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
a_{1} = a_{2} = a_{3
}All at
90° 
13
planes
9 axes
Center 
Isotropic
Singly
refractive 
1 RI
n 
None 
None 
Diamond
Spinel
Garnet 
Tetragonal 
Dimetric: 2 axis lengths
a_{1} = a_{2} ≠ 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
a_{1} = a_{2} = a_{3} ≠ 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
a_{1} = a_{2} = a_{3} ≠ 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 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 oray 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:
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.
This page is http://www.rubysapphire.com/crystal_optics.htm
Page updated
7 March, 2013
