Overview of the crystal systems and their optical properties

by Richard W. Hughes

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° c > b > a	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 c & b axes at 90°; a oblique to their plane	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 c > b > a	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 (neither curve crosses the midpoint), false beta will have a polaroid angle equal to 90°. True beta will have a polaroid angle unequal to 90°.

Finding beta

In biaxial stones, beta is the highest RI of the low curve or the lowest RI of the high curve, where the curve passes a point midway between n_α and n_γ.
In biaxial stones, beta is the point where the two curves meet or cross.
In biaxial stones, if one reading is constant and the other varies, beta is the extreme intermediate point of the variable curve.
If both curves vary and neither crosses the midpoint, 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

Author's Notes

The above technique for determining the optic character and sign with the refractometer comes from Dr. Cornelius Hurlbut:

Hurlbut, C.S. (1984) The jeweler's refractometer as a mineralogical tool. American Mineralogist, Vol. 69, pp. 391–398. <http://www.science.smith.edu/~jbrady/Papers/Hurlbut_AM69_391.pdf>

It was taught in the AIGS classrooms following the appearance of that article (1984 on). The technique has also been described as well by:

Sturman, Darko (2005) Use of the polarizing filter on the refractometer. Journal of Gemmology, Vol. 29, No. 5/6, pp. 341–348.
<http://www.nordskip.com/notes/sturman.pdf>

I have reversed the polaroid angles of Hurlbut as I find it easier to remember relative to the refractometer scale divisions.

This page is http://www.ruby-sapphire.com/crystal_optics.htm
Page updated 7 March, 2013

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