Question

A small portion of a crystal lattice is sketched below. What is the name of the unit cell of this lattice? Your answer must be a word, a very short phrase, or a standard abbreviation. Spelling counts!

Answer 1

This is an incomplete question, the given sketch is shown below.

Answer : The name of given unit cell is, FCC (face-centered cubic unit cell)

Explanation :

Unit cell : It is defined as the smallest 3-dimensional portion of a complete space lattice which when repeated over the and again in different directions produces the complete space lattice.

There are three types of unit cell.

• SCC (simple-centered cubic unit cell)
• BCC (body-centered cubic unit cell)
• FCC (face-centered cubic unit cell)

In SCC, the atoms are arranged at the corners.

$Z=\frac{1}{8}\times 8=1$

The number of atoms of unit cell = Z = 1

In BCC, the atoms are arranged at the corners and the body center.

$Z=\frac{1}{8}\times 8+1=2$

The number of atoms of unit cell = Z = 2

The given unit cell is, FCC because the atoms are arranged at the corners and the center of the 6 faces.

$Z=\frac{1}{8}\times 8+\frac{1}{2}\times 6=4$

The number of atoms of unit cell = Z = 4

Thus, the name of given unit cell is, FCC (face-centered cubic unit cell)