6.11
The activation energy for the diffusion of copper in silver is 193,000 J/mol.
diffusion coefficient at 1250 K (927°C), given that D at 1000 K (727°C) is 1.0 × 10
–14
Calculate the
2
m /s.
Solution
In this problem we are given Qd for the diffusion of Cu in Ag (i.e., 193,000 J/mol) and asked to compute D
at 1250 K given that the value of D at 1000 K is 1.0 x 10–14 m2/s.
It first becomes necessary to solve for D0
using Equation as
D=D0exp(- Qd/RT)
And
D= 1.0 x 10–14 m2/s
T=1000K Qd=193,000 J/mol
Then
D0=(1.0 x 10–14 m2/s)exp[193,000 J/mol/((8.31J/mole-K)(1000K))]
=1.22 × 10–4 m2/s
Now, solving for D at 1250 K (again using Equation 6.8) gives
D=D0exp(- Qd/RT)
D=1.22 × 10–4 m2/s exp[193,000 J/mol/((8.31J/mole-K)(1250K))]
= 1.04 × 10-12 m2/s