Garnet (Nesse, p. 310-312) has the general formula X₃Y₂Z₃O₁₂ where Z is a tetrahedral site generally occupied by Si⁴⁺ or Al³⁺, Y is an octahedral site generally occupied by a cation with 3+ charge (Al³⁺, Cr³⁺, Fe³⁺, or Ti⁴⁺), and X is a deformed cubic site occupied by a cation having a 2+ charge (Mg²⁺, Fe²⁺, Mn²⁺, Ca²⁺).

There are six common varieties of garnet, in two series.
The "pyralspite" garnets all have Al³⁺ as the primary cation in the Y site:

• Pyrope - Mg₃Al₂(SiO₄)₃
• Almandine - Fe₃Al₂(SiO₄)₃
• Spessartine - Mn₃Al₂(SiO₄)₃

• Uvarovite - Ca₃Cr₂(SiO₄)₃
• Grossular - Ca₃Al₂(SiO₄)₃
• Andradite - Ca₃(Fe³⁺,Ti)₂(SiO₄)₃

The Assignment:

Given the above structural information, follow the method of pages 172-174 in Nesse to calculate the structural allocations for the following two garnet chemical analyses:

Oxide	Sample #1	Sample #2
SiO2	41.33	38.96
TiO2	0.28	0.71
Al2O3	21.83	19.93
Cr2O3	1.73	----
Fe2O3	1.44	3.43
FeO	9.00	3.25
MnO	0.44	0.03
MgO	19.60	1.31
CaO	4.40	32.52
Total	100.05	100.14

Please do your calculations in an Excel spreadsheet. Once you've determined the structural assignments, determine which variteies of garnet are present in your sample - which is the most abundant and which is next most abundant? Can you determine anything about the likely paragenesis (origin/tectometamorphic setting) of these garnets?

Due Date: You should be prepared to submit this completed Homework assignment on Monday, November 2 in class.