CN115862783B - Theoretical calculation design method of high-entropy alloy coating with adjustable thermal expansion coefficient - Google Patents

Theoretical calculation design method of high-entropy alloy coating with adjustable thermal expansion coefficient Download PDF

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CN115862783B
CN115862783B CN202211564488.1A CN202211564488A CN115862783B CN 115862783 B CN115862783 B CN 115862783B CN 202211564488 A CN202211564488 A CN 202211564488A CN 115862783 B CN115862783 B CN 115862783B
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entropy alloy
thermal expansion
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吴晓宏
卢松涛
姚忠平
李杨
秦伟
洪杨
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Harbin Institute of Technology
Chongqing Research Institute of Harbin Institute of Technology
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Abstract

The invention provides a theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient. Step 1: determining a crystal structure based on a high-entropy alloy classical descriptor, and establishing a special quasi-random approximate structural model SQS; step 2: optimizing according to the model in the step 1 to obtain a structure of the high-entropy alloy; step 3: predicting the thermal expansion coefficient of the high-entropy alloy along with the temperature change according to the calculation of the structure of the high-entropy alloy in the step 2 and a quasi-simple harmonic approximation method; step 4: determination of FeCrVTiMo according to step 3 x And (3) coating. The method is used for solving the problem that the high-entropy alloy coating in the prior art needs to rely on experimental data to design a long period.

Description

Theoretical calculation design method of high-entropy alloy coating with adjustable thermal expansion coefficient
Technical Field
The invention relates to the field of design of high-entropy alloy coatings, in particular to a theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient.
Background
The high-entropy alloy is a novel solid solution alloy consisting of five or five elements according to equimolar ratio or nearly equimolar ratio, the unique alloy design concept and four core effects (namely high entropy effect in thermodynamics, delayed diffusion effect in dynamics, lattice distortion effect in structure and cocktail effect in performance) attract the wide attention of material workers, and the high-entropy alloy is expected to break through the canyon lock which is difficult to consider the strength and plasticity of the traditional alloy material, has the advantages of good heat stability, irradiation resistance, high strength, corrosion resistance and the like, and has wide application prospect in the fields of surface protection coatings and the like.
The object expands and contracts due to temperature change, and the expansion and contraction degree is measured by the change of length value caused by unit temperature change under equal pressure, namely the thermal expansion coefficient. The thermal expansion coefficient of the coating is matched with that of the matrix, so that the risk of spalling of the coating in the service process can be effectively reduced, and the method has important significance for ensuring the normal service of the coating.
The current research on the field of high-entropy alloy coatings mainly focuses on experimental trial and error, changes the concentration of principal elements or replaces principal components of the alloy based on the existing high-entropy alloy components, has few reports on the research on the thermal expansion coefficient part of the coating, has the problems that the thermal expansion coefficient of the coating is difficult to measure, the change trend of the thermal expansion coefficient along with temperature is unclear and the like, restricts the development of the high-entropy alloy coating and the prediction of the service life of the coating, and therefore, the development, design and adjustment of the thermal expansion coefficient of the high-entropy alloy coating are assisted by theoretical calculation tools such as a first principle, thermodynamic calculation and the like, and finally, the coating with the thermal expansion coefficient similar to that of a substrate at the service temperature is obtained, so that theoretical support and technical support are provided for the practical application of the trend of the high-entropy alloy.
Disclosure of Invention
The invention provides a theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient, which is used for solving the problem that the design period of the high-entropy alloy coating in the prior art is long because of depending on experimental data.
The invention provides a theoretical calculation design system of a high-entropy alloy coating with an adjustable thermal expansion coefficient, which is used for realizing the theoretical calculation design of the high-entropy alloy coating.
The invention is realized by the following technical scheme:
a theoretical computational design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient, the theoretical computational design method comprising the following steps:
step 1: determining a crystal structure based on a high-entropy alloy classical descriptor, and establishing a special quasi-random approximate structure model SQS;
step 2: optimizing according to the model in the step 1 to obtain a stable structure of the high-entropy alloy;
step 3: predicting the thermal expansion coefficient of the high-entropy alloy according to the structure of the high-entropy alloy in the step 2 along with the temperature change;
step 4: determination of FeCrVTiMo according to step 3 x And (3) coating.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient comprises the following steps that step 1 is specifically to judge whether a FeCrVTiMox quinary alloy can form a stable single-phase BCC solid solution according to classical descriptors of the high-entropy alloy, including thermodynamic and structural properties, and determine that a system conforms to the descriptors and tends to form the BCC single-phase solid solution.
A theoretical calculation design method for high-entropy alloy coating with adjustable thermal expansion coefficient, wherein the determination system accords with the descriptor, specifically, is determined by using an empirical judgment formula of high-entropy alloy,
wherein, c i And c j Is the atomic percent of elements i and j; r is (r) i Is the atomic radius of each element;is the average atomic radius; (Tm) i Is the melting point of element i; tm is the average melting point of HEA; />Representing a parameter between i and j;is the mixing enthalpy of binary liquid alloy, delta S mix Is HEA mixed entropy, delta H mix Represents HEA mixing enthalpy; (VEC) i Is the valence electron concentration of the i component, and VEC is the average valence electron concentration of HEA.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient is disclosed, wherein the structure of the high-entropy alloy obtained by optimizing in the step 2 is specifically that a special quasi-random approximate structural model SQS of the high-entropy alloy with a 4 multiplied by 4 BCC structure is constructed, and the structural model meeting the force and energy criteria is obtained by optimizing the structure.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient is characterized in that a special quasi-random approximate structural model of the high-entropy alloy for constructing a 4 multiplied by 4 BCC structure uses a mcsqs module of ATAT software.
A theoretical calculation design method of high-entropy alloy coating with adjustable thermal expansion coefficient, the step 3 is specifically that on the basis of obtaining stable structure, series static self-consistent calculation is carried out near the balance position to obtain the change condition of energy along with volume; based on the change condition data of energy along with the volume, thermodynamic calculation is carried out to obtain the thermal expansion coefficient of the system
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient comprises the steps of performing structural optimization on a high-entropy alloy of a BCC structure by using VASP software;
the series of static self-consistent calculations around the equilibrium position also uses the VASP software.
A theoretical calculation design method of a high-entropy alloy coating with adjustable thermal expansion coefficient is disclosed, wherein the thermodynamic calculation uses GIBBS2 software.
A theoretical calculation design system of a high-entropy alloy coating with an adjustable thermal expansion coefficient, which comprises a special quasi-random approximate structural model unit, an optimized structural unit and a quasi-simple harmonic approximate model prediction unit;
special quasi-random approximation structural model unit: the method is used for determining a crystal structure according to the high-entropy alloy classical descriptor and establishing a special quasi-random approximate structure model;
optimizing a structural unit: the method comprises the steps of optimizing a special quasi-random approximate structural model to obtain a structure of the high-entropy alloy;
a quasi-simple harmonic approximation model prediction unit: determination of FeCrVTiMo for predicting the thermal expansion coefficient of high-entropy alloy with temperature according to the structure thereof x And (3) coating.
A computer readable storage medium having stored therein a computer program which when executed by a processor performs the above-described method steps.
The beneficial effects of the invention are as follows:
according to the method, the classical descriptor of the high-entropy alloy is calculated and combined with the quasi-simple harmonic approximation model through the first sexual principle, the change condition of the thermal expansion coefficient of the high-entropy alloy along with the temperature is calculated independently of experimental data, effective support is provided for development of the high-entropy alloy coating, and the design concept of the high-entropy alloy coating is enriched.
Drawings
Fig. 1 is a schematic structural view of the present invention.
FIG. 2 is a graphical representation of the thermal expansion coefficient of the high entropy alloy coating of the present invention as a function of temperature.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only 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.
A theoretical computational design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient, the theoretical computational design method comprising the following steps:
step 1: determining a crystal structure based on a high-entropy alloy classical descriptor, and establishing a special quasi-random approximate structural model SQS;
step 2: optimizing according to the model in the step 1 to obtain a structure of the high-entropy alloy;
step 3: predicting the thermal expansion coefficient of the high-entropy alloy along with the temperature change according to the calculation of the structure of the high-entropy alloy in the step 2 and a quasi-simple harmonic approximation method;
step 4: determination of FeCrVTiMo according to step 3 x And (3) coating.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient is disclosed, wherein the step 1 is to determine a special quasi-random approximate structural model, specifically, according to a classical descriptor of the high-entropy alloy, including thermodynamic and structural properties, whether a FeCrVTiMox quinary alloy can form a stable single-phase BCC solid solution is judged, and the fact that the system conforms to the descriptor and tends to form the BCC single-phase solid solution is determined.
A theoretical calculation design method for high-entropy alloy coating with adjustable thermal expansion coefficient, wherein the determination system accords with the descriptor, specifically, is determined by using an empirical judgment formula of high-entropy alloy,
wherein, c i And c j Is the atomic percent of elements i and j; r is (r) i Is the atomic radius of each element;is the average atomic radius;(Tm) i is the melting point of element i; tm is the average melting point of HEA; />Representing a parameter between i and j; />Is the mixing enthalpy of binary liquid alloy, delta S mix Is HEA mixed entropy, delta H mix Represents HEA mixing enthalpy; (VEC) i Is the valence electron concentration of the i component, and VEC is the average valence electron concentration of HEA.
A theoretical calculation design method of high-entropy alloy coating with adjustable thermal expansion coefficient, the structure of high-entropy alloy obtained by optimizing in the step 2 is that a special quasi-random approximate structure model of high-entropy alloy of 4 multiplied by 4 BCC structure is constructed, and the structure model meeting the force and energy criteria is obtained by optimizing the structure.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient is characterized in that a special quasi-random approximate structural model of the high-entropy alloy for constructing a 4 multiplied by 4 BCC structure uses a mcsqs module of ATAT software.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient comprises the following steps that 3, on the basis of obtaining a stable structure, series static self-consistent calculation is carried out near an equilibrium position to obtain the change condition of energy along with the volume; based on the change condition data of energy along with the volume, thermodynamic calculation is carried out to obtain the thermal expansion coefficient of the system
The calculation formula of the thermal expansion coefficient:
at a finite temperature and pressure, the free energy of the crystal can be expressed by formula (1):
G(x;p,T)=E sta (x)+PV(x)+F vib (x;T) (1)
f in the formula vi b (x; T) -the contribution of vibration to free energy;
E sta (x) -variation of static energy with internal degrees of freedom;
v (x) -volume;
x-is the internal degree of freedom, such as atomic coordinates, etc.;
p-external pressure.
To simplify the calculation, the change in the internal degrees of freedom is typically reflected in the volume, and other items related to the internal degrees of freedom can be reduced to volume related. Based on the above simplification, various state equations (Equation of state, EOS) have been developed for static energy, such as Birch-musnaghan state equation, below.
In B' 0 -derivative of body elastic modulus with respect to pressure;
U 0 -energy at equilibrium at 0K;
V 0 -volume at equilibrium at 0K;
B 0 -body modulus at equilibrium at 0K;
ξ——(V 0 /V) 1/3
while in the processing of vibration terms, a quasi-harmonic approximation (Quasiharmonic approximation, QHA) is typically used. In QHA, the vibration energy can be expressed by the phonon frequency (ω) in this state, as shown in formula (3). In practical calculation, the change of the free energy of vibration along with the temperature under different volumes can be obtained by adopting the calculation of the state density g (omega) of phonons of crystals under different volumes and carrying out weighted integration on the state density g (omega).
K in B Boltzmann constant;
n-number of atoms in the cell;
n-the number of cells in the unit cell.
However, the phonon spectrum of the crystal is calculated in a large amount, and one common processing method is Debye model (Debye model). In the debye model, it is assumed that the phonon density follows the formula (4) distribution, and under this assumption, the free energy of vibration of the crystal can be expressed by the formula (5).
Omega in DD k B
Θ D Debye temperature.
Where D (y) -Debye integral can be calculated by equation (6).
And the Debye temperature can be approximated by equation (7).
In B of S -body elastic modulus in static state;
m-relative molecular mass;
v-poisson ratio;
and f (v) can be approximated by equation (8).
At finite temperatures and pressures (fixed pressures and temperatures), the volume is varied, a series of volume-energy data is obtained by the above equation,
fitting the volume-energy relation with a state equation under the corresponding temperature and pressure to obtain the balance volume under the temperature and pressure, and obtainingTo the equilibrium volume at different temperatures and pressures to obtain other thermophysical properties, such as body elastic modulus B T Heat capacity C V The specific formulas of the Gruneisen coefficient gamma, the thermal expansion coefficient alpha and the like are shown in formulas (9) to (12). The calculation of the above-described quasi-harmonic approximation was performed using the GIBBS2 software.
A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient comprises the steps of performing structural optimization on a high-entropy alloy of a BCC structure by using VASP software;
the series of static self-consistent calculations around the equilibrium position also uses the VASP software.
A theoretical calculation design method of a high-entropy alloy coating with adjustable thermal expansion coefficient is disclosed, wherein the thermodynamic calculation uses GIBBS2 software.
A theoretical calculation design system of a high-entropy alloy coating with an adjustable thermal expansion coefficient, which comprises a special quasi-random approximate structural model unit, an optimized structural unit and a quasi-simple harmonic approximate model prediction unit;
special quasi-random approximation structural model unit: the method comprises the steps of determining a quasi-simple harmonic approximation model according to a high-entropy alloy classical descriptor;
optimizing a structural unit: the method is used for optimizing the special quasi-random approximate structural model to obtain a stable structure of the high-entropy alloy;
a quasi-simple harmonic approximation model prediction unit: determination of FeCrVTiMo for predicting the thermal expansion coefficient of high-entropy alloy with temperature according to the structure thereof x And (3) coating.
A computer readable storage medium having stored therein a computer program which when executed by a processor performs the above-described method steps.
The crystal structure of the FeCrVTiMox system obtained is a BCC phase and tends to form a single solid solution phase, calculated from the classical descriptors of high-entropy alloys.
On the basis of obtaining a specific crystal configuration, modeling the high-entropy alloy by adopting an mcsqs module of ATAT software, wherein the established structural model is 4 multiplied by 4, and the total number of supercells is 128 atoms.
Converting the established SQS model file of the supercell into a POSCAR format to obtain a model file of the VASP, importing the model file into the VASP, and performing structural optimization to obtain a structural model meeting energy criteria and force criteria, wherein FeCrVTiMo 0.5 As shown in fig. 1, 1 is Fe,2 is Mo,3 is Cr,4 is V, and 5 is Ti.
And (3) performing a series of static self-consistent calculations at the balance position of the stable structural model to obtain the condition that the energy changes along with the supercell volume.
Furthermore, SQS modeling is carried out according to the chemical components and the crystal structure of the 1Cr13 steel, the established structural model is 4 multiplied by 4, the supercell of 128 atoms in total is subjected to structural optimization and static calculation, the thermal expansion coefficient change condition is obtained by combining a quasi-simple harmonic approximation model, and the calculation result is identical with the existing experimental data;
the change condition data of energy along with the volume is subjected to unit conversion, and is imported into GIBBS2 software, and the change condition of the thermal expansion coefficient of the high-entropy alloy coating along with the temperature is obtained by means of a quasi-simple harmonic approximation model, as shown in figure 2. Wherein the thermal expansion coefficient of FeCrVTiMo0.5 is closest to that of the 1Cr13 matrix steel selected.

Claims (9)

1. A theoretical calculation design method of a high-entropy alloy coating with an adjustable thermal expansion coefficient is characterized by comprising the following steps of:
step 1: determining a crystal structure based on a high-entropy alloy classical descriptor, and establishing a special quasi-random approximate structural model SQS;
step 2: optimizing according to the model in the step 1 to obtain a structure of the high-entropy alloy;
step 3: predicting the thermal expansion coefficient of the high-entropy alloy along with the temperature change according to the calculation of the structure of the high-entropy alloy in the step 2 and a quasi-simple harmonic approximation method;
step 3 is specifically that on the basis of obtaining a stable structure, serial static self-consistent calculation is carried out at the balance position, and the change condition of energy along with the volume is obtained; based on the change condition data of energy along with the volume, thermodynamic calculation is carried out to obtain the thermal expansion coefficient of the system;
the calculation formula of the thermal expansion coefficient:
at a finite temperature and pressure, the free energy of the crystal is expressed by formula (1):
G(x;p,T)=E sta (x)+PV(x)+F vib (x;T) (1)
f in the formula vib (x; T) -the contribution of vibration to free energy; e (E) sta (x) -variation of static energy with internal degrees of freedom; v (x) -volume; x-is the internal degree of freedom; p-external pressure;
the change of the internal degree of freedom is reflected on the volume, and all other items related to the internal degree of freedom are simplified to be related to the volume; based on the above simplification, a Birch-musnaghan state equation was developed for static energy, as shown below,
in B' 0 -derivative of body elastic modulus with respect to pressure; u (U) 0 -energy at equilibrium at 0K; v (V) 0 -volume at equilibrium at 0K; b (B) 0 -body modulus at equilibrium at 0K; xi (xi) - (V) 0 /V) 1/3
When the vibration item is processed, a quasi-harmonic approximation QHA is adopted; in QHA, the vibration energy can be expressed by the phonon frequency (ω) in this state, as shown in formula (3); in actual calculation, the change of the vibration free energy along with the temperature under the volume can be obtained by adopting the calculation of the state density g (omega) of phonons of crystals under different volumes and carrying out weighted integration on the phonons;
k in B Boltzmann constant; n-number of atoms in the cell; n-the number of cells in the unit cell;
the phonon spectrometer for calculating the crystal adopts the debye model, and the phonon density is assumed to be compliant with the distribution of the formula (4), under the assumption, the free energy of vibration of the crystal can be expressed by the formula (5),
omega in DD k B ;Θ D Debye temperature;
wherein D (y) -Debye integral can be calculated by formula (6);
whereas the Debye temperature can be approximated by equation (7);
where Bs-bulk modulus at static; m-relative molecular mass; v-poisson ratio;
and f (v) can be calculated by formula (8);
changing the volume at a limited temperature and pressure, obtaining a series of volume-energy data by the above formula,
fitting the volume-energy relation with a state equation under the corresponding temperature and pressure to obtain the balance volume under the temperature and pressure, and obtaining other thermophysical properties and body elastic modulus B according to the balance volumes under the pressure and the temperature T Heat capacity C V The Gruneisen coefficient gamma and the thermal expansion coefficient alpha are shown in the specific formulas (9) to (12); the calculation of the quasi-harmonic approximation is carried out by adopting GIBBS2 software;
step 4: determination of FeCrVTiMo from the thermal expansion coefficient of step 3 x And (3) coating.
2. The theoretical calculation design method of the high-entropy alloy coating with the adjustable thermal expansion coefficient according to claim 1, wherein the step 1 is specifically to judge whether the FeCrVTiMox quinary alloy can form a stable single-phase BCC solid solution according to classical descriptors of the high-entropy alloy, including thermodynamic and structural properties, and determine whether the system conforms to the descriptors to form the BCC single-phase solid solution.
3. The theoretical calculation design method of a high-entropy alloy coating with adjustable thermal expansion coefficient according to claim 2, wherein the determination system conforms to the descriptor, specifically, is determined by using an empirical judgment formula of the high-entropy alloy,
wherein, c i And c j Is the atomic percent of elements i and j; r is (r) i Is the atomic radius of each element;is the average atomic radius; (Tm) i Is the melting point of element i; tm is the average melting point of HEA; />Representing a parameter between i and j; />Is the mixing enthalpy of binary liquid alloy, delta S mix Is HEA mixed entropy, delta H mix Represents HEA mixing enthalpy; (VEC) i Is the valence electron concentration of the i component, and VEC is the average valence electron concentration of HEA.
4. The theoretical calculation design method of the high-entropy alloy coating with the adjustable thermal expansion coefficient according to claim 2, wherein the structure of the high-entropy alloy obtained by optimization in the step 2 is specifically that, and constructing a special quasi-random approximate structural model of the high-entropy alloy of the 4 multiplied by 4 BCC structure, and carrying out structural optimization on the model to obtain a structural model meeting force and energy criteria.
5. The theoretical calculation design method of high-entropy alloy coating with adjustable thermal expansion coefficient according to claim 4, characterized in that, the special quasi-random approximation structural model of the high entropy alloy that builds a 4 x 4 BCC structure uses the mcsqs module of ATAT software.
6. The theoretical calculation design method of the high-entropy alloy coating with the adjustable thermal expansion coefficient according to claim 4, wherein the structural optimization of the high-entropy alloy of the BCC structure uses VASP software;
the series of static self-consistent calculations of the equilibrium position also uses the VASP software.
7. The method for designing a theoretical calculation of a high-entropy alloy coating with an adjustable thermal expansion coefficient according to claim 1, wherein the thermodynamic calculation uses the GIBBS2 software.
8. A theoretical computational design system of a high-entropy alloy coating with an adjustable thermal expansion coefficient, which is characterized in that the theoretical computational design system uses the method as claimed in claim 1, and comprises a special quasi-random approximate structural model unit, an optimized structural unit and a quasi-simple harmonic approximate model prediction unit;
special quasi-random approximation structural model unit: the method is used for determining a crystal structure according to the high-entropy alloy classical descriptor and establishing a special quasi-random approximate structure model;
optimizing a structural unit: the method is used for optimizing the special quasi-random approximate structural model to obtain a stable structure of the high-entropy alloy;
a quasi-simple harmonic approximation model prediction unit: determination of FeCrVTiMo for predicting the thermal expansion coefficient of high-entropy alloy with temperature change based on its structure x And (3) coating.
9. A computer-readable storage medium, characterized in that the computer-readable storage medium has stored therein a computer program which, when executed by a processor, implements the method steps of any of claims 1-7.
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