Question

An alloy in the A-B system is 40% B and is within the α + β two phase field, where the a phase contains 5% B and the β phase contains 90% B. Find the fraction α phase in the structure.

Answer 1

Answer:

0.59

Explanation:

based on Lever's phase rule, we can find the fraction of the α phase in the structure using the following formula:

$w^{\alpha}= \frac{w_{B}-w_{B}^{\beta}}{w_{B}^{\alpha}-w_{B}^{\beta}}$

where

$w_{B}$ =  mass fraction of element B in the entire alloy or mixture = 40%

$w_{B}^{\beta}$ = mass fraction of element B in the β phase = 90%

$w_{B}^{\alpha}$ = mass fraction of element B in the α phase = 5%

hence we have

$w^{\alpha}= \frac{40-90}{5-90}= 0.5882$

∴ The fraction α phase in the structure is ≈ 0.59