# Difference Between Hexagon and Monoclinic Unit Cell

## Main Difference – Hexagon vs Monoclinic Unit Cell

The terms hexagon and monoclinic unit cell are related to crystal systems. A crystal system is each of seven categories of crystals (cubic, tetragonal, orthorhombic, trigonal, hexagonal, monoclinic, and triclinic) classified according to the possible relations of the crystal axes. The unit cell of a crystal system is a portion of the structure which represents the repeating pattern of the crystal system. It is composed of representative atoms and the repeating arrangement of those atoms. The unit cell is a 3D structure, and each and every crystal system has their own unique unit cell structures. A unit cell is a box. It contains atoms arranged in different unique patterns. This unit cell is described with respect to the lattice parameters, which are lengths between the edges of the unit cell and the angles. The main difference between hexagon and monoclinic unit cell is that two of the three axes of a hexagon unit cell have similar length whereas monoclinic unit cell has three axes with unequal lengths.

### Key Areas Covered

1. What is a Unit Cell
– Explanation
2. What is Hexagon Unit Cell
– Definition, Structure, Unique Features
3. What is Monoclinic Unit Cell
– Definition, Structure, Unique Features
4. What is the Difference Between Hexagon and Monoclinic Unit Cell
– Comparison of Key Differences

Key Terms: Crystal System, Hexagon, Lattice Parameters, Monoclinic, Unit Cell

## What is a Unit Cell

A unit cell is a small structure that represents the repeating pattern of a crystal system. It is a box-structure. This box contains all types of atoms that are present in the material. This is a 3D structure. The unit cell is described using lattice parameters. A lattice is a regular repeated three-dimensional arrangement of atoms, ions, or molecules in a metal or other crystalline solid. Lattice parameters are lengths between edges of the unit cell and the angles. Lengths (also called axes) are given by the symbols a, b and c whereas angles are given by alpha(α), beta(β) and gamma(γ).

Figure 1: Lattice Parameters of a Unit Cell

The positions of the atoms inside the cell are described by atomic positions given by X, Y and Z. These points are measured from a reference lattice structure.

## What is Hexagon Unit Cell

Hexagon unit cell is the unit cell of a hexagonal crystal system. It represents the arrangement of atoms in a material with a hexagon crystal structure.  It has two axes with a similar length and one axis with a different length. This axis is perpendicular to other two axes. The angle between two similar axes is 120o.

Figure 2: A Hexagon Unit Cell

In brief, the specific features of hexagon unit cell are;

• a=b≠c
• α= β=90o
• γ=120o.

## What is a Monoclinic Unit Cell

A monoclinic unit cell is the unit cell of monoclinic crystal system. It represents the arrangement of atoms in a material having monoclinic structure. The three axes of the unit cell (a, b and c) are unequal. The monoclinic unit has a rectangular shape with a parallelogram as its base. A parallelogram is a simple structure with two pairs of parallel sides. Therefore, two axes meet each other at 90o angles.

Figure 3: A Monoclinic Unit Cell

In brief, the specific features of hexagon unit cell are:

• a≠b≠c
• α= γ =90o
• β≠90o

## Difference Between Hexagon and Monoclinic Unit Cell

### Definition

Hexagon Unit Cell: Hexagon unit cell is the unit cell of hexagonal crystal system.

Monoclinic Unit Cell: Monoclinic unit cell is the unit cell of monoclinic crystal system.

### Length of Axes

Hexagon Unit Cell: The hexagon unit cell has two axes with similar length and one axis with a different length (a=b≠c).

Monoclinic Unit Cell: The monoclinic unit cell has three axes with unequal lengths (a≠b≠c).

### Angles

Hexagon Unit Cell: The hexagon unit cell has α and β angles equal to 90° and γ equal to 120°.

Monoclinic Unit Cell: The monoclinic unit cell has α and γ angles equal to 90° and β is not equal to 90°.

### Presence of a Parallelogram

Hexagon Unit Cell: Hexagon unit cell has no parallelogram structure in the unit cell.

Monoclinic Unit Cell: Monoclinic unit cell has a parallelogram structure as the base of the unit cell.

### Conclusion

Hexagon and monoclinic unit cells are portions of crystal systems that represent a repeating pattern of the atomic arrangement of a crystal system. The main difference between hexagon and monoclinic unit cell is that a hexagon unit cell has two axes with similar length whereas a monoclinic unit cell has three axes with unequal lengths.

##### References:

1. “Hexagonal crystal family.” Wikipedia, Wikimedia Foundation, 16 Dec. 2017, Available here.
2. “Monoclinic crystal system.” Wikipedia, Wikimedia Foundation, 10 Dec. 2017, Available here.

##### Image Courtesy:

1. “UnitCell” By Mcpazzo – Own work (Public Domain) via Commons Wikimedia
2. “Hexagonal latticeFRONT” By Bor75 – Own work (CC BY-SA 3.0) via Commons Wikimedia
3. “Monoclinic cell” By Monoclinic.png: en: User: Mahleritederivative work: Fred the Oyster – Monoclinic.png (CC BY-SA 3.0) via Commons Wikimedia