The Orthorhombic System: Topaz, Peridot, Aragonite and Sulphur
In the orthorhombic system, the three axes are perpendicular but all of different lengths. Topaz, peridot, alexandrite, aragonite, barite and sulphur are examples.
Key points
| Axes | a ≠ b ≠ c (three different lengths) |
|---|---|
| Angles | α = β = γ = 90° |
| Characteristic symmetry | Three perpendicular two-fold axes (or two mirror planes) |
| Symmetry classes | 3 of 32 |
| Bravais lattices | 4 (primitive, base-centred, body-centred, face-centred) |
| Typical minerals | Topaz, peridot (olivine), chrysoberyl, aragonite, barite, celestine, sulphur, stibnite, iolite, tanzanite |
| Optics | Biaxial: two directions without double refraction, possible trichroism |
A brick with three different dimensions
The orthorhombic system is that of the shoebox: three axes perpendicular to one another, but all of different lengths. It is less symmetrical than the cubic, tetragonal or hexagonal systems, and it is very well represented among minerals, especially among sulphates, carbonates and silicates.
To get a numerical picture: barite has axes of about 8.88 Å, 5.46 Å and 7.16 Å; a forsterite-type peridot has axes of about 4.76 Å, 10.21 Å and 5.98 Å. None of these measurements equals another, and that is what defines the system.
Values to remember
| Quantity | Value |
|---|---|
| Axis lengths | a ≠ b ≠ c |
| Angles between axes | 90°, 90°, 90° |
| Minimum symmetry | Three perpendicular two-fold axes, or two mirror planes and one two-fold axis |
| Symmetry classes | 3 |
| Bravais lattices | 4: P, C (or A, B), I and F |
The lowest symmetry of the system is three two-fold axes (a half turn brings each one back onto itself). The section of an orthorhombic prism is a rectangle or a rhombus, never a square as in the tetragonal system.
Orthorhombic minerals to know
| Mineral | Simplified formula | Mohs hardness | Density | Distinctive feature |
|---|---|---|---|---|
| Topaz | Al2SiO4(F,OH)2 | 8 | 3.5 to 3.6 | Perfect cleavage in one direction |
| Chrysoberyl (alexandrite) | BeAl2O4 | 8.5 | about 3.7 | Colour change in different light |
| Peridot (olivine) | (Mg,Fe)2SiO4 | 6.5 to 7 | 3.2 to 3.4 | Olive green; found in meteorites |
| Iolite (cordierite) | magnesium aluminium silicate | 7 to 7.5 | about 2.6 | Very clear trichroism |
| Tanzanite (zoisite) | Ca2Al3(SiO4)3(OH) | 6.5 to 7 | about 3.35 | Blue-violet after heating |
| Aragonite | CaCO3 | 3.5 to 4 | about 2.95 | Polymorph of calcite, pseudo-hexagonal twins |
| Barite | BaSO4 | 3 to 3.5 | about 4.5 | Very dense for a colourless mineral |
| Celestine | SrSO4 | 3 to 3.5 | 3.95 to 3.97 | Pale blue; geodes from Madagascar |
| Native sulphur | S | 1.5 to 2.5 | about 2.07 | Yellow, very brittle |
| Stibnite | Sb2S3 | 2 | 4.6 to 4.7 | Grey needles; contains antimony |
To go further: topaz, peridot, iolite, tanzanite, aragonite and celestine.
Biaxial crystals and trichroism
An orthorhombic crystal is biaxial: there are two directions, called optic axes, along which double refraction disappears. In all other directions there are two rays. And since the three crystal axes have different lengths, the colour can change along three directions: this is trichroism. Iolite shows it very well, with a violet-blue in one direction, a pale blue in another and a pale yellow in the third. Rough tanzanite also shows several colours depending on orientation, which cutters exploit to obtain the fine blue. See colour and pleochroism.
Topaz, cleavage and fragility
Topaz is hard (8 on the Mohs scale) but has a perfect cleavage perpendicular to its elongation: a sharp knock or a thermal shock can split it cleanly. It is the classic example showing that hardness and resistance to impact are two distinct things. See cleavage and fracture. Also worth knowing: most blue topaz on the market is colourless topaz treated by irradiation and heating. This is a common, documented treatment, and it should be disclosed. See our commitments.
Aragonite and calcite: same formula, different structure
Aragonite and calcite have the same formula, CaCO3, but one is orthorhombic and the other trigonal. They are called polymorphs. Aragonite often forms threefold twins that imitate a hexagonal prism, and it transforms very slowly into calcite on geological timescales. The nacre of shells and pearls is largely made of tiny aragonite platelets bound together by an organic substance. See pearl and nacre.
Traps and precautions
- Desert roses. They are made of gypsum (monoclinic) or barite (orthorhombic), depending on the deposit. The two look alike, but gypsum can be scratched with a fingernail (hardness 2) and barite is markedly heavier.
- Native sulphur, stibnite, cerussite, powdered barite: sulphur is irritating, stibnite contains antimony, cerussite contains lead. Do not put them in your mouth, do not heat them, do not sand them, and wash your hands afterwards.
- Genuine or fake “peridot”: green glass is common. Peridot is strongly birefringent: under a loupe, the back edge of the facets appears doubled, which glass does not show. This is a clue, not proof.
Frequently asked questions
Why is it called orthorhombic?
Because the three axes are perpendicular to one another (“ortho” = straight), and the basic forms are rhombic prisms (with a rhombus as cross-section), with three different lengths.
Is peridot the same mineral as olivine?
Yes. Peridot is the gem variety of olivine, a mineral very common in the Earth’s mantle and in some meteorites.
Does topaz scratch easily?
No, it is hard (8). But it splits easily along its cleavage: avoid knocks and thermal shocks.
What is the difference between aragonite and calcite?
The same formula, CaCO3, but aragonite is orthorhombic, denser (about 2.95 against 2.71) and slightly harder (3.5 to 4 against 3).
Is native sulphur dangerous?
Not in a display case, but it is brittle, irritating to the skin and airways if powdered, and it burns, giving off an irritant gas. Never heat it.
Also read
The meanings mentioned belong to tradition and symbolism. They are neither promises of results nor medical advice. Back to Mineralogy for beginners.