Name:_________________________________________
Geos 306, Mineralogy
Final Exam, Dec 12, 2014
200 pts
1. (9 pts) What are the 4 most abundant elements found in the Earth and
what are their atomic abundances? Create a reasonable hypothetical
charge-balanced chemical formula that uses these four elements in
roughly the same proportions as found in earth.
2. (5 pts) Suppose the illustrated figures represent closest-packed
arrangements of anions. Identify the different locations where cations
could be coordinated with 2, 3, 4, 6, or 12 anions. In the position of the
cation, write its coordination number.
(4 pts) Label the packing type for each of the following diagrams.
3. (20 pts) Magnetite, Fe3O4, is an important spinel, both because it is an
important geological phase on earth, mars, and other parts of the
universe, but also because of its high-tech industrial properties useful in
magnetic storage devices, for instance. Remember that the spinel
structure is ccp anions with both octahedral and tetrahedral cation.
Assume the following radii,
r(O) = 1.35 Å, r(Fe2+) = 0.88 Å, r(Fe3+) = 0.54 Å
a) Write a charge balanced chemical formula for magnetite by
inserting the valence states into the formula Fe3O4.
b) Using Pauling’s rules, argue the relative cases for Fe3+ and Fe2+ in
octahedral or tetrahedral coordination. (ie. Which cation prefers
tetrahedral and which prefers octahedral coordination).
c) What are the relative occupancies of the octahedral and tetrahedral
sites by Fe3+ and Fe2+.
d) What is the tetrahedral FeO bond length?
e) What is the octahedral FeO bond length?
4. (10 pts) From the microprobe analyses of a mineral collected from an
alpine deposit in the Coastal Mountains of British Columbia, the
following oxide weight percent were measured. Determine the chemical
composition of this sample.
SiO2
Al2O3
K2O
Na2O
Weight %
65.92
19.21
14.93
1.43
* 2 pt bonus, name the mineral.
5. (10 pts) Make a careful drawing and use it to derive Bragg’s law for X-
ray diffraction.
6. (20 pts) A basalt rock was found to be composed of 65% olivine,
Mg1.8Fe0.2SiO4, and 35% pyroxene Mg1.4Fe0.5Ca0.1Si2O6. Construct a table
of oxide weight percents that represent the total composition of the rock.
Oxide
FeO
MgO
CaO
SiO2
Weight percent
7. (15 pts) Enstatite, MgSiO3, is an orthorhombic mineral found in
meteorites and as a major component of the upper mantle. The cell
parameters from a fragment of the Bishopville meteorite were carefully
measured as a = 18.210 Å, b = 8.812 Å, c = 5.178 Å and Z = 8. Recall
that Avogadro’s number is 6.023 × 1023 mole-1 and that 108 Å = 1 cm.
a) Determine the cell volume of this mineral.
b) Determine the molecular weight of MgSiO3.
c) Determine its density in units of gm/cm3.
8. (7 pts) Pyrite is a cubic sulfide mineral, FeS2. The (200) peak was
located in a diffraction experiment using Cu radiation, λ = 1.541838 Å, at
2θ = 33.08°
a) determine the d-spacing of (200)
b) determine the cell parameters of pyrite
9. (20 pts) Sketch a diagram showing the structure of the earth. Include the
surface and the center of the earth in your answer. Make a table and
define the boundaries of each region by
a) depth,
b) temperature, and
c) pressure.
d) List the important mineral phases that are found in each of the
different regions.
10. (20 pts) The image provided below is an electron microscopic picture of a
sample of feldspar, of bulk composition ~50% K-spar, ~30% albite, ~20%
anorthite.
a. Identify each of the 3 feldspar phases in the image.
b. Describe and explain their mixing properties. Provide your explanation at
the atomic scale in terms of cation radii. Draw a ternary mixing diagram of
the alkali cations that also shows the temperature effect.
c. Name each of the different phases defined by Al/Si ordering in both the Kspars and albite. Describe the geologic conditions in which you would
expect to find these phases.
11. (20 pts) For each illustration, provide representative mineral name and
chemical formula for each.
5. The following diagram is the phase diagram for silica.
a) (10 pts) Label the various regions.
b) (10
pts) Suppose a diamond crystal was found with a coesite inclusion.
Plot the geotherm onto the silica phase diagram and estimate the
minimum depth that the diamond may have originated. Use the following
table for your estimate of the geotherm:
Depth (km)
P (GPa)
T (K)
(note: 1 GPa = 10 kbar)
0
3
15
24.4
40
80
150
220
310
0
.3
.337
.604
1.122
2.450
4.780
7.110
10.2
300
366
630
743
930
1155
1550
1622
1714
12. (5 pts) Perovskite exhibits the structure of an important high-tech material.
What is the material, and describe a potential application of the property?
13. (5 pts) What is the geotherm?
14. (5 pts) What is the most abundant mineral in Earth?
15. (5 pts) Give the names and formula for 5 different pyroxenes.