Phase Diagrams

Phase diagrams

We generally think of three phases, solid, liquid and gas, when we talk about phases and phase changes. A general description holds that a phase is a unique form of the substance that is uniform in chemical composition and physical state. This description allows that phases are not necessarily limited to the three physical states. For example, two different crystal structures of a substances could be considered two different phases.

No matter what the state, transition between two phases will generally occur at a temperature that depends only on the pressure. For example, ice converts to water at 0ºC if the external pressure is 1 atm. below this temperature, ice dominates were as above 0ºC, water dominates. We would thus expect Gibbs energy to decrease as we go from liquid to solid below 0ºC and also decrease as we go from solid to liquid above 0ºC. The transition temperature, T_trs, which itself is a function of pressure, is the temperature at which the two phases are in equilibrium (no change in Gibbs energy, it's at a minimum for the given pressure).

We can depict the conditions under which phases exist or co-exist using a phase diagram. Where Pressure is the vertical axis and Temperature is horizontal. lines in this diagram represent pressure-temperature conditions where two phases are in equilibrium (Gibbs energy is at a minimum) and spaces between the lines represent single phase regions.

It is also possible to have meta-stable phases, where the transition to another phase may be thermodynamically favored but the rate of the transition so slow as to be not measureable (on the timescale of the experiment). For example, diamond is less a thermodynamically favored form of carbon than graphite, yet, the rate at which diamond spontaneously changes to graphite is immeasurable under normal conditions.

There are several "special" points on a phase diagram that are worth noting:

The Critical point is the point in pressure-temperature space at which the molar volume of the liquid and vapour phases are indistinguishable. at temperatures above the critical temperature, there is only one phase, a super-critical fluid.

The triple point (there can be several of these) represent the conditions where three phases are in equilibrium with each other. The triple point in the diagram above mark the conditions where solid, liquid and gas can exist in equilibrium.

The point at which a phase transition line crosses the 1 atm pressure, are called "normal":

The normal boiling point NBP is the point where the liquid/vapour equilibrium occurs when the pressure is 1 atm.
the normal freezing point NFP is the point where the solid/liquid equilibrium occurs at p = 1 atm.

When equilibrium occurs at 1 bar, it is called "standard". Thus,

Standard freezing point is the point where the solid/liquid equilibrium occurs at a pressure of 1 bar
Standard boiling point is the point where the liquid/vapour equilibrium occurs at a pressure of 1 bar.

Fig. 4.4 (from Atkins) The experimental phase diagram for carbon dioxide. Note that, as the triple point lies at pressures well above atmospheric, liquid carbon dioxide does not exist under normal conditions (a pressure of at least 5.11 atm must be applied).

Carbon dioxide phase diagram:

Look at the features of carbon dioxide's phase diagram. the triple point occurs at a pressure of about 5.11 atm. So we cannot find liquid CO₂ under normal conditions; only solid and vapour. To get liquid CO₂, we need a pressure of at least 5.11 atm. Note also that the critical pressure occurs at a fairly low value of 72.9 atm and slightly above room temperature at 304 K. CO₂ is typically transported, bought and sold under pressure in liquid form. Next time you see a tanker truck on the highway with the words Liquid CO₂, you will know that the truck is not cold, it is pressurized.

Super critical CO₂ is used in many industrial and food based industries such as dry-cleaning and decaffeinating coffee, where it acts as a solvent above the critical point but disappears spontaneously once the pressure is released.

Phase diagram for water

Water has a more complex phase diagram in that there are many forms of water in the solid state. The ice we normally experience is called "ice I" or ice-one. It is the only form of ice that can occur at low pressures. It differes from the other ice analogues in its crystal structure and entropy. Some of the forms of ice are highly ordered and others are disordered. There are also several meta-stable states that are not shown in this diagram but which can exist in some of the space. For example, Ice-nine is metastable under the same conditions as ice-two exists.
http://www.lsbu.ac.uk/water/ice_iii.html#icenine .

Note that there are several triple points in this diagram. For example, see the point where ice X, XI, and VIII all coexist.

The general reasoning for these different polymorphs of water solid is that as the pressure increases, the hydrogen bonds are less and less able to hold the water in place and the molecules assume new formations.

Fig. 4.5 The experimental phase diagram for water showing the different solid phases.

Fig. 4.7 The phase diagram for helium (⁴He). The λ-line marks the conditions under which the two liquid phases are in equilibrium. Helium-II is the superfluid phase. Note that a pressure of over 20 bar must be exerted before solid helium can be obtained. The labels hcp and bcc denote different solid phases in which the atoms pack together differently: hcp denotes hexagonal closed packing and bcc denotes body-centred cubic (see Section 20-1 for a description of these structures).

Helium's phase diagram

The phase diagram for Helium shows other unusual behavior. First of all, the two isotopes of He, 3 and 4 have different phase diagrams.⁴He has two liquid phases with a transition between them (the l-line). Helium's low temperature triple point is the point where
He-II (ℓ), He-I (ℓ) and He(g) coexist. He-II is a superfluid. It flows with zero viscosity.