3. Crystal Structure and Defects

Planar Defects — Quiz

Test your understanding of planar defects with 5 practice questions.

Practice Questions

Question 1

In the coincidence site lattice (CSL) model for grain boundaries in FCC metals, a Σ3 boundary is best described as which of the following?

Question 2

For a low-angle tilt boundary described by Frank’s formula $s=\frac{b}{\theta}$ (with $\theta$ in radians), calculate the dislocation spacing $s$ if the Burgers vector magnitude $b=0.25\,\mathrm{nm}$ and the misorientation angle $\theta=3°$.

Question 3

In an FCC metal with shear modulus $G=26\times10^9\,\mathrm{Pa}$, Burgers vector $b=0.255\times10^{-9}\,\mathrm{m}$, Poisson’s ratio $\nu=0.3$, and stacking fault energy $\gamma_{sf}=45\times10^{-3}\,\mathrm{J/m^2}$, the equilibrium separation $w$ of Shockley partial dislocations is given by $w=\frac{G b^2}{8\pi\gamma_{sf}(1-\nu)}$. What is $w$ in nanometers?

Question 4

Which type of stacking fault in an FCC metal is created by the insertion of an extra close-packed atomic plane?

Question 5

Rank the following diffusion pathways in a polycrystalline metal by decreasing diffusivity at moderate temperatures: I. Lattice, II. Grain boundaries, III. Free surfaces, IV. Dislocation cores.