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JEE Advanced
Exam
JEE Advanced
Subject
Chemistry
Chapter
Solid State

JEE Advanced · Chemistry · Solid State

Titanium crystallizes in a face centred cubic lattice. It reacts...

Titanium crystallizes in a face centred 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 "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?

Correct answer

0.225

Step-by-step solution

(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=1: 2 So, the formula would be TiH2\mathbf{T i H}_{\mathbf{2}} For carbide, Since carbon occupies octahedral holes So, ratio of octahedral hole to atom =1:1=1: 1 The formula of carbide is TiC (b) Since for tetrahedral hole, the limiting ratios, radius ratio r+r−=0.225\frac{r^{+}}{r^{-}}=0.225 to 0.414 Without causing a strain in the host lattice, i.e. r+r−=0.225\frac{r^{+}}{r^{-}}=0.225
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