By B. B. Khina
The objective of this booklet is to explain easy techniques to modelling non-isothermal interplay kinetics in the course of CS of complex fabrics and demonstrate the prevailing controversies and obvious contradictions among assorted theories, on one hand, and among idea and experimental info, nonetheless, and to improve standards for a transition from conventional solid-state diffusion-controlled section formation kinetics (a 'slow', quasi-equilibrium interplay pathway) to non-equilibrium, 'fast' dissolution-precipitation direction.
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Additional info for Combustion Synthesis of Advanced Materials (Chemistry Research and Applications Series)
That is, the inward growth of the TiC layer is insignificant, and we can reasonably assume R0=const. 4. % C). 2, and its volume is VTiC = (4/3)πR03(1+5ρC/ρTiC). 0. 33 and the pore size must be about the initial diameter of carbon particles. 6. 65 , melt spreading and gas release [92,119]. The fraction of closed porosity is usually small: about 1% for SHS in vacuum . Besides, dense titanium carbide articles (with relative density above 95%) can be readily produced by SHS under high pressure Modeling Diffusion-Controlled Formation of TiC… 31 [114,116] or by short-term compaction of a hot pellet immediately after the completion of SHS [3,4 and literature cited therein].
This pattern of diffusion-controlled product formation is sometimes called “the emptying-core mechanism” . e. inward growth of the product layer due to diffusion of Ti atoms across TiC. 5 µm increases the TiC thickness by less than 10%. Thus the diffusion problem can be considered for a semi-infinite rod. The diffusion equations are written for both C and Ti atoms ∂c i ∂t 2 = D i [T ( t )] ∂ ci ∂r , i ≡ C,Ti. 25) The Stefan-type boundary conditions to Eq. 25) are formulated at interfaces Ti(melt)/TiC (r=R1) and C/TiC (r=R0) taking into account that here R0=R0(t) and cC + cTi =1 ( c021 − c10 ) dR 1 dt = − D C[T(t)] , ∂c C ∂r (1 − c023 ) R1(t) dR 0 dt = D Ti [T(t)] .
Temperature profile of the SHS wave in the Ti-C system : 1, analytical solution for a steady-state SHS wave [Eq. 7)] for T≤Tm(Ti); 2, cubic-spline approximation of experimental curve  in the range Tm(Ti)≤T≤TCS. 6. ADIABATIC HEAT RELEASE IN THE REACTION CELL Having the heating law of the reaction cell, we can calculate the heat release due to diffusion-controlled phase layer growth in non-isothermal conditions and thus the maximal temperature attained, and then compare it with experimental TCS.
Combustion Synthesis of Advanced Materials (Chemistry Research and Applications Series) by B. B. Khina