Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions
Ordinary cylindrical specimens with easy-axis anisotropy perpendicular to the axis of a cylinder are studied. As shown, the inhomogeneous long-wave magnetic configurations of harmonic type can be created and observed in such samples. A linear theory is developed to simplify the set of Landau— Lifshi...
Gespeichert in:
| Veröffentlicht in: | Металлофизика и новейшие технологии |
|---|---|
| Datum: | 2016 |
| Hauptverfasser: | , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут металофізики ім. Г.В. Курдюмова НАН України
2016
|
| Schlagworte: | |
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/112623 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions / Yu.I. Dzhezherya, O.Yu. Gorobets, O.P. Kuz, O.S. Klymuk, and Yu.I. Gorobets // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 10. — С. 1379-1393. — Бібліогр.: 18 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860248589061586944 |
|---|---|
| author | Dzhezherya, Yu.I. Gorobets, O.Yu. Kuz, O.P. Klymuk, O.S. Gorobets, Yu.I. |
| author_facet | Dzhezherya, Yu.I. Gorobets, O.Yu. Kuz, O.P. Klymuk, O.S. Gorobets, Yu.I. |
| citation_txt | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions / Yu.I. Dzhezherya, O.Yu. Gorobets, O.P. Kuz, O.S. Klymuk, and Yu.I. Gorobets // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 10. — С. 1379-1393. — Бібліогр.: 18 назв. — англ. |
| collection | DSpace DC |
| container_title | Металлофизика и новейшие технологии |
| description | Ordinary cylindrical specimens with easy-axis anisotropy perpendicular to the axis of a cylinder are studied. As shown, the inhomogeneous long-wave magnetic configurations of harmonic type can be created and observed in such samples. A linear theory is developed to simplify the set of Landau— Lifshitz and Maxwell’s equations to one general equation for a magnetostatic potential. The ranges of magnetic fields and the self-parameters responsible for the inhomogeneous periodic configuration formation are determined when solving a boundary value problem for a magnetostatic potential. Dependence of the period of magnetization wave on a magnetic field value, the constant of anisotropy and diameter of a cylinder is determined. The proposed theory gives qualitative explanation of the experiment when, using the Bitter’s powder-like figures’ method, quasi-periodic distributions of the magnetostatic fields can be observed in samples. These fields arise under external magnetic field of about 1 kOe directed along the axis of a steel cylinder and are absent without external magnetic field. An example of practical application of long-wave magnetic structures for a surface morphology control during chemical etching of ferromagnetic metals in acid solutions is given. The quasi-periodic structure of a corrosion surface of ferromagnetic cylinder corresponds to the period of a long-range magnetic structure.
Досліджено циліндричні зразки з легковісною анізотропією, перпендикулярною до осі циліндру. Показано, що в таких зразках можна створювати і спостерігати неоднорідні довгохвильові магнетні конфіґурації гармонічного типу. Було розвинуто лінійну теорію, яка зводить систему рівнянь Ландау—Ліфшиця та Максвеллових, що описують магнетний стан системи, до одного загального рівняння для магнетостатичного потенціялу. В ході розв’язання крайової задачі для магнетостатичного потенціялу визначено діяпазон магнетних полів і власних параметрів системи, за яких ймовірним є утворення неоднорідної періодичної конфіґурації. Визначено залежність періоду хвилі намагнетованости від амплітуди магнетного поля, константи анізотропії та діяметра циліндру. Запропонована теорія дає якісне пояснення експерименту, коли при застосуванні Біттерової методи порошкових фіґур можливе спостереження квазиперіодичних розподілів магнетостатичних полів, що утворені при прикладанні зовнішнього магнетного поля порядку 1 кЕ вздовж осі сталевого циліндру, тоді як без прикладання зовнішнього магнетного поля магнетостатичні поля відсутні. Наведено приклад практичного застосування довгохвильових магнетних структур для керування морфологією поверхні при хемічному щавленні феромагнетних металів у розчинах кислот. При цьому квазиперіодична структура поверхні кородованого феромагнетного циліндра відповідає періоду його довгомасштабної магнетної структури.
Исследованы цилиндрические образцы с легкоосной анизотропией, перпендикулярной оси цилиндра. Показано, что в таких образцах можно создать и наблюдать неоднородные длинноволновые магнитные конфигурации гармонического типа. Развита линейная теория, которая сводит систему уравнений Ландау—Лифшица и Максвелла, описывающих магнитное состояние системы, к одному общему уравнению для магнитостатического потенциала. В ходе решения краевой задачи для магнитостатического потенциала определён диапазон магнитных полей и собственных параметров системы, при которых вероятным является образование неоднородной периодической конфигурации. Определена зависимость периода волны намагниченности от амплитуды магнитного поля, константы анизотропии и диаметра цилиндра. Предложенная теория даёт качественное объяснение эксперимента, когда при применении метода порошковых фигур Биттера возможно наблюдение квазипериодических распределений магнитостатических полей, образованных при воздействии внешнего магнитного поля порядка 1 кЕ вдоль оси стального цилиндра, в то время как без приложения внешнего магнитного поля магнитостатические поля отсутствуют. Приведён пример практического использования длинноволновых магнитных структур для управления морфологией поверхности при химическом травлении ферромагнитных материалов в растворах кислот. При этом квазипериодическая структура поверхности корродированного ферромагнитного цилиндра соответствует периоду его длинномасштабной структуры.
|
| first_indexed | 2025-12-07T18:40:01Z |
| format | Article |
| fulltext |
1379
PACS numbers:03.50.De, 41.20.Gz,75.10.-b,75.30.Gw,75.60.Ch,75.70.Kw, 81.65.Cf
Periodic Modulations of Magnetostatic Field in Ferromagnetic
Cylinder and Their Influence on Etching Figure Formation
in Acid Solutions
Yu. I. Dzhezherya, O. Yu. Gorobets*, O. P. Kuz*, O. S. Klymuk*,
and Yu. I. Gorobets
Institute of Magnetism, N.A.S. and M.E.S. of Ukraine,
36b
Academician Vernadsky Blvd.,
UA-03142 Kyiv, Ukraine
*National Technical University of Ukraine ‘KPI’,
37 Peremogy Ave.,
UA-03056 Kyiv, Ukraine
Ordinary cylindrical specimens with easy-axis anisotropy perpendicular to
the axis of a cylinder are studied. As shown, the inhomogeneous long-wave
magnetic configurations of harmonic type can be created and observed in
such samples. A linear theory is developed to simplify the set of Landau—
Lifshitz and Maxwell’s equations to one general equation for a magnetostatic
potential. The ranges of magnetic fields and the self-parameters responsible
for the inhomogeneous periodic configuration formation are determined
when solving a boundary value problem for a magnetostatic potential. De-
pendence of the period of magnetization wave on a magnetic field value, the
constant of anisotropy and diameter of a cylinder is determined. The pro-
posed theory gives qualitative explanation of the experiment when, using the
Bitter’s powder-like figures’ method, quasi-periodic distributions of the
magnetostatic fields can be observed in samples. These fields arise under ex-
ternal magnetic field of about 1 kOe directed along the axis of a steel cylinder
and are absent without external magnetic field. An example of practical ap-
plication of long-wave magnetic structures for a surface morphology control
during chemical etching of ferromagnetic metals in acid solutions is given.
Corresponding author: Yuri Ivanovich Dzhezherya
E-mail: dui_kpi@ukr.net
Please cite this article as: Yu. I. Dzhezherya, O. Yu. Gorobets, O. P. Kuz,
O. S. Klymuk, and Yu. I. Gorobets, Periodic Modulations of Magnetostatic Field in
Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid
Solutions, Metallofiz. Noveishie Tekhnol., 38, No. 10: 1379—1393 (2016),
DOI: 10.15407/mfint.38.10.1379.
Металлофиз. новейшие технол. / Metallofiz. Noveishie Tekhnol.
2016, т. 38, № 10, сс. 1379—1393 / DOI: 10.15407/mfint.38.10.1379
Оттиски доступны непосредственно от издателя
Фотокопирование разрешено только
в соответствии с лицензией
2016 ИМФ (Институт металлофизики
им. Г. В. Курдюмова НАН Украины)
Напечатано в Украине.
1380 Yu. I. DZHEZHERYA, O. Yu. GOROBETS, O. P. KUZ et al.
The quasi-periodic structure of a corrosion surface of ferromagnetic cylinder
corresponds to the period of a long-range magnetic structure.
Key words: ferromagnets, domain structure, magnetostatic field, etching.
Досліджено циліндричні зразки з легковісною анізотропією, перпенди-
кулярною до осі циліндру. Показано, що в таких зразках можна створю-
вати і спостерігати неоднорідні довгохвильові магнетні конфіґурації гар-
монічного типу. Було розвинуто лінійну теорію, яка зводить систему рів-
нянь Ландау—Ліфшиця та Максвеллових, що описують магнетний стан
системи, до одного загального рівняння для магнетостатичного потенція-
лу. В ході розв’язання крайової задачі для магнетостатичного потенціялу
визначено діяпазон магнетних полів і власних параметрів системи, за
яких ймовірним є утворення неоднорідної періодичної конфіґурації. Ви-
значено залежність періоду хвилі намагнетованости від амплітуди магне-
тного поля, константи анізотропії та діяметра циліндру. Запропонована
теорія дає якісне пояснення експерименту, коли при застосуванні Бітте-
рової методи порошкових фіґур можливе спостереження квазиперіодич-
них розподілів магнетостатичних полів, що утворені при прикладанні
зовнішнього магнетного поля порядку 1 кЕ вздовж осі сталевого цилінд-
ру, тоді як без прикладання зовнішнього магнетного поля магнетостатич-
ні поля відсутні. Наведено приклад практичного застосування довгохви-
льових магнетних структур для керування морфологією поверхні при хе-
мічному щавленні феромагнетних металів у розчинах кислот. При цьому
квазиперіодична структура поверхні кородованого феромагнетного цилі-
ндра відповідає періоду його довгомасштабної магнетної структури.
Ключові слова: феромагнетики, доменна структура, магнетостатичне по-
ле, щавлення.
Исследованы цилиндрические образцы с легкоосной анизотропией, пер-
пендикулярной оси цилиндра. Показано, что в таких образцах можно со-
здать и наблюдать неоднородные длинноволновые магнитные конфигура-
ции гармонического типа. Развита линейная теория, которая сводит си-
стему уравнений Ландау—Лифшица и Максвелла, описывающих магнит-
ное состояние системы, к одному общему уравнению для магнитостатиче-
ского потенциала. В ходе решения краевой задачи для магнитостатиче-
ского потенциала определён диапазон магнитных полей и собственных
параметров системы, при которых вероятным является образование не-
однородной периодической конфигурации. Определена зависимость пе-
риода волны намагниченности от амплитуды магнитного поля, константы
анизотропии и диаметра цилиндра. Предложенная теория даёт каче-
ственное объяснение эксперимента, когда при применении метода по-
рошковых фигур Биттера возможно наблюдение квазипериодических
распределений магнитостатических полей, образованных при воздей-
ствии внешнего магнитного поля порядка 1 кЕ вдоль оси стального ци-
линдра, в то время как без приложения внешнего магнитного поля магни-
тостатические поля отсутствуют. Приведён пример практического ис-
пользования длинноволновых магнитных структур для управления мор-
фологией поверхности при химическом травлении ферромагнитных ма-
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1381
териалов в растворах кислот. При этом квазипериодическая структура
поверхности корродированного ферромагнитного цилиндра соответствует
периоду его длинномасштабной структуры.
Ключевые слова: ферромагнетики, доменная структура, магнитостатиче-
ское поле, травление.
(Received September 12, 2016)
1. INTRODUCTION
Ferromagnetic materials are known to possess domain structure due to
competition of magnetic interactions of the certain types. On the one
hand, it is the energy of a magnetic anisotropy and exchange interac-
tion; on the other hand, it is dipole—dipole interaction of magnetic
moments of the system. Domain structure acquires the various forms
depending on the contribution of the mentioned interactions, a speci-
men shape and characteristics of external magnetic field [1—4]. It can
be a system of stripe domains, serpentine domain structure, a lattice of
cylindrical domains, spiral domains, etc. Similar structures appear
spontaneously or artificially and correspond to an absolute or a local
minimum of complete energy among the variety of magnetic configu-
rations.
The parameters of certain types of domain structures (DS) and their
separate elements have been widely studied both by experimental and
theoretical methods, for example [1—6]. These papers report on ther-
modynamic properties of ferromagnetic materials, the influence of DS
on their magnetization processes and their practical use in magnetic
devices. Except the practical application, investigation of magnetic
configurations is interesting itself in the theory of the non-linear
equations and theirs soliton-like solutions.
There are some elements of domain structures describing system
magnetization field distribution, which satisfy the joint solution of
the magnetostatic equations and the Landau—Lifshitz non-linear equa-
tions. These are the Néel and Bloch one-dimensional domain walls, the
Shirobokov stripe domain structure, and the Belavin—Polyakov two-
dimensional soliton configurations. However, for real systems with
geometrical restrictions of the samples, the mentioned solutions could
be considered only as certain approach to the real magnetic configura-
tions. Certain simplifications are necessary to take into account fac-
tors of magnetic objects shape and a wide spectrum of magnetic inter-
actions influence. One of the most useful simplifications consists in
representation of a domain wall as geometrical boundary characterized
by a surface energy.
A number of important domain configurations and their elements
have been investigated due to this approach [1, 2, 4].
1382 Yu. I. DZHEZHERYA, O. Yu. GOROBETS, O. P. KUZ et al.
However, there are magnetic configurations with the fundamentally
different magnetization distribution compared to traditional domain
structures, which are formed in ferromagnetic systems under certain
conditions. These are non-uniform magnetic configurations in systems
with biaxial anisotropy.
Inhomogeneous magnetic ordering character of such configurations
is caused by a demagnetizing field in the presence of exchange interac-
tion. These structures are characterized by the sinusoidal type modula-
tion of magnetization components. The existence of such structures in
magnetic films or plates with anisotropy factor lower than unit, were
predicted in papers [7, 8]. The inhomogeneous structure period de-
pendence on the thickness and parameters of material was determined
as well. The development of this theory was the discovery of a magnetic
field influence on the magnetization distribution in such structures
[9].
2. THEORETICAL DETAILS
2.1. Problem Definition
It will be shown further that the inhomogeneous long-wave magnetic
configuration of harmonic type can be created and observed in cylin-
drical samples with ‘easy magnetic plane’ anisotropy, which is perpen-
dicular to the axis of the cylinder. The necessary condition of sinusoi-
dal modulations creation in such systems is the magnetic field directed
along the cylinder axis.
2.2. The Equation for the Magnetostatic Potential
and the Distribution of Magnetization in Ferromagnetic Film
We assume that the system is a ferromagnetic cylinder in an external
magnetic field. The cylinder axis coincides with the direction of the
field and is directed along 0z. It is supposed that while making such a
sample form (by rolling or drawing), uniaxial anisotropy of ‘easy mag-
netization’ occurs in the material in plane that is perpendicular to the
axis of the cylinder.
Thus, the magnetic energy density of the film material consists of
the exchange interaction energy, the Zeeman energy and magnetic ani-
sotropy energy and is given by:
2
2 ,
2 2
M z z
k
w M HM
x
M
(1)
where –a constant of exchange magnetic interaction, M–a system
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1383
magnetization vector, –the uniaxial anisotropy constant, H–
magnetic field value in the direction of cylinder axis 0z.
In case of 0, we have anisotropy of ‘easy plane’ (x0y plane).
The fragment of a cylindrical ferromagnetic sample is shown in Fig. 1.
As, in ferromagnetic systems at fixed temperature, the absolute
value of magnetization is constant,
2 2 2 2 2
0
constx y zM M M M M
(where M0–the saturation magnetization), we can represent Eq. (1) in
form:
2
2 2 2
0
.
2 2
M x y z
k
w M M M HM
x
M
(2)
Based on Eq. (2), we can express effective magnetic field determined
through variation derivative:
eff
,M
i x x y y i
w
M M
H M e e
M
(3)
where i–a potential of a magnetostatic field in the cylinder,
2
i i
x x –the Laplace operator, i –gradient of magnetostatic
potential in the cylinder, describing demagnetizing field of the sample
.m
i i
H
Last term in Eq. (3) determines demagnetizing field caused by mag-
netization inhomogeneities. The first term M is caused by exchange
interactions. When changing of the magnetization modulations at
great space scale (for example, the radius of a cylinder), it makes small
contribution and can be neglected.
Indeed, for cylindrical magnetic system of the radius R, we can es-
timate M as follows:
Fig. 1. The fragment of the ferromagnetic sample of a cylinder shape.
1384 Yu. I. DZHEZHERYA, O. Yu. GOROBETS, O. P. KUZ et al.
2
2
4 ,M
RR
M
M
where
4
(4 ) 10 cm
–the characteristic magnetic length.
Thus, for ferromagnetic rods or wires of the diameter of
2
2 10 cm,R the value of
4
4 10M M is of the same order with
the terrestrial magnetic field.
The self-consistent distribution of magnetostatic fields and system
magnetization in the cylinder is described by the Landau—Lifshitz and
Maxwell’s equation sets, which correspond to a static case:
eff
eff
0,
div 0,
4 ,
.
i
i i z
i z
H
H
M H
B
B e M
H e
(4)
If the macroscopically modulations of a magnetization field with a
wavelength close to the cylinder diameter are considered, then, the
quantities with the second spatial derivatives in an effective field
could be ignored, and the set of equations (4) will be as follows:
( ) ( ),
( ) ( ),
( ) ( ),
4 div .
x y i y x i
x i z x i
y i z y i
i
M M y M M x
M H z M M x
M H z M M y
M
(5)
The potential e and magnetic induction Be satisfy to relations out-
side the sample:
0,
.
e
e e zH
B e
(6)
Requirements of the continuity of potential and the magnetic field
component normal to the surface of the cylinder should be satisfied at
the boundary of two media:
,
4 ,
i e r R
i e
n
r R
M
r r
(7)
where Mn–magnetization vector component normal to the cylinder
surface.
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1385
If magnetic field
H directed along cylinder axis is greater than ani-
sotropy field, H M0, then, ferromagnetic sample obtains homogene-
ous magnetization. Otherwise, H M0, magnetization direction can
deviate from the cylinder axis 0z.
Suppose that such deviations are negligibly small. So, zM
2 2 2
0 0x yM M M M . In such approximation, we excluded terms
2 2
0 0
( ) , ( ) 1.
x y
M M M M (8)
Condition (8) is a soft constraint, because it allows operating with ra-
ther noticeable magnetization modulations: 0
, 0.3x yM M M .
Considering that the magnetostatic potential changes are caused by
magnetization modulations and have a small value as well, let us keep
only the linear terms in the equations (4). As a result, the following re-
lation is obtained between magnetization and magnetostatic potential
components:
4 , 4 ,i i
x y
x y
M M
Q h Q h
(9)
where 0
(4 )h H M –a reduced magnetic field and (4 )Q –a re-
duced anisotropy of the system.
Substituting the relation (9) in (4), the equation for magnetostatic
potential is obtained in the self-contained view:
2 2 2
2
2 2 2
2
0,
1 ( )
.
i i ia
x y z
Q h
a
Q h
(10)
As a system possesses axial symmetry, it makes sense to represent
equations (10) in a cylindrical coordinate system:
2 2
2
2 2 2
1 1
0,i i ia r
r r r r z
where
2 2 , arct ( ).r x y g y x
The equation (10) changes into wave one and can describe spontane-
ous modulation of magnetization of cylindrical sample, if the coeffi-
cient before a bracket has positive value. This condition can be pre-
sented as 0 1Q h or in initial designations:
0 0
0 4 .M H M (11)
1386 Yu. I. DZHEZHERYA, O. Yu. GOROBETS, O. P. KUZ et al.
It follows from (11) that the magnetostatic wave structure cannot
spontaneously be generated without magnetic field presence in a direc-
tion of system axis at large value of anisotropy when 4 . The re-
quirement of occurrence of such magnetization modulation is carried
out starting from some fixed value of the magnetic field.
Taking into account the relations (9), boundary conditions for the
magnetostatic potential (7) on the surface of the cylinder gain the fol-
lowing meaning:
2
,
.
i e r R
i e
r R
a
r r
(12)
Besides, the magnetic field on some distance from the sample should
be converted in zero.
We will search for the solution of the boundary value problem (5),
(10), (12) in case of the axial symmetry in the following form:
0
0
( , ) cos ,
( , ) ( ) cos ,
i
e
kr
r z AJ kz
a
r z BK kr kz
(13)
where Jn(x)–the Bessel functions, and Kn(x)–McDonald’s functions
decaying at r , k–a wave number, A, B–some constants defying
amplitude of modulation.
The given functions turn the equation for the magnetostatic field
potential to identity at any value of a wave number k.
The real value of k is determined from the characteristic equation,
which can be written out from the boundary conditions (12). Substitut-
ing (13) in relations for boundary conditions, the set of the homogene-
ous linear equations is obtained:
0 0
1 1
( ) ( ) 0
.
( ) ( ) 0
J kR a K kR A
aJ kR a K kR B
(14)
The requirement of non-zero solvability of the set (14) leads to the
characteristic equation:
0 1 1 0
( ) ( ) ( ) ( ) 0.J kR a K kR aJ kR a K kR (15)
The equation (15) has a discrete set of solutions concerning a wave
number. We will be restricted by the definition of the minimum of k
value as the configurations with high values of wave numbers are
characterised by greater energy at the account of an exchange interac-
tion.
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1387
2.3. Discussion
It follows from the Eq. (15) that the wave number depends on a mag-
netic field and anisotropy of a material. The dependences of modula-
tion wavelengths on the quality factor Q and magnetic field h for the
first numbers of a discrete spectrum are presented in Fig. 2.
Asymptotic behaviour of the magnetization wavelengths depend-
ences on the external magnetic field can be easily obtained from the
(15).
Thus, having h Q , we can get for the spectrum brunches:
2
,n
n
R
L Q h
P
(16)
where Pn–zeros of the Bessel function J1(x):
1
( ) 0,nJ P 1 2
3.817, 7.0156, ...P P
For the ferromagnetic systems with high anisotropy Q 1, we can
get asymptotic behaviour at ( 1) 0 :h Q
2
,
( 1)
n
n
R
L
G h Q
(17)
where Gn–zeros of the Bessel function J0(x):
0
( ) 0,nJ G 1 2
2.4048, 5.5201, ...G G
It follows from the Eqs. (16), (17) that, at h Q for any mode, the
magnetostatic modulations wavelength tends to zero obeying square-
root law, while, for the systems with 1Q at ( 1) 0h Q , the
wavelength asymptotically tends to .
a b c
Fig. 2. Magnetostatic modulations wavelength dependence for several first
modes of a spectrum.
1388 Yu. I. DZHEZHERYA, O. Yu. GOROBETS, O. P. KUZ et al.
3. EXPERIMENTAL DETAILS
As it has been already mentioned, there are different types of lattices
of magnetic domains in the ferromagnetic materials under certain
conditions: the stripe domain structure, hexagonal lattices of cylindri-
cal magnetic domains, etc. However, the situation is even more typical
when there are more complicated inhomogeneous magnetization pat-
terns in ferromagnets, for which existence of the large-scale qua-
siperiodic ‘over-lattices’ is typically observed ‘against’ micro scale pe-
riodic structure of magnetic domains.
For example, open domain structure with a magnetization direction
perpendicular to the magnetic microwire surface [10]. As a rule, long
ferromagnetic cylinder can have such configurations of domains that
we can see not only the microscale domain structure for the amorphous
magnetic micro wire but the quasi-periodic change of magnetization
direction which is expressed in large-scale quasi-periodic change of the
angle slope of magnetic domains concerning the symmetry axis of a
microwire [10].
Similarly, the long-range magnetic structures of iron and steel cyl-
inders with the Bitter’s method application (a sedimentation method of
highly dispersed paramagnetic powders (Fe2O3) on a ferromagnetic
surface from the distilled water) were revealed [11].
Magnetic structures observed experimentally in [11—16] for thin
iron and steel cylinders are typical in comparison with the structures
observed by other authors [10]. Such long-range domain structures of
steel and iron cylinders as those have been shown in [11—16] can essen-
tially affect the processes in electrolytes in the vicinity of their surfac-
es, in particular the processes of chemical etching in acids solutions.
In the present work with the use of the Bitter’s powder-like figures’
method, we have revealed the quasi-periodic distribution of magneto-
static fields formed by an external magnetic field of about 1—10 kOe
applied along the axis of the steel cylinder and absent when the exter-
nal magnetic field is not applied.
To investigate the magnetic field influence on the surface structure
as a result of metal ferromagnet corrosion, we compared the steel cyl-
inder surfaces as a result of corrosion in the solution of nitric acid
without and with the magnetic field applied along the steel cylinder
axis. Besides, the steel cylinders’ surfaces under the experiments be-
fore the immersion on the solution were controlled by the optical mi-
croscope and the error of the medial diameter was less than 1 micron
along the whole length.
For definiteness, let us consider typical change of the steel cylinder
shape in a magnetic field in a nitric acid solution. The steel that the
cylinder (DSTU 1050-88) has been made of, has the following composi-
tion: iron–98%, other elements (nickel, copper, chrome, carbon,
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1389
phosphorus, sulphur, silicon, manganese)–2%, and a surface before
the experiment had smooth enough structure (Fig. 3, a), the cylinder
length was equal to 18 mm in the experiments which results are given
in Figs. 3, 4 and in Table 1.
The optical images of initial cylinder surface and cylinders after
etching in 7% water solution of nitric acid are given in Figs. 3, b—e.
It is clear that the cylinders corrode uniformly along the axis with
formation of a smooth surface without appreciable dents and hills
without external magnetic field. The diameter of cylinders along the
axis within an error did not depend on coordinate.
Magnetostatic fields’ distribution in dependence on initial diameter
of a ferromagnetic cylinder was visualized by the Bitter’s powder-like
figures’ method. The highly dispersed paramagnetic powder of iron
oxide was used. Powder sedimentation was carried out with and with-
out external magnetic field. Non-magnetized cylinders of different
Fig. 3. The images of the initial cylinder d 550 m (a) and the cylinders after
different duration of etching in a 7% solution of nitric acid without external
magnetic field: b–460 m, c–440 m, d–400 m, e–360 m.
Fig. 4. Allocation of paramagnetic powder on a surface of the not magnetized
cylinder of D 440 m.
1390
diameter
purpose.
The 23
distilled
system o
field app
ized. The
until the
460 m a
ternal ma
It is cl
periodic
The av
the etchi
Accord
periods o
der figur
ders of a
TABLE 1
on the cyl
The cylin
der diam-
eter D, m
460
440
400
360
Yu. I. DZH
rs were fas
3 ml of sus
water were
or in a cons
plied, the cy
e powder se
e saturation
after sedim
agnetic fiel
lear from F
magnetic d
verage dim
ing figures
ding to the
of the struc
res and etc
a wide rang
. The image
linder diame
n-
-
m
The image
visualisat
scale distr
HEZHERYA,
stened on a
spension co
e added to t
stant homo
ylinder tur
edimentatio
n. The opti
mentation o
ld is given i
Fig. 4 that
domain stru
mensional ch
are given i
e results, th
ctures
3
L
ching are id
e of diamet
of the powd
eter.
e of the powd
tion of quasi
ribution of m
fields
O. Yu. GORO
a thread an
ontaining a
the cell, wh
ogeneous m
rned along
on on the c
ical image
of the para
in Fig. 4.
t, without m
ucture of th
haracterist
in Table 2.
he width of
1 2
L L ob
dentical wi
ters in exte
der figures a
der figures f
iperiodic lon
magnetostat
OBETS, O. P. K
nd placed in
a paramag
hich was ou
magnetic fi
its directio
ylinder wa
of the cyli
amagnetic
magnetic f
he steel cyli
tics of the
f elevation
btained by
ithin the e
ernal magn
and the etchi
for
ng
tic
The im
figures
eleva
KUZ et al.
nside a cel
netic powd
utside of a
eld. With
on and was
s carried fo
inder with
powder wit
ield, the la
inder is not
powder fig
s L1, caviti
the method
rror for st
netic field f
ing figures d
mage of the e
s with quasi-
ations and ca
ll for this
der in the
magnetic
magnetic
s magnet-
or 15 min
diameter
thout ex-
arge-scale
t formed.
gures and
ies L2 and
d of pow-
teel cylin-
for homo-
depending
etching
-periodic
avities
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1391
geneous external magnetic field value В 3 kG. The average width of
elevations of the Bitter’s powder figures and elevations of etching fig-
ures is about 100 m. The length of cavities is about 200 m. There-
fore, the cavities are approximately twice wider than elevations. The
length of period of the structures is approximately 300 m.
The regions with the increased and decreased etching rates of fer-
romagnetic cylinder appear due to the inhomogeneous quasi-periodic
magnetostatic-fields’ distribution in the ferromagnetic cylinder. The
nonuniform magnetic fields of cylinder domain structure create the
nonuniform concentration distribution of paramagnetic or effectively
paramagnetic cluster products of chemical etching [17] at the interface
with an electrolyte that leads to the cylinder heterogeneity dissolution
along the axis and to formation of the quasi-periodic structure on its
surface [11—16].
The hysteresis curve of the steel cylinder is presented in Fig. 5. The
Fig. 5. The hysteresis curve of the steel cylinder, coercive forceНс 17 Oe.
TABLE 2. The average dimensional characteristics of the powder figures and
the etching figures.
D,
m
Dimensional characteristics
of the powder figures
Dimensional characteristics
of the etching figures
L1,
m
1,
m
L2,
m
2,
m
L3,
m
3,
m
L1,
m
1,
m
L2,
m
2,
m
L3,
m
3,
m
460 100 10 240 20 340 30 100 10 230 30 320 30
440 100 10 220 20 320 20 100 10 200 20 300 20
400 110 10 220 30 320 30 110 10 200 20 310 20
360 100 10 210 30 310 30 110 10 180 30 310 30
1392 Yu. I. DZHEZHERYA, O. Yu. GOROBETS, O. P. KUZ et al.
hysteresis curve comparison with the results of visualization of the
large-scale distribution of magnetostatic fields by means of the powder
figures gives the possibility to admit that the short-range non-regular
domain structure with the sizes of separate domains less than the cyl-
inder diameter exists in external magnetic fields, lower than critical
field Нcr.
The process of cylinder magnetization is not terminated with the ex-
ternal magnetic field exceeding Нcr, and the large-scale quasi-periodic
domain structure is created, and the magnetization of the sample line-
arly grows at the subsequent increase of an external magnetic field.
4. CONCLUSION
It is shown for cylinders of different diameters (Table 2) that for-
mation of etching figures under external magnetic field is caused by
spatial distribution of their magnetostatic fields. As a result, it is
shown in the present work for the steel cylinders of different diameter
that the quasi-periodic structure of corrode surfaces is created during
their chemical etching in a solution of nitric acid with the constant
magnetic field applied, while the quasi-periodic structure of corrode
surfaces is not formed under the same experimental conditions with-
out magnetic field influence. Besides, the quasi-periodic structure of
the cylinder that is observed due to its etching arises only on ferro-
magnetic samples and the characteristic period of the quasi-periodic
structure equals to the period of the long-range magnetic structure of
ferromagnetic sample.
The results of the present work prove experimentally the possibility
of formation of inhomogeneous boundary conditions for the electric
field potential and a current density, offered in [18], on an interface
metal—electrolyte, if metal is spatially homogeneous with its chemical
compound and mechanical properties.
REFERENCES
1. Ch. Kittel, Phys. Rev., 70, 965 (1946).
2. A. A. Thiele, Bell System Techn. J., 48: 3287 (1969).
3. A. H. Bobeck and E. Della Torre, Magnetic Bubbles (Amsterdam:
North-Holland Publishing Co.: 1975).
4. A. P. Malozemoff and J. C. Slonczewski, Magnetic Domain Walls in Bubble
Materials (New York: Academic Press: 1979).
5. A. N. Eschenfelder, Physics and Technology of Cylindrical Magnetic Domains
(New York: Wiley: 1983).
6. J. A. Cape and G. W. Lehman, J. Appl. Phys., 42: 5732 (1971).
7. Yu. І. Dzhezherya, M. V. Sorokіn, and O. O. Bubuk, Naukovі Visti NTUU ‘KPI’,
4: 51 (2006) (in Ukrainian).
PERIODIC MODULATIONS OF MAGNETOSTATIC FIELD IN CYLINDER 1393
8. Yu. I. Dzhezherya, M. V. Sorokin, and E. A. Bubuk, Zh. Eksp. Teor. Fiz., 133:
844 (2007).
9. Yu. I. Dzhezherya and K. O. Demіshev, Metallofiz. Noveishie Tekhnol., 34,
No. 4: 429 (2012) (in Ukrainian).
10. Yu. Kabanov, A. Zukov, V. Zukova, and J. Gonzalez, International Conference
‘Functional Materials’ (Partenit, The Crimea, Ukraine, 2005), p. 66.
11. M. Yu. Ilchenko, S. V. Gorobets, O. Yu. Gorobets, and O. K. Dvoynenko,
International Conference ‘Functional Matetials’ ICFM-2011 (Partenit, The
Crimea, Ukraine, October 3—8, 2011), p. 393.
12. O. Yu. Gorobets, S. V. Gorobets, D. O. Derecha, and O. M. Brukva,
J. Phys. Chem. C, 112: 3373 (2008).
13. O. Yu. Gorobets and D. O. Derecha, Mater. Sci., 24: 1017 (2007).
14. S. V. Gorobets, O. Yu. Gorobets, O. K. Dvoinenko, and G. L. Lebeda,
Phys. Met. Metallogr., 113: 129 (2012).
15. S. V. Gorobets, O. Yu. Gorobets, S. P. Mazur, and A. A. Slusar, physica status
solidi (c), 1: 3686 (2004).
16. S. V. Gorobets, O. Yu. Gorobets, and O. M. Brukva, Appl. Surf. Sci., 252/2: 448
(2005).
17. O. Yu. Gorobets, Yu. I. Gorobets, I. A. Bondar, and Yu. A. Legenkiy,
J. Magn. Magn. Mater., 330: 76 (2013).
18. О. Yu. Gorobets, Yu. I. Gorobets, and V. P. Rospotnyuk, Metallofiz. Noveishie
Tekhnol., 34, No. 7: 895 (2012) (in Ukrainian).
<<
/ASCII85EncodePages false
/AllowTransparency false
/AutoPositionEPSFiles true
/AutoRotatePages /None
/Binding /Left
/CalGrayProfile (Dot Gain 20%)
/CalRGBProfile (sRGB IEC61966-2.1)
/CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2)
/sRGBProfile (sRGB IEC61966-2.1)
/CannotEmbedFontPolicy /Error
/CompatibilityLevel 1.4
/CompressObjects /Tags
/CompressPages true
/ConvertImagesToIndexed true
/PassThroughJPEGImages true
/CreateJobTicket false
/DefaultRenderingIntent /Default
/DetectBlends true
/DetectCurves 0.0000
/ColorConversionStrategy /CMYK
/DoThumbnails false
/EmbedAllFonts true
/EmbedOpenType false
/ParseICCProfilesInComments true
/EmbedJobOptions true
/DSCReportingLevel 0
/EmitDSCWarnings false
/EndPage -1
/ImageMemory 1048576
/LockDistillerParams false
/MaxSubsetPct 100
/Optimize true
/OPM 1
/ParseDSCComments true
/ParseDSCCommentsForDocInfo true
/PreserveCopyPage true
/PreserveDICMYKValues true
/PreserveEPSInfo true
/PreserveFlatness true
/PreserveHalftoneInfo false
/PreserveOPIComments true
/PreserveOverprintSettings true
/StartPage 1
/SubsetFonts true
/TransferFunctionInfo /Apply
/UCRandBGInfo /Preserve
/UsePrologue false
/ColorSettingsFile ()
/AlwaysEmbed [ true
]
/NeverEmbed [ true
]
/AntiAliasColorImages false
/CropColorImages true
/ColorImageMinResolution 300
/ColorImageMinResolutionPolicy /OK
/DownsampleColorImages true
/ColorImageDownsampleType /Bicubic
/ColorImageResolution 300
/ColorImageDepth -1
/ColorImageMinDownsampleDepth 1
/ColorImageDownsampleThreshold 1.50000
/EncodeColorImages true
/ColorImageFilter /DCTEncode
/AutoFilterColorImages true
/ColorImageAutoFilterStrategy /JPEG
/ColorACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/ColorImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000ColorACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000ColorImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasGrayImages false
/CropGrayImages true
/GrayImageMinResolution 300
/GrayImageMinResolutionPolicy /OK
/DownsampleGrayImages true
/GrayImageDownsampleType /Bicubic
/GrayImageResolution 300
/GrayImageDepth -1
/GrayImageMinDownsampleDepth 2
/GrayImageDownsampleThreshold 1.50000
/EncodeGrayImages true
/GrayImageFilter /DCTEncode
/AutoFilterGrayImages true
/GrayImageAutoFilterStrategy /JPEG
/GrayACSImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/GrayImageDict <<
/QFactor 0.15
/HSamples [1 1 1 1] /VSamples [1 1 1 1]
>>
/JPEG2000GrayACSImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/JPEG2000GrayImageDict <<
/TileWidth 256
/TileHeight 256
/Quality 30
>>
/AntiAliasMonoImages false
/CropMonoImages true
/MonoImageMinResolution 1200
/MonoImageMinResolutionPolicy /OK
/DownsampleMonoImages true
/MonoImageDownsampleType /Bicubic
/MonoImageResolution 1200
/MonoImageDepth -1
/MonoImageDownsampleThreshold 1.50000
/EncodeMonoImages true
/MonoImageFilter /CCITTFaxEncode
/MonoImageDict <<
/K -1
>>
/AllowPSXObjects false
/CheckCompliance [
/None
]
/PDFX1aCheck false
/PDFX3Check false
/PDFXCompliantPDFOnly false
/PDFXNoTrimBoxError true
/PDFXTrimBoxToMediaBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXSetBleedBoxToMediaBox true
/PDFXBleedBoxToTrimBoxOffset [
0.00000
0.00000
0.00000
0.00000
]
/PDFXOutputIntentProfile ()
/PDFXOutputConditionIdentifier ()
/PDFXOutputCondition ()
/PDFXRegistryName ()
/PDFXTrapped /False
/CreateJDFFile false
/Description <<
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
/BGR <FEFF04180437043f043e043b043704320430043904420435002004420435043704380020043d0430044104420440043e0439043a0438002c00200437043000200434043000200441044a0437043404300432043004420435002000410064006f00620065002000500044004600200434043e043a0443043c0435043d04420438002c0020043c0430043a04410438043c0430043b043d043e0020043f044004380433043e04340435043d04380020043704300020043204380441043e043a043e043a0430044704350441044204320435043d0020043f04350447043004420020043704300020043f044004350434043f0435044704300442043d04300020043f043e04340433043e0442043e0432043a0430002e002000200421044a04370434043004340435043d043804420435002000500044004600200434043e043a0443043c0435043d044204380020043c043e0433043004420020043404300020044104350020043e0442043204300440044f0442002004410020004100630072006f00620061007400200438002000410064006f00620065002000520065006100640065007200200035002e00300020043800200441043b0435043404320430044904380020043204350440044104380438002e>
/CHS <FEFF4f7f75288fd94e9b8bbe5b9a521b5efa7684002000410064006f006200650020005000440046002065876863900275284e8e9ad88d2891cf76845370524d53705237300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c676562535f00521b5efa768400200050004400460020658768633002>
/CHT <FEFF4f7f752890194e9b8a2d7f6e5efa7acb7684002000410064006f006200650020005000440046002065874ef69069752865bc9ad854c18cea76845370524d5370523786557406300260a853ef4ee54f7f75280020004100630072006f0062006100740020548c002000410064006f00620065002000520065006100640065007200200035002e003000204ee553ca66f49ad87248672c4f86958b555f5df25efa7acb76840020005000440046002065874ef63002>
/CZE <FEFF005400610074006f0020006e006100730074006100760065006e00ed00200070006f0075017e0069006a007400650020006b0020007600790074007600e101590065006e00ed00200064006f006b0075006d0065006e0074016f002000410064006f006200650020005000440046002c0020006b00740065007200e90020007300650020006e0065006a006c00e90070006500200068006f006400ed002000700072006f0020006b00760061006c00690074006e00ed0020007400690073006b00200061002000700072006500700072006500730073002e002000200056007900740076006f01590065006e00e900200064006f006b0075006d0065006e007400790020005000440046002000620075006400650020006d006f017e006e00e90020006f007400650076015900ed007400200076002000700072006f006700720061006d0065006300680020004100630072006f00620061007400200061002000410064006f00620065002000520065006100640065007200200035002e0030002000610020006e006f0076011b006a016100ed00630068002e>
/DAN <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>
/DEU <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>
/ESP <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>
/ETI <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>
/FRA <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>
/GRE <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>
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
/HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. Stvoreni PDF dokumenti mogu se otvoriti Acrobat i Adobe Reader 5.0 i kasnijim verzijama.)
/HUN <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>
/ITA <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>
/JPN <FEFF9ad854c18cea306a30d730ea30d730ec30b951fa529b7528002000410064006f0062006500200050004400460020658766f8306e4f5c6210306b4f7f75283057307e305930023053306e8a2d5b9a30674f5c62103055308c305f0020005000440046002030d530a130a430eb306f3001004100630072006f0062006100740020304a30883073002000410064006f00620065002000520065006100640065007200200035002e003000204ee5964d3067958b304f30533068304c3067304d307e305930023053306e8a2d5b9a306b306f30d530a930f330c8306e57cb30818fbc307f304c5fc59808306730593002>
/KOR <FEFFc7740020c124c815c7440020c0acc6a9d558c5ec0020ace0d488c9c80020c2dcd5d80020c778c1c4c5d00020ac00c7a50020c801d569d55c002000410064006f0062006500200050004400460020bb38c11cb97c0020c791c131d569b2c8b2e4002e0020c774b807ac8c0020c791c131b41c00200050004400460020bb38c11cb2940020004100630072006f0062006100740020bc0f002000410064006f00620065002000520065006100640065007200200035002e00300020c774c0c1c5d0c11c0020c5f40020c2180020c788c2b5b2c8b2e4002e>
/LTH <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>
/LVI <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>
/NLD (Gebruik deze instellingen om Adobe PDF-documenten te maken die zijn geoptimaliseerd voor prepress-afdrukken van hoge kwaliteit. De gemaakte PDF-documenten kunnen worden geopend met Acrobat en Adobe Reader 5.0 en hoger.)
/NOR <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>
/POL <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>
/PTB <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>
/RUM <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>
/RUS <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>
/SKY <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>
/SLV <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>
/SUO <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>
/SVE <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>
/TUR <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>
/UKR <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>
/ENU (Use these settings to create Adobe PDF documents best suited for high-quality prepress printing. Created PDF documents can be opened with Acrobat and Adobe Reader 5.0 and later.)
>>
/Namespace [
(Adobe)
(Common)
(1.0)
]
/OtherNamespaces [
<<
/AsReaderSpreads false
/CropImagesToFrames true
/ErrorControl /WarnAndContinue
/FlattenerIgnoreSpreadOverrides false
/IncludeGuidesGrids false
/IncludeNonPrinting false
/IncludeSlug false
/Namespace [
(Adobe)
(InDesign)
(4.0)
]
/OmitPlacedBitmaps false
/OmitPlacedEPS false
/OmitPlacedPDF false
/SimulateOverprint /Legacy
>>
<<
/AddBleedMarks false
/AddColorBars false
/AddCropMarks false
/AddPageInfo false
/AddRegMarks false
/ConvertColors /ConvertToCMYK
/DestinationProfileName ()
/DestinationProfileSelector /DocumentCMYK
/Downsample16BitImages true
/FlattenerPreset <<
/PresetSelector /MediumResolution
>>
/FormElements false
/GenerateStructure false
/IncludeBookmarks false
/IncludeHyperlinks false
/IncludeInteractive false
/IncludeLayers false
/IncludeProfiles false
/MultimediaHandling /UseObjectSettings
/Namespace [
(Adobe)
(CreativeSuite)
(2.0)
]
/PDFXOutputIntentProfileSelector /DocumentCMYK
/PreserveEditing true
/UntaggedCMYKHandling /LeaveUntagged
/UntaggedRGBHandling /UseDocumentProfile
/UseDocumentBleed false
>>
]
>> setdistillerparams
<<
/HWResolution [2400 2400]
/PageSize [612.000 792.000]
>> setpagedevice
|
| id | nasplib_isofts_kiev_ua-123456789-112623 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1024-1809 |
| language | English |
| last_indexed | 2025-12-07T18:40:01Z |
| publishDate | 2016 |
| publisher | Інститут металофізики ім. Г.В. Курдюмова НАН України |
| record_format | dspace |
| spelling | Dzhezherya, Yu.I. Gorobets, O.Yu. Kuz, O.P. Klymuk, O.S. Gorobets, Yu.I. 2017-01-24T12:37:24Z 2017-01-24T12:37:24Z 2016 Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions / Yu.I. Dzhezherya, O.Yu. Gorobets, O.P. Kuz, O.S. Klymuk, and Yu.I. Gorobets // Металлофизика и новейшие технологии. — 2016. — Т. 38, № 10. — С. 1379-1393. — Бібліогр.: 18 назв. — англ. 1024-1809 DOI: 10.15407/mfint.38.10.1379 PACS: 03.50.De, 41.20.Gz, 75.10.-b, 75.30.Gw, 75.60.Ch, 75.70.Kw, 81.65.Cf https://nasplib.isofts.kiev.ua/handle/123456789/112623 Ordinary cylindrical specimens with easy-axis anisotropy perpendicular to the axis of a cylinder are studied. As shown, the inhomogeneous long-wave magnetic configurations of harmonic type can be created and observed in such samples. A linear theory is developed to simplify the set of Landau— Lifshitz and Maxwell’s equations to one general equation for a magnetostatic potential. The ranges of magnetic fields and the self-parameters responsible for the inhomogeneous periodic configuration formation are determined when solving a boundary value problem for a magnetostatic potential. Dependence of the period of magnetization wave on a magnetic field value, the constant of anisotropy and diameter of a cylinder is determined. The proposed theory gives qualitative explanation of the experiment when, using the Bitter’s powder-like figures’ method, quasi-periodic distributions of the magnetostatic fields can be observed in samples. These fields arise under external magnetic field of about 1 kOe directed along the axis of a steel cylinder and are absent without external magnetic field. An example of practical application of long-wave magnetic structures for a surface morphology control during chemical etching of ferromagnetic metals in acid solutions is given. The quasi-periodic structure of a corrosion surface of ferromagnetic cylinder corresponds to the period of a long-range magnetic structure. Досліджено циліндричні зразки з легковісною анізотропією, перпендикулярною до осі циліндру. Показано, що в таких зразках можна створювати і спостерігати неоднорідні довгохвильові магнетні конфіґурації гармонічного типу. Було розвинуто лінійну теорію, яка зводить систему рівнянь Ландау—Ліфшиця та Максвеллових, що описують магнетний стан системи, до одного загального рівняння для магнетостатичного потенціялу. В ході розв’язання крайової задачі для магнетостатичного потенціялу визначено діяпазон магнетних полів і власних параметрів системи, за яких ймовірним є утворення неоднорідної періодичної конфіґурації. Визначено залежність періоду хвилі намагнетованости від амплітуди магнетного поля, константи анізотропії та діяметра циліндру. Запропонована теорія дає якісне пояснення експерименту, коли при застосуванні Біттерової методи порошкових фіґур можливе спостереження квазиперіодичних розподілів магнетостатичних полів, що утворені при прикладанні зовнішнього магнетного поля порядку 1 кЕ вздовж осі сталевого циліндру, тоді як без прикладання зовнішнього магнетного поля магнетостатичні поля відсутні. Наведено приклад практичного застосування довгохвильових магнетних структур для керування морфологією поверхні при хемічному щавленні феромагнетних металів у розчинах кислот. При цьому квазиперіодична структура поверхні кородованого феромагнетного циліндра відповідає періоду його довгомасштабної магнетної структури. Исследованы цилиндрические образцы с легкоосной анизотропией, перпендикулярной оси цилиндра. Показано, что в таких образцах можно создать и наблюдать неоднородные длинноволновые магнитные конфигурации гармонического типа. Развита линейная теория, которая сводит систему уравнений Ландау—Лифшица и Максвелла, описывающих магнитное состояние системы, к одному общему уравнению для магнитостатического потенциала. В ходе решения краевой задачи для магнитостатического потенциала определён диапазон магнитных полей и собственных параметров системы, при которых вероятным является образование неоднородной периодической конфигурации. Определена зависимость периода волны намагниченности от амплитуды магнитного поля, константы анизотропии и диаметра цилиндра. Предложенная теория даёт качественное объяснение эксперимента, когда при применении метода порошковых фигур Биттера возможно наблюдение квазипериодических распределений магнитостатических полей, образованных при воздействии внешнего магнитного поля порядка 1 кЕ вдоль оси стального цилиндра, в то время как без приложения внешнего магнитного поля магнитостатические поля отсутствуют. Приведён пример практического использования длинноволновых магнитных структур для управления морфологией поверхности при химическом травлении ферромагнитных материалов в растворах кислот. При этом квазипериодическая структура поверхности корродированного ферромагнитного цилиндра соответствует периоду его длинномасштабной структуры. en Інститут металофізики ім. Г.В. Курдюмова НАН України Металлофизика и новейшие технологии Металлические поверхности и плёнки Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions Періодичні модуляції магнетостатичного поля у феромагнетному циліндрі та їх вплив на формування фіґур щавлення у розчинах кислот Периодические модуляции магнитостатического поля в ферромагнитном цилиндре и их влияние на формирование фигур травления в растворах кислот Article published earlier |
| spellingShingle | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions Dzhezherya, Yu.I. Gorobets, O.Yu. Kuz, O.P. Klymuk, O.S. Gorobets, Yu.I. Металлические поверхности и плёнки |
| title | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions |
| title_alt | Періодичні модуляції магнетостатичного поля у феромагнетному циліндрі та їх вплив на формування фіґур щавлення у розчинах кислот Периодические модуляции магнитостатического поля в ферромагнитном цилиндре и их влияние на формирование фигур травления в растворах кислот |
| title_full | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions |
| title_fullStr | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions |
| title_full_unstemmed | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions |
| title_short | Periodic Modulations of Magnetostatic Field in Ferromagnetic Cylinder and Their Influence on Etching Figure Formation in Acid Solutions |
| title_sort | periodic modulations of magnetostatic field in ferromagnetic cylinder and their influence on etching figure formation in acid solutions |
| topic | Металлические поверхности и плёнки |
| topic_facet | Металлические поверхности и плёнки |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/112623 |
| work_keys_str_mv | AT dzhezheryayui periodicmodulationsofmagnetostaticfieldinferromagneticcylinderandtheirinfluenceonetchingfigureformationinacidsolutions AT gorobetsoyu periodicmodulationsofmagnetostaticfieldinferromagneticcylinderandtheirinfluenceonetchingfigureformationinacidsolutions AT kuzop periodicmodulationsofmagnetostaticfieldinferromagneticcylinderandtheirinfluenceonetchingfigureformationinacidsolutions AT klymukos periodicmodulationsofmagnetostaticfieldinferromagneticcylinderandtheirinfluenceonetchingfigureformationinacidsolutions AT gorobetsyui periodicmodulationsofmagnetostaticfieldinferromagneticcylinderandtheirinfluenceonetchingfigureformationinacidsolutions AT dzhezheryayui períodičnímodulâcíímagnetostatičnogopolâuferomagnetnomucilíndrítaíhvplivnaformuvannâfígurŝavlennâurozčinahkislot AT gorobetsoyu períodičnímodulâcíímagnetostatičnogopolâuferomagnetnomucilíndrítaíhvplivnaformuvannâfígurŝavlennâurozčinahkislot AT kuzop períodičnímodulâcíímagnetostatičnogopolâuferomagnetnomucilíndrítaíhvplivnaformuvannâfígurŝavlennâurozčinahkislot AT klymukos períodičnímodulâcíímagnetostatičnogopolâuferomagnetnomucilíndrítaíhvplivnaformuvannâfígurŝavlennâurozčinahkislot AT gorobetsyui períodičnímodulâcíímagnetostatičnogopolâuferomagnetnomucilíndrítaíhvplivnaformuvannâfígurŝavlennâurozčinahkislot AT dzhezheryayui periodičeskiemodulâciimagnitostatičeskogopolâvferromagnitnomcilindreiihvliânienaformirovaniefigurtravleniâvrastvorahkislot AT gorobetsoyu periodičeskiemodulâciimagnitostatičeskogopolâvferromagnitnomcilindreiihvliânienaformirovaniefigurtravleniâvrastvorahkislot AT kuzop periodičeskiemodulâciimagnitostatičeskogopolâvferromagnitnomcilindreiihvliânienaformirovaniefigurtravleniâvrastvorahkislot AT klymukos periodičeskiemodulâciimagnitostatičeskogopolâvferromagnitnomcilindreiihvliânienaformirovaniefigurtravleniâvrastvorahkislot AT gorobetsyui periodičeskiemodulâciimagnitostatičeskogopolâvferromagnitnomcilindreiihvliânienaformirovaniefigurtravleniâvrastvorahkislot |