Define the following terms in relation to crystal structure: (i) Crystalline, Polycrystalline and amorphous state of matter. (ii) Lattice, basis and crystal structure.

A crystalline material is one of the primary types of solid matter where atoms are arranged in a highly organized, repeating pattern. This long-range order means the atomic structure extends uniformly in all three dimensions. Crystalline materials, such as diamonds and quartz, have distinct and sharp melting points because their atoms are held together in a specific geometric lattice.
Examples of crystalline structures include:

• Salt (sodium chloride) - where the atoms are arranged in a cubic lattice.
• Diamond - with a tetrahedral lattice structure formed by carbon atoms.

Understanding crystalline structures is crucial for fields like material science and solid-state physics because the properties of these materials, such as strength, conductivity, and transparency, are strongly influenced by their atomic arrangement.

Polycrystalline materials consist of many small crystalline regions called grains. Each grain is a crystal with its own orientation, but the overall material does not have a uniform structure. The boundaries between these grains are known as grain boundaries.
Polycrystalline materials are very common in everyday materials, such as:

• Metals (e.g., steel and aluminum) - which have irregular grain boundaries affecting their mechanical properties.
• Ceramics - used in various industrial applications due to their durability.

Grains can vary in size, and controlling grain size can influence the material's properties. For example, smaller grains can lead to harder and stronger materials. The random orientation of grains in polycrystalline materials typically makes them less directionally dependent compared to single crystals.

In an amorphous state, atoms or molecules are arranged in a disordered manner without a long-range repeating pattern. Unlike crystalline and polycrystalline materials, amorphous materials do not have a well-defined structure, which means they lack a definite shape and fixed melting point.
Common examples of amorphous materials include:

• Glass - used in windows and bottles.
• Plastics - utilized in countless everyday items.

Amorphous materials often form when a liquid cools too quickly for the atoms to arrange themselves into a crystalline structure. This rapid cooling is known as quenching. The lack of a long-range order in these materials makes them unique and useful in applications that require flexibility or transparency.

A lattice in a crystal structure is a regular, repeating arrangement of points in three-dimensional space. These points represent the positions of atoms, ions, or molecules within the crystal. The concept of a lattice is foundational in understanding how crystals form and maintain their structure.
Key characteristics of a lattice include:

• Periodicity - the repeated pattern over defined intervals.
• Symmetry - the consistent relationship between lattice points.
• Unit Cell - the smallest repeating unit that can be used to build the entire lattice by translation.

For instance, in a simple cubic lattice, every point has the same surroundings, forming a symmetrical, repeating cubic structure. By translating this unit cell along its edges, the whole lattice can be constructed.
The lattice plays a critical role in determining the physical properties of crystalline materials, such as their mechanical strength and electrical conductivity.

The basis is a group of atoms associated with each point on the lattice. It can consist of a single atom, a molecule, or a group of atoms. The combination of the basis and the lattice is what forms the actual structure of the crystal.
Important points to remember about the basis:

• Different crystals can have the same lattice but different bases, resulting in different structures.
• The basis is repeated throughout the entire crystal, maintaining the periodicity of the lattice.

For example, in a crystal structure like sodium chloride (table salt), the lattice might be simple cubic, but the basis consists of a sodium atom and a chlorine atom at specific positions. When this basis is repeated at each lattice point, the structure representing sodium chloride is created.
Understanding the basis helps in predicting the properties and behavior of different materials because the atomic arrangement influences how the material interacts with external forces and conditions.

A crystal structure is the combination of a lattice and a basis. It represents the ordered arrangement of atoms in a crystalline material. The crystal structure determines many of the material's properties, such as its density, thermal and electrical conductivity, and even its optical properties.
Examples of different crystal structures include:

• Face-Centered Cubic (FCC) - found in metals like aluminum and copper.
• Body-Centered Cubic (BCC) - seen in iron and chromium.
• Hexagonal Close-Packed (HCP) - seen in metals like magnesium and titanium.

The study of crystal structures helps scientists and engineers develop new materials with specific properties for various applications, such as semiconductors for electronics or superhard materials for cutting tools.
By understanding and manipulating the lattice and basis of materials, new innovations and enhancements in technology can be achieved.