JP7147645B2 - Crystal grain analysis device, grain analysis method, and program - Google Patents

Description

The present invention relates to a crystal grain analysis apparatus, a crystal grain analysis method, and a program, and is particularly suitable for use in analyzing the state of crystal grains.

Conventionally, computer analysis of the state of crystal grains of metal materials has been performed. In the case of a metal material that is the subject of crystal grain analysis, for example, the metal material of an electromagnetic steel sheet, it is necessary to increase the grain size of the crystal grain after secondary recrystallization. For this reason, a method of interposing an inhibitor as an inclusion between crystal grains is used.

In this case, as long as the inhibitor is interposed between the grains, grain growth proceeds in a state of being suppressed, so it is necessary to perform calculations in consideration of this inclusion. Patent Documents 1 and 2 disclose techniques for analyzing the state of crystal grains with a computer in consideration of such inclusions.

In Patent Literatures 1 and 2, a point is set at a position corresponding to a grain boundary of a crystal grain, and a line having two points adjacent to each other on the same grain boundary as endpoints is set. Then, when the line passes through the inclusion, a fixed point is generated in the inclusion, and the change processing of the line having the fixed point as an end point is performed. Also, based on the grain boundary energy, a process of releasing the fixed point is performed.

Japanese Patent No. 5298603 Japanese Patent No. 4751355

However, the techniques described in Patent Documents 1 and 2 do not change the inclusions. Therefore, in the techniques described in Patent Documents 1 and 2, only inhibitors that can be observed from images of crystal grains are set. For this reason, when analyzing the state of crystal grains in an environment where inclusions exist, there is a risk that the state of crystal grains will deviate from the actual state. Specifically, for example, in the techniques described in Patent Documents 1 and 2, there is no problem in estimating the final state of crystal growth (secondary recrystallization) according to inclusions (fixed points) set as the initial state. However, when considering the heat treatment conditions for practically controlling the secondary recrystallization, it is necessary to control the temperature and atmosphere according to the progress of the secondary recrystallization over time. The techniques described in Patent Literatures 1 and 2 cannot be applied to practical control of heat treatment conditions because the crystal structure in the middle of such grain growth greatly deviates from the actual state. As a result of considering the cause of this, in order to eliminate the divergence, it was thought that it would be important to analyze inclusions as fixed points that change over time rather than simply recognizing inclusions as fixed points.

The present invention has been made in view of the above problems. The purpose is to suppress

The crystal grain analysis apparatus of the present invention comprises image signal acquisition means for acquiring an image signal of a crystal in a metal material, and an analysis target region based on the image signal corresponding to both end points of a grain boundary of the crystal grain contained in the crystal. and a grain boundary point setting means for setting, as a grain boundary point, a triple point in contact with three crystal grains including the grain, and the grain boundary point set by the grain boundary point setting means for the same grain line setting means for setting a line having two grain boundary points adjacent to each other on a boundary as end points; inclusion setting means for setting inclusions in an analysis target area based on the image signal; and the line setting means. line change processing means for generating a fixed point in the inclusion and changing the line having the fixed point as an end point when the line set by the line passes through the inclusion; and The first grain boundary energy at the grain boundary and the energy when the fixed point is released from the fixed position and moved to the equilibrium position where the grain boundary energy is the minimum at the position in the region excluding the inside of the inclusion grain boundary energy calculation means for calculating a second grain boundary energy at a grain boundary to which the moved fixed point belongs; and when the second grain boundary energy is less than the first grain boundary energy, the fixed fixed point processing means for performing a process of releasing points, wherein the inclusion setting means derives a change in size of the inclusion over time.

A crystal grain analysis method of the present invention includes an image signal acquisition step of acquiring an image signal of a crystal in a metal material, and an analysis target region based on the image signal corresponding to both end points of a grain boundary of a crystal grain contained in the crystal. and a grain boundary point setting step of setting a triple point in contact with three crystal grains including the grain as a grain boundary point; a line setting step of setting a line having two grain boundary points adjacent to each other on a boundary as end points; an inclusion setting step of setting inclusions in an analysis target region based on the image signal; and the line setting step. a line change processing step of generating a fixed point in the inclusion and changing the line having the fixed point as an end point when the line set by passes through the inclusion; and The first grain boundary energy at the grain boundary and the energy when the fixed point is released from the fixed position and moved to the equilibrium position where the grain boundary energy is the minimum at the position in the region excluding the inside of the inclusion a grain boundary energy calculating step of calculating a second grain boundary energy at a grain boundary to which the moved fixed point belongs; and when the second grain boundary energy is less than the first grain boundary energy, the fixed and a fixed point processing step of performing processing to release the point, wherein the inclusion setting step is characterized by deriving a change in size of the inclusion over time.

A program of the present invention is for causing a computer to function as each means of the grain analysis apparatus.

ADVANTAGE OF THE INVENTION According to this invention, when analyzing the state of a crystal grain in the environment where an inclusion exists, it can suppress that the state of a crystal grain diverges from an actual state.

It is a figure which shows notionally an example of the analysis method performed with a grain analyzer. It is a block diagram which shows an example of the functional structure of a crystal grain analysis apparatus. FIG. 3 shows an example of a grain image, double and triple points, lines and grain boundaries; It is a figure explaining an example of the calculation method of the driving force which arises in a double point. It is a figure explaining an example of the calculation method of the driving force which arises in a triple point. FIG. 10 is a diagram illustrating an example of an inhibitor setting method; It is a figure explaining an example of line change processing by a line change processing part. It is a figure explaining an example of the calculation method of grain-boundary energy in case a fixed point is a fixed double point. It is a figure explaining an example of the calculation method of grain-boundary energy in case a fixed point is a fixed triple point. 4 is a flowchart for explaining an example of processing operations performed by a crystal grain analysis apparatus; FIG. 10-1 is a flowchart following FIG. 10-1; FIG. 10B is a flowchart following FIG. 10-2; FIG. FIG. 10-3 is a flowchart following FIG. 10-3;

An embodiment of the present invention will be described below with reference to the drawings. In the embodiments of the present invention described below, a case where an electromagnetic steel sheet manufactured using an inhibitor as an inclusion is applied as an example of a metal material whose crystal grains are to be analyzed will be described.

FIG. 1 is a diagram conceptually showing an example of an analysis method performed by a grain analysis apparatus. For convenience of explanation, only one crystal grain A is shown in FIG. It goes without saying.

In the grain analysis apparatus of this embodiment, grains are modeled as shown in FIG.
First, as shown in FIG. 1A, triple points ia, ie, and if are set at positions corresponding to the end points of the three grain boundaries ua to uc of the crystal grain A, and the midpoints of the grain boundaries ua to uc are set. Grain boundary points of double points ib to id and ig to ii are set at positions corresponding to . Here, the triple points ia, ie, and if refer to points at which three straight lines intersect (that is, points in contact with three crystal grains), and the double points ib to id and ig to ii are points at which the two straight lines intersect. It refers to a point (a point in contact with two crystal grains). Then, a straight line is set to connect adjacent points (grain boundary points) i on the same grain boundaries ua to uc.
As described above, in this embodiment, the double points ib to id, ig to ii are set.

Driving force Fi(t) [N] generated at time t is calculated for each point (double point and triple point) ia to ii of the crystal modeled as described above. Then, based on the calculated driving force Fi(t), the position of each point (double point and triple point) ia to ii after Δt [sec] has passed (time t+Δt) is calculated. Then, the positions of the points (double points and triple points) ia to ii shown in FIG. 1(a) move to the positions shown in FIG. 1(b), for example.

In the crystal grain analysis apparatus of the present embodiment, as described above, the triple points ia, ie, and if corresponding to the end points of the grain boundaries ua to uc included in the crystal grain A, and the intermediate points of the grain boundaries ua to uc Calculating the driving force Fi(t) generated at each of the corresponding double points ib-id and ig-ii, and how the triple points ia, ie and if and the double points ib-id and ig-ii move to parse As a result, for example, the crystal grain Aa shown in FIG. 1(a) changes with time like the crystal grain Ab shown in FIG. 1(b) as accurately as possible without imposing a large computational load. can be parsed into The behavior of crystal grains via inhibitors (inclusions) will be described in detail in the explanation using FIGS. 7 to 9. FIG.

The configuration of the grain analysis apparatus will be described in detail below.
FIG. 2 is a block diagram showing an example of the functional configuration of the grain analysis apparatus of this embodiment. The hardware of the crystal grain analysis apparatus 100 can be realized using an information processing apparatus including a personal computer, CPU, ROM, RAM, hard disk, image input/output board, various interfaces, an interface controller, and the like. . Unless otherwise specified, each block shown in FIG. 2 is implemented by the CPU executing a control program stored in the ROM or hard disk using the RAM. By exchanging signals between the blocks shown in FIG. 2, the following processing is realized.
The main difference between the present embodiment and the techniques described in Patent Documents 1 and 2 is that the inhibitor setting section 118 and the fixed point processing section 120 are added, and the density distribution setting section 124 is added. In the following, for convenience of explanation, the same parts as the techniques described in Patent Documents 1 and 2 will also be explained in detail, but parts other than the parts related to the inhibitor setting section 118, the fixed point processing section 120, and the concentration distribution setting section 124 will be explained. The part is not limited to the contents described below, and for example, the techniques described in Patent Documents 1 and 2 can be applied.

In FIG. 2, the crystal image acquisition unit 101 is obtained by, for example, an EBSP (Electron Back Scattering Pattern) method. A signal and a signal indicating the orientation ξ of each crystal grain A contained in the image signal are acquired and stored in a hard disk or the like. In the following description, the image of the crystal grains A of the magnetic steel sheet and the image of the inhibitor existing between the crystal grains A of the magnetic steel sheet will be referred to as the crystal grain image as necessary. The crystal image acquisition unit 101 may directly acquire the above-described signals from an analyzer that performs crystal analysis by the EBSP method, or may acquire the above-described signals from a removable storage medium such as a DVD or CD-ROM. It may be obtained indirectly.

The crystal image display unit 102 causes the display device 200 to display a crystal grain image based on the crystal grain image signal acquired by the crystal image acquisition unit 101, for example, based on the operation of the operation device 300 by the user. The display device 200 includes a computer display such as an LCD (Liquid Crystal Display). The operation device 300 also includes user interfaces such as a keyboard and a mouse.

The point setting unit 103 allows the user to operate the operation device 300 with respect to the image of the crystal grain A displayed by the crystal image display unit 102 within the analysis target area based on the crystal grain image signal acquired by the crystal image acquisition unit 101. to acquire the specified point (double point and triple point) i using the Or set (store) in the hard disk. In this embodiment, the user can arbitrarily specify the number of points (double points and triple points) i and the initial positions. Also, the setting of the point i may be performed automatically without being specified by the user.

In addition, the point setting unit 103 calculates a vector indicating the position ri(t+Δt) after Δt [sec] at the point (double point or triple point) i to be calculated by the position calculation unit 116 as described later. Then, a vector indicating the position ri(t+Δt) of the point i is set (stored) in the RAM or hard disk. Further, the point setting unit 103 changes the setting of the currently set point i based on inputs from the line change processing unit 119 and the fixed point processing unit 120, which will be described later, and sets (stores) this in the RAM or hard disk. )do.

The line setting unit 104 provides information about a line p specified by two points i adjacent to each other on the same grain boundary u among the points (double points and triple points) i set by the point setting unit 103, Set (store) in RAM or hard disk. Thus, the line p is a straight line having two points i adjacent to each other on the same grain boundary u as both end points. The line setting unit 104 also performs processing for changing the line p when a fixed point is generated in the line change processing unit 119, which will be described later.

The grain boundary setting unit 105 obtains information about the grain boundary u specified by the lines p, which are connected to each other with the triple point i set by the point setting unit 103, among the lines p set by the line setting unit 104. , RAM or hard disk.

FIG. 3 shows a crystal grain image displayed by the crystal image display unit 102 (FIG. 3A) and points (double points and triple points) i set by the point setting unit 103 (FIG. 3B). , a line setting unit 104, and a line p and a grain boundary u set by a grain boundary setting unit 105 (FIG. 3C). For convenience of explanation, in FIGS. 3B and 3C, of the large number of crystal grains A included in the crystal grain image 31 shown in FIG. Only points i, lines p, and grain boundaries u set by In the crystal grain image 31 shown in FIG. 3(a), as an example, inhibitors (k1 to k4), which are inclusions, are shown only around the crystal grain A1, but the inhibitors are actually They are scattered in the grain image 31 .

When the crystal grain image 31 is displayed as shown in FIG. 3(a), the user uses the operation device 300 such as a mouse to specify the positions corresponding to the endpoints of the grain boundary u as the triple point i. Also, the position of the midpoint of the grain boundary u is designated as the double point i. Then, as shown in FIG. is set.

Based on these double points and triple points i1 to i18, lines p1 to p18 and grain boundaries u1 to u4 are set as shown in FIG. 3(c). Here, for example, line p1 is specified by triple point i1 and double point i2. Also, the grain boundary u1 is specified by lines p1 to p4 mutually connected with the triple points i1 and i5 at both ends. Incidentally, as shown in FIG. 3C, the grain boundary u1 is the grain boundary between the crystal grains A1 and A2, the grain boundary u2 is the grain boundary between the crystal grains A1 and A5, and the grain boundary u3 is the grain boundary between the crystal grains A1 and A5. A grain boundary u4 is a grain boundary between the grains A1 and A3.

The analysis temperature setting unit 106 acquires the analysis temperature θ(t) [° C.] of the electromagnetic steel sheet (crystal grain A) to be analyzed based on the operation of the operation device 300 by the user, and sets (stores) it in the RAM or hard disk. )do. Note that the analysis temperature θ(t) acquired by the analysis temperature setting unit 106 may be a constant value that does not depend on time or a value that depends on time (analysis temperature θ(t) change) is fine.

The orientation setting unit 107 determines all the crystal grains A is set (stored) in the RAM or hard disk.

The grain boundary energy (γ) storage unit 108 is an example of a grain boundary energy storage unit. For example, the grain boundary energy γ [J/m] per unit length and two A graph, numeric sequence, formula, or a combination thereof showing the relationship between the absolute value of the difference Δξ of the orientation ξ of the crystal grain A and the analysis temperature θ(t) is stored. In the following description, these graphs, numerical sequences, formulas, or combinations thereof will be referred to as graphs and the like.

For example, the “grain boundary energy γ per unit length” at the grain boundary u1 shown in FIG. By reading the “grain boundary energy γ per unit length” corresponding to the analysis temperature θ(t) set by the temperature setting unit 106 from the graph or the like stored in the grain boundary energy (γ) storage unit 108, can get. Also, the grain boundary energy (γ) storage unit 108 is configured using, for example, a RAM or a hard disk.

The grain boundary energy (γ) setting unit 109 sets the grain boundary based on the orientation ξ of the crystal grain A set by the orientation setting unit 107 and the analysis temperature θ(t) acquired by the analysis temperature setting unit 106. The grain boundary energy γ per unit length of all grain boundaries u set by the unit 105 is read from the graph or the like stored in the grain boundary energy (γ) storage unit 108 as described above. Then, the grain boundary energy (γ) setting unit 109 sets (stores) the read grain boundary energy γ per unit length in the RAM or hard disk.

The mobility storage unit 110 stores the mobility Mi [cm ² /(V·sec)], the absolute value of the difference Δξ between the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u, and Graphs, numerical sequences, formulas, or a combination thereof showing the relationship with temperature θ(t) are stored. In the following description, these graphs, numerical sequences, formulas, or combinations thereof will be referred to as graphs and the like.
For example, the mobility Mi at the grain boundary u1 shown in FIG. The mobility Mi corresponding to the analyzed temperature θ(t) is obtained by reading from the graph or the like stored in the mobility storage unit 110 . It should be noted that the mobility storage unit 110 is configured using, for example, a RAM or a hard disk.

The mobility setting unit 111 causes the grain boundary setting unit 105 to The mobilities Mi of all the set grain boundaries u are read out from the graph or the like stored in the mobility storage unit 110 as described above. Then, the mobility setting unit 111 sets (stores) the read mobility Mi in the RAM or hard disk.

For example, the analysis time setting unit 112 acquires the analysis completion time T [sec] based on the operation of the operation device 300 by the user, and sets (stores) it in the RAM or hard disk. Then, the analysis time setting unit 112 monitors the time t until the analysis completion time T elapses.

The analysis point determination unit 113 sequentially designates all the points (double points, triple points, and fixed points) i set by the point setting unit 103 as points to be calculated without duplication. Then, the analysis point discriminating unit 113 discriminates whether or not the specified point i is a fixed point, and if it is not a fixed point, further discriminates whether it is a double point or a triple point. .

When the analysis point determination unit 113 determines that the point i to be calculated is a double point, the double point driving force calculation unit 114 calculates the driving force Fi(t) generated at the double point.
FIG. 4 is a diagram illustrating an example of a method of calculating the driving force Fi(t) generated at the double point. In FIG. 4, a case of calculating the driving force Fi(t) generated at the double point i will be described as an example.

In FIG. 4, let Ri(t)[m] be the radius of curvature of an arc 41 defined by a double point i and two points i−1 and i+1 adjacent to the double point. Also, the magnitude (absolute value) of the grain boundary energy γ per unit length of the grain boundary u to which the double point i belongs is defined as γi. Then, the magnitude of the driving force Fi(t) generated at the double point i is expressed by the following equation (1). Also, the direction of the driving force Fi(t) generated at the double point i is the direction from the double point i toward the center of curvature O. FIG.

In order to obtain the driving force Fi(t) generated at the double point i using the equation (1), the double point driving force calculator 114 calculates the double point i to be calculated and the two adjacent double points i. Information on two points i−1 and i+1 is read from the point setting unit 103 . Next, the double point driving force calculator 114 calculates the center of curvature O and the radius of curvature Ri(t) of the arc 41 determined by the double point i and the two points i−1 and i+1 adjacent to the double point i. calculate. Further, the double point driving force calculator 114 acquires the grain boundary energy γi per unit length of the grain boundary u belonging to the double point i to be calculated from the grain boundary energy (γ) setting unit 109 .

Then, the double point driving force calculation unit 114 substitutes the radius of curvature Ri(t) and the grain boundary energy γi per unit length into the equation (1) to obtain the driving force Fi(t) generated at the double point i. ). Further, the double point driving force calculator 114 calculates the direction from the double point i to be calculated toward the center of curvature O, and determines the direction of the driving force Fi(t) generated at the double point i.

Returning to the description of FIG. 2, when the analysis point determination unit 113 determines that the point i to be calculated is the triple junction, the triple junction driving force calculation unit 115 calculates the driving force Fi ( t) is calculated.
FIG. 5 is a diagram illustrating an example of a method of calculating the driving force Fi(t) generated at the triple point. In FIG. 5, the case of calculating the driving force Fi(t) generated at the triple point i will be described as an example. Also, in FIG. 5, three points adjacent to the triple point i are indicated by "1", "2", and "3", respectively.

First, the triple point driving force calculation unit 115 reads information on the triple point i to be calculated and the three points 1, 2, and 3 adjacent to the triple point i from the point setting unit 103 . Then, the triple junction driving force calculation unit 115 calculates a unit vector having a direction from the triple junction i to be calculated toward points 1, 2, and 3. FIG. Further, the triple junction driving force calculation unit 115 calculates the magnitude (absolute value) of the grain boundary energies γi1, γi2, and γi3 per unit length at the grain boundary u to which the points 1, 2, and 3 belong, and calculates the grain boundary energy ( γ) Acquired from setting unit 109 .

Then, the triple junction driving force calculation unit 115 calculates the magnitudes (absolute values) of the grain boundary energies γi1, γi2, and γi3 per unit length and the directions from the triple junction i to be calculated toward points 1, 2, and 3. and the unit vector (dij(t)/|dij(t)|) having the following equation (2) to calculate the driving force Fi(t) generated at the triple point i to be calculated.

In equation (2), j is a variable for identifying three points adjacent to the triple point i to be calculated.
Thus, in the present embodiment, the grain boundary energies γi1, γi2, and γi3 per unit length at the grain boundaries u to which the points 1, 2, and 3 belong have the same magnitudes (absolute values), and , the vector sum of three vectors Di1(t), Di2(t), Di3(t) with directions from the triple point i to be computed to points adjacent to that triple point i is the drive produced at the triple point i Calculated as force Fi(t).

Returning to the description of FIG. 2, the position calculator 116 calculates changes in the positions of the double point i and the triple point i over time. First, an example of how to calculate the change in position of the double point i over time will be described.

The position calculator 116 acquires a vector indicating the driving force Fi(t) calculated by the double point driving force calculator 114 (a vector indicating the driving force Fi(t) generated at the double point i to be calculated). Further, the position calculation unit 116 acquires the mobility Mi of the grain boundary u to which the double point i to be calculated belongs from the mobility setting unit 111 . Then, the position calculation unit 116 calculates the mobility Mi of the grain boundary u to which the double point i to be calculated belongs and the vector indicating the driving force Fi(t) of the double point i to be calculated as follows (3): Substitute into the equation to calculate a vector indicating the velocity vi(t) of the double point i to be calculated.

After that, the position calculation unit 116 acquires “the vector indicating the current position ri(t) of the double point i to be calculated” set in the point setting unit 103 . Then, the position calculation unit 116 calculates the vector indicating the velocity vi(t) of the double point i to be calculated, the vector indicating the current position ri(t) of the double point i to be calculated, and the time Δt as follows: (4) to calculate a vector indicating the position ri(t+Δt) where the double point i to be calculated exists when Δt [sec] has passed from the current time t. In this embodiment, the change in the position of the double point i to be calculated over time is calculated in this way. The time Δt defines the timing (interval) for calculating the position of the point i, and is predetermined according to the type of magnetic steel sheet to be analyzed, analysis conditions, analysis accuracy, and the like.

Position calculation section 116 then outputs to point setting section 103 a vector indicating position ri(t+Δt) at which double point i to be calculated exists. By doing so, the point setting unit 103 sets a vector indicating the current position ri(t) of the double point i to be calculated, as described above.

An example of how to calculate the change in position of the triple point i over time will now be described.
The position calculation unit 116 acquires from the mobility setting unit 111 the mobilities Mi1 to Mi3 of the three grain boundaries u to which the triple point i to be calculated belongs.

Then, the position calculation unit 116 calculates the mobility Mi of the triple junction i to be calculated using the mobilities Mi1 to Mi3 of the three grain boundaries u to which the triple junction i to be calculated belongs. Specifically, the position calculation unit 116 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the target triple point i to points 1, 2, and 3, The mobilities Mi1 to Mi3 of the three grain boundaries u to which i belongs are substituted into the following equation (5) to calculate the mobility Mi of the triple junction i to be calculated.

In equation (5), j is a variable for identifying three points adjacent to the triple point i to be calculated.
Further, the position calculation unit 116 obtains a vector indicating the driving force Fi(t) calculated by the triple junction driving force calculation unit 115 (a vector indicating the driving force Fi(t) generated at the triple point i to be calculated). do. Then, the position calculation unit 116 calculates the mobility Mi of the grain boundary u to which the triple junction i to be calculated belongs and the vector indicating the driving force Fi(t) of the triple junction i to be calculated, as described in (3) above. Substitute into the equation to calculate a vector indicating the velocity vi(t) of the triple point i to be calculated.

After that, the position calculation unit 116 acquires “the vector indicating the current position ri(t) of the triple point i to be calculated” set in the point setting unit 103 . Then, the position calculation unit 116 calculates the vector indicating the velocity vi(t) of the triple point i to be calculated, the vector indicating the current position ri(t) of the triple point i to be calculated, and the time Δt as described above. (4) to calculate a vector indicating the position ri(t+Δt) where the triple point i to be calculated exists when Δt [sec] has passed from the current time t. In this embodiment, the change in the position of the triple point i to be calculated over time is calculated in this way. As described above, the time Δt defines the timing (interval) for calculating the position of the point i, and is predetermined according to the type of magnetic steel sheet to be analyzed, analysis conditions, analysis accuracy, etc. It is

Position calculation section 116 then outputs to point setting section 103 a vector indicating position ri(t+Δt) at which triple point i to be calculated exists. By doing so, the point setting unit 103 sets a vector indicating the current position ri(t) of the triple point i to be calculated, as described above.

The analysis time setting unit 112 determines whether the position calculation unit 116 has calculated the position ri(t+Δt) when the analysis completion time T has passed or after the analysis completion time T has passed. By judging whether or not the analysis has been completed until the analysis completion time T is judged.

When the analysis time setting unit 112 determines that the analysis has been completed by the analysis completion time T, the analysis image display unit 117 displays the "vector of the position ri(t+Δt) of the point i" calculated by the position calculation unit 116. Based on this, the display device 200 is caused to display an image showing how the state of the crystal grain A changes during the time t from 0 (zero) to T [sec].

The concentration distribution setting unit 124 sets the concentration distribution of inclusion-constituting elements in the matrix (region other than the region where the inhibitor k exists) within the analysis target region. The inclusion-constituting element is an element that constitutes the inhibitor k. For example, when the inhibitor k is AlN (aluminum nitride), the constituent elements of inclusions are Al and N. In this case, the Al concentration distribution and the N concentration distribution are set. In the following description, the concentration distribution of inclusion-constituting elements in the matrix within the analysis target region will be referred to as an element concentration distribution as necessary.

In this embodiment, the elemental concentration distribution (initial value of the elemental concentration distribution) at time t of 0 (zero) is set based on the operation of the operating device 300 by the user. As the initial value of the element concentration distribution, for example, an element concentration distribution obtained from experimental data for the magnetic steel sheet to be analyzed or a hypothetical element concentration distribution can be used. At the subsequent time t, the concentration distribution setting unit 124 can set the element concentration distribution, for example, assuming that the element concentration distribution changes according to the constituent elements of inclusions coming out of the region to be analyzed as time elapses. . The element concentration distribution at each time t can be determined, for example, using experimental data for the magnetic steel sheet to be analyzed. The element concentration distribution at each time t may be determined analytically by, for example, performing a numerical simulation using the diffusion rate of inclusion-constituting elements.

Further, as will be described later, in this embodiment, the inhibitor setting unit 118 sets (changes) the size of each inhibitor k every time t. Therefore, after the concentration distribution setting unit 124 sets the element concentration distribution as described above, the element concentration distribution at time t (t>0) is calculated (re- setting).
For example, at the current time t, the magnitude of inhibitor k is less than the magnitude at time t−Δt, which is Δt before the current time t. In this case, at the current time t, the inclusion-constituting element is released from the inhibitor k to the surroundings of the inhibitor k. In this case, the amount of the inclusion-constituting element released may be determined according to the amount of decrease in the size of the inhibitor k during time t, t-Δt. In the present embodiment, a case where three-dimensional analysis is performed will be described as an example. Therefore, the size of the inhibitor k becomes the volume. Incidentally, when two-dimensional analysis is performed, the size of the inhibitor k is the area.

On the other hand, suppose that at the current time t, the magnitude of the inhibitor k is greater than the magnitude at the time t-Δt, which is Δt before the current time t. In this case, at the current time t, the inclusion-constituting element is taken into the inhibitor k from the surroundings of the inhibitor k. In this case, the amount of inclusion-constituting element to be taken in may be determined according to the amount of increase in the size of the inhibitor k during time t and t-Δt.
The concentration distribution setting unit 124 calculates the element concentration distribution at the current time t based on the change in the concentration of the constituent element of the inclusion caused by the change in the size of the inhibitor k.
The method of setting the element concentration distribution at each time t is not limited to the above. For example, the element concentration distribution may be calculated by numerical simulation using the finite difference method. Also, in the numerical simulation, a time evolution equation of inclusion constituent elements may be used. At this time, for example, a technique such as the phase field method may be used.

When the user designates an inhibitor k (k1 to k4), which is an inclusion, on the crystal grain image 31 displayed by the crystal image display unit 102 using the operation device 300, the inhibitor setting unit 118 operates the crystal image acquisition unit 118. Based on the grain image signal acquired at 101, the region of the designated inhibitor k is detected. Then, the inhibitor setting unit 118 approximates the area of the detected inhibitor k with a sphere, calculates coordinate information indicating the center-of-gravity position bk of the inhibitor k and information related to the radius r, and sets them in the RAM or hard disk. .

FIG. 6 is a diagram illustrating an example of an inhibitor setting method.
In FIG. 6, the dashed line indicates the region of inhibitor k detected. In this case, the inhibitor setting unit 118 approximates the detection area indicated by the dashed line with a sphere as shown in FIG. . Here, the inhibitor k set by the inhibitor setting unit 118 does not change with the passage of time unlike the grain boundary point.

The inhibitor setting unit 118 sets the center-of-gravity position of the inhibitor k and the radius at the time t=0 as described above. If the inhibitor k is set within the analysis target region based on the crystal grain image signal acquired by the crystal image acquisition unit 101, the position of the center of gravity of the inhibitor k need not be set as described above. For example, each of the center-of-gravity positions of a preset number of inhibitors k may be set randomly. Also, it is not necessary to set the radius of the inhibitor k at time t=0 as described above. For example, the radius of all inhibitors k at time t=0 may be a preset constant value. Further, when the radii of all inhibitors k at time t=0 are set in advance, the radii of inhibitors k at time t=0 may be varied depending on the position of inhibitor k. For example, the radius of the inhibitor k at time t=0 may be varied according to the distance (depth in the plate thickness direction) from the surface of the electromagnetic steel sheet. For example, the closer the inhibitor k is to the surface of the magnetic steel sheet, the smaller the radius at time t=0.

At time t (t>0), the inhibitor setting unit 118 sets (changes) the radius rk of the inhibitor _k every time t. In this embodiment, the inhibitor setting unit 118 calculates the radius rk of the inhibitor _k at time t based on the following equation (6).
r _k =F(f(t), g(m, t), h(s _k' /s _k , d _k' , t), u(y _k )) (6)

In equation (6), F is a function dependent on functions f(t), g(m, t), h( _sk' /sk, _{dk '} , t) and u( _yk ).
The function f(t) is a function that depends on time t (only).
The function g(m, t) is a function that depends on the concentration m of inclusion constituent elements around the inhibitor k and the time t (only). That is, g(m, t) is a function that depends on the concentration m (only) at time t of inclusion constituent elements around inhibitor k. For example, the average concentration of inclusion-constituting elements at each position within a predetermined range from the center of gravity of inhibitor k is calculated for each inclusion-constituting element, and the calculated average concentration of each inclusion-constituting element is calculated as inhibitor k can be adopted as the concentration m of the constituent elements of the inclusions around the . In this case, the number of m is equal to the number of inclusion constituent elements. However, it is not necessary to obtain the concentration m of the inclusion-constituting element around the inhibitor k in this way. Of the plurality of inclusion-constituting elements, only the concentration of some predetermined inclusion-constituting elements may be included in m of the function g(m, t).

The function h(s _k' /s _k ,d _k' ,t) is the ratio s _k' /s _k of the size s _k' of the inhibitor k' around the inhibitor k to the size s _k of the inhibitor k, and It is a function that depends on the distance d _{k ' (of the centroid position) of the inhibitors k, k'} and the time t (only). That is, the function h(s _{k '} /s _k ,d _{k '} ,t) is the ratio s _{k '} /s _k and the distance d _{k' (of the centroid position) of the inhibitors k, k'} (only). As the inhibitor k' around the inhibitor k, for example, the inhibitor k having the largest radius among the inhibitors k whose center of gravity is within a predetermined range from the center of gravity of the inhibitor k can be used. In this embodiment, three-dimensional analysis is performed, so the size of inhibitors k and k' is, for example, the volume of inhibitors k and k'. In the case of two-dimensional analysis, the size of inhibitors k and k' is, for example, the area of inhibitors k and k'.
The function u(y _k ) is a function that depends on the distance y _k (only) from the surface of the magnetic steel sheet to the center of gravity of the inhibitor k.

Let the functions f(t), g(m, t), h(s _k' /s _k ,d _k' ,t), u(y _k ) be the time t−Δt before the current time t by Δt , the radius r _k of the inhibitor _k at time t can be expressed by the following equation (6a), for example.
r _k =r' _k +f(t)+g(m, t)+h(s _k' /s _k ,d _k' ,t)+u(y _k ) (6a)

As the function f(t), for example, a function that becomes a smaller value (negative value with a larger absolute value) as the time t elapses can be adopted. As the function g (m, t), for example, a function that becomes a smaller value (negative value with a larger absolute value) as the concentration m of the constituent elements of inclusions around the inhibitor k at time t becomes lower can be adopted. . As the function h( _sk' /sk, _dk' , t), for example, the ratio _sk' /s of the size sk' of the inhibitor _{k '} around the inhibitor _k to the size sk of the inhibitor k It is possible to employ a function that becomes a smaller value (negative value with a larger absolute value) as _k is larger and the distance dk' between the inhibitor k and the inhibitor k _' is smaller. As the function u(y _k ), a function having a smaller value (negative value with a larger absolute value) as the distance y _k from the surface of the magnetic steel sheet to the center of gravity of the inhibitor k decreases can be employed. The specific function form and coefficients can be determined, for example, by regression analysis using experimental data for the electromagnetic steel sheet to be analyzed. Also, as the specific function form and coefficients, hypothetical ones may be used. Further, while actually operating the crystal grain analysis apparatus 100, a specific function form and coefficients may be determined by trial and error so as to obtain appropriate analysis results (or target analysis results).

The functions f(t), g(m,t), h( _sk' /sk, _{dk '} ,t), u( _yk ) need not all be used, any one or two One or three may be used. As a simple example, if the function F depends only on the function f(t), then the radius r _k of the inhibitor k at time t is given by, for example, equations (6b′) and (6b″) below: can be represented.
r _k =r _k0 (1−t/200) (0<t≦200 [sec]) (6b′)
r _k =0 (t>200 [sec]) (6b'')
where r _k0 is the radius of inhibitor k at time t=0. Formula (6b′) is a formula applied when time t is greater than 0 and 200 [sec] or less, and formula (6b″) is a formula applied when time t is greater than 200 [sec]. is.

The line change processing unit 119 determines whether each line p set by the line setting unit 104 passes through the inhibitor k set by the inhibitor setting unit 118. If the line p passes through the inhibitor k , a process for changing the line p is performed.

FIG. 7 is a diagram illustrating an example of line change processing by the line change processing unit 119. As shown in FIG.
FIGS. 7(1a) to 7(6a) show an example of the line p before processing by the line change processing unit 119. FIG. Also, a first processing example for each line p shown in FIGS. 7(1a) to 7(6a) is shown in FIGS. shown in

Specifically, as shown in FIG. 7(1a), the line change processing unit 119 performs 7(1b) or 7(1c), a double point in is generated at an arbitrary position on the line p to divide the line p into two lines. Then, the line change processing unit 119 moves the generated double point in to the barycentric position (bk) of the inhibitor k, and performs processing for setting this to the fixed point ik. The fixed point ik in this case is a fixed double point forming the end point of the line p and the line. In this case, as shown in FIG. 7(1b) or FIG. 7(1c), a fixed point ik is newly generated, and the line p is divided into two lines p'1 and p'2 whose endpoints are the fixed point ik. divided into

Further, the line change processing unit 119 performs the following operations when the line p passes through the inhibitor k and one end point (grain boundary point) of the line p is inside the inhibitor k ((2a) to (4a) in FIG. 7). ), the end point within the inhibitor k is moved to the center of gravity position (bk) of the inhibitor k, and this is fixed point ik ((2b) to (4b) in FIG. 7 or (2c) to (4c ) is set to the fixed point ik) shown in ). In this case, the line p is changed to a line with the fixed point ik as one end point.

In addition, the line change processing unit 119 determines that when the line p passes through the inhibitor k and both end points (grain boundary points) of the line p are within the inhibitor k (Fig. 7 (5a) and (6a) ), a process is performed to eliminate the line p in the inhibitor k ((5b) and (6b) in FIG. 7, or (5c) and (6c) in FIG. 7). Further, the line change processing unit 119 converts the two points within the inhibitor k into one fixed point ik (Fig. 7 (5b) and Fig. 7 (6b), or 7 (5c) and (6c) as fixed points ik), and a process of constructing a line having each end point of the line p, each end point constituting the line, and the fixed point ik as end points.

That is, when the line p set by the line setting unit 104 passes through the inhibitor k, the line change processing unit 119 generates a fixed point ik having the barycentric position bk as a fixed position in the inhibitor k, and Change processing of the line having the point ik as an end point is performed.

Then, the line change processing unit 119 causes the point setting unit 103 and the line setting unit 104 to perform various resetting processes associated with point change (including disappearance and appearance) and line change (including disappearance and appearance). to do

As will be described later, in this embodiment, when the fixed point ik set as described above satisfies a certain condition, the fixed point ik is made a normal point (movable point), and the fixed point ik release the
Therefore, the effective range setting unit 122 acquires information on the range of the grain boundary u considered when determining whether to release the fixed point ik based on the operation of the operation device 300 by the user, and stores the information in the RAM or hard disk. set to Here, the information about the range of the grain boundary u is acquired based on the operation of the operation device 300, but the grain analysis device 100 is provided with an effective range storage section, from which the previously stored "grain Information on the range of the field u" may be read out. In the following description, this range will be referred to as an effective range as required.
In this embodiment, the effective range is set to be a sphere centered on the barycentric position bk of the inhibitor k. Therefore, the grain boundary energy (E) calculator 121 acquires information about the radius of the effective range from the effective range setting section 122 . This effective range can be determined experimentally. Specifically, of the angles formed by two straight lines connecting a fixed point ik and a point i adjacent to the fixed point ik, what is the sharpest angle (for example, the angle 2β in FIGS. 8 and 10)? To determine experimentally whether or not the fixed point ik is properly released when the angle is 100 degrees, and to determine the effective range in which the fixed point ik is properly released based on the obtained angle. can be done. However, any effective range may be determined as long as it is a region that includes the fixed point ik, is wider than the inhibitor k, and defines an object for which the grain boundary energy is to be calculated.

Further, in the present embodiment, when the fixed point ik is released at the grain boundary u within the effective range set by the effective range setting unit 122 (including immediately before or after), the increase in the grain boundary energy is When it becomes smaller than a certain surmountable predetermined energy (the grain boundary energy when the fixing point ik is released (including immediately before or after) and the grain boundary energy when the fixing point ik is fixed) When the difference becomes smaller than a certain predetermined energy), the fixed point ik is released.
Therefore, the barrier energy setting unit 123 acquires information (energy value) on this predetermined energy based on the operation of the operation device 300 by the user, and sets it in the RAM or hard disk. Here, the information (energy value) about the predetermined energy is acquired based on the operation of the operation device 300, but the grain analysis device 100 is provided with a barrier energy storage unit, from which the barrier energy storage unit is stored in advance. Alternatively, "information on predetermined energy (energy value)" may be read. In the following description, this predetermined energy is called barrier energy.

The grain boundary energy (E) calculation unit 121 obtains the coordinate information of the fixed point ik, the information indicating the positions of the other end points of the line p having the fixed point ik as an end point, and the inhibitor having the fixed point ik as the center of gravity position bk. Get information about k. Also, the grain boundary energy (E) calculator 121 acquires the grain boundary energy γ per unit length of the grain boundary u to which the fixed point ik belongs from the grain boundary energy (γ) setting unit 109 . Furthermore, the grain boundary energy (E) calculator 121 acquires information about the effective range.

Based on the acquired information, the grain boundary energy (E) calculator 121 calculates the grain boundary energy Ei Calculate (calculate)
In this embodiment, the grain boundary energy (E) calculator 121 calculates the grain boundary energy Ei of the grain boundary u to which the fixed point ik belongs within the effective range. In the present embodiment, the grain boundary energy (E) calculator 121 determines that the grain boundary u exists within the inhibitor k (excluding the surface (boundary) of the inhibitor k) having the fixed point ik as the center of gravity bk. Calculation (calculation) of the grain boundary energy Ei is performed assuming that it is not performed.

Here, specifically, using FIGS. 8 and 9, a method for calculating the grain boundary energy Ei when the fixed point ik is a double point (fixed double point) and a triple point (fixed triple point) will be described below.
FIG. 8 is a diagram illustrating an example of a method of calculating the grain boundary energy when the fixed point ik is a fixed double point. FIG. 9 is a diagram illustrating an example of a method of calculating grain boundary energy when the fixed point ik is a fixed triple point. 8 and 9 show an example in which the shape of the inhibitor k is a sphere.

First, when the fixed point ik is a double point, as shown in FIG. Intersection points 802 and 803 between extension lines in the direction of points ir and it of lines pa and pb connecting at the shortest distance and the effective range 801 are obtained. Here, no grain boundary u exists within the inhibitor k. Therefore, the grain boundary energy (E) calculation unit 121 uses the length K between the fixed point ik and the intersection points 802 and 803 as the effective lengths L1 and L2 used when calculating the grain boundary energy Ei. The length of the inhibitor k minus the length of the radius r is obtained.

Also, since the fixed point ik is a double point, the two effective lengths L1 and L2 (=Kr) can be regarded as belonging to the same grain boundary u. Therefore, for example, the grain boundary energy Ei when the fixed point ik is a double point shown in FIG. 8 is calculated by the following equation (7).
Ei=(grain boundary energy γ per unit length of grain boundary u including lines pa and pb)×(L1+L2) (7)
As described above, in the present embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, a virtual line having the fixed point ik as one of its end points (the point ik and the points 802 and 803 are the shortest distance The grain boundary energy Ei is calculated by using the length of the virtual line connecting ) and the grain boundary energy per unit length of the grain boundary to which the fixed point ik belongs. As described above, the length of the radius r of the inhibitor k is set every time t. Therefore, for example, if the radius r of the inhibitor k decreases with the lapse of time t, the effective lengths L1 and L2 used in calculating the grain boundary energy Ei increase. In this case, the grain boundary energy Ei when the fixed point ik is a double point increases with the lapse of time t.

On the other hand, as shown in FIG. 9A, when the fixed point ik is the triple junction, the grain boundary energy (E) calculator 121 calculates , intersecting the equilibrium position w (two imaginary lines defining the region where the equilibrium position exists) and intersections 802 and 803 of the effective range 801 are obtained. The equilibrium position w is the position where the fixed point ik is released from the fixed position (gravity center position bk of the inhibitor k) and the grain boundary energy E is the minimum, excluding the inside of the inhibitor k.
Also, grain boundaries u do not exist within the inhibitor k. Therefore, the grain boundary energy (E) calculation unit 121 uses the length K between the fixed point ik and the intersections 802 and 803 as the effective length used when calculating the grain boundary energy Ei. Obtain the length after subtracting the length of the radius r.

Also, since the fixed point ik is the triple junction, the two effective lengths L1 and L2 (=Kr) can be regarded as belonging to different grain boundaries u. Therefore, for example, the grain boundary energy Ei when the fixed point ik shown in FIG. 9 is the triple junction is calculated by the following equation (8).
Ei=(grain boundary energy γ1 per unit length of grain boundary u including line pa)×L1+(grain boundary energy γ2 per unit length of grain boundary u including line pb)×L2 (8)
As described above, in the present embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, a virtual line having the fixed point ik as one of its end points (the point ik and the points 802 and 803 are the shortest distance The grain boundary energy Ei is calculated by using the length of the virtual line connecting ) and the grain boundary energy per unit length of the grain boundary to which the fixed point ik belongs. As described above, the length of the radius r of the inhibitor k is set every time t. Therefore, for example, if the radius r of the inhibitor k decreases with the lapse of time t, the effective lengths L1 and L2 used in calculating the grain boundary energy Ei increase. In this case, the grain boundary energy Ei when the fixed point ik is the triple junction increases with the lapse of time t.

Further, the grain boundary energy (E) calculation unit 121 calculates (calculates) the grain boundary energy Ei' of the grain boundary to which the released fixed point ik belongs at the equilibrium position w.
In this embodiment, the grain boundary energy (E) calculator 121 calculates the grain boundary energy Ei′ of the grain boundary u to which the fixed point ik belongs within the effective range 801 . In the present embodiment, the grain boundary energy (E) calculator 121 determines that the grain boundary u exists within the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center of gravity bk. The grain boundary energy Ei' is calculated assuming that there is no other inhibitor k and that no other inhibitor k exists.

Here, specifically, using FIGS. 8 and 9, calculation of the grain boundary energy Ei′ when the fixed point i is a double point (fixed double point) and a triple point (fixed triple point) The method is described below.

First, when the fixed point ik is a double point, the grain boundary energy (E) calculator 121 obtains points 802 and 803 and effective lengths L1 and L2 as described above. Here, when the fixed point ik is a double point, it is assumed that the portion of the effective length L1 including the line pa and the portion of the effective length L2 including the line pb belong to the same grain boundary u. can be viewed. Therefore, the equilibrium position w is an arbitrary position on a line (virtual line) 805 connecting the points 802 and 803 at the shortest distance. Here, the length of line (virtual line) 805 is assumed to be Q0. Also, the grain boundary energy γ per unit length of the grain boundary u at the line 805 can be regarded as the grain boundary energy γ per unit length of the grain boundary u including the lines pa and pb.

Therefore, for example, the grain boundary energy Ei' at the equilibrium position w shown in FIG. 8 is calculated by the following equation (9).
Ei′=(grain boundary energy γ per unit length of grain boundary u including lines pa and pb)×(Lw1+Lw2)=(grain boundary energy γ per unit length of grain boundary u including lines pa and pb) x Q0 (9)
As described above, in the present embodiment, the length of the imaginary virtual line of the grain boundary to which the fixed point ik belongs and the imaginary line passing through the equilibrium position w (the imaginary line connecting the points 802 and 803 at the shortest distance) and the fixed The grain boundary energy Ei' is calculated using the grain boundary energy per unit length at the grain boundary to which the point ik belongs.

Although not applicable in the example shown in FIG. 8, when the line 805 passes through the inhibitor k, the length (Q0) of the line 805 minus the length of the portion of the line 805 passing through the inhibitor k is is multiplied by the grain boundary energy γ per unit length.

On the other hand, when the fixed point ik is the triple point as shown in FIG. Ask. Here, when the fixed point ik is a triple point, the portion of the effective length L1 including the line pa and the portion of the effective length L2 including the line pb belong to different grain boundaries u. can be regarded as Here, as an example, the case where the equilibrium position w is the position shown in FIG. 9 will be described.

In this case, the grain boundary energy (E) calculator 121 calculates the shortest line (virtual line) 901 connecting the point 802 and the equilibrium position w, and the shortest line (virtual line) connecting the point 803 and the equilibrium position w. ) 902 and a line (virtual line) 903 connecting the fixed point ik and the equilibrium position w at the shortest distance. At this time, the effective length used to calculate the grain boundary energy Ei' is the length B1 of the line 901, the length B2 of the line 902, and the length obtained by subtracting the radius r of the inhibitor k from the length of the line 903. becomes B3.

The grain boundary energy γ per unit length of the grain boundary u at the line 901 can be regarded as the grain boundary energy γ1 per unit length of the grain boundary u including the line pa. Also, the grain boundary energy γ per unit length of the grain boundary u at the line 902 can be regarded as the grain boundary energy γ2 per unit length of the grain boundary u including the line pb. In addition, the grain boundary energy γ per unit length of the grain boundary u in the portion of the line 903 excluding the inside of the inhibitor k is the grain boundary energy γ of the grain boundary u including the line pc (the line connecting the fixed point ik and the point iv at the shortest distance). It can be regarded as the grain boundary energy γ3 per unit length.

Therefore, for example, the grain boundary energy Ei' when the fixed point ik shown in FIG. 9 is the triple junction is calculated by the following equation (10).
Ei′=(grain boundary energy γ per unit length of grain boundary u including line pa)×B1+(grain boundary energy γ per unit length of grain boundary u including line pb)×B2+ (including line pc Grain boundary energy γ per unit length of grain boundary u)×B3 (10)
As described above, in the present embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, the length of the virtual line (virtual lines 901 to 903) passing through the equilibrium position w, and the length of the grain boundary to which the fixed point ik belongs The grain boundary energy Ei′ is calculated using the grain boundary energy per unit length in .

Furthermore, in the present embodiment, the grain boundary energy (E) calculator 121 calculates the grain boundary energy of the grain boundary u to which the fixed point ik to which the fixed point i is released belongs (including immediately before or after) when the fixed point i is released. Calculate (calculate) the energy Ei''.
In this embodiment, the grain boundary energy Ei'' of the grain boundary u to which the fixed point ik belongs is calculated within the effective range. In the present embodiment, the grain boundary energy (E) calculator 121 determines that the grain boundary u exists within the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center of gravity bk. The grain boundary energy Ei'' is calculated assuming that there are no other inhibitors k.

Here, specifically, using FIG. 8 and FIG. 9, the grain boundary energy Ei'' when the fixed point i is a double point (fixed double point) and a triple point (fixed triple point) A calculation method will be described below.

First, when the fixed point ik is a double point, the grain boundary energy (E) calculator 121 obtains points 802 and 803 and effective lengths L1 and L2 as described above.
Next, the grain boundary energy (E) calculation unit 121 bisects the angle between two lines (virtual lines) connecting the fixed point ik and the points 802 and 803 at the shortest distance, and the inhibitor k. Find the intersection point 804 . In this embodiment, the fixed point ik is assumed to be released to this point 804 . Then, the grain boundary energy (E) calculator 121 obtains lengths M1 and M2 of lines (virtual lines) connecting the point 804 and the points 802 and 803 at the shortest distance. Further, the grain boundary energy (E) calculator 121 obtains the length Q0 of the line (virtual line) connecting the points 802 and 803 at the shortest distance.
Here, since the fixed point ik is a double point, the two effective lengths L1 and L2 (=Kr) can be regarded as belonging to the same grain boundary u. Therefore, for example, the grain boundary energy Ei'' (at the point 804) when the fixed point ik is released shown in FIG. 8 is calculated by the following equation (11).
Ei″=(grain boundary energy γ per unit length of grain boundary u including lines pa and pb)×(M1+M2) (11)
Thus, in this embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, the virtual line having the point 804 as one of its endpoints (the point 804 and the points 802 and 803 are the shortest distance ) and the grain boundary energy per unit length of the grain boundary to which the fixed point ik belongs, the grain boundary energy Ei'' is calculated.

On the other hand, when the fixed point ik is the triple point as shown in FIG. Ask. Further, the grain boundary energy (E) calculator 121 obtains the intersection point 804 as described above. Then, the grain boundary energy (E) calculator 121 obtains lengths M1 and M2 of lines (virtual lines) connecting the point 804 and the points 802 and 803 at the shortest distance.

Here, when the fixed point ik is a triple point, the portion of the effective length L1 including the line pa and the portion of the effective length L2 including the line pb belong to different grain boundaries u. can be regarded as Therefore, for example, the grain boundary energy Ei'' within the effective range 801 of the grain boundary u to which the fixed point i belongs when the fixed point ik is released as shown in FIG. Calculated.
Ei''=(grain boundary energy γ1 per unit length of grain boundary u including line pa)×M1+(grain boundary energy γ2 per unit length of grain boundary u including line pb)×M2 ( 12)
In FIG. 9A, it is assumed that the equilibrium position w is at a point on the line that bisects the angle formed by two lines (virtual lines) connecting the fixed point ik and the points 802 and 803 at the shortest distance. Although shown as an example, the equilibrium position w is not limited to the position on the line that bisects the angle formed by two lines connecting the fixed point ik and the points 802 and 803 at the shortest distance. .
Thus, in this embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, the virtual line having the point 804 as one of its endpoints (the point 804 and the points 802 and 803 are the shortest distance ) and the grain boundary energy per unit length of the grain boundary to which the fixed point ik belongs, the grain boundary energy Ei'' is calculated.

Returning to the description of FIG. 2, the fixed point processing unit 120 compares the grain boundary energy Ei calculated by the grain boundary energy (E) calculation unit 121 with the grain boundary energy Ei', and the grain boundary energy Ei' is the grain boundary energy It is determined whether or not it is less than Ei. That is, the fixed point processing unit 120 determines whether or not the following expression (13) is satisfied.
Ei′<Ei (13)
As a result of this determination, if the grain boundary energy Ei' is not less than the grain boundary energy Ei (Ei'<Ei), the fixing point ik is not released.

On the other hand, when the grain boundary energy Ei′ is less than the grain boundary energy Ei, the fixed point processing unit 120 calculates the grain boundary energy Ei from the grain boundary energy Ei″ calculated by the grain boundary energy (E) calculation unit 121. It is determined whether or not the subtracted value is less than the barrier energy E0 read from the barrier energy setting unit 123 . That is, the fixed point processing unit 120 determines whether or not the following expression (14) is satisfied.
Ei''-Ei<E0 (14)
As a result of this determination, if the value obtained by subtracting the grain boundary energy Ei from the grain boundary energy Ei'' is not less than the barrier energy E0, the fixed point processing unit 120 determines the current time of the inhibitor k to which the fixed point ik belongs. Determine whether the radius r at t is less than or equal to a threshold. This determination is made to prevent the fixed point ik from being released (released) even though the radius of the inhibitor k is small. A threshold value is predetermined from such a point of view. The threshold value may be 0 (zero) or a value exceeding 0 (zero), and can be determined, for example, according to the size of the crystal grain to which the fixed point ik belongs. For example, the fixed point processing unit 120 determines whether the radius r at the current time t of the inhibitor k to which the fixed point ik belongs is 1/n (n is a positive integer) or less of the radius of the circumscribed circle of the crystal grain. can be determined. As a result of this determination, if the radius r at the current time t of the inhibitor k to which the fixed point ik belongs is greater than the threshold, the fixed point processing unit 120 does not release the fixed point ik.
On the other hand, when the value obtained by subtracting the grain boundary energy Ei from the grain boundary energy Ei'' is less than the barrier energy E0, and when the radius r at the current time t of the inhibitor k to which the fixed point ik belongs is equal to or less than the threshold. , a process of canceling (releasing) the fixed point ik is performed.

Specifically, as shown in FIG. 8B, in this embodiment, when the fixed point ik is a double point, the fixed point processing unit 120 moves the fixed point ik to the position of the point 804 and fixes it. is released, and a normal point ik is processed. That is, instead of the fixed point ik, the fixed point processing unit 120 bisects the angle formed by two lines (virtual lines) connecting the fixed point ik and the points 802 and 803 at the shortest distance, and the inhibitor k. At the intersection 804 with , a normal point ik is generated.

Further, as shown in FIG. 9B, in this embodiment, when the fixed point ik is a triple junction, the fixed point processing unit 120 moves the fixed point ik to the position of the point 804 and releases the fixation. Then, the following processing is performed in addition to the normal processing for setting the point ik. That is, the fixed point processing unit 120 generates a fixed double point ix connected to the normal points ik and iv at the center of gravity position bk of the inhibitor k. Here, as shown in FIG. 9(b), point iv is a point that is not connected to normal point ik among points ir, it, and iv adjacent to fixed point ik.

It should be noted that the position of the point after the movement of the fixed point ik is not limited to the position of the point 804. For example, it is applicable even if it is moved to the position of the point where the grain boundary energy Ei'' is the minimum. can. In this case, the grain boundary energy Ei'' is calculated by the above-described formula (11) when the fixed point ik is a double point, and when the fixed point ik is a triple point, the above-described (12) Calculated by the formula.
Further, instead of the expression (14), for example, it may be determined whether or not the absolute value of the value obtained by subtracting the grain boundary energy Ei'' from the grain boundary energy Ei is less than the barrier energy E0. .

As described above, in this embodiment, the condition for releasing the fixed point ik is that both the equations (13) and (14) are satisfied, or that the radius r of the inhibitor k is equal to or less than the threshold.
Returning to the description of FIG. 2, the fixed point processing unit 120 causes the point setting unit 103 to perform resetting according to the change of the fixed point i.

Next, an example of the processing operation performed by the crystal grain analysis apparatus 100 will be described with reference to the flow charts of FIGS. 10-1 to 10-4. It should be noted that the processing of the flowchart shown in FIG. 10A is started when the CPU reads out the control program from the ROM or hard disk and starts executing it based on the operation of the operation device 300 by the user.

First, in step S1 in FIG. 10-1, the crystal image acquisition unit 101 acquires an image signal (crystal grain image signal) of the crystal grain A of the electromagnetic steel sheet and the inhibitor existing between the crystal grains A of the electromagnetic steel sheet, and the image signal is input until a signal indicating the orientation ξ of each crystal grain A contained in is input. When the crystal grain image signal and the signal indicating the orientation ξ of each crystal grain A included in the image signal are input, the process proceeds to step S2.
As described above, in the present embodiment, an example of image signal acquisition means is realized by performing the process of step S1, for example.

When the process proceeds to step S2, the crystal image display unit 102 causes the display device 200 to display the crystal grain image 31 based on the crystal grain image signal acquired in step S1. At this time, the crystal image display unit 102 also causes the display device 200 to display an image for prompting the user to input the analysis temperature θ(t) of the magnetic steel sheet (crystal grain A) to be analyzed and the analysis completion time T. . Here, after the analysis temperature θ(t) and the analysis completion time T are sequentially input, the user can specify the point (double point or triple point) i while referring to the grain image 31. A case will be described as an example.

Next, in step S<b>3 , the analysis temperature setting unit 106 waits until the analysis temperature θ(t) of the electromagnetic steel sheet (crystal grain A) to be analyzed is input based on the operation of the operation device 300 by the user. Then, when the analysis temperature θ(t) of the magnetic steel sheet (crystal grain A) to be analyzed is input, the process proceeds to step S4.

When proceeding to step S4, the analysis temperature setting unit 106 sets the input analysis temperature θ(t) of the electromagnetic steel sheet (crystal grain A) to be analyzed in the RAM or hard disk. 10-1 to 10-4, the case where the analysis temperature θ(t) of the magnetic steel sheet (crystal grain A) to be analyzed is a constant value will be described as an example.

Next, in step S<b>5 , the analysis time setting unit 112 waits until the analysis completion time T is input based on the operation of the operation device 300 by the user. Then, when the analysis completion time T is input, the process proceeds to step S6.

When the process proceeds to step S6, the analysis time setting unit 112 sets the input analysis completion time T in the RAM or hard disk.

Next, in step S7, the point setting unit 103 waits until a point (double point or triple point) i is designated on the crystal grain image 31 displayed by the crystal image display unit . When the point (double point or triple point) i is specified, the process proceeds to step S8.

When the process proceeds to step S8, the point setting unit 103 calculates a vector indicating the position ri(t) of the point i determined to be specified in step S7, and sets it in the RAM or hard disk.

Next, in step S<b>9 , the point setting unit 103 determines whether or not an instruction to end the work of designating the point (double point or triple point) i has been issued based on the operation of the operating device 300 by the user. As a result of this determination, if no instruction to end the work specifying the point i has been issued, the process returns to step S7, and the already specified point (double point or triple point) i and another point (double point or triple point) ) Wait until i is specified.

On the other hand, if the result of determination in step S9 is that an instruction to end the task of designating point i has been issued, the process proceeds to step S10. When the process proceeds to step S10, the point setting unit 103 calculates the number of points (double points or triple points) i determined to be specified in step S7 (that is, the number of times the process of step S7 is performed) NI. , RAM or hard disk.
As described above, in the present embodiment, an example of grain boundary point setting means is realized by performing the processes of steps S7 to S10.

Next, at step S11 in FIG. 10B, the inhibitor setting unit 118 waits until the inhibitor k is specified for the crystal grain image 31 displayed by the crystal image display unit 102. FIG. If the inhibitor k is specified, the process proceeds to step S12.

When the process proceeds to step S12, the inhibitor setting unit 118 detects the region of the inhibitor k determined to be specified in step S11 based on the grain image signal acquired in step S1, and marks this detection region with a sphere. By approximation, coordinate information indicating the center-of-gravity position bk of the inhibitor k and information about its radius r are calculated and set in the RAM or hard disk.

Next, in step S<b>13 , the inhibitor setting unit 118 determines whether or not an instruction to end the work of designating the inhibitor k is given based on the user's operation of the operation device 300 . As a result of this determination, if an instruction to end the work to designate the inhibitor k has not been issued, the process returns to step S11 and waits until another inhibitor k different from the already designated inhibitor k is designated.

On the other hand, if the result of determination in step S13 is that an instruction to end the work of designating inhibitor k has been issued, the process proceeds to step S14. When the process proceeds to step S14, the inhibitor setting unit 118 calculates the number of inhibitors k determined to be specified in step S11 (that is, the number of times the process of step S11 is performed) NK, and sets it in the RAM or hard disk. .
As described above, in the present embodiment, an example of inclusion setting means is realized by performing the processing of steps S11 to S14.

Next, in step S15, the effective range setting unit 122 waits until information regarding the effective range 801 (in this embodiment, information regarding the radius of the effective range 801) is input based on the operation of the operating device 300 by the user. do. Then, when the information regarding the effective range 801 is input, the process proceeds to step S16.

When the process proceeds to step S16, the valid range setting unit 122 sets information regarding the valid range 801 in the RAM or hard disk.
Next, in step S17, the barrier energy setting unit 123 waits until information about the barrier energy E0 (the value of the barrier energy E0 in this embodiment) is input based on the operation of the operation device 300 by the user. Then, when the information about the barrier energy E0 is input, the process proceeds to step S18.
When the process proceeds to step S18, the barrier energy setting unit 123 sets information regarding the barrier energy E0 in the RAM or hard disk.

Next, in step S19, the line setting unit 104 selects a line specified by two points i adjacent to each other on the same grain boundary u among the points (double points or triple points) i set in step S8. Set p and its number NP in RAM or hard disk. Incidentally, the setting of the line p in step S15 is performed without considering the existence of the inhibitor k. Specifically, the line setting unit 104 defines a line p by two points i specifying the line p. For example, the line p1 shown in FIG. 3(c) is defined by the following equation (15).
p1={i1, i2} (15)
As described above, in the present embodiment, an example of line setting means is realized by performing the process of step S19, for example.

Next, in step S20, the grain boundary setting unit 105 selects the grain boundary u specified by the line p, which is connected to each other with the triple point i set in step S8 as both ends, among the lines p set in step S19. is set in RAM or hard disk. Specifically, the grain boundary setting unit 105 defines the grain boundary u by a plurality of lines p specifying the grain boundary u. For example, the grain boundary u1 shown in FIG. 3(c) is defined by the following equation (16).
u1={p1, p2, p3, p4} (16)

Next, in step S21, the orientation setting unit 107 converts the crystal grain image 31 into The orientations ξ of all crystal grains A included are set in the RAM or hard disk.

Next, in step S22, the grain boundary energy (γ) setting unit 109 sets grain From the graph or the like stored in the boundary energy (γ) storage unit 108, the grain boundary energy γ per unit length of all grain boundaries u set in step S20 is read. Then, the grain boundary energy (γ) setting unit 109 sets the read grain boundary energy γ per unit length in the RAM or hard disk.

Next, in step S23, the mobility setting unit 111 stores the mobility based on the orientation ξ of the crystal grain A set in step S21 and the analysis temperature θ(t) set in step S4. From the graph or the like stored in the unit 110, the mobilities Mi of all the grain boundaries u set in step S20 are read. Then, the mobility setting unit 111 sets the read mobility Mi in the RAM or hard disk.
Next, in step S24, the concentration distribution setting unit 124 sets the initial value of the elemental concentration distribution (the elemental concentration distribution when the time t is 0 (zero)).

Next, in step S25 of FIG. 10-3, the analysis time setting unit 112 sets the time t to 0 (zero).

When the analysis time setting unit 112 sets the analysis time t to 0, the process proceeds to step S26. When the process proceeds to step S26, the line change processing unit 119 sets 1 to a variable p indicating the line to be processed. At this time, the line change processing unit 119 acquires from the line setting unit 104 information about the line p set in step S19.

Next, in step S27, the line change processing unit 119 sets ΔNI, which indicates the number of points to be increased or decreased, to 0 (zero), and sets ΔNP, which indicates the number of lines to be increased or decreased, to 0 (zero).

Next, in step S28, the line change processing unit 119 sets 1 to a variable k indicating the inhibitor to be processed. At this time, the line change processing unit 119 acquires from the inhibitor setting unit 118 information about the inhibitor k set in step S12 (coordinate information indicating the center-of-gravity position bk of the inhibitor k and information about its radius r).

Here, in the following description, the diagram shown in FIG. 7 will also be referred to as necessary.
In step S29, the line change processing unit 119 determines whether or not the line p passes through the inhibitor k based on the information regarding the line p acquired in step S26 and the information regarding the inhibitor k acquired in step S28. At this time, it is determined that the surface (boundary) of the inhibitor k is not within the inhibitor k. As a result of this determination, if the line p is not within the inhibitor k (not corresponding to (1a) to (6a) in FIG. 7), the process proceeds to step S39.

On the other hand, if the result of determination in step S29 is that line p passes through inhibitor k, the process proceeds to step S30. When the process proceeds to step S30, the line change processing unit 119 determines whether or not the endpoint of line p is within inhibitor k.

If the end point of line p is not within inhibitor k as a result of the determination in step S30 (the case shown in FIG. 7(1a)), the process proceeds to step S31. When the process proceeds to step S31, the line change processing unit 119 generates a double point (double point in shown in FIG. 7(1b) or FIG. 7(1c)) at an arbitrary position on line p. Line p is thereby split into two lines.

Next, in step S32, the line change processing unit 119 shifts the double point generated on the line p in step S31 (the double point in shown in FIG. 7(1b) or FIG. 7(1c)) to the barycentric position of the inhibitor k. (bk) and set this as a fixed point ik (fixed point ik shown in FIG. 7(1b) or FIG. 7(1c)). The fixed point ik in this case is a fixed double point forming the end point of the line p and the line. As a result, a new fixed point ik is generated and the number of points is increased by one. In addition, since line p is divided into two lines (lines p'1 and p'2 shown in FIG. 7(1b) or FIG. 7(1c), respectively), the number of lines also increases by one. In this case, the line change processing unit 119 also includes information about the newly generated fixed point ik (for example, information indicating that the point is a fixed point and its coordinate information), and information about the newly set line. Information (for example, information indicating that a line is set between each end point of the line p and the fixed point ik) is stored in the RAM or hard disk.

Next, in step S33, since the number of points and the number of lines are increased by one in the processing of steps S31 and S32, the line change processing unit 119 changes the currently set ΔNI indicating the number of points to be increased or decreased. 1 is added to change the ΔNI, and 1 is added to the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP.

On the other hand, if the end point of line p is within inhibitor k as a result of determination in step S30 (cases shown in (2a) to (6a) in FIG. 7), the process proceeds to step S34. When the process proceeds to step S34, the line change processing unit 119 determines whether or not both end points of the line p are within the inhibitor k.

If both end points of line p are not within inhibitor k as a result of determination in step S34, that is, if only one of the end points of line p is within inhibitor k (cases shown in FIGS. 7(2a) to (4a)) , the process proceeds to step S35. When the process proceeds to step S35, the line change processing unit 119 moves the end point within the inhibitor k to the center of gravity position (bk) of the inhibitor k, and sets it to the fixed point ik (FIG. 7 (2b) to (4b) or Let it be fixed points ik) shown in FIGS. 7(2c) to (4c). In the case shown in FIG. 7(3a), the end point within the inhibitor k is located at the barycentric position (bk) of the inhibitor k, so the movement processing is not performed. In this case, since the number of points and the number of lines do not increase or decrease, ΔNI indicating the number of points to be increased or decreased and ΔNP indicating the number of lines to be increased or decreased are not changed. Also, in this case, the line change processing unit 119 stores information indicating that the end point in the inhibitor k has been changed to the fixed point ik in the RAM or hard disk.

On the other hand, if the result of determination in step S34 is that both end points of line p are within inhibitor k (cases shown in FIGS. 7(5a) and (6a)), the process proceeds to step S36. When the process proceeds to step S36, the line change processing section 119 eliminates the line p in the inhibitor k ((5b) and (6b) in FIG. 7, or (5c) and (6c) in FIG. 7). This reduces the number of lines by one.

Next, in step S37, the line change processing unit 119 moves the two points in the inhibitor k to the barycentric position (bk) of the inhibitor k (this example is the first processing example), and One fixed point ik (fixed point ik shown in FIGS. 7(5b) and 7(6b)). In the case shown in FIG. 7(6a), one end point within the inhibitor k is located at the barycentric position (bk) of the inhibitor k, so the one end point is not moved. The processing in step S37 reduces the number of points by one. Also, in this case, the line change processing unit 119 stores information indicating that the two end points of the line p have been changed to one fixed point ik and information indicating that the line p has been eliminated. memorize to

Next, in step S38, since the number of points and the number of lines are reduced by one in the processing of steps S36 and S37, the line change processing unit 119 changes the currently set ΔNI indicating the number of points to be increased or decreased. 1 is subtracted to change the ΔNI, and 1 is subtracted from the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP.

When the process of step S33, step S35, or step S38 is completed, the process proceeds to step S39. When the process proceeds to step S39, the line change processing unit 119 determines whether or not the variable k indicating the inhibitor to be processed is smaller than the number NK set in step S14. As a result of this determination, if the variable k indicating the inhibitor to be processed is smaller than the number NK set in step S14, it is determined that all the inhibitors k set in step S14 have not been processed, and the process proceeds to step S14. Proceed to S40.

When the process proceeds to step S40, the line change processing unit 119 adds 1 to the variable k indicating the inhibitor to be processed to change the inhibitor k to be processed. At this time, the line change processing unit 119 acquires from the inhibitor setting unit 118 information about the inhibitor k set in step S40 (coordinate information indicating the center-of-gravity position bk of the inhibitor k and information about its radius r). Then, the process after step S29 is performed again for the changed inhibitor k.
As described above, in the present embodiment, an example of line change processing means is realized by performing the processes of steps S25 to S40.

On the other hand, if the result of determination in step S39 is that the variable k indicating the inhibitor to be processed is greater than or equal to the number NK set in step S14, it is determined that all inhibitors k set in step S14 have been processed, The process proceeds to step S41.

When the process proceeds to step S41, the line change processing unit 119 determines whether or not the variable p indicating the line to be processed is smaller than the number NP set in step S19. As a result of this determination, if the variable p indicating the line to be processed is smaller than the number NP set in step S19, it is determined that all the lines p set in step S19 have not been processed, and the process proceeds to step Proceed to S42.

When the process proceeds to step S42, the line change processing unit 119 adds 1 to the variable p indicating the line to be processed to change the line p to be processed. At this time, the line change processing unit 119 acquires from the line setting unit 104 information about the line p set in step S42. Then, the process after step S28 is performed again for the changed line p.

On the other hand, if the result of determination in step S41 is that the variable p indicating the line to be processed is greater than or equal to the number NP set in step S19, it is determined that all lines p set in step S19 have been processed, The process proceeds to step S43.

When the process proceeds to step S43, the line change processing unit 119 outputs ΔNI information indicating the number of points currently set to increase or decrease to the point setting unit 103, and the number of points currently set .DELTA.NI indicating the output number of points to be increased or decreased is added to NI to reset the number of points NI. In addition, the line change processing unit 119 outputs ΔNP information indicating the number of lines currently set to be increased or decreased to the line setting unit 104, and the output increase or decrease is added to the number NP of lines set in step S19. ΔNP indicating the number of lines to be processed is added, and the number NP of lines is reset.

Next, in step S44, the line change processing unit 119 instructs the point setting unit 103 and the line setting unit 104 to change points (including disappearance and appearance) and change lines (including disappearance and appearance). Perform various resetting processes.

Specifically, the line change processing unit 119 outputs information regarding the change (including disappearance and occurrence) of the points that occurred in the processing of steps S26 to S43 to the point setting unit 103, and the point i in step S8. be reconfigured. At this time, the point setting unit 103 sets coordinate information indicating the position of the generated fixed point ik in the RAM or hard disk together with information indicating that the point is a fixed point.

In addition, the line change processing unit 119 outputs information regarding the line change (including disappearance and occurrence) that occurred in the processing of steps S26 to S43 to the line setting unit 104, and the line p is reproduced in step S19. make the settings. At this time, the line change processing unit 119 may cause the line setting unit 104 to reset the line based on the point i reset by the point setting unit 103 .

Further, in the grain boundary setting unit 105, the resetting of the point i in the point setting unit 103 and the resetting of the line p in the line setting unit 104 trigger the resetting of the grain boundary u in step S20. Further, in the grain boundary energy (γ) setting unit 109, resetting of the grain boundary u in the grain boundary setting unit 105 triggers the resetting of the grain boundary energy γ per unit length in step S22. Further, in the mobility setting unit 111, the resetting of the grain boundary u in the grain boundary setting unit 105 triggers the resetting of the mobility Mi in step S23.

Next, in step S45 in FIG. 10-4, the analysis point determination unit 113 sets 1 to a variable i indicating a point to be calculated. This sets the point i to be calculated.
Next, in step S46, the analysis point determination unit 113 determines whether or not the point i to be calculated is a fixed point (ik). As a result of this determination, if the point i to be calculated is not the fixed point (ik), the process proceeds to step S47.

When the process proceeds to step S47, the analysis point determination unit 113 determines whether or not the point i to be calculated is a double point. As a result of this determination, if the point i to be calculated is a double point, the process proceeds to step S48.

When the process proceeds to step S48, double point driving force/position calculation processing by the double point driving force calculation unit 114 and the position calculation unit 116 is performed. In the double point driving force/position calculation process, the vector representing the driving force Fi(t) generated at the double point i is calculated by equation (1), and Δt[ sec] has elapsed, a process is performed that includes calculating a vector indicating the position ri(t+Δt) at which the double point i to be calculated lies.
As described above, in the present embodiment, for example, by performing the process of step S48, an example of the driving force calculation means and the position calculation means is realized.

If the result of determination in step S47 is that point i to be calculated is not a double point but a triple point, the process proceeds to step S49.
When the process proceeds to step S49, triple point driving force/position calculation processing by the triple point driving force calculation unit 115 and the position calculation unit 116 is performed. In the triple junction driving force/position calculation process, the vector indicating the driving force Fi(t) generated at the triple junction i to be calculated is calculated by equation (2), and the current time t is calculated by equation (4). When Δt [sec] has passed since , a process including calculating a vector indicating the position ri(t+Δt) at which the triple point i to be calculated exists is executed.
As described above, in the present embodiment, for example, by performing the process of step S49, an example of the driving force calculation means and the position calculation means is realized.

If the point i to be calculated is the fixed point (ik) as a result of the determination in step S46, the process proceeds to step S50.
When the process proceeds to step S50, the fixed point processing unit 120 determines the coordinate information of the fixed point i determined by the analysis point determination unit 113 and the positions of the fixed point i and the other points forming the line p. , is read out from the point setting unit 103 . Then, the fixed point processing unit 120 reads from the inhibitor setting unit 118 information (coordinate information indicating the center of gravity position bk and information on the radius r) of the inhibitor k whose center of gravity position bk is the fixed point i to be processed. Furthermore, the fixed point processing unit 120 reads information on the effective range 801 (information on the radius of the effective range 801) from the effective range setting unit 122. FIG.

Next, in step S51, the grain boundary energy (E) calculator 121 acquires the information read out in step S50, and calculates the grain boundary energy γ per unit length of the grain boundary u to which the fixed point i belongs. Read from the grain boundary energy (γ) setting unit 109 . Then, the grain boundary energy (E) calculation unit 121 uses the grain boundary energy γ per unit length of the grain boundary u to which the fixed point i belongs and the effective lengths L1 and L2 to calculate the fixed point i at the center of gravity position. The grain boundary energy Ei within the effective range 801 of the grain boundary u to which the fixed point i belongs when fixed to bk is calculated (calculated).
Here, when the fixed point i(ik) is a double point, the grain boundary energy Ei is calculated using the equation (7), for example. On the other hand, when the fixed point i(ik) is the triple point, the grain boundary energy Ei is calculated using the equation (8), for example.
As described above, in the present embodiment, for example, the first grain boundary energy is realized by the grain boundary energy Ei, and an example of grain boundary energy calculation means is realized by performing the processing of step S51.

Next, in step S52, the grain boundary energy (E) calculator 121 determines the position (equilibrium position) where the fixed point i is released from the fixed position (the center of gravity position bk of the inhibitor k) and the grain boundary energy E is minimized. , the grain boundary energy Ei′ within the effective range 801 of the grain boundary u to which the released fixed point i belongs is calculated (calculated).
Here, when the fixed point i(ik) is a double point, the grain boundary energy Ei' is calculated using the equation (9), for example. On the other hand, when the fixed point i(ik) is the triple point, the grain boundary energy Ei' is calculated using the equation (10), for example.
As described above, in the present embodiment, for example, the second grain boundary energy is realized by the grain boundary energy Ei′, and an example of grain boundary energy calculation means is realized by performing the process of step S52.

Next, in step S53, the fixed point processing unit 120 compares the grain boundary energy Ei calculated in step S51 with the grain boundary energy Ei' calculated in step S52, and the grain boundary energy Ei' is the grain boundary It is determined whether or not the energy is less than Ei (Ei'<Ei). As a result of this determination, if the grain boundary energy Ei' is not less than the grain boundary energy Ei, the process proceeds to step S60, which will be described later. On the other hand, if the grain boundary energy Ei' is less than the grain boundary energy Ei, the process proceeds to step S54.

When the process proceeds to step S54, the grain boundary energy (E) calculator 121 calculates the grain boundary energy Ei'' within the effective range 801 of the grain boundary u to which the fixing point i belongs when the fixing point ik is released. Calculate (calculate)
Here, when the fixed point i(ik) is a double point, the grain boundary energy Ei'' is calculated using the equation (11), for example. On the other hand, when the fixed point i(ik) is the triple point, the grain boundary energy Ei'' is calculated using the equation (12), for example.
As described above, in the present embodiment, for example, the third grain boundary energy is realized by the grain boundary energy Ei'', and an example of grain boundary energy calculation means is realized by performing the processing of step S54.

Next, in step S<b>55 , fixed point processing section 120 reads information on barrier energy E<b>0 from barrier energy setting section 123 . Then, the fixed point processing unit 120 determines whether or not the value obtained by subtracting the grain boundary energy Ei from the grain boundary energy Ei'' is less than the barrier energy E0. As a result of this determination, if the value obtained by subtracting the grain boundary energy Ei'' from the grain boundary energy Ei'' is not less than the barrier energy E0, the process proceeds to step S60, which will be described later.
On the other hand, if the value obtained by subtracting the grain boundary energy Ei from the grain boundary energy Ei'' is less than the barrier energy E0, the process proceeds to step S56.

When the process proceeds to step S56, the fixed point processing unit 120 determines whether or not the fixed point i(ik) determined in step S46 is a double point. As a result of this determination, if the fixed point i(ik) is a double point, the process proceeds to step S57. When the process proceeds to step S57, the fixing point processing unit 120 moves the fixing point i (ik) to the surface (boundary) of the inhibitor k, releases the fixation, and replaces the normal point i ( ik) (see FIG. 8(b)). Then, the process proceeds to step S61, which will be described later.

On the other hand, if the fixed point i(ik) is not a double point but a triple point, the process proceeds to step S58. When the process proceeds to step S58, the fixation point processing unit 120 moves the fixation point i (ik) to the surface (boundary) of the inhibitor k, releases the fixation, and places the normal point i ( ik). Furthermore, the fixed point processing unit 120 selects a point i(iv) that is not connected to the generated normal point i(ik) among the points i(ir, it, iv) adjacent to the fixed point i(ik). , a fixed double point i(ix) connected to the generated normal point i(ik) is generated at the centroid position (bk) of the inhibitor k (see FIG. 9(b)).
Next, in step S59, the line change processing unit 119 adds 1 to the currently set ΔNI indicating the number of points to be increased or decreased because the number of points and the number of lines are increased by one in the processing of step S58. ΔNI is changed by addition, and 1 is added to the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP. Then, the process proceeds to step S61, which will be described later.
As described above, in the present embodiment, an example of the fixed point processing means is realized by performing the processes of steps S57 and S58, for example.

If it is determined in step S53 that the grain boundary energy Ei' is not less than the grain boundary energy Ei, and in step S55, the value obtained by subtracting the grain boundary energy Ei from the grain boundary energy Ei'' is not less than the barrier energy E0. If so, the process proceeds to step S60. When the process proceeds to step S60, the fixed point processing unit 120 determines whether or not the radius r at the current time t of the inhibitor k to which the fixed point i(ik) belongs is equal to or less than a threshold. As a result of this determination, if the radius r at the current time t of the inhibitor k to which the fixed point i(ik) belongs is equal to or less than the threshold, the process proceeds to step S56 described above. As a result, the fixation by the fixation point i (ik) is released (see steps S57 and S58). On the other hand, if the radius r at the current time t of the inhibitor k to which the fixed point i(ik) belongs is not less than or equal to the threshold, the process proceeds to step S61.

When the process proceeds to step S61 as described above, the analysis point determination unit 113 determines whether or not the variable i indicating the points to be calculated is smaller than the number NI of points currently set by the point setting unit 103. do. As a result of this determination, if the variable i indicating the points to be calculated is smaller than the number NI of points currently set by the point setting unit 103, all the points i currently set by the point setting unit 103 are processed. is not performed, and the process proceeds to step S62.
When the process proceeds to step S62, the analysis point determination unit 113 adds 1 to the variable i indicating the point to be calculated to change the point i to be calculated. Then, the processing after step S46 is performed again for the changed point i.

On the other hand, if it is determined in step S61 that the variable i indicating the points to be calculated is greater than or equal to the number NI of points currently set by the point setting unit 103, the number of points currently set by the point setting unit 103 is It is determined that all points i have been processed, and the process proceeds to step S63.
When the process proceeds to step S63, the fixed point processing unit 120 causes the point setting unit 103 to perform resetting according to the change of the point i in steps S57 and S58. At the same time, the position calculation unit 116 outputs to the point setting unit 103 a vector indicating the position ri(t+Δt) where the point i is calculated in step S48 or S49. As a result, the vector indicating the current position ri(t) of the point i is reset in the point setting section 103 .

Then, the line setting unit 104 resets the line p with the resetting of the point i in the point setting unit 103 as a trigger. Further, in the grain boundary setting unit 105, the resetting of the point i in the point setting unit 103 and the resetting of the line p in the line setting unit 104 trigger the resetting of the grain boundary u. Further, the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 are also reset with the resetting of the grain boundary u by the grain boundary setting unit 105 as a trigger.

Next, in step S64, the analysis time setting unit 112 determines whether the time t is longer than the analysis completion time T set in step S6. That is, it is determined whether or not the analysis completion time T has passed. As a result of this determination, if the time t is not longer than the analysis completion time T set in step S6 (if the analysis completion time T has not passed), the process proceeds to step S65. When the process proceeds to step S65, the analysis time setting unit 112 adds the time Δt to the currently set time t to update the time t.

Next, in step S66, the concentration distribution setting unit 124 derives the element concentration distribution at time t after updating, and changes the element concentration distribution to the derived element concentration distribution.

Next, in step S67, the inhibitor setting unit 118 derives the size (radius r _k ) of the inhibitor k at the updated time t, and changes the size (radius) of the inhibitor k to the derived size (radius r _k ). As described above, in the present embodiment, the inhibitor setting unit 118 derives the size (radius r _k ) of the inhibitor k at the time t after updating, with t in Equation (6) being the time t updated in step S65. do. It should be noted that the inhibitor k whose size is to be changed is the inhibitor k (fixed point i(ik)) reset by the resetting process in the previous step S63.
As described above, in the present embodiment, an example of inclusion setting means is realized by performing the process of step S67, for example.
Note that the processing of steps S66 and S67 may be performed in step S63.
After that, the process returns to step S26, and the processes after step S26 are performed again. Then, until it is determined in step S64 that the time t is greater than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed), the processing from steps S26 to S67 is repeated. .

On the other hand, if the result of determination in step S64 is that the time t is longer than the analysis completion time T set in step S6 (if the analysis completion time T has passed), the process proceeds to step S68. When the process proceeds to step S68, the analysis image display unit 117 changes the time t from 0 (zero) to T[ sec], the display device 200 displays an image showing how the state of the crystal grain A changes. Then, the series of flowcharts shown in FIGS. 10-1 to 10-4 ends.

If the analyzed temperature θ(t) input in step S3 depends on time, for example, after step S65, the analyzed temperature θ(t+Δt) at the time t+Δt set in step S65 is read, and the analyzed temperature θ After resetting the grain boundary energy γ per unit length at (t+Δt) and the mobility Mi, the processing after step S26 may be performed.

As described above, in the present embodiment, the inhibitor setting unit 118, when the line p having both ends at two grain boundary points adjacent to each other on the same grain boundary passes through the inhibitor k, A fixed point ik is generated, and the size (radius r _k ) of the inhibitor k is changed depending on the time t when changing the line p having the fixed point ik as an end point. Therefore, when analyzing the state of the crystal grains in an environment where the inhibitor k is present, it is possible to prevent the state of the crystal grains A from deviating from the actual state. Also, by virtually changing the magnitude of the inhibitor k depending on the time t, it is possible to obtain guidelines for the development of new materials.

In addition, in the present embodiment, the inhibitor setting unit 118 sets the size (radius r _k ) of the inhibitor k to the concentration m of the inclusion-constituting element around the inhibitor k and the inhibitor k′ around the inhibitor k. It is changed according to the size sk', the distance dk' between the inhibitors _k and _{k '} , and the distance yk from the surface of the magnetic steel sheet to the center of gravity of the inhibitor k. Therefore, it is possible to further prevent the state of the crystal grains A from deviating from the actual state.

In this embodiment, the inhibitor setting unit 118 sets the initial size of the inhibitor k according to the initial position (distance from the surface of the electromagnetic steel sheet (depth in the plate thickness direction)). Therefore, it is possible to further prevent the initial state of the crystal grains A from deviating from the actual state.

Further, in this embodiment, the fixed point processing unit 120 cancels (releases) the fixed point ik when the radius r at the current time t of the inhibitor k to which the fixed point ik belongs is equal to or less than the threshold. Therefore, it is possible to prevent the fixed point ik from being released (released) even though the radius of the inhibitor k is small. As a result, it is possible to prevent the state of the crystal grain A from deviating from the actual state because the fixed point ik is not released (released).

[Modification 1]
As in this embodiment, when the size (radius r _k ) of the inhibitor k is changed depending on the time t, the concentration m of the inclusion-constituting element around the inhibitor k and the concentration m of the inclusion-constituting element around the inhibitor k It is preferable to consider the size sk' of the inhibitor _k ', the distance dk' between the inhibitors _k and k _' , and the distance yk from the surface of the magnetic steel sheet to the center of gravity of the inhibitor k. However, this need not necessarily be the case. For example, the concentration m of inclusion constituent elements around the inhibitor k, the size sk ' of the inhibitor k' around the inhibitor k, the distance dk _' between the inhibitors k and k _' , and the magnetic steel sheet One, two, or three of the distances y _k from the surface to the centroid position of the inhibitor k may be considered, and the rest may not be considered. When the distance dk _' between the inhibitors k and _k' is considered without considering the size sk' of the inhibitor k' around the inhibitor _k , the function h( _sk' /sk, _dk' , t) becomes a function h(d _k , t). Conversely, if we consider the size sk' of inhibitor _k ' around inhibitor k without considering the distance dk _' between inhibitors k and _k ', the function h( _sk' /sk , d _k′ , t) becomes the function h(s _k′ /s _k , t). In addition, the size sk' of the inhibitor _{k '} around the inhibitor k is not necessarily the ratio _sk' /sk of the size sk' of the inhibitor k' around the inhibitor _k to the size sk of the inhibitor _k . No need to evaluate. For example, the size sk' of inhibitor _k ' around inhibitor k is evaluated by the difference between the size sk of inhibitor _k and the size sk' of inhibitor _k ' around inhibitor k. The magnitude s _k ' of the inhibitor k' around k may be evaluated.

[Modification 2]
In the present embodiment, the double point is set in order to improve the reproducibility of the grain boundary u, but only the triple point may be set without setting the double point. In this case, for example, steps S47 and S48 in FIG. 10-4 are omitted. Then, instead of steps S58 and S59, the fixed point i is moved to the surface of the inhibitor to generate a normal point i. Further, instead of step S57, the fixed point i is extinguished, and the two lines connecting the fixed point i and the two points adjacent to the fixed point i with the shortest distance are extinguished so that the fixed point i belongs to. After the two grain boundaries are eliminated, a grain boundary (line) connecting two points adjacent to the fixed point i is generated, and 1 is subtracted from ΔNI and ΔNP, which indicate the number of points and lines to be increased or decreased. conduct.

[Modification 3]
In the present embodiment, an electromagnetic steel sheet is taken as an example of a metal material that is an example of a material to be analyzed by the grain analysis apparatus. Any material can be applied as long as it is manufactured using an inclusion such as an inhibitor. When the metal material to be analyzed by the grain analysis device is different, the contents of the graphs stored in the grain boundary energy (γ) storage unit 108 and the mobility storage unit 110 are input to the grain analysis device. The data obtained will be different depending on the material.

[Modification 4]
In the present embodiment, the case where it is determined whether or not the value obtained by subtracting the grain boundary energy Ei from the grain boundary energy Ei'' is less than the barrier energy E0 has been described as an example. However, as in Patent Document 2, such determination may not be performed without considering the barrier energy E0.

[Modification 5]
In this embodiment, the inhibitor setting unit 118 sets the inhibitor k by approximating the detected area of the inhibitor k with a sphere as shown in FIG. 6, but the shape of the inhibitor k is not limited to a sphere. . For example, the approximate shape may be changed according to the shape of the region of the detected inhibitor k. At this time, for example, when approximating the inhibitor k to an ellipsoid, coordinate information indicating the center-of-gravity position (fixed position) of the ellipsoid, information relating to the length of the major axis of the ellipsoid, and short axis of the ellipsoid is calculated, and the inhibitor k is set in the RAM or hard disk. Further, for example, when approximating the inhibitor k to a polyhedron, for example, coordinate information indicating the barycentric position as a fixed position and coordinate information indicating each vertex in the polyhedron are calculated, and the inhibitor k is set in the RAM or hard disk. take the form of In the case of two-dimensional analysis, the ellipsoid is replaced by an ellipse, and the polyhedron is replaced by a polygon.

[Other Modifications]
The embodiments of the present invention described above can be implemented by a computer executing a program. A computer-readable recording medium recording the program and a computer program product such as the program can also be applied as embodiments of the present invention. Examples of recording media that can be used include flexible disks, hard disks, optical disks, magneto-optical disks, CD-ROMs, magnetic tapes, nonvolatile memory cards, and ROMs.
In addition, the embodiments of the present invention described above are merely examples of specific implementations of the present invention, and the technical scope of the present invention should not be construed to be limited by these. It is. That is, the present invention can be embodied in various forms without departing from its technical concept or main features.

100: crystal grain analysis device, 101: crystal image acquisition unit, 102: crystal image display unit, 103: point setting unit, 104: line setting unit, 105: grain boundary setting unit, 106: analysis temperature setting unit, 107: orientation Setting unit 108: Grain boundary energy (γ) storage unit 109: Grain boundary energy (γ) setting unit 110: Mobility storage unit 111: Mobility setting unit 112: Analysis time setting unit 113: Analysis point discrimination unit 114: double point driving force calculation unit 115: triple point driving force calculation unit 116: position calculation unit 117: analysis image display unit 118: inhibitor setting unit 119: line change processing unit , 120: fixed point processing unit, 121: grain boundary energy (E) calculation unit, 122: effective range setting unit, 123: barrier energy setting unit, 124: concentration distribution setting unit, 200: display device, 300: operation device

Claims (9)

an image signal acquiring means for acquiring an image signal of crystals in the metal material;
A grain boundary in which a triple point corresponding to both end points of a grain boundary of a crystal grain contained in the crystal and in contact with three crystal grains including the crystal grain is set as a grain boundary point in the analysis target area based on the image signal. point setting means;
a line setting means for setting a line whose end points are two grain boundary points set by the grain boundary point setting means and which are adjacent to each other on the same grain boundary;
inclusion setting means for setting inclusions in the analysis target area based on the image signal;
line change processing means for generating a fixed point in the inclusion when the line set by the line setting means passes through the inclusion, and changing the line with the fixed point as an end point;
A first grain boundary energy at the grain boundary to which the fixing point belongs, and the fixing point is released from the fixed position and moved to an equilibrium position where the grain boundary energy is the minimum at a position in the region excluding the inclusion. Grain boundary energy calculation means for calculating a second grain boundary energy at the grain boundary to which the moved fixed point belongs when the
fixed point processing means for performing a process of releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy;
The crystal grain analysis apparatus, wherein the inclusion setting means derives a change in size of the inclusion over time. The inclusion setting means determines the size of the inclusion at each time by determining the concentration of elements forming the inclusion around the inclusion, the size of the inclusion different from the inclusion, and the size of the inclusion. 2. The crystal grain analysis apparatus according to claim 1, wherein the derivation is based on at least one of the distance between the inclusion and the inclusion different from the inclusion, and the position of the inclusion. 3. The crystal grain analysis apparatus according to claim 1, wherein said inclusion setting means determines the initial size of said inclusion according to the position where said inclusion is initially arranged. 4. The fixing point processing means, when the size of the inclusion is equal to or less than a threshold value, performs a process of releasing the fixing point within the inclusion. The crystal grain analysis apparatus according to 1. The grain boundary point setting means includes a triple point corresponding to both end points of a grain boundary of a crystal grain contained in the crystal and in contact with three crystal grains including the crystal grain, and a grain of the crystal grain contained in the crystal. 5. The crystal grain according to any one of claims 1 to 4, wherein a double point corresponding to the midpoint of the boundary and in contact with two crystal grains including the crystal grain is set as a grain boundary point. analysis equipment. The grain boundary energy calculation means further calculates a third grain boundary energy at the grain boundary to which the fixed point to be released belongs when the fixed point is released from the inclusion,
The fixed point processing means is such that the second grain boundary energy is less than the first grain boundary energy and a difference between the first grain boundary energy and the third grain boundary energy is less than a threshold. 6. The crystal grain analysis apparatus according to claim 1, wherein a process of releasing the fixed point is performed when the crystal grain analysis is performed. driving force calculation means for calculating the driving force generated at the grain boundary point set by the grain boundary point setting means using the grain boundary energy per unit length of the grain boundary to which the grain boundary point belongs;
7. The method according to any one of claims 1 to 6, further comprising position calculation means for calculating a change in position of said grain boundary point over time using the driving force calculated by said driving force calculation means. 1. A crystal grain analysis apparatus according to claim 1. an image signal acquisition step of acquiring an image signal of crystals in the metal material;
A grain boundary in which a triple point corresponding to both end points of a grain boundary of a crystal grain contained in the crystal and in contact with three crystal grains including the crystal grain is set as a grain boundary point in the analysis target area based on the image signal. a point setting step;
a line setting step of setting a line whose endpoints are two grain boundary points set by the grain boundary point setting step, the grain boundary points being adjacent to each other on the same grain boundary;
an inclusion setting step of setting an inclusion in the analysis target area based on the image signal;
a line change processing step of generating a fixed point in the inclusion when the line set by the line setting step passes through the inclusion, and changing the line with the fixed point as an end point;
A first grain boundary energy at the grain boundary to which the fixing point belongs, and the fixing point is released from the fixed position and moved to an equilibrium position where the grain boundary energy is the minimum at a position in the region excluding the inclusion. a grain boundary energy calculating step of calculating a second grain boundary energy at the grain boundary to which the moved fixed point belongs when the
a fixed point processing step of performing a process of releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy;
The crystal grain analysis method, wherein the inclusion setting step derives a change in size of the inclusion over time. A program for causing a computer to function as each means of the grain analysis apparatus according to any one of claims 1 to 7.

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