BGYCT-133 Solved Assignment 2024
PartA
Answer:
a) Crystallographic axis
Crystallographic axes are imaginary lines used to describe the geometric arrangement of atoms in a crystal lattice. These axes are essential for defining the crystal structure and understanding its properties. In a crystal, atoms are arranged in a repeating pattern, and the crystallographic axes help define the unit cell, which is the smallest repeating unit of the crystal lattice.
There are typically three crystallographic axes, labeled as a, b, and c, which are mutually perpendicular. These axes intersect at a point called the origin, which is often chosen to be the center of the unit cell. Each axis represents a direction in three-dimensional space. The length of these axes, represented by a, b, and c, defines the dimensions of the unit cell.
The orientation of these axes is described by angles between them, known as the axial angles. In most crystal systems, these angles are 90 degrees, indicating orthogonal axes. However, in some crystal systems, such as the tetragonal and hexagonal systems, one or more angles are not 90 degrees.
The crystallographic axes are crucial for understanding the symmetry and properties of crystals. They help determine the symmetry elements present in the crystal lattice, such as mirror planes, rotation axes, and inversion centers. These symmetry elements influence various physical and optical properties of crystals, including their diffraction patterns, birefringence, and thermal conductivity.
Crystallographic axes are also used to define the Miller indices, which are used to describe crystallographic planes and directions within the crystal lattice. The Miller indices provide a systematic way to describe the orientation of planes and directions relative to the crystallographic axes.
In conclusion, crystallographic axes are fundamental to the study of crystallography, providing a framework for describing the arrangement of atoms in a crystal lattice. They play a crucial role in determining the symmetry, properties, and behavior of crystals, making them essential concepts in materials science, geology, and other fields.
b) Interfacial Angles and its measurement
Interfacial angles are the angles between crystal faces in a crystal lattice. These angles are crucial in crystallography as they help identify and classify crystals based on their symmetry and structure. The measurement of interfacial angles is essential for determining the crystal system and lattice parameters of a crystal.
To measure interfacial angles, a goniometer is typically used. A goniometer is a specialized instrument consisting of a rotating stage and a microscope. The crystal face of interest is positioned on the stage, and the microscope is used to align the edges of the crystal face with crosshairs. The stage is then rotated to align the crystal face with a reference axis, and the angle of rotation is read off a scale on the goniometer.
The measurement of interfacial angles is based on the principle of crystallographic symmetry. In crystals, the orientation of crystal faces is determined by the arrangement of atoms within the crystal lattice. The symmetry of the crystal lattice dictates the angles between crystal faces, which can be used to identify the crystal system and space group of a crystal.
Interfacial angles can also be measured using X-ray diffraction. X-ray diffraction is a powerful technique used to study the structure of crystalline materials. When X-rays are incident on a crystal, they are diffracted by the crystal lattice, producing a diffraction pattern. The angles of the diffraction peaks in the pattern can be used to determine the interplanar spacing and interfacial angles of the crystal lattice.
In conclusion, interfacial angles are important in crystallography for characterizing the structure and symmetry of crystals. The measurement of interfacial angles using a goniometer or X-ray diffraction is essential for determining the crystal system, space group, and lattice parameters of a crystal. This information is valuable in understanding the properties and behavior of crystalline materials in various applications.