For each of the crystallographic system listed in Group-I, match the corresponding minimum symmetry in Group-IIGroup-I Group-II [P] Tetragonal [1] 1 two-fold rotation [Q] Cubic [2] 1 three-fold rotation [R] Monoclinic [3] 4 three-fold rotation [S] Rhombohedral [4] 1 four-fold rotation
P-4; Q-3; R-1; S-2
Matching Crystallographic Systems to Minimum Symmetry
This question requires matching each crystallographic system in Group-I with its characteristic minimum symmetry element(s) listed in Group-II.
Group-I: Crystallographic Systems
- [P] Tetragonal
- [Q] Cubic
- [R] Monoclinic
- [S] Rhombohedral
Group-II: Minimum Symmetry Elements
- [1] 1 two-fold rotation
- [2] 1 three-fold rotation
- [3] 4 three-fold rotations
- [4] 1 four-fold rotation
Deriving the Matches
We determine the correct match for each system based on its defining symmetry properties:
- Tetragonal System [P]: This system is defined by the presence of a principal four-fold rotation axis. Therefore, it matches with symmetry element [4].
- Cubic System [Q]: The cubic system exhibits high symmetry, including three unique 4-fold axes and four unique 3-fold axes. The option representing this count is [3].
- Monoclinic System [R]: This system is characterized by a single two-fold rotation axis (or a mirror plane). Thus, it matches with symmetry element [1].
- Rhombohedral System [S]: The defining symmetry feature of the rhombohedral (trigonal) system is a principal three-fold rotation axis. This corresponds to symmetry element [2].
Final Matching
Combining the matches gives us the following correspondence:
- P corresponds to [4]
- Q corresponds to [3]
- R corresponds to [1]
- S corresponds to [2]
This pairing (P-4, Q-3, R-1, S-2) matches Option 4.
Important Questions from Crystallography Stereographic Projection
- Residual stress present in a material can be determined by which one of the following techniques:
A schematic of X-ray diffraction pattern of a single phase cubic polycrystal is given below. The miller indices of peak A is
In a powder diffraction experiment on BCC iron, the first peak occurs at $2\theta = 68.7^\circ$. The wavelength of X-rays is ________ (in nm to three decimal places).
Given: The lattice parameter of iron = $0.287 \text{ nm}$
- For an FCC metal, the ratio of interplanar spacing obtained from the first two peaks of the X-ray diffraction pattern is
X-ray diffraction pattern from an elemental metal with a FCC crystal structure shows the first peak at a Bragg angle $\theta = 24.65^\circ$. The lattice parameter of this metal is ____________ nm.
Given, wavelength of the X-ray used is $0.1543$ nm.
