I have solved using excel .Please find the table below.
Please comment, if you have any doubts.
The dependence of the diffusion coefficient on temperature in given by Qd D=D. exp RT Where m D.- A temperature independent pre exponential S J Qa - The activation energy for diffusion mol J -4 R-Gas constant. 8.31 mol.K T- Absolute temperature (in K) m D. = 8.968 = 8.968x10+ s S kJ = 333.5 mol T =1368+273 = 1641 K D=D. exp RT
-333.5x103 D=8.968x10+ x expl 8.31x1641 4 D=8.968x10+ x exp -333.5x10 13636.71 m D= 2.1505x10-14 S t% C-C = 1-eif C.-C. 2VDt Where, C- concentration of element at distance 'x' from surface at time ty (in W Cg - Surface concentration of element in gas diffusing into the surface (in Wt. %) Co-Initial uniform concentration of elements in solid (in Wt. %) x - Distance from surface (in m) mt D-diffusivity of solve (mixing species) S T - Time (in s) Data's given Cs = 4x1020 atoms/cm Xo = x t=360 hours=360 x 60 x 60=1296000 sec
Co = 0 C = ? x Calculate the surface concentration x, common equation for x C-C = 1- exf C-C. 2/Dt C-0 = 1-erf 4x1020 - 0 212.1505 x 10-14 x 1296000 C = 1-erf 4x1020 202.787x10-6 х C, = 4x10-01-erf 3.3389x104 Modal calculation: For x=0.2R x=0.2R x=0.2 x 520x10-6 x=1.04x104m
C =4x10*[1 - erf 3.3389x104 1.04x10-4 Co2R = 4x1020 | 1-erf 3.3389x10-4 Co2R = 4x1020 [1-erf (0.31148)] Cozx = 4x10> [1–0.340424] Co2R = 2.638x1020 atoms/cm?
Sl.No 0 1 2 3 4 5 X x/3.3E-4 1- error function concentration (Cx) 0 O 0 1 4E+20 0.1 0.000052 0.15573991 0.825676848 3.30271E+20 0.2 0.000104 0.31147983 0.659575738 2.6383E+20 0.3 0.000156 0.46721974 0.508773617 2.03509E+20 0.4 0.000208 0.62295966 0.378318905 1.51328E+20 0.5 0.00026 0.77869957 0.270788956 1.08316E+20 0.6 0.000312 0.93443949 0.186335704 7.45343E+19 0.7 0.000364 1.0901794 0.123135209 4.92541E+19 0.8 0.000416 1.24591931 0.078069975 3.1228E+19 0.9 0.000468 1.40165923 0.047451771 1.89807E+19 1 0.00052 1.55739914 0.027630363 1.10521E+19 6 7 8 9 10