Crystal defects and diffusion

Which statement about diffusion paths in a polycrystalline metal is correct?

  1. AThe activation energy generally increases in the order lattice diffusion < grain boundary diffusion < surface diffusion
  2. BThe lower the temperature, the larger the contribution of grain boundary diffusion relative to lattice diffusion
  3. CThe finer the grains, the smaller the contribution of grain boundary diffusion
Show answer and explanation

Answer: B. The lower the temperature, the larger the contribution of grain boundary diffusion relative to lattice diffusion

The more disordered the atomic packing along a path, the more easily atoms jump, so the activation energy generally increases in the order surface diffusion < grain boundary diffusion < lattice (volume) diffusion. The choice giving lattice < grain boundary < surface has this order reversed. Paths with lower activation energy lose less of their diffusion coefficient as the temperature falls, so the relative contribution of grain boundary diffusion grows at lower temperatures. Finer grains mean a larger total grain boundary area, so the contribution of grain boundary diffusion actually increases. This is why grain boundary diffusion becomes a problem in low-temperature, fine-grained systems such as solder joints and thin-film interconnects.

Report an error

Practice this topic Back to topic

Related calculators

More Crystal defects and diffusion questions

  1. When copper and brass (a Cu-Zn alloy) are bonded and heated, inert markers placed at the original interface move toward the brass side (the Kirkendall effect). What does this phenomenon show?
  2. The Burgers vector of a perfect dislocation in an FCC metal is (a/2)<110>. Which value is closest to its magnitude in aluminum (lattice parameter 0.405 nm)?
  3. Among point defects in ionic crystals, which correctly describes a Frenkel defect?
  4. Which correctly describes the relation between the Burgers vector and the dislocation line of an edge dislocation?
  5. 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.