Answer the following in about 150 words each: (a) How are Miller Indices of a crystal face calculated ? Calculate Miller Indices…

(a) Miller indices describe the orientation of a crystal face relative to the crystallographic axes. Let the intercepts made by the face on the a, b and c axes, measured in axial units, be p, q and r. The method is:

• Determine the intercepts p, q and r.
• Take the reciprocals 1/p, 1/q and 1/r.
• Clear fractions by multiplying by a suitable common factor.
• Reduce the resulting numbers to the smallest integers h, k and l.
• Enclose them in parentheses as (hkl). Negative intercepts are shown by a bar over the index. A face parallel to an axis has infinite intercept, so its reciprocal is zero.

(i) The face intersects all three axes at 3-unit distance. Thus p = 3, q = 3 and r = 3. Reciprocals are 1/3 : 1/3 : 1/3. Multiplying by 3 gives 1 : 1 : 1. Therefore the Miller indices are (111).

(ii) The face intersects the a-axis at 4-unit distance and is parallel to the b and c axes. Thus p = 4, q = ∞ and r = ∞. Reciprocals are 1/4 : 0 : 0. Multiplying by 4 gives 1 : 0 : 0. Therefore the Miller indices are (100).

(b) A solid solution is a single homogeneous crystalline phase in which two or more components are mixed at the lattice scale. Its composition can vary without changing the basic crystal structure. Substitution may be simple, as Mg²⁺ ↔ Fe²⁺ in olivine, Mg₂SiO₄–Fe₂SiO₄; coupled, as Na⁺ + Si⁴⁺ ↔ Ca²⁺ + Al³⁺ in plagioclase; or interstitial, where small atoms or ions occupy voids in the structure. Solid solution is favoured by similar ionic radius and charge, high temperature, suitable crystal structure and, in some cases, pressure. Common examples occur in olivine, pyroxene, amphibole, feldspar and garnet.

Exsolution is the unmixing of an originally homogeneous solid solution into two or more distinct phases on cooling or pressure change. At high temperature, entropy favours mixing. On cooling, the solvus is crossed and diffusion separates the components into lamellae, blebs or patches within a host. It is a solid-state process, not melting. Examples are perthite, where albite lamellae separate from K-feldspar; antiperthite; augite with pigeonite lamellae; and ilmenite–hematite intergrowths. Exsolution textures indicate slow cooling from a high-temperature homogeneous state and help reconstruct thermal history. Thus, solid solution is the mixed state, while exsolution is its later separation.

(c) Intergranular texture: in a mafic rock, plagioclase occurs as randomly oriented laths, and pyroxene fills the angular interstitial spaces between them. The pyroxene does not enclose the plagioclase laths; it merely occupies the remaining pore space. A sketch would show elongated plagioclase rectangles with pyroxene in the wedges and gaps between them.

Sub-ophitic texture: here pyroxene forms larger crystals that partially enclose earlier-formed plagioclase laths. The plagioclase laths are partly embedded in pyroxene, but many still protrude outside; the enclosure is incomplete. In true ophitic texture, plagioclase laths are completely enclosed by pyroxene. A sketch would show a large, irregular pyroxene crystal with several plagioclase laths partly inside and partly outside its boundary.

Both textures may occur in the same mafic rock because plagioclase and pyroxene crystallize nearly simultaneously from the same magma. If plagioclase nucleates first and grows as laths, later pyroxene simply fills the interstices, producing intergranular texture. If pyroxene begins to crystallize before plagioclase growth is complete, it can partially envelop the laths, giving sub-ophitic texture. Local differences in nucleation density, cooling rate, undercooling, melt composition and timing of crystallization can therefore produce both textures together in a dolerite, gabbro or basalt.

(d) Increasing temperature alone promotes solid-state diffusion, recrystallization, grain growth and metamorphic reactions. At constant pressure, hydrous and clay minerals break down, and new anhydrous assemblages form. For example, in pelitic rocks, clay → chlorite → biotite → garnet → staurolite → kyanite/sillimanite with rising temperature. In calcareous rocks, calcite + quartz → wollastonite + CO₂ at high temperature. Temperature thus controls reaction rate and metamorphic grade.

Increasing pressure alone favours denser minerals and high-pressure polymorphs. Examples are quartz → coesite, calcite → aragonite, and basalt/gabbro → eclogite, where plagioclase + pyroxene change to garnet + omphacite. Pressure also influences dehydration and recrystallization, especially under differential stress, producing foliation and preferred mineral orientation.

When pressure and temperature increase jointly, as in regional metamorphism during burial and tectonism, the stable mineral assemblage is fixed by both variables. The P–T path determines the facies series: low-P/high-T Buchan type with andalusite and cordierite; medium-P Barrovian type with kyanite, staurolite and garnet; high-P/low-T blueschist type with glaucophane and lawsonite; and high-P eclogite type. Thus shale may pass through slate → phyllite → schist → gneiss, while basalt may pass through greenschist → amphibolite → eclogite. Pressure and temperature are therefore independent intensive controls on metamorphism.

(e) Sandstones are classified using framework composition and matrix content. Matrix is fine-grained clay or silt, generally less than 0.03 mm, occurring between framework grains. A basic division is:

• Arenite: matrix below the boundary; clean, well-winnowed sandstone. In Pettijohn/Dott the boundary is about 10% matrix; in Folk it is about 15%.
• Wacke: matrix above that boundary; poorly sorted, matrix-rich sandstone.

In Pettijohn’s classification, arenites include quartz arenite, subarkose, sublitharenite, arkose and litharenite. Quartz arenite contains more than about 90–95% quartz and is supermature. Arkose is rich in feldspar, commonly derived from granite. Litharenite is rich in rock fragments. Wackes include quartz wacke, feldspathic wacke and lithic wacke; lithic wacke is commonly called greywacke.

Folk’s classification uses quartz, feldspar and rock fragments for arenites and treats matrix separately. Dott’s scheme recognises quartz arenite, feldspathic arenite, lithic arenite and greywacke. The matrix reflects depositional energy and diagenesis: clean arenites indicate high-energy, winnowed environments, whereas wackes indicate rapid deposition, turbidity currents and low-energy basins. Composition reflects provenance and maturity: quartz-rich sandstones are recycled and mature; feldspar-rich sandstones are arkosic and granitic; lithic-rich sandstones are volcanic or metamorphic in source. Thus, both composition and matrix are essential for sandstone classification.