Method for evaluating stability of corrosion-resistant material

Abstract

A method for evaluating stability of a corrosion-resistant material. The method is implemented by means of a damped Schrödinger equation transformed on the basis of a Mathieu equation. The damped Schrödinger equation transformed on the basis of a Mathieu equation is: equation (1), wherein ψ the molecular motion state of the corrosion-resistant material, formula (2), formula (3), formula (4), the second term c of the equation is a "spatial damping" term, and on the basis of various properties of the corrosion-resistant material, h is a reduced Planck constant, m is the mass of a particle, Ko is a wave number, and Vo is a constant term, so that parameters a and b are calculated. Therefore, the stability of the material can be evaluated.

Description

Method for evaluating stability of corrosion-resistant material TECHNICAL FIELD

[0001] The present application relates to the technical field of corrosion-resistant materials, and more particularly to a method for evaluating the stability of corrosion-resistant materials. BACKGROUND

[0002] The Schrodinger equation is generally applicable to materials at a macroscopic scale. However, at a nanoscale or in special structures such as surfaces and interfaces, the damping between electronic structures can also affect the electronic band structure, and this effect can be ignored in the traditional Schrodinger equation processing. Corrosion is a complex chemical process involving the interaction between multiple substances. The linear Schrodinger equation can only describe the electronic structure inside the material and cannot directly consider the interaction between the material and the external environment.

[0003] Quantum mechanics and classical mechanics are coordinated with each other. First, from Zhang Yongde's 2016 edition of Quantum Mechanics, it is mentioned that when studying the spectrum of a hydrogen-like atom, it is found that the Schrodinger equation theory is approximate and needs to be corrected, such as the Darawin oscillation term correction. Not alone, there is also a band gap problem in the analysis of the Kohn-Sham (KS) equation. In order to overcome this famous band gap problem, in recent years, there have been many research works published in the world, but these articles have not found and eliminated the "cause" from the fundamental mechanism. SUMMARY

[0004] Therefore, the present application provides a method for evaluating the stability of corrosion-resistant materials, which combines classical mechanics and quantum mechanics, establishes an extended Schrodinger equation based on damping, and uses Mathieu instability to establish a parameter analysis diagram of the band structure of corrosion-resistant materials, greatly reducing the quantum computing time and improving the computing efficiency.

[0005] To achieve the above purpose, the present application adopts the following technical solutions:

[0006] A method for evaluating the stability of corrosion-resistant materials, which is realized by a Schrodinger equation based on damping converted based on Mathieu equation, and the Schrodinger equation based on damping converted based on Mathieu equation is:

[0007] ,

[0008] Wherein is the molecular motion state of the corrosion-resistant material, , , , wherein the second term c of the equation is a "spatial damping" term, h is a reduced Planck constant based on properties of the corrosion-resistant material, m is a mass of the particle, k0 is a wave number, and v0 is a constant term, a and b parameters are calculated by substituting the above constants, and the stability of the material is evaluated by substituting the parameters into FIG. 2.

[0009] A method for evaluating the stability of a corrosion-resistant material, the method being obtained by the following steps:

[0010] S1. Constructing a lattice structure representing a material system according to the crystal structure and atomic coordinate parameters of the corrosion-resistant material;

[0011] S2. Establishing a Hamiltonian of the system including a kinetic energy term and a potential energy term according to the selected density functional theory method and pseudo-potential, and introducing a damping term to describe the steady-state behavior of the material in a potential field with damping effect, and establishing a Schrodinger equation based on damping;

[0012] S3. Determining the horizontal and vertical coordinates of the parameter analysis chart of the band structure of the corrosion-resistant material by transforming and solving the Schrodinger equation based on damping through the Mathieu equation;

[0013] S4. Obtaining a parameter chart containing stable and unstable regions of the band structure of the corrosion-resistant material, and analyzing the stability and properties of the corrosion-resistant material.

[0014] Preferably, a method for evaluating the stability of a corrosion-resistant material, the step S4 specifically comprises:

[0015] S41. Determining the value range of the horizontal and vertical coordinates a and b of the Mathieu instability chart and the eigenvalues of the Mathieu equation solution according to the properties h, m, k0 and v0 of the corrosion-resistant material;

[0016] S42. Drawing a stability chart in the parameter space according to the changes of the parameters h, m, k0 and v0, and representing different stable and unstable regions by different colors or other marks;

[0017] S43. Establishing the band structure of the corrosion-resistant material according to the stable and unstable regions of the parameter distribution chart, and determining the parameters and parameter ranges that will cause the material to be unstable.

[0018] Preferably, a method for evaluating the stability of a corrosion-resistant material, the step S2 specifically comprises:

[0019] S21. The Schrodinger equation based on damping is:

[0020] (2),

[0021] wherein is the position coordinate of the particle, For the material density, is a coefficient, is a function of the coordinates and the density, and the remaining parameters are the same as in the potential energy function of equation (1), describes the potential energy of the particle at position x, denotes the energy of the particle in this quantum state.

[0022] S22, using the density functional theory, the damped Schrödinger equation is converted into the Kohn-Sham equation:

[0023] ,

[0024] Both sides are multiplied by The Kohn-Sham equation formula (3) can be obtained as follows:

[0025] ,

[0026] where is a coefficient, related to the coordinates and the density, and the remaining parameters are the same as in equation (1).

[0027] Preferably, the stability evaluation method of the corrosion-resistant material specifically comprises the following steps S3:

[0028] Based on the Mathieu equation, equation (3) is converted into a Schrödinger equation containing damping:

[0029] (1),

[0030] where is the molecular motion state of the corrosion-resistant material, and the second term c of the equation is the "spatial damping" term, corresponding to equation (3), corresponds to , corresponds to , so , corresponds to , where , so , and let = , so , the horizontal and vertical coordinates of the parameter analysis chart of the energy band structure of the corrosion-resistant material are a and b, respectively.

[0031] The beneficial effects of the present application are: the present application takes a different approach, based on the fact that quantum mechanics and classical mechanics are interrelated, using classical wave mechanics theory, to derive the extended Schrodinger equation based on damping. Improving the Schrodinger equation based on wave mechanics theory helps to clarify quantum physical and chemical problems and develop new theoretical equations. The development of solving these problems with less quantum resources has very important significance. Under the driving of this potential utility, quantum computational chemistry is rapidly becoming an interdisciplinary field that requires knowledge of quantum computing and computational chemistry.

[0032] The present application bridges the gap between computational chemistry and quantum computing using the Schrodinger equation based on damping. In addition, one of the most promising applications of quantum computing is to solve classical quantum chemistry problems. This may help to solve the problems related to high-temperature superconductivity, solid-state physics, transition metal catalysis and some biochemical reactions. In turn, this increased understanding may help us to improve or even design new compound materials with scientific and industrial importance.

[0033] The present method can avoid the complex process of solving the Schrodinger equation by transforming the Schrodinger equation based on damping into Mathieu equation, quickly establish the instability parameter analysis chart of the band structure of corrosion-resistant materials, quickly identify the stability of the materials, and effectively reduce the calculation time.

[0034] The present application mainly adds the interaction term (product) of the gradient of the density function and the gradient of the wave function solution in the original (Schrödinger) Schrodinger equation, which is called the space damping term. By studying the Mathieu equation of the simple periodic potential, the parameter plane is divided into stable and unstable parts by the Mathieu stability diagram, and researchers can determine the stability of corrosion-resistant materials through the Mathieu stability diagram.

[0035] When using the present application to predict the stability of corrosion-resistant materials, only the material characteristic parameters need to be substituted into the calculation to easily predict the material stability region. The present application greatly reduces the quantum computing time and improves the computing efficiency, while at the same time being closer to the actual corrosion-resistant material situation, and the evaluation result is more accurate. BRIEF DESCRIPTION OF DRAWINGS

[0036] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description are only embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor on the basis of the provided drawings.

[0037] Figure 1 is a schematic diagram of parameter distribution without damping;

[0038] Figure 2 is a schematic diagram of the parameter distribution of the damping according to the present application. DETAILED DESCRIPTION

[0039] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the scope of protection of the present application.

[0040] Embodiment 1: As shown in Figure 2, the present embodiment discloses a stability evaluation method of a corrosion-resistant material, which is realized by a damping-based Schrodinger equation based on Mathieu equation transformation, and the damping-based Schrodinger equation based on Mathieu equation transformation is:

[0041] ,

[0042] wherein is the molecular motion state of the corrosion-resistant material, , , , the second term c of the equation is a "spatial damping" term, h is the reduced Planck constant based on the properties of the corrosion-resistant material, m is the mass of the particle, k0 is the wave number, v0 is a constant term, a and b parameters are calculated by substituting the above constants, and the stability of the material can be evaluated by substituting Figure 2.

[0043] Embodiment 2: As shown in Figure 2, the present embodiment discloses a stability evaluation method of a corrosion-resistant material, which comprises the following steps:

[0044] S1, constructing a lattice structure representing a material system according to the crystal structure and atomic coordinate parameters of the corrosion-resistant material;

[0045] S2, establishing a Hamiltonian of the system including kinetic energy terms and potential energy terms according to the density functional theory method and pseudo-potential, and introducing a damping term to describe the steady-state behavior of the material in a potential field with damping effect, and establishing a damping-based Schrodinger equation;

[0046] S21, the damping-based Schrodinger equation is:

[0047] (2),

[0048] wherein is the position coordinate of the particle, is the density of the material, is a coefficient, which is a function of the coordinates and the density, and the remaining parameters are the same as those in formula (1) potential energy function, The potential energy of the particle at position x is described, represents the energy of the particle in this quantum state;

[0049] S22, convert the damping-based Schrödinger equation into a Kohn-Sham equation using density functional theory:

[0050]

[0051] Both sides are multiplied by The Kohn-Sham equation formula (3) can be derived as follows:

[0052] (3),

[0053] where is a coefficient related to the coordinates and density, and the remaining parameters are consistent with formula (1).

[0054] S3, determine the horizontal and vertical coordinates of the parameter analysis chart of the energy band structure of the corrosion-resistant material by solving the damping-based Schrödinger equation through the Mathieu equation transformation;

[0055] Based on the Mathieu equation, formula (3) is transformed into a Schrödinger equation containing damping:

[0056] (1),

[0057] where is the molecular motion state of the corrosion-resistant material, and the second term c of the equation is the "spatial damping" term, corresponding to formula (3), corresponding to , corresponding to , so , corresponding to , where , so , and let = , so , the horizontal and vertical coordinates of the parameter analysis chart of the energy band structure of the corrosion-resistant material are a and b, respectively.

[0058] S4, obtain the parameter chart containing the stable and unstable regions of the energy band structure of the corrosion-resistant material, and analyze the stability and properties of the corrosion-resistant material;

[0059] S41, determine the value range of the horizontal and vertical coordinates a and b of the Mathieu instability chart and the characteristic value of the Mathieu equation solution according to the properties h, m, k0, and v0 of the corrosion-resistant material.

[0060] S42, according to the change of parameters h, m, k0, v0, using MATLAB software to draw the stability diagram in the parameter space, and different stability regions and instability regions are represented by different colors or other marks;

[0061] S43, according to the stability region and the instability region of the parameter distribution diagram, the energy band structure of the corrosion-resistant material is established, and the range of parameters (h / k / m / v0) that will cause the material to be unstable is determined.

[0062] The parameter distribution diagram obtained in this embodiment is FIG. 2, in which the horizontal and vertical coordinates a and b are [0, 5] and [0, 5] respectively, and the stable region of the corrosion-resistant material is different blue region, and the unstable region is white region. In practical application, based on the various property parameters h / k / m / v0 of the corrosion-resistant material, the a and b parameters are calculated, and then substituted into FIG. 2, so that the stability of the material can be easily evaluated.

[0063] Comparative Example 1: When the Schrödinger equation does not contain the damping term, the Schrödinger equation based on the Mathieu equation is transformed, and the parameter distribution diagram drawn by using MATLAB software is FIG. 1, in which the horizontal and vertical coordinates a and b are [0, 8] and [0, 6] respectively, and the stable region of the corrosion-resistant material is the yellow region, and the unstable region is the white region.

[0064] As can be seen from FIGS. 1 and 2, FIG. 2 is closer to the actual corrosion-resistant material, and the evaluation result is more accurate.

[0065] The various embodiments in the specification are described in a progressive manner, and each embodiment focuses on the difference from other embodiments. The same or similar parts between the various embodiments can be referred to each other. For the device disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the related parts can be referred to the method part.

[0066] The above description of the disclosed embodiments enables a person skilled in the art to implement or use the present application. Various modifications to the embodiments will be apparent to those skilled in the art, and the general principles defined herein can be implemented in other embodiments without departing from the spirit or scope of the present application. Therefore, the present application will not be limited to the embodiments shown herein, but will conform to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for evaluating stability of a corrosion-resistant material, characterized by, The method is realized by a Mathieu equation transformed damping-based Schrodinger equation, the Mathieu equation transformed damping-based Schrodinger equation is: ， wherein the state of molecular movement of a corrosion-resistant material, ， ， The second term c of the equation is a "space damping" term, h is a reduced Planck constant based on the properties of the corrosion-resistant material, m is the mass of the particle, k0 is the wave number, v0 is a constant term, and the a and b parameters are calculated by substituting the above constants; The method is obtained by the following steps: S1, constructing a lattice structure representing a material system according to the crystal structure and atomic coordinate parameters of the corrosion-resistant material; S2, establishing a Hamiltonian of the system according to the selected density functional theory method and pseudo-potential, including a kinetic energy term and a potential energy term, and introducing a damping term to describe the steady-state behavior of the material in a potential field with damping effect, and establishing a damping-based Schrodinger equation; S3, solving the damping-based Schrodinger equation by Mathieu equation transformation to determine the horizontal and vertical coordinates of the parameter analysis chart of the energy band structure of the corrosion-resistant material; S4, obtaining a parameter chart containing the stable and unstable regions of the energy band structure of the corrosion-resistant material, and analyzing the stability and properties of the corrosion-resistant material; The step S4 specifically includes: S41, determining the value range of the horizontal and vertical coordinates a and b of the Mathieu instability chart and the eigenvalues of the Mathieu equation solution according to the properties h, m, k0 and v0 of the corrosion-resistant material; S42, drawing a stability chart in the parameter space according to the changes of the parameters h, m, k0 and v0, and representing different stable and unstable regions by different colors or other marks; S43, establishing the energy band structure of the corrosion-resistant material according to the stable and unstable regions of the parameter distribution chart, and determining the parameters and parameter range that will cause the material to be unstable.

2. The method for evaluating stability of a corrosion resistant material according to claim 1, characterized by, The step S2 specifically includes: S21, the damping-based Schrodinger equation is: （2）； wherein for the position coordinates of the particles, For material density, is the coefficient, is a function of the coordinates and the density, and the remaining parameters are the same as in equation (1) the potential energy function, The potential energy of a particle at position x is described by E represents the energy of the particle in the quantum state; S22, the damping-based Schrodinger equation is transformed into a Kohn-Sham equation by using the density functional theory: ， Both sides at the same time The Kohn-Sham equation formula (3) is as follows: ， wherein is a coefficient related to the coordinates and density, and the other parameters are consistent with formula (1).

3. The method for evaluating stability of a corrosion resistant material according to claim 1, characterized by, The step S3 specifically includes: The formula (3) is transformed into a Schrodinger equation containing damping based on the Mathieu equation as follows: （1）， wherein The second term c of the equation is the "spatial damping" term, corresponding to equation (3), for the state of molecular motion of the corrosion-resistant material, corresponding ， corresponding therefore ， corresponding wherein therefore , in addition to the above = therefore The horizontal and vertical coordinates of the parameter analysis chart of the energy band structure of the corrosion-resistant material are a and b respectively.

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