Stockton University
Chemistry Program, School of Natural Sciences and Mathematics
101 Vera King Farris Dr, Galloway, NJ
CHEM 3420: Physical Chemistry II — Spring 2016
Solid-state assignment
Due in Class: Wednesday, April 27, 2106
1. Determine the fraction of the total cell volume occupied by atoms for the following structures:
(a) body-centered cubic (assume atoms touch along a body diagonal)
(b) primitive cubic (assume the atoms touch along the cell edge)
2. Iron (ρ= 7.86 g/cm3 ) crystallizes in a BCC unit cell at room temperature. Calculate the radius of
an iron atom in this crystal. At temperatures above 910◦ C iron prefers to be FCC. If we neglect
the temperature dependence of the radius of the iron atom on the grounds that it is negligible, we
can calculate the density of FCC iron. Use this to determine whether iron expands or contracts
when it undergoes transformation from the BCC to the FCC structure.
3. Nickel has an FCC structure with a lattice parameter a = 3.52 Å. A powder sample is irradiated
with Cu Kα radiation (λCuKα = 1.5418 Å) . At what angles (2θ) would you find the diffracted
beams from the (111), (220), and (400) planes.
4. A powder diffraction experiment using incident copper Kα raditation (λCuKα = 1.5418 Å) gave the
following set of reflections expressed as 2θ : 38.40◦ ; 44.50◦ ; 64.85◦ ; 77.90◦ ; 81.85◦ ; 98.40◦ ; 111.20◦ .
(a) Determine the crystal structure.
(b) Calculate the lattice constant, a.
(c) Assume that the crystal is a pure metal and on the basis of the hard-sphere approximation
calculate the atomic radius.
(d) Calculate the density of this element which has an atomic weight of 66.6 g/mol.
I would advise you to use Excel for part (a), but be sure to convert 2θ to θ and use the angle in
radians! This will allow you to use the sin function in Excel, which takes its argument in radians.
Remember, π radians equals 180◦ .
One more on the other side
5. Tying it all together: Vegard’s Law states that in a binary alloy the lattice constant, a, should
vary linearly with composition. As a fully molten nickel-rhodium alloy is cooled, the very first solid
matter to appear is taken from the crucible and subjected to analysis by x-ray diffraction (using
Cr radiation with λ = 2.29 Å). The diffraction pattern shows a plurality of sharp peaks, the first
one corresponding to (111) planes at θ1 = 33.0◦ .
Using the data below along with the phase diagram for Ni–Rh, determine the rhodium concentration
of the original, fully molten Ni–Rh alloy.
Element
Ni
Rh
Structure
FCC
FCC
Lattice Constant, a (Å)
3.53
3.81
Here’s a suggested strategy to solve this problem:
(a) Find the lattice constant of the solid sample
(b) With this lattice constant use Vegard’s Law to find the composition of the solid.
(c) Using the phase diagram, determine the overall alloy composition that first solidifies with solid
of composition calculated in (b).