Which statement about vacancies in crystalline solids is true?

• A. Vacancies can be completely eliminated with proper processing.
• B. All crystalline solids contain vacancies.
• C. Vacancies never occur at low temperatures.
• D. Vacancies are always larger than interstitials in size.

Answer: (B)

Vacancies in crystals are thermodynamically inevitable at any finite temperature. Creating a missing-atom site costs energy, but it also increases the number of ways to arrange atoms, so the configurational entropy gain makes a small but nonzero equilibrium concentration of vacancies favorable. This means there will always be some vacancies present in a crystal unless you are at absolute zero. The vacancy concentration follows roughly a Boltzmann factor, C_v ∝ exp(-Q_v/kT), so it is tiny at low temperatures but never exactly zero at any finite temperature. Therefore, processing cannot completely eliminate vacancies; they persist in real materials. At very low temperatures the number of vacancies is extremely small, but not strictly zero, and at high temperatures it grows, affecting properties like diffusion. The statement that all crystalline solids contain vacancies captures this general, temperature-dependent reality. The other options fail because: processing cannot wipe out vacancies entirely; vacancies can still exist at low but finite temperatures (not “never occur”); and there isn’t a universal rule that vacancies are larger than interstitials—these are distinct defect types with sizes that depend on the specific material and defect.