Name:___________________________________________
Geos 306
2 2009 Midterm (100 pts)
nd
1) (10 pts) Fill in the table that defines the shape and constraints of the unit cell
parameters.
System
Cubic
a
b
c
Hexagonal
Tetragonal
Orthorhombic
Monoclinic
Triclinic
1
α
β
γ
2) (10 pts) Draw a picture of a monoclinic lattice projected onto the a-c plane (i.e.
you do not need to show the b-direction); indicate the origin and the cell edges.
a) Draw and label the vector [-1 0 2].
b) Draw and label the plane (-1 0 2).
2
3) (30 pts) Fill in the missing point group symbols and indicate the crystal system for
the point groups on a given row.
G
GUGi
1
HUG\Hi
n/a
m
⎯3
n/a
4
6/m
2mm
332
4/m2/m2/m
6mm and ⎯62m
332
n/a
3
System
4) (10 pts) Make a careful drawing and derive Bragg’s law for X-ray diffraction.
4
5) (10 pts) Consider a crystal of forsterite with orthorhombic symmetry, a = 4.762 Å,
b = 10.225 Å, c = 5.994 Å.
(a) Draw a figure showing the plane (101).
(b) Show that the d-spacing of (101) is 3.729 Å.
(c) Using Cu radiation, λ = 1.54 Å, what position in 2θ would the (101) peak be
found.
5
6) (15 pts) From the microprobe analyses of a mineral, the following oxide weight
percents were measured. Determine the chemical composition of this sample.
Weight percent
MgO
47.844
SiO2
40.525
FeO
11.630
Bonus point: name the mineral!
6
7) (5 pts) Make a hypothesis of what the first mineral ever formed in the universe
might have been, and give a brief reason for your choice.
7
8) (5 pts) Write down the number of your model and define its point group
symmetry.
9) (5 pts) Electron microprobes and scanning electron microscopes are not able to
detect H, He, Li, and Be. Why not?
8