Answer the following questions in about 150 words each: (a) How are the symmetry elements in a crystal of class 6/m 2/m 2/m…

(a) In the hexagonal setting, the 6-fold axis with its perpendicular mirror, written 6/m, lies along the c-axis, the unique vertical axis. The basal a1, a2 and a3 axes are 120° apart. The first 2/m direction gives three 2-fold axes in the basal plane, perpendicular to c, along a1, a2 and a3; each is perpendicular to a diagonal vertical mirror plane, σd, whose trace bisects the angle between two a-axis lines. The second 2/m direction gives three 2-fold axes bisecting the a-axis lines; each is perpendicular to a vertical mirror plane, σv, that contains the c-axis and one a-axis. In a stereogram projected down c, the c-axis is at the centre; the a-axis lines and σv traces coincide, the bisecting 2-axes and σd traces lie midway between the a-axis lines, and the horizontal mirror is the plane of projection.

(b) Pleochroism is the change in colour of a mineral when light is observed along different crystallographic directions. It occurs only in anisotropic, coloured crystals because their electronic structure, bond strengths and polarizability differ along different axes. A light ray has an electric vibration direction; when that direction is parallel to one principal vibration direction of the crystal, a particular set of wavelengths is absorbed, while a ray vibrating parallel to another direction experiences a different absorption coefficient. Thus the transmitted or reflected colour varies with orientation. Uniaxial minerals have two principal absorption directions, ordinary and extraordinary, while biaxial minerals have three, X, Y and Z. The effect is strongest when the mineral is thick enough to absorb selectively and when the crystal is oriented so that the vibration directions are resolved. Biotite shows brown to black pleochroism, hornblende green to brown, and tourmaline commonly has its strongest absorption parallel to the c-axis. Isotropic minerals lack distinct vibration directions and therefore do not show pleochroism.

(c) In a magnesium-rich magma, olivine crystallizes first along the forsterite-fayalite join of Bowen's reaction series. Early olivine is Mg-rich, so progressive removal of olivine removes both MgO and FeO, but MgO is removed faster; the residual melt is depleted in MgO, Mg# falls, and FeO is relatively enriched, so FeO/MgO rises. Because olivine is silica-poor, the liquid also becomes enriched in SiO2, Al2O3, Na2O, K2O and incompatible elements. This Fe-enrichment drives the magma toward the tholeiitic side of the olivine-pyroxene field; with continued fractionation, clinopyroxene, especially augite, and later orthopyroxene or Fe-Ti oxides enter the liquidus. If water content and pressure favour plagioclase and hydrous phases, the differentiation path can shift toward calc-alkaline compositions. This is why olivine-bearing cumulates are Mg-rich while the residual liquid evolves toward basaltic or andesitic compositions, with eventual pyroxene saturation.

(d) For a mafic protolith such as basalt or gabbro, the facies assemblages record increasing temperature, pressure and dehydration. Greenschist facies, about 300-500 °C and 0.3-0.6 GPa, produces chlorite, actinolite, albite, epidote and quartz; chlorite and actinolite indicate hydrous, low-grade conditions. At amphibolite facies, about 500-700 °C and 0.5-1.0 GPa, chlorite and actinolite break down to hornblende, plagioclase of andesine to labradorite composition, quartz, epidote, and plus or minus garnet or ilmenite; hornblende-plagioclase is diagnostic. In granulite facies, about 700-900 °C and greater than 0.8-1.0 GPa, hydrous minerals disappear; the assemblage is orthopyroxene, clinopyroxene, garnet, plagioclase and quartz, often with ilmenite, reflecting high temperature, low water activity and anhydrous pyroxene stability. Epidote may persist into amphibolite, but is absent in granulite. The sequence is causal: rising P-T drives chlorite and actinolite to hornblende, then hornblende to pyroxene, garnet, plagioclase and quartz, so hydrous minerals are progressively expelled.

(e) Diagenesis in carbonate rocks transforms primary sediment into rock through compaction, cementation, recrystallization and dissolution. Early, shallow diagenesis begins in marine and meteoric settings: micritization coats grains in fine micrite, neomorphism recrystallizes aragonite or high-Mg calcite to low-Mg calcite, and marine cements such as aragonite or high-Mg calcite, or meteoric cements such as low-Mg calcite or dolomite, fill pores. These early cements can preserve primary porosity, while meteoric dissolution can create vadose porosity. Burial diagenesis increases temperature and pressure, causing compaction, pressure solution, and burial cements such as calcite, dolomite, anhydrite or pyrite. Late diagenesis includes dissolution and stylolitization, which reduce porosity and create stylolite seams, and dolomitization, which may create vugs or reduce porosity. In Indian cratonic carbonates, early marine micrite and calcite cements are commonly overgrown by burial calcite and cut by stylolites. Primary interparticle porosity is thus reduced by cementation and compaction, while secondary porosity can form by dissolution, stylolite development or dolomitization. This porosity evolution controls reservoir quality.