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# Titanium crystallizes in a face centered cubic lattice. It reacts with C or H interstitially, by allowing atoms of these elements to occupy holes in the host lattice. Hydrogen occupies tetrahedral holes, but carbon occupies octahedral holes.(a) Predict the formula of titanium hydride and titanium carbide formed by saturating the titanium lattice with either “foreign” element.(b)What is the maximum ratio of “foreign” atom radius to host atom radius that can be tolerated in a tetrahedral hole without causing a strain in the host lattice?

(a)There are 4 – atoms per unit cell and 8-tetrahedral sites per unit cell. So, the ratio of atoms to tetrahedral sites = 1:2
So, the formula would be $TiH_2$
For carbide Since carbon occupies octahedral holes So, ratio of octahedral hole to atom = 1:1
The formula of carbide is TiC
(b) Since for tetrahedral hole
$\large\frac{r^+}{r^-}$$=$$0.225-0.414$
here $r^+$= foreign atom radius
$r^–$ = host atom radius
Without causing a strain in the host lattice i.e.,$\large\frac{r^+}{r^-}$$= 0.225$ (minimum value)