Unit-2: Mineralogy

(a) Crystallography

Definition and Character of Crystals

Crystallography is the scientific branch that deals with the study of the geometric forms, structure, and properties of crystals. A crystal is a solid material whose constituent atoms, molecules, or ions are arranged in an orderly repeating microscopic pattern extending in all three spatial dimensions.

Definition: A crystal is a homogeneous solid of chemical element or compound having a regular atomic or ionic arrangement and bounded by smooth, plane surfaces (crystal faces) meeting at definite angles, formed under favorable physical and chemical conditions.

Character of Crystals:

• Homogeneity: Any small part of a single crystal has the same physical and chemical properties as any other part.
• Anisotropy: Many physical properties of crystals, such as refractive index, electrical conductivity, and thermal expansion, vary with the direction along which they are measured.
• Interfacial Angles: The angle between corresponding faces of crystals of the same substance is constant, regardless of the relative sizes or shapes of the individual faces (Steno's Law of Constancy of Interfacial Angles).

Exam-Oriented Note: Remember that the external regular geometric form is a direct reflection of the internal ordered atomic arrangement.

Crystal Faces, Axes, Axial Ratio, and Interfacial Angle

To describe the external geometry of a crystal, several reference features and terms are used:

• Crystal Faces: The flat, external planar surfaces that bound a crystal, formed during the growth of the crystal.
• Crystal Axes: Imaginary lines passing through the center of a crystal, intersecting each other at specific angles, used as a spatial coordinate system to define the positions of crystal faces.
• Axial Ratio: The relative lengths of the crystallographic axes (a, b, c). One axis is usually taken as unity (standard), and the lengths of the other axes are expressed in proportion to it.
• Interfacial Angle: The angle formed between the normals (perpendicular lines) drawn to two intersecting crystal faces. It is measured using a goniometer and is a constant and characteristic property for a given mineral species.

Practical Example: When examining a quartz crystal, even if one face is larger than the opposing face due to asymmetric growth, the interfacial angle between corresponding prism faces remains precisely constant at 60 degrees.

Symmetry Elements

Symmetry elements are geometric operations that map a crystal onto itself when rotated, reflected, or inverted. A normal crystal class possesses a combination of the following elements:

• Plane of Symmetry (P): An imaginary plane that divides a crystal into two halves such that one half is the exact mirror image of the other.
• Axis of Symmetry (A): An imaginary line around which a crystal can be rotated, resulting in the identical appearance of the crystal a specific number of times in one complete rotation of 360 degrees. These can be 2-fold (dyad), 3-fold (triad), 4-fold (tetrad), or 6-fold (hexad).
• Center of Symmetry (C): A central point within a crystal such that any line passing through it meets identical features, faces, or points at equal distances on opposite sides.

Important Definition: A normal class (holosymmetric class) of a crystal system possesses the maximum possible symmetry elements characteristic of that system.

Parameters and Miller's Indices

To mathematically denote the orientation of crystal faces relative to the crystallographic axes, systems of notation are applied:

• Parameters (Weiss Parameters): The intercepts of a crystal face on the three crystallographic axes (a, b, c), measured in terms of the unit lengths along those axes.
• Miller's Indices: A system of notations using a set of three (or four) integers (h, k, l) that designate a crystal face or a set of parallel planes. They are derived by taking the reciprocals of the Weiss parameters of the face and clearing any fractions to the smallest integers.

Step-by-Step Derivation of Miller's Indices:

1. Find the intercepts of the face along the axes a, b, and c in terms of unit lengths (e.g., 1a, 2b, infinity c).
2. Take the reciprocals of these numbers (1/1, 1/2, 1/infinity).
3. Simplify the reciprocals to the smallest whole numbers by clearing fractions (resulting in 1, 1/2, 0 becomes multiplied by 2 to yield 2, 1, 0).
4. Enclose the resulting integers in parentheses: (2 1 0).

Common Mistake: Do not confuse Weiss parameters (which are relative lengths of intercepts) with Miller's indices (which are reciprocals of intercepts expressed as whole numbers).

Division of Crystals into Crystal Systems

Based on the lengths of the crystallographic axes and the angles between them, all crystals are classified into seven major crystal systems.

Study of Normal Classes (Isometric, Tetragonal, and Hexagonal Systems)

The syllabus requires the detailed study of the normal (holosymmetric) classes of three specific systems:

• Isometric System (Normal Class - Galena Type):
  • Axes: Three mutually perpendicular axes of equal length (a = b = c).
  • Symmetry Elements: 3 rectangular planes of symmetry, 6 diagonal planes of symmetry (Total 9 planes); 3 four-fold axes, 4 three-fold axes, 6 two-fold axes (Total 13 axes); and a center of symmetry.
  • Common forms: Cube, octahedron, dodecahedron.
• Tetragonal System (Normal Class - Zircon Type):
  • Axes: Three mutually perpendicular axes, where the two horizontal axes are equal (a = b) and the vertical axis is longer or shorter (c != a).
  • Symmetry Elements: 1 principal horizontal plane and 4 vertical planes of symmetry (Total 5 planes); 1 four-fold axis and 4 two-fold axes (Total 5 axes); and a center of symmetry.
  • Common forms: Tetragonal prisms, tetragonal pyramids, bipyramids.
• Hexagonal System (Normal Class - Beryl Type):
  • Axes: Four axes total, consisting of three horizontal coplanar axes intersecting at 120-degree angles (a1 = a2 = a3) and one vertical axis perpendicular to them (c != a).
  • Symmetry Elements: 1 horizontal plane and 6 vertical planes of symmetry (Total 7 planes); 1 six-fold axis and 6 two-fold axes (Total 7 axes); and a center of symmetry.
  • Common forms: Hexagonal prisms, hexagonal pyramids, basal pinacoids.

(b) Physical Mineralogy

Definition of a Mineral and Physical Properties

Definition: A mineral is a naturally occurring, inorganic, solid, crystalline substance with a definite chemical composition and a characteristic internal atomic structure.

Physical Properties of Minerals:

• Color: The appearance of the mineral in reflected light; often misleading due to impurities.
• Streak: The color of the powdered mineral when rubbed across an unglazed porcelain streak plate.
• Luster: The quality and intensity of light reflected from the surface of a mineral (e.g., metallic, vitreous, pearly, silky, earthy).
• Hardness: The resistance of a mineral to scratching, measured using Mohs Hardness Scale (from 1 for Talc to 10 for Diamond).
• Cleavage: The tendency of a mineral to break along specific crystallographic planes of weak internal bonding, producing smooth surfaces.
• Fracture: The way a mineral breaks when it does not exhibit cleavage (e.g., conchoidal, uneven, hackly, splintery).
• Specific Gravity: The ratio of the weight of a mineral to the weight of an equal volume of water.

Description of Specific Minerals

The following minerals must be studied with respect to their physical properties, chemical composition, and common use:

• Quartz
  • Chemical Composition: Silicon dioxide (SiO2)
  • Physical Properties: Colorless or variable, vitreous luster, conchoidal fracture, hardness 7, no cleavage.
  • Common Use: Glassmaking, electronic oscillators, abrasive, gemstone.
• Potash Feldspar (Orthoclase)
  Chemical Composition: Potassium aluminum silicate (KAlSi3O8)
  Physical Properties: Pink, white, or grey, hardness 6, two directions of cleavage at 90 degrees, pearly to vitreous luster.
  Common Use: Ceramic industry, porcelain, manufacture of glass.
• Plagioclase Feldspar
  • Chemical Composition: Sodium calcium aluminum silicate ((Na,Ca)(Al,Si)4O8)
  • Physical Properties: White to dark grey, striations often visible on cleavage faces, hardness 6, two cleavage directions at nearly 90 degrees.
  Common Use: Ceramics, building stone, raw material in aggregate.
• Hornblende
  • Chemical Composition: Complex hydrated silicate of calcium, magnesium, iron, and aluminum.
  • Physical Properties: Dark green to black color, vitreous luster, hardness 5 to 6, two directions of cleavage intersecting at approximately 56 and 124 degrees.
  • Common Use: Primarily a rock-forming mineral; minor use as dimension stone.
• Biotite
  • Chemical Composition: Potassium magnesium iron aluminum silicate hydroxide.
  • Physical Properties: Dark brown to black color, flexible elastic sheets, perfect basal cleavage yielding thin elastic laminae, hardness 2.5 to 3.
  • Common Use: Filler in paints, lubricants, and roofing materials.
• Muscovite
  • Chemical Composition: Potassium aluminum silicate hydroxide (KAl2(AlSi3O10)(OH)2)
  • Physical Properties: Colorless to light silvery-yellow, transparent in thin sheets, perfect basal cleavage, hardness 2 to 2.5.
  • Common Use: Electrical insulator, electronics, cosmetics, optical filters.
• Kyanite
  • Chemical Composition: Aluminum silicate (Al2SiO5)
  • Physical Properties: Blue or blue-grey, bladed crystals, variable hardness (4 parallel to the blade length, 6-7 across the blade width), perfect cleavage.
  • Common Use: Refractories, high-temperature porcelain, ceramic spark plugs.
• Sillimanite
  • Chemical Composition: Aluminum silicate (Al2SiO5)
  • Physical Properties: White, grayish, or brownish, fibrous or slender prismatic crystals, hardness 6.5 to 7.5, good cleavage.
  • Common Use: Manufacture of high-grade refractory bricks and ceramics.
• Tourmaline
  • Chemical Composition: Complex borosilicate of aluminum, iron, magnesium, sodium, lithium.
  • Physical Properties: Variable colors, striated prismatic crystals, conchoidal fracture, hardness 7 to 7.5, vitreous luster.
  • Common Use: Gemstone, piezoelectric pressure sensors, scientific instruments.
• Calcite
  • Chemical Composition: Calcium carbonate (CaCO3)
  Physical Properties: Colorless or white, reacts with effervescence to dilute HCl acid, hardness 3, three directions of perfect cleavage yielding rhombohedrons.
  Common Use: Cement manufacture, agricultural lime, construction aggregate, neutralization of acids.
• Garnet
  • Chemical Composition: Silicate of various metals (calcium, magnesium, iron, aluminum).
  • Physical Properties: Deep red, brown, or black, isometric crystal habit (dodecahedron or trapezohedron), hardness 6.5 to 7.5, no cleavage, vitreous luster.
  • Common Use: Abrasive sandpapers, waterjet cutting, gemstone.
• Talc
  • Chemical Composition: Hydrated magnesium silicate (Mg3Si4O10(OH)2)
  • Physical Properties: White, green, or grey, extremely soft (Mohs hardness 1), greasy or soapy feel, perfect basal cleavage.
  • Common Use: Talcum powder, cosmetics, ceramics, paper manufacturing filler.
• Gypsum
  • Chemical Composition: Hydrated calcium sulfate (CaSO4 . 2H2O)
  • Physical Properties: White or colorless, hardness 2, can be scratched with a fingernail, perfect cleavage in one direction.
  • Common Use: Plaster of Paris, drywall/wallboard production, agricultural soil conditioner.
• Fluorite
  • Chemical Composition: Calcium fluoride (CaF2)
  Physical Properties: Variable colors (purple, green, yellow), cubic crystal habit, hardness 4, four directions of perfect octahedral cleavage.
  Common Use: Flux in steel smelting, manufacture of hydrofluoric acid, optical lenses.
• Augite
  • Chemical Composition: Complex silicate of calcium, magnesium, iron, and aluminum (Pyroxene group).
  • Physical Properties: Dark green to black, stubby prismatic crystals, hardness 5.5 to 6, two directions of cleavage at nearly 90 degrees.
  • Common Use: Rock-forming mineral (common in basic igneous rocks like basalt and gabbro); no direct commercial use.
• Pyrite
  • Chemical Composition: Iron disulfide (FeS2)
  • Physical Properties: Pale brass-yellow color ("fool's gold"), metallic luster, dark greenish-black streak, conchoidal fracture, hardness 6 to 6.5.
  • Common Use: Production of sulfur dioxide and sulfuric acid.
Hematite
• Chemical Composition: Iron oxide (Fe2O3)
• Physical Properties: Reddish-brown to steel-gray color, characteristic reddish-brown streak, metallic to earthy luster, hardness 5.5 to 6.5.
• Common Use: Major ore of iron, pigment/paint manufacturing.
• Magnetite
  • Chemical Composition: Iron oxide (Fe3O4)
  • Physical Properties: Iron-black color, strongly magnetic, black streak, metallic luster, hardness 5.5 to 6.5, no true cleavage.
  • Common Use: Important iron ore, heavy media separation, magnetic recording materials.