Question

A hypothetical AX type of ceramic material is known to have a density of 3.55 g/cm3 and a unit cell of cubic symmetry with a cell edge length of 0.39 nm. The atomic weights of the A and X elements are 90.5 and 37.3 g/mol, respectively. On the basis of this information, which one of the following crystal structures is possible for this material?a) fluoriteb) zinc blendc) cesium chloride

Answer 1

Step-by-step explanation:

For AX type ceramic material, the number of formula per unit cells is as follows.

`\rho = (n'(A_(c) + A_(A)))/(V_(C)N_(A))`

or,
`n' = (\rho a^(3)N_(A))/((A_(c) + A_(A)))`

where, n' = no. of formula units per cell

`A_(c)` = molecular weight of cation = 90.5 g/mol

`A_(a)` = molecular weight of anion = 37.3 g/mol

`V_(c)` = volume of cubic cell = 3.55
`g/cm^(3)`

a = edge length of unit cell =
`3.9 * 10^(-8) cm`

`N_(A)` = Avogadro's number =
`6.023 * 10^(23)`

`\rho` = density = 3.55
`g/cm^(3)`

Now, putting the given values into the above formula as follows.

`n' = (\rho a^(3)N_(A))/((A_(c) + A_(A)))`

=
`(3.55 g/cm^(3) * (3.9 * 10^(-8))^(3) * 6.023 * 10^(23))/((90.5 + 37.3))`

= 0.9

= 1 (approx)

Therefore, we can conclude that out of the given options crystal structure of cesium chloride is possible for this material.