Why does an anisotropic mineral, viewed under crossed polars, suffer four times of complete extinction during a 360° rotation of microscope stage? What is pleochroism and how is it determined?

Anisotropy and Extinction under Crossed Polars

Anisotropic minerals possess a refractive index that varies depending on the direction of light propagation. This is described by two refractive indices, n_ω and n_ε, representing the ordinary and extraordinary rays respectively. When light enters an anisotropic mineral, it splits into these two rays, each traveling at a different velocity and with a different refractive index. Under crossed polars, the interference color observed depends on the thickness of the mineral grain and the difference between n_ω and n_ε (birefringence).

Extinction refers to the complete loss of interference color, appearing as a dark area. This happens when the vibration directions of both the ordinary and extraordinary rays are aligned parallel or perpendicular to the polarizer and analyzer. For an anisotropic mineral, extinction doesn’t occur in all orientations. Instead, it occurs at specific angles due to the orientation of the optic axes within the crystal.

Four Extinctions During 360° Rotation

The reason for four extinctions during a 360° rotation of the microscope stage is directly related to the symmetry of the indicatrix, the geometric representation of refractive indices in an anisotropic mineral. The indicatrix is an ellipsoid, and its shape dictates the extinction behavior.

• Optic Axes: Anisotropic minerals have two optic axes, which are directions within the crystal where light travels with equal velocity (n_ω = n_ε).
• Fast and Slow Directions: The directions of fastest and slowest light propagation are perpendicular to the optic axes.
• Rotation and Extinction: As the stage is rotated, the orientation of the mineral’s crystallographic axes relative to the polarizer and analyzer changes.
• Four Extinction Positions: For most uniaxial minerals, complete extinction occurs four times during a 360° rotation. This is because the vibration directions of both rays can be aligned with the polarizer and analyzer in four different orientations. These orientations are related to the symmetry of the crystal and the position of the optic axis.

The angle between successive extinction positions is typically 90° for uniaxial minerals. Biaxial minerals exhibit more complex extinction patterns, but the principle remains the same – extinction occurs when the vibration directions of both rays align with the polarizer and analyzer.

Pleochroism: Definition and Determination

Pleochroism is the optical property of certain anisotropic minerals where the color of the mineral changes when viewed in different polarization directions. This occurs because the mineral absorbs light differently depending on the direction of vibration of the light waves. The absorption of light is related to the electronic structure of the mineral and the wavelengths of light that are absorbed.

How Pleochroism is Determined

Pleochroism is determined by rotating the mineral grain (or the stage) under crossed polars while observing the color changes. The process involves:

• Rotating the Stage: The mineral is rotated 360° while observing its color under the microscope.
• Identifying Color Changes: The observer notes the different colors displayed by the mineral as it is rotated.
• Describing Pleochroic Scheme: The pleochroic scheme is described by listing the colors observed in the directions of maximum and minimum absorption. For example, a mineral might exhibit a pleochroic scheme of "dark green to pale yellow."
• Use of Rotating Stage: A rotating stage is essential for accurately determining pleochroism, as it allows for precise control over the orientation of the mineral.

Pleochroism is a valuable diagnostic tool in mineral identification, particularly for minerals that lack strong cleavage or other easily identifiable features. It is commonly used to identify minerals like tourmaline, biotite, and hornblende.