JP2010091536A - Crystal grain analyzer, crystal grain analysis method, and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To analyze more easily and accurately than conventionally a process of change, with the elapse of time of a crystal grain via an inclusion. <P>SOLUTION: It is determined whether a line p overtakes an inhibitor k, as a result of change of the position of a grain boundary point; when it is overtaken, a fixed point ik is generated at a center position bk of the inhibitor k, and in company therewith, changing the processing of the line passing both end points (grain boundary points) of the line p overtaking the inhibitor k is performed. Consequently, the behavior of a crystal grain A (grain boundary u) near the inhibitor k can be simulated faithfully, as much as possible. <P>COPYRIGHT: (C)2010,JPO&INPIT

Description

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

Conventionally, the state of crystal grains of a metal material has been analyzed by a computer.
Patent Document 1 discloses a technique for annealing a rolled thin steel plate to perform primary recrystallization, and finally annealing the primary recrystallized thin steel plate to obtain a secondary recrystallized thin steel plate. Yes. In such a technique, the particle size distribution of the primary recrystallized crystal grains is statistically obtained. Then, using the particle size distribution of the primary recrystallized grains, the integral value (integrated grain boundary energy) of the grain boundary energy of each primary recrystallized grain is obtained, and the obtained result is used. Estimate the optimal distribution of primary recrystallized grains. And in patent document 1, if it was made to obtain the crystal grain recrystallized primary so that it might become the distribution estimated in this way, the thin steel plate appropriately secondary recrystallized will be obtained. Yes.

  In Patent Document 2, the initial crystal grain size, the holding temperature, the holding time, and various coefficients obtained from the test pieces in each step of the Al slab in the soaking process or the Al plate material in the annealing process and predetermined coefficients are calculated. It is disclosed that the grain size after crystal growth is calculated by substituting into the equation.

  Furthermore, Patent Document 3 calculates the austenite grain size and average dislocation density after rolling based on the size of steel slab, component information and rolling conditions, and based on the calculated results and cooling conditions, the structure of the transformation structure It is disclosed that the fraction of each phase, the average formation temperature and the crystal grain size are calculated, and further, the fraction, particle size and carbide / precipitate size of each phase constituting the final structure are calculated based on the subsequent heat treatment conditions. Has been.

JP-A-6-158165 JP 2002-224721 A JP-A-5-87800

By the way, the primary recrystallized crystal grains grow while taking various behaviors during the secondary recrystallization.
However, the technique described in Patent Document 1 focuses on the primary recrystallized crystal grains, and does not consider the behavior until the primary recrystallized crystal grains are secondary recrystallized. Therefore, it has been difficult to obtain accurate knowledge about how the crystal grains change over time. Further, in the above-described conventional technique, since the particle size distribution of the primary recrystallized crystal grains is obtained statistically, a lot of data based on prior manufacturing and testing is necessary. Therefore, there is a problem that it is difficult to easily analyze the state of crystal grains.

Moreover, the technique described in Patent Document 2 only discloses a calculation model for crystal grain size. Therefore, there is a problem that it is difficult to analyze specifically what shape the crystal grains change with time.
In addition, the technique described in Patent Document 3 has a problem in that it does not indicate what model is used to calculate the crystal grain growth.

  Furthermore, as a metal material to be analyzed for crystal grains, for example, in a metal material of a magnetic steel sheet, it is necessary to enlarge the grain size of the crystal grains after secondary recrystallization. A technique of interposing an inhibitor as an inclusion between grains is used.

  In this case, since the growth of the crystal grains is suppressed while the inhibitor is present between the crystal grains, it is necessary to perform calculation in consideration of the inclusions. In this regard, the conventional technique does not consider such inclusions, and there is a problem that it is difficult to calculate how the crystal grains grow through the inclusions.

  The present invention has been made in view of such a problem, and makes it easier and more accurate to analyze how crystal grains change over time through inclusions. For the purpose.

  The crystal grain analyzer of the present invention corresponds to image signal acquisition means for acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both end points of a grain boundary of the crystal grain included in the crystal. And a triple point in contact with the three crystal grains including the crystal grain, and a double point corresponding to the midpoint of the grain boundary of the crystal grain included in the crystal and in contact with the two crystal grains including the crystal grain. The grain boundary point setting means for setting the specified triple point and double point grain boundary point, and the grain boundary point set by the grain boundary point setting means. A line setting means for setting a line having two grain boundary points adjacent to each other on the same grain boundary, and when the inclusion is designated based on the image signal, the designated intervention Inclusion setting means for setting an object, and the line setting A first line change processing means for generating a fixed point in the inclusion and performing a line change process with the fixed point as an end point when the line set by the step passes through the inclusion; Determining means for determining whether or not the line has passed the inclusion set by the inclusion setting means based on the positions before and after the movement of the line that has not been changed by the first line changing means; When the determination means determines that the line has passed the inclusion set by the inclusion setting means, a fixed point is generated in the inclusion, and the line is changed with the fixed point as an end point. The second line changing means for performing the processing, the first grain boundary energy at the grain boundary to which the fixed point belongs, and the position of the region excluding the inside of the inclusion by releasing the fixed point from the fixed position. Grain boundary energy calculating means for calculating a second grain boundary energy at the grain boundary when moved to an equilibrium position where the grain boundary energy is minimized, and the second grain boundary energy is the first grain boundary. And fixing point processing means for performing processing for releasing the fixed point when the energy is less than energy.

  The crystal grain analysis method of the present invention corresponds to an image signal acquisition step of acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both end points of a grain boundary of the crystal grain included in the crystal. And a triple point in contact with the three crystal grains including the crystal grain, and a double point corresponding to the midpoint of the grain boundary of the crystal grain included in the crystal and in contact with the two crystal grains including the crystal grain. The grain boundary point set by the grain boundary point setting step and the grain boundary point setting step for setting the grain boundary point of the designated triple point and double point when specified based on the image signal. A line setting step for setting a line having two adjacent grain boundary points on the same grain boundary as both end points, and when the inclusion is designated based on the image signal, the designated intervention Inclusion setting step And when the line set by the line setting step passes through the inclusion, a fixed point is generated in the inclusion, and a first line change process for changing the line with the fixed point as an end point is performed. Based on the processing step and the position before and after the movement of the line that has not been changed by the first line changing step, whether or not the line has passed the inclusion set by the inclusion setting step. When the determination step and the determination step determine that the line has passed the inclusion set by the inclusion setting step, a fixed point is generated in the inclusion, and the fixed point is set as an end point. A second line changing step for performing a line changing process, a first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point. Grain boundary energy calculation for calculating the second grain boundary energy at the grain boundary when the grain boundary energy is moved to the equilibrium position where the grain boundary energy is minimized and released from the fixed position. And 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 computer program of the present invention corresponds to an image signal acquisition step of acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both end points of grain boundaries of crystal grains included in the crystal, and The triple point in contact with the three crystal grains including the crystal grain, and the double point corresponding to the intermediate point of the grain boundary of the crystal grain included in the crystal and in contact with the two crystal grains including the crystal grain, When specified based on the image signal, a grain boundary point setting step for setting the specified triple point and double point grain boundary point, and the grain boundary point set by the grain boundary point setting step, A line setting step for setting a line with two grain boundary points adjacent to each other on the same grain boundary, and when the inclusion is specified based on the image signal, the specified inclusion is Inclusion settings to be set And a first line for generating a fixed point in the inclusion and performing a line changing process with the fixed point as an end point when the line set in the line setting step passes through the inclusion. Whether or not the line has passed the inclusion set by the inclusion setting step based on the position before and after the movement of the line that has not been changed by the change processing step and the first line changing step. When the determination step and the determination step determine that the line has passed the inclusion set by the inclusion setting step, a fixed point is generated in the inclusion, and the fixed point is A second line changing step for changing the line as an end point; a first grain boundary energy at a grain boundary to which the fixed point belongs; Grain boundary for calculating the second grain boundary energy at the grain boundary when the fixed point is released from the fixed position and moved to the equilibrium position where the grain boundary energy is the minimum in the region excluding the inside of the inclusion An energy calculation step and 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 are characterized in that a computer is executed. .

  According to the present invention, it is possible to more easily and accurately analyze how the crystal grains change with the passage of time through inclusions.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings. In the embodiment of the present invention described below, a case where an electrical steel sheet manufactured using an inhibitor that is an inclusion is applied as an example of a metal material to be analyzed for crystal grains will be described.
FIG. 1 is a diagram conceptually illustrating an example of an analysis method performed by a crystal grain analysis apparatus. In FIG. 1, for convenience of explanation, only one crystal grain A is shown among the many crystal grains constituting the electromagnetic steel sheet, but actually, the electromagnetic steel sheet is formed by the many crystal grains. Needless to say.

In the crystal grain analysis apparatus of this embodiment, the crystal grains are modeled as shown in FIG.
First, as shown in FIG. 1 (a), triple points ia, ie, if are set at positions corresponding to both end points of three grain boundaries ua to uc of crystal grain A, and intermediate points of grain boundaries ua to uc. The grain boundary points of the double points ib to id and ig to ii are set at positions corresponding to. Here, the triple points ia, ie, and if are points where three straight lines intersect (that is, a point in contact with three crystal grains), and the double points ib to id and ig to ii intersect two straight lines. Points (points in contact with two crystal grains). And the straight line (line) which mutually connects the point (grain boundary point) i mutually adjacent on the same grain boundary ua-uc is set.
As described above, in the present embodiment, not only the positions of both ends of the grain boundaries ua to uc but also the double points ib to id, so that the shape in the middle of the grain boundaries ua to uc can be represented as faithfully as possible. ig to ii are set.

  The driving force Fi (t) [N] generated at the analysis time t is calculated for each point (double point and triple point) ia to ii of the crystal modeled as described above. 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 (analysis time t + Δt) is calculated. If it does so, the position of each point (double point and triple point) ia-ii shown in Drawing 1 (a) will move to the position shown in Drawing 1 (b), for example.

  In the crystal grain analysis apparatus of the present embodiment, as described above, the triple points ia, ie, if corresponding to both 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 are used. The driving force Fi (t) generated at each of the corresponding double points ib to id and ig to ii is calculated, and the triple points ia, ie, if and the double points ib to id and ig to ii move. Is analyzed. Thereby, for example, the state in which the crystal grain Aa shown in FIG. 1 (a) changes with the passage of time as the crystal grain Ab shown in FIG. 1 (b) is as accurate as possible without imposing a large calculation load. Can be analyzed. The behavior of the crystal grains via the inhibitor (inclusion) will be described in detail in the description with reference to FIGS.

Below, the structure of a crystal grain analyzer is demonstrated in detail.
FIG. 2 is a block diagram illustrating an example of a functional configuration of the crystal grain analysis apparatus according to the present embodiment. Note that the hardware of the crystal grain analysis apparatus 100 can be realized by using an information processing apparatus including a personal computer, a CPU, a ROM, a RAM, a hard disk, an image input / output board, various interfaces, an interface controller, and the like. . Unless otherwise specified, each block shown in FIG. 2 is realized by the CPU executing a control program stored in the ROM or the hard disk using the RAM. And the following processes are implement | achieved by exchanging a signal between each block shown in FIG.

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

  For example, 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 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). In addition, the operation device 300 includes a user interface such as a keyboard and a mouse.

  The point setting unit 103 acquires points (double points and triple points) i specified by the user using the operation device 300 for the image of the crystal grain A displayed by the crystal image display unit 102, and the acquired points (Double point and triple point) The number of i and a vector indicating the initial position ri (0) of the point i are set (stored) in the RAM or the hard disk. In this embodiment, the user can arbitrarily designate the number of points (double points and triple points) i and the initial position.

  In addition, the point setting unit 103 calculates a vector indicating the position ri (t + Δt) after Δt [sec] at the calculation target point (double point or triple point) i 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 the hard disk. In addition, the point setting unit 103 sets the currently set point i based on inputs from a line change processing unit 119, a first fixed point processing unit 125, and a second fixed point processing unit 120 described later. Is changed and set (stored) in the RAM or hard disk.

  The line setting unit 104 includes information on the 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. As described above, the line p is a straight line having two points i adjacent to each other on the same grain boundary u. The line setting unit 104 also performs a process of changing the line p based on inputs from a line change processing unit 119, a first fixed point processing unit 125, and a second fixed point processing unit 120 described later.

  The grain boundary setting unit 105 includes information on the grain boundary u specified by the line p connected to each other with the triple point i set by the point setting unit 103 as both ends among the lines p set by the line setting unit 104. Set to RAM or hard disk.

  3 shows a crystal grain image displayed by the crystal image display unit 102 (FIG. 3A), points (double points and triple points) i set by the point setting unit 103, and (FIG. 3B). FIG. 4 is a diagram illustrating an example of a line p and a grain boundary u (FIG. 3C) set by the line setting unit 104 and the grain boundary setting unit 105. For convenience of explanation, in FIGS. 3B and 3C, among the crystal grains A1 included in the crystal grain image 31 shown in FIG. Only the point i, the line p, and the grain boundary u set are shown. In addition, the crystal grain image 31 shown in FIG. 3A shows, as an example, inhibitors (k1 to k4) that are inclusions only around the crystal grain A1, but the inhibitors are actually The crystal grain images 31 are scattered.

  When the crystal grain image 31 is displayed as shown in FIG. 3A, the user designates a position corresponding to both end points of the grain boundary u as a triple point i using the operation device 300 such as a mouse. At the same time, the position of the intermediate point of the grain boundary u is designated as the double point i. Then, as shown in FIG. 3B, for example, double points i2 to i4, i6 to i10, i12 to i15, i17, i18, and triple points i1, i5, i11, i16, and Each grain boundary point 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. Here, for example, the line p1 is specified by the triple point i1 and the double point i2. The grain boundary u1 is specified by lines p1 to p4 connected to each other with the triple points i1 and i5 as both ends. As shown in FIG. 3C, the grain boundary u1 is a grain boundary between the crystal grains A1 and A2, the grain boundary u2 is a grain boundary between the crystal grains A1 and A5, and the grain boundary u3 is a crystal boundary. It is a grain boundary of the grains A1 and A4, and the grain boundary u4 is a grain boundary of the crystal 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 the hard disk. ) 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 (the analysis temperature θ (t) increases with time). It may be changed).

  The orientation setting unit 107, based on the “signal indicating the orientation ξ of each crystal grain A included in the crystal grain image 31” acquired by the crystal image acquisition unit 101, all the crystal grains A included in the crystal grain image 31. 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 adjacent grain boundaries u via the grain boundary u. A graph, a numerical sequence, an equation, 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, numeric strings, formulas, or combinations thereof are referred to as graphs.

  For example, the “grain boundary energy γ per unit length” at the grain boundary u1 shown in FIG. 3C is the absolute value of the difference Δξ between the orientation ξ1 of the crystal grain A1 and the orientation ξ2 of the crystal grain A2, and the analysis. By reading “grain boundary energy γ per unit length” corresponding to the analysis temperature θ (t) set by the temperature setting unit 106 from a graph or the like stored in the grain boundary energy (γ) storage unit 108. can get. 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. The grain boundary energy (γ) setting unit 109 sets (stores) the read grain boundary energy γ per unit length in the RAM or the hard disk.

The mobility storage unit 110 analyzes the mobility Mi [cm ² / (V · sec)], the absolute value of the difference Δξ of the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u, and the analysis. A graph, a numerical string, an expression, or a combination thereof showing the relationship with the temperature θ (t) is stored. In the following description, these graphs, numeric strings, formulas, or combinations thereof are referred to as graphs.
For example, the mobility Mi at the grain boundary u1 shown in FIG. 3C is acquired by the absolute value of the difference Δξ between the orientation ξ1 of the crystal grain A1 and the orientation ξ2 of the crystal grain A2, and the analysis temperature setting unit 106. 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. The mobility storage unit 110 is configured using, for example, a RAM or a hard disk.

  The mobility setting unit 111 is controlled by the grain boundary setting unit 105 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 mobility Mi of all the set grain boundaries u is read 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 the 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 the hard disk. The analysis time setting unit 112 monitors the analysis time t until the analysis completion time T elapses.

  The analysis point discriminating unit 113 sequentially designates all points (double points, triple points, and fixed points) i set by the point setting unit 103 as calculation target points without overlapping. The analysis point determination unit 113 determines whether or not the designated point i is a fixed point. If the specified point i is not a fixed point, the analysis point determination unit 113 further determines whether it is a double point or a triple point. .

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

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

This equation (1) is derived as follows.
First, two vectors having the same size (absolute value) as the grain boundary vector γi of the grain boundary u to which the double point i belongs, and having a direction from the double point i to the points i−1 and i + 1. Assume that the vector sum of fi1 and fi2 is the driving force Fr generated at the double point i (see FIG. 4). Then, the magnitude of the driving force Fr generated at the double point i is expressed by the following equation (2).

Here, l is the length [m] of the straight lines 42 and 43 from the double point i to the point i-1 (or the point i + 1). Α is an angle [°] formed by a straight line connecting the double point i and the center of curvature O and a straight line connecting the point i−1 (or point i + 1) and the center of curvature O.
The driving force generated at the double point i may be defined as in the equation (2). However, if it is defined in this way, the driving force generated at the double point i is changed from the double point i to the point i−1. It depends on the length l of the straight lines 42 and 43 up to (or point i + 1). That is, the driving force generated at the double point i depends on the number of double points i set for one grain boundary u. For example, as shown in FIG. 4C, when three double points i2 to i4 are set for the grain boundary u1, and when five double points are set for the grain boundary u1, The driving force generated at the double point i is different.

  Therefore, the right side of the equation (2) is set so that the driving force generated at the double point i does not depend on the length l of the straight lines 42 and 43 from the double point i to the point i-1 (or the point i + 1). The value divided by 1 was defined as the magnitude of the driving force Fi (t) generated at the double point i (see equation (1)).

  As described above, in order to obtain the driving force Fi (t) generated at the double point i using the equation (1), the double-point driving force calculation unit 114 calculates the double point i to be calculated and its double point. Information on two points i−1 and i + 1 adjacent to i is read from the point setting unit 103. Next, the double-point driving force calculation unit 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. In addition, the double-point driving force calculation unit 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 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 generate a driving force Fi (t ) Is calculated. The double-point driving force calculation unit 114 calculates a direction from the double point i to be calculated toward the curvature center 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 discriminating unit 113 determines that the point i to be calculated is a triple point, the triple-point driving force calculation unit 115 generates the driving force Fi ( t) is calculated.
FIG. 5 is a diagram illustrating an example of a method for calculating the driving force Fi (t) generated at the triple point. In FIG. 5, a case where the driving force Fi (t) generated at the triple point i is calculated will be described as an example. In FIG. 5, three points adjacent to the triple point i are represented by “1”, “2”, and “3”, respectively.

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

  The triple-point driving force calculation unit 115 calculates the magnitude (absolute value) of the grain boundary energy γi1, γi2, and γi3 per unit length and the direction from the triple point i to be calculated toward points 1, 2, and 3. Is substituted for the following equation (3) to calculate the driving force Fi (t) generated at the triple point i to be calculated.

In equation (3), j is a variable for identifying three points adjacent to the triple point i to be calculated.
Thus, in the present embodiment, the grain boundaries u have the same size as the grain boundary energy γi1, γi2, γi3 (absolute value) at the grain boundary u to which the points 1, 2, 3 belong, and A drive in which a vector sum of three vectors Di1 (t), Di2 (t), Di3 (t) having a direction from a triple point i to be calculated to a point adjacent to the triple point i is generated at the triple point i. Calculated as force Fi (t).

  Returning to the description of FIG. 2, the position calculation unit 116 calculates the change in position of the double point i and the triple point i over time. First, an example of a method for calculating the change in position of the double point i with the passage of time will be described.

  The position calculation unit 116 acquires a vector indicating the driving force Fi (t) calculated by the double-point driving force calculation unit 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 determines the mobility Mi of the grain boundary u to which the double point i to be calculated belongs and a vector indicating the driving force Fi (t) of the double point i to be calculated as the following (4). Substituting into the equation, a vector indicating the velocity vi (t) of the double point i to be calculated is calculated.

  Thereafter, the position calculation unit 116 acquires “a 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 a vector indicating the speed vi (t) of the double point i to be calculated, a vector indicating the current position ri (t) of the double point i to be calculated, and a time Δt as follows: Substituting into equation (5), when Δt [sec] has elapsed from the current analysis time t, a vector indicating the position ri (t + Δt) where the double point i to be calculated exists is calculated. In the present embodiment, in this way, the change in the position with the passage of time of the double point i to be calculated is calculated. The time Δt defines the timing (interval) for calculating the position of the point i, and is predetermined according to the type of electromagnetic steel sheet to be analyzed, analysis conditions, analysis accuracy, and the like.

  Then, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the double point i to be calculated exists to the point setting unit 103. In this way, as described above, the point setting unit 103 sets a vector indicating the current position ri (t) of the double point i to be calculated.

Next, an example of a method for calculating a change in the position of the triple point i over time will 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.

  The position calculating unit 116 calculates the mobility Mi of the triple point i to be calculated using the mobility Mi1 to Mi3 of the three grain boundaries u to which the triple point i to be calculated belongs. Specifically, the position calculation unit 116 calculates a unit vector (dij (t) / | dij (t) |) having a direction from the triple point i to be calculated toward the points 1, 2, and 3, and the triple point to be calculated. The mobility Mi1 to Mi3 of the three grain boundaries u to which i belongs are substituted into the following equation (6) to calculate the mobility Mi of the triple point i to be calculated.

In equation (6), 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 point driving force calculation unit 115 (a vector indicating the driving force Fi (t) generated at the triple point i to be calculated). To do. Then, the position calculation unit 116 described above the mobility Mi of the grain boundary u to which the calculation target triple point i belongs and the vector indicating the driving force Fi (t) of the calculation target triple point i (4). Substituting into the equation, a vector indicating the velocity vi (t) of the triple point i to be calculated is calculated.

  Thereafter, the position calculation unit 116 acquires “a 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 obtains 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. Substituting into the equation (5), when Δt [sec] has elapsed from the current analysis time t, a vector indicating the position ri (t + Δt) where the triple point i to be calculated exists is calculated. In the present embodiment, in this way, the change in position with the passage of time of the triple point i to be calculated is calculated. As described above, the time Δt defines the timing (interval) for calculating the position of the point i, and is determined in advance according to the type of the electromagnetic steel sheet to be analyzed, the analysis conditions, the analysis accuracy, and the like. It has been.

  Then, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the triple point i to be calculated exists to the point setting unit 103. In this way, as described above, the point setting unit 103 sets a vector indicating the current position ri (t) of the triple point i to be calculated.

  The analysis time setting unit 112 determines whether or not the position calculation unit 116 has calculated the position ri (t + Δt) after the analysis completion time T has elapsed or after the analysis completion time T has elapsed. By determining, it is determined whether or not the analysis is completed until the analysis completion time T.

  When the analysis time setting unit 112 determines that the analysis is completed until 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, an image showing how the state of the crystal grains A changes during the analysis time t from 0 (zero) to T [sec] is displayed on the display device 200.

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

FIG. 6 is a diagram illustrating an example of an inhibitor setting method.
In FIG. 6, the broken line portion indicates the detected inhibitor k region. In this case, the inhibitor setting unit 118 approximates the detection area indicated by the broken line with a circle as shown in FIG. 6, and calculates information regarding the coordinates indicating the center position bk of the inhibitor k and information regarding the radius r. . Here, unlike the grain boundary point, the inhibitor k set by the inhibitor setting unit 118 does not change its position with time.

  The line change processing unit 119 determines whether or not each line p set by the line setting unit 104 passes through the inhibitor k set by the inhibitor setting unit 118, and when the line p passes through the inhibitor k Then, the process of 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.
7A to 7A show an example of the line p before being processed by the line change processing unit 119. FIG. Moreover, the 1st process example with respect to each line p shown to FIG.7 (1a)-(6a) is shown to FIG.7 (1b)-(6b), and a 2nd process example is shown in FIG.7 (1c)-(6c). It shows.

  Specifically, the line change processing unit 119, as shown in FIG. 7 (1a), is a case where the line p passes through the inhibitor k and the end point (grain boundary point) of the line p is not in the inhibitor k. 7 (1b) or 7 (1c), a double point in is generated at an arbitrary position on the line p, and the line p is divided into two lines. Then, the line change processing unit 119 moves the generated double point “in” to the center position “bk” of the inhibitor “k”, and performs this processing as the fixed point “ik”. In this case, the fixed point ik is an end point of the line p and a fixed double point constituting 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 has two lines p′1 and p′2 whose end points are the fixed point ik. It is divided into.

  Further, the line change processing unit 119 is a case where the line p passes through the inhibitor k, and one end point (grain boundary point) of the line p is in the inhibitor k (FIGS. 7 (2a) to (4a). In this case, the end point in the inhibitor k is moved to the central position bk of the inhibitor k, and this is moved to the fixed point ik (FIG. 7 (2b) to (4b) or FIG. 7 (2c) to (4c). The fixed point ik) shown is performed. In this case, the line p is changed to a line having the fixed point ik as one end point.

  Further, the line change processing unit 119 is a case where the line p passes through the inhibitor k, and both end points (grain boundary points) of the line p are in the inhibitor k (FIGS. 7 (5a) and (6a). In the case shown in FIG. 7, a process of eliminating the line p in the inhibitor k is performed (FIG. 7 (5b) and (6b), or FIG. 7 (5c) and (6c)). Further, the line change processing unit 119 sets two points in the inhibitor k to one fixed point ik (FIG. 7 (5b) and FIG. 7 (6b), or FIG. 5c) and a fixed point ik) shown in (6c), and a process of constructing a line having each end point of the line p and each end point constituting the line and the fixed point ik as an end point is performed.

  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 center position bk as a fixed position in the inhibitor k, and the fixed point A line changing process with the point ik as an end point is performed.

  Then, the line change processing unit 119 performs various reset processes for the point setting unit 103 and the line setting unit 104 according to point changes (including disappearance and occurrence) and line changes (including disappearance and occurrence). To do.

  As described above, in the present embodiment, when it is determined that each line p passes through the inhibitor k as a result of changing the position of the grain boundary point, processing for generating the fixed point ik in the inhibitor k is performed. However, because the size of the inhibitor k is small, the time step Δt for calculating the position of the grain boundary point is large, the line p (grain boundary) is close to the inhibitor k, etc. As a result of changing the position of the point, the inhibitor k may be overtaken (passed). In such a case, the grain boundary that should be captured by the inhibitor k is not captured by the inhibitor k, and the behavior of the grain boundary A may not be analyzed appropriately. Therefore, in the present embodiment, the overtaking determination unit 124 determines such overtaking of the line p.

FIG. 8 is a diagram for explaining an example of a method for determining whether or not the line p has passed (passed) the inhibitor k.
As shown in FIG. 8A, as a result of the calculation by the position calculation unit 116, the line p81 having the grain boundary points i81 and i82 as both end points (the line p81 before movement) has the grain boundary points i83 and i84 as both end points. To the line p82 (the line p82 after movement).
Then, as shown in FIG. 8B, the overtaking determination unit 124 sets one grain boundary point i83 of the moved line p82 and grain boundary points i81 and i82 which are both end points of the line p81 before the movement. It is determined whether or not the center position bk of the inhibitor k is in the triangle 80a as the vertex.

Specifically, in the present embodiment, first, the overtaking determination unit 124 is a vector whose magnitude is the shortest distance between the grain boundary points i83 and i81 and whose direction is the direction from the grain boundary point i83 toward the grain boundary point i81. Aa and a vector Ab whose magnitude is the shortest distance between the grain boundary points i83 and i82 and whose direction is the direction from the grain boundary point i83 to the grain boundary point i82 are obtained.
The overtaking determination unit 124 is a vector whose size is the shortest distance between the grain boundary point i83 and the center position bk of the inhibitor k, and whose direction is the direction from the grain boundary point i83 toward the center position bk of the inhibitor k. A is expressed by using vectors Aa and Ab as shown in the following equation (7).

The overtaking determination unit 124 determines whether or not the coefficients ρ and σ of the equation (7) satisfy all of the following equations (8) to (10).
ρ ≧ 0 (8)
σ ≧ 0 (9)
0 ≦ ρ + σ ≦ 1 (10)
As a result of this determination, when the coefficients ρ and σ in the equation (7) satisfy all of the equations (8) to (10), the overtaking determination unit 124 has the center position bk of the inhibitor k in the triangle 80a. Is determined. Thus, when the center position bk of the inhibitor k exists in the triangle 80a, the calculation target line p has overtaken the inhibitor k.

  On the other hand, when the coefficients ρ and σ in the equation (7) do not satisfy all of the equations (8) to (10), the overtaking determination unit 124 places the inhibitor k in the triangle 80a (including the boundary of the triangle 80a). It is determined that there is no center position bk. In the example shown in FIG. 8B, it is determined that the center position bk of the inhibitor k is not present in the triangle 80a. Thus, when the center position bk of the inhibitor k is not present in the triangle 80a, the overtaking determination unit 124 sets the four grain boundary points i81 to i84 before and after the movement, as shown in FIG. 8C. A triangle 80b obtained by removing the triangle 80a from the quadrangle as a vertex (the grain boundary points i83 and i84 which are both end points of the moved line p82 and one grain boundary point i82 of the line p81 before the movement is a vertex. It is determined whether or not the center position bk of the inhibitor k is in the triangle 80b).

Specifically, in the present embodiment, first, the overtaking determination unit 124 is a vector whose size is the shortest distance between the grain boundary points i83 and i84 and whose direction is the direction from the grain boundary point i83 toward the grain boundary point i84. Ac is determined.
The overtaking determination unit 124 is a vector whose size is the shortest distance between the grain boundary point i83 and the center position bk of the inhibitor k, and whose direction is the direction from the grain boundary point i83 toward the center position bk of the inhibitor k. A is expressed using vectors Ab and Ac as shown in the following equation (11).

The overtaking determination unit 124 determines whether or not the coefficients λ and ω of the equation (11) satisfy all of the following equations (12) to (14).
λ ≧ 0 (12)
ω ≧ 0 (13)
0 ≦ λ + ω ≦ 1 (14)
As a result of this determination, when the coefficients λ and ω in the equation (11) satisfy all of the equations (12) to (14), the overtaking determination unit 124 has the center position bk of the inhibitor k in the triangle 80b. Is determined. Thus, when the center position bk of the inhibitor k exists in the triangle 80b, the calculation target line p has overtaken the inhibitor k. In the example shown in FIG. 8B, it is determined that the center position bk of the inhibitor k is in the triangle 80b.

  On the other hand, when the coefficients λ and ω of the equation (11) do not satisfy all of the equations (12) to (14), the overtaking determination unit 124 determines that the center position bk of the inhibitor k is not present in the triangle 80b. To do. Thus, when the center position bk of the inhibitor k does not exist in the triangle 80b, the center position bk of the inhibitor k does not exist in the quadrangle having the four grain boundary points i81 to i84 as vertices before and after the movement. Therefore, the line p to be calculated does not pass the inhibitor k.

  Returning to the description of FIG. 2, when the overtaking determination unit 124 determines that the line p has overtaken the inhibitor k (in any of the triangles 80a and 80b, the first fixed point processing unit 125 includes the inhibitor k). If the center position bk of the inhibitor k is determined to be present), a fixed point ik is generated at the center position bk of the inhibitor k, and a line passing through the grain boundary point corresponding to both end points of the line p that has passed the inhibitor k. Perform the change process. Hereinafter, a specific example of the processing performed by the first fixed point processing unit 125 will be described.

FIG. 9 is a diagram for explaining an example of processing when the line p overtakes the inhibitor k.
As shown in FIG. 9A, the first fixed point processing unit 125 generates a double point i85 at an arbitrary position on the line p82 (see FIG. 8) that has overtaken the inhibitor k, and sets the line p82 to 2 Divide into two lines. Then, as shown in FIG. 9 (b), the first fixed point processing unit 125 moves the generated double point i85 to the center position bk of the inhibitor k, and performs the process of setting this as the fixed point ik. In this case, the fixed point ik is a fixed double point that constitutes the grain boundary points i83 and i84, which are the end points of the line p82, and the lines p83 and p84. In this case, as shown in FIG. 9B, a fixed point ik is newly generated, and the line p82 is divided into two lines p83 and p84 having the fixed point ik as an end point.

As will be described later, in the present embodiment, when the fixed point ik set as described above satisfies a certain condition, the fixed point ik is changed to a normal point (movable point) and the fixed point ik is set. To release.
Therefore, the effective range setting unit 122 acquires information regarding the range of the grain boundary u to be considered when determining whether or not to release the fixed point ik based on the operation of the operation device 300 by the user, and the RAM or the hard disk Set to. Here, the information regarding the range of the grain boundary u is acquired based on the operation of the operation device 300. However, the effective range storage unit is provided in the crystal grain analysis device 100, and the pre-stored “grain” Information related to the range of the field u may be read out. In the following description, this range is referred to as an effective range as necessary.
In the present embodiment, a circle centered on the center position bk of the inhibitor k is set as the effective range. Therefore, the grain boundary energy (E) calculation unit 121 acquires information regarding the radius of the effective range from the effective range setting unit 122. This effective range can be determined experimentally. Specifically, what is the most acute angle (for example, the angle 2β in FIGS. 10 and 12) between two straight lines connecting the fixed point ik and the adjacent point i to the fixed point ik? It is experimentally determined whether the fixed point ik is appropriately released when the degree is, and the effective range in which the fixed point ik is appropriately released is determined based on the obtained angle. Can do. However, the effective range may be determined in any way as long as it is a region that includes the fixed point ik and is wider than the inhibitor k and that defines a target for calculating the grain boundary energy.

Further, in the present embodiment, the increase in grain boundary energy that occurs when the fixed point ik is released (including immediately before or immediately after) at the grain boundary u within the effective range set by the effective range setting unit 122, The grain boundary energy when the fixed point ik is released (including immediately before or immediately after) and the grain boundary energy when the fixed point ik is fixed The fixed point ik is released when the difference becomes smaller than a predetermined energy.
Therefore, the barrier energy setting unit 123 acquires information (value of energy) related to the predetermined energy based on the operation of the operation device 300 by the user, and sets the information in the RAM or the hard disk. Here, the information (value of energy) related to the predetermined energy is acquired based on the operation of the operation device 300. However, a barrier energy storage unit is provided in the crystal grain analysis device 100 and stored in advance from there. Alternatively, “information on predetermined energy (value of energy)” may be read out. In the following description, this predetermined energy is referred to as barrier energy.

  The grain boundary energy (E) calculation unit 121 includes coordinate information of the fixed point ik, information indicating the position of each other end point of the line p having the fixed point ik as an end point, and an inhibitor having the fixed point ik as the center position bk. Get information about k. Further, the grain boundary energy (E) calculation unit 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) calculation unit 121 acquires information on the effective range.

The grain boundary energy (E) calculation unit 121, based on the acquired information, the grain boundary energy Ei of the grain boundary u to which the fixed point ik belongs when the fixed point ik is restrained and fixed by the inhibitor k. Is calculated (calculated).
In the present embodiment, the grain boundary energy (E) calculation unit 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) calculation unit 121 includes the grain boundary u in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point ik as the central position bk. The grain boundary energy Ei is calculated (calculated) as it is not.

Here, specifically, the calculation method of the grain boundary energy Ei when the fixed point ik is a double point (fixed double point) and a triple point (fixed triple point) using FIG. 10 and FIG. 11. Is described below.
FIG. 10 is a diagram for explaining an example of a method for calculating grain boundary energy when the fixed point ik is a fixed double point. FIG. 11 is a diagram for explaining an example of a method for calculating grain boundary energy when the fixed point ik is a fixed triple point.

  First, when the fixed point ik is a double point, as shown in FIG. 10A, the grain boundary energy (E) calculation unit 121 calculates a fixed point ik and points ir and it adjacent to the fixed point ik. Intersections 802 and 803 of the points ir and the extension lines in the it direction of the lines pa and pb connected at the shortest distance and the effective range 801 are obtained. Here, the grain boundary u does not exist in the inhibitor k. For this reason, the grain boundary energy (E) calculation unit 121 uses the lengths K between the fixed point ik and the intersections 802 and 803 as the effective lengths L1 and L2 used when calculating the grain boundary energy Ei. The length obtained by subtracting the length of the radius r of the inhibitor k is obtained.

In addition, since the fixed point ik is a double point, the two effective lengths L1 and L2 (= K−r) can be regarded as belonging to the same grain boundary u. Therefore, for example, the grain boundary energy Ei shown in FIG. 10 when the fixed point ik is a double point is calculated by the following equation (15).
Ei = (grain boundary energy γ per unit length of grain boundary u including lines pa and pb)
× (L1 + L2) (15)
As described above, in the present embodiment, the virtual line of the grain boundary to which the fixed point ik belongs, and the virtual line (point ik and points 802 and 803) having the fixed point ik as one of the end points is the shortest distance. The grain boundary energy Ei is calculated using the length of the connecting virtual line) and the grain boundary energy per unit length at the grain boundary to which the fixed point ik belongs.

On the other hand, as shown in FIG. 11 (a), when the fixed point ik is a triple point, the grain boundary energy (E) calculation unit 121 includes the lines pa, pb, and pc having the fixed point ik as an end point. The intersections 802 and 803 of the effective ranges 801 with the extension lines of the lines pa and pb (two virtual lines that demarcate the region where the equilibrium position exists) at the position sandwiching the equilibrium position w are obtained. Here, the equilibrium position w is a position in a region excluding the inside of the inhibitor k where the fixed point ik is released from the fixed position (center position bk of the inhibitor k), and the position where the grain boundary energy E is minimum. Say.
Moreover, the grain boundary u does not exist in the inhibitor k. For this reason, 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. The lengths L1 and L2 obtained by subtracting the length of the radius r are obtained.

Further, since the fixed point ik is a triple point, the portions of 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. 11 is a triple point is calculated by the following equation (16).
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
... (16)
As described above, in the present embodiment, the virtual line of the grain boundary to which the fixed point ik belongs, and the virtual line (point ik and points 802 and 803) having the fixed point ik as one of the end points is the shortest distance. The grain boundary energy Ei is calculated using the length of the connecting virtual line) and the grain boundary energy per unit length at the grain boundary to which the fixed point ik belongs.

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 when it is at the equilibrium position w.
In the present embodiment, the grain boundary energy (E) calculation unit 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) calculation unit 121 includes the grain boundary u in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center position bk. The grain boundary energy Ei ′ is calculated on the assumption that no other inhibitor k exists.

  Here, specifically, the grain boundary energy Ei ′ when the fixed point i is a double point (fixed double point) and a triple point (fixed triple point) is calculated using FIGS. 10 and 11. The method will be described below.

  First, when the fixed point ik is a double point, the grain boundary energy (E) calculation unit 121 obtains the points 802 and 803 and the effective lengths L1 and L2 as described above. Here, when the fixed point ik is a double 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 the same grain boundary u. Can be considered. For this reason, the equilibrium position w is an arbitrary position on a line (virtual line) 805 connecting the point 802 and the point 803 with the shortest distance. Here, the length of the line (virtual line) 805 is Q0. The grain boundary energy γ per unit length of the grain boundary u in 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. 10 is calculated by the following equation (17).
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)
× Q0 (17)
As described above, in the present embodiment, the length of a virtual line on the grain boundary to which the fixed point ik belongs, and which passes through the equilibrium position w (a virtual line connecting the points 802 and 803 with 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. 10, when the line 805 passes through the inhibitor k, the length obtained by subtracting the length of the line 805 (Q0) from the portion of the line 805 that passes through the inhibitor k. This is multiplied by the grain boundary energy γ per unit length.

  On the other hand, as shown in FIG. 11, when the fixed point ik is a triple point, the grain boundary energy (E) calculation unit 121 obtains the points 802 and 803 as described above, and sets the effective lengths L1 and L2 as follows. 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 considered. Here, as an example, the case where the equilibrium position w is the position shown in FIG. 11 will be described.

  In this case, the grain boundary energy (E) calculation unit 121 includes a line (virtual line) 901 that connects the point 802 and the equilibrium position w with the shortest distance, and a line (virtual line) that connects the point 803 and the equilibrium position w with the shortest distance. ) 902 and a line (virtual line) 903 connecting the fixed point ik and the equilibrium position w with the shortest distance. At this time, the effective length used for calculating the grain boundary energy Ei ′ is a length B1 of the line 901, a length B2 of the line 902, and a length obtained by subtracting the radius r of the inhibitor k from the length of the line 903. B3.

  The grain boundary energy γ per unit length of the grain boundary u in the line 901 can be regarded as the grain boundary energy γ1 per unit length of the grain boundary u including the line pa. Further, the grain boundary energy γ per unit length of the grain boundary u in 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 with 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. 11 is a triple point is calculated by the following equation (18).
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) × B 2
+ (Grain boundary energy γ per unit length of grain boundary u including line pc) × B3
... (18)
As described above, in this embodiment, the virtual line of the grain boundary to which the fixed point ik belongs, and the length of the virtual line (virtual lines 901 to 903) passing through the equilibrium position w and 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 at.

Furthermore, in this embodiment, the grain boundary energy (E) calculation unit 121, when the fixed point i is released (including immediately before or immediately after), the grain boundary of the grain boundary u to which the released fixed point ik belongs. The energy Ei ″ is calculated (calculated).
In the present 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) calculation unit 121 includes the grain boundary u in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center position bk. The grain boundary energy Ei '' is calculated on the assumption that no other inhibitor k exists.

  Here, specifically, using FIG. 10 and FIG. 11, the grain boundary energy Ei ″ when the fixed point i is a double point (fixed double point) and a triple point (fixed triple point) is shown. The calculation method will be described below.

First, when the fixed point ik is a double point, the grain boundary energy (E) calculation unit 121 obtains the points 802 and 803 and the effective lengths L1 and L2 as described above.
Next, the grain boundary energy (E) calculation unit 121 includes a line that bisects an 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. Find the intersection 804. In the present embodiment, it is assumed that the fixed point ik is released to this point 804. The grain boundary energy (E) calculation unit 121 obtains lengths M1 and M2 of lines (virtual lines) connecting the point 804 and the points 802 and 803 with the shortest distance. Further, the grain boundary energy (E) calculation unit 121 obtains a length Q0 of a line (virtual line) connecting the points 802 and 803 with the shortest distance.
Here, since the fixed point ik is a double point, the portions of the two effective lengths L1 and L2 (= Kr) can be regarded as belonging to the same grain boundary u. Thus, for example, the grain boundary energy Ei ″ (at the point 804) when the fixed point ik is released as shown in FIG. 10 is calculated by the following equation (19).
Ei ″ = (grain boundary energy γ per unit length of grain boundary u including lines pa and pb)
× (M1 + M2) (19)
As described above, in the present embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, and a virtual line (point 804 and points 802 and 803 are the shortest distance) with the point 804 as one of the end points. The grain boundary energy Ei '' is calculated using the length of the virtual line connected by (2) and the grain boundary energy per unit length at the grain boundary to which the fixed point ik belongs.

  On the other hand, as shown in FIG. 11, when the fixed point ik is a triple point, the grain boundary energy (E) calculation unit 121 obtains the points 802 and 803 as described above, and sets the effective lengths L1 and L2 as follows. Ask. Further, the grain boundary energy (E) calculation unit 121 obtains the intersection point 804 as described above. The grain boundary energy (E) calculation unit 121 obtains lengths M1 and M2 of lines (virtual lines) connecting the point 804 and the points 802 and 803 with 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 considered. Therefore, for example, when the fixed point ik shown in FIG. 11 is released, the grain boundary energy Ei ″ within the effective range 801 of the grain boundary u to which the fixed point i belongs is expressed by the following equation (20). 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
... (20)
In FIG. 11A, the equilibrium position w is at a point on a 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 the two lines connecting the fixed point ik and the points 802 and 803 at the shortest distance. .
As described above, in the present embodiment, a virtual virtual line of the grain boundary to which the fixed point ik belongs, and a virtual line (point 804 and points 802 and 803 are the shortest distance) with the point 804 as one of the end points. The grain boundary energy Ei '' is calculated using the length of the virtual line connected by (2) and the grain boundary energy per unit length at the grain boundary to which the fixed point ik belongs.

Returning to the description of FIG. 2, the second fixed point processing unit 120 compares the grain boundary energy Ei obtained by the grain boundary energy (E) calculation unit 121 with the grain boundary energy Ei ′, and the grain boundary energy Ei ′ is obtained. It is determined whether it is less than the grain boundary energy Ei. That is, the second fixed point processing unit 120 determines whether or not the following expression (21) is satisfied.
Ei ′ <Ei (21)
As a result of this determination, when the grain boundary energy Ei ′ is not less than the grain boundary energy Ei (Ei ′ <Ei), the fixed point ik is not released.

On the other hand, when the grain boundary energy Ei ′ is less than the grain boundary energy Ei, the second 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 value obtained by subtracting the energy Ei is less than the barrier energy E0 read from the barrier energy setting unit 123. That is, the second fixed point processing unit 120 determines whether or not the following expression (22) is satisfied.
Ei ″ −Ei <E0 (22)
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 ik is not released. 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, a process of releasing (releasing) the fixed point ik is performed.

  Specifically, as shown in FIG. 10B, in the present embodiment, when the fixed point ik is a double point, the second fixed point processing unit 120 moves the fixed point ik to the position of the point 804. Then, the process of releasing the fixation and setting the normal point ik is performed. That is, the second fixed point processing unit 120 bisects an angle formed by two lines (virtual lines) connecting the fixed point ik and the points 802 and 803 at the shortest distance instead of the fixed point ik. A normal point ik is generated at the intersection point 804 between the point k and the inhibitor k.

  Also, as shown in FIG. 11B, in the present embodiment, when the fixed point ik is a triple point, the second fixed point processing unit 120 moves the fixed point ik to the position of the point 804, In addition to the process of releasing the fixation and setting the normal point ik, the following process is performed. That is, the second fixed point processing unit 120 generates the fixed double point ix connected to the normal point ik and the point iv at the center position bk of the inhibitor k. Here, as shown in FIG. 11B, the point iv is a point that is not connected to the normal point ik among the points ir, it, and iv adjacent to the fixed point ik.

Note 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, the present invention can be applied to a position where the grain boundary energy Ei '' is moved to the minimum. it can. The calculation method of the grain boundary energy Ei '' in this case is calculated by the above-described equation (19) when the fixed point ik is a double point, and is described above when the fixed point ik is a triple point. Calculated by equation (20).
Further, instead of the equation (22), 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, satisfying both the expressions (21) and (22) is the release condition for the fixed point ik. Here, a state when the fixed point ik is released will be described with reference to FIGS. 12 and 13.
FIG. 12 shows the lengths of virtual lines within the effective range 801 (K (= 2K), L (= L1 + L2), M (= M1 + M2), Q (= Q0)) when the fixed point ik is a double point. It is a figure which shows an example of the relationship with the position of the points 802 and 803 on an effective range. FIG. 13 shows the lengths of virtual lines within the effective range 801 (K (= 2K), L (= L1 + L2), M (= M1 + M2), B (= B1 + B2 + B3)) when the fixed point ik is a triple point. It is a figure which shows an example of the relationship with the position of the points 802 and 803 on an effective range.

Here, in FIGS. 12 and 13, the positions of the points 802 and 803 on the effective range are represented by the angle β in FIGS. 10 (a) and 11 (a). In FIGS. 12 and 13, 10 times the effective length (L = L ₁ + L ₂ ) is set to 10 and the diameter (= 2r) of the inhibitor k is set to 2.

In the present embodiment, first, when the grain boundary energy Ei ′ is less than the grain boundary energy Ei and the fixed point ik is at the equilibrium position w, the grain boundary energy Ei ′ of the grain boundary to which the fixed point ik belongs is fixed. The first release condition is that the point ik is lower than the grain boundary energy Ei of the grain boundary to which the fixed point ik belongs when the point ik is fixed. This is because it is physically impossible that the fixed point ik is released when the release condition is not satisfied.
In the example shown in FIG. 12, the first release condition is whether or not the graph of length Q and the graph of length L intersect. On the other hand, in the example shown in FIG. 13, the first release condition is that the graph of length B and the graph of length L intersect.

Further, the second release condition is that the grain boundary energy of the grain boundary u to which the fixed point ik belongs, which temporarily increases when the fixed point ik is released, becomes smaller than the predetermined barrier energy E0. . If this release condition is not satisfied, the barrier energy E0 that must be overcome when the fixed point ik transitions to the equilibrium state (equilibrium position w) cannot be overcome.
In the example shown in FIG. 12, the difference between the values of the length M graph and the length L graph is smaller than the value obtained by dividing the barrier energy E0 by the grain boundary energy γ per unit energy. It becomes a release condition. On the other hand, in the example shown in FIG. 13, the difference between the values of the length M graph and the length L graph is smaller than the value obtained by dividing the barrier energy E0 by the grain boundary energy γ per unit energy. 2 is the release condition.
By introducing the second release condition as described above, the fixed point ik can be released in consideration of the grain boundary energy γ per unit length of the grain boundary u to which the fixed point ik belongs. Become.

FIG. 14 is a diagram illustrating an example of the relationship between the minimum length of the grain boundary u to which the fixed point ik belongs and the pinning time. FIG. 14 shows an example in which the fixed point ik is a double point and the effective lengths L1 and L2 are 3. Further, the minimum length of the grain boundary u to which the fixed point ik belongs represents the minimum value of the length between the double points or between the double point and the triple point at the grain boundary u to which the fixed point ik belongs. The pinning time is the time from when the fixed point ik is generated until it is released.
In FIG. 14, the graph 1201 does not set the effective range 801, and instead of the information of the points 802 and 804, the above calculation is performed using the information of the points ir and it adjacent to the fixed point ik to fix It is a graph at the time of determining whether to release the point ik. On the other hand, as described above, the graph 1202 is a graph when the effective range 801 is set and calculation is performed using the information of the points 802 and 804 to determine whether or not to release the fixed point ik.

  As is apparent from FIG. 14, when the effective range 801 is set, the pinning time can be made substantially constant without depending on the number of double points set for the grain boundary u. Therefore, by setting the effective range 801, the fixed point ik can be released without being affected as much as possible by the length of the line p generated by setting the double point.

  Returning to the description of FIG. 2, the second 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 flowcharts of FIGS. Note that the processing of the flowchart shown in FIG. 15A is started when the CPU reads out the control program from the ROM or the hard disk and starts executing it based on the operation of the operation device 300 by the user.

First, in step S1 of FIG. 15A, the crystal image acquisition unit 101 includes an image signal (crystal image signal) of an inhibitor existing between the crystal grain A of the electromagnetic steel sheet and the crystal grain A of the electromagnetic steel sheet, and the image signal. And a signal indicating the orientation ξ of each crystal grain A included in the. When a crystal grain image signal and a signal indicating the orientation ξ of each crystal grain A included in the image signal are input, the process proceeds to step S2.
Thus, in the present embodiment, for example, an example of the image signal acquisition unit is realized by performing the process of step S1.

  In 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 causes the display device 200 to display an image for prompting the user to input the analysis temperature θ (t) of the electromagnetic 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 designate the point (double point or triple point) i while referring to the crystal grain image 31. A case will be described as an example.

  Next, in step S <b> 3, the analysis temperature setting unit 106 stands by until the analysis temperature θ (t) of the electromagnetic steel sheet to be analyzed (crystal grain A) is input based on the operation of the operation device 300 by the user. And if analysis temperature (theta) (t) of the electromagnetic steel plate (crystal grain A) of analysis object is input, it will progress to step S4.

  In step S4, the analysis temperature setting unit 106 sets the input analysis temperature θ (t) of the analysis target electrical steel sheet (crystal grain A) in the RAM or the hard disk. In the flowcharts of FIGS. 15A to 15D, the case where the analysis temperature θ (t) of the electromagnetic steel sheet (crystal grain A) to be analyzed is a constant value will be described as an example.

  Next, in step S5, the analysis time setting unit 112 stands by until an analysis completion time T is input based on the operation of the operation device 300 by the user. When the analysis completion time T is input, the process proceeds to step S6.

  In step S6, the analysis time setting unit 112 sets the input analysis completion time T in the RAM or the hard disk.

  Next, in step S <b> 7, the point setting unit 103 waits until a point (double point or triple point) i is designated for the crystal grain image 31 displayed by the crystal image display unit 102. When the point (double point or triple point) i is designated, the process proceeds to step S8.

  In 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 the calculated value in the RAM or the hard disk.

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

On the other hand, as a result of the determination in step S9, when an instruction to end the work specifying the point i is made, the process proceeds to step S10. In step S10, the point setting unit 103 calculates the number NI of points (double points or triple points) i determined to have been designated in step S7 (that is, the number of times the process in step S7 has been performed) NI, and the RAM Or set to hard disk.
As described above, in the present embodiment, for example, an example of a grain boundary point setting unit is realized by performing the processes of steps S7 to S10.

  Next, in step S <b> 11 of FIG. 15B, the inhibitor setting unit 118 waits until an inhibitor k is designated for the crystal grain image 31 displayed by the crystal image display unit 102. When the inhibitor k is designated, the process proceeds to step S12.

  In step S12, the inhibitor setting unit 118 detects the area of the inhibitor k determined to be specified in step S11 based on the crystal grain image signal acquired in step S1, and approximates this detection area with a circle. Then, the coordinate information indicating the center position bk of the inhibitor k and the information regarding the radius r are calculated and set in the RAM or the hard disk.

  Next, in step S <b> 13, the inhibitor setting unit 118 determines whether or not an instruction to end the work specifying the inhibitor k has been made based on the operation of the operation device 300 by the user. If the result of this determination is that there is no instruction to end the work specifying the inhibitor k, the process returns to step S11 and waits until another inhibitor k different from the already specified inhibitor k is specified.

On the other hand, as a result of the determination in step S13, if an instruction to end the work specifying the inhibitor k is given, the process proceeds to step S14. In step S14, the inhibitor setting unit 118 calculates the number of inhibitors k determined to have been specified in step S11 (that is, the number of times the processing in step S11 has been performed) NK, and sets the calculated value in the RAM or the hard disk.
As described above, in the present embodiment, an example of the inclusion setting unit is realized by performing the processing of steps S11 to S14, for example.

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

In step S16, the effective range setting unit 122 sets information regarding the effective range 801 in the RAM or the hard disk.
Next, in step S <b> 17, the barrier energy setting unit 123 waits until information related to the barrier energy E <b> 0 (in this embodiment, the value of the barrier energy E <b> 0) is input based on the operation of the operation device 300 by the user. And if the information regarding barrier energy E0 is inputted, it will progress to Step S18.
In step S18, the barrier energy setting unit 123 sets information regarding the barrier energy E0 in the RAM or the hard disk.

Next, in step S19, the line setting unit 104 specifies 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. p and its number NP are set in the RAM or hard disk. Note that the line p is set in step S15 without considering the presence of the inhibitor k. Specifically, the line setting unit 104 defines the line p by two points i that specify the line p. For example, the line p1 shown in FIG. 3C is defined as the following equation (23).
p1 = {i1, i2} (23)
As described above, in the present embodiment, for example, an example of a line setting unit is realized by performing the process of step S19.

Next, in step S20, the grain boundary setting unit 105 identifies the grain boundary u specified by the lines p connected to each other with the triple point i set in step S8 as both ends among the lines p set in step S19. Are set in the RAM or hard disk. Specifically, the grain boundary setting unit 105 defines the grain boundary u by a plurality of lines p that specify the grain boundary u. For example, the grain boundary u1 shown in FIG. 3C is defined as the following equation (24).
u1 = {p1, p2, p3, p4} (24)

Next, in step S21, the orientation setting unit 107 determines the crystal grain image 31 based on the “signal indicating the orientation ξ of each crystal grain A included in the crystal grain image 31” determined to have been input in step S1. The orientation ξ of all the included crystal grains A is set in the RAM or hard disk.
Thus, in the present embodiment, for example, an example of the direction acquisition unit is realized by performing the process of step S21.

Next, in step S22, the grain boundary energy (γ) setting unit 109 determines the grain based on the orientation ξ of the crystal grain A set in step S21 and the analysis temperature θ (t) set in step S4. The grain boundary energy γ per unit length of all grain boundaries u set in step S20 is read from the graph or the like stored in the field energy (γ) storage unit 108. Then, the grain boundary energy (γ) setting unit 109 sets the read grain boundary energy γ per unit length in the RAM or the hard disk.
Thus, in this embodiment, for example, an example of a grain boundary energy setting unit is realized by performing the process of step S22.

  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. The mobility Mi of all the grain boundaries u set in step S20 is read from the graph or the like stored in the unit 110. Then, the mobility setting unit 111 sets the read mobility Mi in the RAM or the hard disk.

  Next, in step S24 of FIG. 15C, the analysis time setting unit 112 sets the analysis time t to 0 (zero).

  When the analysis time t is set to 0 by the analysis time setting unit 112, the process proceeds to step S25. In step S25, the line change processing unit 119 sets the variable p indicating the processing target line to 1. At this time, the line change processing unit 119 acquires information regarding the line p set in step S19 from the line setting unit 104.

  Next, in step S26, the line change processing unit 119 sets ΔNI indicating the number of points to increase / decrease to 0 (zero) and sets ΔNP indicating the number of lines to increase / decrease to 0 (zero).

  Next, in step S27, the line change processing unit 119 sets a variable k indicating the inhibitor to be processed to 1. At this time, the line change processing unit 119 acquires from the inhibitor setting unit 118 information related to the inhibitor k set in step S12 (coordinate information indicating the center position bk of the inhibitor k and information related to the radius r).

Here, in the following description, the description will be made with reference to the diagram shown in FIG. 7 as necessary.
In step S28, the line change processing unit 119 determines whether the line p passes through the inhibitor k based on the information regarding the line p acquired in step S25 and the information regarding the inhibitor k acquired in step S27. 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, when the line p is not within the inhibitor k (when not corresponding to FIGS. 7 (1a) to (6a)), the process proceeds to step S65 described later.

  On the other hand, if the result of determination in step S28 is that the line p passes through the inhibitor k, the process proceeds to step S29. In step S29, the line change processing unit 119 determines whether the end point of the line p is within the inhibitor k.

  If the result of determination in step S29 is that the end point of the line p is not within the inhibitor k (as shown in FIG. 7 (1a)), the process proceeds to step S30. In step S30, 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 the line p. As a result, the line p is divided into two lines.

  Next, in step S31, the line change processing unit 119 determines that the double point (double point in shown in FIG. 7 (1b) or FIG. 7 (1c)) generated on the line p in step S30 is the center position of the inhibitor k. It is moved to bk, and this is set as a fixed point ik (fixed point ik shown in FIG. 7 (1b) or FIG. 7 (1c)). In this case, the fixed point ik is an end point of the line p and a fixed double point constituting the line. As a result, a fixed point ik is newly generated, and the number of points is increased by one. In addition, since the 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 increases by one. In this case, the line change processing unit 119 also relates to information about the newly generated fixed point ik (for example, information indicating that the point is a fixed point and its coordinate information), and 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 the hard disk.

  Next, in step S32, the line change processing unit 119 increases the number of points and the number of lines by 1 in the processing of steps S30 and S31, respectively, so that ΔNI indicating the currently set number of points to be increased or decreased is set. 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, as a result of the determination in step S29, when the end point of the line p is within the inhibitor k (in the case shown in FIGS. 7 (2a) to (6a)), the process proceeds to step S33. In step S33, the line change processing unit 119 determines whether or not both end points of the line p are within the inhibitor k.

  As a result of the determination in step S33, when both end points of the line p are not in the inhibitor k, that is, when only one of the end points of the line p is in the inhibitor k (when shown in FIGS. 7 (2a) to (4a)). The process proceeds to step S34. In step S34, the line change processing unit 119 moves the end point in the inhibitor k to the center position bk of the inhibitor k, and moves it to the fixed point ik (FIG. 7 (2b) to (4b) or FIG. 7 (2c). ) To (4c) as fixed points ik). In the case shown in FIG. 7 (3a), since the end point in the inhibitor k is at the center position bk of the inhibitor k, the movement process 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. 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 the hard disk.

  On the other hand, if the result of determination in step S33 is that both end points of the line p are within the inhibitor k (as shown in FIGS. 7 (5a) and (6a)), the process proceeds to step S35. In step S35, the line change processing unit 119 causes the line p in the inhibitor k to disappear (FIG. 7 (5b) and (6b) or FIG. 9 (5c) and (6c)). This reduces the number of lines by one.

  Next, in step S36, the line change processing unit 119 moves two points in the inhibitor k to the center position bk of the inhibitor k (in this example, the first processing example), Let it be a fixed point ik (fixed point ik shown in FIGS. 7 (5b) and 7 (6b)). In the case shown in FIG. 7 (6a), since one end point in the inhibitor k is at the center position bk of the inhibitor k, the movement process is not performed on the one end point. The number of points is reduced by one by the process of step S36. Also, in this case, the line change processing unit 119 stores information indicating that the two end points in the line p have been changed to one fixed point ik and information indicating that the line p has been deleted from the RAM or the hard disk. To remember.

  Next, in step S37, the line change processing unit 119 reduces the number of points and the number of lines by 1 in the processing in steps S35 and S36, respectively, so that the currently set ΔNI indicating the number of points to be increased or decreased is set. 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 processing of step S32, step S34, step S37, or step S66 described later is completed, the process proceeds to step S38. In step S38, 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. If 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, it is determined that all the inhibitors k set in step S14 have not been processed, and the process proceeds to step S39. move on.

In step S39, the line change processing unit 119 adds 1 to the variable k indicating the inhibitor to be processed, and changes the inhibitor k to be processed. At this time, the line change processing unit 119 obtains information regarding the inhibitor k set in step S39 (coordinate information indicating the center position bk of the inhibitor k and information regarding the radius r) from the inhibitor setting unit 118. And the process after step S28 is performed again with respect to the changed inhibitor k.
As described above, in the present embodiment, for example, an example of the first line change processing unit is realized by performing the processing of steps S24 to S39.

  On the other hand, as a result of the determination in step S38, if the variable k indicating the inhibitor to be processed is equal to or greater than the number NK set in step S14, it is determined that all the inhibitors k set in step S14 have been processed, Proceed to step S40.

  In step S40, the line change processing unit 119 determines whether or not the variable p indicating the processing target line is smaller than the number NP set in step S19. As a result of the determination, if the variable p indicating the processing target line is smaller than the number NP set in step S19, it is determined that all the lines p set in step S15 have not been processed, and the process proceeds to step S41. move on.

  In step S41, the line change processing unit 119 adds 1 to the variable p indicating the processing target line to change the processing target line p. At this time, the line change processing unit 119 acquires information regarding the line p set in step S <b> 37 from the line setting unit 104. And the process after step S27 is performed again with respect to the changed line p.

  On the other hand, if the variable p indicating the processing target line is equal to or larger than the number NP set in step S19 as a result of the determination in step S40, it is determined that all the lines p set in step S19 have been processed. Proceed to step S42.

  In step S42, the line change processing unit 119 outputs ΔNI information indicating the number of points that are currently set to increase or decrease to the point setting unit 103, and sets the number NI of points that are currently set. Then, ΔNI indicating the number of output increasing / decreasing points is added, and the number of points NI is reset. Also, the line change processing unit 119 outputs ΔNP information indicating the number of lines that are currently set to increase / decrease to the line setting unit 104, and outputs the increase / decrease to the number of lines NP set in step S19. ΔNP indicating the number of lines to be added is added, and the number of lines NP is reset.

  Next, in step S43, the line change processing unit 119 causes the point setting unit 103 and the line setting unit 104 to change points (including disappearance and generation) and change lines (including disappearance and generation). Various resetting processes are performed.

  Specifically, the line change processing unit 119 outputs to the point setting unit 103 information related to the change (including disappearance and generation) of the points generated in the processes in steps S25 to S42, and the point i in step S8. Let's reset. At this time, for the generated fixed point ik, the point setting unit 103 sets coordinate information indicating the position of the point in the RAM or the hard disk together with information indicating that the point is a fixed point.

  Further, the line change processing unit 119 outputs to the line setting unit 104 information related to the line change (including disappearance and generation) that has occurred in the processes in steps S25 to S42, and the line change process in step S19 is performed again. Make 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, the grain boundary setting unit 105 resets the grain boundary u in step S20 when the point i is reset by the point setting unit 103 and the line p is reset by the line setting unit 104. Further, the grain boundary energy (γ) setting unit 109 resets the grain boundary energy γ per unit length in step S22 when the grain boundary u is reset by the grain boundary setting unit 105. Further, the mobility setting unit 111 resets the mobility Mi in step S23 when the grain boundary u is reset by the grain boundary setting unit 105.

Next, in step S44 of FIG. 15-4, the analysis point determination unit 113 sets the variable i indicating the calculation target point to 1. Thereby, the point i to be calculated is set.
Next, in step S45, 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 the determination, if the point i to be calculated is not a fixed point (ik), the process proceeds to step S46.

  Next, in step S46, the analysis point determination unit 113 determines whether or not the point i to be calculated is a double point. As a result of the determination, if the point i to be calculated is a double point, the process proceeds to step S47.

  In step S47, double-point driving force / position calculation processing by the double-point driving force calculation unit 114 and the position calculation unit 116 is performed. Here, the detailed processing operation of step S47 will be described with reference to FIG.

  In step S47 of FIG. 15-4, first, in step S431 of FIG. 16, the double-point driving force calculation unit 114 calculates the double point i to be calculated and two points i-1, i + 1 adjacent to the double point. Is read from the point setting unit 103. Then, the double-point driving force calculation unit 114 calculates the center of curvature O and the radius of curvature Ri (t) of the arc 41 defined by the double point i and the two points i−1 and i + 1 adjacent to the double point i. To do.

  Next, in step S432, the double-point driving force calculation unit 114 determines the grain boundary energy γi per unit length of the grain boundary u to which the double point i to be calculated belongs from the grain boundary energy (γ) setting unit 109. read out.

  Next, in step S433, the double-point driving force calculation unit 114 calculates the radius of curvature Ri (t) calculated in step S431 and the grain boundary energy γi per unit length read in step S432 by the equation (1). And the magnitude of the driving force Fi (t) generated at the double point i is calculated.

  The double-point driving force calculation unit 114 reads a vector indicating the current position ri (t) of the double point i to be calculated from the point setting unit 103. Then, the double-point driving force calculation unit 114 calculates the curvature from the double point i to be calculated from the vector indicating the current position ri (t) of the double point i to be calculated and the curvature center O calculated in step S431. The direction toward the center O is calculated, and the direction of the driving force Fi (t) generated at the double point i is determined. Thereby, a vector indicating the driving force Fi (t) generated at the double point i is obtained.

  Next, in step S434, the position calculation unit 116 reads out the mobility Mi corresponding to the grain boundary u to which the double point i to be calculated belongs from the mobility setting unit 111.

  Next, in step S435, the position calculation unit 116 receives a vector indicating the current position ri (t) of the double point i to be calculated from the point setting unit 103.

  Next, in step S436, the position calculation unit 116 firstly calculates the “vector indicating the driving force Fi (t) generated at the double point i to be calculated” obtained in step S433 and the “calculation” obtained in step S434. The mobility Mi of the grain boundary u to which the target double point i belongs is substituted into the equation (4) to calculate a vector indicating the speed vi (t) of the target double point i.

  Then, the position calculation unit 116 calculates a vector indicating the speed vi (t) of the double point i to be calculated, a vector indicating the current position ri (t) of the double point i to be calculated, and a time Δt as follows: Substituting into the equation (5), when Δt [sec] has elapsed from the current analysis time t, a vector indicating the position ri (t + Δt) where the double point i to be calculated exists is calculated. Further, the position calculation unit 116 temporarily stores information on a vector indicating the position ri (t + Δt) where the double point i to be calculated exists in a RAM or the like, and also positions ri where the double point i to be calculated exists. The vector information indicating (t−Δt) is deleted.

By performing the processing from step S431 to step S436, the double-point driving force / position calculation processing shown in step S47 of FIG. 15-4 is performed.
As described above, in the present embodiment, for example, an example of the driving force calculation unit is realized by performing the processes of steps S431 to S433. For example, an example of the position calculation unit is performed by performing the processes of steps S434 to S436. Is realized.

  Returning to the description of FIG. 15-4, if the result of determination in step S46 is that the point i to be calculated is not a double point but a triple point, the process proceeds to step S48.

  In step S48, triple-point driving force / position calculation processing by the triple-point driving force calculation unit 115 and the position calculation unit 116 is performed. Here, the detailed processing operation of step S48 will be described with reference to FIG.

  In step S48 of FIG. 15-4, first, in step S441 of FIG. 17, the triple point driving force calculation unit 115 calculates the grain boundary energy per unit length in the three grain boundaries u to which the triple point i to be calculated belongs. The magnitudes (absolute values) of γi1, γi2, and γi3 are read from the grain boundary energy (γ) setting unit 109. Further, the triple-point driving force calculation unit 115 reads the triple point i to be calculated and information on the three points 1, 2, and 3 adjacent to the triple point i from the point setting unit 103. Then, the triple point driving force calculation unit 115 calculates a unit vector having a direction from the triple point i to be calculated toward the points 1, 2, and 3.

  Next, in step S442, the triple point driving force calculation unit 115 reads the “magnitudes of grain boundary energy γi1, γi2, γi3 per unit length” read out in step S441 and “calculation target” calculated in step S441. The unit vector having a direction from the triple point i to points 1, 2, and 3 ”is substituted into the equation (3) to calculate a vector indicating the driving force Fi (t) generated at the triple point i to be calculated. To do.

  Next, in step S443, the position calculation unit 116 reads the mobilities Mi1 to Mi3 corresponding to the three grain boundaries u to which the triple point i to be calculated belongs from the mobility setting unit 111.

  Next, in step S444, the position calculation unit 116 moves to the points 1, 2, and 3 from the mobility Mi1 to Mi3 of the three grain boundaries u to which the triple point i to be calculated belongs, and from the triple point i to be calculated. A unit vector (dij (t) / | dij (t) |) having a direction is substituted into the equation (6) to calculate the mobility Mi of the triple point i to be calculated. The unit vector having the direction from the triple point i to be calculated toward the points 1, 2, and 3 can be the one calculated in step S441.

  Next, in step S445, the position calculation unit 116 receives a vector indicating the current position ri (t) of the triple point i to be calculated from the point setting unit 103.

  Next, in step S446, the position calculation unit 116 firstly calculates the “vector indicating the driving force Fi (t) generated at the triple point i to be calculated” obtained in step S442 and the “calculation” obtained in step S444. By substituting “the mobility Mi of the target triple point i” into the equation (4), a vector indicating the velocity vi (t) of the target triple point i is calculated.

Then, the position calculation unit 116 calculates a vector indicating the velocity vi (t) of the triple point i to be calculated, a vector indicating the current position ri (t) of the triple point i to be calculated, and a time Δt ( 5) Substituting into the equation, when Δt [sec] has elapsed from the current analysis time t, a vector indicating the position ri (t + Δt) where the triple point i to be calculated exists is calculated. Further, the position calculation unit 116 temporarily stores, in a RAM or the like, vector information indicating the position ri (t + Δt) where the calculation target triple point i exists, and also the position ri where the calculation target triple point i exists. The vector information indicating (t−Δt) is deleted.
Through the processing from step S441 to step S446 described above, the triple point driving force / position calculation processing shown in step S48 of FIG. 15-4 is performed.
As described above, in the present embodiment, for example, an example of the driving force calculation unit is realized by performing the processes of steps S441 and S442, and for example, an example of the position calculation unit is performed by performing the processes of steps S443 to S446. Is realized.

Returning to the description of FIG. 15D, if the result of determination in step S45 is that the point i to be calculated is a fixed point (ik), the process proceeds to step S49.
In step S49, the second fixed point processing unit 120 obtains the coordinate information of the fixed point i determined by the analysis point determining unit 113 and the positions of the other points constituting the fixed point i and the line p. Is read from the point setting unit 103. Then, the second fixed point processing unit 120 obtains information regarding the inhibitor k having the processing target fixed point i as the central position bk (coordinate information indicating the central position bk and information regarding the radius r) from the inhibitor setting unit 118. read out. Further, the second fixed point processing unit 120 reads out information related to the effective range 801 (information related to the radius of the effective range 801) from the effective range setting unit 122.

Next, in step S50, the grain boundary energy (E) calculation unit 121 acquires the information read in step S49 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) calculating 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, and the fixed point i is located at the center position. The grain boundary energy Ei within the effective range 801 of the grain boundary u to which the fixed point i belongs when being fixed to bk is calculated (calculated).
Here, when the fixed point i (ik) is a double point, for example, the grain boundary energy Ei is calculated using the equation (15). On the other hand, when the fixed point i (ik) is a triple point, the grain boundary energy Ei is calculated using, for example, the equation (16).
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 the grain boundary energy calculation unit is realized by performing the process of step S50.

Next, in step S51, the grain boundary energy (E) calculating unit 121 releases the fixed point i from the fixed position (the center position bk of the inhibitor k), and the position where the grain boundary energy E is minimized (equilibrium position). The grain boundary energy Ei ′ in 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, for example, the grain boundary energy Ei ′ is calculated using the equation (17). On the other hand, when the fixed point i (ik) is a triple point, for example, the grain boundary energy Ei ′ is calculated using the equation (18).
Thus, in the present embodiment, for example, the second grain boundary energy is realized by the grain boundary energy Ei ′, and an example of the grain boundary energy calculation unit is realized by performing the process of step S51.

  Next, in step S52, the second fixed point processing unit 120 compares the grain boundary energy Ei calculated in step S50 with the grain boundary energy Ei ′ calculated in step S51, and the grain boundary energy Ei ′. Is less than the grain boundary energy Ei (Ei ′ <Ei). As a result of the determination, if the grain boundary energy Ei ′ is not less than the grain boundary energy Ei, the process proceeds to step S59 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 S53.

In step S53, the grain boundary energy (E) calculation unit 121 calculates 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. (calculate.
Here, when the fixed point i (ik) is a double point, for example, the grain boundary energy Ei ″ is calculated using the equation (19). On the other hand, when the fixed point i (ik) is a triple point, for example, the grain boundary energy Ei ″ is calculated using the equation (20).
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 the grain boundary energy calculation unit is realized by performing the process of step S53.

Next, in step S <b> 54, the second fixed point processing unit 120 reads information on the barrier energy E <b> 0 from the barrier energy setting unit 123. Then, the second 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 the determination, if the value obtained by subtracting the grain boundary energy Ei is not less than the barrier energy E0, the process proceeds to step S59 described later.
On the other hand, if the value obtained by subtracting the grain boundary energy Ei is less than the barrier energy E0, the process proceeds to step S55.

  In step S55, the second fixed point processing unit 120 determines whether or not the fixed point i (ik) determined in step S45 is a double point. As a result of the determination, if the fixed point i (ik) is a double point, the process proceeds to step S56. In step S56, the second fixed point processing unit 120 moves the fixed point i (ik) to the surface (boundary) of the inhibitor k, releases the fixation, and moves the normal point i to the position of the point 804. (Ik) is generated (see FIG. 10B). And it progresses to step S59 mentioned 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 S57. In step S57, the second fixed point processing unit 120 moves the fixed point i (ik) to the surface (boundary) of the inhibitor k, releases the fixation, and moves the normal point i to the position of the point 804. (Ik) is generated. Further, the second fixed point processing unit 120 does not connect 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 (iv) and the generated normal point i (ik) is generated at the central position bk of the inhibitor k (see FIG. 11B).
Next, in step S58, the line change processing unit 119 increases the number of points and the number of lines by 1 in the process of step S57, so 1 is set to ΔNI indicating the currently set number of points to be increased or decreased. Addition is performed 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. Then, the process proceeds to step S59.
As described above, in the present embodiment, for example, an example of a fixed point processing unit is realized by performing the processing of steps S56 and S57.

When the process proceeds to step S59 as described above, the analysis point determination unit 113 determines whether or not the variable i indicating the point to be calculated is smaller than the number of points NI currently set by the point setting unit 103. If the variable i indicating the point to be calculated is smaller than the number of points NI currently set by the point setting unit 103 as a result of this determination, processing is performed for all points i currently set by the point setting unit 103. It is determined that the process has not been performed, and the process proceeds to step S60.
In step S60, the analysis point determination unit 113 adds 1 to the variable i indicating the point to be calculated, and changes the point i to be calculated. And the process after step S45 is performed again with respect to the changed point i.

On the other hand, if it is determined in step S59 that the variable i indicating the point to be calculated is greater than or equal to the number of points NI currently set by the point setting unit 103, the point setting unit 103 currently sets the point. It is determined that all points i have been processed, and the process proceeds to step S61.
In step S61, the second fixed point processing unit 120 causes the point setting unit 103 to perform resetting according to the change of the point i in steps S56 and S57. At the same time, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the point i calculated in step S47 or step S48 is present to the point setting unit 103. Thereby, the vector indicating the current position ri (t) of the point i is reset in the point setting unit 103.

  The line setting unit 104 resets the line p when the point i is reset by the point setting unit 103. Further, the grain boundary setting unit 105 resets the grain boundary u triggered by resetting the point i in the point setting unit 103 and resetting the line p in the line setting unit 104. Furthermore, resetting in the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 is also performed in response to resetting of the grain boundary u in the grain boundary setting unit 105.

  Next, in step S62, the analysis time setting unit 112 determines whether or not the analysis time t is greater than the analysis completion time T set in step S6. That is, it is determined whether or not the analysis completion time T has elapsed. As a result of this determination, if the analysis time t is not longer than the analysis completion time T set in step S6 (if the analysis completion time T has not elapsed), the process proceeds to step 63. In step S63, the analysis time setting unit 112 updates the analysis time t by adding the time Δt to the currently set analysis time t. Then, it returns to step S25 and performs the process after step S25 again. In step S62, the processing from step S25 is repeated until it is determined that the analysis time t is longer than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed).

  On the other hand, if the result of determination in step S62 is that the analysis time t is greater than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed), the process proceeds to step S64. In step S64, the analysis image display unit 117 analyzes the time t from 0 (zero) to T [sec based on the “vector of the position ri (t + Δt) of the point i” calculated in step S47 or step S48. ], An image showing how the state of the crystal grains A changes is displayed on the display device 200. Then, the series of flowcharts of FIGS.

  When the analysis temperature θ (t) input in step S3 depends on time, for example, after step S63, the analysis temperature θ (t + Δt) at the analysis time t + Δt set in step S63 is read and the analysis temperature After resetting the grain boundary energy γ and the mobility Mi per unit length in θ (t + Δt), the processing after step S25 may be performed.

  When it is determined in step S28 of FIG. 15C that the line p is not within the inhibitor k, the process proceeds to step S65. In step S65, the overtaking determination unit 124 determines whether or not the analysis time t is 0 (zero). If the analysis time t is 0 (zero) as a result of this determination, the line p has not overtaken the inhibitor k, so step S66 is skipped and the process proceeds to step S38 described above and set in step S14. It is determined whether or not all the inhibitors k are processed.

On the other hand, if the analysis time t is not 0 (zero), the process proceeds to step S66. In step S66, the overtaking determination unit 124 determines whether or not the calculation target line p has passed the calculation target inhibitor k. Here, the detailed processing operation of this step S66 is demonstrated using FIG.18 and FIG.8.
In step S66 of FIG. 15C, first, in step S451 of FIG. 18, the overtaking determining unit 124, as shown in the equation (7), the vectors Aa and Ab (triangle 80a (first 80a (first)) shown in FIG. Vector A (vector determined by the grain boundary point i83, which is one end point of the moved line p, and the center position bk of the inhibitor k).

Next, in step S452, the overtaking determination unit 124 determines whether or not the coefficients ρ and σ of the equation (7) satisfy all of the equations (8) to (10). Then, it is determined whether or not the center position bk of the inhibitor k exists. As a result of this determination, if the coefficients ρ and σ in the equation (7) satisfy all of the equations (8) to (10) and the center position bk of the inhibitor k is in the triangle 80a, the calculation target It is determined that the line p has passed the calculation target inhibitor k, and the process proceeds to step S67 in FIG.
On the other hand, if the coefficients ρ and σ of the equation (7) do not satisfy all of the following equations (8) to (10) and the center position bk of the inhibitor k is not present in the triangle 80a, the process proceeds to step S453. move on. In step S453, the overtaking determination unit 124 calculates the vector A using the vectors Ab and Ac (vectors determined by the triangle 80b (second triangle)) shown in FIG. 8 as shown in the equation (11). To express.

Next, in step S454, the overtaking determination unit 124 determines whether or not the coefficients λ and ω of the equation (11) satisfy all of the equations (12) to (14). Then, it is determined whether or not the center position bk of the inhibitor k exists. As a result of this determination, if the coefficients λ and ω in the equation (11) satisfy all the equations (12) to (14) and the center position bk of the inhibitor k is in the triangle 80b, the calculation target It is determined that the line p has passed the calculation target inhibitor k, and the process proceeds to step S67 in FIG.
On the other hand, if the coefficients λ and ω of the equation (11) do not satisfy all of the equations (12) to (14) and the center position bk of the inhibitor k is not in the triangle 80b, the line p to be calculated However, it is determined that the inhibitor k to be calculated is not overtaken, and the process proceeds to step S38 in FIG. 15-3 described above, and it is determined whether or not all the inhibitors k set in step S14 have been processed.
As described above, in the present embodiment, for example, an example of a determination unit is realized by performing the processing in step S66 (steps S451 to S454 in FIG. 18).

  As described above, when it is determined that the calculation target line p has passed the calculation target inhibitor k, the process proceeds to step S67 in FIG. 15C, and the first fixed point processing unit 125 passes the inhibitor k. A double point (double point i85 shown in FIG. 9A) is generated at an arbitrary position on the calculation target line p (line p82 shown in FIG. 9A). As a result, the line p is divided into two lines.

  Next, in step S68, the first fixed point processing unit 125 moves the double point (double point i85 shown in FIG. 9A) generated on the line p in step S67 to the center position bk of the inhibitor k. This is set as a fixed point ik (fixed point ik shown in FIG. 9B). The fixed point ik in this case is the end point (the grain boundary points i83 and i84 shown in FIGS. 9A and 9B) of the line p (the line p82 shown in FIG. 9A) and the line (FIG. 9 ( This is a fixed double point constituting the lines p83 and p84) shown in b). As a result, a fixed point ik is newly generated, and the number of points is increased by one. Further, since the line p is divided into two lines (lines p83 and p84 shown in FIG. 9B), the number of lines increases by one. In this case, the first fixed point processing unit 125 also newly sets information regarding the fixed point ik that has been newly generated (for example, information indicating that the point is a fixed point and its coordinate information) and newly setting the fixed point ik. The information regarding the line (for example, information indicating that the line is set between each end point of the line p and the fixed point ik) is stored in the RAM or the hard disk.

Next, in step S69, the first fixed point processing unit 125 increases the number of points to be increased or decreased currently set because the number of points and the number of lines have increased by one in the processing of steps S67 and S68, respectively. 1 is added to the indicated ΔNI 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. Then, the process proceeds to step S38 described above, and it is determined whether or not all the inhibitors k set in step S14 have been processed.
As described above, in this embodiment, for example, an example of the second line change processing unit is realized by performing the processes of steps S67 and S68.

As described above, in the present embodiment, when a line p having two end points adjacent to each other on the same grain boundary passes through the inhibitor k, a fixed point ik is generated in the inhibitor k. Then, the process of changing the line p with the fixed point ik as an end point is performed (for example, see FIG. 9). Thereby, it is possible to simulate a state in which the grain boundary movement of the crystal grains A is inhibited (suppressed) by the inhibitor k.
In particular, in this embodiment, as a result of changing the position of the grain boundary point, it is determined whether or not the line p has overtaken the inhibitor k. If the line p has overtaken, the center position bk of the inhibitor k is determined. Then, a fixed point ik is generated, and along with this, a process of changing a line passing through both end points (grain boundary points) of the line p overtaking the inhibitor k is performed. Therefore, the behavior of the crystal grain A (grain boundary u) in the vicinity of the inhibitor k can be simulated as faithfully as possible, and it is possible to accurately determine how the crystal grain A changes over time through the inhibitor. Can be analyzed.

  In this embodiment, when the fixed point i is fixed at the center position bk, the grain boundary energy Ei of the grain boundary u to which the fixed point i belongs, and the fixed point i are fixed positions (center position of the inhibitor k). bk), the grain boundary energy Ei 'of the grain boundary u to which the released fixed point i belongs when released from the equilibrium position, and the grain to which the fixed point i belongs when the fixed point ik is released The grain boundary energy Ei '' of the boundary u is calculated. Then, when the grain boundary energy Ei ′ is smaller than the grain boundary energy Ei and the difference between the grain boundary energy Ei ″ and the grain boundary energy Ei is smaller than the barrier energy E0, the fixed point i is released. . Therefore, the transition from the state where the grain boundary movement of the crystal grain A is suppressed by the inhibitor to the state where the grain boundary movement of the crystal grain A resumes and the state of the grain boundary movement of the crystal grain A after the transition can be simulated. it can. In particular, it is possible to determine whether or not to release the fixed point ik including the influence of the grain boundary energy γ per unit length.

  As described above, the transition to the state where the grain boundary movement of the crystal grain A is suppressed by the inhibitor k which is an example of the inclusion, and the state where the grain boundary movement of the crystal grain A resumes from the state where the suppression is performed. In addition, since the state of the grain boundary movement of the crystal grain A after the transition can be simulated, it is more easily and accurately analyzed how the crystal grain A changes over time through the inhibitor. be able to.

  In the present embodiment, the grain boundary energy Ei, the grain boundary energy Ei ′, and the grain boundary energy Ei ″ are calculated within the effective range 801, respectively. Therefore, the fixed point ik can be released without being affected as much as possible by the number of double points (the length of each line) set for the grain boundary u.

[Modification 1]
In this embodiment, when the center position bk of the inhibitor k is not in the triangle 80a, it is determined whether or not the center position bk of the inhibitor k is in the triangle 80b. There is no need to do this. For example, when the center position bk of the inhibitor k is not in the triangle 80b (including the boundary of the triangle 80b), it is determined whether or not the center position bk of the inhibitor k is in the triangle 80a. Also good. Further, the vector A that is a direction from the grain boundary point i83 toward the center position bk of the inhibitor k may be expressed by a method other than the expressions (7) and (11). In this case, the determination conditions of the expressions (8) to (10) and (12) to (14) are changed according to the written contents. Further, for example, when a quadrangle having four grain boundary points i81 to i84 as vertices is a rectangle or a square, it is directly (at a time) whether or not the center position bk of the inhibitor k is present in the quadrangle. You may judge. As described above, for example, it is determined whether or not the center position bk of the inhibitor k exists in the quadrangle having the four grain boundary points i81 to i84 as the vertices of the line p before and after the movement. If so, the method of determining whether or not the line p has passed the inhibitor k is not limited to that described above.

[Modification 2]
In this embodiment, as shown in FIGS. 10A and 11A, the lines pa and pb formed by the fixed point ik and the points ir and it adjacent to the fixed point ik are extended. Intersection points 802 and 803 between the line and the effective range 801 are obtained. However, this is not always necessary if the intersection of the line tangent to the grain boundary u including the fixed point ik and the effective range 801 is obtained. For example, in FIG. 10A, for a point corresponding to the intersection 802 (803), an arc passing through the point ir (it) and the fixed point ik and the point iq (iu) adjacent to the point ir (it). Alternatively, the intersection point between the tangent line passing through the fixed point ik and the effective range 801 may be obtained.

[Modification 3]
Further, in the present embodiment, of the lines pa, pb, and pc having the fixed point ik as an end point, the intersections 802 and 803 of the extension lines 801 and 803 at the positions sandwiching the equilibrium position w and the effective range 801. I asked for. However, it is not always necessary to obtain the intersection points 802 and 803 after obtaining the equilibrium position w. For example, the intersection points 802 and 803 can be obtained as follows. Another example of the method for obtaining the intersection points 802 and 803 will be described with reference to FIG.
First, the grain boundary energy (E) calculation unit 121 determines that “the angle between lines pa and pb determined by the fixed point ik and the points ir and it adjacent to the fixed point ik”, “the fixed point ik and the fixed point ik”. "An angle formed by lines pa and pc determined by points ir and iv adjacent to point ik" and "An angle formed by lines pc and pb determined by fixed point ik and points iv and it adjacent to fixed point ik" The angle that is the sharpest angle (the angle formed by the lines pa and pb) is selected. Then, the grain boundary energy (E) calculation unit 121 regards the lines pa and pb constituting the selected angle as a line at a position sandwiching the equilibrium position w, and an extension line of the lines pa and pb and an effective range 801. Intersection points 802 and 803 are obtained.

[Modification 4]
Furthermore, it is not always necessary to obtain the intersection of the effective range 801 with the line in contact with the grain boundary u including the fixed point ik. For example, instead of the intersection points 802 and 803, for example, an intersection point between the effective range 801 and the line p (an intersection point between the effective range 801 and the actually set line p) may be obtained.

[Modification 5]
<Calculation of grain boundary energy Ei>
Further, as shown in the equation (16), in the present embodiment, the grain boundary including the line pc is not taken into consideration when obtaining the grain boundary energy Ei when the fixed point is a fixed triple point. As described above, the grain boundary energy Ei may be obtained in consideration of the grain boundary including the line pc.
FIG. 19 is a diagram illustrating another example of a method for calculating grain boundary energy when the fixed point is a fixed triple point.
The grain boundary energy (E) calculation unit 121 obtains a point 806 in addition to the points 802 and 803. A point 806 is an intersection of an effective line 801 and an extension line of the line pc connecting the fixed point ik and the point iv adjacent to the fixed point ik with the shortest distance.
Here, the grain boundary u does not exist in the inhibitor k. Therefore, the grain boundary energy (E) calculation unit 121 calculates the radius of the inhibitor k from the length K between the fixed point ik and the intersection point 806 as the effective length L3 used when calculating the grain boundary energy Ei. The length obtained by subtracting the length of r is obtained.

Further, since the fixed point ik is a triple point, the portions of the three effective lengths L1, L2, and L3 (= K−r) 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. 11 is a triple point is calculated by the following equation (25).
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
+ (Grain boundary energy γ3 per unit length of grain boundary u including line pc) × L3
... (25)

<Calculation of grain boundary energy Ei '>
In FIG. 11, as shown in the equation (18), in the present embodiment, the fixed point ik is a triple point using a length B3 obtained by subtracting the radius r of the inhibitor k from the length of the line 903. In this case, the grain boundary energy Ei ′ is obtained. However, the grain boundary energy Ei ′ when the fixed point ik is a triple point may be obtained as follows.
As described above, in FIG. 19, the grain boundary energy (E) calculation unit 121 obtains a point 806 in addition to the points 802 and 803. Then, the grain boundary energy (E) calculation unit 121 forms a line (virtual line) 904 that connects the point 806 and the equilibrium position w. At this time, the effective length used for calculating the grain boundary energy Ei ′ is a length B6 obtained by subtracting the length B5 of the portion of the inhibitor k in the line 904 from the length B4 of the line 904.
Then, the grain boundary energy (E) calculation unit 121 substitutes B6 instead of B3 in the above-described equation (18), and calculates the grain boundary energy Ei ′ when the fixed point ik is a triple point.

<Calculation of grain boundary energy Ei ''>
In FIG. 11, as shown in the equation (20), in the present embodiment, the grain boundary including the line pc is taken into account when obtaining the grain boundary energy Ei '' when the fixed point is a fixed triple point. However, the grain boundary energy Ei may be obtained in consideration of the grain boundary including the line pc as follows.
As described above, in FIG. 19, the grain boundary energy (E) calculation unit 121 obtains a point 806 in addition to the points 802 and 803. Then, the grain boundary energy (E) calculation unit 121 sets the length of a line (virtual line) connecting the point 804 and the point 806 at the shortest distance as an effective length used for calculating the grain boundary energy Ei ″. A length M5 obtained by subtracting the length M4 of the portion of the inhibitor k in the line from M3 is obtained.
When the fixed point ik is a triple point, the portion of the effective length L1 including the line pa, the portion of the effective length L2 including the line pb, and the portion of the effective length L3 including the line pc are respectively Can be regarded as belonging to different grain boundaries u. Therefore, for example, when the fixed point ik shown in FIG. 19 is released, the grain boundary energy Ei ″ in the effective range 801 of the grain boundary u to which the fixed point i belongs is expressed by the following equation (26). 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
+ (Grain boundary energy γ3 per unit length of grain boundary u including line pc) × M5
... (26)

[Modification 6]
In this embodiment, the effective range 801 is a circle, but the shape of the effective range 801 is not limited to a circle. Further, if the effective range 801 is set as described above, it is preferable that the fixed point ik can be released without being affected as much as possible by the number of double points set for the grain boundary u. It is not necessary to set the effective range 801. In this case, for example, in FIG. 10 and FIG. 11, the above-described processing is performed using the information of the points ir and it adjacent to the fixed point ik instead of the information of the points 802 and 803. Can do.
In this case, in the example shown in FIG. 10 and FIG. 11, it is a virtual virtual line of the grain boundary to which the fixed point ik belongs, and is a virtual line (point ir, it The grain boundary energy Ei '' is calculated using the length of the virtual line connecting the point 804 and the point 804 at the shortest distance) and the grain boundary energy per unit length at the grain boundary to which the fixed point ik belongs. .

Further, the line of the grain boundary to which the fixed point ik belongs, the length of the lines pa and pb having the fixed point ik as one of the end points, and the grain boundary energy per unit length in the grain boundary to which the fixed point ik belongs By using this, the grain boundary energy Ei is calculated.
Furthermore, it is a virtual virtual line of the grain boundary to which the fixed point ik belongs, the length of the virtual line passing through the equilibrium position w (virtual line connecting the points ir and it with the shortest distance), and 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 at.

[Modification 7]
Further, as in the present embodiment, when the grain boundary energy Ei ′ is smaller than the grain boundary energy Ei and the difference between the grain boundary energy Ei ″ and the grain boundary energy Ei is smaller than the barrier energy E0, the fixed point If i is released, it is possible to determine whether or not to release the fixed point ik including the influence of the grain boundary energy γ per unit length, which is preferable, but it is not always necessary to use the grain boundary energy Ei ″. It is not necessary to determine whether to release the fixed point i. In such a case, when the grain boundary energy Ei ′ is smaller than the grain boundary energy Ei, it is determined that the fixed point i is released, and otherwise, it is determined that the fixed point i is not released. Good.

[Modification 8]
Further, in the present embodiment, the case where the user designates the point i and the inhibitor k using the operation device 300 while viewing the crystal grain image 31 has been described as an example. However, this is not necessarily required. There is no. For example, the crystal grain analysis apparatus 100 (computer) may automatically specify the point i and the inhibitor k based on the crystal grain image signal obtained by the analysis by the EBSP method.

[Modification 9]
In this embodiment, as shown in FIG. 6, the inhibitor setting unit 118 sets the inhibitor k by approximating the detected area of the inhibitor k with a circle. However, the area of the detected inhibitor k is set. The approximate shape may be changed according to the shape. At this time, for example, when the inhibitor k is approximated to an ellipse, coordinate information indicating the center position (fixed position) of the ellipse, information on the length of the major axis of the ellipse, and the length of the minor axis of the ellipse Such information is calculated and the inhibitor k is set in the RAM or the hard disk. For example, when the inhibitor k is approximated to a polygon, for example, coordinate information indicating the center of gravity position as a fixed position and coordinate information indicating each vertex in the polygon are calculated, and the inhibitor k is stored in the RAM or the hard disk. Take the form set to.

[Modification 10]
In this embodiment, the grain boundary u is defined by the grain boundary setting unit 105. However, if the point i, the line p, and the crystal grain A are used, the grain boundary u is naturally determined. There is no need to define u.
[Modification 11]
In the present embodiment, the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 are based on the absolute value of the difference Δξ of the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u. The grain boundary energy γ and the mobility Mi per unit length are set, but the unit is based on the difference Δξ between the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u. You may make it set the grain boundary energy (gamma) per length and the mobility Mi.

[Modification 12]
In this embodiment, the mobility Mi at the triple point i to be calculated is obtained using the equation (6). However, it is easy to correspond to the three grain boundaries u to which the triple point i to be calculated belongs. If the mobility Mi1 to Mi3 is used to determine the mobility Mi of the triple point i to be calculated, this need not necessarily be done. For example, the mobility Mi at the triple point i to be calculated may be obtained using the following equation (27).

[Modification 13]
In this embodiment, the double point is set in order to improve the reproducibility of the grain boundary u. However, only the triple point may be set without setting the double point. In this case, for example, steps S46 and S47 in FIG. Then, instead of steps S57 and S58, the fixed point i is moved to the surface of the inhibitor to generate a normal point i. Further, instead of step S56, the fixed point i disappears, and two lines connecting the fixed point i and two points adjacent to the fixed point i at the shortest distance disappear and the fixed point i belongs. After extinguishing two grain boundaries, a grain boundary (line) connecting the two points adjacent to the fixed point i is generated, and ΔNI and ΔNP indicating the number of points to be increased and decreased and ΔNP are decremented by 1. Do.

[Modification 14]
In the present embodiment, the electromagnetic steel sheet is described as an example of the metal material that is an example of the material analyzed by the crystal grain analysis device. However, the material analyzed by the crystal grain analysis device according to the present invention is as described above. Anything can be applied as long as it is manufactured using an inclusion such as an inhibitor. If the metal material analyzed by the crystal grain analysis device is different, the contents of the graph stored in the grain boundary energy (γ) storage unit 108 and the mobility storage unit 110 are input to the crystal grain analysis device. Depending on the material, the data will vary.

Of the embodiments of the present invention described above, the part executed by the CPU can be realized by the computer executing the program (computer program). Further, means for supplying a program to a computer, for example, a computer-readable recording medium such as a CD-ROM recording such a program, or a transmission medium for transmitting such a program can also be applied as an embodiment of the present invention. . A program product such as a computer-readable recording medium in which the program is recorded can also be applied as an embodiment of the present invention. The above programs, computer-readable recording media, transmission media, and program products are included in the scope of the present invention.
In addition, the above-described embodiments are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

It is a figure which shows the 1st Embodiment of this invention and shows an example of the analysis method performed with a crystal grain analyzer. It is a block diagram which shows embodiment of this invention and shows an example of a function structure of a crystal grain analyzer. It is a figure which shows embodiment of this invention and shows an example of a crystal grain image, a double point, a triple point, a line, and a grain boundary. It is a figure which shows embodiment of this invention and demonstrates an example of the calculation method of the driving force which arises in a double point. It is a figure which shows embodiment of this invention and demonstrates an example of the calculation method of the driving force which arises in a triple point. It is a figure which shows embodiment of this invention and demonstrates an example of the setting method of an inhibitor. It is a figure which shows embodiment of this invention and demonstrates an example of the line change process by a line change process part. It is a figure which shows embodiment of this invention and illustrates an example of the method of determining whether the line passed the inhibitor. It is a figure which shows embodiment of this invention and demonstrates an example of the processing method when the line p overtakes the inhibitor k. It is a figure which shows embodiment of this invention and demonstrates an example of the calculation method of the grain boundary energy in case a fixed point is a fixed double point. It is a figure which shows embodiment of this invention and demonstrates an example of the calculation method of the grain boundary energy in case a fixed point is a fixed triple point. It is a figure which shows embodiment of this invention and shows an example of the relationship between the length of the virtual line in an effective range, and the position of the point on an effective range when a fixed point is a double point. It is a figure which shows embodiment of this invention and shows an example of the relationship between the length of the virtual line in an effective range, and the position of the point on an effective range when a fixed point is a triple point. It is a figure which shows embodiment of this invention and shows an example of the relationship between the minimum length of the grain boundary to which a fixed point belongs, and pinning time. It is a flowchart which shows embodiment of this invention and demonstrates an example of the processing operation which a crystal grain analyzer performs. It is a flowchart which shows embodiment of this invention and follows FIG. It is a flowchart which shows embodiment of this invention and follows FIG. 15-2. FIG. 15 is a flowchart illustrating the embodiment of the present invention and continuing from FIG. It is a flowchart which shows embodiment of this invention and demonstrates an example of the detailed processing operation of step S47 of FIGS. 15-4. It is a flowchart which shows embodiment of this invention and demonstrates an example of the detailed processing operation of step S48 of FIGS. 15-4. It is a flowchart which shows embodiment of this invention and demonstrates an example of the detailed process operation | movement of step S66 of FIG. 15-3. It is a figure which shows embodiment of this invention and demonstrates the other example of the calculation method of the grain boundary energy in case a fixed point is a fixed triple point.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 Crystal grain analyzer 101 Crystal image acquisition part 102 Crystal image display part 103 Point setting part 104 Line setting part 105 Grain boundary setting part 106 Analysis temperature setting part 107 Orientation setting part 108 Grain boundary energy ((gamma)) memory | storage part 109 Grain boundary energy (Γ) setting unit 110 mobility storage unit 111 mobility setting unit 112 analysis time setting unit 113 analysis point determination 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 Second fixed point processing unit 121 Grain boundary energy (E) calculation unit 122 Effective range setting unit 123 Barrier energy setting unit 124 Overtaking determination unit 125 First fixed point processing unit 200 Display device 300 Operating device

Claims (14)

Image signal acquisition means for acquiring image signals of crystals in the metal material and inclusions included in the metal material;
Corresponding to both end points of the grain boundaries of the crystal grains included in the crystal, and corresponding to the midpoint of the grain boundaries of the crystal grains included in the crystal, and a triple point in contact with the three crystal grains including the crystal grains, And when a double point in contact with two crystal grains including the crystal grain is designated based on the image signal, a grain boundary point setting means for setting the designated triple point and double grain boundary point; ,
Line setting means for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary, which is a grain boundary point set by the grain boundary point setting means,
When the inclusion is designated based on the image signal, inclusion setting means for setting the designated inclusion;
When the line set by the line setting means passes through the inclusion, a first line change processing means for generating a fixed point in the inclusion and changing the line with the fixed point as an end point. When,
Determination means for determining whether or not the line has passed through the inclusion set by the inclusion setting means based on the positions before and after the movement of the line that has not been changed by the first line changing means. When,
When it is determined by the determination means that the line has passed the inclusion set by the inclusion setting means, a fixed point is generated in the inclusion, and a line changing process using the fixed point as an end point Second line changing means for performing
The first grain boundary energy at the grain boundary to which the fixed point belongs and the fixed point are released from the fixed position and moved to the equilibrium position where the grain boundary energy is at a position in the region excluding the inside of the inclusion. Grain boundary energy calculating means for calculating a second grain boundary energy at the grain boundary when
A crystal grain analysis apparatus comprising: a fixed point processing unit that performs processing for releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy.   The determination means includes a center of inclusions set by the inclusion setting means in a triangle defined by three grain boundary points among four grain boundary points corresponding to both end points of the line before and after the movement. 2. The line according to claim 1, wherein, when present, it is determined that a line that has not been changed by the first line changing unit has passed the inclusion set by the inclusion setting unit. Crystal grain analyzer.   The determination means includes a grain boundary point corresponding to one end point of the line after movement, and a grain boundary corresponding to both end points of the line before movement, among the grain boundary points corresponding to both end points of the line before and after the movement. When the inclusion center set by the inclusion setting means exists in the triangle defined by the point, the line that has not been changed by the first line changing means is the inclusion setting. 3. The crystal grain analysis apparatus according to claim 2, wherein it is determined that the inclusion set by the means has passed.   In the case where the center of the inclusion set by the inclusion setting means does not exist in the triangle, the determination means determines a triangle obtained by removing the triangle from a quadrangle determined by the four grain boundary points. In the case where the center of the inclusion set by the inclusion setting means exists, a line that has not been changed by the first line changing means is included in the inclusion set by the inclusion setting means 4. The crystal grain analyzer according to claim 2, wherein it is determined that the object has passed.   In the case where there is no inclusion center set by the inclusion setting means in any of the triangles, the determination means is a line that has not been changed by the first line changing means. The crystal grain analysis apparatus according to claim 4, wherein it is determined that the inclusion has not passed through the inclusion set by the inclusion setting means.   The second line changing means generates a fixed point in the inclusion, extinguishes the moved line, a grain boundary point corresponding to both end points of the moved line, and the generated fixed point, The crystal grain analysis apparatus according to claim 1, wherein a line having an end point is generated. 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,
In the fixed point processing means, the second grain boundary energy is less than the first grain boundary energy, and the difference between the first grain boundary energy and the third grain boundary energy is less than a threshold value. In such a case, the crystal grain analyzer according to any one of claims 1 to 6, wherein processing for releasing the fixed point is performed.   The fixed point processing means is a boundary of the inclusions in an area between the lines where the equilibrium position exists among areas defined by the lines having the fixed point as an end point, and an angle formed between the lines. The crystal grain analysis apparatus according to claim 1, wherein a process of moving the fixed point to a position of an intersection with a line segment that bisects the line and releasing the same is performed.   When the fixed point processing means releases the fixed point that is the triple point, the inclusion in the region between the lines where the equilibrium position exists among the regions defined by the lines having the fixed point as an end point The fixed point is moved to the position of the intersection of the line segment that bisects the angle between the lines and released, and the double point connected to the moved fixed point is The crystal grain analysis apparatus according to claim 8, wherein a process for generating the inclusion is performed. A driving force calculating means for calculating the driving force generated at the grain boundary point set by the grain boundary point setting means by using the grain boundary energy per unit length in the grain boundary to which the grain boundary point belongs;
10. The apparatus according to claim 1, further comprising position calculating means for calculating a change in position of the grain boundary point with the passage of time using the driving force calculated by the driving force calculating means. The crystal grain analyzer according to claim 1. Grain boundary energy storage means for storing the relationship between the difference between the orientations of two crystal grains adjacent to each other via the grain boundary and the grain boundary energy per unit length;
Orientation acquisition means for acquiring the orientation of crystal grains included in the image signal;
Grain boundary energy per unit length corresponding to the difference between the orientations of two crystal grains adjacent to each other through the grain boundary, which is the orientation of the crystal grains acquired by the orientation acquisition means, 11. The crystal grain analysis apparatus according to claim 1, further comprising a grain boundary energy setting unit that is determined and set based on a relationship stored by the energy storage unit.   The crystal grain analyzer according to any one of claims 1 to 11, wherein the inclusion does not change its position with the passage of time and is an inhibitor. An image signal acquisition step of acquiring an image signal of a crystal in the metal material and inclusions included in the metal material;
Corresponding to both end points of the grain boundaries of the crystal grains included in the crystal, and corresponding to the midpoint of the grain boundaries of the crystal grains included in the crystal, and triple points in contact with the three crystal grains including the crystal grains And when a double point in contact with two crystal grains including the crystal grain is designated based on the image signal, a grain boundary point setting step for setting the designated triple point and double grain boundary point; ,
A line setting step for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary at the grain boundary point set by the grain boundary point setting step;
When the inclusion is designated based on the image signal, an inclusion setting step for setting the designated inclusion;
A first line change processing step for generating a fixed point in the inclusion and performing a line change process with the fixed point as an end point when the line set in the line setting step passes through the inclusion. When,
A determination step of determining whether or not the line has passed the inclusion set by the inclusion setting step based on the position before and after the movement of the line that has not been changed by the first line changing step. When,
If it is determined by the determination step that the line has passed the inclusion set by the inclusion setting step, a fixed point is generated in the inclusion, and a line changing process using the fixed point as an end point A second line change step for performing
The first grain boundary energy at the grain boundary to which the fixed point belongs and the fixed point are released from the fixed position and moved to the equilibrium position where the grain boundary energy is at a position in the region excluding the inside of the inclusion. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when
A crystal grain analysis method comprising: 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. An image signal acquisition step of acquiring an image signal of a crystal in the metal material and inclusions included in the metal material;
Corresponding to both end points of the grain boundaries of the crystal grains included in the crystal, and corresponding to the midpoint of the grain boundaries of the crystal grains included in the crystal, and triple points in contact with the three crystal grains including the crystal grains And when a double point in contact with two crystal grains including the crystal grain is designated based on the image signal, a grain boundary point setting step for setting the designated triple point and double grain boundary point; ,
A line setting step for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary at the grain boundary point set by the grain boundary point setting step;
When the inclusion is designated based on the image signal, an inclusion setting step for setting the designated inclusion;
A first line change processing step for generating a fixed point in the inclusion and performing a line change process with the fixed point as an end point when the line set in the line setting step passes through the inclusion. When,
A determination step of determining whether or not the line has passed the inclusion set by the inclusion setting step based on the position before and after the movement of the line that has not been changed by the first line changing step. When,
If it is determined by the determination step that the line has passed the inclusion set by the inclusion setting step, a fixed point is generated in the inclusion, and a line changing process using the fixed point as an end point A second line change step for performing
The first grain boundary energy at the grain boundary to which the fixed point belongs and the fixed point are released from the fixed position and moved to the equilibrium position where the grain boundary energy is at a position in the region excluding the inside of the inclusion. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when
When the second grain boundary energy is less than the first grain boundary energy, a computer program causing a computer to execute a fixed point processing step of performing a process of releasing the fixed point.

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