Surface phase diagram creation method, surface phase diagram creation program, and surface phase diagram creation system

Abstract

To provide a surface phase diagram creation method that can efficiently and accurately create a surface phase diagram of a state in which gas or liquid is in contact with a solid surface.SOLUTION: A surface phase diagram creation method repeatedly executes: a surface structure condition proposing step S01 of proposing optimal surface structure conditions using machine learning on the basis of thermodynamic data; a free energy calculation step S02 of searching for the most stable structure under the proposed surface structure conditions and calculating the free energy of the most stable structure searched for; and a surface phase diagram creating step S03 of accumulating combinations of the most stable structure and free energy under the surface structure conditions as thermodynamic data to create a surface phase diagram. In the surface structure condition proposing step S01 from the second time onwards, optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creating step S03 as learning data, and in the surface phase diagram creating step S03, a phase diagram is created from the combination that minimizes the sum of all free energies.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for creating a surface phase diagram, a program for creating a surface phase diagram, and a system for creating a surface phase diagram for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface. [Background technology]

[0002] Phase diagrams show the relationship between the phases of a substance and thermodynamic state quantities, and are important in materials development. In the surface phase diagram in the state where a gas or liquid is in contact with a solid surface, the surface structure, such as the arrangement of the gas or liquid on the solid surface and the number of adsorbed molecules, is very complicated, and it has been difficult to actually conduct experiments, collect data, and create a phase diagram. For this reason, the above-mentioned surface phase diagrams are created by computational science, as described in, for example, Non-Patent Documents 1 and 2.

[0003] For example, Non-Patent Document 1 describes a case in which a phase diagram was created by first-principles calculations for all possible surface structures. Non-Patent Document 2 also describes an example in which a phase diagram was created by calculating a large number of surface structures using first-principles calculations. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] J.Rogal, et al., PHYSICAL REVIEW B 75, 205433 (2007) [Non-patent document 2] J.-H. Lee, et al., PHYSICAL REVIEW Appl. 8, 034010 (2017) Summary of the Invention [Problem to be solved by the invention]

[0005] However, in the cases disclosed in Non-Patent Documents 1 and 2, calculations had to be performed for a large number of surface structures, making it difficult to efficiently create a phase diagram. Furthermore, if it is considered that a solid surface may react with a liquid or gas to form a compound, it is necessary to consider many more surface structures, and it has been difficult to create a surface phase diagram that takes these conditions into account.

[0006] The present invention has been made in consideration of the above-mentioned circumstances, and an object of the present invention is to provide a method for creating a surface phase diagram, a program for creating a surface phase diagram, and a system for creating a surface phase diagram, which are capable of efficiently and accurately creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface. [Means for solving the problem]

[0007] In order to solve the above-mentioned problems, a first aspect of the method for creating a surface phase diagram of the present invention is a method for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface, the method comprising: repeatedly performing a surface structure condition proposing step of proposing optimal surface structure conditions by machine learning based on thermodynamic data; a free energy calculation step of searching for a most stable structure under the surface structure conditions proposed in the surface structure condition proposing step and calculating the free energy of the most stable structure found; and a surface phase diagram creating step of accumulating combinations of the most stable structure under the surface structure conditions and the free energy as thermodynamic data to create a surface phase diagram; and in the surface structure condition proposing step from the second time onwards, optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creating step as learning data, and the surface phase diagram creating step creates a phase diagram from a combination that minimizes the sum of all free energies calculated in the free energy calculation step.

[0008] The surface phase diagram creation method of the first aspect of the present invention is configured to repeatedly perform the following steps: a surface structure condition proposing step of proposing optimal surface structure conditions by machine learning based on thermodynamic data; a free energy calculation step of searching for a most stable structure under the surface structure conditions proposed in the surface structure condition proposing step and calculating the free energy of the most stable structure found; and a surface phase diagram creation step of accumulating a combination of the most stable structure under the surface structure conditions and the free energy as thermodynamic data to create a surface phase diagram.In the surface structure condition proposing step from the second time onwards, the optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creation step as learning data.Therefore, the number of times free energy is calculated in the free energy calculation step can be reduced, and calculations can be performed while fully taking into consideration conditions that need to be considered, making it possible to create a surface phase diagram efficiently and accurately.

[0009] A second aspect of the present invention is a method for creating a surface phase diagram, wherein in the first aspect of the present invention, the surface structure condition proposing step applies Bayesian optimization to propose the surface structure conditions based on conditions that minimize the sum of all free energies in the phase diagram, based on adsorption energies using a lower confidence limit of Gaussian process regression. According to the method for creating a surface phase diagram of the second aspect of the present invention, it is possible to efficiently propose optimal surface structure conditions that minimize the sum of all free energies in the phase diagram based on the obtained thermodynamic data, thereby making it possible to create a surface phase diagram even more efficiently.

[0010] A third aspect of the method for creating a surface phase diagram of the present invention is characterized in that, in the method for creating a surface phase diagram of the first or second aspect of the present invention, the free energy calculation step uses a global optimization method to search for the most stable structure of the solid surface and the adsorbate. According to the method for creating a surface phase diagram of the third aspect of the present invention, in the free energy calculation step, a global optimization method can be used to efficiently search for the most stable structure between the solid surface and the adsorbate, making it possible to create a surface phase diagram more efficiently.

[0011] A fourth aspect of the surface phase diagram creation program of the present invention is a surface phase diagram creation program for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface using a computer, and causes the computer to repeatedly execute the following steps: a surface structure condition proposing step of proposing optimal surface structure conditions by machine learning based on thermodynamic data; a free energy calculation step of searching for a most stable structure under the surface structure conditions proposed in the surface structure condition proposing step and calculating the free energy of the most stable structure found; and a surface phase diagram creation step of accumulating combinations of the most stable structure under the surface structure conditions and the free energy as thermodynamic data to create a surface phase diagram; and in the surface structure condition proposing step from the second time onwards, optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creation step as learning data, and in the surface phase diagram creation step, a phase diagram is created from a combination that minimizes the sum of all free energies calculated in the free energy calculation step. According to the program for creating a surface phase diagram of the fourth aspect of the present invention, it becomes possible to create a surface phase diagram efficiently and accurately using a computer.

[0012] A fifth aspect of the present invention provides a surface phase diagram creation program according to the fourth aspect of the present invention, characterized in that in the surface phase diagram creation program, the surface structure condition proposing step applies Bayesian optimization to propose the surface structure conditions based on conditions that minimize the sum of all free energies in the phase diagram, based on adsorption energy using a lower confidence limit of Gaussian process regression. According to the program for creating a surface phase diagram of the fifth aspect of the present invention, it is possible to efficiently propose optimal surface structure conditions that minimize the sum of all free energies in a phase diagram based on the obtained thermodynamic data, and it becomes possible to create a surface phase diagram more efficiently using a computer.

[0013] A surface phase diagram creation program of a sixth aspect of the present invention is the surface phase diagram creation program of the fourth or fifth aspect of the present invention, characterized in that in the free energy calculation step, a global optimization method is used to search for the most stable structure of the solid surface and the adsorbate. According to the sixth aspect of the program for creating a surface phase diagram of the present invention, in the free energy calculation step, a global optimization method can be used to efficiently search for the most stable structure between the solid surface and the adsorbate, and it becomes possible to create a surface phase diagram more efficiently using a computer.

[0014] A seventh aspect of the present invention provides a surface phase diagram creation system for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface, the system comprising: a surface structure condition proposal unit that proposes optimal surface structure conditions by machine learning based on thermodynamic data; a free energy calculation unit that searches for a most stable structure under the surface structure conditions proposed by the surface structure condition proposal unit and calculates the free energy of the most stable structure found; and a surface phase diagram creation unit that accumulates combinations of the most stable structure under the surface structure conditions and the free energy as thermodynamic data to create a surface phase diagram, wherein the proposal of optimal surface structure conditions by the surface structure condition proposal unit, the search for the most stable structure and calculation of the free energy by the free energy calculation unit, and the creation of a phase diagram by the surface phase diagram creation unit are repeated, and from the second time onwards, the surface structure condition proposal unit proposes optimal surface structure conditions using the free energy of the specific surface structure obtained by the free energy calculation unit as learning data, and the surface phase diagram creation unit creates a phase diagram from the combination that minimizes the sum of all free energies calculated in the free energy calculation step. According to the system for creating a surface phase diagram of the seventh aspect of the present invention, it is possible to create a surface phase diagram efficiently and accurately.

[0015] The surface phase diagram creation system of an eighth aspect of the present invention is characterized in that, in the surface phase diagram creation system of the seventh aspect of the present invention, the surface structure condition proposing unit applies Bayesian optimization and proposes the surface structure conditions based on the condition that minimizes the sum of all free energies in the phase diagram, based on the adsorption energy using a lower reliability limit of Gaussian process regression. According to the eighth aspect of the surface phase diagram creation system of the present invention, it is possible to efficiently propose optimal surface structure conditions that minimize the sum of all free energies in the phase diagram based on the obtained thermodynamic data, thereby making it possible to create a surface phase diagram even more efficiently.

[0016] A ninth aspect of the surface phase diagram creation system of the present invention is the surface phase diagram creation system of the seventh or eighth aspect of the present invention, characterized in that the free energy calculation unit uses a global optimization method to search for the most stable structure of the solid surface and the adsorbate. According to the system for creating a surface phase diagram of the ninth aspect of the present invention, the free energy calculation unit can efficiently search for the most stable structure between the solid surface and the adsorbate by using a global optimization method, making it possible to create a surface phase diagram more efficiently. [Effects of the Invention]

[0017] According to the present invention, it is possible to provide a method for creating a surface phase diagram, a program for creating a surface phase diagram, and a system for creating a surface phase diagram, which are capable of efficiently and accurately creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface. [Brief explanation of the drawings]

[0018] [Figure 1] FIG. 1 is a flowchart showing an example of a method for creating a surface phase diagram according to an embodiment of the present invention. [Figure 2]FIG. 1 is an explanatory diagram illustrating an example of a surface phase diagram creation system according to an embodiment of the present invention. [Figure 3] FIG. 1 is a model diagram of a solid (Pd) and gas (CO, O) that are the subject of a surface phase diagram in an example. [Figure 4] In the examples, a surface phase diagram is created by calculation for all possible surface structures. [Figure 5] 5 is a graph showing the number of calculations (number of cycles) required to obtain the surface phase diagram shown in FIG. 4 in the examples. DETAILED DESCRIPTION OF THE INVENTION

[0019] Hereinafter, a method for creating a surface phase diagram, a program for creating a surface phase diagram, and a system for creating a surface phase diagram according to embodiments of the present invention will be described with reference to the accompanying drawings. The surface phase diagram creation method, the surface phase diagram creation program, and the surface phase diagram creation system according to the embodiments of the present invention create a surface phase diagram in a state where a gas or a liquid is in contact with a solid surface.

[0020] FIG. 1 is a flowchart showing an example of a method for creating a surface phase diagram according to an embodiment of the present invention. As shown in FIG. 1, the method for creating a surface phase diagram of this embodiment includes a surface structure condition proposing step S01, a free energy calculation step S02, and a surface phase diagram creating step S03.

[0021] In the surface structure condition proposing step S01, optimal surface structure conditions are proposed by machine learning based on thermodynamic data. That is, surface structure conditions (e.g., the state of the solid surface, the type and number of gases or liquids adsorbed on the solid surface, etc.) that are predicted to most change the surface phase diagram from the thermodynamic data are proposed. Here, in this embodiment, it is preferable to use Bayesian optimization to propose surface structure conditions based on the conditions that minimize the sum of all free energies in the phase diagram, based on the adsorption energy using the lower confidence bound (LCB) of Gaussian process regression (GPR).

[0022] As the Bayesian optimization program, for example, PHYSBO, a program described in the following document A and available on the website indicated by the following URL, is used. Literature A: Y.Motoyama et al Bayesian optimization package: PHYSBO Computer PhysicsCommunications 278, 108405 (2022) https: / / issp-center-dev.github.io / PHYSBO / manual / master / ja / index.html

[0023] In the free energy calculation step S02, the most stable structure is searched for under the surface structure conditions proposed in the surface structure condition proposal step S01, and the free energy of the most stable structure found is calculated. In this embodiment, a global optimization method is used to search for stable structures of the solid surface and adsorbates according to the surface structure conditions proposed by the surface structure condition proposal unit (state of the solid surface, type and number of gases or liquids adsorbed on the solid surface), and the free energy of the most stable structure found is calculated.

[0024] In the free energy calculation step S02, the most stable structure of the solid surface and the adsorbate is searched for using a factorization machine (FMQA), for example, a program available at the website indicated by the following URL: https: / / github.com / tsudalab / fmqa In addition, the constraint minima hopping method can be used to search for the most stable structure of the solid surface and the adsorbate.

[0025] In the surface phase diagram creation step S03, the combination of the most stable structure and free energy of the surface structure conditions is stored as thermodynamic data, and a phase diagram is created from the combination that minimizes the sum of all free energies calculated in the free energy calculation step S02.

[0026] In this embodiment, the steps of proposing optimal surface structure conditions in the surface structure condition proposing step S01, searching for the most stable structure and calculating the free energy in the free energy calculation step S02, and creating a phase diagram in the surface phase diagram creating step S03 are repeated, and in the surface structure condition proposing step S01 from the second time onwards, the free energy in the specific surface structure obtained in the free energy calculation step S02 is used as learning data to propose optimal surface structure conditions through machine learning. Then, by repeatedly performing the surface structure condition proposing step S01, the free energy calculating step S02, and the surface phase diagram creating step S03, a surface phase diagram in which the total free energy of the phase diagram is minimized is created.

[0027] The program for creating a surface phase diagram according to this embodiment creates a surface phase diagram by repeatedly executing the above-described surface structure condition proposing step S01, free energy calculating step S02, and surface phase diagram creating step S03 using a computer.

[0028] The surface phase diagram creation system of this embodiment implements the surface phase diagram creation method of this embodiment described above. The surface phase diagram creation system of this embodiment is shown in FIG. As shown in FIG. 2, the surface phase diagram creation system 1 of this embodiment includes a surface structure condition proposing unit 11 that performs a surface structure condition proposing step S01, a free energy calculating unit 12 that performs a free energy calculating step S02, and a surface phase diagram creating unit 13 that performs a surface phase diagram creating step S03. By repeatedly performing these steps, a surface phase diagram in which the total free energy of the phase diagram is minimized is created.

[0029] The method for creating a surface phase diagram of this embodiment, configured as described above, is configured to repeatedly perform the following steps: a surface structure condition proposing step S01, in which optimal surface structure conditions are proposed by machine learning based on thermodynamic data; a free energy calculation step S02, in which the most stable structure under the surface structure conditions proposed in the surface structure condition proposing step S01 is searched for and the free energy of the most stable structure found; and a surface phase diagram creating step S03, in which a combination of the most stable structure and the free energy under the surface structure conditions is accumulated as thermodynamic data to create a surface phase diagram. In the surface structure condition proposing step S01 from the second time onwards, optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creating step S03 as learning data. Therefore, the number of times free energy is calculated in the free energy calculation step can be reduced, and calculations can be performed while fully taking into account conditions that need to be considered, making it possible to create a surface phase diagram efficiently and accurately.

[0030] In the method for creating a surface phase diagram according to the present embodiment, when Bayesian optimization is applied in the surface structure condition proposing step S01, and surface structure conditions are proposed based on the conditions that minimize the sum of the total free energy of the phase diagram, based on the adsorption energy using the lower confidence bound (LCB) of Gaussian process regression (GPR), optimal surface structure conditions that minimize the sum of the total free energy of the phase diagram can be efficiently proposed based on the obtained thermodynamic data, and the surface phase diagram can be created even more efficiently.

[0031] In the method for creating a surface phase diagram according to the present embodiment, when the free energy calculation step S02 is configured to use a global optimization method to search for the most stable structure between the solid surface and the adsorbate, the most stable structure between the solid surface and the adsorbate can be efficiently searched for, and the surface phase diagram can be created more efficiently. In particular, when FMQA and constraint minima hopping are applied as global optimization methods, it becomes possible to search for the most stable structure between the solid surface and the adsorbate more efficiently.

[0032] According to the program for creating a surface phase diagram of this embodiment, a surface phase diagram can be created by repeatedly executing a surface structure condition proposing step S01, a free energy calculating step S02, and a surface phase diagram creating step S03 on a computer, and it becomes possible to create a surface phase diagram efficiently and accurately using a computer.

[0033] The surface phase diagram creation system 1 of this embodiment includes a surface structure condition proposing unit 11 that performs a surface structure condition proposing step S01, a free energy calculating unit 12 that performs a free energy calculating step S02, and a surface phase diagram creating unit 13 that performs a surface phase diagram creating step S03. By repeatedly performing these steps, it becomes possible to efficiently and accurately create a surface phase diagram in which the total free energy of the phase diagram is minimized.

[0034] Although the embodiment of the present invention has been described above, the present invention is not limited to this and can be modified as appropriate within the scope of the technical idea of the invention. [Example]

[0035] The results of confirmation experiments conducted to confirm the effects of the present invention will be described below.

[0036] As an example of a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface, we adopted a model in which (gas) and O (gas) are adsorbed on the surface of Pd (solid), as shown in Figure 3. Here, as shown in Figure 3, we assume a structure in which CO and O are adsorbed on the Pd surface as adsorbates, and the number of O atoms is four or more (N O For the condition ≧4), PdO with an oxidized solid surface was selected.

[0037] In the model shown in Figure 3, (N CO ,N O), there are 29 possible patterns. Calculations were performed for all of these patterns in advance, and a surface phase diagram was created in which the sum of all free energies (FOM) in the phase diagram reached its minimum value (-158.72), as shown in Figure 4.

[0038] As an example of the present invention, the method for creating a surface phase diagram described in this embodiment was carried out, and the number of repetitions until the surface phase diagram (FOM=-158.72) shown in FIG. 4 was obtained was confirmed. In Comparative Examples 1 and 2, calculations were performed randomly to repeatedly create a phase diagram, and the number of repetitions until the surface phase diagram (FOM=-158.72) shown in FIG. 4 was obtained was confirmed. The evaluation results are shown in Figure 5.

[0039] In the example of the present invention in which the method for creating a surface phase diagram described in this embodiment was implemented, the number of repetitions required to obtain the surface phase diagram shown in FIG. 4 (FOM=−158.72) was fewer than in Comparative Examples 1 and 2 in which calculations were repeated randomly, confirming that the surface phase diagram could be created efficiently. [Explanation of symbols]

[0040] S01 Surface structure condition proposal step S02 Free energy calculation step S03 Surface phase diagram creation step 1. Surface phase diagram creation system 11 Surface structure condition proposal department 12 Free energy calculation section 13 Surface Phase Diagram Creation Department

Claims

1. A method for creating a surface phase diagram for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface, comprising the steps of: a surface structure condition proposing step that proposes optimal surface structure conditions using machine learning based on thermodynamic data; a free energy calculation step of searching for a most stable structure under the surface structure conditions proposed in the surface structure condition proposal step and calculating the free energy of the most stable structure found; a surface phase diagram creation step of accumulating combinations of the most stable structures and the free energies under the surface structure conditions as thermodynamic data to create a surface phase diagram; Repeatedly carry out In the second or subsequent surface structure condition proposing step, optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creating step as learning data; The method for creating a surface phase diagram, wherein the surface phase diagram creation step creates a phase diagram from combinations that minimize the sum of all free energies calculated in the free energy calculation step.

2. 2. The method for creating a surface phase diagram according to claim 1, wherein in the surface structure condition proposing step, Bayesian optimization is applied to propose the surface structure conditions based on the condition that minimizes the sum of all free energies in the phase diagram, based on the adsorption energy using a lower reliability limit of Gaussian process regression.

3. 3. The method for creating a surface phase diagram according to claim 1, wherein in the free energy calculation step, a global optimization method is used to search for the most stable structure between the solid surface and the adsorbate.

4. A surface phase diagram creation program for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface using a computer, comprising: the computer is caused to repeatedly execute a surface structure condition proposing step of proposing optimal surface structure conditions by machine learning based on thermodynamic data, a free energy calculation step of searching for a most stable structure under the surface structure conditions proposed in the surface structure condition proposing step and calculating the free energy of the most stable structure found, and a surface phase diagram creation step of accumulating combinations of the most stable structure under the surface structure conditions and the free energy as thermodynamic data to create a surface phase diagram, In the second or subsequent surface structure condition proposing step, optimal surface structure conditions are proposed using the thermodynamic data obtained in the surface phase diagram creating step as learning data; A program for creating a surface phase diagram, wherein in the surface phase diagram creation step, a phase diagram is created from a combination in which the sum of all free energies calculated in the free energy calculation step is the smallest value.

5. 5. The program for creating a surface phase diagram according to claim 4, wherein in the surface structure condition proposing step, Bayesian optimization is applied to propose the surface structure conditions based on conditions that minimize the sum of all free energies in the phase diagram, based on the adsorption energy using a lower reliability limit of Gaussian process regression.

6. 6. The program for creating a surface phase diagram according to claim 4, wherein in the free energy calculation step, a global optimization method is used to search for the most stable structure between the solid surface and the adsorbate.

7. A surface phase diagram creation system for creating a surface phase diagram of a state in which a gas or liquid is in contact with a solid surface, comprising: a surface structure condition proposal unit that proposes optimal surface structure conditions using machine learning based on thermodynamic data; a free energy calculation unit that searches for a most stable structure under the surface structure conditions proposed by the surface structure condition proposal unit and calculates the free energy of the most stable structure found; a surface phase diagram creation unit that creates a surface phase diagram by accumulating combinations of the most stable structures and the free energies of the surface structure conditions as thermodynamic data; and the proposal of optimal surface structure conditions by the surface structure condition proposal unit, the search for the most stable structure and calculation of free energy by the free energy calculation unit, and the creation of a phase diagram by the surface phase diagram creation unit are repeatedly performed; In the second and subsequent times, the surface structure condition proposing unit proposes optimal surface structure conditions using the free energy in the specific surface structure obtained by the free energy calculation unit as learning data; The surface phase diagram creation system is characterized in that the surface phase diagram creation unit creates a phase diagram from combinations that minimize the sum of all free energies calculated by the free energy calculation unit.

8. The system for creating a surface phase diagram according to claim 7, characterized in that the surface structure condition proposing unit applies Bayesian optimization to propose the surface structure conditions based on the condition that minimizes the sum of all free energies in the phase diagram, based on the adsorption energy using a lower reliability limit of Gaussian process regression.

9. 9. The system for creating a surface phase diagram according to claim 7, wherein the free energy calculation unit searches for the most stable structure of the solid surface and the adsorbate using a global optimization method.

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