(a) How are the symmetry elements in a crystal of class 6/m 2/m 2/m oriented with respect to its crystallographic axes? (10…

(a) Symmetry elements of the class 6/m 2/m 2/m

This is the dihexagonal dipyramidal class (6/mmm), the highest symmetry of the hexagonal system, as in beryl. The three symbols give the three directions in the Hermann–Mauguin symbol.

(i) First position (c-axis). A 6-fold rotation axis lies along c, the vertical axis, with a mirror plane (m) perpendicular to it, which is the horizontal plane containing the three a-axes (a₁, a₂, a₃), 120° apart.

(ii) Second position (a-axes). Three 2-fold axes lie along a₁, a₂ and a₃, each perpendicular to a vertical mirror plane. The trace of this plane bisects the angle between two a-axes.

(iii) Third position (between the a-axes). Three further 2-fold axes lie in the basal plane midway between the a-axes (30° from each), each perpendicular to a vertical mirror that contains c and one a-axis.

The class thus has one 6-fold axis, six 2-fold axes, seven mirror planes (one horizontal and six vertical) and a centre of symmetry, a total of 24 operations.

(b) Why some minerals show pleochroism

Pleochroism is the change of colour of a coloured, anisotropic mineral in plane-polarised light, when the stage is rotated.

(i) In anisotropic crystals the atomic arrangement and bonding differ from direction to direction. Light vibrating parallel to each principal optical direction is absorbed by a different amount, and in different wavelengths, by the colouring ions such as Fe²⁺, Fe³⁺ and Ti.

(ii) The polariser passes light vibrating in one plane only, so when the stage is rotated, the vibration direction moves through the crystal and a different absorption colour is seen.

(iii) Uniaxial minerals have two colours (dichroic), as in tourmaline, where the ordinary ray (ω) is more strongly absorbed. Biaxial minerals have three colours (trichroic) along X, Y and Z, as in hornblende (yellow-green, green, blue-green) and biotite (pale yellow to dark brown).

Isotropic minerals such as garnet and colourless minerals show no pleochroism. It helps identify minerals in thin sections.

(c) Changes in magnesium-rich magma by progressive removal of olivine

In a primitive picritic or basaltic magma, magnesian olivine (Fo₈₈–₉₀) crystallises first, and if it is removed by settling, the melt changes as follows.

(i) MgO falls rapidly and the Mg number (Mg/(Mg+Fe)) decreases, since olivine has far more MgO than the melt. The olivine itself becomes more iron-rich (less forsteritic).

(ii) FeO/MgO rises, and FeO may rise at first.

(iii) Compatible elements such as Ni and Cr fall sharply, because they are taken into olivine.

(iv) Incompatible components (SiO₂, Al₂O₃, CaO, Na₂O, K₂O, TiO₂, P₂O₅) increase, as olivine is low in them, so silica rises slightly.

The melt moves from picrite to basalt, reaching the cotectic, where clinopyroxene and plagioclase join olivine. The Deccan picritic basalts show such olivine control.

(d) Mineral assemblages of a mafic protolith in metamorphic facies

For basalt or gabbro:

(i) Greenschist facies (about 300–500 °C, low to moderate pressure): chlorite + actinolite + albite + epidote (± quartz, sphene). The green colour comes from chlorite, actinolite and epidote.

(ii) Amphibolite facies (about 500–700 °C): hornblende + plagioclase (oligoclase to andesine), often with garnet, and epidote at the lower grades. Albite gives way to more calcic plagioclase, and actinolite to hornblende.

(iii) Granulite facies (above about 700–800 °C): orthopyroxene + clinopyroxene + plagioclase (± garnet, ± quartz), with little hydrous mineral, as a result of dehydration. High-pressure mafic granulite has garnet + clinopyroxene + plagioclase.

Increasing temperature dehydrates the rock step by step. Indian examples are the Southern Granulite Terrain (Nilgiri, Madras) for granulite, and the Dharwar schist belts for greenschist and amphibolite.

(e) Diagenetic changes in carbonate rocks

Carbonates change quickly and early after deposition, since their minerals (aragonite, high-Mg calcite) are unstable.

(i) Marine phreatic diagenesis: micritisation by boring algae, and fibrous aragonite or high-Mg calcite cement.

(ii) Meteoric diagenesis (after emergence): dissolution of aragonite, which makes moulds and vugs, neomorphism (aragonite and high-Mg calcite change to low-Mg calcite) and precipitation of clear blocky calcite cement.

(iii) Burial diagenesis: mechanical compaction and pressure solution, which form stylolites, late ferroan calcite cement, dolomitisation and silicification.

(iv) Uplift (telodiagenesis): further dissolution.

Cementation reduces porosity, while dissolution and dolomitisation create or preserve it, so diagenesis controls reservoir quality, as in the Bombay High limestone.