On the Decarburization of Iron and Steel (2nd Report)

Abstract

The boundary conditions of Fick’s equation were obtained by using the rate of reaction between decarburizing gas and carbon atoms in austenite, and the results from these equations were compared with experimental data.
The reactions between decarburizing gas and carbon atoms in austenite are represented by the following equations: & C (in γ-Fe)+H_2O \ ightleftarrowsCO+H_2+(γ-Fe),
or & C (in γ-Fe)+2H_2O \ ightleftarrowsCO_2+2H_2+(γ-Fe), and C (in γ-Fe)+2H₂\ ightleftarrowsCH₄+(γ-Fe). The decarburizing process occurring at the surface may be separated into the five steps, the slowest of which will determine the rate of the over-all process. It was pointed out from experiments that the reactions on the surface were the factor determining the over-all rate,when the velocity of gas flow was suitable. Then,the number of carbon atoms reacting on the surface is given by \[\stackrel→k=A·a₀f(p)·e^−Q⁄RTC·N^2⁄3 atoms·cm⁻² sec⁻¹,\]
where a₀ is specific activity of a carbon atom in austenite, N the number of atomes per cc ; f(p) a function of the pressure of the reacting gas,C the atomic fraction of carbon,and A a constant. The number of atoms moving to the surface through a cross section of 1 sq. cm is given by \[N·D·\frac∂c∂x atoms cm⁻² sec,\]
where D is the diffusion constant of carbon.Thus,the obtained Fick’s equation is: & \frac∂c∂t=D \frac∂^2c∂x^2;  at t=0, C=C_O, \left(\frac∂c∂x+hC\ ight)_boundary=0,
& and  h=A ·a_0 ·f(p)e^-Q/RT/DN^1/3
The results of this equation were discussed, comparing with experimantal data. The fact that decarburization ratio increased as the content of water vapour in hydrogen,and the effects of the thickness of sample on decarburization ratio and also on carbon distribution of sample decarburized in hydrogen, can be reasonably illustrated by the equation. The values of both the diffusion constant and activated energy calculated from the solution by using our experimental data agree well with Mehl’s data,but not with those of Bramley and Naito. This discordance would be due to the fact that the latter did not consider the reaction on the surface.
Our result shows that the principal reaction on the surface is represented as : \[C (in γ-Fe)+H₂O→CO+H₂+(γ-Fe),\]
and the rate of the reaction is \[\stackrel→k_(H2O)=5.4×10²⁹P_(H2O)^0.9·(C)e^{−57600⁄RT},\]
where P(H₂O) is the pressure of water vapour in hydrogen,in atmosphere : and (C) is the atomic fraction of carbon at the surface.