Crystal lattice, unit cell, types of crystal systems

A crystal lattice is a three-dimensional arrangement of points that represent the positions of particles (atoms, ions, or molecules) in a crystalline solid.
Each point in the lattice is called a lattice point.
The crystal lattice depicts the geometric arrangement of particles in space.
The regular and repeating pattern of the lattice gives crystals their characteristic shape.
The smallest repeating unit in a lattice is called the unit cell.
There are two main types of lattices: Bravais lattices and non-Bravais lattices.
The Bravais lattices are classified into 14 distinct types, forming the foundation of crystalline structure studies.
Examples of crystal lattices include cubic lattice, hexagonal lattice, and tetragonal lattice.
Every crystal structure can be defined using its lattice and the positions of particles within the unit cell.
The concept of a crystal lattice is fundamental to understanding solid-state physics and materials science.

A unit cell is the smallest repeating structural unit of a crystal lattice.
It is defined by its dimensions along three edges (a, b, c) and the angles between them (α, β, γ).
There are three main types of unit cells: primitive, body-centered, and face-centered.
The primitive unit cell contains particles only at the corners of the cell.
In a body-centered unit cell, an additional particle is present at the center of the cell.
A face-centered unit cell has particles at the center of each face in addition to the corners.
The unit cell determines the overall density and symmetry of the crystal.
The arrangement of atoms within the unit cell is described by the basis of the crystal.
The concept of a unit cell is crucial for calculating properties like packing efficiency and coordination number.
Unit cells are used to define the boundaries of a crystal lattice and its repeating nature.

There are seven crystal systems, each with distinct lattice parameters and symmetry.
The crystal systems are: cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic.
Cubic system: All sides are equal (a = b = c) with angles of 90° (e.g., NaCl, diamond).
Tetragonal system: Two sides are equal (a = b ≠ c) with angles of 90° (e.g., white tin).
Orthorhombic system: All sides are unequal (a ≠ b ≠ c) with angles of 90° (e.g., KNO₃).
Hexagonal system: Two sides are equal (a = b ≠ c) with angles of 120° and 90° (e.g., graphite, ZnO).
Trigonal (rhombohedral) system: All sides are equal (a = b = c), but angles are not 90° (e.g., calcite).
Monoclinic system: All sides are unequal (a ≠ b ≠ c) with two angles of 90° and one angle not 90° (e.g., gypsum).
Triclinic system: All sides and angles are unequal (a ≠ b ≠ c, α ≠ β ≠ γ) (e.g., K₂Cr₂O₇).
Each system can be further divided into Bravais lattices, resulting in 14 possible structures.
The symmetry and geometry of each system influence the material's physical properties.
Crystallography uses these systems to classify and study materials at the atomic level.

A crystal lattice is a three-dimensional arrangement of points representing particles in a crystalline solid.
A unit cell is the smallest repeating unit in a lattice, defined by its dimensions and angles.
The Bravais lattices classify crystal structures into 14 distinct types.
The seven crystal systems are cubic, tetragonal, orthorhombic, hexagonal, trigonal, monoclinic, and triclinic.
Cubic crystals have equal sides and angles of 90° (e.g., NaCl).
Hexagonal crystals have two equal sides and an angle of 120° (e.g., graphite).
The arrangement of particles in the unit cell determines the density and symmetry of the material.
The coordination number and packing efficiency vary with the type of crystal lattice.
Crystallography studies are essential for understanding material properties like hardness, conductivity, and elasticity.
Knowledge of crystal systems is crucial for fields like mineralogy, materials science, and pharmaceuticals.