free volume model. Considering only a single model may be difficult to interpret the results of experimental measurements, nor is the uncertainty of theoretical predicted melt lines estimated. Second, the influence of structural parameters on the high-pressure melting line is not considered; the existing scheme is only suitable for systems with high-symmetry structures such as face-centered cubes and body-centered cubes, and cannot consider the influence of structural parameters which change along with the volume in low-symmetry structures such as close-packed hexagons on the high-pressure melting point;

(2) In mixing to update the liquid phase cooling energy function in the melt volume interval, a simple (linear) mixing scheme is employed. The scheme only mixes the input and the output of a single iteration step, is easy to realize, but cannot utilize the information of an earlier iteration step, so that the problem of slower self-consistent convergence speed is caused. In addition, in the self-consistent iterative solution process of the liquid-phase cold energy, the difference delta G between the free energy of the solid phase Gibbs and the free energy of the liquid phase Gibbs on the melting line corresponds to the current liquid-phase melting volume, and the liquid-phase melting volume is changed along with the change of the liquid-phase cold energy function in the iterative process, so that the implementation of a multi-step mixing scheme is difficult and complicated;

(3) When updating the liquid phase cooling energy outside the liquid phase melting volume interval and on the cooling energy volume interval, delta G data at two ends of a melting line are respectively accumulated to liquid phase cooling energy functions at the positions of two sides of the liquid phase melting volume interval. Through test analysis, errors accompanying the method can be gradually accumulated and diffused along with the self-consistent iterative process, so that the normal form of the liquid-phase cold energy function is destroyed, even the physical pre-judgment that the liquid-phase cold energy is wholly positioned above the solid-phase cold energy is not met, and finally, the self-consistent iterative errors are not reduced any more, and the liquid-phase cold energy calculation result is abnormal.

In order to solve the problems, the embodiment of the invention provides a rapid calculation method of a metal liquid phase state equation and electronic equipment, and the established melting equation considers the influence of different metal solid structures and different Groneisen coefficient theoretical models on a high-pressure melting line, so that compared with the prior art, the confidence of the estimation of the melting line is improved; compared with a single-step scheme adopted in the prior art, the method adopts a multi-step mixed scheme to realize the correction of the liquid-phase cold energy function, and accelerates the iterative convergence of the self-consistent field; and adopting a specific cold energy object state equation model to fit the correction to obtain a new liquid phase cold energy function, compared with the prior art that the liquid phase cold energy function outside the melting volume interval is updated by adopting Gibbs free energy difference values at two ends of the melting line, the non-physical behavior of the liquid phase cold energy function in self-consistent field iteration is avoided, and therefore the calculation precision and efficiency of the metal liquid phase object state equation are improved.

In order to facilitate understanding of the present embodiment, the following describes embodiments of the present invention in detail.

Embodiment one:

the embodiment of the invention provides a rapid calculation method of a metal liquid phase state equation, which is applied to electronic equipment such as a computer, and the rapid calculation method of the metal liquid phase state equation in the embodiment considers the liquid phase state equation in the following form:

Wherein the superscript l denotes the liquid phase, F ^l (V, T) is the free energy of the liquid phase Helmholtz in dependence on the volume V and the temperature T, Is a function of the cold energy of the liquid phase,In the case of an ion item,Is an electron term, -0.8k _B T is the melting entropy, and k _B is the boltzmann constant.

It should be noted that the ionic and electronic items of the free energy of Helmholtz in the liquid phase may be respectively in the same form as the solid phase; if the ion item still adopts an improved average field potential model, the electron state density and the fermi energy of the solid phase are directly used for calculating the liquid-phase electronic item, so that the liquid-phase object state equation is to be quantified as a liquid-phase cold energy function.

The flow chart of the rapid calculation method of the metal liquid phase physical equation shown in fig. 2 mainly describes the determination process of the liquid phase cold energy function; the method comprises the following steps:

Step S202, establishing a melting equation based on the known solid phase Helmholtz free energy of the metal and the solid structure of the metal, solving the melting equation to determine a melting line, and calculating the solid phase Gibbs free energy on the melting line;

Specifically, according to whether the solid structure of the metal is a high symmetrical structure or a low symmetrical structure, respectively, establishing a corresponding melting equation, and solving the corresponding melting equation to determine a melting line. Among them, highly symmetrical structures include, but are not limited to: face centered cubic, body centered cubic, etc., low symmetry structures include closely packed hexagons, etc.

If the solid structure of the metal is a high symmetrical structure, the established melting equation is as follows:

if the solid structure of the metal is a low symmetry structure, the established melting equation is as follows:

Wherein T _m denotes the melting temperature, C denotes the constant, V denotes the volume, R denotes the nearest neighbor atom distance corresponding to the volume V, F ^s(V,T_m) denotes the solid phase Helmholtz free energy depending on the volume V and the melting temperature T _m, η denotes the structural parameter, and varies with the change of the volume V, satisfying Lambda represents an identification parameter for characterizing the type of theoretical model of the gruneisen coefficient used for calculating the gruneisen coefficient. It should be noted that, the free energy of the solid phase Helmholtz known for the metal can be determined by referring to the foregoing formulas (1) - (5), and detailed descriptions of the embodiments of the present invention are omitted herein.

The value of λ includes: -1, 0 and 2, respectively, representing the calculation of said gruneisen coefficients using a slave model, a DM model, a free volume model, since the gruneisen coefficients are related to the melting slope, the uncertainty of the melting line estimate can be evaluated using different theoretical models of the gruneisen coefficients, and the accuracy of the estimate can be improved by appropriate choice of the parameter λ.

And, the above process of solving two melting equations to determine the melting line is similar to the existing scheme, and the main process is as follows: firstly, solid-phase cold energy, electron state density and fermi energy obtained based on a first principle are calculated, and a solid-phase Helmholtz free energy F ^s and partial derivatives thereof about a volume V are obtained by adopting a solid-phase Helmholtz free energy model described in (A1); secondly, performing cubic spline interpolation on the volumes V and R, and calculating derivatives through spline interpolation relationOn this basis, the melting equation is solved to determine the corresponding melting line.

It should be noted that, after determining the melting line, reference may be specifically made to the above (A4) for calculating the free energy of the solid phase Gibbs on the melting line, and the detailed description of the embodiments of the present invention is omitted here.

Therefore, the melting equation established by the embodiment of the invention considers the influence of different metal solid structures and different Gruneisen coefficient theoretical models on the high-pressure melting line, and compared with the prior art, the confidence of the estimation of the melting line is improved, so that the calculation accuracy of the liquid phase state equation is improved.

Step S204, establishing a target equation to be solved based on the condition that the solid phase and liquid phase Gibbs free energies are equal and the relation between Gibbs free energy G (P, T) and Helmholtz free energy F (V, T) on a melting line;

As can be seen from the formula (9), the relation between Gibbs free energy G (P, T) and Helmholtz free energy F (V, T) is G (P, T) =f (V, T) +pv, and the following objective equation to be solved is established by combining the conditions that solid phase and liquid phase Gibbs free energies on the melting line are equal:

Wherein P is pressure, G ^s(P,T_m (P)) represents solid phase Gibbs free energy, Representing the liquid phase melting volume corresponding to pressure P, T _m (P) representing the melting temperature corresponding to pressure P. Since the free energy of the solid phase Gibbs is known, the free energy of the liquid phase Gibbs is to be quantified as the part containing the liquid phase cold energy function, the above objective equation can be used to characterize the correspondence between the free energy difference Δg between the free energy of the solid phase Gibbs and the free energy of the liquid phase Gibbs and the liquid phase cold energy function.

And S206, carrying out self-consistent field iterative solution on the target equation to obtain a liquid-phase cold energy function to be quantified.

Specifically, in the self-consistent field iterative solving process, for each iteration step, calculating the current liquid phase melting volume and the current liquid phase Gibbs free energy at any melting point on the melting line from the current liquid phase cold energy function obtained in the current iteration step, thereby obtaining a current Gibbs free energy difference value delta G (P, T _m(P))＝G^s(P,T_m(P))－G^l(P,T_m (P)) on the melting line, wherein T _m (P) is the melting temperature depending on the pressure P; and carrying out correction limited in a solid-phase melting volume interval on the current liquid-phase cold energy function based on the current delta G and the history information of the previous iteration step, obtaining the liquid-phase cold energy function for the new iteration step based on the correction, and entering the next iteration step; and when judging that the modulus of the delta G is smaller than a preset convergence threshold, ending iteration and outputting the liquid-phase cold energy function at the moment as the liquid-phase cold energy function to be quantified.

In the correction of the self-consistent field iteration solution, a first updated liquid-phase cold energy function is obtained by adopting a mode of mixing input and output of the existing iteration step; and further fitting the first updated liquid phase cold energy function to obtain a second updated liquid phase cold energy function, and taking the second updated liquid phase cold energy function as the liquid phase cold energy function for the new iteration step.

Specifically, a first updated liquid-phase cold energy function is obtained by adopting a mode of mixing a plurality of input and output of the existing iteration steps; and/or fitting the first updated liquid phase cold energy function corresponding to the local correction in the solid-phase melting volume interval to obtain a second updated liquid phase cold energy function. Mixing input and output of a plurality of existing iteration steps in a solid-phase melting volume interval by adopting an Anderson algorithm to obtain a first updated liquid-phase cold energy function; and/or fitting a first updated liquid-phase cold energy function in the solid-phase melting volume interval by adopting a 4-order Poirier-Tarantola cold energy object state equation to obtain a second updated liquid-phase cold energy function.

The method comprises the steps of mixing input and output of a plurality of existing iteration steps in a solid-phase melting volume interval by adopting an Anderson algorithm to obtain a first updated liquid-phase cold energy function; mainly comprises two steps (S1) and (S2); wherein the processes of (S1) and (S2) are as follows:

(S1) if the current iteration step is not 1 (i.e. n+.1), firstly performing a conversion of the current Gibbs free energy difference Δg to a fixed volume point, i.e. a conversion of the current Δg from the liquid phase melt volume to the fixed volume point;

The necessity of the step (1) is that: the Anderson algorithm mixes the liquid phase cold energy and deltag of multiple self-consistent iterative steps, so these quantities need to be taken at a set of fixed volume points, which are taken as solid phase melt volumes by embodiments of the present invention. In particular, Δg calculated from the difference between the solid and liquid phases Gibbs free energy on the melt line corresponds to the current liquid phase melt volume, so when Δg does not reach the convergence threshold, and thus requires continuing the self-consistent iteration, to perform Anderson mixing, Δg needs to be first converted from the liquid phase melt volume to the solid phase melt volume (i.e., the fixed volume point).

Specifically, since Δg is different from cold energy, helmholtz free energy and the like, and fitting cannot be directly performed by using a physical equation model such as Birch-Murnaghan or Poirier-Tarantola and the like to realize conversion of a value point, the process of converting the current Δg from a liquid-phase melting volume to a fixed volume point in the embodiment of the invention is as follows:

① Taking the fixed volume point as the solid phase melting volume corresponding to each melting point on the melting line Wherein, A solid phase melting volume corresponding to a melting temperature T _m (P) dependent on a pressure P;

② Based on the current Gibbs free energy difference DeltaG and the current liquid phase cold energy function, calculation I.e. the value of the current liquid phase cold energy function on the liquid phase melting volumeAdding the calculated current Gibbs free energy difference value delta G (P, T _m (P)) of the current iteration step; wherein, A liquid phase melting volume corresponding to a melting temperature T _m (P) depending on the pressure P;

③ Fitting data points using Birch-Murnaghan or Poirier-Tarantola model To determine a fitting functionThen calculateTo obtain a fixed volume pointThe Gibbs free energy difference of (c) to complete the conversion.

Specifically, a standard cold energy state equation model is adopted, including but not limited to a 3-order or 4-order Birch-Murnaghan model, which is called BM3/BM4 for short; 3-or 4-stage Poirier-Tarantola model, PT3/PT4 for short, etc., fitting the data points obtained in ② above (the value point is on the current liquid phase melting volume)To determine a fitting functionThen the function obtained by fitting is valued on the solid phase melting volume, namelyFinally, willSubtracting the value of the current liquid phase cold energy function on the solid phase melting volumeTo obtain a Gibbs free energy difference ΔG corresponding to the solid phase melt volume to complete the desired conversion.

Note that, in the case of the 1 st iteration step (i.e., n=1), since the initial value of the liquid phase melting volume is the same as that of the solid phase, no conversion is required.

(S2) mixing input and output of a plurality of existing iteration steps in a solid-phase melting volume interval by adopting an Anderson algorithm to obtain a first updated liquid-phase cold energy function; according to an Anderson algorithm, mixing a liquid-phase cold energy function from the current iteration step to the previous step and a value of delta G on a solid-phase melting volume to update the liquid-phase cold energy function in a solid-phase melting volume interval to obtain a first updated liquid-phase cold energy function;

Specifically, the current iteration step is set as an nth step, and n is an integer more than or equal to 1; s is a preset step number, and an integer more than 1 is taken; in the iteration process, if n is more than or equal to s, mixing the liquid-phase cold energy from the current iteration step to the previous step and the value of delta G on the solid-phase melting volume according to an Anderson algorithm to obtain a first updated liquid-phase cold energy function; if n < s, mixing the liquid phase cold energy of the previous n steps from the current iteration step and the value of delta G on the solid phase melting volume according to the Anderson algorithm to obtain a first updated liquid phase cold energy function.

Illustratively, when mixing the liquid phase cold energy and the value of Δg over the solid phase melt volume from the current iteration step to the previous s steps according to the Anderson algorithm, the mixing process is as follows: the value of the liquid phase cooling energy in the solid phase melting volume from the current iteration step to the previous s steps is denoted as x _n,x_n-1,…,x_n-s+1, the value of Δg in the solid phase melting volume from the current iteration step to the previous s steps is denoted as F _n,F_n-1,…,F_n-s+1, that is, the vector composed of the values of the liquid phase cooling energy function in the solid phase melting volume is denoted by x, and the vector composed of the values of Δg in the solid phase melting volume is denoted by F.

Let the first updated liquid phase cold energy function be denoted as x _n+1, then the expression of x _n+1 is as follows:

Wherein alpha represents a mixing coefficient, the value range is (0, 1), AndExpressed as: And The combination coefficient beta _i is determined by solving the equation set Abeta=b, the matrix element of A is A _ij＝(F_n-F_n-i,F_n-F_n-j), and the component of the right-end term vector b of the equation set is b _i＝(F_n-F_n-i,F_n); i, j=1, …, s-1.

Therefore, compared with the single-step scheme adopted in the prior art, the embodiment of the invention can utilize the information of a plurality of iteration steps, thereby accelerating the self-consistent convergence process of the liquid-phase cold energy and further improving the calculation efficiency of the liquid-phase state equation.

Further, for the above-mentioned fitting of the first updated liquid phase cold energy function in the solid phase melting volume interval by using the 4-order Poirier-Tarantola cold energy object state equation, a second updated liquid phase cold energy function is obtained, and the fitting process is as follows: taking as a fitting input data points of the solid phase melt volume interval mixed by the Anderson algorithm, the data points being expressed asWherein, A solid phase melting volume corresponding to a melting temperature T _m (P) dependent on a pressure P; using a 4-order Poirier-Tarantola cold energy object state equation as a fitting function to fit and output a second updated liquid-phase cold energy function, and using the second updated liquid-phase cold energy function as a liquid-phase cold energy function for a new iteration step; the value interval of the liquid-phase cold energy function used for the new iteration step is a cold energy volume interval constructed by an average field potential model.

Specifically, from the foregoing, it is known that the cold energy volume interval [ V _min,V_max ] required for constructing the average field potential g (r, V) is larger than the solid/liquid phase melting volume interval, and thus, what way to obtain the liquid phase cold energy function outside the melting volume range is critical. According to the embodiment of the invention, a 4-order Poirier-Tarantola cold energy object state equation is adopted as a fitting function, the fitting input is data points which are mixed by an Anderson algorithm and are limited in a solid-phase melting volume interval, then a second updated liquid-phase cold energy function is obtained by taking the value of the fitting function, and the second updated liquid-phase cold energy function is a liquid-phase cold energy function on a cold energy volume interval [ V _min,V_max ] required by an average field potential g (r, V), so that the abnormal phenomenon that the liquid-phase cold energy gradually presents non-physical behaviors in an iteration process can be eliminated through the technology, and meanwhile, the self-consistent iteration process is enabled to be normally converged, and the calculation efficiency and the precision of the liquid-phase object state equation are further improved.

In summary, according to the rapid calculation method of the metal liquid phase state equation provided by the embodiment of the invention, the established melting equation considers the influence of different metal solid structures and different Groneisen coefficient theoretical models on a high-pressure melting line, and compared with the prior art, the confidence coefficient of the estimation of the melting line is improved; compared with a single-step scheme adopted in the prior art, the method adopts a multi-step mixed scheme to realize the correction of the liquid-phase cold energy function, and accelerates the iterative convergence of the self-consistent field; and adopting a specific cold energy object state equation model to fit the correction to obtain a new liquid phase cold energy function, compared with the prior art that the liquid phase cold energy function outside the melting volume interval is updated by adopting Gibbs free energy difference values at two ends of the melting line, the non-physical behavior of the liquid phase cold energy function in self-consistent field iteration is avoided, and therefore the calculation precision and efficiency of the metal liquid phase object state equation are improved.

Embodiment two:

based on the above embodiments, the embodiment of the present invention provides another fast calculation method of a metal liquid phase state equation, as shown in fig. 3, including the following steps:

Step S302, inputting solid-phase cold energy, electron state density and Fermi energy;

Step S304, estimating a melting line based on a solid structure of the metal, and calculating solid-phase Gibbs free energy on the melting line;

The foregoing embodiments may be referred to, and the embodiments of the present invention are not described in detail herein.

Step S306, initializing the difference delta G between the liquid-phase cold energy and the solid-liquid-phase Gibbs free energy on the melting line; wherein the liquid phase cold energy is initialized to the solid phase cold energy, the difference between the solid and liquid phase Gibbs free energies on the melting line is initialized to Δg (P _m,T_m)＝k_BT_m lnw, where (P _m,T_m) represents any melting point on the melting line, k _B represents boltzmann constant;

Step S308, updating liquid phase cooling energy in a solid phase melting volume interval by adopting an Anderson algorithm; the process of updating the liquid phase cooling energy by using the Anderson algorithm can refer to the foregoing embodiment, and the embodiment of the present invention is not described in detail herein;

Step S310, fitting liquid-phase cold energy in a solid-phase melting volume interval by using a PT4 object state equation model, and then taking a value of a fitting function to update the liquid-phase cold energy in the cold energy volume interval; fitting a PT4 object state equation model to a first updated liquid-phase cold energy function in a solid-phase melting volume interval, and taking a value of the fitted function to update the liquid-phase cold energy in the cold energy volume interval to obtain a second updated liquid-phase cold energy function, wherein the specific updating process can refer to the foregoing embodiment, and the detailed description of the embodiment of the invention is omitted;

step S312, updating the free energy of the liquid phase Gibbs on the melting line based on the average field potential model;

Step S314, judging whether the mode of the delta G on the melting line is sufficiently small; specifically, whether the modulus of Δg is smaller than a preset convergence threshold is determined, if yes, step S316 is executed; if not, returning to the step S308;

Step S316, outputting the current liquid-phase cold energy; and ending the self-consistent solving process.

Therefore, compared with the prior art in fig. 1, the main improvement points of the rapid calculation method of the metal liquid phase state equation provided by the embodiment of the invention include the following three aspects:

(1) In the prior art, a DM model is adopted to calculate the Groneisen coefficient, the high-pressure melting line of the metal aluminum with the face-centered cubic structure is estimated, as shown in figure 3, L1 represents the high-pressure melting line of the metal aluminum with the face-centered cubic structure estimated by adopting the DM model, L2 represents the high-pressure melting line of the metal aluminum with the face-centered cubic structure estimated by adopting a Slater model, L3 represents experimental measurement results, namely, a reference high-pressure melting line and five-pointed star represents a known melting point estimated to be adopted. In the pressure range of 100GPa-200GPa, the melting point temperature of L1 is obviously lower than that of L3 measured by experiments, and different Groneisen coefficient theoretical models can be considered by adopting the scheme in the embodiment of the application, for example, a Slater model is adopted, and the deviation between the high-pressure melting point theoretical estimated result and the experimental measurement result is obviously reduced according to the L2 and L3, so that the calculation accuracy of a liquid phase state equation is improved.

In addition, the prior art solution cannot consider the change of lattice parameter along with the volume, and as shown in fig. 4, L1 represents the high-pressure melting line of the close-packed hexagonal structure metal beryllium estimated by adopting the fixed structure parameter in the prior art solution, L2 represents the high-pressure melting line of the close-packed hexagonal structure metal estimated by adopting the structure parameter eta along with the change of the volume V in the embodiment of the application, L3 represents experimental measurement results, namely, the reference high-pressure melting line simulated by adopting first principle molecular dynamics, and five-pointed star represents the estimated known melting point. In the pressure range of 150GPa-500GPa, compared with L3, the melting point temperature of L1 is obviously higher; and, because the embodiment of the application considers the influence of the structural parameter change along with the volume on the high-pressure melting line, compared with L2 and L3, the deviation of the theoretical estimated result and the experimental measurement result of the high-pressure melting point is obviously reduced, thereby improving the calculation accuracy of the liquid phase state equation.

(2) The prior art adopts a simple (linear) mixing scheme, and the updating of the liquid phase cold energy only uses the result of a single iteration step. The embodiment of the invention applies the Anderson algorithm to self-consistent mixing, and can utilize the information of a plurality of iteration steps, thereby accelerating the self-consistent convergence process of the liquid phase cold energy.

Specifically, tests on the body-centered cubic structure metal beryllium and the face-centered cubic structure metal aluminum show that the Anderson mixing scheme (the iteration number s=5) can save more than one time compared with the self-consistent iteration convergence step number of the prior art scheme under the condition of adopting the same self-consistent convergence threshold value and the same mixing coefficient (alpha=0.4). Taking aluminum as an example, as shown in fig. 6, L1 represents a self-consistent convergence curve for solving the liquid-phase cold energy of aluminum by adopting an Anderson mixing algorithm, L2 represents a self-consistent convergence curve for solving the liquid-phase cold energy of aluminum by adopting an existing simple (linear) mixing scheme, the convergence threshold is 10 ^-4 eV, the convergence step number of L1 is 7 steps, and the convergence step number of L2 is 17 steps, so that the embodiment of the invention obviously improves the convergence speed of the self-consistent iteration by adopting the Anderson mixing algorithm, thereby improving the calculation efficiency of the liquid-phase state equation.

(3) In the prior art, delta G data at two ends of a melting line are adopted to update liquid-phase cold energy at the positions of the two sides exceeding a melting volume interval respectively, so that the normal form of the liquid-phase cold energy is destroyed. In the embodiment of the invention, a 4-order Poirier-Tarantola cold energy object state equation model is adopted to fit the updated liquid phase cold energy in the solid phase melting volume interval, and then the liquid phase cold energy in the whole cold energy volume interval [ V _min,V_max ] is obtained by taking the value of the fitting function, so that the non-physical behavior of the liquid phase cold energy function in the self-consistent field iteration can be avoided.

The result of solving the liquid-phase cold energy for the face-centered cubic structure metal aluminum is shown in fig. 7, wherein L1 represents the liquid-phase cold energy obtained by fitting the updated liquid-phase cold energy in the solid-phase melting volume interval by adopting a 4-order Poirier-Tarantola cold energy object state equation model; l2 represents liquid-phase cold energy obtained by extrapolation by adopting the prior art scheme, and L3 represents solid-phase cold energy; as can be seen from fig. 7, L1 is integrally located above L3, that is, the technical solution of the embodiment of the present application can obtain the liquid-phase cold energy with correct physical property, while L2 is lower than L1 in part of the volume, that is, the prior art solution causes abnormal liquid-phase cold energy results, which breaks the physical prognosis that the liquid-phase cold energy should be integrally located above the solid-phase cold energy. Therefore, the embodiment of the application adopts the 4-order Poirier-Tarantola cold energy object state equation model to fit the updated liquid phase cold energy in the solid phase melting volume interval, thereby avoiding the non-physical behavior of the liquid phase cold energy function in the self-consistent field iteration and further improving the calculation accuracy of the liquid phase object state equation.

In summary, the rapid calculation method of the metal liquid phase state equation provided by the embodiment of the invention has the following advantages: ① The established melting equation considers the influence of different metal solid structures, different Groneisen coefficient theoretical models and lattice parameters on a high-pressure melting line, and compared with the prior art, the confidence of the estimation of the melting line is improved; ② The Anderson algorithm is adopted to carry out self-consistent mixing of the liquid-phase cold energy, in particular, the volume point conversion technology required by the application of the Anderson algorithm is increased, and thus the self-consistent convergence process of the liquid-phase cold energy is accelerated exponentially; ③ The 4-order Poirier-Tarantola cold energy object state equation model fitting is adopted, so that the calculation of the liquid phase cold energy in the melting volume interval to the liquid phase cold energy in the cold energy volume interval required by the construction of the average field potential is realized, the non-physical behavior of the liquid phase cold energy caused by the prior art scheme is avoided, and the calculation precision and efficiency of the metal liquid phase object state equation are improved.

The embodiment of the invention also provides electronic equipment, which comprises a processor and a memory, wherein the memory stores machine executable instructions which can be executed by the processor, and the processor executes the machine executable instructions to realize the rapid calculation method of the metal liquid phase state equation.

Referring to fig. 8, the electronic device includes a processor 100 and a memory 101, the memory 101 storing machine executable instructions that can be executed by the processor 100, the processor 100 executing the machine executable instructions to implement the rapid calculation method of the metal liquid phase state equation described above.

Further, the electronic device shown in fig. 8 further includes a bus 102 and a communication interface 103, and the processor 100, the communication interface 103, and the memory 101 are connected through the bus 102.

The memory 101 may include a high-speed random access memory (RAM, random Access Memory), and may further include a non-volatile memory (non-volatile memory), such as at least one disk memory. The communication connection between the system network element and at least one other network element is implemented via at least one communication interface 103 (which may be wired or wireless), and may use the internet, a wide area network, a local network, a metropolitan area network, etc. Bus 102 may be an ISA (Industrial Standard Architecture, industry standard architecture) bus, PCI (PERIPHERAL COMPONENT INTERCONNECT, peripheral component interconnect standard) bus, or EISA (Enhanced Industry Standard Architecture, extended industry standard architecture) bus, among others. The buses may be classified into address buses, data buses, control buses, and the like. For ease of illustration, only one bi-directional arrow is shown in FIG. 8, but not only one bus or type of bus.

The processor 100 may be an integrated circuit chip with signal processing capabilities. In implementation, the steps of the above method may be performed by integrated logic circuits of hardware in the processor 100 or by instructions in the form of software. The processor 100 may be a general-purpose processor, including a central processing unit (Central Processing Unit, abbreviated as CPU), a network processor (Network Processor, abbreviated as NP), etc.; but may also be a digital signal Processor (DIGITAL SIGNAL Processor, DSP), application Specific Integrated Circuit (ASIC), field-Programmable gate array (FPGA) or other Programmable logic device, discrete gate or transistor logic device, discrete hardware components. The disclosed methods, steps, and logic blocks in the embodiments of the present invention may be implemented or performed. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like. The steps of the method disclosed in connection with the embodiments of the present invention may be embodied directly in the execution of a hardware decoding processor, or in the execution of a combination of hardware and software modules in a decoding processor. The software modules may be located in a random access memory, flash memory, read only memory, programmable read only memory, or electrically erasable programmable memory, registers, etc. as well known in the art. The storage medium is located in the memory 101, and the processor 100 reads the information in the memory 101 and, in combination with its hardware, performs the steps of the method of the previous embodiment.

The present embodiment also provides a machine-readable storage medium storing machine-executable instructions that, when invoked and executed by a processor, cause the processor to implement the fast calculation method of the metal liquid phase state equation.

The method for quickly calculating the metal liquid phase state equation and the computer program product of the electronic device provided by the embodiments of the present invention include a computer readable storage medium storing program codes, where the instructions included in the program codes may be used to execute the method described in the foregoing method embodiments, and specific implementation may refer to the method embodiments and are not repeated herein.

It will be clear to those skilled in the art that, for convenience and brevity of description, specific working procedures of the above-described system and apparatus may refer to corresponding procedures in the foregoing method embodiments, which are not described herein again.

In addition, in the description of embodiments of the present invention, unless explicitly stated and limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention will be understood in specific cases by those of ordinary skill in the art.

The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer readable storage medium executable by a processor. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.

In the description of the present invention, it should be noted that the directions or positional relationships indicated by the terms "center", "upper", "lower", "left", "right", "vertical", "horizontal", "inner", "outer", etc. are based on the directions or positional relationships shown in the drawings, are merely for convenience of describing the present invention and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.

Finally, it should be noted that: the above examples are only specific embodiments of the present invention, and are not intended to limit the scope of the present invention, but it should be understood by those skilled in the art that the present invention is not limited thereto, and that the present invention is described in detail with reference to the foregoing examples: any person skilled in the art may modify or easily conceive of the technical solution described in the foregoing embodiments, or perform equivalent substitution of some of the technical features, while remaining within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention, and are intended to be included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims

1. A rapid calculation method of a metal liquid phase state equation, wherein the liquid phase state equation is as follows:

The method is characterized in that the liquid-phase cold energy function is used as a quantity to be quantified, and the determining step comprises the following steps:

2. The method for rapidly calculating a metal liquid phase physical equation according to claim 1, wherein the first updated liquid phase cold energy function is obtained by mixing input and output of a plurality of existing iteration steps; and/or fitting the first updated liquid phase cold energy function corresponding to the local correction in the solid-phase melting volume interval to obtain the second updated liquid phase cold energy function, including:

3. The method of claim 2, wherein the establishing a melting equation based on the known solid phase Helmholtz free energy of the metal and the solid structure of the metal, solving the melting equation to determine a melting line, comprises:

4. The rapid calculation method of metal liquid phase physical equation according to claim 3, wherein the establishing the corresponding melting equation according to whether the solid structure of the metal is a high symmetry structure or a low symmetry structure comprises:

5. The method for rapid calculation of a metal liquid phase physical equation according to claim 4, wherein the value of λ comprises: -1, 0 and 2, respectively representing the calculation of said gruneisen coefficients using a slave model, a DM model, a free volume model.

6. The method according to claim 2, wherein before the step of mixing the input and output of the plurality of existing iteration steps in the solid-phase melting volume interval by using Anderson algorithm, if the current iteration step is not the 1 st iteration step, the step of converting the current Gibbs free energy difference Δg to a fixed volume point is performed first, including:

7. The method for rapid calculation of a metal liquid phase state equation according to any one of claims 2-6, wherein the mixing of the input and output of the plurality of existing iteration steps within the solid phase melting volume interval using the Anderson algorithm comprises:

8. The method according to claim 7, wherein the step of mixing the liquid phase cooling energy from the current iteration step to the previous step and the value of Δg on the solid phase melting volume according to the Anderson algorithm to obtain the first updated liquid phase cooling energy function comprises:

And

9. The method of claim 8, wherein fitting the first updated liquid phase cold energy function within the solid-phase melt volume interval to the second updated liquid phase cold energy function using a 4-order Poirier-Tarantola cold energy state equation comprises:

10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the steps of the method for fast calculation of a metal liquid phase state equation according to any of the preceding claims 1-9 when the computer program is executed by the processor.