1st and 2d order phase transitions

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Discussion Overview

The discussion centers on the differences between first and second order phase transitions, exploring definitions, examples, and the characteristics of each type. Participants seek clarification on specific examples and the underlying principles governing these transitions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant requests simple examples of first and second order phase transitions.
  • Another participant suggests that "melting" of glass may be a second order phase transition but questions the continuity of second derivatives of Gibbs potential.
  • A different participant challenges the applicability of equilibrium concepts to glass, noting that glasses are generally not in equilibrium.
  • Concerns are raised about understanding why certain transitions, such as ferromagnetic, superconducting, or superfluid transitions, are classified as second order.
  • Discussion includes the complexity of the van der Waals gas transition and its classification as first order, with a suggestion to examine the discontinuity of free energy derivatives.
  • One participant mentions that second order transitions are often linked to symmetry changes, providing examples from superconductors and ferromagnets.
  • A participant notes that first order transitions release latent heat, while second order transitions do not, but also points out that the classification based on continuity of free energy derivatives may be outdated.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of certain examples (like glass) to the classification of phase transitions. There is no consensus on the best examples or the implications of continuity in derivatives of free energy.

Contextual Notes

Some participants highlight the limitations of applying equilibrium concepts to non-equilibrium systems like glass. The discussion also touches on the complexity of the van der Waals gas transition and the potential divergence of free energy derivatives at transitions.

Who May Find This Useful

Individuals interested in the theoretical aspects of phase transitions, particularly in the context of materials science, thermodynamics, and statistical mechanics.

paweld
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What's the difference between first and second
order phase transitions. Could anyone give me some simple
examples of both?
Thanks.
 
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For homework-type questions, we ask you to show your own reasoning first, then you'll likely get comments on your proposed answers.
 
OK, I'm looking for a simple example of second order phase transition.
Is "melting" of glass a good example? First derivatives of Gibbs potential
are continuous but what about higher. Second derivatives need to be
discontinous. Are they?
 
What in case of van der Waals gas. On the p-V-T plot all transitions are continous.
How about entropy?
 
paweld said:
OK, I'm looking for a simple example of second order phase transition.
Is "melting" of glass a good example? First derivatives of Gibbs potential
are continuous but what about higher. Second derivatives need to be
discontinous. Are they?

I'm not sure a glass is the best example. Glasses aren't at equilibrium (they would generally crystallize except for kinetic limitations), so some object to applying equilibrium concepts like phase transitions to them.

Keep searching; there are one or two transitions that are always used as examples of second-order transitions.
 
Of course there are some examples which are alway used but they are not simple.
I don't have any idea why ferromangetic, superconductor or superfluid phase
transition are second order (how to prove it or at least intuitivly understand?).

How to prove that van der Waals gas transition are first order.
 
The general idea is to take the first (n-th) derivative of the free energy and to see that it is discontinuous. The van der Waals transition is a bit complicated given its coexistence region though. I'm sure the proof is available in some lecture notes online or you can find the details in some book on statistical mechanics.

The Fossheim, Sudbo book gives a very clear idea in its first chapter on the second order transition for superconductors. Quite generally second order transitions are linked to symmetry changes. It's quite intuitively easy to see one in superconductors when the Cooper pairs form and break. You get a similar phenomenon in ferromagnets where domains of aligned magnetic momenta are formed.
 
A first order transition (or discontinuous) will give off latent heat during the transition. A second order transition (or continuous transition) will not give off any heat during the transition.

Classification of transitions based on continuity of the derivatives of the free energy is outdated, as it fails to account for cases in which a derivative of the free energy diverges at the transition.

http://en.wikipedia.org/wiki/First-order_phase_transition#Classifications
 

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