(a) Give a detailed account related to the classification of crystals into different crystallographic systems based on symmetry…

Crystal chemistry is governed by two linked principles: the symmetry of the unit cell and the degree of polymerisation of SiO4 tetrahedra. The seven crystallographic systems are ordered from highest to lowest symmetry and are defined by their characteristic rotation axes, mirror planes and inversion centres; their Hermann-Mauguin symbols encode these elements, with m denoting a mirror plane and -1 an inversion centre. Cubic (m3m) has four 3-fold axes and a=b=c, α=β=γ=90°. Tetragonal (4/mmm) has one 4-fold axis, a=b≠c, all angles 90°. Hexagonal (6/mmm) has one 6-fold axis, a=b≠c, α=β=90°, γ=120°. Trigonal (3m or 32) has one 3-fold axis, a=b=c, α=β=γ≠90°. Orthorhombic (mmm) has three mutually perpendicular 2-fold axes, a≠b≠c, all angles 90°. Monoclinic (2/m) has one 2-fold axis or mirror plane, a≠b≠c, α=γ=90°, β≠90°. Triclinic (1 or -1) has at most an inversion centre, a≠b≠c, α≠β≠γ≠90°. The axial relationships can be visualised as a table, with cubic at the top and triclinic at the bottom; each step reduces symmetry and increases metric freedom. Holohedral forms possess the full symmetry of the system and show all crystal faces allowed by that symmetry; hemihedral forms lack some symmetry elements, often mirrors or inversion, and may occur as enantiomorphic pairs.

Pyroxene structure and orthopyroxene. Pyroxenes are inosilicates built from single chains of corner-sharing SiO4 tetrahedra, (SiO3)2−. A side-view diagram shows each tetrahedron sharing two basal oxygens with neighbours, producing a repeating chain parallel to the c-axis; Mg, Fe, Ca and Mn occupy octahedral sites between chains. In orthopyroxene the orthorhombic structure has two non-equivalent octahedral sites, M1 and M2, occupied mainly by Mg and Fe. The weak inter-chain bonding gives two cleavages at about 87° and 93°, reflecting chain periodicity. This differs from amphiboles, whose double chains (Si4O11)6− are made of two single chains sharing basal oxygens and cleave near 56° and 124°. Orthopyroxene is an orthorhombic MgSiO3–FeSiO3 solid solution, enstatite–ferrosilite, with minor Ca, Mn and Al. It is colourless to pale brown or green, pleochroic, and has low to moderate birefringence: enstatite δ≈0.009–0.011, hypersthene δ≈0.010–0.016, ferrosilite δ≈0.017–0.020. 2Vx is composition-dependent and diagnostic; ferrosilite is biaxial negative with 2Vx≈30–50°, while enstatite has a larger 2Vx. Optically, orthopyroxene shows straight extinction and low first-order interference colours, with 2Vx measured in the XZ section.

Silicate structural classification. Silicates are classified by tetrahedral polymerisation, and the Si:O ratios are the basis for distinguishing silicate classes in thin section and for predicting cleavage, density, petrogenetic behaviour and chemical compatibility in magmas. Nesosilicates have isolated SiO4^4− groups, Si:O=1:4, with no bridging oxygens; olivine (Mg,Fe)2SiO4 occurs in Indian ophiolites and cratonic ultramafics, while zircon is an accessory in peninsular granites. Sorosilicates have paired Si2O7^6− groups, Si:O=2:7, linked by one bridging oxygen; epidote occurs in Indian metamorphic rocks and pegmatites. Cyclosilicates form closed rings, commonly Si6O18^12−, Si:O=1:3; beryl, Al2Be3Si6O18, is found in Indian pegmatites. Inosilicates have chains: single chains (SiO3)2−, Si:O=1:3, as in pyroxenes such as diopside and enstatite, and double chains (Si4O11)6−, Si:O=4:11, as in amphiboles such as hornblende. Phyllosilicates form sheets of Si2O5^2−, Si:O=2:5, with tetrahedral sheets linked by octahedral M layers; muscovite and biotite are classic examples from Indian mica belts. Tectosilicates form three-dimensional frameworks, Si:O=1:2, in which all four apical oxygens are shared; quartz and feldspar dominate Indian granites and peninsular gneisses. Sketches would show isolated tetrahedra, a paired tetrahedron, a six-membered ring, a single chain, a double chain, a sheet, and a fully connected framework.

Thus, symmetry elements define crystal systems, while silicate polymerisation controls mineral structure, cleavage, chemistry and optical behaviour. This structural diversity underlies the petrogenetic significance of silicates in crustal rocks and their roles in magmatic differentiation, from ultramafic olivine to granitic quartz and feldspar.