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Thermodynamics

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Unit Cell Space Lattice

The periodicity of the structure of a crystal is a fundamental feature. Fig. represents a two dimensional pattern of a crystal. A unit cluster of atoms is represented by a dot and two open circles. The parallelogram ABCD is represented with the help of the vectors a and b. By this process, the whole pattern of the crystal structure can be obtained. In this case ABCD forms the unit cell. The areas of all unit cells are equal. Normally, a unit cell is chosen so that the parallelogram has the shortest possible sides. Here,

l = n₁a + n₂b

Similarly, for a three dimensional crystal structure, the distribution of atoms in a unit cell is represented by three vectors a, b and c. The constituent particles in a crystal are represented by points, this representation is called space lattice or crystal describe the whole pattern. This type of three dimensional group of points is known as a, b, c measured along the three edges of the unit cell. The angles give the angles between the pair of edges (b, c), (c, a), and (a, b) respectively.

Thus, a space lattice is defined as an indefinite number of points in space, satisfying the condition that the arrangement of points about a given point is identical with that about any other point.

For a three dimensional crystal structure the lattice vector is given by

l = n₁a + n₂b + n₃c

Here n1, n₂ and n₃ are integers. The complex crystal structure can be obtained by stepwise shifting of the unit cells in all the three directions. Construction of a crystal with the help of unit cells is similar to the construction of a wall with the help of the bricks.