Structural Heterogeneity of an Amorphous-Nanocrystalline Alloy
Fe77Cu1Si16B6 in the Nanometer Range
FROLOV A.M., ANSOVICH A.V., KRAYNOVA G.S., TKACHEV V. V., DOLZHIKOV,
S.V., PLOTNIKOV V.S., RALIN A.YU., FEDORETS A. N.
Far Eastern Federal University
FEFU Campus, 10 Ajax Bay, Russky Island, Vladivostok, 690922,
RUSSIAN FEDERATION
Abstract: In this article, an alloy of the Finemet type Fe77Cu1Si16B6 obtained by quenching from a liquid state
(spinning method) in the initial state is investigated. The main research methods were scanning and transmission
electron microscopy. Methods for describing multiscale structural heterogeneities in amorphous-nanocrystalline
alloys have been developed, allowing the structural state to be described and its influence on the physicochemical
and technical properties to be determined depending on the technological conditions for obtaining these alloys.
Representation of electron microscopic images in the form of Fourier spectra made it possible to reveal the nature of
the formation of short- and middle-order in amorphous-nanocrystalline alloys according to the principle of self-
similar spatial structures. The analysis of electron microscopic images by integral Lebesgue measures revealed
density fluctuations over the alloy volume, which corresponds to the hierarchical representation of structural
inhomogeneities in amorphous metallic alloys.
Keywords: amorphous nanocrystalline alloys, Fourier analysis, anisotropy, heterogeneity, density fluctuations.
Received: April 2, 2021. Revised: November 2, 2021. Accepted: December 13, 2021. Published: January 5, 2022.
1. Introduction
odern scientific and technological progress is
have a pronounced hierarchical structure of various spatial
scales of inhomogeneity, which provides their special physical
properties during the applications [5].
Due to their physical properties, Fe-based alloys have
become the most interesting for practical applications (in
magnetic recording heads, transformers, electronic devices,
etc.) [20], [21]. Knowledge of the correlation of the structure,
as well as the mechanism of its formation, gives a
clear understanding of the known properties of materials,
including Finemet, that will allow them to be improved
and also to obtain new ones with given characteristics and
devices based on them. Thus, the issues related to the study
of the structure of alloys are extremely topical [1], [2], [3],
[13], [14], [15], [16].
The most informative group of methods for studying the
structure is electron microscopy. Electron microscopy
supplemented by analytical methods of statistical analysis
makes it possible to find the regularities of the structural
ordering of materials [3].
This paper aims to investigate the different scale
substructural heterogeneities in the Fe77Cu1Si16B6 alloy
obtained by rapid quenching from the melt. Not only structural
heterogeneities, but also their distribution, anisotropy, form
factor, and their interconnection at different scale levels, are
considered.
2. Objects and research methods
The objects of study were electron microscopic images of a
Maccompanied, on the one hand, by the creation of
fundamentally new technologies and processes, on the other -
requires the use of materials that are more relevant today. The
latest technologies make it possible to improve already known
materials or create new ones.
Partially crystalline alloys (Finemet) are a new class of
materials obtained by rapid quenching from a liquid state.
Moreover, in terms of physical and mechanical properties,
such two-phase systems are superior to the properties of both
nanocrystalline and amorphous materials, thereby creating a
noticeable synergistic effect [1], [2], [3], [4], [5], [6], [7], [8],
[9]. Amorphous metallic alloys present short (0.2 to 0.5 nm.)
and medium range order (0.5 to 2 nm.), it is confirmed by
various experimental methods, including transmission
electron microscopy (TEM) [3], [10], [11], [12]. High-
resolution TEM (HRTEM) makes it possible to
determine the levels of inhomogeneities of different
subnanometer spatial scales in amorphous metallic alloys
obtained by rapid quenching from the melt. The crystalline
phase has an ordered atomic structure, the atomic structure of
the amorphous phaseis devoid of translational symmetry and
has only pronounced topological and compositional short-
range orders. Consequently amorphous-nanocrystalline
materials can be considered natural composites, which have
important properties for practical use [13], [14], [15], [16],
[17], [18], [19]. Such materials
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
8
Volume 17, 2022
spinning tape Fe77Cu1Si16B6 obtained using a TITAN 300
transmission electron microscope (TEM), as well as images of
the interfaces of a spinning tape (contact to the quenching disk
and free from its influence) obtained using a scanning electron
microscope Carl Zeiss Crossbeam 1540XB (SEM) [22], [23],
[24], [25]. The thickness of the samples is ~ 20 μm; therefore,
they were thinned for transmission electron microscopy.
Bright-field images of a spinning ribbon were obtained from
areas near the contact and free interfaces.
For all rapidly quenched alloys, a Fourier spectral analysis
was carried out, including the following: integral frequency
response (IFR), which allows numerically determining the
range of inhomogeneities present in the studied structure and
integrated spatial characteristic (ISC), based on which it is
possible to judge the isotropy / anisotropy of the studied
structure [26], [27], [28], [29], [30].
3. Results and Discussion
The conditions for obtaining alloys by rapid quenching
from the liquid state are highly disbalanced due to significant
cooling rates ~106 deg/s, and gradT ~ 100 deg/μm, and other
factors [1], which can lead to "freezing" of the short-range
order.
The result of the performed X-ray structural analysis of the
Fe77Cu1Si16B6 sample using γ-radiation from Cu (Кα, λ = 1.54
A) is shown in Fig.1. The calculation of the effective
penetration depth of X-ray radiation into the alloy of the given
composition is (3 - 4) microns. Since the thickness of the
spinning tape is ~ 20 μm, the profiles of X-ray diffraction
patterns from the contact and free interfaces of the sample
were obtained, Fig.1. The X-ray diffraction patterns from the
contact surface contain “crystalline” peaks, corresponding to
α-Fe solid solution with a chemical composition similar to the
Fe3Si, the size of the coherent scattering region is 1.5 nm. The
structure of the spinning ribbon on the free-side from the
influence of the cooling cylinder is X-ray amorphous, Fig.1.
Thus, the structure of the spinning Fe77Cu1Si16B6 ribbon at the
atomic level is represented by two components - amorphous
and nanocrystalline. The obtained result suggests the existence
of stratification, and the material can be considered as
amorphous-nanocrystalline. The translational symmetry of the
nanocrystalline phase and its absence in the amorphous matrix
leads to distinctive physical properties of the material [1].
Fig.1. Profiles of X-ray diffraction patterns of a spinning
ribbon Fe77Cu1Si16B6, obtained from various interfaces.
Fig.2. Electron-microscopic image of the structure of a
spinning ribbon Fe77Cu1Si16B6 from area a) close to the
contact surface; b) close to the free surface. Tabs show Fourier
spectrum of image data and integrally spatial characteristic of
periodicities: short wavelength λ1 (c, f); medium wavelength
λ2 (d); long wavelength λ3 (e, g) ranges.
Fig.2 shows electron microscopic TEM images of a
spinning ribbon from regions near the contact (a) and free (b)
surfaces, which demonstrate a homogeneous structure of the
“salt-pepper” type with a clearly distinguishable period of
inhomogeneities (wavelength) λ1 ~ 0.2 nm. A detailed analysis
of the image makes it possible to visualize the combination of
short-wavelength periodicities into larger irregularities with a
period of ~ 0.7 nm and more. However, visual analysis of the
image does not allow us to assess the structure anisotropy.
Fig.2 also shows the results of spectral analysis of the
obtained TEM images of spinning ribbon from regions close
to the interfaces and calculated by IFR and ISC.As a result of
the spectral analysis of electron microscopic images of
spinning ribbons, the following was obtained: the structure of
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
9
Volume 17, 2022
the studied foils consists of inhomogeneities of various sizes,
which correspond to certain frequency modes.
Three ranges of sizes of inhomogeneities were distinguished
– short-wavelength, λ1 = 0.2 nm; medium wavelength, λ2 =
(0.4 - 0.7) nm; long wavelength, λ3 = (1.36 - 2.27) nm.
An analysis of the ISC of the Fourier spectrum for the area
near the contact surface showed a high degree of anisotropy of
the structure for short wavelength and medium wavelength
(Fig.2c,d). The mesoscale inhomogeneities with wavelength λ2
are characterized by the existence of dispersion (~ 200) in their
distribution. For the area near the free interface of the spinning
ribbon, the distribution of inhomogeneities short range order is
isotropic (the anisotropy coefficient ɛ in the two directions is
the same and is, ɛ ~ 1.3, Fig.2f).
Note that the form of the ISC for the periodicities of the
long wavelength range (λ3) with the presence of several
distinguished axes, Fig.2, do not make a significant
contribution to the integral structure anisotropy, Table I.
Table I. Characteristics of nanostructured and
morphological inhomogeneities.
SEM
Contact surface
ɛ
Λ, µm
ɛ
Λ, µm
1
1.75
2.8
1
3.2
2
3
7.2
2
7.7
3
3.6
20.3
3.3
18.1
TEM
The area close to
the contact surface
ɛ
λ, nm
ɛ
λ, nm
1
1.8
0.2
1.3
0.2
2
1.34
0.6
1.14
0.5
3
1
1.8
1
1.62
Spinning ribbons Fe77Cu1Si16B6 have two surfaces with
different morphological. Fig. 3a shows an electron
microscopic image of the contact surface of a spinning ribbon
with a developed relief in the form of rolling strips and
caverns of various sizes, shapes and orientations. An analysis
of the image revealed a spectrum of inhomogeneities: from
small ones with a period of ~ 3 μm (Fig.3a) aligned along the
direction of rolling, to medium ones with a period of ~ 10 μm,
which have a fairly isotropic shape, and long-wavelengths
with a period of ~ 20 μm in the form of non-cubic tetrahedra,
which indicates the presence of anisotropy of the form. The
free surface of the amorphous spinning ribbon is characterized
by a more even tubercle relief, Fig.3b.
Fig. 3. Electron - microscopic image of a) contact surface;
b) free surfacespinning ribbon Fe77Cu1Si16B6. The tabs show
the Fourier spectrum of the images data and the corresponding
ISC and integrally spatial characteristic of periodicities: short
wavelength Λ1 (c, f); medium wavelength Λ2 (d); long
wavelength Λ3 (e, g) ranges.
Spectral Fourier analysis of electron microscopic images of
the interfaces between rapidly quenched alloys, Fig.3a,b,
revealed three ranges of sizes of inhomogeneities of the
morphostructure of spinning ribbons: short-wavelength Λ1,
medium-wavelength Λ2, long-wavelength Λ3, and confirmed
multiscale on the micrometer range, Table I.
Inhomogeneities of the short wavelength range Λ1 of the
contact surface are aligned along the rolling direction of the
spinning ribbon and have an isotropic shape. The periodicities
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
10
Volume 17, 2022
of the long wavelength range Λ3 have an anisotropic form due
to the induced shape anisotropy and the significant influence
of spinning technology on them. Medium and long wave
inhomogeneities are characterized by the presence of a
dispersion of the anisotropy axis (~ 200), which is explained
by the shape of the inhomogeneities (Fig.3d-e). It is shown
that the integral anisotropy of the morphostructure of the
spinning ribbon is determined by the periodicities of the long
wavelength range, Table I.
Short wave inhomogeneities of the free surface are
characterized by a lower anisotropy index (ɛ = 1) compared
with the contact surface (ɛ = 1.75), Table I. The transition to
high-size inhomogeneities leads to an increase in the
anisotropy coefficient. The formation of the middle and long
range order of inhomogeneities of the free surface is
accompanied by a sharp increase in the anisotropy in their
distribution and, by the value of ɛ, reaches the value of the
anisotropy coefficient of the contact surface, Fig.3f-g.
Thus, the behavior of inhomogeneities in the structure of
spinning ribbons in the nanometer range differs from the
morphological level, Fig.4. Anisotropy of this periodicity
scale is formed by short wavelength inhomogeneities, λ1 = 0.2
nm, which have a maximum value of ɛ, both on the contact
and on the free surfaces, Fig. 4b. The formation of mesoscale
and long wavelength structures is accompanied by a decrease
in the anisotropy coefficient, Fig.4b. This dependence pattern
(Fig. 4b) is related to the elimination of uniaxial anisotropy for high-
dimensional homogeneities as shown above, Fig.2. The spectral
analysis of the structure of rapidly quenched alloys at the
morphological level detected opposite regularities, Fig.4a: the
maximum anisotropy coefficient is a characteristic of the long-wave
periodicities. The size reduction of inhomogeneities of the
morphological structure of both spinning ribbon surfaces is
accompanied by a decrease the anisotropy coefficient ɛ, Fig.4а.
Fig. 4. The dependence of the anisotropy coefficient on the
wavelength a) for the contact and free surface of the
amorphous spinning ribbon (SEM); b) for the area close to the
contact surface and the area close to the free surface (TEM).
After analyzing the results obtained, we can say that an
inversion is observed between the structure and
morphostructure of the rapidly quenched Fe77Cu1Si16B6 ribbon
in terms of the value of the anisotropy coefficient, which
manifests itself in a change in the nature of anisotropy for
different size ranges of inhomogeneities.
So, as a result of a spectral analysis of the structure of the
Fe77Cu1Si16B6, the presence of the drawn ranges is shown:
short-wavelength, long-wavelength periodicities, and
mesoscale range. Average values of the lengths revealed
periodicities of the ribbon surfaces: Λ1 - 2.8 μm and 3.2 μm,
Λ2 - 7.2 μm and 7.7 μm, Λ3 - 20.3 μm and 18.1 μm, for the
contact and free surfaces, respectively. Average values of the
wavelengths of the revealed structural periodicities of the
nanoscale: λ1 - 0.2 nm and 0.2 nm, λ2 - 0.6 nm and 0.5 nm, λ3 -
1.8 nm and 1.62 nm, for regions close to the contact and free
surfaces, respectively.
The ratios λ2/λ1 and Λ2/Λ1, λ3/λ1 and Λ3/Λ1, were found for
the wavelengths of the periodicities obtained by analyzing
electron microscopic images from transmission and scanning
electron microscopes, Table II.
It should be noted that these characteristics are close for the
of both inhomogeneities levels: the ratios Λ2/Λ1 and Λ3/Λ1
have similar values both for the contact and free interfaces
(morphological level) and for the regions of structures studied
using a transmission electron microscope, λ2/λ1 and λ3/λ1.
Moreover, the formation of medium and long-range order in
an amorphous-nanocrystalline alloy goes on the principle of
self-similar spatial structures characteristic of modulation-
unstable media [31], [32], [33], [34], [35], as evidenced by
the correspondence of the wavelength ratios, Table II, for
the nanometer and morphological ranges.
Table II. The ratios of the wavelengths ratios of the
inhomogeneities of the nanometer range and the
morphological level.
SEM
Wavelength
ratios
Contact surface
Free surface
Λ2/ Λ1
2.6
2.4
Λ3/ Λ1
7.25
5.7
TEM
Wavelength
ratios
The area close to
the contact surface
The area close to
the free surface
λ2/λ1
3.0
2.5
λ3/λ1
9.0
8.1
The next stage of the study of the amorphous spinning
ribbon with the composition Fe77Cu1Si16B6 is an analysis of
structural changes in local areas. The image, Fig. 2, obtained
in TEM, is a projection of the density of a fragment with a
thickness of (10 – 15) nm: dark portions of the image are
characterized by an increased density of the material
compared to light. The Fourier spectrum, Fig. 2, obtained from
an image measuring (35 x 35) nm, is isotropic with a diffuse
halo located at a distance of 5 nm-1(~ 0.2 nm) and reflects the
nature of the structure in the integral representation, while the
local regions are smaller and can have other characteristics.
To clarify the structural changes in the local areas, we
selected regions of size 8.7 nm × 8.7 nm, which were shifted
half a period in the horizontal direction along the image.
Fourier spectra were obtained for all areas. Fig.5 shows
electron microscopic images and their spectral characteristics
for 2 random local regions of the Fe77Cu1Si16B6 spinning
ribbon near the contact surface. A visual analysis of electron
microscopic images demonstrates differences in their
structure. The obtained spectra, Fig.5b and Fig.5e, are
isotropic, but bright reflections on the selected ring indicate
the presence of local anisotropy. In order to introduce a
quantitative measure of comparison, we use the methodology
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
11
Volume 17, 2022
for calculating integral measures function of Lebesgue (IMFL)
[22], [23], [24], [25], [36]. The starting point for the
comparison procedure was the IFR obtained for seven local
areas of the structure, an example of which is shown in Fig.5c
and Fig.5f.
Fig.5. Electron microscopic images of the structure of a
spinning ribbon Fe77Cu1Si16B6 near the contact surface (8.7
nm x 8.7 nm) from two regions of the image shown in Fig. 1
(a) and the corresponding Fourier spectra (b,e) and IFR (c, f).
In information theory, divergent estimates of proximity and
similarity of distributions are known. One of them is Kullback
divergence (LivI) [23], [24], [25], [29]. To construct it, the
spectral estimate I(k) is chosen with linear IMFL
corresponding to white noise.
Obtained dependence of the LivI on the area number is
shown in Fig. 6a. As can be seen from the figure, the area at
number 4 has the structure farthest from the structure of white
noise. Thus, regions 1, 2, and 7 are the most structurally
disordered. The methodology of our study in constructing the
dependences (Fig. 6) assumes that region 2 consists of half of
region 1 and half of region 3. Analysis of the results (Fig. 6a)
shows that its characteristics are slightly different from region
1 (ΔLiv1-2 = 0.16) and highly different from region 3 (ΔLiv1-3
= 1.74). Therefore, the density projection changes at much
smaller areas of the structure than the ones chosen for the
study (8.7 nm x 8.7 nm).
To confirm the result of a change in the local density
characteristics of the structure of the spinning ribbon, another
base was taken - the IFML of the entire image. That is, an
analysis was made of the difference / similarity of the
structure of local regions from integral ordering. This result is
shown in Fig.6b.
Fig.6. The Kullback divergence obtained from the IFML: a)
the base is white noise, b) the base is the IFML from the
frequency response of the entire image (Fig.2).
In addition to the already stated fact of a local change in the
density projection, Fig.6a can carry additional information
when it is jointly analyzed with Fig.6b. For example, the
parameters of region 7, Fig. 6a, are closest to white noise, but
are farthest from the integral IFML, Fig. 6b. The structure of
region 4 is removed as from white noise, Fig. 6a, and from the
average over the whole image, Fig.6b. Therefore, we can
propose to consider cases of either of ordering, in the case of
region 4, or disordering, in the case of region 7. Most likely, in
terms of the projection of density, region 4 corresponds to a
region with a higher density, and region 7 corresponds to a
region with a lower density.
The above results were obtained for the TEM image from
the structure located close to the contact surface of the
spinning ribbon Fe77Cu1Si16B6. In order to track the change in
the projection of the structure density over the thickness of the
ribbon, a similar procedure was performed for the image
obtained from the structure located close to the free side of the
ribbon, Fig. 2b. Analysis of the of IFML obtained for seven
local regions of the structure near the free surface gave similar
results.
The determined characteristic of structural heterogeneities
of different spatial scales and their interconnection allow to
consider the structure of a rapidly quenched Fe77Cu1Si16B6
alloy as hierarchically arranged. By changing the production
parameters of a rapidly quenched alloy from the melt it is
possible to control the system of hierarchically connected
structural heterogeneities, as well as the characteristics of the
system and its subsystems. The adjustment of the
characteristics of structural heterogeneities will make it
a
b
c)
d
e
f)
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
12
Volume 17, 2022
possible to change the specified functional properties of the
material.
4. Conclusion
Spectral analysis of electron microscopic images of a
spinning ribbon Fe77Cu1Si16B6 showed a complex nature of the
structure, characterized by a wide range of inhomogeneities:
three spatial ranges of sizes of inhomogeneitiesof nano - range
and micro-level were identified: long-wave (λ1 = 1.7 nm; Λ1 =
19.2 μm); medium-wave (λ2 = 0.6 nm; Λ2 = 7.5 μm),short-
wavelength (λ3 = 0.2 nm;Λ3 = 2.8 μm).
The anisotropy of the periodicities of the nanometer range is
determined by short-wave inhomogeneities, λ1 = 0.2 nm,
which have a maximum value of ɛ, both on the contact surface
and on the free one. The formation of mesoscale and long-
wavelength structures is accompanied by a decrease in the
anisotropy coefficient. The integral anisotropy of the
morphostructure of the spinning ribbon is determined by the
inhomogeneities of the long-wavelength range.
A comparison of the spectral characteristics of the local
areas of the structure of the rapidly quenched alloy revealed a
different level of their formation. A change in the nature of
anisotropy for the detected ranges of inhomogeneities of the
nano and micro levels is reflected in the inversion of the
anisotropy coefficient ɛ. The following result has been
obtained: the formation of medium and long-range orders in
an amorphous nanocrystalline alloy occurs on the principle of
self-similar spatial structures characteristic of modulation-
unstable media.
Thus, the proposed TEM image processing technique
allowed us to identify changes in the density projection that
occur in the entire volume of the spinning ribbon
Fe77Cu1Si16B6. Most likely this is due to the wave process of
heat removal during melt spinning.
The methods for describing multiscale structural
heterogeneities in amorphous-nanocrystalline alloys have been
developed, which allows to describe the structural state and
determine its influence on the physicochemical and technical
properties depending on the production of the alloys.
The results allow increasing the reliability in the
investigation of the structure-property correlation of
amorphous-nanocrystalline metal alloys obtained by rapid
quenching from the melt.
References
[1] A. M. Glezer, N. A. Shurygina, Amorphous-
nanocrystalline alloys. CRC Press, 2017, 458p.
[2] F. Zhu, A. Hirata, P. Liu, S. Song, Y. Tian, J. Han, T.
Fujita, M. Chen, Correlation between local structure order
and spatial yeterogeneity in a metallic glass. Phys. Rev.
Lett., 2017, vol. 119, pp. 215501.
[3] L. Tian, C.A. Volkert, Measuring structural
heterogeneities in metallic glasses using transmission
electron microscopy. Metals, 2018, vol.8, 1085, 14 p.
[4] L.L. Pang, A. Inoue, E.N. Zanaeva, F. Wang, A.I. Bazlov,
Y. Han, F.L. Kong, S.L. Zhu, R.B. Shull,
Nanocrystallization, good soft magnetic properties and
ultrahigh mechanical strength for Fe82-85B13-16Si1Cu1
amorphous alloys. J. of Alloys and Compounds, 2019,
vol. 785, pp. 25-37.
[5] S. Cranford, Nature MADE: A Simple guide to biological
design rules Matter, 2020, vol. 2, pр.782–785.
[6] F. Hou, Y. Yang, T. Luo, G. Wang, C. Fan, Z. Xie, Effect
of Ni substitution to Fe on amorphous nanocrystalline soft
magnetic alloy. Physica B, 2020, vol. 595, p.412293.
[7] D.V. Louzgune, Metallic glasses and their composites.
Updated 2nd Edition, Published by Materials Research
Forum LLC, PA 17551, USA, 2021, vol. 85, 340 p.
[8] V. Hasannaeimi, M. Sadeghilaridjani, S. Mukherjee,
Electrochemical and corrosion behavior of metallic
glasses. MDPI: Basel, Switzerland, 2021, 90 p.
[9] Z.X. Dou, Y.L. Li, K. Lv, T. Wang, F.S. Li, X.D. Hui,
Improving the glass formation ability and magnetic
properties by Nb in Fe-Si-B-P-Cu-Nb nanocrystalline
alloys. Materials Science and Engineering, 2021, vol. B
264, p. 114942.
[10] P.H. Gaskell, Medium-range structure in glasses and
low-Q structure in neutron and X-ray scattering data. J. of
Non-Crystalline Solids, 2005, vol. 351, рр. 1003–1013.
[11] H.W. Sheng, W.K. Luo, F. M. Alamgir, J.M. Bai, E. Ma,
Atomic packing and short-to-mediumrange order in
metallic glasses, Nature, 2006, vol. 439, pp. 419-425.
[12] H. Jinwoo, Z.H. Melgarejo, Y.E. Kalay, I. Kalay, M.J.
Kramer, D.S. Stone, P.M. Voyles, Nanoscale structure
and structural relaxation in Zr50Cu45Al5 bulk metallic
glass. PRL, 2012, vol. 108, р. 195505.
[13] I.B. Kekalo, Processes of structural relaxation and
physical properties of amorphous alloys. Publishing
House “MISIS”, 2014, vol. 1, 436 p.
[14] Y.Q. Cheng, E. Ma, Atomic-level structure and structure–
property relationship in metallic glasses. Progress in
Materials Science, 2011, vol. 56, pр. 379-473.
[15] L. Hou, X. Fan, Q. Wang , W. Yang, B. Shen,
Microstructure and soft-magnetic properties of
FeCoPCCu nanocrystalline alloys. J. Mater. Sci.
Technol., 2019, vol.35, Iss. 8, pр. 1655–1661.
[16] D. Azuma, N. Ito, M. Ohta, Recent progress in Fe-based
amorphous and nanocrystalline soft magnetic materials.
J. Magn. Magn. Mater., 2020, vol. 501, p. 166373.
[17] L. Hawelek, T. Warski, P. Wlodarczyk, M. Polak, P.
Zackiewicz, W. Maziarz, A. Wojcik, M. Steczkowska-
Kempka, A. Kolano-Burian, The Structure and magnetic
Properties of Rapidly Quenched Fe72Ni8Nb4Si2B14. Alloy.
Materials, 2021, vol. 14, №5, 10 p.
[18] F. Wang, A. Inoue, F.L. Kong, C.C. Zhao, J.Y. Zhang,
S.L. Zhu, W.J. Botta, C.S. Kiminami, Y.P. Ivanov, A.L.
Greer, Formation, thermal stability and mechanical
properties of high-entropy
(Fe0.25Co0.25Ni0.25Cr0.125Mo0.0625Nb0.0625)100‒xBx (x = 7–14)
amorphous alloys. J. of Alloys and Compounds, 2020,
vol. 825, p. 153858.
[19] E.B. Modin, E.V. Pustovalov, A.N. Fedorets, A.V.
Dubinets, B.N. Grudin, V.S. Plotnikov, S.S. Grabchikov,
Atomic structure and crystallization processes of
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
13
Volume 17, 2022
amorphous (Co, Ni)–P metallic alloy. J. of Alloys and
Compounds, 2015, vol. 641, pp. 139–143.
[20] G. Herzer, Modern soft magnets: Amorphous and
monocrystalline materials. ActaMaterialia, 2013, vol. 61,
pp. 718–734.
[21] S. Kwon, S. Kim, H. Yim, Improvement of saturation
magnetic flux density in Fe–Si–B–Nb–Cu nanocomposite
alloys by magnetic field annealing. Current Applied
Physics, 2020, vol. 20, рр. 37–42.
[22] L.A. Yudina, A.M. Frolov, N.I. Chukhry, V.V. Yudin,
System method for complicated SEM images processing.
Izvestiya Akademii Nauk. Ser. Fizicheskaya, 1998, vol.
62, pp. 455- 460.
[23] A.M. Frolov, G.S. Krainova, S.V. Dolzhikov, Informo-
Dynamics functionals in the study of fields of anisotropy
of a microrelief spinning tapes. Advanced Materials
Research, 2014, vol.1025-1026, pp. 499-503.
[24] E.V. Pustovalov, A.N. Fedorets, V.V. Tkachev, V.S.
Plotnikov, E.B. Modin, Regularities in the disordered
atomic structure of rapidly quenched amorphous cobalt-
based alloys. IEEE Conference Publications, 2017, pp.
142 – 144.
[25] E.V. Pustovalov, E.B. Modin, A.M. Frolov, A.S.
Kosovets, N.B. Kondrikov, N.F. Karpovich, S.A.
Pyachin, S.V. Dolzhikov, G.S. Kraynova, V.S. Plotnikov,
V.V. Tkachev, A.N. Fedorets, N.V. Ilin, Effect of the
process conditions for the preparation of CoNiFeSiB
amorphous alloys on their structure and properties. J. of
Surface Investigation: X-ray, Synchrotron and Neutron
Techniques, 2019, vol. 13, № 4, pp. 600–608.
[26] B.N. Grudin, V.S. Plotnikov, Processing and modeling of
microscopic images. Vladivostok: Dalnauka, 2010,
350p.
[27] B.N. Grudin, V.S. Plotnikov, E.V. Pustovalov, N.A.
Smol’yaninov, S.V. Polishchuk, Simulation and analysis
of images using spectral characteristics. Bulletin of the
Russian Academy of Sciences: Physics, 2012, vol. 76,
№9, pp. 1020-1024.
[28] B. N. Grudin, K.A. Petrov, V.S. Plotnikov, S.V.
Polishchuk, E. B. Modin, Analyzing the fractal properties
of a structure via microscopic images. Bulletin of the
Russian Academy of Sciences: Physics, 2015, vol. 79,
№11, pp. 1345–1349.
[29] A.M. Frolov, A.V. Ansovich, V.V. Tkachev, G.S.
Kraynova, S.V. Dolzhikov, Surface morphology of
spinning tapes Fe- (Cu, Nb) - (Si, B) with different
content of metalloid. Key Engineering Materials, 2019,
vol. 806, p. 124-129.
[30] A.M. Frolov, G.S. Krainova, S.V. Dolzhikov, Anisotropy
of the structural inhomogeneities of rapidly quenched
alloys. J. of Surface Investigation, 2018, vol. 12, p. 370-
376.
[31] M. Popescu, F. Sava, A. Lőrinczi, Self-organization and
anisotropy in amorphous chalcogenides. J. of Non-
Crystalline Solids, 2006, vol. 352, Iss. 9–20, pp. 1506-
1509.
[32] I.E. Gracheva, V.A. Moshnikov, E.V. Maraeva, S.S.
Karpova, O.A. Alexsandrova, N.I. Alekseyev, V.V.
Kuznetsov, G. Olchowik, K.N. Semenov, A.V. Startseva,
A.V. Sitnikov, J.M. Olchowik, Nanostructured materials
obtained under conditions of hierarchical self-assembly
and modified by derivative forms of fullerenes. J. of
Non-Crystalline Solids, 2012, vol. 358, Iss.2, pp. 433-
439.
[33] H.B. Ke, J.F. Zeng, C.T. Liu, Y. Yang, Structure
heterogeneity in metallic glass: Modeling and Experiment
J. Mater. Sci. Technol., 2014, vol. 30 Iss. 6, pp. 560-565.
[34] L. Tang, Z.J. Yang, T.Q. Wen, K.M. Ho, M.J. Kramer,
C.Z. Wang, Short- and medium-range orders in Al90Tb10
glass and their relation to the structures of competing
crystalline phases. Acta Materialia, 2021, vol. 204, p.
116513.
[35] X. Tong, Y. Zhang, Y. Wang, X. Liang, K. Zhang, F.
Zhang, Y. Cai, H. Ke, G. Wang, J. Shen, A. Makino, W.
Wang, Structural origin of magnetic softening in a Fe-
based amorphous alloy upon annealing. J. of Materials
Science & Technology, 2022, vol. 96, рр. 233–240.
[36] N.I. Chukhrii, V.V. Yudin, A.M. Frolov, L.A. Yudina,
Correlation between quickquenched ribbon surfaces and
atomic disordering in spinning processes. Surface
Investigation. X-Ray, Synchrotron and Neutron
Techniques, 2000, vol. 15, pp. 653-665.
Author Contributions:
Frolov A.M. – discuss the results, visualization, funding
acquisition, writing - original draft, writing- review &
editing.
Ansovich A.V.– image processing.
Kraynova G.S.– methodology, writing - review &
editing, image processing
Tkachev V.V. – scanning electron microscopy
investigation, data curation, visualization.
Dolzhikov, S.V. – discuss the results, data curation.
Plotnikov V.S. – discuss the results, data curation,
supervision.
Ralin A.Yu. – transmission electron microscopy
investigation, data curation.
Fedorets A.N. – transmission electron microscopy
investigation, data curation, visualization.
Sources of funding for research presented in a scientific
article or scientific article itself
This work was supported by the state task of the Ministry of
Science and Higher Education of the Russian Federation under
Grant № 0657-2020-0005.
The experimental results were obtained on the equipment of
the Centre of Collective Usage of the Far Eastern Federal
University, registration No. 200556 (Vladivostok).
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the Creative
Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en_US
WSEAS TRANSACTIONS on APPLIED and THEORETICAL MECHANICS
DOI: 10.37394/232011.2022.17.2
Frolov A. M., Ansovich A. V., Kraynova G. S.,
Tkachev V. V., Dolzhikov, S.V., Plotnikov V. S.,
Ralin A. YU., Fedorets A. N.
E-ISSN: 2224-3429
14
Volume 17, 2022
Conflicts of Interest
The authors have no conflicts of interest to
declare