Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification
The modification of the surface structure of the hybrid coating TiN/Al₂O₃ with a low-energy high-current electron beam (NCEB) is performed. The surface roughness is considered as a function of beam current. Surfaces of the obtained samples are investigated within the two-dimensional multifractal det...
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irk-123456789-1208212017-06-14T03:03:22Z Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification Pogrebnjak, A.D. Borisyuk, V.N. Bagdasaryan, A.A. The modification of the surface structure of the hybrid coating TiN/Al₂O₃ with a low-energy high-current electron beam (NCEB) is performed. The surface roughness is considered as a function of beam current. Surfaces of the obtained samples are investigated within the two-dimensional multifractal detrended fluctuation analysis (MF-DFA). The multifractal spectrum of the surface is calculated as a quantitative parameter of the roughness. It is shown that with the increase of the beam energy, the surface become more regular and uniform. Проаналiзовано процес модифiкацiї структури поверхнi гiбридного покриття TiN/Al₂O₃ пiд впливом низькоенергетичного сильнострумового електронного пучка. Шорсткiсть поверхнi розглянуто як функцiю струму пучка. Поверхнi отриманих зразкiв дослiджувались за допомогою двовимiрного мультифрактального флуктуацiйного аналiзу. Для кiлькiсного аналiзу змiни шорсткостi розрахована функцiя мультифрактального спектру. Показано, що зi збiльшенням енергiї пучка поверхня стає бiльш регулярною та рiвномiрною. 2013 Article Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification / A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan // Condensed Matter Physics. — 2013. — Т. 16, № 3. — С. 33803:1-8 . — Бібліогр.: 21 назв. — англ. 1607-324X PACS: 81.40.- z, 81.07.- b, 68.35.-p, 61.46.-w, 05.45.Df, 61.43.Hv DOI:10.5488/CMP.16.33803 arXiv:1310.1235 http://dspace.nbuv.gov.ua/handle/123456789/120821 en Condensed Matter Physics Інститут фізики конденсованих систем НАН України |
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The modification of the surface structure of the hybrid coating TiN/Al₂O₃ with a low-energy high-current electron beam (NCEB) is performed. The surface roughness is considered as a function of beam current. Surfaces of the obtained samples are investigated within the two-dimensional multifractal detrended fluctuation analysis (MF-DFA). The multifractal spectrum of the surface is calculated as a quantitative parameter of the roughness. It is shown that with the increase of the beam energy, the surface become more regular and uniform. |
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Article |
| author |
Pogrebnjak, A.D. Borisyuk, V.N. Bagdasaryan, A.A. |
| spellingShingle |
Pogrebnjak, A.D. Borisyuk, V.N. Bagdasaryan, A.A. Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification Condensed Matter Physics |
| author_facet |
Pogrebnjak, A.D. Borisyuk, V.N. Bagdasaryan, A.A. |
| author_sort |
Pogrebnjak, A.D. |
| title |
Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification |
| title_short |
Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification |
| title_full |
Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification |
| title_fullStr |
Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification |
| title_full_unstemmed |
Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification |
| title_sort |
numerical analysis of the morphological and phase changes in the tin/al₂o₃ coating under high current electron beam modification |
| publisher |
Інститут фізики конденсованих систем НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/120821 |
| citation_txt |
Numerical analysis of the morphological and phase changes in the TiN/Al₂O₃ coating under high current electron beam modification / A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan // Condensed Matter Physics. — 2013. — Т. 16, № 3. — С. 33803:1-8 . — Бібліогр.: 21 назв. — англ. |
| series |
Condensed Matter Physics |
| work_keys_str_mv |
AT pogrebnjakad numericalanalysisofthemorphologicalandphasechangesinthetinal2o3coatingunderhighcurrentelectronbeammodification AT borisyukvn numericalanalysisofthemorphologicalandphasechangesinthetinal2o3coatingunderhighcurrentelectronbeammodification AT bagdasaryanaa numericalanalysisofthemorphologicalandphasechangesinthetinal2o3coatingunderhighcurrentelectronbeammodification |
| first_indexed |
2025-07-08T18:40:34Z |
| last_indexed |
2025-07-08T18:40:34Z |
| _version_ |
1837105210576601088 |
| fulltext |
Condensed Matter Physics, 2013, Vol. 16, No 3, 33803: 1–8
DOI: 10.5488/CMP.16.33803
http://www.icmp.lviv.ua/journal
Numerical analysis of the morphological and phase
changes in the TiN/Al2O3 coating under high current
electron beam modification
A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan
Sumy State University, 2 Rimskii-Korsakov St., 40007 Sumy, Ukraine
Received May 7, 2013, in final form July 10, 2013
A modification of the surface structure of the hybrid coating TiN/Al2O3 with a low-energy high-current electron
beam (NCEB) is performed. The surface roughness is considered as a function of beam current. Surfaces of
the obtained samples are investigated within the two-dimensional multifractal detrended fluctuation analysis
(MF-DFA). The multifractal spectrum of the surface is calculated as a quantitative parameter of the roughness.
It is shown that with an increase of the beam energy, the surface becomes more regular and uniform.
Key words: self-similarity, fractal dimension, hybrid coating, high-current electron beam(s) effect
PACS: 81.40.- z, 81.07.- b, 68.35.-p, 61.46.-w, 05.45.Df, 61.43.Hv
1. Introduction
Many objects and systems in nature exhibit a self-similar or self-affine structure [1, 2]. Self-similarity
means that each segment of the initial set has the same structure as the whole object.The properties of
such structures can be described by specific parameters, such as fractal dimension (or set of dimensions
in the case of the multifractal objects [3]), Hurst exponent and others. Common examples of such objects
are the Koch curve and the Cantor set. The property of self-similarity is inherent not only to topological
structures but also to the phase space of complex stochastic systems with a hierarchical structure and
non participant regions. The stochastic fractals can be illustrated through the Lorenz attractor and non-
stationary time series [4].
The surface roughness characterization is an important problem for both applied and theoretical
science. Many image techniques have been extensively used to investigate the rough surfaces, such as
atomic force microscopy, secondary electron microscopy, optical imaging techniques and others [5]. It
has been established [6] that the roughness parameters based on conventional theories depend on the
sampling interval of a particular measuring instrument used. Using the methods of fractal geometry, this
problem is eliminated because the fractal model includes topological parameters that do not depend on
the resolution of the instrument used. The concept of fractal dimension, in contrast to traditional meth-
ods, has made it possible to explain the physical properties of the system depending on the geometry
of the surface [7, 8]. For this purpose, many methods have been proposed, such as detrended fluctua-
tion analysis (DFA) [9], two-dimensional multifractal detrended fluctuation analysis (2D MF-FDA) [10] a
generalization of the 1D DFA and MF-DFA [11], rescaled range analysis [12] and many more [13].
In the present article we present the investigation of a self-similar structure of the TiN/Al2O3 hybrid
coating surfaces using numerical methods of scaling analysis. Our calculations are based on the algorithm
of two-dimensional multifractal detrended fluctuation analysis (MF-DFA) [9]. This algorithm was initially
was developed for investigation of the time series as a one-dimensional self-similar set [14], and later on
generalized for the analysis of more complicated objects [9]. Our calculations make it possible to present
a quantitative characteristic of the surface roughness, and to compare it for different samples. Earlier
in the work [15] we have considered the dependence of the generalized Hurst exponent surface of the
© A.D. Pogrebnjak, V.N. Borisyuk, A.A Bagdasaryan, 2013 33803-1
http://dx.doi.org/10.5488/CMP.16.33803
http://www.icmp.lviv.ua/journal
A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan
coating TiN/Al2O3 at different beam current densities. However, a complete representation of multifrac-
tal formalism is achieved by calculating the multifractal spectrum f (α) and singularity strength α. This
knowledge would be useful because the roughness of hybrid coatings is an important factor at contact
wear and physical phenomena such as absorption, catalysis and the dissolution of a fractal object.
The paper is organized as follows. In the opening section we briefly describe the object of our re-
search— TiN/Al2O3 hybrid coatings, obtaining through plasma-detonation the technology and additional
treatment by high-current electron beams (HCEB) at different regimes of partial melting. Next, we refer
the main steps of the MF-DFA algorithm and present the results of our calculations, comparing them for
different samples. The final section is devoted to discussion.
2. Samples under investigation
We used the α-Al2O3 powder with a particle size of 27 to 56 microns as initial material for the deposi-
tion, which was applied in the facility “Impulse-5” on the substrate of austenite steel AISI 321 (18 wt.% Cr;
9 wt.% Ni; 1 wt.% Ti; 0.3 wt.% Cr; Fe the rest; 0.3 mm and 2mm thickness) [16–18]. An oxide-aluminum ce-
ramics and other coatings based on titanium carbide and tungsten carbide and nitrides possess a number
of useful properties, which are capable of providing a corrosion protection, high hardness and mechan-
ical strength, low wear and good electro-isolation properties. However, these coatings are characterized
by the presence of macro-, micro- and submicroscopic porosity, and a certain number of defects [19].
For this purpose, to increase the corrosion resistance of protective ceramic coatings and to reduce the
concentration of defects caused by deposition, the surface was coated with TiN layer. The deposition con-
tinued for 20 min in the atmosphere of ionized nitrogen, under 700 K temperature, and about 10−1 to
10−2 operation pressure of the reaction gas. The deposition TiN layer was made by means of the facility
“Bulat-3T” with a vacuum-arc source (Kyiv, Ukraine).
One of the promising methods in solving the problem of adhesion of thin film coatings and reducing
the roughness of the powder sublayer is a thermal treatment of the surface by high-current electron
beams (HCEB) in the regime of partial melting. This technology made it possible to heal the micropores
and to stimulate the diffusion processes between the deposited particles and layers.
It was found that the electron beam melting of hybrid coating surfaces TiN/Al2O3 (20 mA beam cur-
rent) was accompanied by a partial melting of non-uniformities occurring in the surface structure (figu-
re 1). It can be seen that the coating had a layered but melted structure. Regions of pit destruction were
found on the surface (dark points seen in the photo). These craters appeared as a result of degassing
induced by the electron beam melting of the surface layers. In addition, there were found light-color in-
clusions in the coatings. Repeated HCEB meltings of the coatings induced essential (even visible) changes
in the surface relief.
During the second stage of melting, the geometry the surface layers of hybrid coatings depended on
the electron beam power density. Correspondingly, the higher it was, the better these hybrid coating sur-
faces mixed and the more uniform they became. The thermal activation by the electron beam of coatings
with the magnitude of 35 mA is accompanied by intense changes in the geometry of the surface layer.
A complete fusion of the material near the surface is observed. The coating has a developed structure
and represents a smooth alternation of peaks and valleys into each other, which is characterized by an
appreciable decrease in the surface roughness.
3. Image analysis methodology
All surfaces were investigated within two-dimensional multifractal detrended fluctuation analyses
(MF-DFA) methodology [9, 14]. This algorithm allows one to calculate the main parameters of the self-
similar structure [1].
Self-similar surface is considered as a two-dimensional data array X (i , j ), where i , j has discrete va-
lues i = 1,2, . . . , M and j = 1,2, . . . , N . X (i , j ) itself is a surface obtained from the digital electronic mi-
croscopy image by decomposing it according to pixel indexes (i , j ) and brightness level X . This surface is
33803-2
Numerical analysis of the TiN/Al2O3 coating
(a) (b)
(c) (d)
Figure 1. SEM images of surfaces of hybrid TiN/Al2O3 coatings under HCEB modification. The beam cur-
rent in the electron beam quenching of coating surfaces was, respectively: (a) — 20 mA, (b) — 20+15 mA,
(c) — 20+25 mA, (d) — 20+35 mA.
fragmented into Ms ×Ns non-overlapping segments of the sizes s, where Ms = [M/s] and Ns = [N /s] are
integer numbers.
For each segment Xϑ,ω identified by ϑ,ω the cumulative sum uϑω(i , j ):
uϑω(i , j )=
i
∑
k1=1
j
∑
k2=1
Xϑω(k1,k2) (3.1)
is calculated for all segments ϑ,ω. The next step is a detrending procedure for the obtained surface
uϑω(i , j ). The trend can be removed by the fitting procedure, when it is determined by some smooth poly-
nomial function ũϑω(i , j ). There are many possible expressions of the ũϑω(i , j ) function, but we choose
the simplest one, in order to reduce the computational time:
ũϑω(i , j ) = ai +b j +c, (3.2)
where a, b, c are coefficients defined by least-squares fitting algorithm. It should bementioned that more
complicated forms of ũϑω(i , j ) do not provide any significant improvement of the precision of themethod,
but noticeably increase computational time [9]. After detrending we arrive at a residual function:
εϑω(i , j )= uϑω(i , j )− ũϑω(i , j ), (3.3)
and a dispersion of the ϑ,ω segment of length s:
F 2
(ϑ,ω, s) =
1
s2
s
∑
i=1
s
∑
j=1
ε2
ϑω(i , j ). (3.4)
33803-3
A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan
Dispersion of all the segments is calculated through averaging over all surfaces:
Fq (s)=
{
1
Ms Ns
Ms
∑
ϑ=1
Ns
∑
ω=1
[F (ϑ,ω, s)]
q
}1/q
, (3.5)
where q is the deformation parameter initialized to increase the role of the segments with small (when
q < 0) or high (q > 0) fluctuations F 2(ϑ,ω, s), respectively. At q = 0, equation (3.5) takes the form (3.6):
F0(s) =
{
1
Ms Ns
Ms
∑
ϑ=1
Ns
∑
ω=1
ln[F (ϑ,ω, s)]
}
(3.6)
according to l’Hôpital’s rule. For statistically correct results, the values must be varied within the range
from smin = 6 to smax =min(M , N )/s. The dispersion (3.5) and the segment size s are linked through the
scaling relation:
Fq (s) ∼ sh(q)
, (3.7)
where h(q) is the generalized Hurst exponent.
Equation (3.7) can be rewritten according to the standard multifractal formalism through scaling
exponent τ(q) and partition function Zq (s) as [14]:
Zq (s) ∼ sτ(q)
, (3.8)
Zq (s) =
1
M N
M/s
∑
ϑ=1
N/s
∑
ω=1
[F (ϑ,ω, s)]
q
. (3.9)
One can relate the Hölder exponent α and the multifractal spectrum f (α) via Legendre transform
[20, 21], deriving these multifractal parameters as
α= τ′(q), (3.10)
f (α) = qα−τ(q). (3.11)
For monofractal objects, the function τ(q) is a linear dependence which, with the transition to the mul-
tifractal, becomes more curved, keeping the linear sections within q → ∞. In the analyzed structure,
multifractality can be revealed more clearly from the shape of the multifractal spectrum f (α), the width
of which provides a set of fractal dimensions (for example, for monofractal curve f (α) has a δ-function
with the fixed α value).
4. Multifractal analysis of experimental results
In this section we apply the MF-DFA method to analyze the structure of the surface of the hybrid
coating TiN/Al2O3 as shown in figure 1 at different magnitudes of the beam current.
If the object under investigation has a self-similar structure, relation (3.7) is expected to be linear
in double logarithmic scales. Figure 2 illustrates the dependence of the fluctuation function Fq (s) on the
scale s for different values of q , calculated for TiN/Al2O3 surface modified by the beam current I = 20 mA.
As it follows from figure 2, the dependence Fq (s) has a clear linear part, which means that the surface of
a hybrid coating has a self-similar structure. On the other hand, in the range where q < 0, the calculation
is expected to yield a large error.
We have computed the mass exponent τ(q) for different surfaces in the range −20 < q < 20. Figure 3
shows τ(q) as a function of q for hybrid coating surfaces under HCEB modification at different current
magnitudes. The nonlinearity of τ(q) indicates that the surface has a multifractal structure, i.e., it cannot
be completely described by a single value of a fractal dimension α. Different values of α are related to
the segments of the surface with different values of the fluctuation function Fq . The latter is calculated as
the difference of the surface local heights from some smooth fitting function. Thus, the set of the fractal
exponents f (α) can be considered as a quantitative measure of the surface roughness. The strongest
33803-4
Numerical analysis of the TiN/Al2O3 coating
Figure 2. Log-log plot of the fluctuation function Fq (s) versus the scale s for five different values of q ,
calculated for SEM image of the surface of hybrid coating, modified by the beam current I = 20 mA.
Figure 3. Mass exponent τ(q) as a function of q .
Lines 1–4 correspond to the surfaces modificated
by HCEB with current 20 mA, 20 + 15 mA, 20 +
25 mA, 20+35 mA, respectively.
Figure 4. Multifractal spectra of hybrid coat-
ing surfaces TiN/Al2O3 under HCEB modification.
Lines 1–4 correspond to the surfaces modified by
HCEB with current 20 mA, 20+15 mA, 20+25 mA,
20+35 mA, respectively. The curves 2–4 have been
shifted for clarity.
multifractality was observed for the surface being modified with the beam current magnitude I = 20 mA,
becoming more weaker with the growth of the beam current. It is shown that geometry of the surface
layers of hybrid coatings depends on the electron density of the beam power.
We have calculated the values of the singularity strength function α and the multifractal spectrum
f (α) using equations (3.10) and (3.11). Figure 4 shows the spectrum f (α) for four samples under inves-
tigation. As it can be seen, the width of f (α) is different for the samples treated with different density of
the beam current. The more uniform is the surface, the more restricted is the spectrum f (α).
Minimum and maximum values of α(q) are important statistical parameters that describe the multi-
fractal nature of fracture surfaces. These values are the singularity strengths associated with the region
of the sets where the measures are the least and the most singular, respectively [10].
In the formalism of multifractals, αmin is related to the maximum probability measure by Pmax ∼
ε−△α, where ε represents the scale approaching zero and it is a small quantity, whereas αmax is related
to the minimum probability measure through Pmin ∼ εαmax . The width △ α can be used to describe the
range of the probability measures [10]:
Pmax
Pmin
∼ ε−△α . (4.1)
33803-5
A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan
The larger is α, the wider is the probability distribution, and the strongest is the difference between
the highest and the lowest growth probability.
Figure 5. The width of multifractal spectrum △α for surfaces being modified with different beam current
magnitudes.
Figure 5 illustrates the relation between the width of the multifractal spectrum and different values
of the beam current. As it can be seen, the width of the multifractal spectrum decreases with an increase
of the current magnitude. The change of the surface relief, as shown in figure 5, proves the correspon-
dence between the theoretical calculations and experimental results, i.e., with an increase of the beam
current, the surface becomes more regular. A significant reduction of multifractal spectrum width with
the increase of the current magnitude of 25 mA occurs due to remelting which smooths out the craters
produced by degassing. A further increase of the beam current provides only an enhanced homogeneity
of the structure and mass transfer processes between the layers composing the coating matrix. Figure 6
shows the dependence of phase composition on the singularity strength for hybrid coatings after duplex
melting of their surfaces.
Figure 6. The dependence of phase composition for hybrid coatings after duplex melting of their surfaces
with different singularity strengths.
Special attention was paid to the change of concentration of the elements in the hybrid coating after
duplex melting. It was shown in work [16] that the initial composition was about 60 wt. % of Al2O3. All
the other phases and compounds comprised 40 wt. %.
As we can see from figure 6, with an increase of the density of the energy flow and, consequently, a
decrease of the spectrum width, △α was accompanied by an insignificant increase in α-Al2O3 amount.
A further increase of the current led to a decrease in the percentage content of α-phase from 58 wt. % to
50 wt. % and to an increase of γ-Al2O3 from 25 wt. % to 34 wt. %. The concentration of other phases and
compounds underwent insignificant changes. Hence, a non-monotonous change of the phase percentage
33803-6
Numerical analysis of the TiN/Al2O3 coating
content was associated with an increase of the energy density. As a result, the surface of hybrid coating
became more uniform by TiN and Al2O3 coating melting.
5. Conclusion
The mechanical studies demonstrated that hybrid coatings based on corundum and titanium nitride,
which were modified by an electron beam until melted, possessed notably better servicing characteris-
tics. Therefore, this technology could be applied to solve technical problems (for example, to decrease
wear, to protect from corrosion, to increase adhesion and to improve nano- and micro-hardness).
Quantitative parameters of the surface structure obtained by the two-dimensional multifractal fluctu-
ation method can be used to characterize the topology of the interface under modification. As shown by
the numerical analysis, the character of surface morphology changed from high non-uniform roughness
to smoothed regions with a gradual increase of the current density electron beam.
References
1. Feder J., Fractals, Plenum Press, New-York, London, 1998.
2. Olemskoi A., Danylchenko S., Borisyuk V., Shuda I., Metallofiz. Noveishie Tehknol., 2009, 31, 777.
3. Olemskoi A.A., Fractal in Condensed Matter Physics, In: Physics Reviews, 1995, 18, Part 1, 1.
4. Olemskoi A.A., Synergetics of Complex Systems: Phenomenology and Statistical Theory, KRASAND, Moscow, 2009
(in Russian).
5. Arnéodo A., Decoster N., Roux S.G., Eur. Phys. J. B, 2000, 15, 567; doi:10.1007/s100510051161.
6. Jeng Y.R., Tsai P.S., Fang T.H., Microelectron. Eng., 2003, 65, 406; doi:10.1016/S0167-9317(03)00052-2.
7. Pfeifer P., Wu Y.J., Cole M.W., Krim J., Phys. Rev. Lett., 1989, 62, 1997; doi:10.1103/PhysRevLett.62.1997.
8. Borisyuk V.N., Kassi J., Holovchenko A.I., J. Nano-Electron. Phys., 2011, 3, No. 4, 20.
9. Gu G.F., Zhou W.X., Phys. Rev. E, 2006, 74, 061104; doi:10.1103/PhysRevE.74.061104.
10. Liu C., Jiang X.L., Liu T., Zhao L., Zhou W.X., Yuan W.K., Appl. Surf. Sci., 2009, 255, 4239;
doi:10.1016/j.apsusc.2008.11.014.
11. Niu M.R., Zhou W.X., Yan Z.Y., Guo Q.H., Liang Q.F., Wang F.C., Yu Z.H., Chem. Eng. J., 2008, 143, 230;
doi:10.1016/j.cej.2008.04.011.
12. Hurst H.E., Trans. Am. Soc. Civ. Eng., 1951, 116, 770.
13. Olemskoi A., Shuda I., Borisyuk V., Europhys. Lett., 2010, 89, 50007; doi:10.1209/0295-5075/89/50007.
14. Kanthelhardt J.W., Zscheinger S.A., Koscienly-Bunde E., Havlin S., Bunde A., Stanley H.E., Physica A, 2002, 316,
87; doi:10.1016/S0378-4371(02)01383-3.
15. Pogrebnyak A.D., Borisyuk V.N., Bagdasaryan A.A., In: Proceedings of the International Conference “Nanomate-
rials: Applications and Properties” (Alushta, 2012), Vol. 1, 2012, 02NFC27.
16. Pogrebnyak A.D., Kravchenko Yu.A., Kislitsyn S.M., Ruzimov Sh.M., Noli F., Misaelides P., Hatzidimitriou A., Surf.
Coat. Technol., 2006, 201, 2621; doi:10.1016/j.surfcoat.2006.05.018.
17. Pogrebnjak A. D., Ponomarev A.G., Shpak A.P., Kunitskii Yu.A., Phys. Usp., 2012, 55, 270;
doi:10.3367/UFNe.0182.201203d.0287.
18. Pogrebnyak A.D., Sobol O.V., Beresnev V.M., Turbin P.V., Il’yashenko M.V., Kirik G.V., Makhmudov N.A.,
Shypylenko A.P., Kaverin M.V., Tashmetov M.Yu., Pshyk A.V., In: Nanostructured Materials and Nanotechnology
IV: Ceramic Engineering and Science Proceedings, 2010, 31, 127; doi:10.1002/9780470944042.ch14.
19. Kunchenko Yu.V., Kunchenko V.V., Nekliudov I.M., Kartmazov G.N., Andreev A.A., Probl. Atomic Sci. Technol.,
2007, 2, 203.
20. Peitgen H., Jürgens H., Saupe D., Chaos and Fractals: New Frontiers of Sciences, Springer-Verlag, New-York, 1992.
21. Halsey T.C., Jensen M.H., Kadanoff L.P., Procaccia I., Shraiman B.I., Phys. Rev. A, 1986, 33, 1141;
doi:10.1103/PhysRevA.33.1141.
33803-7
http://dx.doi.org/10.1007/s100510051161
http://dx.doi.org/10.1016/S0167-9317(03)00052-2
http://dx.doi.org/10.1103/PhysRevLett.62.1997
http://dx.doi.org/10.1103/PhysRevE.74.061104
http://dx.doi.org/10.1016/j.apsusc.2008.11.014
http://dx.doi.org/10.1016/j.cej.2008.04.011
http://dx.doi.org/10.1209/0295-5075/89/50007
http://dx.doi.org/10.1016/S0378-4371(02)01383-3
http://dx.doi.org/10.1016/j.surfcoat.2006.05.018
http://dx.doi.org/10.3367/UFNe.0182.201203d.0287
http://dx.doi.org/10.1002/9780470944042.ch14
http://dx.doi.org/10.1103/PhysRevA.33.1141
A.D. Pogrebnjak, V.N. Borisyuk, A.A. Bagdasaryan
Чисельний аналiз морфологiчних та фазових перетворень
покриття TiN/Al2O3 пiд час модифiкацiї
низькоенергетичним сильнострумовим електронним
пучком
О.Д. Погребняк, В.М. Борисюк, А.А. Багдасарян
Сумський державний унiверситет , вул. Римського-Корсакова, 2, 40007 Суми, Україна
Проаналiзовано процес модифiкацiї структури поверхнi гiбридного покриття TiN/Al2O3 пiд впливом низь-
коенергетичного сильнострумового електронного пучка. Шорсткiсть поверхнi розглянуто як функцiю
струму пучка. Поверхнi отриманих зразкiв дослiджувались за допомогою двовимiрного мультифракталь-
ного флуктуацiйного аналiзу. Для кiлькiсного аналiзу змiни шорсткостi розрахована функцiя мультифра-
ктального спектру. Показано, що зi збiльшенням енергiї пучка поверхня стає бiльш регулярною та рiвно-
мiрною.
Ключовi слова: самоподiбнiсть, фрактальна розмiрнiсть, гiбридне покриття, НПЕП ефект
33803-8
Introduction
Samples under investigation
Image analysis methodology
Multifractal analysis of experimental results
Conclusion
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