(a) Give the classification scheme of silicate minerals on the basis of atomic structure, Si : O ratio and number of shared…

(a) Classification of silicate minerals

All silicates are built from the SiO₄ tetrahedron. They are classed by how the tetrahedra share oxygen atoms, which fixes the Si : O ratio.

• Nesosilicates (island): isolated tetrahedra, no shared oxygen, SiO₄⁴⁻, Si : O = 1 : 4. Examples: olivine, garnet, zircon, topaz, the Al₂SiO₅ polymorphs (kyanite, sillimanite, andalusite).
• Sorosilicates (group): pairs of tetrahedra sharing one oxygen, Si₂O₇⁶⁻, Si : O = 1 : 3.5. Examples: epidote, melilite, hemimorphite.
• Cyclosilicates (ring): rings sharing two oxygens each, Si₃O₉ or Si₆O₁₈, Si : O = 1 : 3. Examples: beryl, tourmaline, cordierite.
• Inosilicates (chain): single chains share two oxygens, (SiO₃)ₙ²ⁿ⁻, Si : O = 1 : 3, as in pyroxenes (enstatite, augite, diopside); double chains share two or three oxygens alternately (average 2.5), (Si₄O₁₁)ₙ⁶ⁿ⁻, Si : O = 4 : 11, as in amphiboles (hornblende, tremolite).
• Phyllosilicates (sheet): sheets sharing three oxygens each, (Si₂O₅)ₙ²ⁿ⁻, Si : O = 2 : 5. Examples: micas (muscovite, biotite), chlorite, talc, serpentine, clay minerals.
• Tectosilicates (framework): all four oxygens shared, Si : O = 1 : 2 (with Al replacing some Si in feldspars). Examples: quartz, feldspars (orthoclase, plagioclase), feldspathoids (nepheline), zeolites.

As the number of shared oxygens rises from 0 to 4, the structure becomes more polymerised, cleavage changes from none or poor to perfect in one direction (sheets), and the minerals become more silica-rich and generally appear later in the crystallisation sequence.

(b) Birefringence and extinction angle

Birefringence is the difference between the highest and lowest refractive indices of an anisotropic mineral: for uniaxial minerals ne − no, for biaxial nγ − nα. It controls the interference colours: the retardation is Γ = t (n₂ − n₁), where t is the thickness of the section. In standard thin sections (0.03 mm) quartz shows first-order grey–white and calcite high-order pastel colours.

Extinction angle is the angle between the vibration direction of the mineral at extinction (a dark position between crossed polars) and a crystallographic direction, such as a cleavage trace, crystal edge or twin plane. Extinction can be parallel (0°), inclined, or symmetrical.

Measurement under the microscope:

• Choose a grain showing a clear cleavage trace or crystal edge, and the highest interference colour, so that the section is near the optic plane.
• Bring the cleavage trace parallel to a cross-hair using the rotating stage, and note the stage reading.
• Between crossed polars, rotate the stage until the grain goes dark (extinct), and note the new reading.
• The difference between the two readings is the extinction angle.
• Repeat on several grains and take the maximum value as characteristic of the mineral. Sketches show the grain with its cleavage along the cross-hair, then rotated to extinction. Extinction angles help identify minerals, such as hornblende (12–34°) from augite (35–48°).

(c) Twin plane, twin axis, composition plane; twins in feldspars

Twinning is the regular intergrowth of two or more crystals of the same mineral, where the individuals are related by a symmetry operation.

A twin plane is the plane across which the two parts are mirror images. A twin axis is the line about which one individual is rotated, usually 180°, to give the other. The composition plane is the surface along which the twin parts are joined; it may be the twin plane or another plane.

Twins in feldspars:

• Carlsbad twin: a simple twin on the c-axis (twin axis [001]), with composition plane (010), in orthoclase and plagioclase.
• Baveno twin: twin plane (021), a simple twin in orthoclase.
• Manebach twin: twin plane (001), a simple twin in orthoclase.
• Albite twin: polysynthetic (many thin lamellae) with twin plane (010), characteristic of plagioclase.
• Pericline twin: twin axis b [010], with lamellae along the rhombic section, in plagioclase.
• Albite and pericline together produce the cross-hatched (tartan) twinning of microcline.