Copper is face-centred cubic with room-temperature lattice constant (tabulated)

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

Solid State Physics, Ch Symmetry and the classification of crystals

Problem

Copper is face-centred cubic with room-temperature lattice constant a=3.615 A˚a=3.615\,\mathrm{\AA} (tabulated). Using the fcc Brillouin-zone labels Γ=(0,0,0)\Gamma=(0,0,0), X=(1,0,0)X=(1,0,0) and L=(12,12,12)L=(\tfrac12,\tfrac12,\tfrac12), in units of 2π/a2\pi/a: ((a)) Compute the distance ∣ΓX∣|\Gamma X| in A˚−1\mathrm{\AA^{-1}}. ((b)) Compute the distance ∣ΓL∣|\Gamma L| in A˚−1\mathrm{\AA^{-1}}.

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