For a second order phase transition, the order parameter grows continuously to sixth order in the order parameter, the system will undergo a first order phase. PDF | An introductory review of various concepts about first-order phase transitions is given. Rules for classification of phase transitions as second or first order. Continuous phase transitions involve a continuous change in entropy, which means First order transitions have discontinuities in the first derivatives of G.

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Firstly I'd like to know if it's correct. If it is, I have a few questions about it.

Finally, I'd like to know where I can read more about this, i. I'm looking for a text that focuses on the underlying theory, rather than specific examples.

With the interpretation of the second derivative in terms of heat capacity, this is again familiar from classical thermodynamics. So far so uncontroversial.

The part I'm less sure about is how these plots change in a second-order transition. The negative slope of this curve must then look like this, which makes sense of the comment on Wikipedia about a [higher] derivative of the first order phase transition energy "diverging".

If this is what second first order phase transition transitions are like then it would make quite a bit of sense out of the things I've read. In particular it makes it intuitively clear why there would be critical opalescence apparently a second-order phenomenon around the critical point of a liquid-gas transition, but not at other points along the phase boundary.

This is because second-order transitions seem to be "doubly critical", in that they seem to be in some sense the limit of a first-order first order phase transition as the latent heat goes to zero.

However, I've never seen it explained that way, and I have also never seen the third of the above plots presented anywhere, so I would like to know if this is correct. Ehrenfest classification[ edit ] Paul Ehrenfest classified phase transitions based on the behavior of the thermodynamic free first order phase transition as a function of other thermodynamic variables.

### Phase transition

First-order phase transitions exhibit a discontinuity in the first derivative of the free energy with respect to some thermodynamic variable. Second-order phase transitions are continuous first order phase transition the first derivative the order parameterwhich first order phase transition the first derivative of the free energy with respect to the external field, is continuous across the transition but exhibit discontinuity in a second derivative of the free energy.

The magnetic susceptibilitythe second derivative of the free energy with the field, changes discontinuously.

Under the Ehrenfest classification scheme, there first order phase transition in principle be third, fourth, and higher-order phase transitions.

Though useful, Ehrenfest's classification has been found to be an incomplete method of classifying phase transitions, for it does not take into account the case where a derivative of free energy diverges which is only possible in the thermodynamic limit.

## Theory of first-order phase transitions - IOPscience

For instance, in the ferromagnetic transition, the heat capacity diverges to infinity. The same phenomenon is also seen in superconducting phase transition. Modern classifications[ edit ] In the modern classification scheme, phase transitions are divided into two broad categories, named similarly to the Ehrenfest classes: During first order phase transition a transition, a system either absorbs or releases a fixed and typically large amount of energy per volume.

During this process, the temperature of the system will stay constant as heat is added: Familiar examples are the melting of ice or the boiling of water the water does not instantly turn into vaporbut forms a turbulent mixture of first order phase transition water and vapor bubbles.

### Theory of first-order phase transitions

Imry and Wortis showed that quenched disorder can broaden a first-order first order phase transition. That is, the transformation is completed over a finite range of temperatures, but phenomena like supercooling and superheating survive and hysteresis is observed on thermal cycling.

They are characterized by a divergent susceptibility, an infinite first order phase transition length, and a power-law decay of correlations near criticality.

Examples of second-order phase transitions are the ferromagnetic transition, superconducting transition for a Type-I superconductor the phase transition is second-order at zero external field and for a Type-II superconductor the phase transition is second-order for both normal-state—mixed-state and mixed-state—superconducting-state transitions and the superfluid transition.