Crystal Structures

Step 1: Calculate the initial volume of the crystal in the monoclinic phase.
The volume of a crystal with monoclinic structure is given by Substituting the values, Step 2: Calculate the volume of the crystal in the tetragonal phase.
The volume of a tetragonal crystal is given by Substituting the values, Step 3: Calculate the fractional change in volume.
The fractional change in volume is Substituting the values, Step 4: Final Answer.
Thus, the fractional change in the volume is .

Step 1: Understanding the bcc structure.
In a body-centered cubic (bcc) structure, there are 8 corner atoms and 1 atom at the body center. Each corner atom contributes to the unit cell (since each corner atom is shared by 8 cubes).
Step 2: Calculate the total number of atoms per unit cell.

Step 3: Find number of atoms per unit volume.
Since the volume of a unit cell is ,
Step 4: Final Answer.
Hence, the number of atoms per unit volume is .