Advanced Crystallography
Twinning, Miller indices, crystal habits, crystal forms, point groups, and crystal growth mechanisms.
Introduction
Advanced crystallography extends the seven-systems framework to explain how crystals actually grow, what forms they develop, and why they twin. This knowledge directly supports the identification of inclusions, growth features, and crystal morphology in gem testing. Miller indices describe every crystal face and cleavage plane; four-index (Bravais–Miller) notation is required for trigonal and hexagonal systems where three equivalent horizontal axes meet at 120°, with the closure relation i = −(h+k) ensuring symmetry equivalence is explicit. Twinning (the intergrowth of two or more orientations sharing lattice points) produces diagnostic habits: chrysoberyl trillings form the pseudohexagonal star shape characteristic of the species, while polysynthetic twinning in labradorite causes labradorescence. Growth features such as curved striae, chevron zoning, and phantom crystals distinguish natural from synthetic gems under microscopy. The FGA Diploma requires the ability to draw common habits and identify twin laws by name; these visual skills are examined in both the written and practical papers. [1]
Miller Indices
Miller indices describe the orientation of crystal faces relative to crystallographic axes. They are fundamental to describing crystal forms and understanding morphology.
Three-Index Notation {hkl}
For cubic, tetragonal, orthorhombic, monoclinic, and triclinic systems:
- Determine where face intercepts each axis (a, b, c)
- Take reciprocals of these intercepts
- Clear fractions to get smallest integers
- Enclose in braces {hkl} for a form (set of symmetrically equivalent faces)
- Use parentheses (hkl) for a single specific face
Example: Face intercepts a at 1, b at 2, c at ∞
- Reciprocals: 1/1, 1/2, 1/∞ = 1, 0.5, 0
- Clear fractions: multiply by 2 → 2, 1, 0
- Miller index: (210)
Four-Index Notation {hkil}
For hexagonal and trigonal systems, four-index (Miller-Bravais) notation uses three horizontal axes (a₁, a₂, a₃) at 120° plus vertical c-axis:
- h + k + i = 0 (always; i is redundant but clarifies symmetry) [2]
- Negative indices shown with bar: 1̄ or written as -1
Example: {10-10} = {101̄0} = hexagonal prism faces
Common hexagonal/trigonal forms:
- {0001} - Basal pinacoid (top and bottom)
- {10-10} - Hexagonal prism
- {10-11} - Hexagonal dipyramid
- {11-20} - Second-order prism
Crystal Forms
A crystal form is a set of faces that are equivalent by symmetry. Forms can be open (don't enclose space alone) or closed (can exist independently).
Open vs Closed Forms
Open Forms
- Cannot exist alone
- Must combine with other forms
- Examples: prisms, pinacoids
- Require top/bottom faces
Closed Forms
- Can exist independently
- Enclose space completely
- Examples: cube, octahedron
- All faces equivalent
Form Combinations
Real crystals typically show multiple forms in combination:
- Dominant form: Largest faces, determines overall shape
- Modifying forms: Smaller faces, truncate edges/corners
- CDL notation:
{111}@1.0 + {100}@1.3describes relative development
Example: Diamond often shows {111} octahedron with {100} cube faces truncating corners.
Twinning
Twinning occurs when two or more crystals share some lattice points but have different orientations. Twins can form during growth, transformation, or mechanical stress. [1]
Types of Twins
| Type | Description | Examples |
|---|---|---|
| Contact twins | Share a plane; mirror reflection | Spinel twin, quartz Brazil twin |
| Penetration twins | Interpenetrate; share a line/point | Fluorite, staurolite cross |
| Polysynthetic (lamellar) | Multiple parallel thin twins | Plagioclase, labradorite |
| Cyclic twins | Three or more parts around axis | Chrysoberyl trillings, rutile |
Twin Laws
A twin law describes the geometric relationship between twin parts:
- Twin plane: Mirror plane relating the parts
- Twin axis: Rotation axis (typically 180°)
- Contact vs penetration: Whether parts share plane or interpenetrate
Common twin laws include spinel law {111}, Brazil law in quartz, and Carlsbad law in orthoclase.
Important Twins in Gemmology
| Mineral | Twin Type | Appearance | Significance |
|---|---|---|---|
| Spinel | Contact octahedral | Flattened triangular plates | Characteristic habit |
| Chrysoberyl | Cyclic (trillings) | Six-rayed star shape | Common; pseudohexagonal |
| Quartz | Brazil law | Alternating right/left zones | Optical effects |
| Quartz | Dauphiné law | No visible twin plane | Detected by etch figures |
| Rutile | Cyclic (geniculae) | Knee-shaped twins | Common at 60° or 90° |
| Fluorite | Penetration | Interpenetrating cubes | Characteristic |
| Staurolite | Cross penetration | 60° or 90° crosses | Fairy crosses |
| Feldspar | Polysynthetic | Parallel striations | Twinning lamellae |
Twinning Effects
Crystal Habits
Crystal habit describes the overall shape a mineral typically assumes. The same mineral can show different habits depending on growth conditions.
Common Habit Terms
| Term | Description | Examples |
|---|---|---|
| Prismatic | Elongated parallel to c-axis | Tourmaline, beryl |
| Tabular | Flat, plate-like | Mica, topaz |
| Equant | Roughly equal dimensions | Garnet, diamond |
| Acicular | Needle-like | Rutile, actinolite |
| Bladed | Flat, elongated like knife blade | Kyanite |
| Fibrous | Thread-like aggregates | Asbestos, tiger's eye |
| Massive | No visible crystal faces | Jadeite, nephrite |
| Botryoidal | Grape-like rounded masses | Malachite, chalcedony |
Habit Variations
The same mineral may show different habits due to:
- Growth rate: Fast growth → elongated; slow growth → equant
- Temperature: Higher temperatures often favour specific faces
- Impurities: Can block growth on certain faces
- Available space: Constrained environments modify shape
- Supersaturation: Affects relative face development
Species-Specific Habits
Typical Crystal Shapes
- Diamond: octahedron, dodecahedron
- Corundum: barrel-shaped, tabular hexagonal
- Beryl: hexagonal prism with flat termination
- Quartz: hexagonal prism with pyramid
- Tourmaline: triangular prism
- Topaz: orthorhombic prism with dome
- Spinel: octahedron (often twinned)
- Garnet: dodecahedron or trapezohedron
Atypical Habits
- Diamond: cube (rare), flat triangular macles
- Corundum: bipyramidal, prismatic
- Beryl: etched, tapered
- Quartz: sceptre, skeletal, Japan twin
- Tourmaline: slender prismatic, massive
- Spinel: cube (rare)
- Garnet: massive, granular
The 32 Point Groups
Point groups (crystal classes) describe the symmetry elements present at a point. Each crystal system contains multiple point groups.
Point Group Notation
Hermann-Mauguin notation describes symmetry elements:
- Numbers (2, 3, 4, 6): Rotation axes (fold symmetry)
- m: Mirror plane
- Bar notation (-1, -3, -4, -6): Rotoinversion axes
- Combination (4/m): Axis perpendicular to mirror
Crystal Growth
Understanding crystal growth explains many inclusion patterns, zoning features, and quality characteristics observed in gems.
Growth Mechanisms
Crystals grow by atoms/molecules attaching to energetically favourable sites:
- Layer growth: Atoms add to stepped surfaces
- Screw dislocation growth: Spiral growth patterns
- Dendritic growth: Fast growth → branching patterns
- Skeletal growth: Edges grow faster than faces
Growth Features
| Feature | Cause | Example |
|---|---|---|
| Colour zoning | Changing conditions during growth | Sapphire, tourmaline |
| Phantom crystals | Growth interruption and resumption | Quartz phantoms |
| Growth tubes | Inclusions elongated by growth | Tourmaline, beryl |
| Negative crystals | Fluid-filled voids with crystal shape | Spinel, quartz |
| Hourglass zoning | Different impurity uptake on faces | Synthetic corundum |
| Striae | Subtle parallel growth lines | Tourmaline, beryl |
Natural vs Synthetic Growth
Growth features help distinguish natural from synthetic gems:
- Natural: Irregular zoning, varied inclusion suites, geological timeframe
- Flame fusion: Curved striae from rotating growth
- Flux growth: Flux inclusions, metallic platelets
- Hydrothermal: Chevron zoning, seed plates
Crystal Drawing
CDL Crystal Examples
The Crystal Description Language (CDL) provides a notation for describing crystal morphology. These examples show common gem crystal shapes.
Cubic Examples
Diamond octahedron with cube truncations:
cubic[m3m]:{111}@1.0+{100}@1.3 Trigonal Examples
Quartz prism with rhombohedral terminations:
trigonal[32]:{10-10}@1.0+{10-11}@0.8 Hexagonal Examples
Beryl (emerald) hexagonal prism with pinacoid:
hexagonal[6/mmm]:{10-10}@1.0+{0001}@0.5 References
- ↑ 1. Read, P. (2014). Gemmology (3rd ed.). Routledge. DOI: 10.4324/9780080507224.
- ↑ 2. Schwarzenbach, D. (2003). Note on Bravais–Miller indices. Journal of Applied Crystallography, 36(3). DOI: 10.1107/s0021889803014778.
- ↑ 3. Nassau, K. (2001). The Physics and Chemistry of Color: The Fifteen Mechanisms (2nd ed.). Wiley-Interscience. ISBN: 978-0-471-39106-7.