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.