(a) Describe the symmetry elements shown by the normal class of the orthorhombic system. What are the different forms for this…

(a) Orthorhombic normal class

The normal class of the orthorhombic system is 2/m 2/m 2/m (or mmm). It is the holosymmetric class, so all crystal faces occur in symmetrically equivalent pairs. It is the most symmetric orthorhombic class. It has three mutually perpendicular twofold axes (3L2), three mirror planes (3P), and a centre of symmetry (C). The axes a, b and c are unequal and mutually perpendicular. The possible forms are the three pinacoids {100}, {010} and {001}; three rhombic prisms {0kl} (first order), {h0l} (second order) and {hk0} (third order); and the rhombic dipyramid {hkl}, the general form with eight faces. (Domes and sphenoids belong to the lower classes mm2 and 222.) In a sketch stereogram of the general form {hkl}, the class mmm gives eight distinct poles: four in the upper hemisphere and four in the lower hemisphere. Because the class has a horizontal mirror plane, each lower-hemisphere pole lies directly beneath an upper-hemisphere pole, so the stereogram shows four positions, each a dot (upper face) inside a circle (lower face), one in each quadrant.

``svg <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 412" width="640" height="412"> <title>Stereogram of the general form {hkl}, orthorhombic class mmm</title> <style>text{font-family:Arial,Helvetica,sans-serif;font-size:13px;fill:#1f2937}.t{font-size:15px;font-weight:bold}.b{font-weight:bold}.s{font-size:12px;fill:#4b5563}.c{text-anchor:middle}.e{text-anchor:end}.i{font-style:italic}</style> <rect width="640" height="412" fill="#fff"/> <text x="320" y="20" class="t c" style="font-size:14px">Stereogram of the general form {hkl}, orthorhombic class mmm (2/m 2/m 2/m)</text> <circle cx="230" cy="215" r="150" fill="none" stroke="#1f2937" stroke-width="1.8"/> <line x1="80" y1="215" x2="380" y2="215" stroke="#1f2937" stroke-width="1.6"/> <line x1="230" y1="65" x2="230" y2="365" stroke="#1f2937" stroke-width="1.6"/> <ellipse cx="230" cy="65" rx="7" ry="4" fill="#1f2937"/> <ellipse cx="230" cy="365" rx="7" ry="4" fill="#1f2937"/> <ellipse cx="80" cy="215" rx="7" ry="4" fill="#1f2937"/> <ellipse cx="380" cy="215" rx="7" ry="4" fill="#1f2937"/> <ellipse cx="230" cy="215" rx="7" ry="4" fill="#1f2937"/> <text x="392" y="220" class="b">b</text> <text x="236" y="381" class="b">a</text> <text x="240" y="207" class="s">c (centre)</text> <circle cx="302" cy="153" r="8" fill="none" stroke="#1d4e78" stroke-width="2"/> <circle cx="302" cy="153" r="3.5" fill="#b03030"/> <circle cx="158" cy="153" r="8" fill="none" stroke="#1d4e78" stroke-width="2"/> <circle cx="158" cy="153" r="3.5" fill="#b03030"/> <circle cx="302" cy="277" r="8" fill="none" stroke="#1d4e78" stroke-width="2"/> <circle cx="302" cy="277" r="3.5" fill="#b03030"/> <circle cx="158" cy="277" r="8" fill="none" stroke="#1d4e78" stroke-width="2"/> <circle cx="158" cy="277" r="3.5" fill="#b03030"/> <text x="302" y="139" class="c s">hkl</text> <text x="158" y="139" class="c s">h&#773;kl</text> <text x="302" y="299" class="c s">hk&#773;l</text> <text x="158" y="299" class="c s">h&#773;k&#773;l</text> <text x="420" y="70" class="b">Symmetry: 3 L<tspan baseline-shift="sub" font-size="12">2</tspan>, 3 P, C</text> <circle cx="428" cy="96" r="3.5" fill="#b03030"/><text x="440" y="100">upper pole (hkl, face above)</text> <circle cx="428" cy="120" r="7" fill="none" stroke="#1d4e78" stroke-width="2"/><text x="440" y="124">lower pole (hkl&#773;), below</text> <text x="440" y="140" class="s">(horizontal mirror)</text> <line x1="420" y1="160" x2="436" y2="160" stroke="#1f2937" stroke-width="1.6"/><text x="440" y="164">vertical mirrors (100),(010)</text> <ellipse cx="428" cy="184" rx="7" ry="4" fill="#1f2937"/><text x="440" y="188">2-fold axes along a, b, c</text> <text x="420" y="220" class="b">Forms of class mmm</text> <text x="420" y="240" class="s">pinacoids {100} {010} {001}</text> <text x="420" y="258" class="s">prisms {0kl} {h0l} {hk0}</text> <text x="420" y="276" class="s">rhombic dipyramid {hkl}: 8 faces</text> <text x="420" y="312" class="b">Examples</text><text x="420" y="330" class="s">olivine, barite, topaz,</text><text x="420" y="346" class="s">andalusite, aragonite, sulphur</text> <text x="230" y="405" class="c s">8 poles of {hkl}: 4 above, 4 below (dot in circle)</text> </svg> `` The four positions are related by the two vertical mirror planes, and the upper and lower sets by the horizontal mirror and the centre of symmetry. The poles are arranged symmetrically about the three twofold axes. Minerals of this class include olivine, andalusite, sillimanite, barite, topaz, aragonite and sulphur.

(b) Optical properties of hornblende and augite

Under the petrological microscope, hornblende and augite are distinguished by relief, cleavage, extinction and colour. Hornblende is an amphibole; it shows moderate to high relief, two cleavages at about 56° and 124° in basal sections (diamond-shaped outline), and inclined extinction (Z∧c) of about 12–30° to the cleavage traces. It is strongly pleochroic, commonly passing from green to brown. Augite is a clinopyroxene; it shows high relief, two cleavages at nearly 90° (87° and 93°) in basal sections (octagonal outline), and large inclined extinction in longitudinal sections. It has little or no pleochroism, and its cleavage/optic orientation is commonly described by a 45° angle, Z∧c ≈ 45°. In plane-polarised light, hornblende’s green-brown pleochroism is readily visible, whereas augite remains nearly colourless. Both minerals show two cleavage directions, but the extinction angle and pleochroism are the most useful diagnostic features. Both show up to second-order interference colours and simple twinning on {100}; augite is biaxial positive with 2V about 25–60°, hornblende usually biaxial negative with 2V about 50–90°. Augite’s higher relief makes its grain boundaries sharper, while hornblende’s smaller extinction angle is a key distinction in thin section for identification. These properties help identify them in igneous and metamorphic rocks.

(c) Perthite texture and formation

Perthite is an intergrowth in which alkali feldspar is the host and plagioclase occurs as exsolved lamellae; antiperthite is the reverse, with plagioclase host and alkali feldspar lamellae. A neat labelled diagram would show a host alkali feldspar grain containing thin, regularly spaced plagioclase lamellae, with labels for host, exsolution lamellae, and, if present, mesoperthite-scale lamellae. The formation is explained by the Ab-Or phase diagram. At high temperature, albite and orthoclase form a solid solution. On cooling, the composition enters the solvus, the miscibility gap, below about 700 °C. The homogeneous feldspar becomes unstable and separates into two feldspar phases. Slow cooling gives coarser microperthite or macroperthite lamellae, while rapid cooling gives finer cryptoperthite. The phase diagram would show the single-phase feldspar field above the solvus and the two-phase feldspar field below it, with a cooling path crossing the solvus.

``svg <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 640 360" width="640" height="360"> <title>Perthite texture and the Ab–Or solvus</title> <style>text{font-family:Arial,Helvetica,sans-serif;font-size:13px;fill:#1f2937}.t{font-size:15px;font-weight:bold}.b{font-weight:bold}.s{font-size:12px;fill:#4b5563}.c{text-anchor:middle}.e{text-anchor:end}.i{font-style:italic}</style> <rect width="640" height="360" fill="#fff"/> <text x="320" y="20" class="t c">Perthite texture and the Ab–Or solvus (formation by exsolution)</text> <path d="M40,70 L250,60 L270,250 L60,270 Z" fill="#f3eef9" stroke="#333" stroke-width="1.6"/> <path d="M70,78 Q82,165 64,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <path d="M96,78 Q108,165 90,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <path d="M122,78 Q134,165 116,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <path d="M148,78 Q160,165 142,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <path d="M174,78 Q186,165 168,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <path d="M200,78 Q212,165 194,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <path d="M226,78 Q238,165 220,255" stroke="#b03030" stroke-width="7" fill="none" opacity="0.85"/> <text x="150" y="48" class="c s">host alkali feldspar (K-rich, Or)</text> <text x="150" y="292" class="c s">plagioclase (albite-rich) exsolution lamellae</text> <text x="150" y="308" class="c s">(antiperthite: plagioclase host)</text> <text x="150" y="332" class="c b">Perthite (thin section view)</text> <line x1="360" y1="300" x2="610" y2="300" stroke="#1f2937" stroke-width="1.6"/><line x1="360" y1="300" x2="360" y2="70" stroke="#1f2937" stroke-width="1.6"/> <text x="485" y="332" class="c">composition (wt % Or)</text> <text x="360" y="316" class="c s">Ab</text><text x="610" y="316" class="c s">Or</text><text x="485" y="316" class="c s">50</text> <text transform="translate(330,185) rotate(-90)" class="c">temperature (°C)</text> <path d="M365,300 L380,231 L400,180 L422,153 L448,139 L472,144 L498,160 L522,190 L548,231 L572,286 L585,300" fill="#fde8e8" stroke="#8a3324" stroke-width="2.2"/> <text x="354" y="304" class="e s">300</text><line x1="357" y1="300" x2="360" y2="300" stroke="#1f2937"/> <text x="354" y="212" class="e s">500</text><line x1="357" y1="208" x2="360" y2="208" stroke="#1f2937"/> <text x="354" y="120" class="e s">700</text><line x1="357" y1="116" x2="360" y2="116" stroke="#1f2937"/> <text x="485" y="97.6" class="c s">one homogeneous alkali feldspar</text> <text x="455" y="221.8" class="c">solvus</text><text x="455" y="235.6" class="c s">(miscibility gap)</text> <text x="455" y="254" class="c s">Ab-rich + Or-rich</text><text x="455" y="267.8" class="c s">feldspar</text> <line x1="510" y1="74.6" x2="510" y2="240.2" stroke="#5b3a80" stroke-width="2" stroke-dasharray="6 4"/> <polygon points="510,244.8 505,233.3 515,233.3" fill="#5b3a80"/> <text x="520" y="158.4" class="s" style="fill:#5b3a80">cooling</text><text x="520" y="172.4" class="s" style="fill:#5b3a80">path</text> <line x1="380" y1="231" x2="548" y2="231" stroke="#1d4e78" stroke-width="1.4"/> <circle cx="380" cy="231" r="3.5" fill="#1d4e78"/><circle cx="548" cy="231" r="3.5" fill="#1d4e78"/> <text x="376" y="225" class="s" style="fill:#1d4e78">lamellae</text><text x="530" y="225" class="s" style="fill:#1d4e78">host</text> <text x="485" y="352" class="c s">slow cooling: coarse; fast: cryptoperthite</text> </svg> `` This exsolution records the cooling history of granitic rocks: hypersolvus granites and syenites crystallising a single alkali feldspar become strongly perthitic, whereas subsolvus granites crystallise two separate feldspars.

(d) Diagenetic textures of carbonate rocks

A labelled diagram of carbonate diagenesis would show grains and cements modified after deposition. Micrite envelopes are thin carbonate mud coatings around grains; micritization is the replacement or infilling of grains by micrite. Hardgrounds are synsedimentary cemented, bored and encrusted surfaces on the seafloor. (Intraclasts and peloids are depositional grains rather than diagenetic textures, but they are often micritized.) Early marine cements form isopachous fibrous or bladed rims around grains; meteoric vadose cements form meniscus and pendant (gravitational) cements, while meteoric phreatic and burial cements are equant blocky calcite. Cementation includes syntaxial overgrowths, where new calcite grows with the same crystal orientation as the host grain, and drusy mosaic cements, where new crystals grow with differing orientations, coarsening towards pore centres. Pressure solution produces stylolites and sutured grain contacts, where soluble material is removed along grain boundaries. Dissolution of aragonitic grains leaves moldic and vuggy porosity; neomorphism (aggrading recrystallisation) converts micrite to microspar and pseudospar; and dolomitisation produces rhombic dolomite mosaics, often with increased intercrystalline porosity. The diagram would label an ooid with micrite envelope, an intraclast, a peloid, syntaxial cement, and a stylolite.

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l-4,22 l-22,-6 Z" fill="#fde8e8" stroke="#b03030" stroke-width="1.2"/> <path d="M590,346 l22,6 l-4,22 l-22,-6 Z" fill="#fde8e8" stroke="#b03030" stroke-width="1.2"/> <path d="M460,356 C470,306 485,311 480,361 Z" fill="#374151" opacity="0.15" stroke="#374151" stroke-dasharray="3 2"/> <text x="438" y="252" class="s">rhombs; mold (dissolved grain)</text> <text x="320" y="442" class="c s">Also: neomorphism (micrite to microspar), blocky burial cement, hardgrounds (bored seafloor)</text> </svg> `` These features help distinguish marine, shallow-water, and burial diagenetic environments. They also indicate compaction, cementation, and fluid flow during burial. Such textures are common in limestones and dolostones.

(e) Ultrahigh-pressure and ultrahigh-temperature metamorphism

Ultrahigh-pressure metamorphism occurs at pressures above 2.5-4 GPa and temperatures of 600-800 °C, within the eclogite facies (coesite/diamond field). Its diagnostic assemblages include coesite and diamond, minerals stable only at such high pressures. These rocks record rapid subduction of crustal material to mantle depths and later exhumation, as in coesite-bearing eclogites of the Tso Morari complex (Ladakh) and the Kaghan valley in the western Himalaya, and diamond-bearing rocks of Kokchetav (Kazakhstan) and Dabie Shan (China). Ultrahigh-temperature metamorphism occurs at temperatures above 900 °C, up to 1050 °C, at pressures of 0.5-1.2 GPa, in the granulite facies. Characteristic assemblages include osumilite, sapphirine, and spinel plus quartz. Indian examples are the sapphirine-bearing granulites of the Eastern Ghats Mobile Belt (Paderu, Anakapalle) and the Madurai Block of the Southern Granulite Terrain. UHT rocks record intense heating of the lower crust, often associated with mantle-derived magmatism or deep crustal extension. Both UHP and UHT metamorphism indicate extreme tectonic processes, but UHP reflects very high pressure with moderate temperature, while UHT reflects very high temperature at lower pressure. Such assemblages are used to reconstruct P-T paths and tectonic settings. They are important for understanding plate convergence, crustal recycling, and thermal structure. Their preservation requires fast exhumation and limited retrogression.