Question

The energy for vacancy formation in Al is 0.66 eV. Calculate the number of vacancies in a 1 cm3 of Al at 300°C and 600°C

Answer #1

Calculate the energy (in eV/atom) for vacancy formation in some
metal, M, given that the equilibrium number of vacancies at 476oC
is 3.61E+23 m-3. The density and atomic weight for this metal are
20.1 g/cm3 and 92.40 g/mol, respectively.

Calculate the temperature where the number of vacancies per
cubic meter in iron will be 9.40 x 1017 atoms/cm3. The energy for
vacancy formation is 1.08 eV/atom.

(a) Calculate the activation energy, QV, for vacancy formation
in silver, given that the equilibrium number of vacancies at 1073°K
is 3.6 x 1023 m-3. The atomic weight and
density (at 1073°K) of silver are, respectively, 107.9 g/mol and
9.5 g/cm3 .
(b) Suppose that CaO is added as an impurity to Li2O.
If the Ca2+ substitutes for Li+ , what kind of vacancies would you
expect to form? How many of these vacancies are created for every
Ca2+ added?

Consider a metal with an energy for vacancy formation of
(6.0000x10^-1) eV/atom. If the material is originally at
(1.00x10^3) K, calculate the temperature rise (in K) needed to
increase the vacancy fraction by a factor of (8.0000x10^0) .
Note: Do not enter the resulting temperature, just the change in
temperature.

Calculate the equilibrium number of vacancies per cubic meter in
gold(Au) at 25(celcius). For gold, the energy for vacancy formation
is 0.98 eV/atom. Furthermore, the atomic mass and the theoretical
density for gold are 196.9 g/mol and 19.32 g/cm^3(at 25 celcius),
respectively.

Given that for a typical metal the energy for vacancy
formation is on the order of 1 eV/atom, melting point is 10^3 K,
molar mass is 10^2 g/mol and density is 10 g/cm3.
1.) Near melting point the fraction of vacant lattice
sites is:
a) <10^-5
b) 10^-5 to 10^-3
c) 10^-3 to 10^-2
d) 10^-2 to 10^-1
2.) The number of vacant sites per cm^3 is
typically:
a) <10^3
b)10^3 to 10^6
c) 10^6 to 10^9
d) > 10^9...

The energy of formation of Schottky defects in a crystal of CaO
is given as 6.1 eV. Calculate the number of Schottky
defects present in CaO at 1000 oC and 2000
oC. How many vacancies are present at these
temperatures? CaO has a density of 3300
kg*m-3.

Compute the concentration (number density, count per volume) of
vacancies in copper at room temperature if the lattice parameter of
FCC copper is 0.3615 nm at room temperature (25oC, 298 K),
and the activation energy to form a single vacancy is 0.9 eV.
Use 8.617x10-5 eV/(atom-K), exactly, as Boltzmann's Constant.
Note: You could look up the density and atomic weight of copper
to compute the intermediate value of atom concentration you need
for this problem.
But here I give you...

The concentration of vacancies in niobium (Nb)
at 765˚C is 9.836 x 1018 cm-3. If niobium has
a BCC crystal structure and a lattice parameter of 0.3302 nm,
calculate the energy for vacancy formation in
niobium.

Why do vacancies and interstitials have a positive energy of
formation? Why are they present at finite temperatures if they’re
not energetically favored?

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