Multistage kinetics of the synthesis of Ti–TxCy composite

V. N. Demidov, A. G. Knyazeva

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


This work is devoted to the development of a numerical algorithm for the system of kinetic equations corresponding to the formation of the Ti–TxCy composite with the prospect of subsequent using of this algorithm in the model of the technology of the synthesis of composites. In this Ti–C system, irreversible phases can appear under certain conditions typical of composite synthesis. No theoretical works are available however, that would model the synthesis of composites and consider chemical stages eventuating in nonequilibrium phase composition. The present work uses a multistage kinetic model of the formation of nonstoichiometric titanium carbide at a preset temperature. Reaction rates are assumed to be dependent on concentration by the mass action law. Additionally, the reaction rate retardation typical of solid-state reactions is presented with the aid of a special function. This results in nonlinear kinetic equations. The paper suggests an iteration algorithm for numerical embodiment of the kinetic model, as well as 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 carbides TiC, Ti2C, Ti3C2, and 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 conversions.

Original languageEnglish
Pages (from-to)195-218
Number of pages24
JournalNanoscience and Technology
Issue number3
Publication statusPublished - 2019


  • Composite synthesis
  • Kinetic model
  • Multistage kinetics
  • Numerical algorithm
  • Titanium carbide

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials

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