Nuclear Engineering 265
Introduction to Materials for Nuclear Applications
Homework 5
March 3, 2022
10 Points Each
1) Mass and Atom Fraction Estimations:
a. Calculate (in weight percent and atom percent) the composition of an alloy that
contains 104 kg of iron, 0.3 kg of carbon, and 2.0 kg of chromium.
b. Consider a nickel based alloy with the composition Ni-15Fe-10Si-5W-2Ir-1Be
(all numbers in weight percent; Ni is the host). What is the alloy composition in
atom percent?
2) Calculate the fraction of atom sites that are thermodynamically stable as vacancies for
copper just below its melting temperature (e.g., 1084°C) and at room temperature 25°C.
Assume the energy for vacancy formation is 0.90 eV/atom.
3) Estimate the activation energy (Q), in kJ/mole, for vacancy formation in a hypothetical
metal the temperature dependent vacancy concentration, Nv(T), increases by a factor of
1000 when the temperature is raised from 750K to 1000K.
4) Calculate the energy for vacancy formation in silver, given that the equilibrium number
of vacancies at 800°C (1073 K) is 3.6×1023 m-3. The atomic weight and density (at
800°C) for silver are, respectively, 107.9 g/mol and 9.5 g/cm3.
5) Calculate the fraction of lattice sites that are Schottky defects for cesium chloride at its
melting temperature (645°C). Assume an energy for defect formation of 1.86 eV.
6) Using the data given below that relate to the formation of Schottky defects in some oxide
ceramic (having the chemical formula MO), determine the energy for defect formation
(in eV), and the equilibrium number of Schottky defects per cubic meter at 1000ºC.
T(ºC)
Ns (m-3)
ρ (g/cm3)
750
3.50
5.7 x 109
1000
3.45
????
1500
3.40
5.8 x 1017
7) Which of the following systems (i.e., pair of metals) would you expect to exhibit
complete solid solubility? Explain your answers.
(a) Cr–V
(b) Mg–Zn
(c) Al–Zr
(d) Ag–Au
(e) Pb–Pt
8) To provide some perspective on the dimensions of atomic defects, consider a metal
specimen that has a dislocation density (look up the definition) of 105 mm-2. Suppose that
all the dislocations in 1 cm3 were somehow removed and linked end to end.
a. How far (in miles) would this chain extend?
Nuclear Engineering 265
Introduction to Materials for Nuclear Applications
b. What would the length be if the density is increased to 109 mm-2 by cold working?