A crystal's unit cell is spanned by three edge vectors

PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Linear algebra and vector spaces · Linear algebra and vector spaces

Mathematical Methods for Physics, Ch Matrices, determinants and systems of linear equations

Problem

A crystal's unit cell is spanned by three edge vectors, in nanometres, a=(0.20,0,0)\mathbf{a} = (0.20, 0, 0), b=(0.10,0.30,0)\mathbf{b} = (0.10, 0.30, 0) and c=(0,0.10,0.40)\mathbf{c} = (0, 0.10, 0.40). ((a)) Write the 3×33\times 3 determinant whose rows are a\mathbf{a}, b\mathbf{b}, c\mathbf{c}, and evaluate it by expansion along the first row. ((b)) State what the number represents physically, and give the volume of the unit cell with its unit.

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