The present invention is good because it does not artificially subdivide the magnetic domain before and after the secondary recrystallization, but forms crystal grains in a Goss orientation with a limited size, which is desirable in terms of metallographic structure, and subdivides the magnetic domain. It relates to a grain-oriented electrical steel sheet having iron loss characteristics.
Background technology
[0002]
　Electrical steel sheets are widely used mainly as iron core materials for transformers, and their characteristics are rated by iron loss and magnetic flux density. The smaller the iron loss and the higher the magnetic flux density, the greater the value. Generally, when the magnetic flux density is increased, the secondary recrystallization grain size increases, so there is a trade-off relationship that iron loss deteriorates, and the conventional quality improvement technology has been artificially magnetic domain after secondary recrystallization. It is to reduce iron loss by applying means to narrow the width. For example, Patent Document 1 discloses a technique for controlling the width of a magnetic domain by irradiating a laser. However, this magnetic domain control is not suitable for use in performing strain relief annealing because it does not have heat resistance, and the magnetic domain control method having thermal stability of Patent Document 2 has been put into practical use. Further, in Patent Document 3, a method of subdividing the magnetic domain of the secondary recrystallized grains by performing a treatment before the secondary recrystallization has been developed, and the method has been put into practical use. These are excellent in the effect of subdividing magnetic domains, but extra steps are indispensable, cost increase, production limit, decrease in magnetic build-in ratio (yield), destruction and repair (recoating) of insulating film. There are issues such as necessity.
　Further, according to the previous knowledge, it is possible to mix relatively small grains in the secondary recrystallized grains having a grain size of about several centimeters of the grain-oriented electrical steel sheet, but in that case, the orientation of the small grains. Has not been put into practical use because it deviates greatly from the so-called Goss direction ({110} <001>) and the magnetic characteristics deteriorate.
Prior art literature
Patent documents
[0003]
Patent Document 1: Japanese Patent Application Laid-Open No. 55-018566
Patent Document 2: Japanese Patent Application Laid-Open No. 61-117218
Patent Document 3: Japanese Patent Application Laid-Open No. 59-197520
Patent Document 4: Japanese Patent Application Laid-Open No. 33-004710
Patent Document 5 : Japanese Patent Application
Laid-Open No. 59-056522 Patent Document 6: Japanese Patent Application Laid-Open No. 09-287025
Patent Document 7: Japanese Patent Application
Laid-Open No. 58-023414 Patent Document 8: Japanese Patent Application Laid-Open No. 2000-199015
Patent Document 9: Special Fairness 6 -80172
Non-patent literature
[0004]
Non-Patent Document 1: Tadao Nozawa: Tohoku University Dissertation: Dissertation 1979
Non-Patent Document 2: US Patent No. 1965559
Outline of the invention
Problems to be solved by the invention
[0005]
　If the step condition (for example, high cold rolling ratio) that improves the magnetic flux density is adopted for the grain-oriented electrical steel sheet, the Goss orientation of the Goss orientation grains becomes sharp in the primary recrystallization texture, but the frequency of existence of the Goss orientation grains increases. As a result, the secondary recrystallization particle size becomes large, the abnormal eddy current loss increases, and the iron loss deteriorates. That is, although the magnetic flux density becomes high (large), the iron loss deteriorates. This is because the historical loss is improved, but the magnetic domain width is widened, the abnormal eddy current loss is increased (increased), and the total iron loss is deteriorated. Further, in the conventional technique, when fine particles are allowed to exist in the secondary recrystallization structure, the magnetic characteristics are not improved because the orientation of the fine particles is largely deviated or deviated from the Goss orientation. Therefore, in actual industrial production, in order to secure a high magnetic flux density, the secondary recrystallized grains have to be large, and a method of improving iron loss by an artificial additional magnetic domain control method must be adopted. Must be. An example of an artificial additional magnetic domain control method is the application of a tensioning insulating film, and in fact, many electrical steel sheets are produced by this method. However, in this way, in the conventional method, the number of steps increases, the cost increases, or the interlayer resistance deteriorates due to the destruction of the insulating film, and there is a limit to the improvement of iron loss, and improvement thereof has been required.
　An object of the present invention is to provide a grain-oriented electrical steel sheet in which iron loss is remarkably improved by the presence of fine particles in the Goss orientation in the secondary recrystallization structure without deteriorating the magnetic flux density. Hereinafter, the fine grains in the Goss orientation existing in the secondary recrystallization structure are referred to as "sesame grains". In the present invention, sesame seeds have a major axis of 5 mm or less.
Means to solve problems
[0006]
(1) A directional electromagnetic steel plate having a mass% of Si: 2.5 to 3.5%, a balance Fe and unavoidable elements, and a plate thickness of 0.18 to 0.35 mm, and is
a metal after final annealing. The structure contains a matrix grain of GOSS-oriented secondary recrystallized grains,
and the frequency of presence of Goss-oriented crystal grains having a major axis of 5 mm or less in the metal structure in the matrix grain is 1.5 pieces / cm 2 or more. , 8 pieces / cm 2 or less, the magnetic flux density B8 is 1.88 T or more, and the deviation angle of the Goss directional crystal grain from the rolling direction in the [001] direction is
a simple average of the α angle and the β angle. , A directional electromagnetic steel plate characterized by being 7 ° or less and 5 ° or less, respectively.
Here, the α angle and β angle are shown below.
α angle: Angle formed between the longitudinal direction (rolling direction) and the [001] magnetic domain of the Goss directional grain and its orientation projected onto the surface of the rolling surface
β angle: The [001] axis of the Goss directional grain is the rolling surface Angle
The invention's effect
[0007]
　By allowing fine particles in the Goss orientation to be present in the secondary recrystallization structure at a specific frequency, a grain-oriented electrical steel sheet having improved iron loss can be obtained without deteriorating the magnetic flux density.
A brief description of the drawing
[0008]
FIG. 1 is a diagram showing a three-dimensional angular relationship between three directions (rolling, rolled surface normal, and steel plate width direction) of a directional electromagnetic steel sheet and a Goss direction with three angles (α, β, and γ angles).
FIG. 2 is a diagram showing an example of crystal orientation of fine grains (sesame grains) having a sharp Goss orientation having a major axis of 5 mm or less.
FIG. 3 is a diagram showing the relationship between the major axis size of fine grains (sesame grains) having a sharp Goss orientation, the abundance density of sesame grains, and iron loss (W17 / 50).
[Fig. 4] Fig. 4 is a diagram showing a secondary recrystallization macrostructure. The figure below shows the steel of the present invention, and the figure above shows the conventional steel.
FIG. 5 is a diagram showing the relationship between the density of fine particles (sesame grains) having a sharp Goss orientation, iron loss, and magnetic flux density.
[Fig. 6] Fig. 6 is a diagram showing the relationship between the orientation of fine grains (sesame grains) having a sharp Goss orientation and iron loss.
FIG. 7 is a contour graph of iron loss W17 / 50 of an electromagnetic steel sheet (without a tension-applying insulating film).
Mode for carrying out the invention
[0009]
　The grain-oriented electrical steel sheet according to the present invention is based on the diligent studies conducted by the present inventors in order to solve the above-mentioned problems, and its metal structure is a large sharp Goss orientation secondary recrystallized grain (hereinafter referred to as “matrix”). It is composed of "grains"), and in the large secondary recrystallized grains (matrix grains), fine grains with a major axis of 5 mm or less in the same sharp Gossip orientation (hereinafter referred to as "sesame grains") are present. It is a grain-oriented electrical steel sheet with improved magnetic domain structure in large secondary recrystallized grains (matrix grains) and improved iron loss without lowering the magnetic flux density. In other words, it can be said that matrix grains and sesame grains are related to the sea and islands. In other words, sesame grains, which are islands, exist in the matrix grains, which are the sea. In the prior art (for example, Patent Document 9), an electromagnetic steel sheet having a structure in which particles having a large particle size and particles having a small particle size are mixed has been disclosed. However, it should be noted that in the prior art, small particles are present at the grain boundaries of large particles, and the structure of the sea island is not such that small particles (sesame grains) are present in the large particles (matrix grains). The electromagnetic steel plate according to the present invention has a sea-island structure in which small particles (sesame grains) are present in large particles (matrix grains), but it is denied that the small particles are present at the grain boundaries of the large particles. Please also note that this is not the case. Further, the major axis of the matrix grains exceeds at least 5 mm, because the sesame grains having a major axis of 5 mm or less are included. The matrix grains are secondary recrystallized grains and may have a particle size of about several cm, for example, a particle size of about 1 cm to 10 cm.
　Further, a glass coating mainly containing forsterite may be present on the surface of the grain-oriented electrical steel sheet of the present invention. Further, a tension film may be applied on the tension film.
[0010]
　Details will be described below.

　First, the orientation of the secondary recrystallized grains of the grain-oriented electrical steel sheet will be described. Electrical steel sheets utilize the secondary recrystallization phenomenon to form huge Goss oriented grains. This Goss direction is represented by an index of {110} <001>. The Goss orientation integration degree of the grain-oriented electrical steel sheet largely depends on the deviation of the crystal lattice from the rolling direction in the <100> orientation. Specifically, as shown in FIG. 1, the deviation angle is defined by three angles in the three-dimensional space, and the angles of α, β, and γ are defined below (Non-Patent Document 1).
α: An angle between the longitudinal direction (rolling direction) and the [001] axis of the Goss orientation grain and the projection of that orientation on the surface of the sample rolled surface (or rotation around the rolling surface normal axis in the [001] direction). Angle.)
β: The angle formed by the [001] axis of the Goss orientation grain with the rolled surface.
γ: Rotation angle around the [001] axis of the Goss directional grain on the sample surface (cross section perpendicular to the rolling direction)
[0011]
　As described above, the α and β angles include a deviation or deviation from the [001] axis of the Goss orientation grain from the rolling direction or the sample surface. Therefore, when the deviation or deviation becomes large, the easy magnetization axis [001] of the Goss orientation grain becomes large. Is significantly deviated or deviated from the rolling direction, and the magnetic characteristics in the rolling direction are inferior. Correspondingly, the γ angle is an angle around the [001] axis (magnetization easy axis) of the Goss azimuth grain, and therefore does not adversely affect the magnetic flux density. Rather, it is said that the larger the γ angle, the greater the magnetic domain subdivision effect, which is desirable.
　Here, the crystal lattice of the grain-oriented electrical steel sheet is a body-centered cubic crystal. [] And () represent the unique direction and the normal direction, and <> and {} represent the equivalent direction and the normal direction of the cubic crystal. Further, in FIG. 1, unique [100], [010], and [001] directions are defined in the right-handed coordinate system regarding the Goss direction. Furthermore, regarding the "direction", the unique case is defined as "direction", and the equivalent case is defined as "direction".
[0012]
　FIG. 2 shows an example of a {200} pole figure of sesame seeds. (2A) is a case of being manufactured by a conventional method having a rolled shape ratio of less than 7, which will be described later, and (2B) is an example of an electromagnetic steel sheet according to the present invention. Both are orientation measurement values ​​of crystal grains having a major axis of 5 mm or less, and (2B) has extremely better iron loss.
[0013]
The
　component composition will be described below. Hereinafter,% means mass%.
　Si: 2.5 to 3.5%
　Si is an element that increases the natural resistance and contributes to the improvement of iron loss characteristics. If it is less than 2.5%, the natural resistance becomes small and the iron loss deteriorates. .. If it is more than 3.5%, breakage occurs frequently in the manufacturing process, especially in rolling, and commercial production is practically impossible.
[0014]
　The components required for grain-oriented electrical steel sheets are Fe and Si, but the remaining elements that are inevitably present will be described below.
[0015]
　Elements that are inevitably contained in the steel sheet body excluding the surface include Al, C, P, Mn, S, Sn, Sb, N, B, Se, Ti, Nb, Cu, and the like. Is separated into elements that are inevitably mixed in industrial production and those that are artificially added to cause secondary recrystallization of directional electromagnetic steel sheets. And it is desired that these unavoidable elements are unnecessary or small in the final product.
[0016]
　C is necessary in the manufacturing process for texture modification. However, in order to prevent magnetic aging, the final product is required to have a small amount, and the preferable upper limit thereof is 0.005% or less, more preferably 0.003% or less.
[0017]
　Although magnetic aging does not occur, elements that are artificially added and are unnecessary in the final product include P, N, S, Ti, B, Nb, and Se. These upper limits are also preferably 0.005% or less, more preferably 0.0020% or less. Al is not always necessary because it exists in the glass coating as mullite.
[0018]
　Al, Mn, Sn, Sb, and Cu are metallic elements, some of which are unavoidably present and some of which are intentionally added, and remain in the final product. It is better to reduce these in order to reduce the saturation magnetic flux density, but it is inevitable that a maximum of about 0.01% remains in the actual manufacturing. The actual content may be adjusted depending on the manufacturing process.
　The content of each element in the grain-oriented electrical steel sheet according to the present invention and the slab for manufacturing the same shall be measured by a general method and general measurement conditions according to the type of the element. Can be done.
[0019]
<
　Product thickness > The product thickness is up to 0.18 mm in actual production. Although it is possible to produce a steel plate thinner than 0.18 mm, when the roll diameter of the rolling mill is large, it is not possible to roll while sufficiently satisfying the thickness accuracy (plate thickness fluctuation of 5% or less). The upper limit of the thickness is set to 0.35 mm or less, which is the upper limit of the Japanese Industrial Standards, because the absolute value iron loss of the grain-oriented electrical steel sheet becomes large. The technique of the present invention is based on the presence of fine secondary recrystallized grains and a magnetic flux density B8 of 1.88 T or more.
[0020]
As is
　well known, the iron loss of grain- oriented electrical steel sheets consists of history loss, classical eddy current loss, and abnormal eddy current loss.
　Since the classical eddy current loss largely depends on the intrinsic resistance and the plate thickness, it is considered that the Si content and the plate thickness are the same even if the secondary recrystallization grain size is different.
　The history loss and the abnormal eddy current loss largely depend on the secondary recrystallization grain size (more accurately, the grain boundary area). The history loss increases when the grain boundary area is large, and the history loss does not increase due to sesame grains (small grain boundary area). On the other hand, the iron loss of grain-oriented electrical steel sheets depends not only on the grain size but also on the magnetic domain structure in the grains, and more specifically, due to the presence of sesame grains in a sharp Goss orientation, large crystal grains (matrix) The present inventor has found that the effect of narrowing the magnetic domain width of (grain or non-sesame grain) can be obtained. In other words, with only large secondary recrystallized Goss grains, the magnetic domain width within the grains is inevitably widened and abnormal eddy current loss increases, but sesame grains with good orientation (sharp Goss orientation). It is considered that the presence of the magnetic domain narrows the width of the magnetic domain (subdivision of the magnetic domain) in the large grain and improves the abnormal eddy current loss. As described above, while the magnetic domain subdivision effect can be obtained by the sesame seeds, there is a concern that the sesame seeds have the effect of increasing the history loss, but at present, it is difficult to quantitatively compare and explain the two. However, in the present invention, since the sesame seeds have a good orientation, it is presumed that this deterioration is small. In addition, the abnormal eddy current loss improved by the magnetic domain subdivision effect of the sesame grains is proportional to the square of the domain wall movement speed, and the movement speed is considered to be approximately proportional to the movement distance. Is considered to be smaller as the crystal grain size is smaller (the movement distance is shorter), that is, the effect of reducing the abnormal eddy current loss is greater.
[0021]
　When the orientation of the sesame grains is the same as that of the coarse grains (matrix grains) as in the present invention, the total iron loss becomes good due to the magnetic domain subdivision effect even if the abundance density of the sesame grains is considerably large. FIG. 3 shows the reasons for limiting the abundance density and size. The reason why the major axis of the sesame seed is limited to 5 mm or less is that the β angle becomes larger when the major axis is larger than 5 mm. As a result, as shown in FIG. 3, the iron loss deteriorates. At present, it is not clear why the β angle increases.
[0022]
　Further, the number density of sesame grains in the metal structure was set to 1.5 grains / cm 2 or more because the iron loss was good as shown in FIG. In general, the higher the number density, the better the iron loss, and the more preferable number density may be 2.0 pieces / cm 2 or more. The upper limit of sesame grain 8 / cm 2 was set to the eight / cm 2 is for commercial production of electromagnetic steel sheet having a secondary recrystallized structure having a greater good Goss orientation can not be present.
[0023]
　FIG. 3 shows data (sesame grain density) when the grain-oriented electrical steel sheet having a Si content of 3.25 to 3.40% and a plate thickness of 0.27 mm has a magnetic flux density B8 of 1.91 to 1.94 T. , The major axis of sesame seeds and the iron loss (W17 / 50) are summarized. The iron loss (W17 / 50) is the iron loss that occurs when the maximum magnetic flux density is 1.7T and the frequency is 50Hz. means.
[0024]
From FIGS. 3 and 5, the lower limit of the density of sesame grains is 1.5 pieces / cm 2 , and the upper limit is that sesame grains occupy half of the entire metal structure and secondary recrystallization is defective. 8 pieces / cm 2 .
　Assuming that the sesame seeds are rectangular and the average length per side thereof is 2.5 mm, the average area of ​​the sesame seeds is 2.5 × 2.5 = 6.25 mm 2 / piece. Further, if half of the metal structure 100 mm 2 (1 cm 2 ) is occupied by the sesame seeds, the area is 50 mm 2 . Therefore, the density of sesame grains when half of the entire metal structure occupy sesame grain, 50 mm 2 /6.25Mm 2 becomes / number = 8. When the density of sesame seeds is 8 pieces / cm 2 or more, secondary recrystallization is defective and the product cannot be commercialized. The density of sesame grains is measured by visually observing or magnifying the cross section of the steel sheet parallel to the rolling direction, including the total thickness of the sheet.
[0025]
<α angle and β angle> From
　FIG. 6, when the α angle and β angle are 7 ° or less and 5 ° or less, respectively, the iron loss is good (preferably the iron loss is 0.93 or less). Is confirmed. This difference is considered as follows. In α and β, the rotation angle (distance) from the Goss direction to the difficult-to-magnetize axis is larger in α, so the magnetic domain subdivision effect in non-fine grains (matrix grains) is large, and the effect is effective in a wide rotation angle range. Presumed to be. This is because if these upper limits are exceeded, the deviation or deviation from the Goss direction becomes large, and the magnetic flux density often becomes less than 1.88 T.
　The crystal orientation is measured by the single crystal orientation measurement Laue method. In the Laue method, the central region of each grain is irradiated with X-rays and measured for each grain.
[0026]

　A method for obtaining a grain-oriented electrical steel sheet having this characteristic will be described.
　The electromagnetic steel sheet which is the subject of the present invention is related to the one specified in Japanese Industrial Standard JIS C 2553 (oriented electrical steel strip), and is mainly used as an iron core for a transformer. In the standard, a plurality of methods are disclosed and realized as the manufacturing method. Its origin is N. P. It goes back to Non-Patent Document 2 of Goss, and is described in the specification of many inventions such as Patent Document 4 and Patent Document 5 thereafter. The electromagnetic steel sheet of the present invention relates to a directional electromagnetic steel sheet containing AlN as a main inhibitor, and has a final cold rolling ratio of more than 80%. Patent Documents 6 and 7 are related technical examples. , Patent Document 8.
[0027]
　Specifically, for example, as a slab component, C: 0.035 to 0.075%, Si: 2.5 to 3.50%, acid-soluble A1: 0.020 to 0 in weight ratio (mass%). .035%, N: 0.005 to 0.010%, at least one of S and Se 0.005 to 0.015%, Mn: 0.05 to 0.8%, Sn, Sb as required , Cr, P, Cu, Ni at least 1 type is contained in 0.02 to 0.30%, and the balance is prepared as a slab composed of Fe and unavoidable impurities. This slab is heated at a temperature of less than 1280 ° C., hot-rolled, hot-rolled plate annealed, one or more cold-rolled with intermediate annealing in between, and hydrogen under the condition that the strip is run after decarburization annealing. Nitriding is performed in a mixed gas of nitrogen and ammonia. When the slab heating temperature is 1280 ° C. or higher, the nitriding treatment does not have to be performed. Next, an annealing separator containing MgO as a main component is applied to perform final finish annealing. Subsequent final cold rolling is performed by reverse rolling. The work roll radius R (mm) of this cold rolling mill is 130 mm or more, the steel sheet is held at 150 ° C. to 300 ° C. for at least 3 passes out of a plurality of passes, and the steel sheet is held at 150 ° C. to 300 ° C. Manufactured on the basis that the rolling shape ratio of 2 or more passes is 7 or more. FIG. 7 is a contour graph of the iron loss W17 / 50 of an electromagnetic steel sheet having a product thickness of 0.27 mm (without tension-applied insulating coating), the horizontal axis is the steel sheet retention temperature during cold rolling, and the vertical axis is cold. The number of inter-rolling passes. From FIG. 7, a region where the retention temperature is 150 ° C. or higher, the number of passes is 2 to 3 or higher, and the iron loss is good is observed, and based on this, the final cold spreading process for obtaining the above-mentioned electrical steel sheet of the present invention is observed. The conditions have been determined. In FIG. 7, a steel sheet to which the tension-applying insulating film is not applied is used, and the iron loss is inferior to that of the steel sheets having the same thickness in Tables 1 and 2 according to Examples described later.
[0028]
　From the viewpoint of a realistic process, it is difficult to secure a steel sheet at 150 to 300 ° C. for 1 minute or more and 3 passes or more without reverse rolling, and in the final cold rolling process of the steel sheet of the present invention, reverse rolling is substantially performed. Is adopted.
　Further, here, the rolled shape ratio m is defined by the following formula.
[Equation 1]

R: Roll radius (mm), H1: Enter side plate thickness (mm), H2: Outer side plate thickness (mm)
[0029]
　Although not bound by any particular theory, large, sharp Goss orientation secondary recrystallization by manufacturing under the above manufacturing conditions, especially the temperature at final cold rolling, the number of passes, and the rolling shape ratio. Fine grains (sesame grains) having a major axis of 5 mm or less and having a similarly sharp Goss orientation can be present in the grains (matrix grains) at a specific frequency. Since this metal structure improves the magnetic domain structure in the large secondary recrystallized grains, it is considered that a grain-oriented electrical steel sheet with improved iron loss can be obtained without deteriorating the magnetic flux density.
Example
[0030]

　Table 1 shows the results of grain-oriented electrical steel sheets produced according to the above process conditions, with Si contained in the steel sheet being 2.45 to 3.55%. In some comparative examples, grain-oriented electrical steel sheets were manufactured under conditions where the Si content was out of the range of the present invention or the above process conditions (particularly, the number of passes of a rolled shape ratio of 7 or more) were not satisfied. .. Inventive Examples A1 to A7 in which the frequency of presence of sesame grains is within the range of the present invention have good iron loss, whereas Comparative Examples a1 to a5 in which the frequency of presence of sesame grains is outside the range of the present invention have iron loss. Inferior or not a product. The iron loss tends to deteriorate as the plate thickness increases. The reason why the iron loss of Invention Example A4 seems to be inferior is that the plate thickness is thick. Further, in Invention Examples A1 to A7, it was confirmed that sesame grains were present in the large matrix grains as shown in the observation photograph of FIG.
[0031]
[table 1]

[0032]
　
　Table 2 shows the relationship between the abundance frequency, orientation and magnetic characteristics of sesame grains having a major axis of 5 mm or less, and the slab heating temperature was set to 1350 ° C. based on Japanese Patent Publication No. 60-48886. The final cold spreading, without nitriding, is the result of being manufactured under the above process conditions. The number of passes with a rolled shape ratio of 7 or more is as described in the remarks column. The product thickness is 0.27 mm. In this range, the higher the frequency of existence of sesame grains or the smaller the total of the deviation angles α and β, the better the iron loss without deterioration of the magnetic flux density. Further, also in Invention Examples B1 to B4, it was confirmed that sesame grains were present in the large matrix grains as shown in the observation photograph of FIG.
[0033]
[Table 2]

The scope of the claims
[Claim 1]
　A directional electromagnetic steel sheet
consisting of Si: 2.5 to 3.5% by mass, the balance Fe and unavoidable elements, and a plate thickness of 0.18 to 0.35 mm, and the metal structure after final annealing is GOSS. The
frequency of existence of Goss-oriented crystal grains having a major axis of 5 mm or less in the metal structure, which includes matrix grains of azimuth secondary recrystallized grains and is 5 mm or less, is 1.5 pieces / cm 2 or more and 8 pieces. / Cm 2 or less, magnetic flux density B8 is 1.88 T or more,
and the deviation angle of the Goss directional crystal grain from the rolling direction in the [001] direction is
7 ° or less as a simple average of α angle and β angle, respectively. And a directional electromagnetic steel plate characterized by being 5 ° or less.
Here, the α angle and β angle are shown below.
α angle: Angle between the longitudinal direction (rolling direction) and the [001] axis of the Goss directional grain and the projection of that orientation on the surface of the rolling surface
β angle: The [001] axis of the Goss directional grain is the rolled surface The angle to make.