A Python-based statistical method for automated batch calculation of atomic coordination numbers

Abstract

The present invention provides a Python-based automated batch calculation and statistical method for atomic coordination numbers, that is, finding short-range ordered structures from long-range ordered structures, and quantitatively and graphically representing them. The Python-based automated batch calculation and statistical method for similar atomic coordination numbers and atomic coordinates is implemented to study the local ordered structure of alloys with complex components, including: step S1, alloy system selection and atomic occupancy fraction acquisition; step S2, supercell and ordered distribution configuration file construction; step S3, statistical information configuration module; step S4, atomic classification generation module; step S5, interatomic distance calculation file generation module; step S6, statistical various similar atomic coordination number file generation module; step S7, batch output file module; step S8, visualization module.

Description

Technical Field

[0001] The present invention relates to the technical field of metal material calculation and simulation, and particularly to an automated batch calculation and statistical method for atomic coordination numbers based on Python. Background Art

[0002] Metal materials are closely related to the development of human society, and their usage history has accompanied the development of human society for more than 3000 years. With the development of technology, increasing demands, and intensifying international competition, the research and development of new high-performance metal materials are imminent. Traditional metal materials are mainly composed of one or two metal elements, with different alloying elements added to produce different alloys. For example, aluminum alloys mainly based on Al, steel materials mainly based on Fe, titanium alloys mainly based on Ti, or TiAl and intermetallic compounds with nearly equal proportions of Ti and Al. However, traditional alloy systems have been exhausted, and it is urgent to break through the shackles of traditional alloy design thinking. In the past 20 years, high-entropy alloys and high-entropy materials derived from them have broken through the design concepts of traditional materials in terms of composition and structure, setting off a research boom. Many high-entropy alloy and high-entropy material systems exhibit unique microstructural characteristics and special properties, with potential application values. Different from the traditional alloy design concept, high-entropy alloys contain at least five main elements with equal or approximately equal atomic percentages, and there is no obvious difference between solutes and solvents. In 2004, the research teams of Professor Yih-Wey Yeh at Tsinghua University in Taiwan, China, and Professor B. Cantor at the University of Cambridge in the UK independently proposed the design concepts of high-entropy alloys and equimolar multi-principal element alloys at the same time. Their essential ideas in alloy composition design are basically similar. These bold ideas have inspired great interest and practice among materials scientists. Materials scientists have actively carried out rational and quantitative research on the formation mechanism of high-entropy alloys, the relationship between structure and properties, especially for the four major effects of high-entropy alloys proposed by early materials scientists, namely: (1) the high-entropy effect thermodynamically; (2) the sluggish diffusion effect kinetically; (3) the lattice distortion effect structurally; (4) the cocktail effect in terms of properties. Some researchers have also, based on application requirements, inversely explored the composition, microstructure, and corresponding preparation processes of high-entropy alloys that can meet the performance requirements. The basic research and application development of high-entropy materials, including high-entropy alloys, have made remarkable progress. Some high-entropy alloy systems have potential application values in many fields due to their excellent properties such as high strength, fatigue resistance, fracture resistance, thermal stability, high elongation, and radiation resistance. At present, a small number of alloy systems have been applied to metallurgical materials, catalysts, magnetic materials, and nuclear materials, etc., showing initial signs of success.

[0003] Nevertheless, the theoretical foundation for the research and development of high-entropy alloys is very weak. Regarding the aforementioned theories and methods of high-entropy alloys, there are still many controversies and unclear points. For example, regarding the four major effects of the above high-entropy alloys, many scholars have raised doubts and even directly given counterexamples that do not match. The main reason for the controversy is that there is a lot of speculation and a lack of quantitative description methods.

[0004] It is generally believed that due to the high mixing entropy, high-entropy alloys have stable properties and simple structures. However, this is based on the assumption that atoms randomly occupy lattice sites, and the theoretical basis is lacking or even impossible because the lattice and sublattices of different crystal structures with different atomic species are different, and there must be a random solid solution of multi-components with preferred site occupation (i.e., site-occupying preference). The ideal configurational entropy of such a solid solution is:

[0005]

[0006] where R is the gas constant, x Mi is the mole fraction of element Mi, and n is the number of components. When x M1 = x M2 =... = x Mn the entropy of the system reaches its maximum value. That is, for an equiatomic high-entropy alloy system, the configurational entropy can be expressed as:

[0007] S conf = Rln(n)

[0008] Theoretical and experimental results show that a higher mixing entropy in the alloy promotes the formation of a random solid solution phase with a simple structure (such as FCC, BCC, HCP), thus reducing the number of phases. The properties of high-entropy alloys are closely related to their phase structures. High-entropy alloys with an FCC phase have high plasticity and low hardness, while high-entropy alloys with a BCC phase have high strength and low plasticity. High-entropy alloys with a mixed-phase structure can achieve a combination of high strength and high plasticity. In the simplest description, the local chemical environment of high-entropy alloys can be considered to represent the random distribution of different types of atoms at lattice sites, that is, the maximum configurational entropy state. However, some scholars believe that the atomic configuration in a truly random high-entropy alloy should not support any type of nearest-neighbor pairs. Taking CrFeMnNi as an example, there should be a certain number of like-atom XX pairs (such as Cr-Cr, Mn-Mn, Fe-Fe, and Ni-Ni) and unlike-atom pairs XY (such as Cr-Mn, Cr-Fe, Cr-Ni, Mn-Fe, Mn-Ni, and Fe-Ni). With the continuous in-depth study of high-entropy alloy systems, a small number of scholars have found the existence of local order in the alloy and believe that local order is closely related to the properties of the alloy, but they are at a loss as to how to decipher the local ordered structure, which is like an encrypted code.

[0009] The research group of the inventors has been engaged in research in the field of high-entropy alloys for more than 10 years. On the one hand, considering that in high-entropy alloys, the types and contents of constituent elements are diverse, and the atomic radii, nuclear outer electron structures, electronegativities of constituent atoms, and the binding energies between different atoms are all different, and some even have significant differences.

[0010] On the other hand, considering that FCC, BCC or HCP alloy phases all have clear sublattice structures, it is considered that alloy atoms must have a certain tendency to occupy positions on the sublattice, either strong or weak, and cannot be completely randomly distributed. Aiming at the complex mechanism of the alloying process, an attempt is made to establish a quantitative internal relationship among the four elements of "alloy composition - process - structure - performance".

[0011] There must be a certain tendency to occupy positions (that is, the ability to compete for positions on different sublattices is not equal). Some atoms tend to occupy one sublattice, while some atoms tend to occupy another sublattice, that is, the so-called ordered occupation behavior. The inventors, as previous workers, have applied for and obtained authorization for an invention patent on a quantitative prediction method for the ordered occupation behavior of atoms in high-entropy alloys: ZL 2021100207115 A method for calculating the configurational entropy of high-entropy alloys based on the ordered occupation behavior of atoms. Based on this invention patent, when a high-entropy alloy with a given composition reaches phase equilibrium at a certain heat treatment temperature, a supercell is constructed by calculating and predicting the occupation fractions, and then atoms are distributed, and the coordination of its atoms is statistically analyzed, and the statistical law of the coordination numbers of the same type of atoms is given and displayed graphically, so as to discover the quantity and distribution of local ordered structures from the long-range ordered structure described by the occupation fractions, push the research of high-entropy alloys deeper, lay a solid fine structure foundation for performance regulation, and realize the rational, quantitative and graphical research of high-entropy alloys, and promote the research process of new high-entropy alloy materials. The present invention not only quantitatively describes the occupation behavior of different types of atoms on different sublattices, but also can further graphically display the atomic distribution configuration, obtain the local ordered structure of atoms when the heat treatment reaches the equilibrium state, and solve the deficiencies in previous literatures that ignore the differences in the types of constituent atoms and the alloy phase structure, and generally use the method of ideal mixing to quantitatively calculate the rough method of high-entropy effect, and are even more helpless in the research of local ordered structures. Summary of the Invention

[0012] In view of this, the purpose of the present invention is to provide a method for extracting the coordination information of the same type of atoms from the complex high-entropy alloy configuration with ordered occupation characteristics, that is, to find the short-range ordered structure from the long-range ordered structure, and quantitatively and graphically characterize it. And an automated batch calculation and statistical method for the coordination numbers and atomic coordinates of the same type of atoms based on Python is realized, which is used to study the local ordered structure of alloys with complex compositions.

[0013] To achieve the above object, the present invention adopts the following technical solutions: An automated batch calculation and statistics method for atomic coordination numbers based on Python, comprising the following steps:

[0014] Step S1, alloy system selection and obtaining atomic site fractions: Establish a supercell of an appropriate size of a FCC, BCC or HCP prototype structure for the position occupancy distribution of atoms;

[0015] Step S2, construction of supercell and ordered distribution configuration files: According to the site fraction data of each type of alloy atom on different sublattices in the alloy phase calculated by phase equilibrium prediction, perform rounding conversion on the number of atoms of various types on various types of sublattices of the corresponding supercell;

[0016] Step S3, statistical information configuration module: Configure the types of elements to be calculated, the distance of the first nearest neighbor atoms, the length of the basis vectors, and the atomic coordination numbers;

[0017] Step S4, atomic classification generation module: Extract the three-dimensional coordinate data of each type of element from the POSCAR file, and store the three-dimensional coordinate data of each type of element into an atomic coordinate Excel file respectively;

[0018] Step S5, atomic distance calculation file generation module: Calculate the distance between every two atoms, and store the atomic information that meets the distance of the first nearest neighbor atoms into an atomic first nearest neighbor Excel file, including three-dimensional coordinate data, atomic type, atomic serial number, and atomic distance;

[0019] Step S6, statistical various types of atomic coordination number file generation module: According to the coordination numbers of the same type of atoms, count the number of coordination pairs of each atom at a specified coordination number, and output the coordination data information as an atomic coordination csv file;

[0020] Step S7, batch output file module: Control the batch calculation of the coordination pairs of the same type of atoms of different element types at different coordination numbers;

[0021] Step S8, visualization module: Collect and summarize the three-dimensional coordinate data of the same type of atoms with a specified coordination number and greater than the number of coordination pairs into a cluster structure file, and apply the primitive vectors of the POSCAR of the supercell to the corresponding positions of the POSCAR of the same type of atomic cluster. Note that at this time, the low coordination numbers actually include the high coordination numbers, that is, the atomic information in the high coordination numbers is a subset of the atomic set in the low coordination numbers; then use the VESTA software package to visually express the corresponding same type of atomic cluster.

[0022] In a preferred embodiment, in step S5, the pandas library is required to convert the atomic coordinate Excel file into a DataFrame and a list, and output the atomic first nearest neighbor Excel file.

[0023] In a preferred embodiment, the step of generating the atomic coordination number file in step S6 includes the following steps:

[0024] Step S61: Calculate the number of occurrences of each atom, and store the atom serial number as the key value and the number of occurrences of the atom as the value in a dictionary;

[0025] Step S62: Screen out the atom serial numbers that meet the coordination number from the dictionary and store them in a list;

[0026] Step S63: Use the atom serial numbers in the list as indexes to find the data rows where the atoms are located and record them in the atomic coordination csv file.

[0027] The present invention has the following beneficial effects:

[0028] The present invention is based on Python technology. By using Python libraries, it calculates the interatomic distance values of a large number of different elements, classifies and statistically analyzes them according to different coordination numbers, obtains the atomic information under the condition of meeting the coordination number, and further provides quantitative calculations for studying the site ordering behavior of atoms, which has important guiding significance for accurately predicting the phase formation mechanism and microstructure of high-entropy alloys.

[0029] The calculation process of the present invention strictly follows the alloy phase crystallographic structure information and alloy thermodynamics theory, quantitatively calculates the atomic coordination number of high-entropy alloys, and is expected to rationally and quantitatively study the phase formation mechanism of high-entropy alloys from the essence, forming a universal calculation method. This method saves research costs, improves research efficiency, provides new ideas for further quantitative research on other effects of high-entropy alloys, and lays a solid fine structure foundation, thus accelerating the research and development of new high-entropy alloy materials. Description of the Drawings

[0030] Figure 1 It is a flowchart of a preferred embodiment of the present invention

[0031] Figure 2 It is a single cell diagram formed by the sublattice nesting of the ordered FCC_VCoNi of the preferred embodiment VCoNi of the present invention

[0032] Figure 3 It is an atomic configuration diagram of the 20×20×20 supercell process of V and Co in the preferred embodiment VCoNi of the present invention

[0033] Figure 4 It is a construction diagram of the 20×20×20 supercell of the preferred embodiment VCoNi of the present invention

[0034] Figure 5 It is a fragment diagram of the POSCAR file of all atoms in the preferred embodiment VCoNi of the present invention

[0035] Figure 6 Distribution of each atom in the FCC lattice of the preferred embodiment VCoNi of the present invention

[0036] Figure 7 Fragment diagram of the V atom POSCAR file of the preferred embodiment VCoNi of the present invention

[0037] Figure 8 Fragment diagram of the Co atom POSCAR file of the preferred embodiment VCoNi of the present invention

[0038] Figure 9 Fragment diagram of the Ni atom POSCAR file of the preferred embodiment VCoNi of the present invention

[0039] Figure 10 Diagram of the information configuration module of the preferred embodiment VCoNi of the present invention

[0040] Figure 11 Diagram of the same-kind atomic cluster with M*-8M coordination of preferred site occupation of the preferred embodiment VCoNi of the present invention

[0041] Figure 12 Diagram of the same-kind atomic cluster with M*-8M and above coordination of random site occupation of the preferred embodiment VCoNi of the present invention

[0042] Figure 13 Diagram of the same-kind atomic cluster with M*-7M and above coordination of preferred site occupation of the preferred embodiment VCoNi of the present invention

[0043] Figure 14 Diagram of the same-kind atomic cluster with M*-7M and above coordination of random site occupation of the preferred embodiment VCoNi of the present invention Detailed implementation manners

[0044] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0045] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0046] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should also be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0047] An automated batch calculation and statistical method for atomic coordination numbers based on Python, referring to Figures 1 to 14 , includes the following steps:

[0048] Step S1, alloy system selection and obtaining atomic site fractions: Establish a supercell of an appropriate size of an FCC, BCC, or HCP prototype structure for the position occupancy distribution of atoms;

[0049] Step S2, building the supercell and ordered distribution configuration file: According to the site fraction data of each type of alloy atom on different sublattices in the alloy phase calculated by phase equilibrium prediction, perform rounding conversion of the number of atoms of various types on various types of sublattices of the corresponding-sized supercell.

[0050] Step S3, statistical information configuration module: Configure the types of elements to be calculated, the distance of the first-nearest neighbor atoms, the length of the basis vectors, and the atomic coordination numbers;

[0051] Step S4, atomic classification generation module: Extract the three-dimensional coordinate data of each type of element from the POSCAR file and store the three-dimensional coordinate data of each type of element into an atomic coordinate Excel file respectively;

[0052] Step S5, atomic distance calculation file generation module: Calculate the distance between every two atoms, and store the atomic information that meets the distance of the first-nearest neighbor atoms into an atomic first-nearest neighbor Excel file, including three-dimensional coordinate data, atomic type, atomic serial number, and atomic distance;

[0053] Step S6, statistical various types of like-atom coordination number file generation module: According to the like-atom coordination numbers, count the number of coordination pairs of each atom at a specified coordination number, and output the coordination data information as an atomic coordination csv file;

[0054] Step S7, batch output file module: Control the batch calculation of the like-atom coordination pairs of different element types at different coordination numbers;

[0055] Step S8, Visualization module: Collect and summarize the coordinate data of like atoms with a specified coordination number and more than this coordination number into a cluster structure file, and apply the primitive vectors of the POSCAR of the supercell to the corresponding positions of the POSCAR of the like-atom cluster. Note that at this time, the lower coordination numbers actually include the higher coordination numbers, that is, the atomic information in the higher coordination numbers is a subset of the atomic set in the lower coordination numbers. Then use the VESTA software package to visually represent the corresponding like-atom clusters.

[0056] In step S5, the pandas library is needed to convert the atomic coordinate Excel file into a DataFrame and a list, and output the Excel file of the first nearest neighbors of the atoms.

[0057] The atomic coordination number file generation module in step S6 includes the following steps:

[0058] Step S61: Calculate the number of times each pair of atoms appears, and store the atomic serial number of the key value and the number of times the atom appears in the dictionary;

[0059] Step S62: Screen out the atomic serial numbers of the key values that meet the coordination number from the dictionary and store them in a list;

[0060] Step S63: Use the atomic serial numbers in the list as indexes to find the data rows where the atoms are located and record them in the atomic coordination csv file.

[0061] In this embodiment, taking the VCoNi multi-principal element alloy with FCC structure (also called medium-entropy alloy or high-entropy alloy by some scholars) as an example, an automated batch calculation and statistics method for atomic coordination numbers based on Python is provided, including the following steps:

[0062] Step S1, Selection of the VCoNi alloy system with FCC structure and acquisition of atomic site fractions. This alloy is relatively unique, and its site occupation behavior is not affected by temperature, with constant and ordered site occupation, and the theoretical prediction results are in good agreement with the experimental reported results. While the site occupation behaviors of other alloy systems may change with temperature.

[0063] Step S2, Construction of supercell and ordered distribution configuration files: According to the site fraction data of each type of alloy atom on different sublattices in the alloy phase calculated by phase equilibrium prediction, convert and round up the number of atoms of various types on various types of sublattices of the corresponding-sized supercell. The site occupation details and visualization are as Figure 2 shown. Based on the existing computing resources, this embodiment establishes a 20x20x20 supercell of the FCC prototype structure of VCoNi for the position occupation distribution of atoms.

[0064] The formatted POSCAR file fragment is as Figure 5As shown in the figure. Various atoms in the 20×20×20 CoNiV_FCCMPA supercell were separately stripped out, and visualized and data files were created, that is, the three-dimensional coordinate information in the POSCAR file was extracted and stored in the atomic coordinate Excel files corresponding to V, Co, and Ni for further analysis.

[0065] The formatted fragment diagram of the POSCAR file with various atoms stripped out is as Figures 7 to 9 shown.

[0066] Step S3: Following a similar idea to the construction of the 20×20×20 supercell, a 3×3×3 supercell of this structure was established, and the cell volume was optimized to obtain the first-nearest neighbor atomic distance of

[0067] Step S4: Through the configuration module, the element types were set as V, Co, and Ni. Based on the optimized cell volume of the 3×3×3 supercell in Step S3, the first-nearest neighbor atomic distance obtained was The lattice constant of the supercell was By extrapolation, the first-nearest neighbor atomic distance of the 20×20×20 supercell was still The basis vector length was Then, the coordination information of the same-type atoms (i.e., the first-nearest neighbor atoms) of various atoms was searched, and the coordination numbers were set as: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, where 12 is the maximum number of first-nearest neighbor atoms in the FCC pure element unit cell.

[0068] Step S5: Through the atomic distance file generation module, the distances between every two atoms in each type of atom were calculated by traversal, and the data of the atoms that satisfied the first-nearest neighbor atomic distance were stored in the atomic first-nearest neighbor Excel file, including three-dimensional coordinate data, atomic type, atomic serial number, and atomic distance.

[0069] Step S6: Through the atomic coordination number file generation module, the atomic sequences that satisfied the conditions were separately counted for coordination numbers of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, and the ones that met the coordination number quantity were output as an atomic coordination csv file.

[0070] Partial coordination number information of the VCoNi alloy system is shown in Table 1. It can be seen that the higher the coordination number n, the fewer the number of coordination clusters (Group numbers). And under the assumption of random occupancy, the number of coordination clusters is significantly more, but this assumption does not match the significant tendency of ordered occupancy of different atoms in this system and can only be used as a control result. Generally speaking, under the condition of heat treatment reaching equilibrium, the alloy has a tendency of ordered occupancy, and the maximum coordination number does not exceed 8. The coordination of the same-type atoms in other alloy systems can be statistically analyzed according to these steps:

[0071] Table 1

[0072]

[0073]

[0074] Step S7: Statistically analyze the probability of the formation of clusters by atoms of the same type under a specified coordination number to characterize the local order characteristics.

[0075] For atoms of the same type, the probability calculation formula for 8-fold coordination is as follows:

[0076] P(M*-8M) = [N g ×(1 + 8) / 10667]×1000‰ = N g ×0.843‰, (1)

[0077] P(V*-8V) = N g ×0.843‰ = 40×0.843‰ = 33.72‰,

[0078] P(Co*-8Co) = N g ×0.843‰ = 8×0.843‰ = 6.74‰,

[0079] P(Ni*-8Ni) = N g ×0.843‰ = 8×0.843‰ = 6.74‰.

[0080] Step S8: Graphical representation of coordination clusters. The following separately conducts graphical representations of the atomic clusters of atoms of the same type under a specified coordination number. Note that the cluster configurations at higher coordination numbers also meet the requirements of lower coordination number clusters. Therefore, the information of higher coordination numbers is also included in the images of lower coordination number clusters. Figure 11 It is a diagram of atomic clusters of atoms of the same type with M*-M8 and above coordination under the preferred occupancy of VCoNi. Figure 12 It is a diagram of atomic clusters of atoms of the same type with M*-M8 and above coordination under the random occupancy of VCoNi. Figure 13 It is a diagram of atomic clusters of atoms of the same type with M*-M7 and above coordination under the preferred occupancy of VCoNi. Figure 14 It is a diagram of atomic clusters of atoms of the same type with M*-M7 and above coordination under the random occupancy of VCoNi.

[0081] The above are only the embodiments of the present invention. All equivalent changes and modifications made according to the scope of the patent application of the present invention shall fall within the scope covered by the present invention.

Claims

1. A Python-based automated batch calculation statistical method for atomic coordination numbers, characterized in that: The following steps are involved: Step S1, alloy system selection and atomic site occupancy fraction acquisition: establishing a supercell of FCC, BCC or HCP prototype structure of appropriate size for atomic site occupancy distribution; Step S2, supercell and ordered distribution configuration file construction: according to the occupancy fraction data of each type of alloy atoms on different sublattices in the alloy phase calculated by phase equilibrium prediction, the number of atoms of various types on various types of sublattices of supercells of corresponding sizes is converted and rounded; Step S3, statistical information configuration module: configure the calculation element type, first nearest neighbor atomic distance, basis vector length and atomic coordination number; Step S4, atomic classification generation module: extracting the three-dimensional coordinate data of each element from the POSCAR file, and storing the three-dimensional coordinate data of each element into an atomic coordinate Excel file; Step S5, interatomic distance calculation file generation module: calculate the distance between every two atoms, and store the atomic information that meets the first-neighbor atomic distance into the atom first-neighbor Excel file, including three-dimensional coordinate data, atomic type, atomic number and atomic distance; Step S6, a module for generating files for counting coordination numbers of various similar atoms: according to the coordination numbers of similar atoms, the number of coordination pairs of each atom under the specified coordination number is counted, and the coordination data information is output as an atomic coordination csv file; Step S7, batch output file module: controlling batch calculation of similar atomic coordination pairs of different element types at different coordination numbers; Step S8, visualization module: collect and summarize the coordinate data of similar atoms with a specified coordination number and a coordination pair number greater than the specified coordination number into a cluster structure file, and apply the initial basis vectors of the POSCAR of the supercell to the corresponding positions of the similar atomic clusters POSCAR. Note that at this time, the low coordination pair number actually contains the high coordination pair number, that is, the atomic information in the high coordination pair number is a subset of the atomic set in the low coordination pair number; then use the VESTA software package to visualize the corresponding similar atomic clusters.

2. According to the Python-based automated batch calculation statistical method for atomic coordination numbers in claim 1, it is characterized in that: In step S5, the pandas library is used to convert the atomic coordinate Excel file into a DataFrame and a list, and output the atomic first neighbor Excel file.

3. The method for automatic batch calculation of atomic coordination numbers based on Python according to claim 1, characterized in that: The module for generating the statistical atomic coordination number file in step S6 includes the following steps: Step S61: Calculate the number of occurrences of each atom, and store the key value atom number and the value value atom occurrence number in the dictionary; Step S62: Filter out the atomic numbers of the key values ​​that match the coordination number from the dictionary and store them in a list; Step S63: Use the atomic number in the list as an index to find the data row where the atom is located and record it in the atomic coordination csv file.

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