Use the data in the Table describing the temperature dependence of Cu diffusion

Question

Use the data in the Table describing the temperature dependence of Cu diffusion in FCC Al to estimate the average distance a Cu atom will diffuse during a period of 60 minutes in an Al – 5 wt% Cu alloy aged (annealed) at:

(i) T=500 o C; and

(ii) room temperature (20 o C).

Table 6.2 Diffusing A Tabulation of Host Metal Do (m2/s) (J/mol Species Diffusion Data Interstitial Diffusion Fe (a or BCC) 1.1 x 10 87,400 Fe (r or FCC) 2.3 X 10 148,000 77,000 Fe (a or BCC) 5.0 x 10 Fe (r or FCC) 9.1 X 10 168,000 Self-Diffusion Fe (a or BCC) 251,000 Fe 2.8 X 10 Wiley PLUS Fe (r or FCC Fe 5.0 x 10 284,000 Tutorial Video Cu 200,000 Cu (FCC) 2.5 X 10 How to Use 144,000 Al Al (FCC) 2.3 x 10 Tabulated Diffusion Mg Mg (HCP) 136.000 1.5 X 10 Data? 94,000 Zn (HCP) Zn 1.5 X 10 Mo (BCC) Mo 1.8 x 10 461,000 Ni (FCC) 1.9 X 10 285,000 Ni Interdiffusion (Vacancy) Cu (FCC) Zn 2.4 X 10 189,000 Zn (HCP) 124,000 Cu 2.1 x 10 6.5 x 10 Al (FCC) 136,000 Cu Mg All (FCC) 130,000 1.2 x 10 2.7 x 10 Ni (FCC) Cu 256,000 Cu (FCC) 1.9 x 10 230,000 Ni "There are two sets of diffusion coefficients for iron because iron experiences a phase trans- formation at 912 C, at temperatures less than 912 C, BCCa-iron exists; at temperatures higher than 912°C, FCC r-iron is the stable phase. Y. Adda and J. Philibert, Diffusion Dans Les Solides, Universitaires de France, Paris, 1966. CE. A. Brandes and G. B. Brook (Editors), Smithells Metals Reference Book, 7th edition, Butterworth-Heinemann, Oxford, 1992. J. Askill, Tracer Diffusion Data for Metals, Alloys, and Simple oxides, IFI/Plenum, New York, 1970.

Explanation / Answer

If D=diffusion coefficient,x=average distance ,t=time

then,according to fick's second law of diffusion,

Cx-C0/Cs-C0=1- erf[(x/2)((Dt)^-1/2]...................(1)

Cx=concentration of diffused species at a distance x,Cs=constant surface concentration of the diffused species,C0=intial concentration of diffused species

For a certain concentration of the diffused species,Cx-C0/Cs-C0=constant=1- erf[(x/2)((Dt)^-1/2]

or,constant=1- erf[(x/2)((Dt)^-1/2]

or,x^2 /Dt =constant

Also D depends on Temperature(T) as well as host material,activation energy (Qd).

D=D0 exp(-Qd/RT)

D0=6.5*10^-5 m2/s,Qd=136000J/mol,R=universal gas constant=8.314J/K.mol,T=500+273=773K

D=(6.5*10^-5 m2/s)exp(-136000J/mol/8.314J/K.mol*773K) =4.19*10^-14 m2/s

Cx=5 wt% Cu

Cs=100wt%

x=?

t=60min=60*60=3600s

C0=0 wt%

using eqn (1)

Cx-C0/Cs-C0=1- erf[(x/2)((Dt)^-1/2].

or,5wt%-0/100wt%-0=1-erf[(x/2)((4.19*10^-14 m2/s*3600s)^-1/2].=1-erf[(x *11.31]

0.05=1-erf[(x *11.31]

or,0.95=erf[(x *11.31]

erf(1.4)=0.95

so,x*11.31=0.95

x=0.95/11.31=0.084 m=8.4cm

D=4.19*10^-14 m2/s(At T=500 deg C)

ii)Similarly ,at T=20 deg C=273+20=293K

D=(6.5*10^-5 m2/s)exp(-136000J/mol/8.314J/K.mol*293K) =0 m2/s (no diffusion can take place at such low temperature)

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