Materials Science/Thermodynamics

Thermodynamics of Material

Phase Diagrams

Phase diagrams provide a graphical means of presenting the results of experimental studies of complex natural processes, such that at a given temperature and pressure for a specific system at equilibrium the phase or phases present can be determined.

SYSTEM - Any portion of the universe which is of interest and can be studied experimentally.

PHASE- any particular portion of a system, which is physically homogeneous, has a specific composition, and can be mechanically removed or separated from any other phase in the system.

• e.g. A system containing a mixture of ol and pl in equilibrium contains two phases - ol and pl.

In petrology we generally deal with primary phases - any crystalline phase which can coexist with liquid, i.e. it formed/crystallized directly from the liquid.

EQUILIBRIUM - The condition of minimum energy for the system such that the state of a reaction will not change with time provided that pressure and temperature are kept constant.

In experimental petrology there are three practical criteria used to test for equilibrium.

1. Time - with time the system does not change its physical or chemical makeup. 2. Approach equilibrium from two directions, e.g., the melting point of Albite.

• begin with a liquid of Ab composition (Na₂O-Al₂O₃-6SiO₂) and cool until Ab crystallizes - T=1100°C
• begin with the same mixture of solid Albite and heat it up until liquid forms - T=1120°C. Melting point of albite = 1110°C + 10°C.

3. Attainment of equilibrium by using different reactants and procedures. To determine the melting temperature of Albite

• grind up a sample of pure albite
• combine powdered oxides to give pure Ab composition

Use both to determine Ab melting point.

One final term to be defined prior to examining phase diagrams.

COMPONENT - the smallest number of independent variable chemical constituents necessary to define any phase in the system.

• components may be oxides, elements or minerals, dependent on the system being examined.

For example, experiments carried out in the H₂O system, show that the phases which appear over a wide temperature and pressure range are ice, liquid water and water vapour. The composition of each phase is H₂O and only one chemical parameter or component is required to describe the composition of each phase. Systems which can be defined by a single component are called Unary Systems. H₂O System In this system pressures from 0 to 15 kbars seven phases, each with the same composition - H₂O have been recognized:

• Ice I
• Ice II
• Ice III
• Ice IV (actually does not exist)
• Ice V
• Water
• Steam

SiO₂ System In the one component SiO₂ system in the temperature range from 0 to 2,000°C and a pressure range from 0 to 30 kbars six phases of SiO₂ are recognized. At pressures > 30 kbar a seventh phase, stishovite, exists. The six phases of SiO₂ are:

• coesite
• alpha quartz (Trigonal)
• beta quartz (hexagonal)
• tridymite
• cristobalite
• anhydrous melt