The Solid State

Space lattice or Crystal lattice and Unit Cell

A crystalline solid has a very special structure, that gives it the unique properties of a solid. This structure is made up of repeating units which we call a unit cell. Let us study this special lattice structure in detail.

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Crystal Lattice

As we have studied in the previous topic, solids are basically of two shapes. One is an amorphous solid which has no specific shape or structure. Another is a crystalline structure or crystals which have a specific organized structure of their particles. Let us take a look.

Crystals have a structure made up of a regular arrangement of their atoms (or particles). When such an arrangement of atoms is represented in a three-dimensional structure, this is a crystal lattice. So a lattice is an array of points in a particular order which describes the arrangement of particles of a crystalline solid.

Now Auguste Bravais was French scientist who found out that there are a total of fourteen possible three-dimensional lattices. These 14 arrangements are the Bravais Lattice. They have six basic shapes. The following diagram shows you the fourteen arrangements.

Crystal Lattice and unit Cell : Bravias Lattices

Characteristics of Crystal Lattice

The fourteen Bravais Lattices show some similar characteristics. These are

  • Each point on the lattice represents one particle of the crystal, This is a lattice point.
  • This particular particle may be an atom, a molecule or even ions
  • These lattice points of a crystal are joined together by straight lines.
  • By joining of these points we get the geometry (or shape) of the crystal
  • Every one of the fourteen lattices has such a unique geometry

solid state

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Unit Cell

A unit cell is the most basic and least volume consuming repeating structure of any solid. It is used to visually simplify the crystalline patterns solids arrange themselves in. The entire of the space lattice is built by the repeating arrangement of unit cells. A unit cell is a geometric shape even by itself. It has three edges. And these three edges form three respective angles. The edges of a unit cell are as follows

  • A: edges defined by lattice vectors b and c
  • B: edges defined by lattice vectors a and c
  • C: edges defined by lattice vectors a and b

The interfacial angles of the unit cell are as follows:

  • α: the angle between edges b and c
  • β: angle between edges a and c
  • γ: angle between edges a and b

Primitive Unit Cells

A primitive unit cell only has atoms, molecules or ions at the corners of the lattice. There are no particles located at any other position in a primitive unit cell. So essentially primitive unit cell has only one lattice point.

Non-Primitive Unit Cells

In this type of unit cell, there are particles not only at the corners of the lattice but in other positions as well. These additional constituent particles are either on the face of the unit cell or inside the unit cell. So there is more than one lattice point in a non-primitive unit cell. There are actually three types of non-primitive unit cells, namely:

  • Body Centered: It has one particle at the center of the body. Other particles (one or more) are at the corner of the lattice
  • Face Centered: This contains particles on every face of the lattice and other particles on the corners
  • End Centered: Has particles at the corners and one particle at the center of the opposite faces.

Solved Question for You

Q: How many kinds of space lattices are possible in a crystal?

  1. 14
  2. 29
  3. 08
  4. 24

Ans: The correct option is “A”. There are fourteen types of lattices possible in a crystal. These are known as Bravias Lattices.

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