Hypothetical metal calculations

  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. 23 A 6.022 10 ; ; 58.6934 c Ni A nA N atoms mol V A l N     g mo    Determine density of FCC Ni-structure and use it as concentration in nickel side.  Use zero concentration of Ni in Tantalum side  Determine J, diffusion flux and determine the number of atoms that will cross through the given area of cross-section.) 9. An impermeable cylinder 3 cm in diameter and 10 cm long contains a gas that includes 0.5  1020 N atoms per cm3 and 0.5  1020 H atoms per cm3 on one side of an iron membrane as shown. Gas is continuously introduced to the pipe to assure a constant concentration of nitrogen and hydrogen. The gas on the other side of the membrane includes a constant 1  1018 N atoms per cm3 and 1  1018 H atoms per cm3 . The entire system is to operate at 700oC, where the iron has the BCC structure. Design an iron membrane that will allow no more than 1% of the nitrogen to be lost through the membrane each hour, while allowing 90% of the hydrogen to pass through the membrane per hour.