1. Pyroxene

2. Pyroxene: Structure and classification
Pyroxenes are the most significant and abundant group of rock-forming ferromagnesian silicates. They are found in almost every variety of igneous rock and also occur in rocks of widely different compositions formed under conditions of regional and contact metamorphism.
Pyroxenes have a basic structural unit consisting of linked SiO4 tetrahedra that each share 2 of their oxygens in such a way as to build long chains of SiO4. The basic structural group is thus Si2O6 with. Pyroxenes have a general structural formula of: XYZ2O6 where X = Na+, Ca2+, Mn2+, Fe2+, or Mg2+ filling octahedral sites called M2 Y = Mn2+, Fe2+, Mg2+ , Al3+, Cr3+, or Ti4+ filling smaller octahedral sites called M1 Z = Si4+ or Al3+ in tetrahedral coordination.

3. M1 site (Y)
Fe, Mg, Ca
M2 sites (X)
XYZ2O6

4. Pyroxene I Beam
All pyroxenes show perfect (110) cleavage. When viewed looking down the c-crystallographic axis, the cleavages intersect at near 90° angles (the angles are actually 92 – 93° and 87 – 88°). This 90 degree cleavage angle is most useful in distinguishing pyroxenes from amphiboles (in amphiboles the cleavages are at 56° and 124°. 

5. The most important natural pyroxene minerals are formed from solid solutions involving Mg, Fe2+, and Ca. The range of compositions can be represented by the pyroxene quadrilateral. There are three important solid solutions contained within the quadrilateral: the orthopyroxene solid solution (often referred to as hypersthene), the pigeonite solid solution, and the augite solid solution. 
The pyroxenes can be divided into several groups based on chemistry and crystallography: • Clinopyroxenes are monoclinic pyroxenes and are either calcic or sodic. Clinopyroxenes include augite, diopside, pigeonite, hedenbergite, aegirine, jadeite and omphacite. Augite, pigeonite and diopside can contain exsolution lamellae of orthopyroxene if cooled slowly.

6. Sodic Pyroxenes

7. • Orthopyroxenes are orthorhombic pyroxenes
• Orthopyroxenes are orthorhombic pyroxenes. They are low-Ca ferromagnesian pyroxenes. The maximum birefringence of orthopyroxenes increases with Fe content. Orthopyroxenes consist of a range of compositions between enstatite - MgSiO3 and ferrosilite -FeSiO3

9. Amphiboles - W0-1X2Y5Z8O22(OH,F)2
There are 5 major groups of amphibole leading to 76 chemically defined end-member amphibole compositions.
Because of the wide range of chemical substitutions permissible in the crystal structure, amphiboles can crystallize in igneous and metamorphic rocks with a wide range of bulk chemistries. 

10. Amphiboles constitute the most chemically complex group in nature,
These are double chain silicates .
Along the chain, successive tetrahedra share two and three oxygen ions, respectively, so that the chemical formula for the infinite chain is (Si4O11)6-. The chain are elongated along c direction, with the bases of the tetrahedra nearly in the bc plane. 
The general formula for amphiboles is: W0-1X2Y5Z8O22(OH,F)2 W = Na1+ or K1+ in the A site with 10 to 12 fold coordination. X = Ca2+, Na1+, Mn2+, Fe2+, Mg2+, Fe3+, in an M4 site with 6 to 8 fold coordination Y = Mn2+, Fe2+, Mg2+, Fe3+, Al3+ or Ti4+ in an M1 octahedral coordination site.  Z = Si4+ and Al3+ in the tetrahedral site.

11. W0-1X2Y5Z8O22(OH,F)2
The structure is characterized by several cationic sites, called A, M4, M1, M2, M3 and Z
A: 12-fold A site is occupied by K or Na or vacant
M4 (large octahedra): 8-fold M4 sites is occupied by X cations (Ca2+, Na1+, Mn2+, Fe2+, Mg2+, Fe3+ )
M1,M2,M3: are medium and small octahedral site and containing Y cations (Mg2+, Fe2+, Mg2+, Fe3+, Al3+, Ti4+)

12. The principal classification of amphiboles is based on the chemistry of the X cations.
If X sites is occupied by Ca we have Calcium amphiboles: • Tremolite Ca2Mg5Si8O22(OH)2 – Ferroactinolite Ca2Fe5Si8O22(OH)2 • Hornblende Na0-1(Ca,Na)2(Mg,Fe2+,Fe3+, Al)5(Si,Al)8O22(OH)2
If X sites is occupied by Na we have Sodium or alkali amphiboles: • Glaucophane Na2Mg3Al2Si8O22(OH)2 • Ferroglaucophane Na2Fe2+Al2Si8O22(OH)2 • Riebeckite Na2Fe2+Fe2+Si8O22(OH)2 • Magnesioriebeckite Na2Mg3Fe3+Si8O22(OH)2 • Arfvedsonite Na3Fe2+Fe3Si8O22(OH)2 If X sites is occupied by Ca and Na we have Calcium-Sodium amphiboles: • Richterite Na(Na,Ca)Mg5Si8O22(OH)2 If X sites is occupied by Fe, Mg, Mn we have Iron-magnesium amphiboles: • Antophyllite Mg7Si8O22(OH)2 • Cummingtonite Mg7Si8O22(OH)2 - Grunerite Fe7Si8O22(OH)2

13. The amphiboles differ chemically from the pyroxenes in two major respects.
Amphiboles have hydroxyl groups in their structure and are considered to be hydrous silicates that are stable only in hydrous environments where water can be incorporated into the structure as (OH)-.
The second major compositional difference is the presence of the A site in amphiboles that contains the large alkali elements, typically sodium cations and at times potassium cations. The pyroxenes do not have an equivalent site that can accommodate potassium.
The presence of hydroxyl groups in the structure of amphiboles decreases their thermal stability relative to the more refractory (heat-resistant) pyroxenes. Amphiboles decompose to anhydrous minerals (mainly pyroxenes) at elevated temperatures. 
All of the amphiboles except Anthophyllite are monoclinic, and all show the excellent prismatic cleavage on (110). The angles between the cleavages, however are 56° and 124° making all amphiboles easy to distinguish from the pyroxenes. Looking at faces that show only a single cleavage trace would show inclined extinction, except in Anthophyllite.