The Phase Rule and 1- and 2-Component Systems
(Chapter 6)

last update:09/21/05

Crystallization behavior of magma from a basaltic lava lake
(Wright and Okamura, 1977)

Makaopuhi Lava Lake
Temperature vs. %Glass in the quenched sample

 

Crystallization Behavior of Melts

1. Cooling melts crystallize from a liquid to a solid over a range of temperatures (and pressures)

2. Several minerals crystallize over this T range, and the number of minerals increases as T decreases

3. The minerals that form do so sequentially, with considerable overlap

4. Minerals that involve solid solution change composition as cooling progresses

5. The melt composition also changes during crystallization

6. The minerals that crystallize (as well as the sequence) depend on T and composition of the melt

7. Pressure can affect the types of minerals that form and the sequence

8. The nature and pressure of the volatiles can also affect the minerals and their sequence

The Phase Rule

F = C - P + 2

F = # degrees of freedom

The number of intensive parameters that must be specified in order to completely determine the system

P = # of phases

phases are mechanically separable constituents

C = minimum # of components (chemical constituents that must be specified in order to define all phases)

2 = 2 intensive parameters

Usually = temperature and pressure for geologists

One-component systems

The SiO2 system.
Inclusion of coesite (cs), quartz (qtz) and chalcedony (cha) in an inclusion within pyrope from Dora Maira Massif (Italy).

This locality has reached ultrahigh P metamorphic conditions of >30 kb.

CL image from a hot-cathode CL system

 

From Schertl et al. (2004) Eur. J. Mineral.

 

Two-component systems

Binary system with a complete solid solution

Sample OL-4 - crossed nicols

Sample OL-4 - Backscattered electron image

 

For equilibrium crystallization

Bulk composition a = An60

= 60 g An + 40 g Ab

XAn = 60/(60+40) = 0.60

F = 2

1. Must specify 2 independent intensive variables (e.g. T and XAn) in order to completely determine the system = a divariant situation

2. Can vary 2 intensive variables independently without changing P, the number of phases

 

Get new phase joining liquid:

first crystals of plagioclase: = 0.87 (point c)

F = 2 - 2 + 1 = 1 ("univariant")

Must specify only one variable from among:

T, XAbLiq, XAbPl, XAnLiq, XAnPl

(P = constant)

 

At 1450oC, liquid d and plagioclase f coexist at equilibrium

A continuous reaction of the type:

liquidA + solidB = liquidC + solidD

 

 

When the composition of solid plagioclase approaches h, then the solid plagioclase approaches the bulk composition.

The last liquid to crystallize at point g (1340 C) has a composition of An20.

 

Equilibrium melting

 

Fractional crystallization 
(sinking or floating of crystals as they form)

Another effective manner of fractional crystallization of plagioclase is through compositional zoning such that the An-rich core of a plagioclase is effectively isolated from the liquid (i.e. normal zoning).

Sample OL-4 - crossed nicols

Sample OL-4 - Backscattered electron image

 

Fractional or Partial melting
(immediate extraction of melt)

Partial melting will generate a residue plagioclase enriched in An.

 

Sample OL-4 - crossed nicols

Sample OL-4 - Backscattered electron image
Fo - Fa (Mg2SiO4 - Fe2SiO4)

also a solid-solution series

 

 

 

Binary eutectic systems

Example: Diopside - Anorthite
Isobaric (P=0.1 MPa) and no solid solution

 

(1) a = bulk composition = An70

(2) Cool to 1455oC (point b)

(3) Continue cooling as Xliq varies along the liquidus;

(4) Continuous rxn: liqA ® anorthite + liqB
(5) at 1274oC, P = 3 so F = 2 - 3 + 1 = 0 (invariant)

(P) T and the composition of all phases is fixed

Must remain at 1274oC as a discontinuous reaction proceeds until a phase is lost

Discontinuous Reaction: all at a single T

 

Left of the eutectic get a similar situation
  

(left) Texture expected to the left of the eutectic
(right) Texture expected to the right of the eutectic
The last melt to crystallize in any binary eutectic mixture is the eutectic composition

Equilibrium melting is the opposite of equilibrium crystallization

Thus the first melt of any mixture of Di and An must be the eutectic composition as well

For fractional crystallization, the initial crystals will accumulate somewhere and the final melt will be fixed at the eutectic point composition.

For partial melting, the initial melt has the eutectic composition and removed until one the components is removed (An or Di). Then, the remaining solid would be one component and would not melt again until the melting point of the pure phase.

 

Binary Peritectic System
Possible solid phases: Forsterite (Fo) - Enstatite (En) - Silica (S)

Peritectic reaction: Mg2SiO4 + SiO2 = 2 MgSiO3
 i.e. the composition of En is between Fo and SiO2, and quartz should never coexist with forsterite!)

Isobaric T-X phase diagram of the system Fo-Silica at 0.1 MPa.
For bulk composition f equilibrium crystallization ultimately results in Forsterite + Enstatite

 

i = "peritectic" point

1557oC have colinear Fo-En-liq

geometry indicates a reaction: Fo + liq = En

consumes olivine (and liquid) ® resorbed textures

 

Fractional crystallization of composition f will generate a layer of Fo, then En and then En + SiO2.

Incongruent Melting of Enstatite (i.e.

Melt of En does not ® melt of same composition
Rather En ® Fo + Liq i at the peritectic

Partial Melting of Fo + En (harzburgite) mantle

En + Fo also ® first liq = i

Remove i and cool

Result = ?

 

Pressure Effects

Different phases have different compressibilities

- Raises melting point

- Shift eutectic position (and thus X of first melt, etc.)

 

Solid Solution with a Eutectic

Albite - orthoclase (the alkali feldspar system)

T-X phase diagram of the system albite-orthoclase at 0.2 GPa H2O pressure.

The solvus relations of the feldspars are a potential geothermometer

 

 

Effect of PH2O on Ab-Or
At relatively low PH2O, a single feldspar will crystallize and then undergo further exsolution (a, b) [hypersolvus]

 
At relatively high PH2O, two feldspars will crystallize with possible further exsolution of each phase (c) [subsolvus]