Mineralogy

Mineralogy

1. Two dimensional packing of equal-sized spheres (20 points): This is an exercise on
understanding a two-dimensional packing of equal-sized spheres. I will give one example, and
you will answer the rest of the questions.
Example:
Answering the following questions:
1-A 1. Geometry of array:
2. In the array outline the shape of
coordinating spheres
3. Coordination number (C.N.) :
4. Sketch the shape of the interstice:
1-B 1. Geometry of Array:
2. In the array outline the shape of
coordinating spheres
3. Coordination number (C.N.) :
4. Sketch the shape of the interstice
(Hint: there are more than one kind):
1-C 1. Geometry of Array:
2. In the array outline the shape of
coordinating spheres
3. Coordination number (C.N.) :
4. How does this array relate to 1-A
(hint: rotate by how many degree):
5. Sketch the shape of the interstice:
2. Three dimensional packing of equal-sized spheres(30 points):
1-D 1. Geometry of Array:
2. In the array outline the shape of
coordinating spheres
3. Coordination number (C.N.) :
4. How does this array relate to 1-B
(hint: rotate by how many degree):
5. Sketch the shape of the interstice:
2-A

1. Outline unit cell in model and
give name of its shape:
2. C.N. of interstice of model:
3. Sketch of packing along the
plane A1A1’A2A2’
Plane view
A1
A’
1
Three dimensional stacking
A1
A1′
A2
A2′
2-B

1. Outline unit cell in model and
give name of its shape:
2. C.N. of central (shaded) sphere
(B):
3. Sketch of packing along the
plane A1A1’A2A2’
4. What differentiates this
packing from that shown in 2-A?
Plane view
B
A1
A’
1
Three dimensional stacking
B
A1
A2′
A2
A1′
2-C
1. Outline the smallest unit cell
choice in plane-view and give
name of its shape:
2. C.N. of sphere S in the twolayer
sequence:
3. Sketch of packing along the
plane A1A1’A2A2’
4. After adding a third layer
below the plane A1A1’, what
becomes of the C.N. of sphere
S:
Plane view
A1 S A1′
Three dimensional stacking
A1
A1′
A2 A ‘ 2
2-D
C.N. of shaded sphere is:
One layer of spheres; B is the
location of voids Two-layer stacking AB
2-E
2-F
One layer of spheres with all void spaces identified
In three-layer stacking ABA , C.N. of any
sphere is:
Three-layer stacking ABA
(hexagonal close-packed)
1. Giving stacking sequence of this two layer
stack (using A and B notation):
2. This stacking has two different types of
interstices with difference coordination
numbers. Locate these two types throughout
the drawing and give their C.N.

A
B
Instead of stacking a sequence of AB
AB AB …., we can stack a somewhat
different sequence ABC ABC ….
What is the C.N. of any sphere in such
A A A a sequence?
A A
A A
B
B B
C
C C
B
C

3. (25 points) Calculating the bond-strength (electrostatic valance, e.v.): Please calculate the
average bond strengths of the following radicals: 1) CO3 with C4+ and O2- ; 2) BO3 with B3+ and
O2-
; 3) SO4 with S6+ and O2-
; 4) PO4 with P5+ and O2-
; 5) SiO4 with Si4+ and O2-
. In each calculation,
also estimate the valence of the radicals.
4. (25 points): Based on the ionic radius of elements (see attached), please calculate the radius
ratios for the following compounds and predict the coordination number.
1) ZnS; 2) SiO2; 3) Al2O3; 4) Fe2O3; 5) FeO; 6) CaO; 7) MgO; 8) TiO2; 9) NaCl; 10) CaF2; 11) CsCl; 12)
CuCu(metal)
In the schematic
projection of such a
sequence, label the
atomic positions with
A, B and C
A
B
C
The ABC ABC sequence is
known as cubic close-packed

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