JP7452412B2 - How to search for diffusion routes - Google Patents

Description

The present invention relates to a diffusion route search method.

In order to further improve the performance of various materials, the search for new materials and the search for substitution elements that replace some of the elements constituting substances are actively being conducted.

As mentioned above, when searching for new materials and substitution elements, it is important to consider the routes through which atoms that affect the desired reaction, function, etc. move and diffuse within the crystal of the desired substance. It is preferable to know exactly what to do.

However, the elements inside the crystal are often tightly packed, and there appear to be only small gaps between the atoms that make up the crystal. For this reason, if you estimate the size of an atom whose diffusion path you want to investigate using its atomic radius, ionic radius, or van der Waals radius, you can compare the sizes of multiple gaps in the crystal to determine the diffusion path of the atom. It was difficult to identify.

In view of the problems of the above-mentioned conventional techniques, one aspect of the present invention aims to provide a method for searching for diffusion paths that can efficiently search for diffusion paths of atoms within a crystal.

According to one aspect of the present invention to solve the above problems,
an initial structure setting step of setting the positions of multiple atoms included in the crystal used for diffusion route search;
a calculation step of performing molecular dynamics calculations using the plurality of atoms whose positions were set in the initial structure setting step;
an analysis step of performing wavelet analysis on the coordinate data of the plurality of atoms obtained in the calculation step and determining a direction in which the plurality of atoms are likely to move;
a structural model creation step of creating a plurality of structural models in which the plurality of atoms are located in directions where they are likely to move, based on the results of the analysis step;
The present invention provides a method for searching for a diffusion path, which includes a diffusion path searching step of searching for an atomic diffusion path from the plurality of structural models created in the structural model creation step.

According to one aspect of the present invention, it is possible to provide a method for searching for diffusion paths that can efficiently search for diffusion paths of atoms within a crystal.

FIG. 1 is a hardware configuration diagram of a simulation device according to an embodiment of the present invention. FIG. 1 is a block diagram showing the functions of a simulation device according to an embodiment of the present invention. FIG. 2 is a schematic diagram showing the initial structure of LiMn ₂ O ₄ in which a diffusion path was searched in Example 1. FIG. 2 is a schematic diagram showing the diffusion path of Li atoms in LiMn ₂ O ₄ determined in Example 1.

Hereinafter, modes for carrying out the present invention will be described. However, the present invention is not limited to the following embodiments, and various modifications and variations may be made to the following embodiments without departing from the scope of the present invention. Substitutions can be added.

The diffusion route search method of this embodiment can include the following steps.
Initial structure setting step to set the positions of multiple atoms included in the crystal used for diffusion route search.
A calculation process in which molecular dynamics calculations are performed using multiple atoms whose positions were set in the initial structure setting process.
An analysis process that performs wavelet analysis on the coordinate data of multiple atoms obtained in the calculation process to determine the direction in which multiple atoms are likely to move.

A structural model creation process in which multiple structural models are created based on the results of the analysis process, in which multiple atoms are positioned in directions where they are likely to move.
Diffusion path search step to search for atomic diffusion paths from multiple structural models created in the structural model creation step.

The inventor of the present invention has conducted extensive studies on an efficient method for searching for the diffusion path of atoms within a crystal. If you look at the crystal structure at the atomic level, the atoms are tightly packed. However, when atoms move in concert, a transitional space is formed within the crystal, which often serves as a diffusion path. Therefore, by converting the fluctuations of a group of atoms into multiple characteristic movements and analyzing these movements, it becomes possible to discover specific phenomena.

Therefore, in the diffusion path search method of this embodiment, the movement of a plurality of atoms within a crystal is analyzed using wavelet analysis based on the results of the molecular dynamics method. As a result, the researchers discovered that it is possible to efficiently derive the diffusion path by deriving the direction in which multiple atoms are likely to move, and searching for the diffusion path from a structural model in which atoms are placed in the direction in which they are likely to move, thereby completing the present invention. .

Each step will be explained below.
(Initial structure setting process)
In the initial structure setting step, the positions of a plurality of atoms included in the crystal used for diffusion route searching can be set. That is, the initial coordinates of atoms included in the crystal used in the calculation process can be set.

In the initial structure setting step, a specific method for setting the positions of a plurality of atoms included in the crystal used for diffusion route search is not particularly limited. For example, the atomic arrangement of each atom can be set based on the crystal structure of the crystal, which has been experimentally determined or disclosed in literature, etc., to obtain the initial structure.

The initial structure set in the initial structure setting step may or may not contain diffusion atoms, which are atoms that search for diffusion paths. That is, it may be only a skeletal structure excluding diffused atoms. In the diffusion route search method of this embodiment, the diffusion route is searched based on the size of the space formed by the movement of atoms other than the diffusing atoms. This is because there is no big difference in the results.
(calculation process)
In the calculation step, molecular dynamics calculations can be performed using a plurality of atoms whose positions were set in the initial structure setting step.

Molecular dynamics calculation is a computer simulation method of the physical movement of atoms, and by numerically solving Newton's equation of motion, it is possible to determine the evolution of the position of atoms over time. Therefore, by performing the calculation step, it is possible to obtain time-series changes in the coordinates of a plurality of atoms set in the initial structure setting step.

In molecular dynamics calculations, information about atoms and interactions between atoms is represented by a functional form for describing potential energy and its parameter set (force field).

The type of force field used in the molecular dynamics calculation in the calculation process is not particularly limited, and various force fields can be used. For example, metal/alloy systems include EAM and MEAM, inorganic compound systems include Buckingham, BKS, Clay-FF, CVFF_aug, etc., semiconductor systems include Tersoff, and organic compound systems include PCFF, Compass, MMFF, OPLS-AA, AMBER, CHARMM, etc. UFF etc. can be used. In addition, forces selected from existing force fields such as polarization force fields such as X-Pol, AMBER polarization force field, and CHARMM polarization force field, and reaction force fields such as ReaxFF, as well as force fields created by yourself as necessary. You can use the field.

Existing force fields may not specify the charge of the target atom. In that case, RESP (Restrained ElectroStatic Potential) charges, AM1-BCC (Bond Charge Correction) charges, etc. can also be used.

The program (software) used for molecular dynamics calculations is not particularly limited, but for example, it may be selected from existing programs such as LAMMPS, DL_POLY, Gromacs (Groningen Machine for Chemical Simulations), AMBER, CHARMM, NAMD, etc., or a self-made program. A program can be used.

The setting environment for performing molecular dynamics calculations can be, for example, vacuum or periodic boundary conditions if a solvent is included.

The numerical integration method for solving Newton's equation of motion when performing molecular dynamics calculations is not particularly limited, but may be selected from, for example, the Berlet method, the velocity Berlet method, the Leap-frog method, the predictor-modifier method, etc. Other methods can be used.

Although the time span for performing molecular dynamics calculations is not particularly limited, it is preferably selected so that the directions in which the plurality of atoms constituting the crystal tend to move can be grasped and calculation costs can be suppressed. The time width for performing the molecular dynamics calculation can be, for example, 0.5 fs or more and 2 fs or less.

Further, the temperature control method is not particularly limited, but may be selected from, for example, the rate scaling method, the Nose-Hoover hot bath method, the Nose-Hoover chain method, the Berendsen hot bath method, the Andersen hot bath method, the Langevin kinetic method, etc. Other methods can be used.

The method of controlling the pressure under periodic boundary conditions is not particularly limited either, but for example, a method selected from the Berendsen method, the Parinello-Rahman method, etc. can be used.

A cutoff method can be used to calculate long-range interactions such as electrostatic interactions and van der Waals interactions. In particular, the Particle-Mesh Ewald method, the multipole expansion method, etc. can be used to calculate electrostatic interactions under periodic boundary conditions.

Molecular dynamics calculation in the calculation process uses, for example, a CPU (Central Processing Unit), a RAM (Random Access Memory), various storage media such as a hard disk, an output device such as a display, an input device such as a keyboard, various peripheral devices, etc. It can be carried out using a conventional computer system equipped with a computer system. Note that examples of the computer system include a network server, a workstation, a personal computer, and the like.

Specifically, for example, a program for the molecular dynamics calculation described above is stored in a storage medium, and the program is executed by a CPU, and an input device such as a keyboard or the like is stored in a storage medium such as a RAM. This can be achieved by reading the initial structure and conditions input from .
(Analysis process)
In the analysis step, wavelet analysis is performed on the coordinate data of the plurality of atoms obtained in the calculation step, and the directions in which the plurality of atoms tend to move can be determined.

Wavelet analysis is one of the frequency analysis methods, and is an analysis method that can simultaneously extract signal information related to time and frequency. Wavelet is translated as ``ripple'' and is a temporary wave that is created and disappears in the flow of time. Wavelet transform expresses arbitrary time series data as a sum of wavelets. The Fourier transform, which is often compared, represents arbitrary time-series data as a sum of infinite waves. Wavelet transform is an effective method for analyzing data that exhibits irregular fluctuations. The wavelet transform will be explained below.

Assume that there is a signal f(t) that changes with time t. When Fourier transform is performed on the signal f(t), information regarding the spectrum, that is, information regarding the frequency can be obtained, but information regarding the time is lost. Therefore, the window Fourier transform was devised. In order to analyze an object over time, a part of the signal is cut out using a "window function," and the spectrum of the signal is analyzed one after another while shifting this window. However, since the frequency resolution is generally inversely proportional to the size of the window function, the resolution for various frequencies is not constant in window Fourier transform using a window function of a fixed size.

On the other hand, wavelet transform uses a wavelet function called the mother wavelet Ψ(t) that scales and moves the basis function in parallel, making it possible to perform analysis adapting to the time width tailored to each frequency. , the resolution with respect to frequency is constant. The wavelet function is defined as shown in equation (1) below using two real parameters a and b that determine expansion and position.

ウェーブレット変換でのウェーブレット係数Ｗ（ａ，ｂ）は、対象となる信号ｆ（ｔ）とウェーブレット関数の内積で以下の式（２）のように定義される。

The wavelet coefficient W(a,b) in the wavelet transform is defined as the inner product of the target signal f(t) and the wavelet function as shown in Equation (2) below.

式（２）中のＷ（ａ，ｂ）は、ｔ＝ｂにおいてｆ（ｔ）の中にΨ_ａ，ｂ（ｔ）の成分がどれだけ含まれるかを表す。

W(a,b) in equation (2) represents how many components of Ψ _a,b (t) are included in f(t) at t=b.

Wavelet transforms include continuous wavelet transform and discrete wavelet transform. Main wavelets used in continuous wavelet transform include Mexican Hat, Meyer wavelet, and Morlet wavelet. Each mother wavelet has differences in calculation speed and information obtained in each time-frequency domain, but the general criteria for determining which mother wavelet is suitable for which data is not clear, and judgments must be made on a case-by-object basis. become. In the diffusion route search method of this embodiment, a Morlet wavelet defined by the following equation (3) can be used.

式（３）中のσは窓関数の窓の中に入っている波の数を表す。ウェーブレット変換では周波数に合わせた解析が可能であるため、振幅に合わせて周波数が変化するような非調和的な動きの解析も対象となる。

σ in equation (3) represents the number of waves falling within the window of the window function. Since wavelet transform allows analysis according to frequency, it can also be used to analyze non-harmonic movements where the frequency changes according to the amplitude.

In the wavelet coefficient W(a,b) described above, the range of t is from −∞ to ∞. However, the data actually used for analysis has a finite range. For this reason, the reliability of data near the boundaries decreases, so it is preferable to remove the edge portions of the time series during analysis. Furthermore, in general, in data analysis with a finite width, low frequencies are particularly affected by boundaries, and at high frequencies, the number of data in one wave becomes small and discrete, resulting in low data reliability. Therefore, it is preferable to perform analysis using the low frequency and high frequency parts removed.

Here, it is assumed that time-series position data q _n (t) (n=0, . . . , 3N) is obtained from a collection of N objects. First, wavelet transform is performed on each degree of freedom to obtain transformed data q'n(t, ωl), ωl=2πl/T. Here, T is the length of time series data, and in actual calculation, continuous wavelet transform is approximated by M pieces of discrete time series data. Also, for the above reasons, the range of frequency ωl is defined as l=M1,...,M2 (0<M1<M2≦(M/2)-1) and l=M-M2,..., Apply a low-pass filter set to M-M1. A matrix A={An, l} is created using the above wavelet components. If it is within the above frequency, A _n,l = q'n(t, ωl), otherwise it is 0.

In the analysis step, it is preferable to determine the direction in which atoms move easily, that is, the direction in which atoms move significantly. In general, slow motion has a large amplitude, that is, it moves slowly and greatly. In order to extract slow movements from the time series data obtained by wavelet transformation, singular value decomposition defined by the following equation (4) is used.

行列Ａは上記の通り、あるタイムステップにおける時系列データの対象物の自由度を行成分に、周波数を列成分に持つ。Ａの左特異ベクトルＵは時系列データの空間での動きの特徴を示す。また、右特異ベクトルＶは周波数での振幅の特徴を表し、Σは振幅を表す。

As described above, the matrix A has the degree of freedom of the object of time series data at a certain time step as a row component, and the frequency as a column component. The left singular vector U of A indicates the characteristics of the movement of time series data in space. Further, the right singular vector V represents the characteristic of amplitude at frequency, and Σ represents the amplitude.

The U and V column vectors corresponding to a certain amplitude represent the spatial motion and frequency characteristics having that amplitude, respectively. By projecting the signal in the direction of the column vector of U, the dynamic properties in that direction can be obtained.

As described above, in the analysis step, the dynamic properties of the atoms constituting the crystal can be analyzed by performing wavelet analysis on the coordinate data of a plurality of atoms obtained in the calculation step. In the analysis step, in order to find the direction in which the atoms tend to move, that is, the direction in which the atoms move significantly, for example, a left singular vector having a large singular value can be found, and a projection trajectory projected onto the left singular vector can be calculated.
(Structural model creation process)
In the structural model creation process, it is possible to create multiple models of structures in which multiple atoms are located in directions where they can easily move, based on the results of the analysis process.

Specifically, for example, a structural model in which the coordinates of multiple atoms set in the initial structure setting process are changed in the direction in which each atom can easily move, calculated in the analysis process, is can be created.

The purpose of the diffusion route search method of this embodiment is to search for diffusion routes of diffused atoms. Therefore, in the structural model creation step, it is preferable to create a structural model in which at least some of the atoms constituting the crystal, which can serve as diffusion paths, have large amplitudes. Therefore, among the results obtained in the analysis step, it is preferable to create a structural model in which the atoms are moved in the direction of the left singular vector having a large singular value.
(Diffusion route search process)
In the diffusion route searching step, it is possible to search for the diffusion route of the atom whose diffusion route is being searched, that is, the diffusion route of the diffusing atom, from the plurality of structural models created in the structure creation step. Specifically, for example, by comparing multiple structural models that have been created, it is possible to identify as the diffusion route the part where the interatomic distance is wider than the atomic radius of the diffusing atoms for atoms that make up the crystal other than the diffusing atoms. can.

According to the diffusion path search method of the present embodiment described above, the direction in which atoms are likely to move is derived using wavelet analysis based on the results of molecular dynamics calculation, and the structural model that moves in that direction is used to diffuse diffusion. Searching for a route. Therefore, it is possible to efficiently search for diffusion paths that are difficult to find from static crystal structures obtained through experiments in which atoms exist at average positions.

Furthermore, as described above, diffusion paths are searched using a structural model that reflects atomic fluctuations based on molecular dynamics calculation results, making it possible to search for diffusion paths in a structure that is closer to reality.
[Simulation device]
The simulation apparatus of this embodiment is a simulation apparatus for efficiently searching for diffusion paths of atoms within a crystal. Therefore, it can be called a diffusion route search device and can include the following members.

An initial structure setting section that sets the positions of multiple atoms included in the crystal used for diffusion route search.

A calculation section that performs molecular dynamics calculations using multiple atoms whose positions are set in the initial structure setting section.

The analysis section performs wavelet analysis on the coordinate data of multiple atoms calculated by the calculation section to determine the direction in which multiple atoms are likely to move.

The structural model creation department creates multiple structural models in which multiple atoms are positioned in directions where they can easily move, based on the results of the analysis department.

The diffusion path search unit searches for atomic diffusion paths from multiple structural models created by the structural model creation unit.

As shown in the hardware configuration diagram shown in FIG. 1, the simulation device 10 of the present embodiment is configured of, for example, an information processing device (computer), and physically includes a CPU (Central Processing Unit) that is an arithmetic processing unit. : processor) 11, RAM (Random Access Memory) 12 and ROM (Read Only Memory) 13 which are main storage devices, auxiliary storage device 14, input/output interface 15, display device 16 which is an output device, etc. Can be configured as a computer system. These are interconnected by a bus 17. Note that the auxiliary storage device 14 and the display device 16 may be provided externally.

The CPU 11 controls the overall operation of the simulation device 10 and performs various information processing. The CPU 11 can execute, for example, a program (simulation program) to be described later, which is stored in the ROM 13 or the auxiliary storage device 14, to perform molecular dynamics calculations, wavelet analysis, search for diffusion paths, and the like.

The RAM 12 is used as a work area for the CPU 11 and may include a nonvolatile RAM that stores main control parameters and information.

The ROM 13 can store programs (simulation programs) and the like.

The auxiliary storage device 14 is a storage device such as an SSD (Solid State Drive) or an HDD (Hard Disk Drive), and can store various data, files, etc. necessary for the operation of the simulation device.

The input/output interface 15 includes both a user interface such as a touch panel, keyboard, display screen, and operation buttons, and a communication interface that takes in information from an external data recording server and outputs analysis information to other electronic devices. .

The display device 16 is a monitor display or the like. The display device 16 displays an analysis screen, and the screen is updated in accordance with input/output operations via the input/output interface 15.

The functions of the simulation device 10 shown in FIG. This can be realized by reading and writing and operating the input/output interface 15 and display device 16.

FIG. 2 shows a functional block diagram of the simulation device 10 of this embodiment.

As shown in FIG. 2, the simulation device 10 can include a reception section 21, a processing device 22, and an output section 23. Each of these parts can be executed by executing a simulation method or a program stored in advance by the CPU in an information processing device such as a personal computer equipped with a CPU, a storage device, various interfaces, etc., which the simulation device 10 has. Software and hardware work together to achieve this.

The configuration of each part will be explained below.
(A) Reception Unit The reception unit 21 receives input of commands and data from a user related to processing executed by the processing device 22. The reception unit 21 includes a keyboard and a mouse that are operated by the user to input commands, a communication device that inputs via a network, and a reading device that inputs from various storage media such as CD-ROM and DVD-ROM. Can be mentioned.
(B) Processing device The processing device 22 can include an initial structure setting section 221, a calculation section 222, an analysis section 223, a structural model creation section 224, and a diffusion path search section 225.
(B-1) Initial Structure Setting Unit The initial structure setting unit 221 can set the positions of a plurality of atoms included in the crystal used for diffusion route search.

The data regarding the positions of a plurality of atoms set by the initial structure setting section may be data stored in a database or the like, or may be calculated values calculated from experimental results.
(B-2) Calculation section The calculation section can perform molecular dynamics calculations using a plurality of atoms whose positions are set in the initial structure setting section. Since the molecular dynamics calculation has already been explained, the explanation will be omitted here.
(B-3) Analysis Unit The analysis unit 223 performs wavelet analysis on the coordinate data of the plurality of atoms calculated and obtained by the calculation unit 222, and can determine the direction in which the plurality of atoms are likely to move. Since the wavelet analysis has already been explained, the explanation will be omitted here.
(B-4) Structural Model Creation Unit The structural model creation unit 224 can create a plurality of structural models in which a plurality of atoms are located in directions where they can easily move, based on the analysis results in the analysis unit 223.
(B-5) Diffusion Path Search Unit The diffusion path search unit 225 can search for atomic diffusion paths from the plurality of structural models created in the structural model creation process. Specifically, for example, by comparing multiple structural models created in the structural model creation section, for atoms constituting the crystal other than the diffusing atoms, the diffusion path is determined by determining the part where the interatomic distance is wider than the atomic radius of the diffusing atoms. It can be certified as
(C) Output unit The output unit 23 can have a display or the like. The search results obtained by the diffusion route search section 225 can be output to the output section 23. Although the contents of the simulation results to be output are not particularly limited, for example, the searched route can be outputted and displayed as an image to the output unit 23 as shown in FIG.

According to the simulation apparatus of this embodiment described above, the direction in which atoms are likely to move is derived using wavelet analysis based on the results of molecular dynamics calculation, and the diffusion path is searched using a structural model moved in that direction. It is carried out. Therefore, it is possible to efficiently search for diffusion paths that are difficult to find from static crystal structures obtained through experiments in which atoms exist at average positions.

Furthermore, as described above, diffusion paths are searched using a structural model that reflects atomic fluctuations based on molecular dynamics calculation results, making it possible to search for diffusion paths in a structure that is closer to reality.
[program]
Next, the program of this embodiment will be explained.

The program of this embodiment relates to a program for efficiently searching for diffusion paths of atoms within a crystal, and can cause a computer to function as the following units.

An initial structure setting section that sets the positions of multiple atoms included in the crystal used for diffusion route search.

A calculation section that performs molecular dynamics calculations using multiple atoms whose positions are set in the initial structure setting section.

The analysis section performs wavelet analysis on the coordinate data of multiple atoms calculated by the calculation section to determine the direction in which multiple atoms are likely to move.

The structural model creation department creates multiple structural models in which multiple atoms are positioned in directions where they can easily move, based on the results of the analysis department.

The diffusion path search unit searches for atomic diffusion paths from multiple structural models created by the structural model creation unit.

The program of this embodiment can be stored in various storage media such as a main storage device or an auxiliary storage device such as RAM or ROM of the above-mentioned simulation device, for example. By loading such a program and executing it by the CPU, it is possible to read and write data in a RAM, etc., and to operate and execute an input/output interface and a display device. For this reason, the explanation of the matters already explained with respect to the simulation device will be omitted.

The program of this embodiment described above may be provided by being stored on a computer connected to a network such as the Internet and downloaded via the network. Furthermore, the program of this embodiment may be configured to be provided and distributed via a network such as the Internet.

The program of this embodiment may be distributed while being stored in an optical disk such as a CD-ROM or a recording medium such as a semiconductor memory.

According to the program of this embodiment described above, the direction in which atoms are likely to move is derived using wavelet analysis based on the results of molecular dynamics calculation, and the diffusion path is searched using a structural model moved in that direction. Is going. Therefore, it is possible to efficiently search for diffusion paths that are difficult to find from static crystal structures obtained through experiments in which atoms exist at average positions.

Furthermore, as described above, diffusion paths are searched using a structural model that reflects atomic fluctuations based on molecular dynamics calculation results, making it possible to search for diffusion paths in a structure that is closer to reality.

Hereinafter, the present invention will be described in more detail with reference to Examples. However, the present invention is not limited to the following examples.
[Example 1]
The following procedure was used to search for the diffusion route of Li atoms in LiMn ₂ O ₄ .
(Initial structure setting process)
The initial structure of LiMn ₂ O ₄ was set. Specifically, as shown in FIG. 3, an initial structure 30 of LiMn ₂ O ₄ in which lithium atoms 31, manganese atoms 32, and oxygen atoms 33 were arranged was set in the cell. In addition, in FIG. 3, atoms with the same hatching indicate atoms of the same type.
(calculation process)
Next, using molecular dynamics calculation, time-series changes in the coordinates of the lithium atom 31, the manganese atom 32, and the oxygen atom 33 whose positions were set in the initial structure setting step were determined.

Molecular dynamics calculations were performed using LAMMPS as software and a force field developed by Ishizawa et al., Nagoya University. Then, the coordinates of each atom were entered to set the environment in the crystal.

In addition, the velocity Berlet method was used as a velocity calculation method when performing molecular dynamics calculations, and the time width was set to 1 fs. The Nose-Hoover chain method was used as a temperature control method, and the set temperature was 300K.

The Particle-Mesh Ewald method was used to calculate long-range interactions.

Molecular dynamics calculations were performed for 10 nanoseconds under the above conditions.
(Analysis process)
Wavelet analysis was performed on the changes in the coordinates of multiple atoms obtained during the calculation process, and the directions in which multiple atoms tend to move were determined.

Note that when the results obtained in the calculation process were submitted to the analysis process, they were corrected using the following equation (5) so that the average value was 0.

なお、上記式中のｘ（ｔ）は、ウェーブレット解析で使用したトラジェクトリ、ｘ´（ｔ）は計算工程で得られたトラジェクトリ、＜ｘ´＞はその時間平均を表す。

Note that x(t) in the above formula represents the trajectory used in the wavelet analysis, x'(t) represents the trajectory obtained in the calculation process, and <x'> represents its time average.

A self-written Python code was used for wavelet analysis calculations, and the Python numerical calculation library Numpy was used for singular value decomposition. The length of the entire time series is 1 ns, and the number of time series is M=200. The time series data used for analysis was 0.1 ns or more and 0.9 ns or less. Furthermore, a low-pass filter with M ₁ =15 and M ₂ =50 was used.
(Structural model creation process)
From the results of the analysis process, the coordinates of multiple atoms set in the initial structure setting process are calculated in the analysis process. Created.
(Diffusion route search process)
We searched for diffusion paths of diffusing atoms from multiple structures created in the structure creation process.

In general, slow movements have large amplitudes, ie, slow and large movements. Therefore, in the analysis step, projection trajectories were calculated by projecting the trajectories obtained in the calculation step onto 10 left singular vectors having large singular values. In the diffusion route searching step, it was confirmed whether a space that could serve as a diffusion route could be obtained among them. Specifically, in the structural model creation process, atoms are moved in the direction of the left singular vector, and in the diffusion path search process, from the lithium atom 31A placed in the center in FIG. It was confirmed whether a continuous space was formed between the other four lithium atoms 31.

FIG. 4 shows the diffusion paths of the diffused atoms obtained in the diffusion path search step.

As shown in FIG. 4, diffusion paths 411 to 414 were found as diffusion paths for lithium atoms. These diffusion paths connect the lithium atoms 31A (see FIG. 3) located in the center of the cell and the lithium It is formed so as to connect the lithium atoms arranged around the atom 31A.

These diffusion paths 411 to 414 are consistent with the diffusion paths of lithium atoms in LiMn ₂ O ₄ that have been reported so far, and the method of searching for diffusion paths used in this example is based on actual phenomena. I was able to confirm that.

Claims (1)

an initial structure setting step of setting the positions of multiple atoms included in the crystal used for diffusion route search;
a calculation step of performing molecular dynamics calculations using the plurality of atoms whose positions were set in the initial structure setting step;
an analysis step of performing wavelet analysis on the coordinate data of the plurality of atoms obtained in the calculation step and determining a direction in which the plurality of atoms are likely to move;
a structural model creation step of creating a plurality of structural models in which the plurality of atoms are located in directions where they are likely to move, based on the results of the analysis step;
A diffusion route search method comprising: a diffusion route search step of searching for an atomic diffusion route from the plurality of structural models created in the structural model creation step.

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