Difference Between Uniaxial and Biaxial Crystals

The key difference between uniaxial and biaxial crystals is that uniaxial crystals have a single optic axis whereas biaxial crystals have two optic axes.

The optic axis of a crystal is the direction that the light propagates through the crystal without facing double refraction. All the light waves that are parallel to this axis do not undergo double refraction. In other words, the light beam passes in this direction with a speed that does not depend on the polarisation.

 

CONTENTS

1. Overview and Key Difference
2. What are Uniaxial Crystals
3. What are Biaxial Crystals
4. Side by Side Comparison – Uniaxial vs Biaxial Crystals in Tabular Form
5. Summary

What are Uniaxial Crystals?

A uniaxial crystal is an optical element that has a single optic axis. In other words, a uniaxial crystal has one crystal axis different from other two crystallographic axes. Ex: na=nb≠ nc. This unique axis is known as an extraordinary axis. When a light beam passes through a uniaxial crystal, that light beam splits into two fractions such as the ordinary ray and extraordinary ray. The ordinary ray (o-ray) passes through the crystal without any deviation. The extraordinary ray (e-ray) deviates at the air-crystal interface.

There are two forms of uniaxial crystals named as negative uniaxial crystal and positive uniaxial crystal. If the refraction index of o-ray (no) is larger than that of the e-ray (ne), then it is a negative uniaxial crystal. But if the refraction index of e-ray (ne) is smaller than that of the e-ray, then it is a positive uniaxial crystal.(Refractive index is the ratio of the velocity of light in a vacuum to its velocity in the crystal). Examples of negative uniaxial crystals include calcite (CaCO3), ruby (Al2O3), etc. Examples of positive uniaxial crystals include quartz (SiO2), sellaite (MgF2), rutile (TiO2), etc.

What are Biaxial Crystals?

A biaxial crystal is an optical element which has two optic axes. When a light beam passes through a biaxial crystal, the light beam splits into two fractions, being both fractions are extraordinary waves (two e-rays). These waves have different directions and different speeds. The crystalline structures such as orthorhombic, monoclinic, or triclinic are biaxial crystal systems.

The Refractive Indices for a Biaxial Crystal are as follows:

  1. The smallest refractive index is α (the corresponding direction is X)
  2. The intermediate refractive index is β (the corresponding direction is Y)
  3. The largest refractive index is γ (the corresponding direction is Z)

Figure 01: The Indicatrix of a Biaxial Crystal. (Indicatrix is an imaginary ellipsoidal surface whose axes represent the refractive indices of a crystal for light following different directions concerning the crystal axes)

However, these optical directions and refractive indices are different from the crystallographic axes on the nature of the crystal system.

  • Orthorhombic crystal system –optical directions correspond to crystallographic axes. Ex: X,Y or Z directions (α, β and γ refractive indices) may parallel to any of the crystallographic axes (a, b or c).
  • Monoclinic crystal system – one of the X, Y and Z directions (α, β and γ refractive indices) is parallel to the b crystallographic axis while other two direction is not parallel to any crystallographic direction.
  • Triclinic crystal system –none of the optical directions coincide with crystallographic axes.

There are two types of biaxial crystals such as, negative biaxial crystal and positive biaxial crystals. Negative biaxial crystals have their β closer to γ than to α. Positive biaxial crystals have their β closer to α than to γ.

What is the Difference Between Uniaxial and Biaxial Crystals?

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 Uniaxial vs Biaxial Crystals
A uniaxial crystal is an optical element that has a single optic axis. A biaxial crystal is an optical element that has two optic axes.
Negative Form
A negative uniaxial crystal has the refraction index of o-ray (no) larger than that of the e-ray (ne). A negative biaxial crystal has its β closer to γ than to α.
Splitting the Light Beam
When a light beam passes through a uniaxial crystal, the light beam splits into two rays named as ordinary ray (o-ray) and the extraordinary ray (E-ray). When a light beam passes through a biaxial crystal, the light beam splits into two rays being both are extraordinary rays (e-rays).
  Positive Form
A positive uniaxial crystal has the refraction index of e-ray (ne) is smaller than that of the e-ray (ne). A positive biaxial crystal has its β closer to α than to γ.
Examples
Quartz, calcite, rutile, etc. All the monoclinic, triclinic an orthorhombic crystal systems

Summary – Uniaxial vs Biaxial Crystals

Crystals are substances whose atoms are arranged in a well-ordered manner. Furthermore, these two crystals are in two types as uniaxial crystals and biaxial crystals, based on the number of optic axes present in the crystal structure. The difference between uniaxial and biaxial crystals is that uniaxial crystals have a single optic axis whereas biaxial crystals have two optic axes.

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