Question

Given that the primitive basis vectors of a lattice are
a=(a/2)i
b=(a/2)j
c=(a/2)k
Where I,j,k are unit vectors in coordinate system
Determine the bravais lattice
Calculate the volume of the primitive unit cell

Answer 1

Answer on Question #63595, Physics / Solid State Physics

Given that the primitive basis vectors of a lattice are

a=(a/2)i

b=(a/2)j

c=(a/2)k

Where I,j,k are unit vectors in coordinate system

Determine the bravais lattice

Calculate the volume of the primitive unit cell

**Solution:**

The primitive unit cell has a shape of cube.

Volume of primitive unit cell:

$$V = a \times b \times c \quad (1)$$ $$\text{Of} \quad (1) \Rightarrow V = \frac{a^3}{8}$$

**Answer:**

$$\frac{a^3}{8}$$

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