All images that I didn’t draw are from
Klein, 2002 or Blatt and Tracy 1996 unless
otherwise indicated.
Mineralogy Notes
Go over syllabus
Play game: Name that rock or mineral
1 point for each mineral identified, 1 point for composition
1 point for each rock identified, 1 point for story it tells.
15-18, including mostly straightforward, but with azurite (striking) and siderite
Physical Properties of Minerals
Review of concept of lattice vs amorphous material.
Definition of a mineral.
Crystal faces: faces are planes in the crystal with particular ion/atom densities and
arrangements. In general, faces will be the planes with lowest surface energy. However,
planes are also affected by growth rates. Are also constrained by the area available for
growth.
Faces reflect underlying symmetry of the crystal
Overhead: point out different faces, expressed to different degrees, or growing faster or
slower than comparable faces gives more complex appearance, or distorted appearance.
Habit: Malformations, differential growth rates, restrictions of growth area
euhedral
subhedral
anhedral
1
Form: group of faces that all have the same relationship to underlying symmetry
Can be either open or closed (e.g. pinacoid open, 2 horizontal planes, prismatic is open
with any number of planes parallel to one axis, sphenoid has 2 planes intersecting in
“hat”)
Form names (not same as form): prismatic (3, 4,6, 8, 12 planes parallel to one axis),
rhombohedral (closed form 6 faces, three faces on top alternate with 3 on bottom offset
by 60 degrees), cubic, octahedral, pinacoidal (2-sided forms with faces parallel),
sphenoid (2 planes not parallel)
Twinning: symmetrical intergrowth of two or more crystals of the same substance, often
on mirror plane or axis of rotation.
show examples of albite twinning (polysynthetic twinning- composition planes of twin
are parallel), show contact twinning (Qz- definite surface separates two individual
crystals), and penetration twin (carlbad twinning in orthoclase-individuals joined along
an irregular surface such that they appear intergrown)
State of Aggregation
(overhead, point out styles)
2
Luster, color, streak
luster: way light reflected, metallic and nonmetallic: vitreous (Qz), resinous (sphalerite),
pearly (talc), greasy silky (milky qz), adamantine (refractive index)
color: a few are diagnostic (azurite, malachite, turquoise), some vary according to
exposure to air (bornite), some by trace composition (Quartz, sapphire, ruby), some by
major composition (pyroxene-talk about effect of amount and color)
streak: color of powder, especially useful for oxides. E.g. hematite always has red
streak, but color not always red.
translucency: metallic oxides often opaque, most silicates, carbonates, sulfates, others
are transparent or translucent if sliced thin enough.
Diffraction among amorphous hydrated silica spheres in opal. (didn’t get to)
3
Chatoyancy and Asterism
oriented (parallel) elongate inclusions in a mineral can give optical (reflectance) effects.
elongate minerals give reflective line perpendicular to orientation of inclusions
(chatoyancy). If have three sets of oriented inclusions, can get 6 sided star (asterism) E.g.
“star” sapphire, has elongate rutile crystals
Fluorescence and phosphorescence
If you excite an electron to a higher energy state, it can return to ground state in series of
small steps in which energy is transferred e.g. to heat (no fluorescence), by releasing a
photon (which may be in visible range or not). If the spin state of the electron is
different in the ground state than the excited state, the decay is slower,
get phosphorescence.
Fluorescence that produces visible light usually results from excitation
in the ultraviolet range. The wavelength of light is proportional to the
inverse of the energy of the photon. The energy of the photon depends
on the amount of change in the energy level from excited to less
excited states.
Cleavage, parting, fracture
Planes of weakness in the crystal,
parting is breaking along other planes of weakness, such as twinning surface, exsolution
surface.
fracture-no planes of relative weakness (Qz)
break along planes with weaker bonds, e.g. Van der Waals bonding in graphite, easily
cleaves along that plane.
OrthoPyroxene (Mg2Si2O6): cleavage planes is between more ionic Mg-O bonds, not
more covalent Si-O bonds.
Hardness
Mohs scale
4
Related to bond strength. Different bonds in different directions, so hardness may
depend on direction (kyanite), or which crystal face (calcite)
In general, in increasing bond strength/hardness
Van der Waals, hydrogen bonds, ionic bonds, covalent bonds
Tenacity
brittle, malleable, sectile, ductile
Specific gravity
depends on how closely packed atoms are and atomic mass of atoms. (compare to mass=
like dividing by mass of H2O, makes dimensionless, but because water has a density of
1g/cc, you get the same number)
Magnetism: diamagnetic (paired electrons, opposes imposed field direction),
paramagnetic( unpaired electrons attracted to imposed magnetic field), Ferromagnetic
(retains magnetic alignment even in absence of imposed field if below Curie T)
radioactivity, solubility in HCl
Piezoelectric
non-conductor, otherwise it shorts itself out. Must not have center of symmetry (that is,
its atomic arrangement is different in one direction from the other along some axis, or
polar). Used in altimeters, pressure gauges, timer in watches and computers.
Hydroxyapatite is piezoelectric, important in bone formation.
5
Mineralogy Lab 1 Mineral Scavenger Hunt
Get into groups of 3
Each group must accumulate each of the following sets:
Each group must collect one of each of the following
Oxide
Sulfide
Halide
Sulfate
Carbonate
Silicate
Each group must collect one of each the following:
Nesosilicate
Sorosilicate
Cyclosilicate
Inosilicate
Phylosilicate
Tectosilicate
Each group must collect a mineral containing each of the following elements as a major
constituent
Pb
Mg
K
Ca
Zn
Al
Fe
Cu
To confirm the "winner", you will go through naming each mineral and what it's made of.
6
Mineralogy and Petrology.
Physical Properties of Minerals, Lab #2
Mineral hardness:
Mohs Hardness scale consists of 10 “standard” minerals, with hardnesses that increase in
a roughly exponential fashion.
These are Talc, gypsum, calcite, fluorite, apatite, orthoclase, quartz, topaz, corundum and
diamond.
1) Examine the Mohs sample set with the intent of becoming familiar with these (please
don’t scratch these samples)
2) Fingernails are roughly 2.2-2.5, a pocketknife or nail is roughly 5.1, a glass plate is
roughly 5.5. For each of the following minerals, test its hardness against each of these to
see if it is harder or softer. Then, check the actual hardness for that mineral given in your
text book to be sure you got it right.
M2 (gypsum)
M3 (fluorite)
M14 (orthoclase)
49-1652 Wards (Kyanite). This sample has a hardness that is strikingly different in
different directions. Parallel to the crystal blades it is about 5 (softer than knife or nail),
perpendicular to the blades it is about 7 (harder than knife or nail). Test it in both
directions until you ‘get’ it. The difference in hardness is due to differences in bond
strength in the different directions.
State of Aggregation:
3) Look at the following samples and think about their growth habit
Examine the two varieties of gypsum, alabaster and selenite (M1 and M2). Make sure
you know which is which. Also look at the satin spar sample 97 Wards in the Mineral
Cabinet (from East Bridgeford England).
Use the Figure in your book to identify which type of aggregation or growth character
that each of the following might exhibit.
49-1652 Wards (Kyanite),
46-E-4894 Wards (Malachite) This sample is fragile, be careful with it.
Wards (Hematite)
Asbestos (25 Wards Mineral Cabinet).
Twinning:
Look at the samples of Staurolite Garnet Schist (R11), Find the twinned staurolite
crystals present in a few samples (called cruciform twins).
7
Look at the samples of albite (M9). Make sure you can see and understand the
polysynthetic twinning.
Look at the samples of orthoclase (M14). Find a carlsbad twin.
Crystal faces, cleavage, and fracture:
Examine the Quartz crystals (M8). These samples exhibit both crystal faces, and
conchoidal fracture. Quartz doesn’t have cleavage because the covalent bond strength is
equal in all directions.
Examine the Pyrite crystals (49E3167 Wards). Also look at the bottom where the
fracture (no cleavage) is apparent. DON’T DAMAGE THIS SAMPLE, DON’T
SCRATCH IT, BASH IT, WHATEVER. Compare this sample with sample (188 in
wards mineral cabinet). Sketch the different crystal forms.
Look at the samples of Orthoclase (M14). These samples exhibit both crystal faces and
cleavage planes. Learn to tell them apart. Two cleavage planes are at nearly right angles.
Crystal faces are NOT at right angles. Cleavage will appear in areas of breakage. Crystal
faces clearly will not have been broken.
Examine three different samples of fluorite (49E1631 Wards; M3, and 49-1645 Wards).
One sample shows crystal growth form (cubic), one shows cleavage (octahedral), and one
is a more typical sample.
Think about the differences.
Look at the atomic structure for fluorite shown in your book.
Examine two different samples of Calcite, M16 and 49E1602 Wards (PLEASE,
PLEASE, PLEASE DO NOT SCRATCH, PUT ACID ON, OR CRUSH THIS SAMPLE,
OR ANYTHING ELSE BAD!!!!!). M16 shows mostly crystal forms, 49E1602 is a
cleavage rhomb.
Also look at sample 83 Wards Mineral Cabinet, from Chihuahua Mexico. Notice its
hexagonal form.
Look at the atomic structure diagram for calcite in your book showing the relationship
between the hexagonal and rhombic forms.
Think about it. Talk about it with someone.
Examine several samples of m11. Notice the stubby prisms of the pyroxene crystals, as
they grew in an igneous rock. Also, notice the cleavage.
Pyroxene is distinguished from amphibole on the basis of its two cleavage planes at
nearly right angles to each other. This shows up most obviously as a stairstep appearance
to the cleavage surfaces.
Cleavage in pyroxene (Mg2Si2O6) occurs at the ionic bonds between Mg and oxygen, not
at the covalent bonds between Si and O. Examine the picture below from your text. lines
on this diagram represent covalent bonds between Si and O. Oxygen atoms are
represented by the smaller open circles and Si atoms by small black dots. The larger
8
black dots represent octahedrally-coordinated sites in the crystal (called M1 by
mineralogists), and the larger open circles represent a structurally-different octahedral
site (called M2). Mg goes into both M1 and M2. No lines are drawn for the more ionic
bonds between Mg and O. With a pencil, draw how the mineral will break on the righthand image (don’t cross any covalent bond lines! Remember that cleavage planes are at
roughly right angles when seen on the big scale, cleavage planes pass through the M1
sites, not the M2 sites).
Color and Streak:
Look at the samples that are referenced.
Color is sometimes diagnostic of a mineral, but usually not. It is diagnostic for
Malachite (49E1553, Wards) and
Azurite (49H5760 Wards).
It is not diagnostic for Quartz (samples M8,
and the following samples from the Mineral Cabinet:
45 amethyst,
46 milky quartz,
47 Smoky Qz,
48 rose quartz.
Observe both the color and streak for two varieties of hematite:
specular hematite (46E3877 Wards)
oolitic hematite (46E3867 Wards)
Density:
Two factors influence density: The molecular weight of the ions in the mineral, and the
closeness of the packing of ions. Metamorphic minerals often are more closely packed
because higher-density minerals are usually more stable at higher pressure.
Examine the samples that are referenced.
9
M10 (Galena) Dense due to high molecular weight of Pb (PbS).
It has the same atomic structure as Halite (M15). Compare them.
46E1022 (Wards) Barite is dense due to the high molecular weight of Ba
(BaSO4).
Gypsum (M2) is also a sulfate mineral (CaSO4۰2H2O) but is less dense that Barite.
Compare them.
Look up the molecular weights for Ba and Ca on a periodic table. Values:
____________________.
Another sulfate is Anhydrite (CaSO4) Because Ca is so much smaller (as well as
less massive) than Ba, the coordination number of Ca (the number of SO42- ions around
Ca) is much lower than the coordination number for Ba. Therefore, the structures of the
two sulfates, Barite and Anhydrite, are very different, even though Ca and Ba have very
similar chemical properties (they are in the same column of the periodic table).
Garnet and Kyanite are Alumino-silicate minerals (contain aluminum and silicon bound
with oxygen) that have high-densities due to close packing of the ions. They both form
under high-pressure metamorphic conditions. Compare them with a lower-density
alumino-silicate mineral, Albite.
Garnet = M18
Kyanite = 49-1652 Wards
Albite=M9
Other Cool Stuff
Birefringence:
Due to the electrical fields generated in crystals by the arrangement of ions, light
travels through crystals at different speeds in different directions. When speed changes,
the light will bend (refract) just like light bends when it goes from air into water (the
“bent pencil” effect when you put it in a glass of water) or like seismic waves refract as
they pass through the Earth. This can produce a “double vision” affect.
Calcite (49E1602 Wards): DO NOT DAMAGE THESE SAMPLES!! Place the Calcite
rhomb over a sample of text. Rotate the crystal and watch the double images rotate
around each other. (Side note: There is one axis in calcite along which this double image
effect does not occur: the c axis. This is because light passing in this direction travels
the same speed regardless of the direction of light vibration. Trilobites, which had an eye
lens made of calcite, had a lens oriented such that it looked parallel to the c axis.)
Exsolution Lamillae: Perthite (46E0514 Wards)
Sometimes a mineral that is stable at high temperature, reacts to form two structurally
similar but chemically different minerals at lower temperature. This process is called
exsolution (meaning, that the second mineral does not dissolve in the first, but exsolves).
Chemically, this is similar to how water will dissolve in air at high temperature, but will
condense out at low temperature. We will talk lots more about exsolution later in the
10
course. Feldspar commonly shows an exsolution texture. A composite feldspar at high
temperature exsolves to form Perthite, which is a mixture of long, thin laminae of albite
(the more Na-rich feldspar) and orthoclase (the more K-rich feldspar). Examine the
examples of Perthite until you can spot the whitish stringers of albite and the pinkish
stringers of orthoclase.
Labradorescence and Opalescence:
look up the composition of labradorite. _____________________________
One variety of plagioclase feldspar, labradorite, often has very tiny exsolution lamilae
(too small to see). These laminations form tiny layers in the mineral which will act as a
diffraction grating for incoming light. Diffraction is the effect that causes rainbow colors
in an oil slick in a wet parking lot.
Look at sample 49-1654 Wards (polished Labradorite),
as well as the more typical sample 46E4514 Wards.
Find the rainbow colors. You should see really striking yellows, greens, and cobalt blues.
Sample 46E4514 also has great polysynthetic twinning! Can you find it?
Sample of Opal in the Ore Mineral Cabinet, 213.
Find an opal that opalesces (Not all of them do)
The rainbow colors of opal are also from diffraction from layers in the sample. Opal is
actually not a mineral because it is amorphous. However, layers are made of tiny round
beads of hydrated silicate that form a diffraction grating in a similar fashion to the layers
in Labrodorite.
Idea of diffraction. When light “reflects” off of multiple layers, some of the light beams
will be in-phase and some out-of-phase when the light emerges from the rock. Whether it
is in our out of phase depends on both the angle the light enters and the wavelength of the
light. The colors of light that are in-phase will show up as brighter, giving the sample a
rainbow appearance.
11
Elements of Crystal Chemistry
Review of the atom: protons (+), neutrons, electrons (-), ions, atomic number, atomic
mass, isotopes. Examples: what element if atomic mass is 3 and has 1 electron when
neutrally charged? What element if atomic mass is 87 and it has 49 neutrons? What
element if atomic mass = 86 and it has 48 neutrons?
hydrogen
Spectroscopic lines from elements indicates that energy is discrete. Leads to idea of
quantized energy states, that is, electrons can’t exist in any energy state, but only in
particular ones. The energy of a particular photon is related to the wavelength by the
expression E=hc/.
Bohr postulated that electrons exist only in particular shells (or orbits). The more distant
from the nucleus, the higher the energy, until the electron escapes from the nucleus
entirely.
E=-A/n2
where n is the quantum number, related to the mass and charge. Notice that as n goes to
infinity, energy goes to 0 (escapes from nucleus). As n goes to 1, E approaches its
maximum.
From this, it can be seen that it is easiest to remove the outermost electrons. More and
more energy is required to remove inner electrons. Ionization potential: energy to
remove easiest-to-remove electron.
12
Notice, the easiest to remove (such as Li and Na) are those that form positive ions. Those
hardest to remove (such as Ne, and Kr) don’t generally form ions at all). Ones like F, Cl
tend to form negative ions.
valence electrons, are the outer electrons most easily removed. Produces a charged ION.
Elements typically lose a characteristic number of electrons, giving ion a typical valence
(e.g.Na+, K+, Cl-, Br-, Ca++, Mg++, Ni++, Sc+++) Some elements may lose a different
number of electrons under different conditions, giving it more than one valence (e.g.
Fe++, Fe+++, Ti3+, Ti4+,
Go through electromagnetic spectrum and common energy levels absorbed by rotational
quantum levels=microwave, vibrational=infrared, electronic (outer electrons=visible,
inner electrons = X-ray), nuclear quantum levels = gamma.
Schrodinger model of the atom (briefly)
Electron can be thought of as wave like. Schrodinger equation describes position as a
wave, predicting only the probability it is at any particular location. The distance of
highest probability corresponds to the Bohr distance from nucleus.
4 quantum numbers for electronic energy levels. one corresponds to Bohr’s energy levels
(K, L, M, N, O), others orbital shape (s, p, d, f, g), magnetic (determines number of
orientations of and shapes, e.g. s=1, p=3, d=5, f=7), and electron spin (only two values,
so only two electrons possible per orbital).
Explain how typical ionic charge relates to the number of electrons in the outer shell (K,
L, M, etc). Examples of Na, Mg, Al, Cl). Explain how it gravitates toward form of noble
gases (most stable configuration). Do electron orbital fill exercise. For each atom,
indicate its likely valence (charge).
13
Li
O
He
Ar
Na
Ne
Mg
Al
14
Brief review (like Physical Geology) of closest packing, unit cell (motif), shapes that
fill up space in 2-D (called lattice system) (square, rectangle, hexagonal (rhombus), and
oblique). Shapes that fill space in 3-D (called crystal system or lattice system) (isometric,
tetragonal, orthorhombic, hexagonal, monclinic, triclinic)
Types of Bonds
Notice that noble gases are very inert, stable.
ionic bond: Transfer of electrons from one atom to another so that both achieve an
electronic configuration like noble gas. This is related to filled s and p orbitals in the
outer shell. This gives each a charge, and bonding results from electrostatic interaction.
energy = (AZ+Z-/d) Z = charge, d = interatomic distance, A is madelung constant which
depends on crystal structure.
force (strength of bond) = AZ+Z-/d2)
Which will be stronger, bond between Na and Cl or between Na and I?
reflected in melting T: NaCl melts at 801C, NaI at 651 C (melting is when short range
order lost).
typical of ionic bonds: Non-conductive (no easy exchange of electrons once noble-gaslike configuration achieved). soluble (many are called ‘salts’), electrons are not shared,
but go to one atom, distributed over atom, making bond nondirectional so symmetry of
resulting minerals are often high. Moderate hardness (not as strong as covalent bonds,
but stronger than other types of bonds). Once dissolved, the free ions provide electrical
conductance in the solution.
Often, geochemists approximate energy of crystals from ionic model even when they are
not perfectly ionic.
U = N(AZ+Z-/d + sye-d/p)
second term is a repulsion term. If try to cram large ion into too small a space, the
electrons bump into each other. Since like charges repel, this results in a repulsion term.
Repulsion is shorter-range term. There is some “balance” distance (minimum energy).
15
Side note on my research: Trying to understand and predict how easily trace elements
substitute into a particular crystal. I proposed that it could be understood in terms of
electrostatic energy:
Relative ease with which different elements substitute into olivine I found that there is a
best-fit size about at size of Ni, getting smaller to either side of that, so that both bigger
and littler cations fit less well Repulsion energy higher if crammed too tightly,
electrostatic energy higher if too large.
Goldschmidts rule: Substitution of one element for another in a lattice: will subst. better
if of similar size and charge.
covalent bond
Share electrons, such that some electrons do double duty filling outer shells of more than
one atom.
e.g. C
16
Covalent bonds are very strong, very hard (like diamond), high melting T. No free
electrons, so do not conduct electricity well.
In reality, all bonds have some ionic and some covalent character.
Some atoms have a strong tendency to attract electrons (electronegativity), others a much
weaker ability. The more different two are (one that tends to attract electrons and one
that doesn’t), the more ionic the bond. The closer they are, the more covalent the bond.
metallic bond
valence electrons “swim” freely among the nuclei and bound non-valence electrons. The
cloud of electrons allows easy movement of atoms (plasticity, tenacity, ductility) and the
movement of electrons provides conductivity (both heat and electricity). Weaker bonds
yield much softer materials. Only native metals (in nature) exhibit this behavior.
Van der waals bond
These bonds form in neutrally charged atoms or molecules when the motion of electrons
becomes synchronized such at one adjacent sides of atoms or molecules gain slightly
opposite charges. They are very weak bonds, yielding soft materials and usually low
melting temperatures (such as for cooled dimers of Cl2 or O2)
e.g. Graphite (one out of 3 C-C bonds is a double bond- actually 4rth valence electron
'wanders' over the plane of bonds, creating electrical conductivity, which diamond lacks)
17
has covalent bonds in plane, with planes bound by Van der Waals forces. The mineral
easily cleaves in this plane, making graphite an excellent lubricant. Also used as pencil
‘lead’. Layers for many clay minerals are held together by VanderWaals (e.g. kaolinite,
gibbsite, pyrophyllite, brucite, talc).
hydrogen bond
Hydrogen, when it loses its electron, becomes an unshielded proton (positive charge).
This exposed positive charge can bond with negative ions, or polar molecules that have a
negative pole. Polar molecules are ones that are not the same on all sides, and have
positive and negative ends. e.g. H2O. This bond is weaker than covalent or ionic, but
stronger than Van der Waals.
briefly mention a couple of
Pauling’s rules: Local charge
balance and polyhedra sharing
corners>sharing edges>sharing
sides
18
Mineralogy and Petrology.
Thinking about atoms, energy levels, and crystal structure, Lab #3
For each atom: Fill in the missing information without looking at a periodic table.
Atom 1:
Symbol = Mg
Atomic mass =
Atomic number=
Number of neutrons = 12
number of electrons = 10
number of protons =
valence of the atom = +2
Atom 2:
Symbol =
Atomic mass = 24
Atomic number=
Number of neutrons =
number of electrons = 12
number of protons = 12
valence of the atom = 0
Atom 3:
Symbol =
Atomic mass = 87
Atomic number = 37
Number of neutrons =
number of electrons = 36
number of protons =
valence of the atom = +1
Atom 4:
Symbol = Cl
Atomic mass = 36
Atomic number=
Number of neutrons = 19
number of electrons =
number of protons =
valence of the atom = -1
Atom 5:
Symbol =
Atomic mass = 14
Atomic number=
Number of neutrons =
number of electrons = 6
number of protons =
valence of the atom = 0
Checking the periodic table, how many neutrons does the most common isotope of this element
contain? ______
19
The quantum numbers for atoms are the following
n =1, 2, 3, 4, 5, (corresponds to the K, L, M, N, O shells)
(primary Bohr energy levels ~ 'distance' from nucleus)
l = 0, 1, 2, 3 (corresponds to the s, p, d, f orbitals)
(orbital shape quantum number)
m = for s (m), for p (m1, m2, or m3), for d (m1, m2, m3, m4, m5), f(m1-m7)
(orbital magnetic quantum number)
s = -1/2 or +1/2 (only two electrons can be in one orbital)
(electron spin magnetic quantum number)
In General, lowest energy are K electrons, highest energy is O shell electrons, however, their are some
complexities to the energy levels when considered in detail.
From lowest energy to highest:
1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, f5, 6d, 7p
Using this energy scheme, fill up the shells as follows: put s orbitals at 12 oclock, p orbitals at 3, 6, and 9
oclock, d orbitals at 1:30, 4:30, 7:30, 10:30, and the last pair put just below the s orbital at 12 oclock. f
orbitals at 1, 2, 4, 5, 7, 8, and 10 oclock. Label each orbital pair. In general, the energetically equivalent
orbitals (like the p orbitals), will fill up one electron in each orbital first, then fill each orbital with 2
electrons.
Do the following elements: Ca, Fe, Rb, Au.
Ca
Rb
Fe
Au
20
One of the important discoveries of the 1800s was the spectroscope. Suddenly, color was not
uniform, but rather particular wavelengths (lines) were found to be brighter than others.
Elements, when excited by temperature or other energy, glowed in particular lines characteristic
of each element. Below is the spectrum, showing spectral lines (absorption lines), for the bluewhite star, Sirius. Can you identify one or two elements that must be present in that star based
on its spectrum? Selected elemental spectra and a spectrum resulting from absorption by Earth’s
atmosphere are shown. The spectrum for Sirius is modified from a lithograph published in 1870
as found in the Cambridge Illustrated History of Astronomy. Spectral lines are simulated from
data in the CRC Handbook of Chemistry and Physics, 63rd and from James B. Kaler, Stars and
their Spectra, Cambridge Univ. Press, Cambridge, 1989.
Red
Blue
21
ultraviolet
blue
red
The figure above shows additional lines occurring in the non-visible
ultraviolet range (not exactly the same scale so they don't line up
exactly in the visible range, although they should).
There are two types of lines, basically at the same wavelengths
(energies): emission and absorption lines. Those shown above are
dark, meaning that light at that wavelength is being absorbed.
Absorption lines occur when the energy kicks an electron to a
higher energy orbital (thus it absorbs energy). Emission lines occur
when the electron is already in a higher energy orbital and it falls to
lower energy (releasing energy).
Remembering that red is a longer wavelength than blue
(and thus lower energy), correlate each of the observed lines in the
visible spectrum (H alpha through H delta), with one of the electron
transition shown at right (write answer on the graph).
Notice that the lines on the spectrum are not separated by equal distances. Explain briefly why
this is so.
Where do the extra lines in the ultraviolet range (left side of the spectrum above) come from?
Remembering that E of a photon is proportional to 1/ and E of an electron is proportional to
1/n2, write a simple expression for what the wavelength of the absorption line will be
proportional to in terms of n for the excited state and n for the unexcited state (n=2). (In 1885,
Johann Balmer figured this formula out without any understanding of how atoms worked. These
absorption lines are called the Balmer sequence after him).
It makes sense that some electrons would start out in the n=1 state. Where would the absorption
lines for this transition occur?
22
Coordination number:
For ionic compounds, the number of nearest neighbors is determined by the relative sizes of ions.
This number is called the coordination number.
consider the diagram from your book.
Consider how the coordination of the alkali atom changes in alkali chloride as the size of the
cation changes (keeping the size of the anion the same).
Does the coordination number of Cs increase or decrease relative to Na?
Is Cs larger or smaller than Na?
Is this consistent with the diagram from your book?
Draw atoms on the shown faces below for NaCl and CsCl. Use open circles for Cl and filled
circles for Na and Cs.
NaCl
CsCl
23
Close Packing:
Another way to think of crystal packing is to consider that the anions (usually O2-, but sometimes
Cl- etc) are packed in some type of “closest packing” arrangement, and cations then fit into
interstitial areas of various shape (tetrahedral, octahedral).
There are two types of closest-packing: Cubic closest packing and hexagonal closest
packing. Both of these represent the most closely-packed that equal-sized spheres can be.
Consulting with figures 3.37 and 3.38 from your text book (shown in small form below), Use
equal-sized styrofoam balls to construct three layers of each type of packing (hint, the first two
layers is the same for both of them-only the third layer differs). Balls have been attached in
groups of three to aid stacking.
Polyhedral models:
The interstitial spaces between the close-packed anions often have simple geometric shapes
(although sometimes distorted), such as tetrahedral and octahedral. Due to its covalent bonding
with 4 oxygens, Si often fills tetrahedral spots. 6-coordinated cations (Al and Mg often) occupy
octahedral spots. Examine the shapes below to verify that 4-coordination results in shapes with 4
sides (tetrahedral), and 6-coordination results in shapes with 8 sides (octahedral).
These polyhedra can share corners (left two pictures), edges (middle two pictures) or
sides (right two pictures). Make sure you understand this and can see it.
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Crystal structure can be shown either by ball-and-stick models, showing atoms and bonds, or by
polyhedral models, showing the polyhedra formed by groups of atoms.
NaCl is shown below in both models, from your book.
Unit Cell:
A unit cell is the unit that can be copied over and over to fill up space, thus making up the entire
crystal. It reflects the overall symmetry and form of the crystal. On the ball-and-stick picture of
NaCl above, draw the boundaries of the unit cell that has the octahedron in it. There is a Na
atom at each corner of the unit cell.
How many corners does the unit cell have?
With how many unit cells is each corner Na shared?
How many edges does each unit cell have?
With how many unit cells is each edge Cl shared?
How many sides does each unit cell have?
With how many unit cells is each side Na shared?
There is one atom that is entirely within the unit cell. What is it?
Unit cells for NaCl and CsCl are shown. Notice how they differ. The total number of Na, Cl,
and Cs in each are shown. Make sure that you understand how this number is derived by
thinking of fractions of atoms shared with more than one unit cell.
NaCl
8x⅛+6x½ =4Cl
12x¼ +1 = 4Na
CsCl
8x⅛+2x½= 2Cs
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4x½ = 2Cl
Mineralogy and Petrology Lab # 4: Ball and stick models. ATTENTION:
BE VERY CAREFUL WITH THE MODELS. Together, they cost over $1500!
Halite Model (NaCl)
green = Chlorine (Cl)
gray = Sodium (Na)
What is the coordination number (number of nearest neighbors) for Na?
for Cl?
Find the octahedra around the Na or Cl. Visualize it.
Find the octahedral planes (there are 4 of them). Rotate such that you see the plane of Na
atoms and plane of Cl atoms. These are the octahedral planes.
At what angle are these planes to the sides of the cube?
Relate the chemical composition of Halite to the number of Na and Cl you see in the
model.
Halite is in the isometric system. This system has very high symmetry. Examine the
block models 1, 2, and 3. Think about how the crystal form is related to the planes of the
cube and octahedral.
Graphite and diamond models
Neither of these two is closest packed. Which of these two is denser?
Which will be favored at higher pressure?
Examine the graphite model.
Find the layers in graphite. To how many other 'closest neighbor' carbon atoms is each
atom bonded?
Examine the bottom layer of graphite. What can you notice about the pattern of atoms in
one layer?
Look one layer up? Is this layer on top of the underlying layer?
How many layers up do you have to go before you find a repeat of the first layer?
The 6 crystal systems that "fill up space" in three dimensions are isometric (like a cube),
hexagonal, tetragonal (like a cube stretched in one dimension), orthorhombic (like a cube
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stretched in two dimensions), monoclinic (like a box squished over so angles in one
direction are no longer 90 degrees), and triclinic (no angles equal 90 degrees). To which
does graphite belong?
Look up the common crystal habit of graphite. _________________________
Examine the diamond model.
What is the coordination number of each C atom?
Imagine how a tetrahedron fits around each C atom.
Diamond is isometric (the unit cell is shown on the model). It has a face-centered cubic
unit cell, meaning that each face has one C at each corner and another C in the center.
Look toward each of the faces of the cube and note how the atomic arrangement looks the
same. In each case, you should see the C atoms line up in rows diagonal to the sides of
the cube.
Notice that each face has a 4-fold axis of symmetry coming out at you, meaning that can
rotate it four times and it looks the same. (Actually it is a 4 fold axis with perpendicular
mirror plane, but we'll get to that later).
Look down the model from cube corner to corner and note how each corner looks the
same.
Notice that each corner has a 3-fold axis of symmetry coming out at you, meaning that
you can rotate it three times and see the same image. This is the characteristic symmetry
of the isometric system.
Look down the model from cube-edge to cube edge. You should see hexagonal rings.
Now look down the octahedral face of the cube (Remember where the octahedral face
relative to the sides of the cube in the isometric halite structure). This is basically
looking down a corner of the cube, but instead of looking to the far corner, look to a spot
in the center of the opposite face. You should see bumpy layers of C atoms that are
farther apart than any of the other layers. Because they are farther apart, these planes are
weaker. Diamond cleaves along these planes, producing diamond's pronounced
octahedral cleavage. Crystals may be octahedral, cubic, or dodecahedral.
Sphaelerite and Wurtzite Models
Look at the sphaelerite model (grey= Zn yellow =S). What is the coordination number
for Zn?
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Sphaelerite has the same structure as Diamond, with half the C replaced by Zn and half
replaced by S. What crystal system is sphaelerite in?
Try to find the face-centered cubic unit cell for sphaelerite.
Compare to the model for wurtzite (a polymorph of sphaelerite). Has the coordination
number changed?
Has the crystal system changed?
To which crystal system might wurtzite belong?
Wurtzite atoms can be thought of as filling a hexagonally close-packed structure. Find
the planes of stacking. (Hint: find the c axis of the crystal, this is the axis with the
distinct hexagonal columns. move the model so that the c axis runs left and right. Rotate
the model until you see flat planes of atoms that are equally spaced. Unlike a perfect
close-pack structure, the rows of atoms zig-zag a bit.
Think of the stacking of these planes, does the stacking follow an AB-AB-AB stacking
structure or an ABC-ABC stacking structure?
Beta-Quartz Model
black = Silicon (Si)
red = Oxygen (O)
Notice the tetrahedra formed by the four oxygens around each Si. Think about the
polyhedral model.
How many sides, corners, edges does each tetrahedron share with adjacent tetrahedra?
(the answer, to be read only when you have thought about it, is..............no sides, no
edges, 4 corners)
What is the chemical formula for Beta-Quartz, based on the number of oxygens and Si
present in the model? (also, think about how many O there must be for each Si, if every
O is shared with one other Si). Check its composition in your book to see if you are
right.
Framework silicates, like quartz, have tetrahedra that share all corners, and have a ratio of
tetrahedral cations (Si), to anions (O) of 1:2.
Notice the unit cell shown on the model. Each unit cell contains 3 Si, and 6O, many of
them shared with adjacent unit cells. Make sure that you can count them up, and figure it
out! Think about how many unit cells that a particular atom is shared with.
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Alpha-Quartz Model
This form of Quartz is a polymorph of Beta Quartz, that is, it has the same composition
but a different atomic structure. Alpha-quartz is the form that occurs at lower
temperatures (below 500 C). Which has higher entropy, alpha or beta quartz?
Also, the alpha quartz is slightly preferred at higher pressure, such that at 8kbars pressure
it occurs below about 800C. This is because the alpha-quartz is slightly denser than the
beta-quartz (the atoms packed together more tightly).
The two forms are very similar. Notice, as with beta-quartz, the shared tetrahedron
corners (all four corners are shared).
As with beta-quartz, there are no shared sides or edges.
The basic shape of the unit cell is similar.
To notice the difference, count the number of Si and O in each unit cell, as you did with
beta-quartz, and notice that different fractions of particular atoms are shared with
adjacent unit cells. Beta quartz is slightly more symmetrical.
Rotate the model so that the Si atoms line up. You should be looking at the
rhombohedral unit cell from the side. With the model in this orientation, you are
looking approximately in the “c” direction of the crystal. When quartz grows into
hexagonal prisms, the prisms grow in the c direction, and the hexagonal outline will be
perpendicular to the c direction.
Do you see any hints of hexagonal form?
Forsterite Model (one end of the Olivine solid solution series)
black = silicon (Si), red = oxygen (O), silver = magnesium (Mg)
Try to infer the chemical formula for Forsterite based on the proportions of atoms that
you see. Check your book to see if you are right.
Find the Si tetrahedra. What is the coordination number for Si?
Find the Mg octahedra. What is the coordination number for Mg?
Try to visualize the polyhedral model for Forsterite.
How many sides, corners, or edges do Si tetrahedra share with other Si tetrahedra?
(And the answer is, not to be read before you think about it.........no edges, no sides, no
corners)
Look at the model end-on in such a way that the Oxygen atoms line up. Think about
what it would look like if projected onto a flat sheet of paper (the way crystal structures
are often shown in books).
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Look at the model sideways such that the Mg atoms line up. As above, think about the
projection onto a flat page. Notice the “apparent” hexagons around Mg?
Nesosilicates like Forsterite have tetrahedra that do not share any corners, edges, or sides.
The ratio of tetrahedral cations (Si) to anions (O) is 1:4.
Illite Model (a mica-like clay mineral, very similar to muscovite and montmorillinite in
composition and structure. Use of this mineral name has a problematic history.)
black = silicon (Si)
red = oxygen (O)
silver = aluminum (Al)
aquamarine = hydroxyl group (OH-)
gold = potassium (K)
orange = other large cations maybe Na, Ca
Find the silica tetrahedra.
how many corners, edges, sides do they share with other silica tetrahedra?
Notice that some of the Si has been substituted by Al. Typically, 10-15% of the Si is
replaced by Al.
Find the Al octahedrons.
How many corners, edges, sides do octahedral share with other octahedral?
(the answer is, which you shouldn’t read until looking, is share edges, no sides, no
corners)
How many corners, edges, sides, do octahedra share with tetrahedra?
(share 4 corners)
With how many octahedrons is any one octahedron-oxygen shared? (we will talk later in
the term about dioctahedral and trioctahedral sheet silicates).
It is very common for sheet silicates (micas and clays) to be made of up various sets of
tetrahedral and octahedral layers (covalent or strong ionic bonds) that make characteristic
“sandwiches” that are in turn bound by much weaker ionic bonds, or even hydrogen
bonds. See if you can find the layers of tetrahedral and octahedral and figure out the
pattern.
The stacking sandwiches for illite (which is like muscovite) is roughly the following:
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Make sure you can find and see these layers in the model.
Think about how the strong cleavage in micas and clays results from this layering.
Montmorillinite (the super-water absorbing clays in bentonite) is similar in structure but
lacks the K layer, having instead much more weakly bonded water layer between the
sandwiches.
The c axis is perpendicular to the sheets. Look into the crystal in the c direction (you
won’t see the layers). Notice how any plane cutting through the crystal in this direction
must cut across the covalent bonds of the tetrahedra and octahedra. Therefore, there is no
good cleavage in these directions.
Look how big a unit cell must be!!! Observe how far you go before the crystal repeats,
the entire size of the model!
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32
Mineral Reactions, Stability, and Behavior:
Crystallization:
Concept of phases: phases are macroscopically homogeneous regions bounded by
distinct edges.
gases, liquids, solids are the examples of phases you learn in high school. But a
particular material can exist in more than one solid or liquid phase. For example,
graphite and diamond are two solid phases with the same composition (polymorphs).
In gases, individual molecules or atoms have no long range order, and are not bonded to
nearby molecules or atoms.
In liquids, molecules or atoms have no long range order but are bonded to nearby
molecules or atoms but those bonds are not strong enough or persistent enough to
maintain a regular long-range order, although a short-range order often exists.
In solids, molecules and atoms are bonded to nearby modecules and atoms, most
normally establishing both local and long range order (crystals). Some solid materials do
not have long range order (although short range order typically exists). These amorphous
materials are called glass.
Crystallization occurs when a material goes from a gaseous or liquid state to a solid,
ordered state. This occurs when T, P, composition or other properties change in such a
way that the solid state is energetically favored over the former state.
For example, evaporating water from salt water increases the concentration of Na and Cl
dissolved in the water to the point that salt crystals will form.
Cooling magma will bring the temperature to a value where crystals begin to form in the
melt.
Energy of a crystal is related to the bond energy as well as the arrangement of atoms in
the crystal.
We can also think of the bulk energy, the energy of a block of essentially infinite size,
and the surface energy, the energy of the material where it encounters something else (air,
water, another mineral, etc). Generally, the atoms at the very edge of a crystal are less
stable (higher energy).
Think about what the effect of surface energy will have on tiny crystals versus big
crystals. (think about volume increases by cube, surface area by square: use example
sizes e.g. cube 1x1x1 vs cube 2x2x2 what is surface area and volume of each?)
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The surface energy makes tiny beginning crystals less energetically favorable. This is
what makes crystals tend to grow into a few big ones instead of many small ones. But it
also makes the “starting” step of crystal growth difficult. This step is called nucleation.
E.g. of nucleation in weather. Seeding clouds in the 60’s, still done in some countries.
Lowers surface energy. Supercooled air then forms ice crystals or water droplets.
Sometimes, air can become supercooled. It is below T at which ice crystals should form,
but due to surface energy, they crystals don’t form.
Big perfect crystals, usually form from slow growth, lots of space to grow in to, and ideal
growing conditions (such as the T, P, composition are held persistently where the crystals
grows slowly at a regular rate). They are rare.
Phase Diagrams, graphical illustration of crystallization reactions and phase transitions.
One-component reactions (different phases of a single chemical component)
Primary variables are T and P.
In general, the phase preferred at higher pressure will be the denser phase.
The phase preferred at higher temperature will be the less well-ordered phase and/or the
phase with higher energy bonding.
Parameters other than T and P can also affect equilibrium, and could be plotted, but are
generally not significant in natural situations (e.g. magnetic field, gravitational field,
electrostatic field, etc.).
Water overhead: Phase diagrams illustrate fields of T and P where phases are stable.
Lines represent reactions, such as the reaction in which liquid water freezes to ice (find
that reaction). The triple point is invariant, meaning there only one T and P where all
three (liquid, gas, solid) can coexist. Lines are univariant, curves of T and P where e.g.
liquid and gas can coexist. Critical point is T and P beyond which liquid and gas are not
separated by a distinct phase transition (they become like each other). Based on the ideas
discussed above, which is more random, and/or has higher energy bonding, liquid water
or vapor water? Does this make sense? Which is more dense, ice or liquid water? Does
this make sense? Below 6 millibars, what happens to ice as you heat it up? This is the
state of H2O on most of Mars surface.
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Broader H2O phase diagram, overhead.
Which is denser, Ice I (normal ice that we know), Liquid H2O, Which is denser, Ice I or
ice III? How about Ice VI? Which is denser liquid water, or ice VI?
Is ice deep inside a moon of Jupiter likely to have a density of less than, equal to, or
greater than 1g/cc?
C phase diagram, overhead
Which is more dense, graphite or diamond? Which is less ordered and/or more energy in
bonding? Which is more dense, C melt, or diamond? Which is more dense, graphite or
C melt? In which will the atoms of C be packed more closely, diamond or Carbon III?
Notice the C vapor. What will happen to vapor at a single T if pressure increases?
Metamorphic reactions among different
polymorphs of Al2SiO5. Which is the
most dense? Which is the least ordered
and/or highest energy in bonds? Which
is the least dense? Which is the most
ordered and/or lowest energy in bonds?
Which would form in a contact
metamorphic aureole? Which would
form in dynamic metamorphic
environment (like a subduction zone)?
35
SiO2 phase diagram overhead.
At pressure of around 10kbars (about 29 kilometers depth), what will happen to pure
SiO2 as T falls from around 1800 (tell the story). What would happen at about 3 Kbar?
Stishovite generally forms in meteorite impacts, is a fingerprint for impact. 80-90 kbar is
a pressure 250 km deep or more, where SiO2 generally does not occur as a distinct phase.
CaCO3 overhead.
Which is more stable at high P, aragonite or Calcite? Which is the more dense structure?
Which is more stable at low pressure? Why does aragonite occur is many gastropod
shells?
2-component Phase diagrams (two compositional components)
Can only easily show 2 variables on 2-dimensional page. With only 1 component, you
can show both T and P and composition doesn’t change. With 2 components, can’t easily
show both T and P as well as composition. So often show a diagram that is valid at only
a single pressure (often 1-atm pressure).
Solid-solution series: (e.g. olivine and plagioclase)
36
Same structure, but Fe substitutes for Mg as go from Forsterite to Fayalite.
Above both curves, there is a single phase, melt, that has the composition of the bulk
material.
As T decreases, the upper curve is encountered. It is called the liquidus, the temperature
at which all solid disappears during melting, or where the first solid appears during
cooling.
At this T, solid olivine begins to form. You can determine the composition of that olivine
(remember, it’s a solid solution) by drawing a horizontal line at that temperature. The
intersection of the horizontal line with the lower curve (called the solidus) indicates the
composition of the olivine.
As T continues to fall, the composition of both the residual melt and the olivine solid
solution must change. At any T, the equilibrium composition of melt and solid is
indicated by the intersection of the horizontal line with the liquidus and solidus
respectively.
Eventually, a temperature is reached where the solid olivine has the same composition as
the bulk starting material. At this temperature, the last of the liquid material will solidify
(or, if we are melting solid material, it is at this temperature that the first melting will
occur).
What reaction does the liquidus and solidus lines represent? (liquid olivine = solid
olivine).
Notice that, in general, solids in 2 or more component systems will not have the same
composition as the bulk liquid. Therefore, as the solid crystallizes, the composition of
the residual melt must change since the total of solids+liquids must always equal the
initial bulk composition.
How many phases are present above the liquidus?
How many phases below the liquidus but above the solidus?
How many phases below the solidus?
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Handout of Plagioclase phase diagram, one for each person.
Questions:
Which melts at a higher T, pure anorthite or pure albite?
What happens to the melting T of Albite as you add more Ca-Al to it?
What happens to the melting T of anorthite as you add more Na-Si to it?
Consider 40%An, 60% Ab. At what temperature would such a mineral begin to melt?
(about 1229C)
If it was all completely melted, at what temperature would it start to freeze? (about
1413C)
At what temperature would it completely freeze? (about 1229C)
What would be the composition of plagioclase at about 1413C when the first plagioclase
crystals start to form? (about 76.2% An)
What would the composition of the melt be at about 1413C when the first plagioclase
crystals start to form? (40% An)
Are the plagioclase crystals more Ca rich or more Na rich than the melt? Is that always
true? So, if the solid has more Ca in it than the melt, how must the melt change as more
plagioclase crystallizes from it?
Will the composition of the plagioclase stay the same once it starts to crystallize, or will
it change?
How will it change? (more Na rich at lower T)
what is the composition of the melt at 1300C? (15.3% An)
What would be the composition of plagioclase at about 1229C when the last melt
solidifies? (40% An)
What would be the composition of plagioclase at about 1300C? (54.3% An)
Non-solid-solution binary systems: phase diagram overhead.
Pick a couple of compositions and decrease T, showing
first phase to appear on liquidus, zone of freezing, and
encounter of solidus.
Two different phases on the liquidus, depending on the
starting bulk composition.
Last drop of melt will always be at the invariant point
where liquid, phase A and phase B all coexist
(remember, other invariant point was where three things
coexisted).
38
Albite-Qz phase diagram overhead.
What form of quartz if went to even lower T? (high quartz then low quartz) (show other
phase diagram if necessary)
What if at higher Pressure? what would be different? (high Qz instead of cristobalite and
tridymite).
Didn’t get to the following, but will probably do these when we cover igneous rocks.
Two solid solution series plus a subsolidus exsolution curve. See Albite-Orthoclase
overhead, and also draw a simplified schematic version on the blackboard. Note where
various phases occur, including polymorphic transitions. High albite, less ordered Si-Al,
low albite has more ordered Si-Al.
If slow cooling occurs, microcline occurs in rock. More rapid cooling from higher T
results in orthoclase, or even sanidine.
Bunny rabbit overhead with simplified schematic on blackboard. Effect of pressure
(H2O pressure) on the curve (5 kbar H2O). Explain how this results in a single feldspar
at low water pressure, and two feldspars at high water pressure. Perthite forms when
crystallizes at low P, then cools below solidus curve. If the rock cools at depth with
H2O, 2 feldspars form to start with and perthite does not occur.
39
Ternary systems (overhead):
plot three components, with temperature plotted as contour lines. Composition is
resolved as illustrated.
Other types of phase diagrams. phase diagrams in which two compositional variables are
shown (at T and P are constant), are called fence diagrams. Often, pH and Eh are the
compositional variables.
40
Mineralogy and Petrology.
Phase Diagrams, Lab #5
1) Construct a one-component phase diagram (T on the x-axis, P on the y-axis), showing
a typical gas-liquid-solid system for the typical case in which the solid is denser than the
liquid.
2) Construct a one-component phase diagram of a material that exists as three solid
phases for the following case:
For Entropy:
Phase A<B<C
For Density
Phase B<A<C
3) Two-component phase diagram - case of solid solution
a) How many phases are present in a bulk composition that is 10% Fa and 90% Fo at
1800C?
b) How many phases are present in a bulk composition that is 50% Fa and 50%Fo at
1800C?
c) List the variables of the system that you can change in the case above without
changing the number or type of phases present.
41
d) Between what two temperatures will the composition in (b) have only a single degree
of freedom (ignoring P which is held constant)?
e) For the bulk composition in (b), what is the highest T at which some crystals exist at
equilibrium?
f) For the bulk composition in (b), how many degrees of freedom are there at 1600C?
g) For the bulk composition in (b), what phase(s) is (are) present at 1600C?
h) For the bulk composition in (b), what is the composition of olivine at 1650C?
i) For the bulk composition in (b), what is the composition of melt at 1650?
j) For the bulk composition in (b), what is the composition of solid at 1650?
k) For the bulk composition in (b), what is the proportion solidified at 1650?
l) For the bulk composition in (b), what is the composition of solid at 1500C?
m) For the bulk composition in (b), what is the composition of melt at 1500C?
n) For the bulk composition in (b), what is the proportion solidified at 1500C?
o) Consider that lava periodically erupts from a cooling magma chamber beneath
Kileaua, Hawaii. How will the composition of olivine differ in the later eruption?
p) For the bulk composition in (b), what is the composition of solid (olivine) at 1200C?
q) For the bulk composition in (b), what is the composition of melt at 1850C?
42
r) For the bulk composition in (b), at what temperature will the composition of the
olivine be 75% Fa?
Fa=Fayalite=Fe2SiO4
Fo=Forsterite=Mg2SiO4
43
4) Two-component phase diagram - case of no solid solution. Because there is no solid
solution, the solid is either pure A or pure B, thus there is no solidus curve along which
solid composition changes. Liquid composition is defined by the liquidus curves.
a) How many phases and degrees of freedom are there above TB (assume that P is
constant, so don't include pressure as one of the degrees of freedom)?
b) How many phases and degrees of freedom are there at composition M and
temperature T1?
c) How many phases and degrees of freedom are there at point c (called the eutectic
point)?
d) How many phases and degrees of freedom are there at temperatures below Tc? How
does this differ from the subsolidus state in a solid solution series?
e) Suppose that you start with 90%B and 10% A. What will the composition of the solid
be at T1?
f) Suppose that you start with 90%B and 10% A. What will the composition of the melt
be at T1?
g) Suppose that you start with 90%B and 10% A. What will be the proportion solidified
at temperature T1?
h) Suppose that you start with 90%B and 10% A. What will the composition of the melt
be just a tiny fraction above Tc?
i) Suppose that you start with 90%B and 10% A. What will the composition of the solid
be just a tiny fraction above Tc?
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j) Does the melt get richer in A or B as temperature decreases for composition
90%B+10%A?
k) Suppose that you start with composition M. What will the composition of the melt be
just slightly above Tc?
l) Suppose that you start with 10%B and 90%A. How will the composition of the melt
change as temperature decreases?
m) What will the composition of the melt be at temperature Tc?
5) Binary phase diagram with liquid immiscibility and incongruent melting.
Often, cooling results in freezing of a liquid into one or more solid phases. However,
sometimes the melt will divide into two separate liquids that don't mix with each other,
like oil and water. This happens at high SiO2 concentrations in the system Fo-SiO2.
Sometimes a solid phase will "back-react" with the melt and produce a different solid
phase. This is called incongruent melting reaction. This happens between oliving and
protoenstatite (Pr) at 1157C. The reaction that happens at this T is the following:
Olivine + melt ↔ Protoenstatite + a melt of a different composition
Look over this diagram. Figure out what solids form, and how melt composition will
change in any given situation. Ask questions where necessary.
45
6) Review Bowens reaction series, either in an introductory Physical Geology textbook,
or the more complete version in your text book (in my edition, its in Chapter 4, pg 108).
Think about how changes in the discontinuous series is reflected in the diagram above
(increasing SiO2 of melt, reaction from olivine to pyroxene). Think about how the
continuous series is related to the plagioclase phase diagram that we did in class.
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Mineralogy. Review sheet for Exam 1.
Sure Bets (80% of exam):
(This category basically includes the key concepts that we have learned so far)
Be able to fill electron shells for a selected atom, predict that atom’s typical valence, and
explain qualitatively what electron “shells” are.
Be able to describe and explain the different types of bonding, including each of their
properties and a description of how the bond works, with illustrations, giving an example
of each.
Be able to interpret a single-component phase diagram (P-T), including understanding of
the relationship between lines on the diagram and the relative densities and enthalpyentropy characteristics of phases (that is, we simplified concepts of free energy to think
about the higher-T phase being the one that is less ordered and/or has more energy in its
bonds).
Based on single-component phase diagrams, be able to predict under what conditions
different phases will exist.
Be able to interpret a binary phase diagram with complete solid solution (like Fo-Fa, or
An-Ab), including reading off the diagram the temperature of initial crystal formation
and temperature of final solidification (for any particular composition), and the
composition of melt and composition of solid (for any particular temperature). Be able to
predict how composition of the melt will change with either crystallization or melting.
Be able to interpret a binary phase diagram with no solid solution.
Other Stuff (20% of exam):
(This category basically includes the important information and language that we have
learned so far......there is a lot, of course!)
I can’t reproduce here all the things that fall into this category. But I have listed some
obvious ones to give you an idea of what I mean by “information and language”.
Be able to illustrate, explain, and/or identify twinning, various types of aggregation,
crystal faces (and crystal form), cleavage, fracture, hardness, density, streak, habit,
birefringence, exsolution, labradorescence, fluorescence.
Know what euhedral, subhedral, anhedral mean
Especially, be able to explain the difference between a crystal face and a cleavage face.
Understand what causes fluorescence.
Be able to identify the mineral group to which a particular composition belongs.
Be able to explain why elements in stars produce characteristic spectra.
Know what the expression E=-A/n2 tells us about electronic energy levels.
Understand the relationship between quantum chemistry and spectroscopic lines.
47
Given their position on the periodic table, be able to predict the relative ionic or covalent
character of particular bonds.
Know, conceptually, the difference between the Bohr model and the Schrodinger model
for atoms.
Know what electronegativity means and how it varies across the periodic table.
Understand what the expression AZ+Z-/d tells us about the energy of an ionic bond.
Be able to recognize features in ball-and-stick models, including number of nearest
neighbors (coordination number), presence of tetrahedra and octahedra, shared
corners, edges, or sides of tetrahedra or octahedra.
Be able to count the number of other unit cells that a particular atom in a unit cell will be
shared with (such as a corner atom, and edge atom, or a side atom in a cubic unit
cell).
Know what a phase is.
Know what a phase transition is.
Be able to explain solid, liquid, and gas phases in terms of long and short range order.
Be able to explain qualitatively why small crystals may not grow even if they are
thermodynamically favored (considering nucleation).
48
Mineralogy and Petrology. Lab # 6
Becoming familiar with Crystal Systems
Some shapes fill up space and others do not. The crystals systems are the basic types of
shapes that can fill up space in three dimensions. There are 6 of them.
In two dimensions, there are only 4 unique shapes that fill up space. For example, the
square fills up space:
Draw pictures showing that each of the following DO NOT fill up space in two
dimensions:
Circle:
Octagon:
Pentagon:
suggestion: (trace over the pentagon on a separate sheet of paper, then cut out the result
to act as a drawing template)
Try to figure out what the other three shapes are that fill up space in two dimensions.
Demonstrate with pictures that they do fill up space.
The other three shapes that fill up space in two dimensions are:
49
The rectangle
The rhombohedron (called hexagonal)
The non-rhombohedral parallelogram (called oblique)
You might be thinking, Wait! Don't triangles and hexagons fill up space? Yes, they do,
however they are not unique shapes, that is, they can be made with the other shapes.
Use the wooden rhombohedrons in the lab to construct hexagons to demonstrate this.
Can you make a square or a rectangle with the rhombs.
Drawing of rhombohedrons making hexagons:
Show with pictures of three differently shaped parallelograms that taking any two
triangles of the same shape can be used to make a parallelogram.
In 3 dimensions, the 6 crystal systems are:
Isometric
Hexagonal
Tetragonal
Orthorhombic
Monoclinic
Triclinic
We will look at these one at a time:
Important concepts to know:
a mirror plane is an imaginary plane that can be drawn through a shape such that one
side of the shape looks exactly like a reflection of the other side.
an axis of rotational symmetry is a an imaginary axis drawn through shape such that
rotation around this axis yields basically the same view several times in a single rotation.
For example, looking down on a cube with the axis of rotation coming up at us, it can be
seen that we get basically the same view 4 times as we rotate it, thus this is a 4-fold axis
2
of rotational symmetry.
1
3
4
50
The isometric system is cube-like. Its key features are sides of equal length and angles
at 90˚. The identifying symmetry element for this system is four 3-fold axes of
symmetry. The picture from my notes, is given below
There are three wooden models in the isometric system, models 1, 2, and 3.
Look at model 1, an octahedron (remember the octahedral-cube relationship in halite?)
It has three 4-fold axes of rotation. Find them (they go from corner to corner).
There are 4 three-fold axes of symmetry (the characteristic symmetry for this system).
Find them (they go from face to face. Hold the model with your fingers on two opposing
faces and rotate the sample, counting the number of faces that turn to face you (or
upward-pointing corners, or downward pointing corners).
There are also 6 2-fold axes of symmetry. Find them (they go from edge to edge).
There are lots of mirror planes. Find some of them.
Look at model 2, a cube (with the octahedral planes showing at the corners of the cube).
It also has three 4-fold axes of rotation. Find them (they go from face to face).
It has four 3-fold axes of rotation (the characteristic symmetry for this class). Find them
(they go from corner to corner).
There are 6 2-fold axes of symmetry. Find them (they go from edge to edge).
There are lots of mirror planes. Find some of them.
Look at model 3, a pyrotohedron (triangles are the octahedral planes, squares are the
cubic planes).
It also has three 4-fold axes of rotation. Find them (they go from square face to face).
51
It has four 3-fold axes of rotation (the characteristic symmetry for this class). Find them
(they go from triangular face to triangular face).
There are 6 2-fold axes of symmetry. Find them (they go from corner to corner).
There are mirror planes, but not as many. Find some of them.
Find some planes that lack mirror symmetry.
The tetragonal system is a rectangular prism. Its key features are two sides of equal
length and angles at 90˚. The identifying symmetry element for this system is one 4-fold
axis of symmetry. The picture from my notes is given below
There are two wooden models of this system, 4 and 5. Look at both together.
Find the single 4-fold axis of rotation in each model (the characteristic symmetry for this
system).
There are two 2-fold axes of rotation in each of the wooden models. Find them (going
from face to face and edge to edge).
Find the mirror planes (including the one that is perpendicular to the 4-fold axis of
rotation and the ones that are parallel to this axis)
The orthorhombic system is a non-cubic box. Its key features are sides of un-equal
length and angles at 90˚. The identifying symmetry element for this system is three
perpendicular axes with binary symmetry. The picture from my notes is given below
52
There are two wooden models of this system, 8 and 9. Look at both together.
Both of these samples have both a mirror plane (one type of binary symmetry) and a twofold rotation axis (another type of binary symmetry) associated with each axis.
Find the long axis of each. Notice that this axis is a 2-fold axis of rotation.
Notice the mirror plane perpendicular to this axis.
Find the short axis of each. Notice that this axis is a 2-fold axis of rotation.
Notice the mirror plane perpendicular to this axis.
Find the middle-length axis of each. Notice that this axis is a 2-fold axis of rotation.
Notice the mirror plane perpendicular to this axis.
The monclinic system is a box squished over in one dimension. Its key features are
sides of un-equal length and an angle between two of the axes that is not 90˚. The
identifying symmetry element for this system is either a two-fold b axis, or a mirror plane
perpendicular to b axis. The picture from my notes is given below
There are two wooden models of this system, 10
and 11. Both of these models have the same
symmetry.
Compare the two models. At first they will not
appear to have the same symmetry.
Look at model 10. The b axis goes through the
wide faces. Notice that this is a two-fold axis of
symmetry.
Notice the mirror plane perpendicular to the b axis.
Lay the model on its flat face. You are looking down on the b axis. Notice that the c axis
(the longer axis) is perpendicular to this. Notice that the a axis (going from corner to
corner in the shorter dimension) is NOT perpendicular to the c axis.
Look at model 11. At first, the angle of the sides of the model might seem to suggest
that there must not be any axes at 90°. However, the true axes are not parallel to the sides
of the model. Look at the model end-on so that you see the diamond shape. The b axis
goes through the long axis of the diamond.
Rotate about this axis in order to see the 2-fold axis of symmetry.
53
Find the mirror plane perpendicular to this axis.
The triclinic system is a box squished over in two dimension. Its key features are
sides of un-equal length and no angles between axes of 90˚. The identifying symmetry
element for this system is its lack of rotational or mirror plane symmetry. The picture
from my notes is given below
There is one wooden model of this system, 12.
(we are going to compare this to model 11, so get
both). To see this lack of symmetry, compare
model 12 with model 11. Hold sample 11 so that
its b axis is up and you are looking at the
diamond-shaped end of the model. Now, hold
sample 12 in the same orientation. Compare
them. Notice that 11 has a mirror plane
perpendicular to the b axis, but 12 does not.
Rotate 12 around the b axis and notice that it does not have a 2-fold axis of symmetry,
but model number 11 does.
The hexagonal system is a hexagonal or trigonal prism. The identifying symmetry
element for this system is either a single 6-fold or 3-fold axis of symmetry. The picture
from my notes is given below
There are two wooden models of this system, 6 and 7.
Look at model 6.
Find the 6-fold axis of symmetry (you don't need any hints):
Find some 2-fold axes of symmetry.
Find some mirror planes.
Look at model 7.
Find the 3-fold axis of symmetry (hold the points of the long axis and rotate)
54
Find the 3 2-fold axes of rotation
Find a mirror plane (there are three)
Look at crystals from each of these Crystal Systems and think about how cleavage and/or
crystal habit reflects this symmetry:
Isometric:
Almandine Garnet (wards cabinets 27)
Galena (wards cabinets 27)
Halite (class mineral cabinet 15)
Tetragonal:
Vesuvianite (wards cabinets 33)
Orthorhombic: Stibinoconite (wards cabinets 66) (oxidized stibnite pseudomorph)
Cerussite (wards cabinets 29)
Monclinic:
Gypsum (selenite) (wards cabinets 95 and my sample)
Triclinic:
Microcline (wards cabinets 107)
Kyanite (wards cabinets 111)
Hexagonal:
Quartz (wards cabinets 44)
Calcite (cleavage rhomb, 84 and dogtooth crystals 83, in Wards cabinets)
55
Save for a later lab:
Make patterns with the rhombs.
Fill up space with the rhombs by translating (moving without rotating) a rhomb-shape.
Translate with a 180 degree rotation (the blue dot will not always appear in the same
corner).
Put two rhombs in a relationship to each other that represents reflection. Imagine that
you could draw a line between them such that each side of the line looks like a reflection
of the other. There is more than one way to do this.
Make a hexagon with the rhombs. What operations (translation, rotation, reflection), did
you have to use?
Crystal symmetry:
Crystallography is (arguably) the second oldest science, after astronomy.
Crystals can be thought of as made of motifs (a unit pattern of atoms) which are
periodically repeated to construct the entire crystals. The periodic array of points to
which the motif is copied is called a lattice. Imaginary lines constructed between these
points will enclose only a limited number of shapes. The unit cell is one possible
repeating pattern which can fill up space. The environment around each unit cell will be
identical to that around all other unit cells. The motif, and the lattice, will have symmetry
and dimensions which is characteristic of each crystal.
Symmetry operations (illustrated in 2-D, for 3-D illustrations, see your book)
Rotation:
2-D: 1 fold, 2 fold, 3-fold, 4-fold, 6 fold axes of rotational
symmetry
Reflection:
56
Can consider mirror planes. Some motifs may have more than
one. Consider mirror planes in the 2-D figures:
Inversion (in 2-D it is like rotation, but is more complex in 3-D):
Rotoinversion (in 2-D it is like a rotation, but is more complex in 3-D):
The symmetry above can be related to the symmetry of a particular motif. However, to
fully understand a crystal, we also have to consider the operations by which the motif is
copied through a crystal.
Translation and glide.
57
Translation and screw (only occurs in 3-D)
Consider the following 2-D motifs. What symmetry do they have? (i4; i4mm)
Hermann-Maugin notation (or the international symbols)
numbers refer to axes of rotation. e.g. 222 refers to three separate axes of rotation, each
of which is two fold. Show with an orthorhombic box. A bar over the number designates
an axis of rotoinversion (rotation and inversion).
m refers to mirror planes. e.g. 4mm refers to a four fold axis of symmetry with mirror
planes in two different orientations (it could be more than two mirror planes). 4/m refers
to a mirror plane that is perpendicular to the 4-fold axis.
i refers to a center of inversion. It is usually not listed if higher orders of symmetry are
present.
Only certain shapes fill up space (lattice systems or crystal systems).
Of those shapes that fill up space, only certain organizations of points within the lattice
are possible (lattices).
In addition, only certain types of motif symmetry are possible (point groups, or crystal
classes)
Considering the different types of possible lattices and the different point groups, and
considering the way that unit cells can be moved by translation, glide, and screw, there
are only a limited number of possible types of crystals (plane groups or space groups)
2-D
3-D
lattice system or
4
6
these are the basic
crystal system
shapes
lattices or Bravais
5
14
number of nonlattices
identical periodic
arrays of points
point groups or
10
32
number of different
crystal classes
symmetries possible
for motifs.
plane groups or
17
230
combines the
space groups
number of point
arrays with the
different
symmetries, and the
effects of
translation, glide,
58
and screw
For example, in two dimensions the 4 basic shapes are square (a=b, =90º), rectangular
(a≠b, =90º), oblique (a≠b, ≠90º), and hexagonal (the shape is a rhombus, a=b, =60º).
Although other shapes can fill up space, all other possible shapes are equivalent to one of
these.
(5 lattices in 2-D, also includes the centered rectangle, or diamond lattice, can't center
square, because that simply yields 4 smaller uncentered squares)
Examples of the different levels of crystal organization for a two dimensional square
shape:
lattice system square, has only one lattice type (square)
it has two point groups. (4mm, and 4). 4 refers to axis of rotation, first m to vertical and
horizontal mirror planes and second m to diagonal mirror planes: The illustration of
possible atom configurations is symbolic, showing possible symmetries.
The
square lattice has three plane groups
(analogous to space groups in 3-D). These
include the ways that the square shape can
combine with point groups, including also the operations of translation, glide, and screw.
p4, p4gm, and p4mm. 4 refers to the axis of rotation, the first m to the mirror planes
perpendicular to the sides of the square, the second m refers to diagonal mirror planes,
either through the corners (for p4mm), or between the corner and center point (for p4gm),
g refers to glide planes parallel to the sides but between the center and the sides.
For comparison in 3-D, in the cubic (isometric) system, there are 5 different crystal
classes (compared to 2 in the 2-D point groups), and 36 space groups (compared to 3 in
2-D squares).
Consider the highest symmetry example: P432. it has 3 4-fold axes of symmetry, 4 3fold axes of symmetry, and 6 2-fold axes of symmetry (show with a cube). There are lots
59
of mirror planes, however these are not given in the Hermann-Maugin notation because
the mirror plane symmetry is already implied by the rotational symmetry.
The six crystal systems in 3-D
(from least to most symmetry)
show lack of symmetry with parallelogram in 2-D (although point out rotation axis).
60
note: notation meaning for hexagonal may be wrong: should be 2nd number is parallel
to a, 3rd is perpendicular to a, (noting that perpendicular to a3 is between a1 and a2).
14 Bravais lattices in 3D:
Primitive: simple primitive shape with points at corners (or for hexagonal also in center
at ends)
Body-Centered: Primitive with point in center for monoclinic, orthorhombic, tetragonal
and isometric
Side-Centered: Primitive with points at two ends, orthorhombic
Face-Centered: Primitive with points in all sides, orthorhombic and isometric
Rhombohedral:
61
Crystallographic notation for planes, Miller indices - go through cubic and octahedral
examples for isometric system only.
Consider the intersection of the plane of a crystal face (or a planar feature within a crystal
or unit cell) and a line drawn perpendicularly through that plane from the origin of the a,
b, c axes within the figure. Take the inverse of the point of intersection for each axis, a,
b, and c. Adjust the points of intersection such as to yield only integers and only integers
with no common denominator other than 1. This is the Miller Index for the plane.
Example in Isometric system: planes of the cube and planes of the octahedral expression
of that system. e.g. first figure: intersection of b axis is at 1, a and c are at ∞. 1/1 = 1,
1/∞ = 0. Second figure: intersection of a, b, and c are all at 0.5. 1/0.5 = 2. These have 2
as a common denominator. Dividing by 2 yields (111). A bar over the number indicates
it is negative.
62
Miller Indices game
1 point for each done correctly (in teams)
Miller Index for each Plane:
DCGH
ABEF
DBGF
EFHG
Parallel to ADGF but above it slightly
Parallel to ADGF but below it slightly
Parallel to ABGH but above it slightly
Parallel to DCEF but below it slightly
IJHG
AHF
CHF
ICH
Define one cubic-face plane
Define one octahedral-face plane
Which plane is (1,0,-1)
Which plane is (1,1,-1)
63
Example Test Exercise Questions for the section on Symmetry and crystallography.
Illustrate a motif in 2-D that has a three-fold axis of rotation and 3 mirror planes.
Illustrate a motif in 2-D that has a three-fold axis of rotation but no mirror planes.
Illustrate a rectangular figure in 2-D, with motifs at the corners, that has only a single mirror plane.
Illustrate the three 2-D point groups for the square, using motifs different from those we used in class.
Illustrate the similarities and differences between the orthorhombic and tetragonal systems.
Draw a perspective view of a cube (isometric system). Use dashed lines for edges that are hidden. For
each of the 2-fold axes of symmetry, put a dot where the axis emerges from the cube. Number the dots
such that the two dots associated with each of the axes have the same number (i.e. the first axis has two
dots each labeled with a “1”, etc.).
Match the space group (hermann-maugin notation) with the appropriate crystal system. Choose from the
following crystal systems for each
isometric, orthorhombic, tetragonal, hexagonal (not rhombohedral), hexagonal (rhombohedral),
monoclinic, triclinic. (NOTE: These can be figured out simply from the rules that I discussed in class for
each crystal system)
P432
_________________________
P6/m
_________________________
Pmm2
_________________________
P2/m
_________________________
P422
_________________________
P4mm
_________________________
P3m
_________________________
P622
_________________________
P23
_________________________
P32
_________________________
P4
_________________________
P1
_________________________
Pm
_________________________
P6
_________________________
Match the indicated faces with the proper miller index (three faces in the isometric
system). Presume that the “a” axis is emerging from the figure (negative = going into the
figure) and the “c” axis goes upward (negative = downward). Positive “b” axis is toward
the right. Possible indices are (100), (111), (110), (211), (222), (010), (001), (101), (110),
and (422). Mark each of the lettered faces.
64
Lab #7: Hermann-Maugin notation, Miller Indices, and
Stereographic projection
Miller Indices
Give the Miller Index for each Plane (with the origin in the center of the cube and
the a axis parallel to x axis, the b parallel to y, and c parallel to z.
DCGH
ABEF
DBG
EFHG
Parallel to ADGF but above it slightly
Parallel to ADGF but below it slightly
Parallel to ABGH but above it slightly
Parallel to DCEF but below it slightly
IJHG
AHF
CHF
ICH
Define one cubic-face plane
Define one octahedral-face plane
Which plane is (1,0,-1)
Which plane is (1,1,-1)
65
Match the indicated faces with the proper miller index (three faces in
the isometric system). Presume that the “a” axis is emerging from
the figure (negative = going into the figure) and the “c” axis goes
upward (negative = downward). Positive “b” axis is toward the
right. Possible indices are (100), (111), (110), (211), (222), (010),
(001), (101), (110), and (422). Mark each of the lettered faces.
Illustrate a motif in 2-D that has a three-fold axis of rotation and 3 mirror planes.
Illustrate a motif in 2-D that has a three-fold axis of rotation but no mirror planes.
Illustrate a rectangular figure in 2-D, with motifs at the corners, that has only a single mirror plane.
Draw a perspective view of a cube (isometric system). Use dashed lines for edges that are hidden. For
each of the 2-fold axes of symmetry, put a dot where the axis emerges from the cube. Number the dots
such that the two dots associated with each of the axes have the same number (i.e. the first axis has two
dots each labeled with a “1”, etc.).
Match the space group (hermann-maugin notation) with the appropriate crystal system. Choose from the
following crystal systems for each
isometric, orthorhombic, tetragonal, hexagonal (not rhombohedral), hexagonal (rhombohedral),
monoclinic, triclinic. (NOTE: These can be figured out simply from the rules that I discussed in class for
each crystal system)
P432
_________________________
P6/m
_________________________
Pmm2
_________________________
P2/m
_________________________
P422
_________________________
P4mm
_________________________
P3m
_________________________
P622
_________________________
P23
_________________________
P32
_________________________
66
P4
_________________________
P1
_________________________
Pm
_________________________
P6
_________________________
Use the figure below in the following exercises.
67
Concept of a stereographic projection: Imagine
that all lines and surfaces in a crystal intersect a
surrounding sphere (upper left). Now, think
about the projection of those points and lines on
the sphere onto a circle at the equator of the
sphere (upper right). The projection onto the
circle at the equator is done as shown in the
diagram at left.
Stereographic plot of a 432 isometric crystal (you can also look at the procedures for
stereographic projection in your text). Get one of the models of isometric crystals to look
at and also look at the illustrations above for isometric crystals. For this exercise, what
you are really doing is transcripting the projected image on the equatorial surface above
onto a stereographic circle. Thus, the "answer" is apparent in the figure above. Go
through the steps below to help you visualize what you are doing.
1) Choose an axis that you will project down (we are going to choose the 001, or c, axis).
2) Place tracing paper on a Wulff Stereographic net. Mark the center of the circle and
draw the outer circle. Mark the 010 axis and draw a line through the center to mark your
zero meridian.
68
3) use a tiny square to indicate a 4-fold axis of symmetry. Draw the location of the 4fold axis that passes through the center of the 001 face. (hint: what part of the circle will
this line hit, and where will that project on the paper.
4) Do the same for the 4-fold axis that pass through the other faces. Notice that these
lines are in the equatorial plane, and thus will appear on both sides of the circle (that is,
we get 2 squares for each one axis since we see both ends of the line).
5) For the plot of each of the following points, think first about which direction the point
will lie from the center of the circle, then, think about how far it will lie from the center.
Direction: think about projection onto a surrounding sphere. In which direction will the
intersection of the axis line with the sphere lie?
Distance: your book explains the trigonometry of measuring distance. However, you can
also use the Wulff stereographic net to simply draw the distance given the angle. Rotate
the Wulff net until the distance degree curves are in the direction of the point you want to
plot, then plot the point.
a) 110, īī0, ī10, 1 ī 0 (these are the edges, with two fold axes of symmetry, plot with a
vertical "eye" shape, the symbol for 2-fold axis)
b) 101, 011, ī 01, 0 ī 1 (these are the edges, with two fold axes of symmetry, plot with a
vertical "eye" shape, the symbol for 2-fold axis)
There are only 6 2-fold axes of symmetry in the 432 system. Explain why you have 8
plotted on your diagram.
c) 111, ī 11, ī ī 1, 1 ī 1 (these are the corner-corner axes of a cube or faces of an
octahedron, with three fold axes of symmetry, plot with a small triangle the symbol for 2fold axis)
d) Draw the traces of the 2 vertical mirror planes that pass through the center of the
upper face (001) and the other faces (010 etc).
e) now draw the traces of the 2 vertical mirror planes that pass through the center of the
upper face (001) and the corners of the upper face (111 etc).
f) Draw the traces of the 4 non-vertical mirror planes that pass through the center of the
other faces (not the upper face, 001) and the corners corresponding to those faces.
69
70
Mineralogy and Petrology.
Mineral identification, occurrence, and properties, Lab #8
For each of the listed minerals (61), you should create a neat record of the mineral’s
features (including composition, crystal class, typical crystal form, hardness, color,
streak), and its occurrence (what type of rocks it is found in, under what geological
conditions it forms). You should also examine the examples of this mineral that we have
in the lab, and make notes about your observations. You can use these notes on exams.
This lab is due in 3 weeks. At 3 hours of lab per week, this gives you about nine to ten
minutes per mineral. Feel free to spend more time on some and less on others. You have
already looked at many of these in Lab #1.
You might use a form like the one on the attached page:
All the minerals listed below should be available in the mineral cabinet (mc), the ore
mineral cabinets (omc), or the introductory mineral cabinet (imc). You will have to
identify the imc samples in order to find them, which is a good exercise anyway. There
are multiple samples for many of the minerals. You should look at all the different
samples, because they won’t all look the same. Please don’t scratch, streak, or apply
acid to any samples other than those from the introductory mineral cabinet.
Oxides:
cuprite (omc 21), corundum (omc 201, 202, mc 54, 55, imc), hematite (omc 46, 47,
48, 49, imc, imc, mc 61, 62, 63, 64), ilmenite (mc 59), chromite (omc60, mc
58), cassiterite (omc 39, 40), magnetite (omc 44, 45, imc, imc, mc 56, 57),
bauxite (omc 41)
Sulfides:
bornite (omc 17, imc), galena (omc 26, 27, imc), sphalerite (omc 27, 32, 33, imc,
imc), covellite (omc18), cinnabar (omc73), stibnite (omc65, imc), arsenopyrite
(omc 67, imc-THIS IS A POISON-WASH YOUR HANDS) pyrrhotite
(omc15, mc 70, imc), chalcopyrite, pyrite
Sulfates:
barite (omc 82, 176, imc, mc 99), gypsum (mc 95, 96, 97, imc, imc), anhydrite (mc
98)
Carbonates:
calcite (omc 36, 179, mc 83, 84, 85, 89, imc), siderite (omc 54, mc 93, imc),
magnesite (omc 112, mc 94), cerussite (omc 29), dolomite (omc 28, mc 91,
92), malachite (omc 23), azurite (omc 22)
halides:
halite (omc 182, 183, imc, mc 100), Fluorite
71
Silicates:
nesosilicates: olivine(forsterite-fayalite) (mc 26), garnet [almandine omc 203, imc,
mc27, mc28; andradite mc29; grossularite mc30], andalucite (mc 35, 36),
silliminite (omc 110, mc 38), kyanite (omc 111, mc 37), staurolite (mc 34).
sorosilicates: epidote (mc 31)
cyclosilicates: beryl (omc69), tourmaline (omc 181, mc 39, 40, 41)
inosilicates: pyroxene [wollastonite mc29, diopside-hedenburgite (mc 18, 19),
augite (mc 20, imc), enstatite-ferrosilite (mc 17)] amphibole (mc 22, 23, 24,
25, imc)
phylosilicates: micas [biotite (omc 172, mc 15, imc), phlogopite (omc 171, mc 16),
muscovite (omc 170, mc 13, imc), chlorite (mc 75), lepidolite (omc 86, mc 14,
41)], talc (omc 173, 174, 175, imc, mc 78, 79), kaolinite (omc 99, 100, mc 73),
serpentine (mc 76, chrysotile, omc 166, mc 77)
tectosilicates: quartz(omc1,2, 4, 180, 208, 215, 216, mc 44, 45, 46, 47, 48, 49, 50,
51, 52, imc) , feldspars [orthoclase (imc), microcline (omc 107, mc 3, 4),
sanidine (mc 1), albite (omc 107, mc 5, imc), anorthite (mc 8)] leucite (mc 12),
nepheline (omc 43, mc 10), sodalite (mc 11)
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Mineral:
Chemical composition:
crystal system (and Hermann-Maugin symmetry if you choose):
typical habit and appearance:
hardness:
color and streak:
Typical occurrence (include rock types and geological environments of formation)
Notes on your observations of this mineral (include how many different types of samples
you looked at).
Mineral:
Chemical composition:
crystal system (and Hermann-Maugin symmetry if you choose):
typical habit and appearance:
hardness:
color and streak:
Typical occurrence (include rock types and geological environments of formation)
Notes on your observations of this mineral (include how many different types of samples
you looked at).
73
Classification of Minerals:
Crystal structure and symmetry are not the only important characteristics of a mineral.
Chemical composition is also important. Minerals are often classified into mineral
groups.
Mineral groups are based on the primary anion (not cation) of the crystal. This is because
minerals with a common cation usually have more in common in terms of properties than
do minerals with common cations (for example, compare cerrusite and siderite to galena
and pyrite). Also, the anion more consistently reflects the geological environment of
formation. That is, sulfides tend to occur together in one type of environment, whereas
carbonates occur together in a different environment, and silicates in a third environment.
Native elements (metals and nonmetals) (no anion)
e.g. Cu, Au, Fe, Fe-Ni
e.g. S, C
bonds are metallic in metals, or covalent or other in nonmetals
Crystal structures for the metals are often based on closest packing structures like
hexagonal or cubic closest packing (12 nearest neighbors), or other simple packing
structures like body-centered cubic (8 nearest neighbors). Structures in S or C are
controlled by covalent bonding angles and typically have 3 or 4 nearest neighbors.
Degree of solid solution is primarily controlled by similarities of atom size, thus
Au and Ag have complete solid solution, but the much smaller Cu does not dissolve
significantly in Au or Ag. Fe and Ni substitute fairly readily for each other, being of very
similar size. etc.
Sulfides (and sulfarsenides, aresenides, antimonides, selenides, and tellurides) (S, As, Sb,
Se and Tl are anions)
e.g. FeS2 (pyrite or marcasite), ZnS (sphalerite or wurtzite), arsenopyrite (FeAsS arsenic substitutes for S), CuS (covellite), Cu2S (Chalcocite), Cu5FeS4 (bornite). Other
cations can include the metals cobalt (Co), nickel (Ni), molybdenum (Mo), silver
(Ag), cadmium (Cd), tin (Sn), platinum (Pt), gold (Au), mercury (Hg), tellurium (Tl), and
lead (Pb) (for example), or the semimetals arsenic (As), antimony (Sb), and bismuth (Bi).
bonds are mainly ionic, although there are also covalent bonds and metallic
bonds.
Usually opaque with distinctive streaks and colors
Structures can often, but not always, be thought of as metals in octahedral or
tetrahedral coordination in the interstices between S anions (polygons often are distorted
though).
associated with low Eh environments, with high S. Is usually aqueous, often
hydrothermal. Is a primary ore-forming mineral group, especially for Cu, Zn, Pb, Ag,
Hg, and many others.
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Structures of Sphaelerite, Chalcopyrite, and Wurtzite.
Wurtzite
hexagonal
Sphalerite
isometric
Chalcopyrite,
tetragonal
Note that Sphaelerite and Wurtzite (ZnS) differ in that the Zn cations have a facecentered cubic arrangement in sphaelerite, but a hexagonal closest packing in Wurtzite
(remember that these differ in that the third layer up is different for hexagonal closest
packing, but returns to be like layer one in cubic closest packing).
Chalcopyrite differs from sphalerite in that Fe and Cu replace Zn. Because the
top and bottom atoms in the sphalerite-sized cell are different (Fe and Cu) and thus
adjacent cells wouldn’t have exactly the same environments (criteria for unit cell), the
actual unit cell for Chalcopyrite must be twice as big (also formula CuFeS2). Notice that
you couldn’t stack just half-cells on each other and have it make sense because you
would end up with a half-Fe-half-Cu atom between the cells.
Structures of Pyrite and Marcasite
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Pyrite is isometric (2/m3, most common crystal types are cube, pyritohedron, and
octahedron), Marcasite is orthorhombic (2/m2/m2/m, crystals often tabular). Pyrite has
structure like Halite with covalently-bonded S pairs occupying Cl positions and Fe in Na
positions. The S pairs in pyrite decrease symmetry from 432. The three-fold axis of
rotation (in this case, rotoinversion) is the characteristic symmetry of the isometric class).
The three axes of binary symmetry are the characteristic of the orthorhombic class.
Sulfosalts As, Sb, or Bi (semimetals) substitute not for the anion S, but onto the metal
lattice sites.
Oxides (and hydroxides)
e.g. Fe2O3 (hematite), Al2O3 (corundum), Ilmenite (FeTiO3), Magnetite (Fe3O4),
cassiterite (SnO2), goethite (FeO(OH)).
The structure can be understood as deriving from oxygens that take on some closepacking configuration, with metal cations occupying various tetrahedral or octahedral
interstitial spaces. Close packing of O with octahedra interstices in Geothite (see
overhead).
bonds are mostly very strong ionic bonds. These minerals are often very hard. Oxides
are usually very stable minerals.
Oxides are important ore minerals, including Fe, Cr, Mn, U, Sn, Al (although the stability
means that substantial energy investment must be made to separate the metal from the
oxygen). Ruby and Sapphire are members of this group.
May be grouped either as simple oxides (one metal plus oxygen), and complex oxides
(more than one metal cation).
Or they may be grouped according to the cation-oxygen ratio (e.g. Divalent cations yield
1:1, trivalent 2:3, or mix of divalent and trivalent 3:4, tetravalent 1:2).
periclase-hematite-corundum structure: Hexagonal closest-packed oxygens, with metal
cations occupying octahedra.
Considering all octahedral sites, each oxygen is shared with six octahedra. So, what
valence charge is associated with each octahedra? (each oxygen contributes -2,
distributed over 6 octahedra, each octahedra has 6 closest neighbor oxygens = 2/6 x 6 = 2). Therefore, each octahedron can be filled with a divalent cation (e.g. periclase =
MgO), or 2/3 of the octahedrons can be filled with trivalent cations (e.g. Hematite,
corundum). Note: periclase has the same structure as Halite....see if you can count the
octahedra around a particular Cl ion.
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Brucite-gibbsite structures.
OH- groups in place of oxygens. Different charge, but octahedra connect only in a plane,
rather than in 3-D like in the oxides discussed above. (the individual planes are
connected by Van der Waals bonds). Therefore, each OH- at the corners of the octahedra
are shared with only 3 octahedrons. This leaves an anion charge associated with each
octahedron of -2. Therefore, all can be filled with Mg (Brucite), or two thirds can be
filled with Al (Gibbsite). These layers are called trioctahedral and dioctahedral layers
respectively.
Conditions: how will CuS and Cu2S differ in environment of formation? How Cu2O
and Cu2S differ?
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Halides
The halides include F, Cl, Br, I, etc. e.g. NaCl (halite), KCl (sylvite), CaF2
(fluorite)
Bonding is the most completely ionic of any of the mineral groups because the
electronegativities of the constituent elements are the most different.
This group has the highest crystal symmetries because ions are spherical and bonds are
symmetrical. Symmetry decreases as cations of higher valence than 1 are involved, and
the bonds become more covalent.
Have the characteristics of ionic solids: e.g. low hardness, poor conductors
Carbonates: (and nitrates)
e.g. CaCO3 (calcite, aragonite), FeCO3 (siderite), CaMg(CO3)2 (dolomite),
Cu2CO3(OH)2 (malachite), Cu3(CO3)2(OH)2 (Azurite).
Triangular anionic complexes bound more strongly than the complexes are bound
to other ions. Each oxygen has a residual charge of -2/3. Bonding of the CO3 group is
not as strong as CO2 bond, so in presence of H+, the carbonate group becomes unstable,
breaking down to form CO2 and water.
Bonds in the complex are covalent, bonds between complex and metal cations are
ionic.
Calcite structure: Like halite, but with CO3 groups in place of Cl and Ca in place
of Na. Symmetry of the triangular CO3 groups produces a rhombohedral rather than
isometric crystal. Pseudohexagonal structure of calcite derives from the near-hexagonal
close packing of the Ca cations.
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Other two groups: Dolomite is also rhombohedral, aragonite is orthorhombic.
Larger cations (or Ca at higher T) tend to organize into the aragonite-type structure.
Ca very different in size from Mg and Fe. Therefore, there is little solid solution.
Dolomite and Ankarite result when Ca and Mg or Fe don’t mix, but occupy distinct
layers in the crystal.
As T increases (at high CO2 pressure so crystals don’t become unstable), the
amount of mixing increases, and a solid solution exists at sufficiently high pressure.
Sulfates:
e.g. BaSO4 (Barite), CaSO4 (Anhydrite), CaSO4۰2H2O (Gypsum).
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non-polymerizing complexes.
Nitrates, Borates, chromates, tungstates, molybdates, phosphates, arsenates,
vanadates.
anionic complexes bound more strongly than the complexes are bound to other ions.
Tidbits: borates can polymerize. Nitrates triangular like carbonates.
80
Mineralogy and Petrology. Review sheet for Exam 2.
Covering crystallography , oxides, halides, sulfides, sulfates, and carbonates
Be able to reproduce a drawing and explanation of each of the six crystal systems,
including the key symmetry elements of that group and the angular and dimensional
qualities that set them apart.
Given a crystal shape, or its description, be able to identify key symmetries and the
Crystal system.
Be able to read Hermann-Maugin notation sufficiently to identify which crystal system it
belongs to, or, given a crystal system, to give an example of Hermann-Maugin
symmetry in that system.
Be able to recognize features in ball-and-stick models, related to symmetry.
Be able to relate unit cells to underlying crystals systems
Be able to draw 2-D plane groups that have indicated symmetries (square system).
Know and be able to use the ideas of motif, lattice, and unit cell.
Know the differences and relationships between a crystal system, Bravais lattice, crystal
classes, and space groups.
Draw examples in 2-D of various types of symmetry. For example, be able to illustrate
mirror planes, rotation, and center of inversion.
Be able to illustrate an example of a lattice system, a point group, and a plane group in 2D (preferably in the square system).
Know what mineral groups are.
Be able to identify key characteristics of sulfates, carbonates, halides, oxides, sulfides,
and native elements.
Be able to explain the difference between dioctahedral and trioctahedral packing in
oxides and hydroxides, including being able to predict what percent of octahedral will
be occupied for a given cation.
Be able to interpret a stereographic projection enough to recognize which crystal system
is portrayed (this is really not very hard and not much different from being able to use
Hermann-Maugin notation!).
81
82
Silicates:
Key idea: whether and how the silica tetrahedra are connected to each other by strong
covalent bonding, or whether the corners of tetrahedra connect to octahedral or other sites
occupied by usually-larger cations by ionic bonds.
Show overhead. Key things to note, the sharing of tetrahedral corners (means that two Si
are linked to each other by a single oxygen). The number of oxygens shared between
tetrahedra determines the Si-O ratio. For example, with no sharing, then each Si has 4
oxygens, if two Si share one O, then each 2 Si has 7 oxygens, etc.
comment on the unit cell shown for phyllosilicates. Notice how each corner of the
rhombus is surrounded by a “motif” of silica tetrahedrons arranged in a hexagon.
Also comment on what I teach in Physical Geology: the idea of tetrahedrons connected
in 0, 1, 2, and 3 dimensions corresponding to island, chain, sheet, and framework
silicates.
Nesosilicates: olivine
remind of model that we looked at. Show overhead. Point out that tetrahedra share
corners with octahedra (M1 and M2), not other tetrahedra.
Inosilicates: Single Chain Silicates: The pyroxenes.
Draw on board:
show cleavage, cutting down through M1 sites at angles
such that cleavage is at nearly right angles (remind of lab
activity).
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The clinopyroxenes (monoclinic) and orthopyroxenes (orthorhombic):
Draw illustration:
immiscibility gap: Mg and Fe are near the same size, so they mix in solid solution series,
but Ca is much different, resulting in a miscibility gap between the DiopsideHedenbergite series and the Enstatite-Ferrosilite series. Tie lines show coexisting
pyroxenes at a particular temperature (Compositions of coexisting pyroxenes can be used
as a geothermometer recording temperature of formation).
Primary compositional components:
Diopside (CaMgSi2O6), orthopyroxene ((Fe2+,Mg)2Si2O6)
but can substitute Na, Al, Fe3+, Li for M1 and M2 sites, and Al on tetrahedral sites
Putting Ca in M2 site, much larger than Mg or Fe, distorts lattice resulting in the lower
symmetry of clinopyroxenes (including diopside, augite, and pigeonite).
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(note: putting Ca in M1 site also distorts chains, resulting in the even lower symmetry,
triclinic, of the pyroxenoid, wollastonite)
Augite: is mostly in the series CaMgSi2O6-CaFeSi2O6, but with some substitution of
Na and Al.
But must charge balance. So, for example, if Na or Li is substituted for Ca (2+), a
trivalent cation, such as Fe3+ or Al must substitute for Mg or Fe2+.
Tschermacks substitution: Can substitute Al for Mg on the M1 site, and charge balance
by substituting Al for Si4+ on a tetrahedral site.
M2 is bigger (show picture of jadeite): Na in bigger M2, small Al in M1. Point out
shared tetrahedral corners and where chains are connected by octahedra.
Phyllosilicates (sheet silicates)
Structure of micas:
Similar to the structure of illite looked at in lab (triangles represent tetrahedra in 2-D,
diamonds represent octahedra in 2-D).
85
Muscovite KAl2(AlSi3O10)(OH)2 - K between covalent octahedra-tetrahedra
sandwiches, OH substituting for some O in octahedra, Al in octahedra, other Al
substituting for Si in tetrahedra. Dioctahedral because Al is trivalent, not all octahedral
sites are occupied (2 of 3). Is the Si-O ratio correct? Have to compensate for the Al on
the tetrahedral sites. So better to think of the T-O ratio.
Phlogopite KMg3(AlSi3O10)(OH)2 - what has changed? Mg in octahedral sites, it is
divalent, so this is a Trioctahedral structure, all the octahedral sites are filled.
Biotite K (Mg, Fe)3 (AlSi3O10)(OH)2 - what has changed? Is this dioctahedral or
trioctahedral?
Igneous Minerals:
Bowens reaction Series.
Have them try to predict which pyroxenes are possible (Na+, Fe3+, Al3+, Mg2+, Fe2+,
Ca2+)
review ideas of charge balance, lattice sites, and sizes of lattice sites - Goldschmidts
rules?) Tschermaks substitution and others)
Do with Plagioclases, how coupled charge balance works.
Go over Phase diagrams for plagioclase series relate to bowens reaction series , then Kspar-Albite series at low and high H2O pressure.
Go over SiO2-MgO diagram, relate to bowens reaction series, particularly reaction curve
and changes in SiO2 in melt with T.
Discuss difference between equilibrium and fractional crystallization as pertains to phase
diagrams. Discuss zonation in feldspars or pyroxenes.
Discuss origins of basalt and komatiite as pertains to phase diagrams. Which will be
more SiO2 rich, lower temperature or higher T partial melt? Which rich in SiO2, partial
melt or bulk composition?
Sedimentary Minerals - Rough stability trend is reverse of Bowen's reaction series
Metamorphic Minerals:
Review Andalucite-Kyanite-Silliminite diagram. Which has higher density? Which has
higher entropy?
86
Dewatering reactions
e.g. Al2Si2O5(OH)4 Al2SiO5 +SiO2+ H2O (Kaolinite Andalucite + Quartz + water
De-carbonation reactions
e.g. CaCO3 + SiO2 CaSiO3 + CO2
87
Pick several reactions, which has higher density/entropy. What sequence of minerals
might you get as metamorphic grade increases? How might you constrain P-T conditions
(first minerals, then composition of garnet).
88
Mineralogy and Petrology.
Minerals under the Microscope Lab #9
Thin Sections:
Using a petrographic microscope entails not only looking at the sample in polarized light
(called 'Plane' light), but looking at the sample under "crossed polars" or "crossed
Nichols". Polarized light is light which is vibrating in only a single direction (polarizing
sunglasses only allow light through that is vibrating in a particular direction). The light
source for a petrographic microscope is polarized. This "plane" light goes through the
crystalline samples, which can split the plane light into new light components that may not
be polarized in a single plane any more. "Crossing the Nichols" involves inserting a lens
between your eye and the sample which only lets light pass when it is vibrating in a
direction perpendicular to the original plane light (this means that if you look into the
scope with no sample and with the polarizers crossed, you will see only blackness since
none of the plane-polarized light is allowed to pass the "analyzer" lens, which is what the
second polarizing lens is called. Because the way that the crystal changes the light depends
on the exact details of the crystal structure, the light-polarizing and analyzing capabilities
of the petrographic microscope give one all kinds of ways to learn about crystals.
Basic idea of how to use a petrographic microscope: lenses, focus, polarizing lenses,
condenser lenses, quartz wedge,
Review of key things to notice under the microscope:
In plane light:
cleavage or fracture . euhedral,
subhedral, anhedral crystal form
color, zoning, birdseye, opacity
relief
Under Crossed Polars (crossed Nichols)
How crystals go to extinction (strained crystals, twinning, and large poikilitic crystals), or
for isotropic, always extinct
interference colors
optic axis figures
89
Thin Sections 3, Gabbro
Find the Olivine: it has an erratic fracture pattern (not the regular linear fractures
indicative of good cleavage). It is a faint greenish color in plane light. Under crossed
Nichols it has high interference colors, red/blue/green.
Find Plagioclase: it is lath-shaped, or rectangular. It has low interference colors under
crossed Nichols (grey/white). It exhibits very distinctive polysynthetic twinning, visible
under crossed Nichols by the alternating bands of extinction as the sample is rotated.
Find Biotite: It is brown or green and pleochroic. It has a birds-eye texture in plain light
(resembles birds-eye maple).
Notice the opaque minerals.
Find the pyroxene: it is a light brown color in plane light. It has medium
interference colors under crossed Nichols (orangish). fractures run parallel to
each other, indicating cleavage. In many grains, two sets of fractures intersect
at nearly right angles (2 cleavage planes at right angles to each other).
There is some of another type of feldspar, generally without polysynthetic twinning,
which contains poikilitically enclosed olivine crystals.
Thin Section 1, Granite
Find the quartz: equant crystals with low interference colors (grey to yellow). No
cleavage planes, usually don't show an extensive fracture pattern either.
Find the feldspar: there are two kinds. Na-rich plagioclase shows polysynthetic
twinning. K-spar grains are quite large and have a mottled extinction appearance under
crossed Nichols.
Thin Section 2, Diorite
find the amphibole (hornblende): light brown to dark brown or green,
pleochroic, cleavage fractures run at angles of about 124 degrees. Medium
(orangish) interference colors.
There is a particularly large hornblende grain. Find it, and notice that it is
ZONED(meaning that its compositions changes outward from the middle of the crystal).
This is due to changes in the melt during crystallization. Notice also that there are
abundant poikilitic inclusions in the greener-colored rim. The rim is probably richer in Na
and Fe than the interior (think about charge-balancing substitutions!).
There is some biotite. You can distinguish it from hornblende (although not easily at
first) because it will generally have slightly different pleochroic colors, only one
dominant cleavage is apparent (and pleochroic colors will be darkest when the cleavage
90
plane of the sample is aligned with the polarizing lens), birds eye appearance, and higher
interference colors than hornblende (red/blue). Also, the grain will go to extinction when
the cleavage planes are parallel to the polarizing lens (parallel to the cross hairs), whereas
amphibole goes extinct when there is a distinct angle between the cleavage planes and the
polarized light orientation (parallel to the cross hairs).
Find the polysynthetically-twinned Plagioclase
Notice that quite a few of the opaques (ilmenite and magnetite) are diamond shaped.
Based on their crystal systems, are the diamond shaped opaques more likely to be
ilmenite or magnetite?
In Plane light, find some the hexagonal poikilitic crystals in hornblende. These are
apatite (check out the crystal system for apatite in your book). Notice that many of the
most perfect hexagons are always black under crossed Nichols. This occurs when you
look right down the c axis of the crystal.
I also found a grain of titanite (diamond shape, high interference colors), light brownish
color.
Wards 44E7310 rhyolite tuff
Find the subhedral to anhedral Si02 grains (low interference colors,
white/yellow). I think that at least some of these are cristobalite (the high
T form of Si02). This is based on the presence of a "tile" structure seen in
some of the grains with crossed Nichols (near the bottom middle when
the number is placed to the right). This tile structure is characteristic of
cristobalite. (what does that tell you about its formation?)
Find the K-spar (some with Carlsbad twinning). (lath shaped often, grey/white in crossed
Nichols)
Wards 44E 7327 Hornblende Andesite
Phenocrysts include muscovite (clear in plane light, high interference colors under
crossed Nichols and may show birdseye like biotite), plagioclase (lath shape,
polysynthetic twinning), hornblende (equant crystals with orange/yellow interference
colors)
Many of the hornblende grains are altered (chemical reaction in a late stage of eruption or
weathering), and many have reaction rims (corona texture).
6: Gneiss In this sample, notice the following:
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Biotite and Amphibole. Both are strongly pleochroic. But amphibole shows two
directions of cleavage, not at right angles, and the crystal goes to extinction NOT
PARALLEL TO THE CLEA V AGE. Biotite has only a single obvious cleavage direction
and extinction IS PARALLEL TO CLEA V AGE.
There is some feldspar in this sample. Unlike in igneous rocks, these can't be
identified by their characteristic twinning (twins are annealed away during
metamorphism). You can distinguish it from quartz on the basis of cleavage plane lines,
which the quartz lacks.
There are two "high-relief' minerals. These minerals stand out from the
surrounding minerals (high-relief) because they have a distinctly higher refractive index
(that is, light travels much more slowly through th~m, thereby refracting the light more).
These two minerals look very similar in plane light, both occurring as small, equant
crystals.
One of these minerals is garnet. Garnet occurs as roughly equant crystals (often
hexagonal-looking), more often associated with the quartz than with biotite or amphibole,
and is isotropic. Isotropic minerals are high-symmetry minerals that do not break light into
separate beams, because oftheir high symmetry. Therefore, garnet always appears black
under crossed Nichols, regardless of stage rotation.
The second high-relief minerals occurs often in association with biotite or
amphibole in this thin section. It is not isotropic, but has high interference colors. I think
that this mineral is clinopyroxene, although there isn't much cleavage apparent.
44 W 6173 Marble
Most ofthis rock is composed of calcite. Notice the rhombohedral cleavage and
twinning pattern (cross-hatched pattern). Calcite has very high interference colors (so high
that most of the color disappears and is called 'high-order white' - a sort of grungy
gray-white). In some of the cross-hatched twins you can get hints of the high interference
colors in that you can see glints or red, blue, etc.
There are a few muscovite grains (high interference colors and birdseye under crossed
Nichols, clear in plane light).
44 E 7386 KvaniteOuartzite
Kyanite is the high relief, medium-to-Iow interference-color mineral (yellowish
under crossed Nichols). It has prominent cleavage planes, and common poikiloblasts of
quartz (in igneous rocks we refer to poikilocrysts - in metamorphic rocks we refer
to poikiloblasts).
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