Mineralogy and Petrology Notes



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.

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Habit: Malformations, differential growth rates, restrictions of growth area

euhedral

subhedral

anhedral

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.

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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)

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)

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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

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.

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.

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).

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 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 right-hand 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).

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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.

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 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.

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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?

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/λ.

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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.

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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).

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-gas-like 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).

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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.

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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

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)

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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.

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? ______

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.

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 blue-white 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.

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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/λ 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?

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.

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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).

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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.

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.

[pic][pic]

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.

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.

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 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?

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.

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).

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:

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!

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?)

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?

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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?

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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.

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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)

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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?

Handout of Plagioclase phase diagram, one for each person.

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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).

Albite-Qz phase diagram overhead.

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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.

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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.

Ternary systems (overhead):

plot three components, with temperature plotted as contour lines. Composition is resolved as illustrated.

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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.

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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 ................
................

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