uniaxial crystals_crossed polars

Uniaxial Crystals Between Crossed Polars

Optical Mineralogy Lecture/ LaboratoryAdamson University

08 February 20132nd Sem

Course Outline

• Lecture PART 1

• Theories of Light• Isotropic and Anisotropic Substances• Uniaxial minerals: indicatrix, interference figures, optic

sign • Biaxial minerals: optic sign, 2V angles, optical

orientation, dispersion of biaxial minerals

Course Outline

• LaboratoryPART 1

• The polarizing microscope• Orthoscopic examination of minerals under plane

polarized light• Orthoscopic examination of minerals under crossed

polarized light• Conoscopic examination of minerals I: Uniaxial crystals• Conoscopic examination of minerals II: Biaxial crystals

Course Outline• Lecture

PART 2• Introduction to optical properties of common rock forming

minerals– Neso-silicates: Olivine group, Garnet group, Al2Sio5 group,

staurolite– Soro-silicates: Epidote group, Ring silicates: Tourmaline– Chain-silicates: Pyroxene group, Amphibole group– Sheet-silicates: Mica group (Muscovite, biotite, talc), chlorite group– Tecto-silicates: Silica group, feldspar groups, feldspathoids– Non-silicates Carbonate, sulfates, phosphate (apatite), opaque

minerals, spinel, rutile; volcanic glass

Course Outline• Laboratory

PART 2• Optical properties of common rock forming minerals

– Optical examination of comon rock-forming minerals (I): Nesosilicates, sorosilicates and cyclosilicates

– Optical examination of common rock-forming minerals (II): inosilicates: pyroxene and amphibole

– Optical examination of common rock-forming minerals (III) phylosilicates

– Optical examination of common rock-forming minerals (IV): tectosilicates

– Plagioclase composition determination– Optical examination of common rock-forming minerals (V): non-

silicates

Extinction

• Isotropic crystals remain dark in all positions between crossed polars

• Anisotropic crystals however also behave (i.e. remain dark) when viewed between crossed polars

• When? • WHEN LIGHTS MOVES PARALLEL TO THE OPTIC AXIS• How? • Light from polarizer passes through the crystal and

is completely cut out by the analyzer

Extinction

• WHEN VIBRATION DIRECTION OF LIGHT FROM THE POLARIZER COINCIDES EXACTLY WITH ONE OF THE VIBRATION DIRECTION OF THE CRYSTAL

• How?• Light passes through the crystal as either the

O ray or the E ray to be completely eliminated by the analyzer

Extinction

Quartz grain experiencing extinction

Extinction

• Parallel Extinction – when traces of the cleavage planes appear as irregularly shaped parallel lines. Extinction along cleavage planes occurs because these are parallel to the vibrations direction of the polars.

Extinction


• Inclined or Oblique Extinction – When cleavages or crystal boundaries lie at oblique angles to the planes of vibration of the two polars.

Extinction


Hornblende (left); Hedenbergite (right)

Extinction



• Symmetrical Extinction – Minerals forming cleavage patterns with rhombic cross sections

Elongation

• Occurs in minerals which exhibit elongated habit and straight edges (i.e. lathlike, needles, long crystals etc.)

• Positive elongation – When vibration direction of the slow ray of the crystal is parallel to the long direction (a.k.a. length slow)

• Negative elongation – when vibration direction of the slow ray lies across the crystal in the short direction (a.k.a. length fast)

Elongation

• Hexagonal and tetragonal crystals are often elongated on the c-axis or have prismatic cleavage that forms splintery fragments parallel to the c-axis

Interference Color

– Colors produced when analyzer is inserted – Generated as a result of birefringence, where ray

of light is retarded relative to the other– Different degrees in retardation give different

interference colors– Used to identify certain minerals

Interference Color

• Phase difference: P=Δ/ λwhere, Δ=t (n2-n1),

where t=thickness of mineral converted to millimicrons (1mμ=10-6 mm), n2 is the greater index of refraction, n1 is the lesser index of refraction for a particular orientation

Interference Color

• If one ray is an integral number of wavelengths (nλ) behind the other, the interference results in darkness

• If the path difference is (2n-1) λ /2 (i.e. λ/2, 3 λ/2…), the waves reinforce one another to produce maximum brightness

Interference Color

• Interference colors appear as complementary colors when one wavelength in the spectrum is eliminated (i.e. when darkness appears)

• Different orders of interference:– 1st order: 1 λ– 2nd order: 2 λ– 3rd order: 3 λ…

Interference Color

• Dependent on:– Orientation– Thickness – BirefringenceRelationship: For a given orientation, the thicker the

crystal and the greater the birefringence, the higher the order of interference color

Interference Color

• Accessory Plates – Indicate fast- and slow-ray vibration direction and are mounted in frames between the objective and the analyzer– Gypsum – Mica– Quartz

– NOTE: when the positions of the vibration directions of the rays are known, turn mineral from extinction to maximum interference color

Interference Color

• Accessory Plates– Gypsum – Mica– Quartz

• Made by cleaving a gypsum to such thickness that in white light it produces a uniform red interference color (i.e. red of first order) •Employed in cases where there is strong double refraction

Interference Color


• Made with thin mica flake, cleaved to a thickness that for yellow light it yields a path difference of a quarter of a wavelength (λ/4). •Used when there is weak double refraction

Interference Color


• Elongated wedge-shaped piece of quartz with vibration direction of the fast ray (omega) parallel to its length and the slow ray (epsilon) across its length•Used when there is very strong double refraction

Interference Color

Quartz Wedge:a. Cross sectionb. In monochromatic light

λ=560 nmc. Colors in white light

Interference Color

As thicker portions of the wedge are placed in the

optical path, the path difference of the rays

passing through it also increases, producing

succession of interference colors. The

number of orders depends on the wedge angle: The greater the angle the more orders

per unit of length

Interference Color

When viewed between crossed polars in

monochromatic light, it is crossed by alternating

dark and light bands: dark where the path difference is n λ and brightest where the

path difference is (2n – 1) λ / 2

Interference Color

In white light, a succession of interference colors is observed that resemble

colors seen in thin oil films on water

Interference Color

Microscope set-up and apparent interference

colors resulting from insertion of quartz

wedge and/or analyzer

From Kerr

Δ=t (n2-n1)

Interference Color

The difference between wavelengths of opposite ends of the spectrum is:

First dark band for violet occurs almost in

first position of maximum intensity for

red

Δ=t (n2-n1)

Violet band: ~410 mμRed band: ~700 mμResulting interference: Orange = ~620 mμ

Interference ColorBirefringence

Path difference

Thickness in Micrometers

Anomalous Interference Color

• Abnormal production of interference colors, often in low order

• May be produced as a result of strain in the minerals

• Example: Vesuvianite – Berlin Blue (interference color does not follow the color chart); Chlorite, zoisite, brucite etc.

Uniaxial Crystals in Convergent Polarized Light

• Interference figures are seen when properly oriented crystal sections are examined in convergent polarized light

• To see interference figures: – set microscope to conoscopic mode– Using high power objective


• Interference figures are seen when properly oriented crystal sections are examined in convergent polarized light

• Principal interference figure of uniaxial crystal, the optic axis figure, is seen when one views the crystals parallel to the c-axis


Black cross superimposed on the rings of interference color: Radial dashes indicate the vibration direction of the E ray and those at right angle with the vibration

directions of the O ray. WHERE THESE VIBRATION DIRECTIONS ARE PARALLEL OR NEARLY PARALLEL TO THE VIBRATION DIRECTIONS OF THE POLARIZER AND THE ANALYZER, NO LIGHT PASSES AND THUS THE FORMATION OF THE DARK CROSS.



Interference of these rays produce concentric circles of interference colors. The center is black with no interference, but moving outward there is a progression from 1st order to 2nd and so forth, interference colors.



If crystal section is of uniform thickness, no change will be noted as it is moved horizontally. HOWEVER, if thickness varies, the positions of the colors change with horizontal movement. Increase in thickness will result to higher order interference colors.


• Figures below show centered optic axis figures as obtained on a crystal plate whose axis coincides with the axis of the microscope; as the stage is rotated, no movement of the figure (cross) is seen.


• When the optic axis of the crystal makes an angle with the axis of the microscope, the black cross is no longer symmetrically located in the field of view.

• The center of the cross moves as stage is rotated, where the bars of the cross remain parallel to the vibration directions of the polarizer and analyzer.


• Flash Figure – an interference figure produced by uniaxial crystals when optic axis is normal to the axis of the microscope.

• How does it look like? • When the crystal is at extinction, the figure is an ill-defined

cross occupying a large space; Upon stage rotation, the cross breaks into two hyperbolas, which immediately leave quadrants with optic axis.

Determination of Optic Sign

• Accessory plates may be used to determine optic sign• How is this done?• With the use of an accessory plate, where the vibration

directions of the slow ray and fast ray are known, you can determine whether the E ray of the crystal is slower (positive crystals) or faster (negative crystals) than the O ray and thus determine the optic sign.

Determination of Optic Sign

• Accessory plates may be used to determine optic sign• How is this done?• With the use of an accessory plate, where the vibration

directions of the slow ray and fast ray are known, you can determine whether the E ray of the crystal is slower (positiv crystals) or faster (negative crystals) than the O ray and thus determine the optic sign.

• Example:

The most marked effect produced by the mica plate is the formationof two black spots near the center of the black cross in the quadrants where subtraction occurs

Questions?

Biaxial Crystals

Biaxial Indicatrix

•Biaxial indicatrix is a triaxial ellipsoid with its 3 axes•Lengths of the semiaxes are proportional to the refractive indices alpha along x, beta along y, and gamma along z. •Planes xy, yz, xz•They all are ellipses and each has the length of its semimajor and semiminor axes proportional to refractive indices.

Biaxial Characteristics

Acute bisectrix interference figureParallel position; 45 degrees position

Relation of 2VTo 2E

Curvature of isogyre n optic axis figureFrom 0 degrees to 90 degrees 2V

Optic sign determination of negative crystal with gypsum plateAcute bisectrix figure (a)Optic axis figure (b)

uniaxial crystals_crossed polars

Documents

oblique extinction

minerals v

extinction alo

minerals iv

opaque minerals

minerals nesosilicates

cleavage planes

optic sign biaxial minerals