X ray crystallography

1. X- Ray Crystallography

2. Elements of Symmetry

3. Symmetry
The term symmetry is derived from the Greek word “symmetria” which means
“measured together”. An object is symmetric if one part (e.g. one side) of it is the
same as all of the other parts. All nature is in symmetry.

4. Elements of Symmetry
A Symmetry element (imaginary line/axis) is a point of
reference about which symmetry operations (rotation of
molecule through this point of reference) can take place
that generates the same representation of an object.
It tells us about the external shape of a crystal.
Types of elements of symmetry:
• Centre of Symmetry
• Plane of symmetry
• Rotation axis of symmetry
• Rotation-Reflection axis of symmetry
• Rotation-Inversion axis of symmetry

5. Centre of Symmetry
It is a point such that any line drawn through it will met at surface of cube at
equal distance on either side. For unit cell, the point of body center represents
the center of Symmetry.

6. Plane of symmetry
A cube is set to have a plane of symmetry when it is divided by
an imaginary plane in to two halves such one is the mirror
image of the other.

7. Rotation axis of symmetry
This is an axis’s passing through cube such that if the cube is
rotated around it through some angle the crystal remains
unchanged.

8. Rotation-Reflection axis of symmetry

9. Rotation-Inversion axis of symmetry

10. Space Lattice and Unit cell
The regular arrangement of points (i.e. Ions, atoms or molecules) constituting the crystal in
Three dimensional space within the crystal is called the space lattice or crystal lattice.
The smallest portion of the complete space lattice which has all the elements of symmetry and
which when repeated over and again in different directions produces the complete space lattice
is called the Unit Cell.

11. Unit Cell
Bio-molecules are composed of monomer units which act as unit cells. Proteins are
composed of amino acids. Each and every amino acid in a protein represents a unit cell. By
combining all unit cells (amino acids) we get the structure of whole protein molecule.
amino acid
amino acid
amino acid

12. Crystal Systems & Bravais Lattice
Crystal system is a method of classifying
crystalline substances on the basis of their unit
cell.
There are seven unique crystal systems. The
simplest and most symmetric, the cubic (or
isometric) system, has the symmetry of a cube.
The other six systems, in order of decreasing
symmetry, are hexagonal, tetragonal, trigonal
(also known as rhombohedral), orthorhombic,
monoclinic and triclinic.

13. Crystal Systems
Crystal Systems Axial Character Angles
Cubic a=b=c α=β=λ=90ᵒ
Tetragonal a=b≠c α=β=λ=90ᵒ
Orthorhombic a≠b≠c α=β=λ=90ᵒ
Monoclinic a≠b≠c α=λ=90ᵒ≠β
Triclinic a≠b≠c α≠β≠λ≠90ᵒ
Hexagonal a=b≠c α=β=90ᵒλ=120ᵒ
Rhombohedral a=b=c α=β=90ᵒ≠λ

14. Bravais Lattice
Before it, we knew there are points
only at the corners of a crystal. But
Bravais discovered there are points
present at the center of faces or
within the body of unit.
1. Simple: When Points are present at
Corners of unit cell
2. Face-centred: in addition to points
at corners, when Points at the Centre
of each Face of unit cell
3. End-centred: in addition to points
at corners, when Points at the Centre
of the End Face of unit cell
4. Body-centred: in addition to points
at corners, there is one point present
within the body of each unit cell

18. X-Ray Crystallography
It is a method for studying the three-dimensional,
atomic structure of molecules.
Visible light (400-700 nm) cannot produce an
image of protein molecules, in which bonded atoms
are about 1.5Å apart (0.15 nm). Electromagnetic
radiation of this wavelength falls into the X-ray
range.

19. Bragg’s Law