Question

An ax ceramic compound has the rock salt crystal structure. if the radii of the a and x ions are 0.137 nm and 0.241 nm, respectively, and the respective atomic weights are 22.7 g/mol and 91.4 g/mol, what is the density of this material? 0.571 g/cm3

Answer 1

P = n'∑Ac + ∑AA/VcNA
= n'(∑Ac + ∑AA)/9³NA
=n'(∑Ac + ∑AA)/(2(rA + rX))³ NA
n' = number of atoms per unit cell
= 4(assumption)
rA = 0.137 × 10⁻⁷ cm
rX = 0.241 × 10⁻⁷ cm
NA = Avagadros number
= 6.022 × 10²³
∑Ac = Atomic weight of all cations
∑AA = Atomic weight of all anions
p = n'(∑Ac + ∑∑AA)/(2(rA + rx))³NA
= 4(22.7 + 91.4/(2(0.137 × 10⁻⁷ + 0.241 × 10⁻⁷))³ 6.022× 10²³
= 1.75 gm/cc