The tie line between basis point to solid solution. for example, in CaO-CuO-TiO2 ternary system; the projection tie line from CaO (1,0,0) to solid solution type (12.75, 37.25, 50), so how to create an equation from this line.
tqvm
I don't know that i find out your purpose correctly. I think that, you can create an equation for three or more tie lines after defined X and Y for two equilibrium phase. X and Y may be defined as the following:
X=mass of CaO/(mass of CaO + m of CuO and m of TiO2) in phase of Alpha and Y defined same as X for Beta phase (assumed Alpha and Beta to be two equilibrium phases).
Actually I want to know how to create linear equation from point CaO (1,0,0) to point CCTO solid solution (0.1275, 0.3725, 0.5).
You must work with only two coordinates, because the other is defined as 1 minus the sum of the two selected coordinates.
for example, (x0, y0, z0) and (x1, y1, z1), an equation is: x = (z - z0)*(x1 - x0)/(z1 - z0) + x0, and y = 1 - x - z.
For your case, for values of TiO2 fraction (z) from 0 to 0.5:
CaO fraction = (z - 0)*(0.1275 - 1)/(0.5 - 0) + 1 = 1 - 1.745*z
CuO fraction = 1 - (1 - 1.745*z) - z = 0.745*z
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