(a) Explain the process of manganese nodules formation and give their major occurrences in the world. (10 marks) (b) Describe the…

(a) Manganese nodules: formation and world occurrence

Manganese nodules are rounded concretions of Mn and Fe oxides, a few centimetres across, lying on the deep-sea floor at 4000–6000 m. A nucleus such as a shark tooth, a shell or a fragment of basalt is coated in concentric layers.

Formation.

(i) Hydrogenetic: Mn, Fe, Co, Ni and Cu are precipitated slowly from oxygenated seawater, at about 1–10 mm per million years.

(ii) Diagenetic: metals released from organic-rich sediment, by reduction in pore water, rise and are precipitated in oxidised conditions near the surface, at a far faster rate, up to about 100 mm per million years, and the nodules are richer in Ni and Cu, with a high Mn/Fe ratio.

Low rates of sedimentation, oxic bottom water and abundant nuclei favour them.

Major occurrences. The Clarion–Clipperton Zone of the north-east Pacific, the Peru Basin, the Penrhyn Basin of the Pacific, the Blake Plateau of the Atlantic, and the Central Indian Ocean Basin, where India holds an exploration area allotted by the International Seabed Authority.

(b) Replacement textures in ore minerals and their criteria

Replacement is the process by which a new mineral forms in place of an older one, by dissolution and deposition, often simultaneously, as hydrothermal or supergene fluids react with the host. The volume is kept in the change, and the old form may be retained.

Textures.

(i) Pseudomorphs, where the new mineral keeps the crystal shape of the old, as in martite (haematite after magnetite) and goethite after pyrite.

(ii) Rim replacement along grain edges, cracks and cleavage, as in covellite and chalcocite after chalcopyrite and pyrite.

(iii) Relics and islands of the old mineral in the new.

(iv) Atoll and skeletal forms, where the rim or the core is replaced and the other remains.

Criteria of recognition. Irregular, embayed contacts; relics of the older mineral, in optical continuity; preserved structures, cleavage and twinning crossing the boundary; replacing veinlets following cleavage or fractures; and pseudomorphs. Open-space filling shows no such features.

(c) Kriging method of ore-reserve estimation

Kriging is a geostatistical method, developed from the work of D. G. Krige on gold and formalised by G. Matheron, that estimates the grade at an unsampled point or block as a weighted average of nearby samples. It gives the best linear unbiased estimate, meaning that the weights sum to one and the estimation variance is the least.

Steps.

(i) Compute the experimental semivariogram, γ(h) = (1/2N) Σ [z(x) − z(x + h)]², which shows how grade differences grow with distance.

(ii) Fit a model (spherical or exponential) with nugget, sill and range. Samples farther than the range do not influence each other.

(iii) Solve the kriging equations with the model, for the weights, which account for the distance to the target and for the clustering of samples.

(iv) Estimate each block and its kriging variance.

Types are ordinary, simple, universal and block kriging. Its advantage over inverse distance or polygons is that it gives a measure of reliability and is used for resource classification and mine planning.

(d) Environmental impacts of urbanisation and their mitigation

Land. Loss of agricultural land and green cover; sealing of soil by pavement; subsidence from the extraction of groundwater, as in Kolkata; landslide and subsidence from building on unstable hill slopes, as at Joshimath in 2023; and waste dumps and landfills.

Water. More runoff and less recharge, causing urban floods, as in Mumbai (2005), Chennai (2015) and Bengaluru (2022); falling water tables; and pollution of surface and groundwater from sewage and industrial waste. Wetlands and lakes are lost.

Mitigation. Carrying-capacity-based planning and hazard zonation, with no building on hazardous slopes or flood plains. Protection of wetlands and drainage channels. Permeable surfaces, parks and green roofs, with rainwater harvesting, which is mandatory in Tamil Nadu. Sewage treatment and reuse. Solid waste management in line with the Solid Waste Management Rules, 2026, and regulation of groundwater extraction.

(e) Coordination number and the ratio of ionic radii

In an ionic crystal, each ion tends to surround itself by as many oppositely charged ions as touch it without the anions touching each other. The coordination number (CN) of a cation therefore depends on the radius ratio r⁺/r⁻.

Pauling's radius-ratio rules give the ranges:

(i) 0.155–0.225: CN 3, triangular.

(ii) 0.225–0.414: CN 4, tetrahedral.

(iii) 0.414–0.732: CN 6, octahedral.

(iv) 0.732–1.0: CN 8, cubic.

For NaCl, Na⁺ is 1.02 Å and Cl⁻ is 1.81 Å; the ratio is 0.56 and CN is 6. For CsCl, Cs⁺ is 1.74 Å, so the ratio is 0.96 and CN is 8. The rules are approximate because bonds are partly covalent and ions are polarised, as in the SiO₄ tetrahedron.