In the mathematical analysis on the carburization and decarburization of Th-W filaments, it must be recongnized that the carburized layer is distinguished from the decarburized and that the carbon content does not vary continuously. This differs from the carburization and decarburization of the common metals such as iron, so that the conventional solution on the Fick’s equation of diffusion is not applicable. Therefore, we obtain the following solution, using the Stefan’s method of the calculation about the formation of ice. \left. rl & \dfrac4ktR^2C_0=s+(1-s) log_e (1-s)
& K=D(C_1-C_2), S=\dfrac1f \left(1-\dfrac1λ_0\
ight) for carburization
and & K=D_1C_2, S=\dfrac1f-\dfrac1λ_0 \left(\dfrac1λ_t-1\
ight) for decarburization\
ight}\labeleq1Where,
C1 represents the concentration of carbon at the surface (g/cm
3),
C2, the concentration of carbon dissolved in the tungsten and not present as W
2C,
C0, the amount of carbon required to convert unit volume of W into W
2C,
D and
D1, the diffusion constants of carbon into W
2C and W respectively,
R, the radius of Th-W filament,
t, the time of carburization and decarburization,
S, the ratio of area of carburized sheath and total section for carburization and the ratio of area of decarburized sheath and total section for decarburization, λ
0, the ratio of resistance after and before cecarburization, λ
t,the ratio of resistance after and before decarburizaton and
f,the constant related with specific resistance.
Analysing the carburization data by equation (\
efeq1), we get
D(
C1−
C2)=7.52×10
−9, 5.36×10
−8 and 2.178×10
−7 cm
2 g/sec for 1700°, 1850° and 2000°K respectively.
Applying the Vant’ Hoff’s equation on the thermodynamical equilibrium, we obtain
Q=32300 cal as an activation energy on the diffusion of carbon into W
2C. Similarly, in the case of the decarburization in hydrogen, we get
D1C2=1.6×10
−10, 3.76×10
−9 and 2.8×10
−8 cm
2 g/sec for 1650°, 2000° and 2150°K respectively and
Q=24430 cal.
抄録全体を表示