# A New Approach to Measure Fundamental Microstructural Influences on the
Magnetic Properties of Electrical Steel using a Miniaturized Single Sheet
Tester

N. Leuning<EMAIL_ADDRESS>M. Heller  M. Jaeger  S. Korte-
Kerzel  K. Hameyer  Institute of Electrical Machines (IEM), RWTH Aachen
University, D-52062 Aachen, Germany  Institute for Physical Metallurgy and
Materials Physics (IMM), RWTH Aachen University, D-52062 Aachen, Germany

###### Abstract

Magnetic properties of electrical steel are usually measured on Single Sheet
Testers, Epstein frames or ring cores. Due to the geometric dimensions and
measurement principles of these standardized setups, the fundamental
microstructural influences on the magnetic behavior, e.g., deformation
structures, crystal orientation or grain boundaries, are difficult to separate
and quantify. In this paper, a miniaturized Single Sheet Tester is presented
that allows the characterization of industrial steel sheets as well as from in
size limited single, bi- and oligocrystals starting from samples with
dimensions of 10 x 22 . Thereby, the measurement of global magnetic properties
is coupled with microstructural analysis methods to allow the investigation of
micro scale magnetic effects. An effect of grain orientation, grain boundaries
and deformation structures has already been identified with the presented
experimental setup. In addition, a correction function is introduced to allow
quantitative comparisons between differently sized Single Sheet Testers. This
approach is not limited to the presented Single Sheet Tester geometry, but
applicable for the comparison of results of differently sized Single Sheet
Testers. The results of the miniaturized Single Sheet Tester were validated on
five industrial electrical steel grades. Furthermore, first results of
differently oriented single crystals as well as measurements on grain-oriented
electrical steel are shown to prove the additional value of the miniaturized
Single Sheet Tester geometry.

###### keywords:

Electrical steel , Miniaturized Single Sheet Tester , Single Crystals ,
Deformation , Grain boundaries , Electrical steel , FeSi

††journal: Journal of Magnetism and Magnetic Materials

##  1 Introduction

Magnetic properties of non-grain oriented (NO) and grain oriented (GO)
electrical steels are usually obtained by measurements on standardized
measurement sensors according to international standards, such as IEC-60404.
For the macroscopic evaluation of the magnetic properties of electrical steel
sheet this is sufficient. However, for a more detailed consideration of
microstructural effects on the magnetic properties these standardized sensors
are not suitable as the results are insufficiently spatially resolved. In
order to improve the understanding of the interrelations between grain
orientation, grain boundaries and deformation mechanisms on the one hand and
magnetic properties on the other hand, a miniaturized Single Sheet Tester
(SST) was constructed and initial results are presented in this paper.

Electrical steel sheet is used as magnetic core material for electrical
machines, thus the magnetic properties are of main concern in the material
selection [1]. Electromagnetic simulations are performed during the design
stage of electrical machines to determine the relation between design,
material choice and operational behavior of the machine. For such
electromagnetic simulations, the magnetic properties of the electrical steel
sheet material in question have to be modeled based on magnetic measurements
of the magnetic permeability and iron loss [2]. These characteristic values
are used to compare different electrical steel grades. With standardized
measurement setups, the non-linear material behavior can be analyzed,
different grades can be compared and iron loss models can be parameterized.
Consequently, standardized measurements are crucial for the general
application of electrical steel in electrical machines. For the development of
improved electrical steel grades and advanced material models, advanced
magnetic characterization approaches have to be utilized that go beyond
standardized characterization techniques. Advanced methods that are used today
include the consideration of vector characteristics of magnetic flux $B$ and
magnetic field $H$, two-dimensional excitation conditions, rotating magnetic
fields or local magnetic properties [3, 4, 5]. However, these techniques are
mainly designed for polycrystalline sheet materials. In order to further study
fundamental magnetization mechanisms of NO and GO steel another approach has
to be developed that enables the quantification of effects on a grain scale.

In order to study individual fundamental microstructure influences, we
developed a Miniature Single Sheet Tester (Mini-SST). The minimum sample size
is 10 x 23 . These sample dimensions allow the investigation of grown single
crystals with specific orientations, grown bi-crystals with defined grain
boundaries or oligocrystals with specifically adjusted deformation structures
[6]. The measurements of the magnetic properties are not locally resolved
within the 10 x 17 measurement area of the sample, but the Mini-SST results
are coupled with materials science microstructure investigation methods, i.e.,
hardness measurements, optical microscopy, X-ray diffraction, or electron
backscatter diffraction (EBSD) [6]. This approach allows a correlation between
crystallographic texture [7], grain boundaries [8] and deformation mechanisms
[9] with the magnetic properties. In addition, due to the small sample size,
characterization of polycrystalline materials on a laboratory or industrial
scale becomes possible even if the sample volume is small, e.g. during sample
preparation of a manufactured motor.

##  2 Miniaturization of a SST

###  2.1 Standardized Measurement Setups

In general, three methods are used for the standardized magnetic
characterization of electrical steel, namely Epstein frames, SST and ring core
measurements. In this study, the SST was miniaturized to allow the
investigation of fundamental microstructural effects. In practice, none of the
three standardized characterization methods outperformed the others, as they
all have different advantages and disadvantages. Detailed information on these
methods can be found in DIN EN 60404 [10], nevertheless a brief comparison is
made here to illustrate the idea of the Mini-SST.

The measurement principle of all three methods can be summarized as follows: A
magnetic field is generated by a current running through a copper winding
(magnetization coil). The rectangular or ring shaped electrical steel sample
is placed in this magnetic field and a secondary copper winding (induction
coil) is placed as close as possible to the sample. The voltage, which is
induced in this secondary induction winding is proportional to the flux
density within the sample. Differences between the setups stem from the sample
geometry on the one hand and the magnetic flux path on the other hand. In a
ring shaped sample, the magnetic flux is closed entirely by the sample. In an
Epstein frame, four electrical steel strip legs are positioned in a rectangle
with overlapping edges to close the magnetic flux path entirely by the sample
material. In a SST, there is only one sheet sample, which makes it impossible
to close the magnetic path over the sample, thus, a double c-yoke is required.
These macroscopically different magnetic flux paths lead to differences in the
magnetic flux distribution across the sample cross sections. For example, due
to the different magnetic path length at the outer and inner circumference of
the ring cores and on the four legs of an Epstein frame, a flux concentration
at the inner diameter occurs before the material is fully saturated. The
resulting flux density distribution in the sample cross sections is
inhomogeneous and thus, describes an averaged flux density within the sample.
For the purpose of this study, it is necessary to have a homogenous flux
density condition within the sample. In a SST, the flux density distribution
is homogeneous over the cross section. However, the yoke that is needed to
close the magnetic flux can lead to additional losses and are determined by
the yokes geometry. This is an effect that needs to be accounted for during
the validation of the Mini-SST setup and is discussed in the following
sections. Sample sizes for a SST can be as large as 500 x 500 , whereas
samples for the Epstein frame are 280 x 30 . The newly designed Mini-SST
allows a minimum size of 10 x 22 .

###  2.2 Mini SST - Geometry

The purpose of the Mini-SST is to enable a detailed characterization of the
magnetic properties of single, bi- and oligo-crystals with dimensions
achievable by crystal growth [6]. Since the size of samples produced by
crystal growth are in the range of $2\text{\,}{\mathrm{cm}}^{2}$, a
correspondingly small SST was developed in cooperation with Brockhaus
Measurements. The outer distance between the magnet yoke legs of the Mini-SST
is about $22\text{\,}\mathrm{mm}$ defining the minimum sample length, however,
the free magnetic path length $l_{\text{m}}$ between the yoke poles is about
$16\text{\,}\mathrm{mm}$. Consequently, the pole thickness is
$3\text{\,}\mathrm{mm}$ on each side. Both, the primary winding $N_{1}$ and
secondary winding $N_{2}$ have 60 turns each. The Mini-SST is controlled by an
MPG 200 test bench from Brockhaus Measurements. A picture of the Mini-SST is
displayed in Fig. 1.

Magnetic properties are measured by means of electric measurements, i.e.,
electric current and voltage. The required current is supplied by a power
amplifier. Thereby, a magnetic field is created by the primary magnetization
winding. The current is measured by means of a temperature-stable, low
inductivity precision resistor. Polarization is determined by measuring the
induced voltage in the secondary induction winding. The parallel recording of
magnetic field $H$ and magnetic polarization $J$ with separate analogue-
digital converters enables simultaneous measurement. A control algorithm is
used to ensure sinusoidal excitation, where the secondary voltage can be
checked and constantly regulated in accordance with the nominal value. The
nominal voltage is supplied by a highly stable, digital frequency generator.
Amplitude and frequency are set by software according to the sample data
entered and the default values, according to the MPG 200 and MPG Expert
Software.

Figure 1: Photograph of the 10 x 22 Mini-SST.

##  3 Description of the Correction Function

It is well known that the characterization of magnetic properties strongly
depends on the geometric conditions of the measurement setup, e.g., Epstein
frame to SST as well as differently sized SST, which are summarized in [11].
Even different laboratories with similar geometric conditions, as presented in
[12] for Epstein measurements, come to different results. Therefore, the
comparability between measurement results becomes a matter of reference
samples as well as measurement and correction techniques. To ensure
comparability between the Mini-SST measurements and previous measurements of
the authors, a general correction function is developed and parameterized to
the reference SST of the Institute of Electrical Machines (IEM).

In Fig. 2, magnetization curves tested at $50\text{\,}\mathrm{Hz}$ are
displayed for three differently sized SST s of 120 x 120 , 60 x 60 and 10 x 20
. To ensure comparability, the same sample was measured on all SST s. A strip
of $d_{\text{strip}}=$ $10\text{\,}\mathrm{mm}$ and $l_{\text{strip}}=$
$120\text{\,}\mathrm{mm}$ was utilized for this. To account for the cut-edge
effect, the sample for the filled 120 x 120 SST consisted of 12 sample strips
each with a width of $10\text{\,}\mathrm{mm}$ and a length of
$120\text{\,}\mathrm{mm}$ that are taped together according to [13]. When
looking at the magnetization curves, two effects can be observed. At low
magnetic fields $H$, as can be seen in Fig. 2 (a), the smaller SST s generally
show lower magnetization compared to larger SST s. Furthermore, the curves for
one $10\text{\,}\mathrm{mm}$ sample strip are identical to those for a fully
filled SST (12 $\times$ $10\text{\,}\mathrm{mm}$) at low magnetic fields. At
high magnetic fields $H$, the fully filled reference SST shows the hardest
magnetization behavior right before the 10 x 20 SST. Both, the 60 x 60 SST and
the reference SST with just one sample strip need much lower field strengths
to seemingly magnetize the sample to $1.8\text{\,}\mathrm{T}$.

The observed behavior is attributed to two separate effects. The first one is
linked to the magnetic resistance of the yoke, whereas the second effect is
linked to the influence of stray flux within the unfilled coil cross section.
Due to the required size of the yoke’s pole width, non-ideal conditions in the
ratio of the free magnetic path length and the yoke height occur, when the SST
is downscaled. Thereby, the permeability of the yoke becomes an important
factor. Moreover, at high magnetic fields, the air flux needs to be
considered. The free space in the coil depends on the solenoid housing, which
is fixed and the respective sample cross section (i.e. sample thickness and
width). This explains the strong difference between the results for the filled
and non-filled reference SST, as well as for the differently sized SST s with
different solenoid housing.

(a) Low magnetic fields. (b) High magnetic fields.

Figure 2: Measurements of a M330-50A (M1) reference sample of
$d_{\text{strip}}=$ $1\text{\,}\mathrm{cm}$ on differently sized SST s for the
low (a) and high magnetic field region (b) and a measurement of 12 strips
resp. of $d_{\text{strip}}=$ $1\text{\,}\mathrm{cm}$.

To account for these differences and ensure comparability, a correction
function for the $B(H)$ measurement results has been developed and
parametrized to the 120 x 120 IEM SST, which, as previously stated, serves as
the reference SST within this study. Again, the correction function for the
Mini-SST is necessary to account for the magnetic resistance of the yoke and
the air flux in the solenoid, which enables a quantitative comparison to the
reference SST. The proposed method describes a general approach, that can be
transferred to other research facilities and SST sizes to improve
comparability between measurement setups and research facilities.

For a designated reference SST, certain assumptions have to be made. Firstly
that the reference SST is ideal and only measures the resistance of the
sample. Hence, there is no stray flux outside the yoke, which has a
permeability $\mu_{\text{r}}=\infty$. Therefore, the magnetic resistance is
only composed of the resistance of the sample and the air in the coil. As a
framework for the correction function a magnetic equivalent circuit is used
(Fig. 3), where:

  * 1.

Mini-SST geometry is known: $A_{\text{yoke}}$ $l_{\text{yoke}}$

  * 2.

Sample geometry is known: $A_{\text{sample}}$ $l_{\text{sample}}$

  * 3.

Magnetic flux is known: $\Phi=I\cdot N$ and

  * 4.

Total flux linkage $\Psi=\Psi_{\text{Air}}+\Psi_{\text{Sample}}$

with $A$ representing a cross section, $l$ representing a length, $I$
describing an electric current and $N$ the number of turns. The magnetic
resistance can generally be calculated using the following equation:

$R_{\text{mag}}=\frac{l}{\mu_{0}\mu_{\text{r}}A}~{}.$ (1)

Figure 3: Magnetic equivalent circuit framework to calculate a SST correction
function.

###  3.1 Correction of the Magnetic Field Strength

The measured magnetization curves $B_{\text{meas.}}(H_{\text{meas.}})$ of the
Mini-SST cannot be directly compared to the reference, as previously stated,
thus a corrected $B_{\text{meas., corr.}}(H_{\text{meas., corr.}})$ has to be
calculated. Inputs for the calculation of the corrected magnetic field
$H_{\text{meas.,corr.}}$ are the measured flux density $B_{\text{meas.}}$ in T
and the measured magnetic field strength $H_{\text{meas.}}$ in A/m. With the
following equations the corrected field strength can be determined.

The total flux linkage $\Psi$ can be calculated from the flux density
$B_{\text{meas.}}$ in the sample as given by the measurement system and the
cross section of the sample $A_{\text{sample}}$, which is determined
geometrically (thickness $x$ width).

$\Psi=B_{\text{meas.}}\cdot A_{\text{sample}}$ (2)

The magnetic flux $\Phi$ is the product of the measured magnetic field
strength $H_{\text{meas.}}$ and the magnetic path length $l_{\text{m}}$
between the yoke legs of the Mini-SST according to

$\Phi=H_{\text{meas.}}\cdot l_{\text{m}}~{}.$ (3)

With the information of $\Psi$ (eq. (2)) and the cross section of the yoke
pole surfaces $A_{\text{yoke}}$, the magnetic flux density in the yoke
$B_{\text{yoke}}$ can be calculated

$B_{\text{yoke}}=\frac{\Psi}{A_{\text{yoke}}}$ (4)

For the calculation of the magnetic field in the yoke $H_{\text{yoke}}$, the
permeability of the yoke needs to be determined. As this value cannot be
directly measured, a fitting has been performed. As depicted in Fig. 4, the
permeability of the yoke is fitted to $B_{\text{yoke}}$ measurement values
below $0.07\text{\,}\mathrm{T}$ of two materials and can be described by the
following empirical equation:

$\mu_{\text{r, yoke}}=\frac{7750}{1+2^{-160\cdot B_{\text{yoke}}}}-2000$ (5)

$H_{\text{yoke}}=\frac{B_{\text{yoke}}}{\mu_{\text{r,
yoke}}\cdot\mu_{\text{0}}}$ (6)

With equations (2) to (6), all the variables needed to calculate the corrected
magnetic field taking the yoke permeability into account are known, resulting
in the following equation:

$H_{\text{meas.,corr.}}=\frac{1}{l_{\text{m}}}\cdot(\Phi-
H_{\text{yoke}}l_{\text{yoke}})~{}.$ (7)

Figure 4: Determination of the fitting function to account for the
permeability of the Mini-SST yoke.

###  3.2 Correction of the Magnetic Flux Density

To account for the influence of stray flux, $H_{\text{stray}}$ (8) and
$B_{\text{stray}}$ (9) are calculated with the help of the magnetic flux
$\Phi$ and the properties of the yoke. These parameters are used to
subsequently determine the flux $\Psi_{\text{stray}}$ and
$\Psi_{\text{sample}}$ in equations (10) and (11).

$H_{\text{stray}}=\frac{1}{l}_{\text{stray}}\cdot(\Phi-
H_{\text{yoke}}l_{\text{yoke}})$ (8)

$B_{\text{stray}}=H_{\text{stray}}\cdot\mu_{0}$ (9)

$\Psi_{\text{stray}}=B_{\text{stray}}\cdot A_{\text{coil}}$ (10)

$\Psi_{\text{sample}}=\Psi-\Psi_{\text{stray}}$ (11)

The value for the length of the magnetic stray lines $l_{\text{stray}}$ is
based on the assumption that the flux lines are longer than the direct
connection between the poles of the magnetic yoke $l_{\text{m}}$, which is
$16\text{\,}\mathrm{mm}$. A value of $+12.5\%$ is assumed, which, in our case,
corresponds to $18\text{\,}\mathrm{mm}$. The free cross section of the
solenoid $A_{\text{coil}}$ is approximated with the help of geometrical
measurements to be $42\text{\,}{\mathrm{mm}}^{2}$. Finally, the corrected flux
density $B_{\text{meas. corr}}$ in the sample can be determined according to
(12):

$B_{\text{meas. corr.}}=\frac{\Psi_{\text{sample}}}{A_{\text{sample}}}~{}.$
(12)

(a) Low magnetic fields. (b) High magnetic fields.

Figure 5: Measurements and corrected $B(H)$-curves of Material 1 (M330-50A).

In Fig. 5 results of the corrected $B(H)$-curves are displayed in comparison
to the uncorrected measurements on the Mini-SST and measurements of the same
material on the reference SST. It is evident that the identified and fitted
parameters of the correction function lead to a measurement data correction
that enables a quantitative comparison between the differently sized SST s. In
both the low and high $H$ region, the curves for the reference and corrected
$B(H)$ characteristics are virtually congruent.

##  4 Validation of the Correction Function

Figure 6: Measurements and corrected $B(H)$-curves of Material 2. Figure 7:
Measurements and corrected $B(H)$-curves of Material 3. Figure 8: Measurements
and corrected $B(H)$-curves of Material 4. Figure 9: Measurements and
corrected $B(H)$-curves of Material 5.

In order to validate the correction function, the approach is tested on a
total of five different materials with different chemical compositions, grain
sizes, sheet thicknesses and resulting magnetic properties. An overview of the
tested materials is given in Table 1.

| $d_{\text{sheet}}$ | orientation | $d_{\text{GS}}$
---|---|---|---
Material M1 | $0.50\text{\,}\mathrm{mm}$ | NO, RD | 52 $\muup$m
Material M2 | $0.35\text{\,}\mathrm{mm}$ | NO, RD | 69 $\muup$m
Material M3 | $0.27\text{\,}\mathrm{mm}$ | NO, RD | 134 $\muup$m
Material M4 | $0.20\text{\,}\mathrm{mm}$ | NO, RD | 95 $\muup$m
Material M5 | $0.18\text{\,}\mathrm{mm}$ | GO, TD | $1\text{\,}\mathrm{cm}$
Table 1: Nominal thickness $d_{\text{sheet}}$, orientation and mean grain
diameter $d_{\text{GS}}$ of the studied materials.

In Fig 6 to Fig. 9 the results are displayed for all materials. In general,
the correction function improves the compatibility for all materials, however,
the results for M1 show the best result. This could be due to the small grain
size, together with the effect of crystal orientation and resulting stray
fields. This is a topic that can further be studied with the validated Mini-
SST. The correction function can also be applied to GO material, which helps
the interpretation of results for single crystals due to the large grains and
variable sample orientation. As the purpose of the Mini-SST is the
characterization of samples that cannot be tested on a reference SST due to
their size, the function cannot be parametrized on each material but must be
generally applicable. The results presented suggest that a quantitative
comparison is enabled with sufficient accuracy.

##  5 Measurements of undeformed single crystals and GO material

In this section, preliminary results of Mini-SST measurements of single
crystal as well as GO material coupled with EBSD measurements are presented.

(a) Low magnetic fields (IEM Mini-SST results). (b) High magnetic fields
comparison of IEM and Honada et al. results. (c) Low magnetic fields (after
[14].

Figure 10: Results of single crystal measurements and comparison to literature
data [14].

The single crystals were produced on a self build induction furnace that works
according to the Bridgman Stockbarger method. Subsequently, the sheet
geometry, necessary for the Mini-SST, was cut out of the cylindric crystal
growth geometry with the help of an electrical discharging machine. To make
sure that no heat affected layer or deformation layer remains the sample was
etched with nitric acid ($100\text{\,}\mathrm{mL}$ HNO3,
$150\text{\,}\mathrm{ml}$ H2O), mechanically grinded and polished and the
final surface finish for EBSD was achieved with electro polishing (A2 without
water for $15\text{\,}\mathrm{s}$ at $24\text{\,}\mathrm{V}$). A detailed
description can be found in [6, 15]. The GO material was cut from industrial
transformer sheets with a strong Goss texture along different orientations
relative to rolling direction (RD).

The single crystals were characterized on the Mini-SST at
$50\text{\,}\mathrm{Hz}$ with peak inductions between $0.1\text{\,}\mathrm{T}$
and $1.5\text{\,}\mathrm{T}$ in $0.1\text{\,}\mathrm{T}$-steps. The
magnetization curves $J(H)$ are shown in Fig. 10 (a). The magnetic anisotropy
of the three common axes is clearly visible. Magnetization of the [100] single
crystal is easiest, as expected. At first sight, the curves for the [110] and
[111] single crystals show an unexpected behavior as the magnetization in
[110] seems to be harder compared to the [111] direction. In order to examine
this behavior further, the results have been compared to the data of Honda et
al. [14] and their work on the magnetization behavior of single crystalline
iron, which is shown in Fig. 10 (b). It can be seen that the results actually
show similar behavior when looking at higher field strengths. Due to the
different measurement setup, Honda was able to measure higher field strength
up to saturation. The slight differences of the curves can stem from the
difference in chemical composition as well as the manufacturing and
preparation of samples. Looking at the low magnetic field region, as displayed
in Fig. 10 (c) the same initial crossing of the [110] and [111] curves can be
observed, which could have been due to measurement scatter of Honda’s results
but shows a smooth transition for the Mini-SST measurements. In ongoing work,
the single crystals, from which the here analyzed samples have been cut, are
subsequently plastically deformed in several steps. After each step, one sheet
sample is cut for Mini-SST measurements. This is an additional advantage of
the Mini-SST setup as all deformed samples can be cut out of the same single
crystal  [15].

(a) EBSD measurements of the pole figures and exemplary sample preparation.
(b) Magnetization curves at $50\text{\,}\mathrm{Hz}$.

Figure 11: Results of industrial GO sheet measurements.

In a second example, results of industrial GO Mini-SST measurements are
displayed in Fig. 11. Six samples per sheet direction in RD ($None$),
transverse direction (TD) ($None$) and diagonal sheet plane direction ($None$)
have been cut from industrial GO sheet. Due to the crystallographic
orientation of the present Goss grains, the sample directions along
magnetization direction correspond to the [100], [110] and [111] direction of
the unit cells. EBSD measurements were performed on the samples to validate
the crystallographic orientation. Inverse pole figures, as depicted in Fig. 11
(a), show which crystallographic plane normal is parallel to a particular
sample axis, in this case the rolling direction. Therefore, points in the
triangle show the exact orientation of these crystallographic plane normals
relative to the rolling direction and the colour groups them into near 100
(red), 110 (green) and 111 (blue). The corresponding magnetization curves are
shown in Fig. 11 (b). These results correspond very well to the single crystal
measurements in Fig. 10 (a). Both, GO and the single crystals have pronounced
crystal orientations. With a SST, magnetic field $H$ and magnetic polarization
$J$ are treated as scalar properties, although they are actually vectors. For
the [100] single crystal and GO cut in RD, the vector and scalar values are
expected to be equal, as the easy magnetization direction, an thus,
orientation of magnetic domains are aligned parallel with the magnetic field
generated perpendicular to the magnetizing coil. For differently oriented
single crystals and GO which is cut in unfavourable directions, this is not
the case and the domains want to align in the easy directions, which are not
parallel to the induced magnetic field. Only the polarizations vector
component parallel to the magnetic field is obtained. When the sample
approaches saturation, the domains are forced out of the easy directions into
the direction of the applied magnetic field. As a result, the mismatch of
vector and scalar properties decreases at high polarizations. The systematic
error of neglecting vector properties needs to be accounted for in the
evaluation and interpretation of results of SST measurements in general.
However, this systematic error is inherent of the SST setups and its scalar
consideration of vector properties. As the approach wants to enable a
comparison between different SST, the fundamental measurement principle is not
changed.

In the examples given, the chemical composition and sample preparation are
different, nevertheless both examples show how the influence of orientation
can be analyzed without the influence of high angle grain boundaries. In
ongoing work, bi-crystals have been successfully grown and subsequently
deformed to study the effect of high angle grain boundaries as well as their
deformation behavior. In the future, these measurements may be correlated in
more detail with microstructural parameters that can be controlled and
quantified in such small samples, such as dislocation density and domain
distribution. The measurements and validations shown here highlight that small
scale characterisation is a promising method to better understand the
characteristics of microstructural parameters of electrical steel.

##  6 Conclusions

In this paper a miniaturized SST is presented that has been designed to study
fundamental microstructural effects on the magnetic properties of electrical
steels. A correction function is developed to account for the non-ideal
geometric conditions of the setup, i.e., the air flux in the solenoid and the
yoke pole to sample ratio, to allow a comparison to a reference SST. A
validation of the correction function is performed on five industrial
materials. The results of this paper can be summarized in the following
points:

  * 1.

The validation shows that measurement results of the Mini-SST can be
quantitatively compared to those established reference SST setups, after a
one-time parametrization on industrial steel sheet.

  * 2.

The correction function approach can be transferred to other SST setups, as it
mainly depends on geometric conditions and a measurement at low magnetic
fields to determine a fitting function for the permeability of the yoke.

  * 3.

Fundamental micro magnetic effects of orientation, deformation and grain
boundaries can be assessed as sample the minimum sample size allows the
analysis of grown single-, bi- and oligo crystals. Additional microstructural
analysis is necessary to link the effects to the magnetic results.

  * 4.

In case of industrial NO and GO material, the Mini-SST can be useful in cases
where sample material is sparse, i.e., experimentally produced laboratory
grades or materials of manufactured machines.

With the Mini-SST and parametrized correction function, studies of the
microstructure influences and of industrial NO can be performed analogous to
usually sized SST. A quantitative comparison is enabled. The challenge in the
transfer of the correction function to various sized SST lies in the
determination of the geometric parameters and especially in the assumption of
the stray field length. The value cannot be directly measured so needs to be
fitted empirically or possibly simulated.

## Acknowledgement

The Mini-SST was funded by the Deutsche Forschungsgemeinschaft (DFG, German
Research Foundation) as part of the DFG-research group – ”FOR 1897 – Low-Loss
Electrical Steel for Energy-Efficient Electrical Drives”.

##  7 References

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URL https://arxiv.org/pdf/2302.03808