Question

A certain solid has a structure in which $X$ atoms are located at the corners of the cubic cell, $O$ at the edge centres and $Y$ at the body centres. Then the formula of the cell is $X_a{Y}_b{O}_c$.
If $O$ atoms are missing from any two edge centres per unit cell, the formula is $X_x{Y}_y{O}_z$.
Find the value of $(a+b+c)+(x+y+z)$.

Answer 1

$a=\frac{1}{8}\times 8=1$
$b=1\times 1=1$
$c=\frac{1}{4}\times 12=3$
Then the formula of the cell is $X_1{Y}_1{O}_3$.
When $O$ is missing from any two edge centre, total of 10 atoms are left. So here $x=a,y=b,$ and $z=\frac{1}{4}\times 10=2.5$
We get Molecular formula as $XY{O}_{2.5}$
Since the molecular formula can never be a fraction, so multiply it by 2.
Now Molecular formula becomes as $X_2{Y}_2{O}_5$ and
$(a+b+c)+(x+y+z)=14$