6. Solid-liquid equilibria of two component mixtures

Mixed crystal, solid- and liquid curve, eutectic phase diagram, crystallization, slush bath

The study of solid-liquid equilibria in two-component systems is fundamental in physical chemistry and materials science.

Solid-liquid equilibria of two component mixtures

·       In two dimensions one is the concentration, one is either p or T, the other is kept constant

·       In this case p dependence is small

·       L:

o   Freezing point/liquid curve, above it only liquids, on it the liquid is in equilibrium with the solid

·       Freezing point:

o   That temperature where the given liquid is in equilibrium with the solid (the first crystal appears from the liquid, unless the system is supercooling)

·       S:

o   Melting point/solid curve, below it only solids, on it the solid is in equilibrium with the liquid

·       Melting point:

o   The temperature where the given solid is in equilibrium with the liquid (where the first droplet of liquid appears)

·       X₁/X₂:mol fractions

o   at a given concentration freezing point and boiling point differs

o   in equilibrium the concentration of solid and liquid differs

o   in the solid phase the components might be mixed in any ratio

Mixed crystal:

·       A mixed crystal, or solid solution, is a solid phase where two or more components are miscible and form a homogeneous crystalline structure

·       The composition of the solid solution can vary, resulting in different properties compared to pure components

·       They are very rare and important at freezing point depression

·       For example: Ag-Au

Eutectic phase diagram

·       A eutectic phase diagram illustrates the equilibrium between solid and liquid phases in a binary mixture

o   It highlights the eutectic point

o   eutectic point:

§  The lowest temperature at which the liquid phase can coexist with solid phases of both components

§  At this composition, the liquid freezes into a mixture of the two solid phases at a single temperature.

o   eutectic temperature:

§  The temperature at the eutectic point

o   eutectic composition:

§  The specific ratio of the two components that forms the eutectic mixture

o   hypoeutectic and hypereutectic compositions: Compositions with a lower (hypo) or higher (hyper) proportion of the component with the higher melting point compared to the eutectic composition.
 

Crystallization:

·       a process where practically solid pure crystals freeze out of the solution

·       so the liquid phase transforms into the solid phase

·       a great purification method

·       also used to form solid solutions/mixed crystals
           

·       cooling crystallization:

o   achieved by lowering the temperature until we get under the liquid curve (moving down on the s-l diagram)

·       evaporative crystallization:

o   achieved by evaporating solvent, so the concentration changes until we end up below the liquid line (moving right on the s-l diagram)

Slush bath

·       a mixture of solid and liquid phases to achieve a low-temperature, stable mixture

·       commonly used in laboratories for cooling or maintaining a specific low temperature

·       for example:

o   Ice-salt mixture (-20°C)

o   Ice.MgCl₂ (-40°C)

§    During the process ice is melting so the mixture becomes diluted