Silicon has shear modulus , Poisson ratio

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Condensed Matter, Materials & Soft Matter · Crystal structure, bonding and diffraction

Solid State Physics, Ch Point defects, dislocations and alloys

Problem

Silicon has shear modulus G=64 GPaG=64\,\mathrm{GPa}, Poisson ratio ν=0.28\nu=0.28, and glides on {111}⟨110⟩\{111\}\langle110\rangle with Burgers vector b=a/2=3.84 A˚b=a/\sqrt2=3.84\,\mathrm{\AA} (diamond-cubic lattice constant a=5.43 A˚a=5.43\,\mathrm{\AA}). ((a)) Taking α=1/2\alpha=1/2, as for copper, estimate the dislocation line energy per unit length 12Gb2\tfrac12Gb^2, and convert it to an energy per atomic length bb, in eV. ((b)) Silicon's narrow, directional covalent bonds give a dislocation core width of about one Burgers vector, w≈bw\approx b. Using τP≈2G1−νe−2πw/b\tau_P\approx\dfrac{2G}{1-\nu}e^{-2\pi w/b}, estimate the Peierls stress and express it as a fraction of GG. ((c)) Copper's measured Peierls stress is below 10−5G10^{-5}G. Using the two fractions, explain why silicon is brittle at room temperature while copper remains ductile even at 4 K4\,\mathrm{K}.

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