HW 2 Inorganic Materials
Chemistry
Name:
Points: C7780 Due date: 23.11.2022
Max. 100 points Fall 2022 A
1. (10 pts) Copper metal crystallizes with a cubic close packed (ccp or fcc) structure having a
lattice parameter a = 3.6147 Å. Calculate the Cu-Cu distance (separation) between nearestneighbor
Cu atoms in the crystal. Hint: nearest-neighbor Cu atoms are any two within the same
close-packed layer (plane).
2. (10 pts) Molybdenum metal crystallizes with a body-centered cubic (bcc) structure having a
lattice parameter a = 3.1469 Å. Calculate the Mo-Mo distance (separation) between nearestneighbor
Mo atoms in the crystal. Hint: the nearest-neighbor atoms are aligned along the body
diagonal of the bcc unit cell.
3. (20 pts) Derive the first three terms of the series to calculate the Madelung constant for CsCl.
Use interionic separation d (d = rCs+ + rCl) as the distance parameter in the Coulomb equation.
4. (10 pts) Should it be possible to convert -cristobalite to some of the other modifications by
applying high pressure?
Modification of SiO2 Density / g cm1
-quartz 2.65
-quartz 2.53
-tridymite 2.27
-cristobalite 2.33
Vitreous 2.20
5. (15 pts) a) Write balanced chemical equation for a solid state reaction:
ZnC2O4 + Fe(OH)3  ZnFe2O4
b) What is the driving force in this reaction?
c) Cubic spinel ZnFe2O4 crystallizes with 8 formula units in the cubic unit cell. The cell parameter
a = 8.42 Ǻ. Calculate the density in g cm3
of the material.
NA = 6.022141 1023
mol1
, Ar(Zn) = 65.41, Ar(Fe) = 55.85, Ar(O) = 15.999.
6. (15 pts) The cell parameter for cubic spinel ZnFe2O4 is a = 8.42 Ǻ, for MnFe2O4 a = 8.50 Ǻ.
a) Suggest a reason for the difference.
b) What would be the cell parameter for the mixed-metal phase (MnxZn1x)Fe2O4 when x = 0.25,
0.50, and 0.75.
7. (20 pts) Gibbs free energy change for nucleation GN is given by two terms – surface and
volume. GN = 4r2
SL + 4/3r3
GV
SL = the solid/liquid interfacial energy
ΔGV – the free energy change between the ‘monomer’ in solution and unit volume of bulk
crystal
S – supersaturation = the quotient (ratio) of the actual concentration and the concentration of the
respective species at equilibrium conditions, indicates how far away from equilibrium the system
is.
Vm – molar volume of the bulk crystal, r – nucleus radius
a) Explain what is a critical radius of nuclei rC – draw a graph of GN versus r.
b) Suggest a way how to control the critical nucleation radius rC by changing some reaction
parameter.
m
V
V
SRT
G
ln
