Dear Venkatesan,

as you already stated the Gibbs energy is always minimised, therefore, it decides about the state of aggregation. If we have a mixture the Gibbs energy becomes a function of composition. Starting with an ideal, binary mixture the chemical potential of each component becomes: mu_i=mu_i^star+RT ln(x_i) where mu_i^star is the chemical potential of the pure substance at given T and p. The molar Gibbs energy of one phase of a binary mixture is therefore: Gm=x_i mu_i+x_j mu_j=x_i mu_i^star+x_iRTln(x_i)+... So, G_m already varies with x_i and x_j=1-x_i.

If the mixture is not ideal then one has to use the activity a_i and the Gibbs energy of the mixture (1 phase) becomes:

G_m = x_i G_m,i+x_j G_m,j=x_i mu_i^star+x_iRTln(a_i)+...= x_i mu_i^star+x_iRTln(x_i)+x_iRTln(gamma_i)+...

where gamma_i is the activity cefficient. The third term is the excess contribution. Often this contribution is expressed by the Porter ansatz which is Ax_i(1-x_i). The excess contribution has to vanish for x_i --> 0 and x_i--> 1. A is just a constant and can be positive or negative and depends on pressure p and temperature T. A positive A is causing a miscibility gap.

Now you have G_m for the liquid and the solid phase which are both depending on x_i and x_j=1-x_i and in general have different A(p,T). If you plot such two G_m over x_i (for the two phases) you will see that the distance between the two curves varies with x_i. This gives you already an idea why the melt temperature varies with composition. A change in p or T will basically shift the Gibbs energy curves upwards or downwards and changes the distance between the curves. Very roughly speaking a crossing point indicates a phase transition. You just have to be careful and obye that the total Gibbs energy of the whole system is minimized. This might be a linear combination of the Gibbs energy's of the two phases. Then the liquid and solid phase coexist but show diffenrent compositions.

The attached figure (which was created by G. Zifferer) shows the phase transition form green to red phase in dependence of the composition and temperature for an ideal mixture.

I hope this simplified system gives you already an idea how the composition influences the melting temperature.

Best regards,

Werner Müller

 my dear , i agree with Hans Werner Müller

Dear Hans Werner Müller ·, 

Thank you for your effort to explain it in detail. I am aware of the concept you explained here  but your explanation is excellent and easily understandable.  

i am specially looking for the system like Fe-C where melting temperature decreases upto 4.1%C and then started to increase. 

Do you have any Gibbs energy diagram for this system ? 

Thank you

Dear Venkatesan,

I have no specific data for the Fe-C system.

Best regards,

Hans Werner Müller

Dear Hans Werner Müller

Thank you for your response.