CN113868850B - High-flux elastic property calculation method based on symmetry and standard orientation - Google Patents
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Abstract
The invention discloses a high-flux elastic property calculation method based on symmetry and standard orientation, and belongs to the field of material calculation. First, the crystallographic structure information of the crystal S is extracted, and the symmetry of the crystal structure is analyzed based on the set symmetry analysis precision, so as to determine the space group and crystal system of the unit cell. Then, based on symmetry of the input crystal structure, automatically redefining the input structure as an IEEE standard orientation, and automatically setting corresponding distortion modes, and applying a strain matrix to each distortion mode generates a series of distortion structures. And calculating the total energy of each distortion structure and the corresponding strain energy of the unit volume to obtain strain energy-strain curves of the unit volume in different distortion modes, and removing the unstable distortion modes in the strain energy-strain curves to obtain final strain energy-strain curves of the unit volume. And performing quadratic term fitting on the final strain energy-strain curve of unit volume, and calculating the elastic constant and other elastic property parameters. The invention has high calculation efficiency and low cost.
Description
Technical Field
The invention belongs to the field of material calculation, and particularly relates to a high-flux elastic property calculation method based on symmetry and standard orientation.
Background
Elastic properties are fundamental properties describing the reversible response of a crystal to external loads within the elastic limit and play an important role in the design of structural materials. For example, pugh ratio (ratio of shear modulus to bulk modulus) is a simple parameter that quantifies the toughness and brittleness of a material; in a pegbase dislocation model describing dislocation slip properties, the elastic energy factor K of the dislocation is measured by shear modulus and poisson's ratio; the elastic properties of crystals are also key parameters related to interatomic forces, phonon dispersion, elastic stability, crystal cohesion, etc. [ Physics Reports 826,1-49 (2019) ]. However, since the measurement of the elastic properties of crystals by experiments is time-consuming and labor-consuming and is more difficult to measure for metastable phase structures, it is difficult to meet the requirement of large data on the elastic properties of three-dimensional materials and two-dimensional materials in the "materials genome project".
Disclosure of Invention
The invention provides a high-flux elastic property calculation method based on symmetry and standard orientation in order to realize automatic calculation of elastic constants and other elastic properties of a crystal structure and realize efficient screening of high-performance materials.
The high-flux elastic property calculation method based on symmetry and standard orientation comprises the following steps:
step one, preparing a structure file of a certain crystal S, preprocessing the structure file to enable the crystal structure to be fully relaxed, and reading crystallographic structure information of the structure;
Step two, based on the read crystallographic structure information and the set symmetry analysis precision, automatically analyzing the symmetry of the input crystal structure by utilizing SPGLIB interface program to determine the space group and crystal system of the unit cell;
step three, according to symmetry of the crystal structure input, automatically converting the crystal structure into IEEE standard orientation;
And step four, according to the symmetry of the input crystal structure, automatically setting corresponding distortion modes, and applying a strain matrix to each distortion mode to generate a series of distortion structures.
The number of distortion modes is equal to the number of independent elastic constants.
The distortion structure is specifically generated by:
First, a strain matrix epsilon is applied to the original lattice basis vector a i to obtain a strained lattice basis vector a i', i=1, 2,3:
wherein I is a 3×3 identity matrix; epsilon is the strain matrix:
Then, outputting distortion structures of different strain values, which are named as POS_ [ display_mode ] _ [ strain_value ]; wherein the distortion_mode is a distortion mode number, and the strain_value is a strain value.
Step five, respectively carrying out structural relaxation on each distorted structure through first sexual principle computing software, computing the total energy of the structure, and judging whether the atomic stress in the distorted structure is converged or not; if yes, extracting total energy of each distorted structure after relaxation, and executing a step six; if not, copying the structure into a first principle structure file, and carrying out structure relaxation again until the stress of atoms in the distorted structure is converged.
For structural relaxation, only the atomic positions are relaxed while the lattice basis vector of the distorted structure remains unchanged.
And step six, after the total energy of each distortion structure is calculated, calculating the strain energy of the unit volume corresponding to each distortion structure, and obtaining strain energy-strain curves of the unit volumes in different distortion modes.
Strain energy per unit volume: Δe= (E i-E0)/V0
E i is the total energy of the distorted structure at the strain value, E 0 is the total energy of the zero strain structure, and V 0 is the volume of the zero strain structure.
Step seven, judging whether the strain energy-strain curves of each unit volume have bad data or unstable distortion modes, deleting the bad data if the strain energy-strain curves of each unit volume have the bad data, regenerating a final strain energy-strain curve of each unit volume, and executing the step eight; if the unstable distortion mode exists, stopping operation and outputting error information; if neither exists, a final strain energy-strain curve per unit volume is obtained, and step eight is performed.
The unstable distortion mode comprises a unit volume strain energy and strain value non-quadratic relation, an input structure in an unbalanced state and an unstable distortion mode.
Step eight, performing quadratic term fitting on the final strain energy-strain curve of unit volume, calculating an elastic constant, and obtaining an elastic constant matrix;
The unit volume strain energy-strain curve fitting yields a quadratic equation: Δe=aδ 2 +bδ+c
Wherein δ is the strain value; Δe is strain energy per unit volume; a. and b and c are correlation fitting coefficients.
The linear combination of the binomial coefficients a in the quadratic equation yields the value of the elastic constant.
Step nine, obtaining other elastic property parameters of the crystal structure based on the determined elastic constant;
the other elastic property parameters comprise elastic modulus, pugh ratio, elastic stability criterion and elastic anisotropy coefficient.
The invention has the advantages and beneficial effects that:
The invention can realize high-flux calculation of the elastic property of the crystal, provides an efficient and low-cost way for solving the elastic property of the three-dimensional material and the two-dimensional material, can improve the efficiency of screening and designing the high-rigidity material, and shortens the research and development application period of the new material.
Drawings
FIG. 1 is a schematic diagram of a high-throughput elastic property calculation method based on symmetry and standard orientation in accordance with the present invention;
FIG. 2 is a flow chart of a high throughput elastic property calculation method based on symmetry and standard orientation according to the present invention;
FIG. 3 is a graph showing criteria for four unstable distortion modes in the present invention; (a) poor data exists, (b) the unit volume strain energy and the strain value are not in a quadratic relation, (c) the input structure is in an unbalanced state, and (d) an unstable distortion mode exists.
Detailed Description
The invention will be further described with reference to the drawings and specific examples.
The invention discloses a high-flux elastic property calculation method based on symmetry and standard orientation, which is shown in a figure 1, and comprises the steps of reading crystal structure information, analyzing the symmetry of crystals, automatically setting IEEE standard orientation and distortion mode, judging unstable distortion mode and calculating the elastic property with high flux.
A high-throughput elastic property calculation method based on symmetry and standard orientation, as shown in fig. 2, comprising the steps of:
step one, preparing a structure file of a certain crystal S, preprocessing the structure file to enable the crystal structure to be fully relaxed, and reading crystallographic structure information of the structure;
The crystallographic structure information includes: the name, three-dimensional or two-dimensional material, lattice basis vector, element type, number of element species, total atomic number, number of atoms of different elements, whether SELECTIVE DYNAMICS is selected (selection dynamics), type of atomic coordinates, and atomic position constraints are noted.
The atomic coordinate types are classified into Cartesian coordinates or fractional coordinates, and if Cartesian coordinates are used for inputting the structural atomic coordinates, the atomic coordinates are automatically converted into fractional coordinates. If SELECTIVE DYNAMICS is selected, it is automatically deleted.
Step two, based on the read crystallographic structure information and the set symmetry analysis precision, automatically analyzing the symmetry of the input crystal structure by utilizing SPGLIB interface program to determine the space group and crystal system of the unit cell; and thirdly, automatically converting the crystal structure into an IEEE standard orientation according to the symmetry of the input crystal structure.
Since the value of the elastic constant c ij depends on the choice of structure coordinate system and lattice vector, the input structure is automatically reconverted to the IEEE standard orientation.
For three-dimensional and two-dimensional materials, the IEEE standard orientations are set as shown in table 1:
TABLE 1
For the three-dimensional material, under the orientation of IEEE standard, the number of independent elastic constants and the value of the independent elastic constants of different symmetrical structures are respectively as follows:
If the space group number is 1-2, the three-dimensional material is triclinic, the number of independent elastic constants is 21, c11、c12、c13、c14、c15、c16、c22、c23、c24、c25、c26、c33、c34、c35、c36、c44、c45、c46、c55、c56 and c 66 respectively.
If the space group number is 3-15, the three-dimensional material is monoclinic, the number of independent elastic constants is 13, c11、c12、c13、c15、c22、c23、c25、c33、c35、c44、c46、c55 and c 66 respectively.
If the space group number is 16-74, the three-dimensional material is orthorhombic, the number of independent elastic constants is 9, and c 11、c12、c13、c22、c23、c33、c44、c55 and c 66 are respectively.
If the space group number is 89-142 and the three-dimensional material is tetragonal system I type, the number of independent elastic constants is 6, and c 11、c12、c13、c33、c44 and c 66 are respectively.
If the space group number is 75-88, the three-dimensional material is tetragonal system II type, the number of independent elastic constants is 7, and c 11、c12、c13、c16、c33、c44 and c 66 are respectively.
If the space group numbers are 149-167 and the three-dimensional material is rhombohedral system I type, the number of independent elastic constants is 6, and c 11、c12、c13、c14、c33 and c 44 are respectively. And c 66＝(c11-c12)/2.
If the space group numbers are 143-148 and the three-dimensional material is rhombohedral system II type, the number of independent elastic constants is 7, and c 11、c12、c13、c14、c15、c33 and c 44 are respectively. And c 66＝(c11-c12)/2.
If the space group number is 168-194 and the three-dimensional material is hexagonal, the number of independent elastic constants is 5, and c 11、c12、c13、c33 and c 44 are respectively. And c 66＝(c11-c12)/2.
If the space group numbers are 195-230, the three-dimensional material is cubic, the number of independent elastic constants is 3, and c 11、c12 and c 44 are respectively.
For two-dimensional materials, under the orientation of IEEE standard, the number of independent elastic constants and the value of the independent elastic constants of different symmetrical structures are respectively
If the space group number is 3-15 and the two-dimensional material is in oblique symmetry, the number of independent elastic constants is 6, and c 11、c12、c22、c16、c26 and c 66 are respectively adopted.
If the space group number is 16-74 and the two-dimensional material is orthogonal symmetrical, the number of independent elastic constants is 4, and c 11、c12、c22 and c 66 are respectively.
If the space group number is 75-142 and the two-dimensional material is tetragonal symmetric, the number of independent elastic constants is 3, and c 11、c12 and c 66 are respectively.
If the space group numbers are 143-194 and the two-dimensional material is in hexagonal symmetry, the number of independent elastic constants is 2, and c 11 and c 12 are respectively. And c 66＝(c11-c12)/2.
And step four, according to the symmetry of the input crystal structure, automatically setting corresponding distortion modes, and applying a strain matrix to each distortion mode to generate a series of distortion structures.
The number of distortion modes is equal to the number of independent elastic constants.
In order to improve the calculation efficiency, the symmetry of the structure is maintained to the greatest extent when the distortion mode is considered.
The specific steps for generating the distortion structure are as follows:
Applying a strain matrix epsilon to the original lattice basis vector a i, and obtaining a lattice basis vector a i' after strain through matrix operation:
wherein I is a 3×3 identity matrix; epsilon is the strain matrix:
Outputting distortion structures of different strain values, which are named as POS_ [ display_mode ] _ [ strain_value ]; wherein the distortion_mode is a distortion mode number, and the strain_value is a strain value.
Step five, respectively carrying out structural relaxation on each distorted structure through first sexual principle computing software, computing the total energy of the structure, and judging whether the atomic stress in the distorted structure is converged or not; if yes, extracting total energy of each distorted structure after relaxation, and executing a step six; if not, copying the structure into a first principle structure file, and carrying out structure relaxation again until the stress of atoms in the distorted structure is converged.
For structural relaxation, only the atomic positions are relaxed while the lattice basis vector of the distorted structure remains unchanged.
Step six, after the total energy of all the distortion structures is calculated, calculating the strain energy of the unit volume corresponding to each distortion structure, and obtaining strain energy-strain curves of the unit volume in different distortion modes;
Strain energy per unit volume: Δe= (E i-E0)/V0
Wherein E i is the total energy of the distorted structure under the strain value, E 0 is the total energy of the zero-strain structure, and V 0 is the volume of the zero-strain structure.
Step seven, judging whether the strain energy-strain curves of each unit volume have bad data or unstable distortion modes, deleting the bad data if the strain energy-strain curves of each unit volume have the bad data, regenerating a final strain energy-strain curve of each unit volume, and executing the step eight; if the unstable distortion mode exists, stopping operation and outputting error information; and if the poor data and the unstable distortion mode do not exist, obtaining a final strain energy-strain curve of unit volume, and executing the step eight.
The unstable distortion mode comprises a unit volume strain energy and strain value non-quadratic relation, an input structure in an unbalanced state and an unstable distortion mode.
Poor data and 3 criteria for unstable distortion modes, as shown in fig. 3:
(a) There are bad data: if the value of the strain energy per unit volume exceeds the range of 0 to 1, the data point is defined as poor data calculated by the first sexual principle;
(b) Unit volume strain energy and strain value are not quadratic: if the regression square sum of the quadratic term fit of the strain energy and the strain value of the unit volume exceeds 0.1, judging that the strain energy and the strain value of the unit volume are not in quadratic relation;
(c) The input structure is in an unbalanced state: if the value of-b/2 a in the quadratic equation delta E=aδ 2 +bδ+c obtained by fitting exceeds the range of-0.004 to 0.004, the input crystal structure is judged to be in an unbalanced state;
(d) There are unstable distortion modes: if the sign of the slope between two adjacent data points changes more than twice, then an unstable distortion mode is determined to exist.
Step eight, performing quadratic term fitting on the final strain energy-strain curve of unit volume, solving to obtain an elastic constant, and obtaining an elastic constant matrix;
The unit volume strain energy-strain curve fitting yields a quadratic equation: Δe=aδ 2 +bδ+c
Wherein δ is the strain value; a. and b and c are correlation fitting coefficients.
The linear combination of the binomial coefficients a in the quadratic equation yields the value of the elastic constant.
Step nine, obtaining other elastic property parameters of the crystal structure based on the determined elastic constant;
the other elastic property parameters comprise elastic modulus, pugh ratio, elastic stability criterion and elastic anisotropy coefficient.
Claims (4)
1. A high-throughput elastic property calculation method based on symmetry and standard orientation, which is characterized by comprising the following steps:
step one, preparing a structure file of a certain crystal S aiming at the crystal S, so that the crystal structure is fully relaxed, and reading the crystallographic structure information of the structure;
The structure relaxes, only relaxes the atomic position and keeps the lattice basis vector of the distorted structure unchanged;
Step two, based on the read crystallographic structure information and the set symmetry analysis precision, automatically analyzing the symmetry of the input crystal structure by utilizing SPGLIB interface program to determine the space group and crystal system of the unit cell;
step three, according to symmetry of the crystal structure input, automatically converting the crystal structure into IEEE standard orientation;
Step four, according to symmetry of the input crystal structure, automatically setting corresponding distortion modes, and applying a strain matrix to each distortion mode to generate a plurality of distortion structures;
Step five, respectively carrying out structural relaxation on each distorted structure through first sexual principle computing software, computing the total energy of the structure, and judging whether the atomic stress in the distorted structure is converged or not; if yes, extracting total energy of each distorted structure with good relaxation; if not, copying the distorted structure into a first principle structure file, and carrying out structural relaxation again until the stress of atoms in the distorted structure is converged;
Step six, after the total energy of all the distortion structures is calculated, calculating the strain energy of the unit volume corresponding to each distortion structure, and obtaining strain energy-strain curves of the unit volume in different distortion modes;
Strain energy per unit volume: Δe= (E i-E0)/V0
Wherein E i is the total energy of the distorted structure under the strain value, E 0 is the total energy of the zero-strain structure, and V 0 is the volume of the zero-strain structure;
Step seven, judging whether the unit volume strain energy-strain curve of each distortion mode has bad data or an unstable distortion mode, if so, deleting the bad data, regenerating a final unit volume strain energy-strain curve, and executing step eight; if the unstable distortion mode exists, stopping operation and outputting error information; if the strain energy and the strain energy are not present, a final strain energy-strain curve of unit volume is obtained, and the step eight is executed;
step eight, performing quadratic term fitting on the final strain energy-strain curves of each unit volume, calculating an elastic constant, and obtaining an elastic constant matrix;
The unit volume strain energy-strain curve fitting yields a quadratic equation: Δe=aδ 2 +bδ+c
Wherein δ is the strain value; Δe is strain energy per unit volume; a. b and c are correlation fitting coefficients;
The linear combination of the binomial coefficient a in the quadratic equation is used for obtaining the value of the elastic constant;
and step nine, obtaining other elastic property parameters of the crystal structure based on the determined elastic constant.
2. The method for calculating high-throughput elastic properties based on symmetry and standard orientation according to claim 1, wherein the generating distortion structure in the fourth step is specifically:
First, a strain matrix ε is applied to a primary lattice basis vector a i to obtain a strained lattice basis vector a i':
wherein I is a 3×3 identity matrix; epsilon is the strain matrix:
Then, outputting distortion structures of different strain values, which are named as POS_ [ display_mode ] _ [ strain_value ]; wherein the distortion_mode is a distortion mode number, and the strain_value is a strain value.
3. The method of claim 1, wherein the unstable distortion mode comprises a unit volume strain energy and strain value non-quadratic relationship, an input structure in an unbalanced state, and an unstable distortion mode.
4. A method of high throughput elastic property calculation based on symmetry and standard orientation according to claim 1, wherein said other elastic property parameters of the crystal structure include elastic modulus, pugh ratio, elastic stability criterion and elastic anisotropy coefficient.
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Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| JPH11272723A (en) * | 1998-03-20 | 1999-10-08 | Fujitsu Ltd | Device for calculating modulus of elasticity and storage medium |
| WO2007071095A1 (en) * | 2005-12-22 | 2007-06-28 | Eidgenössische Technische Hochschule Zürich | Method for crystal structure determination |
| CN107665274A (en) * | 2017-09-08 | 2018-02-06 | 东南大学 | A kind of method for designing low elastic modulus titanium alloy |
| KR20200092536A (en) * | 2019-01-25 | 2020-08-04 | 연세대학교 산학협력단 | Method and apparatus for analyzing perovskite and pseudo-perovskite material |
| WO2020228140A1 (en) * | 2019-05-10 | 2020-11-19 | 北京大学深圳研究生院 | Method for describing crystal structure of material and application thereof |
| CN113160904A (en) * | 2021-03-17 | 2021-07-23 | 北京航空航天大学 | High-throughput calculation method for surface property based on automatic modeling technology |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| JPH11272723A (en) * | 1998-03-20 | 1999-10-08 | Fujitsu Ltd | Device for calculating modulus of elasticity and storage medium |
| WO2007071095A1 (en) * | 2005-12-22 | 2007-06-28 | Eidgenössische Technische Hochschule Zürich | Method for crystal structure determination |
| CN107665274A (en) * | 2017-09-08 | 2018-02-06 | 东南大学 | A kind of method for designing low elastic modulus titanium alloy |
| KR20200092536A (en) * | 2019-01-25 | 2020-08-04 | 연세대학교 산학협력단 | Method and apparatus for analyzing perovskite and pseudo-perovskite material |
| WO2020228140A1 (en) * | 2019-05-10 | 2020-11-19 | 北京大学深圳研究生院 | Method for describing crystal structure of material and application thereof |
| CN113160904A (en) * | 2021-03-17 | 2021-07-23 | 北京航空航天大学 | High-throughput calculation method for surface property based on automatic modeling technology |
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