1. 1 Crystals possess different symmetry elements. The definite ordered arrangement of the faces and edges of a crystal is known as `crystal symmetry’. CRYSTAL SYMMETRY

2. 2 WHAT IS A SYMMETRY OPERATION ? A `symmetry operation’ is an operation performed on an object which brings it to a position which is absolutely indistinguishable from the old position.

3. 3 The seven crystal systems are characterized by three symmetry elements. They are Centre of symmetry Planes of symmetry Axes of symmetry.

4. 4 CENTRE OF SYMMETRY It is a point such that any line drawn through it will meet the surface of the crystal at equal distances on either side. Since centre lies at equal distances from various symmetrical positions it is also known as `centre of inversions’.

5. 5 CENTRE OF SYMMETRY

6. 6 PLANE OF SYMMETRY A crystal is said to have a plane of symmetry, when it is divided by an imaginary plane into two halves, such that one is the mirror image of the other. In the case of a cube, there are three planes of symmetry parallel to the faces of the cube and six diagonal planes of symmetry

7. 7 PLANE OF SYMMETRY 3 plane of symmetry parallel to the plane 6 diagonal plane of symmetry

8. This is an axis passing through the crystal such that if the crystal is rotated around it through some angle, the crystal remains invariant. If n=1, the crystal has to be rotated through an angle = 360º, about an axis to achieve self coincidence. Such an axis is called an `identity axis’. If n=2, the crystal has to be rotated through an angle = 180º about an axis to achieve self coincidence. Such an axis is called a `diad axis’.Since there are 12 such edges in a cube, the number of diad axes is six. If n=3, the crystal has to be rotated through an angle = 120º about an axis to achieve self coincidence. Such an axis is called is `triad axis’. In a cube, the axis passing through a solid diagonal acts as a triad axis. Since there are 4 solid diagonals in a cube, the number of triad axis is four. If n=4, for every 90º rotation, coincidence is achieved and the axis is termed `tetrad axis’. a cube has `three’ tetrad axes. AXIS OF SYMMETRY 8

9. 9 SYMMETRICAL AXES OF CUBE Tetrad axis = 3 Diad axis = 6 Triad axis = 4

10. 10 SYMMETRICAL ELEMENTS OF CUBE (a) Centre of symmetry 1 (b) Planes of symmetry 9 (Straight planes -3,Diagonal planes -6) (c) Diad axes 6 (d) Triad axes 4 (e) Tetrad axes 3 ---- Total number of symmetry elements = 23 ---- Thus the total number of symmetry elements of a cubic structure is 23.