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Titanium monoxide has a rock−salt structure. X−ray diffraction data show that the length of one edge of the cubic unit cell for TiO with a 1:1 ratio of Ti to O is 4.18$A^{\large\circ}$, and the density as determined by volume and mass measurements is 4.92 g $cm^{–3}$. Do the data indicate that defects are present? If so, are they vacancy or interstitial defects? [Ti = 47.88 u].

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The presence of vacancies (Schottky defects) at the Ti and O sites should be reflected in a lower measured density than that calculated from the size of the unit cell and the assumption that every Ti and O site is occupied. Interstitial (Frenkel) defects would give little of any difference between the measured and theoretical densities. There are four formula units per unit all so theoretical
density is d=$\large\frac{4(47.88+16)}{6.023\times 10^{23}(4.18\times 10^{23})}=$$4.81gcm^{-3}$
This is significantly greater than the measured density. The crystal must, therefore, contain numerous vacancies. Because the overall composition of the solid is TiO, there must be equal number of vacancies on cation and anion sites.
answered Jun 3, 2014 by sreemathi.v

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