Method for optimizing microstructure of multiferroic material and multiferroic material structure

Abstract

To provide an optimization method of a microscopic structure of a multiferroic material capable of obtaining a new microscopic structure capable of obtaining a larger macroscopic material property value, and a multiferroic material structure based on the method.SOLUTION: In an optimization method of a microscopic structure of a multiferroic material, a unit cell model of a microscopic structure composed of a piezoelectric phase and a compression phase is constructed, and a series of two scales of a microscopic structure and a macroscopic structure in which the microscopic structure is periodically and repeatedly arranged is formulated, and a numerical solution for the obtained partial differential equations of both scales is obtained by a finite element method, by using an extreme value search method in which a macroscopic material characteristic value is used as an objective function, and the microscopic structure is used as a variable, a calculation process is performed in which the microscopic structure is sequentially changed to maximize the macroscopic material property value.SELECTED DRAWING: Figure 5

Description

Technical Field

[0001] The present invention relates to the microscopic structure of a multiferroic material having an electromagnetic effect (also referred to as the "ME effect").

Background Art

[0002] In recent years, multiferroic materials having the ME effect have attracted attention. A multiferroic material is a functional material composed of, for example, a plurality of materials such as a ferroelectric material and a ferromagnetic material, and is capable of obtaining an excellent ME effect that cannot be obtained with a single material.

[0003] Regarding such multiferroic materials, various studies have been conducted. For example, Non-Patent Document 1 shows that in a multiferroic material, a macroscopic material property value (for example, a macro ME constant) becomes relatively large by making a microscopic structure composed of a ferroelectric phase (also referred to as the "FE phase") and a ferromagnetic phase (also referred to as the "FM phase") a uniformly oriented laminated structure (a structure in which the material arrangement is layered and the polarization direction is uniformly oriented in a predetermined direction).

Prior Art Documents

Patent Documents

[0004]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] For multiferroic materials, it is desirable to find a new microscopic structure capable of obtaining larger macroscopic material property values.

[0006] It is also desirable to find a microscopic structure capable of obtaining even larger macroscopic material property values.

[0007] Therefore, an object of the present invention is to provide an optimization method for the microscopic structure of a multiferroic material capable of finding a new microscopic structure capable of obtaining larger macroscopic material property values, and a multiferroic material structure based thereon.

Means for Solving the Problems

[0008] (1) The optimization method for the microscopic structure of a multiferroic material according to the present invention constructs a unit cell model of a microscopic structure composed of a piezoelectric phase (specifically, an FE phase) and a piezomagnetic phase (specifically, an FM phase), formulates the coupling of two scales between the microscopic structure and the macroscopic structure formed by periodically repeating and arranging the microscopic structure, and the obtained Maximize the macroscopic material property value In the optimization method for the microscopic structure of a multiferroic material, with the macroscopic material property value as the objective function and the microscopic structure as the variable, a calculation process is performed using an extreme value search method to sequentially change the microscopic structure to maximize the macroscopic material property value. When the macroscopic material property value is maximized by the extreme value search method, if the distribution of the polarization directions of the piezoelectric phase and the piezomagnetic phase in the (001) pole figure obtained from the microscopic structure is a specific pattern in which the polarization direction of the piezoelectric phase and the polarization direction of the piezomagnetic phase are concentrated in each of a plurality of specific regions, perform a simplification process on the microscopic structure, and then use the extreme value search method again to sequentially change the microscopic structure to perform a calculation process of maximizing the macroscopic material property value. The simplification process includes determining, for each azimuth region in the pole figure, any value including an average value, a median value, a maximum value, a minimum value, or a mode value as a representative value, and replacing the azimuths of the integration points within each azimuth region with the representative value It is characterized by the above.

[0009] According to the configuration of (1), for example, for a multiferroic material made of a predetermined material, when the microscopic structure is a predetermined structure (for example, a uniformly oriented laminated structure), a macroscopic material property value exceeding the maximum value of the macroscopic material property value obtained in the research before the filing of the present application can be obtained, and it is possible to find a microscopic structure of a new structure different from the predetermined structure. That is, it is possible to find a new microscopic structure capable of obtaining larger macroscopic material property values.

[0010] (2) In the optimization method for the microscopic structure of a multiferroic material described in (1) above,The simplification process is When the macroscopic material property value is maximized by the extreme value search method, the distribution of the polarization directions of the piezoelectric phase and the piezomagnetic phase in the (001) positive pole figure obtained from the microscopic structure is in the range of angle 30 to 60 degrees such that the polarization direction of the piezoelectric phase and the polarization direction of the piezomagnetic phase are 5% concentrated above in a specific pattern in each of a plurality of specific regions within is performed This is the gist.

[0011] According to the configuration of (2), it is possible to obtain a microscopic structure that provides an even larger macroscopic material property value.

[0012] In the method for optimizing the microscopic structure of the multiferroic material according to (3) above, when the distribution of the polarization directions in the (001) positive pole figure is different from the specific pattern, the optimization process of the microscopic structure is terminated. This is the gist.

[0013] According to the configuration of (3), for example, when further optimization of the microscopic structure when the macroscopic material property value is maximized by the extreme value search method is not required, the optimization of the microscopic structure is terminated, and it is possible to efficiently perform the optimization of the microscopic structure.

[0020] ( 4 ) The multiferroic material structure according to the present invention is barium titanate (hereinafter sometimes referred to as "BTO") forming a piezoelectric phase and cobalt ferrite (hereinafter sometimes referred to as "CFO")It is a multiferroic material structure composed of a piezomagnetic phase formed by [material name], with the direction of applying a magnetic field or an electric field as the input direction, and the electric flux density or magnetic flux density generated thereby as the output direction, and exhibiting an electromagnetic constant in which the input direction and the output direction are parallel. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are alternately arranged so that the same phase does not adjacent to each other. The polarization orientation of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization orientation of the piezomagnetic phase belongs to four orientation regions that exist in the four quadrants in the (001) pole figure and are symmetric with respect to each other with respect to the coordinate axes or the origin.

[0021] ( 5 ) The multiferroic material structure according to the present invention is composed of a piezoelectric phase formed by barium titanate and Terfenol-D (Registered trademark. Hereinafter sometimes referred to as "TFD") It is a multiferroic material structure composed of a piezomagnetic phase formed by [material name], and exhibiting an electromagnetic constant in which the input direction and the output direction are parallel. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are continuously arranged in the same phase in one direction among the three orthogonal coordinate axes, and are alternately arranged in the remaining two directions so that the same phase does not adjacent to each other. The polarization orientation of the piezomagnetic phase and the polarization orientation of the piezoelectric phase respectively belong to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution.

[0022] ( 6 ) The multiferroic material structure according to the present invention is lead zirconate titanate (hereinafter sometimes referred to as "PZT")It is a multiferroic material structure composed of a piezoelectric phase made of [material name] and a piezomagnetic phase made of cobalt ferrite, and exhibits electromagnetic constants with the input direction and the output direction being parallel. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are arranged such that the same phase is continuously arranged in one direction among the three orthogonal coordinate axes, and in the remaining two directions, the same phase is not adjacent to each other, or alternately arranged such that in one of the two directions, the same phase is not adjacent to each other and in the other direction, the same phase is partially adjacent. The polarization orientation of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure representing the orientation distribution, and the polarization orientation of the piezomagnetic phase belongs to four orientation regions that exist in the four quadrants in the (001) pole figure and are symmetric with respect to the coordinate axes or the origin.

[0023] ( 7 ) The multiferroic material structure according to the present invention is a multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of Terfenol-D, and exhibits electromagnetic constants with the input direction and the output direction being parallel. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are alternately arranged such that the same phase is not adjacent to each other. The polarization orientation of the piezomagnetic phase and the polarization orientation of the piezoelectric phase each belong to one orientation region existing at the position of the origin and two orientation regions existing on the coordinate axes and being symmetric with respect to the origin in the (001) pole figure representing the orientation distribution.

[0024] ( 8)The multiferroic material structure according to the present invention is a multiferroic material structure composed of a piezoelectric phase made of barium titanate and a piezomagnetic phase made of cobalt ferrite, and exhibits electromagnetic constants in which the input direction and the output direction are orthogonal. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are alternately arranged so that the same phase is not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure.

[0025] ( 9 )The multiferroic material structure according to the present invention is a multiferroic material structure composed of a piezoelectric phase made of barium titanate and a piezomagnetic phase made of Terfenol-D, and exhibits electromagnetic constants in which the input direction and the output direction are orthogonal. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are arranged such that the same phase is continuously arranged in one of the three orthogonal coordinate axes, and alternately arranged in the remaining two axes so that the same phase is not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to one orientation region that exists at the position of the origin in the (001) pole figure.

[0026] ( 10)The multiferroic material structure according to the present invention is a multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of cobalt ferrite, and exhibits electromagnetic constants in which the input direction and the output direction are orthogonal. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are alternately arranged so that the same phase is not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution, and the polarization direction of the piezomagnetic phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure.

[0027] ( 11 )The multiferroic material structure according to the present invention is a multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of Terfenol-D, and exhibits electromagnetic constants in which the input direction and the output direction are orthogonal. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are alternately arranged so that the same phase is not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution, and the polarization direction of the piezomagnetic phase belongs to one orientation region that exists at the position of the origin in the (001) pole figure.

Effect of the Invention

[0032] According to the present invention, it is possible to provide an optimization method for the microscopic structure of a multiferroic material that can seek a new microscopic structure capable of obtaining a larger macroscopic material property value, and a multiferroic material structure based thereon.

Brief Description of the Drawings

[0033]

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Mode for Carrying Out the Invention

[0034] An optimization method for the microscopic structure of a multiferroic material according to an example of the present invention, and a multiferroic material structure based thereon will be described with reference to the drawings and the like.

[0035] <Regarding the Multiferroic Material> First, before explaining the optimization method for the microscopic structure of the multiferroic material according to an example of the present invention, the multiferroic material will be explained.

[0036] The multiferroic material (multiferroic composite material) according to the present invention is composed of a piezoelectric body (specifically, a ferroelectric body) and a piezomagnetic body (specifically, a ferromagnetic body). In the multiferroic material, an electromagnetic effect (hereinafter referred to as the "ME effect") can be obtained by generating mechanical strain between the piezoelectric phase (specifically, the ferroelectric phase) and the piezomagnetic phase (specifically, the ferromagnetic phase). For example, when a magnetic field is applied to the multiferroic material, strain (in other words, deformation) occurs in the ferromagnetic phase due to the piezomagnetic effect. Then, strain occurs in the ferroelectric phase in response to the strain in the ferromagnetic phase, and electric flux density is generated due to the piezoelectric effect. Conversely, when an electric field is applied to the multiferroic material, strain occurs in the ferroelectric phase due to the piezoelectric effect. Then, strain occurs in the ferromagnetic phase in response to the strain in the ferroelectric phase, and magnetic flux density is manifested due to the piezomagnetic effect. Utilizing such properties, the multiferroic material can be used in various technologies such as sensors, memories, and energy harvesters, for example, in automobiles, IT devices, medical devices, and the like. Note that the piezomagnetic phase is also referred to as the "magnetostrictive phase". In addition, in this specification, the ferroelectric phase is also referred to as the "FE phase", and the ferromagnetic phase is also referred to as the "FM phase". Also, the FE phase and the FM phase may each be a single crystal (a single domain or an aggregate of multiple domains), or may be a polycrystal (an aggregate of multiple crystallites).

[0037] Note that hereinafter, the linear combination problem among displacement, electric potential, and magnetic potential will be discussed. Specifically, for the piezoelectric-piezomagnetic elastic body with respect to stress σ ij , strain ε ij , electric flux density D i , electric field E i , magnetic flux density B i and magnetic field H i , the following linear relationships of equations (1) to (3) hold.

[0038]

Equation

Equation

Equation

[0039] C ijmn is a fourth-order tensor of elastic stiffness coefficients, K ij and μ ij are second-order tensors of permittivity and permeability, e mij and q mij are third-order tensors of piezoelectric and piezomagnetic coupling constants. Also, a mn is a second-order tensor of the ME coupling constant. When m = n, the input direction and the output direction are parallel, and when m ≠ n, the input direction and the output direction are orthogonal.

[0040] FIG. 1 is a conceptual diagram for explaining the macroscopic structure (hereinafter also referred to as "macrostructure") and microscopic structure (hereinafter also referred to as "microstructure") of a multiferroic material, etc. The macroscopic structure of the multiferroic material is sufficiently larger than the microscopic structure and occupies a region (macroscopic region) Ω. The microscopic structure is defined as a region (microscopic region) Y that is periodically repeated in a small cycle within the macroscopic structure. In other words, the macroscopic structure is composed of the microscopic structures being periodically repeated in a small cycle. Note that the coordinates of the macroscopic structure are x = (x1, x2, x3) T and the coordinates of the microscopic structure (coordinates defined for all unit cells) are y = (y1, y2, y3) T Let. Also, in this specification, the three-dimensional directions are indicated in a right-handed orthogonal coordinate system. In the macroscopic structure, the first axis is the x1 axis, the second axis is the x2 axis, and the third axis is the x3 axis. Also, in the microscopic structure, the first axis is the y1 axis, the second axis is the y2 axis, and the third axis is the y3 axis.

[0041] The macroscopic structure has a homogeneous (homogeneous in general view) structure. In contrast, the microscopic structure has a heterogeneous structure. Also, the microscopic structure is modeled as an aggregate of FE phase 20 (see FIG. 1) and FM phase 30.

[0042] The micro-structure is a unit cell (representative volume element) in a multiferroic material, and is composed of the respective positions (arrangements), ratios (specifically, the ratios between the FE phase 20 and the FM phase 30), and polarization orientations (polarization directions) of the FE phase 20 and the FM phase 30. The polarization orientation (direction of electric polarization) of the FE phase 20 and the polarization orientation (direction of magnetic polarization) of the FM phase 30 are each defined by Euler angles (φ, θ, ψ). Note that, in the case of a single-crystal material, the polarization orientation is the "crystal direction with spontaneous polarization", and in the case of a polycrystalline material, the polarization orientation is the polarization orientation obtained by synthesizing the polarization orientations of all the crystallites in the aggregate.

[0043] Also, the material properties of the components of the micro-structure are determined by the ratio (proportion) between the FE phase and the FM phase defined by the material index (material variable) ξ. Note that in each of the following figures, the material index is shown in red the closer it is to "0.0" (FM phase), and in blue the closer it is to "1.0" (FE phase). However, in FIG. 1, for convenience of illustration, the material index is shown in white the closer it is to "0.0" (FM phase), and in black the closer it is to "1.0" (FE phase).

[0044] In this embodiment, a multiferroic material structure in which the FE phase is made of barium titanate (BaTiO3; hereinafter referred to as "BTO") and the FM phase is made of cobalt ferrite (CoFe2O4; hereinafter referred to as "CFO") is exemplified. BTO is a material having a tetragonal crystal structure, and CFO is a material having a hexagonal crystal structure. Also, the spontaneous polarization (spontaneous magnetic polarization, spontaneous electric polarization) of both materials appears in the

[0001] crystal direction. Note that, also for the hexagonal crystal structure, for convenience, a three-index expression is applied based on the conversion rule from the four-index expression.

[0045] Also, these materials have strong anisotropy in mechanical, magnetic, and electrical properties. In particular, the piezomagnetic constant and the piezoelectric constant change greatly depending on the polarization orientation. The crystal orientation dependence of the material constants differs between BTO and CFO and also differs depending on their components. Below, the respective orientation dependences of the FM phase and the FE phase will be described in detail.

[0046] First, the crystal orientation dependence of the piezomagnetic strain constant of single-crystalline CFO will be described with reference to FIG. 2.

[0047] On the left side of FIG. 2, the coordinate transformation values of the piezomagnetic strain constant are shown three-dimensionally in a rectangular coordinate system, and its surface is shown such that the distance from the origin in all directions is equal to the absolute value of the material constant. Also, FIGS. 2(A), (B), and (C) show three independent components f 311 , f 333 , f 131 of the piezomagnetic strain constant. f 311 is a component that relates the magnetic field H3 and the perpendicular strain ε 11 , and f 333 is a component that relates the magnetic field H3 and the perpendicular strain ε 33 . Also, f 131 is a component that relates the magnetic field H1 and the shear strain ε 31 .

[0048] Note that on the left side of FIG. 2, the coordinate transformation values of the three-dimensionally displayed piezomagnetic strain constant are shown in colors corresponding to the piezomagnetic strain constant. In this embodiment, as an example, the closer the piezomagnetic strain constant is to 0 (nA / m), the more it is shown in green. Also, as the piezomagnetic strain constant increases in the positive direction, it changes from green to yellow and red, and conversely, as the piezomagnetic strain constant increases in the negative direction, it changes from green to light blue and blue.

[0049] On the left side of FIG. 2(A), two circular peaks 111 and 112 appear, and a convex peak 113 appears along the y3-axis direction. Note that the component f 311On the other hand, a similar convex peak exists on the opposite side of peak 113 in the y3-axis direction (see the right side of Fig. 2(A)), but it is not shown on the left side of Fig. 2(A) due to the presence of circular peak 112. The central part of circular peak 111 is shown in green and gradually changes to blue as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the negative direction). Also, the central part of circular peak 112 is shown in green and gradually changes to red as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the positive direction). Further, the root part of convex peak 113 is shown in green and gradually changes to yellow as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the positive direction).

[0050] On the left side of Fig. 2(B), two circular peaks 121 and 122 appear, and two convex peaks 123 and 124 appear along the y3-axis direction. The central part of circular peak 121 is shown in green and gradually changes to orange as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the positive direction). Also, the central part of circular peak 122 is shown in green and gradually changes to light blue as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the negative direction). Further, the root part of convex peak 123 is shown in green and gradually changes to blue as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the negative direction). Also, the root part of convex peak 124 is shown in green and gradually changes to red as it goes towards the tip part (the piezomagnetic strain constant gradually increases in the positive direction).

[0051] Also, on the left side of Fig. 2(C), two circular peaks 131 and 132 appear, and a convex peak 133 appears along the y3-axis direction. Note that component f 131On the other hand, a similar convex peak appears on the opposite side of peak 133 in the y3-axis direction (see the right side of Fig. 2(C)). However, on the left side of Fig. 2(C), it is not shown due to the presence of circular peak 132. The central part of circular peak 131 is shown in green and gradually changes to blue toward the tip (the piezomagnetic strain constant gradually increases in the negative direction). Also, the central part of circular peak 132 is shown in green and gradually changes to red toward the tip (the piezomagnetic strain constant gradually increases in the positive direction). Further, the root part of convex peak 133 is shown in green and gradually changes to red toward the tip (the piezomagnetic strain constant gradually increases in the positive direction).

[0052] On the right side of Fig. 2, a cross-sectional view (a cross-sectional view perpendicular to the y1-axis of the microstructure) for explaining the direction and magnitude of each peak with respect to the piezomagnetic strain constant of single-crystalline CFO is shown. As shown on the right side of Fig. 2, six peaks appear in all components in this cross-sectional view. Specifically, for example, in the case of component f 311 , there are four equivalent maximum peaks at angles of 58°, 122°, 238°, and 302° with respect to the y3-axis, and the other two peaks along the y3-axis are smaller than these four maximum peaks. Also, in the case of component f 333 , the two peaks along the y3-axis are larger than the other four peaks in the oblique direction. Furthermore, in the case of component f 131 , six equivalent peaks appear at intervals of 60°.

[0053] Next, the crystal orientation dependence of the piezoelectric strain constant of single-crystalline BTO will be described with reference to Fig. 3.

[0054] Figs. 3(A), (B), and (C) show three independent components d 311 , d 333 , d 131 of the piezoelectric strain constant. d 311 is a component that relates the electric field E3 and the perpendicular strain ε 11 , and d 333 is a component that relates the electric field E3 and the perpendicular strain ε33 is a component that associates them. Also, d 131 is a component that associates the electric field E1 with the shear strain ε 31 is a component that associates them. The component d in Fig. 3 311 , d 333 shows similar trends to each other. On the other hand, the component d 131 is different from the other two components. Note that, similar to the three-dimensional display on the left side of Fig. 2 (color display method according to the piezomagnetic strain constant), the three-dimensional display on the left side of Fig. 3 is shown in colors according to the piezoelectric strain constant.

[0055] On the left side of Fig. 3(A), two circular peaks 141 and 142 appear. The central part of peak 141 is shown in green and gradually changes to blue towards the tip (the piezoelectric strain constant gradually increases in the negative direction). Also, the central part of peak 142 is shown in green and gradually changes to red towards the tip (the piezoelectric strain constant gradually increases in the positive direction).

[0056] On the left side of Fig. 3(B), two circular peaks 151 and 152 appear. The central part of peak 151 is shown in yellow and gradually changes to red towards the tip (the piezoelectric strain constant gradually increases in the positive direction). Also, the central part of peak 152 is shown in green and gradually changes to blue towards the tip (the piezoelectric strain constant gradually increases in the negative direction).

[0057] On the left side of Fig. 3(C), two convex peaks 161 and 162 appear in opposite directions along the y3-axis direction. The root part of peak 161 is shown in green and gradually changes to red towards the tip (the piezoelectric strain constant gradually increases in the positive direction). Also, the root part of peak 162 is shown in green and gradually changes to blue towards the tip (the piezoelectric strain constant gradually increases in the negative direction).

[0058] Also, in the right cross-sectional view of FIG. 3, component d 311 has four equivalent maximum peaks at angles of approximately 50°, 130°, 230°, and 310°, and component d 333 also has four equivalent maximum peaks at similar angles. On the other hand, component d 131 has two equivalent maximum peaks at angles of 0° and 180° with respect to the y3 axis.

[0059] <Regarding the method for optimizing the microstructure> Next, a method for optimizing the microstructure according to an example of the present invention will be described. Specifically, in this embodiment, the microstructure is optimized in the multi-scale coupling analysis to obtain a new microstructure capable of increasing the ME constant (an example of macroscopic material property values) of the macrostructure.

[0060] Here, the manifestation of a huge magnetoelectric effect is obtained by the synergistic effect of the coupling (piezoelectric and piezomagnetic) characteristics in the micro-inhomogeneous structure, and the microstructure exceeding the conventional uniformly oriented laminated structure is (at least at the time of filing this application) unexplored. However, in a multiferroic material where displacement, electric potential, and magnetic potential interfere with each other, the coupling effect inside the material changes greatly and complexly by controlling the material arrangement and polarization orientation. Therefore, there is a potential ability to significantly improve the macroscopic material property values through advanced design of the microstructure, and a breakthrough microstructure design has been demanded.

[0061] Therefore, the inventor of the present application applied the homogenization theory to the scale coupling analysis described below, and searched for an optimal microstructure that maximizes the electromagnetic effect using a numerically-analyzed program developed independently. Specifically, the inventor of the present application performed the coupling (multiphysics) of three fields, namely displacement, electric potential, and magnetic potential, in a composite of a piezoelectric body and a piezomagnetic body, and also performed the coupling (multiscale) of two scales, namely a macrostructure and a microstructure (that is, it is possible to perform two types of coupling). A numerically-analyzed program was developed. Then, as will be described in detail below, the inventor of the present application realized the optimization of the microstructure using the numerically-analyzed program. By developing such a numerically-analyzed program, the coupling between multiple materials and the coupling between multiple scales (so-called, multiscale) for an arbitrary heterogeneous structure were realized, and it became possible to efficiently perform virtual experiments on a computer for various design variables. In addition, the present invention can dramatically improve the electromagnetic effect of a multiferroic material, which is the core of the development of next-generation new devices, and realize material development led by numerical analysis. Furthermore, the multiferroic material having the obtained optimal structure (digital composite structure) can be developed for new creation by 3D printing or the like.

[0062] Hereinafter, the optimization method of the microstructure of the multiferroic material will be described in detail.

[0063] Generally, in a composite material in which electricity and magnetism are polarized in the same direction, as non-zero components of the ME effect, there are three components of a 11 , a 22 and a 33 . Typical composite materials such as a polycrystalline random structure, a polycrystalline layered structure, and a single-crystalline layered structure (uniform orientation laminated structure) have in-plane isotropy. a 11 and a 22 are equivalent components, and a 33 is different from the other two components. These electromagnetic constants (ME constants) a 11 , a 22 and a 33is a material constant in which the input direction (specifically, the y1-axis direction or the y2-axis direction) for applying a magnetic field (or an electric field) and the output direction of the resulting electric flux density (or magnetic flux density) are parallel. In the present embodiment, an example of a multiferroic material structure that exhibits an ME constant (specifically, a 11 ) in which the input direction and the output direction are parallel will be illustrated. a 11 is a material constant that relates the magnetic field H1 to the electric flux density D1 or the electric field E1 to the magnetic flux density B1 on the first axis. Note that the polycrystalline random structure is a structure in which both the material arrangement and the crystal orientation of the ferroelectric and the ferromagnetic are random. The polycrystalline layered structure is a structure in which the material arrangement of the ferroelectric and the ferromagnetic is layered and the crystal orientation is random. The single-crystalline layered structure (uniform orientation laminated structure) is a structure in which the material arrangement of the ferroelectric and the ferromagnetic is layered and the crystal orientation is uniformly oriented in a predetermined direction (for example, the y3-axis direction).

[0064] In the optimization of the microstructure, first, a unit cell model of the microstructure (that is, on a microscopic scale) is constructed (the first step). The unit cell is also referred to as the "representative volume element".

[0065] Note that the material properties of the microstructure, which are the elastic stiffness coefficient, the permittivity, the permeability, and the piezoelectric / piezomagnetic coupling coefficient micro X continuously changes according to the following equation using a trigonometric function of the material index ξ.

[0066]

Equation

[0067] X FE represents the material properties of the FE phase, and X FMshows the material properties of the FM phase. The material properties are periodically changed at a predetermined interval (e.g., 2.0 interval) of two material indices. For example, focusing on the first half interval of the material index ξ from 0.0 to 1.0, the elements of the microstructure model correspond to the complete FM phase at the material index ξ = 0.0, and in the reverse case, correspond to the complete FE phase at the material index ξ = 1.0. Also, the intermediate value of the material index ξ between 0.0 and 1.0 indicates a virtual mixed state of the FE phase and the FM phase. In this way, the material properties of all elements of the microstructure model are changed by the material index. As a result, a non-uniform microstructure is reconstructed, and its effect is reflected in the characteristic function. Note that in the optimization calculation, the material variable ξ is treated as a continuous value, but after the optimization calculation is completed, the material variable ξ of each element is binarized to 0.0 or 1.0 based on a threshold value. Therefore, the optimized structure is a composite material composed only of the FE phase and the FM phase, and in this state, the volume fractions of both phases occupying the whole are determined.

[0068] Next, for the multiphysics coupling problem in which three fields of displacement, electric potential, and magnetic potential interfere with each other due to the piezoelectric effect and the piezomagnetic effect, the coupling (coupling analysis) of two scales of the microscopic scale (microstructure) and the macroscopic scale (macrostructure formed by periodically repeating and arranging the microstructure) is formulated using, for example, the multiscale coupling method, and a numerical solution is obtained for the partial differential equations of both scales obtained by the finite element method (second step). Specifically, in this second step, when analyzing the optimization problem of the microstructure with the macroscopic material property value (specifically, the macro ME constant) as the objective function and the microstructure as the variable, a calculation process is performed to sequentially change the microstructure to maximize the macroscopic material property value using an extreme value search method. This calculation process is realized by using a numerical analysis program independently developed by the inventor of the present application.

[0069] First, the asymptotic homogenization theory (homogenization method) is used as an example of the multiscale coupling method for scale bridging between the microstructure (microscopic scale) and the macrostructure (macroscopic scale), and based on the asymptotic homogenization theory, the macro equation and the micro equation are formulated.

[0070] The macro equations are derived from the virtual work principle equations representing the equilibrium state of the object, and using the volume-averaged material properties of the microstructures, give the displacements, electric potentials, and magnetic potentials of the macrostructure under boundary conditions. On the other hand, the micro equations must satisfy the micro perturbations of the displacements, electric potentials, and magnetic potentials in the heterogeneous structure, and the micro perturbations are assumed to vary proportionally with respect to the mechanical strain, electric field, and magnetic field of the macrostructure. The proportionality constant χ(x,y), which is a microstructure characteristic function, is obtained by solving the micro equations under periodic boundary conditions, and in the case of a homogeneous body, the characteristic function becomes zero. And by using the characteristic function, the macro-homogenized material properties can be estimated as the volume average of the microstructures, and the response of the microstructures to the macro external loads can be evaluated. The macro-homogenized material properties are shown by the following equations (5) to (10).

[0071]

Number

Number

Number

Number

Number

Number

[0072] In each case, the superscript "micro" means the material properties of each phase in the microstructural coordinate system, and the superscript "macro" means the material properties (macro-homogenized material properties) in which the parameters are homogenized in the macrostructural coordinate system. Also, χ(x,y) is a proportionality constant that relates the microscopic perturbations of displacement, electric potential, and magnetic potential to the macro-strain, electric field, and magnetic field. Note that the material properties calculated from equations (5) to (10) are in complete agreement with the calculation results by the "Mori-Tanaka theory" (Reference 1: J. Y. Kim, Micromechanical analysis of effective properties of magneto-electro-thermo-elastic multilayer composites, International Journal of Engineering Science, 49 (2011), 1001-1018.), and the validity of these calculated values has been confirmed. The "Mori-Tanaka theory" is a theory for estimating the material properties of composite materials, and its validity and reliability are widely recognized and practically applied to various materials. As an example, Fig. 4 shows a comparison between the literature values and the calculated values by the Mori-Tanaka theory regarding the electromagnetic constants of a BTO / CFO composite material having a multi-layered structure. The vertical axis on the left in the figure represents the electromagnetic constant of a 11 and the vertical axis on the right represents the electromagnetic constant of a 33 , and the horizontal axis indicates the volume fraction of the FE phase in the overall structure. The solid line and the dotted line (the "AHM" in Fig. 4) in the figure are the calculated values obtained by this numerical analysis method (specifically, the solid line is for a 33 and the dotted line is for a 11 ), and the round plots (the "MT" in Fig. 4) are the literature values obtained by the Mori-Tanaka theory. As shown in Fig. 4, in all ranges where the volume fraction of the FE phase is from 0% to 100%, both components of a 11 and a 33 are in complete agreement with the literature values. Note that the calculated values for the elastic modulus, permittivity, permeability, piezoelectric constant, and piezomagnetic constant are also in complete agreement with the literature values, and their validity has been confirmed.

[0073] Then, numerical solutions are obtained for the macro equation and the micro equation (i.e., the partial differential equations at both scales) obtained as described above by the finite element method. Specifically, an optimal microstructure composed of FE phase and FM phase is searched for, and the macro homogenized ME constant (homogenized macro ME constant) is maximized. This multi-scale optimization can be expressed as follows.

Number

[0074] Here, macro a ij is the macro homogenized ME constant (electromagnetic constant) obtained from Equation (10). Also, ξ k is the material index (ratio), and E k represents the Euler angle (polarization direction) of the k-th element (or integration point within the element) in the microstructure model defined as follows.

[0075]

Number

[0076] Then, with the macro homogenized ME constant as the objective function and the microstructure as the variable (design variable), an analytical process (multi-scale optimization process) of the optimization problem for searching for the state where the macro homogenized ME constant is maximized is performed. In the present embodiment, among the microstructures composed of the respective arrangements, ratios (material indices), and polarization directions of the FE phase and the FM phase, the material index (the material index changing from the FE phase to the FM phase) and the respective polarization directions of the FM phase and the FE phase are used as variables.

[0077] Specifically, a calculation process is performed in which the microstructure (more specifically, material indices and polarization directions) is sequentially changed (more specifically, updated) using an extreme value search method to maximize the macro-homogenized ME constant. In the present embodiment, the steepest descent method is adopted as the extreme value search method for searching for the state in which the macro-homogenized ME constant is maximized. Note that the present invention is not limited to this, and as the extreme value search method, a random approach, a dimension division constant width hill climbing method, a probabilistic hill climbing method, a GA (genetic algorithm), a conjugate gradient method, or the like may be adopted.

[0078] FIG. 5 is a diagram showing the relationship (numerical results) between the macro-homogenized ME constant and the number of trials in the multi-scale optimization process for the BTO / CFO multiferroic material. In FIG. 5, the vertical axis represents the macro-homogenized ME constant a 11 which is the objective function, and the horizontal axis represents the number of trials n for updating the microstructure (more specifically, polarization direction and material indices).

[0079] Further, FIG. 6 is a diagram showing the distribution of polarization directions and the macro-homogenized ME constant in the microstructure at each stage (point O to point C) of the multi-scale optimization process.

[0080] First, the polarization directions (electric polarization direction, magnetic polarization direction) are generated in the (001) positive pole figure (more specifically, the (001) positive pole figure with the y3 axis as the normal direction), and are input to each element (or each integration point within the element) of the microstructure using a random generator (random number generator).

[0081] Here, in the microstructure, a hexahedral first-order element is used to regularly divide and model the composite structure of the piezoelectric phase and the piezomagnetic phase. As an example, for the hexahedral first-order element, 2×2×2 integration points are set within the element, and material properties and polarization directions are input as variables. In the microstructure shown in the upper part of Fig. 7, in the case of 4×4×4 element division (the number of elements is 64), different material properties and polarization directions are set for each integration point within the element, and the regions are divided and displayed with 8×8×8 integration points (the number of integration points is 512 points) as a unit. Also, in the upper part of Fig. 12 to be described later, in the case of 4×4×4 element division (the number of elements is 64), the same material properties and polarization directions are set for the integration points within the element, and the regions are divided and displayed with 4×4×4 elements as a unit. Note that the element division method is not limited to this, and it may be coarser than 4×4×4 (for example, 2×2×2) or finer (for example, 16×16×16). When the element division is made coarser, the accuracy of the calculated value of the ME constant decreases. However, in the optimization process, since the search is based on the relative change of the calculated value with the same element division, it is considered that there is no significant difference in the finally obtained optimal structure. On the other hand, when the element division is made finer, although the accuracy is improved, it requires calculation time and is likely to fall into various local solutions. And in the (001) pole figure, the orientation distribution (orientation distribution of the polarization direction) of a plurality of elements (in other words, the integration points included in each element) constituting the microstructure is represented by points. In this specification, the "(001) pole figure" is also simply referred to as the "(001) pole figure" or "pole figure", etc.

[0082] At the initial point O, the initial distribution of the polarization direction has substantially isotropy (see Fig. 6) and corresponds to the non-polarized state. Also, the material indices of all elements (all integration points) are set to "0.0" (FM phase) or "1.0" (FE phase). Note that the assignment (material arrangement) of the FE phase and the FM phase to each element is also determined using a random generator. At the initial point O, macroscopically, there is no polarity, and it is in a magnetically and electrically neutral state. At this time, the ME effect does not occur, and the macro-homogenized ME constant a 11 becomes zero.

[0083] Then, the macro-homogenized material properties obtained from equations (5) to (10) are evaluated from the above microstructural model. Specifically, the gradient vector of the objective function in the steepest descent method is estimated using specific increments of Euler angles and material indices. Then, the microstructure is updated based on the gradient vector and a specific displacement amount, and for the updated new microstructure, the macro-homogenized ME constant a 11 is newly obtained.

[0084] Such a calculation process (microstructure update process) using the steepest descent method is repeated until the variation of the macro-homogenized ME constant, which is the objective function, becomes sufficiently small (for example, until the change rate of the macro-homogenized ME constant is below a reference value). In this embodiment, when the number of trials (in other words, the number of repetitions) n reaches 1000, the variation of the macro-homogenized ME constant becomes sufficiently small (see Figure 5).

[0085] Specifically, first, through multi-scale optimization, the macro-homogenized ME constant a 11 rapidly increases until the number of trials n approaches about 50. And at point A where the number of trials n reaches about 300, the macro-homogenized ME constant a 11 reaches 58.7 (nNs / VC). This value "58.7 (nNs / VC)" is the maximum value of the macro ME constant obtained in the research before the filing of this application for a multiferroic material composed of BTO / CFO with a microstructural uniform orientation laminated structure.

[0086] At point A, in the (001) pole figure (refer to the column of point A in Figure 6), the polarization directions of the FE phase (blue) are in a plane perpendicular to the y1 axis, and they are arranged approximately linearly (in other words, rod-shaped) along the y1 axis. On the other hand, most of the polarization directions of the FM phase (red) are inclined in the positive or negative direction of the y1 axis with respect to the y2 axis. Note that the (001) pole figure is measured using, for example, the electron backscatter diffraction method (EBSD method) or the X-ray diffraction method, etc.

[0087] After that, as shown in FIG. 5, the macrohomogenization ME constant a 11 continued to increase beyond the maximum value (58.7) of the macro ME constant of the multiferroic material composed of uniformly oriented laminated BTO / CFO. At point B where the number of trials n reached 1000, it became 5.0% larger than the maximum value. That is, it was confirmed that there exists a new microstructure capable of obtaining a macro ME constant exceeding the maximum value of the macro ME constant when the microstructure is the conventional structure (specifically, the uniformly oriented laminated structure). At this time, in the (001) pole figure of FIG. 6, the polarization directions (blue) of the FE phase are concentrated in two orientation regions A1 and A2, and the polarization directions (red) of the FM phase are concentrated in four orientation regions B1 to B4.

[0088] FIG. 7 is a diagram showing the arrangement (material index ξ) and the distribution of the polarization directions of the FM phase and the FE phase in the optimized microstructure at point B in FIG. 6. In the grayscale display of FIG. 7, in the diagram showing the arrangement (phase composition) of the FM phase and the FE phase in the microstructure, the FE phase is displayed in a relatively dark color, and the FM phase is displayed in a relatively light color.

[0089] Here, in this specification, a method of indicating the polarization directions of the FE phase and the FM phase in the optimized microstructure of the multiferroic material structure by color will be briefly described. The "color mapping of the (001) pole figure" at the bottom of FIG. 7 is a diagram for indicating the polarization direction by hue. The left pole figure in the "color mapping of the (001) pole figure" shows the inclination with respect to the positive direction of the y3 axis (a view from the positive direction of the y3 axis, and those having an inclination component of the polarization direction in the positive direction of the y3 axis), and the right pole figure shows the inclination with respect to the negative direction of the y3 axis (a view from the negative direction of the y3 axis, and those having an inclination component of the polarization direction in the negative direction of the y3 axis). Both of these figures are made to be able to map the orientation by color, and the inclination with respect to the y1 axis direction and the inclination with respect to the y2 axis direction are shown using a circular gradient. The color becomes brighter as it goes in the positive direction of the y3 axis and darker as it goes in the negative direction of the y3 axis.

[0090] Also, with respect to the y1 axis, red is zone - distributed around approximately 0 degrees, green around approximately 120 degrees, and blue around approximately 240 degrees. Between red (approx. 0 degrees) and green (approx. 120 degrees), between green (approx. 120 degrees) and blue (approx. 240 degrees), and between blue (approx. 240 degrees) and red (approx. 0 degrees (i.e., 360 degrees)), there are new mixed - color hues. That is, the counter - clockwise angle from the y1 axis of the main hues and color synthesis by RGB are as follows. · Red 0 degrees (255, 0, 0) · Yellow 60 degrees (255, 255, 0) · Green 120 degrees (0, 255, 0) · Cyan 180 degrees (0, 255, 255) · Blue 240 degrees (0, 0, 255) · Magenta 300 degrees (255, 0, 255) · Orange 45 degrees (230, 121, 40) · Violet 280 degrees (167, 87, 168)

[0091] As a result, for example, the intermediate color orange has a positive y1 and a positive y2 and is distributed in a direction approximately 45 degrees from the y1 axis. Therefore, those showing the color representation of orange in the figure indicate an inclination in this direction. Those showing the color representation of other colors also indicate the direction shown by the color in the color mapping of the polar diagram in the same way, indicating that the polarization azimuth is inclined in that direction. Note that the "color" described in words in each figure is a rough representation for the convenience of illustration and does not only show that "color".

[0092] In the microstructure at point B, in many phases, the material index ξ was either approximately 0.0 or 1.0, and the content ratios of the two phases were approximately uniform. Also, as shown by the microstructure in the upper row (the column of combinations of each phase) of Fig. 7, no regularity was recognized in the phase composition of the FM phase and the FE phase in the microstructure at point B. On the other hand, regarding the polarization orientation, there was a clear difference in the orientation regions in the (001) pole figure between the FM phase and the FE phase. Specifically, as shown by the (001) pole figure in the upper row of Fig. 7, the polarization orientation of the FM phase belongs to four orientation regions B1 to B4 existing in the positive or negative direction of the y1 axis, while the polarization orientation of the FE phase belongs to two orientation regions A1 and A2 existing in the positive or negative direction of the y2 axis. The orientation regions B1 to B4 are regions existing in each of the four quadrants and symmetric (line symmetry or point symmetry) to each other with respect to the coordinate axes or the origin, and the orientation regions A1 and A2 are regions existing on the coordinate axes (here, on the y2 axis) and point-symmetric to the origin.

[0093] Specifically, the distribution of the polarization orientation of the microstructure at point B optimized using the steepest descent method is · In the (001) positive pole figure, the FE phase (green in Fig. 7) oriented in the positive direction of the y2 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FE phase (blue in Fig. 7) oriented in the negative direction of the y2 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (orange in Fig. 7) oriented in the positive direction of the y1 axis, the positive direction of the y2 axis (i.e., the first quadrant) and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (green in Fig. 7) oriented in the negative direction of the y1 axis, the positive direction of the y2 axis (i.e., the second quadrant) and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (light blue in Fig. 7) oriented in the negative direction of the y1 axis, the negative direction of the y2 axis (i.e., the third quadrant) and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (purple in Fig. 7) oriented in the positive direction of the y1 axis, the negative direction of the y2 axis (i.e., the fourth quadrant) and the positive direction (or negative direction) of the y3 axis, and It is composed of. In other words, the microstructure optimized for the multiferroic material composed of BTO / CFO is composed of the FM phase and the FE phase as described above.

[0094] Also, in the central figure at the lower part of FIG. 7, the orientation of each integration point (the orientation of the FM phase or the polarization orientation of the FE phase) of the 8×8×8 integration points is represented by the hue. Thus, the orientation of each integration point in the microstructure optimized in the first stage can be understood. The meaning of the orientation represented by the hue is the orientation shown by the hue in the left pole figure and the right pole figure in the “(001) pole figure color mapping” at the lower part of FIG. 7, as described in the explanation of the above “(001) pole figure color mapping”. For details of the polarization orientation of each FM phase and FE phase, refer to FIG. 9 (Euler angles).

[0095] Also, in the microstructure at point B, there is no regularity in the arrangement of the polarization orientation of the FM phase and the polarization orientation of the FE phase (refer to the microstructure in the lower part of FIG. 7). However, when analyzing the numerical values of the polarization orientation, that is, the Euler angles, the inventor of the present application found that the microstructure is classified into four rectangular regions 51 to 54 along the y3 axis, and these four rectangular regions 51 to 54 are periodically repeated (refer to FIG. 8). Specifically, all regions respectively have an FE phase with a specific polarization orientation in one orientation region A i and FM phases with polarization orientations in two orientation regions B k ,B l , that is, the inventor of the present application found that all rectangular regions are respectively composed of three types of polarization orientations.

[0096] FIG. 9 is a diagram showing the combination of the polarization orientations of the FM phase and the FE phase in each rectangular region 51 to 54 in the optimized microstructure at point B in FIG. 6. In FIG. 9, the average value of the Euler angles of the polarization orientations of each orientation region is shown.

[0097] The combination of the FE phase and the FM phase depends on the rectangular region. For example, focusing on the rectangular region 51, the polarization direction of the FE phase belongs to the orientation region A1, and the polarization direction of the FM phase belongs to the orientation regions B3 and B4. Similarly, other rectangular regions have the specified combination between the FM phase and the FE phase. And in the rectangular region 51, the polarization directions of the FM phase and the FE phase face outward from each other, and also in the rectangular region 53, the polarization directions of the FM phase and the FE phase face outward. In contrast, the polarization directions of the rectangular regions 52 and 54 face inward from each other.

[0098] And as shown in FIG. 6, the macroscopic homogenized ME constant at point B is 61.8, and a macroscopic ME constant exceeding the maximum value (58.7) obtained in the research before the filing of the present application for a multiferroic material composed of BTO / CFO with a microstructure as a uniform orientation laminated structure is obtained.

[0099] As described above, in the present embodiment, in optimizing the microstructure of the multiferroic material, a calculation process is performed to sequentially change the microstructure using an extreme value search method to maximize the macroscopic ME constant. As a result, for a multiferroic material made of a predetermined material, when the microstructure is set to a predetermined structure, a macroscopic ME constant exceeding the maximum value of the macroscopic ME constant of the multiferroic material obtained in the research before the filing of the present application is obtained, and it is possible to obtain a microstructure of a new structure different from the predetermined structure. For example, in the above embodiment, for a multiferroic material composed of BTO / CFO, when the microstructure is a uniform orientation laminated structure, a macroscopic ME constant exceeding the maximum value (58.7) of the macroscopic ME constant obtained in the research before the filing of the present application is obtained, and a microstructure of a new structure different from the uniform orientation laminated structure is obtained. That is, it is possible to provide a method for optimizing the microstructure capable of obtaining a new microstructure having a larger macroscopic ME constant compared to the conventional structure (uniform orientation laminated structure). Also, it is possible to provide a multiferroic material structure having a new microstructure with a larger macroscopic ME constant.

[0100] Now, referring back to Fig. 5 again.

[0101] In this embodiment, multi-scale optimization is performed in two stages.

[0102] Specifically, when the distribution in the (001) pole figure obtained from the microstructure when the macro-homogenized ME constant is maximized in the first stage is a specific pattern (described later), the optimization process of the second-stage microstructure is performed. Hereinafter, the criteria for determining whether to perform the optimization process of the second stage and the like will be described.

[0103] Fig. 10 is a diagram for explaining the criteria for determining whether to perform the optimization of the second-stage microstructure. Fig. 10(A) shows the (001) pole figure obtained from the microstructure in the initial state where the material arrangement and polarization orientation are random. As described above, optimization by the extreme value search method is performed for such a microstructure, and when the convergence determination conditions such as the change rate of the macro material properties (macro-homogenized ME constant) becoming equal to or less than the reference value are satisfied, the first stage of the microstructure optimization ends.

[0104] Then, in the pole figure obtained from the microstructure optimized in the first stage (the pole figure representing the orientation distribution of the polarization directions of the FE phase and the FM phase), it is confirmed whether or not there is localization of the polarization direction, that is, whether or not the distribution of the polarization directions of each phase (the orientation distribution of the material) is a specific pattern. The "specific pattern" (localization of the polarization direction) is, for example, a state (pattern) in which the polarization directions of the FE phase and the FM phase (here, 512 polarization directions) are concentrated at a predetermined ratio or more in each of a plurality of specific regions within a predetermined angle. The "predetermined angle" is preferably 30 to 60 degrees, more preferably 50 degrees. Also, the predetermined ratio is preferably 5 to 20%, more preferably 10%. These numerical values were found by the present inventor based on the inflection points of the curve shown in Fig. 16(B) described later and experience.

[0105] For example, in the upper part of FIG. 10(B), there is localization of orientation in the pole figure, and the distribution in the pole figure has a specific pattern. When such a pole figure is obtained from the micro-structure optimized in the first stage, it is considered possible to perform further optimization on the micro-structure when the macro-homogenized ME constant is maximized in the first stage, and the optimization process of the second stage is carried out. In the present embodiment (regarding the multi-ferroic material of BTO / CFO), as shown in FIG. 6, orientation groups (orientation groups of the FM phase) are formed in each of the four quadrants in the (001) pole figure, and two orientation groups (orientation groups of the FE phase) are formed along the y2 axis. And for each of the six orientation groups, it is obtained by analysis that the orientation difference is within 50 degrees and the orientation of 10% or more of the total number of orientations (all integration points) is concentrated. That is, it is determined that the distribution in the (001) pole figure (refer to the pole figure at point B in FIG. 6) obtained from the micro-structure when the macro-homogenized ME constant is maximized in the first stage has a specific pattern. Then, the optimization process of the micro-structure in the second stage is carried out.

[0106] In the upper part of Fig. 10(C), in the pole figure, the orientations are discretely distributed in a plurality of regions, but the range of a predetermined angle is wide, and it is difficult to directly find a specific pattern as in Fig. 10(B). However, instead of the entire pole figure, for each discrete region, it is possible to confirm the presence or absence of localization of the orientation within the region. That is, when the polarization orientations of the FE phase and the polarization orientations of the FM phase are concentrated at a predetermined ratio or more in a local ratio based on the number of orientations within the region in each of a plurality of partial specific regions within a predetermined angle in the discrete region, it is determined that there is partial localization of the orientation within the region. A secondary pattern in which the orientation is localized within the region is regarded as a specific pattern, simplified in the same manner as in the case of Fig. 10(B), and the second-stage optimization process is carried out. In the present embodiment (regarding the PZT / CFO multiferroic material), as shown in Figs. 23(A) and 24(A), a linear orientation group (the orientation group of the FE phase) along the y2 axis and two arc-shaped orientation groups (the orientation groups of the FM phase) inclined with respect to the y1 axis are formed. The orientation difference in any of the orientation groups is 100 degrees or more, and it is not a direct specific pattern. However, as shown in Fig. 23(B), in the orientation group of the FE phase, the orientations are concentrated at a ratio of about 20% in two regions where the orientation difference is within 30 degrees, and in the two orientation groups of the FM phase, the orientations are concentrated at a ratio of about 20% in two regions where the orientation difference is within 30 degrees respectively, as obtained by analysis. That is, it is determined that there is partial localization of the orientation within the orientation group, and a secondary pattern in which the orientation is localized within the orientation group is regarded as a specific pattern. Then, the second-stage optimization process of the microstructure is carried out.

[0107] On the other hand, in Fig. 10(D), there is no overall localization of the orientation in the pole figure, and there is no partial localization of the orientation in the discrete region, and the distribution in the pole figure is different from a specific pattern. When such a pole figure is obtained from the microstructure optimized in the first stage, the microstructure when the macro-homogenized ME constant is maximized in the first stage is regarded as the optimal structure, and here, the optimization calculation of the microstructure ends.

[0108] In the second stage, the microstructure (the microstructure at point B in Fig. 5) when the macro-homogenized ME constant is maximized using the steepest descent method in the first stage is simplified (in other words, cleaned), and using the obtained microstructure as a new variable, iterative calculations using the steepest descent method are performed again.

[0109] Specifically, the microstructure when the macro-homogenized ME constant is maximized in the first stage is simplified using the following three methods.

[0110] First, for each orientation region (azimuth region) A1, A2, B1 - B4 in the (001) pole figure (see Fig. 7) obtained from the microstructure at point B, a representative value (representative azimuth) of the orientation is determined, and the orientations of all integration points within each orientation region in a specific pattern are corrected (replaced) with the representative value. That is, the variation within each orientation region is eliminated, and the orientation effect on the macro material properties (macro-homogenized ME constant) is sharpened. In this embodiment, the average value is adopted as the "representative value". Note that it is not limited to this, and for example, the median value, maximum value, minimum value, or most frequent value, etc. may be adopted as the representative value.

[0111] Specifically, in each orientation region, the Euler angles θ, φ of the final optimized microstructure in the first stage (specifically, the optimized microstructure at point B in Fig. 5) are corrected (cleaned) to their average values and reset as new variables in the steepest descent method. For example, for the FM phase, the Euler angle θ is reset to 39°, 141°, 219°, and 321°, and the Euler angle φ is reset to 75.5° and 104.5°. For the FE phase, the Euler angle θ is reset to 90° and 270°, and the Euler angle φ is reset to 63.5° and 116.5°. That is, the FM phase and FE phase of the microstructure are rearranged. As a result of cleaning the polarization orientation, the FM phase becomes 4 points in the (001) pole figure, and considering the positive and negative directions of the y3 axis, it includes 8 polarization orientations. The FE phase becomes 2 points in the (001) pole figure and includes 4 polarization orientations.

[0112] In addition, a material index (material constant) that quantifies the mixed state of the FE phase and the FM phase is binarized based on a threshold value. Specifically, the material index at each integration point of the microstructure at point B is replaced with either "0.0" or "1.0" (specifically, the closer value of "0.0" and "1.0"). For example, when the material index is "0.1", it is replaced with "0.0", and when the material index is "0.9", it is replaced with "1.0".

[0113] Furthermore, regarding the material arrangement of the FE phase and the FM phase in the microstructure at point B, it is simplified based on connectivity (the connection of materials in each axial direction in the rectangular coordinate system). That is, the material arrangements of the FE phase and the FM phase are rearranged to have a simpler arrangement.

[0114] Then, using the steepest descent method, iterative calculations are performed again with the microstructure simplified (cleaned) as described above as a new variable (new initial state). In this embodiment, when simplifying the microstructure, in addition to averaging the crystal orientations in the pole figure and binarizing the material index, the material arrangement is rearranged, but it is not limited to this, and the rearrangement of the material arrangement may not be performed.

[0115] As a result of performing the calculation process to maximize the macro-homogenized ME constant with the simplified microstructure as a new variable, in this embodiment, when the number of trials n reached 1250 times (see point C in FIG. 5), the iterative calculations ended. The details of the iterative calculations by the steepest descent method in the second stage are the same as those in the first stage, and the description is omitted.

[0116] As a result of optimizing the microstructure in the second stage, as shown in FIG. 5, the macro-homogenized ME constant of the optimized microstructure at point C is 71.2 (nNs / VC), which is 21% larger than the macro-homogenized ME constant at point A (that is, the maximum value of the macro ME constant when the microstructure is a uniform orientation laminated structure composed of BTO / CFO, which is 58.7).

[0117] FIG. 11 is a conceptual diagram showing a (001) pole figure obtained from an optimized microstructure for a multiferroic material composed of BTO / CFO. Further, FIG. 12 is a diagram showing the arrangement (material index) of the FM phase and the FE phase and the distribution of the polarization directions in the optimized microstructure at point C in FIG. 6.

[0118] Hereinafter, the optimized microstructure at point C in FIG. 6 will be described.

[0119] After point B, there is no change in the phase composition of the microstructure, and the phase composition holds the microstructure rearranged by the cleaning process at point B until point C. That is, in the optimized microstructure at point C optimized for the multiferroic material composed of BTO / CFO, as shown in the upper microstructure in FIG. 12, the FE phase and the FM phase are alternately arranged (i.e., not a two-layer structure) and have regularity. Specifically, the FE phases are not adjacent to each other (not continuously arranged), the FM phases are not adjacent to each other, and the connectivity indicating the connection relationship (connection of each material) between the FE phase and the FM phase is "0-0" (in other words, the FE phase and the FM phase are arranged so that the same material does not continue on all of the y1-axis to y3-axis). Also, the content ratio of the FE phase in the entire composite material is 50%.

[0120] Also, in the microstructure optimized for the multiferroic material composed of BTO / CFO, in the (001) positive pole figure, the polarization directions of the FE phase and the polarization directions of the FM phase are distributed so as to concentrate on each of a plurality of orientation regions 40 (see FIG. 11) that are discrete from each other inside the periphery of the polar coordinates.

[0121] Here, FIG. 40 is a conceptual diagram showing the (001) pole figure of the microstructure of the conventional structure. For example, when the microstructure is a polycrystalline random structure, as shown in FIG. 40(A), the polarization directions of the FE phase and the FM phase are randomly dispersed and distributed. When the microstructure is a two-layer structure, as shown in FIG. 40(B), the polarization directions of the FE phase and the FM phase concentrate only at the origin, or as shown in FIG. 40(C), they concentrate only at two points, i.e., the intersection of the periphery of the polar coordinates and the y2 axis and the origin. In FIG. 40(C), for the sake of illustration, the regions where the polarization directions of the FE phase and the FM phase concentrate protrude from the periphery of the polar coordinates, but actually, these regions do not protrude from the periphery of the polar coordinates and exist on the periphery.

[0122] Thus, in the microstructure optimized in this embodiment, the distributions of the FE phase and the FM phase are completely different from the (001) pole figure of the microstructure of the conventional structure. With a microstructure having such a distribution, it is possible to provide a multiferroic material with an excellent macro ME constant as compared with at least a multiferroic material structure of a polycrystalline random structure.

[0123] More specifically, the polarization directions of the FE phase and the FM phase are distributed such that a predetermined ratio (e.g., 10%) or more of all the integration points concentrates in each of a plurality of specific regions (orientation regions) 40 (see FIG. 11) where the azimuthal difference is within a predetermined angle (e.g., 50 degrees). Specifically, as shown in the upper pole figure of FIG. 12, the optimized microstructure is composed of the FM phase belonging to four orientation regions B1 to B4 that exist in the four quadrants and are symmetric with respect to the coordinate axes or the origin, and the FE phase belonging to two orientation regions A1 and A2 that exist on the y2 axis (the second axis) and are point-symmetric with respect to the origin. The polarization directions of the FM phase and the FE phase slightly change from the polarization direction at point B (see FIG. 7).

[0124] In addition, in the case of the optimized microstructure (point C) at the second stage for the multiferroic material composed of BTO / CFO, as shown in the (001) positive electrode pole figure at the bottom of Fig. 12, the distribution of the polarization orientations of the optimized microstructure is · an FE phase (green in Fig. 12) oriented in the positive direction of the y2 axis and the positive direction (or negative direction) of the y3 axis in the figure, · an FE phase (blue in Fig. 12) oriented in the negative direction of the y2 axis and the positive direction (or negative direction) of the y3 axis in the figure, · an FM phase (orange in Fig. 12) oriented in the positive direction of the y1 axis, the positive direction of the y2 axis (i.e., the first quadrant), and the positive direction (or negative direction) of the y3 axis in the figure, · an FM phase (green in Fig. 12) oriented in the negative direction of the y1 axis, the positive direction of the y2 axis (i.e., the second quadrant), and the positive direction (or negative direction) of the y3 axis in the figure, · an FM phase (blue in Fig. 12) oriented in the negative direction of the y1 axis, the negative direction of the y2 axis (i.e., the third quadrant), and the positive direction (or negative direction) of the y3 axis in the figure, · an FM phase (purple in Fig. 12) oriented in the positive direction of the y1 axis, the negative direction of the y2 axis (i.e., the fourth quadrant), and the positive direction (or negative direction) of the y3 axis in the figure, and is composed of.

[0125] Also, in the central figure at the bottom of Fig. 12, the orientation of each of the 4×4×4 elements (the polarization orientation of the FM phase or the polarization orientation of the FE phase) is represented using the hue. Thereby, the orientation of each integration point in the microstructure optimized at the second stage can be known. Note that the meaning of the orientation represented by the hue is the orientation indicated by the hue in the left pole figure and the right pole figure in the "Color mapping of the (001) pole figure" at the bottom of Fig. 12, as described in the explanation of the "Color mapping of the (001) pole figure" above. For details of the polarization orientations of each FM phase and FE phase, refer to Fig. 14 (Euler angles).

[0126] Also, as shown in Fig. 13, the microstructure optimized at the second stage is classified into four rectangular regions 61 to 64 along the y3 axis, and these four rectangular regions 61 to 64 are periodically repeated.

[0127] Further, FIG. 14 is a diagram showing combinations of polarization directions of the FM phase and the FE phase in each rectangular region 61 to 64 in the optimized microstructure at point C. In FIG. 14, it can be confirmed that the Euler angle φ is larger than the Euler angle φ (see FIG. 9) at point B.

[0128] Here, hereinafter, the influence of the specific polarization direction averaged as described above on the ME effect will be explained.

[0129] First, the influence of the polarization direction of the FM phase on the macro-homogenized ME constant will be described. FIG. 15 is a diagram showing changes in the (001) pole figure when the Euler angle φ of the FM phase is changed from 0° to 90°. The Euler angle φ of the FM phase is changed from 0° to 90° while maintaining the initial value of the Euler angle θ. Accordingly, in the (001) pole figure, each distance from the center to each point of the FM phase changes (specifically, becomes longer).

[0130] Here, the macro-homogenized ME constant a 11 is defined as a constant that associates the input of the magnetic field H1 on the first axis with the output of the electric flux density (electric displacement) D1, or a constant that associates the input of the electric field E1 on the first axis with the output of the magnetic potential B1. Here, focusing on the former case, the internal strain and electric flux density of the FE phase in the microstructure when an external magnetic field is applied to the macrostructure will be described.

[0131] The electric flux density D1 is generated in the FE phase using the strain ε ij and the piezoelectric stress constant e 1ij . When the polarization direction of the FE phase corresponds to the y3 axis of the microstructure coordinate system, that is, when the Euler angles φ = 0° and θ = 90°, only two components e 113 , e 131 become non-zero, and the other components become zero. On the other hand, when the polarization direction of the FE phase inclines to the y2 axis (φ = 63.5° or 116.5°, θ = 90°), two components of e 112 and e 121 also become non-zero, as well as e 113 and e 131becomes non-zero. As a result, two shear strains ε 31 , ε 12 govern the generation of the electric flux density D1.

[0132] FIG. 16 is a diagram showing the changes in the strain ε 31 , ε 12 and the electric flux density D1 of the FE phase with respect to the Euler angle φ of the FM phase. FIG. 16(A) shows the change in the strain ε 31 , ε 12 , and FIG. 16(B) shows the change in the electric flux density D1.

[0133] The strains ε 31 , ε 12 occur in the FE phase through transmission from the FM phase deformed by the magnetic effect in response to the external magnetic field H1 in the macrostructure. Note that the magnetic field H1 is set to, for example, 10 MA / m. In FIG. 16(A), due to the direction dependence of the piezomagnetic effect and the piezoelectric effect (see FIGS. 2 and 3) and the magnitude relationship of the elastic stiffness between the FM phase and the FE phase, it is shown that the strain ε 31 and the strain ε 12 become different curves with respect to the Euler angle φ. Specifically, the strain ε 31 has a maximum peak near the Euler angle φ = 60°, while the strain ε 12 has a maximum peak at the Euler angle φ = 90°.

[0134] When the piezoelectric stress constants converted to the oblique coordinate system (φ = 63.5° or 116.5°, θ = 90°) are multiplied by these strains, the electric flux density D1 generated in the FE phase becomes a curve as shown in FIG. 16(B). Specifically, the electric flux density in response to the magnetic field, that is, the ME effect, is the two strains ε 31 , ε 12Due to the synergistic effect of [[ID=]], the FM phase has a maximum peak at the Euler angle φ = 75.5° corresponding to the optimized angle in Fig. 14. This indicates that the optimized microstructure can exhibit a large ME effect exceeding that of the conventional layered structure. That is, in the layered structure, only one component of the micro-internal strain acts on the macro ME effect. On the other hand, in the optimized structure, two components of the strain inside the microstructure contribute synergistically to the macro ME effect. Similarly, from the Euler angle θ of the FM phase, two micro shear strains act on the macro ME effect. The synergistic effect of the two strains is maximized at the specified angle, which corresponds to the optimized angle in Fig. 14.

[0135] Next, the influence of the polarization orientation of the FE phase on the macro-homogenized ME constant is also investigated. Fig. 17 is a diagram showing the change in the (001) pole figure when the Euler angle φ of the FE phase is changed from 0° to 90°. The Euler angle φ of the FE phase changes from 0° to 90° while maintaining the initial value of the Euler angle θ. Accordingly, in the (001) pole figure, the distance from the center to each point of the FE phase changes (specifically, it becomes longer).

[0136] Also, Fig. 18 shows the changes in the shear strain and electric flux density of the FE phase with respect to the Euler angle φ. Specifically, the shear strains ε 12 , ε 31 show different dependencies on the Euler angle φ (see Fig. 18(A)). Also, the electric flux density D1 shows a maximum peak at the specified angle (for example, 63.5°) corresponding to the optimized angle in Fig. 14 (see Fig. 18(B)). Note that a similar phenomenon can also be confirmed for the Euler angle θ of the FE phase.

[0137] As described above, in this embodiment, in the first stage, the microstructure when the macro ME constant is maximized by the extreme value search method is simplified, and the obtained microstructure is used as a new variable to perform iterative calculations by the extreme value search method again to maximize the macro ME constant. As a result, for example, in the microstructure optimized in the second stage for a multiferroic material composed of BTO / CFO, a macro ME constant that is 21% larger than that in the case of the conventional structure (uniformly oriented laminated structure) is obtained, and a macro ME constant that is 15% larger than that in the case of the optimized microstructure in the first stage is obtained (see Fig. 5). Therefore, it is possible to obtain a microstructure that gives an even larger macro ME constant.

[0138] In the above embodiment, the same type of extreme value search method (steepest descent method) is used in the first and second stages, but this is not essential, and different types of extreme value search methods may be used in the first and second stages. For example, the steepest descent method may be used as the extreme value search method in the first stage, and the conjugate gradient method may be used as the extreme value search method in the second stage.

[0139] <Modification Example> The embodiments of the present invention have been described above, but the present invention is not limited to the above-described embodiments, and various modifications are possible as long as they are within the scope described in the claims. For example, the following modification examples may be implemented.

[0140] In the above embodiment, a multiferroic material structure in which the FE phase is made of barium titanate (BTO) and the FM phase is made of cobalt ferrite (CFO) was exemplified, but it is not limited thereto. For example, a multiferroic material structure composed of a combination of materials as shown in the following (1) to (3) may be used.

[0141] (1) For example, a multiferroic material structure in which the FE phase is made of barium titanate (BTO) and the FM phase is made of Terfenol-D (registered trademark. Hereinafter referred to as "TFD") may be used. Note that TFD is a product of ETREMA Products, Inc., Tbx Dy 1-x A material that is a DyFe₂(x≒0.3) alloy and has a cubic crystal structure.

[0142] FIG. 19 is a diagram showing the relationship between the macro ME constant and the number of trials in the multi-scale optimization process for a multiferroic material composed of BTO / TFD. For the multiferroic material composed of BTO / TFD, when the microstructure is a uniformly oriented laminated structure, the maximum value of the macro ME constant obtained in the research before the filing of the present application was 122.7 (nNs / VC). FIG. 20 is a conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of BTO / TFD. FIG. 21(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point B in FIG. 19, and FIG. 21(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point C in FIG. 19.

[0143] Regarding the multiferroic material composed of BTO / TFD, multi-scale optimization was performed in the same manner as in the above embodiment, and the following results were obtained. Specifically, in the optimization process of the microstructure in the first stage, although it did not exceed the maximum value "122.7" of the macro ME constant in the conventional structure (for example, a uniformly oriented laminated structure), in the optimization process of the microstructure in the second stage, a macro ME constant (123.7) exceeding the maximum value "122.7" was obtained. More specifically, since the distribution in the pole figure obtained from the optimized microstructure at point B in FIG. 19 is a specific pattern, it is determined (decided) to perform the optimization process of the microstructure in the second stage. Then, a cleaning process (simplification process) is performed on the optimized microstructure in the first stage, and using the obtained microstructure as a new variable, the calculation process for maximizing the macro ME constant is executed again. As a result, a macro ME constant (123.7) exceeding the maximum value "122.7" of the macro ME constant in the conventional structure was obtained.

[0144] At this time, as shown in FIG. 21(B), the microstructure has regularity in the arrangement configuration of the FM phase and the FE phase. Specifically, in the microstructure optimized for the multiferroic material composed of BTO / TFD, the FM phase and the FE phase arranged along the y1 axis are alternately arranged. That is, for each of the FE phase and the FM phase, the same material (the same phase) is not continuously arranged on the y2 axis and the y3 axis, while the same material is continuously arranged on the y1 axis, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "1-1". Also, the content ratio of the FE phase in the entire composite material is 50%.

[0145] Also, in the microstructure optimized for the multiferroic material composed of BTO / TFD, in the (001) pole figure, the polarization directions of the FE phase and the FM phase are distributed so as to concentrate by a predetermined ratio (for example, 10%) or more in each of a plurality of specific regions (orientation regions) 43 (see FIG. 20) within a predetermined angle (for example, 50 degrees). Specifically, as shown in FIG. 21(B), the arrangement of the polarization directions of the microstructure optimized for the multiferroic material composed of BTO / TFD is · In the (001) positive pole figure at the lower part of FIG. 21(B), the FE phase and the FM phase (green in FIG. 21(B)) oriented in the positive direction of the y2 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FE phase and the FM phase (purple in FIG. 21(B)) oriented in the negative direction of the y2 axis and the positive direction (or negative direction) of the y3 axis, and are composed.

[0146] Thus, also for the multiferroic material composed of BTO / TFD, when the microstructure is a uniform orientation laminated structure, a macro ME constant exceeding the maximum value (122.7) of the macro ME constant obtained in the research before the filing of the present application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniform orientation laminated structure.

[0147] (2) Further, the FE phase may be made of lead zirconate titanate (Pb(Zr,Ti)O3; hereinafter referred to as "PZT"), and the FM phase may be a multiferroic material structure made of cobalt ferrite (CFO). Note that PZT is a material having a property that the piezoelectric constant becomes extremely large near the morphotropic phase boundary, and its crystal structure is a perovskite structure.

[0148] FIG. 22 is a diagram showing the relationship between the macro ME constant and the number of trials in the multi-scale optimization process for a multiferroic material composed of PZT / CFO. For the multiferroic material composed of PZT / CFO, when the micro-structure was a uniformly oriented laminated structure, the maximum value obtained in the research before the filing of the present application was 44.1 (nNs / VC). Further, FIG. 23(A) is a conceptual diagram showing the (001) pole figure obtained from the micro-structure in which the first-stage optimization process was performed for the multiferroic material composed of PZT / CFO. FIG. 23(B) is a conceptual diagram showing the (001) pole figure obtained from the micro-structure in which the second-stage optimization process was performed for the same material. Further, FIG. 24(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized micro-structure at point B in FIG. 19, and FIG. 24(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized micro-structure at point C in FIG. 19.

[0149] Regarding the multiferroic material structure composed of PZT / CFO, as a result of optimizing the microstructure in the same manner as in the above embodiment, in the first-stage optimization process, a macro ME constant exceeding the maximum value "44.1" of the macro ME constant in the conventional structure (uniformly oriented laminated structure) was obtained (see point B in Fig. 22). When the design requirements are satisfied with the obtained macro ME constant, the calculation can be terminated only with the first-stage optimization process. On the other hand, when further improving the macro ME constant, a cleaning process (simplification process) is performed on the optimized microstructure in the first stage, and with the obtained microstructure as a new variable, the calculation process for maximizing the macro ME constant is executed again. As a result, a macro ME constant of "54.8" (nNs / Vc) was obtained (see point C in Fig. 22).

[0150] At this time, as shown in Fig. 24(B), the microstructure has regularity in the arrangement configuration of the FM phase and the FE phase. Specifically, in the optimized microstructure of the multiferroic material composed of PZT / CFO, the FM phase and the FE phase arranged along the y1 axis are alternately arranged. That is, for each of the FE phase and the FM phase, the same material (the same phase) is continuously arranged along the y1 axis. Also, along the y2 axis, the same phase is alternately arranged so as not to be adjacent to each other (not continuously arranged), and along the y3 axis, the same phase is alternately arranged so as to be partially adjacent. Here, the content ratio of the FE phase in the entire composite material is 60%, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "2-1". Here, by setting the content ratio to 60%, the same phase is arranged so as to be partially adjacent along the y3 axis. However, when not considering the content ratio, in the two directions of the y2 axis and the y3 axis, the same phase is alternately arranged so as not to be adjacent to each other. The connectivity in this case is "1-1".

[0151] Also, as shown in Fig. 23(B), the polarization directions of the FE phase in the microstructure optimized for the multiferroic material composed of PZT / CFO belong to two orientation regions 41 that exist on the y2 axis (the second axis) in the (001) pole figure and are symmetric with respect to the origin in a point-symmetric manner. Further, the polarization directions of the FM phase belong to four orientation regions 42 that exist in the four quadrants in the (001) pole figure and are symmetric with respect to each other (line symmetry or point symmetry) with respect to the y1 axis (the first axis) or the origin.

[0152] Specifically, for the multiferroic material composed of PZT / CFO, the distribution of the polarization directions in the optimized microstructure is · In the (001) pole figure at the lower part of Fig. 24(B), the FE phase (black in Fig. 24(B)) oriented in the positive direction of the y2 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FE phase (white in Fig. 24(B)) oriented in the negative direction of the y2 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (brown in Fig. 24(B)) oriented in the positive direction of the y1 axis, the positive direction of the y2 axis, and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (pink in Fig. 24(B)) oriented in the positive direction of the y1 axis, the negative direction of the y2 axis, and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (green in Fig. 24(B)) oriented in the negative direction of the y1 axis, the positive direction of the y2 axis, and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (light blue in Fig. 24(B)) oriented in the negative direction of the y1 axis, the negative direction of the y2 axis, and the positive direction (or negative direction) of the y3 axis, and is composed of. By the microstructure showing such a distribution, it becomes possible to provide a multiferroic material having an excellent macro ME constant as compared with at least a multiferroic material structure of a polycrystalline random structure.

[0153] Thus, regarding the multiferroic material structure composed of PZT / CFO as well, it is possible to seek a microstructure that can obtain a larger macro ME constant. Specifically, for the multiferroic material composed of PZT / CFO, when the microstructure is a uniform orientation laminated structure, a macro ME constant exceeding the maximum value (44.1) of the macro ME constant obtained in the research before the filing of this application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniform orientation laminated structure.

[0154] (3) Further, the multiferroic material structure may be such that the FE phase is made of lead zirconate titanate (PZT) and the FM phase is made of Terfenol-D (TFD).

[0155] FIG. 25 is a diagram showing the relationship between the macro ME constant and the number of trials in the multi-scale optimization process for the multiferroic material composed of PZT / TFD. For the multiferroic material composed of PZT / TFD, when the microstructure is a uniform orientation laminated structure, the maximum value of the macro ME constant obtained in the research before the filing of this application was 92.9 (nNs / VC). Further, FIG. 26 is a conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of PZT / TFD. Further, FIG. 27(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point B in FIG. 25, and FIG. 27(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point C in FIG. 25.

[0156] Regarding the multiferroic material composed of PZT / TFD, multi-scale optimization was performed in the same manner as in the above-described embodiment, and the following results were obtained. Specifically, in the optimization process of the microstructure in the first stage, although it did not exceed the maximum value "92.9" of the macro ME constant in the conventional structure (for example, a uniform orientation laminated structure), in the optimization process of the microstructure in the second stage, a macro ME constant (94.9) exceeding the maximum value "92.9" was obtained.

[0157] The microstructure at this time has regularity in the arrangement configuration of the FM phase and the FE phase, as shown in the "material arrangement" in Fig. 27(B). Specifically, in the optimized microstructure of the multiferroic material composed of PZT / TFD, the FM phase and the FE phase are alternately arranged, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "0-0", similar to the multiferroic material composed of BTO / CFO. Also, the content ratio of the FE phase in the entire composite material is 50%.

[0158] Also, in the optimized microstructure of the multiferroic material composed of PZT / TFD, in the (001) pole figure, the polarization directions of the FE phase and the FM phase are distributed so as to concentrate at a predetermined ratio (for example, 10%) or more in each of a plurality of specific regions (orientation regions) 44 (see Fig. 26) within a predetermined angle (for example, 50 degrees). Specifically, as shown in the lower part of Fig. 27(B), the arrangement of the polarization directions of the optimized microstructure of the multiferroic material composed of PZT / TFD is · In the (001) positive pole figure in the lower part of Fig. 27(B), the FE phase and the FM phase (white in Fig. 27(B)) oriented only in the positive direction of the y3 axis, and · In the same figure, the FE phase and the FM phase (black in Fig. 27(B)) oriented only in the negative direction of the y3 axis, and · In the same figure, the FE phase and the FM phase (green in Fig. 27(B)) oriented in the positive direction of the y2 axis and the positive (or negative) direction of the y3 axis, and · In the same figure, the FE phase and the FM phase (purple in Fig. 27(B)) oriented in the negative direction of the y2 axis and the positive (or negative) direction of the y3 axis, and It is composed of

[0159] As described above, also regarding the multiferroic material composed of PZT / TFD, when the microstructure is a uniformly oriented laminated structure, a macro ME constant exceeding the maximum value (92.9) of the macro ME constant obtained in the research before the filing of the present application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniformly oriented laminated structure.

[0160] In particular, as can be seen from the above (1) and (3), in the optimization process of the microstructure in the first stage, even when the macro ME constant of the multiferroic material having the microstructure of the conventional structure is not exceeded, in the optimization process of the microstructure in the second stage, a macro ME constant exceeding it was obtained. That is, by re-optimizing the microstructure using the microstructure obtained by cleaning the microstructure optimized in the first stage as a new variable, it is possible to obtain a microstructure that can surely exceed the macro ME constant of the multiferroic material having the microstructure of the conventional structure (for example, a uniformly oriented laminated structure). That is, by performing multi-scale optimization in two stages, it is possible to obtain a microstructure that can surely exceed the macro ME constant of the multiferroic material having the microstructure of the conventional structure.

[0161] In FIG. 28, a list for each material combination of the optimized microstructure in the multiferroic material structure that exhibits the above-mentioned ME constant a 11 is shown. Note that the right figure in the (001) positive electrode point figure of FIG. 28 is a positive electrode point figure with the y2 axis as the normal direction, and the "(001) positive electrode point figure" in the claims corresponds to the left figure (positive electrode point figure with the y3 axis as the normal).

[0162] In FIG. 28, although the polar diagrams of the optimized microstructures differ according to the material combinations, in each case, the polarization directions of the piezoelectric phase or the piezomagnetic phase are inclined with respect to the input direction or the output direction. As a result, for a magnetic input or an electrical input, two or more shear components of the piezomagnetic constant or the piezoelectric constant become non-zero components, and as a result, magnetism and electricity can be converted through two or more shear strains. Therefore, while magnetism and electricity are converted through one shear strain in the conventional structure, it becomes possible to exhibit an excellent ME constant due to the synergistic effect of two or more shear strains in the optimized microstructure.

[0163] In the above embodiment, a multiferroic material structure that exhibits an ME constant in which the input direction and the output direction are parallel has been exemplified, but the present invention is not limited thereto. For example, an ME constant in which the input direction and the output direction are orthogonal (specifically, a 31 multiferroic material structure that exhibits may also be used. For example, an ME constant a 31 that associates a magnetic field H1 with an electric flux density D3, or an electric field E1 with a magnetic flux density B3. Here, as a multiferroic material structure that exhibits a 31 a multiferroic material structure composed of the material combinations shown in (4) to (7) below will be exemplified. As described in (4) to (6) below, for a multiferroic material structure that exhibits an ME constant a 31 it was possible to obtain a macro ME constant that greatly exceeds the maximum value of the macro ME constant of the conventional structure.

[0164] (4) For example, a multiferroic material structure in which the FE phase is made of BTO and the FM phase is made of CFO may be used.

[0165] FIG. 29 is a diagram showing the relationship between the macro ME constant and the number of trials in the multi-scale optimization process for a multiferroic material composed of BTO / CFO. For the multiferroic material composed of BTO / CFO, when the microstructure is a uniformly oriented laminated structure, the maximum value of the macro ME constant obtained in the research before the filing of the present application was 0.34 (nNs / VC). FIG. 30 is a conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of BTO / CFO. FIG. 31(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point B in FIG. 29, and FIG. 31(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point C in FIG. 29.

[0166] Regarding the multiferroic material composed of BTO / CFO, as a result of performing the multi-scale optimization process in the same manner as in the above embodiment, in the first-stage optimization process, a macro ME constant that greatly exceeds the maximum value "0.34" of the macro ME constant in the conventional structure (uniformly oriented laminated structure) was obtained (see point B in FIG. 29). Then, a cleaning process (simplification process) is performed on the optimized microstructure in the first stage, and using the obtained microstructure as a new variable, the calculation process for maximizing the macro ME constant is executed again. As a result, a macro ME constant of "75.9" (nNs / Vc) was obtained (see point C in FIG. 29).

[0167] At this time, the microstructure has regularity in the arrangement configuration of the FM phase and the FE phase, as shown in the "material arrangement" in FIG. 31(B). Specifically, in the optimized microstructure for the multiferroic material composed of BTO / CFO, the FM phase and the FE phase are alternately arranged so that the same phase is not adjacent to each other, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "0-0". Also, the content ratio of the FE phase in the entire composite material is 50%.

[0168] Also, as shown in FIG. 30, in the optimized microstructure of the multiferroic material composed of BTO / CFO, the polarization direction of the FE phase belongs to two orientation regions 45 that exist on the y1 axis (the first axis) in the (001) positive pole figure and are symmetric with respect to the origin. Also, the polarization direction of the FM phase also belongs to two orientation regions 46 that exist on the y1 axis in the (001) positive pole figure and are symmetric with respect to the origin. Note that these two orientation regions 46 exist inside (the origin side) of the two orientation regions 45, respectively.

[0169] Specifically, for the multiferroic material composed of BTO / CFO, the distribution of the polarization direction in the optimized microstructure is · In the (001) positive pole figure at the lower part of FIG. 31(B), the FE phase (red in FIG. 31(B)) oriented in the positive direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FE phase (light blue in FIG. 31(B)) oriented in the negative direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (brown in FIG. 31(B)) oriented in the positive direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (green in FIG. 31(B)) oriented in the negative direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and is composed of.

[0170] Thus, also for the multiferroic material composed of BTO / CFO, when the microstructure is a uniformly oriented laminated structure, a macro ME constant exceeding the maximum value (0.34) of the macro ME constant obtained in the research before the filing of the present application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniformly oriented laminated structure.

[0171] (5) Also, a multiferroic material structure in which the FE phase is composed of BTO and the FM phase is composed of TFD may be used.

[0172] FIG. 32 is a diagram showing the relationship between the macro ME constant and the number of trials in the multi-scale optimization process for a multiferroic material composed of BTO / TFD. For the multiferroic material composed of BTO / TFD, when the microstructure is a uniformly oriented laminated structure, the maximum value of the macro ME constant obtained in the research before the filing of the present application was 0.150 (nNs / VC). FIG. 33 is a conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of BTO / TFD. FIG. 34(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point B in FIG. 32, and FIG. 34(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point C in FIG. 32.

[0173] Regarding the multiferroic material composed of BTO / TFD, as a result of performing the multi-scale optimization process in the same manner as in the above-described embodiment, in the first-stage optimization process, a macro ME constant that greatly exceeds the maximum value "0.150" of the macro ME constant in the conventional structure (uniformly oriented laminated structure) was obtained (see point B in FIG. 32). Then, a cleaning process (simplification process) was performed on the optimized microstructure in the first stage, and using the obtained microstructure as a new variable, the calculation process for maximizing the macro ME constant was executed again. As a result, a macro ME constant of "123" (nNs / Vc) was obtained (see point C in FIG. 32).

[0174] At this time, the microstructure has regularity in the arrangement configuration of the FM phase and the FE phase, as shown in the "Material Arrangement" of FIG. 34(B). Specifically, in the microstructure optimized for the multiferroic material composed of BTO / TFD, the FM phase and the FE phase arranged along the y1 axis are alternately arranged. That is, for each of the FE phase and the FM phase, the same material (the same phase) is not continuously arranged on the y2 axis and the y3 axis, while the same material is continuously arranged on the y1 axis, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "1-1". Also, the content ratio of the FE phase in the entire composite material is 50%.

[0175] Also, as shown in FIG. 33, in the microstructure optimized for the multiferroic material composed of BTO / TFD, the polarization orientation of the FE phase belongs to two orientation regions 47 that exist on the y1 axis (the first axis) in the (001) positive pole figure and are symmetric with respect to the origin. Also, the polarization orientation of the FM phase belongs to one orientation region 48 that exists at the origin position in the (001) positive pole figure.

[0176] Specifically, for the multiferroic material composed of BTO / TFD, the distribution of the polarization orientation of the optimized microstructure is · In the lower (001) positive pole figure of FIG. 34(B), the FE phase (red in FIG. 34(B)) oriented in the positive direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FE phase (light blue in FIG. 34(B)) oriented in the negative direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (black in FIG. 34(B)) oriented only in the positive direction of the y3 axis, and is composed of these.

[0177] Thus, even for a multiferroic material composed of BTO / TFD, when the microstructure is a uniformly oriented laminated structure, a macro ME constant exceeding the maximum value (0.150) of the macro ME constant obtained in the research before the filing of the present application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniformly oriented laminated structure.

[0178] (6) Further, it may be a multiferroic material structure in which the FE phase is made of PZT and the FM phase is made of CFO.

[0179] FIG. 35 is a diagram showing the relationship between the macro ME constant and the number of trials in the multi-scale optimization process for a multiferroic material composed of PZT / CFO. For the multiferroic material composed of PZT / CFO, when the microstructure is a uniformly oriented laminated structure, the maximum value of the macro ME constant obtained in the research before the filing of the present application was 0.49 (nNs / VC). Further, FIG. 36(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the azimuth distribution by material, the arrangement of the polarization azimuth, and the color map of the azimuth in the optimized microstructure at point B in FIG. 35, and FIG. 36(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the azimuth distribution by material, the arrangement of the polarization azimuth, and the color map of the azimuth in the optimized microstructure at point C in FIG. 35. The conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of PZT / CFO is the same as the conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of BTO / CFO and is shown in FIG. 30.

[0180] Regarding the multiferroic material composed of PZT / CFO, as a result of performing the multi-scale optimization process in the same manner as the above-described embodiment, in the first-stage optimization process, a macro ME constant exceeding the maximum value "0.49" of the macro ME constant in the conventional structure (uniformly oriented laminated structure) was obtained (see point B in FIG. 35). Then, a cleaning process (simplification process) is performed on the optimized micro-structure in the first stage, and with the obtained micro-structure as a new variable, the calculation process for maximizing the macro ME constant is executed again. As a result, a macro ME constant of "53.3" (nNs / Vc) was obtained (see point C in FIG. 35).

[0181] At this time, the micro-structure has regularity in the arrangement configuration of the FM phase and the FE phase, as shown in the "material arrangement" in FIG. 36(B). Specifically, in the micro-structure optimized for the multiferroic material composed of PZT / CFO, the FM phase and the FE phase are alternately arranged so that the same phase is not adjacent to each other, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "0-0". Also, the content ratio of the FE phase in the entire composite material is 50%.

[0182] Further, as shown in FIG. 30, in the micro-structure optimized for the multiferroic material composed of PZT / CFO, the polarization orientation of the FE phase belongs to two orientation regions 45 that exist on the y1 axis (first axis) in the (001) positive pole figure and are symmetric with respect to the origin. Also, the polarization orientation of the FM phase also belongs to two orientation regions 46 that exist on the y1 axis in the (001) positive pole figure and are symmetric with respect to the origin.

[0183] Specifically, regarding the multiferroic material composed of PZT / CFO, the distribution of the polarization orientation of the optimized micro-structure is · In the (001) positive pole figure at the lower part of FIG. 36(B), the FE phase (red in FIG. 36(B)) oriented in the positive direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, an FE phase (light blue in Fig. 36(B)) oriented in the negative direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, · In the same figure, an FM phase (pink in Fig. 36(B)) oriented in the positive direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, · In the same figure, an FM phase (green in Fig. 36(B)) oriented in the negative direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, are configured.

[0184] Thus, even for a multiferroic material composed of PZT / CFO, when the microstructure is a uniformly oriented laminated structure, a macro ME constant exceeding the maximum value (0.49) of the macro ME constant obtained in the research before the filing of the present application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniformly oriented laminated structure.

[0185] (7) Further, it may be a multiferroic material structure in which the FE phase is made of PZT and the FM phase is made of TFD.

[0186] FIG. 37 is a diagram showing the relationship between the macroscopic ME constant and the number of trials in the multi-scale optimization process for a multiferroic material composed of PZT / TFD. Note that, for the multiferroic material composed of PZT / TFD, when the microstructure is a uniformly oriented laminated structure, the maximum value of the macroscopic ME constant obtained in the research before the filing of the present application was 0.190 (nNs / VC). Further, FIG. 38(A) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point B in FIG. 37, and FIG. 38(B) is a diagram showing the material arrangement of the FM phase and the FE phase, the orientation distribution by material, the arrangement of the polarization orientation, and the color map of the orientation in the optimized microstructure at point C in FIG. 37. Note that the conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of PZT / TFD is the same as the conceptual diagram showing the (001) pole figure obtained from the optimized microstructure for the multiferroic material composed of BTO / TFD and is shown in FIG. 33.

[0187] Regarding the multiferroic material composed of PZT / TFD, as a result of performing the multi-scale optimization process in the same manner as in the above embodiment, in the first-stage optimization process, a macroscopic ME constant that greatly exceeds the maximum value "0.190" of the macroscopic ME constant in the conventional structure (uniformly oriented laminated structure) was obtained (see point B in FIG. 37). Then, a cleaning process (simplification process) was performed on the optimized microstructure in the first stage, and using the obtained microstructure as a new variable, the calculation process for maximizing the macroscopic ME constant was executed again. As a result, a macroscopic ME constant of "92.8" (nNs / Vc) was obtained (see point C in FIG. 37).

[0188] At this time, the microstructure has regularity in the arrangement configuration of the FM phase and the FE phase, as shown in the "Material Arrangement" of FIG. 38(B). Specifically, in the microstructure optimized for the multiferroic material composed of PZT / TFD, the FM phase and the FE phase are alternately arranged so that the same phase does not adjacent to each other, and the connectivity indicating the connection relationship between the FE phase and the FM phase is "0-0". Also, the content ratio of the FE phase in the entire composite material is 50%.

[0189] Also, as shown in FIG. 33, in the microstructure optimized for the multiferroic material composed of PZT / TFD, the polarization orientation of the FE phase belongs to two orientation regions 47 that exist on the y1 axis (the first axis) in the (001) positive pole figure and are symmetric with respect to the origin, similar to the multiferroic material composed of BTO / TFD. Also, the polarization orientation of the FM phase belongs to one orientation region 48 that exists at the origin position in the (001) positive pole figure.

[0190] Specifically, for the multiferroic material composed of PZT / TFD, the distribution of the polarization orientation of the optimized microstructure is · In the (001) positive pole figure at the lower part of FIG. 38(B), the FE phase (red in FIG. 38(B)) oriented in the positive direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FE phase (light blue in FIG. 38(B)) oriented in the negative direction of the y1 axis and the positive direction (or negative direction) of the y3 axis, and · In the same figure, the FM phase (black in FIG. 38(B)) oriented only in the positive direction of the y3 axis are composed of.

[0191] Thus, also for the multiferroic material composed of PZT / TFD, when the microstructure is a uniform orientation laminated structure, a macro ME constant exceeding the maximum value (0.190) of the macro ME constant obtained in the research before the filing of the present application can be obtained, and it is possible to provide a multiferroic material structure having a microstructure with a new structure different from the uniform orientation laminated structure.

[0192] In Fig. 39, a for the cases exemplified in (4) to (7) above 31 shows a list for each material combination of the optimized microstructures in the multiferroic material structure that exhibits. In the right figure of the (001) positive pole figure in Fig. 39, the figure on the right side is a positive pole figure with the y2 axis as the normal direction, and the "(001) positive pole figure" in the claims corresponds to the figure on the left side (positive pole figure with the y2 axis as the normal direction). As shown in the list in Fig. 39, for the multiferroic material structure that exhibits the ME constant a 31 in the optimized microstructure, the polarization orientation of the FE phase is distributed so as to concentrate in two orientation regions that exist on one coordinate axis in the (001) positive pole figure and are at point-symmetric positions with respect to the origin. Also, the azimuthal distribution of the FM phase is distributed so as to concentrate in one or a plurality of regions that are discrete from each other on the periphery of the polar coordinates or on the coordinate axes in the (001) positive pole figure.

[0193] In Fig. 39, the pole figures of the optimized microstructures differ depending on the material combination, but in any case, the polarization orientation of the piezomagnetic phase is almost oriented along the y1 axis, and the polarization orientation of the piezoelectric phase is almost oriented along the y3 axis. As a result, for magnetic input or electrical input, the shear component functions in the piezomagnetic constant or piezoelectric constant, and as a result, magnetic and electrical can be converted through shear strain. Therefore, in the conventional structure, the vertical component with a small absolute value in the piezomagnetic constant or piezoelectric constant functions to convert magnetic and electrical, whereas in the optimized microstructure, by functioning the shear component with a large absolute value, it is possible to exhibit an excellent ME constant. When the piezomagnetic phase is CFO, since the polarization orientation of the piezoelectric phase or piezomagnetic phase is inclined with respect to the input direction or output direction, there is also an effect of converting magnetic and electrical through two or more shear strains and increasing the ME constant as their synergistic effect.

Explanation of symbols

[0194] 20 FE phase 30 FM phase

Claims

1. Construct a unit cell model of a microscopic structure composed of a piezoelectric phase and a piezomagnetic phase, Formulate the coupling of two scales between the microscopic structure and the macroscopic structure formed by periodically repeating and arranging the microscopic structure, and maximize the obtained macroscopic material property values. In an optimization method for the microscopic structure of a multiferroic material, Taking the macroscopic material property value as the objective function, using the microscopic structure as a variable, and using an extreme value search method, perform a calculation process of sequentially changing the microscopic structure to maximize the macroscopic material property value. When the distribution of the polarization directions of the piezoelectric phase and the piezomagnetic phase in the (001) positive pole figure obtained from the microscopic structure when the macroscopic material property value is maximized by the extreme value search method is a specific pattern in which the polarization directions of the piezoelectric phase and the piezomagnetic phase are concentrated in each of a plurality of specific regions, perform a simplification process on the microscopic structure, and then use the extreme value search method again to sequentially change the microscopic structure to perform a calculation process of maximizing the macroscopic material property value. The simplification process includes, for each azimuth region in the pole figure, determining any one of values including the average value, median value, maximum value, minimum value, or most frequent value as a representative value, and replacing the azimuths of the integration points within each azimuth region with the representative value. An optimization method for the microscopic structure of a multiferroic material, characterized by the above.

2. The simplification process is Performed when the distribution of the polarization directions of the piezoelectric phase and the piezomagnetic phase in the (001) positive pole figure obtained from the microscopic structure when the macroscopic material property value is maximized by the extreme value search method is a specific pattern in which the polarization directions of the piezoelectric phase and the piezomagnetic phase are concentrated by 5% or more in each of a plurality of specific regions within an angular range of 30 to 60 degrees. The optimization method for the microscopic structure of a multiferroic material according to Claim 1, characterized by the above.

3. When the distribution in the (001) positive pole figure is different from the specific pattern, end the optimization process of the microscopic structure. The optimization method for the microscopic structure of a multiferroic material according to Claim 2, characterized by the above.

4. A multiferroic material structure composed of a piezoelectric phase made of barium titanate and a piezomagnetic phase made of cobalt ferrite, and exhibiting electromagnetic constants in which the input direction and the output direction are parallel. In its microscopic structure, The piezoelectric phase and the piezomagnetic phase are alternately arranged so that the same phase is not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to four orientation regions that exist in the four quadrants in the (001) pole figure and are symmetric with respect to the coordinate axes or the origin. A multiferroic material structure characterized by this.

5. A multiferroic material structure composed of a piezoelectric phase made of barium titanate and a piezomagnetic phase made of Terfenol-D, which exhibits electromagnetic constants with the input direction and the output direction being parallel. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are arranged such that the same phase is continuously arranged in one of the three orthogonal coordinate axes, and in the remaining two directions, the same phases are arranged alternately so as not to be adjacent to each other. The polarization direction of the piezomagnetic phase and the polarization direction of the piezoelectric phase each belong to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. A multiferroic material structure characterized by this.

6. A multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of cobalt ferrite, which exhibits electromagnetic constants with the input direction and the output direction being parallel. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are arranged such that the same phase is continuously arranged in one of the three orthogonal coordinate axes, and in the remaining two directions, the same phases are arranged alternately so as not to be adjacent to each other, or in one of the two directions, the same phases are not adjacent to each other and in the other direction, the same phases are partially adjacent. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to four orientation regions that exist in the four quadrants in the (001) pole figure and are symmetric with respect to the coordinate axes or the origin. A multiferroic material structure characterized by this.

7. A multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of Terfenol-D, which exhibits electromagnetic constants with the input direction and the output direction being parallel. In its microscopic structure, The piezoelectric phase and the piezomagnetic phase are alternately arranged such that the same phase does not adjacent to each other. The polarization direction of the piezomagnetic phase and the polarization direction of the piezoelectric phase each belong to one orientation region existing at the position of the origin and two orientation regions existing on the coordinate axes and at positions point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. A multiferroic material structure characterized by this.

8. A multiferroic material structure composed of a piezoelectric phase made of barium titanate and a piezomagnetic phase made of cobalt ferrite, which exhibits electromagnetic constants with the input direction and the output direction being orthogonal, In its microscopic structure, The piezoelectric phase and the piezomagnetic phase are alternately arranged such that the same phase does not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions existing on the coordinate axes and at positions point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to two orientation regions existing on the coordinate axes and at positions point-symmetric with respect to the origin in the (001) pole figure. A multiferroic material structure characterized by this.

9. A multiferroic material structure composed of a piezoelectric phase made of barium titanate and a piezomagnetic phase made of Terfenol-D, which exhibits electromagnetic constants with the input direction and the output direction being orthogonal, In its microscopic structure, The piezoelectric phase and the piezomagnetic phase are arranged such that the same phase is continuously arranged in one direction among the three orthogonal coordinate axes, and alternately arranged in the remaining two directions such that the same phase does not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions existing on the coordinate axes and at positions point-symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to one orientation region existing at the position of the origin in the (001) pole figure. A multiferroic material structure characterized by this.

10. A multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of cobalt ferrite, which exhibits electromagnetic constants with the input direction and the output direction being orthogonal, In its microscopic structure, The piezoelectric phase and the piezomagnetic phase are alternately arranged such that the same phase does not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure. A multiferroic material structure characterized by the above. **Claim 11**: A multiferroic material structure composed of a piezoelectric phase made of lead zirconate titanate and a piezomagnetic phase made of Terfenol-D, which exhibits electromagnetic constants with the input direction and the output direction being orthogonal. In its microscopic structure, the piezoelectric phase and the piezomagnetic phase are alternately arranged so that the same phases do not adjacent to each other. The polarization direction of the piezoelectric phase belongs to two orientation regions that exist on the coordinate axes and are symmetric with respect to the origin in the (001) pole figure representing the orientation distribution. The polarization direction of the piezomagnetic phase belongs to one orientation region that exists at the origin position in the (001) pole figure. A multiferroic material structure characterized by the above.

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