1. Materials Contributions by:
John L. Falconer & Will Medlin Department of Chemical and Biological Engineering University of Colorado Boulder, CO

2. Sample A is an equimolar physical mixture of Si and Ge
Sample A is an equimolar physical mixture of Si and Ge. Sample B is a Si0.5Ge0.5 solid solution. Which measurements will be different for the two samples?
Elemental analysis and x-ray diffraction
X-ray diffraction
Absorption spectrum
Absorption spectrum and x-ray diffraction
Elemental analysis
ANSWER: D. Absorption spectrum and x-ray diffraction
The solid solution will have different lattice parameters and thus different XRD patterns.

3. Below is a 2-dimensional representation of a crystal structure where each circle represents a single atom. Each lattice/unit cell contains ________ atoms. 1 2 3 4
ANSWER: A. 1
The each corner of a unit cell contains an atom, but not all of the atom is within the unit cell. With each atom centered on the corner, only 1/4th of an atom in each cell. 4 x 1/4th means one atom per cell.

4. A unit cell of a simple cubic crystal is represented below
A unit cell of a simple cubic crystal is represented below. If each corner contains an atom, how many atoms are there per unit cell? 1 2 3 4 8
ANSWER: A. 1
The each corner of a unit cell contains an atom, but not all of the atom is within the unit cell. With each atom centered on the corner, only 1/8th of an atom is in each cell. 8 x 1/8th means one atom per cell.

5. A unit cell of a simple cubic crystal structure is represented below
A unit cell of a simple cubic crystal structure is represented below. If each corner contains an atom, what is the coordination number of each atom? 4 6 8 10 12
ANSWER: B. 6
Coordination number of an atom is the number of other atoms in contact with the atom of interest. For a simple cubic structure, this is 6. For the unit cell pictured, each atom is currently connected to three other atoms, each 90° from each other. For a sphere, there can be 6 such connections.

6. In a space-filling representation, the unit cell size is limited by the close-packing of spherical atoms, where the surfaces of the atoms are in contact. For a simple cubic unit cell of this type, how are atom center distance, d, and atom radius, r, related?
d = r
d = 2r
d = 3r
d = 4r
ANSWER: B. d=2r d

7. A corner atom is part of how many unit cells in this simple cubic structure?1 2 4 8
ANSWER: D. 8
Each corner atom has 1/8th of its volume within the unit cell pictured. Therefore the rest of the atom will be contained within 7 other unit cells, bringing the total to 8.

8. In the face-centered cubic (FCC) crystal structure, an atom is on each corner and each side of the unit cell. How many atoms are in the unit cell? 1 2 4 14
None of the above
ANSWER: C. 4
Each corner atom is shared with 8 unit cells so 1/8th x 8 corner atoms = 1 atom
Each atom on the face is shared with 2 unit cells. So ½ x 6 face atoms = 3 atoms
Total 3 + 1= 4 atoms

9. In a face-center cubic structure, the atoms are close-packed along the face diagonal. What is the coordination number of a metal atom in this structure? 2 4 6 8 12
ANSWER: E.12
The coordination number of an atom is the number of other atoms in contact with the atom of interest. For a face-center cubic structure, this is 12. Look at the bottom face-centered atom. It is touching the 4 green atoms in it’s same plane. It also touches 4 atoms in the plane above it, and 4 atoms in the plane below it for a total of 12.

10. In the body-centered cubic (BCC) crystal structure, an atom is on each corner and one atom (blue atom) is in the center of the unit cell. How many atoms are in the unit cell? 1 2 4 8 9
ANSWER: B. 2
Each corner atom is shared with 8 cells so 1/8th in each cell. The center atom is entirely within the unit cell so (1/8th x 8) + 1 = 2 atoms

11. In the body-centered cubic (BCC) crystal structure, an atom is on each corner and one atom (blue atom) is in the center of the unit cell. What is the coordination number for each atom? 4 6 8 12
ANSWER: C. 8
The center atom is in contact with all the corner atoms in the unit cell for a total of 8 atoms

12. Which crystal structure is body center cubic?
ANSWER: A.
The blue atom is at the center of the cell and coordinates with 8 total atoms

13. A zinc sulfide crystal structure is shown
A zinc sulfide crystal structure is shown. What type of unit cell is defined by just the green sulfide ions?
Simple cubic
Body-centered cubic
Face-centered cubic
None of the above
ANSWER: C. Face-centered cubic
The sulfide ions are on the corners and the faces of the structure shown.

14. A layer sequence for an FCC metal is shown
A layer sequence for an FCC metal is shown. A close-packed plane is comprised of six atoms. If atoms 2, 4, 5 are three of the six atoms, which other three atoms are need to define the plane?
Z = 0 1 2 4 3 5
11, 13, 14
6, 9, 12
7, 8, 14
6, 9, 10
Z = 1/2
Z = 1
ANSWER: D.
These atoms form the close packed (111) plane. Along this plane that cuts diagonally through the FCC structure, atoms 2, 5, 4 are the base and atoms 6 and 9 nestle into the spaces diagonally (and to the viewer’s left) and above those atoms. Atom 10 nestles between 6 and 9 on the same diagonal to form a close-packed plane along the (111) plane. Note: atom 1 is the origin. 6 7 9 8 10 11 14 13 12

15. Which structure is the FCC (110) plane?B
ANSWER: B. The (110) plane cuts along the bottom, horizontal plane of the unit cell. This means that the green atom is surrounded on all sides by blue atoms, all on the same plane. Picture B shows this repeating pattern.
FCC unit cell

16. Which structure is the FCC (001) plane?B
ANSWER: A. The plane (001) cuts through vertically from the back left corner to the front right corner of the shown unit cell. This means that the blue atoms form a square grid, as shown in A.
FCC unit cell

17. Which structure is the FCC (111) plane?B
ANSWER: C. The (111) plane cuts diagonally through the unit cell with the blue atoms forming a triangle at each “corner” of the plane and the green, face centered atoms forming a projected triangle that fills in between the blue atoms. This is the close packing plane.
FCC unit cell

18. In a zinc sulfide (ZnS) crystal structure, each zinc ion (blue) sits between four sulfide ions (white). Given a ZnS layer sequence, which sulfide ions surround the indicated zinc ion? 1 2 4 5 3
1, 4, 7, 8
1, 3, 4, 7
1, 3, 6, 7
1, 4, 7, 9
Z = 0
Z = 1/4
ANSWER: C. 1, 3, 6, 7 The layer sequences show that at z = ¼ the indicated zinc ion nestles between the sulfide ions 1 and 3. The next plane up is z = ½ , and the sulfide ions 6 and 7 would be touching on either side of the indicated zinc ion. 6 8 7 9
Z = 1/2
Z = 3/4

19. How many sulfide ions (green) are in a zinc sulfide unit cell?1 2 3 4
ANSWER: D. 4
Sulfide ions are the green ones. Each corner atom is shared with 8 unit cells so 1/8th x 8 corner atoms = 1 atom
Each atom on the face is shared with 2 unit cells. So ½ x 6 face atoms = 3 atoms
Total 3 + 1= 4 atoms

20. Vanadium, molybdenum, and sodium all have a body-centered cubic structure. Given the following atomic radii, which two metals are most likely to form a sold solution?
Metal
Atomic radii V
0.131 Mo
0.136 Na
0.186
Vanadium, molybdenum
Vanadium, sodium
Molybdenum, sodium
ANSWER: A. Vanadium, molybdenum
Vanadium and molybdenum have similar atom radii. Therefore, they are more likely to be able to form a BCC crystal structure together and thus form a solid solution

21. For a two-plane, octahedron arrangement of identical spheres, there will be two differently-sized gaps. One gap will be within the plane, the other gap will be between planes. Which gap will be smaller?
Between planes
Within plane
Within the plane
Between the planes
The gaps are the same size
ANSWER: B. Between the planes
Within the plane x radius
Between the planes– x radius

22. When a copper wire is heated, it becomes more malleable because ___________________________.
the bonds have been weakened
the wire has fewer atomic level defects
the wire has more atomic level defects
the density is lower
there is more space inside the crystal lattice
ANSWER: B. the wire has fewer atomic level defects. Heating the metal allows the atoms to settle into a more regular arrangement which decreases the number of grain boundaries, or defects. Fewer grain boundaries means a softer metal.

23. Atoms in a solid _____________________________.
cannot move, only electrons move
may move through vacancies in a crystal lattice
may move in the spaces between atoms in a crystal lattice
can move through both vacancies and in the spaces between atoms in a crystal lattice
none of the above
ANSWER: B. may move through vacancies in a crystal lattice. These are called dislocations.

24. If 0 < x < 1, which gallium alloys could be solid solutions?
Gallium(Ga) can be mixed with two other elements to form a solution. Possible elements include aluminum(Al), arsenic(As), and phosphate(P).
If 0 < x < 1, which gallium alloys could be solid solutions? B
6 C
7 N
8 O
13 Al
14 Si
15 P
16 S
31 Ga
32 Ge
33 As
34 Se
49 In
50 Sn
51 Sb
52 Te
GaxAl1-xAs ; GaAlxAs1-x
GaxAl1-xAs ; GaPxAs1-x
GaPxAs1-x ; GaAlxAs1-x
GaPxAs1-x ; GaxP1-xAs
ANSWER: B.
The structure has the compostion of GaAs or AlP or any replacement of Ga by Al or As by P so that the sum of Ga + Al =1 and the sume of P + As = 1

25. Buckminsterfullerene, C60, is face-centered cubic in crystalline form
Buckminsterfullerene, C60, is face-centered cubic in crystalline form. If a fullerene was saturated with potassium, by placing a potassum atom in every tetrahedral hole and every octahedral hole, the chemical formula would be ____.
KC60
K2C60
K3C60
K4C60
K6C60
ANSWER: C. K3C60
The FCC structure has 2 tetrahedral sites and one octahedral site for each atom for a total of 3 sites.

26. How many zinc ions (green) are in a zinc sulfide unit cell?1 2 3 4
ANSWER: D. 4
There is an atom on every corner, with only 1/8th of that atom contributing to unit cell. 8 * 1/8th = 1 atom
There is a zinc atom on each face contributing ½ to the unit cell. 6 * ½ = 3 atoms
Total atoms = = 4 atoms

27. How many atoms are in the following layer sequence of a diamond structure?4 6 8 13
Z = 0
Z = 1/4
ANSWER: C. 8 atoms.
1 atom from corner atoms (8 corner atoms, shared with 7 other unit cells, so 1/8th of each corner atom in this unit cell)
3 atoms from faces (6 atoms, each shared with another unit cell so 6 x ½)
4 atoms inside the unit cell (atoms on the z =1/4 and z= ¾ levels)
Z = 1/2
Z = 3/4

28. What is the coordination number for a diamond structure?4 6 8 10
ANSWER: A
The diamond structure can be considered an FCC lattice with half the tetrahedral holes filled by four interstitial C atoms. Each carbon atom bonds to 4 other carbon atoms

29. What is the coordination geometry of a diamond structure?
Tetrahedral
Square
Octahedral
Cubic
ANSWER: A. Tetrahedral The inner carbon atoms are at the center of a tetrahedron.

30. In the two-dimensional square packing shown below, what is the coordination number of the central atom? 2 4 6 8
ANSWER: B. 4 The central atom is actually only in contact with 4 atoms, not all 8 that surround it.

31. Which part of a face-centered cubic crystal surface is likely to chemically etch faster?
111 plane
100 plane
Grain boundary
Vacancy
ANSWER: C. Grain Boundary
The etching solution will attack the surface at dislocations. These dislocations occur at grain boundaries in crystal structures.

32. A system contains an equimolar vapor/liquid mixture of components A and B. The saturated pressure of A is greater than that of B. If the system is an ideal gas, which plot represents the effect of raising the system pressure on the vapor/liquid fractions of component A?
1.0
1.0 yA xA C.
1.0 xA yA yA xA A. B.
ANSWER: A.
The mole fraction of A in the vapor should be higher than in the liquid and high pressure should be all liquid with the same compostion as the starting vapor P P P
1.0
1.0 yA xA yA xA
Pasat > PBsat D. E. P P

33. Temperature
Liquid
Solid
100% Cu
100% Ni
50/50
For this Cu/Ni phase diagram, which cooling curve results for a 50/50 mixture?
Temp.
Time A
Time B
Temp.
Time C
Temp.
ANSWER: D.
The slope should change and the temperature should drop more slowly as solid starts to form. From the phase diagram, solidificaiton takes place over a temperature range. The slope should change again when all solid and change based on the heat capacity of the solid.
Time D
Temp.
Time E
Temp.

34. Magnesium and silicon form Mg2Si under certain conditions
Magnesium and silicon form Mg2Si under certain conditions. What phases and how much of each will be present for a 60 mol% Si mixture at 1000 K?
xSi
Temperature (K) 1
Liquid
800
1700
1 phase that is 57% Si
2 phases; 57% is Mg2Si
2 phases; 40% is Mg2Si
2 phases; 57% is pure Mg
2 phases; 57% is pure Si
ANSWER: B.
Mixture of 2 solid phases, Mg2Si and pure Si. Lever rule indicates more Mg2Si than Si so B is correct answer. It’s about 57% Mg2Si. Mg Si

35. A Pt/Ag alloy containing 62% Ag is initially at 1600°C
A Pt/Ag alloy containing 62% Ag is initially at 1600°C . As it cools, what phases are observed? L represents liquid and α and β are solids.
1800
L+α, L+α+β, L+β, β, α+β
L+α, L+β, α, α+β
L+α, L+α+β, L+β, α+β
L+α, L+β, α+β
L+α, L+β, β , α+β L
L+α α
Temp. (°C)
L+β
α+β
ANSWER: A. L+α, L+α+β, L+β, β, α+β
In the transition from L + alpha to L + beta, must have L +alpha+beta β
Wt % Ag
100

36. (β) solid. Given some of the phases, what phase(s)
Cu/Pb alloys can form several combinations of phases between two liquids (L1 and L2) and alpha (α) and beta
(β) solid. Given some of the
phases, what phase(s)
is/are present at the point
indicated?
Wt % Pb
100
Temperature
L+ α L
α + β
L2+α
L1+β
L1+L2
α+β
ANSWER: C. L1+L2
In the region that has liquid on both sides, get two liquid phases that do not mix so the indicated point represents liquid phases L1 and L2.

37. A Si-Mg mixture containing 40 mol% Si at 1000 K (the blue dot in the figure) contains ____________.
1700
Liquid
a single solid phase
a mixture of pure Si and pure Mg
a mixture of Si and Mg2Si
none of the above
Temperature (K)
ANSWER: C.
At 40 mol% Si and 1000 K, the mixture is in the rectangular region, which is all solid. It is mostly solid Mg2Si with some solid pure Si. There are two solid phases present.
800
xSi 1
Mg2Si

38. For the binary phase diagram for components A and B, what fraction of the mixture is liquid at point indicated by the black dot? 1
Weight frac B
Temperature
Liquid
Solid
30%
45%
50%
55%
70%
ANSWER: E
Use the lever rule to determine the amount. The black dot is much closer to the liquid line than the vapor line so only possible answer is E.