## Face Centred Cubic Unit Cell – Class 12 | Chapter – 1 | Chemistry Short Notes Series PDF for NEET & JEE

Face Centred Cubic Unit Cell: The face centred cubic unit cell is a type of unit cell that is characterized by a cubic lattice with atoms located at each corner of the cube and at the center of each face. In other words, an FCC unit cell contains one lattice point or one atom at each of its eight corners and an additional atom at the center of each of its six faces. Therefore, the number of atoms in an face centred cubic unit cell is equal to four.

The edge length (a) of an FCC unit cell can be determined using the relationship between the lattice constant (a) and the atomic radius (r) of the atoms in the crystal. In an FCC unit cell, the distance between two adjacent lattice points (or the edge length of the unit cell) is equal to 2√2 times the atomic radius. Therefore, the edge length (a) of an FCC unit cell can be expressed as:

a = 2√2∙r

The coordination number of the atoms in an FCC lattice is equal to 12, as each atom is in contact with 12 neighboring atoms. The packing fraction of an FCC lattice is relatively high, at around 0.74, meaning that there is relatively little empty space in the lattice.

Examples of materials that have an FCC lattice include copper, aluminum, gold, and silver. The FCC unit cell is also a useful model for understanding more complex crystal structures, as it provides a simple and easy-to-understand example of a crystal lattice with atoms located at both the corners and the faces of the cube.

## Properties of Face Centred Cubic Unit Cell

Some of the key properties of the face centred cubic unit cell are:

• Coordination Number: The coordination number of the atoms in an face centred cubic unit cell lattice is 12, which is higher than the coordination number in the primitive cubic and body-centered cubic lattices. This results in a more closely packed structure and higher density.
• Packing Fraction: The packing fraction of an FCC lattice is relatively high, at around 0.74. This means that there is relatively little empty space in the lattice, and the atoms are more closely packed together than in the primitive cubic or body-centered cubic lattices.
• Density: The FCC lattice has a higher density compared to the primitive cubic and body-centered cubic lattices, as there are more atoms per unit cell. This makes it a useful structure for materials that require high density, such as metals.
• Mechanical Properties: Materials that have an FCC structure tend to have high ductility and toughness, making them useful in applications where strength and toughness are important. FCC metals also tend to be good conductors of electricity and heat.
• Thermal Expansion: FCC materials tend to have a relatively low coefficient of thermal expansion, which means that they are less likely to expand or contract significantly with changes in temperature. This property can be useful in applications where dimensional stability is important.
• Optical Properties: Some materials that have an FCC structure, such as gold and silver, exhibit unique optical properties, such as strong reflection and absorption of certain wavelengths of light. This makes them useful in applications such as jewelry and electronics.

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