diffusion example problems

diffusion example problems - A Diffusion Problem Consider a...

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A Diffusion Problem Consider a dilute solution of Ni atoms in FCC Fe. At point x the local composition is 0.3 atomic % Ni and at point y the composition is 0.2 atomic % Ni. If the distance from x to y is 1 mm, what is the flux of atoms between x and y at 1000ºC? Note: D 1000 = 2 x 10 -12 cm 2 /sec a Fe = 3.7Å a/o distance x y 0.3 0.2 1 mm Sketch of physical situation
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Step 1: Calculate the number of atoms per volume (this is what we need for our flux calculations). Note: since we are told that the Fe in this case is FCC we know that there are 4 atoms/ unit cell. # atoms/cm 3 = 4 atoms/unit cell (3.7x10 -8 cm) 3 /unit cell = 8 x 10 22 atoms/cm 3
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Calculate the number of atoms of Ni at position y: 0.2 atomic % Ni = 0.002 Ni atoms/atom [0.002 Ni atoms/atom] x [8 x 10 22 atoms/cm 3 ] = 1.6 x 10 20 Ni atoms/cm 3 0.3 atomic % Ni = 0.003 Ni atoms/atom [0.003 Ni atoms/atom] x [8 x 10 22 atoms/cm 3 ] = 2.4 x 10 20 Ni atoms/cm 3 Similarly:
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Step 2: Calculate the concentration gradient. The concentration gradient is the change in concentration divided by the distance over which it changes. 1.6 x 10 20 Ni atoms/cm 3 2.4 x 10 20 Ni atoms/cm 3 0.1 cm = - 8 x 10 20 Ni atoms/cm 4 = dc/dx
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Step 3. Calculate the flux.
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diffusion example problems - A Diffusion Problem Consider a...

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