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Crystal defects and diffusion

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?

  1. AThe two kinds of atoms diffuse at different rates, and diffusion proceeds by the vacancy mechanism
  2. BAtoms diffuse only by the interstitial mechanism, and the number of lattice sites on each side does not change
  3. CThermal stress generated at the bonded interface during heating is pushing the inert markers toward the brass side
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Answer: A. The two kinds of atoms diffuse at different rates, and diffusion proceeds by the vacancy mechanism

Zinc diffuses into copper faster than copper diffuses into brass, so more atoms leave the brass side than enter it. Substitutional diffusion proceeds by exchange with vacancies, so vacancies flow opposite to the net flow of atoms; lattice planes are lost on the brass side and the markers shift toward the brass. This historic experiment showed that diffusion proceeds by the vacancy mechanism. With only the interstitial mechanism, the number of lattice sites would not change and the markers would not move. Excess vacancies that coalesce form Kirkendall voids, which degrade the reliability of solder joints and similar structures.

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More Crystal defects and diffusion questions

  1. 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)?
  2. Among point defects in ionic crystals, which correctly describes a Frenkel defect?
  3. Which correctly describes the relation between the Burgers vector and the dislocation line of an edge dislocation?
  4. 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.
  5. 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.