An optimized iterative method and system for the structure factor of a flat crystal X-ray diffraction with an arbitrary lattice structure

Abstract

The present application provides an optimized iterative method and system for the structure factor of a flat crystal X-ray diffraction with an arbitrary lattice structure. The method includes: calculating the structure factor of the crystal unit cell class, calculating the structure factor of the crystal unit cell class according to the material structure information of the crystal unit cell; microcrystal shaping, which is used to calculate the structure factor of the microcrystal according to the structure factor of the crystal unit cell class; crystal scale magnification, which is used to calculate the structure factor of the crystal after crystal scale magnification according to the structure factor of the microcrystal class; and crystal scale magnification iterative operation, which is used to calculate the structure factor of the crystal of the actual material according to the known crystal size. The advantages of the present application are: the calculation result of the structure factor is accurate and reliable; it has the advantages of low redundancy in the calculation process, low time complexity, and a space complexity of O(n<supgt;3< / supgt;).

Description

Technical Field

[0001] This application belongs to the technical field of X-ray detection, and specifically relates to an optimized iterative method and system for the structure factor of a flat crystal X-ray diffraction with an arbitrary lattice structure. Background Art

[0002] X-ray crystal optical diffraction calculation is an important basic technology in the science of microscopic structures. Based on X-ray crystal optics, to calculate the diffraction process of X-rays and crystal materials, it is necessary to calculate the structure factor of the crystal materials. Currently, in the method for calculating the diffraction of X-rays on a flat crystal with an arbitrary lattice structure, although there are many methods for calculating the structure factor of crystal materials, there is no method that can both integrate all atomic information of the crystal material and calculate quickly and accurately. To a certain extent, all methods effectively approximate the atomic information, which may lead to the loss of non-trivial crystallographic information. In fact, on the millimeter scale, a crystal material has more than 10 20 atoms. Based on X-ray crystal optics, performing a fast and accurate integral calculation of all atomic information in the crystal material will help to more quickly and finely conduct numerical simulation analysis to discover new characteristics of the microscopic structure of substances, provide comprehensive and reliable simulation preparations for carrying out relevant experimental measurements, and provide a more efficient method for reconstructing the microscopic structure and distribution of unknown substances. Summary of the Invention

[0003] The purpose of this application is to overcome the defect that the existing method may lead to the loss of non-trivial crystallographic information when quickly and accurately calculating the diffraction structure factor of X-rays on an arbitrary crystal structure. An optimized iterative method for the structure factor of a flat crystal X-ray diffraction with an arbitrary lattice structure is proposed. Based on the basic physical principles of X-ray crystal optics, considering the geometric and physical information of each atom in the actual material during the calculation process, it can efficiently and accurately calculate the diffraction structure factor of X-rays on an arbitrary crystal structure.

[0004] To achieve the above purpose, this application proposes an optimized iterative method for the structure factor of a flat crystal X-ray diffraction with an arbitrary lattice structure. The method uses X-rays as the incident light source to irradiate a flat crystal with an arbitrary lattice structure, and calculates the structure factor of the material for the diffraction process. The method includes:

[0005] Step 1: Calculate the structure factor of the microscopic crystal unit cell structure with atoms as the basic unit;

[0006] Step 2: Perform a shaping operation on the microscopic crystal and calculate the structure factor of the microscopic crystal;

[0007] Step 3: Iteratively magnify the scale of the microscopic crystal, and iteratively calculate the structure factor of the crystal after the crystal scale is magnified, and finally obtain the structure factor of the actual material crystal.

[0008] As an improvement of the above method, step 1 includes:

[0009]

[0010] where is the structure factor of the microcrystal unit cell class; j refers to the j-th atom, and the Σ integral ranges from 1 to the last atom; is the position vector of the j-th atom; is the scattering wave vector; is the structure factor of the j-th atom; c represents the atom as the basic unit.

[0011] As an improvement of the above method, in step 2, the shaping operation on the microcrystal includes:

[0012] Taking the geometric center of the microcrystal as the origin of the coordinate system and using the unit cell as the basic unit, perform a structure factor-like translation operation to obtain a microcrystal stacked by multiple unit cells.

[0013] As an improvement of the above method, in step 2, the calculation of the structure factor of the microcrystal includes:

[0014] Taking the unit cell as the basic unit, calculate the structure factor of each basic unit respectively, and finally sum to obtain the structure factor of the microcrystal after the shaping operation of the microcrystal.

[0015]

[0016] where is the structure factor of the m-th basic unit; is the weight of the structure factor of the m-th basic unit in the total structure factor of the basic units; N is the number of iterations in step 3.

[0017] As an improvement of the above method, in step 3, the calculation of the structure factor of the crystal after crystal scale magnification includes:

[0018] Taking the crystal after scale magnification in the previous iteration as the basic unit, calculate the structure factor of each basic unit, and finally sum to obtain the structure factor of the crystal after the crystal scale magnification operation.

[0019]

[0020] where is the structure factor of the n-th basic unit in the previous iteration; M - 1 represents the remaining number of iterations.

[0021] As an improvement of the above method, obtaining the pseudo structure factor of the actual material crystal in step 3 includes:

[0022]

[0023] wherein, is the pseudo structure factor of the actual material crystal; is the static structure factor.

[0024] This application also provides an optimized iterative system for the flat crystal X-ray diffraction structure factor of any lattice structure, which is implemented based on the above method. The system includes:

[0025] A module for calculating the pseudo structure factor of the microscopic crystal unit cell, which is used to calculate the pseudo structure factor of the microscopic crystal unit cell with atoms as the basic unit;

[0026] A module for calculating the pseudo structure factor of the microscopic crystal, which is used to calculate the pseudo structure factor of the microscopic crystal after performing a shaping operation on the microscopic crystal;

[0027] A module for calculating the pseudo structure factor of the actual material crystal, which is used to iteratively calculate the pseudo structure factor of the crystal after the crystal scale is enlarged, and finally obtain the pseudo structure factor of the actual material crystal.

[0028] Compared with the prior art, the advantages of this application are as follows:

[0029] 1. In the calculation process of the method of the present invention, integration is performed on all atomic information of the crystal material, and the calculation result of the structure factor is accurate and reliable;

[0030] 2. The method of the present invention proposes an iterative optimization method for the crystal geometric scale, which transforms the NP-hard calculation problem of traversing all atomic information of the crystal material into a calculation process with a time complexity of O(n 3 ), a fast and accurate calculation process, with the advantages of low redundancy in the calculation process, low time complexity, and a space complexity of O(n 3 );

[0031] 3. The method of the present invention can perform fine numerical simulation on material crystallography, discover non-trivial microscopic structure characteristics of substances that have not been measured in experiments, and provide a new direction for X-ray crystal experimental measurement. Description of the Drawings

[0032] Figure 1 Shown is a flow chart of the optimized iterative method for the flat crystal X-ray diffraction structure factor of any lattice structure;

[0033] Figure 2 Shown is a schematic diagram of establishing a Cartesian rectangular coordinate system in three-dimensional space. Detailed Embodiments

[0034] The technical solution of the present application will be described in detail below with reference to the accompanying drawings.

[0035] Embodiment 1

[0036] As Figure 1 shown, for the optimization iteration method of the structure factor of a flat crystal X-ray diffraction with any lattice structure, before specifically describing the method, it is necessary to specify the application scenario and application initial conditions of the method.

[0037] The application scenario of the method: Using X-rays as the incident light source to irradiate a flat crystal with any lattice structure, and calculating the structure factor of the material for the diffraction process;

[0038] The application initial conditions of the method include the lattice structure information (including the shape factor distribution of the contained atoms) of the crystal material that has been generated, set, or obtained; all the geometric information of the application scenario of the method is known.

[0039] As Figure 1 shown, the optimization iteration method of the structure factor of a flat crystal X-ray diffraction with any lattice structure is applied in the above application scenario. After giving the above application initial conditions, the method is used to perform optimization iteration calculation on the diffraction structure factor of a flat crystal with any lattice structure. This method sequentially executes five processes: establishing a crystal material coordinate system, calculating the structure factor of the crystal unit cell class, microcrystal shaping, crystal scale magnification, and crystal scale magnification iteration.

[0040] Calculating the structure factor of the crystal unit cell class means calculating the structure factor of the class with atoms as the basic unit within the periodically distributed unit cells of the crystal material, which is used to provide the initial calculation basic unit for microcrystal shaping.

[0041] Microcrystal shaping means using the unit cell in the process of calculating the structure factor of the crystal unit cell class as the basic unit. In the crystal material coordinate system, with the origin of the coordinate system as the geometric center of the stacked material, the structure factor translation operation is performed on the basic unit, and microcrystals with the same ratio of length, width, and height as the actual material are stacked, and the structure factor of the class of the microcrystals is calculated, which is used to provide the initial basic unit with the same length, width, and height as the actual crystal material for the crystal scale magnification operation.

[0042] Crystal scale magnification means using a crystal with a certain geometric size as the basic unit. In the crystal material coordinate system, with the origin of the coordinate system as the geometric center of the stacked material, the structure factor translation operation is performed on the basic unit, and a crystal with a length, width, and height that are all N scl times that of the microcrystal is stacked, and the structure factor of the class of the stacked crystal is calculated, which is used to provide the initial basic unit for the crystal scale magnification iteration operation. This process finally realizes the scale magnification operation through translation operations in 6 directions on the XYZ three axes.

[0043] Crystal scale amplification iteration means taking a crystal with a certain geometric size as the basic unit. In the crystal material coordinate system, with the origin of the coordinate system as the geometric center of the stacked material, setting the iteration number iter, performing crystal scale amplification operations on the basic unit, and stacking a crystal with the same length, width, and height as the basic unit crystal times, and calculating the pseudo structure factor and structure factor of the stacked crystal.

[0044] Process 1: Establish a crystal material coordinate system. The specific steps are as follows:

[0045] Step 1) As Figure 2 shown, establish a Cartesian rectangular coordinate system O-XYZ in three-dimensional space, with the geometric center of the crystal material as the origin O of the coordinate system; the positive direction of the X-axis points to the geometric center of the detector receiving plane and is perpendicular to the detector receiving plane; the Y-axis and Z-axis are parallel to the detector receiving plane.

[0046] Process 2: Calculate the pseudo structure factor of the crystal unit cell. The specific steps are as follows:

[0047] Step 2) In the crystal material coordinate system, the crystal material is periodically distributed. Set the geometric center of any unit cell as the origin of the coordinate system, and calculate the pseudo structure factor with the atom as the basic unit:

[0048]

[0049] Among them, is the pseudo structure factor; i refers to the i-th atom, and the Σ integral ranges from 1 to the last atom; is the vector from the i-th atom to the origin of the coordinate; is the scattering wave vector; is the structure factor of the i-th atom; c represents the atom as the basic unit.

[0050] Process 3: Microscopic crystal shaping. The specific steps are as follows:

[0051] Step 3) In the crystal material coordinate system, the microscopic crystal after the microscopic crystal shaping operation is periodically distributed. Set the geometric center of the microscopic crystal formed by the microscopic crystal shaping operation as the origin of the coordinate system;

[0052] Step 4) With the geometric center of the microscopic crystal as the origin of the coordinate system, using the unit cell as the basic unit, perform a pseudo structure factor translation operation to obtain a microscopic crystal stacked by M x in length, M y in width, and M z unit cells in height; using the unit cell in Step 2) as the basic unit, calculate the pseudo structure factor of each basic unit respectively, and finally sum them up to obtain the pseudo structure factor after the microscopic crystal shaping operation

[0053]

[0054] Among them, is the class structure factor of the m-th basic unit; is the weight of the class structure factor of the m-th basic unit in the total class structure factors of the basic units.

[0055] Process Four: Crystal scale amplification, and the specific information of the steps is as follows:

[0056] Step 5) Set the crystal after microcrystal shaping as the basic unit; in the crystal material coordinate system, specify that the origin of the coordinate system is the geometric center of the material after crystal scale amplification; specify that the crystal after crystal scale amplification is stacked by N scl basic units in length, width, and height;

[0057] Step 6) For the basic unit set in Step 5), perform the class structure factor scale amplification operation, calculate the class structure factor of each basic unit respectively, and finally sum them up to obtain the class structure factor after the crystal scale amplification operation

[0058]

[0059] Among them, is the class structure factor of the m-th basic unit.

[0060] Process Five: Crystal scale amplification iteration, and the specific information of the steps is as follows:

[0061] Step 7) Set the crystal after crystal scale amplification as the basic unit; in the crystal material coordinate system, specify that the origin of the coordinate system is the geometric center of the crystal material after the crystal scale amplification iteration operation; specify the number of iterations iter;

[0062] Step 8) For the basic unit in Step 7), perform the crystal scale amplification operation to obtain the crystal class structure factor after one crystal scale amplification operation; use the obtained crystal as the basic unit and perform the crystal scale amplification operation to obtain the crystal class structure factor after two crystal scale amplification operations; perform iter iterations to obtain the crystal class structure factor after iter crystal scale amplification operations, that is, the class structure factor of the actual crystal material

[0063] Step 9) Calculate the structure factor of the actual crystal material

[0064]

[0065] Among them, is the static class structure factor of the operating atom.

[0066] Through simulation and experimental verification, the method of the present invention can quickly and accurately calculate the structure factor of material diffraction in the X-ray flat crystal diffraction process of any lattice structure, so as to realize the optimization iteration of the structure factor of the flat crystal X-ray diffraction of any lattice structure.

[0067] Example 2

[0068] The present application also provides an optimization iteration system for the structure factor of flat crystal X-ray diffraction of any lattice structure, which is implemented based on the above method. The system includes:

[0069] A module for calculating the structure factor of the microscopic crystal unit cell class, which is used to calculate the structure factor of the microscopic crystal unit cell class with atoms as the basic unit;

[0070] A module for calculating the structure factor of the microscopic crystal class, which is used to calculate the structure factor of the microscopic crystal class after performing a shaping operation on the microscopic crystal; and

[0071] A module for calculating the structure factor of the actual material crystal class, which is used to iteratively calculate the structure factor of the crystal after the crystal scale is enlarged, and finally obtain the structure factor of the actual material crystal.

[0072] The present application can also provide a computer device, including: at least one processor, a memory, at least one network interface, and a user interface. Each component in the device is coupled together through a bus system. It can be understood that the bus system is used to realize the connection and communication between these components. In addition to the data bus, the bus system also includes a power bus, a control bus, and a status signal bus.

[0073] Among them, the user interface may include a display, a keyboard, or a pointing device. For example, a mouse, a trackball, a touchpad, or a touch screen, etc.

[0074] It can be understood that the memory in the disclosed embodiments of the present application can be a volatile memory or a non-volatile memory, or can include both volatile and non-volatile memories. Among them, the non-volatile memory can be a Read-Only Memory (ROM), a Programmable ROM (PROM), an Erasable PROM (EPROM), an Electrically EPROM (EEPROM), or a flash memory. The volatile memory can be a Random Access Memory (RAM), which is used as an external cache. By way of example but not limitation, many forms of RAM are available, such as Static RAM (SRAM), Dynamic RAM (DRAM), Synchronous DRAM (SDRAM), Double DataRate SDRAM (DDRSDRAM), Enhanced SDRAM (ESDRAM), Synchlink DRAM (SLDRAM), and Direct Rambus RAM (DRRAM). The memory described herein is intended to include but not be limited to these and any other suitable types of memory.

[0075] In some embodiments, the memory stores the following elements, executable modules, or data structures, or subsets or supersets thereof: an operating system and application programs.

[0076] Among them, the operating system includes various system programs, such as a framework layer, a core library layer, a driver layer, etc., and is used to implement various basic services and process hardware-based tasks. The application programs include various application programs, such as a Media Player, a Browser, etc., and are used to implement various application services. The program for implementing the method of the disclosed embodiments of the present application can be included in the application programs.

[0077] In the above embodiments, by calling the programs or instructions stored in the memory, specifically, the programs or instructions stored in the application programs, the processor is configured to:

[0078] Execute the steps of the above method.

[0079] The above method can be applied to a processor or implemented by a processor. The processor may be an integrated circuit chip with the ability to process signals. During implementation, the steps of the above method can be completed by the integrated logic circuit of the hardware in the processor or instructions in the form of software. The above-mentioned processor may be a general-purpose processor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components. It can implement or execute the various methods, steps, and logic block diagrams disclosed above. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. Combining the steps of the above-disclosed method can be directly embodied as being executed and completed by a hardware decoding processor, or executed and completed by a combination of hardware and software modules in the decoding processor. The software module may be located in a mature storage medium in the art such as random access memory, flash memory, read-only memory, programmable read-only memory, or electrically erasable programmable memory, registers, etc. This storage medium is located in the memory, and the processor reads the information in the memory and combines its hardware to complete the steps of the above method.

[0080] It can be understood that the embodiments described in this application can be implemented using hardware, software, firmware, middleware, microcode, or a combination thereof. For hardware implementation, the processing unit can be implemented in one or more application specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), general-purpose processors, controllers, microcontrollers, microprocessors, other electronic units for performing the functions described in this application, or a combination thereof.

[0081] For software implementation, the technology of this application can be implemented by executing the functional modules of this application (such as procedures, functions, etc.). The software code can be stored in the memory and executed by the processor. The memory can be implemented inside or outside the processor.

[0082] The present application can also provide a non-volatile storage medium for storing a computer program. When the computer program is executed by a processor, each step in the above method embodiments can be implemented.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application and not to limit them. Although the present application has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present application does not depart from the spirit and scope of the technical solutions of the present application, and they should all be covered within the scope of the claims of the present application.

Claims

1. An iterative method for optimizing the X-ray diffraction structure factor of a flat crystal with an arbitrary lattice structure, wherein the method uses X-rays as an incident light source to enter a flat crystal with an arbitrary lattice structure, and calculates the material structure factor according to the diffraction process; the method comprises: Step 1: Calculate the microscopic crystal cell structure factor using atoms as the basic unit; Step 2: Perform shaping operations on the microscopic crystal and calculate the quasi-structure factor of the microscopic crystal; Step 3: Iteratively scale up the microscopic crystal, iteratively calculate the quasi-structure factor of the crystal after the crystal scale is scaled up, and finally obtain the structure factor of the actual material crystal; The step 1 comprises: in, is the microscopic crystal cell-like structure factor; j refers to the jth atom, and Σ is integrated from 1 to the last atom; is the position vector of the jth atom; is the scattered wave vector; is the structure factor of the jth atom; c represents the atom as the basic unit; i is the imaginary unit; The calculation of the class structure factor of the microscopic crystal described in step 2 includes: Taking the cell as the basic unit, the quasi-structure factor of each basic unit is calculated separately, and finally summed up to obtain the quasi-structure factor of the microscopic crystal after the microscopic crystal shaping operation. in, is the class structure factor of the mth basic unit; is the weight of the class structure factor of the mth basic unit in the total class structure factors of basic units; N is the number of iterative operations in step 3; The calculation of the crystal-like structure factor after the crystal scale is enlarged as described in step 3 includes: The crystal after the scale enlargement in the previous iteration is used as the basic unit, and the quasi-structure factor of each basic unit is calculated. Finally, the quasi-structure factor of the crystal after the crystal scale enlargement operation is obtained by summing them up. in, is the class structure factor of the nth basic unit in the previous iteration; M-1 represents the remaining number of iterations.

2. The iterative method for optimizing the structure factor of a flat crystal X-ray diffraction of an arbitrary lattice structure according to claim 1, characterized in that: The shaping operation of the microscopic crystals described in step 2 includes: Taking the geometric center of the microscopic crystal as the origin of the coordinate system and the cell as the basic unit, a structure factor-like translation operation is performed to obtain a microscopic crystal composed of multiple cells stacked together.

3. The iterative method for optimizing the structure factor of a flat crystal X-ray diffraction of an arbitrary lattice structure according to claim 1, characterized in that: The structure factor of the actual material crystal obtained in step 3 includes: in, is the structure factor of the actual material crystal; The static class structure factor for the operation atom; is the quasi-structure factor of actual crystalline materials.

4. An iterative system for optimizing the structure factor of a flat crystal X-ray diffraction of an arbitrary lattice structure, implemented based on the method described in any one of claims 1 to 3, characterized in that: The system comprises: The module for calculating the structure factor of microscopic crystal cells is used to calculate the structure factor of microscopic crystal cells with atoms as the basic unit; A module for calculating the quasi-structure factor of a microscopic crystal, used for calculating the quasi-structure factor of the microscopic crystal after performing a shaping operation on the microscopic crystal; and The module for calculating the quasi-structure factor of the actual material crystal is used to iteratively calculate the quasi-structure factor of the crystal after the crystal scale is enlarged, and finally obtain the structure factor of the actual material crystal.

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