# Dynamics of phase transitions

1. Oct 29, 2013

### aaaa202

I'm merely starting to research this field. Phase transitions have always been a mystery for me. Which kinds of dynamics govern when a material will undergo a phase transition? e.g., why is it exactly at the temperature T0 and pressure p0 that the substance X goes from one phase to the other?
Typically it would seem like the ΔT/ΔU is zero during phase change. Why is this? Is it consistent with the 2nd law? Somehow my intuition tells me that heating a substance should increase its temperature - but it has been a long time since I studied the actual thermodynamic equations.
And finally, and most important, do YOU know any good introductory texts in this topic that you woud recommend?

2. Nov 1, 2013

### DrDu

In general, a phase transition happens when the pressure, temperature and chemical potential of the two phases are equal. The difference of the chemical potentials is the free enthalpy $\Delta G=\mu_2-\mu_1$, which is itself a function of T and P. So if we take the equality of T and P for granted, The equation $\Delta G(T,P)=0$ selects the line of phase equilibrium.
A simple example, where $\Delta G$ can be worked out analytically is the van der Waals gas.
There are also models of phase transitions in spin lattice models which can partly be treated analytically.

3. Nov 11, 2013

### aaaa202

I don't understand. I don't know much about phases but how can we speak of T,p and μ of one phase and that these parameters should in general be different for those of another phase?
All we have is a thermodynamical system, the laws of thermodynamics do not say that we have different phases of a system?
I hope you follow, or can at least understand why I am confused.

4. Nov 11, 2013

### aaaa202

Let me maybe try and explain what it is I don't understand about phase transitions.
The problem is that I don't understand why we have this "discontinous" behaviour of the physical system. Why is it that at one temperature, the system suddenly "decides" to let all energy be directed into changing its physical properties drastically, rather than this being a process that happened continously as we increased temperature. I just seems weird to me that there actually exists one temperature that separates 2 systems with very different physical properties.

5. Nov 11, 2013

### DrDu

Well, this is a very difficult question.
This sudden change happens only in macroscopic (="infinitely" large) systems. For microscopic systems, all phase transitions are smooth. Depending on the system, phase transitions also require a minimal number of dimensions.
The theory is simpler for second order phase transitions, e.g. for the ferromagnetic-paramagnetic transition.
Relatively easy to understand is the Landau theory of phase transitions. Basically, the free energy of the material is a 4th order polynomial. Below the transition temperature, it only has one minimum, above, it has two stable minima and the original minimum becomes a maximum. E.g. if the low temperature minimum corresponds to vanishing magnetization, above the transition temperatures, two stable minima exist with finite (and opposite) magnetization.
It is quite clear that this "deformation" of the function graph is perfectly continuous. Nevertheless, the magnetization has a discontinuous derivative wrt temperature.