Chapter 5

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Polarized light microscopy

microscopy technique that uses polarized light to study specimens; allows us to see otherwise undiscernible characteristics. One approach includes examining grains of crystals to better see details

Opaque minerals

Minerals with metallic luster; will not transmit light unless the mineral grains are much thinner than normal thin sections. Appear black under a microscope (magnetite)

Non-opaque minerals

Minerals that do transmit light. Can be isotropic (having the same properties in all directions) or anisotropic (having different optical properties in different directions)

Anisotropic subdivisions

uniaxial and those that are biaxial, and according to whether minerals have a positive or negative optic sign

Microscopic relationships between mineral grains allow us to determine the order in which

minerals crystallized from a magma, and we can identify minerals produced by alteration or weathering long after the crystals first formed

When the velocity of light is altered as it passes from one medium (for example, air) to another…

the wavelength changes, but the frequency remains the same

If wavelengths corresponding to all the primary colors are present with equal intensities

The light appears white

Polychromatic

Many-colored light; contains a range, or spectrum, of wavelengths. Polychromatic light can be separated into different wavelengths in many ways

Monochromatic

Light with one color. When one wavelength is isolated

Phase

whether a wave is moving up or down at a particular time

In-phase wave

If two waves move up and down at same times. If not, they are out of phase

Interference phenomena

the optical properties of minerals that result from the passing of light waves through them

Constructive interference

When waves are in phase, no energy is lost

Destructive interference

When waves are out of phase, both waves appear to “consume” each other’s energy (law of conservation of energy)

For perfect constructive or destructive interference to occur, waves must be

of the same wavelength but they may have different amplitudes

Refractive index (n)

the ratio of the velocity (v) of light in a vacuum to the velocity in the crystal. Always has a value greater than 1. High values of n correspond to materials that transmit light slowly

n = v_air / v_crystal

Refraction

Objects that appear to bend as they pass from air into another medium—When light rays pass from one medium to another (for example water and air) with a different refractive index

When refraction occurs, a light beam bends toward the medium with

Higher refractive index, where the light travels slower, because one side of the beam moves faster than the other

Angle of incidence (θ_i)

the angle between the beam and a perpendicular to the interface

Angle of refraction (θ_r)

After crossing the interface, the angle between the beam and a perpendicular to the interface

θ_r = sin^-1[(n_i/n_r) x sin θ_i]

Snell’s Law

Relationship between the angle of incidence (θ_i) and the angle of refraction (θ_r)

sin(θ_i) / sin(θ_r) = v_i / v_r = n_r / n_i

where v_i and v_r are the velocities of light through two media, and n_i and n_r are the indices of refraction of the two media

Internal reflection

If the angle of incidence is small (drawing b), most light escapes and is refracted at some angle to the crystal face, but some light reflects back into the crystal

As the angle of incidence increases, the proportion of light that is reflected increases. True or False?

True

Critical angle of refraction

The limiting value of θ_i. Common method for determining refractive index of a mineral

Why do some crystals (diamond) with a high refractive index exhibit internal reflection that makes them sparkle?

If the angle of incidence is greater, none of the light will escape; the entire beam will be reflected inside the crystal (figure e and f)

Dispersion

How the velocity of light in a crystal varies with the light’s color. Different colors of light follow different paths through a crystal because they refract at different angles

Dispersion and refractive index determine

the play of colors (fire). For example, diamond has high dispersion and high refraction. If not for dispersion, diamonds might sparkle, but the sparkles would all be the same color

Minerals with low dispersion generally appear

dull, no matter how well-cut or faceted

Polarizing filter

Causes light waves that pass through to be filtered/stopped. Some waves reflect, whether horizontal or vertical, depending on the surface. Eliminates glare and helps to isolate one wave

Characteristics Seen in Plane Polarized (PP) Light

• If a mineral is opaque or non-opaque

• Crystal shape/habit

• Cleavage

• Color and pleochroism (some colors appear differently from different angles. Amphiboles are an example)

• Relief/Becke lines (how well grains stand out)

(High) positive relief

Minerals with high refractive indices; their index of refraction is greater than that of the epoxy. They also show structural flaws, such as scratches, cracks, or pits, unlike those with low refractive indices (garnet, biotite, quartz)

Negative relief

Minerals with very low refractive indices show high relief (termed negative relief) in thin section because their index of refraction is much lower than that of the epoxy

Characteristics Seen in Cross Polarized (XP) Light

• If a mineral is anisotropic or isotropic

• Viewing a mineral with crossed polars (upper polarizer)

• Detecting presence of interference colors

• Detecting anomalous interference colors (not represented)

• Twinning, zoning, and undulatory extinction

Undulatory extinction

different parts of a crystal go to extinction at different times with stage rotation

Minerals whose crystals belong to the cubic system are

isotropic; their atomic arrangement is the same along all crystallographic axes (garnet, sphalerite, and fluorite). Minerals in other systems are anisotropic

Interference colors

Unrelated to true mineral color. Pigments that shift colors when viewed from different angles/through XP light. Depend on grain orientation

Anomalous interference colors

not represented on color chart. May result if minerals have highly abnormal dispersion, are deeply colored, or for several other reasons (chlorite, epidote, zoisite, jadeite, tourmaline, and sodic amphiboles)

Double refraction

the splitting of a light beam into two perpendicularly polarized rays (all randomly oriented anisotropic minerals)

Apparent birefringence

The difference in the indices of the fast ray and the slow ray. (slow-fast). Varies depending on the atomic orientation in the crystal and the direction light is traveling

Michel-Lévy Color Chart

Horizontal axis is retardation; it directly correlates with interference color (shown as vertical color swatches). The vertical axis is grain thickness. The diagonal lines and numbers on the top and right side of the chart show birefringence

Maximum interference colors for common minerals

First-order colors

If retardation is slightly greater than white → grey, yellow, orange, or red interference colors will appear when we rotate the stage. Correspond to a retardation of 200 nm-550 nm

Second and third-order colors

violet to red interference colors

Uniaxial minerals

Tetragonal or hexagonal crystal systems. One optic axis that coincides with the c-axis. Maximum value of birefringence in uniaxial crystals is the absolute value of the difference between ω (parallel to optic) and ε (perp to optic)

Two uniaxial classes

f ω < ε, the mineral is uniaxial positive ( + ).

If ω > ε , the mineral is uniaxial negative (-)

Biaxial minerals

Two optic axes; orthorhombic, monoclinic, and triclinic systems. Axes are not coincident with crystallographic axes (a, b, or c). Have refractive indices that vary between two limiting values that change in orientation to light.

The indices of refraction for light vibrating parallel to X, Y, and Z are α, β, γ

Two biaxial classes

In biaxial positive minerals, the intermediate refractive index β is closer in value to α than to γ.

In biaxial negative minerals, it is closer in value to γ

Parallel extinction

Some hexagonal, tetragonal, and orthorhombic minerals. Go extinct when their cleavages or directions of elongation are parallel to the upper or lower polarizer

Inclined extinction

Many monoclinic and all triclinic crystals. Go extinct when their cleavages or directions of elongation are at angles to the upper and lower polarizer

Symmetrical extinction

Minerals that go extinct at angles symmetrical with respect to cleavages or crystal faces

Isogyres

Dark bands or curves that appear in interference figures. Indicate where light waves that are vibrating parallel to the polarizer have passed through a crystal

How to determine optic sign (+ or -)

For positive minerals, colors move inward in the southwest and northeast quadrants and outward in the northwest and southeast quadrants. For negative minerals, the motion is opposite