Homework Sourse2 The diffusion coefficient at the melting point for materia
2) The diffusion coefficient at the melting point for materials is approximately constant, with the value D =10-12 m 2 /s. What is the diffusion distance if a material is held for 12 hours at just below its melting temperature? This distance gives an idea of the maximum distance over which concentration gradients can be smoothed by diffusion
Solution
Diffusion time, t = x2 / qiD
where,
x2 - mean-square displacement
(x is the mean distance from the starting point that a molecule will have diffused in time, t)
qi - numerical constant which depends on dimensionality: qi = 2, 4, or 6, for 1, 2, or 3 dimensional diffusion.
D - diffusion coefficient (m2/s)
t - time.
Here, given D = 10-12 m2/s ; time t = 12 hrs = 12 x 60 x 60 sec and qi = 2 for 1 dimension
Therefore, the diffusion distance, x = (qi x D x t )0.5
= (2 x 10-12 x 12 x 60 x 60)0.5
= 0.000294 m = 0.294 mm
