A crystal has primitive vectors , , : a lattice oblique in the -plane

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

Condensed Matter Physics, Ch The reciprocal lattice and the Brillouin zone

Problem

A crystal has primitive vectors a1=(4.00,0,0) A˚\mathbf{a}_1=(4.00,0,0)\,\mathrm{\mathring{A}}, a2=(1.50,3.00,0) A˚\mathbf{a}_2=(1.50,3.00,0)\,\mathrm{\mathring{A}}, a3=(0,0,5.00) A˚\mathbf{a}_3=(0,0,5.00)\,\mathrm{\mathring{A}}: a lattice oblique in the xyxy-plane, repeating with a different period along zz. Construct its reciprocal lattice vectors b1\mathbf{b}_1, b2\mathbf{b}_2 and b3\mathbf{b}_3, and verify that b1⋅a1=2π\mathbf{b}_1\cdot\mathbf{a}_1=2\pi and b1⋅a2=0\mathbf{b}_1\cdot\mathbf{a}_2=0.

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