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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 [94], melt spreading and gas release [92,119]. The fraction of closed porosity is usually small: about 1% for SHS in vacuum [117]. 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” [115]. 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 [60]: 1, analytical solution for a steady-state SHS wave [Eq. 7)] for T≤Tm(Ti); 2, cubic-spline approximation of experimental curve [88] 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.

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