Optical properties of Minerals under Cross Polarized Light (CPL)

The CPL arrangement of the microscope is withe analyzer in the "In" position. The optical properties that can be observed under this arrangement are as follows,

1.  Isotropic and Anisotropic Minerals
All minerals are either Isotropic or Anisotropic. Isotropic minerals are the minerals that do not show any colour under the CPL arrangement whatsoever. These minerals appear dark. Isotropic minerals are the minerals that are very symmetric and usually belong to the cubic crystal system. Examples include Garnet and Spinel. (Garnet having pink as its optic colour turns dark when the analyzer is in. This property is used to identify garnet).
Anisotropic minerals are the minerals that show colours under the CPL arrangement. These colours are known as interference Colours. Anisotropic minerals belong to crystal systems having lower crystal symmetry. (Systems other than Cubic)

2.  Extinction Position and Angle.
Extinction position is a position reached when the microscope stage is rotated under the CPL arrangement and no colours are seen (dark positions). All Anisotropic minerals have extinction positions. All minerals show 4 extinction positions in a single rotation (90 degrees apart). At he extinction position the vibration directions of the mineral are parallel to the planes of polarization of the polarizer and the analyzer. Therefore no light reaches the eyepiece thereby giving the dark extinction position.

The extinction angle is the angle between one of the cross-hairs and the lines of cleavage of the mineral at the extinction position.

3.  Interference Colours
The colours that anisotropic minerals show under the CPL arrangement are known as Interference Colours. The maximum intensity of these colours are seen in between two extinction positions. (at 45 degree positions).

4.  Birefringence
Birefringence is the difference between the maximum and minimum Refractive index value shown by a mineral. The interference colours shown by a mineral depend on its birefringence and therefore birefringence is very useful in mineral identification.

5.  Optic Sign
Double refraction of all anisotropic minerals results in them having two refractive indices RIO and RIE. According to these values, The Optic sign is determined as follows.
RIO  >  RIE.  -  Negative (-)
RIO  <  RIE.  -  Positive (+)

6.  Interference Figures
Interference figures are important optical properties that are used in the identification of minerals, as well as to determine other properties of minerals such as,
-  Optic Sign
-  Whether a mineral is Uniaxial or Biaxial
-  2V angle of a mineral (2V angle is the angle between the two optic axes of a mineral)
Interference figures are observed under the Conoscopic Arrangement of the microscope. The thin sections have to be specifically prepared in order to observe Interference figures.

The Becke Line Method

Becke line is a band of light seen along the mineral grain boundary under the PPL arrangement when the microscope is slightly out of focus. Depending on the way the microscope is focused, the Becke line may lie within or outside the grain boundary.

The Becke line method is used to determine the relative refractive indices of two minerals. This is performed by lowering the microscope stage or increasing the focal distance (increasing the distance between the section and the objective). When this is done the Becke line will appear to move towards the material with the higher refractive index. This method is used to compare the refractive indices of two minerals or to compare the mineral with a medium with known refractive index such as Canada Balsam or Epoxy glue.

Conoscopic arrangement of the Petrological Microscope

Observing interference figures of minerals is done under the Conoscopic view of the petrological microscope. The conoscopic arrangement is set up as follows,

1.  The medium or low power objective is selected and selected grain is brought to the centre of the cross-hairs.

2.  The light intensity is increased by using the concave mirror or the intensity controller of the electric bulb.

3.  The objective is now changed to high power and brought very close to the the thin section (almost touching it).

4.  The analyzer is put to the "IN" position.

5.  The Bertrand Lens is also put to the "IN" position. (This will make the viewing scope small)

Optic Axes of a Mineral

When double refraction is observed using a calcite crystal and when its rotated and tilted at one point the two images (the Ordinary image and the Extraordinary image) coincide and appears as one image. This direction in which no double refraction can be observed is the Optic Axis direction. While some minerals have only a single optical axis while others have two optic axes. Minerals are thus classified as follows
1.  Uniaxial Minerals - one optic axis
2.  Biaxial Minerals - two optic axes
Minerals that belong to the tetragonal and hexagonal crystal systems are uniaxial while minerals that belong to monoclinic, triclinic and orthorhombic crystal systems are biaxial.
eg.  quartz, calcite - hexagonal - uniaxial   pyroxene - orthorhombic and monoclinic - biaxial
 

Double Refraction in Minerals

Double refraction is the splitting of a single ray of light into two refracted rays when passing through an anisotropic mineral. All anisotropic minerals exhibit double refraction.
Double refraction can be practically observed by placing a transparent Calcite (Iceland spar) crystal on a sheet of paper with a black dot on it. When the dot is viewed through the crystal, two dots are seen. Also when the crystal is either rotated or tilted one of those images moves while the other remains stationary. This implies that the mineral has two refractive indices, one constant and one that varies with direction. The fixed image is called the "Ordinary image" and the moving image is called the "Extraordinary image". Similarly the rays that produce the images are also named "O-ray" and "E-ray". The Refractive indices are also identified as RIO and RIE. The relative magnitudes of RIO and RIE determine the Optic Sign of the mineral.

calcite crystal showing double refraction. image from : wikipedia

Isotropic and Anisotropic Minerals under the CPL arrangement

In the CPL arrangement of the petrological microscope, Isotropic minerals do not show any colour while anisotropic minerals show interference colours.
Isotropic minerals have high symmetry and therefore as shown in the diagram below does not alter the plane of vibartions of light that comes from the polarizer. When this light reaches the analyzer, it cannot pass through because the plane of polarization of the analyzer is perpendicular to that of the polarizer. Therefore no light moves through to the eyepiece resulting in the mineral becoming dark.

Anisotropic minerals have low symmetry and therefore alters the plane of vibration of light that passes through it. Therefore when this "altered" light reaches the analyzer, the light that has the same vibration direction as the analyzer passes through to the eyepiece. Therefore colours are seen in this case.

Birefringence

Anisotropic minerals have a range of Refractive index values at different directions. Out of these values, the Maximum RI value and the minimum RI value can be observed. The difference between the maximum and minimum values is defined as "Birefringence". The interference colours shown by a mineral depends on its birefringence. Thus based on the birefringence, all interference colours are put into a scale known as "Newton's scale of interference colours".
Anisotropic minerals are classified according to their birefringence values as,
0-0.018 - low birefringence - gives colours of high order in the scale
0.018-0.036 - moderate birefringence
0.036-0.055 - high birefringence
0.055< - very high birefringence - gives colours of high order in the scale.

birefringence chart

Note that as birefringence increases, the colours in the chart repeat but the shades become pale.

It should also be noted that when the thickness of the section of the same mineral is increased, its birefringence also increases producing the above colour scale. Therefore the above scale can also be produced with a single mineral of varying section thickness.

Optical properties of Minerals under Plane Polarized Light (PPL)

The PPL arrangement of the Petrological microscope is with the Analyzer in the "out" position. The optical properties that can be seen under this arrangement are as follows,

1.  Optic Colour
This is the colour of the mineral as seen through the microscope. Often the optic colour is different to the physical colour of the mineral.
eg.  Feldspar - Colourless,  Quartz - Colourless,  Biotite - Brown,  Hornblende - Green/Yellow,  Alamandine Garnet - Pale pink

2.  Pleochroism
The change in optic colour or colour intensity when observed under the PPL arrangement while rotating the microscope stage is known as Pleochroism. This occurs when the absorption of light varies with the direction of   observation.
eg.  Feldspar, Quartz - No pleochroism  Biotite - Strongly pleocroid (yellow to dark brown)  Hypersthene - Strongly pleochroid (pink to green)  Hornblende - Moderately pleochroid (yellow to green)  Garnet - Weakly pleochroid (pale pink to pink)

3.  Relief
The effect of the mineral grain standing out with respect to the surrounding minerals or medium when viewed under the PPL arrangement is known as Relief. The relief depends on the difference between the Refractive Index of the mineral and that of the surrounding medium. If the refractive index is high with respect to the surrounding medium, so is the relief. Relief is categorized as High, Moderate and Low.

4.  Twinkling
The change in relief observed when the microscope stage is rotated is known as Twinkling. The reason for this is the variation of the refractive index of the mineral with the direction observed. Only certain minerals exhibit twinkling.
eg.  Calcite

5.  Cleavage
 The planes along which a mineral shows a tendency to split (planes of relative weakness) are known as cleavage planes. These planes can be observed as straight lines under the microscope. Cleavage angles help to identify the minerals.
eg.  Hornblende - 120degree cleavage sets.  Biotite - parallel cleavages  Pyroxene - 90 degree cleavage sets

6. Shape
The shape of the crystal also helps in the identification process.
eg.  Accicular(needle shaped) silimanite  Rounded grains of Garnet.

Preparing a Thin Section of a Rock

Thin sections of rocks are prepared in order to observe them in Petrological Microscopes. Thin sections are prepared by grinding rocks to a thickness of micrometers  (0.03mm) so that its features such as mineral grains, cleavages, twinning and optical properties of those minerals can be observed.

thin section of Gabbro - image from wikipedia

The procedure adopted in preparing thin sections is explained below.

1.  The sample to be sectioned and is determined and the direction of the cut is selected such that it is cut across structures such as layering, foliation, cleavages etc.

2.  A rectangular slice having a size of about 3x2x0.5 cm is cut using a diamond wheel.

3.  One surface of the slice is polished using Carborundum powder from coarse to fine varieties.

4.  The polished specimen is mounted onto a glass slide, polished side down using epoxy glue. (Care should be taken to avoid air bubbles)

5.  The other side of the rock specimen is ground and polished using carborundum powder to bring the thickness of the section to 0.03mm.

6.  The cover slip is fixed onto the polished section using Canada Balsam. (The cover slip protects the thin section)

The following diagram depicts the prepared thin section (thicknesses are exaggerated for clarity)

thin section 

This method is used for preparing thin sections of hard rocks. In order to prepare a thin section from a soft rock, first the rock must be strengthened using a glue, and the same procedure must be followed.

Sand grains can be directly mounted on Canada Balsam and polished if necessary before covering with a cover slide. This method is used to observe the interior of individual grains of sand.

Parts of a Petrological Microscope

A Petrological Microscope also called a Polarizing Microscope is an essential instrument in optical mineralogy and Petrology. It is used to observe thin sections of rocks under polarized light and to identify their physical and optical properties. The microscope is widely used to identify and classify rocks and minerals. Given below is a schematic diagram of a petrological microscope and its parts.

parts of  a petrological microscope

The function of each part are as follows,

Light Source - Provides light into the microscope for viewing. Usually an electric bulb or a two sided(plane and concave) mirror.

Polarizing unit 1 - This converts normal light into plane polarized light and is situated below the microscope stage.

Condenser System - This removes the effects of interference of light by changing the phase of light.

Diaphragm Lever - This lever is used to control the intensity of light.

Microscope Stage - This is a graduated, rotatable disk on which the thin sections are mounted for viewing purposes.

Objective - This contains several objective lenses of different magnifying power that can be selected. These lenses are of usually of three types. Low power objectives(3.5x) that provide a large coverage of the thin section where the micro-structures and grain percentages can be observed, Medium power objectives(10x) that shows several grains in considerable detail and can be used for identification purposes, and High power objectives(40x-50x) that show a single grain in very fine detail and used for advanced analysis.

Slot - the slot is used to insert accessory plates for different viewing purposes.

Analyzer (polarizing unit 2) - This is also a light polarizing unit. However the plane of polarization is perpendicular to that of the polarizing unit that is situated below the microscope stage. This can be set in either "in" or "out" positions.

Bertrand lens - This is a special lens system that is used to observe interference figures. This too can be ste in either "in or "out" positions. When the Bertrand lens is in the "in" position, the view seen from the eyepiece is smaller.

Eye piece - This is the lens through which the observer views the thin section. It has a circular view with centre cross-hairs to help viewing.

The petrological microscope can be set up in two arrangements depending on viewing purposes and optical properties of the minerals. They are,
1.  PPL arrangement (Plane Polarized Light) - analyzer is out, Bertrand lens is out
2.  CPL arrangement (Cross Polarized Light) - analyzer is in Bertrand lens is out.