JP7314963B2 - CRYSTAL STRUCTURE SEARCHING DEVICE AND CRYSTAL STRUCTURE SEARCHING METHOD - Google Patents

Description

The present invention relates to a crystal structure searching apparatus and a crystal structure searching method.

A crystal structure search is performed to search for a stable crystal structure in designated compound composition information (Patent Documents 1 to 3, Non-Patent Documents 1 and 2). For example, a method of estimating a material structure based on radiation commentary data and a method of estimating a common crystal structure for multiple compounds contained in a database by applying a multiple parameter optimization method by a genetic algorithm (hybrid GA) are disclosed. Further, for example, a method of searching for a crystal structure using a generative model such as VAE (Variational Auto-Encoder) or GAN (Generative Adversarial Network), and a structure refinement technique applying Rietveld analysis are disclosed.

Japanese Patent No. 5055556 U.S. Patent Publication No. 2019/220484 Japanese Patent No. 4576194

Chem. Sci., 2020, 11, 4871-4881 Journal of the Ceramic Society of Japan, 1994, 102, 1184, 401-404

By the way, in the prior art, there is a problem that the search efficiency is low because the crystal structure search process is not performed in a search space that satisfies invariance with respect to translational movement, rotational movement, and unit cell selection.

Moreover, when machine learning is used, there is a problem that a huge amount of training data is required, which increases the calculation cost. In addition, there is also a problem that machine learning needs to be tuned according to desired physical properties, and lacks versatility.

In addition, in the process of refining the crystal structure, the estimated initial structure must be a globally optimal structure, and there is a problem that it is difficult to converge to the optimal structure if the initial structure is not appropriate. Therefore, the experience and wisdom of a skilled engineer were required when setting the initial structure.

One aspect of the present invention is a crystal structure searching apparatus characterized by searching for a crystal structure in a search space composed of crystal structures obtained by interpolating between a plurality of crystal structures using a distance index of SOAP theory.

Here, the distance index is preferably a distance index that reflects the translational invariance, unit cell selection invariance, and rotational invariance of the crystal.

Also, using a point set χ ₁ and a point set χ ₂ of the intensity of reciprocal lattice points obtained by transforming two different crystal structures into a reciprocal space,
Using the overlap integral (hatted R is a rotation operator) of formula (1),
Preferably, the distance index is the power spectral distance d _ps represented by Equation (2).

Also, using a point set χ ₁ and a point set χ ₂ of the intensity of reciprocal lattice points obtained by transforming two different crystal structures into a reciprocal space,
Using the overlap integral (hatted R is a rotation operator) of formula (3),
Preferably, the distance index is the SOAP distance d _SOAP represented by Equation (4).

Further, it is preferable to obtain a structure interpolated between the plurality of crystal structures by updating reciprocal lattice vectors and atomic positions indicating the crystal structure using gradient information obtained by differentiating the distance index.

Further, it is preferable to search for the crystal structure so that the feature amount indicating the crystal structure obtained by interpolating between the plurality of crystal structures approaches the target feature amount.

Further, it is preferable that the feature amount is an X-ray diffraction spectrum.

According to another aspect of the present invention, it is preferable to search for crystal structures in a search space composed of crystal structures obtained by interpolating between a plurality of crystal structures using the distance index of SOAP theory.

According to the present invention, crystal structures can be efficiently searched in a search space that mathematically satisfies crystal invariance.

1 is a diagram showing the configuration of a crystal structure searching device according to an embodiment of the present invention; FIG. 4 is a flow chart showing a crystal structure searching method according to an embodiment of the present invention; FIG. 4 is a diagram showing an example of a list of crystal structures used in the examples of the present invention; FIG. 3 shows the XRD spectrum and corresponding crystal structure targeted for the search used in the examples of the present invention; FIG. 2 shows an optimized crystal structure and its XRD spectrum obtained by searching in an example of the present invention;

A crystal structure searching apparatus 100 according to the embodiment of the present invention includes a processing unit 10, a storage unit 12, an input unit 14, an output unit 16 and a communication unit 18, as shown in FIG. The processing unit 10 includes means for performing arithmetic processing such as a CPU. By executing the crystal structure search program stored in the storage unit 12, the processing unit 10 implements the functions of the crystal structure search method according to the present embodiment. The storage unit 12 includes storage means such as a semiconductor memory and a memory card. The storage unit 12 is connected to the processing unit 10 so as to be accessible, and stores a crystal structure search program and information necessary for the processing. The input unit 14 includes means for inputting information. The input unit 14 includes, for example, a keyboard, a touch panel, buttons, and the like for receiving input from the user. The output unit 16 includes means for outputting the processing result of the crystal structure search apparatus 100, such as a user interface screen (UI) for receiving input information from the user. The output unit 16 includes, for example, a display that presents images to the user. The communication unit 18 includes an interface for communicating information with an external information processing device via the information communication network 102 . Communication by the communication unit 18 may be wired or wireless.

Various devices can be applied to the crystal structure searching device 100 as long as they are information processing devices capable of executing a crystal structure searching program. For example, a stationary or portable personal computer (PC), a tablet computer, or the like can be used as the crystal structure searching apparatus 100 .

The crystal structure searching method according to the present embodiment will be described below. In the crystal structure search method, a crystal structure search program is executed in the crystal structure search device 100 to search for a crystal structure interpolated between known crystal structures based on the distance index of SOAP theory.

When a crystal structure in which n atoms exist in a unit cell expressed by Gaussian (standard deviation σ) is converted into a reciprocal lattice space, it can be expressed as a point set χ having an intensity expressed by Equation (5) at a reciprocal lattice point Gi. Here, v _uc is the unit cell volume, r is the atomic coordinate, b is the reciprocal lattice defining vector, and M(M ₁ , M ₂ , M ₃ ) is an arbitrary integer.

Since the reciprocal lattice space corresponds to the discrete Fourier transform of the real lattice, it satisfies the translational invariance and unit cell selection invariance of the crystal structure. Therefore, the overlap integral of Equation (6) is calculated to mathematically satisfy the remaining rotational invariance among the invariants of the crystal structure. where the hated R is the rotation operator.

Define the power spectrum distance d _ps or the SOAP distance d _SOAP in equation (7) using the overlap integral.

This power spectrum distance d _ps or SOAP distance d _SOAP has a smaller value when the two crystal structures are similar, and a larger value when they are different. Therefore, a crystal structure interpolated between different crystal structures can be searched by updating reciprocal lattice vectors and atomic positions using the gradient descent method or the like based on the gradient information calculated from the differential of the power spectrum distance d _ps or the SOAP distance d _SOAP .

Here, let us consider the defining vector of the point set χ on the reciprocal lattice space and minute changes in the intensity by means of Equation (8).

The derivative of the power spectrum distance d _ps or the SOAP distance d _SOAP when the point set χ1 representing one crystal structure is fixed and the point set χ2 representing the other crystal structure is slightly changed is represented by Equation (9).

Therefore, in order to obtain the differential of the power spectrum distance d _ps or the SOAP distance d _SOAP , it is sufficient to know the differential of the overlap integral L expressed by Equation (6). The differentiation of the overlap integral L with respect to the basis vectors is given by Equation (10).

Expression (11) is obtained by explicitly expressing the components of the minute transformation matrix t (hat).

Also, the differentiation of the overlap integral L with respect to the point intensity is represented by Equation (12). However, g _n is a direct radial basis, Y _i ^m is a spherical harmonic function, and l is a modified spherical Bessel function.

The derivative of the power spectrum distance d _ps or the SOAP distance d _SOAP used for the steepest descent method is defined as in Equation (13).

The basis vectors of the reciprocal lattice can be updated by Equation (14) using an arbitrary parameter δt related to convergence. Since the basis vectors bη in the reciprocal lattice space can be converted one-to-one with the basis vectors ai in the real space, the crystal structure in the real space of the unit cell can be restored.

The intensity at the reciprocal lattice point Gi shown in Equation (5) can be similarly updated. However, the atomic positions in the real space cannot be restored due to lack of phase information. Therefore, the power spectrum distance d _ps or the SOAP distance d _SOAP may be differentiated with respect to the atomic position r, and the atomic position r may be directly updated by Equation (15) so as to reduce the distance between the crystal structures.

The required differentiation of the overlap integral L with respect to the atomic position r is given by Equation (16).

In addition, in the case of a multi-element system, the calculation may be performed by dividing it into a two-element system. For example, a five-element system can be divided into ₅ C ₂ =10 combinations as a two-element system. The point intensity and point set in the reciprocal lattice space can be expressed by Equation (17), where (α, β) is the pair of elements that make up the system. However, _Aj is a positive/negative sign for discriminating the types of the two elements.

The power spectrum distance d _ps or the SOAP distance d _SOAP and its derivative in the case of a multicomponent system are defined as in Equation (18). Differentiation of the overlap integral L may be performed using the above equation.

[Example]
An example of processing for searching for a crystal structure interpolated between known crystal structures based on the distance index of SOAP theory will be described below.

FIG. 2 is a flow chart showing a process of searching for a crystal structure interpolated between crystal structures in the embodiment. In this embodiment, a process of searching for a crystal structure is performed based on a spectrum indicating the crystal structure obtained by X-ray diffraction (XRD) analysis.

In step S10, a process of obtaining a list of crystal structures forming a crystal structure search space is performed. Through the processing in this step, the crystal structure search device 100 functions as a crystal structure list obtaining means. Here, the crystal structure constituting the crystal structure search space is a crystal structure that serves as a basis for interpolation when searching for a crystal structure. A list of crystal structures may be created by the user using the input unit 14, or a list of crystal structures pre-stored in an external device may be acquired via the communication unit 18. FIG.

In this example, as shown in FIG. 3, a list of five crystal structures other than Triangular from the tetraatomic Archimedean lattice of Trellis, Ladybug, Honeycomb, Square and CaVO was used.

In step S12, a process of acquiring a physical property value that is a search target is performed. Through the processing in this step, the crystal structure searching apparatus 100 functions as physical property value acquiring means. Here, the physical property value to be searched for is the physical property value exhibited by the crystal structure to be searched for. The physical property value to be the search target may be obtained by the user using the input unit 14, or the physical property value to be the search target stored in advance in an external device via the communication unit 18. It may be acquired.

In this example, as shown in FIG. 4, the XRD spectrum obtained when the target crystal structure was subjected to X-ray diffraction (XRD) analysis was used as the target physical property value for the search. In this embodiment, an XRD spectrum of a known crystal structure was used to confirm the effectiveness of the crystal structure searching apparatus 100. FIG. FIG. 4 shows the XRD spectrum of the target crystal structure along with the known crystal structure corresponding to the XRD spectrum.

In step S14, a process of setting the order of the crystal structures forming the crystal structure search space is performed. Through the processing in this step, the crystal structure searching apparatus 100 functions as crystal structure ranking means. For each crystal structure included in the list of crystal structures acquired in step S10, the physical property value corresponding to the physical property value acquired in step S12 is obtained, and the similarity to the physical property value to be searched acquired in step S12 is calculated. Then, the crystal structures included in the crystal structure list are ranked in descending order of similarity.

In this example, Trellis, Ladybug, Honeycomb, Square, and CaVO are ranked in descending order of similarity.

In step S16, a process of optimizing the crystal structure interpolated between the two crystal structures is performed. Through the processing in this step, the crystal structure searching apparatus 100 functions as crystal structure searching means. That is, in a search space consisting of a crystal structure serving as a starting point and a crystal structure serving as an end point, a crystal structure is obtained by interpolating between a crystal structure serving as a starting point and a crystal structure serving as an end point, and among the crystal structures obtained by the interpolation, a crystal structure exhibiting physical property values closest to the physical property values to be searched is obtained. In the process of interpolating the crystal structure, a crystal structure interpolated between different crystal structures is searched for by updating reciprocal lattice vectors and atomic positions using the steepest descent method or the like based on the gradient information calculated from the differentiation of the power spectrum distance d _ps or the SOAP distance d _SOAP based on the above SOAP theory.

When the search process in this step is performed first, the crystal structure with the highest degree of similarity to the target physical property value of the search in the list of crystal structures whose order is set in step S14 is set as the starting point, and the crystal structure with the second highest degree of similarity is set as the end point. Then, an optimization process is performed to obtain a crystal structure exhibiting a physical property value closest to the target physical property value of the search from the crystal structure interpolated between the crystal structure serving as the starting point and the crystal structure serving as the end point.

In step S18, a process of updating the list of crystal structures is performed. Through the processing in this step, the crystal structure searching apparatus 100 functions as crystal structure list updating means. The crystal structures used as the start and end points in the search in step S16 are deleted from the list. Furthermore, among the crystal structures optimized by the search in step S16, that is, the crystal structures interpolated between the crystal structure serving as the starting point and the crystal structure serving as the end point, the crystal structure showing the physical property values closest to the physical property values targeted for the search is added to the list.

In step S20, it is determined whether or not to continue the search process. Through the processing in this step, the crystal structure searching apparatus 100 functions as end determination means. If only one crystal structure remains in the crystal structure list, the process proceeds to step S22, and if two or more crystal structures remain, the process returns to step S16 to continue the search process.

Here, when the process is returned to step S16 to continue the search process, the crystal structure optimized in the previous search process (the crystal structure added to the list of crystal structures in step 18) is set as the starting point, and the crystal structure with the next highest degree of similarity is set as the ending point. Then, an optimization process is performed to obtain a crystal structure exhibiting a physical property value closest to the target physical property value of the search from the crystal structure interpolated between the crystal structure serving as the starting point and the crystal structure serving as the end point.

In this embodiment, by repeating the crystal structure search process in step S16, as indicated by the circles and arrows in FIG. 3, a crystal structure exhibiting an XRD spectrum similar to the target XRD spectrum to be searched can be obtained based on the crystal structures of Trellis, Ladybug, Honeycomb, Square, and CaVO.

FIG. 5 shows the crystal structure and its XRD spectrum obtained as a result of the search in this example. The crystal structure obtained as a result of the search was very close to the crystal structure corresponding to the targeted XRD spectrum. Moreover, the XRD spectrum of the crystal structure obtained as a result of the search showed a similarity of 99.76% to the target XRD spectrum of the search.

As described above, according to the crystal structure searching apparatus 100 and the crystal structure searching method using the same in the present embodiment, it is possible to efficiently search for a crystal structure in a search space that mathematically satisfies crystal invariance. In addition, unlike supervised learning, it does not require a large amount of teacher data, and the cost of calculation can be suppressed.

10 processing unit, 12 storage unit, 14 input unit, 16 output unit, 18 communication unit, 100 crystal structure search device, 102 information communication network.

Claims (8)

the computer,
Using the point set χ ₁ and the point set χ ₂ of the intensity of the reciprocal lattice points obtained by converting the two different crystal structures into the reciprocal space ,
Using the overlap integral (hatted R is a rotation operator) of formula (1),
In a search space composed of crystal structures obtained by interpolating between a plurality of crystal structures using the power spectrum distance dps represented by Equation (2) _as a distance index ,
A crystal structure searching apparatus characterized by searching for a crystal structure so that a feature quantity indicating a crystal structure obtained by interpolating between the plurality of crystal structures approaches a target feature quantity by updating reciprocal lattice vectors and atomic positions indicating the crystal structure using gradient information obtained by differentiating the distance index, and functioning as means for obtaining a structure obtained by interpolating between the plurality of crystal structures. the computer,
Using the point set χ ₁ and the point set χ ₂ of the intensity of the reciprocal lattice points obtained by converting the two different crystal structures into the reciprocal space ,
Using the overlap integral (hatted R is a rotation operator) of formula (3),
In a search space composed of crystal structures obtained by interpolating between a plurality of crystal structures using the SOAP distance d _SOAP represented by Equation (4) as a distance index ,
A crystal structure searching apparatus characterized by searching for a crystal structure so that a feature quantity indicating a crystal structure obtained by interpolating between the plurality of crystal structures approaches a target feature quantity by updating reciprocal lattice vectors and atomic positions indicating the crystal structure using gradient information obtained by differentiating the distance index, and functioning as means for obtaining a structure obtained by interpolating between the plurality of crystal structures. The crystal structure searching device according to claim 1 or 2 ,
A crystal structure search apparatus, wherein the distance index is a distance index reflecting translational invariance, unit cell selection invariance, and rotational invariance of a crystal. The crystal structure search device according to any one of claims 1 to 3 ,
The crystal structure search apparatus, wherein the feature amount is an X-ray diffraction spectrum. to the computer,
Using the point set χ ₁ and the point set χ ₂ of the intensity of the reciprocal lattice points obtained by converting the two different crystal structures into the reciprocal space ,
Using the overlap integral (hatted R is a rotation operator) of formula (1),
In a search space composed of crystal structures obtained by interpolating between a plurality of crystal structures using the power spectrum distance dps represented by Equation (2) _as a distance index ,
A crystal structure searching method, wherein the crystal structure is searched so that the feature amount indicating the crystal structure obtained by interpolating between the plurality of crystal structures approaches a target feature amount by updating the reciprocal lattice vector indicating the crystal structure and the atomic positions using the gradient information obtained by the differentiation of the distance index, and performing a process of obtaining the structure interpolated between the plurality of crystal structures. to the computer,
Using the point set χ ₁ and the point set χ ₂ of the intensity of the reciprocal lattice points obtained by converting the two different crystal structures into the reciprocal space ,
Using the overlap integral (hatted R is a rotation operator) of formula (3),
In a search space composed of crystal structures obtained by interpolating between a plurality of crystal structures using the SOAP distance d _SOAP represented by Equation (4) as a distance index ,
A crystal structure searching method, wherein the crystal structure is searched so that the feature amount indicating the crystal structure obtained by interpolating between the plurality of crystal structures approaches a target feature amount by updating the reciprocal lattice vector indicating the crystal structure and the atomic positions using the gradient information obtained by the differentiation of the distance index, and performing a process of obtaining the structure interpolated between the plurality of crystal structures. The crystal structure search method according to claim 5 or 6,
A crystal structure searching method, wherein the distance index is a distance index reflecting translational invariance, unit cell selection invariance, and rotational invariance of a crystal. The crystal structure search method according to any one of claims 5 to 7,
The crystal structure search method, wherein the feature amount is an X-ray diffraction spectrum.