# Difference between revisions of "Phase transition"

Entry to be completed by Kevin Tian

Written by Kevin Tian, AP 225, Fall 2011

Generally speaking, a Phase Transition is the the process through which a thermodynamic system changes from one Phase to another. Here we are defining a "phase" to be a set of states of a macroscopic system that have (relatively) uniform composition and physical properties[0]. The most common and easily observed manifestations of this are the various transitions between the various states of matter (solid, liquid, gas, plasma). However though the most visible, states-of-matter transitions are not representative of all phase transitions. For example one is not necessarily limited to a single phase changing to another (different) single phase. There are transitions where a two component system of single phase transforms to two solid phases, among many others.

## Definition

Figure 1: Taken from [1]. Illustrates the names of the phase transitions between the 4 states of matter: Solid, Liquid, Gas, and Plasma.

The most commonly observed phase transitions are the phase changes of the 3/4 states of matter. If we were to consider a one component system (let's say water), and we alter the external conditions imposed upon the system (such as increase the temperature) then the system will undergo a phase transition (with our example, the water will eventually boil). In essence, as one changes the properties of a system, eventually the system will no longer be in equilibrium. The new phase that forms will be more stable than the phase the system was in previous to the phase transition.

The conditions under which phase transitions occur essentially depend on the system being considered, and what the thermodynamic free energy of the system is (which relates to its temperature, pressure, chemical potential etc.). Most of this would be rather obscure were it not for Phase diagrams.

Figure 2: Taken from [2]. Illustrates an arbitrary 2D phase diagram with Temperature vs. Pressure. The lines indicate equilibrium between two phases.

Phase diagrams are extremely useful for observing phase transitions, since built into the diagram are the boundaries between different phases. A phase transition is quite simply what happens when a system crosses from one side of a phase boundary to the other (crossing an equilibrium line amounts to a phase transition).. Figure 2 is one such example of a 2D phase diagram with most features common to a phase diagram, such as the triple point and critical point. These points are special since they indicate conditions under which multiple phases are in equilibrium with each other. When moving along lines or at a particular point of equilibrium between states, Gibbs' phase rule must hold.

## Phase Transition Classification

It is generally accepted that there are two 'orders' of phase transitions. These are aptly named 'first order' and 'second order', named similarly to the Ehrenfest classification (which has now been found to be inaccurate)[3].

• First Order
• This is any transition that involves a Latent heat, where the system takes in heat but the temperature remains constant.
• The system does not entirely transition to the new phase all at once in a smooth fashion (regions of both phases exist simultaneously)
• There is a discontinuity in the state variables of the system (such as temperature or pressure)
• Examples include melting of ice and the boiling of water (not all ice melts instantaneously nor does all water turn to steam immediately).
• Second Order
• These transitions occur in a continuous fashion.
• The entire system transitions to the new phase continuously.
• This order of transitions encompasses those where thermodynamic quantities diverge (such as susceptibility, heat capacity, etc.)
• Examples include the ferromagnetic transition at the Curie Temperature, superconductivity and superfluids. The critical point shown in Figure 2 is also a second order transition.

There are higher order phase transitions, such as the Kosterlitz–Thouless transition that belong to the class of infinite order phase transitions". However phase transitions in this class only exist in two spatial dimensions, and thus are typically not of concern to for those that work in three dimensions (though it is applicable for 2D electron gasses in quantum mechanics for example).

Some processes/transformations that are phase transitions:

• Eutectic transform: Two component, single phase liquid is cooled and transitions into two (different) solid phases.
• Eutectoid transform: Two component, single phase solid is cooled and transitions into two (different) solid phases.
• Peritectic transform: Two component single phase solid is heated and transitions into a mixture of a solid phase and a liquid phase.
• Spinodal decomposition: Single phase system is cooled and phase separates into two different compositions of the original phase.
• The transition from conductivity to Superconductivity below the critical temperature.
• Bose-Einstein Condensation.