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 = a3
All 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
nω and nε
+ = nε > nω

– = nε < nω

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
nω and nε

 

+ = nε > nω

– = nε < nω

 

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

nω and nε

+ = nε > nω

– = nε < nω

 

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

nα, nβ, nγ

+ = nβ closer to nα

– = nβ closer to nγ

± = nβ midway to nα & nγ
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

nα, nβ, nγ

+ = nβ closer to nα

– = nβ closer to nγ
± = nβ midway to nα & nγ

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

nα, nβ, nγ

+ = nβ closer to nα

– = nβ closer to nγ
± = nβ midway to nα & nγ

May be trichroic Axinite

Labradorite

Optic character/sign with the Refractometer

Optic character/curve variations: Uniaxial or biaxial

  1. Two constant curves = Uniaxial
  2. Two variable curves = Biaxial
  3. One constant/one variable, which meet but do not cross = Uniaxial
  4. One constant/one variable which don't meet
  5. 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

  1. High RI curve varies = (+)
  2. Low RI curve varies = (-)
  3. 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

  1. If nβ is closer to nα, the gem is (+)
  2. If nβ is closer to nγ, the gem is (-)
  3. If nβ is halfway between nα and nγ, the gem is (±)
  4. 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

  1. 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 nα and nγ.
  2. In biaxial stones, beta is the point where the two curves meet or cross.
  3. In biaxial stones, if one reading is constant and the other varies, beta is the extreme intermediate point of the variable curve.
  4. 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

  • nω = omega, the constant RI of a uniaxial crystal
  • nε = epsilon, the variable RI of a uniaxial crystal

Biaxial crystals

  • nα = alpha, the lowest RI of a biaxial crystal
  • nβ = beta, the intermediate RI of a biaxial crystal
  • nγ = 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:

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

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

 

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Page updated 7 March, 2013