CN113192578A - Method and device for determining crystal symmetry and energy band path - Google Patents
Method and device for determining crystal symmetry and energy band path Download PDFInfo
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- CN113192578A CN113192578A CN202110626051.5A CN202110626051A CN113192578A CN 113192578 A CN113192578 A CN 113192578A CN 202110626051 A CN202110626051 A CN 202110626051A CN 113192578 A CN113192578 A CN 113192578A
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Abstract
The invention provides a method and a device for determining crystal symmetry and an energy band path, wherein the method comprises the following steps: determining a standard crystallographic unit cell of a target crystal based on structural parameters of the target crystal; acquiring initial elementary cells corresponding to the standard crystallography unit cells; and determining a point group of the target crystal based on the initial elementary cells. The method and the device for determining the crystal symmetry and the energy band path provided by the embodiment of the invention are based on the group representation theory, determine the crystal point group to which the periodic material belongs, and can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standard energy band path, avoiding the k point loss, completely representing the electronic structure information of the obtained energy band path, and avoiding the misjudgment of the energy band structure caused by the k point loss and the imperfection of the energy band path.
Description
Technical Field
The invention relates to the technical field, in particular to a method and a device for determining crystal symmetry and an energy band path.
Background
The symmetry of a crystal (including point groups and space groups) is closely related to its physical properties. In the physical property study of periodic materials, the point group and space group of crystals are very important basic parameters. When microscopic properties of materials are simulated by using quantum mechanics or classical mechanics, the symmetry of a material model must be determined firstly, and the electronic structure of the materials can be determined on the basis; when an electron band structure is plotted, a highly symmetric k-point is generally selected to form a band path, which represents the distribution of electron energy along the band path.
In the existing crystal symmetry and energy band path determining method, high-symmetry k points and connecting paths thereof are manually selected and determined by personnel according to experience, and existing k points are missing, so that even if the same crystal is adopted, the representation of an electronic structure may have an enormous difference due to non-uniform energy band path selection. Furthermore, there is a disadvantage of k-point deletion in the manner of manual selection and determination empirically.
When the band gap of the semiconductor is judged by utilizing the energy band, if the path selection of the energy band is improper, the represented information of the electronic structure is easily judged by mistake; 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 influenced.
In summary, the defects of k-point missing and band path imperfection in the prior art can cause information missing and misjudgment of electronic structure when the electronic band is represented.
Disclosure of Invention
The invention provides a method and a device for determining crystal symmetry and an energy band path, which are used for overcoming the defect of k point deficiency in the prior art and realizing more complete acquisition of high-symmetry k points.
The invention provides a method for determining crystal symmetry and an energy band path, which comprises the following steps:
determining a standard crystallographic unit cell of a target crystal based on structural parameters of the target crystal;
acquiring initial elementary cells corresponding to the standard crystallography unit cells;
and determining a point group of the target crystal based on the initial elementary cells.
According to the method for determining crystal symmetry and energy band path provided by the present invention, after determining the point group of the target crystal based on the initial elementary cell, the method further comprises:
determining a spatial population of the target crystal based on the point population of the target crystal.
According to the method for determining crystal symmetry and energy band path provided by the present invention, after obtaining the initial elementary cell corresponding to the standard crystallographic unit cell, the method further comprises:
and acquiring an energy band path corresponding to the initial base unit cell based on the initial base unit cell.
According to the method for determining the crystal symmetry and the energy band path, the determining the point group of the target crystal based on the initial elementary cell specifically comprises the following steps:
determining an effective symmetric operation based on a target operation matrix and the atomic coordinates of the target crystal;
determining a point group of the target crystal based on the effective symmetry operations and the atomic coordinates of the primary elementary cells.
According to the method for determining the crystal symmetry and the energy band path provided by the invention, the determining the spatial group of the target crystal based on the point group of the target crystal specifically comprises the following steps:
and determining the space group where the initial elementary cells are located based on the atomic coordinates of the target crystal and the point group to which the initial elementary cells belong.
According to the method for determining the crystal symmetry and the energy band path, the standard crystallographic unit cell of the target crystal is determined based on the structural parameters 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 crystallography unit cell based on the minimum lattice vector.
According to the method for determining crystal symmetry and energy band path provided by the invention, the obtaining of the energy band path corresponding to the initial elementary cell based on the initial elementary cell specifically comprises:
determining k points and the band paths connecting the k points based on the Bravais lattice type of the target crystal.
The invention also provides a crystal symmetry and energy band path determining device, comprising:
a normalization module for determining a standard crystallographic unit cell for a target crystal based on structural parameters of the target crystal;
the crystal cell reduction module is used for acquiring initial elementary cells corresponding to the standard crystallography crystal cells;
and the point group determining module is used for determining the point group of the target crystal based on the initial elementary cells.
The invention also provides an electronic device, which comprises a memory, a processor and a computer program stored on the memory and capable of running on the processor, wherein the processor executes the computer program to realize the steps of any one of the crystal symmetry and energy band path determination methods.
The present invention also provides a non-transitory computer readable storage medium having stored thereon a computer program which, when executed by a processor, performs the steps of the crystal symmetry and band path determination method as described in any of the above.
The method and the device for determining the crystal symmetry and the energy band path provided by the invention are based on the group representation theory, determine the crystal point group to which the periodic material belongs, and can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standard energy band path, avoiding the k point loss, completely representing the electronic structure information of the obtained energy band path, and avoiding the misjudgment of the energy band structure caused by the k point loss and the imperfection of the energy band path.
Drawings
In order to more clearly illustrate the technical solutions of the present invention or the prior art, the drawings needed for the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are some embodiments of the present invention, and those skilled in the art can also obtain other drawings according to the drawings without creative efforts.
FIG. 1 is a schematic flow chart of a method for determining crystal symmetry and band path according to the present invention;
FIG. 2 is a schematic diagram of a crystal symmetry and band path determining apparatus provided in the present invention;
fig. 3 is a schematic structural diagram of an electronic device provided in the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are some, but not all embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the 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", and the like indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, and are only for convenience of describing the embodiments of the present invention and simplifying the description, but do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and thus, 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 the description of the embodiments of the present invention, it should be noted that, unless explicitly stated or limited otherwise, the terms "mounted," "connected," and "connected" are to be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; they may be connected directly or indirectly through intervening media, or they may be interconnected between two elements. Specific meanings of the above terms in the embodiments of the present invention can be understood in specific cases by those of ordinary skill in the art.
In order to overcome the problems in the prior art, the invention provides a method and a device for determining crystal symmetry and a band path.
Fig. 1 is a schematic flow chart of a crystal symmetry and band path determining method according to the present invention. The crystal symmetry and band path determination method of an embodiment of the present invention is described below with reference to fig. 1. As shown in fig. 1, the method includes: step 101, determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal.
Specifically, the target crystal is a crystal for which symmetry and band path are to be determined.
The structural parameters of the target crystal may be unit cell parameters expressed by three-dimensional vector form, instead of the conventional a, b, c, α, β, γ form.
The structural parameters of the target crystal are normalized to determine a standard crystallographic unit cell for the target crystal.
It should be noted that the atom type, the number of atoms in each type, the total number of atoms, and the coordinate position of each atom of the target crystal can also be obtained.
Specifically, a standardized cell is called a primordial cell if it contains only one minimal repeating unit. The primordial germ cells are the basic unit of the crystal; crystallographically, in order to express a crystal with as high a symmetry as possible, a unit cell is likely to contain a plurality of minimal repeating units, and such a unit cell is called a complex unit cell. The standardized cells corresponding to 14 Bravais lattices are mostly expressed by polycrystalline cells.
The minimum repeating unit corresponding to the standard crystallography unit cell can be obtained through crystal axis sequencing, and the common unit cell (unit cell) is converted into a standardized primary cell (primary cell) to obtain each primary cell.
It should be noted that, according to the group representation theory of crystal symmetry analysis, symmetry analysis of a crystal is complicated, and it is necessary to determine symmetry information of the crystal strictly in accordance with constraints on crystal axes and atom positions of crystal systems (7 types), Bravais lattice types (14 types), point groups (32 types), and space groups (230 types) to which the crystal belongs, while considering a, b, and c axes of the minimum repeating unit of the crystal and atom positions in the crystal. And due to the difference of the a, b and c axes, the representation of various point groups and space groups has difference. By converting the common unit cell into a standardized initial unit cell, the non-uniqueness of the space group representation can be eliminated, and the minimum translation vector allowed by the target crystal (i.e., the effective minimum translation vector) can be determined.
Obtaining the initial elementary cells corresponding to the standard crystallographic unit cell may include determining unit cell parameters of the initial elementary cells, the number of initial elementary cells included in the unit cell, a basic transformation relationship between the unit cell and the initial elementary cells, and a translation relationship of each initial elementary cell.
The atomic type with the least atomic number and the corresponding atomic number can be determined by translating the coordinate origin to the center of the primitive cell according to the coordinate positions of all atoms.
The allowed translation relation (namely, effective translation relation) of the target crystal can be determined, namely, the translation vector relation of each atom to the first atom is determined by taking the position of the first atom in the atom with the least atomic number as a reference; and applies the translation relationship to all atoms, checking for the translation relationship actually permitted.
The translation vector and the number of primitive cells can be determined, that is, all translation vectors are counted and recorded, and the minimum vector in three directions is determined, so that the minimum translation amount is determined. The number of allowed primary primitive cells in a unit cell can be determined by the minimum translation vector.
And 103, determining a point group of the target crystal based on the primary elementary cells.
In particular, crystal symmetry determination may include determining a point group for a target crystal.
All the macroscopic symmetric elements contained in the crystal intersect at least at one point, and various combinations of all the symmetric elements converging at one point are called point groups (point groups) of the crystal, or symmetrical types.
In crystallography, a group of crystallographic points is a collection of symmetric operations (e.g., rotation, reflection). These operations move the fixed center in other directions to restore the crystal, and are therefore called symmetric operations. For a true crystal (not a quasi-crystal), manipulation of the clusters of dots must be such as to maintain the three-dimensional translational symmetry of the crystal. After any manipulation in its cluster of points, the macroscopic properties of the crystal remain exactly the same as before the manipulation. In the classification of crystals, each kind of dot group is also called a crystal class.
And sequentially acting on all the atomic coordinates of the target crystal according to the operation matrix corresponding to the group elements of the 32 point groups, and comparing the acted coordinate positions with the original atomic positions, wherein if the atomic positions are overlapped, the target crystal is allowed to be symmetrical (namely, effective symmetrical operation).
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 symmetric operations to obtain a symmetric operation matrix group to form a point group to which the target crystal belongs (namely the point group of the target crystal).
The embodiment of the invention determines the crystal point group to which the periodic material belongs based on the group representation theory, can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standardized energy band path, avoiding k point loss, completely representing electronic structure information by the obtained energy band path, and avoiding misjudgment of the energy band structure caused by k point loss and energy band path imperfection.
Based on the content of any of the above embodiments, after determining the point group of the target crystal based on the primitive translation unit cell, the method further includes: 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 space group of the target crystal.
The collection of all symmetric elements in the internal structure of a crystal is called a space group. Specifically, the combination of all the symmetric elements in the unit cell.
There are only 230 different combinations of symmetric elements in all crystal structures, i.e. 230 space groups.
According to the point-group operation, a spatial group shift operation (i.e., a valid shift operation) that confirms permission of the target crystal can be checked.
Traversing all the symmetrical operations permitted by the space group, and according to the corresponding relation between the point group and the space group in the group representation theory: the same point group may be mapped to multiple spatial groups. The coordinate position of the minimum repeating unit in the crystal is checked through matrix transformation, and the translation operation specific to the space group to which the crystal belongs is searched and determined, so that the space group to which the crystal belongs (namely the space group of the target crystal) can be determined.
Based on the point group of the target crystal, determining the spatial group of the target crystal may include:
determining a transformation matrix of the standard crystallography unit cell under a rectangular coordinate system according to the crystal system;
determining a transformation matrix and an inverse matrix between standard crystallography unit cells and initial unit cells;
determining a transformation matrix of the initial base unit cell under a rectangular coordinate system;
transforming the inverse matrix of the transformation matrix between the standard crystallography unit cell and the initial elementary cell into the initial elementary cell for representation;
reducing the atomic coordinates of the target crystal to the smallest primary unit cell;
searching the minimum atom type and counting the atom number;
determining a translation vector permitted by the least atom type;
determining a transformation matrix permitted by the minimum atom type, and transforming the transformation matrix into a rectangular coordinate system;
obtaining all atom coordinates by using a transformation matrix permitted by the minimum atom type;
using the transformation matrix permitted by the minimum atom type to act on the transformation matrix of the initial primitive cell under the rectangular coordinate system to obtain a new transformation matrix of the initial primitive cell under the rectangular coordinate system;
aiming at various Bravais lattices, exhausting corresponding point groups and symmetrical operations thereof;
converting the symmetrical operation of the point group to which the target crystal belongs into the primary elementary cell representation;
checking the relation between all atoms and the symmetrical operation, and determining a 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 allowable point group operation of the target crystal, and respectively converting the point group operation into the standard crystallography unit cell and the initial unit cell representation;
determining a space group to which a target crystal belongs;
all atomic coordinates are transformed to the original coordinate representation using the inverse of the above operation.
It should be noted that after the space group of the target crystal is determined, the point group-space group transformation matrix of the target crystal may be determined.
The embodiment of the invention determines the crystal space group to which the periodic material belongs based on the group representation theory, can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standardized energy band path, avoiding k point deletion, completely representing electronic structure information by the obtained energy band path, and avoiding misjudgment of the energy band structure caused by k point deletion and energy band path imperfection.
Based on the content of any of the above embodiments, after obtaining the initial elementary cells corresponding to the standard crystallographic unit cell, the method further includes: and acquiring an energy band path corresponding to the initial base cell based on the initial base cell.
Specifically, on the basis of completing symmetry judgment, a set of k points and a connection mode thereof can be quickly determined through traversal.
Enumerating all k points and connection modes required by the standardized energy bands for each set of point group, traversing all k points with high symmetry, ensuring minimum repetition, and determining a set of k points and connection modes thereof as each k point and connecting the k points into an energy band path.
The set of k points can be applied to electronic energy band calculation of quantum mechanics.
The embodiment of the invention determines the energy band path of the crystal based on the symmetry of the crystal, can more efficiently and completely determine the k point with high symmetry and connect the k point with the k point to form a standard energy band path, can avoid k point loss, can completely represent electronic structure information by the obtained energy band path, and can avoid misjudgment of the energy band structure caused by k point loss and imperfection of the energy band path.
Based on the content of any of the above embodiments, determining a point group of the target crystal based on the primitive translation unit 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 symmetry operation of the elements of the point group is an effective operation, that is, the symmetry operation is applied to all atomic positions of the unit cell, and whether the operation is an effective symmetry operation.
For a symmetric operation of any point group element, the operation is effectively a symmetric operation if the symmetric operation can act on all atomic positions of the unit cell; if the symmetry operation cannot be applied to all atomic positions of the unit cell, the operation is not an effective symmetry operation.
And determining the point group of the target crystal based on the effective symmetrical operation and the atomic coordinates of the primary elementary cells.
Specifically, the point group to which the effective symmetric operation belongs is judged, that is, if the operation can realize the coincidence of all the atomic positions, the operation belongs to the point group operation; if the operation needs additional translation operation to realize complete atom position coincidence, the operation belongs to translation group operation; if the operation cannot achieve full atomic position coincidence, then the operation also does not belong to a point group operation.
Whether the position conversion requirements of all the atoms of the crystal are met by the check point group or not is checked. If so, it may be determined that the point cloud is a point cloud for the target crystal.
The embodiment of the invention determines the crystal point group to which the periodic material belongs based on the group representation theory, can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standardized energy band path, avoiding k point loss, completely representing electronic structure information by the obtained energy band path, and avoiding misjudgment of the energy band structure caused by k point loss and energy band path imperfection.
Based on the content of any of the above embodiments, determining the spatial group of the target crystal based on the point group of the target crystal specifically includes: and determining the space group where the primary elementary cells are located based on the atomic coordinates of the target crystal and the point group to which the primary elementary cells belong.
Specifically, an effective translation operation can be confirmed based on the atomic coordinates of the target crystal and the point group to which the primitive translation cells belong.
And based on effective translation operation, eliminating the non-uniqueness of the space group representation, and determining the space group where the initial elementary cells are positioned as the space group of the target crystal.
The embodiment of the invention determines the crystal point group to which the periodic material belongs based on the group representation theory, can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standardized energy band path, avoiding k point loss, completely representing electronic structure information by the obtained energy band path, and avoiding misjudgment of the energy band structure caused by k point loss and energy band path imperfection.
Based on the content of any one 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: determining Bravais lattice type of the target crystal based on the structural parameters of the target crystal, and obtaining a standard crystallography unit cell based on the minimum lattice vector.
Specifically, the structural parameters of the target crystal can determine the Bravais lattice type and the crystal system to which the crystal belongs, and the unit cell parameters a, b, c, alpha, beta and gamma.
The corresponding minimum unit cell parameter (i.e., the minimum lattice vector) for a unit cell is searched and determined, and the minimum unit cell is converted to a corresponding crystallographically normalized unit cell representation.
According to the embodiment of the invention, the standard crystallography unit cell of the target crystal is determined, the initial unit cell can be determined based on the standard crystallography unit cell, and the non-uniqueness of space group representation can be eliminated.
Based on the content of any of the above embodiments, based on the initial base cell, acquiring the energy band path corresponding to the initial base cell specifically includes: and determining the k point and an energy band path connecting the k point based on the Bravais lattice type of the target crystal.
Specifically, after the Bravais lattice is determined for each type of crystal, the normalized k-point path of the electron band structure representation can be given in a list form.
The embodiment of the invention determines the energy band path of the crystal based on the symmetry of the crystal, can more efficiently and completely determine the k point with high symmetry and connect the k point with the k point to form a standard energy band path, can avoid k point loss, can completely represent electronic structure information by the obtained energy band path, and can avoid misjudgment of the energy band structure caused by k point loss and imperfection of the energy band path.
The crystal symmetry and band path determining apparatus provided by the present invention will be described below, and the crystal symmetry and band path determining apparatus described below and the crystal symmetry and band path determining method described above may be referred to in correspondence with each other.
Fig. 2 is a schematic structural diagram of a crystal symmetry and band path determining apparatus according to an embodiment of the present invention. Based on the content of any of the above 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, wherein:
a normalization module 201 for determining a standard crystallographic cell of the target crystal based on the structural parameters of the target crystal;
a cell reduction module 202 for obtaining initial elementary cells corresponding to standard crystallographic cells;
and the point group determining module 203 is used for determining the point group of the target crystal based on the primary elementary cells.
Specifically, the normalization module 201, the cell reduction module 202, and the dot group determination module 203 are electrically connected in sequence.
The normalization module 201 can normalize the structural parameters of the target crystal and determine a standard crystallographic unit cell for the target crystal.
The cell reduction module 202 may obtain the minimum repeating unit corresponding to the standard crystallographic cell by ordering through the crystal axis, and convert the common cell into the standardized primary cell to obtain each primary cell.
The point group determining module 203 may sequentially act on all the atomic coordinates of the target crystal according to the operation matrix corresponding to the group elements of the 32 point groups, and compare the acted coordinate positions with the original atomic positions, and if the atomic positions coincide, the operation is a symmetric operation allowed by the target crystal (i.e., an effective symmetric operation).
The point group determining module 203 may obtain a symmetric operation matrix group by traversing all effective 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 an energy band path corresponding to the initial base cell based on the initial base cell.
Optionally, the point group determining module 203 includes:
a symmetric operation determination unit for determining an effective symmetric operation based on a target operation matrix and the atomic coordinates of the target crystal;
a point group determination unit for determining a point group of the target crystal based on the effective symmetry operation and the atomic coordinates of the primary elementary cells.
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 coordinates of the target crystal and the point group to which the primitive cell belongs.
Optionally, the normalization module 201 comprises:
a lattice determination unit for determining Bravais lattice type of a target crystal based on structural parameters of the target crystal;
a normalization unit for obtaining the standard crystallographic unit cells based on a minimum lattice vector.
Optionally, the path determining module is specifically configured to determine a k point and the energy band path connecting the k point based on a Bravais lattice type of the target crystal.
The crystal symmetry and energy band path determining apparatus provided in the embodiment of the present invention is used for executing the crystal symmetry and energy band path determining method provided in the embodiment of the present invention, and an implementation manner of the crystal symmetry and energy band path determining apparatus is consistent with that of the crystal symmetry and energy band path determining method provided in the embodiment of the present invention, and the same beneficial effects can be achieved, and details are not repeated here.
The crystal symmetry and band path determining apparatus is used in the crystal symmetry and band path determining method of the foregoing embodiments. Therefore, the descriptions and definitions in the crystal symmetry and band path determination methods in the foregoing embodiments can be used for understanding the execution modules in the embodiments of the present invention.
The embodiment of the invention determines the crystal point group to which the periodic material belongs based on the group representation theory, can more efficiently and accurately determine the symmetry of the crystal, thereby more efficiently and completely determining the k point with high symmetry on the basis of the symmetry of the crystal and connecting the k point with high symmetry to form a standardized energy band path, avoiding k point loss, completely representing electronic structure information by the obtained energy band path, and avoiding misjudgment of the energy band structure caused by k point loss and energy band path imperfection.
Fig. 3 illustrates a physical structure diagram of an electronic device, which may include, as shown in fig. 3: a processor (processor)310, a communication Interface (communication Interface)320, a memory (memory)330 and a communication bus 340, wherein the processor 310, the communication Interface 320 and the memory 330 communicate with each other via the communication bus 340. The processor 310 may invoke logic instructions stored in the memory 330 and executable on the processor 310 to perform the crystal symmetry and band path determination methods 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; acquiring initial elementary cells corresponding to standard crystallography unit cells; and determining the point group of the target crystal based on the primary elementary cells.
In addition, the logic instructions in the memory 330 may be implemented in the form of software functional units and stored in a computer readable storage medium when the software functional units are sold or used as independent products. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The processor 310 in the electronic device provided in the embodiment of the present invention may call the logic instruction in the memory 330, and the implementation manner of the method for determining crystal symmetry and energy band path is consistent with that of the method for determining crystal symmetry and energy band path provided in the present invention, and the same beneficial effects may be achieved, and details are not described here.
In another aspect, an embodiment of the present invention further provides a computer program product, where the computer program product includes a computer program stored on a non-transitory computer-readable storage medium, the computer program includes program instructions, and when the program instructions are executed by a computer, the computer can execute the crystal symmetry and energy band path determining method provided by the above-mentioned method embodiments, and the method includes: determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal; acquiring initial elementary cells corresponding to standard crystallography unit cells; and determining the point group of the target crystal based on the primary elementary cells.
When the computer program product provided by the embodiment of the present invention is executed, the method for determining crystal symmetry and energy band path is implemented, and the specific implementation manner thereof is consistent with the implementation manner described in the foregoing method embodiment, and the same beneficial effects can be achieved, which is not described herein again.
In another aspect, an embodiment of the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored, where the computer program is implemented by a processor to execute the crystal symmetry and energy band path determining method provided in the foregoing embodiments, and the method includes: determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal; acquiring initial elementary cells corresponding to standard crystallography unit cells; and determining the point group of the target crystal based on the primary elementary cells.
When the computer program stored on the non-transitory computer-readable storage medium provided in the embodiments of the present invention is executed, the method for determining crystal symmetry and energy band path described above is implemented, and the specific implementation manner of the method is consistent with the implementation manner described in the embodiments of the foregoing method, and the same beneficial effects can be achieved, which is not described herein again.
The above-described embodiments of the apparatus are merely illustrative, and the units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
Through the above description of the embodiments, those skilled in the art will clearly understand that each embodiment can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware. With this understanding in mind, the above-described technical solutions may be embodied in the form of a software product, which can be stored in a computer-readable storage medium such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the methods described in the embodiments or some parts of the embodiments.
Finally, it should be noted that: the above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present 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 solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.
Claims (10)
1. A method for determining crystal symmetry and energy band path, comprising:
determining a standard crystallographic unit cell of a target crystal based on structural parameters of the target crystal;
acquiring initial elementary cells corresponding to the standard crystallography unit cells;
and determining a point group of the target crystal based on the initial elementary cells.
2. The method of claim 1, wherein the determining the point group of the target crystal based on the primitive translation cell further comprises:
determining a spatial population of the target crystal based on the point population of the target crystal.
3. The method of claim 1, wherein the obtaining of the initial elementary cells corresponding to the standard crystallographic unit cell further comprises:
and acquiring an energy band path corresponding to the initial base unit cell based on the initial base unit cell.
4. The method for determining crystal symmetry and energy band path according to claim 1, wherein the determining a point group of a target crystal based on the primitive translation cell specifically comprises:
determining an effective symmetric operation based on a target operation matrix and the atomic coordinates of the target crystal;
determining a point group of the target crystal based on the effective symmetry operations and the atomic coordinates of the primary elementary cells.
5. The method of claim 2, wherein the determining the spatial group of the target crystal based on the point group of the target crystal comprises:
and determining the space group where the initial elementary cells are located based on the atomic coordinates of the target crystal and the point group to which the initial elementary cells belong.
6. The method of claim 1, wherein determining a standard crystallographic unit cell of the target crystal based on the structural parameters of the target crystal comprises:
determining the Bravais lattice type of the target crystal based on the structural parameters of the target crystal, and acquiring the standard crystallography unit cell based on the minimum lattice vector.
7. The method for determining crystal symmetry and energy band path according to claim 6, wherein the obtaining the energy band path corresponding to the primitive cell based on the primitive cell specifically includes:
determining k points and the band paths connecting the k points based on the Bravais lattice type of the target crystal.
8. A crystal symmetry and energy band path determining apparatus, comprising:
a normalization module for determining a standard crystallographic unit cell for a target crystal based on structural parameters of the target crystal;
the crystal cell reduction module is used for acquiring initial elementary cells corresponding to the standard crystallography crystal cells;
and the point group determining module is used for determining the point group of the target crystal based on the initial elementary cells.
9. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor when executing the program performs the steps of the crystal symmetry and band path determination method of any of claims 1 to 7.
10. 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 7.
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