Method for extracting phases of material structure, device for extracting phases of material structure, and microscope device

Abstract

To provide a method for extracting phase of material organization having robustness against noise and taking advance information of phases into consideration, a device for extracting phase of material organization, and a microscope device.SOLUTION: A method for extracting phase of material organization includes: a first input step (S1) to obtain mapping information from a material organization; a second input step (S2) to obtain phase information of the material organization; an evaluation function definition step (S3) to define an evaluation function based on the mapping information and the phase information; and a phase extraction step (S5) to extract a phase of the material organization based on the evaluation function.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to a method for extracting a phase of a material structure, an apparatus for extracting a phase of a material structure, and a microscope apparatus. [Background technology]

[0002] The internal structure of a material has a significant effect on its properties. For example, the steel material Transformation Induced Plasticity (TRIP) steel has a composite structure consisting of martensite or bainite and retained austenite (residual γ), and exhibits an excellent balance between strength and ductility due to the processing-induced martensitic transformation of the residual γ. It is known that ductility strongly depends on the fraction of the residual γ, and it has been pointed out that the distribution and morphology of austenite during the tempering process contribute to the formation of the residual γ. In order to understand the properties of materials, it is extremely important to analyze the fraction, distribution and morphology of the phases in the material structure with high precision.

[0003] With the recent development of various image analysis technologies and machine learning, methods have been disclosed for automatically or semi-automatically clustering and extracting phases of material structures from mapping information such as structural images of metal materials and concentration distribution of metal material components. For example, there are methods for extracting phases of material structures using perceptrons, deep learning, random forests, and support vector machines. By utilizing these methods, extraction of phases of material structures, which previously required time-consuming work by skilled engineers, is becoming possible with less labor and at higher speeds.

[0004] On the other hand, the Phase Field (PF) method, which is based on the variational principle of thermodynamics and free energy, is a method for accurately simulating the formation process of a structure in a metal material. The PF method makes it possible to simulate the formation process of various structures by appropriately selecting the free energy. In addition, the PF method has a mathematical structure similar to the Mumford-Shah segmentation model (Non-Patent Document 1), which is one of the segmentation methods robust to noise, and is therefore considered to be applicable to the extraction of phases in a material structure. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] J. Lie et al., “A binary level set model and some applications to Mumford-Shah image segmentation” IEEE Transactions on Image Processing 15 (2006), p.1171-1181 Summary of the Invention [Problem to be solved by the invention]

[0006] However, although a machine learning model created based on a teacher image of a material structure can extract the phases of the material structure with high accuracy, it is often unable to extract the appropriate phases of the material structure for images with different measurement conditions from the teacher image. This is because the phases of the material structure shown in the teacher image and the phases of the material structure with different measurement conditions are identified as different phases. A skilled engineer can identify and extract the phases of the material structure even when the measurement conditions change in this way. This is because a skilled engineer comprehensively identifies the phases of the material structure based on knowledge of the analytical device and materials, images of the material structure obtained by other analytical devices, etc. If the phases of the material structure can be identified and extracted based on such multifaceted information, it is thought that the accuracy of the extraction of the phases of the material structure by a computer will be improved.

[0007] In view of the above circumstances, an object of the present disclosure is to provide a method for extracting phases of a material structure that is robust to noise and takes into account prior information about the phases, an apparatus for extracting phases of a material structure, and a microscope apparatus. [Means for solving the problem]

[0008] The present inventors have intensively studied ways to solve the above problems, and as a result, have found that the phases of a material structure can be extracted with high accuracy by using, as prior information, the fraction of the phase calculated by thermodynamic calculation or numerical analysis, the concentration of a component contained in the phase, or information obtained by measurement or analysis using an analytical device such as XRD (X-ray Diffraction) or EPMA (Electron Probe Micro Analyzer).

[0009] More specifically, a method for extracting material structure phases according to an embodiment of the present disclosure includes: A first input step of acquiring mapping information from a material structure; A second input step of acquiring information on the phases of the material structure; an evaluation function definition step of defining an evaluation function based on the mapping information and the phase information; a phase extraction step of extracting a phase of the material structure based on the evaluation function; Equipped with.

[0010] According to one embodiment of the present disclosure, an apparatus for extracting material phases comprises: an input unit for acquiring mapping information from a material structure and acquiring information on the phases of the material structure; an evaluation function definition unit that defines an evaluation function based on the mapping information and the phase information; a phase extraction unit that extracts a phase of the material structure based on the evaluation function; Equipped with.

[0011] A microscope apparatus according to an embodiment of the present disclosure includes: The mapping information is obtained by the material structure phase extraction device described above. Effect of the Invention

[0012] According to the present disclosure, it is possible to provide a method for extracting phases of a material structure that is robust to noise and takes into account prior information about the phases, an apparatus for extracting phases of a material structure, and a microscope apparatus. [Brief description of the drawings]

[0013] [Figure 1] FIG. 1 is a flow chart illustrating the process of a material structure phase extraction method according to one embodiment of the present disclosure. [Figure 2A] FIG. 2A is a flowchart showing detailed calculation procedures for some steps of the method for extracting phases of the material structure in FIG. [Figure 2B] FIG. 2B is a flowchart showing detailed calculation procedures for some steps of the method for extracting phases of the material structure of FIG. [Diagram 3] FIG. 3 is a diagram comparing the results of phase extraction of material structure according to one embodiment of the present disclosure and other methods. [Figure 4] FIG. 4 is a diagram comparing the results of phase extraction of material structure according to one embodiment of the present disclosure and other methods. [Diagram 5] FIG. 5 is a schematic diagram showing a configuration example of a material structure phase extraction system including a material structure phase extraction device according to an embodiment of the present disclosure. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0014] Hereinafter, a method for extracting a phase of a material structure, an apparatus for extracting a phase of a material structure, and a microscope apparatus according to embodiments of the present disclosure will be described with reference to the drawings. The embodiments described below are exemplary embodiments of the present disclosure, and do not limit the contents of the present disclosure.

[0015] [Method of extracting phases of material structure] FIG. 1 is a flow chart showing a method for extracting phases of a material structure according to the present embodiment. The method for extracting phases of a material structure includes a step of acquiring mapping information from the material structure (first input step, step S1), a step of acquiring information on the phases of the material structure (second input step, step S2), a step of defining an evaluation function based on the mapping information and the phase information (evaluation function definition step, step S3), and a step of extracting phases of the material structure based on the evaluation function (phase extraction step, step S5). Here, as in the present embodiment, a step of determining initial conditions by preliminary calculation (initial condition determination step, step S4) may be inserted before the step of extracting phases. Also, as in the present embodiment, a step of outputting information on the extracted phases (output step, step S6) may be included.

[0016] 2A and 2B are flowcharts showing detailed calculation procedures for the initial condition determination step and the phase extraction step. Each step will be explained below, and FIGS. 2A and 2B will be referred to in the explanation of the initial condition determination step and the phase extraction step.

[0017] (Process for obtaining mapping information from material structure) The mapping information is distribution information that is correlated with the component distribution of the material structure. The distribution information may be, for example, a concentration distribution of the component. ob =(X1 ob ,…,X N ob ) consists of N measurement points, which is one or more. Also, the measurement value X at a certain measurement point n is n ob =(X n,1 ob ,…,X n,M ob ) is composed of a vector with 1 or more M components. In what follows, the parameter n indicating the measurement point can take values ​​from 1 to N. Similarly, with K being 1 or more, the parameter k indicating the phase can take values ​​from 1 to K. For example, Σ k means the sum when the parameter k is changed from 1 to K.

[0018] Mapping Information X obThe mapping information X is physical information such as the concentration distribution of components contained in the tissue obtained by measurement or analysis using various analytical devices such as EPMA and SEM (Scanning Electron Microscope), tissue images, etc. ob may be information obtained by further processing physical information, tissue images, and the like through machine learning or numerical analysis.

[0019] (Process for obtaining information on the phase of material structure) The information on the phases of the material structure is information obtained by thermodynamic calculation, numerical analysis, or an analytical device. The information on the phases of the material structure may be, for example, a fraction or a component concentration. The information on the phases of the material structure may be information obtained by an arbitrary number N A Average information of each phase A ob =(A i ob ,…,A NA ob The information on the phase of the material structure can be physical information X, which is predicted from a thermodynamic database, numerical analysis, or experiments such as XRD or neutron diffraction, and is represented by the following formula (1): ref can be a probability density function of

[0020]

number

[0021] Here, the parameter θ in equation (1) ref The composition of depends on the type of probability density function. ob or the parameter θ of the probability density function ref The phase information represented by the mapping information X ob It is preferable to use physical quantities related to phases as information on phases, such as the fraction of a phase in a material structure obtained by measurement or analysis using XRD, the concentration of a component contained in a phase obtained by measurement or analysis using EPMA or SEM-EDS, the fraction of a phase calculated by thermodynamic calculation using a thermodynamic database, or the concentration of a component contained in a phase, calculated by numerical analysis, etc.

[0022] The disclosed method further comprises the step of extracting the appropriate material structure phase information from the mapping information X obtained from the material structure. ob By integrating this, it becomes possible to extract phases of the material structure with greater accuracy.

[0023] (Process of defining the evaluation function) The evaluation function F is the mapping information X ob The term L separates the phases of the material structure based on the statistical distribution of the phases, and the term F suppresses noise and smooths the interface. int It includes two terms, and is expressed by the following equation (2).

[0024]

number

[0025] The term L for separating the phases of the material structure can be given using log-likelihood, logarithm of posterior probability, mutual information, Kullback-Leibler divergence, etc., but it is preferable to use the logarithm of the posterior probability. Below, we will explain an example in which the term L for separating the phases of the material structure is the logarithm of the posterior probability.

[0026] Mapping Information X ob is considered to contain measurement error and noise, and the true distribution that cannot be observed in reality is X * =(X1 * ,…,X N * )

[0027] where X n * represents the true value at measurement point n. Also, the true distribution X * is the probability density function p[X * |θ * ]. Here, assuming that there are K types of phases in the structure, θ * =(θ1 * ,…,θ K * ) is a set of parameters of the true probability density function, and the information on the phase k represented by the parameters of the probability density function is k *The probability that the kth phase exists at the measurement point n is expressed as h n,k Then, the set is H=(h n,1 ,…,h n,K )

[0028] Here, the true distribution X * The probability density function is the probability of the existence of a phase h n,k and the probability density function p[X n * |θ k * ] and is approximately given by the following equation (3).

[0029]

number

[0030] Mapping information actually measured X ob is the true distribution X * Therefore, the actually measured mapping information X ob The probability of measuring is described by equation (4) below.

[0031]

number

[0032] Here, θ noise is the actual measured mapping information X ob and the true distribution X * is a parameter of the probability density distribution function that indicates the error of the measurement and depends on the precision and accuracy of the measurement device.

[0033] By Bayes' theorem, the parameter θ noise , θ * , the posterior probability of H is approximately expressed by the following equation (5).

[0034]

number

[0035] Here, the parameter θ noise , θ * and p[θ noise ], p[θ * ] and p[H] are the characteristics of the measurement error and the true distribution X * describes the shape of the probability density function of , the distribution of phases. By taking the logarithm of equation (5), the term L that separates the phases can be easily determined by the following equation (6).

[0036]

number

[0037] Next, we add a term F int This corresponds to the interfacial energy term in the PF method. There are models using double-well potential or double obstacle potential for the definition of the interfacial energy term in the PF method, but here we will explain using Steinbach's Multi-Phase Field (MPF) method as an example. In Steinbach's MPF method, the term F int is defined by the following equation (7).

[0038]

number

[0039]

number

[0040] Next, a method of introducing information on the phase of the material structure into the evaluation function, which is one of the features of this disclosure, will be explained. Specifically, for the prior probability of the third and fourth terms on the right side of equation (6), the parameter θ ref , or the average information of the phase A ob By incorporating the above, information on the phase of the material structure can be introduced into the evaluation function. Here, the second term on the right side of formula (6) may be input when it can be estimated from, for example, past performance data.

[0041] The probability density function p[X n ref |θ k ref ] can be estimated. Here, the parameter θ k ref and the true parameter θ k * It is possible to estimate the error and variance of p[θ * ] can be defined by the following equation (9).

[0042]

number

[0043] Σ ref is θ k ref and θ k * The error between k ref It is determined by the accuracy of the prediction model. ref One example of a method for deriving is the use of a thermodynamic database. A thermodynamic database is a database that accumulates data such as free energy or activity when temperature or composition is given. If the target system is near thermal equilibrium, then according to statistical thermodynamics, it will be in state X * The probability of occurrence of p[X *] is the free energy f[X * ] is expressed by the following equation (10).

[0044]

number

[0045] where k B is the Boltzmann coefficient. T is the temperature at which the tissue forms. When a quadratic approximation is applied to the free energy f, p[X * |θ * ] is X * The equilibrium state is taken as the expected value, and the Gaussian distribution has the variance-covariance matrix given by the following equation (11).

[0046]

number

[0047] In this case, Σ is determined based on the non-equilibrium nature of the system or the accuracy of the thermodynamic database. ref In the case of a stronger non-equilibrium state, the true distribution X can be determined by using the Scheil model, numerical analysis of reaction-diffusion systems, or the Phase Field method. * It is possible to predict the probability density of

[0048] On the other hand, the average information A ob If is known, the average information A is calculated by p[H] in equation (6). ob where the effect of the appropriate function A k ref [X ob ,H] to obtain the average information A ob X ob It can be inferred from H that the function A k pre By defining the average information A pre is predicted as follows:

[0049]

number

[0050] Therefore, A k pre [X ob ,H] prediction accuracy and measurement error parameter Σ A pre Using this, p[H] can be expressed by the following equation (13).

[0051]

number

[0052] Add p[θ * ] and p[H], the true distribution X * By deriving a function L that takes into account prior knowledge such as the probability density of the phase and the average phase information, the evaluation function F can be defined.

[0053] (A process for determining initial conditions through preliminary calculations) From the viewpoint of efficiency, a preliminary calculation is performed with the parameter θ noise and θ * Here, if an initial value is available, the initial value may be acquired (step S11 in FIG. 2A). In the preliminary calculation, the spatial distribution of the parameter H is not taken into account, and the phase ratio π=(π1, ..., π K ) to h n,k = π k In the preliminary calculation, the evaluation function F' in this step is determined based on the above evaluation function F (step S12 in FIG. 2A). For example, the evaluation function F' is calculated by using the first term of the formula (2) as follows: noise , θ * and is determined as a function of π by the following equation (14).

[0054]

number

[0055] With the evaluation function F' as a constraint, Σ k π kBy minimizing θ noise , θ * and π are determined (step S13 in FIG. 2A). The minimization calculation method may be appropriately selected from, for example, the Newton method, the conjugate gradient method, etc. Then, when it is determined that the value of the evaluation function F' has converged, an initial value is determined (step S14 in FIG. 2A). However, it does not have to be the minimum value, and may be a quasi-optimal solution.

[0056] (Process for extracting phases of material structure) Next, the actual calculation is performed taking into account the spatial distribution of tissue. In this calculation, an interpolation function q[Φ n,k ], h n,k is expressed as the following equation (15).

[0057]

number

[0058] Order variable Φ=(Φ1,…,Φ n ,…,Φ N ), Φ n =(Φ n,1 ,…,Φ n,k ,…,Φ n,K ) is a parameter for extracting the type of phase, and Σ k Φ n,k = 1. Also, Φ n,k satisfies the following equation (16).

[0059]

number

[0060] The initial value of the order parameter Φ is determined by the preliminary calculation. noise , θ * It is efficient to define F by the following formula (17) in terms of F and π (step S21 in FIG. 2B). Also, the evaluation function F in this process is determined as a function of the order parameter Φ by the following formula (18) (step S22 in FIG. 2B).

[0061]

number

[0062] Here, Σ k Φ n,k To impose the constraint of =1, we use the Lagrangian L g is defined as the following equation (19).

[0063]

number

[0064] A solution that satisfies the conditions of the following formula (20) is numerically analyzed to obtain the minimum value of the evaluation function F under the constraint conditions (step S23 in FIG. 2B). When it is determined that the value of the evaluation function F has converged, the order parameter Φ is determined (step S24 in FIG. 2B). However, it does not have to be the minimum value, and a quasi-optimal solution may be acceptable.

[0065]

number

[0066] By extracting the maximum order parameter from the finally obtained order parameters of each coordinate, the phase type k at the measurement point n is determined by the following equation (21). n (Step S25 in FIG. 2B), where argmax is the order parameter Φ n,k This means a function that outputs the k that maximizes

[0067]

number

[0068] (A process for outputting extracted phase information) Phase type k at estimated measurement point n n The information is output so that the user can confirm it. The extracted phase information may be displayed on a display device such as various displays.

[0069] [Material structure phase extraction device] 5 is a schematic diagram showing a configuration example of a material structure phase extraction system 1 (hereinafter, may be simply referred to as "extraction system 1") including a material structure phase extraction device 10 according to an embodiment of the present disclosure. The material structure phase extraction method described above is performed by the material structure phase extraction device 10 (hereinafter, may be simply referred to as "extraction device 10").

[0070] The extraction system 1 includes an extraction device 10 and a microscope device 30. The extraction device 10 includes an input unit 11, an output unit 12, and a calculation unit 13. The calculation unit 13 includes an evaluation function definition unit 14, an initial condition determination unit 15, and a phase extraction unit 16.

[0071] (Microscope Equipment) The microscope device 30 obtains the mapping information acquired by the extraction device 10. As described above, the mapping information is physical information such as the concentration distribution of components contained in the material structure, a structure image, and the like. The microscope device 30 is, for example, an EPMA or SEM, but is not limited to these as long as it is a device that measures or analyzes the mapping information. The microscope device 30 may be, for example, a device that performs elemental analysis of the material structure using X-rays, etc.

[0072] (Input section) The input unit 11 is an input interface of the extraction device 10, and executes a first input step and a second input step. That is, the input unit 11 acquires mapping information from the material structure, and acquires information on the phases of the material structure.

[0073] (Output section) The output unit 12 is an output interface of the extraction device 10, and executes an output step. That is, the output unit 12 displays the phase information extracted by the calculation unit 13 on a display device such as various displays.

[0074] (calculation section) The calculation unit 13 performs calculations to extract the phases of the material structure. The calculation unit 13 may also have a function as a control unit that controls the entire extraction device 10. The calculation unit 13 may be one or more processors. The processor may be, for example, a general-purpose processor or a dedicated processor specialized for a specific process, but is not limited to these and may be any processor.

[0075] As described above, in this embodiment, the calculation unit 13 includes the evaluation function definition unit 14, the initial condition determination unit 15, and the phase extraction unit 16. The functions of the evaluation function definition unit 14, the initial condition determination unit 15, and the phase extraction unit 16 may be realized by software. For example, one or more programs may be stored in a storage device accessible to the calculation unit 13. When the program stored in the storage device is read by the calculation unit 13, which is a processor, it may cause the calculation unit 13 to function as the evaluation function definition unit 14, the initial condition determination unit 15, and the phase extraction unit 16.

[0076] (Evaluation function definition part) The evaluation function definition unit 14 executes an evaluation function definition step, that is, the evaluation function definition unit 14 defines an evaluation function based on mapping information and phase information.

[0077] (Initial condition determination part) The initial condition determination unit 15 executes an initial condition determination step. That is, the initial condition determination unit 15 determines an initial condition by a preliminary calculation before the phase extraction step.

[0078] (Phase extraction part) The phase extraction unit 16 executes a phase extraction step, that is, the phase extraction unit 16 extracts phases of the material structure based on the evaluation function.

[0079] Here, the extraction device 10 is not limited to a specific device, but may be realized by a computer as an example. The computer may be, for example, a commercially available general-purpose computer. The computer includes, for example, a storage device such as a memory and a hard disk drive, a CPU, and an input / output device. The calculation unit 13 may be realized by the CPU. The program read by the calculation unit 13 may be stored in the storage device. Furthermore, the input unit 11 and the output unit 12 may be realized by an input / output device.

[0080] [Example] In this embodiment, the probability density function p[X ob |θ noise ,θ * ,H], and the probability density function p[θ noise ], p[θ * ], p[H] were determined. Parameter θ noise =(θ1 noise ,θ2 noise ,…) and θ * =(θ1 * ,θ2 * ,…) was given by a combination of the mean and variance.

[0081] Example 1 In Example 1, calculations were performed to extract the phases of the material structure from the mapping information using average information based on the calculation results obtained from the thermodynamic database. The mapping information of the carbon concentration in the steel in the α-γ two-phase region ((a-0) in FIG. 3) was used. The parameter θ * Equation (10) was used to estimate the free energy function, and a quadratic approximation was used. The estimated parameters θ * and the parameter θ calculated from thermodynamic data pre is assumed to follow a Gaussian distribution.

[0082] (a-0) in FIG. 3 is a reference element map, and data (processed data) was prepared by adding noise as (a-1), scratches as (a-2), and a numerical shift as (a-3) to the reference element map. In order to show that the method of the present disclosure is robust against changes in measurement conditions, a comparative calculation was performed with a random forest. Random forest was trained using unprocessed actual data, not processed data. (c-0) to (c-3) are the results of the random forest, and it can be seen that they are strongly influenced by noise, scratches, and numerical shifts. In contrast, the results of Example 1, (b-0) to (b-3), were roughly equal under all conditions. In other words, it was shown that Example 1 can perform robust tissue extraction against noise and changes in measurement conditions. This is because the parameter θ noise and F int In Fig. 3, (b-0) to (b-3) and (c-0) to (c-3), the white color indicates the austenite phase, and the black color indicates the ferrite phase.

[0083] Example 2 In Example 2, the mapping information of the C concentration obtained by FE-EPMA (field emission electron probe microanalyzer) was combined with the average information of the structure obtained by XRD measurement to perform phase extraction calculation of the material structure. FIG. 4(a) shows the distribution of carbon element in a high tensile steel sheet. FIG. 4(b-1) is a comparative example, in which p[θ noise ], p[θ * ] and p[Φ] are fixed values. The black areas are areas where C is concentrated and are thought to correspond to the residual γ phase. However, while the amount of residual γ measured by XRD was 6.03%, the fraction of the C-enriched areas detected in Figure 4 (b-1) was approximately 25.4%. In other words, there is a large difference in the information regarding the C-enriched areas (amount of residual γ), and the information is not consistent.

[0084] Therefore, according to the method for extracting the phases of the material structure in the above embodiment, the amount of residual γ measured by XRD was 6.03% and the C concentration in the residual γ was 0.63 wt%. k pre [X n ob ]=1 gives the information on the amount of residual γ measured by XRD, and θ ref The information on the average concentration of residual γ measured by XRD was added to this. Figure 4 (b-2) shows the result of structure extraction using the prior information from XRD. In Figure 4 (b-2) as well, the black color indicates the C-enriched regions (corresponding to the residual γ phase). The proportion of the C-enriched regions extracted in Figure 4 (b-2) is 6.1%, which is almost the same as the amount of residual γ measured by XRD, and appropriate phase extraction has been performed for the purpose of predicting the distribution of residual γ.

[0085] As described above, the material structure phase extraction method, material structure phase extraction device, and microscope device of this embodiment integrate mapping information obtained from the material structure with prior information on the phases of the material structure, thereby providing consistency between the mapping information and the information on the phases of the material structure and robustness to noise.

[0086] Although the embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art can easily make various modifications or corrections based on the present disclosure. Therefore, it should be noted that these modifications or corrections are included in the scope of the present disclosure. For example, the functions included in each component or each step can be rearranged so as not to be logically inconsistent, and multiple components or steps can be combined into one or divided. The embodiments of the present disclosure can also be realized as a storage medium on which a program executed by a processor included in the device is recorded. It should be understood that these are also included in the scope of the present disclosure. [Explanation of symbols]

[0087] 1. Material structure phase extraction system 10. Material structure phase extraction device 11 Input section 12 Output section 13 Arithmetic section 14 Evaluation function definition section 15 Initial condition determination section 16 Phase extraction section 30 Microscope Equipment

Claims

1. A first input step of acquiring mapping information from a material structure; A second input step of acquiring information on the phases of the material structure; an evaluation function definition step of defining an evaluation function based on the mapping information and the phase information; a phase extraction step of extracting a phase of the material structure based on the evaluation function; Equipped with The method for extracting phases of a material structure, wherein the evaluation function includes a term for separating phases of the material structure based on a statistical distribution of the mapping information, and a term for suppressing noise and smoothing an interface.

2. The method for extracting phases in a material structure according to claim 1 , wherein the mapping information is distribution information correlated with a component distribution in the material structure.

3. The method for extracting phases in a material structure according to claim 2 , wherein the distribution information is a concentration distribution of components.

4. The method for extracting phases of a material structure according to claim 1 , wherein the information on the phases of the material structure is information obtained by thermodynamic calculation, numerical analysis, or an analytical device.

5. The method for extracting phases in a material structure according to claim 4 , wherein the information on the phases in the material structure is a fraction or a component concentration.

6. 2. The method for extracting phases in a material structure according to claim 1, wherein the term separating the phases in the material structure is the logarithm of the posterior probability.

7. an input unit for acquiring mapping information from a material structure and acquiring information on the phases of the material structure; an evaluation function definition unit that defines an evaluation function based on the mapping information and the phase information; a phase extraction unit that extracts a phase of the material structure based on the evaluation function; Equipped with The evaluation function includes a term for separating phases of the material structure based on a statistical distribution of the mapping information, and a term for suppressing noise and smoothing an interface.

8. A microscope apparatus for obtaining the mapping information obtained by the material structure phase extraction apparatus of claim 7.

9. The microscope apparatus according to claim 8 , wherein elemental analysis of the material structure is performed.

Images