(a) How does one designate mirror plane, rotational axes of symmetry and centre of symmetry in Hermann-Mauguin notation? A…

(a) Hermann–Mauguin notation and the tetragonal crystal

In Hermann–Mauguin (international) notation: a rotation axis is written by its fold, 1, 2, 3, 4 or 6; a mirror plane is written m; a centre of symmetry (inversion) is written 1̄; an axis with a mirror plane perpendicular to it is written n/m; and a mirror plane parallel to the axis is written n m. Axes are listed in the order of the crystallographic directions.

The crystal has one 4-fold axis, four 2-fold axes (two along the horizontal axes and two diagonal), five mirror planes (one horizontal and four vertical) and a centre. Its symbol is 4/m 2/m 2/m, written 4/mmm. This is the ditetragonal dipyramidal class, the highest symmetry of the tetragonal system.

On a stereographic projection: draw the primitive circle with the central 4-fold axis (square symbol), the horizontal mirror plane as the circle itself, two vertical mirror planes along the axes and two along the diagonals as straight lines through the centre, and the 2-fold axes as ellipses at the ends of those lines. The general form {hkl} has 16 equivalent faces: eight upper poles, shown as dots, and eight lower, shown as open circles, placed symmetrically in each quadrant.

(b) Crystallisation of Diopside 70–Anorthite 30 at 1 atm

Diopside–anorthite is a simple binary eutectic system (Bowen). Diopside melts at about 1,392 °C and anorthite at about 1,553 °C; the eutectic is at about 1,274 °C and about 58 per cent diopside.

A melt of Di70 An30 lies on the diopside side of the eutectic. On cooling it first meets the diopside liquidus, so diopside crystallises first. As diopside separates, the liquid becomes richer in anorthite and its composition moves along the liquidus toward the eutectic. At the eutectic temperature the liquid has Di58 An42 and diopside and anorthite crystallise together at constant temperature until the liquid is used up. By the lever rule, (70 − 58)/(100 − 58) = about 29 per cent is early diopside, and about 71 per cent is eutectic intergrowth.

The final rock is made of diopside crystals that grew first, in a finer eutectic intergrowth of diopside and anorthite, a porphyritic or ophitic-type texture, with all of the melt consumed.

(c) Bowen's reaction series

Bowen (1922) showed the order in which minerals crystallise from a cooling basaltic magma, in two branches that merge.

Discontinuous series: olivine → pyroxene → amphibole → biotite. At each stage the earlier mineral reacts with the melt and changes to a new mineral with a different crystal structure.

Continuous series: calcium-rich plagioclase (anorthite) → sodic plagioclase (albite), by gradual substitution of Na and Si for Ca and Al in the same framework structure.

After both series, the remaining liquid yields potassium feldspar, muscovite and quartz.

Why the names: the plagioclase series is continuous because the crystal structure stays the same and only the composition changes gradually by solid solution. The ferromagnesian series is discontinuous because each step requires an abrupt change of structure, from isolated tetrahedra (olivine) to single chains (pyroxene), double chains (amphibole) and sheets (biotite).

(d) Prograde and retrograde metamorphism; metasomatism

Prograde metamorphism is a change of a rock to higher grade as temperature and pressure rise, usually with loss of water. The usual path is shale → slate → phyllite → schist → gneiss, with chlorite → biotite → garnet → staurolite → kyanite → sillimanite.

Retrograde metamorphism is a return of the rock to lower grade as temperature and pressure fall, usually with the return of water to the minerals; it needs fluid. Examples: garnet replaced by chlorite, amphibolite replaced by greenschist-facies minerals, and olivine altered to serpentine.

Metasomatism is the change in the bulk chemical composition of a rock by addition or removal of elements by fluids moving through it, without melting. It is a chemically open process by infiltration or diffusion. Examples: skarn formation, in which limestone next to granite gains silicon, iron and magnesium to form garnet and pyroxene; fenitisation around carbonatite; and albitisation or greisenisation.

(e) Folk's classification of limestones

Folk (1959, 1962) classifies limestones by their allochems (grains) and the material between them.

Allochems: intraclasts (i), ooids (o), fossils or bioclasts (bio) and pellets (p). Matrix: micrite (microcrystalline lime mud, from low energy) or sparite (clear calcite cement, from clear water and higher energy).

Names combine the two: intrasparite, intramicrite, oosparite, oomicrite, biosparite, biomicrite, pelsparite and pelmicrite. If allochems make up less than 10 per cent the rock is micrite; and rocks built in place by organisms, such as reefs, are biolithites. Grain rounding and sorting give a further textural stage.

The name shows both the grain type and the energy of the environment: sparry types indicate strong currents, and micritic types calm water.