OPTICAL PROPERTIES OF MINERALS



OPTICAL PROPERTIES OF MINERALS

▪ Nature of light (EM Radiation)

▪ To account for all properties of light we need wave theory and corpuscular theory

▪ We use wave theory to explain the optical behavior of crystals

▪ Assume that visible light travels in straight lines with a transverse motion (vibrates at right angles to direction of propagation)

▪ Waves in light are like waves in water:

Wavelength = ( (distance between successive crests)

Amplitude = displacement on either side of the equilibrium

( =frequency= #of waves /sec passing a point

v=velocity= frequency x wavelength v=((

▪ However, with light, transverse vibrations takes place ( to the direction of propagation in all possible directions

▪ R O Y G B I V

( 7700Å 3900 Å

▪ White light = all wavelengths between 7700 and 3900 Å

▪ Single wavelength = monochromatic

C= speed of light = 3 x 108 m/sec

▪ When light passes through a mineral, ( (wavelength) changes but ( (frequency) remains the same

INTERFERENCE

▪ Phase character of light (wave moving up or down at a particular time ) in phase vs. out of phase

▪ 2 waves in phase = Constructive interference

← increased intensity

▪ 2 waves out of phase = Destructive interference

(if waves are of same (, perfect C or D might occur)

POLARIZATION OF LIGHT AND THE POLARIZING MICROSCOPE

▪ Polarized light vibration of light is ( to direction of propagation. With light, vibration is in all different directions

▪ We can filter or alter light to make all waves vibrate in one direction || to a particular plane = plane polarized light

HOW?

1) BY REFLECTION: light vibrates in planes || to the reflecting surface, light traveling in other directions is absorbed (polarizing sunglasses reduce glare)

2) BY ABSORPTION: all directions absorbed by an anisotropic crystal. Two polarized rays are created one is absorbed, one emerges

3) BY DOUBLE REFRACTION: light is bent by an anisotropic crystal 2 polarized rays at different angles, and we use one

▪ We utilize filters. With one filter our eyes can’t tell if light is polarized.

With a second filter we can!

▪ If the 1st and 2nd filters are in || directions, then maximum light is emitted / passes through.

▪ If the 2nd filters are ( to the 1st filter, then no light passes

▪ Intermediate angles intermediate amounts of light

POLARIZING MICROSCOPE (PETROGRAPHIC MICROSCOPE)

▪ Magnify with a white light source

▪ Lower polarizer – plane polarized light vibrating in only one plane

▪ Typically in an E-W (Left-Right) direction

▪ Fixed condensing lens and diaphragm helps concentrate light on the sample

ORTHOSCOPIC ILLUMINATION – UNFOCUSED BEAM

▪ Light travels from the substage through the sample and up the microscope tube

▪ All light travels orthogonal (( to) stage

CONOSCOPIC lens + illumination = Condenser lens

Light converges on a small spot with a cone of nonparallel rays

▪ Rotate stage to change orientation of the sample relative to polarized light

▪ Because most minerals are anisotropic (non-cubic) light vibrates unequally in different directions, thus interaction with light varies with stage rotation

OBJECTIVE LENSES (2x –50x typically)

N.A. (Numerical aperture) = describes angles at which light can enter a lens (N.A. =.85 is most common)

OCULAR LENSES (8x,10x ,15x etc) in the eye piece

Total magnification = ocular x objective

(e.g. 10x X 20x = 200X)

Upper polarizer = Analyzer (insert or remove)

Typically at 90˚ to lower polarizer

▪ If no sample is on the stage and the upper polarizer is in, no light can pass.

▪ If a sample is on the stage, it typically changes the polarization of the light

▪ If isotropic – no light passes

▪ If anisotropic – some light passes

ACCESSORY PLATE

▪ Full wave plate (used to be gypsum plate)

▪ Bertrand lens + diaphragm (conoscopic study) (pin hole)

▪ Only polarizer = Plane Polarized Light (PPL)

▪ Both polarizers = Crossed Polar Light (CPL or XPL)

▪ PPL grain size, shape, color, cleavage

▪ PPL refractive index, pleochroism

▪ CPL with conoscopic + Bertrand lens retardation, optic sign, 2V

▪ Grain mounts + thin sections

Grains with refractive index oil and cover slip

T sections are 30(m thick (thickness affects color)

▪ Colors in PPL + CPL

PPL in thin sections most minerals are weakly colored to colorless

Changes in color under PPL with stage rotation are due to changes in the minerals orientation with respect to polarized light

= Pleochroism (useful for Identification of some minerals)

For uniaxial minerals = 2 hues

for biaxial minerals = 3 hues (XYZ Pleochroic formula)

light vibrates || to 3 directions that are numerically perpendicular.

CPL INTERFERENCE COLORS

▪ Not caused by absorption of different wave lengths, but by interference of light waves passing through the upper polarizer

[pic]

▪ Differ based on grain orientation

▪ Vary with grain thickness

▪ Need T-Sections of uniform thickness

VELOCITY OF LIGHT IN CRYSTALS + REFRACTIVE INDEX

▪ When EMR passes near an atom, it causes electrons to oscillate. This causes Energy to be absorbed from the light and the wave slows down.

[pic]

▪ A waves velocity through a crystal is described by the

Refractive index (n) of the crystal and it depends on chemical

composition, crystal structure and bond type

n = VVacuum /VCrystal

Because light in a vacuum is faster n is always > 1

( in air n = 1.00029 ( speed in vacuum, common reference)

n = Vair /VCrystal

▪ As light passes through most non opaque crystals its V decreases by about 1/3 to ½ (n= 1.5 to 2 typically)

* Because the frequency of light (() is unchanged, ( must

decrease because v=( (

▪ Refractive index is most useful for grain mounts (with oils)

▪ R.I. also varies with ( of the light used (need to eliminate this)

▪ Velocity of light in a crystal varies with light’s color (dispersion)

e.g. a prism separates white light into a rainbow

[pic]

▪ Different (’s are bent (refracted) at different angles

Diamond = high dispersion

Fluorite = low dispersion

ISOTROPIC MINERALS (Cubic minerals, glass, epoxy + plastic)

▪ Have essentially random atomic structure

▪ Remain extinct (dark) as the stage rotates, no matter what their orientation

ANISOTROPIC MINERALS

▪ Go extinct (briefly) every 90˚ of stage rotation (however if they are oriented parallel to optic axis they will remain extinct and appear isotropic)

▪ Anisotropic minerals may have only one (uniaxial) or two (biaxial) optic axes. When in doubt if anisotropic or isometric, use conoscopic light, as anisotropic minerals will transmit some conoscopic light and display interference figures (isotropic minerals do not)

SNELL’S LAW + LIGHT REFRACTION

▪ Objects appear to bend as they pass from air into water = refraction, as light passes from one medium into another, with different R.I.’s

▪ If light strikes the interface at an angle ≠ 90˚,it changes direction

[pic]

▪ the light beam bends towards the medium with the higher R.I. because one side of the beam moves faster than the other.

[pic]

▪ The angle between the incoming beam and a perpendicular to the interface is (i the angle of incidence

▪ The angle between the outgoing beam and a perpendicular to the interface is the angle of refraction=(r

▪ The relation between the two angles is

Sin (i / Sin (r = Vi/Vr = nr/ni

where Vi and Vr are velocities of light through the two media

ni and nr are the indices of refraction of the two media

= Snell’s law (Dutch 1621)

by rearranging, we calculate the angle of refraction:

(r = sin-1 [ ni/nr Sin (i ]

by definition, Sin values of (i must be ( 1.0

for some/average values of (i there is no solution.

The limiting value of (i is the critical angle of refraction.

▪ If the angle is greater no light escapes and the entire beam is reflected inside the crystal= high R.I. of diamond and adamantine luster (sparkling appearance).

▪ We can use a refractrometer to measure the angle.

RELIEF AND BECKE LINES

▪ Isotropic minerals in liquid of the same R.I. disappear (unless they are distinctly colored) as their edges don’t stand out.

▪ If the grains have a significantly different R.I. than the liquids light will refract and reflect at the edge of the grain and the boundary becomes more pronounced.

RELIEF

▪ Contrast between a mineral and its surroundings (high vs. low)

▪ Also true in T-sections relative to epoxy or other minerals

If a grain is in a liquid, some light rays bend towards the medium with higher R.I.

Light interacts with the grains as if they were small lenses. If

Nmineral >nliquid, rays are refracted and converge after passing through the grain.

We can see this feature if we slowly lower the microscope stage, shifting the focus to a point above the mineral grain.

A bright narrow band of light called a BECKE LINE appears at the mineral-liquid interface and moves towards the material with the higher R.I.

( A complimentary but harder to see, dark band moves towards the material with the lower R.I.)

▪ We can do the same thing in a T-Section by focusing and at a grain boundary.

▪ We can employ a variety of oils of differing R.I. to identify the R.I. of an unknown mineral grain.

INTERACTION OF LIGHT AND CRYSTALS

DOUBLE REFRACTION

Upon entering an anisotropic mineral, light is normally split into two polarized rays, each traveling through the crystal along a slightly different path with a slightly different velocity and R.I.

[pic]

For uniaxial minerals we call the two rays:

O (ordinary) ray ( and

E (extraordinary) ray (’

The O ray travels a path predicted by Snell’s law, while the E ray does not. The O ray and the E ray vibration directions depend on the direction that light is traveling through the crystal structure, but the vibration direction of the two rays are always perpendicular to each other.

▪ We call the splitting of a light beam into 2 perpendicularly polarized rays, double refraction. All randomly oriented anisotropic minerals cause double refraction.

▪ Calcite is one of the few common minerals that exhibit double refraction that is easily seen without a microscope.

▪ As the two rays pass through an anisotropic crystal, they travel at different velocities (unless they are parallel to an optic axis)

▪ We call the two rays the slow ray and the fast ray.

▪ Because they travel at different velocities, their R.I’s must be different

▪ The difference in the indices of the fast and slow rays (nslow- nfast) is the apparent birefringence ((’)

▪ The maximum birefringence (() is a diagnostic property of minerals.

▪ When the slow ray emerges from the anisotropic crystal, the fast ray has already emerged and traveled some distance. This distance is the retardation ((). Retardation is proportional to both the thickness (t) of the crystal and to the birefringence in the direction the light is traveling ((’).

(=t x ((’)=t x (ns-nf)

For isotropic crystals, ( and ( = 0

All light passes through them with the same velocity

(see table inside back cover of the book for interference colors, which are a function of birefringence)

CRYSTALS BETWEEN CROSSED POLARS

Under CPL we can differentiate isotropic and anisitropic crystals (isotropic remains dark through 360( of stage rotation)

When we view an anisotropic crystal with CPL (unless down an optic axis) light is split into 2 rays. The 2 rays, after emerging from the crystal, travel up to the upper polariser where they are resolved into one ray with N-S polarization. Because the vibration directions of the rays are not normally perpendicular to the upper polarizer, components of both pass through it to produce the light reaching our eyes.

As we rotate the microscopic stage, the relative intensity of the two rays vary. Every 90( the intensity of one is zero and the other is vibrating parallel to the lower polarizer.

Consequently, no light passes through the upper polarizer and the crystal appears extinct every 90( (at 45( to the extinction positions, we see maximum brightness)

INTERFERENCE COLORS

When white light passes through an anisotropic mineral, all wavelengths are split into 2 polarized rays vibrating at 90( to each other.

▪ Different colors have different (, so some colors may be retarded (though most will not)

▪ When the N-S component of the two rays are combined at the upper polarizer C.I. occurs for some colors and D.I. for others

▪ If we see a mineral of uniform thickness under CPL, we see one color the interference color.

▪ Depends on retardation, which depends on orientation, birefringence and the thickness of the crystal.

▪ Interference colors change intensity and hue as we rotate the stages they disappear every 90(

▪ Normal interference colors are shown in a Michel – Levy color chart

▪ Very low order interference colors (retardation of < 200nm) are gray + white

▪ The interference color of a mineral with very low birefringence changes from white to black every 90(

▪ Minerals with slightly greater birefringence show yellow, orange or red interference colors upon rotation (retardation of 200-550 nm) = first order colors

▪ As retardation increases further, colors repeat every 550nm (average wavelength of visible light) going from violet to red (second order) and then from violet to red again (3rd order)

▪ They become more pastel as order increases.

▪ 4th order colors appear white

▪ Calcite ((=.172) with high order pastels and quartz ((=.011) with 1st order gray-white.

▪ If in doubt insert a full wave plate

▪ (’s 1st order white to yellow or blue, but has no effect on high order white

▪ some minerals have anomalous interference colors (due to high dispersion or if they are deeply colored): chlorite, epidote, zoisite, jadeite, tourmaline, sodic plagioclase

UNIAXIAL & BIAXIAL MINERALS

▪ Isotropic crystals have the same R.I. in all directions because they have the same light velocity in all directions.

▪ Anisotropic minerals do not

For uniaxial minerals we need 2 indices of refraction to describe the mineral R.I. (( and ( ). For biaxial minerals we need three ((, ( and ()

Optic axes are directions that light can travel through a crystal without being split into 2 rays

[pic]

▪ In some uniaxial minerals, the O.A. is parallel or perpendicular to crystal faces

▪ In biaxial minerals, the 2 optic axis rarely are parallel or perpendicular to crystal faces

Light traveling parallel to O.A. of a uniaxial mineral travels as an ordinary ray with a unique R.I. (

[pic]

Light traveling in other directions is doubly refracted 2 rays: ( and (’ R.I.’s

(’ is a value between ( and ( (light perpendicular to O.A.)

▪ If (( = uniaxial (-)

[pic]

▪ POLE (positive = omega less than epsilon)

▪ NOME (negative = omega more than epsilon)

Maximum possible bifringence, (, =|(-(| (if O.A. is parallel to stage)

Most minerals are biaxial. We describe their optical properties in terms of 3 perpendicular directions (x, y, z)

Fig. 7.23[pic]

▪ The vibration direction of the fastest ray is X; the slowest is z

▪ The R.I. for light vibrating parallel to x, y and z are (, ( and (

▪ Thus ( has the lowest R.I., ( the highest, and ( intermediate. (R.I. of light perpendicular to an O.A.)

▪ Normally light that passes through a randomly oriented biaxial crystals is split into two rays, neither of which vibrates parallel to x, y, and z.

▪ Thus their R.I.’s will be some value between ( and (

▪ If light travels parallel to y, the rays will have R.I’s equal to ( and ( as they vibrate parallel to x and z

▪ In this case the crystal will experience maximum retardation

▪ If light travels parallel to an optic axis, no double refraction occurs and it has a single R.I. (

▪ There will be no birefringerence or retardation and the mineral will appear extinct

In biaxial minerals we call the plane that contains x and z, and the 2 optic axis the optic plane

[pic][pic]

▪ The acute angle between the optic axis is 2V

▪ A line bisecting the acute angle must parallel either z (biaxial +) or X (biaxial -)

▪ In biaxial (+) minerals ( is closer in value to ( than to (

▪ In biaxial (-) minerals, ( is closer in value to (

▪ The maximum possible value of birefengerence in biaxial minerals (() is always ( - (

Accessory plates and sign of elongation

▪ When inserted above the objective lens, the slow and fast vibration directions of the plate are at 45( to the upper and lower polarizers.

▪ A full wave plate has a retardation of 550 nm (avg wavelength of light)= first order red interference colors

▪ Quartz wedge has variable thickness with retardation from 0 to 3500 nm

▪ Inserting a plate adds or subtracts to the retardation.

[pic]

▪ We can determine which direction in the crystal permits polarized light to travel the fastest

▪ If crystals have a long dimension we can determine if the mineral is length fast (negative elongation) or length slow (positive elongation)

UNIAXIAL INTERFERENCE FIGURES

▪ Optic sign (+ or -) is another useful characteristic to identify anisotropic crystals.

▪ Interference figure use conoscopic light with upper polarizer in and a Bertrand lens (refocuses rays + magnifies I.F)

▪ To determine the optic sign of a uniaxial mineral it is best to look down the optic axis=optic axis figure =O.A. = uniaxial cross

[pic]

▪ Should be easy to find because uniaxial minerals appear isotropic when we look down the O.A. or have low order interference colors if we are close to O.A.

Melatope = center of cross where O.A. emerge

Isogyre = dark bands forming cross

Isochromes colored rings (if present) (bands of equal retardation caused by light entering at different angles)

▪ Minerals with low birefringence (e.g. quartz) may not display isochromes

To determine (+) or (-) sign we use an accessory plate

[pic]

▪ Usually O.A. is not perfectly centered

[pic]

▪ If O.A. is parallel to the stage of the microscope we get an optic normal figure = flash figure

[pic]

▪ Appears as a vague cross or blob that nearly fills the field of view when the grain is at extinction (= when the O.A. is perpendicular to one of the polarizers)

▪ Upon stage rotation it splits into 2 curved isogyres flashing in and out of the field of view with a few degrees of stage rotation

▪ Looks like a BXO figure

BIAXIAL INTERFERENCE FIGURES

▪ It is more difficult to find grains oriented in a useful way for biaxial crystals.

[pic]

3 general types of biaxial interference figures: optic axis; acute bisectrix (Z axis); and optic normal (Y axis)

[pic]

ACUTE BISECTRIX FIGURE (BXA)

[pic]

Z axis is perpendicular to the polarizer or analyzer (you are looking down optic plane (X-Z)

▪ Black cross is similar to uniaxial I.F.

▪ Upon rotation cross splits into 2 isogyres that move apart and may leave the field of view

▪ After 45( rotation isogyres are at max separation, another 45( resume +

▪ the maximum amount of isogyre separation 2V depends on RI and K (constant based on numeric aperture of objective lens)

[pic]

▪ if 2 V is , 60( , iosgyres stay in the field of view on rotation BXA figures for topaz [2v=60(] and muscovite [2v =40(]

▪ The points on the isogyres closest to the center of a BXA (or BXO), the melatopes are points corresponding to the orientations of the optic axes

▪ If the crystal retardation is great, isochromes circle the melatopes

[pic]

▪ Interference colors increase in order, moving away from the melatopes because retardation is greater as the angle to the optic axis increases

Optic Axis Figure – Maximum curvature of isogyre can also be used to estimate 2V angle

[pic] [pic]

OBTUSE BISECTRIC FIGURE (BXO)

▪ The isogyres in a BXO figure always leave the field of view on rotation because, by definition, an obtuse angle separates the optic axis in the BXO direction

[pic]

▪ If isogyres remain on rotation=BXA

▪ If not = either a BXA with 2V >60( or BXO

▪ Perfectly centered BXO or BXA are rare. It may be possible to see only one isogyre clearly

DETERMINIG OPTIC SIGN FROM A BXA

= does the BXA correspond to fast direction (-) or slow direction (+)?

▪ Need a useful for BXA when isogyres remain in field of view

[pic]

[pic]

Or

Find a grain with a centered optic axis figure (OA)

▪ Amount of curvature =2V

▪ More curvature = lower 2V

[pic]

DETERMINIG OPTIC SIGN FROM A BXO

[pic]

[pic]

OPTIC NORMAL FIGURE

▪ Looking down Y axis, perpendicular to plane with 2 optic axis

▪ Grain with maximum retardation poorly resolved BXA, but isogyres leave the field of view with only slight rotation.

▪ Appear similar to the uniaxial flash figures.

EXTINCTION ANGLES

– Uniaxial Minerals - Biaxial Minerals

[pic]

Uniaxial - Sign of Elongation

[pic]

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