Physical quantity calculation method, physical quantity calculation program, and physical quantity calculation device

Abstract

This physical quantity calculation method comprises: a step (S12) for acquiring data indicating an electronic state of a material calculated on the basis of an arrangement of atoms constituting the material; a step (S14) for adjusting a parameter indicating a Fermi level in the acquired data; and a step (S18) for calculating a physical quantity indicating a physical property of the material on the basis of the acquired data and the adjusted parameter indicating the Fermi level.

Description

Physical quantity calculation method, physical quantity calculation program, and physical quantity calculation device

[0001] The present disclosure relates to a physical quantity calculation method, a physical quantity calculation program, and a physical quantity calculation device.

[0002] Lithium transition metal oxides are used as electrode materials for batteries. To improve energy efficiency, electrode materials with excellent properties such as electrical conductivity are being developed.

[0003] Georg KH Madsen et. al., Comput. Phys. Commun., 231, 140-145 (2018)R. Amin et. al., J. Electrochem. Soc., 162 (7), 1163-1169 (2015)

[0004] The electrical conductivity of lithium transition metal oxides calculated by the method described in Non-Patent Document 1 deviates significantly from the experimental value described in Non-Patent Document 2, particularly in the region where the amount of lithium ions is small. Therefore, the conventional method cannot accurately predict the electrical conductivity when the battery is discharged and lithium ions are released. In order to develop new electrode materials with excellent properties, a technology is needed to predict physical quantities such as electrical conductivity with higher accuracy.

[0005] The present disclosure provides a technique for improving the accuracy of calculating a physical quantity.

[0006] The physical quantity calculation method in the present disclosure includes the steps of acquiring data representing an electronic state of a material calculated based on the arrangement of atoms constituting the material, adjusting a parameter representing a Fermi level in the acquired data, and calculating a physical quantity representing a physical property of the material based on the acquired data and the adjusted parameter representing the Fermi level.

[0007] The physical quantity calculation device according to the present disclosure includes an acquisition unit that acquires data representing an electronic state of a material calculated based on an arrangement of atoms constituting the material, an adjustment unit that adjusts a parameter representing a Fermi level in the data acquired by the acquisition unit, and a calculation unit that calculates a physical quantity representing a physical property of the material based on the data acquired by the acquisition unit and the parameter representing the Fermi level adjusted by the adjustment unit.

[0008] Any combination of the above components, and conversion of the present disclosure into a method, device, system, recording medium, computer program, etc., are also valid aspects of the present disclosure.

[0009] According to the technology of the present disclosure, it is possible to improve the accuracy of calculating physical quantities.

[0010] FIG. 1 is a flowchart showing the procedure of a physical quantity calculation method according to the first embodiment; FIG. 2 is a diagram showing an example of the atomic arrangement of a lithium transition metal oxide; FIG. 3 is a diagram showing an example of the band structure of a lithium transition metal oxide; FIG. 4 is a diagram showing an example of the conductivity of a lithium transition metal oxide; and FIG. 5 is a diagram showing the configuration of a physical quantity calculation device according to the first embodiment.

[0011] Hereinafter, embodiments will be described in detail with reference to the drawings. However, unnecessary detailed description may be omitted. For example, detailed description of well-known matters or redundant description of substantially the same configuration may be omitted.

[0012] The accompanying drawings and the following description are provided to enable those skilled in the art to fully understand the present disclosure, and are not intended to limit the subject matter described in the claims.

[0013] First Embodiment Hereinafter, a first embodiment will be described with reference to FIGS.

[0014] 1 is a flowchart showing the steps of a physical quantity calculation method according to the first embodiment. The physical quantity calculation method according to the first embodiment is executed by a physical quantity calculation device implemented by a program or the like installed in a computer. In the first embodiment, a case will be described in which the conductivity of a lithium transition metal oxide used as a positive electrode of a lithium ion battery is calculated as an example of a physical quantity.

[0015] [Step S10: Determining Atomic Arrangement] In step S10, the physical quantity calculation device determines the arrangement of atoms constituting the target material. Specifically, the physical quantity calculation device creates a structure file of the lithium transition metal oxide. The structure file may be acquired from a crystal structure database. The structure file may be created using crystal structure drawing software or the like based on information described in literature such as academic papers. The structure file may be created by referring to the atomic arrangement of a material whose atomic arrangement is known and whose constituent atoms are similar. The structure file may also be created by any other method.

[0016] Figure 2 shows an example of the atomic arrangement of lithium transition metal oxides: LiCoO ２ and LiNiO ２ As shown in Figure 2, lithium transition metal oxides such as these have a layered rock-salt structure (α-NaFeO) in which transition metals and lithium are regularly arranged in the <111> direction of a cubic rock-salt structure to form a two-dimensional plane. ２ A structure file may also be created for lithium transition metal oxides in which the transition metal sites are substituted with other transition metal elements, assuming that they have a similar atomic arrangement.

[0017] [Step S12: Calculation of Electronic State] In step S12, the physical quantity calculation device calculates the electronic state of the material. The electronic state of the material may be calculated using known first-principles calculation software that performs first-principles band calculations according to any calculation method. The first-principles calculation software inputs the initial atomic arrangement represented by a structure file, the potential of each atom, and calculation conditions, and calculates a stable atomic arrangement, electronic structure, energy, etc. based on density functional theory (DFT) or the like. The first-principles calculation software calculates the force acting on each atom by calculating the electronic state based on the initial atomic arrangement, and then moves each atom by the calculated force to obtain a more stable atomic arrangement. This process is repeated, and the atomic arrangement when the force acting on each atom becomes equal to or less than a reference value is considered to be a stable atomic arrangement, and the electronic structure, energy, etc. at that time are output.

[0018] Figure 3 shows an example of the band structure of a lithium transition metal oxide. In Figure 3, the density of states of the transition metal, calculated taking into account electron spin, is shown by a thick solid line, and the density of states of oxygen is shown by a thin solid line. Lithium transition metal oxides are semiconductors, and the Fermi level exists in the band gap between the electron-filled valence band and the empty conduction band.

[0019] [Step S14: Adjustment of Fermi Level] In step S14, the parameters representing the Fermi level are adjusted.

[0020] Fermi level E of intrinsic semiconductor ｉ is the energy at the bottom of the conduction band E Ｃ , the energy at the top of the valence band E Ｖ , effective density of states N Ｃ , N Ｖ Using this, it is expressed by the following equation: The second term is small enough that the Fermi level E ｉ is located near the center of the band gap.

[0021] Fermi level E of a doped semiconductor Ｆ is the intrinsic carrier density n ｉ , the electron density n in the conduction band, and the hole density p in the valence band, are expressed by the following equation: The higher the doping concentration of impurities, the closer the Fermi level is to the band edge. That is, the higher the electron density n in the conduction band, the closer the Fermi level is to the bottom of the conduction band, and the higher the hole density p in the valence band, the closer the Fermi level is to the top of the valence band.

[0022] Therefore, the Fermi level of lithium transition metal oxides can vary depending on the density of states, energy, electron spin, valence, bond length, local strain, point defects, composition, etc. of the material.

[0023] Furthermore, when a lithium transition metal oxide is used as the positive electrode of a lithium ion battery, lithium ions enter and exit during charging and discharging, which changes the hole density p in the valence band and causes the Fermi level to fluctuate. The Fermi level can also change depending on the materials, such as the electrolyte and negative electrode, that are in electrical contact with the positive electrode.

[0024] Thus, when calculating the conductivity of an electrode material for a primary or secondary battery that has a deficiency of carrier ions, such as a lithium transition metal oxide in a lithium ion battery, it is not sufficient to simply set an appropriate Fermi level value in consideration of the Fermi-Dirac distribution at the temperature at which the battery is used, as has been done conventionally. As described above, the calculated value will deviate significantly from the experimental value, particularly in the region where the amount of carrier ions is small.

[0025] To solve this problem, in the physical quantity calculation method of the first embodiment, a parameter representing the Fermi level is adjusted based on at least one of the density of states, energy, electron spin, valence, bond length, local strain, point defects, and composition of a target material and a material in contact with the target material. This allows the conductivity of the material to be calculated with higher accuracy. Furthermore, it allows the change in conductivity due to the desorption or insertion of carrier ions to be predicted with higher accuracy.

[0026] The physical quantity calculating device may adjust the parameters so that the Fermi level is closer to the valence band than to the center of the band gap. The physical quantity calculating device may adjust the parameters so that the Fermi level is at a position 0%, 5%, 10%, 15%, 20%, 25%, 30%, 35%, 40%, 45%, or 50% of the band gap from the top of the valence band. The physical quantity calculating device may adjust the parameters so that the Fermi level is closer to the top of the valence band as the hole density, local strain, or point defects of the material increases. The physical quantity calculating device may adjust the parameters so that the Fermi level is closer to the top of the valence band as the amount of desorption of lithium ions increases.

[0027] [Step S16: Adjustment of Carrier Density] In step S16, the physical quantity calculation device adjusts the parameter representing the carrier density in consideration of holes generated due to desorption of lithium ions, thereby enabling more accurate prediction of changes in conductivity due to charging and discharging of a lithium-ion battery using a lithium transition metal oxide as a positive electrode.

[0028] [Step S18: Calculation of Electrical Conductivity] In step S18, the physical quantity calculation device calculates the electrical conductivity of the lithium transition metal oxide based on the data calculated in step S12, the parameter representing the Fermi level adjusted in step S14, and the parameter representing the carrier density adjusted in step S16. The physical quantity calculation device may calculate the electrical conductivity using any known method.

[0029] FIG. 4 shows an example of the conductivity of a lithium transition metal oxide. In FIG. 4, black squares represent experimental values, black circles represent values ​​calculated by the physical quantity calculation method of embodiment 1, and gray circles represent values ​​calculated by the conventional method. The conventional method does not take into account the effects of lithium ion desorption on the Fermi level and carrier density, so the smaller the amount of lithium ions, the more it deviates from the experimental value. The value calculated by the physical quantity calculation method of embodiment 1 is almost equal to the experimental value. It has been shown that the physical quantity calculation method of embodiment 1 can calculate conductivity with higher accuracy even in a state where carrier ions are desorbed.

[0030] [Step S20: Selection of Promising Materials] In step S20, promising materials for the electrode are selected based on the conductivity calculated in S18. For example, materials that exhibit high conductivity over a wide range, even when the amount of lithium ions changes due to lithium ion desorption or insertion, may be selected as promising materials. This allows for efficient selection of novel materials with excellent properties, thereby reducing the time, effort, and cost required for battery design.

[0031] 5 shows the configuration of the physical quantity calculation device 100 according to the first embodiment. The physical quantity calculation device 100 includes a communication device 101, a display device 102, an input device 103, a processing device 160, and a storage device 170. The physical quantity calculation device 100 may be any computer such as a personal computer or a server device.

[0032] The communication device 101 controls communication with other devices via a communication network. The communication device 101 may perform communication using any wired or wireless communication method. The display device 102 displays a screen generated by the processing device 160. The display device 102 may be a liquid crystal display device, an organic EL display device, or the like. The input device 103 transmits instructions input by a user of the physical quantity calculation device 100 to the processing device 160. The input device 103 may be a mouse, a keyboard, a touchpad, or the like. The display device 102 and the input device 103 may be implemented as touch panels.

[0033] The storage device 170 stores programs, data, etc. used by the processing device 160. The storage device 170 may be a semiconductor memory, a hard disk, or the like.

[0034] The processing device 160 includes an atomic arrangement determination unit 161, an electronic state calculation unit 162, a Fermi level adjustment unit 163, a carrier density adjustment unit 164, a physical quantity calculation unit 165, and a material selection unit 166. These components are realized as hardware by any circuit, a computer CPU, memory, other LSIs, etc. These components are realized as software by programs loaded into memory, etc. Here, functional blocks realized by their cooperation are depicted. Therefore, it will be understood by those skilled in the art that these functional blocks can be realized in various ways, such as hardware alone or a combination of hardware and software.

[0035] The atomic arrangement determination unit 161 determines the arrangement of atoms constituting the target material in step S10 of the physical quantity calculation method according to the first embodiment.

[0036] The electronic state calculation unit 162 calculates the electronic state of the material based on the atomic arrangement determined by the atomic arrangement determination unit 161 in step S12 of the physical quantity calculation method of the first embodiment.

[0037] The Fermi level adjusting unit 163 adjusts the parameters representing the Fermi level among the data calculated by the electronic state calculating unit 162 in step S14 of the physical quantity calculating method according to the first embodiment.

[0038] In step S16 of the physical quantity calculation method of embodiment 1, the carrier density adjustment unit 164 adjusts the parameters representing the carrier density from the data calculated by the electronic state calculation unit 162, taking into account carriers generated due to the desorption of atoms or ions.

[0039] In step S18 of the physical quantity calculation method of the first embodiment, the physical quantity calculation unit 165 calculates the physical quantity of the material based on the data calculated by the electronic state calculation unit 162, the parameter representing the Fermi level adjusted by the Fermi level adjustment unit 163, and the parameter representing the carrier density adjusted by the carrier density adjustment unit 164.

[0040] The material selection unit 166 selects materials with excellent properties based on the physical quantities calculated by the physical quantity calculation unit 165 .

[0041] [Effects] As described above, in this embodiment, the physical quantity calculation method includes the steps of: acquiring data representing the electronic state of a material calculated based on the arrangement of atoms constituting the material (S12); adjusting a parameter representing the Fermi level in the acquired data (S14); and calculating a physical quantity representing a physical property of the material based on the acquired data and the adjusted parameter representing the Fermi level (S18). This makes it possible to calculate the physical quantity of the material with higher accuracy. Furthermore, it is possible to predict with higher accuracy changes in the physical quantity due to desorption or insertion of atoms or ions.

[0042] In this embodiment, the step (S18) of adjusting the parameters representing the Fermi level includes a step of adjusting the parameters representing the Fermi level based on at least one of the density of states, energy, electron spin, valence, bond length, local strain, point defects, and composition of the material and a material in contact with the material. This allows the physical quantities of the material to be calculated with higher accuracy. Furthermore, it allows the changes in the physical quantities associated with the desorption or insertion of atoms or ions to be predicted with higher accuracy.

[0043] In this embodiment, the material is a material used in an electrode of a lithium ion battery, and the physical quantity calculation method further includes a step (S16) of adjusting a parameter representing carrier density in the acquired data, taking into account holes generated in the material due to desorption of lithium ions, and the step (S18) of calculating the physical quantity includes a step of calculating a physical quantity representing a physical property of the material further based on the adjusted parameter representing carrier density. This makes it possible to calculate the physical quantity of the material with higher accuracy. Also, it is possible to predict with higher accuracy a change in the physical quantity due to desorption or insertion of lithium ions.

[0044] In this embodiment, the data acquisition step (S12) includes a step (S10) of determining the atomic arrangement of the material and a step (S12) of calculating the electronic state of the material based on the determined atomic arrangement. This allows the physical quantities of the new material to be calculated with higher accuracy. Furthermore, it allows the changes in physical quantities associated with the desorption and insertion of atoms or ions to be predicted with higher accuracy.

[0045] In this embodiment, the physical quantity is the conductivity. This allows the conductivity of the material to be calculated with higher accuracy. Also, the change in conductivity due to the desorption or insertion of atoms or ions can be predicted with higher accuracy.

[0046] In this embodiment, the physical quantity calculation program causes a computer to execute the following steps: acquiring data representing the electronic state of a material calculated based on the arrangement of atoms constituting the material (S12); adjusting a parameter representing the Fermi level in the acquired data (S14); and calculating a physical quantity representing a physical property of the material based on the acquired data and the adjusted parameter representing the Fermi level (S18). This allows the physical quantity of the material to be calculated with higher accuracy. Furthermore, it allows the change in the physical quantity due to the desorption or insertion of atoms or ions to be predicted with higher accuracy.

[0047] Furthermore, in this embodiment, the physical quantity calculating device 100 includes an electronic state calculating unit 162 that acquires data representing an electronic state of a material calculated based on the arrangement of atoms constituting the material, a Fermi level adjusting unit 163 that adjusts a parameter representing a Fermi level in the data calculated by the electronic state calculating unit 162, and a physical quantity calculating unit 165 that calculates a physical quantity representing a physical property of the material based on the data calculated by the electronic state calculating unit 162 and the parameter representing the Fermi level adjusted by the Fermi level adjusting unit 163. This makes it possible to calculate the physical quantity of the material with higher accuracy. Furthermore, it is possible to predict with higher accuracy a change in the physical quantity due to desorption or insertion of atoms or ions.

[0048] (Other Embodiments) As described above, the first embodiment has been described as an example of the technology disclosed in the present application. However, the technology in the present disclosure is not limited to this, and can be applied to embodiments in which modifications, substitutions, additions, omissions, etc. are made. Furthermore, it is also possible to combine the components described in the first embodiment above to create new embodiments.

[0049] Therefore, other embodiments will be exemplified below.

[0050] Although the first embodiment has been described mainly in relation to the calculation of the conductivity of a lithium transition metal oxide, the technique of the present disclosure can be widely applied to the calculation of physical quantities that represent the electrical, magnetic, and mechanical properties of materials such as semiconductors and insulators. In particular, when atoms or ions contained in a material are desorbed, the technique can accurately predict changes in the physical quantities that accompany the desorption of atoms or ions.

[0051] It should be noted that the above-described embodiments are intended to illustrate the technology of the present disclosure, and various modifications, substitutions, additions, omissions, etc. may be made within the scope of the claims or their equivalents.

[0052] (Additional Notes) The above embodiments disclose the following techniques. (Technology 1) A physical quantity calculation method including: acquiring data representing an electronic state of a material calculated based on the arrangement of atoms constituting the material; adjusting a parameter representing a Fermi level in the acquired data; and calculating a physical quantity representing a physical property of the material based on the acquired data and the adjusted parameter representing the Fermi level. This allows the physical quantity of the material to be calculated with higher accuracy. It also allows for more accurate prediction of changes in the physical quantity associated with desorption or insertion of atoms or ions. (Technology 2) The step of adjusting the parameter representing the Fermi level includes adjusting the parameter representing the Fermi level based on at least one of density of states, energy, electron spin, valence, bond length, local strain, point defects, and composition of the material and a material in contact with the material. This is the physical quantity calculation method according to Technology 1. This allows the physical quantity of the material to be calculated with higher accuracy. It also allows for more accurate prediction of changes in the physical quantity associated with desorption or insertion of atoms or ions. (Technology 3) The physical quantity calculation method according to Technology 1 or 2, wherein the material is a material used in an electrode of a lithium ion battery, and further includes a step of adjusting a parameter representing a carrier density in the acquired data, taking into account holes generated in the material upon desorption of lithium ions, and wherein the step of calculating the physical quantity includes a step of calculating a physical quantity representing a physical property of the material further based on the parameter representing the adjusted carrier density. This allows the physical quantity of the material to be calculated with higher accuracy. Also, it allows for higher accuracy prediction of changes in the physical quantity associated with desorption or insertion of atoms or ions. (Technology 4) The physical quantity calculation method according to any one of Technology 1 to 3, wherein the step of acquiring data includes a step of determining an atomic arrangement constituting the material, and a step of calculating an electronic state of the material based on the determined atomic arrangement. This allows for higher accuracy calculation of the physical quantity of a new material. Also, it allows for higher accuracy prediction of changes in the physical quantity associated with desorption or insertion of atoms or ions.(Technology 5) The physical quantity calculation method according to any one of Techniques 1 to 4, wherein the physical quantity is electrical conductivity. This allows the electrical conductivity of a material to be calculated with higher accuracy. Furthermore, it also allows for more accurate prediction of changes in electrical conductivity associated with the desorption or insertion of atoms or ions. (Technology 6) A physical quantity calculation program for causing a computer to execute the following steps: acquiring data representing the electronic state of the material calculated based on the arrangement of atoms constituting the material; adjusting a parameter representing the Fermi level in the acquired data; and calculating a physical quantity representing a physical property of the material based on the acquired data and the adjusted parameter representing the Fermi level. This allows the physical quantity of the material to be calculated with higher accuracy. Furthermore, it also allows for more accurate prediction of changes in the physical quantity associated with the desorption or insertion of atoms or ions. (Technology 7) A physical quantity calculation device comprising: an acquisition unit that acquires data representing an electronic state of a material calculated based on the arrangement of atoms constituting the material; an adjustment unit that adjusts a parameter representing a Fermi level in the data acquired by the acquisition unit; and a calculation unit that calculates a physical quantity representing a physical property of the material based on the data acquired by the acquisition unit and the parameter representing the Fermi level adjusted by the adjustment unit. This makes it possible to calculate the physical quantity of the material with higher accuracy. Also, it is possible to predict with higher accuracy changes in the physical quantity due to desorption or insertion of atoms or ions.

[0053] The present disclosure can be used as a physical quantity calculation device for calculating the physical quantity of a material that can be used as an electrode or the like.

[0054] REFERENCE SIGNS LIST 100 Physical quantity calculation device 101 Communication device 102 Display device 103 Input device 160 Processing device 161 Atomic arrangement determination unit 162 Electronic state calculation unit 163 Fermi level adjustment unit 164 Carrier density adjustment unit 165 Physical quantity calculation unit 166 Material selection unit 170 Storage device

Claims

1. A step of obtaining data representing the electronic state of the material calculated based on the atomic arrangement constituting the material; a step of adjusting a parameter representing the Fermi level in the obtained data; and a step of calculating a physical quantity representing the physical properties of the material based on the obtained data and the parameter representing the adjusted Fermi level. A method for calculating a physical quantity including these steps.

2. The step of adjusting the parameter representing the Fermi level includes the step of adjusting the parameter representing the Fermi level based on at least one or more of the density of states, energy, electron spin, valence, bond distance, local strain, point defects, and composition of the material and the material in contact with the material. The method for calculating a physical quantity according to claim 1.

3. The material is a material used for an electrode of a lithium-ion battery, and further includes a step of adjusting a parameter representing the carrier density in consideration of holes generated in the material as lithium ions are desorbed in the obtained data. The step of calculating the physical quantity includes the step of calculating a physical quantity representing the physical properties of the material based on the parameter representing the adjusted carrier density. The method for calculating a physical quantity according to claim 1 or 2.

4. The step of obtaining the data includes a step of determining the atomic arrangement constituting the material and a step of calculating the electronic state of the material based on the determined atomic arrangement. The method for calculating a physical quantity according to claim 1 or 2.

5. The physical quantity is conductivity. The method for calculating a physical quantity according to claim 1 or 2.

6. A program for calculating a physical quantity for causing a computer to execute a step of obtaining data representing the electronic state of the material calculated based on the atomic arrangement constituting the material, a step of adjusting a parameter representing the Fermi level in the obtained data, and a step of calculating a physical quantity representing the physical properties of the material based on the obtained data and the parameter representing the adjusted Fermi level.

7. An acquisition unit that acquires data representing the electronic state of the material calculated based on the arrangement of atoms constituting the material; an adjustment unit that adjusts a parameter representing the Fermi level in the data acquired by the acquisition unit; and a calculation unit that calculates a physical quantity representing the physical properties of the material based on the data acquired by the acquisition unit and the parameter representing the Fermi level adjusted by the adjustment unit. A physical quantity calculation device comprising the above components.

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