=Paper=
{{Paper
|id=Vol-3896/short11
|storemode=property
|title=Information System for Design of Thin Multilayer Film Processes Parameters Management based on Diffusion
|pdfUrl=https://ceur-ws.org/Vol-3896/short11.pdf
|volume=Vol-3896
|authors=Mykhaylo Petryk,Vitalii Chyzh,Halyna Tsupryk,Oksana Petryk
|dblpUrl=https://dblp.org/rec/conf/ittap/PetrykCTP24
}}
==Information System for Design of Thin Multilayer Film Processes Parameters Management based on Diffusion==
https://ceur-ws.org/Vol-3896/short11.pdf
Information System for Design of Thin
Multilayer Film Processes Parameters
Management based on Diffusion
Mykhaylo Petryk1, Vitalii Chyzh1, Halyna Tsupryk1, Oksana Petryk1
1
Ternopil Ivan Puluj National Technical University, 56 Ruska str., Ternopil 46001, Ukraine
Abstract
This designing investigates the diffusion phenomena within multilayer films, emphasizing the
crucial role of mathematical modeling and computational simulation techniques. By considering the
transitions between adjacent layers, our approach incorporates advanced modeling methods and
software frameworks, including integral transformations, to accurately depict diffusion processes.
Theoretical insights are validated through experimental data analysis and solution identification
based on the theory of state control of multicomponent systems. Our results reveal close agreement
between modeled and experimental aluminum concentration distributions, particularly as the
duration of multilayer formation approaches completion. Furthermore, our findings suggest
practical applications, including enhancing the efficiency of experimental studies and exploring
properties of emerging nanomaterials. This study underscores the synergy between theoretical
modeling and experimental validation, offering insights into complex transport phenomena and
paving the way for advancements in materials science and engineering.
Keywords
Multilayer Films, Computational Simulation, Software Frameworks, Data-Driven Analysis, Complex
Diffusion Mechanisms 1
1. Introduction
Addressing the complexities inherent in investigating diffusion within multilayer films
demands advancements in modern modeling techniques, computation algorithms software
frameworks, enabling accurate depiction of phenomena while accounting for transitions
between adjacent layers [1, 2]. Integral transformations stand out among the efficacious
methods employed to comprehensively tackle these challenges, serving to derive solutions for
diverse boundary value problems in mathematical physics concerning homogeneous
structures. This encompasses diffusion scenarios across various environments, thereby
facilitating their mathematical representation.
1
ITTAP’2024: 4th International Workshop on Information Technologies: Theoretical and Applied Problems, October 23-
25, 2024, Ternopil, Ukraine, Opole, Poland ∗
∗
Corresponding author.
†
These authors contributed equally.
petrykmr@gmail.com (M. Petryk); vitalik.c@gmail.com (V. Chyzh); galyna.tsupryk@gmail.com (H. Tsupryk);
oopp3@ukr.net (O. Petryk)
0000-0001-6612-7213 (M. Petryk); 0009-007-2308-7363 (V. Chyzh); 0000-0002-8106-5628 (H. Tsupryk); 0000-0001-
8622-4344 (O. Petryk)
© 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
ceur-ws.org
Workshop ISSN 1613-0073
Proceedings
Moreover, alongside the indispensable role of advanced modeling techniques and software,
sophisticated computational approaches play a crucial role in tackling the challenges of
studying diffusion within multilayer media. Leveraging cutting-edge methodologies in
computer programming and software architecture, these approaches elevate the capabilities of
mathematical methods, such as integral transformations, to unprecedented levels of precision
and efficiency. This symbiotic relationship between mathematical modeling and
computational innovation not only enhances our ability to accurately represent diffusion
phenomena within multilayer structures but also paves the way for new avenues of
exploration and analysis [3, 4].
Furthermore, the integration of modern modeling techniques with state-of-the-art
computational tools facilitates a deeper understanding of diffusion processes across diverse
material compositions and environmental conditions. Through harnessing the power of
numerical simulations and data-driven analyses, researchers can unlock insights into
previously inaccessible complex diffusion mechanisms. This multidisciplinary approach
empowers scientists and engineers to not only address fundamental questions in materials
science and engineering but also devise innovative strategies for optimizing the performance
and functionality of multilayer films across various technological applications.
In this article, the authors endeavor to amalgamate complex mathematical models with
best practices in software development to address the challenge of computer simulation of
diffusion transport processes within multilayer nanofilms.
2. Disogning Methidology and Physics Problem
Formulation
In this conceptual framework, mutual diffusion occurs between adjacent layers of the
multicomposite at each interface. The mechanisms governing this mutual transfer are
influenced by the variable gradients and rates of concentration change at the interface
boundaries between layers. By integrating changes in concentrations and their gradients over
time into the boundary and interface conditions, it becomes feasible to model the mechanisms
of this additional mutual transport alongside the fundamental transport equations.
When devising a mathematical model for diffusion transfer within oxide films, the
consideration of a multilayer configuration is essential. Assuming that the diffusion of atoms
of constituent components (such as aluminum, molybdenum, and silicon) primarily governs
system mixing, concentration profiles for such a multilayer system can be derived from the
Fick equations. These equations incorporate boundary conditions at the outer layers and
account for contact conditions between successive layers. This methodological approach
results in a mathematical model that comprehensively describes the diffusion transfer process
within a planar multilayered medium.
Figure 1: Schema of multilayer nanofilm
(1)
Within domain ( )
Here:
Ck represents diffusion concentrations; Dk represents diffusion coefficients; k2 define
mass distribution coefficient (at first attempt ).
The initial and boundary condition of proposed model are:
(2)
(3)
(4)
With boundary conditions across variable x
; (5)
Here:
are coefficients which determines boundary and contact
conditions on the multilayer media.
diffusion coefficients in direction of z axis;
diffusion coefficient in direction of x axis;
─ thikness of k-th layer; ─ media thickness.
Solution of the formulated mathematical problem can be found by applying Fourier
transforms following algorithm detail described at [5].
(6)
Еhe following functions are used here
- Cauchy's function
(7)
- Green’s functions
(8)
3. Computer identification of parameters
According to the results of experimental data and using the solution identification
methodology were carried out using the theory of state control of multicomponent systems
[5].
The identified diffusion coefficients distributions correspond to experimental data, are used
as input parameters of the obtained mathematical solution of model (1)-(5) for modeling and
analysis of concentration distributions for aluminum component of nanofilms media.
In fig. 2 the distributions of diffusion coefficients for the constituent components of
nanofilm (aluminum) are presented, reproduced using the methods of optimal control of the
state of multicomponent transport systems, the analytical solution of model and the data of
experimental observations [6]. Both heat and corrosion resistance of result alloys are
determined by the level of aluminum, which ensures the formation of protective surface
oxides. Let us consider the results of computer modeling and parameters identification of
aluminum concentration distributions in each of the five points.
Figure 2: Diffusion coefficients distribution in Aluminum sample at five different points
Special software framework was developed for numerical modeling of concentration
distributions in aluminum using the obtained distributions of diffusion coefficients. To achieve
good accuracy and high performance, multi-threaded parallelization [7] were used for the
modular software architecture, following software engineering best practices [8]. The
individual results of numerical modeling are shown in the figures below.
Figure 3: Concentration of aluminum in film (point 2)
Figure 4 : Concentration of aluminum in film (point 4)
In fig. 3-5 show the results of numerical modeling and use traces of experimental observations
(exp) reflecting the aluminum content. Presented distributions were constructed for different
formation times of technological multilayer of nanofilm: the given time equal to (1T)
corresponds to the experimental time (20 days). The duration of the formation of the
technological multilayer of the nanofilm due to the molecular diffusion of the specified
components is divided into 5 periods, which include the formation of the protective multilayer
from the initial period (0.25 T) to the final period (1 T).
Figure 5: Concentration of aluminum in film (point 5)
As can be seen on the plots, distribution characteristic is in complete correlation with
aluminum content at a depth after 100 μm at the reduced time of 0.25T and 0.33T, which
corresponds to one third of the experiment duration. In addition, content is close to zero. The
notable increase in aluminum content are for time from 0.33T to 0.75T.
The profiles obtained by modeling aluminum concentration distributions are well agreed
with the corresponding experimental profiles in the cases of multilayer formation time
reaching the period of completion of the formation of the nanofilms protective multilayer. The
maximum deviation is around 2-5%, which points on the reliability of the mathematical model
and the proposed simulation software. Consequentially, the obtained results have options for
practical use. Such simulations can be used to improve the efficiency of experimental studies
of transport in multicomponent multi composites and to study the properties of new
nanomaterials
Conclusions
The convergence between modeled and experimental aluminum concentration
distributions underscores the efficacy of our approach, particularly as the duration of
multilayer formation approaches the completion phase of the nanofilm's protective layer.
With maximum deviations are in small range, and our findings attest to the reliability of both
the mathematical model and the simulation software employed. These results not only
validate our methodology but also signal its potential for practical utilization.
Moving forward, the implications of our information systems software extend beyond
mere validation; they open doors to practical applications. Using leveraging simulations, we
can enhance the efficiency of experimental investigations into transport phenomena within
multicomponent composites. Furthermore, our approach offers a systematic means of
studying the properties of emerging nanomaterials, thereby contributing to advancements in
materials science and engineering.
As we continue to refine and expand upon these methodologies and control systems of
designing, we are poised to make significant strides in our understanding of multilayer film
dynamics and the development of novel nanomaterials with tailored properties for diverse
applications.
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