Model Answer
0 min readIntroduction
Crystallography, the science of crystals, relies heavily on understanding the symmetry inherent within their structures. Symmetry elements are geometric operations (rotation, reflection, inversion, glide planes, screw axes) that, when applied to a crystal, leave it unchanged. These elements dictate the external forms a crystal can exhibit. The orthorhombic crystal system, one of the seven crystal systems, is characterized by three unequal axes, all intersecting at right angles. Within this system, different classes exist based on the presence or absence of specific symmetry elements. The ‘normal’ class, also known as the mmc class, is a fundamental class within the orthorhombic system, and understanding its symmetry and forms is essential for mineral identification and classification.
Orthorhombic System and Symmetry Elements
The orthorhombic system is defined by three unequal crystallographic axes (a ≠ b ≠ c) that are mutually perpendicular. This leads to a rectangular prism as the general crystal shape. The symmetry elements present determine the specific class within the orthorhombic system. The normal class (mmc) is characterized by the following symmetry elements:
- Three mutually perpendicular twofold rotation axes (2): These axes are parallel to the crystallographic axes (a, b, and c).
- Three perpendicular mirror planes (m): These planes are perpendicular bisectors of the crystallographic axes.
- A center of symmetry (i): A point within the crystal such that any line drawn through the point intersects the crystal surface at two points equidistant from the center.
Symmetry Elements – Sketches
Below are sketches illustrating the symmetry elements of the normal class of the orthorhombic system:
Figure: Illustration of symmetry elements in the normal class of the orthorhombic system. (a) Twofold rotation axis, (b) Mirror plane, (c) Center of symmetry.
Forms of the Normal Class (mmc)
The combination of these symmetry elements results in a variety of possible crystal forms. Some of the common forms include:
- Pinacoid {hk0}: These are forms parallel to the c-axis, resulting from mirror planes perpendicular to the c-axis.
- Prism {hkl}: These are forms parallel to the c-axis, but not necessarily perpendicular to other axes.
- Pyramid {hkl}: Forms that intersect the c-axis at an angle.
- Scalenohedron {hkl}: Forms with faces that are not parallel to any crystallographic axis.
Illustrative Sketches of Common Forms
Figure: Common crystal forms observed in the normal class of the orthorhombic system. (a) Pinacoid, (b) Prism, (c) Pyramid.
Minerals of the Normal Class (mmc)
Several minerals crystallize in the normal class of the orthorhombic system. Three examples are:
- Barite (BaSO4): Commonly forms tabular crystals with well-developed pinacoids and prisms.
- Celestite (SrSO4): Similar to barite in appearance, often forming elongated prismatic crystals.
- Stibnite (Sb2S3): Forms prismatic or acicular (needle-like) crystals, often with a metallic luster.
The symmetry of these minerals dictates their cleavage, habit, and other physical properties, aiding in their identification.
Conclusion
In conclusion, the normal class of the orthorhombic system is defined by its three twofold rotation axes, three mirror planes, and a center of symmetry. These elements lead to a variety of crystal forms, including pinacoids, prisms, and pyramids. Minerals like barite, celestite, and stibnite exemplify this class, showcasing the importance of symmetry in understanding mineral structures and properties. A thorough understanding of crystal symmetry is fundamental to the field of mineralogy and geology, enabling accurate mineral identification and interpretation of geological processes.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.