Mineralogy & Optical Mineralogy: Crystal Structures, Phase Diagrams, and Optics

Hexagonal Close-Packed (HCP)

ABAB... stacking arrangement. Exhibits 6-fold rotational symmetry, belonging to the Hexagonal crystal system. Coordination number is 12.

Cubic Close-Packed (CCP)

ABCABC... stacking sequence (equivalent to face-centered cubic, FCC). Exhibits 3-fold symmetry along body diagonals, belonging to the Isometric (Cubic) crystal system. Coordination number is 12.

Chemical zoning

Occurs when a crystal grows in a changing environment, resulting in spatial variations in chemical composition from core to rim.

Simple Substitution

Direct 1:1 exchange of ions of similar charge and ionic radius.

Cationic Simple Substitution

Mg²⁺ ↔ Fe²⁺ (e.g., Olivine series).

Anionic Simple Substitution

F⁻ ↔ OH⁻ (e.g., Fluorapatite to Hydroxylapatite).

Coupled Substitution

Two or more ions swap simultaneously to maintain overall charge balance when substituting ions of different valence states (e.g., Plagioclase feldspars: Na⁺ + Si⁴⁺ ↔ Ca²⁺ + Al³⁺).

Interstitial Solid Solution

Small ions fit into structural voids or channels without displacing existing framework atoms (e.g., Na⁺ or K⁺ fitting into ring channels of beryl).

Omission Solid Solution

A higher-charge cation replaces two or more lower-charge cations, leaving structural site vacancies to preserve neutrality (e.g., Pyrrhotite, Fe₁₋ₓS).

Polymorphism

Minerals with identical chemical compositions but different crystal structures.

Displacive Polymorphic Transformation

Structural adjustment involves slight bending or distortion of bonds without breaking them. Rapid, fully reversible, and requires low activation energy (e.g., α-quartz ↔ β-quartz).

Reconstructive Polymorphic Transformation

Requires breaking structural bonds and reassembling the crystal lattice. Slow, non-reversible without high thermal energy, often preserving metastable phases (e.g., Quartz → Coesite → Stishovite; Calcite ↔ Aragonite).

Isostructuralism

Isostructural (or isomorphous) minerals share the exact same crystal structure type and symmetry but possess completely different chemical compositions (e.g., Halite NaCl and Galena PbS, or the Calcite group minerals).

Surface Free Energy (γ)

Atoms at a crystal surface have unsatisfied bonds (higher potential energy). Growth naturally minimizes total surface free energy, favoring smooth, low-index faces with lower energy density.

Growth Kinetics

High supersaturation leads to rapid growth and dendritic or skeletal forms; low supersaturation promotes slow, equilibrium growth producing euhedral faces.

Schottky Defect

A vacancy pair where an equal number of cations and anions are missing from the lattice, maintaining charge neutrality.

Frenkel Defect

An ion leaves its normal lattice site and occupies a nearby interstitial vacancy, leaving a vacancy behind.

Interstitial Defect

An extra atom/ion squeezes into a site not normally occupied in the ideal crystal structure.

Substitutional Defect

A foreign ion occupies a standard lattice site in place of the primary ion.

Twinning

A symmetrical intergrowth of two or more separate crystals of the same species along a shared structural plane or axis.

Contact Twins

Two crystal segments joined across a single, well-defined planar boundary (composition plane), often appearing as mirror images (e.g., Gypsum 'swallow-tail' twins).

Penetration Twins

Two or more individual crystals intergrow and pass through each other, sharing a central volume (e.g., Staurolite cross, Orthoclase 'Carlsbad' twins).

Ternary diagrams

Graphical representation that maps compositional variations using normalized molar or weight percentages.

Mineral Stability Diagrams (P-T and T-X)

P-T Diagrams: Pressure-Temperature diagrams show boundary lines (phase boundaries) where reactions occur (ΔG = 0).

T-X Diagrams

Temperature-Composition diagrams show phase relationships across chemical mixing series at fixed pressure, illustrating solidus and liquidus curves, eutectic points, and peritectic reactions.

Nature of Light

Light behaves both as a wave and a stream of particles (photons).

Transverse Electromagnetic Wave

Light is modeled as a transverse electromagnetic wave with mutually perpendicular electric ($\vec{E}$) and magnetic ($\vec{B}$) vectors.

Unpolarized Light

Electric field vectors vibrate in all random directions perpendicular to the propagation axis.

Plane-Polarized Light (PPL)

Electric field vector vibrates within a single plane containing the line of propagation.

Reflection

Angle of incidence equals angle of reflection ($\theta_i = \theta_r$).

Refraction

Bending of light as it passes from one medium to another due to a change in propagation speed.

Snell's Law

Relates angles of incidence ($\theta_1$) and refraction ($\theta_2$) to refractive indices ($n_1, n_2$): $n_1 \sin\theta_1 = n_2 \sin\theta_2 \quad \text{where } n = \frac{c}{v}$.

Dispersion

The variation of refractive index with the wavelength of light ($\lambda$).

Isotropic Materials

Light travels at equal speeds in all crystallographic directions; refractive index ($n$) is identical everywhere.

Anisotropic Materials

Light velocity and refractive index vary with crystallographic orientation.

Double Refraction (Birefringence)

When unpolarized light enters an anisotropic mineral, it splits into two mutually perpendicular plane-polarized rays traveling at different velocities.

Ordinary Ray ($o$-ray)

Obeys Snell's Law; velocity is constant regardless of direction.

Extraordinary Ray ($e$-ray)

Disobeys Snell's Law; velocity changes depending on propagation direction.

Retardation ($\Delta$)

Distance by which the slower ray lags behind the faster ray upon exiting the crystal: $\Delta = t \times (n_{slow} - n_{fast})$.

Interference Color

Under Crossed Polarized Light (XPL), recombined rays interfere constructively or destructively depending on $\Delta$.

Birefringence ($\delta$)

Absolute numerical difference between the maximum and minimum refractive indices ($\delta = n_{max} - n_{min}$).

Michel-Lévy Chart

Used to determine thickness and birefringence by identifying the highest-order interference color.

Parallel Extinction

Cleavage line or crystal elongation extinguishes parallel to the crosshairs ($0^\circ / 90^\circ$).

Inclined Extinction

Mineral extinguishes at an angle relative to cleavage or crystal faces.

Symmetrical Extinction

Cleavage or face intersections bisect the extinction angles evenly.

Undulatory Extinction

Wavy, irregular extinction patterns sweeping across a crystal during rotation due to internal lattice strain.

Optical Indicatrix

A 3D geometric construct (ellipsoid) where radius vectors represent refractive index magnitudes.

Interference Figures

Formed under XPL using high power with a Bertrand lens inserted and conoscopic illumination.

Melatopes

Points where optic axes emerge through the field of view; dark spots around which isochromes form.

Isogyres

Dark bands forming brushes or crosses across the field of view representing extinction directions.