# Calculating the radius of a crystal structure

1. Some hypothetical metal has the simple cubic crystal. If its atomic
weight is 70.4 g/mol and the atomic radius is 0.126 nm, compute its
density.
2. Calculate the radius of a vanadium atom, given that Vhas a BCC crystal
structure, a density of 5.96 g/cm3
, and an atomic weight of 50.9 g/mol.
3. Calculate the radius of an iridium atom, given that Ir has an FCC crystal
structure, a density of 22.4 g/cm3
, and an atomic weight of 192.2 g/mol.
4. (a) Derive linear density expressions for FCC [100] and [111] directions
in terms of the atomic radius R.
(b) Compute and compare linear density values for these same two
directions for silver. The atomic radius for silver is 0.144 nm.
5. (a) Derive planar density expressions for FCC (100) and (111) planes
in terms of the atomic radius R.
(b) Compute and compare planar density values for these same two
planes for nickel.
6. A sheet of steel 2.5-mm thick has nitrogen atmospheres on both sides
at 900oC and is permitted to achieve a steady-state diffusion condition.
The diffusion coefficient for nitrogen in steel at this temperature is
10 2
1.85 10 m s 
 , and the diffusion flux is found to be 7 2
10 kg m s 
. Also,
it is known that the concentration of nitrogen in the steel at the highpressure
surface is 2 kg/m3
. How far into the sheet from this highpressure
side will the concentration be 0.5 kg/m3
? Assume a linear
concentration profile.
7. Consider a diffusion couple between silver and a gold alloy that
contains 10 wt% silver. This couple is heat treated at an elevated
temperature and it was found that after 850 s, the concentration of silver
had increased to 12 wt% at 10 m from the interface into the Ag–Au
alloy. Assuming pre-exponential and activation energy values of
6 2
7.2 10 m s 
 and 168,000 J mol , respectively, compute the temperature
of this heat treatment.
8. A 0.05 cm layer of magnesium oxide (MgO) is deposited between
layers of nickel (Ni) and tantalum (Ta) to provide a diffusion barrier
that prevents reactions between the two metals as shown. At 1400 oC,
nickel ions are created and diffuse through the MgO ceramic to the
tantalum. Determine the number of nickel ions that pass through the
MgO per second. The diffusion coefficient of nickel ions in MgO is 9
 10-12 cm2
/s, and the lattice parameter of nickel at 1400oC is 3.6  10-8
cm. Nickel has FCC structure.