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Crystal defects and diffusion

Among point defects in ionic crystals, which correctly describes a Frenkel defect?

  1. AA pair consisting of a cation vacancy and an anion vacancy, formed together so as to keep the whole crystal electrically neutral
  2. BA pair of a vacancy and an interstitial ion, formed when an ion moves from its lattice site into an interstitial position
  3. CA substitutional impurity defect, in which an ion of an element different from the host occupies a lattice site in place of a host ion
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Answer: B. A pair of a vacancy and an interstitial ion, formed when an ion moves from its lattice site into an interstitial position

A Frenkel defect forms when an ion (usually the smaller cation) moves from its lattice site to an interstitial position, creating a vacancy and an interstitial ion as a pair. Ag⁺ in AgCl and AgBr is the well-known example. A pair of a cation vacancy and an anion vacancy is a Schottky defect, which occurs mainly in NaCl and MgO. Both combinations preserve the electrical neutrality of the crystal as a whole. Substitution by a foreign ion is impurity solid solution; when the valences differ, vacancies or other defects are introduced to compensate the charge.

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More Crystal defects and diffusion questions

  1. Which correctly describes the relation between the Burgers vector and the dislocation line of an edge dislocation?
  2. A metal has a vacancy formation energy of 0.90 eV. Using n/N = exp(−Q/kT), which value is closest to the equilibrium vacancy concentration (the fraction of lattice sites that are vacant) at 1000 K? Take Boltzmann's constant as k = 8.617×10⁻⁵ eV/K.
  3. Carbon diffuses at steady state through a 5.0 mm thick steel plate whose two faces are held at carbon concentrations of 1.2 kg/m³ and 0.8 kg/m³. If the diffusion coefficient is 3.0×10⁻¹¹ m²/s, which value is closest to the diffusion flux of carbon? Assume the concentration varies linearly through the thickness.
  4. The diffusion coefficient of carbon in γ-iron follows the Arrhenius form D = D₀exp(−Q/RT) with D₀ = 2.3×10⁻⁵ m²/s and activation energy Q = 148 kJ/mol. Which value is closest to the diffusion coefficient at 927 °C? Take the gas constant as R = 8.314 J/(mol·K).
  5. The diffusion coefficient of an element was 1.0×10⁻¹⁴ m²/s at 800 K and 4.0×10⁻¹³ m²/s at 1000 K. Assuming the Arrhenius form D = D₀exp(−Q/RT), which value is closest to the activation energy Q? Take R = 8.314 J/(mol·K).