JP7597995B2 - Method and system for analyzing magnetic domain structure of grain-oriented electrical steel sheet - Google Patents

Description

The present invention relates to grain-oriented electrical steel sheets, and a method and system for analyzing the magnetic domain structure of grain-oriented electrical steel sheets.

Grain-oriented electrical steel sheet is a steel sheet that contains 7 mass% or less of Si and has a secondary recrystallized texture in which secondary recrystallized grains are concentrated in the {110}<001> orientation (Goss orientation). The magnetic properties of grain-oriented electrical steel sheet are greatly affected by the degree of concentration in the {110}<001> orientation. In recent years, in grain-oriented electrical steel sheets that have been put into practical use, the angle between the crystal's <001> direction and the rolling direction is controlled to be within a range of about 5°.

Grain-oriented electrical steel sheets are laminated and used in transformer cores, etc., and in addition to the main magnetic properties of high magnetic flux density and low core loss, they are also required to have low magnetostriction, which causes vibration and noise. It is known that crystal orientation has a strong correlation with these properties, and precise orientation control techniques have been disclosed, for example, in Patent Documents 1 to 3.

Furthermore, grain-oriented electrical steel sheets are used in various devices, and various methods have been proposed for evaluating the magnetic domain structure of grain-oriented electrical steel sheets in order to improve the performance of the devices. For example, Patent Documents 4 and 5 disclose techniques that improve iron loss by specifying the area ratio of magnetic domains that meet certain conditions.

JP 2001-192785 A JP 2005-240079 A JP 2012-052229 A JP 2000-345306 A JP 2004-225154 A

In response to the demand for smaller transformers, there is a demand to make the iron core itself smaller. To achieve the same magnetic behavior, a smaller iron core requires that it be operated in a stronger magnetic field. For this reason, there is a demand for improved magnetic properties in high magnetic field regions for the grain-oriented electrical steel sheets used as transformer core materials.

It is generally known that reducing the thickness of grain-oriented electrical steel sheets reduces iron loss, and the application of thin grain-oriented electrical steel sheets is expanding.

The inventors of the present application conducted a detailed study of the characteristics of transformer cores manufactured from thin steel sheets in the high magnetic field region. As a result, they recognized that even when using steel sheets with favorable crystal orientation controlled according to conventional technology, there is still room for improvement, particularly in noise reduction.

When it comes to the impact of materials on the noise of transformer cores, magnetostriction of grain-oriented electromagnetic steel sheets is often considered. The present inventors conducted research from this perspective, and found that noise in high magnetic field regions from iron cores made from thin steel sheets differs from noise made when the material sheet is relatively thick and used in low magnetic field regions, and has a relatively low correlation with the magnetostriction of the material.

After further investigation into the cause, it was discovered that the problematic noise was caused by vibrations outside the plane of the steel plate, rather than vibrations within the plane of the steel plate, which is the direction of magnetostriction of the material, i.e., the magnetization direction.

After observing this phenomenon in detail, the following was found: In a transformer core, the steel sheets are arranged to form a closed magnetic circuit. That is, in a so-called stacked core, the steel sheet blocks are assembled into a square shape, and in a so-called wound core, the steel sheets are bent into an approximately square shape. This core is then fixed to a copper wire coil and a case. As a result, the raw steel sheets are constrained in the in-plane direction, especially at the ends in the magnetization direction.

Considering the cause of the steel plate vibrating out of its plane in this situation, it is expected that a dimensional change occurs that causes the steel plate to stretch, causing the steel plate to bend out of its plane. It is generally known that magnetostriction in steel plates causes the steel plate to distort so that its dimensions shrink in areas with low magnetic fields, but that in high magnetic fields, this shifts from shrinkage distortion to expansion distortion. Furthermore, because noise becomes an issue when the material plate is thin, the inventors of this application have concluded that the bending out of the steel plate's plane due to this expansion magnetostriction is the cause of the noise that needs to be eliminated.

Following this conclusion, we investigated ways to reduce magnetostriction in the same way as with conventional technology, but we were unable to achieve a significant reduction in elongation magnetostriction, even in steel sheets where the overall magnetostriction was controlled to be small. As a result, we were unable to achieve the same level of improvement in noise caused by out-of-plane vibration of the steel sheets as when the material sheet thickness was relatively thick and used in a low magnetic field. We also investigated the simple correlation between the magnitude of elongation magnetostriction and noise, but the simple magnitude of elongation magnetostriction alone was insufficient as a guideline for reducing noise when used in a high magnetic field.

It is known that the magnitude and shape of elongation magnetostriction are related to the amount of closure domains and magnetization rotation that occur in steel sheets in a demagnetized state. Therefore, if it were possible to control the state of the closure domains and the amount of magnetization rotation, it would be possible to effectively suppress noise when used in high magnetic fields. However, there were the following obstacles:

While there have traditionally been several technologies for controlling the characteristics of grain-oriented electrical steel sheets by focusing on the magnetic domain structure, it cannot be said that sophisticated control technologies for magnetic domain structure have been sufficiently developed. In other words, most conventional technologies specify average information about the magnetic domain structure, such as the average spacing, area ratio, and angle of the 180° magnetic domains, which are the main magnetic domains of grain-oriented electrical steel sheets, and there are few that characterize the spatial distribution and non-uniformity of the magnetic domain structure of grain-oriented electrical steel sheets. In particular, it can be said that there are no quantitative evaluation methods that include highly non-uniform magnetic domain structures such as closure domains.

For example, Patent Documents 4 and 5 specify the area ratio of magnetic domains that satisfy certain conditions, but do not specify the distribution state of such magnetic domains (whether it is one integrated magnetic domain or multiple magnetic domains), and there is no method to quantitatively determine this.

Given this situation, the inventors of the present application considered quantifying the magnetic domain structure from the following perspectives:

The crystal structure of grain-oriented electrical steel sheets is composed of relatively large crystal grains with a highly uniform crystal orientation. Each crystal grain can be considered as a single crystal, and the majority of the magnetic domain structure is occupied by 180° magnetic domains, which are simple magnetic domain structures. In this case, closure domains, which are relatively complex magnetic domain structures, tend to occur near the grain boundaries, and the amount of magnetization rotation corresponds to the angle between the 180° magnetic domain and the RD (rolling direction) axis. In other words, a simple method of suppressing closure domains is to increase the crystal grain size and reduce the proportion of grain boundary regions, and to suppress the amount of magnetization rotation, the 180° magnetic domain and the RD axis should be made parallel. However, simply increasing the crystal grain size will increase the generation of closure domains in the areas near the grain boundaries due to continuous orientation changes caused by coil sets, etc., which will increase the crystal orientation changes at the grain boundaries, and will actually increase noise in high magnetic fields.

Upon observing the magnetic domains in more detail, it was discovered that there are grain boundaries where closure domains are likely to form and grain boundaries where closure domains rarely form. This indicates that, depending on a wide range of factors including the morphology and orientation of the grain boundaries, precipitates, surface properties, and distortion, even if there are grain boundaries, that is, even if there are discontinuous changes in the crystal orientation, magnetic domains may be able to exist continuously while maintaining their morphology.

As a result of examining various steel sheet manufacturing conditions from this perspective, it was found that, under certain manufacturing conditions, it is possible to control the crystal structure so that the crystal grain boundaries, where the generation of closure domains is suppressed, predominate. Furthermore, a means of quantifying the magnetic domain structure was examined, and an analysis method and analysis system were established that show a very high correlation with noise in the high magnetic field region of an iron core manufactured from a thin steel sheet to be controlled in this invention, and that can identify a range that is favorable for reducing said noise.

The present invention has been made in consideration of the above problems, and aims to provide a grain-oriented electromagnetic steel sheet that enables the manufacture of iron cores with improved noise in high magnetic field regions (magnetic fields of about 1.9 T), and an analysis method and analysis system for the magnetic domain structure of grain-oriented electromagnetic steel sheet.

The grain-oriented electrical steel sheet according to an embodiment of the present invention has the following composition, by mass%, Si: 2.0-7.0%, Nb: 0-0.030%, V: 0-0.030%, Mo: 0-0.030%, Ta: 0-0.030%, W: 0-0.030%, C: 0-0.0050%, Mn: 0-1.0%, S: 0-0.0150%, Se: 0-0.0150%, Al: 0-0.0650%, N: 0-0.0050%, Cu: 0-0.4 0%, Bi: 0-0.010%, B: 0-0.080%, P: 0-0.50%, Ti: 0-0.0150%, Sn: 0-0.10%, Sb: 0-0.10%, Cr: 0-0.30%, Ni: 0-1.0%, and the balance being Fe and impurities. The alloy has a texture oriented in the Goss orientation, and the average diameter of identical magnetic domain angle domains derived by a specified method is 5.0 mm or more. A specified method for deriving identical magnetic domain angle regions is to: a) extract multiple partial regions corresponding to multiple positions in a magnetic domain image of a grain-oriented electromagnetic steel sheet that is binarized with two types of colors or expressed in three or more gradations; b) obtain multiple partial Fourier images by performing a two-dimensional Fourier transform on each of the multiple partial regions; c) derive the spatial distribution of the 180° magnetic domain angle of the grain-oriented electromagnetic steel sheet based on the peak positions of the spots of each of the multiple partial Fourier images; and d) derive, based on the spatial distribution of the 180° magnetic domain angle, consecutive regions of the magnetic domain image where the 180° magnetic domain angle is within a predetermined range as identical magnetic domain angle regions.

The method for analyzing the magnetic domain structure of a grain-oriented electromagnetic steel sheet according to an embodiment of the present invention comprises the steps of: a) extracting a plurality of partial regions corresponding to a plurality of positions in a magnetic domain image of the grain-oriented electromagnetic steel sheet, the partial regions being binarized with two colors or expressed in three or more gradations; b) obtaining a plurality of partial Fourier images by performing a two-dimensional Fourier transform on each of the plurality of partial regions; c) deriving the spatial distribution of the 180° magnetic domain angle of the grain-oriented electromagnetic steel sheet based on the peak positions of the spots of each of the plurality of partial Fourier images; and d) deriving, based on the spatial distribution of the 180° magnetic domain angle, consecutive regions of the magnetic domain image in which the 180° magnetic domain angle is within a predetermined range as identical magnetic domain angle regions.

The analysis system for the magnetic domain structure of grain-oriented electromagnetic steel sheet according to an embodiment of the present invention includes a calculation unit that extracts a plurality of partial regions corresponding to a plurality of positions in a magnetic domain image of the grain-oriented electromagnetic steel sheet, which is binarized with two types of colors or expressed in three or more gradations, obtains a plurality of partial Fourier images by performing a two-dimensional Fourier transform on each of the plurality of partial regions, derives the spatial distribution of the 180° magnetic domain angle of the grain-oriented electromagnetic steel sheet based on the peak position of each spot in the plurality of partial Fourier images, and derives, based on the spatial distribution of the 180° magnetic domain angle, consecutive regions of the magnetic domain image in which the 180° magnetic domain angle is within a predetermined range as identical magnetic domain angle regions.

In this specification, the term "180° magnetic domain" refers to a magnetic domain whose magnetization direction is in the <100> crystal direction and which is sandwiched between two 180° magnetic domain walls that are substantially parallel to the rolling direction.
The "angle" of the 180° magnetic domain refers to the orientation of the 180° magnetic domain with respect to the reference magnetization direction. In general, in the case of grain-oriented electrical steel sheets, the reference magnetization direction is parallel to the RD (rolling direction).

According to the present invention, by extracting partial regions at each position from the magnetic domain image of the grain-oriented magnetic steel sheet and performing a two-dimensional Fourier transform, the grain-oriented magnetic steel sheet can be identified by a method that quantitatively derives continuous regions where the magnetic domain angle of 180° is within a specified range and their positions, thereby making it possible to reduce noise in the high magnetic field region of the transformer core and to favorably control the noise characteristics.

1 is a block diagram showing a configuration of an analysis system according to an embodiment of the present invention. FIG. 2 is a block diagram showing a hardware configuration of the image acquisition device shown in FIG. 1 . FIG. 2 is a block diagram showing a hardware configuration of the analysis device shown in FIG. 1 . 10A and 10B are schematic diagrams illustrating a method for extracting a plurality of partial regions from a magnetic domain image. 13 is an example of a plurality of partial Fourier images obtained by performing a two-dimensional Fourier transform on each of a plurality of partial regions cut out from a magnetic domain image. This is an example of an image of almost uniform magnetic domains without grain boundaries, and an example of an image of non-uniform magnetic domains with grain boundaries. 7 is a graph showing the spatial distribution of the angle of the 180° magnetic domain derived using a short-range two-dimensional Fourier transform (ST2DFT) for each of the two magnetic domain images shown in FIG. 6 . 7 is a table comparing the analysis results of the magnetic domain structure by the line segment method and the analysis results of the magnetic domain structure by the ST2DFT for each of the two magnetic domain images shown in FIG. 6 . 1 is a flow chart illustrating a method for manufacturing a grain-oriented electrical steel sheet according to an embodiment of the present invention.

A preferred embodiment of the present invention will be described in detail. However, the present invention is not limited to the configuration disclosed in this embodiment, and various modifications are possible without departing from the spirit of the present invention. The numerical ranges described below include lower and upper limits. Values indicated as "greater than" or "less than" are not included in the numerical range. Furthermore, "%" in relation to chemical composition means "mass %" unless otherwise specified.

(1) Chemical Composition of Grain-Oriented Electrical Steel Sheet First, the chemical composition of the grain-oriented electrical steel sheet according to the present embodiment will be described. The grain-oriented electrical steel sheet according to the present embodiment has a chemical composition that includes basic elements, optionally includes optional elements, and the balance is Fe and impurities.

The grain-oriented electrical steel sheet according to this embodiment contains, as a base element (major alloy element), 2.00% to 7.00% Si (silicon) by mass fraction.

The Si content is preferably 2.0-7.0% to concentrate the crystal orientation in the {110}<001> direction.

In this embodiment, the chemical composition may contain impurities. Note that "impurities" refer to elements that are mixed in from raw materials such as ores and scraps, or from the manufacturing environment, during industrial production of steel. The upper limit of the total impurity content may be, for example, 5%.

In addition to the basic elements and impurities described above, this embodiment may contain selective elements. For example, instead of a portion of the remaining Fe, C, Mn, S, Se, Al, N, Cu, Bi, B, P, Ti, Sn, Sb, Cr, Ni, Nb, V, Mo, Ta, W, etc. may be contained as selective elements.

C (carbon): 0 to 0.0050%
Mn (manganese): 0-1.0%
S (sulfur): 0-0.0150%
Se (selenium): 0 to 0.0150%
Al (acid-soluble aluminum): 0 to 0.0650%
N (nitrogen): 0 to 0.0050%
Cu (copper): 0 to 0.40%
Bi (Bismuth): 0 to 0.010%
B (boron): 0 to 0.080%
P (phosphorus): 0-0.50%
Ti (titanium): 0 to 0.0150%
Sn (tin): 0 to 0.10%
Sb (antimony): 0 to 0.10%
Cr (chromium): 0-0.30%
Ni (nickel): 0-1.0%
Nb (niobium): 0-0.030%
V (vanadium): 0 to 0.030%
Mo (molybdenum): 0 to 0.030%
Ta (tantalum): 0 to 0.030%
W (tungsten): 0-0.030%
These selective elements may be contained according to known purposes. There is no need to set a lower limit for the content of these selective elements, and the lower limit may be 0%. In addition, these selective elements may be impurities. Even if it is contained as such, the above effects are not impaired.

In addition, grain-oriented electrical steel sheet undergoes decarburization annealing and purification annealing during secondary recrystallization in the manufacturing process, which causes a relatively large change in chemical composition (reduction in content). Depending on the element, purification annealing can reduce the content to a level that cannot be detected by general analytical methods (1 ppm or less). The above chemical composition of grain-oriented electrical steel sheet is the chemical composition of the final product. In general, the chemical composition of the final grain-oriented electrical steel sheet differs from the chemical composition of the starting material, the slab (described below), but is basically the remaining elements that were contained in the slab, and is adjusted by the slab composition and manufacturing conditions.

The chemical composition of grain-oriented electrical steel sheets can be measured using a general steel analysis method. For example, the chemical composition of grain-oriented electrical steel sheets can be measured using Inductively Coupled Plasma-Atomic Emission Spectrometry (ICP-AES). Specifically, the chemical composition can be determined by measuring a 35 mm square test piece taken from the grain-oriented electrical steel sheet using a Shimadzu ICPS-8100 or other measuring device under conditions based on a previously prepared calibration curve. C and S can be measured using the combustion-infrared absorption method, and N can be measured using the inert gas fusion-thermal conductivity method.

The above chemical composition is the composition of grain-oriented electrical steel sheet. If the grain-oriented electrical steel sheet to be measured has an intermediate layer made of oxides or an insulating coating on the surface, these are removed using the method described below before measuring the chemical composition.

For example, the insulating coating can be removed by immersing the grain-oriented electrical steel sheet having the coating in a high-temperature alkaline solution. Specifically, the insulating coating can be removed from the grain-oriented electrical steel sheet by immersing the sheet in an aqueous sodium hydroxide solution containing 30 to 50 mass % NaOH and 50 to 70 mass % H ₂ O at 80 to 90° C. for 5 to 10 minutes, followed by rinsing with water and drying. The time for immersion in the aqueous sodium hydroxide solution can be changed depending on the thickness of the insulating coating.

For example, one method for removing the intermediate layer is to immerse the magnetic steel sheet from which the insulating coating has been removed in hot hydrochloric acid. Specifically, the concentration of hydrochloric acid suitable for removing the desired intermediate layer is determined in advance, and the intermediate layer can be removed by immersing the sheet in hydrochloric acid of this concentration, for example 30-40% by mass hydrochloric acid, at 80-90°C for 1-5 minutes, followed by rinsing with water and drying. Typically, different treatment solutions are used to remove each coating, such as an alkaline solution to remove the insulating coating and hydrochloric acid to remove the intermediate layer.

(2) Magnetic Domain Structure of Grain-Oriented Electrical Steel Sheet As described above, the magnetic domain structure defined by grain-oriented electrical steel sheet has not been sufficiently quantified to identify a special steel sheet. Therefore, in the following, we will first explain the method for quantifying the magnetic domain structure used in this embodiment (see (2-1) below), then verify the validity of the quantification parameters obtained by the quantification method (see (2-2) below), and further explain the definition of grain-oriented electrical steel sheet based on the quantification method (see (2-3) below).

(2-1) Method for Quantifying Magnetic Domain Structure of Grain-Oriented Electrical Steel Sheet Hereinafter, a method for quantifying a magnetic domain structure used in an embodiment of the present invention will be described with reference to the drawings.

<System Configuration>
First, a configuration of a system for implementing the method for quantifying (analyzing) a magnetic domain structure according to this embodiment will be described.

Figure 1 shows the configuration of an analysis system 100 according to this embodiment. The analysis system 100 is a system that analyzes the magnetic domain structure of a grain-oriented electrical steel sheet, and as shown in Figure 1, it includes an image acquisition device 20 and an analysis device 30, which are connected via a cable.

As shown in FIG. 2, the image acquisition device 20 has a light source unit 21, a magneto-optical (MO) sensor 23, an image sensor 25, and a signal processing unit 27.

The light source unit 21 has a light source consisting of a light emitting diode (LED) and irradiates the MO sensor 23 with light with a uniform polarization plane.

The MO sensor 23 is a device for measuring the structure of magnetic materials such as grain-oriented electromagnetic steel sheets, and has an observation surface on which the magnetic material sample to be measured is placed. Light irradiated from the light source unit 21 passes through the inside of the MO sensor 23 and is reflected by the reflective layer, and the reflected light passes through the inside of the MO sensor 23 again and is output to the outside of the MO sensor 23. When a grain-oriented electromagnetic steel sheet as a magnetic material sample is placed on the observation surface of the MO sensor 23, a leakage magnetic field corresponding to the direction of spontaneous magnetization of the grain-oriented electromagnetic steel sheet is generated inside the MO sensor 23, and this leakage magnetic field rotates the polarization plane of the reflected light.

The image sensor 25 is a complementary metal-oxide-semiconductor (CMOS) image sensor that forms an image of the reflected light from the MO sensor 23 on its light receiving surface, photoelectrically converts it, and outputs the analog signal after photoelectric conversion to the signal processing unit 27. By detecting the reflected light with a rotated polarization plane using the image sensor 25, the spatial distribution of the leakage magnetic field can be obtained, as described below, and the magnetic domain structure of the grain-oriented electromagnetic steel sheet becomes clear.

The signal processing unit 27 has an amplifier, an AD converter, a digital signal processor (DSP), etc. The analog signal output from the image sensor 25 is amplified by the amplifier and converted into a digital signal by the AD converter. This digital signal is subjected to a predetermined digital processing by the DSP to generate an image signal. The image signal generated by the signal processing unit 27 is output to the analysis device 30 via a connector.

The analysis device 30 is a computer device such as a personal computer (PC), and as shown in FIG. 3, has a calculation unit 31, a memory 33, a display unit 35, an input unit 37, and a communication I/F 39.

The calculation unit 31 has a central processing unit (CPU) and executes a method for analyzing the magnetic domain structure according to a program stored in the memory 33. The method for analyzing the magnetic domain structure executed by the calculation unit 31 will be described in detail later.

The memory 33 includes a Read Only Memory (ROM) and a Random Access Memory (RAM). The ROM stores programs executed by the CPU of the calculation unit 31 and data required when these programs are executed. The programs and data stored in the ROM are loaded into the RAM and executed.

The memory 33 may include a magnetic memory such as a hard disk drive (HDD) or an optical memory such as an optical disk. Alternatively, the program and data may be stored in a computer-readable recording medium that is detachable from the analysis device 30. Alternatively, the program executed by the calculation unit 31 may be received from a network via the communication I/F 39.

The display unit 35 has a display such as a liquid crystal display (LCD), a plasma display, or an organic electroluminescence (EL) display, and displays an image based on the image signal output from the image acquisition device 20, and also displays the analysis results of the magnetic domain structure by the calculation unit 31.

The input unit 37 includes input devices such as a mouse and a keyboard.
The communication I/F 39 is an interface for transmitting and receiving data to and from external devices via a network such as a Local Area Network (LAN), a Wide Area Network (WAN), or the Internet.

In addition, instead of general-purpose hardware such as a CPU, the calculation unit 31 may be dedicated hardware such as an Application Specific Integrated Circuit (ASIC) or a Field Programmable Gate Array (FPGA) specialized for analyzing magnetic domain structures.

Furthermore, the image acquisition device 20 and the analysis device 30 may be connected via wireless communication.
Furthermore, while FIG. 1 shows an example in which the image acquisition device 20 and the analysis device 30 are provided separately, a system in which the image acquisition device 20 and the analysis device 30 are integrated may also be employed.

<Method of analyzing magnetic domain structure>
Next, a method of analyzing the magnetic domain structure executed by the calculation unit 31 will be described.
When dealing with a magnetic material with a periodic magnetic domain structure, such as grain-oriented electrical steel sheet, it is effective to evaluate the magnetic domain structure using the Fourier transform.

First, we will explain the short-term Fourier transform (hereinafter referred to as "STFT"). STFT is a technique for analyzing a data string to be analyzed by moving a window function, and is one of the signal processing methods that has long been used for the time-frequency analysis of audio signals.

In STFT, a window function Wa(k) in the range 0≦k≦N-1 (N is a natural number) is used to divide a discrete signal data sequence x(k) into short intervals and analyze its frequency structure. The Hamming window, Hanning window, Blackman window, etc. can be used as the window function Wa(k).

ここで、ｎ（整数）はデータ列のインデックスを表し、Ｓ（整数）は窓関数のシフト量を表す。 In STFT, as expressed in equation (1), a window function Wa(k) is shifted by nS and multiplied by a discrete signal data sequence x(k), to obtain a data sequence x _n (k-nS) extracted from x(k) for the range nS≦k≦nS+N-1.

Here, n (an integer) represents the index of the data string, and S (an integer) represents the shift amount of the window function.

ここで、ｆは空間周波数である。 By defining the extracted section as _xn (n')= _xn (k-nS) and performing a discrete Fourier transform (DFT) as in equation (2), a frequency spectrum corresponding to data position nS is obtained.

where f is the spatial frequency.

In this embodiment, as described below, the magnetic domain structure of grain-oriented electrical steel sheets is analyzed using a short interval two-dimensional Fourier transform (hereinafter referred to as "ST2DFT"), which is an extension of STFT to the two-dimensional domain.

In the following, the image represented by the image signal acquired by the image acquisition device 20 (hereinafter referred to as the magnetic domain image) is expressed as a data string of two-dimensional coordinates (k-l coordinates) as x(k,l). The magnetic domain image to be analyzed in this embodiment is an image binarized with two types of colors, such as grayscale, or an image expressed in three or more gradations (multiple gradations).

In order to analyze the magnetic domain structure of the grain-oriented electrical steel sheet according to this embodiment, the calculation unit 31 executes the following steps (A-1), (A-2), (A-3) and (A-4).
(A-1) cutting out a plurality of partial regions from a magnetic domain image;
(A-2) performing ST2DFT;
(A-3) A step of deriving the spatial distribution of the angles of the 180° magnetic domains;
(A-4) Step of deriving identical magnetic domain angle regions.
Each step will now be described in detail.

(A-1) Step of extracting a plurality of partial regions from a magnetic domain image In order to extract a plurality of partial regions from a magnetic domain image and analyze the frequency structure of each of them, a rectangular window function Wa(k, _l ) is used in which the range in the k direction is 0≦k≦ _Nk -1 and the range in the l direction is 0≦l≦Nl-1 ( _Nk and _Nl are natural numbers). As the window function Wa(k,l), a Hamming window, a Hanning window, a Blackman window, etc. can be used.

If the observation position in the data sequence x(k,l) of the magnetic domain image is represented by index (n,m) and the shift amounts of the window function Wa(k,l) in the k and l directions are represented by S _k and S _l , respectively (n, m, S _k , and S _l are integers), then a data sequence x _nm (k-nS k ,l-mS l ) of a partial region cut out from the magnetic domain image in the range nS _k ≦k≦nS _k +N _k -1, mS _l ≦l≦mS _l + _{N l} - ₁ can be obtained as shown in equation (3).

Figure 4 shows an example of partial regions cut out from the magnetic domain image G, each corresponding to the observation positions (n,m) = (1,1), (2,2), (3,3), ..., (P,Q) (P and Q are natural numbers).

In this embodiment, N _k and N _l that define the range of the window function Wa(k, l) are parameters that correspond to the number of pixels in the k direction and the number of pixels in the l direction, respectively, in the partial region.

ここで、ｆ_ｋ及びｆ_ｌは空間周波数である。空間周波数ｆ_ｋの分解能をΔｆ_ｋ、空間周波数ｆ_ｌの分解能をΔｆ_ｌと表記すると、それぞれ、式（５）及び式（６）のように定義される。

ここで、Δｋ及びΔｌは、それぞれ、磁区画像におけるｋ方向の空間分解能及びｌ方向における空間分解能である。 (A-2) Step of performing ST2DFT By defining the data sequence of the partial region as x _nm (n', m') = x _nm (k-nS _k , l-mS _l ) and performing a two-dimensional Fourier transform on x _nm (n', m'), a partial Fourier image X(f _k , f _l , n, m) corresponding to the partial region at the observation position (n, m) is obtained as shown in equation (4).

Here, f _k and f ₁ are spatial frequencies. If the resolution of the spatial frequency f _k is expressed as Δf _k and the resolution of the spatial frequency f ₁ is expressed as Δf ₁ , they are defined as in Equation (5) and Equation (6), respectively.

Here, Δk and Δl are the spatial resolutions in the k and l directions, respectively, of the magnetic domain image.

For example, when a two-dimensional Fourier transform is applied to the data sequence x _nm (k-nS _k , lmS _l ) of each partial region shown in FIG. 4, a partial Fourier image X(f _k , f _l , n,m) is obtained for each observation position (n, m), as shown in FIG.

(A-3) Step of deriving spatial distribution of 180° magnetic domain angle Once the partial Fourier image X(f _k , f _l , n,m) is obtained, the coordinates of the peak position of the spot in the partial Fourier image X(f _k , f _l , n,m) (k component f _k ^max (n,m) and l component f _l ^max (n,m)) are determined.

Then, from the spatial frequency resolution defined in equations (5) and (6) and the peak position of the spot of the partial Fourier image, the spatial distribution θ(n,m) of the 180° magnetic domain angle is derived as shown in equation (7).

(A-4) Step of deriving identical magnetic domain angle regions Next, based on the spatial distribution θ(n,m) of the 180° magnetic domain angles obtained in step (A-3), consecutive regions in the magnetic domain image G in which the 180° magnetic domain angles are within a predetermined range are derived as identical magnetic domain angle regions. The range of magnetic domain angles that defines the identical magnetic domain angle regions will be described later.

As described above, according to the method for analyzing magnetic domain structures of this embodiment, the spatial distribution θ(n,m) of the 180° magnetic domain angles is quantitatively derived while maintaining the position information of the magnetic domain image by using a short interval two-dimensional Fourier transform (ST2DFT), and further, based on the spatial distribution θ(n,m) of the 180° magnetic domain angles, consecutive regions in the magnetic domain image G where the 180° magnetic domain angles are within a predetermined range are derived as identical magnetic domain angle regions. This makes it possible to quantitatively determine identical magnetic domain angle regions and their positions (n,m), which can be used as a guideline for controlling the iron loss of grain-oriented electrical steel sheets.
(2-2) Validity of parameters for quantifying magnetic domain structure

Next, using the analysis system 100, two types of magnetic domain structures (i) and (ii) of grain-oriented electrical steel sheet are analyzed as follows, and the effectiveness (validity) of the quantitative derivation method using ST2DFT is verified by comparing it with the conventional line segment method.
(i) A nearly uniform magnetic domain structure without grain boundaries;
(ii) Non-uniform magnetic domain structure with grain boundaries.

The size of the observation surface of the MO sensor 23 is 55.68 mm x 40.37 mm, and the spatial distribution of the leakage magnetic field in this area can be obtained at 3200 pixels x 2320 pixels. In this case, the spatial resolution of the magnetic domain image is Δk = Δl = 17.4 μm.

The magnetic domain image obtained by the image acquisition device 20 is 3200 pixels x 2320 pixels, but in this embodiment, in order to clarify the analysis results in (i) and (ii), the image was trimmed to a range of 512 pixels x 512 pixels.

Figure 6 shows examples of magnetic domain image D00 corresponding to (i) and magnetic domain image D01 corresponding to (ii) obtained from image acquisition device 20. In Figure 6, "RD" represents the rolling direction of the grain-oriented electromagnetic steel sheet. Magnetic domain image D00 has a nearly uniform magnetic domain structure, but magnetic domain image D01 contains a grain boundary in the center of the image, so the magnetic domain structure differs greatly between the upper and lower parts of the image.

In the conventional method, three line segments parallel to the magnetic domains were drawn for the magnetic domain structure obtained from magnetic domain image D00, and the angle of the line segments was calculated using the line segment method to obtain the angle of the 95% confidence interval. The width of the 180° magnetic domain, which represents the distance between adjacent magnetic domain walls (magnetic domain wall spacing), was also derived. For the width of the 180° magnetic domain, three line segments parallel to the magnetic domain were similarly drawn, and the width of the 180° magnetic domain in the 95% confidence interval (average magnetic domain width) was derived using the line segment method. For the magnetic domain structure of magnetic domain image D01, measurements were performed for each magnetic domain region in the same way as for magnetic domain image D00, and the average magnetic domain width and angle were derived for each magnetic domain.

The average domain width and angle of the 180° domains derived from magnetic domain image D00 using the line segment method were 175 μm to 189 μm and 0.13° to 1.5°, respectively. When the line segment method was also used for magnetic domain image D01, the average domain width and angle of the 180° domains in the upper part of the image were 131 μm to 138 μm and 10.6° to 12.5°, respectively, and the average domain width and angle of the 180° domains in the lower part of the image were 243 μm to 249 μm and 0.63° to 1.7°, respectively.

On the other hand, in ST2DFT, the parameters were set as follows:
Spatial resolution: Δk=Δl=17.4 μm;
Size of partial region cut out from magnetic domain image: N _k =N _l =64;
Window function shift amount: S _k = S _l = 1.
Here, the size of the partial region cut out from the magnetic domain image was set to N _k =N ₁ =64 because analysis cannot be performed unless at least one period of 180° magnetic domain is included in the cut out partial region.

Figure 7 shows the spatial distribution θ(n,m) of the 180° magnetic domain angle for each of the magnetic domain images D00 and D01. From θ(n,m) of the magnetic domain image D01 shown in Figure 7, it can be seen that even in magnetic domains that contain grain boundaries, the grain boundary portions can be clearly distinguished.

In addition, by using ST2DFT to analyze the magnetic domain structure, it is possible to map the relationship between the angle (deg) of the 180° magnetic domain and its position (n, m), as shown in Figure 7, making it possible to easily derive identical magnetic domain angle regions and their positions (n, m).

Figure 8 shows a comparison of the results of the analysis of the magnetic domain structure using the line segment method and the results of the analysis of the magnetic domain structure using ST2DFT (Figure 7).

In Figure 8, the upper part of magnetic domain image D01 shows the region where the m coordinate is greater than 200, and the lower part of magnetic domain image D01 shows the region where the m coordinate is 0 to 200. The analysis results by ST2DFT in Figure 8 show, for magnetic domain image D00, the width (indicated as "magnetic domain width" in Figure 8) and angle of the 180° magnetic domain at observation position (n, m) = (200, 200), for the upper part of magnetic domain image D01, the magnetic domain width and angle at observation position (n, m) = (200, 350), and for the lower part of magnetic domain image D01, the magnetic domain width and angle at observation position (n, m) = (200, 100).

From FIG. 8, the line segment method and ST2DFT show similar results for the angle of the 180° magnetic domain, but the line segment method has a higher angular resolution. This is due to the tendency that when calculating the angle, n and m substituted into formula (7) are integers and tend to be values near the origin. If the width of the 180° magnetic domain is assumed to be 135 μm, the angular resolution is about ±6°, which is very rough compared to the actual angular change of the magnetic domain. To solve this problem, it is considered effective to use a method such as interpolating by assuming a distribution when acquiring the peak position of the partial Fourier image, or taking the center of gravity by considering the intensity of adjacent Fourier spots. This method allows the peak position to be acquired continuously, so it is possible to increase the angular resolution of the 180° magnetic domain.
Due to the resolution problem as described above, in this embodiment, the peak position is derived by determining the spot positions (excluding the origin) and intensities of 10 high intensity points in the partial Fourier image, and then determining the center of gravity taking into account the intensity and position.

As such, the results of the analysis of the magnetic domain structure using ST2DFT are better than those of the conventional line segment method, and it is clear that the quantitative derivation method of the 180° magnetic domain angle using ST2DFT is effective.

(2-3) Definition of grain-oriented electrical steel sheet Next, the result of the analysis of the magnetic domain structure by the ST2DFT is defined as an identical magnetic domain angle region, which is a continuous region where the 180° magnetic domain angle is within a predetermined range. An identical magnetic domain angle region is a region that is generally considered to be a region of different crystal grains, but where the magnetic domain angle is considered to be substantially the same, and can be recognized as a concept similar to that of a "colony" in terms of crystal orientation.

The same magnetic domain angle region varies depending on the size of the observation region, the size at which the partial Fourier image is divided, and how the angles considered to be the same are determined. In this embodiment, the realistic size of the magnetic domain, the size of the crystal grains, and the strength of the correlation with the magnetic properties are taken into consideration, and are defined as follows.

(2-3-1) Observation area The size of the observation area to be measured in the magnetic domain image is 500 mm x 500 mm. This size generally corresponds to the size of a sample when measuring magnetic properties based on the Single Sheet Tester (SST) method specified in JIS C 2556:2015. In addition, the k direction is parallel to the direction perpendicular to the rolling direction (TD direction), and the l direction is parallel to the RD direction, and the observation is performed.

(2-3-2) Size of Fourier Image The size of the observation area of a steel plate of 500 mm x 500 mm is set so that the spatial resolution per pixel of the magnetic domain image is 25 μm or less, and the image is acquired in gray scale. The acquired magnetic domain image is expressed in 256 continuous gradations, including black and white. In the subsequent numerical processing, black is treated as 0 and white as 255 (dimensionless quantity). If it is difficult to observe the above measurement range in one measurement, magnetic domain images measured multiple times may be combined and treated as one magnetic domain image. In this case, it is natural to adjust the observation position so that there is no inconsistency at the joints between the images.

(2-3-3) Sample to be observed Since the magnetic domain structure is easily affected by distortion, it is natural to select the observation area as an area that is hardly affected by distortion caused by handling the steel sheet and cutting out the sample, such as the edge of the steel sheet or the edge of the observation sample. In addition, the magnetic domain image of this embodiment is observed in a demagnetized state by exciting the sample with a magnetic field of 1.9 T or more at 50 Hz and then gradually decreasing the magnetic field.

(2-3-4) Size of the partial Fourier image The size of the partial Fourier image is set to 2 mm x 2 mm. This size is large enough to include at least one period of 180° magnetic domains in the partial region. The shift amount of the window function is set to 25 μm or less.

(2-3-5) Magnetic domain angle regarded as the same magnetic domain angle region The magnetic domain angle obtained for the partial region is divided into three regions: 0 deg to less than 1 deg, 1 deg or more to less than 5 deg, and 5 deg or more. When adjacent partial regions are in the same region, it is determined that the magnetic domain angles are continuous, that is, in one same magnetic domain angle region. In this embodiment, whether adjacent partial regions are in one same magnetic domain angle region or not does not depend on the difference in magnetic domain angle between the adjacent partial regions. For example, partial regions with magnetic domain angles of 0.0 deg and 0.9 deg form continuous same magnetic domain angle regions, while partial regions with magnetic domain angles of 0.9 deg and 1.1 deg are not continuous, although the difference in magnetic domain angle is 0.2 deg, and this boundary is the boundary of the same magnetic domain angle region.

The reason that the sections of the regions are discontinuous is that grain-oriented electrical steel sheets are highly concentrated in the Goss orientation, so a change in orientation of 0.5 degrees in the region from 0 degrees to less than 1 degree has a significantly different effect on the magnetic properties than a change in orientation of 0.5 degrees in the region of 5 degrees or more. In particular, the change in angle in the region from 0 degrees to less than 1 degree has the greatest effect on the magnetic properties, so the closer to 0 degrees the section is, the shorter it is.

It should be noted that although the boundaries of the same magnetic domain angle regions are basically determined as described above, in actual steel sheets, minute same magnetic domain angle regions are observed to exist within large same magnetic domain angle regions due to the measurement of the closure domains occurring within the 180° magnetic domain, scratches on the steel sheet surface, noise during measurement, etc. Such minute regions observed become a disturbance factor in the evaluation of the average diameter of the same magnetic domain angle regions to be controlled in this embodiment for the purpose of noise reduction, and significantly reduce the correlation between the noise in the high magnetic field region and the average diameter of the same magnetic domain angle regions found in this embodiment. For this reason, in this embodiment, regions with an area of 10.0 ^mm2 or less in the above operation are treated as having no boundaries surrounding the regions. In other words, regions observed with an area of 10.0 ^mm2 or less are treated as the same magnetic domain angle region as the surrounding regions, and are not counted as "the number of same magnetic domain angle regions existing in the observation region" in the derivation of the average diameter described below.

(2-3-6) Average diameter of identical magnetic domain angle regions The average diameter of identical magnetic domain angle regions is the equivalent circle diameter of the identical magnetic domain angle regions in the observation region. That is, the average identical magnetic domain angle region area S _A is calculated by (area of observation region)/(number of identical magnetic domain angle regions present in the observation region), and d for which S _A = ^πd2 is defined as the average diameter of the identical magnetic domain angle regions. In this case, for identical magnetic domain angle regions that contact the outermost boundary of the observation region, the colonies are considered to be connected with mirror symmetry to the outside of the observation region, and the number is calculated as "0.5".

In this embodiment, the average diameter of the same magnetic domain angle region is set to 5.0 mm or more. This effectively suppresses elongation magnetostriction in the high magnetic field region, and significantly reduces noise due to out-of-plane vibration of the steel sheet. It is preferably 8.0 mm or more, and more preferably 10.0 mm or more. There is no need to particularly limit the upper limit of the average diameter of the same magnetic domain angle region, and from the viewpoint of exerting the effect of this embodiment, the larger the average diameter of the same magnetic domain angle region, the more preferable it is. For example, it can be said that it is technically an ideal state for the entire steel sheet manufactured by the coil to be recognized as a single same magnetic domain angle region. However, it is also clear that it is not realistic for the entire coil, which has a width of several hundred mm and a length of several hundred meters or more, to become a single same magnetic domain angle region in the current practical grain-oriented electromagnetic steel sheet, whose crystal grain size is only about 100 mm. The realistic maximum diameter of the same magnetic domain angle region in the grain-oriented electromagnetic steel sheet manufactured by the current manufacturing process is about 500 mm, or even about 300 mm. In this embodiment, the observation area is set to 500 mm x 500 mm, taking into consideration the realistic maximum diameter of the same magnetic domain angle area.

The reason why the noise caused by out-of-plane vibration of steel sheets is suppressed when the same magnetic domain angle area is large is not clear, but it is assumed as follows. Closure domains are likely to occur in areas where the atomic arrangement in the crystal is disturbed. The grain boundaries, which are areas where the atomic arrangement is disturbed in the crystal structure of oriented electrical steel sheets, are areas where closure domains are likely to occur, but their occurrence frequency is affected by orientation changes across the grain boundaries, element segregation, strain accumulation, and even the surface properties of the steel sheet. For this reason, there are grain boundaries where closure domains are likely to occur and grain boundaries where they are not likely to occur, and even if the crystal grain size is the same (the frequency of occurrence of grain boundaries is the same), the frequency of occurrence of closure domains will decrease if the proportion of grain boundaries where closure domains are not likely to occur is high. If closure domains are unlikely to occur at grain boundaries, the 180° magnetic domains will occupy a continuous space across the grain boundaries with almost no change in magnetic domain angle. This situation is a situation in which the average diameter of the same magnetic domain angle region defined in this embodiment is large, and since the proportion of closure domains is small, elongation magnetostriction is suppressed, and as a result, noise caused by out-of-plane vibration of the steel sheet in the high magnetic field region is reduced. Furthermore, the closer the 180° magnetic domain angle is to 0 deg, the less likely magnetization rotation occurs when excited to the high magnetic field region. Magnetization rotation generates harmonic components in the magnetostriction waveform and leads to increased noise, so it is preferable to reduce it. Therefore, it can be said that it is desirable to maximize the area of the 0 to 1 deg region. Specifically, in a preferred embodiment of the present invention, the area of the 0 to 1 deg region is 70% or more of the total area. In a particularly preferred embodiment, it is 90% or more. However, as mentioned above, noise caused by out-of-plane vibration of the steel sheet in the high magnetic field region cannot be suppressed simply by reducing the elongation magnetostriction, and we believe that a comprehensive change in the magnetic domain structure as described below is necessary to suppress noise caused by out-of-plane vibration of the steel sheet in the high magnetic field region.

The magnetic domain structure obtained by this embodiment acts independently of the coarsening of the crystal grain size. Generally, as the crystal grain size becomes coarser, the same magnetic domain angle region also becomes coarser. However, when the coarsening of the same magnetic domain angle region in this embodiment is achieved by the coarsening of the crystal grain size, it is considered that it does not necessarily contribute to the suppression of noise caused by the out-of-plane vibration of the steel sheet in a high magnetic field region. This is because it is presumed that the coarsening of the same magnetic domain angle region only by the coarsening of the crystal grain size is insufficient to reduce the closure domain caused by the crystal orientation difference with the adjacent crystal grains. Therefore, the coarsening of the same magnetic domain angle region in this embodiment occurs regardless of the presence or absence of grain boundaries. Ideally, it is ideal that the same magnetic domain angle region exists across the grain boundaries. Therefore, in order to evaluate this ideal state, the effect is evaluated by taking the ratio of the crystal grain size Rc of the grain-oriented electrical steel sheet to the average diameter d of the same magnetic domain angle region, as shown in formula (8).
d/Rc≧1.1 (8)
Here, Rc is the average equivalent circle diameter of the grain-oriented electrical steel sheet, the average grain area S _B is calculated, and Rc for which S _B = πRc ² is defined as the grain size. Note that, in the case where the surface of the base steel sheet has a primary coating (glass coating, intermediate layer), insulating coating, etc. made of oxides or the like, these are removed by a known method, and then the above grain size Rc is measured visually.

Generally, when the magnetic domain angle increases, the adverse effect of a decrease in magnetic properties (increased hysteresis loss) cannot be avoided. On the other hand, the continuous state of the magnetic domain structure across the grain boundaries, which is a feature of this embodiment, continues while maintaining the magnetic domain angle, so even if the same magnetic domain angle region becomes coarse, the magnetic domain angle itself does not increase. Therefore, the decrease in magnetic properties (increased hysteresis loss) caused by the expansion of the magnetic domain angle is essentially not a problem.

As mentioned above, there is no need to set a specific upper limit for the average diameter of the same magnetic domain angle region, but a larger same magnetic domain angle region leads to a lower frequency of closure domains, which is favorable for reducing noise caused by out-of-plane vibration of the steel sheet in high magnetic field regions. However, the average diameter of the same magnetic domain angle region that can be achieved with a practical steel sheet is about 100 mm, which is the realistic upper limit.

Furthermore, the magnitude of the variation in the magnetic domain angle is defined as follows by the partial region determined as above.
(2-3-7) Fluctuation in magnetic domain angle With respect to the observation area, when the total sum of the absolute values of the differences in magnetic domain angles of adjacent partial regions in the l direction parallel to the RD direction is Δθl (deg), the total sum of the absolute values of the differences in magnetic domain angles of adjacent partial regions in the k direction parallel to the TD direction is Δθk (deg), and the total sum of the areas of the partial regions used to derive the same magnetic domain angle region is S ( ^mm2 ), it is a preferred embodiment that the following formula (9) is satisfied.
(Δθl+Δθk)/S≦1.0degmm ^-2 …(9)

The value of formula (9) represents the magnitude of the magnetic domain angle variation per unit area in the l direction, i.e., the rolling direction of the steel sheet, and as described above, it is an index representing the continuity of the magnetic domain structure, excluding the influence of the crystal grain size. The smaller this value is, the smaller the variation in the magnetic domain angle is, and corresponds to a situation in which the occurrence of closure domains at the boundary of the same magnetic domain angle region is suppressed. Formula (9) is preferably 0.8 deg.mm ^-2 or less, more preferably 0.6 deg.mm ^-2 or less. There is no need to particularly limit the lower limit of formula (9), and from the viewpoint of exerting the effect of this embodiment, it can be said that the ideal state is zero, that is, the observation area of 500 mm x 500 mm is a single same magnetic domain angle region, and further, there is no variation in the magnetic domain angle even within the same magnetic domain angle region. However, it is difficult to achieve such a state in a practical grain-oriented electrical steel sheet, and it can be said that it is difficult to completely eliminate the variation in the magnetic domain angle caused by the influence of the crystal orientation difference between adjacent crystal grains and the grain boundary form even within one crystal grain, and further the shape variation such as the surface roughness. A realistic lower limit value of formula (9) for grain-oriented electrical steel sheets manufactured by current manufacturing processes is about 0.01 degmm ^-2 , or even about 0.005 degmm ^-2 .

In this specification, the term "high magnetic field region" is used assuming a magnetic field in the grain-oriented electromagnetic steel sheet of 1.9 T or more. However, in an actual iron core, there is no situation in which all parts of the grain-oriented electromagnetic steel sheet used as a material are 1.9 T or more. In an actual iron core, there are variations in the magnetic flux density, and it is natural that the magnetic flux density is less than 1.9 T in parts where the magnetic flux is difficult to pass. Even taking such a situation into consideration, the noise caused by the out-of-plane vibration of the steel sheet in the high magnetic field region, which is an effect of this embodiment, is understood to be vibration caused by dimensional changes in the steel sheet when at least a part of the steel sheet is magnetized with a magnetic flux density of 1.9 T or more in a situation in which at least a part of the steel sheet is restrained.

(3) Thickness of Grain-Oriented Electrical Steel Sheet As described above, the effect of making the magnetic domain structure continuous at the grain boundaries in this embodiment suppresses the bending of the steel sheet out of the plane due to the magnetization of the steel sheet, thereby suppressing noise. Also, as described above, the thinner the steel sheet, the easier it is to bend, so the effect of this embodiment is more likely to be exhibited with a thin steel sheet. Strictly speaking, the effect of this embodiment is exhibited even if the sheet is thick. Since the noise of interest in this embodiment also depends on the degree of constraint in the in-plane direction of the steel sheet, including the core design and core structure, the presence or absence of a practical noise improvement effect cannot be determined only by the sheet thickness of the grain-oriented electrical steel sheet, but a target thickness of 0.35 mm or less can be cited as a guide for the grain-oriented electrical steel sheet that exhibits a sufficient effect in a general iron core. The effect of this embodiment is clear with a steel sheet of 0.25 mm or less, and the merit of this embodiment is remarkable with a steel sheet of 0.15 mm or less.

(4) Manufacturing Method of Grain-Oriented Electrical Steel Sheet Next, a manufacturing method of the grain-orientated electrical steel sheet according to this embodiment will be described.

Figure 9 is a flow chart illustrating a method for manufacturing a grain-oriented electrical steel sheet according to this embodiment. As shown in Figure 9, the method for manufacturing a grain-oriented electrical steel sheet (silicon steel sheet) according to this embodiment includes a casting process (S11), a hot rolling process (S12), a hot-rolled sheet annealing process (S13), a cold rolling process (S14), a decarburization annealing process (S15), an annealing separator application process (S16), a finish annealing process (S17), and an insulating coating formation process (S21). In addition, if necessary, a nitriding treatment may be performed at any timing between the decarburization annealing process and the finish annealing process, and a magnetic domain control process (S22) may be further performed at any timing after the cold rolling process.

In order to favorably control the magnetic domain structure, which is a feature of the steel sheet of this embodiment, it is important to control the tension in the insulating coating formation process. As for other manufacturing conditions, conventional known manufacturing methods for grain-oriented electrical steel sheets can be applied. For example, there are manufacturing methods that use MnS or AlN formed by high-temperature slab heating as an inhibitor, and manufacturing methods that use AlN formed by low-temperature slab heating and subsequent nitriding treatment as an inhibitor. The switching that is a feature of this embodiment can be applied to any manufacturing method and is not limited to a specific manufacturing method. Below, a manufacturing method that applies nitriding treatment will be described as an example.

(Casting process)
In the casting step (S11), a slab is prepared. An example of a method for producing a slab is as follows. Molten steel is produced (smelted). A slab is produced using the molten steel. The slab may be produced by a continuous casting method. An ingot may be produced using the molten steel, and the ingot may be bloomed to produce a slab. The thickness of the slab is not particularly limited. The thickness of the slab is, for example, 150 to 350 mm. The thickness of the slab is preferably 220 to 280 mm. As the slab, a so-called thin slab having a thickness of 10 to 70 mm may be used. When a thin slab is used, rough rolling before finish rolling can be omitted in the hot rolling step.

The chemical composition of the slab can be the same as that used in the manufacture of general grain-oriented electrical steel sheets. For example, the chemical composition of the slab contains the following elements:

C: 0-0.0850%
Carbon (C) is an effective element for controlling the primary recrystallization structure during the manufacturing process, but excessive C content in the final product adversely affects the magnetic properties. Therefore, the C content of the slab is set to 0. The preferred upper limit of the C content is 0.0750%. C is purified in the decarburization annealing process and the final annealing process described below, and after the final annealing process, the C content is 0.0050% or less. When C is contained, in consideration of the productivity in industrial production, the lower limit of the C content may be more than 0% or may be 0.0010%.

Si: 2.0-7.0%
Silicon (Si) increases the electrical resistance of grain-oriented electrical steel sheets and reduces iron loss. If the Si content is less than 2.0%, austenite transformation occurs during final annealing, and the crystallization of the grain-oriented electrical steel sheets is reduced. On the other hand, if the Si content exceeds 7.0%, the cold workability decreases and cracks tend to occur during cold rolling. The upper limit of the Si content is preferably 4.50%, and more preferably 4.0%.

Mn: 0. ~1.0%
Manganese (Mn) combines with S or Se to produce MnS or MnSe, and functions as an inhibitor. The Mn content may be 0 to 1.0%. When Mn is contained, Mn When the content is within the range of 0.05 to 1.0%, the secondary recrystallization is stabilized, which is preferable. In this embodiment, part of the inhibitor function is carried out by nitrides of Nb group elements. In this case, the strength of MnS or MnSe as a general inhibitor is controlled to be weak. Therefore, the upper limit of the Mn content is preferably 0.50%, more preferably 0.20%. %.

S: 0-0.0350%
Se: 0-0.0350%
Sulfur (S) and selenium (Se) combine with Mn to produce MnS or MnSe, and function as inhibitors. The S content may be 0 to 0.0350%, and the Se content may be 0 to 100%. When at least one of S and Se is contained, it is preferable that the total content of S and Se is 0.0030 to 0.0350%, since this stabilizes secondary recrystallization. In this embodiment, it is possible for part of the inhibitor function to be carried out by the nitride of an Nb group element. In this case, the strength of MnS or MnSe as a general inhibitor is controlled to be weak. Therefore, the upper limit of the total content of S and Se is preferably 0.0250%, and more preferably 0.010%. If S and Se remain after final annealing, they form compounds and deteriorate the core loss. Therefore, it is preferable to reduce S and Se as much as possible by purification during final annealing.

Here, "the total content of S and Se is 0.0030-0.0350%" may mean that the chemical composition of the slab contains only one of S or Se, and the total content of either S or Se is 0.0030-0.0350%, or that the slab contains both S and Se, and the total content of S and Se is 0.0030-0.0350%.

Al: 0-0.0650%
Aluminum (Al) combines with N to precipitate as (Al,Si)N, and functions as an inhibitor. The Al content may be 0 to 0.0650%. When Al is contained, the content of Al is When the amount of Al is within the range of 0.010 to 0.065%, AlN, which acts as an inhibitor formed by nitriding as described below, expands the secondary recrystallization temperature range, and secondary recrystallization in particular in the high temperature range is prevented. From the viewpoint of stability of secondary recrystallization, the preferred lower limit of the Al content is 0.020%, and more preferably 0.0250%. %, and more preferably 0.030%.

N: 0-0.0120%
Nitrogen (N) combines with Al and functions as an inhibitor. The N content may be 0 to 0.0120%. Since N can be added by nitriding during the manufacturing process, the lower limit is On the other hand, when N is contained, if the N content exceeds 0.0120%, blisters, which are a type of defect, tend to occur in the steel sheet. The preferred upper limit of the N content is 0.010 %, and more preferably 0.0090%. N is purified in the final annealing process, and the N content is 0.0050% or less after the final annealing process.

The remainder of the chemical composition of the slab consists of Fe and impurities. Note that "impurities" here refer to elements that are inevitably mixed in from components contained in the raw materials or components mixed in during the manufacturing process when the slab is industrially manufactured, and that do not substantially affect the effects of this embodiment.

The slab may contain known selective elements in place of part of the Fe, taking into consideration not only solving manufacturing problems, but also strengthening the inhibitor function through compound formation and the effect on magnetic properties. Examples of selective elements include the following elements:

Cu: 0-0.40%
Bi: 0~0.010%
B: 0-0.080%
P: 0 to 0.50%
Ti: 0~0.0150%
Sn: 0-0.10%
Sb: 0-0.10%
Cr: 0-0.30%
Ni: 0 to 1.0%
Nb: 0-0.030%
V: 0-0.030%
Mo: 0-0.030%
Ta: 0-0.030%
W: 0-0.030%
These optional elements may be contained according to known purposes. There is no need to set a lower limit for the content of these optional elements, and the lower limit may be 0%.

(Hot rolling process)
The hot rolling step (S12) is a step of hot rolling a slab heated to a predetermined temperature (e.g., 1100 to 1400°C) to obtain a hot rolled steel sheet. In the hot rolling step, for example, after the casting step, the heated silicon steel material (slab) is roughly rolled, and then finish-rolled to obtain a hot rolled steel sheet having a predetermined thickness, for example, 1.8 to 3.5 mm. After the finish rolling is completed, the hot rolled steel sheet is coiled at a predetermined temperature.

Since MnS strength as an inhibitor is not particularly necessary, taking productivity into consideration, it is preferable to set the slab heating temperature to 1100°C to 1280°C.

(Hot-rolled sheet annealing process)
The hot-rolled sheet annealing step (S13) is a step in which the hot-rolled steel sheet obtained in the hot rolling step is annealed under predetermined temperature conditions (for example, at 750 to 1200° C. for 30 seconds to 10 minutes) to obtain a hot-rolled annealed sheet.

(Cold rolling process)
The cold rolling step (S14) is a step of obtaining a cold-rolled steel sheet having a thickness of, for example, 0.10 to 0.50 mm by performing a single cold rolling process on the hot-rolled annealed sheet obtained in the hot-rolled sheet annealing process, or performing multiple cold rolling processes (two or more times) via annealing (intermediate annealing) (for example, a total cold rolling rate of 80 to 95%).

(Decarburization annealing process)
The decarburization annealing step (S15) is a step of performing decarburization annealing (for example, at 700 to 900°C for 1 to 3 minutes) on the cold-rolled steel sheet obtained in the cold rolling step to obtain a decarburization annealed steel sheet in which primary recrystallization has occurred. By performing decarburization annealing on the cold-rolled steel sheet, C contained in the cold-rolled steel sheet is removed. The decarburization annealing is preferably performed in a moist atmosphere in order to remove "C" contained in the cold-rolled steel sheet.

(Nitriding)
The nitriding treatment is carried out in order to adjust the strength of the inhibitor in the secondary recrystallization. In the nitriding treatment, the nitrogen content of the steel sheet may be increased to about 40 to 300 ppm at any timing between the start of the above-mentioned decarburization annealing and the start of the secondary recrystallization in the finish annealing described below. Examples of the nitriding treatment include a treatment of annealing a steel sheet in an atmosphere containing a gas having a nitriding ability such as ammonia, and a treatment of finish annealing a decarburization annealed steel sheet coated with an annealing separator containing a powder having a nitriding ability such as MnN.

When the slab contains Nb group elements in the above numerical range, the nitrides of Nb group elements formed by the nitriding process function as inhibitors that lose their grain growth inhibition function at relatively low temperatures, so secondary recrystallization begins at a lower temperature than before. These nitrides also have an advantageous effect on the selectivity of the nucleation of secondary recrystallized grains, and may possibly contribute to achieving high magnetic flux density. In addition, AlN is formed during the nitriding process, and this AlN functions as an inhibitor that continues to inhibit grain growth up to relatively high temperatures. To obtain these effects, it is preferable to set the amount of nitride after the nitriding process to 130 to 250 ppm, and more preferably 150 to 200 ppm.

(Annealing separator application process)
The annealing separator application step (S16) is a step of applying an annealing separator to the decarburized annealed steel sheet. As the annealing separator, for example, an annealing separator mainly composed of MgO or an annealing separator mainly composed of alumina can be used.

When an annealing separator containing MgO as the main component is used, a forsterite film ( _a film mainly containing _Mg2SiO4 ) is likely to be formed as an intermediate layer by final annealing, and when an annealing separator containing alumina as the main component is used, an oxide film (a film mainly containing SiO2) is likely to be formed as an intermediate layer by final annealing. These intermediate layers may be removed as necessary.

After the annealing separator is applied, the decarburized annealed steel sheet is wound into a coil and finish annealed in the next finish annealing process.

(Finish annealing process)
The final annealing step (S17) is a step in which the decarburized annealed steel sheet coated with the annealing separator is subjected to final annealing to cause secondary recrystallization. In this step, the growth of the primary recrystallized grains is suppressed by an inhibitor, and the secondary recrystallization is allowed to proceed, thereby preferentially growing {100}<001> oriented grains and dramatically improving the magnetic flux density.

(Insulating film formation process)
The insulating coating forming step (S21) is a step of forming an insulating coating on the grain-oriented electrical steel sheet (finish annealed steel sheet) after the finish annealing step. An insulating coating mainly made of phosphate and colloidal silica or an insulating coating mainly made of alumina sol and boric acid may be formed on the steel sheet by a known method.

However, this step can be used to favorably control the magnetic domain structure, which is a feature of the steel sheet of this embodiment, and is an important step in the manufacturing method described in this specification. In order to realize the magnetic domain structure defined in this embodiment, tension control in this step, which is the final heat treatment in steel sheet manufacturing, is the key. First, the maximum tension of the steel sheet before heating is controlled to be 30 MPa or less, and then the sheet is passed through with a tension of 6.5 to 13.0 MPa at all times in the temperature range of 750°C or more, and the maximum absolute value of the time derivative is 3.0 MPa/s or less. The data for determining this tension change is obtained by continuously measuring the tension during passing through the sheet using a general method, and the tension at a specific time t is the average value of the tension for 10 seconds going back to time t-10 seconds. The reason for such averaging for 10 seconds is that unintended stress fluctuations (hunting) may occur during passing through the sheet, and the effect of this is mitigated.

By controlling the tension before heating and during the cooling process in the final heat treatment process as described above, the magnetic domain structure defined in this embodiment is preferable. The reason why such a change occurs is not clear, but the following reasons are considered. The yield stress at room temperature of the steel sheet containing 2% or more Si, which is the subject of this embodiment, exceeds 200 MPa, and the tension of 30 MPa, which is the allowable load on the steel sheet before heating, is a stress that can be judged to be within elastic deformation. However, even with this level of stress, in the microregions inside the steel sheet, especially in the grain boundaries where the constituent elements and dislocations are arranged in a special structure, slight structural changes occur due to the stress within the elastic deformation, and it is thought that this affects the changes during the subsequent heat treatment process in the high temperature range. In addition, in the temperature range of 750 ° C or more, the grain boundary movement (crystal grain growth and crystal orientation change) hardly occurs, but the structural change due to the tension applied before heating also affects the shape of the grain boundary, the dislocation structure on the grain boundary, element segregation to the grain boundary, precipitation on the grain boundary, etc., which affect the continuity of the magnetic domain. The tension in this temperature range affects the effect of this embodiment through atomic movement, including dislocation formation near the grain boundaries. If the tension is too low, the above-mentioned grain boundary changes themselves are unlikely to occur. If the tension is too high, it will cause inadvertent proliferation of dislocations near the grain boundaries, which will have a significant adverse effect on the continuity of the magnetic domain angle across the grain boundaries. In low temperature conditions, atomic movement is unlikely to occur, so the effect on the effect of this embodiment is small. In high temperature conditions, atomic movement becomes active and the preferable special grain boundary structure itself is eliminated, so the effect on the effect of this embodiment is small. Furthermore, it is believed that the change further affects the preferable enhancement of changes in grain boundary characteristics by fluctuating the tension within an appropriate range, and as a result, the continuity of the magnetic domains across the grain boundaries is increased. Basically, it is believed that the grain boundary morphology becomes smooth, the dislocation density decreases, and the segregation becomes uniform, but direct detection has not been possible.

The maximum tension applied to the steel sheet before heating is preferably 25 MPa or less, and more preferably 20 MPa or less. A lower tension is preferable, but a typical insulating coating heat treatment line has the following structure: "finishing annealing coil discharge reel → bridle roll → removal of excess annealing separator → bridle roll → entry looper → bridle roll → coating raw material application → annealing → bridle roll → exit looper → bridle roll → take-up reel." Because of the handling of the steel sheet from discharge to coating raw material application, it is difficult to make the load tension less than 5 MPa.

The fluctuation range of the tension at all times in the temperature range of 750°C or higher is preferably 7.0 to 11.0 MPa, more preferably 7.5 to 10.0 MPa. The maximum value of the time derivative of the tension is preferably 2.5 MPa/s or less, more preferably 2.0 MPa/s or less.

The manufacturing method according to this embodiment may further include a magnetic domain control process, if necessary.

(Magnetic domain control process)
The magnetic domain control step (S22) is a step of performing a process for subdividing the magnetic domains of the grain-oriented electrical steel sheet. For example, localized micro-distortions or localized grooves may be formed in the grain-oriented electrical steel sheet by a known method such as laser, plasma, mechanical method, or etching. Such a magnetic domain subdivision process does not impair the effect of this embodiment.

The manufacturing method of grain-oriented electrical steel sheet shown in FIG. 9 shows an example in which the insulating film forming process is essential to control the magnetic domain structure in the insulating film forming process. However, if the method can manufacture grain-oriented electrical steel sheet having the above-mentioned magnetic domain structure, the insulating film forming process is not necessarily required.

Next, the effects of this embodiment will be described in detail using examples. The conditions in this example are an example of conditions adopted to confirm the feasibility and effects of the present invention, and the present invention is not limited to this example of conditions. Various conditions can be adopted in the present invention as long as they do not deviate from the gist of the present invention and achieve the object of the present invention.

Grain-oriented electrical steel sheets with the chemical composition shown in Table 2 were manufactured using slabs with the chemical composition shown in Table 1 as the raw material. In Tables 1 and 2, "-" indicates that no control or manufacturing was performed with the content in mind, and no content measurement was performed, and values with "<" indicate that control and manufacturing were performed with the content in mind, and content measurement was performed, but a measurement value with sufficient reliability for the content could not be obtained (the measurement result was below the detection limit).

The grain-oriented electrical steel sheets were basically manufactured according to known manufacturing conditions: a slab was cast, hot-rolled, and hot-rolled sheet annealed.
Furthermore, the steel sheets were subjected to cold rolling and decarburization annealing, and some of the steel sheets after the decarburization annealing were subjected to nitriding treatment (nitriding annealing) in a mixed atmosphere of hydrogen-nitrogen-ammonia.

Furthermore, an annealing separator mainly composed of MgO was applied to the steel sheet, and the steel sheet was subjected to finish annealing. In the final process of the finish annealing, the steel sheet was held in a hydrogen atmosphere at 1200°C for 20 hours (purification annealing), and then naturally cooled.

A coating solution for forming an insulating film, mainly composed of phosphate and colloidal silica and containing chromium, was applied onto the primary coating (intermediate layer) formed on the surface of the manufactured grain-oriented electrical steel sheet (finish annealed steel sheet), and the solution was heated and held in an atmosphere of 75% by volume hydrogen:25% by volume nitrogen, and then cooled to form an insulating film.

When viewed on a cut surface with the cutting direction parallel to the sheet thickness direction, the produced grain-oriented electrical steel sheet had an intermediate layer arranged in contact with the grain-oriented electrical steel sheet (silicon steel sheet) and an insulating coating arranged in contact with the intermediate layer. The intermediate layer was a forsterite coating with an average thickness of 2 μm, and the insulating coating was an insulating coating mainly composed of phosphate and colloidal silica with an average thickness of 1 μm.

(B-1) Magnetic Properties of Grain-Oriented Electrical Steel Sheet The magnetic properties of the grain-oriented electrical steel sheet were measured based on the Single Sheet Tester (SST) specified in JIS C 2556:2015.

As a magnetic property, the magnetic flux density B8 (T) in the rolling direction of the steel sheet was measured when excited at 800 A/m.

(B-2) Magnetic Domain Structure of Grain-Oriented Electrical Steel Sheet The magnetic domain structure of the grain-oriented electrical steel sheet was quantified by the above-mentioned analysis method, and the same magnetic domain angle region was measured.

(B-3) Noise characteristics of the core A three-phase, three-leg stacked core was created using each steel plate as the material. The size of the core was 750 mm in overall height, 750 mm in width, 150 mm in width for the U-phase, V-phase, and W-phase, and 40 mm in thickness. To fix the core, both sides were surrounded by a wooden frame and fixed with clamps and bolts. The tightening torque for the clamps and bolts was adjusted so that the average tightening pressure on the core surface was 0.30 MPa. The core joint was a six-stage step lap, with one sheet stacked at the same time. Eight microphones were placed at equal intervals 30 cm away from the core surface for each core, and the noise was measured.

(Measurement Example 1)
When manufacturing steel sheets of steel types A, B, C, and D with a thickness of 0.35 mm or less, the tension in the insulating coating formation process was changed to manufacture four types of steel sheets (A, B, C, D)-(1 to 4) with different average diameters d of the same magnetic domain angle region. In this case, the tension fluctuations in each steel type were controlled to be relatively small and almost constant. Since the only condition that changed during the manufacturing process in each steel type was the tension in the insulating coating formation process, the magnetic flux density, iron loss, and magnetostriction were almost the same characteristic values in each steel type. The magnetic domain structure of these steel sheets was analyzed, and iron cores were manufactured and noise was measured. The measurement results are shown in Table 3. It can be seen that within each steel type, the change in noise is strongly correlated with d. In other words, it can be seen that controlling d within an appropriate range is effective in reducing the noise of iron cores manufactured with thin steel sheets.

(Measurement Example 2)
When manufacturing steel sheets of steel types A, B, and D with a thickness of 0.35 mm or less, the tension in the insulating coating formation process was changed to manufacture four types of steel sheets with different d, (A, B, D)-(11-14), (B, D)-(15-18), and (D19-D22). In this case, the absolute value of the tension was kept constant for each steel type, and only the maximum value of the time derivative was controlled to vary. In addition, for magnetic domain refinement, local strain was imparted or local grooves were formed in a line or point shape extending in a direction intersecting the rolling direction under the following conditions. Note that the pitch is the interval in the rolling direction, Ua is the energy density, the mechanical groove formation was performed by the gear press method, and the chemical groove formation was performed by the electrolytic etching method. The magnetic domains of steel sheets B15 to B18 were controlled using etching, an electron beam, mechanical strain, and a laser, respectively. The conditions of the electron beam irradiation were irradiation pitch = 4 mm, Ua = 7 mJ/ ^mm2 , the conditions of the laser irradiation were irradiation pitch = 4 mm, Ua = 2.0 mJ/ ^mm2 , the conditions of the mechanical groove formation were pitch = 4 mm, groove depth = 20 μm, no grains under the groove, and the conditions of the chemical groove formation were pitch = 4 mm, groove depth = 20 μm. After the mechanical groove formation and the chemical groove formation, an insulating coating was formed under the following conditions. The mechanical groove formation was performed by forming an aluminum phosphate insulating coating by baking annealing at 850 ° C for 30 seconds. The chemical groove formation was performed by forming an aluminum phosphate insulating coating by baking annealing at 850 ° C for 60 seconds.

The only condition that changed during the manufacturing process for each steel type was the tension during the insulating coating formation process, so the magnetic flux density, iron loss, and magnetostriction were approximately the same characteristic values for each steel type. The magnetic domain structure of these steel sheets was analyzed, and iron cores were manufactured and noise was measured. The measurement results are shown in Table 4. It can be seen that even if d is the same for each steel type, noise is reduced when (Δθl + Δθk)/S satisfies equation (9).

According to the above aspect of the present invention, a grain-oriented magnetic steel sheet can be identified by a method for quantitatively deriving the areas and their positions where the magnetic domain angles are within a predetermined range from the magnetic domain image of the grain-oriented magnetic steel sheet, and it is possible to reduce noise in the high magnetic field area of the transformer core and favorably control the noise characteristics, which has high industrial applicability.

20 Image acquisition device 21 Light source unit 23 MO sensor 25 Image sensor 27 Signal processing unit 30 Analysis device 31 Calculation unit 33 Memory 35 Display unit 37 Input unit 39 Communication I/F
100 Analysis System

Claims (3)

A method for analyzing a magnetic domain structure of a grain-oriented electrical steel sheet, comprising the steps of:
a) cutting out a plurality of partial regions corresponding to a plurality of positions in a magnetic domain image of the grain-oriented electrical steel sheet, the magnetic domain image being binarized with two types of colors or represented in three or more gradations;
b) obtaining a plurality of partial Fourier images by performing a two-dimensional Fourier transform on each of the plurality of partial regions;
c) deriving a spatial distribution of the angle of the 180° magnetic domain of the grain-oriented electrical steel sheet based on the peak positions of the spots of the plurality of partial Fourier images;
d) deriving, based on the spatial distribution of the 180° magnetic domain angles, continuous regions in the magnetic domain image in which the 180° magnetic domain angles are within a predetermined range as identical magnetic domain angle regions;
The analysis method comprises: The magnetic domain image is represented by a data string x(k, l) of two-dimensional coordinates (k, l);
The observation position in the magnetic domain image is (n, m),
The window function is Wa(k,l),
The shift amounts of the window function in the k direction and the l direction are S _k and S _l , respectively.
If the parameters corresponding to the number of pixels in the k direction and the number of pixels in the l direction of each of the plurality of partial regions are expressed as N _k and N _l , respectively, then
In the step a),
A range of nS _k ≦k≦nS _k +N _k -1, mS _l ≦l≦mS _l +N _l -1 is extracted from the magnetic domain image using the window function, and a data string x _nm (k-nS _k ,l-mS _l ) is obtained for each of the plurality of partial regions as shown in the following formula:

In the step c),
The spatial distribution θ(n,m) of the angle of the 180° magnetic domain is derived as follows:

Δf _k and Δf _l represent the resolution in the k direction and the l direction of the spatial frequency of the magnetic domain image, respectively;
Δk and Δl represent the spatial resolution in the k direction and the l direction of the magnetic domain image, respectively;
The analysis method according to claim 1 , wherein f _k ^max (n,m) and f _l ^max (n,m) respectively represent the k component and the l component of a peak position of a spot in each of the plurality of partial Fourier images. A system for analyzing a magnetic domain structure of a grain-oriented electrical steel sheet, comprising:
A plurality of partial regions corresponding to a plurality of positions in the magnetic domain image of the grain-oriented electrical steel sheet are cut out from the magnetic domain image binarized with two types of colors or expressed in three or more gradations,
obtaining a plurality of partial Fourier images by performing a two-dimensional Fourier transform on each of the plurality of partial regions;
deriving a spatial distribution of the angle of the 180° magnetic domain of the grain-oriented electrical steel sheet based on peak positions of the spots of the plurality of partial Fourier images;
and a calculation unit that derives, based on a spatial distribution of the 180° magnetic domain angles, continuous regions in the magnetic domain image in which the 180° magnetic domain angles are within a predetermined range as identical magnetic domain angle regions.

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