Among the following the incorrect statement is

For an “incorrect statement” type question we must check every option against the standard facts of solid-state chemistry.

Option A : Frenkel defect involves displacement of a smaller ion (generally a cation) from its normal lattice point to an interstitial void.
• Mass of the unit cell remains unchanged (no ion leaves the crystal).
• Volume of the unit cell is also unchanged.
Hence density $$\rho=\frac{\text{mass}}{\text{volume}}$$ remains the same. Statement A is correct.

Option B : Packing efficiency of a body-centred cubic (BCC) lattice is obtained from

$$\text{Packing efficiency}= \frac{\text{volume occupied by atoms}}{\text{volume of unit cell}}\times100\%$$

For BCC this value is $$68\%$$, therefore the unoccupied (void) space is $$100\%-68\% = 32\%$$. Statement B is correct.

Option C : A Schottky defect means equal numbers of cations and anions are missing from their lattice sites.
• Mass of the unit cell decreases (some ions have left).
• Unit-cell volume is unaffected.
Therefore density decreases. Statement C is correct.

Option D : Temperature dependence of electrical conductivity ($$\sigma$$) is opposite for metals and intrinsic semiconductors.

• Metals: $$\sigma$$ decreases with increase in temperature because lattice vibrations (phonons) scatter conduction electrons more.

• Semiconductors: $$\sigma$$ increases with temperature because thermal energy generates more electron-hole pairs.

The statement “electrical conductivity of semiconductors and metals increases with temperature” is therefore wrong for metals. Statement D is incorrect.

Hence, the incorrect statement is:
Option D which is: Electrical conductivity of semiconductors and metals increases with increase in temperature.