Hexagonal Crystal System Unit Cell Parameters Explained
The hexagonal crystal system is defined by specific relationships between its unit cell edge lengths and interaxial angles.
Defining Hexagonal Lattice Parameters
- Axes Lengths: In the hexagonal system, two of the unit cell axes lying in the basal plane are equal in length, while the third axis, perpendicular to the basal plane, has a different length. This is represented as: $a = b \neq c$
- Interaxial Angles: The angles between the unit cell axes are also specific. The angles between the axes in the basal plane are not 90 degrees, but rather 120 degrees. The angles involving the axis perpendicular to the basal plane are 90 degrees. This is represented as: $\alpha = \beta = 90^\circ, \gamma = 120^\circ$
Correct Parameter Combination
Combining these conditions, the unit cell parameters for the hexagonal crystal system are:
$a = b \neq c$ and $\alpha = \beta = 90^\circ, \gamma = 120^\circ$
This combination corresponds to Option 2.
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