Question

Below are listed the atomic weight, density, and atomic radius for three hypothetical alloys at room temperature. For each determine whether its crystal structure is FCC, BCC, or simple cubic and then justify your answer.

Alloy	Atomic weight	Density	Atomic radius
	(g/mol)	(g/cm3)	(nm)
A	195.08	21.45	0.139
B	209	9.32	0.335
C	55.85	7.87	0.124

Answer 1

For alloy A,

Edge length = 1.39 x 10^-8 cm x 2(sq.rt.(2)) = 3.93 x 10^-8 cm

Volume of unit cell = (3.93 x 10^-8)^3 = 6.07 x 10^-23 cm^3

mass of alloy = 21.45 x 6.07 x 10^-23 = 1.30 x 10^-21 g

Number of atoms in unit cell = 1.30 x 10^-21 x 6.023 x 10^23/195.08 = 4

The the crystal structure is an FCC type.

For alloy B

It does not fit into the FCC or BCC type crystal and thus, it would be a simple cubic trpe of crystal structure.

For alloy C

Edge length = 1.24 x 10^-8 x 4/sq.rt.(3) = 2.86 x 10^-8 cm

Volume of unit cell = 2.34 x 10^-23 cm^3

mass of alloy in unit cell = 2.34 x 10^-23 x 7.87 = 1.84 x 10^-22 g

number of atoms in a unit cell = 1.84 x 10^-22 x 6.023 x 10^23/55.85 = 2

So, the crystal structure is a BCC.