Overview of the crystal systems and their optical properties

Structure	Structure type Crystal axes Angles	Symmetry (of highest crystal class)	Optic character	Refractive index (RI)	Optic sign	Pleochroism	Gem examples
Amorphous	No order No axes	No symmetry	Isotropic Singly refractive	1 RI n	None	None	Glass Amber
Cubic	Isometric: 1 axis length a₁ = a₂ = a₃All at 90°	13 planes 9 axes Center	Isotropic Singly refractive	1 RI n	None	None	Diamond Spinel Garnet
Tetragonal	Dimetric: 2 axis lengths a₁ = a₂ ≠ c All at 90°	5 planes 5 axes Center	Anisotropic Doubly refractive Uniaxial	2 RIs n_ω and n_ε	+ = n_ε > n_ω – = n_ε < n_ω	May be dichroic	Zircon
Hexagonal	Dimetric: 2 axis lengths a₁ = a₂ = a₃ ≠ c a axes at 60°; c axis at 90° to their plane	7 planes 7 axes Center	Anisotropic Doubly refractive Uniaxial	2 RIs n_ω and n_ε	+ = n_ε > n_ω – = n_ε < n_ω	May be dichroic	Beryl Apatite
Trigonal	Dimetric: 2 axis lengths a₁ = a₂ = a₃ ≠ c a axes at 60°; c axis at 90° to their plane	3 planes 4 axes Center	Anisotropic Doubly refractive Uniaxial	2 RIs n_ω and n_ε	+ = n_ε > n_ω – = n_ε < n_ω	May be dichroic	Corundum Quartz Tourmaline
Orthorhombic	Trimetric: 3 axis lengths a ≠ b ≠ c All at 90°	3 planes 3 axes Center	Anisotropic Doubly refractive Biaxial	3 RIs n_α, n_β, n_γ	+ = n_β closer to n_α – = n_β closer to n_γ ± = n_β midway to n_α & n_γ	May be trichroic	Topaz Zoisite Olivine (peridot)
Monoclinic	Trimetric: 3 axis lengths a ≠ b ≠ c 2 axes at 90°; 1 oblique	1 axis 1 plane Center	Anisotropic Doubly refractive Biaxial	3 RIs n_α, n_β, n_γ	+ = n_β closer to n_α – = n_β closer to n_γ± = n_β midway to n_α & n_γ	May be trichroic	Orthoclase Spodumene
Triclinic	Trimetric: 3 axis lengths a ≠ b ≠ c all axes oblique	No planes No axes Center	Anisotropic Doubly refractive Biaxial	3 RIs n_α, n_β, n_γ	+ = n_β closer to n_α – = n_β closer to n_γ± = n_β midway to n_α & n_γ	May be trichroic	Axinite Labradorite

Optic character/sign with the Refractometer

Optic character/curve variations: Uniaxial or biaxial

Two constant curves = Uniaxial
Two variable curves = Biaxial
One constant/one variable, which meet but do not cross = Uniaxial
One constant/one variable which don't meet
Check the polaroid angle of the constant curve
- Biaxial = polaroid angle of constant curve = 90°
- Uniaxial = polaroid angle of constant curve ≠ 90°

RI readings of corundum

RI readings for different faces on corundum. Corundum is uniaxial negative.
Illustration © Richard W. Hughes

Optic sign

Uniaxial stones

High RI curve varies = (+)
Low RI curve varies = (-)
Both curves constant: At 0° polaroid angle, only the o-ray is seen
- a. If low curve is seen = (+)
- b. If high curve is seen = (-)

Biaxial stones

If n_β is closer to n_α, the gem is (+)
If n_β is closer to n_γ, the gem is (-)
If n_β is halfway between n_α and n_γ, the gem is (±)
If two possible betas exist, false beta will have a polaroid angle equal to 90°. True beta will have a polaroid angle unequal to 90°.

Polaroid angle

0° polaroid angle is when the transmission direction of the polaroid plate is parallel to the refractometer scale divisions.
90° polaroid angle is when the transmission direction of the polaroid plate is perpendicular to the refractometer scale divisions.

Symbols

Uniaxial crystals

n_ω = omega, the constant RI of a uniaxial crystal
n_ε = epsilon, the variable RI of a uniaxial crystal

Biaxial crystals

n_α = alpha, the lowest RI of a biaxial crystal
n_β = beta, the intermediate RI of a biaxial crystal
n_γ = gamma, the highest RI of a biaxial crystal

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Page updated 11 March, 2010