Crystal structures. The metal Cobalt undergoes a structural transition from the

Question

Crystal structures. The metal Cobalt undergoes a structural transition from the FCC (high
temperature) to the HCP crystal structure (low temperature) at 450°C, but samples that are
quenched fast to room temperature frequently consist of mixtures of the FCC form and the HCP
form. At 20°C, the FCC lattice parameter was determined as follows:
FCC: a = 3.5442 Å
(a) What is the nearest-neighbor distance in FCC Co?
(b) Calculate the unit cell volume of FCC Co at 20°C. What is the mass density of FCC Co?
(mass of Co atoms in unit cell per unit cell volume, in kg/m3)
(c) Assume that a hypothetical BCC Co phase has the same nearest-neighbor distance as the
FCC Co phase described above. Calculate the lattice parameter of this hypothetical BCC
phase. What is its mass density?

Explanation / Answer

(a) nearest-neighbor distance in FCC Co is 2.5064 Angstrom

(b) Volume of unit cell = a^3 = (3.5442 x 10^-10)^3 = 4.45 x 10^-29 m^3

Mass of unit cell = 59 * 4 / 6.022 x 10^23 = 3.92 x 10^-22 = 3.92 x 10^-25 kg

Mass density = 3.92 x 10^-25 / 4.45 x 10^-29 = 8.81 x 10^3 kg/m^3

(c)

d = root(3) * a / 2

2.5064 * 2 /root(3) = a

a = 2.894 x 10^-10 m

Volume = 2.424 x 10^-29 m^3

Mass of unit cell = 59 * 2 / 6.022 x 10^23 = 1.96 x 10^-22 g = 1.96 x 10^-25 kg

MAss Density = 1.96 x 10^-25 kg / 2.424 x 10^-29 m^3 = 8.01 x 10^3 kg/m^3

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