Question

Iron (Fe) undergoes an allotropic transformation at 912°C: upon heating from a BCC (a phase) to an FCC (y phase). Accompanying this transformation is a change in the atomic radius of Fe-from Recc=0.12584 nm to RFcc0.12894 nm-and, in addition, a change in density (and volume). Compute the percentage volume change associated with this reaction. Indicate a decreasing volume by a negative number.

Answer 1

To calculate the percentage volume change for iron transforming from BCC to FCC, find the volume of a unit cell for each phase using the atomic radius and the formulas for BCC and FCC lattices. Compute the volume change and express it as a percentage of the initial BCC volume.

To compute the percentage volume change when iron (Fe) undergoes an allotropic transformation from BCC to FCC, we must first determine the volume of a unit cell for each phase using the provided atomic radii (RBCC = 0.12584 nm and RFCC = 0.12894 nm). For BCC, the unit cell's volume, VBCC, is given by (4R/√3)³ since the body diagonal is equal to 4 times the atomic radius (R) divided by the square root of 3, and there are 2 atoms per unit cell.

For FCC, the volume VFCC is given by (2√2R)³, as the face diagonal is 4 times the atomic radius and there are 4 atoms per unit cell. The volume change ΔV is then VFCC - VBCC. To find the percentage volume change, divide the volume change by the initial BCC volume and multiply by 100%

Percent volume change:
((VFCC - VBCC) / VBCC) * 100%