12 November 2019

[Optic] – An Introduction to Optical Crystallography

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Optical Cristallography - Codex International

The technique is particularly useful in petrology – the study of the composition and properties of rock – which studies the appearance of thin, transparent sections of rocks with a polarized light microscope. The use of this microscope restricts the light that passes through the mineral specimens to waves that vibrate in a single direction and enables chemists and mineralogists to identify substances based on how they refract or bend light.
Typical transparent media such as glass is isotropic: in this simple cubic crystal, the atomic arrangement is such that light behaves the same way no matter which way it travels through the medium.
Properties of Crystals
Crystals, however, are often naturally anisotropic, and their atoms are closer together in some planes more than others. This means their optical properties are different depending on which way the light travels through them. Anisotropy can be defined as a difference, when measured along different axes, in a material’s physical or mechanical properties.
Classical physics suggest the progress of an electromagnetic wave through a material involves the displacement of electrons. In anisotropic materials, the forces acting against this movement depend on the direction, and consequently, the velocity of light is different in different directions and different states of polarization.
In isotropic mediums, light from a point source spreads out in a spherical shell and thus possesses no principal axes to relate to the crystallographic axes. In anisotropic crystals, it spreads out in two wave surfaces, one of which travels at a faster rate than the other.
The way that light travels through minerals is entirely dependent on the crystalline structure of the minerals; they might be cubic, hexagonal, trigonal, tetragonal, or orthorhombic, where there are three unequal axes at right angles, monoclinic or triclinic.
Generally, in a transparent anisotropic medium, the dielectric constant – the ability of a substance to store electrical energy in an electric field – is different along each of the three orthogonal axes, thus the light vector is orientated along each direct, so the velocity of light is different and so there are different indices of refraction.
The index of refraction – which describes how fast the light travels through the medium – depends on both the composition and crystal structure. It is visualized as a bend in the light as it travels from one material to another. Anisotropic minerals might be uniaxial – relating to one axis – or biaxial, relating to two.
Classification of Crystals
Crystals can be classified according to how they transmit plane-polarized light; all crystals may be assigned to one of five groups, which correspond to the seven systems of crystallization (group 2 includes three different systems):
Optically isotropic crystals: these exhibit only one index of refraction for the light of each color.

Optically uniaxial crystals, which includes tetragonal, hexagonal and rhombohedral systems: these display double refraction and yield two refractive indices for the light of each color, one parallel to the optical axis and one perpendicular.

Optically biaxial crystals – all of which exhibit three principal refractive indices, one along each of the mutually perpendicular optical axis – in which three optical axes correspond to the three crystallographic axes. This is known as an orthorhombic system.

Optically biaxial crystals in which only one of the three optical axes correspond to a crystallographic axis – known as a monoclinic system.

Optically biaxial crystals with no fixed and definite relationship between the optical and crystallographic axes, a triclinic system.

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