How to use this calculator
At the alloy temperature draw a horizontal tie line across the two-phase region. Enter the alloy composition and the compositions where the tie line meets the phase boundaries on each side, all in the same weight-percent scale.
Formulas
Left phaseWleft = (Cright − C0) / (Cright − Cleft)
Right phaseWright = (C0 − Cleft) / (Cright − Cleft)
Volume fractionVi = (Wi/ρi) / Σ(W/ρ)
Worked example
Cu–Ni alloy, 35 wt% Ni at 1250 °C: liquid 32 wt% Ni, α 43 wt% Ni
- WL = (43 − 35)/(43 − 32) = 8/11 = 0.727.
- Wα = (35 − 32)/(43 − 32) = 3/11 = 0.273.
- They add to 1, as they must.
Frequently asked questions
Why the opposite arm?
The alloy is a balance point: the closer it sits to one phase’s composition, the more of that phase it contains, so each fraction uses the lever arm on the far side.
Does it work on the iron–carbon diagram?
Yes, for any two-phase field, for example α + Fe₃C below the eutectoid with 0.022 and 6.70 wt% C at the ends.