introduction to optical mineralogy

Gabi (Gelu) Costin

- 2011 -

Introduction to Optical Mineralogy

GLC 201 - Introduction to Optical Mineralogy

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Contents

INTRODUCTION _________________________________________________________________ 4

Recommended textbooks, websites; pracs, tests & exam info ______________________________ 5

Objectives of the course_____________________________________________________________ 5

1. WHAT IS LIGHT? ______________________________________________________________ 6

1.1. Light as a wave ........................................................................................................................ 6

1.2. Light as particle ....................................................................................................................... 7

1.3. Polarized light .......................................................................................................................... 7

2. ISOTROPIC AND ANISOTROPIC MATERIALS ____________________________________ 8

3. INTERACTION BETWEEN LIGHT AND MINERAL ________________________________ 9

3.1. Reflected light .......................................................................................................................... 9

3.2. Absorbed light ....................................................................................................................... 10

3.3. Refracted light ....................................................................................................................... 11 3.3.1. Refractive index ............................................................................................................................. 11 3.3.2. Important things to know about the refraction taking place in minerals ............................................ 12

3.4. Transmitted light ................................................................................................................... 14 3.4.1. Thin section for optical studies in transmitted light.......................................................................... 14

4. VECTORIAL AND CONTINUOUS CHARACTER OF REFRACTION ________________ 15

4.1. Indicatrix ............................................................................................................................... 15

4.2. Interference colours (IF); birefringence (δ) .......................................................................... 17

5. PETROGRAPHIC MICROSCOPE _______________________________________________ 21

6. MINERAL IDENTIFICATION USING THE PETROGRAPHIC MICROSCOPE ________ 23

6.1. Orthoscopic study .................................................................................................................. 23

6.1.1. Observations using plane polarized light (PPL) mode ______________________________ 23

a) Transparency ........................................................................................................................... 23

b) Shape, habit, size ...................................................................................................................... 23

c) Cleavage ................................................................................................................................... 25

d) Colour (absorption colour) ...................................................................................................... 28

e) Pleochroism .............................................................................................................................. 28

f) Relief ......................................................................................................................................... 28 Becke line; Becke method for estimating the relief .................................................................................... 29 Twinkling (relief changing) ...................................................................................................................... 30 Chagrin (roughness in appearance of the mineral surfaces)...................................................................... 30

g) Inclusions, alterations .............................................................................................................. 31

6.1.2. Observations using crossed polarized light (XPL) mode ____________________________ 32

a) Isotropy/anisotropy .................................................................................................................. 32

b) Extinction angle ....................................................................................................................... 32 Determination of the extinction angle ....................................................................................................... 32

c) Birefringence ............................................................................................................................ 34 Colour of interference (colours of birefringence) ...................................................................................... 34 Finding the value of birefringence (δ)....................................................................................................... 35


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d) Twinning/zoning ...................................................................................................................... 36 Twinning ................................................................................................................................................. 36 Zoning (compositional zoning) ................................................................................................................. 37

e) Orientation of nγ and nα ........................................................................................................... 38

f) Optical elongation ..................................................................................................................... 40

6.2. Conoscopic mode ................................................................................................................... 40 6.2.1. Interference Figures ........................................................................................................................ 41 Interference figure for uniaxial crystals .................................................................................................... 41 Interference figure for biaxial crystals ...................................................................................................... 41

Determination of the optic sign .................................................................................................... 42

Estimation of the 2V angle ........................................................................................................... 44

Useful charts for mineral identification: the Tröger Chart _______________________________ 46

27 Key minerals species ____________________________________________________________ 47

Key Characteristics of common minerals: Speeding up mineral identification_______________ 48

A few hints for the relation chemical composition - optical properties _____________________ 48

Tips for discriminate between different mineral groups _________________________________ 49

Mineral association: helpful in identifying minerals ____________________________________ 49

Mineral Identification – A Beginner’s Guide __________________________________________ 50

Identification Tables for Common Minerals in Thin Section _____________________________ 53

Tables for Common Minerals in Thin Section _________________________________________ 54


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INTRODUCTION

Why study minerals/crystal optics?

1) They assist in the identification of minerals – study their optical properties under the

microscope.

• Minerals are inorganic chemical compounds having a certain lattice shape, size and

symmetry, being a result of the geometrical arrangement of the constituents (chemical

elements such as Si, Al, O, etc).

• Lattice (symmetry) + chemistry (nature of the chemical elements of the lattice)

combine to make a unique mineral phase. The lattice (internal symmetry) of the mineral

is reflected not only in the symmetry of the external crystal shape but also in the

symmetry of optical properties of the mineral; therefore, determining the optical

properties of an unknown phase assists in identifying the mineral phase;

• Mineral identification is needed in petrological studies, structural geology, mineral

exploration etc…

2) Microscopic study is the cheapest and fastest method for identifying minerals; however, there

are limitations to the optical method, such as constraints of very small size (sub-

microscopic) of minerals, or complex solid solutions, etc.

3) Microscopic study is required for textural (natural arrangements of minerals) analysis; it is

useful in determining the rock type, the crystallization sequence, deformation history or

observing frozen-in reactions, constraining pressure-temperature history, noting

weathering/alteration, etc.

4) Because the principles of light refraction and reflection are also relevant to seismicity

(geophysics and geological exploration), water behaviour (groundwater management),

and even to real life!

Remember that minerals have an ordered internal lattice (with an internal symmetry) which is also

reflected in the external shape of the crystals. Therefore, it is expected that the optical properties of

minerals somehow demonstrate this internal symmetry. In order to “see” the symmetry of the optical

properties, and to determine the symmetry of a mineral, we need to understand:

a) What light is, and especially polarized light;

b) The difference between isotropic and anisotropic media (optical and other properties of minerals

can be isotropic and anisotropic);

c) The concept of vectorial and continuous properties;

d) The tool of studying the optical properties of minerals (the petrographic microscope);

e) The use of specific charts of physical properties in order to identify unknown minerals;

f) A few specific optical properties which can help in quick identification of the common rock-

forming minerals.

This handout represents a compilation realized by Dr. Gelu Costin from different resources:

previous versions of power-point presentations and notes: Dr. Steffen Bütner, Dr. Stephen

Prevec. Dr. Emese Bordy, Prof. Goonie Marsh

internet resources

several text explanations and some figures were added by Dr. Gelu Costin


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Recommended textbooks, websites; pracs, tests & exam info

A) Recommended TEXT BOOKS and WEBSITES

1) Perkins, D. & Henke, K.R. (2004): Minerals in Thin Section. Prentice Hall.

2) Deer, Howie & Zussman (1992): Introduction to rock forming minerals

3) Heinrich (1965): Microscopic identification of minerals

On short loan:

Bloss, F. D.: Optical crystallography 548.9 BLO

Shelley, D.: Optical mineralogy 549.125 SHE

Others:

Gribble, C.D. & Hall, A.J.: Optical mineralogy: principles and practice

Battey, M.H. & Pring, A.: Mineralogy for students

B) Lectures & Pracs

* All material presented in the lectures is relevant for the pracs. Polarisation Microscopy is a method used in:

1. 201 Mineralogy/Geochemistry

2. 201 Introductory Igneous Petrology

3. 202 Sedimentology

4. 202 Igneous Petrology

5. 301 Structural Geology

6. 301 Metamorphic Petrology

7. 302 Economic Geology

8. Almost all modules on Honours level

9. More or less all studies on Masters/PhD level and beyond

1. Optical properties of some common mineral species on the Web: http://www.brocku.ca/earthsciences/people/gfinn/minerals/database.htm

http://funnel.sfsu.edu/courses/geol426/Handouts/mintable.pdf

http://www.geolab.unc.edu/Petunia/IgMetAtlas/mainmenu.html

http://sorrel.humboldt.edu/~jdl1/minerals.list.html

http://geology.about.com/od/thinsections/Thin_Sections.htm

2. More or less everything about minerals:

http://webmineral.com/determin.shtml

3. More thin section photos + optical properties

http://www.und.nodak.edu/instruct/mineral/320petrology/opticalmin/

4. First aid for conoscopy problems

http://users.skynet.be/jm-derochette/conoscopy.htm

C) Tests & Exams

No formal 45 min theory test

Instead: daily quickies (5 minute tests)

Thin section microscopy work can be expected as main part of the GLG 201/202 Prac Exam

Objectives of the course

understanding the behaviour of minerals under transmitted polarized light

understanding and practicing the determination of optical properties of crystalline solids

identification of unknown minerals using optical property determinations and catalogues of

physical properties

rapid identification of common minerals in thin section

http://www.brocku.ca/earthsciences/people/gfinn/minerals/database.htm

http://funnel.sfsu.edu/courses/geol426/Handouts/mintable.pdf

http://www.geolab.unc.edu/Petunia/IgMetAtlas/mainmenu.html

http://sorrel.humboldt.edu/~jdl1/minerals.list.html

http://geology.about.com/od/thinsections/Thin_Sections.htm

http://webmineral.com/determin.shtml

http://www.und.nodak.edu/instruct/mineral/320petrology/opticalmin/

http://users.skynet.be/jm-derochette/conoscopy.htm


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1. WHAT IS LIGHT?

Light may be seen as electromagnetic waves and/or as particles (quantum theory).

1.1. Light as a wave

A wave* (Fig. 1) can be characterized by four parameters**: wavelength, frequency, velocity and

intensity.

* any kind of wave (e.g. optical, mechanical, thermal, acoustic, seismic etc) can be characterized by

these above-mentioned parameters

**a parameter is a physical property which can be measured

a) wavelength (λ - lambda): distance between two neighbouring points experiencing vibrations of

the same amount and in the same direction. Such points are said to be in phase. The wavelength is

important in optical mineralogy, since it is this that affects our perception of colour. (coherent light =

in phase, incoherent = not in phase).

Figure1. Graphical representation of light. λ = wavelength.

a= amplitude (related to ε = intensity or energy of the wave).

Visible (white) or polychromatic light (Fig. 2) with wavelengths between 390 and 780nm (nano

meter = 10-9

m = 1 billionth of a meter) is a small part of the electromagnetic spectrum which

includes gamma- and X-rays, ultraviolet as well as infrared light, radio- and micro-waves. Sunlight

contains the entire visible spectrum plus ultraviolet light and infrared light as well.

Visible light includes 7 monochromatic lights which correspond to the 7 primary colours of the

rainbow (as recognised by Sir Isaac Newton): violet, indigo, blue, green, yellow, orange, red.

Figure 2. Colours of the visible spectrum with their corresponding wavelength (in black and white).

The wavelength range of the colors from the visible spectrum are:

Violet: 390 - 420 nm

Indigo: 420 - 440 nm

Blue: 440 - 490 nm

Green: 490 - 570 nm

Yellow: 570 - 585 nm

Orange: 585 - 620 nm

Red: 620 - 780 nm


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b) Frequency (η - nu): number of wavelengths passing a fixed point in 1 second; “pulse rate”

c) Velocity (c) is related to frequency (η) and wavelength (λ) by: c = ηλ

The velocity of light in a vacuum is higher than in any other substance (2.99773 x 108 m/s);

(Slowing down waves = shortening their wavelength)

d) Intensity (ε = the amplitude of the wave). The amplitude of the wave is related to the energy

(the “higher” wave has more energy). The wave energy of light is given by the moving photons and

therefore, the amplitude (intensity) of the wave makes the connection between wave and particle

nature of light.

1.2. Light as particle

Light is interacting with the electric fields produced by the nuclei and electrons of atoms it will

slow down light passing through them the more atoms and/or e- that are in a given volume the

more the light rays will decelerate. Density of atoms in the mineral lattice and number of e- per atom

in the material are important (note that the number of e- per atom is directly dependent on the atomic

number of the element -see the Periodic Table of the Elements). As the atomic number is higher, the

mass of the element is higher, and consequently the mass of the compound made by the heavy

elements will be higher. Since density = mass/volume, this also reduces to considering density as the

main factor in slowing down the light speed within materials.

1.3. Polarized light

Natural light vibrates (oscillates) in all the directions perpendicular to the direction of propagation

(fig. 3). Therefore we can say that there is infinity of planes of vibrations (all possible planes that

intersects/contain the direction of propagation.

Figure 3: Propagation and vibration of natural light; note vibration in all directions perpendicular to

the direction of propagation (all vibration directions are perpendicular on the propagation line).

Plane polarized light (PPL) has one single plane of vibration, in which the direction of vibration is

always perpendicular to the direction of propagation (fig. 4). We can use this plane of vibration as a

geometrical reference for the optical properties of mineral. Keeping this plane fixed and rotating

(changing the orientation of) the mineral, all of the mineral‟s optical properties can be measured or

related to such a plane. Note that we can polarize light with a special designed material, called a

nicol or polarizer. The name “nicol” comes from Nicol (Nicol‟ prism), a French scientist who first

built a kind of prism of calcite, made of two halves of the same calcite crystal, adjusting the angles

of the prism to a convenient value in order to eliminate all other planes of vibration but one. More

commonly, these days, materials called polaroids are used for manufacturing polarisers (microscopic

oriented crystals of iodoquinine sulphate embedded in a nytrocelulose polymer film).

Note that the polariser does not absorb light (or the absorption is negligible), so it does not affect the

observed colour of the mineral (fig. 5a). See the difference between a polariser and a colour filter

(fig. 5b).

Direction of propagation


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Figure 4: Polarized light (plan polarized light -PPL)

Figure 5: a) Polariser: the light exiting from the polariser has one single plane of

vibration; The intensity of the light (amplitude of wave) is not affected; b)

colour filter: the intensity of polarised light entering the filter is attenuated

(some energy of the light was absorbed and the out light will be coloured but

still polarised). The amplitude of the wave will therefore decrease.

In order to relate the optical properties of a mineral to a particular symmetry, we need to find an

external optical-geometrical element (such as a reference plane – e.g. plane of polarization of the

incident light) and to relate to it all the optical properties that we want to consider for a mineral.

2. ISOTROPIC AND ANISOTROPIC MATERIALS

Isotropic (in a general sense) means that any physical property of the material is the same at any

point and in any direction through the material (it is independent of orientation). Concerning mineral

optics, the word “isotropic” refers to the optical properties of the mineral, which are the same and

independent of the orientation (e.g. isotropic minerals). However, if a mineral is isotropic, it means

that ALL of its physical properties are the same at any point. Minerals that are isotropic are the

minerals with cubic symmetry (remember the symmetry of minerals crystallized in the cubic system

have a=b=c and α=β=γ=90°), and materials that do not have a geometrical arrangement of the atoms,

so they do not have an internal lattice (e.g. non-crystalline materials), such as glass, liquids, and

gasses. Accordingly, an isotropic mineral has the same refractive index, the same absorption of light

(and the same for any other physical property) at any point and for any direction in the mineral.

Anisotropic (in a general sense) means that the properties of the material are not the same at all

points or directions, but may vary continuously with changing direction (orientation) of observation

(all minerals other than cubic are anisotropic). Examples of anisotropic behaviour when changing

orientation include different absorption of light, different refractive indexes, etc.

Anisotropic crystals have variable refractive indices because light travelling through the crystals will

do so at different speeds, depending on the direction of travel (the orientation of the crystal to the

incident light).

Plane of vibration

Direction of propagation

Direction of vibration

a)


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All minerals, other than those belonging to the isometric system, are anisotropic. But some of them

are “more anisotropic” than others, and the isotropy-anisotropy is related to the symmetry of

crystals. For example, all minerals can be grouped based on their symmetry according to 7 systems

of symmetry, and beyond that, we can subgroup the symmetry according to the presence or absence

of high order fold axes (A3, A4, A6):

-minerals with superior symmetry (cubic or isometric system: a=b=c and α=β=γ=90°); several high

order fold axes are present: 3 A4 or 3Ai4 and 4 A3.

-minerals with medium symmetry (trigonal, tetragonal and hexagonal systems); all of them have

one main axis of symmetry, only: A3, A4 or A6, respectively.

-minerals having inferior symmetry (orthorhombic, monoclinic and triclinic); no high order axis is

present (no fold axis superior to A2); among these, the symmetry decreases as the number of

A2 axes decreases: orthorhombic: maximum 3 A2; monoclinic: maximum 1 A2; triclinic has

the lowest symmetry, with no A2 axis.

3. INTERACTION BETWEEN LIGHT AND MINERAL

As light intersects an isotropic material (let‟s say glass or an isotropic mineral, such as garnet), the

light suffers several optical phenomena, and is decomposed into several components. The intensity

(or the energy) of the incident light splits up accordingly (Fig. 6):

a) Some fraction of the incident light is reflected by the surface of the mineral. The intensity

of the reflected light is (εrl)

b) Another component of light entering the mineral is refracted (εr): this refracted light is

plane polarized!!

c) a variable component of the light that enters the mineral is absorbed (εa)

d) The remaining light (intensity), if any, succeeds in escaping from/through the mineral

grain. This light is called transmitted light (εt); the transmitted light is also polarized by

the mineral (the mineral acts like a complex polarizer).

Thinking in terms of energies (or intensities), the budget of the initial incident light is:

εi = εrl + εr + εa + εt

3.1. Reflected light

The reflection depends on the surface properties of the mineral but also on its nature (some minerals

reflects more light than others). The strongly reflective minerals are those which reflect all (or

almost all) of the incident light and no other light component is able to cross through and exit the

mineral (no transmitted light). This means that the mineral is opaque to light. We can define

reflectivity (or reflectance) as the fraction of incident light (in terms of energy or intensity) which is

reflected from a surface. Reflectivity is therefore proportional to the intensity of the light reflected

by the mineral. The reflectivity index (R) is the ratio between reflected light intensity versus incident

light intensity (R= εrl/εi), a ratio which is lower than 1. However,typically R is expressed in

percentages; R= εrl/εi x 100 %. In order to study opaque minerals we need to analyze the light

reflected by the mineral (we need therefore to polish one surface of the mineral as well as possible in

order to get the best reflectivity). The opaque minerals are studied with the chalcographic (reflected


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light) microscopes (you will learn to use chalcographic microscopes another time, not within this

term).

Common experience (such as mirror imaging) tells us that the angle of incidence is equal to the

angle of reflection. However, at a certain incident angle, the incident ray is refracted at 90 ; this is

termed total reflection. The incident angle at which total reflection occurs is called the critical angle

(θi-cr).Total reflection is used to determine the refractive index of an unknown material:

θr = 90, nair ~ 1

ni sinθi-cr = nair sinθr sin θi-cr= 1 / ni

Figure 6: Light intensities splitting out at the interface of light with the mineral. Notice

the difference between the incidence angle (θi) and the refraction angle (θr). When

exiting the mineral, the (transmitted) light will resume propagation at the original

θi angle to the surface.

3.2. Absorbed light

One fraction of the light that enters the mineral is absorbed. This absorption is responsible for the

colours of materials that we see around us. How does it work? Inspired by the colours of the

rainbow, Newton decomposed the natural light into its components using an optical prism. Looking

at figure 2, we see that several colours can be distinguished in the visible spectrum (wavelengths

between ~400 nm (violet) to ~800 nm (red). All of them are the components of the yellow light. If

all the coloured lights from the visible spectrum are combined, we get a wave with an approximate

average value of wavelength λ~(400+800)/2~600 nm (the real value is 575 nm). This is the

wavelength of the yellow light (or natural light from the sun). It means that the yellow light contains

a combination of waves that include all the wavelengths from the visible spectrum.

incident light (εi) reflected light (εrl)

used by

CHALCOGRAPHIC

MICROSCOPE

absorbed light (εa)

transmitted light (εt) used by PETROGRAPHIC

MICROSCOPE

Plane perpendicular on the mineral surface

(and on the boundary) between air and mineral)

AIR

AIR

θr

θi

nair nm

θi

εo εe

refracted light (εr=εo+εe)

Isotropic MINERAL (or gass)


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When an incident yellow light (natural light from the window or the light emitted by a lamp) enters a

material, some of the wavelength components can be absorbed by the material (the electromagnetic

components of certain wavelengths of the incident light are consumed/combined into the

electromagnetic field produced by the atoms and molecules of the material or we can understand this

as the energy of the incident photons which is transferred to the electrons of the material, making

them moving faster; the result of this absorption of energy is heat). The interaction of the light with

the discrete nature of material is more complicated. For example, the transfer of energy from

incident photons to the electrons of the material can produce not only increasing vibration of the

molecules, but, if intensity of the incident photons is high enough, they can displace some electrons

from their position (moving one e- from an orbital to another). This happens with X-ray emission

(other photons vibrating with wavelengths in the X-ray spectrum (see fig. 2). The combination of the

remaining wavelength components which were not absorbed gives the colour of the material that we

observe. In other words, the colours that we observe around us are produced by selective absorption

of light by different objects, and the selectivity of absorption depends on the composition of the

material. If a material absorbs all the (visible) wavelengths in (proportionally) the same amount, the

material will be colourless. If the material absorbs more from the lower visible spectrum (violet,

blue), the colour of the material would be a combination of the remaining wavelengths from yellow

to red (the observable colour would then be orange). If a material does not absorb any components of

light at all, it would be… invisible. Well, this is not yet possible since the electromagnetic radiation

will interact with the atoms and electrons of the material, so at least some absorption has to take

place.

The wavelengths of the reflected light also affect the appearance of colour. Note that the thickness of

the medium can affect the eyes‟ interpretation of colour. Hence, many minerals which we are

accustomed to seeing as coloured are colourless in thin section (for example, the various coloured

varieties of quartz, such as amethyst).

3.3. Refracted light

A component of the non-reflected light is refracted into the mineral. Refraction is a fundamental

optical property of any medium which transmits light.

3.3.1. Refractive index

Refractive Index (R.I. or n) is a measure of refraction. The refractive index (n) is the ratio between

the velocity of light in vacuum (cv) and the velocity of light in the material (cm):

n = cv / cm In optical mineralogy we can‟t actually measure the speed of light, but we can utilise this ratio of the

speed of light in a mineral related to the speed in a vacuum. Since the speed of light in a vacuum, cv,

is the maximum possible speed of light, the refractive index will be always greater than 1.

Sometimes R.I. is defined as the ratio of “the velocity of light in air / the velocity of light in a

medium” (i.e., any physical material other than air, as distinct from “a person who talks to ghosts”),

as there is little difference for purposes of optical mineralogy (cvacuum almost = cair nvacuum= 1; nair

= 1.0003; nwater = 1.33). As we can see even from the above example, c depends largely on the

density of the material. The higher the density is, the more difficult it is for light to travel within

the material, so it gets slowed down. Since the cm is at the denominator in the definition of n, it

means that n is higher when cm is lower (therefore, when the density of the material is higher).

Accordingly, common sense tells as that nsolid > nliquid > nair.


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The direct optical effect of observing refraction is that, looking at an object

through a non-opaque material (liquid or solid), the margin of the object is

observed as “displaced or moved” if you look at it from the side (i.e., away

from the axis perpendicular to the material surface). The apparent

“displacement” is higher when the angle is higher and when the refractive

index of the material (or rather, the contrast in refractive indices) is higher.

For example, if you see a fish in the river and want to touch it, be sure that

you are exactly above him (and not laterally positioned) because otherwise

what you see is not actually there where you see it, it is a “displaced”

image of the fish produced by the difference in the refractive indices of air

and water. The “displaced” imaged is due to the refraction angle which is always different from the

incidence angle (see fig. 6). If you see a fish while looking through your petrographic microscope,

it‟s probably time to take a rest.

The angle of refraction (θr = angle of deviation from the incident direction) always depends on the

refractive index (n). As nm gets higher, the angle of refraction will also get higher (as the light is

“deflected” inside of the material). Therefore, given that n is related to cm, instead of measuring the

velocity of light in the material (which is not an easy task), we can measure the angle of refraction

and find the cm and n. Using Snell’s Law we have:

nair sinθi = nm sinθr

After measuring θi and θr, then:

nm = nair x sinθi / sin θr

The same is proceed for any two environments with different refractive indexes, ni and nr.

If ni < nr, light is going to be deflected towards the plane normal (┴) to the boundary on entering the

refracting medium. If ni > nr, light is going to be deflected away from the plane normal (┴) to the

boundary.

Note: if two materials in contact with one another have identical refractive indices, the optical

boundary (meaning the sharpness of the boundary, and not, for example, a colour difference)

between them is not observable. As the difference between the two refractive indexes gets greater,

the boundary between the two materials is sharper and appears to get “thicker”.

3.3.2. Important things to know about the refraction taking place in minerals

1. The light which enters the mineral is refracted (slowed down) according to the density of the

mineral (so also therefore according to the refractive index).

2. Light entering an isotropic media (glass or cubic minerals) produces a double refraction, such that

the incident light is separated into two components, or rays. Both of the rays are polarized. One ray

continues in the direction of incidence, and it is called the ordinary ray (εo); the other ray is

refracted, and it is called the extraordinary ray (εe). These rays display a special characteristic: the

polarization plane of the ordinary ray is always perpendicular to the polarization plane of the

extraordinary ray (fig. 7)! This is due to the nature of any electromagnetic wave, which has a

magnetic vector perpendicular to its electric vector. Since the refractive index is the same in any

direction in an isotropic material, the two rays travel with the same speed and when they exit the

mineral, there will be no delay between them. Therefore we can say that there is no retardation (Δ).

The term “retardation” comes from the French word “retarder” meaning “to delay”). Because the

retardation is zero, the isotropic materials are called “monorefringent” (because the refractive index

corresponding to the extraordinary ray is identical to the refractive index corresponding to the

ordinary ray; i.e., there is only one R.I. involved).


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Figure 7: Two plane polarized rays: the polarization planes are perpendicular to each other

3. The minerals with medium symmetry will also produce a double refraction, where the incident

light splits into an ordinary ray and an extraordinary ray, as in the isotropic media. However, since

the refractive index varies with orientation in anisotropic minerals, the extraordinary ray will also be

slowed down in comparison to the ordinary ray (Fig. 8b). In this case, the retardation (Δ) is different

from (greater than) zero. We call these minerals birefringent. The value of (Δ) should be directly

related to the difference between the refractive indices along the direction of the ordinary ray (with

the lowest refractive index, called nα) and that of the extraordinary ray (representing the highest

refractive index direction, called nγ). So, the retardation is therefore proportional to (nγ-nα), which is

known as the birefringence. The minerals with medium symmetry are called uniaxial, where the

main (A3, A4 or A6) symmetry axis of the lattice (known as the “c axis”) is always in the direction

of (i.e., parallel to) either nγ or nα.

4. The minerals of inferior symmetry produce one ordinary ray and two extraordinary rays (Fig. 8c),

all of them polarized (the three polarization planes being perpendicular to each other). Each of these

three rays corresponds to three different refractive indexes: the lowest one is nα and it corresponds to

the direction of the ordinary ray, the intermediate refractive index nβ corresponds to the least delayed

extraordinary ray, and nγ corresponds to the most delayed extraordinary ray. The minerals with

inferior symmetry are called biaxial (see explanations for the indicatrix and the optic axis). For the

orthorhombic minerals, the c, b and a axes are parallel to nγ, nβ and nα. For monoclinic crystals a

maximum of two of the crystallographic axis can be parallel to two of the nγ, nβ or nα directions. For

triclinic crystals, a maximum of one of their crystallographic axes can be parallel (or not) to any of

the nγ, nβ or nα directions (remember that for triclinic crystals the angles between the crystallographic

axis are α≠β≠γ≠90°, but nγ, nβ and nα are always mutually perpendicular).

Figure 8: Double refraction in minerals: a) in isotropic minerals or materials (nγ=nα); b) in

anisotropic uniaxial minerals (nγ>nα); c) in anisotropic biaxial minerals (nγ>nβ>nα)

O E O E O E2

E1

nα nγ=nα nα

nγ

nα

nγ nβ

a b c


14

5. If the incident light is perpendicular to the surface of the mineral, according to Snell‟s Law, the

ordinary ray should then be also perpendicular to the surface of the mineral.

3.4. Transmitted light

The light that remains after some fractions of it have been reflected or absorbed then exits the

mineral. This is called transmitted light, and it has always a lower intensity than did the original

incident light. The ordinary and extraordinary ray(s) also recombine as they emerge from the crystal,

and since these rays are polarized, their recombined product is therefore also polarized (as either two

or three planes of polarization, perpendicular one to each other). Note that since light is slowed down

when passing through a material due to the refractive index contrast, and also part of the light is

absorbed, the thickness of the medium therefore affects the transmitted light. If the material is thick,

more of the energy of the light will be absorbed, and less light will exit the material. For example, a

thin glass is transparent to light but the same glass at 10 m thickness will probably not let light pass

through it. If a material (such as a mineral) has a high refractive index compared to air, it is likely to

be transparent to light only in thin section. When it is, such as in hand specimen, the mineral will

generally not allow light to be transmitted through it (although some minerals can be translucent in

hand specimen, allowing some light through).

The transmitted light intensity is related to the absorption, so measuring the intensity (energy) of the

transmitted light allows us to calculate the absorption (providing the principles of absorption

spectroscopy, infrared spectroscopy, etc.). However, since the transmitted light intensity is also

dependent upon the mineral thickness, slices of materials (known as thin sections) should be both

thin (for enhanced light transmission) and consistently the same thickness (or thinness). By

convention, mineral thin sections are made at a standard thickness of 30 microns.

3.4.1. Thin sections for optical studies in transmitted light Minerals are the constituents of rocks, and usually a rock is composed of several mineral species. In

order to study minerals we need to cut a slice of the rock, grind and polish a flat surface of it down to

30 microns thick, and glue it, using a polymerized resin, onto a glass slide (fig. 9). The refractive

index of the resin must be known, in order to estimate correctly the (unknown) refractive indexes of

minerals in thin sections (usually resin is 1.542 if the resin is Canada Balsam, as was traditionally

used, or around 1.54-1.55 if other resins are used, such as araldite). A cover slip is usually glued on

top of the thin section (with the same resin) in order to protect the sample from „weathering‟ but also

to have the same (known) refractive index below and above the sample.

Figure 9: Profile through a thin section

The optical methods normally used do not measure the intensity of the transmitted light, but instead

use this light to provide information about the optical behaviour of minerals. The microscopes using

transmitted light are called petrographic microscopes and they are used for studying the transparent

minerals (remember that for study of the opaque minerals, which do not transmit light, we would use

the chalcographic, or reflected light, microscopes).

Cover glass (<1mm; n~1.55)

Glass slide (~2 mm; n~1.55)

Synthetic resin; a few µm; n~1.55) Sample (~30 µm; n variable / unknown)

Synthetic resin; a few µm; n~1.55)


15

4. VECTORIAL AND CONTINUOUS CHARACTER OF REFRACTION

Refraction is a vectorial, and continuous, property. A vectorial property is a property that varies with

direction (a different n is expected in any anisotropic material for each different direction of the

incident light coming through the mineral).

A continuous property is one which varies continuously and gradually (from a minimum value to a

maximum value) within the material (such as refractive index). By contrast, a non-continuous

property would abruptly change from one point to another (such as the cleavage of a mineral).

4.1. Indicatrix

We must imagine a geometrical figure which can depicts the continuous variation of a property with

a continuous variation of direction (orientation). Let‟s take the refractive index (n) as the optical

property that we want to graphically represent. First, we can attribute a vector direction to any

possible direction within the mineral. Secondly, we can attribute to each vector a value (length)

proportional to the refractive index on each direction. If we consider an infinite number of vectors

radiating from a central point within a medium, where each vector length is proportional to n, we

can imagine a geometrical figure given by the surface connecting the tips of the vectors. This

geometrical figure is called the indicatrix, and it graphically represents the variation in refractive

indices in a crystal. The indicatrix is a method of rationalising optical phenomena, and provides a

framework whereby optical phenomena of transparent media may be interpreted, remembered and

predicted.

If n has the same value in any direction, it means that all of the vectors (radiating from a point in the

mineral) would have the same length, and consequently will describe a sphere (fig. 10a). This is the

case for the isotropic minerals: the crystal has only one RI, and is optically isotropic. This applies to

the cubic minerals (garnet, spinel, sodalite etc), where all possible sections through a cubic crystal

produce a circular indicatrix section.

If n varies continuously from a minimum value (nα) to a maximum value (nγ) the indicatrix will have

the shape of an ellipsoid (fig. 10b), where the long axis is nγ and the short axis is nα. Different types

and shapes of ellipsoids (indicatrixes) can be imagined for the anisotropic minerals (fig. 10b,c).

However, two specific sections of the indicatrix are important for making the connection to the

symmetry of the mineral: a) the section that contains the maximum possible values of nγ and nα

which is called section of maximum birefringence and b) the sections with a circular shape (called

the isotropic section). The perpendicular direction on such sections is called optical axis (or

direction of monorefringence). Three main types of indicatrixes are possible (see Fig. 10a,b,c):


16

Figure 10: a) indicatrix for an isotropic mineral (nγ=nα); b) indicatrix for an anisotropic mineral (nγ>nα)

called uniaxial indicatrix; by convention, always the higher refractive index is written as nγ , the

minimum refractive index is nα; c) indicatrix for anisotropic minerals (nγ> nβ >nα), called biaxial

indicatrix; nβ is the intermediate refractive index, being the radius of the circular section (and

always perpendicular to the optical axis).

Isotropic indicatrix (any section of the

sphere is a circle; n=radius of the

circle (fig. 10a).

Uniaxial indicatrix (revolution/rotation ellipsoid).

the direction perpendicular

to circle section is called the optic

axis.

If the optic axis is parallel to

(contains) the maximum R.I.,

nγ, then it is a positive

uniaxial indicatrix (a rugby

ball shape, positioned for a

penalty kick).

If the optical axis is parallel to

(contains) the minimum R.I.,

nα, then it is a negative

uniaxial indicatrix (a rugby

ball being passed?).

Biaxial indicatrix If the bisectrix of the 2V angle

is parallel to nγ, then it is a

positive biaxial indicatrix

(imagine a flattened rugby

ball; an ellipsoid elongated

in one direction (nγ) and

flattened from a perpendicular

direction (nα);

If the bisectrix of the 2V angle

is parallel to nα, then it is a

negative biaxial indicatrix

(imagine a sphere flattened

from one direction (nβ) and

even more flattened from a

perpendicular direction (nα).

Figure 10 a)

Figure 10 b)

Figure 10 c)

Biaxial positive Biaxial negative


17

Optically positive? (slightly off-centred)

and negative

4.2. Interference colours (IF); birefringence (δ)

Interference colours are produced when the mineral is placed between two polarisers, having the

polarization planes orientated mutually perpendicular (i.e, perpendicular to one another). By

convention, the polarizer closest to the light source is called “the polarizer”, and the other one is

called “the analyzer”.

-The polarizer has a E-W privileged direction producing E-W oscillating white light waves.

-The analyser is consists of a polariser with a N-S privileged direction.

-The sample (thin section of a mineral) is in-between the polarizer and analyzer and can be

rotated to change its orientation (the nγ and nα orientation in relation to the polarization planes

of polarizer and analyzer) in a petrographic microscope.

Remember that:

-Transparent minerals are, in effect, polarisers with TWO privileged directions

-These privileged directions are ALWAYS mutually perpendicular

-Their orientation depends upon crystal lattice properties

-A polarised (E-W) light wave is split into two waves which can pass through the crystal along

its privileged directions

-The two waves pass through at different velocities, so that there is a faster wave with a lower

RI (nα) and a slower one with a higher RI (nγ)

Let us follow the behaviour of polarized light on its way from the polarizer through the sample and

on to the analyzer:

The EW-polarized white light leaves the polarizer with the normal speed of light in air (nair~1) and

hits the sample. Here (Fig. 11) the light is refracted and one ordinary (fast) ray and one extraordinary

(slow) ray (or two, if the crystal is biaxial) are created.

The vibration planes of the rays produced will always be mutual perpendicular. These polarized rays

will exit the sample with the speed of light in air and be recombined, but the extraordinary ray(s)

will have been delayed by the sample; therefore there will now be a difference in the „phase‟ of their

wavelengths, proportional to the retardation (the delay of the extraordinary –or slow) ray. This

difference in phase (also called path difference or retardation, Δ or R) is manifested as a wavelength

difference (in the range of microns to hundred of microns).


18

Figure 11: Maximum interference colours obtained at 45° between nγ or/and nα and the N-S (and E-W)

polarization planes.

When hitting the analyzer, the mutually perpendicular rays coming from the sample will arrive at the

N-S “gate” of the analyzer. What will be the outcome? It will depend on the orientation of the

sample and its crystal lattice (and hence the orientation of the mutual perpendicular rays coming

from the sample). If nγ or nα comes out along the N-S plane (or the W-E plane, since nγ and nα are

mutually perpendicular), the two rays will be eliminated by the analyzer, such that the nγ and nα of

the sample will be compensated by the nγ and nα of the analyzer (Fig. 12, right). The result will be a

dark image (black or dark gray). This situation (or orientation) is called extinction (as the light has

become switched off; “extinct” comes from Latin extinct meaning „switched off, terminated,

ended‟).

Figure 12: Amplification (giving the increase of the intensity,) and

extinction (mutually compensation/annihilation of the intensity of the

light).

When the stage is rotated from this position, the grain will start to increase its light intensity and

become coloured. The colours are the result of interference (adding and/or subtracting wavelengths)

between the nγ or nα rays of the sample, which are forced to pass through the N-S plane only. The

AAmmpplliiffiiccaattiioonn EExxttiinnccttiioonn

W3 =0

E-W oscillation white light leaves the polariser

with normal speed of light (n=1)

The E-W wave hits the crystal and gets split up

into the faster nα wave and the slower nγ wave

Both waves pass through the crystal at different

velocity; nγ is getting delayed

Waves leave the crystal with a path difference:

the retardation Δ (or R) [nm]

The privileged directions nγ and nα of the crystal

at 45° to polariser and analyser

nγ and nα waves both propagate at the same velocity

(n=1) and hit the analyser at diagonal angles

The waves are forced into N-S direction;

because of Δ interference occurs interference colour!

polarizer

analyzer

mineral


19

interference colours will be at their maximum (Fig. 12, left) when nγ or nα of the sample are at

exactly 45° to the N-S plane of the analyzer (the N-S diameter of the field of view in the

microscope). In this position we observe the maximum intensity of the interference colours (IF),

called the birefringence colours (Fig. 13 - Michel Levy chart).

From the maximum interference position, continuing to rotate the stage in the same direction, the

intensity of the colours gradually decreases til we return to total extinction. After rotating the stage

for 45° from the maximum illumination position, another extinction position is obtained (i.e., the

grain becomes dark again).

When rotating the stage through 360°, all anisotropic minerals show 4 positions of extinction,

(interference = 0) one at every 90°, alternating with 4 positions of maximum interference colours

(interference = maximum) also at every 90° from one another. Between each position of extinction

and the following position of maximum interference there are 45° of rotation.

Note that:

1) There is no interference colour produced without the analyser!

2) The interference colour depends on the retardation Δ (i.e., the distance between nα and nγ when

leaving the crystal).

3) Only waves propagating in the same plane can interfere!

4) The maximum brightness of the crystal in the microscope if nγ and nα are at 45° to polariser and

analyser! At this position we observe the maximum birefringence.

Birefringence (δ) is the difference between nγ and nα , so δ = nγ - nα

nγ - nα = Retardation (Δ) x Thickness of the crystal (d)

δ = Δ / d and (Δ) correlates with the interference colour (IF)

Graphically, δ is a straight line, in a chart (Michel-Levy) where Δ and d are the x and y axes,

respectively. The line crosses the origin of graph (see the Interference Colour Chart, also known as

the birefringence chart or Michel LLéévvyy cchhaarrtt)).. The Michel-Levy table contains 4 orders of colours

(each order has a total wavelength of 550 nm). The orders are separated by a violet colour and, as we

can see in the chart (fig.13), as we go to higher retardation (Δ), the colours become more pale and

mixed, sometimes difficult to describe.

Figure 13: the Michel LLéévvyy cchhaarrtt

,, ,, dd,, IIFF ccoolloouurr:: aallll oonn tthhee MMiicchheell LLéévvyy cchhaarrtt!!

1st Order 2nd Order 3rd Order , IF

d

= 0.026


21

5. PETROGRAPHIC MICROSCOPE

The petrographic microscope is used to analyze the properties of the transparent minerals. The main

components of petrographic microscopes are shown in Fig. 14. The light source (1) is on the bottom

of the microscope, under the blue filter. The blue filter is needed for absorbing the strong yellow-

orange component of the light emitted by the electric bulb, in order to produce normal-looking

white-coloured light (and therefore „normal‟ interference colours). The 2nd

diaphragm is used for

reducing the intensity of light (useful sometimes, for evaluating properties such as relief and

chagrin). Similar effects can also be obtained by using the light intensity control dial (2).

Let‟s once again follow the light on its way up to our eye (along the optical axis of the microscope);

The white light coming up from the blue filter passes through a group of other diaphragms and

apertures (13) also used for adjusting the light intensity and homogeneity. On its way up, the light

passes through the polarizer (3), which is mounted so that the polarization plane is East-West in the

image we see through the eye-piece, or ocular (fig. 15). Above the polarizer is mounted a mobile

lens (convergent lens, 4). In normal use, this lens is kept out of the way of the light path. Above the

convergent lens there is a rotating plate (11), which is the stage, and is graduated (360°) so that

angular measurements can be made. In the middle of the plate there is a round hole where the

polarized light goes through. Here we put the thin section (sample), so that the light from below can

pass up through the sample. The polarized light will interact with the sample and the resulted light

will continue upwards. To magnify the light transmitted through the sample, an objective (or a set of

objectives) is normally used (5), having different powers of magnification (usually 2.5x, 6.3x, and

10x, 20x, 40x or more). Up to 4 objectives are mounted on a typical nosepiece (6). Above the

objective, the analyzer (10) is mounted. It also polarizes light, and is mounted so that its plane of

polarization is perpendicular to the polarization plane of the polarizer (i.e., the analyzer has the

polarization plane mounted N-S -fig. 15). The analyzer is mobile, so it can be pushed in (or pulled

out) so that observations can be made either with or without the analyzer. The final magnification of

the image is provided by the ocular (9), which typically provides 10x additional magnification. The

total power of magnification of the microscope is equal to the power of magnification of the

particular objective in use, multiplied by the power of magnification of the ocular; these values are

written on both the objective and the ocular. For some specific determinations, the lamda plate (λ-

plate = gypsum plate, or λ/4-plate = muscovite plate; 7) and the Bertrand lens (8) can be used. In

normal use, these pieces are all kept out of the light path. The focused image through the

microscope is achieved by using the focus knobs (12) (one large, for coarse focusing, and one

smaller, for fine focus).

Looking through the microscope without any thin section present, and having all the mobile

components (the convergent lens, analyser, lambda plate, and Bertrand lens) kept out of the light

path, we should see a white field, homogenously lit (we see the white light, polarized by the

polarizer). This microscope mode is known as plane polarized light = PPL.

Introducing only the analyser, we get the microscope mode for crossed polarized light (CPL, or

colloquially XPL). With no sample, the observed field in the microscope should now be dark (all

light eliminated by the crossed polariser and analyser). Why? The analyser lets pass through only the

light vibrating in the N-S plane (the analyzer polarization plane). However, it does not receive any

vibrations in that plane since the incoming light from the polarizer is vibrating only in the W-E

plane. This is how we confirm the 90° angle between the polarization planes of the two nicols, the

polarizer and the analyzer (since the analyser can be rotated, this need not always be the case).

Both the above modes (PPL and XPL/CPL) use plane polarized light which is transmitted through

the mineral in mutual perpendicular planes. For this reason, the study of minerals using either of

these modes, or setups, is called orthoscopic study.


22

In contrast, introducing the convergent lens and the Bertrand lens to the XPL mode, we get the

conoscopic mode (for identifying the optical symmetry of minerals using convergent polarized

light). The study of minerals using this mode is called conoscopic study.

The λ-plate (gips), as well as the λ/4 plate (muscovite) are called compensators. They can be used for

certain observations in both orthoscopic and/or conoscopic modes.

Figure 14: Petrographic microscope: main components

Figure 15: N-S and E-W direction of the polarization planes as seen at the microscope; polarizer has the

polarization plane oriented E-W and the analyzer has the polarization plane mounted N-S.

9) Ocular (eyepiece)

10) Analyser

11) Rotating stage

12) Focus

13) Diaphragm / aperture

8) Bertrand lens

7) Lambda (λ-) plate

(accessory plate)

5) Objective lens

4) Condenser lens

1) Light source & filter

2nd

diaphragm

2) Light intensity control dial

3) Polariser

Petrographic microscope

6) Objective nosepiece

N

S

W E


23

6. MINERAL IDENTIFICATION USING THE PETROGRAPHIC MICROSCOPE

6.1. Orthoscopic study

-Condenser lens and the Bertrand lens are OUT!-

6.1.1. Observations using plane polarized light (PPL) mode

-Analyser is OUT!-

The observations typically made in PPL are transparency, shape/habit/size, colour,

pleochroism, cleavage, relief (Becke line, Chagrin), and inclusions/alterations.

a) Transparency

A mineral is opaque if it appears totally black and stays black regardless of the rotation of the

stage). The light cannot pass through the mineral, at all. Since the petrographic microscope is

designed for studying the transparent minerals only, we cannot get diagnostic reflected light

information here. However, we can observe shape, habit, and transparent inclusions, where

present. Usually the opaque minerals are either sulphides (e.g. pyrite, chalcopyrite, etc.), oxides

(e.g. magnetite, hematite, or ilmenite), or graphite.

If the mineral appears anything other than totally black (no matter what other colour is

observed!) it means that the light passes through the mineral, so the mineral is transparent.

b) Shape, habit, size

Shape: euhedral (or, if metamorphic, we call it idiomorphic), subhedral (hypidiomorphic)

or anhedral (xenomorphic);

Habit: isometric, prismatic, tabular, sheeted, etc.

Size: estimated in mm, based on the field of view determined from the magnification by the

objective and ocular lenses.

Looking at the mineral boundaries, we can see the shape of the analyzed grain. Remember that

the mineral as seen in thin sections is just a section through the mineral, which can have

different orientations related to the 3-dimensional (3-D) shape of the grain. In order to estimate

the habit, several grains of the same mineral should be examined. The shape can be regular

(geometrical features such as squares, rectangles, triangles, or combinations of these); different

regular sections of grains seen in the same thin section suggest a euhedral grain (all grain

boundaries are linear crystallographic faces with predictable interfacial angles). If the grain

shows irregular boundaries only, the grain is anhedral (xenomorphic). If the grain has both

regular and irregular boundaries, it is subhedral (hypidiomorphic) - see tables below. The

shape and size of the grains are related to the conditions of growth (crystallization). When

crystals grow, depending on how favourable the conditions are, they may develop all of their

crystal faces, or none of them at all (no preferred faces, so crystal grows as a shapeless blob =

anhedral growth), or anything in between.


24

Crystal habits

Degree of crystal development Igneous minerals

(crystallised from a

liquid)

Metamorphic minerals

(crystallised by solid state

diffusion)

shaded grains as

examples

grain has most/all well-developed

crystal faces (i.e., linear grain

boundaries whose orientations are

controlled by the crystallography

of the particular mineral)

euhedral

(idiomorphic)

idioblastic

grain has some well-developed

crystal faces

subhedral

(subidiomorphic)

subidioblastic

(hypidioblastic)

grain has no well-developed

crystal faces (its boundaries are

defined by the shapes of the

adjacent crystals)

anhedral

(allotriomorphic)

xenoblastic

Straight, or linear, grain boundaries can occur by a variety of mechanisms:

Well-developed crystal faces;

grain should show the same or

similar shape throughout the rock,

and the same relationship to

cleavages (where present); the

shape is controlled by crystal

symmetry of the mineral.

Linear boundaries can be found in

interstitial grains adjacent to euhedral

or subhedral grains; the interstitial

grain is anhedral, and its shape is

controlled by its neighbours (and is

therefore not consistent throughout

the rock, and not consistent with

respect to cleavages, etc.).

Recrystallisation (solid-state

modification of grains to

accommodate energy from heating

or deformation) can result in linear

grain boundaries, but these will not

reflect the crystal symmetry of the

mineral, and will usually not

produce consistent mineral shapes

euhedral

interstitial (anhedral)

recrystallised (anhedral)


25

More common crystal/grain habits

Name Description Shape

equant equidimensional (i.e., a ~ b ~ c)

columnar elongate in one direction, “blocky”, with

other two dimensions similar (i.e., c > a = b)

tabular rectangular, but flat (“table-like”) (i.e., c > a

> b).

lath-shaped Thin, narrow and flat (so a variant of

tabular, but specifically a narrow type).

(Actual laths are strips of wood).

fibrous elongate in one direction, tapering

acicular elongate and “pointy”, needle-like

prismatic elongated, with pyramidal pointed

terminations

sheaf radiating collection of elongate grains

rosette radiating collection of elongate grains

skeletal the framework of a mineral; partially

internally replaced

c) Cleavage

Cleavages are planar surfaces of low cohesion produced by weaker atom bonds across them.

They are visible when the cleavage is more or less vertical in the thin section. Cleavages seen

in thin sections are linear expressions of the intersection of particular planes of crystal faces

with the cut surface of the thin section; these faces have low surface energies and are therefore

favoured to “express themselves” in the crystal as preferred planes of growth and preferred

planes of splitting of the crystal. Not all faces have equal surface energies; some minerals may

have three “good” cleavages (e.g., calcite), some have a “perfect” cleavage (e.g., micas), and

some may have no cleavages at all (e.g., olivine, which therefore has no “preferred” planes of


26

splitting, and gets fractured, instead). All cleavage planes of a mineral must match that

mineral's symmetry. The same mineral will always have the same cleavage.

Cleavage is said to be basal when it occurs perpendicular to the major axis of the mineral, and

prismatic when it occurs parallel to the major axis. Multiple cleavages that produce geometric

polygons are referred to using the name of the geometric polygon, such as octahedral cleavage

in the mineral fluorite, cubic cleavage in the mineral halite, or rhombohedral cleavage in

calcite.

Cleavage, being related to structure, can be important in the correct identification of a mineral's

symmetry. Remember, cleavage must obey the symmetry of the mineral and must be parallel to

a possible crystal face. A mineral of the isometric symmetry class can either have no cleavage

or at least three directions of identical cleavage that form a closed three-dimensional polygon.

A mineral of a uniaxial class (trigonal, tetragonal or hexagonal) will potentially have a

cleavage perpendicular to the dominant axis and/or prismatic cleavage of either 3, 4 or 6

directions respectively, running parallel to the axis. Other cleavage directions are possible, but

will always be controlled by the symmetry of the crystal (Fig. 16). A biaxial mineral, those

belonging to orthorhombic, monoclinic or triclinic classes, cannot have more than two

identical cleavage directions.

Figure 16: Mineral cleavage: left: enstatite, with prismatic cleavage (parallel to the prismatic

faces) and two basal cleavages. Right: biotite, with one perfect basal cleavage.

The cleavage (quality and number of different cleavage planes) is diagnostic of some mineral

species. From the shape of the observed grain in thin section and the quality and orientation of

the cleavage(s), we can have an idea of the orientation of the section cut through the 3-D grain

morphology. In figure 17 we can see basal sections of amphibole (left) and pyroxene (right),

displaying two characteristic sets of cleavages.

a

ab

b

cc

d

d

Figure 17: Basal face with basal cleavage (two intersecting cleavages). Left: amphibole, where the angle

between the two cleavages is ~ 60° or 120°. Right: pyroxene, where the angle between the two cleavages is ~ 90°;

Enstatite (Opx) Biotite


27

A crystal with one perfect

basal cleavage, such as a

phyllosilicate, could be

depicted as shown below:

When seen in a cross-section

cut parallel to the c-axis, we

would see this system of

cleavages represented as a set

of parallel lines of ~equal

spacing: planes or faces.

Although the mineral has 4

sets of faces (labelled a to d),

only 2 of them form

prominent cleavages (b and

d). In thin section, we might

see 2 cleavages at ~90° angles

to one another, or we might

see only one of them (with

the other poorly developed, or

absent), or none at all,

depending on how the crystal

has grown, and how it has

been cut, relative to the

orientations of these cleavage

c-axis

c-axis

basal cleavage

a

ab

b

cc

d

d

The quality of the cleavage is estimated observing the density, continuity and width of the

cleavage lines (which are always parallel lines) in thin section (Fig. 18). Remember, this

estimation should be done on grains cut almost perpendicular to the cleavages. The quality of

cleavage is described as perfect, imperfect, good, distinct, indistinct, poor, or absent. The

quality decreases from perfect (dense, almost continue and thin lines of cleavage) to weak

cleavage (few, disperse segments of thicker lines) to absent (no cleavage, different curved

and/or broken thick lines). For example:

Perfect cleavage: micas, all phyllosilicates;

Good cleavage: feldspars, pyroxenes, amphiboles;

Weak cleavage: apatite, sodalite, olivine;

Absent: quartz

Figure 18: Left: one good cleavage in K-feldspar (kfs) and absent cleavage in garnet (grt); Right: good cleavage

(prismatic) in pyroxenes (note that the centre of the image shows a whole in the thin section).

kfs

grt

px


28

d) Colour (absorption colour)

The mineral is colourless if it appears white (we see the white light source!). If any other

colour is observed, the mineral is coloured (and the colour can be described). The observed

colour is the absorption colour (absorption of a part of the white spectrum). The observed

colour should be described as colour, nuances and intensity. For example: pale yellowish

brown, bluish light grey, etc. If when rotating the stage, the colour changes, then the mineral

has pleochroism (see below) and the range of colours should be described, rather than a single

colour.

e) Pleochroism

The term “pleochroism” comes from the Greek: pleos – many; chromos – colours. A mineral

shows pleochroism when the absorption colour (colour or nuance, or/and intensity) changes

when the stage is rotated. It means that absorption of specific light wavelengths depends on the

crystal orientation. This happens when the mineral is anisotropic. All anisotropic coloured

minerals have pleochroism. However, the intensity of pleochroism (the changing of colour) can

be different (from strong to weak). Common examples shown below include strong

pleochroism of biotite and hornblende (Fig. 19 and 20). We describe the pleochroism as ther

strong, moderate or weak, and try to describe the colour variation from the lightest to the

darkest colour/nuance (e.g. pleochroism from light yellowish green to dark bluish green).

Figure 19: Strong pleochroism of biotite, as stage is rotated 90°.

Figure 20: Strong pleochroism of hornblende, at 90° of rotation.

f) Relief

Refractive index (RI, n) is a measure of the speed of light in material relatively to the speed of

light in vacuum. The higher the RI, the slower the light propagation in the mineral.

“Relief” refers to the relative difference in RI between neighbouring crystals.

Examine the grain boundaries for the relief of a crystal (Fig. 21, 22):


29

Figure 21: Crystals with higher RI (n) seem embossed compared to low-RI minerals or resin; Here:

Clinopyroxene (Cpx) has a high relief compared to the resin but does not have a high relief

compared to other Cpx crystals.

Figure 22: Left: low relief of quartz (it can hardly be distinguished from the resin because the

refractive indexes of quartz and resin are very similar). Right: High relief of garnet comparing

to the resin. It boundary appears extremely distinct and thick.

Becke line; Becke method for estimating the relief

The Becke line is a narrow bright line along grain boundaries caused by light refraction and

scattering along the crystal surface. When lowering the rotating stage (using the fine focus), the

Becke line migrates into the phase of higher RI (Fig. 23). This is called Becke method and it is

a very sensitive method (determines n to ± ~0.02).

The microscope mode for the Becke line test:

• PPL setup mode

• High power objective lens (40x or higher)

• Close the diaphragm for better contrast

Resin (hole) n=1.55

Cpx n~1.7

Cover glass (<1mm; n~1.55)

Glass slide (~2 mm; n~1.55)

Synthetic resin; a few µm; n~1.55)

Sample (~30 µm; n variable)

n=1.55

n=1.55

n=1.55

n=1.7


30

Figure 23: Becke line observed at the boundary between garnet (Grt) and quartz-feldpar (Qtz/Fsp)

aggregate. The Becke line moves into the garnet (into the mineral with higher refractive index)

when slightly defocusing the image as the stage is lowered. Note also fine bright lines (also Becke lines) between the quartz and feldspar grains.

Although relief is most useful as a comparative term (some minerals show higher relief than

others), the relief can be positive or negative compared to a reference material of fixed and

known RI. This reference standard is the resin, which has a known refractive index (n = 1.54-

1.55). All minerals with relief higher than the resin have positive relief and all minerals with

lower relief than the resin, have negative relief. In order to determine if the relief is positive or

negative, we need therefore to directly compare the mineral with the resin (using the Becke

method). We should therefore look in the thin section where the unknown mineral is in direct

contact with the resin (usually look at the margin of the thin section, or look for holes in the

thin sections, if any).

Twinkling (relief changing)

This property is specific (diagnostic) for carbonates (calcite, dolomite, magnesite, etc). When

a mineral has nγ much higher than ~1.54 (nresin) and nα lower than ~1.54, it will show a

changing of relief (from positive to negative) when rotating the stage (Becke line moves from

one side to the other at the mineral boundaries, cleavage lines, or micro-fractures. This

movement of the Becke line when rotating the stage (and NOT when lowering the stage!)

produces a variation of the white light intensity (boundary and cleavages turn from fine to

thicker lines) and the mineral appears to have “pleochroism” (from colourless to light gray).

However, the phenomenon is not actually related to absorption, but to the high difference

between nγ and nα.

Chagrin (degree of rough appearance of the mineral surfaces)

Chagrin is a rarely used but an often useful term! It is produced by light refraction between the

mineral surface and the resin at the top (or bottom) of the thin section, as well as between the

mineral and very small cracks in it which are filled with resins. Fine, irregular, dense Becke

lines will form along micro-cracks, giving the image of a rough, irregular surface. The chagrin

is most obvious in minerals with strong relief and with absent or weak cleavages (where micro-

cracks are widespread in the volume of the grain). Olivine, apatite, sphene and garnet show

characteristic chagrin (all have high relief and absent or weak cleavage!). However, the chagrin

can be positive (olivine, apatite, sphene, garnet) or negative (sodalite, fluorite), depending on

the relief of the mineral (Fig. 24, 25).

Focused Stage slightly lower

Grt

Qtz/Fsp

Becke line

moves into Grt


31

Figure 24: Positive and negative chagrin ordered by relief (relief ~zero is albite ~ resin).

Figure 25: Olivine (Ol): strong positive relief, weak or absent cleavage, strong positive chagrin

(roughness surface); clinopyroxene (Cpx): positive relief, good cleavage, weaker chagrin. Is

the grain in the middle of the image olivine or clinopyroxene? Why?

g) Inclusions, alterations

Minerals can have inclusions, which can be solid (other finer-grained minerals) or fluid (liquid

and/or gas) inclusions. Choose a higher magnification objective and describe the inclusions, if

present (transparent or opaque, colourless or coloured, relief, etc.).

If altered, other minerals (alteration minerals) can appear at the margin of the analyzed

mineral, or along its cleavages or cracks. Describe the alteration mineral separately using a

higher magnification objective.

Ol

Ol

Cpx

Cpx


32

6.1.2. Observations using crossed polarized light (XPL) mode

-Analyser is IN!-

The observations in crossed nicols are: isotropy/anisotropy, extinction angle, birefringence colour,

twinning/zoning, finding the orientation of nγ and nα , optical elongation, and specific textures.

a) Isotropy/anisotropy

A transparent isotropic mineral is dark gray or black in crossed nicols, and the colour doesn‟t

change during rotation of the stage (there are no interference colours, since nγ=nα). NOTE: do not

confuse an isotropic mineral (or an isotropic section through an anisotropic mineral) with an

opaque mineral! An opaque mineral is totally black whether the analyser is in OR out, while the

transparent, isotropic mineral is not opaque!

If the mineral is anisotropic, it shows 4 positions of extinction and 4 positions of maximum

interference when rotating the stage.

b) Extinction angle

The extinction angle is the angle between one vibration direction of the mineral (nγ or nα) and the

N-S polarization plane of the analyzer (the N-S direction of the microscopic view).

The extinction can be parallel, symmetric or oblique.

In order to measure the extinction angle, we need to identify crystallographic features of the

mineral, such as cleavage planes, crystallographic faces or twinning planes (crystallographically-

controlled orientation). These features serve as reference directions. We rotate the stage to set the

crystallographic reference (e.g. an elongated face parallel to a cleavage, as shown in Fig. 26a)

parallel to the N-S (vertical) or E-W (horizontal) direction of the microscopic field (ensuring that

the cleavage lines are more or less either vertical or horizontal). Is the crystal in this position at

maximum extinction? If yes, it means that the angle of extinction is zero (or 90°), and the

extinction is called parallel extinction, meaning that the nγ or nα, (we don‟t know yet at this point

which one is which) is parallel to the N-S polarization plane. If in the vertical position the crystal is

not in maximum extinction but it shows an interference color, it means that the angle between nγ or

nα is different from zero (or 90°). We should rotate (incline) the crystal in order to find its

extinction position. It means that the crystal has an inclined extinction.

a) Parallel extinction: the cleavage is in N-S or E-W orientation when the crystal is

in extinction position

b) Oblique extinction: the cleavage is not // N-S or E-W when the crystal is in

extinction position. The extinction angle is usually <45%

c) Symmetrical extinction: When the nγ and nγ are parallel to the bisectrix of two

identical faces.

-Requires ALWAYS two (2!) equivalent crystallographic surfaces (cleavages, crystal

faces). -A crystal shows symmetrical extinction if both cleavages/crystal faces show

the same angle to the crosshairs at extinction.

Figure 26: a) Parallel extinction; b) Oblique extinction; c) symmetrical extinction.

It is as simple as that: what it is the position of the crystal when it is in extinction, compared to the

N-S plane of the microscopic view? Is it parallel to the N-S plane? If yes, the extinction is parallel


33

(angle of extinction is zero), if not, the extinction is oblique (Fig. 26b). The angle of extinction will

be the angle we have to rotate the stage in order to get the nearest extinction position. Some

specific sections in minerals (e.g. basal faces) show symmetrical extinction (Fig. 26c).

Determination of the extinction angle

Move the stage so that the crystallographic reference (e.g. the crystal face, cleavage, etc.) is

aligned N-S (Fig.27, left). Record the position of the stage. Then rotate the stage (in the sense

where the crystal arrives faster in the extinction position) until the crystal has its maximum

extinction (remember that there are four positions of extinction at each 90°). In this second

position, when the crystal is extinct, record the stage position again (Fig. 27, right). The

difference between the two readings is the extinction angle.

Fig. 27: Extinction angle = angle between Reading 1 and Reading 2.

The extinction angle is characteristic for each anisotropic mineral. However, it can differ even

within the same mineral group (i.e., olivines, pyroxenes, etc.), because of compositional

differences caused by solid solution substitutions that also influence the mineral‟s crystal structure.

For example, see the variations in extinction angles in the pyroxene group (Fig. 28), below.

Figure 28: Variation of the extinction angle within the pyroxene group (Saggerson, p. 24).

Reading 1 Reading 2


34

c) Birefringence

In order to describe the birefringence we should be able to: 1) describe the colour of

interference (also called colour of birefringence) and 2) find the value of the birefringence.

Interference colour (birefringence colour)

First, we need find the crystals of our particular unknown mineral with the highest interference

colours, using both PPL and XPL settings to identify grains of the same mineral (same relief,

absorption colour, pleochroism, cleavage, etc.). Then, we describe birefringence by comparing

the interference colours observed with the microscope with those within the Michel-Levy chart

(e.g. first order yellow). But how do we know it is first order yellow (as distinct from the other

order yellows)? Colours in the Michel-Levy chart are repeated in each order. ****. Remember

that although the colours usually repeat in each order, they are pale and diffuse as the order

gets higher (e.g. compare the yellow from each order). We have two methods to establish the

order of the interference colour: a) using the isochromatic lines (called isochromates, or

isochromes) and b) using the λ-plate.

a) using isochromates

The margin of grains are usually oblique to the light path, and because of this, the polarized

light is dispersed (as in the dispersion in Newton‟s prism; Fig. 29). A white light ray entering

an optically denser medium and leaving by a plane inclined to that of entry will have its

colours separated, analyzed, spread out. This is because each colour has a different wavelength

and so is differently slowed down (refracted) by the medium. Red (longest wavelength) is

slowed the least and violet (shortest wavelength) the most.

Figure 29: Dispersion of light at an oblique boundary of a refringent material.

Observing the dispersion of the interference colour of the mineral at oblique grain boundaries

allows us to estimate the order of birefringence by counting the number of violet colour bands

and adding 1. For instance, in Fig. 30a we observe a plagioclase with a gray colour of

birefringence (no violet isochromates at its boundary). The order of colour is therefore 0+1=1.

In Fig. 30b we have a muscovite. The bluish green colour of birefringence is in the second

order (we observe one violet isochromate, so the order is 1+1=2). In Fig. 30c we see calcite

with a diffuse, white-greyish colour of birefringence. At its rim, we notice 3 violet

isochromates, so the order of birefringence is 3+1=4.


35

Figure 30a-c: Identifying the order of the interference colour using the isochromates (see text).

Finding the value of birefringence (δ)

Knowing the thickness of the thin section “d” (which is standard, 30 microns) and observing

the birefringence colours in Michel-Levy chart, we can graphically obtain the value of

birefringence (values written at the top and right of the Michel-Levy chart) by intersecting the

band of the observed colours with the “d” value horizontal line (Fig. 31). From that point,

going up right on the chart following the line δ=Δ / d, we get the value of δ (birefringence). For

example, the maximum interference colour of quartz is first order white. We look for the

intersection of the first order white band in the Michel-Levy table with the horizontal (d) line

corresponding to 30 microns thickness. From that point, going up (interpolating between the

radiating lines), we get a birefringence value of 0.009, as written at the top of the chart.

Looking in the same sample, we will also find grains of quartz with lower birefringence (gray)

which means that their orientation is different (the section is not cut parallel to the optic axis,

and therefore, our view is not completely perpendicular to the optic axis).

If we want to know what maximum colour of birefringence to expect from a particular mineral

(knowing the value of δ from mineral tables), we go down from the value on the δ line until we

intersect the d line. At this intersection we see the colour of birefringence that corresponds to a

particular δ value.

IMPORTANT:

-The standard thickness of thin sections is 30 microns (the “d” horizontal line of interest is at

30 microns!)

- The Michel-Levy chart is made for maximum birefringence of minerals, only!! Do not try

to memorize a mineral using a specific unique birefringence colour. It is pointless and wrong!

Always remember that different colours can be possible for differently-cut orientations.

What does this mean? Some specific cuts of anisotropic minerals (sections perpendicular to the

optic axis, called sections of monorefringence – circular sections of the optical indicatrix)

behave isotropically. For example, apatite (calcium phosphate) has a prismatic habit,

crystallized in the hexagonal system (with medium symmetry, so it has a uniaxial indicatrix). If

the section is cut parallel to the prism faces, it will show maximum interference colours

(section parallel with the optical axis). If the cut is perpendicular to the prism, the section will

be isotropic. We can understand from here that the interference colours of one mineral

species depends on the orientation of the section cut, so that the interference colours can

a) 1st order IF colours b) Isochromates indicate

Green 2nd

order c) High order white

in calcite

a b c


36

vary from isotropic (black) when the cut is perpendicular to the optic axis, up to the maximum

interference colours when the cut is parallel to the optic axis.

d) Twinning/zoning

Twinning

A twin is a symmetrical growth of two or more crystals of the same mineral. The common

plane of the twinned crystals (which is called the twinning plane) is a symmetry plane, seen in

thin section as a straight line separating two identical crystals (e.g. crystal (1) and crystal (2))

which have a symmetrical optical orientation to the twinning plane, i.e., the indicatrices of the

two twinned crystals are symmetrical to the twinning plane. This is observable by rotating the

stage (Fig. 32); when crystal (1) is in extinction, its twin crystal (2) shows interference colours.

Continuing the rotation of the stage, crystal 1 shows interference colours and crystal (2) will

enter into a position of extinction. If the section is cut perpendicular to the twinning plane, the

extinction angles of crystal (1) and crystal (2) should be identical (if the crystallographic

reference for measuring the extinction is the twinning plane!). If the section cut is not

perpendicular to the twinning plane, the extinction angles will be different. If the section is cut

parallel to the twinning plane, the twin cannot be observed at all, in the plane of the thin

section.

Figure 32: Polysynthetic twins in plagioclase; section ~ perpendicular to the twinning plane

(useful for measuring the anorthite content in plagioclase)

FFiigguurree 3311:: SSkkeettcchh ooff tthhee MMiicchheell--LLeevvyy ttaabbllee sshhoowwiinngg tthhee ggrraapphhiiccaall mmeetthhoodd ttoo iiddeennttiiffyy tthhee bbiirreeffrriinnggeennccee vvaalluuee

((ffrroomm SSaaggggeerrssoonn ((11998833))


37

If more than two crystals are twinned, having parallel twinning planes, the twinning is called

polysynthetic (sometimes also called lamellar twinning). Plagioclase commonly shows this

type of twinning, called the Albite Twin Law, with {010} as the twin plane. Such twinning is

one of the most diagnostic features of plagioclase (Fig. 33). Several laws of twinning are

possible and they can be recognized using the microscope (e.g. Polysynthetic twins after the

“albite” and “pericline” laws in plagioclase, Carlsbad twins in plagioclase or orthoclase, cyclic

twins in leucite, etc.).

Orthoclase (K-feldspar)

Plagioclase (Na-Ca-feldspar)

Two ~ perpendicular polysynthetic

twin sets

(albite-law twins perpendicular to the

pericline-law twins)

Carlsbad twinning in plagioclase

(also common in orthoclase)

Polysynthetic albite-type twins in

plagioclase

(Tartan twinning, typical of

microcline – K-feldspar)

Figure 33: Examples of twinning in feldspars.

Zoning (compositional zoning)

Compositional variation within a crystal can be shown by different interference colours (Fig.

34). Zoning is possible in minerals which consist of solid solutions, where the compositional

differences reflect variation of major element ratios: e.g. Mg/Fe, Na/Ca, etc.). Note that the

difference in composition is visible as differences in the interference colours under the

petrographic microscope only if the symmetry of the crystal is low (it is visible for inferior

symmetry minerals, rarely visible for those with medium symmetry, and never visible in high

symmetry – isometric crystals, such as garnet, which is commonly zoned, but this is not

evident in thin section).

Figure 34: Compositional zoning in amphibole (a) and twinned plagioclase (b)


38

e) Orientation of nγ and nα

What we know from maximum brightness and total extinction of a mineral under the

petrographic microscope in XPL mode is that, at complete extinction the privileged directions

nα and nγ are N-S and E-W, and at maximum brightness nα and nγ are NW-SE and NE-SW

oriented. However, we don‟t know which is which!

Why do we need to find the nα and nγ of a crystal? Because it is the only way to establish the

optical elongation, which is a characteristic of any anisotropic crystal!

How do we find out which is nα and which nγ?

The microscope is designed so that the input of the λ-plate is always at 45° to the polarizer and

analyzer. Looking at the λ-plate, we can read the orientation of nγ of the plate (Fig. 35).

Figure 35: λ-plate, showing the orientation of nγ of the plate. In

this case, nγ is perpendicular to the direction of input, meaning

that it is at 45° to the N-S and E-W polarization planes.

We rotate the crystal into its position of maximum brightness. Now, either nα and nγ is oriented

NE-SW, meaning parallel to nγ of the λ-plate. Note that:

- The wavelength of the λ-plate is 550 nm (~575 nm is the extent of one order in the

Michel-Levy table!);

- When introduced, nα and nγ of the λ-plate will interfere with the nα and nγ of the

mineral, modifying the retardation (Δ)

- The wave can combine their wavelengths by addition (increasing retardation) or

subtraction (decreasing retardation). The addition or subtraction will only be by 550

nm, meaning by 1 λ.

- Adding retardation is when nα and nγ of the plate are parallel with nα and nγ of the

mineral.

- Subtracting retardation is when nγ of the plate is parallel to nα of the mineral (and nα of

the plate is parallel to nγ of the mineral).

- Increasing or decreasing the retardation can be seen by the changes in the interference

colours in the Michel-Levy table (to the left with 550 nm or to the right with 550 nm

starting to the interference colours observed for the mineral).

Let us take an example (Fig 36a-c):

1) First, bring the mineral to total extinction (this example is for a crystal with parallel

extinction). Here, we know that the two directions of vibration of the mineral are vertical,

and also horizontal (but we don‟t know which is nα and nγ)(Fig. 36a)

2) Rotate the stage exactly 45° (preferably bringing the longest faces of the crystal parallel

with the direction of the introduction of the plate (meaning NW-SE). In this position the

two directions of vibration of the mineral will be at 45° to the N-S and E-W lines and the

mineral will show its maximum interference colours (Fig. 36b).

3) Observe and locate the interference colour in the Michel-Levy table (pay attention to the

order of the colour!)

4) Introduce the plate (λ-plate or λ/4-plate)(Fig. 36c)

nslow


39

5) Observe the changed colour and locate this new colour in the Michel-Levy table

If the new colour is situated at the right of the first observed one, it means that the wavelengths

of the mineral and the plate were added (the retardation increased in the Michel-Levy table).

This means that nγ of the mineral is parallel with the nγ of the plate (Fig. 36c). Knowing the nα

is perpendicular to nγ we have determined now the position of both nα and nγ of the mineral.

Note that if we rotate the crystal another 90°, having already introduced the plate, the nγ of the

mineral will now be parallel to the nα of the plate, and so the wavelength will subtract one from

the other and the retardation will decrease (the interference colour will appear further to the

left, by 550 nm).

Figure 37: a) Bring first the mineral to total extinction (this example is for a crystal with

parallel extinction); in this position nγ and nα will ALWAYS be vertical for one, and the other

horizontal (at this stage, however, we don‟t know which direction is nγ or nα); b) rotate the stage

by 45° to arrive at maximum interference and identify the colour of interference in the Michel-

Levy chart; in this position, the nγ and nα will ALWAYS be positioned at 45° relative to N-S

polarisation planes of the nicols (therefore, one of the two will be EXACTLY along the

direction in which we introduce the λ-plate); c) introduce the plate and identify the modified colour using the Michel-Levy chart: check if the retardation (Δ) has increased or decreased. If Δ

increased (colour moved to the right in the Michel-Levy chart), then we know that nγ of the

mineral is parallel to nγ of the plate.

Variable birefringence in anisotropic minerals:

the problem of crystal orientation in thin sections

Figure 38: left: XPL image of plagioclase crystal showing cleavage (centre of the image); middle: same image

after introducing λ-pate colour moved to the right in the Michel-Levy chart (from grey to yellow), so we know

that in this position, the interference of λ-plate with the crystal produced an addition of (Δ) therefore, the nγ of

the crystal is parallel to the NE-SW direction of the microscope view (meaning parallel to the orientation of nγ

shown on the λ-plate). Relating this observation to the reference direction (cleavage) of the crystal, we can say

that nγ of the crystal is parallel to the cleavage; right: crystal rotated by 90°. Note that the interference colours

changed; in this position we get subtraction of Δ (colour moved to the left in the Michel-Levy chart) nγ of the

crystal is parallel to nα of the λ-plate. Don‟t be confused… No matter how we rotate the stage, even colour

changes, the orientation of nγ and nα of the crystal in relation to crystal shape or reference (cleavage) always stays

the same (in this example nγ of the crystal is always parallel to the cleavage, no matter how the stage is rotated).

nslow

nγ


40

See the example in Fig. 38, for the grain in the centre of the microscope view (left: no plate;

middle: plate introduced; right: crystal rotated by 90°).

f) Optical elongation

Since we have determined the orientation of nα and nγ in the crystal, is easy now to derive the

optical elongation. Remember that nγ is higher than nα. The two directions of vibration

represent the two main axes of the indicatrix (ellipsoid). We now relate the determined

ellipsoid to the mineral form!

We know that the exterior form of crystals is directly related to its symmetry (therefore to its

a,b and c crystallographic axes). Usually (but not always), the longer faces are parallel (or

displaced by the extinction angle value) to the c axis.

How are nα and nγ placed in relation to the direction in which the crystal is more developed

(longer), in relation to the c axis? If nγ is parallel (or at the extinction value angle) with the

direction of the longer faces, we say that the crystal has a positive optical elongation (the

elongation of the ellipsoid corresponds to the direction of the c axis). This crystal can also be

described as “length-fast” (the long axis of the crystal is parallel to the direction of the lowest

R.I.). If nα is parallel to the c axis, then the optical elongation is negative (Fig. 39), and the

crystal is “length slow”.

Figure 39: a) parallel extinction, positive optical elongation; b) parallel extinction, negative

optical elongation; c) oblique extinction, positive optical elongation; d) oblique extinction,

negative optical elongation.

Question: what is the optical elongation of the plagioclase shown in figure 38?

6.2. Conoscopic mode

Microscope setup: XPL (crossed nicols), high magnification (powerful objective)

Convergent lens in! Bertrand Lens in!

Chose a coarser grain and make certain that the rotating stage and the objective are centred (by

rotating the stage, the crystal should remain at or near the crosshairs in the centre of the

microscopic field).

Conoscopic study helps us to see if a crystal is uniaxial or biaxial. (Note that a 2-D section

through a 3-D uniaxial (circular ellipsoid) or biaxial indicatrix (flattened ellipsoid) would have

the same (elliptical) form).

In conoscopic mode, light penetrates the crystal in a conical shape, not as parallel rays as in

orthoscopic mode. This gives a kind of three-dimensional impression of light propagation in

the crystal. Details can be found in the literature; here we will only discuss

the practical side of thin section conoscopy.

We can derive the real shape of the indicatrix by using the interference figures and determining

the optical sign.

c- axis c- axis c- axis c- axis

a) b) c) d)


41

6.2.1. Interference Figures

The conical (convergent) shape of light interferes with the sample and the shape of the

interference result is an image (interference figure) that forms somewhere between the analyzer

and ocular. In order to bring the interference image closer to the ocular, the Bertrand Lens is

used.

An interference figure consists of two dark diffuse intersecting lines (or curves) called isogyres

(regions of zero path difference) and circular coloured rings called isochromates, representing

regions of identical path difference; The higher the (Δ), the more isochromates there are (e.g.

Fig. 40).

Interference figures for uniaxial crystals

Uniaxial interference figures ideally look like this:

Figure 40: Interference figure for calcite (section perpendicular to the optic axis).

When the section is perpendicular to the optical axis of an uniaxial crystal (e.g. calcite, which

is trigonal), the interference figure is a cross (Fig. 40) centred in the middle of the view.

Rotating the stage, the cross, as well the isochromates, do not move. At the intersection of the

isogyres is the optic axis (which corresponds to the A3 fold axis of symmetry of the calcite)

If the section is oblique to the optic axis, the cross will be out of view and we have to rotate the

stage. By rotating the stage, we will observe one vertical “arm” of the cross, moving

horizontally as we rotate the stage, and when it disappears, a horizontal arm will show up,

moving vertically (fig. 41).

Figure 41: Interference figure for a uniaxial crystal, section oblique to the optic axis. The optic

axis is outside the interference figure but the vertical and horizontal black lines move horizontally and vertically, respectively, as the stage is rotated.

Interference figure for biaxial crystals

If the section is perpendicular to one of the optic axes, the interference figure will appear as a

curved, dark, diffuse arm that rotates within the image view. If the curvature is high, it means

that the angle between the two optical axes (the 2V angle) is small, and if the curvature is

small, then the 2V angle is high. (Fig. 42).

Isochromates

Isogyres (regions of zero path difference)

Rotation of the stage does not

change the image

Optic axis


42

Figure 42: Interference figure for a biaxial crystal, section perpendicular to one of the optic axes.

The most useful biaxial interference figures are those for sections perpendicular to the 2V

bisectrix (the bisectrix of the acute angle between the two optic axes). In these figures we can

see both optic axes (Fig. 43a).

How do we find the section cut most closely perpendicular to the acute bisectrix? Trial and

error! Start with the lowest interference colour section you can find and, in the Conoscopic

Mode, work your way up until you find the right (i.e., most useful) interference figure.

Determination of the optic sign

-using the λ-plate-

The optic sign can be either positive or negative, and this tells us if nγ or nα, respectively, is

parallel to the 2V bisectrix.

After finding the interference figure, we introduce the λ-plate. The wavelength introduced by

the plate can produce either addition or substraction in the retardation of the isochromates (Fig.

44)!

What does the optic sign mean? It shows the shape of indicatrix in relation to the optic axis of

the crystal. For uniaxial crystals: is the optical axis parallel or not with the nγ or nα? For

biaxial crystals: is the bisectrix of the acute 2V angle parallel with nγ or nα? See the shape of

biaxial indicatrices in Fig. 45.

Figure 43a: Position of the optic axes

SShheelllleeyy 11999933

Figure 43b: Movement of isogyres during stage rotation.

From top to bottom, the 2V angle increases.


43

Figure 44: Determination of the optic sign

Observe the upper right or lower left quadrant:

Add the λ-plate

-Constructive (addition) colours indicate a positive

optic sign;

-destructive (subtraction) colours indicate a negative

optic sign.

Figure 45: Positive and negative optical sign

a) Crystal biaxial positive : Acute bisectrix: nγ nα and nβ T acute bisectr, δ > 0

b) Crystal biaxial negative Acute bisectrix: nα nβ and nγ T acute bisectr. δ > 0

A quick reference for the determination of the optic sign of minerals with low birefringence (IF

1st order grey-white) is provided in figure 46.


44

Figure 46: Determination of the optic sign for crystals with low birefringence.

Estimation of the 2V angle

This estimation is an approximation using the interference figures. The best sections are those

perpendicular to the acute bisectrix (Fig. 47a). The estimate is done by comparison with

images from Fig. 47.

a) 2V=90: one straight line rotating in the opposite direction compared to the rotation of the

stage;

b) There is a moderate 2V angle if the isogyres are moderately curved;

c) There is a low 2V angle if the two wings of the cross meet and break slightly as we rotate

the stage. The two wings do not leave the interference figure when rotating the stage only if

the section is ~ perpendicular to the acute bisectrix (i.e. a uniaxial-like interference figure).

a) Uniaxial to optic axis

c) Biaxial to optic axis

b) Biaxial to acute bisectrix

Figure 47: Estimation of the 2V angle (see text). After Shelley (1993).


45

Is the interference figure good enough for seeing the optical character and determining

the optical sign? Interference figures: The Good, the Bad and the Ugly (Fig. 48):

Figure 48: Types of possible sections obtained for biaxial crystals. Which one is good?

The Good: Section to the acute bisectrix

The Bad: Section oblique to the acute bisectrix

Another Good one: Section ± to OA

The Ugly: “Flash Figure”

Section to the obtuse bisectrix (biaxial minerals) or

parallel to the OA (uniaxial minerals): confusion

guaranteed.


46

Useful charts for mineral identification: the Tröger Chart

A (sometimes dangerous) shortcut to identify minerals with the petrographic microscope

involves using the Tröger Chart, which has the refractive index on the x axis and birefringence

values on the y axis. The zero value of birefringence (isotropic crystals) positioned at the

middle of the chart, so that the birefringence values increase from zero up but also decrease

from zero down in the chart. In the upper part are found minerals with positive optical sign,

while in the lower part of the chart are minerals with negative optical sign. To make a

distinction between uniaxial and biaxial crystals, the uniaxial are represented with bold circles.

The steps to take are:

a) Check refractive index (n)/chagrin (low, medium, high); for n(RI)<1.65 use part one of

the chart (Fig. 49a) and for n>1.65 use part two of the chart (Fig. 49b)

b) Check the maximum birefringence (birefringence colour; then estimate the value of

birefringence using the Michel-Levy chart)

c) Determine the optic character (uni- or biaxial) and the optic sign

d) Find the region on the Tröger Chart corresponding to these determined values

e) Check the optical characteristics of minerals occurring in that region

f) Check the likelihood of the determined mineral occurring in the rock type investigated

g) Don‟t forget: there are more mineral species than shown on the charts!

Figure 49a: Tröger Chart part 1 (refractive indexes from 1.45 to 1.65)


47

Figure 49b: Tröger Chart part 1 (refractive indexes from 1.65 to 2.80)

27 Key mineral species

It is useful to know the key optical characteristics for the minerals listed below (the common

rock-forming minerals).

1. Quartz 2. Plagioclase*

3. K-feldspar* 4. Cordierite*

5. Biotite* 6. Tourmaline*

7. Amphibole* 8. Muscovite

9. Talc 10. Chlorite*

11. Garnet* 12. Spinel*

13. Staurolite 14. Rutile

15. Chloritoid 16. Calcite/Dolomite

17. Titanite 18. Zircon/Monazite

19. Olivine* 20. Cpx*

21. Opx* 22. Epidote*

23. Apatite 24. Kyanite

25. Sillimanite 26. Andalusite

27. Nepheline

* Solid solutions with variable optical properties

Italics: learn formula; the rest: learn the general composition


48

Key Characteristics of common minerals: Speeding up mineral identification

Many common mineral phases have unique characteristics (or combinations of two or three)

which make them unmistakable.

Examples

Quartz: low RI (~like the resin); low birefringence (1st order IF colour); uniaxial positive; no

(visible) twins.

Plagioclase: low RI and birefringence (~like Qtz); lamellar twinning; biaxial positive or

negative.

Staurolite: pale yellow pleochroism; high RI; frequently idiomorphic.

Carbonates: very high birefringence, relief changes when you turn the stage; uniaxial negative.

Identify the key characteristics and note them in your mineral catalogue.

A few hints for the relationship between chemical composition - optical properties

Some cations from the Transition Elements in the Periodic Table (including Fe, Cr, V, Ti, etc.)

which have several possible valence states in rocks, produce more intense but variable

absorption of light, and are called chromophores. The result is that minerals rich in these

elements will be more strongly coloured in thin sections (in PPL mode): Fe2+

gives gray,

yellow to greenish colours, depending on its concentration and on the absorption produced by

other cations (e.g. in olivine, pyroxene, amphibole, chlorite). Fe3+

gives brown colours (in

oxydated hornblende = brown hornblende) or green in oxydized biotite. Cr3+

gives pale green

colours (e.g. in spinels, Cr-diopside, fuxite (Cr-mica), Cr-staurolite, Cr-cordierite); Ti produces

reddish-brown colours (such as in Ti-rich biotite).

In addition to the strong selective absorption, the presence of these cations also increases the

refractive indices of the mineral, causing higher relief. This is useful in composition

estimations for minerals that are part of solid solutions. For example, in olivine or pyroxene,

Fe2+

shares a structural position with Mg2+

(so Fe2+

can substitute for Mg in any proportion).

The Mg-rich end member of the solution will be colourless, but the solid solution becomes

more coloured and the refractive index increases as it has more Fe2+

instead of Mg. The Fe2+

end members will be green with higher relief.

When dealing with silicates (as we usually are in rocks), coloured minerals as seen in PPL can

be expected to have a positive relief (have refractive indices superior to the resin). There are

few exceptions: the bluish hauyine and nosean from the sodalite group have negative relief, but

the bluish colour is given by the absorption produced by small amounts of the [SO4] molecule.

The silicates with Al, Ca, Mg, or with Ca, Na, K (note the absence of chromophores) are

typically colourless (e.g. all feldspars, feldspathoids, white mica).

The substitution of Ca for Na in plagioclase solid solutions produces no colour change, but

does induce an increase in the refractive index (relief) and the extinction angle. Michel-Levy

proposed a method to estimate the Ca-end member (Anorthite CaAl2Si2O8) in a plagioclase,

based on the extinction angle.

The carbonates always show twinkling (a modification of relief from positive to negative)

when the stage is rotated. Together with the high order birefringence (4th

order), the twinkling

is diagnostic for carbonates.


49

Tips for discriminate between different mineral groups

All cubic minerals are isotropic.

All orthorhombic minerals, as well as all uniaxial minerals (medium symmetry: trigonal,

tetragonal, hexagonal), have parallel extinction (except for basal sections, which have

symmetrical extinction).

All monoclinic and triclinic minerals have oblique extinction (except for basal sections which

have symmetrical extinction).

All phyllosilicates have parallel extinction and perfect basal cleavage; the extinction is not total

(smooth) but „rough‟ (small bright coloured spots are present across its entire surface).

All orthosilicates have relatively high refractive indices (relief)

All tectosilicates have low or medium-low refractive indices (relief)

Sulphates (e.g. gypsum) have usually negative refractive indices (relief)

Heavy elements (down periods in the periodic table) produce high relief (Ba, U, REE etc) in

their host mineral

Sulphides are all opaque (as some of the oxides: magnetite, hematite, ilmenite); yellowish-

brown alterations on fissures (no pleochroism, no birefringence) are usually Fe-hydroxides

(goethite, lepidocrocite etc) or hematite (dark reddish).

Mineral associations: helpful in identifying minerals

Not all minerals can be naturally associated in a rock. Most rocks have 2-5 abundant minerals

and a few other minerals as possible accessories or alteration. The natural association of

minerals in rocks is controlled by their stability, which mainly depends on chemistry, pressure

(including water pressure), and temperature.

-olivine and quartz are never found together in equilibrium in the same thin section (one is

undersaturated in SiO2, the other is super-saturated in SiO2, respectively).

-feldspathoids (nepheline, sodalite, cancrinite, etc.) are never found together with quartz (same

explanation as above);

-if olivine has been recognised (medium-high relief, no cleavage, strong chagrin, high

birefringence), it is frequently associated with pyroxenes (no chagrin, good cleavage, similar

relief, parallel extinction = orthopyroxene; oblique extinction (30-45°) = clinopyroxene) and/or

amphiboles (longer prisms, stronger pleochroism, typical basal sections with 120° angle

between cleavages, medium relief, lower extinction angle), and/or plagioclase (colourless, low

birefringence first order, polysynthetic twinning)

-grid twinning is typical for microcline (K-feldspar), and is commonly associated with quartz

and (sodic) plagioclase

-perthitic textures - fine lamellae of albite (relief zero or negative) in a host of K-feldspar

(stronger negative relief than albite); perthites are typical for K-feldspar (orthoclase,

microcline, rare in sanidine).


50

Mineral Identification – A Beginner’s Guide

to Identifying the Common Rock-Forming Minerals using Transmitted Light Microscopy

Is your mineral?:

COLOURLESS? COLOURED?

ISOTROPIC? low relief? hole in slide, or basal section of

a non-isotropic mineral ISOTROPIC? green? spinel

high relief? garnet black? “opaque” (oxides, sulphides)

NON-ISOTROPIC? NON-ISOTROPIC?

UNIAXIAL? UNIAXIAL?

LOW RELIEF? (relief masked by mineral colour)

positive? quartz pleochroic brown, green, orange (pseudo-

uniaxial or very low 2V)?

biotite

negative? nepheline, scapolite pleochroic pale brown to colourless? phlogopite

MODERATE RELIEF? BIAXIAL?

positive, usually as laths muscovite, talc very pale green to colourless, very

weakly pleochroic?

cpx, chlorite, chloritoid,

muscovite, serpentine

HIGH RELIEF? pleochroic pale pink to pale green to colourless?

hypersthene

Positive-negative (“relief

pleochroisme”, with distinct cleavages

calcite pleochroic yellow-brown to colourless? staurolite

BIAXIAL? pleochroic distinctly green, brown, blue-green?

hornblende, tourmaline

LOW RELIEF?

may have polysynthetic twinning feldspars, cordierite pleochroic brown to colourless, often

euhedral, very high δ?

titanite

HIGH RELIEF? reddish-brown needles, very high δ? rutile

conchoidal fracture? olivine pleochroic blue, purple? riebeckite, glaucophane

idio- to subidioblastic, in a

metamorphic rock?

Al2SiO5: andalusite, sillimanite,

kyanite

AMORPHOUS (no optic sign)

granular, with anomalous 1st order

colours? clinozoisite, epidote opaque interior, brown at thin edges chromite

up to 2 distinct cleavage directions opx, cpx, wollastonite, all

amphiboles other than

hornblende

red hematite

fine-grained, granular, with very high δ zircon, monazite


51

A Birefringence Primer

Interference colours (birefringence) produced when the polariser and analyser are both “in” (crossed nicols, or crossed polars).

For mineral diagnostic purposes, the colours refer to “maximum birefringence”, produced only when mineral grains are aligned perpendicular to

their c-axis (i.e., many grains will show interference colours below the maximum, but the „average” or typical colour seen in a thin section is

usually close enough.

In strongly-coloured minerals, interference colours may be masked by the mineral colour; if the apparent interference colour looks “odd”,

compare it with the actual mineral colour in plane-polarised light, to avoid confusion.

Birefringence

(nγ - nα = δ)

0 to 0.005 0.005 to 0.01 0.01 to 0.015 0.015 to 0.018 0.018 to 0.028 0.028 to 0.08 0.08 to 0.2

“Order” Lower 1st Order Upper 1

st

Order

Lower 2nd

Order

Upper 2nd

Order

3rd

Order 4th

Order and beyond

Interference

Colours

black, grey, white

+ anomalous

colours: “Berlin”

or Prussian blue-

grey, green-grey

“straw

yellow”, red

purple to blue,

green

yellow,

orange/red

blue, green,

yellow, red

pale green,

pink

“bright brown”

Common

minerals

quartz,

plagioclase

feldspar,

microcline,

cordierite,

chlorite,

clinozoisite,

andalusite,

nepheline,

scapolite

quartz,

orthoclase

(yellow or

lower);

sillimanite,

opx,

wollastonite

kyanite,

amphiboles,

cpx, biotite

muscovite,

olivine

talc zircon titanite, calcite,

rutile

Some common problems:

How can I tell if I’m looking at “1st order” red, or 2

nd or 3

rd order colours?

Look at the edges of the grains, or along fractures, where they are thinnest; you should see fine rings of the lower interference colours

(e.g., so if it‟s 1st order red, there will be no blue-indigo edges)

Look at conoscopic figure; isochromes correspond to the same colour bands (usually these are subtle, but it works well in come cases, like

calcite & biotite, for example)

Lower order colours are “deeper”, higher order “brighter”, higher orders are pale, mixed, diffuse.


52

If a mineral is black, does that mean it is automatically “1st order Black”?

Not necessarily; it could also be

o an opaque mineral (light is not transmitted through it), so it is also black under plane-

polarised light (i.e., with analyser “out”)

o an isotropic mineral is always black under cross-polars; it has no birefringence and is

therefore not “1st order” per se

o basal-orientated sections (looking directly down the c-axis, in general) can be 1st Order

black, but this is not the maximum birefringence for that particular mineral.

o a hole in the slide, often the result of “plucking” of certain minerals, or where there are

void spaces (not uncommon in volcanic rocks and sediments); it will have “very low

relief” and no crystal shape or other properties.

Got it narrowed down yet?

Yes? – Good! Now go look up the detailed properties of the possible minerals, and match them to

the observed properties & associated minerals and textures.

No? – Is it similar to anything? (probably); There may be some common “similar” minerals not

listed here in related mineral groups, other solid solution end-members, etc., so start with the

mineral(s) it looks the most similar to, and work from there.

Still stumped? Follow the identification Table for Common Minererals in Thin Sections. If still

stumped....Ask a petrologist…


53

Identification Tables for Common Minerals in Thin Section

These tables provide a concise summary of the properties of a range of common minerals. Within the

tables, minerals are arranged by colour so as to help with identification. If a mineral commonly has a

range of colours, it will appear once for each colour.

To identify an unknown mineral, start by answering the following questions:

(1) What colour is the mineral?

(2) What is the relief of the mineral?

(3) Do you think you are looking at an igneous, metamorphic or sedimentary rock?

Go to the chart, and scan the properties. Within each colour group, minerals are arranged in order of

increasing refractive index (which more or less corresponds to relief). This should at once limit you to

only a few minerals. By looking at the chart, see which properties might help you distinguish between the

possibilities. Then, look at the mineral again, and check these further details.

Notes (refer to notations and observations in the tables below):

(i) Name: names listed here may be strict mineral names (e.g., andalusite), or group names (e.g.,

chlorite), or distinctive variety names (e.g., titanian augite). These tables contain a selection of some of

the more common minerals. Remember that there are more than 4000 minerals, although 95% of these

are rare or very rare. The minerals in here probably make up 95% of medium and coarse-grained rocks in

the crust.

(ii) IMS: this gives a simple assessment of whether the mineral is common in igneous (I), metamorphic

(M) or sedimentary (S) rocks. These are not infallible guides - in particular many igneous and

metamorphic minerals can occur occasionally in sediments. Bear this in mind, even if minerals are not

marked as being common in sediments.

(iii) Colour in thin sections (TS): the range of colours for each mineral is given, together with a

description of any pleochroism. Note that these are colours seen in thin-section, not handspecimen.

The latter will always be much darker and more intense than thin section colours.

(iv) RI: the total range of refractive index shown by the mineral with this coulour is shown: This covers

any range due to compositional variation by solid solution, as well as the two or three refractive indices of

anisotropic minerals.

(v) Relief : is described verbally, followed by a sign indicating whether the relief is positive or negative

(ie greater or less than the mounting medium of the thin-section - 1.54). Minerals with refractive indices

close to 1.54 have low relief, those with much higher or lower refractive indexes will have high relief.

(vi) Extinction: angles are only given where minerals usually show a linear feature such as a cleavage

and/or long crystal faces. For plagioclase feldspars (stippled) the extinction angles given are those

determined by the Michel-Levy method (see a textbook for details).

(vi) Int. Figure: this gives details of the interference figure. Any numbers given refer to the value of 2V

(normally a range is given), followed by the optic sign. For uniaxial minerals the word "Uni" is given,

followed by the sign. Your course may or may not have covered interference figures. If not, ignore this

section!

(vii) Birefr: Birefringence is described verbally. In some cases the maximum is given as a colour, in

other cases you will need to cross-refer to an interference colour chart.

(viii) Twinning etc.: a few notes about twinning, or other internal features of crystals may be given. If no

twinning is mentioned, then the phenomenon is not common in thin section, but this does not mean that it

NEVER occurs.

(ix) Notes: general tips on appearance, occurrence and distinguishing features. May include indication of

whether the mineral is length fast or slow - again a feature not covered in all courses - but a useful and

easily-determined property.


54

Tables for Common Minerals in Thin Section


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bisectrix dominatrix optical dominatrix optical indicatrix

introduction to optical mineralogy

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