18 - Lecture notes for GEOL 3010

Klein and Hurlbut (21st Ed) p. 236-24, 318-324, 330-332, 448-449, 532-543

Two-component diagrams - Presented in two dimensions.

The understanding two component systems requires holding one degree of freedom (variable) constant.

When pressure is held constant (known as isobaric conditions), then T and X are varied.

Recall that when two components can mix on an atomic scale then they are considered miscible phases and a solution results.

Points to make:

1. Liquidus Diagram

2. liquidus - upper portion where melt is in equilibrium with crystalline phase.

3. solidus - lower portion where crystalline phase is in equilibrium with melt.

4. Path depicts the evolution of melt and crystalline phase composition.

5. Note: that this is scenario operates assuming constant re-equilibration and a closed system.

6. subsolidus - region below solidus where all solid-state transformations may take place.

Olivine Series is an example of solid-solution series that is maintained over regardless of temperature (also includes high temperature portion of the plagioclase series).

Example from an actual olivine grain:

Core: Mg1.63 Fe0.36

Rim: Mg1.01 Fe0.78

Zonation in the olivine crystal shows us that equilibrium conditions did not exist. This potentially tells us information about cooling rate.

Coexistance without mixing is known as immisciblity.

At high temperature - 1. structure expands, 2. Vibration of atoms larger, 3. distinct structural sites become similar.

Consequence is that cation of different size can occupy the same site.

e.g., Na+ (1.18Å) and K+ (1.33Å) in feldspars

Exsolution - As tempertures decrease, diffusion of atoms within crystal occurs. Inital solid-solutions undergo "unmixing" into two separate, distinct crystalline phases.

Analogy: Vigourously shaken oil and water mixture will mix for a short time. With time they will "unmix"

See figure 5.21 (page 238). Subsolidus - phase diagram.


1. Miscibility gap - region in T-X space where solid-solution compositions are not formed due to exsolution.

2. Phase changes take place in the subsolidus

Examples: hornblende - grunerite, Labradorite An47-An58

No solid-solution

Silica* - albite system

* Silica as quartz never crystallizes from solution in water free systems (crystobilite and tridymite). But, for the purpose of our discussion (i.e., a binary system) we will ignore the third component water.

  1. Imagine a melt containing the ions Na+ , Al3+ , Si4+ , O2- with equal amounts of Na and Al and excess Si and enough O to keep things electrically neutral.
  2. Above the melting temperature vigorous particle motion keeps forming and breaking of the Si-O bonds and Al and Na prevent the Si-O bonds from firmly locking into bonds.
  3. As the temperature cools Si-O bonds lock and SiO2 crystals start forming.
  4. The growth of SiO2 crystals change the composition of the remaining liquid. (i.e., the liquid is impoverished in Si and enriched in Al and Na).
  5. If the temperature does not drop any more, then no additional SiO2 crystals will form.
  6. The process does not occur in steps, but is continuous. Therefore, in the first figure below there is a line from X1 to X2 .
  7. The line becomes steeper as crystallization proceeds.
  8. A similar crystallization process occurs for albite in melts that are enriched in Al and Na.
  9. The completed pathway is shown on the second diagram below.
  10. The location marked Z is a point in T-X space where both crystals will grow. This point is known as the eutectic point.
  11. The curve that represents the loci of points between melt and solid regions (i.e., phase fields) is termed the liquidus.
  12. The arrows on the boundaries of the phase fields represent the crystallization paths with decreasing temperature.
  13. Note that this diagram represent isobaric conditions. The phase relations will change with changing pressure. In the final diagram, lets consider a system in the state at point D in the diagram below.
  14. At a low pressure the system will exist as a single phase (liquid) state.
  15. If the pressure is raised, then two phases can coexist (liquid and silica) and crystallization will occur.

Caveats -

16. The effect of changing pressure (increased or decreased) can cause melting or crystallization. The effect is dependent upon all components in the system.

17. In an ideal binary system, usually the effect of increased pressure will cause crystallization (at the same temperature).

18. The presence of water (a third component) is likely to significantly alter the behavior of a system.