What you need to learn:

• The essentials of the olivine and garnet structure.
• The concept of an ideal solid solution and configurational entropy.
• How to interpret a binary melting diagram.
• The high pressure phase transitions of olivine that occur in the Earth's mantle.

Olivine Structure:

Below is a unit cell of the olivine structure.

The olivine structure is based on isolated SiO4 tetrahedra (blue) which link chains of (Fe,Mg)O6 octahedra. There are two octahedral cation sites: M1 (yellow) and M2 (orange). Both sites accomodate Fe2+ and Mg2+ cations and there is complete disorder of Fe and Mg over the M1 and M2 sites. Olivine is orthorhombic and therefore will show parallel or symmetric extinction under crossed polarized light.

Solid solution and configurational entropy

The cation disorder over the M1 and M2 sites gives olivine a slightly higher stability at elevated temperatures because of the increased configurational entropy associated with disorder.

There are two sites for Mg and Fe in olivine, M1 and M2. The configurations Fe(M1)Mg(M2) and Fe(M2)Mg(M1) have almost the same energy. Both the M1 and M2 sites will have equal amounts of Mg or Fe. Olivine is a good example of a nearly ideal solid solution.

Now, let X_M1 be the mole fraction of Mg in the M1 site; let X_M2 be the mole fraction of Mg in the M2 site. The configurational entropy will be

S = [X_M1lnX_M1 + (1-X_M1)ln(X_M1) + X_M2lnX_M2 +(1-X_M2)ln(1-X_M2)]

Since there is no partitioning between the M1 and M2 sites,

X_M2 = X_M1 = X

so that

S = 2R[XlnX+(1-X)ln(1-X)]

Effect of solid solution on melting

Optical Properties of Olivine

Olivine can be recognized by its

• High relief
• Moderate Birefringance
• Absence of good cleavage directions.
• In volcanic rocks, olivine crystals may be euhedral and show symmetrical extinction.

High-Pressure Phase Transitions of Olivine

Under the pressure conditions of the Earth's mantle, olivine undergoes several phase transitions to denser structures. These phase transitions give rise to several important seismic discontinuities. Indeed, the transition from the olivine to the spinel structure is responsible for deep focus earthquakes. It is probably worthwhile, both for this course and for others in the next two years, that you memorize the diagram below:

The spinel (ringwoodite) polymorph

(Fe,Mg)2SiO4 in the spinel structure is known as ringwoodite. Here, Si atoms occupy the tetrahedral sites (yellow) and Fe and Mg atoms occupy the edge-sharing octahedral sites (blue).

Wadsleyite

Intermediate between the olivine and spinel (ringwoodite) structure is a phase known as wadsleyite (beta (Mg,Fe)₂SiO₄ The wadsleyite (or beta-spinel) structure is currently of great interest because it is being invoked as a reservior of water (as chemically bound OH) in the Earth's mantle.

In the wadsleyite structure, the octahedra (yellow) contain Mg and Fe; the tetrahedra (blue) contain Si. One of the oxygens in the structure, however, receives an incomplete Pauling bond strength. It is coordinated to four Mg cations to get a total PBS of 4*(2/6) = 1.333. This oxygen readily becomes protonated (hydrogenated) as shown by the pink spheres. It is believed that wadsleyite might store vast quantities of water in the Earth's mantle.

There is more polyhedral sharing in the wadsleyite and spinel structures than in the olivine structure. According to Paulings Rules, therefore, these structures should have a higher internal energy than the olivine structure. They form because at high pressure, phases with a lower volume (higher density) will have a lower free energy.

The pressure of the phase transitions to ringwoodite and wadsleyite varies with composition (Fe/Mg ratio). This has implications for the sharpness of these transitions in the Earth's mantle and is currently of research interest:

Garnets

Crystal Chemistry

General formula is X₃Y₂Z₃O₁₂ where X = Ca²⁺, Mg²⁺, Fe²⁺, Mn²⁺ (Dodecahedral Site) Y = Fe³⁺, Al³⁺, Cr³⁺ (Octahedral Site) Z = Si⁴⁺, Ti⁴⁺ (Tetrahedral Site) Nomenclature:

• Pyrope Mg-Al
• Almandine Fe²⁺-Al
• Spessertine Mn²⁺-Al
• Grossular Ca-Al
• Andradite Ca-Fe³⁺
• Uvarovite Ca-Cr³⁺

There is complete solid solution between pyrope-almandine and spessertine ("pyralspite") and also between grossular, andradite and uvarovite ("ugrandite"). The reason there is no solid solution between the "pyralspite" and "ugrandite" systems is because of the ionic radii differences between Ca and (Mg, Fe²⁺ or Mn²⁺).

Crystallographic and Optical Properties:

Garnets are cubic. In thin section, garnets have high relief and are optically isotropic. They show no cleavage and have variable colours depending on the transition metal present. Rarely, they are slightly optically anistropic...

Garnet Paragenesis

Garnets occur in a variety of igneous and metamorphic environments:

• Pyrope - ultrabasic rocks such as peridotite
• Almandine - pelitic schists
• Spessartine - granitic pegmatites
• Grossular - contact and regionally metamorphosed impure calcareous rocks.
• Andradite - metasomatism of impure calcareous rocks accompanied by metasomatism (introducing Fe³⁺): CaCO₃ + SiO₂ + Fe₂O₃ --> Ca₃Fe₂Si₃O₁₂ + 3CO₂

There is also a garnet structure of MgSiO₃ at high pressure:
(Mg^VIII)₃ (Si^VI)₂(Si^IV)₃O₁₂
This is called "majorite" and exists in the upper mantle and transition zone.