Iron Transformation Volume Change Calculation
This solution calculates the percentage volume change when pure iron transforms from a Body Centered Cubic (BCC) structure to a Face Centered Cubic (FCC) structure, using the provided lattice parameters. The calculation focuses on the change in volume per atom.
BCC Phase Volume per Atom
First, calculate the volume of the BCC unit cell.
Given the BCC lattice parameter $ a_{BCC} = 0.293 \text{ nm} $. The volume is:
$ V_{BCC} = a_{BCC}^3 = (0.293 \text{ nm})^3 \approx 0.02515 \text{ nm}^3 $
Since a BCC unit cell contains 2 atoms, the volume per atom is:
$ V_{atom, BCC} = \frac{V_{BCC}}{2} = \frac{0.02515 \text{ nm}^3}{2} \approx 0.01258 \text{ nm}^3 $
FCC Phase Volume per Atom
Next, calculate the volume of the FCC unit cell.
Given the FCC lattice parameter $ a_{FCC} = 0.363 \text{ nm} $. The volume is:
$ V_{FCC} = a_{FCC}^3 = (0.363 \text{ nm})^3 \approx 0.04783 \text{ nm}^3 $
Since an FCC unit cell contains 4 atoms, the volume per atom is:
$ V_{atom, FCC} = \frac{V_{FCC}}{4} = \frac{0.04783 \text{ nm}^3}{4} \approx 0.01196 \text{ nm}^3 $
Volume Change Calculation
Calculate the percentage change in volume per atom relative to the BCC phase.
The formula for percentage volume change is:
$ \% \Delta V = \frac{V_{atom, FCC} - V_{atom, BCC}}{V_{atom, BCC}} \times 100 $
Substitute the calculated volumes per atom:
$ \% \Delta V = \frac{0.01196 \text{ nm}^3 - 0.01258 \text{ nm}^3}{0.01258 \text{ nm}^3} \times 100 $
$ \% \Delta V = \frac{-0.00062}{0.01258} \times 100 \approx -4.92\% $
Rounding the result to one decimal place gives -4.9%.
Important Questions from Crystal Structure Density Atomic Packing Factor
- Match the crystal systems in Column I with the corresponding axial lengths (a, b, c) and interaxial angles ($\alpha$, $\beta$, $\gamma$) provided in Column II
Column I Column II (P) Tetragonal (1) $a \neq b \neq c$, $\alpha = \beta = \gamma = 90^\circ$ (Q) Rhombohedral (2) $a = b \neq c$, $\alpha = \beta = \gamma = 90^\circ$ (R) Orthorhombic (3) $a \neq b \neq c$, $\alpha = \gamma = 90^\circ \neq \beta$ (S) Monoclinic (4) $a = b = c$, $\alpha = \beta = \gamma \neq 90^\circ$ - The coordination number for an octahedral site in pure copper is __________.
The lattice parameter of face-centered cubic iron ($\gamma$-Fe) is 0.3571 nm. The radius (in nm) of the octahedral void in $\gamma$-Fe is _______________
- For a bcc metal the ratio of the surface energy per unit area of the (100) plane to that of the (110) plane is ________
- If saturation magnetization of iron at room temperature is $1700 \text{ kA m}^{-1}$, the magnetic moment (in $A \text{ m}^2$) per iron atom in the crystal is: _________ $ \times 10^{-23}$
(round off to 1 decimal place).
(Given: Lattice parameter of iron at room temperature = 0.287 nm)
