LECTURE NOTES 1ST SEMESTER UNIT 4

Silicate Structures and Structural Formula As we discussed in a previous lecture, the relative abundance of elements in the Earth's crust determines what minerals will form and what minerals will be common. Because Oxygen and Silicon are the most abundant elements, the silicate minerals are the most common. Thus, we will spend some time here discussing the structure, chemistry, and occurrence of silicate minerals. Our systematic discussion of the common rock forming minerals will follow in the lectures throughout the remainder of the course.

Element Wt% Atomic% Volume%

O 46.60 62.55 ~94

Si 27.72 21.22 ~6

Al 8.13 6.47

Fe 5.00 1.92

Ca 3.63 1.94

Na 2.83 2.34

K 2.59 1.42

Mg 2.09 1.84

Total 98.59 100.00 100

In order to discuss the silicates and their structures it is first necessary to remember that the way atoms are packed together or coordinated by larger anions, like oxygen depends on the radius ratio of the cation to the anion, Rx/Rz.

Rx/Rz C.N. Type

1.0 12 Hexagonal or Cubic Closest Packing

1.0 - 0.732 8 Cubic

0.732 - 0.414

6 Octahedral

0.414 - 0.225

4 Tetrahedral

0.225 - 0.155

3 Triangular

<0.155 2 Linear

Since oxygen is the most abundant element in the crust, oxygen will be the major anion that coordinates the other other cations. Thus, for the major ions that occur in the crust, we can make the following table showing the coordination and coordination polyhedra that are expected for each of the common cations.

Ion C.N. (with

Oxygen)

Coord. Polyhedron

Ionic Radius, Å

K+ 8 - 12 cubic to closest

1.51 (8) - 1.64 (12)

Na+ 8 - 6 cubic to octahedral

1.18 (8) - 1.02 (6)

Ca+2 8 - 6 1.12 (8) - 1.00 (6)

Mn+2 6

Octahedral

0.83

Fe+2 6 0.78

Mg+2 6 0.72

Fe+3 6 0.65

Ti+4 6 0.61

Al+3 6 0.54

Al+3 4 Tetrahedral

0.39

Si+4 4 0.26

C+4 3 Triangular 0.08 The radius ratio of Si+4 to O-2 requires that Si+4 be coordinated by 4 O-2 ions in tetrahedral coordination.

In order to neutralize the +4 charge on the Si cation, one negative charge from each of the Oxygen ions will reach the Si cation. Thus, each Oxygen will be left with a net charge of -1, resulting in a SiO4

-4 tetrahedral group that can be bonded to other cations. It is this SiO4

-4 tetrahedron that forms the basis of the silicate minerals.

Since Si+4 is a highly charged cation, Pauling's rules state that it should be separated a far as possible from other Si+4 ions. Thus, when these SiO4

-4 tetrahedrons are linked together, only corner oxygens will be shared with other SiO4

-4 groups. Several possibilities exist and give rise to the different silicate groups.

Nesosilicates (Island Silicates)

If the corner oxygens are not shared with other SiO4-4

tetrahedrons, each tetrahedron will be isolated. Thus, this group is often referred to as the island silicate group. The basic structural unit is then SiO4

-4. In this group the oxygens are shared with octahedral groups that contain other cations like Mg+2, Fe+2, or Ca+2. Olivine is a good example:

(Mg,Fe)2SiO4.

Sorosilicates (Double Island Silicates)

If one of the corner oxygens is shared with another tetrahedron, this gives rise to the sorosilicate group. It is often referred to as the double island group because there are two linked tetrahedrons isolated from all other tetrahedrons. In this case, the basic structural unit is Si2O7

-6. A good example of a sorosilicate is the mineral hemimorphite - Zn4Si2O7(OH).H2O. Some sorosilicates are a combination of single and double islands, like in epidote - Ca2(Fe+3,Al)Al2(SiO4)(Si2O7)(OH).

Cyclosilicates (Ring Silicates)

If two of the oxygens are shared and the structure is arranged in a ring, such as that shown here, we get the basic structural unit of the cyclosilcates or ring silicates. Shown here is a six membered ring forming the structural group Si6O18

-12. Three membered rings, Si3O9

-6, four membered rings, Si4O12

-8, and five membered rings Si5O15-10 are

also possible. A good example of a cyclosilicate is the mineral Beryl - Be3Al2Si6O18.

Inosilicates (Single Chain Silicates)

If two of the oxygens are shared in a way to make long single chains of linked SiO4 tetrahedra, we get the single chain silicates or inosilicates. In this case the basic structural unit is Si2O6

-4 or SiO3-2. This group is the

basis for the pyroxene group of minerals, like the orthopyroxenes (Mg,Fe)SiO3 or the clinopyroxenes

Ca(Mg,Fe)Si2O6.

Inosilicates (Double Chain Silicates)

If two chains are linked together so that each tetrahedral group shares 3 of its oxygens, we can from double chains, with the basic structural group being Si4O11

-6. The amphibole group of minerals are double chain silicates, for example the tremolite - ferroactinolite series - Ca2(Mg,Fe)5Si8O22(OH)2.

Phyllosilicates (Sheet Silicates)

If 3 of the oxygens from each tetrahedral group are shared such that an infinite sheet of SiO4 tetrahedra are shared we get the basis for the phyllosilicates or sheet silicates. In this case the basic structural group is Si2O5

-2. The micas, clay minerals, chlorite, talc, and serpentine minerals are all based on this structure. A good example is biotite - K(Mg,Fe)3(AlSi3)O10(OH)2. Note that in this structure, Al is substituting for Si in one of the tetrahedral groups.

Tectosilicates (Framework Silicates)

If all of the corner oxygens are shared with another SiO4 tetrahedron, then a framework structure develops. The basic structural group then becomes SiO2. The minerals quartz, cristobalite, and tridymite all are based on this structure. If some of the Si+4 ions are replaced by Al+3 then this produces a charge imbalance and allows for other ions to be found coordinated in different arrangements within the framework structure. Thus, the feldspar and feldspathoid minerals are also based on the tectosilicate framework.

General Formula for Silicates

Based on these basic structural units, we can construct a general structural chemical formula for the silicates. But one substitution in particular tends to mess things up a bit. This is Al+3, the third most abundant element in the Earth's crust. Al+3 has an ionic radius that varies between 0.54 and 0.39 depending on the coordination number. Thus, it could either fit in 6-fold coordination with oxygen or 4-fold coordination with oxygen. Because Al+3 will go into 4-fold coordination with oxygen, it sometimes substitutes for Si+4. If such a substitution takes place, it creates a charge imbalance that must be made up elsewhere in the silicate structure.

The other common elements in the Earth's crust that enter the silicates do so in other types of coordination. Ions like Al+3, Mg+2, Fe+2, Fe+3, Mn+2, and Ti+4 enter into 6-fold or octahedral sites. Larger ions like Ca+2, and Na+1, are found in octahedral coordination or 8-fold, cubic coordination sites. Very large cations like K+1, Ba+2, and sometimes Na+1 are coordinated by 12 oxygens in 12-fold coordination sites.

We can thus write a general structural formula for the silicates as

follows:

XmYn(ZpOq)Wr

where X represents an 8 to 12 fold coordination site for large cations like K+, Rb+, Ba+2, Na+, and Ca+2.

Y represents a 6-fold (octahedral) site for intermediate sized cations like Al+3, Mg+2, Fe+2, Fe+3, Mn+2, and Ti+4. Z represents the tetrahedral site containing Si+4, and Al+3.

the ratio p:q depends on the degree of polymerization of the silica (or alumina) tetrahedrons, or the silicate structural type as discussed above.

O is oxygen,

and W is a hyrdoxyl (OH-1) site into which can substitute large anions like F-1 or Cl-1.

The subscripts m, n, and r depend on the ratio of p to q and are chosen to maintain charge balance.

This is summarized in the table shown here. In this table note that there is very little substitution that takes place between ions that enter the X, Y, and Z sites. The exceptions are mainly substitution of Al+3 for Si+4, which is noted in the Table, and whether the X site is large enough to accept the largest cations like K+1, Ba+2, or Rb+1.

Site C.N. Ion

Z 4 Si+4

Al+3

Y 6

Al+3

Fe+3

Fe+2

Mg+2

Mn+2

Ti+4

X

8 Na+1

Ca+2

8 - 12

K+1

Ba+2

Rb+1

Nesosilicates (Island Silicates)

We now turn our discussion to a systematic look at the most common rock forming minerals, starting with the common nesosilicates. Among these are the olivines, garnets, Al2SiO5 minerals, staurolite, and sphene (the latter two will be discussed in the last lecture on accessory minerals).

As discussed above, the nesosilicates or island silicates are based on the isolated SiO4

-4 tetrahedral groups. In the olivines, the remaining corner oxygens form octahedral groups that coordinate Mg+2 and Fe+2 ions.

Olivines

The olivines consist of a complete solid solution between Mg2SiO4 (forsterite, Fo) and Fe2SiO4 (fayalite, Fa). There is limited substitution of the following end members:

Ca2SiO4 - larnite

Mn2SiO4 - tephroite

CaMgSiO4 - monticellite (which is commonly found in metamorphosed dolomites)

Also found substituting in octahedral sites are Ni+2 and Cr+3, particularly in Mg-rich olivines.

The phase diagram for the common end members of the olivine solid solution series shows that pure forsterite melts at 1890oC and pure fayalite melts at 1205oC. Thus, the olivines are sometimes seen be be zoned from Mg-rich cores to more Fe-rich rims, although such zoning is usually limited to 5 to 10% difference between the cores and the rims.

Occurrence Pure forsterite is limited to metamorphosed Mg-rich limestones and dolomitic metamorphic rocks. Fo90 - 95 is found in ultrabasic igneous rocks, particularly dunites (>90% by volume olivine), and peridotites (Olivine + Cpx + Opx). Fo60 - 90 is found in basic igneous rocks likes basalts and gabbros, and sometimes in andesites, where it occurs with plagioclase and pyroxene. Fa100 - 40 is found in Fe-rich siliceous igneous rocks like rhyolites and granites. Mg-rich olivines rarely occur in quartz bearing rocks and quartz rarely occurs with Mg-rich olivine because the reaction shown below runs to the right for most pressures and temperatures.

Mg2SiO4 + SiO2 <=> 2MgSiO3

Fo Qtz En

Note however, that Fe-rich olivines can occur with quartz.

Structure The structure of the olivines is illustrated on page 439 of Klein and Dutrow. Note that 2 different kinds of octahedral sites occur. One is a regular octahedron, labeled M2, and the other is a distorted octahedron, labeled M1. Fe+2 and Mg+2 have no particular preference for either site, but if Ca+2 is present it prefers the M2 site.

Identifying Properties The olivines are orthorhombic (2/m2/m2/m) and usually green colored in hand specimen. The most characteristic property in thin section is their surface texture that kind of looks like a piece of sandpaper (see photo on the back wall of the Mineralogy lab). Because of their good {010} cleavage and common {100} parting, they show parallel extinction relative to the cleavage or parting. Maximum birefringence as seen in the interference colors in thin section varies between 3rd order blue (for Fo rich varieties) and 3rd order yellow (for Fa-rich varieties), but remember that this is the maximum birefringence that will only be seen for grains with and parallel to the microscope stage. Fo-rich olivines are usually clear in thin section, but Fa-rich olivines show pale yellow, greenish yellow, or yellow amber

absorption colors and sometimes show pleochroism with = = pale yellow, = orange, yellow, or reddish brown. Because optical properties vary with composition of the olivine, 2V is useful in distinguishing olivine compositions. Look at the graph on page 11 of Deer, Howie, and Zussman. From the graph you can see that very Fo-rich olivines(>Fo90) are optically positive with a 2V between 82 and 90o. Between Fo90 and Fa100 the olivine is optically negative with 2V between 90 and 130 (2V between 90o and 50o. Thus, by estimating the 2V, you should be able to estimate the composition of the olivine. Olivines are distinguished from orthorhombic pyroxenes (opx) easily because olivines show higher maximum birefringence and do not show the characteristic {110} cleavage of the pyroxenes. They are distinguished from the clinopyroxenes (Cpx) which show inclined extinction relative their {110} cleavage and show a biaxial positive character with a 2V of 50 to 60o.

Garnets

Garnets are isometric minerals and thus isotropic in thin section, although sometimes they are seen to be weakly birefringent (slightly anisotropic). They are also nesosilicates, and therefore based on the SiO4 structural unit. The general formula for garnets is:

A3B2(Si3O12)

where the A sites are cubic sites containing large divalent cations, usually Ca, Fe, Mg, or Mn, and the B sites are octahedral sites occupied by smaller trivalent cations, like Al and Fe+3.

Garnets with no Ca in the A site and Al in the B site are called the

pyralspite series. These consist of the end members:

Pyrope - Mg3Al2Si3O12

Almandine - Fe3Al2Si3O12

Spessartine - Mn3Al2Si3O12

Garnets with Ca in the A site are called the ugrandite series and consist of the end members:

Uvarovite - Ca3Cr2Si3O12

Grossularite - Ca3Al2Si3O12

Andradite - Ca3Fe+32Si3O12

Limited solid solution exists between end members of each series.

Occurrence The garnets occur mostly in metamorphic rocks where they are often seen to form euhedral (well-formed) crystals. The Mg-rich garnet, pyrope, is found in metamorphic rocks formed at high pressure and in eclogites (basalts metamorphosed at high pressure) and peridotites (ultrabasic rocks containing olivine, Opx, Cpx, and garnet).

The Fe-rich garnet, almandine, is the most common garnet and is found in metamorphic aluminous schists.

The Mn-rich variety, spessartine, is limited to Mn-rich metamorphic rocks like meta-cherts.

Identifying Properties

Garnets are generally isotropic although some may be weakly birefringent. In hand specimen they exhibit a wide range of colors and these are sometimes seen in thin section. Color is controlled by the amounts of Fe+2, Fe+3, Mg+2, and Cr+3 present. Pyrope is usually pinkish red to purplish in hand specimen and is usually clear in thin section. Almandine is usually deep red to brownish black in hand specimen and pink in thin section. Spessartine ranges from black to red to brown and orange and is usually pink in thin section. Grossularite has a color in hand specimen that reflects the amount of Fe and Mn present and thus ranges from brown to yellow to pink. If Cr is present, the color is usually green. In thin section grossularite varies in color from clear to brown or green in Cr-rich varieties. Uvarovite, with high Cr concentration is usually deep green in hand specimen and green in thin section. Andradite ranges from yellow to dark brown, but if appreciable amounts of Ti are present, the color could be black in hand specimen and brown in thin section. The composition and identity of the garnets is best determined either by association with other minerals or by more sophisticated techniques such as electron microprobe or XRD. Garnets are easily distinguished from other minerals by their high relief, isotropic character, and common euhedral habit.

Al2SiO5 Minerals

The Al2SiO5 minerals are common in aluminous metamorphic rocks (meta-shales and meta-mudstones) and sometimes found in aluminous igneous rocks.

In metamorphic rocks the Al2SiO5 polymorphs provide rather general estimates of the pressure and temperature of metamorphism, with Kyanite indicating relatively high pressure, andalusite indicating low temperature and pressure, and sillimanite indicating high temperature. Better estimates of pressure and temperature are provided if two of the minerals are present in the same rock.

Sillimanite Sillimanite is orthorhombic with a good {010} cleavage. It generally occurs in long fibrous crystals that are length slow, with extinction parallel to the {010} cleavage. In sections lying on {001}that show well-developed {110} forms, the cleavage is usually seen to cut across the crystal as shown here. Maximum birefringence is generally seen to be between 2o yellow to 2o red. Sillimanite is biaxial positive with a 2V of 21 - 31o.

Andalusite

Andalusite is also orthorhombic , but shows a length fast character. It generally tends to occur as euhedral blocky crystals with a maximum birefringence in thin section between 1o yellow and 1o red. It sometimes shows weak pleochroism with = rose-pink, = = greenish yellow. Some varieties show a cross, termed the chiastolite cross, which is made up of tiny carbonaceous inclusions oriented along crystallographic directions (see illustration on page 492 of Klein & Dutrow). Andalusite generally occurs as euhedral crystals with an almost square prism. It is biaxial negative with 2V = 73 - 86o.

Kyanite Kyanite is triclinic and thus shows inclined extinction relative to its good {100}and {010}cleavages and {001} parting. In hand specimen kyanite is commonly pale blue in color, but is clear to pale blue in thin section. Because of its good cleavages and parting, two cleavages or partings are seen in any orientation of the crystal in thin section. These cleavages intersect at angles other than 90o and thus look like parallelograms in two dimensions. Because Kyanite has high relief relative to other minerals with which it commonly occurs, it stands out in thin section and sometimes appears to have a brownish color. This color is more due to its high relief and numerous cleavages rather than due to selective absorption. Kyanite is biaxial negative with 2V = 78 -83o

Staurolite (Mg,Fe)2Al9Si4O22(OH)2 Staurolite is a common mineral in medium grade metamorphic rocks, usually metamorphosed shales.

In hand specimen and in thin section it characteristically is seen to show

staurolite twinning, either the right-angle cross, twinned on {031} or the oblique cross, twinned on {231}

It is monoclinic, but its optical properties are those of an orthorhombic mineral. It has moderate {010} cleavage, which if present, will cause parallel extinction. It's most distinguishing property is its pleochroism, with = colorless, = pale yellow, and = golden yellow. Less distinctive are its positive optic sign and 2V = 82 - 90o. In many rocks Staurolite shows twinning, and commonly forms euhedral crystals with well developed {100} and {010} crystal faces. In thin section Staurolite is commonly seen to contain tiny inclusions of other minerals, usually quartz. There are very few minerals which can be confused with Staurolite.

Sorosilicates

Sorosilicates are the double island silicates. Only one important mineral group, the epidote group, has this structure.

Epidote, Clinozoisite, Zoisite

The important minerals in the epidote group are epidote, clinozoisite, and zoisite. Since the sorosilicates are based on the Si2O7

-6 group, the structural formula can be written as:

Ca2(Al,Fe+3)Al2O(SiO4)(Si2O7)(OH)

Thus, the epidote group contains both the double tetrahedra and the single tetrahedron, separated by groups of AlO6 octahedra and Ca in nine to 10 fold coordination with Oxygen or OH.

The formula can be rewritten as:

Ca2(Al,Fe+3)Al2Si3O12(OH)

Epidote is the Fe-rich variety and has the above general formula.

Clinozoisite is the Fe-free variety with the chemical formula:

Ca2Al3Si3O12(OH)

Both clinozoisite and epidote are monoclinic (2/m). Zoisite has the same chemical formula as clinozoisite, but is orthorhombic.

Epidote is usually pistachio green in color with perfect {001} cleavage and imperfect {100} cleavage. It is optically negative with a 2V of 64 - 90o. It usually shows pleochroism with - colorless to pale yellow, - greenish yellow, and - yellowish green, and shows high relief relative to feldspars and quartz. It's birefringence is high enough to show 3rd order interference colors. It usually shows an anomalous blue extinction.

Clinozoisite shows similar relief and cleavage to epidote, but it is optically negative with a 2V of 14 to 90o, shows no pleochroism, and lower birefringence (1st to 2nd order interference colors). Zoisite is similar to clinozoisite, except it will show parallel extinction relative to faces parallel to the crystallographic axes.

Epidote is a common mineral in low grade metamorphic rocks, particularly metamorphosed volcanic rocks and Fe-Al rich meta shales. Both Clinozoisite and epidote occur as alteration products of plagioclase and as veins in granitic rocks.

Cyclosilicates

The cyclosilicates are based on rings of SiO4 tetrahedra, with a Si:O ratio of 1:3 The most common minerals based on this structure are Beryl, Cordierite, and Tourmaline.

Beryl

Be3Al2Si6O18 is hexagonal (6/m2/m2/m) with a strong prismatic habit with the form {10 0} usually the only form present. It is usually deep green to yellowish green in color. Beryl forms different gemstones depending on color - Aquamarine when it is pale greenish-blue, Morganite if pink, and emerald if deep green and transparent. Beryl is a common constituent of coarse grained granitic rocks and pegmatites and is found in aluminous mica schists.

In thin section, Beryl shows higher relief than quartz, and is distinguished from quartz by its negative optic sign and length-fast character. The only other mineral that it can be confused with is apatite, but apatite shows even higher relief than Beryl.

Cordierite

Cordierite is (Mg,Fe)2Al4Si5O18.nH2O. It is orthorhombic

(2/m2/m2/m), but shows a pseudohexagonal character due to its common cyclical twinning on {110}. In thin section it may show a twinning that looks like albite twinning, which makes it hard to distinguish from plagioclase. But, cordierite is usually dusted with tiny opaque inclusions. In thick sections it shows a pale -yellow, violet, pale blue pleochroism. It can be distinguished from quartz by its biaxial character.

Cordierite is a common constituent of aluminous metamorphic rocks. It is common in contact metamorphic rocks where it is commonly associated with sillimanite or andalusite, feldspars and micas.

Tourmaline

Tourmaline - Na(Mg,Fe,Mn,Li,Al)3Al6Si6O18(BO3)3(OH)4 is hexagonal (3m) and is commonly found as well-formed prismatic crystals, with a rounded triangular cross section perpendicular to the c crystallographic axis.

Tourmaline is a common mineral in pegmatites (SiO2 - rich igneous rocks with large grain size), where it is associated with quartz and alkali feldspar. It is also found in metasomatized rocks of all types, where it is precipitated from a Boron and Silica - rich fluid phase.

It's most distinguishing properties are its uniaxial negative optical character and its pleochroism with = dark green or dark blue and = yellow or violet. Tourmaline usually forms in euhedral crystals with well developed prism faces and extinction parallel to the prism faces.

COMPILED BY GDC HANDWARA

LECTURE NOTES

1ST

SEMESTER

UNIT 4

Inosilicates (Single Chain Silicates)

The single chain silicates have a basic structural unit consisting

of linked SiO4 tetrahedra that each share 2 of their oxygens in

such a way as to build long chains of SiO4. The basic structural

group is thus Si2O6 with an Si:O ratio of 1:3. The most

important inosilicates are the pyroxenes. These have a general

structural formula of:

XYZ2O6

where X = Na+, Ca

+2, Mn

+2, Fe

+2, or Mg

+2 filling octahedral sites called M2

Y = Mn+2

, Fe+2

, Mg+2

, Al+3

, Cr+3

, or Ti+4

filling smaller octahedral sites called

M1

Z = Si+4

or Al+3

in tetrahedral coordination.

The pyroxenes can be divided into several groups based on chemistry and

crystallography:

Orthorhombic Pyroxenes (Orthopyroxenes - Opx)

These consist of a range of compositions between enstatite - MgSiO3 and

ferrosilite - FeSiO3

Monoclinic Pyroxenes (Clinopyroxenes - Cpx)

The Diopside- Hedenbergite series - Diopside (CaMgSi2O6) -

Ferrohedenbergite (CaFeSi2O6)

The Sodic Pyroxenes - Jadeite (NaAlSi2O6) and Aegerine (NaFe+3

Si2O6)

Augite is closely related to the diopside - Hedenbergite series with addition

of Al and minor Na substitution - (Ca,Na)(Mg,Fe,Al)(Si,Al)2O6

Pigeonite is also a monoclinic pyroxene with a composition similar to the

orthopyroxenes with more Ca substituting for Fe, and Mg.

The compositional range of the Ca-

rich, Al-free pyroxenes in shown in

the triangular composition diagram

here. Note that there is complete

Mg-Fe substitution and small

amounts of Ca substitution into the

Orthopyroxene solid solution series.

Mg-rich varieties of orthopyroxene

are called hypersthene, whereas Fe-

rich varieties are called Ferrosilite.

There is also complete Mg-Fe solid

solution between Diopside and

Ferrohedenbergite, with some

depletion in Ca. CaSiO3 is the

chemical formula for wollastonite,

but wollastonite does not have a

pyroxene structure.

There is complete Mg-Fe solid solution between the pyroxenes, and as with most

Mg-Fe solid solutions, the Mg-rich end members crystallize at higher

temperatures than the Fe-rich end members.

Solid immiscibility is present between the Diopside - Hedenbergite series and the

Orthopyroxene series. This is seen in the phase diagram below which shows a

hypothetical phase diagram running from the orthopyroxenes to the

clinopyroxenes. Note the solvi. Pigeonite is only stable at higher temperatures

and inverts to orthopyroxene if cooled slowly to lower temperatures. Thus,

pigeonite is only found in volcanic and shallow intrusive igneous rocks, or as

exsolution lamellae in a host augite or opx (more commonly in augite).

When pigeonite or augite exsolve they may form exsolution lamellae that form

parallel to the (001) plane. At lower temperature the exsolution of Opx or augite

result in exsolution lamellae that are parallel to the (100) plane.

All pyroxenes show perfect {110} cleavage.

When viewed looking down the c-

crystallographic axis, the cleavages intersect at

near 90o angles (the angles are actually 92 - 93

o

and 87 - 880). This 90 degree cleavage angle is

most useful in distinguishing pyroxenes from

amphiboles (in amphiboles the cleavages are at

56o and 124

o.

Distinguishing Opx from Cpx in

thin section is accomplished by

noting that in all orthorhombic

pyroxenes the prismatic {110}

cleavage will show parallel

extinction. If looking down the c-

axis the extinction will be

symmetrical relative to the two

cleavage traces.

In Cpx, however, one would see

inclined extinction on all faces

except {100}. Thus, one should

check several grains for extinction

before concluding that the mineral

is Opx, since there is always a

slight chance that one is looking at

a {100} face. Note that in Cpx,

the maximum extinction angle will

only be observed if one is looking

at a {010} face.

Occurrence and Distinction of the Pyroxenes

Augite - is commonly found in both plutonic and volcanic igneous rocks,

as well as high grade meta-igneous rocks like gneisses and granulites. It is

easily distinguished from amphiboles by the nearly 90ocleavage angles, and

is distinguished from Opx by inclined extinction relative to the {110}

cleavage, as discussed above. Augite also has higher maximum

birefringence than Opx, and shows 2nd

to 3rd

order interference colors.

Augite is optically positive with a 2V of about 60o. It shows high relief,

relative to quartz and feldspars and is commonly colorless to brown or

green in thin section, showing no pleochroism.

Hypersthene - is commonly found in both plutonic and volcanic igneous

rocks and in meta-igneous rocks as well. It is distinguished from augite by

its lower interference colors and lack of inclined extinction relative to

{110}. Hypersthene is sometimes pleochroic, showing light pink to light

green colors. The chemical composition of hypersthene can be estimated

using 2V (see p. 163 of DHZ). Compositions close to Enstatite are

optically positive with a 2V of 60 to 90o, whereas intermediate

compositions are optically negative with a 2V of 50 to 90o.

Pigeonite - is generally only found in volcanic igneous rocks, although, as

mentioned above, it can occur as exsolution lamellae in augites of more

slowly cooled igneous rocks. Pigeonite is distinguished from augite by its

lower 2V of 0 to 30o, and is distinguished from hypersthene by its lack of

pleochroism, lower 2V and inclined extinction relative to the {110}

cleavage.

Aegerine (acmite) - Aegerine Augite - are sodic pyroxenes and thus are

found in alkalic igneous rocks associated with sodic amphiboles, alkali

feldspars, and nepheline. The mineral is common in alkali granites, quartz

syenites, and nepheline syenites (all alkalic plutonic rocks), and are also

found in sodic volcanic rocks like peralkaline rhyolites.

Aegerine is distinguished from other clinopyroxenes by a low extinction

angle relative to the {110} cleavage (0 -10o, with augite having an

extinction angle of 35 - 48o), and by the green brown pleochroism present

in aegerine. Aegerine is also optically negative with a 2V of 60 to 70o,

whereas Aegerine-augite has a higher 2V and can be optically positive or

negative. It is distinguished from the pleochroic sodic amphiboles by its

nearly 90o pyroxene cleavage angle.

Jadeite - is a sodium aluminum

pyroxene that is characterized by its

presence in metamorphic rocks

formed at relatively high pressure. It

can form by a reaction of Albite to

produce :

NaAlSi3O8 = NaAlSi2O6 + SiO2

Albite Jadeite Quartz

Jadeite has a lower refractive index

than all other pyroxenes, and has low

birefringence, showing low order 1st

and 2nd

order interference colors.

It is monoclinic with an extinction angle of 33 to 40o, and can thus be

easily distinguished form hypersthene. It is usually colorless in thin

section, helping to distinguish it from augite and aegerine, and has lower

birefringence than augite and aegerine.

Inosilicates (Double Chain Silicates) - The Amphiboles

The amphibole group of minerals is based on the double-chain silicate structure

as shown here. The basic structural unit is (Si4O11)-6

. The structural formula can

be written as:

W0-1X2Y5Z8022(OH,F)2

where W = Na+1

or K+1

in the A site with 10 to 12

fold coordination.

X = Ca+2

, Na+1

, Mn+2

, Fe+2

, Mg+2

, Fe+3

, in an M4 site

with 6 to 8 fold coordination.

Y = Mn+2

, Fe+2

, Mg+2

, Fe+3

, Al+3

. or Ti+4

in an M1 octahedral coordination site.

Z = Si+4

and Al+3

in the tetrahedral site.

There is complete solid solution between Na and Ca end members and among Mg

and Fe end members, with partial substitution of Al+3

for Si+4

in the tetrahedral

site, and partial substitution of F for OH in the hydroxyl site.

The composition of the

common (non-sodic)

amphiboles are shown in the

diagram here. Note the

similarity to the pyroxene

compositional diagram,

above. Actinolite is the solid

solution between Tremolite

[Ca2Mg5Si8O22(OH)2] and

Ferroactinolite

[Ca2Fe5Si8O22(OH)2.]

Cummingtonite - Grunerite is

a solid solution between

Anthophyllite

[Mg7Si8O22(OH)2] and

Grunerite [Fe7Si8O22(OH)2].

Hornblende is the most common amphibole and has more in common with the

Tremolite - Ferroactinolite series, with Al substituting into the Y sites and the

tetrahedral site. It thus has the complicated formula:

(Ca,Na)2-3(Mg,Fe,Al)5Si6(Si,Al)2O22(OH,F)2

The sodic amphiboles have the following formulae:

Glaucophane - Na2Mg3Al2Si8O22(OH)2

Riebeckite - Na2Fe3+2

Fe2+3

Si8O22(OH)2

Arfvedsonite - NaNa2Fe4+2

Fe+3

Si8O22(OH)2

All of the amphiboles except Anthophyllite are

monoclinic, and all show the excellent prismatic

cleavage on {110}. The angles between the

cleavages, however are 56o and 124

o making all

amphiboles easy to distinguish from the

pyroxenes. Looking at faces that show only a

single cleavage trace would show inclined

extinction, except in Anthophyllite.

Occurrence and Distinction of the Amphiboles

Tremolite - Occurs almost exclusively in low grade metamorphic rocks,

particularly those with a high Ca concentration, such as meta-dolomites,

meta-ultrabasic rocks. Tremolite in hand specimen is white in color and

shows a fibrous habit and the characteristic amphibole cleavage. In thin

section it is distinguished from wollastonite and diopside by its amphibole

cleavage. In thin section it is clear with no pleochroism, which

distinguishes it from other amphiboles. It shows high relief, inclined

extinction, and is optically negative with a 2V of about 85o.

Actinolite - Also occurs almost exclusively in low grade metamorphic

rocks, particularly in meta-basalts and meta-gabbros where it is commonly

associated with chlorite. It is green in hand specimen and shows the

characteristic amphibole cleavage, usually showing an elongated habit. In

thin section it shows a characteristic pale yellow to green pleochroism, has

high relief, and is optically negative with a 2V of 60 to 85o.

Hornblende - is a common mineral in both igneous and metamorphic

rocks. In igneous rocks it is found in andesites, dacites, and rhyolites, as

well as in gabbros, diorites, and granites. In metamorphic rocks it is a

common constituent of meta-basalts that have been metamorphosed to

intermediate grades of regional metamorphism (amphibolites). It is also

found in some ultrabasic rocks. In hand specimen it is dark brown to black

in color and shows the characteristic amphibole cleavage. In thin section,

it shows high relief with a characteristic green - brown - yellow

pleochroism. Optic sign and 2V angle cover a wide range and not very

useful in the distinction of hornblende.

Basaltic Hornblende (also called Oxy-hornblende)- is a dark brown to

reddish brown variety of hornblende that results from oxidation during

crystallization of basalts, andesites, dacites, and rhyolites. It usually has a

dark reaction rim that consists of opaque oxide, and is characteristically

pleochroic in yellow to brown to reddish brown colors.

Anthophyllite - does not occur in igneous rocks, but is a constituent of

metamorphic rocks. It is the only orthorhombic amphibole so it is easily

characterized by its parallel extinction relative to the {110} cleavage.

Cummingtonite - Grunerite - is more common in metamorphosed

igneous rocks where members of the series occur with hornblende. It has

been found in siliceous volcanic rocks as well. Cummingtonite is optically

positive, while grunerite is optically negative. Members of this series can

be distinguished from orthorhombic Anthophyllite by the inclined

extinction of the monoclinic Cummingtonite-Grunerite series, and can be

distinguished from tremolite and actinolite by the higher refractive indices

and higher birefringence of the Cummingtonite Grunerite series.

Glaucophane - Riebeckite - Glaucophane is a common mineral in

blueschist facies metamorphic rocks that result from low temperature, high

pressure metamorphism along ancient subduction zones. Riebeckite is

found in alkali granites, syenites, and peralkaline rhyolites. Glaucophane is

easily distinguished from the other amphiboles by its characteristic blue-

lavender pleochroism. Glaucophane is length slow, whereas Riebeckite is

length fast.

Arfvedsonite - occurs most commonly in peralkaline volcanic rocks and

alkaline plutonic igneous rocks, where it typically occurs with the sodic

pyroxene aegerine. Its blue green to yellow green pleochroism distinguish

it from the other amphiboles.

The chart below, also found in your lab assignments, summarizes the properties

used to distinguish the amphiboles.

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UNIT 4

Phyllosilicates (Sheet Silicates)

The phyllosilicates, or sheet silicates, are an important group of minerals that includes the

micas, chlorite, serpentine, talc, and the clay minerals. Because of the special importance of

the clay minerals as one of the primary products of chemical weathering and one of the more

abundant constituents of sedimentary rocks, they will be discussed in more detail in the next

lecture.

The basic structure of the phyllosilicates is based on

interconnected six member rings of SiO4-4

tetrahedra that

extend outward in infinite sheets. Three out of the 4

oxygens from each tetrahedra are shared with other

tetrahedra. This leads to a basic structural unit of Si2O5-2

.

Most phyllosilicates contain hydroxyl ion, OH-, with the OH

located at the center of the 6 membered rings, as shown here.

Thus, the group becomes Si2O5(OH)-3

. When other cations are

bonded to the SiO4 sheets, they share the apical oxygens and

the (OH) ions which bond to the other cations in octahedral

coordination. This forms a layer of cations, usually Fe+2

,

Mg+2

, or Al+3

, that occur in octahedral coordination with the O

and OH ions of the tetrahedral layer. As shown, here, the

triangles become the faces of the octahedral groups that can

bind to the tetrahedral layers.

The octahedral layers take on the structure

of either Brucite [Mg(OH)3], if the cations

are +2 ions like Mg+2

or Fe+2

, or Gibbsite

[Al(OH)3], if the cations are +3 like Al+3

.

In the brucite structure, all octahedral sites

are occupied and all anions are OH-1

. In

the Gibbsite structure every 3rd

cation site

is unoccupied and all anions are OH-1

.

This gives rise to 2 groups of sheet silicates:

1. The trioctahedral sheet silicates where each O or OH ion is surrounded by 3 divalent

cations, like Mg+2

or Fe+2

.

2. The dioctahedral sheet silicates where each O or OH ion is surrounded by 2 trivalent

cations, usually Al+3

.

We can build the structures of the various sheet silicates by starting with the octahedral layers

similar to the structures of brucite or gibbsite, as shown below.

The trioctahedral phyllosilicates are based on the

structure where the octahedral layers are similar to

brucite, where Mg+2

occupies the cation position.

The dioctahedral phyllosilicates are based on the

structure where the octahedral layers are similar to

gibbsite, where Al+3

occupies the cation position.

The octahedral sheets in both cases are held together by weak Van der Waals bonds.

If we start with the brucite and

gibbsite structures shown above,

and replace 2 of the OH ions with

O, where the Oxygens are now the

apical Oxygens of the tetrahedral

sheets, then we get the structure of

the serpentine mineral, Lizardite,

if the octahedral layer is

trioctahedral, containing Mg+2

. If

the octahedral layer is

dioctahedral, containing Al+3

, the

structure of the clay mineral

Kaolinite, is obtained.

This leads to a tetrahedral - octahedral (T-O) structure, where each T-O layer is bonded to the

top (or bottom) of another T-O layer by Van der Waals bonds.

If 2 more of the OH ions in the octahedral

layer are replaced by O, and these O

become the apical Oxygens for another

tetrahedral layer, the this builds the

trioctahedral phyllosilicate talc or the

dioctahedral pyrophyllite. This becomes a

T-O-T layer that can bond to other T-O-T

layers by weak Van der Waals bonds.

If an Al+3

is substituted for every 4th

Si+4

in the tetrahedral layer, this causes an excess -1

charge in each T-O-T layer. To satisfy the charge, K+1

or Na+1

can be bonded between 2 T-O-T

sheets in 12-fold coordination.

For the trioctahedral sheet silicates this becomes Phlogopite (Mg-biotite), and for the

dioctahedral sheet silicates this becomes Muscovite. This makes a T-O-T - T-O-T layer that,

again can bind to another T-O-T - T-O-T layer by weak Van der Waals bonds. It is along these

layers of weak bonding that the prominent {001} cleavage in the sheet silicates occurs.

Replacing 2 more Si+4

ions with Al+3

ions in the tetrahedral layer results in an excess -2 charge

on a T-O-T layer, which is satisfied by replacing the K+1

with Ca+2

.

This results in the trioctahedral sheet silicate - Clintonite and the dioctahedral sheet silicate -

Margarite.

Because of the differences in charge balance between the trioctahedral and dioctahedral sheet

silicates, there is little solid solution between the two groups. However, within the

trioctahedral sheet silicates there is complete substitution of Fe+2

for Mg+2

and limited

substitution of Mn+2

into the octahedral sites. Within the dioctahedral sheet silicates there is

limited substitution of Fe+3

for Al+3

in octahedral sites. In addition, F- or Cl

- can substitute for

(OH)- in the hydroxyl site. As previously discussed, substitution of F

-1 stabilizes the mineral to

higher pressures and temperatures.

Another group of phyllosilicates that is more of mixture of structural types is the chlorite

group. Although chlorite is complex in that the amount of Al that can substitute Mg and Si is

variable, one way of looking at the chlorite structure is shown below.

Here, the chlorite structure is depicted as

consisting of a brucite-like layer (with some

Al) sandwiched between tetrahedral layers

that are similar to phlogopite.

Another important sheet silicate structure is that of vermiculite. This is similar to the talc

structure, discussed above, with layers of water molecules occurring between each T-O-T

layer.

Similarly, insertion of layers of water molecules between the T-O-T sheets of pyrophyllite

produces the structure of smectite clays. The vermiculite and smectite groups are therefore

expanding type sheet silicates and as the water is incorporated into the structure the mineral

increases its volume.

Although we have shown that the octahedral layers fit perfectly between the tetrahedral layers,

this is an oversimplification. If the tetrahedral layers were stacked perfectly so that apical

oxygens were to occur vertically aligned, then the structure would have hexagonal symmetry.

But, because this is not the case, most of the phyllosilicates are monoclinic.

Serpentine Group

The serpentine group of minerals has the formula - Mg3Si2O5(OH)4. Three varieties of

serpentine are known. Antigorite and Lizardite are usually massive and fine grained, while

Chrisotile is fibrous. As discussed above, the imperfect fit of the octahedral layers and the

tetrahedral layers causes the crystal structure to have to bend.

In Antigorite the bending

of the sheets is not

continuous, but occurs in

sets, similar to

corrugations, as shown

here.

In Chrisotile, the bending of the sheets

is more continuous, resulting in

continuous tubes that give the mineral

it's fibrous habit. The Chrisotile variety

is commonly referred to as asbestos.

Occurrence - Serpentine is found as an alteration product of Mg-rich silicates like pyroxene

and olivine. It results due to hydration. For example:

2Mg2SiO4 + 3H2O <=> Mg3Si2O5(OH)4 + Mg(OH)2

Olivine water Serpentine Brucite

Thus, serpentine is commonly found pseudomorphed after olivines and pyroxenes in altered

basic and ultrabasic igneous rocks, like altered peridotites, dunites, and sometimes basalts and

gabbros. It is commonly associated with minerals like magnesite (MgCO3), chromite, and

magnetite. If the rock is made up almost entirely of serpentine, it is called a serpentinite.

Properties - Because the serpentines usually occur either as fine-grained aggregates or fibrous

crystals, optical properties are difficult to determine. Most of the time, serpentine can be

distinguished by its characteristic pseudomorphing of other crystals like olivines and

pyroxenes. In hand specimen it generally tends to have a dark green color with a greasy luster.

In thin section it is clear to pale green to pale yellow, but does not show pleochroism, shows a

generally low relief compared to minerals like olivine and pyroxene with which it is associated,

and show very low order interference colors due to its low birefringence.

Talc

Talc has the chemical formula - Mg3Si4O10(OH)2. It is probably best know for its low

hardness. Although it has a micaceous structure, it is so easily deformed, that crystals are

rarely seen.

Occurrence - Like serpentine, talc requires an environment rich in Mg. It is therefore found in

low grade metamorphic rocks that originated as ultrabasic to basic igneous rocks. Rocks

composed almost entirely of talc have a greasy feel and are referred to as soapstone.

Properties - Talc is most easily distinguished in hand specimen by its low hardness, greasy

feel, and association with other Mg-bearing minerals. When crystals are present they show the

characteristic micaceous cleavage on {001}. In thin section, talc is colorless, biaxial negative

with a 2V of 0 to 30o. Like other sheet silicates, it shows the well developed {001} cleavage.

Maximum interference colors, consistent with a birefringence of 0.05 is 3o yellow. Muscovite

has a higher birefringence and higher 2V, properties which easily distinguish the 2 minerals.

Mica Group

The micas can be divided into the dioctahedral micas and the trioctahedral micas, as discussed

above. Muscovite, Paragonite, and Margarite are the white micas, and represent the

dioctahedral group, and Biotite and Clintonite (Xanthophyllite) the black or brown mica,

represents the trioctahedral group. Muscovite and Biotite are the most common micas, but the

Lithium- rich, pink mica, Lepidolite, K(Li,Al)2AlSi3O10(OH)2 is also common, being found

mostly in pegmatites.

Muscovite

Muscovite, KAl3Si3O10(OH)2, and Paragonite, NaAl3Si3O10(OH)2, are two potential end

members of the solid solution series involving K and Na. But, there is a large miscibility gap

between the two end members with Muscovite being between 65% and 100% of K-rich end

member, and Paragonite showing compositions between about 80% and 100% of the Na-rich

end member.

Occurrence - Muscovite is common constituent of Al-rich medium grade metamorphic rocks

where is found in Al-rich schists and contributes to the schistose foliation found in these rocks.

Muscovite is also found in siliceous, Al-rich plutonic igneous rocks (muscovite granites), but

has not been found as a constituent of volcanic rocks. In these rocks it is commonly found in

association with alkali feldspar, quartz, and sometimes biotite, garnet, andalusite, sillimanite, or

kyanite.

Properties - Muscovite is easily identified in hand specimen by its white to sometimes light

brownish color and its perfect {001} cleavage. In thin section, the {001} cleavage is easily

seen and it's high birefringence is exhibited by the large change in relief on rotation of the stage

and it's 2nd to 4th order interference colors. It is clear and shows no pleochroism (which

distinguishes it from Biotite), and it is biaxial negative with a 2V between 28 and 50o. One of

the most diagnostic properties of the micas, including muscovite, is the mottled or birds-eye

extinction exhibited by these minerals.

Biotite

Biotite is a solid solution between the end members Phlogopite KMg3AlSi3O10(OH)2 and

Annite KFe3AlSi3O10(OH)2, although pure Annite does not occur in nature. In addition, small

amounts of Na, Rb, Cs, and Ba may substitute for K, and like in other minerals, F can substitute

for OH and increase the stability of Biotite to higher temperatures and pressures.

Occurrence - Nearly pure phlogopite is found in hydrous ultrabasic rocks like kimberlite, and

is also found in metamorphosed dolomites. Biotite, with more Fe-rich compositions is

common in dacitic, rhyolitic, and trachytic volcanic rocks, granitic plutonic rocks, and a wide

variety of metamorphic rocks. In metamorphic rocks, biotite usually shows a preferred

orientation with its {001} forms parallel to the schistose foliation.

Properties - In hand specimen, Biotite is brown to black and shows the perfect {001}

micaceous cleavage. In thin section, it shows the perfect cleavage and mottled extinction

typical of all micas. It's most characteristic property is its pleochroism, showing yellow to

brown to green colors. Hornblende shows similar pleochroic colors, but is distinguished from

biotite by the differences in cleavage of the 2 minerals. Biotite is biaxial negative with a low

2V of 0o to 25

o.

Chlorite Group

As discussed above, the Chlorite group has a structure that consists of phlogopite T-O-T layers

sandwiching brucite-like octahedral layer. There is substantial substitution of Mg for Fe, and

Al can substitute for (Mg, Fe) in both the octahedral sites, as well as for Si in the tetrahedral

sites. Thus, chlorite can have a rather complicated formula - (Mg,Fe,Al)3(Si,Al)4O10(OH)6.

Occurrence- Chlorite is a common mineral in low grade metamorphic rocks, where it occurs in

association with minerals like actinolite, epidote, and biotite. It also forms as an alteration

product of pyroxenes, amphiboles, biotite, and garnet in igneous as well a metamorphic rocks.

Properties - In hand specimen, chlorite is recognized by its green color, micaceous habit and

cleavage, and association with other minerals like actinolite and epidote. In thin section,

Chlorite shows low relief and low birefringence, with a characteristic midnight blue to black

anomalous interference color. It shows some pleochroism in the range of green to pale yellow.

It is easily distinguished from biotite by its lower relief and anomalous interference color.

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Tectosilicates (Framework Silicates)

The tectosilicates or framework silicates have a structure wherein all of

the 4 oxygens of SiO4-4

tetrahedra are shared with other tetrahedra. The

ratios of Si to O is thus 1:2.

Since the Si - O bonds are strong covalent bonds and since the structure is

interlocking, the tectosilicate minerals tend to have a high hardness.

SiO2 Minerals

There are nine known polymorphs of SiO2, one of which does not occur naturally. These are:

Name Crystal System Density

(g/cm3)

Refractive

Index

(mean)

Stishovite Tetragonal 4.35 1.81

Coesite Monoclinic 3.01 1.59

Low () Quartz Hexagonal 2.65 1.55

High () Quartz Hexagonal 2.53 1.54

Kaetite (synthetic) Tetragonal 2.50 1.52

Low () Tridymite Monoclinic or Orthorhombic 2.26 1.47

High () Tridymite Hexagonal 2.22 1.47

Low () Cristobalite Tetragonal 2.32 1.48

High () Cristobalite Isometric 2.20 1.48

Stishovite and Coesite are high pressure forms

of SiO2, and thus have much higher densities

and refractive indices than the other

polymorphs. Stishovite is the only polymorph

where the Si occurs in 6 fold (octahedral)

coordination with Oxygen, and this occurs due

to the high pressure under which the mineral

forms. Both Stishovite and Coesite have been

found associated with meteorite impact

structures.

At low pressure with decreasing temperature, SiO2 polymorphs change from high Cristobalite -

Low Cristobalite - High Tridymite - Low Tridymite - High Quartz - Low Quartz. The high to

low transformations are all displacive transformations. Since displacive transformations

require little rearrangement of the crystal structure and no change in energy, the high ()

polymorphs do not exist at the surface of the earth, as they will invert to the low ()

polymorphs as temperature is lowered.

Transformations between Cristobalite, Tridymite, and Quartz, however, as well as

between the high pressure polymorphs and Quartz, are reconstructive transformations. Since

reconstructive transformations require significant structural rearrangement and significant

changes in energy, they occur slowly, and the high temperature and high pressure polymorphs

can occur as metastable minerals at the Earth's surface.

Quartz

Quartz is hexagonal and commonly occurs as crystals ranging in size form microscopic to

crystals weighing several tons. Where it crystallizes unhindered by other crystals, such as in

cavities in rock or in a liquid containing few other crystals, it shows well-developed hexagonal

prisms and sometimes showing apparent hexagonal pyramids or dipyramid. When it

crystallizes in an environment where growth is inhibited by the surroundings, it rarely show

crystal faces. It is also found as microcrystalline masses, such as in the rock chert, and as

fibrous masses, such as in chalcedony.

As visible crystals, Quartz is one of the more common rock forming minerals. It occurs in

siliceous igneous rocks such as volcanic rhyolite and plutonic granitic rocks. It is common in

metamorphic rocks at all grades of metamorphism, and is the chief constituent of sand.

Because it is highly resistant to chemical weathering, it is found in a wide variety of

sedimentary rocks.

Several varieties of Quartz can be found, but these are usually only distinguishable in hand

specimen.

Rock Crystal - clear Quartz in distinct crystals - usually found growing in open cavities

in rock.

Amethyst - violet colored Quartz, with the color resulting from trace amounts of Fe in

the crystal.

Rose Quartz - a pink colored variety, that usually does not show crystal faces, the color

resulting from trace amounts of Ti+4

.

Smokey Quartz - a dark colored variety that may be almost black, usually forming well-

formed crystals. The color appears to result from trace amounts of Al+3

in the structure.

Citrine - a yellow colored variety.

Milky Quartz - a white colored variety with the color being due to fluid inclusions.

Milky Quartz is common in hydrothermal veins and pegmatites.

A fibrous variety of Quartz is called Chalcedony. It is usually brown to gray to translucent

with a waxy luster. It is found lining or filling cavities in rock where it was apparently

precipitated from an aqueous solution. When it shows bands of color, it is commonly called by

the following names:

Carnelian - red colored Chalcedony

Chrysoprase - apple-green colored as a result of coloration from NiO.

Agate - alternating curving layers of Chalcedony with different colors or different

porosities.

Onyx - alternating layers of Chalcedony of different colors or porosities arranged in

parallel planes.

Bloodstone - green Chalcedony containing red spots of jasper (see below)

Very fined grained aggregates of cryptocrystalline quartz makes up rock like Flint and Chert.

Flint occurs as nodules in limestone, whereas chert is a layered rock deposited on the ocean

floor. The red variety of flint is called Jasper, where the color results from inclusions of

hematite.

Optical Properties

Quartz is uniaxial positive with a low relief and low birefringence, thus exhibited only 1o gray

to 1o white interference colors. In thin section it is almost always colorless when viewed

without the analyzer inserted. One of its most distinguishing properties in thin section is that it

usually has a smooth, almost polished-like surface texture. Quartz is easily distinguished from

the Feldspars by the biaxial nature of feldspars, and from Nepheline which is uniaxial

negative. Apatite, has similar birefringence to quartz, but is uniaxial negative and has a very

high relief.

In Chalcedony, the fibers are usually elongated perpendicular to the c-crystallographic axis and

thus are length fast. Normal quartz, when it show an elongated habit, is elongated parallel to

the c axis, and is thus length slow.

Tridymite

Tridymite is the high temperature polymorph of SiO2. Thus, it is only commonly found in

igneous rocks that have been cooled rapidly to surface temperatures, preventing the slow

transformation to quartz, the stable form of SiO2 at surface temperatures. Because of this, we

only expect to find Tridymite in siliceous volcanic rocks like rhyolites, where it commonly

occurs as wedge shaped crystals in cavities in the rock. In volcanic rocks, Tridymite is

commonly associated with Cristobalite and Sanidine.

Optical Properties

Tridymite usually occurs as orthorhombic or monoclinic wedge shaped crystals with a positive

2V between 40 and 90o. The wedge shape of the crystals is the result of twinning on {110},

and usually as 2 to 3 twinned individuals. Although it has similar birefringence to quartz and

feldspar, it has lower refractive indices, and thus shows negative relief compared to quartz and

feldspars.

Cristobalite

Cristobalite is also a high temperature SiO2 polymorph, and thus has a similar occurrence to

Tridymite. It also occurs in thermally metamorphosed sandstones. In volcanic rocks it can

occur both as a lining in open cavities, and as fine grained crystals in the groundmass of the

rock.

Optical Properties

Cristobalite is tetragonal and thus uniaxial. It has a negative optic sign and shows lower relief

than quartz, but has similar birefringence.

Opal

Opal is amorphous, and thus a mineraloid, with a formula - SiO2.nH2O.

Feldspars

The feldspars are the most common minerals in the Earth's crust. They consist of three end-

members:

KAlSi3O8 - Orthoclase (or), NaAlSi3O8 - Albite (ab), and CaAl2Si2O8 -Anorthite (an)

KAlSi3O8 and NaAlSi3O8 form a complete solid solution series, known as the alkali feldspars

and NaAlSi3O8 and CaAl2Si2O8 form a complete solid solution series known as the plagioclase

feldspars.

The feldspars have a framework structure, consisting of SiO4 tetrahedra sharing all of the

corner oxygens. However, in the alkali feldspars 1/4 of the Si+4

ions are replaced by Al+3

and

in the plagioclase feldspars 1/4 to 1/2 of the Si+4

ions are replaced by Al+3

. This allows for the

cations K+, Na

+, and Ca

+2 to be substituted into void spaces to maintain charge balance.

Compositions of natural feldspars are shown in the diagram below based on the 3 components -

NaAlSi3O8, - Albite (ab), KAlSi3O8 - Orthoclase (or) and CaAl2Si2O8. The Alkali Feldspars

form a complete solid solution between ab and or, with up to 5% of the an component. The

high temperature more K-rich variety is called Sanidine and the more Na-rich variety is called

anorthoclase.

The plagioclase feldspars are a complete solid solution series between ab and an, and can

contain small amounts of the or component. Names are given to the various ranges of

composition, as shown here in the diagram are:

Albite - ab90 to ab100

Oligoclase - ab70 to ab90

Andesine - ab50 to ab70

Labradorite - ab30 to ab50

Bytownite - ab10 - ab30

Anorthite - ab0 to an10

Plagioclase Feldspars

Plagioclase is the most common feldspar. It forms initially by crystallization from magma. The

plagioclase solid solution series is coupled solid solution where the substitution is:

Na+1

Si+4

<=> Ca+2

Al+3

Thus, the general chemical formula for plagioclase can be written as:

CaxNa1-xAl1+xSi3-xO8

where x is between 0 and 1.

The phase diagram for

the plagiocalse series is

shown here, and shows

that the Anorthite

component has a higher

melting temperature the

than the Albite

component. Thus, on

crystallization, higher

temperatures will favor

more An-rich plagioclase

which will react with the

liquid to produce more

Ab-rich plagioclase on

cooling.

Plagioclase occurs in basalts, andesites, dacites, rhyolites, gabbros, diorites, granodiorites, and

granites. In most of these igneous rocks, it always shows the characteristic albite twinning.

Plagioclase also occurs in a wide variety of metamorphic rocks, where it is usually not twinned.

In such rocks where the plagioclase is not twinned, it is difficult to distinguish from the alkali

feldspars. Plagioclase can be a component of clastic sedimentary rocks, although it is less

stable near the Earth's surface than alkali feldspar and quartz, and usually breaks down to clay

minerals during weathering.

Properties

In hand specimen, plagioclase is most commonly white colored and

shows perfect {100} and good {010} cleavage. It is most easily

identified and distinguished from quartz, sanidine, orthoclase, and

microcline, by its common polysynthetic twinning on {010}. If this

twinning is not present, plagioclase can still be distinguished from

quartz by its cleavage, but cannot easily be distinguished from the

alkali feldspars. If both plagioclase and alkali feldspar occur in the

same rock, the two can usually be distinguished by differences in

color or differences in the extent of weathering.

In thin section, plagioclase commonly shows the characteristic albite

polysynthetic twinning. This twinning is the most characteristic

identifying feature of plagioclase, and makes its identification easy

when present. Although some cross-hatched twinning may also

occur in plagioclase, it is always very simple with only one or two

cross twins per grain. Thus, be careful not to identify plagioclase as

microcline. The cross-hatched twinning in microcline is always

much more complex.

Plagioclase often shows zoning. This is exhibited by the extinction position changing from the

rim to the core of the crystal. Remember that zoning is caused by incomplete reaction of

crystals with liquid during cooling of a solid solution. Often the zoning is very complex, and is

sometimes oscillatory. Normal zoning would show Ca - rich cores and Na - rich rims, but

reverse zoning is possible under certain conditions.

In metamorphic rocks plagioclase may not show twinning making it difficult to distinguish

from orthoclase. The two can be distinguished by staining the thin section with stains that

make the K-feldspars one color and the more Ca-rich feldspars another color. In this class, we

will not have time to look at these staining techniques. You should, however, be aware, that

such staining techniques exist, so that if you need them in the future, you can use them.

The optical properties of the plagioclase series vary widely as a function of composition of the

plagioclase. In general, all plagioclases show low order interference colors, and thus, low

birefringence. Optic sign and 2V vary widely, and are thus, not very distinguishing features of

plagioclase. Although, as you have seen in lab, it is possible to estimate the composition of

plagioclase from a combination of extinction angle and twinning.

Alkali Feldspars (K,Na)AlSi3O8

As an alkali feldspar cools from high temperature to lower temperature, the crystal structure

changes from that of sanidine, which is monoclinic, through orthoclase, also monoclinic, but

with a different crystal structure than sanidine, to microcline, which is triclinic. These

transformations are order-disorder transformations, and thus require large amounts of time.

Furthermore, if the feldspar is allowed to cool very slowly, then exsolution will occur, and the

solid solution will separate into a Na-rich phase and a K-rich phase. Thus, one expects to find

sanidine in rocks that were cooled very rapidly from high temperature, i.e. volcanic rocks.

Orthoclase and microcline will be found in plutonic igneous rocks (cooled slowly at depth in

the earth) and in metamorphic rocks. In addition, in the plutonic rock types if the cooling takes

place slowly enough, then perthitic exsolution lamellae may also form.

All of the alkali feldspars have low relief and low birefringence. Thus the interference colors

may range up to 1o white. Since this is the same interference color we expect for quartz, care

must be taken to avoid confusing feldspars and quartz.

Sanidine

Sanidine generally occurs with an equant habit (almost square) and shows perfect {001} and

{010} cleavages, which readily distinguish it from quartz. Rarely does sanidine show twinning,

but when it does, it is usually simple twinning. Optic axis figures will only be found on sections

showing both cleavages. Sanidine is optically negative with a 2V of 20 - 50o. This distinguishes

it from quartz, which is uniaxial positive, and from the other alkali feldspars which show larger

values of 2V.

Orthoclase

Orthoclase is a common alkali feldspar in granitic rocks and K - Al rich metamorphic rocks. It

often shows perfect {001} and {010} cleavages which will distinguish it from quartz. Also,

quartz usually shows a smooth surface texture, while orthoclase appears much rougher.

Orthoclase is also biaxial, which further distinguishes it from quartz. The 2V of orthoclase

varies from 60 to 105o, and thus it may be either positive or negative. The 2V angle

distinguishes orthoclase from sanidine, but is otherwise not very useful because of the its wide

range.

Microcline

Microcline is the lowest temperature form of alkali feldspar. Upon cooling, orthoclase must

rearrange its structure from monoclinic to triclinic. When this happens, twinning usually

results. The twinning characteristic of microcline is a combination of albite twinning and

pericline twinning. This results in a cross-hatched pattern (often called tartan twinning) that is

the most distinguishing characteristic of microcline.

Anorthoclase

Anorthoclase is a Na - rich feldspar with approximately equal amounts of the Anorthite (Ca)

and orthoclase (K) components. Generally anorthoclase occurs in Na - rich volcanic rocks. Like

the other alkali feldspars, it has perfect {001} and {010} cleavages. Sections showing both of

the cleavages are best for determining the optic sign and 2V. Anorthoclase sometimes shows

twinning, but generally not the multiple twinning seen in the plagioclase feldspars, but a cross-

hatched twinning similar to that seen in microcline, but on a very fine scale. Anorthoclase, like

sanidine shows a low 2V of 5 to 20o, and is optically negative. Anorthoclase can sometimes be

distinguished from sanidine by the fact that anorthoclase usually forms crystals with a tabular,

elongated habit, while sanidine forms crystals with a more equant habit.

Feldspathoids

The feldspathoid group of minerals are SiO2 poor, alkali rich minerals that occur in low SiO2,

high Na2O - K2O igneous rocks. In general, these minerals are not compatible with quartz, and

therefore, are rarely, if ever, seen in rocks that contain quartz. They do, however, often occur

with feldspars. Because of the alkalic nature of the rocks that contain feldspathoids, associated

pyroxenes and amphiboles are of the sodic variety, i.e. aegerine or riebeckite.

The main feldspathoids are Nepheline (Na,K)AlSiO4, Kalsilite KAlSi2O6, and Leucite

KAlSi2O6. At high temperature there is complete solid solution between Nepheline and

Kalsilite, but at low temperature Nepheline can contain only about 12 wt% K2O.

Other similar members of the feldspathoid group are:

Sodalite 3NaAlSiO4.NaCl

Nosean 3NaAlSiO4.NaSO4

Haüyne 3NaAlSiO4.Ca(Cl,SO4)

Nepheline

Nepheline occurs in both volcanic and plutonic alkaline igneous rocks. In hand specimen,

Nepheline is difficult to distinguish from the feldspars, and thus must usually be identified by

its association with other alkalic minerals. Nepheline has a yellowish colored alteration

product, called cancrinite. Nepheline is hexagonal, and thus uniaxial, making it easy to

distinguish from the feldspars. Furthermore, it is optically negative, making it distinguishable

from quartz. It usually shows no cleavage, has low birefringence, and low relief (refractive

indices are smaller than the feldspars). The only other common mineral with which nepheline

could be confused is apatite, which is also uniaxial negative. Apatite, however, shows much

higher relief than does nepheline.

Sodalite

Sodalite occurs predominantly in alkali-rich plutonic igneous rocks, like syenites, but can also

be found in volcanic rocks. It is essentially 3 nepheline molecules with an added NaCl

molecule. It is a clear colored isometric mineral with low relief. Thus, the only thing sodalite

might be confused with is a hole in the thin section. The blue color of sodalite in hand

specimen and its association with other alkali-rich minerals is usually necessary to detect its

presence in a rock.

Leucite

Leucite is found in alkalic volcanic rocks, and is rarely found in plutonic rocks. It is a

tetragonal mineral, however, its refractive indices and are so close together that it almost

always appears isometric. It usually occurs as small, slightly rounded, low relief grains that go

extinct upon insertion of the analyzer. Commonly, leucite contains tiny inclusions within the

mineral, and sometimes shows a slight twinning, barely visible with the analyzer inserted.

Oxides

The oxide minerals are very common and usually occur as accessory minerals in all kinds of

rocks. The most common oxide minerals are the following:

Corundum - Al2O3

Corundum is hexagonal and optically negative. It occurs in Al-rich igneous and metamorphic

rocks. If transparent blue, it is the gemstone sapphire, if transparent red, it is the gemstone

ruby. When it occurs as an accessory mineral it usually shows its hexagon shaped outline when

looking down the c-axis. It has high refractive indices, thus shows very high relief in thin

section. But it has low birefringence and commonly shows lamellar twinning.

Spinel - MgAl2O4

Spinel is an isometric mineral that occurs ultrabasic rocks like peridotite, and in many low

silica ignoeous rocks like basalts, where it contains high concentrations of Cr. It is also found

in Al-rich contact metamorphic rocks. It shows a wide variety of colors depending on trace

amounts of other ions substituting for both Mg and Al. Because of the isometric nature, Spinel

is difficult to distinguish from garnet, although spinel tends to occur as much smaller crystals.

Chromite - Fe+2

Cr2O4

Chromite is a major ore of Cr. It is found in in low silica, Mg-rich igneous rocks, usually

associated with Olivine. Often it is seen as small inclusions in Olivine, indicating that it is an

early crystallizing phase in basaltic and gabbroic magmas. Chromite is isometric, and usually

opaque in thin section. Electron Microprobe analysis is usually necessary to distinguish it from

other opaque oxide minerals.

Magnetite - Fe3O4

Magnetite is one of the most common oxide minerals. It is a major ore of Fe, and is found as

an accessory mineral in all rock types. It is isometric and commonly crystallizes with an

octahedral habit. In hand specimen it is most easily identified by its strongly magnetic nature,

black color, and hardness of 6. In thin section it is opaque and thus difficult to distinguish from

the other opaque oxide minerals. As discussed below, it forms a solid solution with Ulvospinel

- Fe2TiO4.

Ilmenite - FeTiO3

Ilmenite is a major ore of Ti. It is found as a common accessory mineral in a wide range of

igneous volcanic and plutonic rocks, as well as metamorphic and clastic sedimentary rocks. It

forms a solid solution series with Hematite, as will be discussed below, and commonly occurs

along with Magnetite. Ilmenite is hexagonal, but is usually opaque which makes its distinction

from other oxide minerals difficult. Ilmenite, however, often shows an elongated or acicular

habit, whereas Magnetite usually crystallizes as more equant crystals with an octahedral habit.

Hematite - Fe2O3

Hematite is one of the most important ores of Fe. It is more oxidized than Magnetite, and thus

forms as an alteration product of magnetite as well as other Fe bearing minerals. In most

unaltered igneous rocks, hematite occurs as a component of Ilmenite in solid solution.

Hematite is hexagonal, but rarely occurs in crystals where its symmetry can be determined. It

is found in a variety of forms, ranging from oolitic spherules, to massive fine grained

aggregates, to botryoidal masses. It is most easily distinguished by its black to dark red color

and reddish brown streak. In thin section it is not easily distinguished from other opaque oxide

minerals.

Iron-Titanium Oxide Geothermometer

Under magmatic conditions, Ilmenite and Hematite form a complete solid solution series, often

called the rhombohedral series since both minerals crystallize in the hexagonal system.

Similarly Magnetite and Ulvospinel form a complete solid solution series, called the spinel

series.

The possible ranges of solid solution are

shown in the diagram to the right.

Coexisting compositions (as illustrated

by the tie line) depend on temperature

and the fugacity (similar to partial

pressure) of Oxygen. If magma is

rapidly cooled so as to preserve the

compositions of the high temperature

solid solutions, it is possible to calculate

the temperature and fugacity of Oxygen

that were present just before eruption of

the magma. Minerals that allow for

determination of the temperature of

formation of minerals are referred to as a

geothermometer. The example

illustrated here is an important one,

called the Iron-Titanium Oxide

Geothermometer.

Carbonates

The carbonates are an important group of minerals near the Earth's surface. Carbonate minerals

make up the bulk of limestones and dolostones. Are found as cementing agents in clastic

sedimentary rocks, and make up the shells of many organisms. The carbonates are based on

the CO3-2

structural unit, which has carbon surrounded by 3 oxygens in triangular

coordination. Thus each Oxygen has a residual charge of -2/3. In the carbonate structure, no

two triangles share the corner oxygens and the C-O bonds are highly covalent.

There are three structural types of carbonates:

Calcite Group Aragonite Group Dolomite Group

Calcite CaCO3 Aragonite CaCO3 Dolomite CaMg(CO3)2

Magnesite MgCO3 Witherite BaCO3 Ankerite CaFe(CO3)2

Siderite FeCO3 Strontianite SrCO3

Rhodochrosite MnCO3 Cerussite PbCO3

Smithsonite ZnCO3

In addition, there are the hydroxyl Cu carbonates - Malachite, Cu2CO3(OH)2 and Azurite

Cu3(CO3)2(OH)2.

The Calcite Group

The calcite group minerals are all hexagonal. They have Ca, Mg, Fe, Mn, or Zn divalent

cations in 6-fold coordination with the CO3-2

groups, in a structure that is similar to that of

NaCl. All members of this group show rhombohedral cleavage {01 2}, thus breaking into

rhomb-shaped cleavage blocks.

Calcite CaCO3- The most common carbonate mineral is calcite. It is the principal constituent

of limestone and its metamorphic equivalent - marble. Deposits of fine grained calcite in

powder form are referred to as chalk. It forms the cementing agent in many sandstones, and is

one of the more common minerals precipitated by living organisms to form their skeletal

structures.

Calcite is also precipitated from groundwater where it form veins, or in open cavities like caves

and caverns can form the cave decorations - like stalactites and stalagmites, and encrustations.

It is also precipitated from hot springs where it is called travertine.

Calcite does occur in rare igneous rocks called carbonatites. These form from carbonate

magmas. Calcite is also precipitated from hydrothermal fluids to form veins associated with

sulfide bearing ores.

Properties

In hand specimen, calcite is distinguished by its rhombohedral cleavage, its hardness of 3, and

by its effervescence in dilute HCl. It can range in color from white, to slightly pink, to clear,

but dark colored crystals can also occur. In thin section it is most readily distinguished by its

high birefringence, showing high order white interference colors, by its rhombohedral cleavage

and its uniaxial negative character. Because of its high birefringence, it shows a large change

in relief on rotation of the stage. Furthermore, its refractive index direction (low RI

direction) when parallel to the polarizer shows a negative relief when compared to the

mounting medium of the thin section. Calcite can be distinguished from Aragonite by the lack

of rhombohedral cleavage and biaxial nature of Aragonite.

Magnesite MgCO3

Magnesite is a common alteration product of Mg-rich minerals on altered igneous and

metamorphic rocks. Like calcite, it shows perfect rhombohedral cleavage, but unlike calcite, it

does not readily effervesce in dilute HCl. It does, however, effervesce in hot HCl. These

properties and its association with Mg-rich minerals and rocks make it distinguishable from

Calcite.

Siderite FeCO3

Siderite forms complete solid solution series with Magnesite, although the environment in

which the two minerals occur usually determines that either Mg-rich Magnesite or Fe-rich

Siderite will form, and one rarely sees intermediate end members. In hand specimen, siderite is

usually brown colored and effervesces only in hot HCl. In thin section it resembles Calcite, but

has a much higher refractive index than Calcite and is commonly pale yellow to yellow

brown in color without the analyzer inserted.

Rhodochrosite MnCO3

Rhodochrosite is the Mn bearing carbonate, and is thus found only in environments where there

is an abundance of Manganese. It is relatively rare and occurs as hydrothermal veins and as an

alteration product of Mn rich deposits. In hand specimen it show a distinctive pink color along

with the rhombohedral cleavage common to the Calcite group minerals. Hot HCl is required to

make the mineral effervesce.

The Aragonite Group

The Aragonite group of minerals are all orthorhombic, and can thus be distinguished from

minerals of the calcite group by their lack of rhombohedral cleavage. Aragonite (CaCO3) is the

most common mineral in this group.

Aragonite is the higher pressure form of CaCO3 but,

nevertheless occurs and forms at surface temperatures and

pressures. When found in metamorphic rocks it is a good

indicator of the low temperature, high pressure conditions of

metamorphism, and is thus commonly found in Blueschist

Facies metamorphic rocks along with Glaucophane. Water

containing high concentrations of Ca and carbonate can

precipitate Aragonite. Warm water favors Aragonite, while

cold water favors calcite, thus Aragonite is commonly found

as a deposit of hot springs. Aragonite can also form by

biological precipitation, and the pearly shells of many

organisms are composed of Aragonite. Fine needle-like

crystals of Aragonite are produced by carbonate secreting

algae.

Properties

In hand specimen, Aragonite, like calcite effervesces in cold HCl. But, unlike Calcite,

Aragonite does not show a rhombohedral cleavage. Instead it has single good {010} cleavage.

It is usually transparent to white in color and forms in long bladed crystals. Twinning is

common on {110}, and this can produce both cyclical twins, which, when present, make it look

pseudohexagonal, and single twins. In thin section Aragonite is distinguished by its high

birefringence, showing high order white interference colors, its biaxial character with a 2V of

about 18o, and extinction parallel to the {010} cleavage.

The Dolomite Group

Dolomite - CaMg(CO3)2 and Ankerite - CaFe(CO3)2 form a complete solid solution series,

although because Mg-rich environments are much more common than Fe-rich environments,

Mg-rich dolomites are much more common than Ankerites. Ankerite is common mineral in

Pre-Cambrian iron formations. Dolomite is a common constituent of older limestones, probably

the result of secondary replacement of original calcite. It is also found as dolomitic marbles,

and in hydrothermal veins..

Dolomite is a unique chemical composition, as

can be seen in the Magnesite - Calcite phase

diagram shown here. Two solvi exist at low

temperatures. Thus, any high Mg-calcite -

dolomite solid solutions that might exist at high

temperatures would form nearly pure calcite

and pure dolomite at surface temperatures, and

similarly, any Magnesite - Dolomite solid

solutions that might exist at high temperatures

would form nearly pure Magnesite and pure

Dolomite at low temperatures. Thus,

Magnesite and Dolomite commonly occur

together, as do Calcite and Dolomite.

PropertiesDolomite, and therefore rocks containing large amounts of dolomite, like dolostones,

is easily distinguished by the fact that dolomite only fizzes in cold dilute HCl if broken down to

a fine powder. Also, dolostones tend to weather to a brownish color rock, whereas limestones

tend to weather to a white or gray colored rock. The brown color of dolostones is due to the

fact that Fe occurs in small amounts replacing some of the Mg in dolomite.

In thin section it is more difficult to distinguish from calcite, unless it is twined. In order to

facilitate its identification in thin section, the sections are often stained with alizarin red S.

This turns calcite pink, but leaves the dolomite unstained.

If calcite and dolomite

are twinned, they are

easily distinguishable

from one

another. Calcite shows

twin lamellae that are

parallel to the

rhombohedral cleavage

traces and parallel to

the long direction of

the cleavage rhombs.

Thus, the lamellae bisect the acute angle between the cleavages. Dolomite also has twins

parallel to the cleavage faces and parallel to the long direction of the rhombs, but also has twin

lamellae that are parallel to the short dimension of the rhomb. Thus, dolomite would also show

twin lamellae that would bisect the obtuse angle between the cleavage traces.

Accessory Minerals

Zircon ZrSiO4

Zircon is a common accessory mineral in nearly all kinds of rocks, particularly the more

siliceous igneous rocks, like granites, granodiorites, and syenites. Still, it is not often found in

thin section because it is so hard that it gets plucked out during the grinding of the section.

Zircon usually contains high amounts of radioactive elements like U and Th. Thus, when it is

found as inclusions in minerals like biotite, it produces pleochroic haloes in the biotite as seen

in thin section. Because it contains high concentrations of U and Th, it is very useful in

obtaining U-Pb and Th-Pb radiometric dates on old rocks. It is very resistant to weathering and

may also survives during metamorphism, allowing for dates to be obtained on the original rock

prior to metamorphism (often called the protolith).

In hand specimen Zircon usually occurs as tiny reddish colored crystals. In thin section, it

shows extremely high relief, with = 1.923 to 1.960 and = 1.968 to 2.015. and is uniaxial

positive. Zircon has high birefringence, with interference colors in the higher orders (lots of

reds, pinks and light greens). It is commonly colorless to pale brown or pinkish brown in

polarized light without the analyzer. Generally it occurs as small crystals with relief higher than

almost anything else in the thin section. This latter property should tip you off to its presence.

Sphene (Titanite) CaTiSiO4(OH)

Sphene is another common accessory mineral in plutonic igneous rocks like granites,

granodiorites, and syenites. It is also found as larger crystals in metamorphic gneisses and

chlorite bearing schists.

In hand specimen as an accessory mineral, it is usually seen as small wedge-shaped crystals

with a resinous to adamantine luster and brown to yellow brown color. In thin section,

Sphene, has a relief similar to that of zircon, and is usually found in small crystals with an

elongated diamond shape. It is generally brownish in color, shows a well developed {110}

cleavage, and high order interference colors.

Apatite Ca5(PO4)3(OH,F)

Apatite is another very common and almost ubiquitous (always present) accessory mineral in

igneous rocks and many metamorphic rocks. If the rock contains any phosphorous it is usually

found in apatite. Apatite is hexagonal, hence uniaxial with a negative optic sign. Its refractive

indices = 1.624 to 1.666 and = 1.629 to 1.667 are higher than both quartz and nepheline,

giving apatite a higher relief than these minerals. Its birefringence, expressed as 1o gray

interference colors is similar to that of quartz and nepheline. Quartz, however, is optically

positive. Nepheline, while optically negative, shows much lower relief than does apatite. The

crystal form of apatite is usually distinctive. If cut parallel to {0001}, it usually has a

hexagonal outline. If cut parallel to the C axis, it appears as doubly terminated prisms.

COMPILED BY

GDC HANDWARA

LECTURE NOTES

1ST

SEMESTER

UNIT 4

Pleochroism

With the upper polar removed, many coloured anisotropic minerals display a

change in colour - this is pleochroism or diachroism.It Produced because the two

rays of light are absorbed differently as they pass through the coloured mineral and

therefore the mineral displays different colours. Pleochroism is not related to the

interference colours.

UNIAXIAL OPTICS

Uniaxial minerals have only one optic axis, and belong to the hexagonal and

tetragonal systems.

Minerals in this group include:

nepheline NaAlSiO4

apatite Ca5(PO4)3(F,Cl,OH)

calcite CaCO3

dolomite (Ca,Mg)CO3

quartz SiO2

zircon ZrSiO4

tourmaline - borosilicate

On rotating the calcite rhomb one dot remained stationary but the other dot rotated

with the calcite about the stationary dot.

The ray corresponding to the image which moved is called the Extraordinary

Ray - epsilon.

The ray corresponding to the stationary image, which behaves as though it

were in an isotropic mineral is called the Ordinary Ray - omega.

The vibration direction of the ordinary ray lies in the {0001} plane of the calcite

and is at right angles to the c-axis.

The extraordinary ray vibrates perpendicular to the ordinary ray vibration direction

in the plane which contains the c-axis of the calcite.

If instead of using a calcite rhomb we had used a slab of calcite which had been cut

in a random orientation and placed that on the dots, two images would still appear.

If the random cuts were such that they were perpendicular to the c-axis, then light

travelling through the calcite, along the c-axis would produce only one image

andwould not become polarized.

The c-axis coincides with the optic axis, which is the direction through the mineral

along which light propogates without being split into two rays.

For calcite,

1. The index of refraction for the ordinary ray is uniform omega = 1.658,

regardless of the direction through the grain that the light follows.

2. The index of refraction for the extraordinary ray, epsilon, is variable ranging

from 1.486 to 1.658. The index is dependant on the direction that the light

travels through the mineral.

o If light travels perpendicular to c-axis, epsilon = 1.486.

o If the light travels along the the c-axis, epsilon = 1.658.

o For intermediate directions through the grain epsilon will fall between

the two extremes.

Calcite is used as an example of the formation of the two rays because of the large

difference between the refractive indices (birefringence (delta)).

for calcite, delta = 0.172.

For minerals with a lower birefringence, e.g. quartz, delta = 0.009, the two images

are still produced but show very little separation. The quartz would have to be 20-

25X as thick as the calcite to see the same separation of the dots.

UNIAXIAL OPTIC SIGN

LIGHT PATHS THROUGH UNIAXIAL MINERALS

nepsilon refers to the maximum or minimum index of refraction for the extraordinary

ray,.

nepsilon' refers to an index of refraction for the extraordinary ray which is between

nomega and nepsilon.

For uniaxial minerals any orientation will provide nw, but only one orientation, cut

parallel to the c-axis will yield nepsilon maximum. This orientation is the one which

exhibits the highest interference colour as delta (birefringence), is greatest, and

therefore DELTA (retardation) is greatest

(DELTA = d(ns-nf))

In Calcite omega > epsilon, 1.658 versus 1.485. In other minerals, e.g. quartz, omega < epsilon, 1.544 versus 1.553.

This difference in this refractive index relationship provides the basis for defining the optic sign of uniaxial minerals.

Optically positive uniaxial minerals omega < epsilon

Optically negative uniaxial minerals omega > epsilon

Alternatively,

if extrordinary ray is the slow ray, then the mineral is optically positive.

if extraordinary ray is the fast ray, then the mineral is optically negative.

epsilon refers to the maximum or minimum index of refraction for the extraordinary ray, the value recorded in the mineral

descriptions in the text.

epsilon' refers to an index of refraction for the extraordinary ray which is between omega and epsilon.

For uniaxial minerals any orientation will provide omega, but only one orientation, cut parallel to the c-axis will yield

epsilon maximum. This orientation is the one which exhibits the highest interference colour as delta (birefringence), is

greatest, and therefore retardation (DELTA) is greatest.

(DELTA = d(ns-nf))

Hexagonal and tetragonal systems are characterized by a high degree of symmetry

about the c-axis. Within the 001 or 0001 plane, at 90° to the c-axis, uniform

chemical bonding in all directions is encountered.

Light Paths Through a Mineral

Light travelling along the c-axis is able to vibrate freely in any direction within the

001 or 0001 plane.

No preferred vibration direction allows light to pass through the mineral as if it

were isotropic, this orientation has the lowest interference colour - black to dark

grey.

If the light passes at some angle to the c-axis, it encounters a different electronic

configuration and is split into two rays of different velocities.

The vibration vector of the ordinary ray is parallel to the 001 or 0001 plane, i.e.

perpendicular to the c-axis. The extraordinary ray vibrates across these planes,

parallel to the c-axis.

The ordinary ray has the same velocity regardless of the path it takes, because it

always vibrates in the same electronic environment.

The extraordinary ray velocity varies depending on the direction. If the light travels

nearly parallel to the c-axis, the extraordinary ray vibrates ~ parallel to 001 or

0001, so that nepsilon'~nomega.

If the light travels at right angles to the c-axis, the extraordinary ray vibrates across

the 001 or 0001 plane and nepsilon is most different from nomega.

For intermediate angles to the c-axis:

nomega > nepsilon'

and, nepsilon' > nepsilon.

Whether the extraordinary ray has a higher or lower RI than the ordiniary ray

depends on the chemical bonding and the crystal structure.

In the lab you will determine the indices of refraction for a uniaxial mineral using

grain mounts and the immersion method.

UNIAXIAL INDICATRIX

The indicatrix is a geometric figure, constructed so that the indices of refraction are

plotted as radii that are parallel to the vibration direction of light.

In isotropic minerals the indicatrix was a sphere, because the refractive index was

the same in all directions.

In uniaxial minerals, because nomega and nepsilon are not equal, the indicatrix is an

ellipsoid, the shape of which is dependant on its orientation with respect to the

optic axis. In positive uniaxial minerals, the Z indicatrix axis is parallel to the c-

crystallographic axis and the indicatrix is a prolate ellipsoid, i.e. it is stretched out

along the optic axis.

All light travelling along the Z axis (optic axis), has an index of refraction of nomega,

whether it vibrates parallel to the X or Y axis, or any direction in the XY plane.

The XZ and the YZ planes through the indicatrix are identical ellipses with

nomega and nepsilon as their axes, with the radii of the ellipses equal to the magnitude

of the RI for the ray.

Plotting the indices of light travelling in all directions produces the prolate

ellipsoid, whose axis of revolution is the optic axis, for uniaxial positive minerals;

nomega < nepsilon.

For optically negative minerals the X indicatrix axis corresponds to the optic axis

and the indicatrix is an oblate ellipsoid, i.e. flattened along the optic axis, and

nomega > nepsilon

In each case, for positive and negative minerals the circular section through the

indicatrix is perpendicular to the optic axis and has a radius = nomega.

The radius of the indicatrix along the optic axis is always nepsilon.

Any section through the indicatrix which includes the optic axis is called a

principal section, and produces an ellipse with axes nomega and nepsilon.

A section through the indicatrix perpendicular to the optic axis produces a circular

section with radius nomega.

A random section through the indicatrix will produce an ellipse with axes

nomega and nepsilon

The indicatrix is oriented so that the optic axis is parallel to the c crystallographic

axis.

Random Section Vibration Directions

Random section through the uniaxial indicatrix will give nomega and nepsilon'.

Light travelling from the origin of the indicatrix outwards, construct a wave normal

to the wave front.

A slice through the centre of the indicatrix, perpendicular to the wave normal

forms an ellipse with axes of nomega and nepsilon.

omega vibrates at 90° to the optic axis = short axis of the ellipse

epsilon' vibrates parallel to the optic axis = long axis of the ellipse.

The magnitude of the axes = nomega and nepsilon

BIREFRINGENCE AND INTERFERENCE COLOURS

Birefringence, difference between the index of refraction of the slow and fast rays

and the interference colours for uniaxial minerals is dependant on the direction that

light travels through the mineral.

1. In a sample which has been cut perpendicular to the optic axis, the bottom

and top surfaces will be parallel. The angle of incidence for the light

entering the crystal = 0° and the wave front are not refracted at the interface

and remain parallel to the mineral surface.

o A cut through the indicatrix, parallel to the bottom of the mineral, will

yield the indices and vibration directions of the light. A slice through

the indicatrix is a circular section, with radius nomega.

o No preferred vibration direction, so light passes along the optic axis as

an ordinary ray and retains whatever vibration direction it had

originally.

o Between crossed polars the light passing through the mineral is

completely absorbed by the upper polar and will remain black on

rotation of the stage, The birefringence = 0.

2. Cutting the sample such that the optic axis is parallel to the surface of the

section the following is observed.

o The indicatrix section is a principle section, as it contains the optic

axis. The indicatrix forms an ellipse with axes = nomega and nepsilon,

with the incident light being split into two rays such that:

the ordinary ray vibrates perpendicular to the optic axis,

the extraordinary ray vibrates parallel to the optic axis.

o The birefringence is at a maximum, and in thin section this grain

orientation will display the highest interference colour.

3. A mineral cut in a random orientation, with normally incident light;

o The ordinary ray produced has an index, nomega and vibrates

perpendicular to the optic axis.

o The extraordinary ray has an index nepsilon' and vibrates in the plane

containing the optic axis.

o nepsilon < nomega maximum or minimum, the birefringence is

intermediate between the two extremes.

EXTINCTION IN UNIAXIAL MINERALS

Uniaxial minerals will exhibit all four types of extinction discussed earlier.

The type is dependent on:

1. the orientation that the mineral is cut

2. the presence of cleavage(s) in the grain

Tetragonal minerals

1. Zircon ZrSi04- poor prismatic

2. Rutile Ti02 - good prismatic

o are prismatic and either elongate or stubby II to c axis.

o display prismatic (parallel to c)

o or pinacoidal (perpendicular to c) cleavage.

Depending on how the crystal is cut, and how its indicatrix is cut, dictates what

will be seen in thin section.

Hexagonal Minerals

1. Quartz - SiO2 - no cleavage

2. Apatite - Ca5(PO4)3(F,C1,OH) - rare pinacoidal, prism

3. Calcite - CaC03 - 1 of two cleavages rhombohedral

4. Nepheline - NaAlSiO4 - no cleavage

Hexagonal minerals will exhibit the following forms prisms, pinacoids, pyramids

and rhombohedrons which will exhibit prismatic, pinaciodal and rhombohedral

cleavages.

The birefringence, interference colours and any cleavage displayed by hexagonal

minerals is a function of how the grain has been cut.

PLEOCHROISM IN UNIAXIAL MINERALS

Pleochroism is defined as the change in colour of a mineral, in plane light, on

rotating the stage. It occurs when the wavelengths of the ordinary &

extraordinary rays are absorbed differently on passing through a mineral,

resulting in different wavelengths of light passing the mineral.

Coloured minerals, whether uniaxial or biaxial, are generally pleochroic.

To describe the pleochroism for uniaxial minerals must specify the colour which

corresponds to the ordinary and extraordinary rays.

e.g. Tourmaline, Hexagonal mineral

o omega = dark green

o epsilon = pale green

If the colour change is quite distinct the pleochroism is said to be strong.

If the colour change is minor = weak pleochroism.

For coloured uniaxial minerals, sections cut perpendicular to the c axis will show a

single colour, corresponding to ordinary ray.

Sections parallel to the c crystallographic axis will exhibit the widest colour

variation as both omega and epsilon are present.

BIAXIAL MINERALS

Include orthorhombic, monoclinic and triclinic systems, all exhibit less symmetry

than uniaxial and isotropic minerals.

Minerals in these crystal systems exhibit variable crystal structure, resulting in

variable chemical bonding.

The crystallographic properties of orthorhombic, monoclinic and triclinic minerals

are specified by means of the unit cell measured along the three crystallographic

axes.

It is also necessary to specify 3 different indices of refraction for biaxial minerals:

alpha, beta, gamma are used in text.

where alpha < beta < gamma

A variety of other conventions have been used or suggested, make sure that you are

aware of the convention used in the text you are using, if it is not Nesse.

The maximum birefringence of a biaxial mineral is defined by

(gamma - alpha)

Clarification

1) It takes 3 indices of refraction to describe optical properties

of biaxial minerals, however, light that enters biaxial minerals

is broken into two rays - FAST and SLOW.

2) Ordinary - extraordinary terminology is not used. Both

rays behave as the extraordinary ray did in uniaxial minerals.

The rays are both extraordinary and are referred to as SLOW

RAY and FAST RAY.

o slow = gamma' , between beta and gamma (higher RI)

gamma > gamma' > beta

o fast = alpha' , between alpha and beta (lower RI)

alpha < alpha' < beta

BIAXIAL INDICATRIX

The biaxial indicatrix is similar to the uniaxial indicatrix, except now there are

three principal indices of refraction instead of two. The biaxial indicatrix is

constructed by plotting the principal indices along 3 mutually perpendicular axes.

nalpha plotted along X

nbeta plotted along Y

ngamma plotted along Z

again, nalpha < nbeta < ngamma

So that the length of X<Y<Z.

Indicatrix is a triaxial ellipsoid elongated along the Z axis, and flattened along the

X axis.

Indicatrix has 3 principal sections, all ellipses:

X - Y axes = nalpha & nbeta

X - Z axes = nalpha & ngamma

Y - Z axes = nbeta & ngamma

Random sections through the indicatrix also form ellipses.

The uniaxial indicatrix exhibited a single circular section, a biaxial indicatrix

exhibits two circular sections with radius = nbeta; the circular sections intersect

along the Y indicatrix axis, which also has a radius of nbeta.

Look at the X - Z plane in the above image.

The axes of the ellipse are = nalpha & ngamma.

The radii vary from nalpha through nbeta to ngamma.

Remember that nalpha < nbeta < ngamma, so a radii = nbeta must be present on the X - Z

plane.

The length of indicatrix along the Y axis is also nbeta, so the Y axis and radii nbeta in

X - Z plane defines a circular section, with radius nbeta.

In the biaxial indicatrix the directions perpendicular to the circular sections define

the OPTIC AXES of the biaxial mineral. Optic axes lie within the X - Z plane,

and this plane is the OPTIC PLANE.

The acute angle between the optic axes is the optic or 2V angle.

The indicatrix axis, either X or Z, which bisects the 2V angle is the ACUTE

BISECTRIX or Bxa.

The indicatrix axis, either X or Z, which bisects the obtuse angle between the optic

axes is the OBTUSE BISECTRIX or Bxo.

The Y axis is perpendicular to the optic plane and forms the OPTIC NORMAL.

OPTIC SIGN

For biaxial minerals optic sign is dependant on whether the X or Z indicatrix axis

is the acute bisectrix.

if Bxa is X, mineral is -ve

if Bxa is Z, mineral is +ve

In the special case where 2V = 90°, mineral is optically neutral.

Another convention used is to identify the angle between the optic axes bisected by

the X axis as the 2VX angle; and the Z axis as 2VZ angle.

These two angles can vary from 0 to 180°, such that the following relationship

holds:

2VX + 2VZ = 180°

Using this convention the optic sign is determined by the following:

if 2VZ < 90°, the mineral is +ve.

if 2VZ > 90°, the mineral is -ve.

Light travelling through biaxial minerals is split into two rays -

FAST and SLOW rays which vibrate at 90° to each other.

The vibration directions of the FAST and SLOW rays are defined, or determined,

by the axes of the ellipse or section through the indicatrix, which is oriented at 90°

to the wave normal.

The Refractive Index corresponding to the FAST ray will be between nalpha and

nbeta, and is referred to as nalpha'.

The Refractive Index corresponding to the SLOW ray will be between nbeta and &

ngamma, and is referred to as ngamma'.

With this convention the following relationship will be true for all biaxial minerals:

1. X - will always correspond to the fast ray and will have the lowest RI.

o RI = nalpha, always fast

2. Y - will be either the fast or the slow ray depending on which other

indicatrix axis it is withand its refractive index will be between the lowest

and highest RI for the mineral.

o RI = nbeta, either fast or slow

3. Z - will always correspond to the slow ray and will have the highest RI.

o RI = ngamma, always slow.

COMPILED BY

GDC HANDWARA

LECTURE NOTES

1ST

SEMESTER

UNIT 4

REFLECTION AND REFRACTION

At the interface between the two materials, e.g. air and water, light may be reflected at the interface

or refracted (bent) into the new medium.

For Reflection the angle of incidence = angle of reflection.

For Refraction the light is bent when passing from one material to another, at an angle other than

perpendicular.

A measure of how effective a material is in bending light is called the Index of Refraction (n),

where:

Index of Refraction in Vacuum = 1 and for all other materials n > 1.0.

Most minerals have n values in the range 1.4 to 2.0.

A high Refractive Index indicates a low velocity for light travelling through that particular medium.

Snell's Law

Snell's law can be used to calculate how much the light will bend on travelling into the new medium.

If the interface between the two materials represents the boundary between air (n ~ 1) and

water (n = 1.33) and if angle of incidence = 45°, using Snell's Law the angle of refraction =

32°.

The equation holds whether light travels from air to water, or water to air.

In general, the light is refracted towards the normal to the boundary on entering the material

with a higher refractive index and is refracted away from the normal on entering the material

with lower refractive index.

In labs, you will be examining refraction and actually determine the refractive index of

various materials.

ISOTROPIC INDICATRIX

To examine how light travels through a mineral, either isotropic or anisotropic, an indicatrix

is used.

INDICATRIX - a 3 dimensional geometric figure on which the index of

refraction for the mineral and the vibration direction for light travelling

through the mineral are related.

Isotropic Indicatrix

Indicatrix is constructed such that the indices of refraction are plotted on lines from the origin that are

parallel to the vibration directions.

It is possible to determine the index of a refraction for a light wave of random orientation travelling

in any direction through the indicatrix.

1. a wave normal, is constructed through the centre of the indicatrix

2. a slice through the indicatrix perpendicular to the wave normal is taken.

3. the wave normal for isotropic minerals is parallel to the direction of propagation of light ray.

4. index of refraction of this light ray is the radius of this slice that is parallel to the vibration

direction of the light.

For isotropic minerals the indicatrix is not needed to tell that the index of refraction is the same in all

directions.

Anisotropic minerals differ from isotropic minerals because:

1. the velocity of light varies depending on direction through the mineral;

2. they show double refraction.

When light enters an anisotropic mineral it is split into two rays of different velocity which vibrate at

right angles to each other.

In anisotropic minerals there are one or two directions, through the mineral, along which

light behaves as though the mineral were isotropic. This direction or these directions are

referred to as the optic axis.

Hexagonal and tetragonal minerals have one optic axis and are optically UNIAXIAL.

Orthorhombic, monoclinic and triclinic minerals have two optic axes and are

optically BIAXIAL.

Calcite Rhomb Displaying Double Refraction

Light travelling through the calcite rhomb is split into two rays which vibrate at right angles

to each other. The two rays and the corresponding images produced by the two rays are

apparent in the above image. The two rays are:

1. Ordinary Ray, labelled omega w, nw = 1.658

2. Extraordinary Ray, labelled epsilon e, ne = 1.486.

Vibration Directions of the Two Rays

The vibration directions for the ordinary and extraordinary rays, the two rays which exit the

calcite rhomb, can be determined using a piece of polarized film. The polarized film has a

single vibration direction and as such only allows light, which has the same vibration

direction as the filter, to pass through the filter to be detected by your eye.

1. Preferred Vibration Direction NS

With the polaroid filter in this orientation only one row of dots is visible within the

area of the calcite rhomb covered by the filter. This row of dots corresponds to the

light ray which has a vibration direction parallel to the filter's preferred or permitted

vibration direction and as such it passes through the filter. The other light ray

represented by the other row of dots, clearly visible on the left, in the calcite rhomb is

completely absorbed by the filter.

2. Preferred Vibration Direction EW

With the polaroid filter in this orientation again only one row of dots is visible, within

the area of the calcite coverd by the filter. This is the other row of dots thatn that

observed in the previous image. The light corresponding to this row has a vibration

direction parallel to the filter's preferred vibration direction.

It is possible to measure the index of refraction for the two rays using the immersion oils, and

one index will be higher than the other.

1. The ray with the lower index is called the fast ray

o recall that n = Vvac/Vmedium

If nFast Ray = 1.486, then VFast Ray = 2.02X1010 m/sec

2. The ray with the higher index is the slow ray

o If nSlow Ray = 1.658, then VSlow Ray = 1.8 1x1010 m/sec

Remember the difference between:

vibration direction - side to side oscillation of the electric vector of the plane light

and

propagation direction - the direction light is travelling.

Electromagnetic theory can be used to explain why light velocity varies with the direction it

travels through an anisotropic mineral.

1. Strength of chemical bonds and atom density are different in different directions for

anisotropic minerals.

2. A light ray will "see" a different electronic arrangement depending on the direction it

takes through the mineral.

3. The electron clouds around each atom vibrate with different resonant frequencies in

different directions.

Velocity of light travelling though an anisotropic mineral is dependant on the interaction

between the vibration direction of the electric vector of the light and the resonant frequency

of the electron clouds. Resulting in the variation in velocity with direction.

Can also use electromagnetic theory to explain why light entering an anisotropic mineral is

split into two rays (fast and slow rays) which vibrate at right angles to each other.

PACKING

As was discussed in the previous section we can use the electromagnetic theory for light to

explain how a light ray is split into two rays (FAST and SLOW) which vibrate at right

angles to each other.

The above image shows a hypothetical anisotropic mineral in which the atoms of the

mineral are:

1. closely packed along the X axis

2. moderately packed along Y axis

3. widely packed along Z axis

The strength of the electric field produced by the electrons around each atom must

therefore be a maximum, intermediate and minimum value along X, Y and Z axes

respectively, as shown in the following image.

With a random wavefront the strength of the electric field, generated by the mineral, must

have a minimum in one direction and a maximum at right angles to that.

Result is that the electronic field strengths within the plane of the wavefront define an ellipse

whose axes are;

1. at 90° to each other,

2. represent maximum and minimum field strengths, and

3. correspond to the vibration directions of the two resulting rays.

The two rays encounter different electric configurations therefore their velocities and indices

of refraction must be different.

There will always be one or two planes through any anisotropic material which show

uniform electron configurations, resulting in the electric field strengths plotting as a circle

rather than an ellipse.

Lines at right angles to this plane or planes are the optic axis (axes) representing the direction

through the mineral along which light propagates without being split, i.e., the anisotropic

mineral behaves as if it were an isotropic mineral.

INTERFERENCE PHENOMENA

the colours for an anisotropic mineral observed in thin section, between crossed polars

are called interference colours and are produced as a consequence of splitting the light

into two rays on passing through the mineral.

RETARDATION

Monochromatic ray, of plane polarized light, upon entering an anisotropic mineral is

split into two rays, the FAST and SLOW rays, which vibrate at right angles to each

other.

Development of Retardation

Due to differences in velocity the slow ray lags behind the fast ray, and the distance

represented by this lagging after both rays have exited the crystal is the retardation - D

The magnitude of the retardation is dependant on the thickness (d) of the mineral and

the differences in the velocity of the slow (Vs) and fast (Vf) rays.

The time it takes the slow ray to pass through the mineral is given by:

during this same interval of time the fast ray has already passed through the mineral

and has travelled an additional distance = retardation.

substituting 1 in 2, yields

rearranging

The relationship (ns - nf) is called birefringence, given Greek symbol lower case d

(delta), represents the difference in the indices of refraction for the slow and fast rays.

In anisotropic minerals one path, along the optic axis, exhibits zero birefringence,

others show maximum birefringence, but most show an intermediate value.

The maximum birefringence is characteristic for each mineral.

Birefringence may also vary depending on the wavelength of the incident light.

INTERFERENCE AT THE UPPER POLAR

Now look at the interference of the fast and slow rays after they have exited the anisotropic

mineral.Fast ray is ahead of the slow ray by some amount = D.Interference phenomena are

produced when the two rays are resolved into the vibration direction of the upper polar.

Interference at the Upper Polar - Case 1

1. Light passing through lower polar, plane polarized, encounters sample and is split into

fast and slow rays.

2. If the retardation of the slow ray = 1 whole wavelength, the two waves are IN PHASE.

3. When the light reaches the upper polar, a component of each ray is resolved into the

vibration direction of the upper polar.

4. Because the two rays are in phase, and at right angles to each other, the resolved

components are in opposite directions and destructively interfere and cancel each other.

5. Result is no light passes the upper polar and the grain appears black.

Interference at the Upper Polar - Case 2

1. If retardation of the slow ray behind the fast ray = ½ a wavelength, the two rays are OUT

OF PHASE, and can be resolved into the vibration direction of the upper polar.

2. Both components are in the same direction, so the light constructively interferes and

passes the upper polar.

MONOCHROMATIC LIGHT

If our sample is wedged shaped, as shown above, instead of flat, the thickness of the

sample and the corresponding retardation will vary along the length of the wedge.

Examination of the wedge under crossed polars, gives an image as shown below, and

reveals:

1. dark areas where retardation is a whole number of wavelengths.

2. light areas where the two rays are out of phase,

3. brightest illumination where the retardation of the two rays is such that they are

exactly ½, 1½, 2½ wavelengths and are out of phase.

The percentage of light transmitted through the upper polarizer is a function of the

wavelength of the incident light and retardation.

If a mineral is placed at 45° to the vibration directions of the polarizers the mineral

yields its brightest illumination and percent transmission (T).

POLYCHROMATIC LIGHT

Polychromatic or White Light consists of light of a variety of wavelengths, with the

corresponding retardation the same for all wavelengths.

Due to different wavelengths, some reach the upper polar in phase and are cancelled, others

are out of phase and are transmitted through the upper polar.

The combination of wavelengths which pass the upper polar produces the interference

colours, which are dependant on the retardation between the fast and slow rays.

Examining the quartz wedge between crossed polars in polychromatic light produces a range

of colours. This colour chart is referred to as the Michel Levy Chart and may be found as

Plate I in Nesse.

At the thin edge of the wedge the thickness and retardation are ~ 0, all of the wavelengths of

light are cancelled at the upper polarizer resulting in a black colour.

With increasing thickness, corresponding to increasing retardation, the interference colour

changes from black to grey to white to yellow to red and then a repeating sequence of

colours from blue to green to yellow to red. The colours get paler, more washed out with

each repetition.

In the above image, the repeating sequence of colours changes from red to blue at

retardations of 550, 1100, and 1650 nm. These boundaries separate the colour sequence into

first, second and third order colours.

Above fourth order, retardation > 2200 nm, the colours are washed out and become creamy

white.

The interference colour produced is dependant on the wavelengths of light which pass the

upper polar and the wavelengths which are cancelled.

The birefringence for a mineral in a thin section can also be determined using the equation

for retardation, which relates thickness and birefringence.

Retardation can be determined by examining the interference colour for the mineral and

recording the wavelength of the retardation corresponding to that colour by reading it

directly off the bottom of Plate I. The thickness of the thin section is ~ 30 µm. With this the

birefringence for the mineral can be determined, using the equation:

See the example below.

This same technique can be used by the thin section technician when she makes a thin

section. By looking at the interference colour she can judge the thickness of the thin

section.

The recognition of the order of the interference colour displayed by a mineral comes

with practice and familiarity with various minerals. In the labs you should become

familar with recognizing interference colours.

EXTINCTION

Now we want to examine other properties of minerals which are useful in the

identification of unknown minerals.

Anisotropic minerals go extinct between crossed polars every 90° of rotation. Extinction

occurs when one vibration direction of a mineral is parallel with the lower polarizer. As a

result no component of the incident light can be resolved into the vibration direction of

the upper polarizer, so all the light which passes through the mineral is absorbed at the

upper polarizer, and the mineral is black.

Upon rotating the stage to the 45° position, a maximum component of both the slow and

fast ray is available to be resolved into the vibration direction of the upper polarizer.

Allowing a maximum amount of light to pass and the mineral appears brightest.

The only change in the interference colours is that they get brighter or dimmer

with rotation, the actual colours do not change.

Many minerals generally form elongate grains and have an easily recognizable cleavage

direction, e.g. biotite, hornblende, plagioclase.

The extinction angle is the angle between the length or cleavage of a mineral and the

minerals vibration directions.

The extinction angles when measured on several grains of the same mineral, in the same thin

section, will be variable. The angle varies because of the orientation of the grains. The maximum

extinction angle recorded is diagnostic for the mineral.

Types of Extinction

1. Parallel Extinction

The mineral grain is extinct when the cleavage or length is aligned with one of the

crosshairs.

The extinction angle (EA) = 0°

e.g.

o orthopyroxene

o biotite

2. Inclined Extinction

The mineral is extinct when the cleavage is at an angle to the crosshairs.

EA > 0°

e.g.

o clinopyroxene

o hornblende

3. Symmetrical Extinction

The mineral grain displays two cleavages or two distinct crystal faces. It is possible to

measure two extinction angles between each cleavage or face and the vibration

directions. If the two angles are equal then Symmetrical extinction exists. EA1 = EA2

e.g.

o amphibole

o calcite

4. No Cleavage

Minerals which are not elongated or do not exhibit a prominent cleavage will still go

extinct every 90° of rotation, but there is no cleavage or elongation direction from which

to measure the extinction angle.

e.g.

o quartz

o olivine

Exceptions to Normal Extinction Patterns

Different portions of the same grain may go extinct at different times, i.e. they have

different extinction angles. This may be caused by chemical zonation or strain.

Chemical zonation

The optical properties of a mineral vary with the chemical composition resulting in

varying extinction directions for a mineral. Such minerals are said to be zoned.

e.g. plagioclase, olivine

LECTURE NOTES

1ST

SEMESTER

UNIT 4

RELIEF

Refractometry involves the determination of the refractive index of minerals, using

the immersion method. This method relys on having immersion oils of known

refractive index and comparing the unknown mineral to the oil.

If the indices of refraction on the oil and mineral are the same light passes through

the oil-mineral boundary un-refracted and the mineral grains do not appear to stand

out.

If noil <> nmineral then the light travelling though the oil-mineral boundary is

refracted and the mineral grain appears to stand out.

RELIEF - the degree to which a mineral grain or grains

appear to stand out from the mounting material, whether it is

an immersion oil, Canada balsam or another mineral.

When examining minerals you can have:

1. Strong relief o mineral stands out strongly from the mounting medium,

o whether the medium is oil, in grain mounts, or other minerals in thin

section,

o for strong relief the indices of the mineral and surrounding medium

differ by greater than 0.12 RI units.

2. Moderate relief o mineral does not strongly stand out, but is still visible,

o indices differ by 0.04 to 0.12 RI units.

3. Low relief o mineral does not stand out from the mounting medium,

o indices differ by or are within 0.04 RI units of each other.

A mineral may exhibit positive or negative relief:

+ve relief - index of refraction for the material is greater than the index of

the oil.

- e.g. garnet 1.76

-ve relief nmin < noil

- e.g. fluorite 1.433

It is useful to know whether the index of the mineral is higher or lower that the oil.

This will be covered in the second lab section - Becke Line and Refractive Index

Determination.

BECKE LINE

In order to determine whether the idex of refraction of a mineral is greater than or

less than the mounting material the Becke Line Method is used

.

BECKE LINE - a band or rim of light visible along the grain

boundary in plane light when the grain mount is slightly out

of focus.

Becke line may lie inside or outside the mineral grain depending on how the

microscope is focused.

To observe the Becke line:

1. use medium or high power,

2. close aperture diagram,

3. for high power flip auxiliary condenser into place.

Increasing the focus by lowering the stage, i.e. increase the distance between the

sample and the objective, the Becke line appears to move into the material with the

higher index of refraction.

The Becke lines observed are interpreted to be produced as a result of the lens

effect and/or internal reflection effect.

LENS EFFECT

Most mineral grains are thinner at their edges than in the middle, i.e. they have a

lens shape and as such they act as a lens.

If nmin > noil the grain acts as a converging lens, concentrating light at the centre of

the grain.

If nmin < noil, grain is a diverging lens, light concentrated in oil.

INTERNAL REFLECTION

This hypothesis to explain why Becke Lines form requires that grain edges be

vertical, which in a normal thin section most grain edges are believed to be more or

less vertical.

With the converging light hitting the vertical grain boundary, the light is either

refracted or internally reflected, depending on angles of incidence and indices of

refraction.

Result of refraction and internal reflection concentrates light into a thin band in the

material of higher refractive index.

If nmin > noil the band of light is concentrated within the grain.

If nmin < noil the band of light is concentrated within the oil.

BECKE LINE MOVEMENT

The direction of movement of the Becke Line is determined by lowering the stage

with the Becke Line always moving into the material with the higher

refractive index. The Becke Line can be considered to form from a cone of light

that extends upwards from the edge of the mineral grain.

Becke line can be considered to represent a cone of light propagating up from the

edges of the mineral.

If nmin < noil, the cone converges above the mineral.

If nmin > noil, the cone diverges above the mineral.

By changing focus the movement of the Becke line can be observed.

If focus is sharp, such that the grain boundaries are clear the Becke line will

coincide with the grain boundary.

Increasing the distance between the sample and objective, i.e. lower stage, light at

the top of the sample is in focus, the Becke line appears:

in the mineral if nmin >noil

or in the oil if nmin << noil

Becke line will always move towards the material of higher RI upon

lowering the stage.

A series of three photographs showing a grain of orthoclase:

1. Photo 1 – The grain is in focus, with the Becke line lying at the grain

boundary.

2. Photo 2 – The stage is raised up, such that the grain boundary is out of

focus, but the Becke line is visible inside the grain.

3. Photo 3 – The stage is lowered, the grain boundary is out of focus, and

the Becke line is visible outside the grain.

When the RI of the mineral and the RI of the mounting material are equal,

the Becke line splits into two lines, a blue line and an orange line. In order to see

the Becke line the microscope is slightly out of focus, the grain appears fuzzy, and

the two Becke lines are visible. The blue line lies outside the grain and the orange

line lies inside the grain. As the stage is raised or lowered the two lines will shift

through the grain boundary to lie inside and outside the grain, respectively.

Index of Refraction in Thin Section

It is not possible to get an accurate determination of the refractive index of a

mineral in thin section, but the RI can be bracket the index for an unknown mineral

by comparison or the unknown mineral with a mineral whoseRI is known.

Comparisons can be made with:

1. epoxy or balsam, material (glue) which holds the sample to the slide n =

1.540

2. Quartz

o nw = 1.544

o ne = 1.553

Becke lines form at mineral-epoxy, mineral-mineral boundaries and are interpreted

just as with grain mounts, they always move into higher RI material when the stage

is lowered.

OPTICS

In Isotropic Materials - the velocity of light is the same in all directions. The

chemical bonds holding the material together are the same in all directions, so that

light passing through the material sees the same electronic environment in all

directions regardless of the direction the light takes through the material.

Isotropic materials of interest include the following isometric minerals:

1. Halite - NaCl

2. Fluorite - Ca F2

3. Garnet X3Y2(SiO4)3, where:

o X = Mg, Mn, Fe2+

, Ca

o Y = Al, Fe3+, Cr

4. Periclase - MgO

If an isometric mineral is deformed or strained then the chemical bonds

holding the mineral together will be effected, some will be stretched, others

will be compressed. The result is that the mineral may appear to be

anisotropic.

COMPILED BY

GDC HANDWARA

LECTURE NOTES

1ST

SEMESTER

UNIT 4

PHYSICAL PROPERTIES OF MINERALS

1. Introduction

The physical characteristics of minerals include traits which are used to identify and describe

mineral species. These traits include color, streak, luster, density, hardness, cleavage, fracture,

tenacity, and crystal habit.

Certain wavelengths of light are reflected by the atoms of a mineral's crystal lattice while

others are absorbed. Those wavelengths of light which are reflected are perceived by the viewer

to possess the property of color. Some minerals derive their color from the presence of a

particular element within the crystal lattice. The presence of such an element can determine

which wavelengths of light are reflected and which are absorbed. This type of coloration in

minerals is termed idiochromatism; different samples of an idiochromatic mineral species will all

display the same color. Other minerals are colored by the presence of certain elements in

mixture. Different samples of such a species may exhibit a range of similar colors. Still other

mineral species may usually be colorless, but may display several different and startling colors

when trace amounts of impurities, or elements which are not an integral part of the crystalline

lattice, are present. Coloration which is caused by the presence of an element foreign to the

crystal lattice, whether in mixture or in trace amounts, is termed allochromatism. Certain

elements are strong pigmenting agents and may lend vivid colors to specimens when they are

present, whether as a part of the crystal lattice, in mixture, or as an impurity. These elements are

termed the chromophores.

Streak is the color which a mineral displays when it has been ground to a fine powder. Trace

amounts of impurities do not tend to affect the streak of a mineral, so this characteristic is usually

more predictable than color. Two different specimens of the same species may be expected to

possess the same streak, whereas they may display different colors.

Minerals are either opaque or transparent. A thin section of an opaque mineral such as a

metal will not transmit light, whereas a thin section of a transparent mineral will. Typically those

minerals which possess metallic bonding are opaque whereas those where ionic bonding is

prevalent are transparent. Relative differences in opacity and transparency are described as

luster. The characteristic of luster provides a qualitative measure of the amount and quality of

light which is reflected from a mineral's exterior surfaces. Luster thus describes how much the

mineral surface 'sparkles'.

The property of density is defined as mass per unit volume. Certain trends exist with respect

to density which may sometimes aid in mineral identification. Native elements are relatively

dense. Minerals whose chemical composition contains heavy metals, or atoms possessing an

atomic number greater than iron (Fe, atomic number 26), are relatively dense. Species which

form at high pressures deep within the earth's crust are in general more dense than minerals

which form at lower pressures and shallower depths. Dark-colored minerals are typically fairly

dense whereas light-colored ones tend to be less dense.

Hardness is defined as the level of difficulty with which a smooth surface of a mineral

specimen may be scratched. Hardness has historically been measured according to the Mohs

scale. Mohs' method relies upon a scratch test to relate the hardness of a mineral specimen to the

hardness of one of a set of reference minerals. Hardness may also be measured according to the

more quantitative but less accessible diamond indentation method.

Cleavage refers to the splitting of a crystal along a smooth plane. A cleavage plane is a plane

of structural weakness along which a mineral is likely to split. The quality of a mineral's

cleavage refers both to the ease with which the mineral cleaves and to the character of the

exposed surface. Not every mineral exhibits cleavage.

Fracture takes place when a mineral sample is split in a direction which does not serve as a

plane of perfect or distinct cleavage. A mineral fractures when it is broken or crushed. Fracture

does not result in the emergence of clearly demarcated planar surfaces; minerals may fracture in

any possible direction.

The characteristic of tenacity describes the physical behavior of a mineral under stress or

deformation. Most minerals are brittle; metals, in contrast, are malleable, ductile, and sectile.

The term crystal habit describes the favored growth pattern of the crystals of a mineral

species. The crystals of particular mineral species sometimes form very distinctive, characteristic

shapes. Crystal habit is also greatly determined by the environmental conditions under which a

crystal develops.

2. Color:

When different wavelengths of visible light are incident upon the eye they are perceived as

being of different colors. Three different varieties of color receptors in the eye correspond to

light possessing wavelengths of approximately 660 nm (red), 500 nm (green), and 420 nm (blue-

violet). The eye then interprets the color of incident light according to which color receptors have

been stimulated. For example, if monochromatic light which stimulated the red and green color

receptors equally and did not affect the blue-violet receptors was detected, then the eye would

interpret this light as possessing a wavelength halfway between those of red and green light. The

eye would therefore register an incident light wave with a wavelength of approximately 580 nm

and the viewer would percieve the incoming light as yellow. Incident polychromatic light which

stimulated the red and green color receptors equally and did not affect the blue-violet ones would

also be interpreted as yellow light, regardless whether or not the incoming light actually

contained a component with a wavelength close to 580 nm. The incident polychromatic light

might possess only a red and a green component of equal intensity; it would nevertheless be

interpreted by the eye as yellow light. The phenomenon called color is thus a description of the

differentiation by the eye between various wavelengths and combinations of wavelengths of

visible light.

When light is incident upon a mineral specimen, some wavelengths are absorbed by the

atoms of the crystal lattice while others are reflected. Those wavelengths which were not

absorbed are reflected off of the mineral's surfaces and enter the eye of the viewer. The color

which is perceived by the viewer depends on the wavelengths of light which are reflected rather

than absorbed by the mineral. The property of color in minerals is thus due to the absorption of

particular wavelengths of light and the reflection of others by the atoms of the crystal lattice.

The color exhibited by certain mineral species may depend upon which crystallographic axis

is transmitting the light. Such species may demonstrate several different colors as light is

transmitted along various different axes. This phenomena of directionally selective absorption is

termed pleochroism.

Idiochromatism and the Chromophores

The color of many mineral species is derived directly from the presence of one or more of the

elements which constitute the crystal lattice. The color of such minerals is a fundamental

property directly related to the chemical composition of the species. Minerals which exhibit this

type of coloration are called idiochromatic minerals. Idiochromatic coloration is a property

possessed by a mineral species as a whole. In such species color can successfully be utilized as a

means of identification.

Ions of certain elements are highly absorptive of selected wavelengths of light. Such

elements are called chromophores; they possess strong pigmenting capabilities. The elements

vanadium (V), chromium (Cr), manganese (Mn), iron (Fe), cobalt (Co), nickel (Ni), and copper

(Cu) are chromophores. A mineral whose chemical formula stipulates the presence of one or

more of these elements may possess a vivid and distinctive color.

Examples of idiochromatic minerals abound. For instance, the copper carbonate malachite is

consistently green; the copper carbonate azurite and the copper silicate chrysocolla are each a

distinctive and predictable blue. Rhodochrosite is always red or pink; samples of sulphur are a

bright, recognizable yellow. Each of these distinctive colors is due to the fact that the chemical

composition which defines the mineral species specifies inclusion of one of the chromophores

within the lattice structure.

Allochromatism

Most minerals which are composed entirely of elements other than the chromophores are

nearly colorless. However, certain specimens are sometimes observed to possess vivid

coloration. Color in such instances is due to the presence of an impurity. If one of the

chromophores is present within a mineral whose chemical formula does not include it, then the

foreign element constitutes an impurity or a defect in the lattice structure. Coloration in minerals

which is due to the presence of a foreign element is termed allochromatism. In such cases the

color of the mineral may differ radically from the nearly colorless shade expected of the species.

Some minerals demonstrate a range of colors due to the presence in mixture of one of the

chromophores. For example, the substitution of a quantity of iron for zinc atoms within the

crystal lattice of sphalerite (ZnS) implements a change from white to yellow in the color of the

mineral. Proportionally larger inclusions of iron will progressively result in a brown and

eventually a black mineral specimen. In such cases the color of the sample is directly

proportional to the amount of the pigmenting element which is present in the crystal lattice.

Not all allochromatism in minerals is due to presence of substantial amounts of a

chromophore in mixture, however. The property of color may sometimes be highly dependent on

the inclusion of trace amounts of impurities. The presence of even a minute quantity of a

chromophore within the crystal lattice can cause a mineral specimen to exhibit vivid color. For

example, trace inclusions of chromium (Cr) in beryl are responsible for the deep green of

emerald, while the purple of amethyst is due to trace amounts of iron (Fe) in quartz and the pink

of rose quartz is due to trace inclusions of titanium (Ti). Samples of the mineral corundum which

include tiny amounts of chromium are deep red, and the gem is then called a ruby, while samples

containing iron or titanium impurities produce blue gems termed sapphire.

Trace amounts of an impurity do not affect the basic chemical composition or the chemical

formula of a mineral, and thus do not affect its classification as a species. Trace amounts of the

various chromophores, however, can cause several samples of a single species to differ radically

in color. (Beryl, corundum, and quartz provide examples of this possibility.) Because it varies so

widely, color is a property which is sometimes of little use in identification. However, the

idiochromatic minerals are consistently of distinctive color. The green of malachite, the blue of

azurite, the pink of rhodocrosite, and the yellow of sulphur are easily recognized and are

therefore quite useful in the identification of these species.

3. Streak

Streak is the color of a mineral substance when it has been ground to a fine powder.

Typically an edge of the sample will be rubbed across a porcelain plate, leaving behind a 'streak'

of finely ground material. The material in a streak sample thus consists of a powder composed of

randomly oriented microscopic crystals rather than a lattice structure containing the uniformly

oriented unit cells which compose a macroscopic crystal.

Although color is a property which may vary widely between two different specimens of the

same mineral, streak generally varies little from sample to sample. The presence of trace

amounts of an impurity may radically affect the property of color in a macroscopic crystal

because each unit cell is aligned within the crystal structure, thereby forming a diffraction

grating. Minute amounts of a strongly absorptive impurity within the structure may highly affect

which wavelengths of light are reflected from this diffraction grating. This change may greatly

modify the absorption of certain wavelengths of incoming light, altering the percieved color of

the specimen. In a streak sample, however, each of the microscopic crystal grains of the sample

is randomly oriented and the presence of an impurity does not greatly affect the absorption of

incoming light. Because it is not typically affected by the presence of an impurity, streak is a

more reliable identification property than is color.

4. Luster

Minerals may be categorized according to whether they are opaque or transparent. A thin

section of an opaque mineral such as a metal will not transmit light, whereas a thin section of a

transparent mineral will. The absorption index of an opaque mineral is high. Light which is

incident upon an opaque mineral such as a metal is unable to propagate through the mineral due

to this high rate of absorption, and will thus be reflected. Opaque minerals typically reflect

between 20% to 50% or more of the light incident upon them. In contrast, most of the light

which is incident upon a transparent mineral passes into and through the mineral; transparent

minerals may reflect as little as 5% of the incident light and as much as 20%. Typically those

minerals which possess metallic bonding are opaque whereas those where ionic bonding is

prevalent are transparent.

Relative differences in opacity and transparency are described as luster. The term luster

refers to the quantity and quality of the light which is reflected from a mineral's exterior surfaces.

Luster provides an assessment of how much the mineral surface 'sparkles'. This quality is

determined by the type of atomic bonds present within the substance. It is related to the indices

of absorption and refraction of the material and the amount of dispersion from the crystal lattice,

as well as the texture of the exposed mineral surface.

Minerals are primarily divided into the two categories of metallic and nonmetallic luster.

Minerals possessing metallic luster are opaque and very reflective, possessing a high absorptive

index. This type of luster indicates the presence of metallic bonding within the crystal lattice of

the material. Examples of minerals which exhibit metallic luster are native copper, gold, and

silver, galena, pyrite, and chalcopyrite. The luster of a mineral which does not quite possess a

metallic luster is termed submetallic; hematite provides an example of submetallic luster.

The property of streak can aid in distinguishing whether a specimen has a metallic or a

nonmetallic luster. Metals tend to be soft, implying that more powdered material may be

obtained from the streak sample of a metal than a nonmetal. Metals are also opaque, transmitting

no light. Minerals which possess a metallic luster therefore tend to exhibit a thick, dense, dark

streak whereas those which possess a nonmetallic luster tend to produce a thinner, less dense

streak which is also lighter in color.

Adjectives such as "vitreous', 'dull', 'pearly', 'greasy', 'silky' or 'adamantine' are frequently

used to describe various types of nonmetallic luster.

Dull or Earthy :

Minerals of dull or earthy luster reflect light very poorly and do not shine. This type of luster is

often seen in minerals which are composed of an aggregate of tiny grains.

Resinous

A surface of resinous luster possesses a sheen resembling that of resin. Such materials have a

refractive index greater than 2.0. Sphalerite (ZnS) demonstrates a resinous luster.

Pearly

Pearly luster appears iridescent, opalescent, or pearly. This is typically exhibited by mineral

surfaces which are parallel to planes of perfect cleavage. Layer silicates such as talc often

demonstrate a pearly luster on cleavage surfaces.

Greasy

A surface which possesses greasy luster appears to be covered with a thin layer of oil. A light-

scattering surface which is slightly rough, such as that of nepheline, may exhibit greasy luster.

Silky

Silky luster occurs when light is reflected off of an aggregate of fine parallel fibers; malachite

and serpentine may both exhibit silky luster.

Vitreous

Vitreous luster occurs in minerals with predominant ionic bonding and resembles the reflective

quality of broken glass. The refractive index of such minerals is 1.5 to 2.0. Many silicates

possess this type of luster; quartz and tourmeline both demonstrate vitreous luster.

Adamantine or brilliant

A brilliant luster such as the sparkling reflection of diamond is known as adamantine. Minerals

of adamantine luster have high refractive indices (1.9-2.6) and are highly dispersive and

translucent. Covalent bonding or the presence of heavy metal atoms or transition elements may

result in adamantine luster.

Metallic lustre

Metallic (or splendant) minerals have the lustre of polished metal, and with ideal surfaces will

work as a reflective surface. Examples include galena,6[6] pyrite[7] and magnetite

Submetallic lustre

Submetallic minerals have similar lustre to metal, but are duller and less reflective. A

submetallic lustre often occurs in near-opaque minerals with very high refractive indices,2such

as sphalerite, cinnabar and cuprite.

Waxy lustre

Jade

Waxy minerals have a lustre resembling wax. Examples include jade[11] and chalcedony.[12]

Optical phenomena

Asterism

Sapphire cabochon

Asterism is the display of a star-shaped luminous area. It is seen in some sapphires and rubies,

where it is caused by impurities of rutile.[12][13] It can also occur in garnet, diopside and spinel.

Aventurescence

Aventurine

Aventurescence (or aventurization) is a reflectance effect like that of glitter. It arises from

minute, preferentially oriented mineral platelets within the material. These platelets are so

numerous that they also influence the material's body colour. In aventurine quartz, chrome-

bearing fuchsite makes for a green stone and various iron oxides make for a red stone.

Chatoyancy

Tiger's eye

Chatoyant minerals display luminous bands, which appear to move as the specimen is rotated.

Such minerals are composed of parallel fibers (or contain fibrous voids or inclusions), which

reflect light into a direction perpendicular to their orientation, thus forming narrow bands of

light. The most famous examples are tiger's eye and cymophane, but the effect may also occur in

other minerals such as aquamarine, moonstone and tourmaline.

Color change .

.Alexandrite

Color change is most commonly found in Alexandrite, a variety of chrysoberyl gemstones.

Other gems also occur in color-change varieties, including (but not limited to) sapphire, garnet,

spinel. Alexandrite displays a color change dependent upon light, along with strong pleochroism.

The gem results from small scale replacement of aluminium by chromium oxide, which is

responsible for alexandrite's characteristic green to red color change. Alexandrite from the Ural

Mountains in Russia is green by daylight and red by incandescent light. Other varieties of

alexandrite may be yellowish or pink in daylight and a columbine or raspberry red by

incandescent light. The optimum or "ideal" color change would be fine emerald green to fine

purplish red, but this is exceedingly rare.

Schiller

Labradorite

Schiller, from German for "twinkle", is the metallic iridescence originating from below the

surface of a stone, that occurs when light is reflected between layers of minerals. It is seen in

moonstone and labradorite and is very similar to adularescence and aventurescence.[14]

5. Density

The property of density is defined as mass per unit volume:

µ = m/V

The geometric structure of the unit cell of a mineral determines the volume which it occupies.

The masses of the atoms which compose the unit cell decree the mass of each cell. The identity

of the atoms which compose the unit cell is specified by the chemical formula of the mineral.

Density is therefore directly related to both the physical structure of the unit cell and the

chemical composition of each species of mineral.

One method of measuring the density of a sample entails the use of one dense liquid and

another miscible liquid of lower density. A solution of the two substances is created in which a

crystal of the mineral in question remains suspended and neither sinks nor floats. The weight of a

known volume of the solution is then measured, and the density of the solution and thus the

density of the crystal are calculated from this information. Bromoform (CHBr3, density 2.9

g/cm3), soluble in acetone; di-iodomethane (CH2I2, density 3.3 g/cm3), soluble in chloroform,

CHCl3; and Clerici's solution (a solution of thallium formate and thallium malonate; density 4.4

g/cm3), soluble in water, are some heavy liquids and their solvents which are commonly used in

this process.

Density has historically been equated by mineralogists with the concept of specific gravity.

Specific gravity is a unitless quantity which is defined as the ratio of the weight of a substance to

the weight of an equal volume of water at a temperature of 4° Celsius. This ratio is equal to the

ratio of the density of the substance to the density of water at 4° Celsius.

G = µ / µwater

Specific gravity has therefore classically been measured by weighing a mineral specimen on a

balance scale while it is submerged first in air and then in water. The difference between the two

measurements is the weight of the volume of water which was displaced by the sample. The

specific gravity of the mineral specimen is thus:

G = mair / [mair - mwater]

Because the density of water at 4° Celsius is 1.00 g/cm3, the density of a mineral in units of

grams per centimeter cubed (g/cm3) is equal to its (unitless) specific gravity.

The field geologist sometimes uses a very rough estimation of the density of a hand-held

sample as a lue to identification. Certain rough trends relating mineral density to various other

factors are sometimes useful. Native elements, which contain only one type of atom and whose

molecular structure is that of cubic or hexagonal closest packing, are relatively dense. Minerals

whose chemical composition contains heavy metals - atoms of greater atomic number then iron

(Fe, atomic number 26) - are more dense than atoms whose chemical composition does not

include such elements. Minerals which formed at the high pressures deep within the earth's crust

are in general more dense than minerals which formed at lower pressures and shallower depths.

A general trend relating color to density is also prevalent; this trend states that dark-colored

minerals are often fairly heavy whereas light-colored ones are frequently relatively light. A

geologist is thus given cause to remark upon a sample which seems to reverse this trend. For

example, graphite is dark colored but of low density (C; 2.23 g/cm3) while barite is light in color

but unexpectedly heavy (BaSo4; 4.5 g/cm3). The noted oddity of unexpectedly high or low

density with respect to color provides the field geologist with a clue as to the identification of

such atypical materials.

6. Hardness

Hardness has traditionally been defined as the level of difficulty with which a smooth surface

of a mineral specimen may be scratched. The hardness of a mineral species is dependent upon

the strength of the bonds which compose its crystal structure. Hardness is a property

characteristic to each mineral species and can be very useful in identification.

Certain trends exist in hardness with respect to mineral class. (For a description of the

various classes of minerals, please refer to the discussion on mineral classification contained in

Section 4.) Native elements are typically soft, although iron (Fe) and platinum (Pt) are relatively

hard and diamond (C) is exceptionally hard. Compounds of heavy metals are soft. Sulphides and

sulpho-salts, with the exception of pyrite, are relatively soft; halides are soft; carbonates and

sulphates are usually soft. Oxides are typically hard while hydroxides are softer. Anhydrous

silicates tend to be hard, while hydrous silicates are softer.

The Mohs Scale

The property of hardness has historically been measured according to the Mohs scale, which

was created in 1824 by the Austrian mineralogist Friedrich Mohs. Mohs based his system for

measuring and describing the hardness of a sample upon the definition of hardness as resistance

to scratching. Mohs' method thus relies upon a scratch test in order to relate the hardness of a

mineral specimen to a number from the Mohs scale.

In order to define his scale, Mohs assembled a set of common reference minerals of varying

hardnesses and labled these in order of increasing hardness from 1 to 10. The reference minerals

of the Mohs scale are as follows:

Talc

Gypsum

Calcite

Fluorite

Apatite

Orthoclase

Quartz

Topaz

Corundum

Diamond

Each reference mineral will scratch a test specimen with a Mohs hardness less than or equal to its

own. Each reference mineral can be scratched by a specimen with a hardness equal to or greater

than its own. If a reference mineral both scratches and can be scratched by a certain test

specimen, then the specimen is assumed to possess a hardness equal to that of the reference

mineral in question.

The set of reference minerals of the Mohs' scale can be supplemented by a few common

household items. A fingernail has a Mohs hardness of 21/2; a copper penny 3, window glass

51/2, and a knife blade approximately 6.

The hardness of an unknown sample can be determined to within 1/2 increment by using the

scratch test. Mineral hardnesses determined by the scratch test should never be given in decimal

form, because the Mohs scale does not provide measurements of such precision.

The hardness of a mineral may vary with direction and crystallographic plane. This effect is

usually small. However, species exist in which the variance in the hardness along different axes

is notable. For example, the mineral kyanite (Al2OSiO4) typically forms elongated crystals. The

Mohs hardness parallel to the length of a kyanite crystal is 5, whereas the Mohs hardness

perpendicular to the length of such a crystal is 7. A second example is provided by the mineral

halite, which is softer parallel to its cleavage planes than it is at a 45° angle to the cleavage

planes.

The Diamond Indentation Method

Investigations more recent than those completed by Mohs have used the diamond indentation

method to quantitatively determine hardness. According to this method, a diamond point is

pushed into a planar mineral surface under the weight of a known load. The diameter of the

indentation thereby produced is then measured under a microscope. The diamond indentation

hardness of a sample is equal to the mass of the load applied divided by the surface area of the

indentation produced. The units in which diamond indentation hardness is recorded are therefore

kilograms per millimeter squared (kg/mm2).

Tests utilizing the diamond indentation method have shown that in order for a point

fashioned from a certain material to scratch a surface the hardness of its constituent material

must be 1.2 times that of the surface. Thus on an ideal hardness scale, each subsequent reference

material would have a hardness of approximately 1.2 times that of the material preceeding it. It

must be noted that the intervals between reference points on the Mohs scale are not, in fact,

equal. The interval between subsequent reference points on the scale increases as the hardness of

the reference materials increases. The skill with which Mohs chose his reference materials

becomes apparent when one notes that each of his samples is approximately 1.6 times the

hardness of the last.

The Mohs scale provides a means of testing hardness which is far more readily available to

amateur geologists than the diamond indentation method. It has therefore remained the standard

scale by which hardness is measured.

7. Cleavage

A cleavage plane is a plane of structural weakness along which a mineral is likely to split

smoothly. Cleavage thus refers to the splitting of a crystal between two parallel atomic planes.

Cleavage is the result of weaker bond strengths or greater lattice spacing across the plane in

question than in other directions within the crystal. Greater lattice spacing tends to accompany

weaker bond strength across a plane, because such bonds are unable to maintain a close

interatomic spacing.

Both the positioning of crystal faces in a mineral and the property of cleavage are derived

from the crystalline structure of the species. However, despite the fact that every mineral belongs

to a specified crystal system, not every mineral exhibits cleavage. A mineral such as quartz may

demonstrate beautiful, well-developed crystals and yet possess no distinct planes of cleavage.

Cleavage planes, if they exist, are always parallel to a potential crystal face. However, such

planes are not necessarily parallel to the faces which the crystal actually displays. Fluorite, for

example, has octahedral cleavage yet forms cubic crystals. Nonetheless, the property of cleavage,

if it is present, can offer important information about the symmetry and inner structure of a

crystal.

The quality of a mineral's cleavage refers to both the ease with which the mineral cleaves and

to the character of the exposed cleavage surface. The quality of a sample's cleavage is typically

described by terms such as 'eminent,' 'perfect,' 'distinct,' 'difficult,' 'imperfect,' or 'indistinct.'

'Eminent' cleavage describes the case in which cleavage always occurs readily and is in fact

difficult to prevent from occurring. The mineral mica, for example, cleaves readily into thin, flat

sheets. A mineral which demonstrates 'perfect' cleavage breaks easily, exposing continuous, flat

surfaces which reflect light. Fluorite, calcite, and barite are minerals whose cleavage is perfect.

'Distinct' cleavage implies that cleavage surfaces are present although they may be marred by

fractures or imperfections. 'Difficult' or 'indistinct' cleavage produces surfaces which are neither

smooth nor regular; samples possessing such cleavage tend to fracture rather than split.

Cleavage may be determined by the examination of surfaces which have actually broken. It

may also be determined by inspection of the interlacing systems of cracks which permeate the

structure of certain specimens. These systems of cracks are beautifully apparent within

transparent crystals such as fluorite or calcite.

8. Fracture

A mineral fractures when it is broken or crushed. Fracture takes place when a mineral sample

is split in a direction which does not serve as a plane of perfect or distinct cleavage. In other

words, fracture takes place along a plane possessing difficult, indistinct, or nonexistant cleavage.

The difference between fracture and indistinct cleavage is not clearly delineated.

Unlike perfect or distinct cleavage, fracture does not result in the emergence of clearly

demarcated planar surfaces which run parallel to possible crystal faces. Fracture is

nondirectional: minerals which do not possess distinct cleavage may fracture in any possible

direction.

Fractured surfaces may in some minerals possess a characteristic appearance which can aid

in identification. Examples of distinctive types of fracture are 'conchoidal,' 'irregular,' and

'hackly' fracture.

Conchoidal

Conchoidal fracture results in a series of smoothly curved concentric rings about the stressed

point, generating a shell-like appearance. The familiar ripples of a broken glass bottle

demonstrate this type of fracture. Quartz and olivine are two mineral species which possess

conchoidal fracture.

Irregular

Irregular or uneven fracture results in a rough, rugged surface.

Hackly

The term 'hackly' describes a fractured surface with multiple small, sharp and jagged

irregularities.

9. Tenacity

The property of tenacity describes the behavior of a mineral under deformation. It describes

the physical reaction of a mineral to externally applied stresses such as crushing, cutting,

bending, and striking forces. Adjectives used to characterize various types of mineral tenacity

include 'brittle,' 'flexible,' 'elastic,' 'malleable,' 'ductile,' and 'sectile'.

Brittle

Most mineral species are brittle, and will crumble or fracture under pressure or upon the

application of a blow. Such materials break or powder easily.

Flexible

A mineral which is flexible rather than brittle will flex as opposed to breaking under the

application of stress. However, a mineral which is merely flexible and not also elastic will be

unable to return to its original shape when the stress is removed. Flakes of molybdenite and

scales of talc are two substances which are flexible but inelastic.

Elastic

An elastic mineral will deform under external stress but will resume its original shape after the

stress is removed. If it is bent, it will flex, but will return to its previous position when the stress

dissappears. The mineral called mica is both flexible and elastic.

Malleable

Native metals such as copper, silver, and gold are easily flattened with a hammer. This type of

tenacity is termed malleable. Metallic-bonded minerals tend to be malleable, and may be

pounded out into thin, flat sheets.

Ductile

Some malleable materials are also ductile, and may be drawn out into a thin wire without

crumbling.

Sectile

Some minerals may be sliced into smooth sheets with a knife, although these may possibly still

crumble under a blow from a hammer. Materials possessing this rare type of tenacity are called

sectile minerals. The species chlorargyrite (AgCl) offers an example of a sectile mineral.

10. Crystal Habit

The term crystal habit describes the favored growth pattern of the crystals of a mineral

species, whether individually or in aggregate. It may bear little relation to the form of a single,

perfect crystal of the same mineral, which would be classified according to crystal system. Subtle

evidence of the crystal system to which a mineral species belongs is, however, frequently

observed in the habit of the crystals which a specimen displays.

The terminology used to describe crystal habit is not intended to replace the precise

nomenclature of crystallography. Instead, it is intended as a supplement to this system.

Discussions of crystal habit are more descriptive than precise; for this reason the terminology is

suited to the discussion of mineral samples discovered in the field. Naturally formed specimens

are rarely quantitatively perfect.

The crystals of particular minerals species sometimes form very distinctive, characteristic

shapes. Crystal habit is thus often useful in identification.

Although each mineral species typically forms according to a few preferred shapes, crystal

habit is largely determined by the environmental conditions under which a crystal develops. For

example, aqueous solutions near or surrounding a crystal contain the elemental substances which

it needs to continue growth. The direction from which a growing crystal may obtain such

solutions is a factor which will affect its eventual shape. Higher environmental temperatures

during formation increase ion mobility and aid in crystal formation; the rate at which the

environment cools determines how much time a mineral is allowed to form large crystals. The

amount of space available for a crystal to fill affects its final shape and size. Surface energy

relations are also quite important to the direction of crystal growth; this process is not yet fully

understood.

Adjectives used to describe the habit of individual crystals are 'equant,' 'prismatic,' and

'tabular.' Aggregates of crystals may also be termed equant or prismatic, while aggregates of thin,

flat, tabular crystals may be 'bladed.' Thin sheets, flakes or scales are termed 'foliated,'

'micaceous,' and, if feathery or delicate, 'lamellar' or 'plumose.' Crystal aggregates resembling

long, slender needles, hair, or thread are termed 'acicular,' filiform,' 'capillary,' or 'fibrous.' An

aggregate of crystals forming a network or lattice is 'reticulated;' one composed of branches

which radiate starlike from a central point is 'stellated' while a branching and treelike mineral

growth is 'dendritic.' 'Colloform' crystal habits termed 'botryoidal,' 'mamillary,' and 'reniform'

display spherical, bulbous or globular lumps. Smaller spherical forms are of 'pisolitic' or 'oolitic'

habit; ovoid clusters or formations are 'amygdaloidal.' Tapered, column-like formations are

'stalactitic' or 'columnar' while concentrically banded formations are of 'concretionary' habit.

Minerals whose flat crystal faces are covered with shallow, parallel grooves are 'striated;' a fine

furry layer of crystals growing over a massive lump constitutes a formation of 'drusy' habit.

Following is a list of descriptive terms which are applied when discussing crystal habit.

Equant

A crystal which is equant or equidimensional possesses approximately the same side length in

every direction. Crystals of garnet are often of equant habit.

Prismatic

A prismatic crystal is elongated in one direction like a prism. The mineral tourmaline often forms

crystals of such habit.

Tabular

Tabular crystals appear tabular or platelike in shape.

Bladed

A specimen displaying bladed habit possesses a collection of elongated, flat crystals suggestive

of knife blades. Gypsum often displays crystals of bladed habit.

Foliated

Crystals of foliated habit are separable into leafy structures or display leaflike projections. The

word 'foliated' is derived from the Latin term folium, meaning 'leaf.'

Micaceous

Minerals of micaceous habit form as thin, flat sheets or flakes which are easily peeled or split off

the larger mass. Muscovite provides an example of micaceous habit.

Lamellar or lamelliform

Crystals of lamellar habit form thin scales or plates which may resemble gills or lamellae. The

term is derived from the Latin word lamina, meaning 'thin plate.'

Plumose

A mineral specimen of plumose habit displays fine, feathery scales resembling plumes. 'Plumose'

is derived from the Latin term pluma, or 'feather.'

Acicular

The adjective 'acicular' means needlelike in shape. An acicular aggregate of crystals contains

many long, slender crystals which may radiate out like needles or bristles from a common base.

Acicular crystals are typically long and narrow like a pine leaf and seem to possess a sharp point.

The mineral natrolite often exhibits acicular crystals.

Capillary

An aggregate of crystals of capillary habit resembles an intricate network of tubules. Capillary

crystals appear long, slender, and fine, like delicate hairs. The term 'capillary' is derived from the

Latin word capillus, 'hair.'

Filiform

A mineral possessing crystals of filliform habit exhibits many hairlike or threadlike filaments.

"Filiform' is derived from the Latin word filum, 'thread.'

Fibrous

Specimens possessing fibrous habit exhibit clumps of sinewy, stringy, or hairlike fibers.

Reticulated

A mineral specimen of reticulated habit seems to display a lattice, net, or network of small

crystals. The word 'reticulated' is derived from the Latin term rete, or 'net.'

Stellated

A mineral of stellated habit possesses several branches which radiate outwards from the center in

a pattern resembling a star. The word 'stellated' stems from the Latin term stella, or 'star.'

Dendritic

Dendritic crystals form a divergent branching structure reminiscent of an arborescent, organic

growth such as a tree or a dendrite. Native copper sometimes exhibits this habit.

Colloform

Specimens of colloform habit exhibit spherical, rounded, or bulbous shapes. Botryoidal,

reniform, and mammillary habits are subsets of this category.

Botryoidal

The word 'botryoidal' means 'resembling a bunch of grapes,' or globular. Specimens of malachite

frequently provide examples of botryoidal crystals. The Greek word botrus, 'bunch of grapes,'

provides the linguistic root of botryoidal.

Mammillary

Samples possessing mammillary crystal habit display soft, rounded curves.

Reniform

Reniform crystal habit displays the shape of a kidney. The mineral species hematite provides

samples which exemplify both mammillary and reniform habit. 'Reniform' is derived from the

Latin renes, 'kidney.'

Oolitic

Crystals of oolitic habit form small spheres or grains which resemble fish roe. Oolites are often

found in limestones.

Pisolitic

A mineral of pisolitic habit develops round, pea-shaped forms. These are larger and slightly more

uneven than an oolite and are usually composed of calcium carbonate. The word 'pisolitic' is

derived from the Greek term pisos, 'pea.'

Amygdaloidal

A mineral of amygdaloidal crystal habit demonstrates small almond-shaped nodules called

amygdules. The term stems from the Latin word amygdala, or 'almond.'

Stalactitic

Stalactitic or columnar crystal habit refers to the tall, tapered, columlike appearance of an icicle

or a limestone stalactite. Such formations are built up by the dripping of mineral-laden solution.

The minerals calcite and aragonite (CaC03) typically form stalactites. The term is derived from

the Greek word stalaktos, 'dripping.'

Concretionary

A concretion develops when mineral matter is concentrically deposited around a nucleus and

colored and banded layers are build up. Malachite often exhibits such formations.

Striated

Minerals whose crystals are of striated habit display shallow parallel grooves or lines along flat

crystal faces. Pyrite often demonstrates square, striated crystals.

Drusy

A sample exhibiting drusy habit displays a surface covered with a fine furry layer of tiny

crystals.

Massive

Massive or earthy habit describes a large, lumpy mass which has no apparent crystal form. In

such a sample the crystals are too tiny to be observable by the eye and are interlocked and

mingled; the specimen lacks visible crystals.

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LECTURE NOTES

1ST

SEMESTER

UNIT 4

POLARIZATION OF LIGHT

All of this introductory material on light and its behavior brings us to the most critical

aspect of optical mineralogy - that of Polarization of Light.

Light emanating from some source, sun, or a light bulb, vibrates in all directions at

right angles to the direction of propagation and is unpolarized.

In optical mineralogy we need to produce light which vibrates in a single direction

and we need to know the vibration direction of the light ray. These two requirements

can be easily met but polarizing the light coming from the light source, by means of a

polarizing filter.

Three types of polarization are possible.

1. Plane Polarization

2. Circular Polarization

3. Elliptical Polarization

Three Types of Polarized Light

In the petrographic microscope plane polarized light is used. For plane polarized light

the electric vector of the light ray is allowed to vibrate in a single plane, producing a

simple sine wave with a vibration direction lying in the plane of polarization - this is

termed plane light or plane polarized light.

Plane ploarized light may be produced by reflection, selective absorption, double

refraction and scattering.

When light travels through any other medium it is slowed down, to maintain

constant frequency the wavelength of light in the new medium must al

1. Reflection

Unpolarized light strikes a smooth surface, such as a pane of glass, tabletop,

and the reflected light is polarized such that its vibration direction is parallel to

the reflecting surface.

The reflected light is completely polarized only when the angle between the

reflected and the refracted ray = 90°.

2. Selective Absorption

This method is used to produce plane polarized light in microscopes, using

polarized filters.

Some anisotropic materials have the ability to strongly absorb light vibrating in

one direction and transmitting light vibrating at right angles more easily. The

ability to selectively transmit and absorb light is termed pleochroism, seen in

minerals such as tourmaline, biotite, hornblende, (most amphiboles), some

pyroxenes.

Upon entering an anisotropic material, unpolarized light is split into two plane

polarized rays whose vibratioin directions are perpendicular to each other, with

each ray having about half the total light energy.

If anisotropic material is thick enough and strongly pleochroic, one ray is

completely absorbed, the other ray passes through the material to emerge and

retain its polarization.

This method of producing plane polarized light was employed prior to selective

absorption in microscopes. The most common method used was the Nicol

Prism. See page 14 and Figure 1.14 in

3. Scattering

Polarization by scattering, not relevant to optical mineralogy, is responsible for

the blue colour of the sky and the colours observed at sunset.

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