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Nanoscience and Technology: An International Journal
ESCI SJR: 0.219 SNIP: 0.484 CiteScore™: 0.37

ISSN Print: 2572-4258
ISSN Online: 2572-4266

Nanoscience and Technology: An International Journal

Formerly Known as Nanomechanics Science and Technology: An International Journal

DOI: 10.1615/NanoSciTechnolIntJ.2019031220
Forthcoming Article

Multi-stage kinetics for composite Ti-TxCy synthesis

Anna G Knyazeva
Institute of Strength Physics and Materials Science SB RAS; Tomsk Polytechnik University
Valery N Demidov
Tomsk Polytechnik University


This work is devoted to the development of numerical algorithm for kinetic equation system corresponding to composite Ti-TxCy formation with the perspective of following using of this algorithm in the model of technology process of composite synthesis. In this system Ti-C, irreversible phases could appear in some conditions typical for composite synthesis. However, there are no theoretical works on modeling the synthesis of composites that would consider chemical stages eventuating to nonequilibrium phase composition. The present work uses a multi-stage kinetic model for the formation of nonstoichiometric titanium carbide at a preset temperature. Reaction rates are assumed depending on concentration by mass action law. Additionally the reaction rate retardation typical for solid – state reactions is assumed with the help of special function. As a result we come to nonlinear kinetic equations. The paper suggests an iteration algorithm for numerical embodiment of the kinetic model and its special variants corresponding to different initiation conditions and initial data. Depending on the temperature and time of the synthesis, the final product contains the following carbides TiC, Ti2C, Ti3C2, TiC2 in various proportions. Among the irreversible carbides, the most stable one is TiC2. Taking into account the retardation of the reactions by the layer of products in the kinetic functions only extends the time necessary for the conversions.