CN113851199B - Crystal dissociation and slip energy barrier automatic calculation method based on lattice redirection - Google Patents
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Abstract
The invention discloses an automatic calculation method of crystal dissociation and slip energy barrier based on lattice redirection, belonging to the field of material calculation, and specifically comprising the following steps: firstly, inputting a structural file of a crystal aiming at the crystal, and reading crystallographic structure information; determining the slip direction of the dissociation plane or the slip plane of the crystal structure according to the read crystallographic structure information; the redirection of the lattice basis vector is further automated. Then, the redirected crystal structure Shi Jiajie is strained or slipped to generate a strained structure file; carrying out structural relaxation and static calculation on the strain structure file in parallel by a first sexual principle method to obtain a dissociation energy χ (d) -strain d curve or a stacking fault energy gamma (u) -strain u curve; finally, fitting a dissociation energy χ (d) -strain d curve and a stacking fault energy gamma (u) -strain u curve to obtain dissociation and slippage energy barriers and corresponding critical stress; the invention not only can realize high-flux calculation of the mechanical properties of the material, but also can be used for rapidly screening three-dimensional materials with high strength/high hardness.
Description
Technical Field
The invention belongs to the field of material calculation, and particularly relates to an automatic calculation method of crystal dissociation and slip energy barrier based on lattice redirection.
Background
The dissociation energy barrier and critical stress at dissociation strain determine: the energy barrier and critical stress required to cleave the chemical bond between given crystal planes; the slip energy barrier and critical stress at slip strain represent: the energy barrier and critical stress of a given crystal plane along a specific slip direction. Moreover, the dislocation energy curve calculated based on the slip strain determines the misfit energy of the dislocation, which is a main determining parameter for dislocation nucleation and slip.
However, to date, the prior art has only used dissociation and slip energy barriers and corresponding critical stresses to study specific materials and structures [ Physics Reports 826,1-49 (2019) ], lacking the research effort of high-throughput computing. This not only severely limits the application of dissociation and slip energy barriers and corresponding critical stresses in studying material dislocation properties and toughening mechanisms, but also makes it difficult to meet the requirements for dissociation and slip energy barriers and corresponding critical stress big data in the "materials genome project".
Disclosure of Invention
Aiming at the problems, the invention provides an automatic calculation method of the dissociation and slip energy barrier of the crystal based on lattice redirection, which not only provides an efficient and low-cost way for solving the dissociation and slip energy barrier of the crystal material and the corresponding critical stress, but also can improve the efficiency of screening and designing the high-strength/high-toughness material and shorten the research and development application period of new materials.
The crystal dissociation and slip energy barrier based on lattice redirection and the corresponding critical stress automatic calculation method specifically comprise the following steps:
step one, inputting a structural file of a crystal aiming at the crystal, and reading crystallographic structure information;
The structure information includes tag name, lattice basis vector, element type, number of element types, total number of atoms, number of atoms of different elements, whether SELECTIVE DYNAMICS is selected, type of atomic coordinates, atomic position constraints, and the like.
Step two, determining the slip direction of the dissociation plane or the slip plane of the crystal structure according to the read crystallographic structure information;
The determining method comprises the following steps: according to the minimum intrinsic strength of the crystal tensile strain and the shearing strain, acquiring a destabilization structure and a chemical bond breaking position of a crystal structure under the strain along the weakest tensile and shearing directions, judging the weakest bonding position in the crystal structure, and selecting the crystal face crystal orientation of the weakest bonding position as a slip direction of a dissociation plane or a slip plane; or automatically analyzing the crystal face with the largest face spacing in the crystal structure as a dissociation face or a slip face;
and thirdly, automatically redirecting lattice basis vectors according to the slip direction of the dissociation plane or the slip plane.
For the dissociation strain, the redirection of the lattice basis vector is:
Firstly, two non-collinear crystal directions [ u c1vc1wc1 ] and [ u c2vc2wc2 ] located on a dissociation surface (h ckclc) are automatically set, and the conditions are satisfied:
uc1hc+vc1kc+wc1lc＝0
uc2hc+vc2kc+wc2lc＝0
The lattice basis vectors are then redirected to [ u c1vc1wc1]、[uc2vc2wc2 ] and [ h ckclc ], the crystal orientation [ u c1vc1wc1 ] is placed in the x-axis direction, and the crystal orientation [ u c2vc2wc2 ] is placed on the x-y plane, with the dissociation plane (h ckclc) parallel to the x-y plane.
For slip strain, the redirection of the lattice basis vector is:
Firstly, automatically setting a crystal direction [ u s1vs1ws1 ] which is positioned on a slip plane (h sksls) and is not collinear with the slip direction [ u svsws ], and meeting the conditions:
ushs+vsks+wsls＝0
us1hs+vs1ks+ws1ls＝0；
Then, the lattice basis vectors are automatically redirected to [ u svsws]、[us1vs1ws1 ] and [ h sksls ], the crystal orientation [ u svsws ] is placed in the x-axis direction, and the crystal orientation [ u s1vs1ws1 ] is placed on the x-y plane, and the slip plane (h sksls) is parallel to the x-y plane.
Step four, separating strain or sliding strain from the redirected crystal structure Shi Jiajie to generate a strain structure file;
The strain process is divided into two steps, specifically as follows:
The first step is: atoms in the crystal structure are divided into two parts according to the position p z of the dissociation plane or slip plane parallel to the x-y plane relative to the cartesian z-axis, i.e. atoms with z-axis coordinates smaller than p z are the "lower half" and atoms with z-axis coordinates greater than p z are the "upper half".
For dissociation strain, the "upper half" atoms are applied with dissociation displacement d, i.e., p z is changed to p z +d;
For slip strain, the "upper half" atoms are subjected to slip displacement u, i.e., p x and p y are changed to p x+ux and p y+uy, respectively, wherein u x is the component of slip distance u in Cartesian x, and u y is the component of slip distance u in Cartesian y-axis; thereby obtaining atomic coordinates after strain.
The second step is: the strain matrix epsilon is applied to lattice basis vector a i, i=1, 2,3, resulting in strained lattice basis vector a' i:
wherein I is a3 x 3 identity matrix and for the dissociated strain, the strain matrix epsilon is: Wherein ε zz＝d/Lcz,Lcz is the component of the redirected lattice basis vector c in the Cartesian z-axis;
For slip strain, the strain matrix ε is: Wherein ε zx＝ux/Lcz and ε zy＝uy/Lcz.
The strained atomic coordinates and lattice basis vector are output together as a strain structure file to generate a series of strain structure sets with different dissociation strain values or slippage strain values, which are named as POS_ [ d ] and POS_ [ u x]_[uy ] respectively
Step five, carrying out structure relaxation and static calculation on the strain structure set POS_ [ d ] and POS_ [ u x]_[uy ] in parallel by a first sexual principle method to obtain a dissociation energy χ (d) -strain d curve or an stacking fault energy γ (u) -strain u curve;
for the non-relaxed mode, the lattice base vector and atomic positions in the strained structure remain unchanged throughout.
For the relaxation mode, under dissociation strain, only the atomic coordinates near the lattice basal vector and dissociation plane are relaxed; under slip strain, only the unit cell basal vector and the atomic coordinates perpendicular to the slip plane direction are relaxed.
Fitting a dissociation energy χ (d) -strain d curve and a stacking fault energy gamma (u) -strain u curve to obtain dissociation and slippage energy barriers and corresponding critical stress;
First, for the dissociation energy χ (d) -strain d curve, the following formula is used for fitting:
Wherein m i and n are unknown parameters;
for the stacking fault energy γ (u) -strain u curve, the following formula fit is used:
And satisfies γ (0) =0 and dγ/du u＝0 =0; wherein R 0、Ri and I i are unknown parameters.
Then, carrying out numerical derivation on the fitted dissociation energy curve or the fault energy curve to obtain a dissociation stress curveAnd slip stress curve/>
Finally, utilizing the dissociation stress curveAnd slip stress curve/>Calculating dissociation energy barriers and critical stresses, and sliding energy barriers and critical stresses;
the dissociation energy barrier and critical stress are respectively:
Slip energy barrier and critical stress are γ US =max { γ (u) } and respectively
The invention has the advantages that:
1) The crystal dissociation and slip energy barrier automatic calculation method based on lattice redirection can calculate the crystal dissociation and slip energy barrier and the corresponding critical stress of any symmetrical three-dimensional crystal.
2) The automatic calculation method of the crystal dissociation and slip energy barrier based on lattice redirection not only can realize high-flux calculation of the mechanical properties of materials, but also can meet the requirements of the material genome project on the crystal dissociation and slip energy barrier and the corresponding critical stress big data.
3) The automatic calculation method of the crystal dissociation and slip energy barrier based on lattice redirection can be used for rapidly screening three-dimensional materials with high strength/high hardness, and has guiding significance for designing superhard materials and high-performance structural materials.
Drawings
FIG. 1 is a schematic diagram of an automatic calculation method of crystal dissociation and slip energy barrier based on lattice redirection according to the present invention;
FIG. 2 is a flow chart of an automatic calculation method of crystal dissociation and slip energy barrier based on lattice redirection according to the present invention;
fig. 3 is a schematic diagram of the present invention for automatically performing a reorientation of the lattice basis vector.
FIG. 4 is a schematic diagram of the present invention with dissociation strain and slip strain.
Detailed Description
The invention is described in further detail below with reference to examples and figures;
The invention discloses a crystal dissociation and slip energy barrier automatic calculation method based on lattice redirection, which comprises the steps of reading information of a crystallographic structure, analyzing symmetry of crystals, automatically redirecting the crystal lattice, generating a series of strain structures, selecting a parallel relaxation mode, calculating convergence by a first principle, calculating dissociation energy or stacking fault energy curve fitting and deriving, and automatically solving dissociation and slip energy barriers and critical stress, as shown in figure 1. Not only can provide a high-efficiency and low-cost way for solving the dissociation and slippage energy barrier and critical stress of the crystal material, but also can improve the efficiency of screening and designing the high-strength/high-toughness material and shorten the research and development application period of the new material.
As shown in fig. 2, the specific steps are as follows:
step one, inputting a structural file of a crystal aiming at the crystal, and reading crystallographic structure information;
The structure information includes tag name, lattice basis vector, element type, number of element types, total number of atoms, number of atoms of different elements, whether SELECTIVE DYNAMICS is selected, type of atomic coordinates (cartesian coordinates or fractional coordinates), atomic coordinates and atomic position constraints (determining whether to allow atomic movement during relaxation), etc.
If fractional coordinates are used for the input structure atomic coordinates, the conversion is automatically to Cartesian coordinates. If SELECTIVE DYNAMICS is selected, it is removed.
Step two, analyzing the symmetry of the crystal, and determining the slip direction of the dissociation plane or the slip plane of the crystal structure according to the read crystallographic structure information;
And according to the read crystallographic structure information and the set symmetry analysis precision, the symmetry of the input structure is determined by SPGLIB interface programs. The determining method comprises the following steps: according to the minimum intrinsic strength of the crystal tensile strain and the shearing strain, acquiring a destabilization structure and a chemical bond breaking position of a crystal structure under the strain along the weakest tensile and shearing directions, judging the weakest bonding position in the crystal structure, and selecting the crystal face crystal orientation of the weakest bonding position as a slip direction of a dissociation plane or a slip plane; or automatically analyzing the crystal face with the largest face spacing in the crystal structure as a dissociation face or a slip face;
and thirdly, automatically redirecting lattice basis vectors according to the slip direction of the dissociation plane or the slip plane.
As shown in fig. 3, for the dissociation strain, the redirection of the lattice basis vector is:
Firstly, two non-collinear crystal directions [ u c1vc1wc1 ] and [ u c2vc2wc2 ] located on a dissociation surface (h ckclc) are automatically set, and the conditions are satisfied:
uc1hc+vc1kc+wc1lc＝0
uc2hc+vc2kc+wc2lc＝0
The lattice basis vectors are then redirected to [ u c1vc1wc1]、[uc2vc2wc2 ] and [ h ckclc ], the crystal orientation [ u c1vc1wc1 ] is placed in the x-axis direction, and the crystal orientation [ u c2vc2wc2 ] is placed on the x-y plane, with the dissociation plane (h ckclc) parallel to the x-y plane.
For slip strain, the redirection of the lattice basis vector is:
Firstly, automatically setting a crystal direction [ u s1vs1ws1 ] which is positioned on a slip plane (h sksls) and is not collinear with the slip direction [ u svsws ], and meeting the conditions:
ushs+vsks+wsls＝0
us1hs+vs1ks+ws1ls＝0；
Then, the lattice basis vectors are automatically redirected to [ u svsws]、[us1vs1ws1 ] and [ h sksls ], the crystal orientation [ u svsws ] is placed in the x-axis direction, and the crystal orientation [ u s1vs1ws1 ] is placed on the x-y plane, and the slip plane (h sksls) is parallel to the x-y plane.
In order to reduce the size of the reorientation supercell as much as possible and improve the calculation efficiency, the crystal orientation index is allowed to be a fraction (such as 1/2) for a specific structure and a crystal orientation based on the analysis of the symmetry of the crystal.
Step four, applying a series of dissociation strain or slip strain to the redirected crystal structure to generate a strain structure file;
The strain process is divided into two steps, specifically as follows:
The first step is: atoms in the crystal structure are divided into two parts according to the position p z of the dissociation plane or slip plane parallel to the x-y plane relative to the cartesian z-axis, i.e. atoms with z-axis coordinates smaller than p z are the "lower half" and atoms with z-axis coordinates greater than p z are the "upper half".
The application of the dissociation strain separates two adjacent crystal planes by a distance d in the dissociation direction, while the application of the slip strain slips two adjacent crystal planes (slip planes) by a distance u in the slip direction while maintaining the relative positions of the other atomic layers unchanged.
The method comprises the following steps: for dissociation strain, the "upper half" atoms are applied with dissociation displacement d, i.e., p z is changed to p z +d;
For slip strain, the "upper half" atoms are subjected to a slip displacement u, i.e., p x and p y are changed to p x+ux and p y+uy, respectively, where u x is the component of the slip distance u in Cartesian x; u y is the component of the slip distance u on the Cartesian y-axis, thereby obtaining the strained atomic coordinates.
The second step is: strain is applied to the cell structure by matrix operation, i.e. the strain matrix epsilon is applied to the lattice basis vector a i, i=1, 2,3, resulting in a strained lattice basis vector a' i:
wherein I is a3 x 3 identity matrix and for the dissociated strain, the strain matrix epsilon is: Wherein ε zz＝d/Lcz,Lcz is the component of the redirected lattice basis vector c in the Cartesian z-axis;
For slip strain, the strain matrix ε is: Wherein ε zx＝ux/Lcz and ε zy＝uy/Lcz.
The strained atomic coordinates and lattice basis vector are output together as a strain structure file to generate a series of strain structure sets of different dissociated strain values or slip strain values, respectively designated as pos_ [ d ] and pos_ [ u x]_[uy ], as shown in fig. 4.
Step five, carrying out structure relaxation and static calculation on the strain structure set POS_ [ d ] and POS_ [ u x]_[uy ] in parallel by a first sexual principle method to obtain a dissociation energy χ (d) -strain d curve or an stacking fault energy γ (u) -strain u curve;
for the calculation of the crystal dissociation and slip energy barrier and critical stress, the non-relaxation mode and the relaxation mode may be selected. For the non-relaxed mode, the lattice base vector and atomic positions in the strained structure remain unchanged throughout.
For the relaxation mode, under dissociation strain, only the atomic coordinates near the lattice basal vector and dissociation plane are relaxed; under slip strain, only the unit cell basal vector and the atomic coordinates perpendicular to the slip plane direction are relaxed.
And (3) carrying out structure relaxation (only in a relaxation mode) and static calculation on the strain structure POS_ [ d ] and POS_ [ u x]_[uy ] in parallel through first sexual principle (from the head) calculation software, acquiring energy and stress values of the strain structure, and judging whether the structure is converged or not. If yes, extracting energy of the relaxed structure, otherwise, copying the structure into a first sexual principle structure file, and carrying out structure relaxation again.
Fitting a dissociation energy χ (d) -strain d curve and a stacking fault energy gamma (u) -strain u curve to obtain dissociation and slippage energy barriers and corresponding critical stress;
Firstly, based on the first principle calculation results of structures with different strain values, a dissociation energy χ (d) -strain curve or an stacking fault energy γ (u) -strain curve is automatically obtained.
For the dissociation energy χ (d) -strain d curve, the following formula fit is used:
Wherein m i and n are unknown parameters; the size of n determines the fitting accuracy.
For the stacking fault energy γ (u) -strain u curve, the following formula fit is used:
And satisfies γ (0) =0 and dγ/du| u＝0 =0; wherein R 0、Ri and I i are unknown parameters.
Then, carrying out numerical derivation on the fitted dissociation energy curve or the fault energy curve to obtain a dissociation stress curveAnd slip stress curve/>
Finally, utilizing the dissociation stress curveAnd slip stress curve/>Calculating dissociation energy barriers and critical stresses, and sliding energy barriers and critical stresses;
The dissociation energy barrier and critical stress are respectively: chi C＝limd→∞ chi (d) and
Slip energy barrier and critical stress are γ US =max { γ (u) } and respectively
Examples:
(1) Pretreatment: preparing a crystal structure file, fully relaxing the structure, and the like.
(2) The crystallographic structure information of the input structure file is read, including the name of the mark, the vector of the lattice basis vector, the type of the element, the number of the element types, the total number of atoms, the number of atoms of different elements, whether SELECTIVE DYNAMICS is selected, the type of the atomic coordinates, the atomic position constraint, and the like.
(3) The SPGLIB interface procedure was used to determine the spatial group of unit cells.
(4) According to the input dissociation plane (hkl) and the slip path (hkl) [ uvw ], lattice redirection is automatically carried out, and the redirected structure is copied into ALIPOS files to serve as an initial structure of dissociation or slip strain.
(5) A series of strain structures are automatically generated that dissociate or slip the strain, and are designated POS_ [ d ] and POS_ [ u x]_[uy ], respectively.
(6) Calculating the energy of the strain structure of the series of dissociated or slipped strains in parallel, constructing a separate folder for each strain value, and performing the steps (7) - (9) in parallel under each folder.
(7) The relaxation mode is selected.
(8) The strain cells are subjected to structural relaxation and the energy and stress values of the strain cells are calculated by first principles (from the head) calculation software.
(9) And judging whether the strain structure is converged or not. If yes, extracting energy of the relaxed structure; otherwise, the structure is copied into a first principle structure file, and the structure relaxation is performed again.
(10) And outputting a dissociation energy-strain curve or a stacking fault energy-strain curve after all the strain values are calculated. And fitting and deriving the dissociation energy curve or the fault energy curve, and automatically obtaining a dissociation stress curve or a slip stress curve.
(11) Based on the dissociation energy and dissociation stress curve or the stacking fault energy and the slip stress curve, the crystal dissociation and slip energy barrier and the critical stress are automatically acquired.
Claims (4)
1. The automatic calculation method of the crystal dissociation and slip energy barrier based on lattice redirection is characterized by comprising the following specific steps:
Step one, inputting a structural file of a crystal aiming at the crystal, and reading crystallographic structure information; determining the slip direction of the dissociation plane or the slip plane of the crystal structure according to the read crystallographic structure information; further, according to the slip direction of the dissociation plane or the slip plane, the redirection of the lattice basis vector is automatically carried out;
for the dissociation strain, the redirection of the lattice basis vector is:
First, two dissociation surfaces are automatically set Is not collinear with the crystal orientation/>And/>And satisfies the conditions:
；
；
Then, the lattice basis vectors are redirected to 、/>And/>And will crystal orientation/>Placed in the x-axis direction to make the crystal orientation/>Placed on the x-y plane, the dissociation plane/>Parallel to the x-y plane;
for slip strain, the redirection of the lattice basis vector is:
first, automatically setting a sliding surface And is connected with the slip direction/>Non-collinear Crystal orientation/>The conditions are satisfied:
；
；
Then, the lattice basis vectors are automatically redirected to 、/>And/>And will crystal orientation/>Placed in the x-axis direction to make the crystal orientation/>Placed on the x-y plane, slip plane/>Parallel to the x-y plane;
Step two, separating strain or sliding strain from the redirected crystal structure Shi Jiajie to generate a strain structure file; the structural relaxation and static calculation are carried out on the strain structural file in parallel through a first sexual principle method, so that dissociation energy is obtained Strain d curve or stacking fault energy/>-A strain u-curve;
The strain process is divided into two steps, and is specifically as follows:
the first step is: according to dissociation or slip planes parallel to the x-y plane relative to Cartesian Position of shaft/>The atoms in the crystal structure are divided into two parts, i.e. the z-axis coordinates are smaller than/>The atoms of (2) are the lower half, and the z-axis coordinate is greater than/>The upper moiety of the atoms of (a);
for dissociation strain, the upper half of atoms are applied with dissociation displacement I.e./>Change to/>；
For slip strain, the upper half of atoms are applied with slip displacementI.e./>And/>Respectively change to/>And/>Wherein/>Is slip distance/>In Cartesian/>Components of (2); /(I)Is slip distance/>In Cartesian/>The component of the axis, thereby obtaining strained atomic coordinates;
The second step is: will strain matrix Applied to lattice basis vector/>On/>Obtaining the lattice basis vector/>, after strain：
；
Wherein the method comprises the steps ofIs a 3 x3 identity matrix, and for dissociated strain, a strain matrix/>The method comprises the following steps: /(I)Wherein/>，A component of the redirected lattice basis vector c in the cartesian z-axis;
For slip strain, the strain matrix The method comprises the following steps: /(I)Wherein/>And/>；
The strained atomic coordinates and lattice basis vector are output together as a strain structure file to generate a series of strain structure sets with different dissociated strain values or slippage strain values, which are respectively named asAnd/>；
Step three, for dissociation energyStrain d-curve and stacking fault energy/>Strain/>Fitting a curve to obtain dissociation and slippage energy barriers and corresponding critical stress;
the method comprises the following steps:
First, with respect to dissociation energy -A strain d curve fitted using the following formula:
；
Wherein the method comprises the steps of And/>Is an unknown parameter;
for the fault energy Strain/>Curve fitting using the following formula:
；
And satisfy the following And/>; Wherein/>R i and I i are unknown parameters;
Then, carrying out numerical derivation on the fitted dissociation energy curve or the fault energy curve to obtain a dissociation stress curve And slip stress curve/>；
Finally, utilizing the dissociation stress curveAnd slip stress curve/>Calculating dissociation energy barriers and critical stresses, and sliding energy barriers and critical stresses;
the dissociation energy barrier and critical stress are respectively: And/> ；
The slip energy barrier and critical stress are respectivelyAnd/>。
2. The method of claim 1, wherein the structural information includes a tag name, a lattice basis vector, an element type, a number of element types, a total number of atoms, a number of atoms of different elements, whether SELECTIVE DYNAMICS is selected, a type of atomic coordinates, and atomic position constraints.
3. The method for automatically calculating the dissociation and slip energy barrier of crystal based on lattice redirection according to claim 1, wherein the specific method for determining the slip direction of the dissociation plane or slip plane comprises the following steps: according to the minimum intrinsic strength of the crystal tensile strain and the shearing strain, acquiring a destabilization structure and a chemical bond breaking position of a crystal structure under the strain along the weakest tensile and shearing directions, judging the weakest bonding position in the crystal structure, and selecting the crystal face crystal orientation of the weakest bonding position as a slip direction of a dissociation plane or a slip plane; or automatically analyzing the crystal face with the largest face spacing in the crystal structure as a dissociation face or a slip face.
4. The method for automatically calculating the dissociation and slip energy barrier of crystals based on lattice redirection according to claim 1, wherein the parallel structure relaxation of the first principle of nature on the strain structure file is specifically as follows:
for the non-relaxation mode, the lattice base vector and the atomic position in the strained structure are always kept unchanged;
For the relaxation mode, under dissociation strain, only the atomic coordinates near the lattice basal vector and dissociation plane are relaxed; under slip strain, only the unit cell basal vector and the atomic coordinates perpendicular to the slip plane direction are relaxed.
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| 冲击载荷下TATB晶体滑移和各向异性的分子动力学研究;周婷婷等;物理化学学报;20170215;33(05);949-959 * |
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