Zone refining and phase diagrams

[twohaha]

Homework Statement

From Ashby's "Engineering Materials"[/B]

Homework Equations

$k=C_o/C_s=m_1/m_2$

The Attempt at a Solution

Solving for k
$m_1=(660-548)/(0-32)=-3.5$
$m_2=(660-548)/(0-7)=-16$
$k=m_1/m_2=0.219$

$C_s=C_o*(1-(1-0.219)exp(-xL/0.219))$How do I proceed from there? Also, how do I incorporate the $C_l$ term in the equation?

Thanks!

 

[KataKoniK]

To proceed, you can use the equation for C_s that you have derived and plug in the value of k that you calculated. Then, you can also plug in the value of xL for the specific material you are working with. This will give you the value of C_s for that material.

To incorporate the C_l term, you can use the equation C_l = C_o - C_s, where C_o is the initial concentration and C_s is the concentration at a specific distance xL. This will give you the concentration gradient of the material at that specific distance.

Alternatively, you can also use the equation C_l = k*C_o*exp(-xL/k), where k is the same constant that you calculated earlier. This equation takes into account the concentration gradient and can be used to calculate the concentration at any distance xL.

Hope this helps!