# Calculating the diffusivity of hydrogen through an alloy coating on a steel container

1. Dec 29, 2009

1. The problem statement, all variables and given/known data

Constant for the diffusion of hydrogen through steel is D(steal) = 4 x 10^5 cm²/s. They try to improve steel tanks for hydrogen storage by applying the coating based on TiAlN alloys. What is the diffusion coefficient Dp of such coating, if the permeability of hydrogen is reduced by 19,000 times? In this attempt the steel had a thickness of
d(steal) = 0.5 mm, and the thickness of the alloys was d(alloy)= 10 nm.

2. Relevant equations

s²= 2Dt

3. The attempt at a solution

x= 19,000, D(steal) = 4 x 10^5 cm²/s, s(steal)= 0.5 mm, s(alloy)= 10 nm, D(alloy)= ?

s(steal)²= 2D(steal)t
s(steal)² + s(alloy)²= 2D(alloy)xt

s(steal)²/ [s(steal)² + s(alloy)²]= 2D(steal)t/ 2D(alloy)xt
s(steal)²/ [s(steal)² + s(alloy)²]= D(steal)/ D(alloy)x
D(alloy)= D(steal) [s(steal)² + s(alloy)²]/ s(steal)²x
D(alloy)= 21.1 cm²/s

Are my calculations correct?

Thank you for helping!