Crystal Geometry and crystal structure.

Crystal Geometry and Crystal structure:

Crystal Geometry includes different factors which help to find the crystal system and crystal structure. Crystal Geometry is the combination of Crystal, Lattice, Basis, Crystal System and Crystal Structure.
Crystal geometry is used to find the behavior of materials and there is a lot of properties depending upon the crystal structures.
To know about the Crystal system and Crystal structure there is a basic thing to understand is Lattice.
Lattice:
Lattice is a 3-D Periodic arrangement of the points in the space. and it is used to find geometrical properties.
Lattice is introduced by Bravais.
Depending upon the arrangement of lattice points they are divided.
Crystal:
Crystal is the Arrangement of 'ATOMS' in 3-D periodically.
For 2-D Lattice, it should have translation simulation property.
For 3-d Lattice, it should have an infinite regularly spaced array of points.
In order to obtain the crystal structure and material, the addition of atoms or ions in the lattice point leads to generating a crystal structure.
             Crystal = Basis + Lattice.

Based on the space filling arrangement 7 types of crystal system and 14 types of crystal structures are obtained.

7types of Crystal Systems:

1) Cube:

In this system all axis are equal and all angles are equal.
i.e,Axis  a=b=c and Angles Q=R=S.

2) Tetragonal:

In this system, two axis are equal (a=b) but b is not equal to c.

3) Orthohombic:

In this system, All axis are unequal (a#b#c).
and All angles are 90 degrees.

4) Rhombohedral:

In this system, all axis are equal (a=b=c). but all angles are not equal to 90 degrees.

5) Hexagonal:

In this system, a=b but b is not equal to c and both q and r angles are equal to 90 degrees but s=120 degrees.

6) Mono-clinic:

In this system, all angles are unequal and q,s angles are equal to 90 degrees but s is not equal to 90 degrees.

7) Tri-clinic: 

In this system all angles unequal and all axis are unequal.
By placing the lattice points on the different places on crystal system we can obtain 14 types of crystal structures.

14 Types of Crystal Structures:

1) Cube:

We can arrange 3 different places on crystal structure of cube. they are
1) Simple Cube.  2) Face-Centered Cube.  and 3) Body Centered Cube.

2) Tetragonal:

We can arrange 2 different places on tetragonal crystal structure. they are 1) Simple Tetragonal  and 2) Body-centered tetragonal.

3) Orthohombic:

We can arrange 4 different places on the Orthorhombic crystal structure. they are 1) Simple Orthorhombic  2) Body-Centered Orthorhombic  3) Base Centered Orthohombic and  4) Face-Centered Orthorhombic.

4) Rhombohedral:

There are only one type of Rhombohedral arrangement is possible in crystal structure.

5) Hexagonal:

There is only one type of Hexagonal arrangement is possible in crystal structure.

6) Mono-clinic:

There are two types of mono-clinic arrangement is possible in crystal structure. they are 1) Simple Mono-clinic and  2) Base Centered mono-clinic.

7) Tri-clinic:

There is only one type of tri-clinic arrangement is possible in crystal structure.