Geology 3411 - Petrology - Fall 2002 Chapter Outline for Raymond Text
Chapter 4.  The Phase Rule and Phase Diagrams

1. Introduction
   1. Phase = homogeneous material that can be separated by mechanical means from other phases
   2. Component = chemical species
   
   
2. Systems and the Phase Rule
   1. System = any part of the universe selected for study / observation
      1. Isolated system = cannot exchange energy or matter with surroundings (theoretical only)
      2. Closed system = can exchange energy, but not matter, with surroundings
      3. Open system = can exchange both energy and matter with surroundings
   2. Intensive variable = property of the system that can be changed and is independent of the size of the system, such as temperature, pressure, composition
   3. Degree(s) of freedom = minimum number of variables needed to define a specific state of the system.
   4. The Phase Rule:  F = C - P + 2 , where F = degrees of freedom, C = number of components, and P = number of phases.
   
   
3. Unary Systems = one-component systems.  For example, H2O can exist as solid, liquid or gas.  Freezing/melting, vaporization/condensation, or sublimation/deposition are the processes of changing from one phase to another.  These take place at various combinations of temperature and pressure that map out as phase boundaries between the stability fields in a phase diagram.
   1. Pressure and temperature can vary independently inside one-phase fields (F = 2)
   2. Along a linear boundary between one-phase fields, two phases can coexist and pressure and temperature vary dependently (one must change if the other does, in order to keep the pressure-temperature coordinates on the line: F = 1. The linear boundaries are called univariant (one degree of freedom) curves.
   3. An invariant point (or triple point), F = 0:  Pressure and temperature must both have particular values for three phases to coexist.
   
   
4. Binary Systems = two-component systems.  Most commonly we portray they system at a fixed pressure and let composition and temperature vary.  The diagrams typically show compostion varying horizontally and temperature varying vertically: vertical lines in such a graph are constant-temperature lines or isopleths, and horizaontal line are constant temperature lines, or isotherms.
   1. Binary systems with eutectic point are one common basic type frequently seen in geology:
      1. The pure "end-member" components do little by themselves except melt or freeze at their respective melting/freezing points.
      2. For mixtures of the end-members, the solidus "curve" is typically a flat line that marks the temperature at which melting begins, from solid material that contains both solid phases.
      3. The eutectic point represents the temperature and composition of the first liquid to form by melting, or the last to crystallize.
      4. As heating progresses, melting continues with no temperature increase, until one or the other of the solid phases is completely melted.  If the bulk composition of the system is the same as that represented by the eutectic point, both solids are completely melted at the same time.
      5. Whatever solid phase is left begins to melt on its own, and this is accompanied by a rise in temperature and shift of liquid composition away from the eutectic composition, following one branch or other of the liquidus curve.
      6. Melting is complete when the composition of the liquid becomes the same as the isopleth that represents the total system, and the temperature is defined where this line crosses the liquidus curve.
   2. Binary solid-solution systems are another geologically common type.  In this type of system the solidus and liquidus make a football-like shape.  As in other systems the liquid counts as one phase, but the solid also counts as one phase, a "solid solution" that can contain variable proportions of the end-member components.
      1. When crystallization begins on cooling in this type of system, the first crystals are richer in the high-melting component, so that the liquid composition is driven toward the low-melting component's side of the system.
      2. As the liquid composition changes, the crystals forming in equilibrium with it are also shifted toward the lower-temperature end-member.
      3. Crystallization is complete when the crystals form with the same composition as the original liquid.
      4. To do exactly as the phase diagram shows, the solid phase must continually react and stay in equilibrium with the liquid.  In real magmatic situations, especially with volcanics amd shallow intrusions, crystallization happens too fast and "zoned" crystals result.
   
   
5. Ternary and Other Multicomponent Systems - are shown with triangular diagrams, with isothermal contous to portray the liquidus surface.
   1. One-component fields are separated by cotectic lines
   2. Cotectic lines may run into each other to form eutectics, or simply have "sags" called minima.  One of the most notable of these occurs in the system SiO2-albite-orthoclase, occupying a bulk composition that characterizes many granites.
   
   
6. Bowen's Reaction Series - can be portrayed in terms of the phase relations among mafic minerals (in the discontinuous series, best manifested by olivines, Mg-Fe pyroxenes and Ca-rich pyroxenes), The plagioclase (continuous) series, and the quartz-Kspar-plag system.

Last revised October 31, 2002 by MAJordan