Liquid Solid Phase diagrams

At the lower region on the temperature scale, the liquids can freeze into the solid state.  Just as in the liquid vapour phase diagrams, the composition has a role to play in what phases are present.  A simple first idea comes from colligative properties that says that in the dilute limit, the melting point lowers, as a factor only of the solvent and the amount of solute.  The particular kind of solute is not an issue.  Thus, as we look at the liquid-solid phase diagram a common feature is a slope down in temperature as the composition moves away from pure solvent.

There are several regions in this diagram (from Atkins Fig. 6.29). 

The uppermost region is the only single phase region. All other regions are two-phase regions, either solid-liquid or solid-solid phases.  Consider a system with overall composition represented by the vertical line running through points a₁ ... a₅. 

• At the upper-most point, a₁, the system is in the single phase region and consists of a liquid solution with the composition x_b .
• At a₂, the solution has cooled to the freezing point at it's composition.  Any solid that freezes out will be pure B, resulting in the solution slowly becoming more concentrated in A and hence, the melting point slowly lowers as more and more b freezes out
• After a significant amount of solid has frozen, we reach a point like a₃, where there are two distinct phases, one at composition b₃ and one of pure B. the relative amounts of the two phases can be determined via the lever rule.
• Point a₄ is the lowest temperature that will allow us to find liquid phase.  The temperature will stop here until all the liquid has frozen out as either pure A or pure B. from that point on, the relative amounts of the two solids are un changing and can be calculated by the lever rule.  In this region, the relative amounts of the two phases is simply given by the mole fractions of the overall system.
• One extra point e is the eutectic point.  as mentioned, it is the lowest temperature at which we can find liquid solution.

In the case where the two substances A and B react in condenced phase to form a new compound C, we can consider the resulting phase diagram as simply two phase diagrams, side by side.  all the considerations given above to the un-reacting system can be applied here.  Now, there are two different solid phase regions, both with P=2.  one has Pure A and Pure C as the two solid phases and the other has pure B and pure C solid phases.

An example of this behaviour can be found in the GaAs semiconductor system.

Other mixtures have behaviours similar in that there are multiple solid phase regions but at the melting points, the composition of the resulting liquid is not the same as that of the solid.  This is an incongruent melting system.

In any of the two phase regions, the two phases can always be determined by looking at where a tie line might intersect at either side of the region. 

Consider the phase diagram for the sodium/potassium  there are several regions where two solid phases exist.  in some cases, the phases are merely solid solutions (of K in Na or of Na in K).  In this case, there is a solid state compound Na₂K (note not 1:1). 

• Thus, as we consider a system composition "a", we find that at the higher temperatures, a single phase of composition a exists. 

• At T₂, the point a₂ represents the point where the liquid begins to freeze.  The solid that freezes out is actually a solid solution of some K in Na and as the temperature lowers, the composition of both the liquid and the solid solutions change.

• The temperature T₃ represents the lowest temperature at that particular isopleth (constant composition) system were liquid phase exists.  In fact, three phases can exist at this temperature.  Liquid solution and two solid phases: solid Na₂K and solid solution of K in Na.  Below T₃, only the two solid phases can exist.h

If we follow an isopleth at composition b, we find  a slightly different sequence. 

• Point b₁ is single phase liquid solution

• Point b₂ (at T'₂) indicates the initial melting point of the solution.

• As the temperature reaches T₃, again, three phases are present: liquid solution, solid compound Na₂K and some solid solution of K in Na.

• Below, T₃, the liquid continues to freeze and form solid Na₂K.  The two phases present (plus probably a bit of K in Na solution) are liquid solution and solid Na₂K.

• below T₄, the eutectic temperature, the two phases are pure Na₂K solid compound and a solution of Na in K.

At no point do we find liquid compound Na₂K.  It is only stable in the solid phase.

Liquid Crystals

Liquid crystals form from compounds whose molecules have distinct non-spherical morphology and/or distinct differences in the kind of intermolecular forces from one part of the molecules to another.  These compounds can form a mesophase, intermediate between solid phase and liquid phase, where the molecules have more freedom than in the solid phase but are generally still aligned one to the other in a repeating array.  Two general types of such molecules are long thin molecules (1) and disk-like molecules (2).  These tend to align such that there is long-range disorder in at least one dimension but order in the short range. 

This type of molecule forms "Calamitic liquid crystals

This type of molecules forms discotic liquid crystals.

Some kinds of compounds are created or changed by a change in temperature.  These are called Thermotropic liquid crystals.  These are used in displays like temperature strips, which change color to indicate when a child has a fever.

Some compounds form liquid crystals that change with composition.  These are called lyotropic liquid crystals.

Nematic phase liquid crystals occur at higher temperatures where there is thermal disorder in the planes of the structure

Smectic liquid crystals form long-range order on one plane only.  The molecules slide over one another to give a soapy low friction phase.  These generally are lower temperature phases. than nematic phase.

The cholesteric phase liquid crystals form layers that are rotated one to the other by some angle, in a helical long range structure.  These layers can be nematic layers or smectic layers.  The helical structure rotates the polarization of light that passes through.  Additionally, some molecules can change the angle of this twist with applied electrical charge or change in pressure.

LCD displays use this property to create their visible effects.  A "Twisted Nematic" display consists a thin layer of the liquid crystal material held between to polarized plates whose angle of polarization is set to allow the desired effect (for example, it may be set to cancel all light).  Transparent electrodes in the glass allow for the twist angle to be changed with the application of a small charge, thus changing the amount of light that passes through the array.

Solutions of liquid crystal materials can sometimes allow for larger useable temperature ranges for the material.  Thus, the figure to the right (from Atkins, fig 6.34).  some concentrations show a wider nematic range than either pure substance.

Finally, melting properties can be used to purify materials.  Fibre optics requires ultra pure quartz or the signal will degrade to zero before it reaches the end of the fibre.  Consider that a typical glass window absorbs as much as 40% of the light that passes through its thickness of .3 mm, yet light passes for many kilometers through the ultrapure fibre optics cable before it must be boosted.  Similarly, the semiconductor industry must work with ultrapure materials for things like micro-processors in computers, to keep the number of failed units do an acceptable limit.

To purify these materials, a method called Zone refining is used.  the material is repeatedly melted in one region at a time.  as the melted region moves, it tends to drag impurities along with it because the impurities are more soluble in the melt than in the solid phase.

This also explains the presence of bubbles in the middle of ice cubes.  as the ice freezes, from the outside first, the impurities (dissolved gas) are pushed to the middle.  eventually, the vapour pressure is enough that the gases separate out of the remaining liquid but are trapped by the surrounding ice and remain there in the cube.  Ultrapure water is needed to form ice with no bubbles for things like ice sculptures.