Question

What is the Bravais lattice formed by all lattice points which have the Cartesian
coordinates (x,y,z) such that
i) x,y and z are all even numbers
ii) x,y and z are either all even numbers or all odd numbers.

Answer 1

Answer on Question #51567, Physics, Solid State Physics

What is the Bravais lattice formed by all lattice points which have the Cartesian coordinates $(x,y,z)$ such that

i) $x,y$ and $z$ are all even numbers

ii) $x,y$ and $z$ are either all even numbers or all odd numbers.

Answer:

i) The lattice will be simple cubic with lattice constants $a = 2$, if $(x, y, z)$ are all even.

ii) The lattice will be body-centered cubic with lattice constants $a = 2$, if $(x, y, z)$ are all even or all odd. We will get a lattice with $(x, y, z)$ all odd, and each new lattice point is in the center of the cubic of old lattice, if we shift the lattice in part (i) as $(x, y, z) \to (x + 1, y + 1, z + 1)$. Hence we obtain a body-centered cubic lattice.

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