Name: ____________________________
Geosciences 306, Mineralogy
Final Exam, 2011
200 pts
1. (20 pts)
a. What are the 4 most abundant elements in the Earth and what are their atomic
percentages?
b. For each of the four elements, name one mineral that contains the element.
c. Write 8 charge-balanced hypothetical ideal chemical formulas that contain
combinations of only these elements. Four of the formulas must contain all four of
the elements.
2. (20 pts) Describe the electronic structures of atomic sulfur (S), arsenic (As) and iron
(Fe) using spin diagrams. There are two common ionic states for sulfur, one as an
anion, and one as a cation. Give the valence and make spin diagrams for these two
states.
3. (10 pts) Derive the radius-ratio rule parameter (r /r = .414) for an octahedral 6C A
coordinated cation. Draw a picture and carefully label everything so that your answer
can be evaluated properly.
4. (5 pts) Draw a schematic binary phase diagram for the isostructural rocksalt minerals
lime CaO and periclase MgO. One melts at ~2570 C and the other at ~2950 C.
Assign these numbers to the diagram.
5. (25 pts) Draw a picture of an orthorhombic lattice projected onto the b-c plane and
indicate the origin and the cell edges, assuming a = 4 Å, b = 3 Å, c = 5 Å.
a) Draw and label the vector [0 1 2].
b) Draw and label the plane (0 1 2).
c) Calculated the length of the [0 1 2] vector.
d) Calculate the d-spacing of the (0 1 2) plane using geometry.
e) Using Bragg’s equation with Cu radiation, λ = 1.54 Å, what position in 2θ
would the (0 1 2) peak be found.
6. (10 pts) One of the diffraction patterns below was recorded on a cubic mineral; the
other is from a triclinic mineral. Identify which pattern is from the cubic mineral and
give a reason for your choice. For a hint, think about the positions of the (100), (010)
and (001) peaks.
7. (10 pts) Below is a Raman spectrum of topaz, Al2SiO4F2.
a. Describe the origin of Raman peaks.
b. What is the strongest bond in topaz?
c. Indicate the position of the peak on the Raman spectrum that corresponds to the
strongest bond.
8. 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
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. (10 pts) For each illustration, provide representative mineral name and chemical formula
for each.
11. (20 pts) Using the bulk chemistry of the Earth, assuming all Fe is metal or Fe2+, and
aside from Si, all other metals are 2+, derive the radius of the core.
12. (20 pts) From the microprobe analyses of a mineral, the following oxide weight
percents were measured. Determine the chemical composition of this sample and
name the mineral.
Weight percent
MgO
16.81
Al2O3
32.12
Cr2O3
36.20
FeO
13.66
Fe2O3
1.06
13. (10 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.