guide to thin section microscopy - Mineralogical Society of America

Guide to Thin Section Microscopy
Optical properties: basic principles
Crystals of orthorhombic, monoclinic and triclinic symmetry
The propagation of both waves in crystals of such symmetry is direction-dependent. The
resulting 3D two-surface models of ray velocities are complicated and have not had any
impact on practical work. Microscopists prefer the single-surface indicatrix model for the
explanation of optical phenomena (Fig. 4-7).
Figure 4-7. Optically biaxial crystals, crystal symmetry and indicatrix
The indicatrix of crystals with orthorhombic, monoclinic and triclinic symmetry is respresented
in a coordinate system with axes X, Y, Z that are orthogonal to each other. The geometry
of the triaxial ellipsoid is defined by the proportional lengths of the refractive indices n x , n y ,
n z on X, Y and Z. Thus, the symmetry of the ellipsoid is generally orthorhombic. The
refractive indices are defined as n z > n y > n x (or n γ > n β > n α ).
There are two circular sections with the radius n y . Orthogonal to these circular sections, light
propagates with the same velocity as in an isotropic substance. These two directions correspond
to the two optic axes A. The low-symmetry crystals are therefore optically anisotropicbiaxial.
Raith, Raase & Reinhardt – February 2012
The optic axes lie in the ZX plane (= optic axial plane OAP). Y is orthogonal to the OAP. The
angle between the optic axes (2V) is mineral-specific and can attain values between 0˚ and
90˚. If Z dissects the acute angle (2V z < 90˚), the crystal is biaxial-positive; if X dissects the
acute angle (2V x < 90˚), the crystal is biaxial-negative. If the axial angle is 90˚, the crystal is
optically neutral.
The spatial orientation of the indicatrix in a crystal is defined by the crystal's symmetry:
• In crystals of orthorhombic symmetry, the ellipsoid axes (X, Y, Z) correspond to the
crystallographic axes (a,b,c). Which indicatrix axis is parallel to which crystallographic
axis depends on the specific mineral.
• In crystals of monoclinic symmetry, it is only the crystallographic b axis and one of the
indicatrix axes that are parallel (commonly Y). The other two axes lie in the symmetry
plane (010) and form angles with the crystallographic axes a and c.
• In triclinic crystals, none of the axes of the orthorhombic indicatrix is parallel to any of the
crystallographic axes. The indicatrix axes form mineral-specific angles with the crystallographic
axes.
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