Crystallography & Mineralogy

Hardness of a mineral is its resistance to scratching (abrasion). It depends on the strength of the chemical bonds and the atomic structure of the mineral.

Moh's scale

In 1812 Friedrich Mohs proposed a relative scale of ten standard minerals, in which each mineral scratches those below it.

Field aids

• Fingernail: about 2.5
• Copper coin: about 3.5
• Knife blade / glass: about 5.5
• Steel file: about 6.5

Notes

• It is a relative, ordinal scale: the gap between 9 and 10 is much larger than between 1 and 2.
• To test an unknown mineral, find which standard mineral or object scratches it and which it scratches; its hardness lies between them.
• Test a fresh surface and not a weathered or powdery one.

Symmetry in a crystal is the repetition of faces, edges and angles when the crystal is rotated or reflected. The imaginary features about which this repetition occurs are the elements of symmetry.

1. Plane of symmetry

An imaginary plane that divides a crystal into two equal halves, each the mirror image of the other.

• Axial (principal) plane: passes through two crystallographic axes.
• Diagonal plane: passes through one axis and bisects the angle between two others.
• A cube has 9 planes (3 axial, 6 diagonal).

2. Axis of symmetry

An imaginary line through the centre about which the crystal, when rotated through 360°, shows the same appearance more than once.

A cube has 3 tetrad, 4 triad and 6 diad axes, total 13 axes.

3. Centre of symmetry

A point at the centre of the crystal such that any line through it meets identical faces, edges or corners at equal distances on opposite sides. A cube has 1 centre.

  Cube (isometric): 9 P + 13 A + 1 C = 23 elements
   P = planes, A = axes, C = centre

The symmetry of a crystal decides which of the 7 crystal systems it belongs to.

The physical properties of minerals depend on chemical composition and crystal structure, and are used to identify minerals in hand specimens.

1. Colour

Appearance in reflected light. Idiochromatic minerals have constant colour (malachite green); allochromatic minerals vary because of impurities (quartz can be white, pink, purple). Colour is not always reliable.

2. Streak

Colour of the powder of a mineral, seen on an unglazed porcelain plate. It is more constant than colour: hematite is red-brown streak although it may be black.

3. Lustre

Appearance of a fresh surface in reflected light.

• Metallic (galena, pyrite).
• Non-metallic: vitreous (quartz), pearly (talc), silky (asbestos), resinous, greasy, earthy (kaolin), adamantine (diamond).

4. Transparency

Transparent, translucent or opaque.

5. Hardness

Resistance to scratching, measured on Moh's scale 1 to 10.

6. Cleavage

Tendency to split along smooth planes of weak bonding. Described as perfect (mica, one direction), good (feldspar, two directions), poor or absent. Calcite has three directions, not at right angles.

7. Fracture

Irregular breaking where there is no cleavage: conchoidal (quartz), uneven, splintery, hackly.

8. Tenacity

Behaviour under stress: brittle, malleable, sectile, flexible, elastic.

9. Specific gravity

Ratio of the mineral's density to that of water (quartz 2.65, galena 7.5).

10. Form / habit

Crystal shape: prismatic, tabular, fibrous, granular, massive.

11. Other properties

Magnetism (magnetite), taste (halite), effervescence with dilute HCl (calcite), feel (talc greasy), and fluorescence.

The isometric (cubic) system is the most symmetrical crystal system. It has three crystallographic axes of equal length, mutually perpendicular (all at 90°).

        c
        |   b
        |  /
        | /
        |/____ a
   a = b = c, all at 90 deg

Symmetry elements (of the normal class, hexoctahedral)

• Planes of symmetry: 9 (3 axial planes + 6 diagonal planes).
• Axes of symmetry: 13
  • 3 tetrad (4-fold) axes through the centres of opposite faces,
  • 4 triad (3-fold) axes through opposite corners,
  • 6 diad (2-fold) axes through the mid-points of opposite edges.
• Centre of symmetry: 1.
• Total: 23 elements.

Common forms and minerals

• Cube, octahedron, dodecahedron.
• Minerals: galena, pyrite, fluorite, halite (rock salt), garnet, diamond, magnetite.

A crystal is a homogeneous solid body of a chemical element or compound whose atoms, ions or molecules are arranged in a regular, repeating three-dimensional pattern (space lattice), and which is bounded by natural, smooth plane faces that follow geometric rules. Examples: quartz, calcite, halite (common salt).

Features:

• Definite internal atomic arrangement.
• Flat faces meeting at fixed angles (law of constancy of interfacial angles).
• Definite symmetry and a definite chemical composition.

A mineral is a naturally occurring, inorganic, homogeneous solid with a definite chemical composition (or a narrow range) and a regular internal atomic structure, usually formed by geological processes. Example: quartz (SiO₂), calcite (CaCO₃).

Rock-forming minerals are the few mineral groups that make up most of the rocks of the Earth's crust, about 20-30 in number. The main ones are:

• Silicates: quartz, feldspars, micas, amphiboles, pyroxenes, olivine.
• Carbonates: calcite, dolomite.
• Others: clay minerals, gypsum, oxides.

Silicates alone make up about 90% of the crust.

Crystals are classified into seven systems by the length and mutual inclination of their three (or four) crystallographic axes a, b, c.

Sketches of axes

 Isometric        Tetragonal       Orthorhombic
  c                c                 c
  |__b             |__b              |__b
 /a=b=c           /a=b<>c           /a<>b<>c
 all 90           all 90            all 90

 Monoclinic       Triclinic         Hexagonal
  c                c                  c
  |  /b            |  /b              | a2
 /|/               | /                 |/__a1
 a  beta<>90       a  none 90        a3 (120 deg)

Some books group the trigonal system under hexagonal, giving six systems.

The properties of rock-forming minerals decide the strength, durability and behaviour of rocks used in foundations, tunnels and construction materials.

• Quartz (SiO₂): very hard (7), chemically stable, no cleavage. Rocks rich in quartz (granite, quartzite, sandstone) are strong, durable and resistant to weathering, so good for aggregate, foundations and building stone. Its abrasive nature wears drilling tools and crushers. Reactive (amorphous) silica can cause alkali-aggregate reaction in concrete.
• Calcite (CaCO₃): soft (3), perfect cleavage, dissolves in acidic water. Limestone and marble make cement, lime and building stone. Solution cavities in limestone cause reservoir leakage and foundation settlement, a risk for dams.
• Feldspar: hardness 6, two cleavages; weathers to clay minerals, so feldspar-rich rocks lose strength with weathering. Clay formed is weak, swells and is slippery, and cause of slope failure.
• Mica: very perfect cleavage, soft, flaky. Rocks rich in mica (schist, phyllite) split easily, are weak along foliation, and cause slope and tunnel instability. Mica in aggregate reduces concrete strength.

Minerals in hand specimen are identified by their physical properties, many of which relate to the way they interact with light (optical properties).

Physical properties

• Colour: general appearance; may vary with impurities (quartz).
• Streak: colour of powder on unglazed porcelain; more constant than colour.
• Hardness: resistance to scratching on Moh's scale (1 to 10).
• Cleavage: splitting along smooth planes (mica one, feldspar two, calcite three directions).
• Fracture: irregular breakage without cleavage (conchoidal in quartz).
• Tenacity: brittle, malleable, flexible, elastic.
• Specific gravity: relative density (quartz 2.65, galena 7.5), tested by heft.
• Habit/form: shape of crystal aggregates (prismatic, fibrous, granular).
• Others: magnetism, taste, feel, effervescence with HCl.

Optical properties

• Lustre: metallic (galena), vitreous (quartz), pearly (talc), silky (asbestos), resinous, greasy, earthy, adamantine.
• Transparency: transparent (clear quartz), translucent (milky quartz), opaque (pyrite).
• Colour and play of colour: opalescence, iridescence, asterism.
• Refraction and double refraction: calcite shows two images of an object seen through it.
• Fluorescence and phosphorescence: glow under ultraviolet light (fluorite).
• Pleochroism: change of colour with viewing direction (seen under the microscope).

Silicate and carbonate minerals can be distinguished in the field by a few simple tests.

The fastest field test is the acid test with a drop of dilute HCl, together with a knife scratch.

Feldspar group

The most abundant minerals of the crust (about 50-60%). They are aluminosilicates of potassium, sodium and calcium.

• Types: potassium feldspars (orthoclase, microcline) and plagioclase (albite to anorthite, a series of sodium-calcium feldspars).
• Crystal system: monoclinic (orthoclase), triclinic (microcline, plagioclase).
• Hardness: 6. Specific gravity: 2.55-2.76.
• Cleavage: two good cleavages at about 90° (or near 86° in plagioclase); plagioclase shows fine striations.
• Colour: white, pink, cream or grey; vitreous to pearly lustre; white streak.
• Occurrence: granite, gneiss, syenite, basalt.
• Engineering: durable when fresh, but weathers to clay, lowering rock strength.

Mica group

Sheet silicates with very perfect cleavage in one direction, splitting into thin, flexible, elastic sheets.

• Types: muscovite (white mica, light) and biotite (black mica, iron-magnesium rich).
• Crystal system: monoclinic.
• Hardness: 2-3. Specific gravity: 2.7-3.1.
• Lustre: pearly to vitreous; colourless to brown or black.
• Occurrence: granite, schist, gneiss, phyllite, sandstone.
• Engineering: mica-rich rocks split easily along planes, are weak and slippery, so unsuitable as foundation, aggregate or for stable slopes.

These two terms belong to different fields: structural geology and mineralogy.

The strike of a bed is always at 90° to its true dip direction. Streak is more reliable than the colour of a mineral because it stays constant.

Orthorhombic system

The orthorhombic system has three crystallographic axes, mutually perpendicular but all of different lengths.

        c
        |
        |_____ b
       /
      a        a, b, c unequal, all 90 deg

Symmetry of the normal class: 3 planes of symmetry (parallel to the axes), 3 diad axes (along a, b, c) and 1 centre of symmetry. The crystals are prisms with rectangular or rhombic cross-section. Minerals: topaz, barite, olivine, sulphur, aragonite.

Three monoclinic minerals

The monoclinic system has $a \ne b \ne c$, with $\alpha = \gamma = 90^\circ$ and $\beta \ne 90^\circ$. Examples:

1. Gypsum
2. Orthoclase feldspar
3. Mica (muscovite or biotite). Hornblende and augite are also monoclinic.

Orthorhombic system

The orthorhombic system has three crystallographic axes at right angles to each other, all of different lengths.

        c
        |
        |_____ b
       /
      a        a, b, c unequal, all 90 deg

Symmetry of the normal class: 3 planes of symmetry, 3 diad axes and 1 centre of symmetry (7 elements). Typical forms are rhombic prisms and pyramids. Minerals: topaz, barite, olivine, sulphur, aragonite.

Three isometric minerals

The isometric (cubic) system has $a = b = c$, all axes at 90°. Examples:

1. Galena (PbS)
2. Pyrite (FeS₂)
3. Halite (NaCl); fluorite, garnet, magnetite and diamond are also isometric.

Axis of symmetry

An axis of symmetry is an imaginary straight line through the centre of a crystal about which, when the crystal is rotated through 360°, the same appearance is repeated two, three, four or six times.

 Diad   (2-fold): 180 deg, repeats 2 times
 Triad  (3-fold): 120 deg, repeats 3 times
 Tetrad (4-fold):  90 deg, repeats 4 times
 Hexad  (6-fold):  60 deg, repeats 6 times

   Cube:   tetrad axis through face centres
           |
        +--|--+
        |  |  |
        +--|--+

Isometric (cubic) system

• Three crystallographic axes of equal length, all at 90°: $a = b = c$, $\alpha = \beta = \gamma = 90^\circ$.
• Most symmetrical system; normal class has 9 planes, 13 axes (3 tetrad, 4 triad, 6 diad) and 1 centre of symmetry.
• Forms: cube, octahedron, dodecahedron.
• Minerals: galena, pyrite, fluorite, halite, garnet, diamond.

Elements of symmetry

Symmetry is the repetition of faces and edges in a crystal. There are three elements.

1. Plane of symmetry: a plane dividing the crystal into two mirror-image halves. Axial planes pass through two axes; diagonal planes pass through one axis and bisect the angle between the other two.
2. Axis of symmetry: a line about which rotation by 360° repeats the form 2 (diad, 180°), 3 (triad, 120°), 4 (tetrad, 90°) or 6 (hexad, 60°) times.
3. Centre of symmetry: a point at which any line through it meets similar faces at equal distance on both sides.

A cube has 9 planes, 13 axes and 1 centre.

Crystal systems

 Isometric     Tetragonal    Orthorhombic   Monoclinic
   c             c              c              c  /
   |_b           |_b            |_b            |_/b
  /a=b=c        /a=b<>c       /a<>b<>c        /a   beta<>90

Engineering significance of rock-forming minerals

• Quartz: hard, stable, no cleavage; gives strong, durable rocks; may react with cement alkalis if amorphous.
• Feldspar: common, hardness 6, but weathers to clay and weakens rock.
• Mica: perfect cleavage; mica-rich rocks (schist, phyllite) are weak and cause slope and tunnel failures.
• Calcite: soft and soluble; limestone makes cement but has cavities that cause leakage.
• Amphibole/pyroxene/olivine: dense and strong, good in dark rocks like basalt, but weather faster.

Physical properties of minerals

• Colour and streak (colour of powder).
• Lustre: metallic or non-metallic (vitreous, pearly, silky, earthy).
• Hardness: Moh's scale 1-10.
• Cleavage and fracture.
• Tenacity: brittle, malleable, elastic.
• Specific gravity.
• Transparency and crystal habit.
• Special: magnetism, taste, effervescence in HCl.

Symmetry elements of the orthorhombic system

Axes: $a \ne b \ne c$, all at 90°. The normal class has:

• 3 planes of symmetry (each parallel to a pair of axes).
• 3 diad axes (along the a, b and c axes).
• 1 centre of symmetry. Total of 7 elements.

Tenacity is the resistance of a mineral to breaking, bending, cutting or crushing, that is, how it behaves when force is applied. Types:

• Brittle: breaks or powders (quartz, calcite).
• Malleable: can be hammered into sheets (gold, copper).
• Sectile: can be cut with a knife into shavings (gypsum, talc).
• Flexible: bends and stays bent (talc, chlorite).
• Elastic: bends and returns to shape (mica).

Hardness is the resistance of a mineral to scratching or abrasion. It is measured relatively on Moh's scale of ten minerals: talc (1), gypsum (2), calcite (3), fluorite (4), apatite (5), orthoclase (6), quartz (7), topaz (8), corundum (9) and diamond (10).

Minerals are classified in several ways.

1. Based on abundance and role in rocks

• Rock-forming minerals: abundant, form the bulk of rocks (quartz, feldspar, mica, amphibole, pyroxene, olivine, calcite).
• Accessory minerals: occur in small amounts (zircon, apatite, magnetite).
• Ore minerals: contain metals of economic value (galena, hematite, chalcopyrite).

2. Chemical classification (most common)

• Native elements (gold, graphite), sulphides (pyrite), oxides (hematite), halides (halite), carbonates (calcite), sulphates (gypsum), phosphates (apatite) and silicates (the largest group, about 90% of the crust).

3. Colour-based

• Felsic (light-coloured: quartz, feldspar) and mafic (dark: pyroxene, olivine, biotite).

1. Strong chemical structure: quartz is made of SiO₂ in a three-dimensional framework of strong Si-O covalent bonds, giving high hardness (7) and chemical stability; it hardly reacts with water or weak acids.
2. No cleavage: quartz breaks with a conchoidal fracture, with no planes of weakness along which weathering and disintegration can start. Hence it remains as sand grains when other minerals weather to clay.

A hard mineral does not always mean a strong rock; a quartz-rich but weakly cemented sandstone has low strength.