- #1

spaghetti3451

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## Homework Statement

Given that the primitive basis vectors of a lattice are ##\mathbf{a} = \frac{a}{2}(\mathbf{i}+\mathbf{j})##, ##\mathbf{b} = \frac{a}{2}(\mathbf{j}+\mathbf{k})##, ##\mathbf{c} = \frac{a}{2}(\mathbf{k}+\mathbf{i})##, where ##\mathbf{i}##, ##\mathbf{j}##, and ##\mathbf{k}## are the usual three unit vectors along cartesian coordinates, what is the Bravais lattice?

## Homework Equations

## The Attempt at a Solution

There are seven different crystal systems and fourteen different Bravais lattices.

The common length of the primitive unit cell is ##a##, so the crystal system is either cubic or trigonal (rhombohedral).

Furthermore, the basis vectors are oriented at ##90°## to each other, so the crystal system must be cubic.

Finally, the Bravais lattice is face-centred cubic, because, if the basis vectors originate from one corner of the primitive unit cell, then they point to lattice sites at the centre of three adjacent (to the corner) faces of the primitive unit cell.

Is my answer correct?