CN113192578B - Crystal symmetry and band path determination method and device - Google Patents
Crystal symmetry and band path determination method and device Download PDFInfo
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Abstract
The invention provides a method and a device for determining symmetry and energy band paths of crystals, wherein the method comprises the following steps: determining a standard crystallographic unit cell of a target crystal based on a structural parameter of the target crystal; obtaining primary elementary cells corresponding to the standard crystallographic unit cells; based on the primitive cells, a point group of a target crystal is determined. According to the method and the device for determining the symmetry of the crystal and the energy band path, which are provided by the embodiment of the invention, the symmetry of the crystal can be determined more efficiently and accurately by determining the crystal point group to which the periodic material belongs based on the group representation theory, so that the k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form the standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent the electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Description
Technical Field
The present invention relates to the technical field, and in particular, to a method and apparatus for determining symmetry of a crystal and an energy band path.
Background
Symmetry of the crystal (including point clusters and space clusters) is closely related to its physical properties. In the physical property research of periodic materials, the point group and the space group of crystals are very important basic parameters. When the microscopic properties of the material are simulated by utilizing quantum mechanics or classical mechanics, the symmetry of a material model must be determined firstly, and the electronic structure of the material can be determined on the basis; when drawing an electron energy band structure, a high-symmetry k point is generally selected to form an energy band path, which represents the distribution of electron energy along the direction of the energy band path.
The existing crystal symmetry and energy band path determination method is that for high symmetry k points and connection paths thereof are manually selected and determined by personnel according to experience, k points which will exist are absent, so that even if the same crystal is in the same state, due to non-uniformity of energy band path selection, the representation of electronic structures may have a huge difference. Moreover, the deficiency of k point deletion exists according to the manner of manual selection and determination of experience.
When the band gap of the semiconductor is judged by using the energy band, if the energy band path is improperly selected, misjudgment of the electronic structure representation information is easily caused; with the development of machine learning technology, electronic structure information is optimized by using materials with the same crystal structure, and if electronic energy band data based on the same k-point path cannot be provided, the efficiency of comparing and improving the electronic performance of a system by a computer algorithm is greatly affected.
In summary, the defects of k point missing and imperfect energy band path in the prior art may cause information missing and misjudgment of electronic structure during electronic energy band representation.
Disclosure of Invention
The invention provides a crystal symmetry and energy band path determining method and device, which are used for solving the defect of k point deficiency in the prior art and realizing more complete acquisition of high-symmetry k points.
The invention provides a crystal symmetry and energy band path determining method, which comprises the following steps:
Determining a standard crystallographic unit cell of a target crystal based on a structural parameter of the target crystal;
obtaining primary elementary cells corresponding to the standard crystallographic unit cells;
based on the primitive cells, a point group of a target crystal is determined.
According to the method for determining symmetry and band path of a crystal provided by the invention, after determining the point group of the target crystal based on the primary unit cell, the method further comprises the following steps:
a spatial population of the target crystal is determined based on the point population of the target crystal.
According to the method for determining symmetry and band path of crystal provided by the invention, after the primary unit cells corresponding to the standard crystallographic unit cells are obtained, the method further comprises the following steps:
and acquiring the energy band path corresponding to the primitive cell based on the primitive cell.
According to the method for determining symmetry and band path of crystal provided by the invention, the point group of the target crystal is determined based on the primary primitive cell, and the method specifically comprises the following steps:
determining effective symmetric operation based on a target operation matrix and atomic coordinates of the target crystal;
A population of points of the target crystal is determined based on the effective symmetry operation and the atomic coordinates of the primitive cells.
According to the method for determining symmetry and energy band path of the crystal provided by the invention, the space group of the target crystal is determined based on the point group of the target crystal, and the method specifically comprises the following steps:
and determining the space group where the primary primitive cell is based on the atomic coordinates of the target crystal and the point group where the primary primitive cell belongs.
According to the method for determining symmetry and band path of a crystal provided by the invention, the standard crystallographic unit cell of the target crystal is determined based on the structural parameter of the target crystal, and the method specifically comprises the following steps:
Determining the Bravais lattice type of the target crystal based on the structural parameters of the target crystal, and acquiring the standard crystallographic unit cell based on a minimum lattice vector.
According to the method for determining symmetry and energy band path of crystal provided by the invention, the energy band path corresponding to the primary primitive cell is obtained based on the primary primitive cell, which comprises the following steps:
and determining a k point and the energy band path connecting the k point based on the Bravais lattice type of the target crystal.
The invention also provides a crystal symmetry and energy band path determining device, which comprises:
a normalization module for determining a standard crystallographic unit cell of a target crystal based on a structural parameter of the target crystal;
the unit cell reduction module is used for obtaining primary unit cells corresponding to the standard crystallographic unit cells;
And the point group determining module is used for determining the point group of the target crystal based on the primary primitive cells.
The invention also provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the steps of any one of the crystal symmetry and energy band path determination methods described above are realized when the processor executes the computer program.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the steps of any of the crystal symmetry and band path determination methods described above.
According to the method and the device for determining the symmetry of the crystal and the energy band path, the crystal point group to which the periodic material belongs is determined based on the group representation theory, so that the symmetry of the crystal can be determined more efficiently and accurately, k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form the standardized energy band path, k point deletion can be avoided, the obtained energy band path can completely represent electronic structure information, and erroneous judgment of the energy band structure caused by k point deletion and imperfect energy band path is avoided.
Drawings
In order to more clearly illustrate the invention or the technical solutions of the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are some embodiments of the invention, and other drawings can be obtained according to the drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of a method for determining symmetry and band path of a crystal according to the present invention;
FIG. 2 is a schematic diagram of a crystal symmetry and band path determining device according to the present invention;
fig. 3 is a schematic structural diagram of an electronic device provided by the present invention.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the present invention more apparent, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is apparent that the described embodiments are some embodiments of the present invention, 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.
In describing embodiments of the present invention, it should be noted that the terms "center", "longitudinal", "lateral", "length", "width", "thickness", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings are merely for convenience in describing the embodiments of the present invention and simplify description, and do not indicate or imply that the devices or elements referred to must have a specific orientation, be configured and operated in a specific orientation, and therefore should not be construed as limiting the embodiments of the present invention. Furthermore, the terms "first," "second," and "third" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance, and not order.
In describing embodiments of the present invention, it should be noted that, unless explicitly stated and limited otherwise, the terms "mounted," "connected," and "connected" should be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in embodiments of the present invention will be understood in detail by those of ordinary skill in the art.
In order to overcome the above problems in the prior art, the invention provides a method and a device for determining symmetry and band path of a crystal, which are characterized in that the point group and the space group to which a calculation target crystal belongs are automatically judged, and standardized k points and connection modes (i.e. band paths) thereof are determined according to corresponding Bravais grids.
FIG. 1 is a schematic flow chart of a method for determining symmetry and band path of a crystal according to the present invention. The crystal symmetry and band path determination method according to the embodiment of the present invention will be described with reference to fig. 1. As shown in fig. 1, the method includes: step 101, determining standard crystallographic unit cells of the target crystal based on the structural parameters of the target crystal.
Specifically, the target crystal is a crystal whose symmetry and energy band path are to be determined.
The structural parameters of the target crystal may be unit cell parameters represented by three-dimensional vector forms, rather than the conventional a, b, c, α, β, γ forms.
The structural parameters of the target crystal are standardized, and standard crystallographic unit cells of the target crystal are determined.
It is to be noted that the atom type of the target crystal, the number of atoms of each type, the total number of atoms, and the coordinate position of each atom may also be obtained.
Step 102, obtaining primitive cells corresponding to standard crystallographic unit cells.
Specifically, if the normalized unit cell contains only one minimal repeating unit, it is called a primordial primitive cell. Primordial primordia are the basic unit of the crystal; in crystallography, in order to represent crystals with as high symmetry as possible, it is likely that multiple minimal repeating units are contained in one unit cell, which is called a complex unit cell. The standardized cells corresponding to the 14 Bravais lattices are represented by polycells.
The minimum repeating unit corresponding to the standard crystallographic unit cell can be obtained by crystal axis sequencing, and the normal unit cell (unit cell) is converted into a standardized primitive cell (PRIMTIVE CELL) to obtain each primitive cell.
The symmetry analysis of the crystal is complicated according to the group representation theory of the crystal symmetry analysis, and the symmetry information of the crystal must be determined according to the constraints of the crystal system (7 types), the Bravais lattice type (14 types), the point group (32 types) and the space group (230 types) of the crystal to the crystal axis and the atomic position by considering the a, b and c axes of the minimum repeating unit of the crystal and the atomic position in the crystal. And the representation of various point groups and space groups can be different due to the difference of a, b and c axes. By converting the normal unit cell into a normalized primitive cell, the non-uniqueness of the space group representation can be eliminated, and the minimum allowable translation vector (i.e., the effective minimum translation vector) of the target crystal can be determined.
Obtaining the elementary cells corresponding to standard crystallographic cells may include determining cell parameters of the elementary cells, the number of elementary cells comprised by the cells, a basic transformation relationship between the cells and the elementary cells, and a translation relationship of each elementary cell.
The atomic type with the least number of atoms, i.e. the atomic type with the least number of atoms and the corresponding number of atoms, can be determined by translating the origin of coordinates to the center of the primordial primordium according to the coordinate positions of all atoms.
The allowable translation relationship (namely effective translation relationship) of the target crystal can be determined, namely, the position of the first atom in the atoms with the least atomic number is taken as a reference, and the translation vector relationship of other atoms and the first atom is determined; and applies the translation relationship to all atoms, checking the translation relationship for actual permissions.
The translation vector and primordial primitive cell number can be determined, i.e., all translation vectors are counted and recorded, and the minimum vector in three directions is determined, thereby determining the minimum translation amount. The number of allowed primordial primordia in the unit cell can be determined from the minimum translation vector.
Step 103, determining the point group of the target crystal based on the primitive cells.
In particular, crystal symmetry determination may include determining a point group of the target crystal.
All macroscopic symmetry elements contained in the crystal intersect at least at one point, and various combinations of all symmetry elements that converge at one point are called point groups of the crystal, or symmetry types.
In crystallography, a crystallography point group is a collection of symmetric operations (e.g., rotation, reflection). These operations, which move the crystal in the other direction with a fixed center, are called symmetrical operations. For a true crystal (not quasi-crystal), the operation of the point group must be able to maintain the three-dimensional translational symmetry of the crystal. After any manipulation of its point clusters, the macroscopic properties of the crystal remain exactly the same as before the manipulation. In the classification of crystals, each group of points is also referred to as a crystal class.
According to the operation matrix corresponding to the group elements of the 32 point groups, all the atomic coordinates of the target crystal are acted in sequence, the acted coordinate positions are compared with the original atomic positions, and if the atomic positions are overlapped, the symmetrical operation (namely effective symmetrical operation) permitted by the target crystal is realized.
It should be noted that, for non-primitive cells, the allowable translation operation (i.e., the effective translation operation) of the target crystal may be determined.
And traversing all effective symmetrical operations to obtain a symmetrical operation matrix group to form a point group to which the target crystal belongs (namely the point group of the target crystal).
According to the embodiment of the invention, the crystal point group to which the periodic material belongs is determined based on the group representation theory, so that the symmetry of the crystal can be determined more efficiently and accurately, and k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form a standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Based on the foregoing in any of the foregoing embodiments, after determining the dot group of the target crystal based on the primitive cell, further comprising: based on the point group of the target crystal, a spatial group of the target crystal is determined.
In particular, crystal symmetry determination may also include determining a spatial group of target crystals.
The collection of all symmetric elements in the internal structure of the crystal is called space group. Specifically, it is a combination of all symmetric elements in the unit cell.
In total, only 230 different symmetrical element combinations, namely 230 space groups, can be provided in all crystal structures.
From the point group operation, a space group panning operation (i.e., a valid panning operation) confirming the permission of the target crystal can be checked.
Traversing the symmetry operation of all space group permissions, and according to the corresponding relation between the point group and the space group in the group representation theory: the same point group may map to multiple spatial groups. The coordinate position of the minimum repeated unit in the crystal is checked through matrix transformation, and the special translation operation of the space group of the crystal is found and determined, so that the space group of the crystal (namely the space group of the target crystal) can be determined.
Determining the spatial group of the target crystal based on the point group of the target crystal may include:
determining a transformation matrix of the standard crystallographic unit cell under a rectangular coordinate system according to the crystal system;
Determining a transformation matrix between standard crystallographic unit cells and primitive unit cells and an inverse matrix thereof;
determining a transformation matrix of the primary primitive cells under a rectangular coordinate system;
Transforming the inverse of the transformation matrix between standard crystallographic cells and primitive cells to a primitive cell representation;
Approximating the atomic coordinates of the target crystal into a minimum primitive cell;
retrieving the least atom types and counting the atom numbers;
determining a translation vector for the least atomic type permissions;
Determining a transformation matrix of the least atomic type permission, and transforming the transformation matrix into a rectangular coordinate system;
Acquiring all atomic coordinates by using a transformation matrix permitted by the least atomic types;
Using a transformation matrix permitted by the least atomic types to act on the transformation matrix of the primary primitive cells under the rectangular coordinate system to obtain a new transformation matrix of the primary primitive cells under the rectangular coordinate system;
aiming at various Bravais grids, the corresponding point groups are exhausted and the symmetrical operation is performed;
transforming the symmetrical operation of the point group to which the target crystal belongs into a primitive cell representation;
Checking the relation between all atoms and symmetrical operation, and determining the point group to which the target crystal belongs;
checking whether the current point group has additional translation operation according to the known translation operation;
Determining the final allowed point group operation of the target crystal, and converting the point group operation into standard crystallographic unit cells and primitive unit cell representations respectively;
Determining a space group to which the target crystal belongs;
All atomic coordinates are transformed to the original coordinate representation using the inverse of the above operation.
After determining the space group of the target crystal, the point group-space group transformation matrix of the target crystal may be determined.
According to the embodiment of the invention, the crystal space group to which the periodic material belongs is determined based on the group representation theory, so that the symmetry of the crystal can be determined more efficiently and accurately, and k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form a standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Based on the foregoing in any of the embodiments, after obtaining the primitive cell corresponding to the standard crystallographic unit cell, the method further comprises: based on the primary primitive cells, energy band paths corresponding to the primary primitive cells are obtained.
Specifically, on the basis of completing symmetry judgment, a set of k points and connection modes thereof can be rapidly determined through traversal.
For each set of point groups, enumerating k points and connection modes required by all standardized energy bands, traversing all high-symmetry k points, ensuring minimum repetition, and determining a set of k points and connection modes thereof as each k point and connecting the k points into energy band paths.
The set of k points can be applied to electronic energy band calculation of quantum mechanics.
According to the embodiment of the invention, based on the symmetry of the crystal, the energy band path of the crystal is determined, the k points with high symmetry can be more efficiently and completely determined and connected to form the standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Based on the foregoing in any of the embodiments, determining a point group of the target crystal based on the primitive cell specifically includes: based on the target operation matrix and the atomic coordinates of the target crystal, an effective symmetric operation is determined.
Specifically, it is checked whether the symmetric operation of the point group element is a valid operation, i.e., the symmetric operation acts on all atomic positions of the unit cell, and whether the operation is a valid symmetric operation.
For a symmetric operation of any point group element, if the symmetric operation can act on all atomic positions of the unit cell, the operation is a valid symmetric operation; if the symmetric operation cannot be applied to all atomic positions of the unit cell, the operation is not an efficient symmetric operation.
The point group of the target crystal is determined based on the effective symmetry operation and the atomic coordinates of the elementary cells.
Specifically, judging the point group to which the effective symmetrical operation belongs, namely if the operation can realize the coincidence of all the atomic positions, the point group operation belongs; if the operation needs additional translation operation to realize complete atomic position coincidence, the operation belongs to translation group operation; if the operation cannot achieve all atomic position coincidence, then the operation does not belong to the point group operation either.
It is checked whether the point group satisfies the position conversion requirement of all atoms of the crystal. If so, it can be determined that the cluster is the cluster of the target crystal.
According to the embodiment of the invention, the crystal point group to which the periodic material belongs is determined based on the group representation theory, so that the symmetry of the crystal can be determined more efficiently and accurately, and k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form a standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Based on the foregoing in any of the embodiments, determining a spatial group of the target crystal based on the point group of the target crystal specifically includes: and determining the space group where the primitive cell is located based on the atomic coordinates of the target crystal and the point group where the primitive cell belongs.
Specifically, an effective translation operation can be confirmed based on the atomic coordinates of the target crystal and the dot group to which the primitive cell belongs.
Based on the effective translation operation, the non-uniqueness of the space group representation is eliminated, and the space group where the primitive cell is located is determined as the space group of the target crystal.
According to the embodiment of the invention, the crystal point group to which the periodic material belongs is determined based on the group representation theory, so that the symmetry of the crystal can be determined more efficiently and accurately, and k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form a standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Based on the content of any of the above embodiments, determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal, specifically includes: the Bravais lattice type of the target crystal is determined based on the structural parameters of the target crystal, and a standard crystallographic unit cell is obtained based on the minimum lattice vector.
Specifically, the structural parameters of the target crystal can determine the Bravais lattice type and crystal system to which the crystal belongs, and the unit cell parameters a, b, c, α, β, γ.
The corresponding minimum cell parameters (i.e., the minimum lattice vectors) of the cells are searched and determined, and the minimum cells are converted to the corresponding crystallographically standardized cell representations.
The embodiment of the invention can determine primitive unit cells based on standard crystallographic unit cells by determining the standard crystallographic unit cells of the target crystal, and can eliminate the non-uniqueness of space group representation.
Based on the foregoing in any one of the foregoing embodiments, based on the primitive cell, obtaining an energy band path corresponding to the primitive cell specifically includes: the k point and the energy band path connecting the k points are determined based on the Bravais lattice type of the target crystal.
Specifically, after determining the Bravais lattice, each type of crystal can give a normalized k-point path of the structural representation of the electron band in the form of a list.
According to the embodiment of the invention, based on the symmetry of the crystal, the energy band path of the crystal is determined, the k points with high symmetry can be more efficiently and completely determined and connected to form the standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
The crystal symmetry and band path determining device provided by the invention will be described below, and the crystal symmetry and band path determining device described below and the crystal symmetry and band path determining method described above can be referred to correspondingly.
Fig. 2 is a schematic structural diagram of a crystal symmetry and band path determining device according to an embodiment of the present invention. Based on the foregoing in any of the embodiments, as shown in fig. 2, the apparatus includes a normalization module 201, a unit cell reduction module 202, and a point group determination module 203, where:
A normalization module 201 for determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal;
A unit cell reduction module 202 for obtaining primary unit cells corresponding to standard crystallographic unit cells;
the point group determining module 203 is configured to determine a point group of the target crystal based on the primitive cell.
Specifically, the normalization module 201, the unit cell reduction module 202, and the point group determination module 203 are electrically connected in sequence.
The normalization module 201 may normalize structural parameters of the target crystal to determine a standard crystallographic unit cell of the target crystal.
The unit cell reduction module 202 may obtain the minimum repeating unit corresponding to the standard crystallographic unit cell by crystal axis sequencing, and convert the normal unit cell into the standardized primitive cell to obtain each primitive cell.
The point group determining module 203 may sequentially act on all the atomic coordinates of the target crystal according to the operation matrices corresponding to the group elements of the 32 point groups, and compare the coordinate positions after the acting with the original atomic positions, if the atomic positions coincide, the operation is a symmetry operation (i.e. an effective symmetry operation) permitted by the target crystal.
The point group determining module 203 may obtain a symmetric operation matrix group by traversing all valid symmetric operations, and form a point group to which the target crystal belongs (i.e., a point group of the target crystal).
Optionally, the apparatus further comprises:
and the space group determining module is used for determining the space group of the target crystal based on the point group of the target crystal.
Optionally, the apparatus further comprises:
And the path determining module is used for acquiring the energy band path corresponding to the primary primitive cell based on the primary primitive cell.
Optionally, the point group determining module 203 includes:
A symmetric operation determination unit configured to determine an effective symmetric operation based on a target operation matrix and an atomic coordinate of the target crystal;
and a point group determining unit for determining a point group of the target crystal based on the effective symmetric operation and the atomic coordinates of the primitive cell.
Optionally, the space group determining module is specifically configured to determine a space group in which the primitive cell is located based on the atomic coordinate of the target crystal and a point group to which the primitive cell belongs.
Optionally, the normalization module 201 includes:
A lattice determining unit configured to determine a Bravais lattice type of a target crystal based on a structural parameter of the target crystal;
And the normalization unit is used for acquiring the standard crystallographic unit cell based on the minimum lattice vector.
Optionally, the path determining module is specifically configured to determine a k point and the energy band path connected to the k point based on a Bravais lattice type of the target crystal.
The device for determining the symmetry and the band path of the crystal provided by the embodiment of the invention is used for executing the method for determining the symmetry and the band path of the crystal, the implementation mode of the device is consistent with the implementation mode of the method for determining the symmetry and the band path of the crystal provided by the invention, and the same beneficial effects can be achieved, and the detailed description is omitted.
The crystal symmetry and band path determination device is used for the crystal symmetry and band path determination method of the foregoing embodiments. Therefore, the descriptions and definitions in the crystal symmetry and the band path determination method in the foregoing embodiments may be used for understanding each execution module in the embodiments of the present invention.
According to the embodiment of the invention, the crystal point group to which the periodic material belongs is determined based on the group representation theory, so that the symmetry of the crystal can be determined more efficiently and accurately, and k points with high symmetry can be determined more efficiently and completely on the basis of the symmetry of the crystal and connected to form a standardized energy band path, the k point deficiency can be avoided, the obtained energy band path can completely represent electronic structure information, and the erroneous judgment of the energy band structure caused by the k point deficiency and the imperfect energy band path is avoided.
Fig. 3 illustrates a physical schematic diagram of an electronic device, as shown in fig. 3, where the electronic device may include: processor 310, communication interface (Communications Interface) 320, memory 330 and communication bus 340, wherein processor 310, communication interface 320 and memory 330 communicate with each other via communication bus 340. Processor 310 may invoke logic instructions stored in memory 330 and executable on processor 310 to perform the crystal symmetry and band path determination methods provided by the various method embodiments described above, the method comprising: determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal; obtaining primary primitive cells corresponding to standard crystallographic unit cells; based on the primitive cells, a population of points of the target crystal is determined.
Further, the logic instructions in the memory 330 described above may be implemented in the form of software functional units and may be stored in a computer-readable storage medium when sold or used as a stand-alone product. Based on this understanding, the technical solution of the present invention may be embodied essentially or in a part contributing to the prior art or in a part of the technical solution, in the form of a software product stored in a storage medium, comprising several instructions for causing a computer device (which may be a personal computer, a server, a network device, etc.) to perform all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a usb disk, a removable hard disk, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), a magnetic disk, or an optical disk, or other various media capable of storing program codes.
The processor 310 in the electronic device provided by the embodiment of the present invention may call the logic instruction in the memory 330, and its implementation manner is consistent with the implementation manner of the crystal symmetry and energy band path determining method provided by the present invention, and may achieve the same beneficial effects, which are not described herein again.
In another aspect, embodiments of the present invention also provide a computer program product comprising a computer program stored on a non-transitory computer readable storage medium, the computer program comprising program instructions which, when executed by a computer, enable the computer to perform the crystal symmetry and band path determination method provided by the above-described method embodiments, the method comprising: determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal; obtaining primary primitive cells corresponding to standard crystallographic unit cells; based on the primitive cells, a population of points of the target crystal is determined.
When the computer program product provided by the embodiment of the present invention is executed, the above crystal symmetry and band path determining method is implemented, and the specific implementation manner thereof is consistent with the implementation manner described in the foregoing embodiment of the method, and the same beneficial effects can be achieved, which is not described herein.
In yet another aspect, embodiments of the present invention further provide a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, is implemented to perform the crystal symmetry and band path determination method provided by the above embodiments, the method comprising: determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal; obtaining primary primitive cells corresponding to standard crystallographic unit cells; based on the primitive cells, a population of points of the target crystal is determined.
When the computer program stored on the non-transitory computer readable storage medium provided by the embodiment of the present invention is executed, the above method for determining crystal symmetry and band path is implemented, and the specific implementation manner is consistent with the implementation manner described in the embodiment of the foregoing method, and the same beneficial effects can be achieved, which is not repeated here.
The apparatus embodiments described above are merely illustrative, wherein the elements illustrated as separate elements may or may not be physically separate, and the elements shown as elements may or may not be physical elements, may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art will understand and implement the present invention without undue burden.
From the above description of the embodiments, it will be apparent to those skilled in the art that the embodiments may be implemented by means of software plus necessary general hardware platforms, or of course may be implemented by means of hardware. Based on this understanding, the foregoing technical solution may be embodied essentially or in a part contributing to the prior art in the form of a software product, which may be stored in a computer readable storage medium, such as ROM/RAM, a magnetic disk, an optical disk, etc., including several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method described in the respective embodiments or some parts of the embodiments.
Finally, it should be noted that: the above embodiments are only for illustrating the technical solution of the present invention, and are not limiting; although the invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present invention.
Claims (7)
1. A method for determining symmetry and band path of a crystal, comprising:
Determining a standard crystallographic unit cell of a target crystal based on a structural parameter of the target crystal;
obtaining primary elementary cells corresponding to the standard crystallographic unit cells;
determining a point group of the target crystal based on the primitive cells;
the method for determining the standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal specifically comprises the following steps:
Determining the Bravais lattice type of the target crystal based on the structural parameter of the target crystal, and acquiring the standard crystallographic unit cell based on a minimum lattice vector;
after the primary unit cell corresponding to the standard crystallographic unit cell is obtained, the method further comprises:
based on the primary primitive cells, obtaining energy band paths corresponding to the primary primitive cells;
The obtaining the energy band path corresponding to the primary primitive cell based on the primary primitive cell specifically comprises the following steps:
and determining a k point and the energy band path connecting the k point based on the Bravais lattice type of the target crystal.
2. The method for determining symmetry and band path according to claim 1, wherein after determining a point group of a target crystal based on the elementary cells, further comprising:
a spatial population of the target crystal is determined based on the point population of the target crystal.
3. The method for determining symmetry and band path of crystals according to claim 1, wherein said determining a point group of a target crystal based on said elementary cells comprises:
determining effective symmetric operation based on a target operation matrix and atomic coordinates of the target crystal;
A population of points of the target crystal is determined based on the effective symmetry operation and the atomic coordinates of the primitive cells.
4. The method for determining symmetry and band path of crystals as defined in claim 2, wherein determining a spatial group of the target crystals based on the point group of the target crystals comprises:
and determining the space group where the primary primitive cell is based on the atomic coordinates of the target crystal and the point group where the primary primitive cell belongs.
5. A crystal symmetry and band path determination device, comprising:
a normalization module for determining a standard crystallographic unit cell of a target crystal based on a structural parameter of the target crystal;
the unit cell reduction module is used for obtaining primary unit cells corresponding to the standard crystallographic unit cells;
the point group determining module is used for determining the point group of the target crystal based on the primary primitive cells;
The normalization module includes:
A lattice determining unit configured to determine a Bravais lattice type of a target crystal based on a structural parameter of the target crystal;
a normalization unit for obtaining the standard crystallographic unit cell based on a minimum lattice vector;
the system further comprises a path determination module for:
based on the primary primitive cells, obtaining energy band paths corresponding to the primary primitive cells;
The obtaining the energy band path corresponding to the primary primitive cell based on the primary primitive cell specifically comprises the following steps:
and determining a k point and the energy band path connecting the k point based on the Bravais lattice type of the target crystal.
6. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor performs the steps of the crystal symmetry and band-path determination method of any one of claims 1 to 4 when the program is executed.
7. A non-transitory computer readable storage medium having stored thereon a computer program, wherein the computer program when executed by a processor implements the steps of the crystal symmetry and band-path determination method of any of claims 1 to 4.
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