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) $a = b = c$, $\alpha = \beta = \gamma \neq 90^\circ$
To match the crystal systems with their axial lengths and interaxial angles, we need to recall the defining characteristics of each system.
Matching Crystal Systems: Axial Lengths and Angles
We will analyze each crystal system from Column I and find its corresponding definition in Column II based on the relationships between axial lengths ($a$, $b$, $c$) and interaxial angles ($\alpha$, $\beta$, $\gamma$).
- (P) Tetragonal System: This system is defined by two equal axes and one different axis, all mutually perpendicular. The conditions are $a = b \neq c$ and $\alpha = \beta = \gamma = 90^\circ$. This matches condition (2) in Column II.
- (Q) Rhombohedral System (Trigonal): This system has all three axes equal in length, and all interaxial angles are equal but not necessarily $90^\circ$. The conditions are $a = b = c$ and $\alpha = \beta = \gamma \neq 90^\circ$. This matches condition (4) in Column II.
- (R) Orthorhombic System: This system features three unequal axes that are mutually perpendicular. The conditions are $a \neq b \neq c$ and $\alpha = \beta = \gamma = 90^\circ$. This matches condition (1) in Column II.
- (S) Monoclinic System: In the monoclinic system, the three axes are unequal in length, and two interaxial angles are $90^\circ$, while the third angle is different. The conditions are $a \neq b \neq c$ and $\alpha = \gamma = 90^\circ \neq \beta$. This matches condition (3) in Column II.
Final Crystal System Matching
Based on the analysis above, the correct matching is:
- P corresponds to 2
- Q corresponds to 4
- R corresponds to 1
- S corresponds to 3
This corresponds to the option P-2, Q-4, R-1, S-3.
Important Questions from Crystal Structure Density Atomic Packing Factor
- 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 ________
- Pure iron transforms from body centered cubic (BCC) to face centered cubic (FCC) crystal structure at $912 \text{ °C}$. If the lattice parameter of the BCC phase is $0.293 \text{ nm}$ and that of the FCC phase is $0.363 \text{ nm}$, the associated volume change is ________ (in % to one decimal place)
- 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)
