This document discusses the crystalline structure of materials and symmetry elements in crystals. It defines a crystal as a solid with atoms, molecules, or ions arranged in a highly ordered microscopic structure called a lattice. Crystals can be isotropic, with uniform properties in all directions, or anisotropic, with properties that vary by orientation. The flat surfaces that bound a crystal are called faces. Crystals exhibit symmetry through repetitive patterns of atomic arrangement. There are three types of symmetry elements: planes of symmetry that divide the crystal into mirror images, axes of symmetry where rotation around the axis presents the same appearance multiple times, and centers of symmetry at the crystal's center point.

1. Dr Shelma R
Assistant Professor
KSMDB College, Sasthamcotta

2. Crystalline state
 A crystal or crystalline solid is a solid material
whose constituents, such as atoms, molecules or ions,
are arranged in a highly ordered microscopic structure,
forming a crystal lattice that extends in all directions.

3. Isotropy and anisotropy
 Iso means same and tropic means direction
 when the properties of a material are the same in all
directions, the material is said to be isotropic
 When the properties of a material vary with different
crystallographic orientations, the material is said to
be anisotropic.

5. External features of crystal
 Face: crystal face One of the relatively flat surfaces by
which a crystal is bounded.
Like face Unlike face

6. Symmetry
 When the faces of a crystal can be arranged in a
repetitive and regular pattern around the center of the
crystal, the crystal has symmetry
 Crystals have an ordered internal arrangement of
atoms. This ordered arrangement shows symmetry
 The atoms are arranged in a symmetrical fashion on a
three dimensional network referred to as a lattice.

7. Elements of symmetry:
 A geometrical entity such as a line (or axis),a plane or a
point with respect to which one or more symmetry
operations may be carried out is called a symmetry
element.
 A crystal possess following three types of symmetry
 Plane of symmetry, axis of symmetry and centre of
symmetry

8. Plane of symmetry
 It is an imaginary plane which passes through the
centre of a crystal can divides it into two equal
portions which are exactly the mirror images of each
other.

9. Axis of symmetry
 An axis of symmetry or axis of rotation is an imaginary line,
passing through the crystal such that when the crystal is
rotated about this line, it presents the same appearance
more than once in one complete revolution i.e., in a
rotation through 360°.
 Suppose, the same appearance of crystal is repeated, on
rotating it through an angle of 360°/n, around an
imaginary axis, is called an n-fold axis where, n is known as
the order of axis. By order is meant the value of n in so that
rotation through gives an equivalent configuration.

10. Thank You......