CN112349352A - High-entropy alloy lattice distortion quantity calculation method based on atom occupying ordering behavior - Google Patents
High-entropy alloy lattice distortion quantity calculation method based on atom occupying ordering behavior Download PDFInfo
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Abstract
The invention relates to a method for calculating lattice distortion of a high-entropy alloy based on atom occupying ordering behavior, which comprises the following steps: s1, constructing a corresponding thermodynamic model; step S2, calculating discrete values of Gibbs free energy thermodynamic data of each end compound and elementary substance element in the high-entropy alloy; step S3, constructing a thermodynamic database of the high-entropy alloy end group compound; step S4, calculating and obtaining the occupation fraction of each element in the high-entropy alloy on the sublattice under the conditions of given components and temperature; s5, constructing a structural model of the actual distribution of atoms in the high-entropy alloy; and S6, obtaining a structure model after structure optimization, and S7, substituting a preset lattice distortion formula according to the structure model after structure optimization, and calculating to obtain the total distortion, the average distortion and the relative lattice distortion of the high-entropy alloy. The invention realizes the quantitative calculation of the lattice distortion effect of the high-entropy alloy.
Description
Technical Field
The invention relates to the field of metal material microstructure design, in particular to a method for calculating lattice distortion of a high-entropy alloy based on atom occupying ordering behavior.
Background
The high-entropy alloy is a novel metal material developed in recent 20 years, is an epoch-making alloy component and structure design concept, and breaks through the bottleneck of limited alloy types faced by the traditional alloy research idea. Since the first official report in 2004, the study has attracted a lot of attention in the international academic field, and a research enthusiasm has been raised. The high-entropy alloy has unique alloy component characteristics, consists of a plurality of elements with equal atomic ratio or near equal atomic ratio, has relatively simple phase structure, takes a face-centered cubic structure (FCC), a body-centered cubic structure (BCC) or a close-packed hexagonal structure (HCP) as main component phases, is added with a small amount of ordered intermetallic compounds, has different performance characteristics, has high strength in some systems, good plasticity in some systems, corrosion resistance or oxidation resistance in some systems, good radiation damage resistance in some systems, excellent soft magnetic property in some systems and multiple unique properties in some systems.
The variety of the types and the contents of the constituent elements in the high-entropy alloy and the complex mechanism of the alloying process have no precise understanding and grasp about the internal relation among the four elements of alloy composition, process, structure and performance. In the field of materials science, the high-entropy alloy is considered to have four major effects, namely a high-entropy effect on thermodynamics, a lattice distortion effect on a structure, a delayed diffusion effect on kinetics and a cocktail effect on performance, the effects determine the internal relation between the structure and the performance of the high-entropy alloy, but the method also introduces wide disputes, most documents are developed and researched in a stir-frying way, and the mechanism research report is few. The main reason for the disputes is the assumption that there is a lack of quantitative description.
Regarding the occupancy ordering behavior of atoms on sublattices in the high-entropy alloy, it is considered that the sizes, electronic structures, crystal structures, and bonding energies between different atoms of the various components constituting the high-entropy alloy are different from each other, and some atoms are even significantly different from each other, so that different kinds of atoms cannot be perfectly mixed on the crystal lattice, and there is necessarily a certain occupancy tendency that some atoms tend to occupy one sublattice and some atoms tend to occupy another sublattice, that is, the so-called occupancy ordering behavior. Quantitative description is carried out from the statistical significance, and the occupancy ordering behavior is expressed by occupancy probability, also called occupancy fraction. Through the calculation of the occupancy fraction, the occupancy behaviors of different kinds of atoms on different sub-lattices can be described quantitatively, and the configuration entropy of a high-entropy alloy system can be further calculated, namely the entropy of the high-entropy effect is known to be actually high, so that the defect that the high-entropy effect is calculated by adopting ideal mixing in the past literature is overcome.
With respect to lattice distortion, i.e., atoms deviate from the ideal lattice position. In the multi-principal-element high-entropy alloy with complex composition, the alloy can be more serious than the conventional traditional alloy with one element as the main component. High entropy effect high entropy alloys readily produce single phase solid solutions, whether of the structure BCC, FCC, or HCP. Meanwhile, each atom in the multi-principal-element sublattice can be surrounded by atoms of different types and is influenced by various factors such as lattice strain and stress, and besides the difference of atom sizes, the asymmetry of adjacent atoms such as electronic structures, crystal structures and different binding energies among the constituent elements can influence the atom positions, so that more obvious lattice distortion is caused. Whereas in conventional alloys most of the matrix atoms (or solvent atoms) are of the same atomic type as their neighbors, this results in a much smaller overall lattice distortion than in high entropy alloys. Therefore, how to determine the occupation behavior of each atom on the sublattice is important for quantitatively researching the lattice distortion effect of the high-entropy alloy.
Disclosure of Invention
In view of the above, the present invention aims to provide a method for calculating lattice distortion of a high-entropy alloy based on an atom occupying ordering behavior on a sublattice, which combines crystallographic structure information of an alloy phase, quantum mechanics first principle calculation, density functional perturbation theory and alloy thermodynamic theory to realize quantitative calculation of lattice distortion effect of the high-entropy alloy, and provides a solid foundation for accelerating research and development of a new high-entropy alloy material.
In order to achieve the purpose, the invention adopts the following technical scheme:
a method for calculating lattice distortion of a high-entropy alloy based on the space-occupying ordering behavior of atoms on sublattices comprises the following steps:
s1, constructing a corresponding thermodynamic model based on the phase structure of the high-entropy alloy;
step S2, obtaining discrete values of Gibbs free energy thermodynamic data of each end group compound and elementary substance element in the high-entropy alloy through phonon spectrum calculation of a density functional perturbation theory;
step S3, fitting thermodynamic data based on a specific function model, and deducting the reference state function values of the constituent elements to construct a high-entropy alloy end group compound thermodynamic database;
step S4, calculating and obtaining the occupation fraction of each element in the high-entropy alloy on the sublattice under the conditions of given components and temperature based on a terminal compound thermodynamic database and a thermodynamic phase equilibrium principle;
step S5, according to the fractional value of the occupation of the elements on the sublattice, forming atom random occupation patterns on the sublattice, nesting the sublattice together to form an integral structure, and constructing a structural model of the actual distribution of atoms in the high-entropy alloy;
s6, based on the total energy minimization principle, carrying out volume optimization on the structural model of the atomic actual distribution in the high-entropy alloy, and then carrying out shape and atomic position optimization to obtain a structural model after structural optimization;
and step S7, substituting the structure model after the structure optimization into a preset lattice distortion formula to calculate the total distortion, the average distortion and the relative lattice distortion of the high-entropy alloy.
Further, the function model is as follows:
G(T)=A+BTlnT+CT2+DT3+ET-1+FT
wherein G (T) represents Gibbs free energy of an elemental element or an end group compound as a function of temperature in J/(mol. atom), T represents Kelvin temperature (K), A, B, C, D, E and F are parameters obtained by fitting.
Further, the step S3 is specifically:
s31, fitting thermodynamic data of the high-entropy alloy end group compound and the composition simple substance elements to obtain various parameter values of a function expression;
step S32, data processing is carried out on the fitted terminal compound function, the stable structure of the simple substance elements forming the terminal compound at room temperature is taken as a reference state, and the Gibbs free energy function value at room temperature, namely the reference state value, is obtained by a thermodynamic function expression;
and S33, deducting the reference state value by using the function expression of each terminal compound, and finally writing the deducted relative Gibbs free energy function expression of the terminal compound into a terminal compound thermodynamic database.
Further, the step S4 is specifically to calculate the occupancy fraction of each element on different types of sub-lattices of the given alloy system at different temperatures based on the constructed high-entropy alloy database.
Further, the step S6 is specifically:
step S61, fixing the position and shape of the crystal cell, optimizing the volume of the crystal cell to obtain the smallest volume of the system, namely the balance volume, and simultaneously obtaining the atom position coordinate when the crystal lattice is not distorted and the first adjacent distance between atoms;
and step S62, fixing the shape and the volume of the unit cell, and optimizing the atomic position of the unit cell to obtain the atomic position coordinates after the atomic position is optimized, namely the lattice is allowed to be distorted.
Further, the step S7 is specifically:
the total lattice distortion quantity calculation formula is as follows:
wherein n is the total atomic number minus the number of fixed atoms, dxi、dyi、dziRepresenting the difference of the corresponding coordinate components of the same atom before and after optimization, d0Denotes the distance of the first adjacent atom when no lattice distortion occurs, D andall units of (A) are angstroms
Compared with the prior art, the invention has the following beneficial effects:
the method combines the crystallographic structure information of the alloy phase, the calculation of the first principle of quantum mechanics, the density functional perturbation theory and the thermodynamic theory of the alloy to realize the quantitative calculation of the lattice distortion effect of the high-entropy alloy and provide a solid foundation for accelerating the research and development of new high-entropy alloy materials.
Drawings
FIG. 1 is a flow chart of a method of the present invention;
FIG. 2 shows an embodiment of the present inventionEnd group CoCr of FCC Structure in examples3A schematic diagram of a thermodynamic model;
fig. 3 is a schematic diagram of a calculation path of thermodynamic calculation of a FCC structure cocrfermni alloy in an embodiment of the present invention, wherein (r) (+ c);
FIG. 4 is a schematic diagram of the POSCAR principle constructed by the FCC structure CoCrFeMnNi supercell in one embodiment of the present invention;
FIG. 5 is a schematic diagram of an original position of a 973K-CoCrFeMnNi high-entropy alloy in an embodiment of the present invention;
FIG. 6 is a schematic diagram showing the comparison of the (100) direction (front view) after the optimized positions of the atoms before and after the 973K-CoCrFeMnNi high-entropy alloy are superposed.
Detailed Description
The invention is further explained below with reference to the drawings and the embodiments.
The invention provides a method for calculating lattice distortion of a high-entropy alloy based on an atom occupying ordering behavior, which comprises the following steps of:
s1, constructing a corresponding thermodynamic model based on the phase structure of the high-entropy alloy;
step S2, obtaining discrete values of Gibbs free energy thermodynamic data of each terminal compound and elementary substance element in the high-entropy alloy through phonon spectrum calculation of a density functional perturbation theory;
step S3, fitting thermodynamic data based on a preset function model, and deducting the reference state function values of the constituent elements to construct a high-entropy alloy end group compound thermodynamic database;
step S4, calculating and obtaining the occupation fraction of each element in the high-entropy alloy on the sublattice under the conditions of given components and temperature based on a terminal compound thermodynamic database and a thermodynamic phase equilibrium principle;
step S5, according to the fractional value of the occupation of the elements on the sublattice, forming atom random occupation patterns on the sublattice, nesting the sublattice together to form an integral structure, and constructing a structural model of the actual distribution of atoms in the high-entropy alloy;
s6, based on the total energy minimization principle, carrying out volume optimization on the structural model of the atomic actual distribution in the high-entropy alloy, and then carrying out shape and atomic position optimization to obtain a structural model after structural optimization;
and step S7, substituting the structure model after the structure optimization into a preset lattice distortion formula to calculate the total distortion, the average distortion and the relative lattice distortion of the high-entropy alloy.
In this embodiment, the step S1 specifically includes: the thermodynamic model is based on CoCrFeMnNi as FCC structure and AuCu3Is AB3_L12The prototype structure is taken as an example, and CoCr with the same structure is used here3As an illustration, as shown in fig. 2. In addition, there is an AB _ B2 structure using NiAl as a prototype, MgCu2Is AB of the prototype2The structure of (i.e., Laves phase) of (a) _ C15, and the like.
In this embodiment, the step S2 specifically includes: calculating discrete values of Gibbs free energy thermodynamic data of each end compound and elementary substance element in the high-entropy alloy by combining a first linear principle VASP calculation software package and a phonon calculation software package Phonopy;
preferably, the high-entropy alloy is a single-phase high-entropy alloy, such as a CoCrFeMnNi high-entropy alloy, and only an FCC phase exists, or a MoNbTaVW high-entropy alloy, and only a BCC phase exists. If phase separation or multi-phase high-entropy alloy occurs, the description of the lattice distortion becomes complex and is not considered for the moment; dat is a document of gibbs-temperature, the temperature step is 10K, and Gibbs free energy values at different temperatures are mainly referred to as thermodynamic data discrete values. In the specific implementation process, a Density Functional Perturbation Theory (DFPT) method or an atomic displacement method is generally adopted when the phonon spectrum is calculated.
In this embodiment, in step S3, software such as Matlab is used to fit thermodynamic data, the reference state function values of the constituent elements are subtracted, and then a high-entropy alloy end group compound thermodynamic database is constructed;
specifically, the specific fitting function model is as follows:
G(T)=A+BTInT+CT2+DT3+ET-1+FT
wherein G (T) represents Gibbs free energy of elemental elements or terminal compounds as a function of temperature in J/(mol. atom), T represents Kelvin temperature (K), and values for parameters A, B, C, D, E and F are fitted by software such as Matlab; the method specifically comprises the following steps:
s31, fitting thermodynamic data of the high-entropy alloy end group compound and the composition simple substance elements to obtain various parameter values of a function expression;
step S32, data processing is carried out on the fitted terminal compound function, the stable structure of the simple substance elements forming the terminal compound at room temperature (298.15K) is taken as a reference state, and the Gibbs free energy function value at room temperature, namely the reference state value, is obtained by a thermodynamic function expression;
and S33, deducting the reference state value by using the function expression of each terminal compound, and finally writing the deducted Gibbs free energy function expression of the terminal compound into a terminal compound thermodynamic database.
In this example, the end group compound Co is in the FCC structure3For example, Mn is calculated as Δ G relative Gibbs free energyT(Co3Mn)=[GT(Co3Mn)-3×G298.15(Co)-G298.15(Mn)]/4, wherein Δ GT(Co3Mn) as end group compound Co3Relative Gibbs free energy function expression of Mn, GT(Co3Mn) as a base compound Co3Gibbs free energy function expression of Mn, G298.15(Co) is the Gibbs free energy function value corresponding to the Hexagonal Close Packed (HCP) stable structure of pure element Co at room temperature (298.15K), G298.15(Mn) is a Gibbs free energy function value corresponding to a stable structure CBCC _ A12 of pure element Mn at room temperature (298.15K), and thermodynamic units are normalized units, J/(mol. atom).
In this embodiment, the step S4 is specifically to calculate, based on a thermodynamic database of end compounds and a thermodynamic phase equilibrium principle, the occupancy fractions of various elements in the high-entropy alloy on the sublattice under given compositions and temperature conditions by using thermodynamic software Pandat or Thermo-Calc;
preferably, the database is in a TDB format recognized and called by a thermodynamic software package Pandat or Thermo-Calc, and the thermodynamic principle of path transformation for thermodynamic model solution is as follows: according to the property of the thermodynamic function, the thermodynamic function is a state function, and the change of the thermodynamic function value in the reaction process is independent of the reaction path and only related to the initial state and the final state of the reaction. Therefore, the thermodynamic function of the high-entropy alloy compound with the complex structure generated by the pure simple substance element can be converted into the thermodynamic function of the end group compound generated by the pure element, and the thermodynamic function of the high-entropy alloy compound with the complex structure generated by the end group compound is further added to obtain the high-entropy alloy compound with the complex structure through a two-step approach. As shown in fig. 3;
after the high-entropy alloy database is imported into thermodynamic calculation simulation software, the occupancy fraction of each element on the sublattice at different temperatures from 173K to 1473K is calculated, and a configuration expression is further constructed.
Taking CoCrFeMnNi high-entropy alloy as an example, taking the existing calculation resources and the calculation amount of lattice distortion into consideration, carrying out 3 × 3 × 3 supercell, wherein the total number is 108 atoms, and the occupying configuration expression and the rounding result are as follows:
under the thermodynamic equilibrium state at 173K, the occupancy fraction configuration of CoCrFeMnNi is (Co)0.031Cr0.680Fe0.031Mn0.149Ni0.109)1a(Co0.256Cr0.040Fe0.256Mn0.217Ni0.230)3c
Is converted into (Co)1Cr18Fe1Mn4Ni3)1a(Co21Cr3Fe21Mn17Ni19)3c
Under the thermodynamic equilibrium state at 1073K, the occupancy fraction configuration of CoCrFeMnNi is (Co)0.233Cr0.246Fe0.141Mn0.200Ni0.180)1a(Co0.189Cr0.185Fe0.220Mn0.200Ni0.207)3c
Is converted into (Co)6Cr7Fe4Mn5Ni5)1a(Co15Cr15Fe18Mn16Ni17)3c
In this embodiment, in step S5, according to the fractional occupancy value of the element on the sublattice, the random occupancy pattern of atoms is formed on the sublattice, and the sublattices are nested together to form an overall structure, so as to construct a structural model file POSCAR of the actual distribution of atoms in the high-entropy alloy, which is schematically shown in fig. 4;
the method comprises the following steps of constructing a structural file POSCAR of the high-entropy alloy:
(1) taking the existing calculation resources and the calculation amount of lattice distortion into consideration, the unit cell of the high-entropy alloy CoCrFeMnNi with the 108-atom FCC structure is constructed as an example. Splitting an FCC protocell POSCAR-unit cell consisting of 4 atoms into two sublattices POSCAR-1a and POSCAR-3c, wherein the sublattices POSCAR-1a and POSCAR-3c respectively contain 1 atom and 3 atoms, and performing 3 x 3 supercell on the POSCAR-1a and POSCAR-3c respectively, wherein the atomic number ratio of the two sublattices is as follows: 27:81.
(2) And multiplying the atomic number of each sublattice by the atomic ratio in the sublattice at the determined temperature, and rounding to obtain the number of atoms of different elements under different sublattices.
(3) And randomly arranging atomic coordinates in the superlattice by using a random function in Excel, and then defining the atomic coordinates from top to bottom as corresponding elements according to the atomic number of each element in the superlattice and the sequence of Co, Cr, Fe, Mn and Ni. Two sublattices POSCAR of the high-entropy alloy CoCrFeMnNi with 108 atoms, namely POSCAR-1a and POSCAR-3c, can be obtained, and then position coordinates on the sublattices of the same element 1a and 3c are respectively integrated together, so that a complete crystal structure file POSCAR of the high-entropy alloy CoCrFeMnNi with 3 x 3 supercells containing 108 atoms can be obtained.
In this embodiment, the step S6 is based on the total energy minimization principle, and the volume optimization is performed on the crystal structure file POSCAR by using the VASP software package, and then the shape and the atomic position optimization are performed to obtain the structure file CONTCAR after the structure optimization. Step S6 specifically includes:
and step S61, fixing the position and the shape of the unit cell and optimizing the volume of the unit cell. During optimization, the ISIF in the INCAR is set to be 7, the volume of the system which can be always minimum, namely the balance volume, is obtained, and meanwhile, the atom position coordinates when the crystal lattice is not distorted and the first adjacent distance between atoms are also obtained;
and step S62, fixing the shape and the volume of the unit cell, optimizing the atomic position of the unit cell, setting ISIF (intermediate frequency) -2 in INCAR during optimization, and obtaining the atomic position coordinates after the atomic position is optimized, namely the lattice is allowed to be distorted.
The optimized coordinates are shown in table 1:
TABLE 1973K-CoCrFeMnNi high-entropy alloy coordinate partial data before and after two optimizations
In this embodiment, the step S7 substitutes the optimization result into a predetermined lattice distortion formula, which strictly follows physics and mathematics to calculate the total distortion, the average distortion and the relative lattice distortion of the high-entropy alloy, specifically:
the total lattice distortion quantity calculation formula is as follows:
where n is the total number of atoms minus a fixed number of atoms (typically we fix 1 atomic coordinate as the origin), dxi、dyi、dziRepresenting the difference of the corresponding coordinate components (Cartesian coordinates) of the same atom before and after optimization, d0Denotes the distance of the first adjacent atom when no lattice distortion occurs, D andall units of (A) are angstroms
TABLE 2973K-CoCrFeMnNi high entropy alloy lattice distortion calculation process partial data processing
Based on the atomic coordinate optimization in the examples, and n 108-1 107, d0Calculated as 2.47Dr=1.781%
In order to further visually display the high-entropy alloy lattice distortion effect, a data file is led into VESTA software to obtain an occupied visual image of the high-entropy alloy unit cell elements, atomic position schematic diagrams in (100) projection directions are respectively shown in fig. 5 and fig. 6 before and after lattice distortion, and it can be seen that position views among atomic layers before lattice distortion are overlapped, atomic positions are dislocated to a certain degree after lattice distortion, and atomic projection positions with obvious distortion are marked in the diagrams. In addition, other projection directions have similar distortion characteristics.
The above description is only a preferred embodiment of the present invention, and all equivalent changes and modifications made in accordance with the claims of the present invention should be covered by the present invention.
Claims (6)
1. A method for calculating lattice distortion of a high-entropy alloy based on atom occupying ordering behavior is characterized by comprising the following steps:
s1, constructing a corresponding thermodynamic model based on the phase structure of the high-entropy alloy;
step S2, obtaining discrete values of Gibbs free energy thermodynamic data of each end group compound and elementary substance element in the high-entropy alloy through phonon spectrum calculation of a density functional perturbation theory;
step S3, fitting thermodynamic data based on a preset function model, and deducting the reference state function values of the constituent elements to construct a high-entropy alloy end group compound thermodynamic database;
step S4, calculating and obtaining the occupation fraction of each element in the high-entropy alloy on the sublattice under the conditions of given components and temperature based on a terminal compound thermodynamic database and a thermodynamic phase equilibrium principle;
step S5, according to the fractional value of the occupation of the elements on the sublattice, forming atom random occupation patterns on the sublattice, nesting the sublattice together to form an integral structure, and constructing a structural model of the actual distribution of atoms in the high-entropy alloy;
s6, based on the total energy minimization principle, carrying out volume optimization on the structural model of the atomic actual distribution in the high-entropy alloy, and then carrying out shape and atomic position optimization to obtain a structural model after structural optimization;
and step S7, substituting the structure model after the structure optimization into a preset lattice distortion formula to calculate the total distortion, the average distortion and the relative lattice distortion of the high-entropy alloy.
2. The method for calculating the lattice distortion quantity of the high-entropy alloy based on the atom occupying ordering behavior according to claim 1, wherein the function model is as follows:
G(T)=A+BTlnT+CT2+DT3+ET-1+FT
wherein G (T) represents Gibbs free energy of an elemental element or an end group compound as a function of temperature, T represents Kelvin temperature (K), and A, B, C, D, E and F are parameters obtained by fitting.
3. The method for calculating the lattice distortion quantity of the high-entropy alloy based on the atomic occupying ordering behavior according to claim 1, wherein the step S3 is specifically as follows:
s31, fitting thermodynamic data of the high-entropy alloy end group compound and the composition simple substance elements to obtain various parameter values of a function expression;
step S32, data processing is carried out on the fitted terminal compound function, the stable structure of the simple substance elements forming the terminal compound at room temperature is taken as a reference state, and the Gibbs free energy function value at room temperature, namely the reference state value, is obtained by a thermodynamic function expression;
and S33, deducting the reference state value by using the function expression of each terminal compound, and finally writing the deducted relative Gibbs free energy function expression of the terminal compound into a terminal compound thermodynamic database.
4. The method for calculating lattice distortion of a high-entropy alloy based on atomic occupying ordered behavior as claimed in claim 1, wherein the step S4 is specifically to calculate occupying fractions of various elements of a given alloy system on different types of sublattices at different temperatures based on the constructed high-entropy alloy database.
5. The method for calculating the lattice distortion quantity of the high-entropy alloy based on the atomic occupying ordering behavior according to claim 1, wherein the step S6 is specifically as follows:
step S61, fixing the position and shape of the crystal cell, optimizing the volume of the crystal cell to obtain the smallest volume of the system, namely the balance volume, and simultaneously obtaining the atom position coordinate when the crystal lattice is not distorted and the first adjacent distance between atoms;
and step S62, fixing the shape and the volume of the unit cell, and optimizing the atomic position of the unit cell to obtain the atomic position coordinates after the atomic position is optimized, namely the lattice is allowed to be distorted.
6. The method for calculating the lattice distortion quantity of the high-entropy alloy based on the atomic occupying ordering behavior according to claim 1, wherein the step S7 is specifically as follows:
the total lattice distortion quantity calculation formula is as follows:
wherein n is the total number of atoms-the number of fixed atoms, dxi、dyi、dziRepresenting the difference of the corresponding coordinate components of the same atom before and after optimization, d0Denotes the distance of the first adjacent atom when no lattice distortion occurs, D andall units of (a) are angstroms.
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