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Original papers Advanced structural materials, materials for extreme conditions
УДК 536.46:546.05:621.762.2 DOI: 10.17277/jamt.2023.04.pp.324-332
Synthesis of the TiC + 20 % NiCr composite from a granular mixture
© Nail I. Abzalova, Boris S. Seplyarskiia^, Roman A. Kochetkova, Tatiana G. Lisinaa, Mikhail I. Alymova
a Merzhanov Institute of Structural Macrokinetics and Materials Science RAS (ISMAN), 8, Academician Osipyan St., Chernogolovka, 142432, Russian Federation
И seplb1@mail.ru
Abstract: For the first time, the synthesis of the TiC + 20 % NiCr composite from a granular mixture with titanium of different dispersion, containing different amounts of impurity gases, was carried out. The features of the combustion process of a granular charge are explained by its structure - the presence of physically separated cells (granules) with a powder mixture, which can ignite because of conductive heat transfer from granule to granule or convective heating by gas released from the charge. The combustion front in the powder and granular charge based on titanium with a smaller characteristic size of titanium particles propagated at a higher rate, despite the higher content of impurity gases in it. The effect of impurity gas release on the combustion rate of powder mixtures is explained using a convective-conductive combustion model. It is shown that the combustion of the studied mixtures with granules 0.6 and 1.7 mm in size took place in a safe conductive mode, making it possible to scale the process. X-ray phase analysis of the combustion products showed that the phase composition of the synthesis products did not depend on the size of the granules. When using a granular mixture containing finely dispersed titanium powder, synthesis products were obtained without side phases of intermetallic compounds, which were easily crushed to micron sizes and could be used for plasma spraying of wear-resistant coatings.
Keywords: combustion synthesis; protective coating; granules; titanium particle size; impurity outgassing.
For citation: Abzalov NI, Seplyarskii BS, Kochetkov RA, Lisina TG, Alymov MI. Synthesis of the TiC + 20 % NiCr composite from a granular mixture. Journal of Advanced Materials and Technologies. 2023;8(4):324-332. DOI: 10.17277/jamt.2023.04.pp.324-332
Синтез композита Т1С + 20 % МСг из гранулированной шихты
© Н. И. Абзалова, Б. С. Сеплярскийа^, Р. А. Кочеткова, Т. Г. Лисинаа, М. И. Алымова
а Институт структурной макрокинетики и проблем материаловедения им. А. Г. Мержанова Российской академии наук (ИСМАН), ул. Академика Осипьяна, 8, Черноголовка, Московская область, 142432, Российская Федерация
И seplb1@mail.ru
Аннотация: Впервые проведен синтез композита ТЮ + 20 % №Сг из гранулированной шихты с титаном разной дисперсности, содержащим разное количество примесных газов. Особенности процесса горения гранулированной шихты объяснены ее структурой - наличием физически выделенных ячеек (гранул) с порошковой смесью, воспламенение которых может происходить вследствие кондуктивной передачи тепла от гранулы к грануле или конвективного нагрева газом, выделяющимся из шихты. Фронт горения в порошковой и гранулированной шихте на основе титана с меньшим характерным размером частиц титана распространялся с более высокой скоростью, несмотря на более высокое содержание примесных газов в ней. Влияние примесного газовыделения на скорость горения порошковых смесей объяснено с использованием конвективно-кондуктивной модели горения. Показано, что горение исследованных смесей с гранулами размером 0,6 и 1,7 мм проходило в безопасном кондуктивном режиме, позволяющем масштабировать процесс. Рентгенофазовый анализ продуктов горения показал, что фазовый состав продуктов синтеза не зависел от размера гранул. При использовании гранулированной шихты, содержащей мелкодисперсной порошок титана, получены продукты синтеза без побочных фаз интерметаллидов,
которые легко дробились до микронных размеров и могут быть использованы для плазменного напыления износоустойчивых покрытий.
Ключевые слова: СВС; защитное покрытие; гранулы; размер частиц титана; примесное газовыделение.
Для цитирования: Abzalov NI, Seplyarskii BS, Kochetkov RA, Lisina TG, Alymov MI. Synthesis of the TiC + 20 % NiCr composite from a granular mixture. Journal of Advanced Materials and Technologies. 2023;8(4):324-332. DOI: 10.17277/jamt.2023.04.pp.324-332
1. Introduction
Materials based on transition metal carbides with metal binders are increasingly used as a substitute for hard alloys based on tungsten and chromium carbides [1-14]. To reduce brittleness and increase adhesion during spraying of protective coatings, metal binders such as Ni, Mo, NiCr, Cu, etc. are introduced into titanium carbide-based powders. [15-19]. A promising area of application of TiC-NiCr composite powders is their use for protective coatings on parts of industrial equipment and machinery to protect against wear and corrosion [20]. The addition of NiCr to carbide coatings increases their resistance in oxidizing environments as Cr2O3 is formed, which is especially important for the use of parts at high temperatures [21, 22]. Self-propagating high-temperature synthesis (SHS, also called "combustion synthesis") is one of the methods of producing such powders [23]. SHS is characterized by a combination of low energy consumption, high process speed, purity and homogeneity of the product obtained in one technological cycle [24-40]. In the process of synthesis, easily fusible metal binder is melted, which provides melt spreading and dispersion of initial reagents in the products. The microstructure of coatings obtained by sputtering of synthesized powders is characterized by the spherical shape of carbide grains and their homogeneous distribution over the volume of the metal matrix, which reduces the pitting of carbide inclusions [25, 41]. However, refractory and strong sintered materials produced by SHS from powder components must be crushed to micron sizes for use in sputtering [25], which requires significant energy inputs and additional operations for cleaning from the substance of grinding bodies.
Scaling up the process of obtaining composite materials by SHS requires reproducibility of combustion parameters, predictability of the properties of the obtained products, and reduction of the cost of milling the synthesis products. These objectives can be achieved by changing the structure of the mixture from powder to granular, which levels the influence of the content of impurity gases and moisture in the charge and ensures the stability of the properties of the obtained products [42]. When using granular mixtures based on titanium, the phase
composition of synthesis products depended on the dispersity and morphology of titanium powder particles [43-45]. The brittle sinter obtained as a result of synthesis was easily separated into separate granules, their grinding was not difficult and was not accompanied by contamination of grinding bodies [46]. However, depending on the content of gas-emitting components in the charge and the organic binder used in granulation, combustion can switch to a convective mode, in which the combustion rate depends quadratically on the gas mass flow [45, 47]. Since the combustion time of granules behind the ignition front is almost independent of the gas flow rate, there is a positive feedback between the combustion rate and the flow of gas filtered through the front: the higher the combustion rate, the greater the gas flow, and vice versa [48]. Therefore, in order to avoid uncontrolled growth of the combustion rate, it is necessary to carry out synthesis in the conductive mode. The authors formulated the critical conditions for the transition of combustion to the convective mode in [49].
There are no data on synthesis of titanium carbide with nichrome bond from granular mixtures (Ti + C) + 20 % NiCr in scientific literature. Therefore, the aim of the present work is, firstly, in one process operation to synthesize metal-ceramics of TiC + 20 % NiCr composition, and secondly, to find out the influence of dispersity and morphology of titanium powder and granule size on combustion modes of Ti + C + 20 % NiCr mixtures with titanium of different dispersity, phase composition of their synthesis products and the possibility of their grinding.
2. Materials and Methods
2.1. Experimental method
The combustion patterns were studied using the original experimental setup (Fig. 1).
The experiments were carried out according to the following procedure: the mixture under study 8 was poured into a vertically mounted transparent quartz tube (outer diameter - 19 mm, height - 90 mm, wall thickness - 2 mm), on a substrate of mineral wool (Al2O3 base) 9.
Fig. 1. Diagram of the experimental setup: 1 - cylinder with nitrogen; 2 - cylinder with argon; 3 - computer for recording the video; 4 - computer for recording sensor readings with an ADC; 5 - flow and pressure sensors; 6 - digital video camera; 7 - electric element for igniting a mixture; 8 - charge; 9 - layer of mineral wool; 10 - metal grid; 11 - gas switch (position I, nitrogen; II, argon; III, supply of gas is blocked)
Signals from sensors 5 and LEDs informing about the position of the gas supply switch 11 were fed to the computer 4 via ADC in real time mode. The thermal pulse from the tungsten spiral 7 started the combustion process from the upper end of the sample. Before each experiment, the sample was purged with a stream of argon at a pressure drop of 1 atm to avoid shrinkage of the unburned part of the backfill during combustion and to obtain stable results. The height of the initial mixture (both powder and granular) after blowing was (40 ± 5) mm.
The combustion process was recorded using a digital video camera 6 SONY FDR AX-700 (shooting speed 100-250 fps). Based on the frame-by-frame processing of the video recordings, the velocity of the combustion front was calculated.
2.2. Starting materials
The Russia-manufactured powders used in this work and their brief characteristics are given in Table 1.
Figure 2 shows the particle size distribution of the initial metal components in percentage of the total mass of the investigated powder. Further in the text and in calculations of the necessary and sufficient conditions for heating the particles of powder mixture components, their values at the point of maximum of the distribution function are used as characteristic sizes: d(Ti) = 60 and 120 ^m, d(NiCr) = 90 ^m.
The external view of titanium particles with d(Ti) = 60 and 120 ^m, obtained using scanning electron microscopy, is shown in Fig. 3.
Table 1. Substances and reagents used
Particle size, ^m
Components Grade up to up to
50 wt. % 90 wt. %
Titanium: d = 60 ^m d = 120 ^m
PTM (Polema, Tula)
Soot
Nichrome, d = 90 ^m
< 54 < 86 <105 <169
P-803 (YATU, Yaroslavl) Ni80Cr20 (Polema, Tula) Polyvinylbutyral (POLYMER-DZ, Dzerzhinsk) Ethyl alcohol technical 95 % (Ferein, Elektrogorsk)
< 2.5
< 75
< 4
< 142
16 14 12 10 8 6 4 2
P, wt. % Ti(60 ym
Ti(120 |im )
Ni80Cr20
0
d, |am
Fig. 2. Particle size distribution of the initial metal components as a percentage of the total mass of the powder under study
Wf&MM ■h^fc 1 jM r Ww *
HLr fl Lfl N m
^hhbpjva^^^^v" »jiOji. * 1/ ■■ ^rW.tM^ fm
|>- ™< 100 urn wd- es mm ekt - wooku sgnjia-sea dm nf«b»ijr»-ii j«s I v.«- mix 100 urn wo - 6.» mm eht- joookv snjrul* - SE2du ii mtymj3ti™ 13» Hi
(a) (b)
Fig. 3. Micrographs of titanium powders with d(Ti) = 120 ^m (a) and with d(Ti) = 60 ^m (b)
As can be seen from the photographs, titanium particles with d(Ti) = 120 ^m have a lentil-like shape, which is smoother than that of dendritic particles with d(Ti) = 60 ^m. To determine the amount of impurity gases in titanium powders of different dispersity, a sample weighing (100 ± 0.01) g was placed in a vacuum chamber under standard conditions and the pressure was reduced to 2.6 Pa. At 300 °C, the sample was kept in vacuum for 40 min. The sample was then heated to 850 °C and held at this temperature for 60 minutes. After the chamber had cooled to room temperature, the sample was removed and reweighed to determine the mass loss during processing.
2.3. Granulation
Granulation of the compositions was carried out as follows: preliminary initial powder mixture was mixed for 4 h in a gravity-type mixer. Then a four per cent (wt.) solution of polyvinyl butyral in ethyl alcohol was added to the obtained mixture. The pastelike mass obtained after mixing was rubbed through a sieve with mesh size of 1.25 and 1.6 mm. The obtained particles were rolled on a rotating horizontal surface to give them spherical shape. The particles were then air dried for 10 h and dispersed on a vibrating screen. The content of polyvinyl butyral in the dry mixture was about 1 %. Granules with sizes of 0.4-0.8 and 1.4-2.0 mm were used for the experiments. The half sum of the upper and lower size limits, i.e., 0.6 and 1.7 mm, respectively, was taken as the characteristic size of the granule fraction.
The stoichiometry of initial mixtures was calculated for obtaining metal-ceramics of 80 % TiC + 20 % NiCr composition. Thermodynamic calculations were performed using the THERMO software package (http://www.ism.ac.ru/thermo/). The calculated maximum combustion temperature of the mixture Tad = 2890 K.
2.4. Methods of analysis
To determine the particle size distribution of the components, a laser analyser Microsizer-201C (VA Instalt, St. Peterburg, Russia) was used. The phase composition of the final product was studied on X-ray diffractometer DRON-3M (IC Bourevestnik, St. Peterburg, Russia) using monochromatic CuKa-radiation. The diffractograms were taken in step-scanning mode in the range of angles 29 = 20-80° with an imaging step of 0.2°. The obtained data were analysed using PDF-2 database. Microstructure of titanium powders was investigated by SEM method on Ultra Plus microscope by Carl Zeiss (Cermany). The obtained synthesis products were milled in a planetary mill Pulverisette by Fritsch (Cermany) for 5 minutes with zirconium oxide balls of 8 mm diameter with a weight ratio of balls and mixture 30:1, rotor speed 320 rpm.
3. Results and Discussion
At the first stage, initial titanium powders used in the mixtures were thermovacuum-treated. The mass loss due to heat treatment was about 0.7 wt.% at d(Ti) = 60 ^m and 0.2 % at d(Ti) = 120 ^m.
The external view and combustion shots of titanium-based powder and granulated charge at d(Ti) = 60 ^m are shown in Fig. 4. The mixtures with d(Ti) = 120 ^m look almost the same.
The rate of propagation of the combustion front is the most important macrokinetic parameter of the combustion process. Synthesis of mixtures with d(Ti) = 60 ^m (a) and 120 ^m (b), both powder and granular mixtures was carried out in steady-state regime. The shape of the combustion front is flat, which allowed reliable measurement of the position of the combustion front at different moments of time and determination of its propagation rate.
Fig. 4. External view of a quartz tube and frames of combustion of (Ti + C) + 20 % NiCr mixtures with d(Ti) = 60 ^m (a) and 120 ^m (b, c): the initial powder mixture (a), granular mixture with D = 0.6 mm (b),
and granular mixture with D = 1.7 mm (c)
Table 2. Combustion rates Up of powder and Ugr(D) mixtures with granules of size D; combustion rate Ucom of the substance of the granules
d(Ti), ^m Up, mm-s1 Ugr (0.6 mm), mm-s1 Ugr (D = 1.7 mm), mm-s1 Ucom, mm-s1 Ucom/Up 60 20 32 39 44 2.2
120 8 17 20.5 23 2.9
The values of combustion rates used in the calculations are averages from 3-4 experiments, the value spread is not more than 10 %. Table 2 shows the experimental values of combustion rates of powder and granular mixtures of 80 % (Ti + C) + + 20 % NiCr with titanium particles of 60 and 120 pm in size.
At the same nichrome content, the combustion rates of titanium-based powder mixtures with d(Ti) = 60 pm are almost twice as high as those with d(Ti) = 120 pm. To explain the difference in the combustion rates of powder mixtures with titanium particles of different sizes, we shall use the convective-conductive combustion model (CCCM) [50]. In accordance with this model, the propagation of the combustion wave front in a powder mixture is the movement of the melt of a fusible component under the action of capillary forces and pressure difference of impurity gases in front of and behind the melt layer. An increase in the pressure of impurity gases in front of the reaction front leads to a decrease in the combustion rate, and a decrease in pressure leads to an increase in the combustion rate. Usually, the influence of impurity gas emitted behind the melt layer (combustion front) can be neglected because it does not create increased pressure due to the high gas permeability of combustion products [51].
In accordance with [52], we consider that in a powder mixture the particles of initial components
have time to heat up and release impurity gas before the combustion front if two conditions are simultaneously fulfilled:
d < L, (1)
th < t. (2) Here d is the characteristic particle size of the powder mixture, L = aJUp is the width of the heating zone, Up is the experimental combustion rate, ac is the thermal diffusivity coefficient of the heterogeneous powder mixture, 'h(d) = d /4a is the thermal relaxation time of the particle, a is the thermal diffusivity coefficient of the particle substance and t = L/Up = ac/Up is the characteristic time of the particle in the heating zone [1]. During calculations, the value of ac was assumed to be the same, equal to ac = 10-6 m2-s—1 [53].
Calculation of the heating condition (1) showed that for titanium particles (a(Ti) = 8-10-6 m2-s—1 [54], the width of the heating zone L = 50 pm for mixtures with d(Ti) = 60 pm and L = 125 pm for mixtures with d(Ti) = 120 pm. Thus, L < d(Ti) for 60 pm titanium particles and L > d(Ti) for 120 pm titanium particle sizes. Soot particles (d(C) = 3-4 pm, a(C) =
—7 2 —1
= 2-10 m -s [55]) are heated and release impurity gas ahead of the combustion front in both cases. Nichrome contains 80 % Ni, and Ni particles release negligible amounts of impurity gas compared to
titanium and soot [42], so the effect of outgassing from nichrome can be neglected. The heating condition (2) is fulfilled for all components. Thus, inhibition of the combustion front by impurity gases from titanium for mixtures with d(Ti) = 120 pm and its absence for mixtures with d(Ti) = 60 pm explains the difference in the combustion rate of powder mixtures 80 % (Ti + C) + 20 % NiCr. A quantitative assessment of the influence of impurity outgassing on the combustion rates of these mixtures can be obtained by comparing them with the combustion rates of granular mixtures.
Table 2 shows that the combustion rates of granular mixtures were higher than those of powder mixtures of the same composition. This is due to a different mechanism of propagation of the combustion front in granular mixtures, in which the combustion rate is determined by both the combustion rate of individual granules and the rate of heat transfer from granule to granule. A granular mixture consists of individual cells (granules) containing the powder mixture and the pore space between them. It is precisely because of the discrete nature of granular mixtures and the difference in the size of the granules and grains of the resulting product that surface tension forces prevent the melt from flowing beyond the individual granules. Therefore, the high gas permeability of such charge practically does not change during the combustion process. Since the size of granules (about 1 mm) is much larger than the particle size of the initial powders, the combustion process of an individual granule can be considered similar to the combustion process of a powder mixture [44]. However, the granule has better conditions for the removal of impurity gases from the combustion zone compared to the powder charging, since the length of the filtration zone does not exceed half of the granule diameter D. In combination with the high gas permeability of the entire charging, this leads to an insignificant influence of the impurity gas release both on the combustion process of the granules themselves and on the whole sample [44]. However, a granule has better conditions for the removal of impurity gases from the combustion zone compared to a powder sample, since the length of the filtration zone does not exceed half the diameter of the granule D. In combination with the high gas permeability of the entire sample, this leads to a slight effect of impurity gas release on both levels of the combustion process: the granules themselves and the sample [56]. If in the powder mixture there is no gas release in the heating zone, granulation will lead to a decrease in the combustion rate of the sample. This is due to the presence of a granule to granule combustion transfer stage. In contrast, for the
composition where impurity gases are released in the heating zone and have an inhibitory effect, granulation leads to an increase in the combustion rate. Consequently, the observed ratio Ugr > Up (Table 2) results from the levelling of the impurity gas influence, which is released before the melt layer from soot particles, and in the mixture with d(Ti) = 120 pm - also from titanium particles.
During the combustion process, the granules of
the studied mixtures retained their size and sintered
lightly with each other. Therefore, it is assumed that
the heat transfer between them occurred mainly at the
contact points of the granules and is determined by
a conductive mechanism. An upper estimate of the
1/2
granule heating depth H = (acD/Ugr) by the time of ignition [44] gives H = 0.19 mm for granules of size D = 0.6 mm and H = 0.17 mm for D = 1.7 mm, that is, H < D. Therefore, the heating of the granule up to the moment of ignition is described by the semiinfinite body model. Then the combustion rate of the granule substance Ucom and the time of transfer of combustion between granules tig can be considered the same for granules of different sizes. Considering that the total burning time of the granule tb = D/Ugr is the sum of the combustion time of the granule substance D/Ucom and the combustion transfer time from granule to granule tig, i.e.
tb = D/Ucom + ^
(3)
com and tig to the
we obtain an expression relating Uc combustion rate of the granular mixture Ugr [44]:
Ugr = Ucom/(1 + Ucomtig/D).
(4)
By solving the system of two equations with two unknowns, obtained by successive substitution of D and Ugr values for two fractions of granules of the same composition into (4), the values Ucom = 44 mm-s-1, tig = 5 ms for d(Ti) = 60 pm, and Ucom = 23 mm-s-1, tig = 9 ms for d(Ti) = 120 pm are obtained. These results allow to assume that a conductive combustion mechanism is realized in the investigated sample-scale mixtures.
The ratio of the combustion rate of the granule substance and the powder mixture gives a quantitative estimate of the inhibitory effect of impurity gas release on the combustion rate of the powder mixture: Ucom/Up = 2.2 and 2.9 at d(Ti) = 60 and 120 pm, respectively. These estimates are close, and it is due to the rather low impurity gas content in titanium with d(Ti) = 120 pm (0.2 %), which inhibits the combustion.
The data of X-ray phase analysis (XRF) of combustion products of powder and granular mixtures are shown in Fig. 5.
It was found that the phase composition of the synthesis products of 80 % (Ni + C) + 20 % NiCr mixtures is strongly influenced by the particle size of the initial titanium powder and the type of mixture. Thus, for d(Ti) = 60 pm the composition of combustion products of powder and granular charge was the same and included phases TiC and NisCr, which coincides with the data of thermodynamic calculations. So, the observed difference in the dependence of combustion rates of powder and granular mixtures cannot be explained by a change in the phase composition of the combustion products, thus supporting the proposed explanation - the influence of impurity gas released during combustion from the components of the mixtures. In turn, d(Ti) = 120 pm is characterized by faint NisCr bond peaks, as well as by-product phases of intermetallides, which are particularly abundant in the
• • Ti
powder mixture. As in [43], there is a correlation between the smaller titanium particle size, higher combustion rate of the mixture, and the absence of intermetallic side phases.
Combustion products' samples from granules of different sizes for titanium-based mixtures of the same dispersity had similar phase composition (Fig. 6).
Thus, to obtain the target phase composition of combustion products of the studied mixtures, as in the case of nickel-bonded titanium carbide [44], it is necessary to use granular mixtures based on finely dispersed titanium powder. For the studied mixture, a safe conductive mode of combustion is realised irrespective of the granule size in the range of 0.6-1.7 mm.
As in the case of previously investigated Ti-C-Ni mixtures [57], synthesis from the granular mixture yields a sample in which the granules retain their dimensions, fuse only at the contact points, and are easily separated from each other (Figs. 7, 8).
• • TiC ■ Ni3Cr
•
1 1 I v2
1 .. JLjl/
20 40 60 29, °
Fig. 5. Results of X-ray phase analysis of combustion Fig. 6. Results of X-ray phase analysis of the combustion
products of a granular mixture of Ti + C + 20 % NiCr products of the Ti + C + 20 % NiCr granular mixture
with 1.7 mm granules at d(Ti) = 120 pm (1) based on titanium with d(Ti) = 60 pm:
and at d(Ti) = 60 pm (2) 1 - 0.4-0.8 fraction granules; 2 - 1.4-2.0 fraction granules
(a) (b) Fig 7. Samples of powder (a) and granular (b) mixtures with D = 1.7 mm after combustion
-H- » '»jSSir
(a) (b)
Fig. 8. Photographs of a granular mixture of 80 % (Ti + C) + 20 % NiCr composition with D = 1.7 mm before (a) and after (b) synthesis
After the synthesis of composites from powder and granular mixtures, a comparison of the milling efficiency of the obtained products was performed. The samples were milled in a planetary mill for 5 minutes, with a rotor speed of 320 rpm. At milling of the combustion product of titanium-based powder mixture with d(Ti) = 60 pm the yield of fraction < 250 pm was 5 %, and from the granular one with granules of size D = 1.7 mm - 94 % of the total mass of the sample.
4. Conclusion
The studies have shown that granulation of the initial charge 80 % (Ti + C) + 20 % NiCr (granule size 0.6-1.7 mm) on the basis of titanium with a specific particle size of 60 pm provides the synthesis of titanium carbide with nichrome bonding in a safe conductive mode, i.e. provides the possibility of scaling the process. Facilitated micron-size crushing of synthesis products from granular charges makes the process attractive for obtaining fine powders for wear-resistant coatings [3].
5. Funding
This study received no external funding.
6. Acknowledgements
The study was carried out using the equipment of the Distributed Core Facility Centre of the Merzhanov Institute of Structural Macrokinetics and Materials Science.
7. Conflict of interests
The authors declare no conflict of interest.
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Information about the authors / Информация об авторах
Nail I. Abzalov, Cand. Sc. (Phys. and Math), Junior Researcher Associate, Merzhanov Institute of Structural Macrokinetics and Materials Science RAS (ISMAN), Chernogolovka, Russian Federation; ORCID 00000003-0970-3709; e-mail: abzalov396@mail.ru
Абзалов Наиль Илдусович, кандидат физико-математических наук, научный сотрудник, Институт структурной макрокинетики и проблем материаловедения им. А. Г. Мержанова РАН (ИСМАН), Черноголовка, Российская Федерация; ORCID 00000003-0970-3709; e-mail: abzalov396@mail.ru
Boris S. Seplyarskii, Cand. Sc. (Phys. and Math), Leading Researcher, ISMAN, Chernogolovka, Russian Federation; ORCID 0000-0003-0852-184X; e-mail: seplb1@mail.ru
Roman A. Kochetkov, Cand. Sc. (Phys. and Math), Senior Researcher, ISMAN, Chernogolovka, Russian Federation; ORCID 0000-0003-4364-7464; e-mail: numenor@list.ru
Tatiana G. Lisina, Cand. Sc. (Phys. and Math), Senior Researcher, ISMAN, Chernogolovka, Russian Federation; ORCID 0000-0003-0454-6273; e-mail: lisina@ism.ac.ru
Mikhail I. Alymov, D. Sc. (Eng.), Professor, Corresponding member of RAS, Director ISMAN, Chernogolovka, Russian Federation; ORCID 00000001-6147-5753; e-mail: alymov@ism.ac.ru
Сеплярский Борис Семенович, кандидат физико-математических наук, ведущий научный сотрудник, ИСМАН, Черноголовка, Российская Федерация; ORCID 0000-0003-0852-184X; e-mail: seplb1@mail.ru
Кочетков Роман Александрович, кандидат физико-математических наук, старший научный сотрудник, ИСМАН, Черноголовка, Российская Федерация; ORCID 0000-0003-4364-7464; e-mail: numenor@list.ru
Лисина Татьяна Геннадиевна, кандидат физико-математических наук, старший научный сотрудник, ИСМАН, Черноголовка, Российская Федерация; ORCID 0000-0003-0454-6273; e-mail: lisina@ism.ac.ru
Алымов Михаил Иванович, доктор технических наук, профессор, член-корр. РАН, директор ИСМАН, Черноголовка, Российская Федерация; ORCID 00000001-6147-5753; e-mail: alymov@ism.ac.ru
Received 30 June 2023; Accepted 07 September 2023; Published 15 December 2023
Copyright: © Abzalov NI, Seplyarskii BS, Kochetkov RA, Lisina TG, Alymov MI, 2023. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Территория распространения - Российская Федерация, зарубежные страны Distributed is the Russian Federation and foreign countries
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