MONOCHROMATIC AND POLYCHROMATIC DIFFRACTION

1. MONOCHROMATIC AND POLYCHROMATIC DIFFRACTION

2. CONRAD RÖNTGEN, X-RAYS and MAX von LAUE

3. Constructive interference Destructive interference WAVES, INTERFERENCE, and all that

4. HUYGENS’ PRINCIPLE

6. PATH DIFFERENCE & SCATTERING ANGLE WITH SLITS

7. LATTICE PLANES IN A 3D CRYSTAL Bragg described diffraction as ‘reflection’ from a set of planes. These planes are parallel, equally spaced planes, drawn through lattice points, or fractionally between planes of lattice points. (2,3,3) lattice planes (x,y,z) Lattice planes are given indices hkl, for the number of intersections they make along each axis between lattice points.

8. The directions in which X-rays are scattered from a set of planes depends on: (1) the wavelength of the rays, (2) the angle at which they hit the crystal, (3) the spacing of atoms within the crystal lattice BRAGG’S LAW: 2d sin  = n Incoming wave front Reflected wave front 2d sin  = n 1/2 path difference Bragg's law allows one to calculate details about the crystal structure, or if the crystal structure is known, to determine the wavelength of the x-rays incident upon the crystal.

9. BRAGG’S LAW Bragg assumed that diffracted X-rays would interfere constructively (that is, form a reflection) only if they traveled distances that differ by an integral number of wavelengths

10. RELATIVE INTENSITY OF SCATTERED RADIATION Atoms lying on Bragg planes hkl contribute to reflection hkl. If planes hkl are densely occupied with atoms, the hkl reflection is intense, unless there are atoms on planes midway between.

11. Rotation X-ray photograph of a crystal of RuBisCO EACH SPOT ON THIS FILM IS PRODUCED BY X-RAYS REFLECTED FROM A PARTICULAR SET OF LATTICE PLANES

12. 3,1 The set of points so determined constitutes the RECIPROCAL LATTICE 2,1 1,1 0,1 1/d3,1 1/d2,1 1/d1,1 1/d0,1 d1,1 d2,1 Consider normals to all possible direct lattice planes (hkl) to radiate from some lattice point taken as the origin (O). Terminate each normal at a point at a distance 1/dhkl from this origin. THE RECIPROCAL LATTICE CAN BE DEFINED AS FOLLOWS: Each POINT in the RECIPROCAL LATTICE corresponds to a family of LINES/PLANES in the direct lattice 0,1 d0,1 O 1,1 3,1 2,1

13. Rotation X-ray photograph of a crystal of RuBisCO EACH SPOT ON THIS FILM IS PRODUCED BY X-RAYS REFLECTED FROM A PARTICULAR SET OF LATTICE PLANES

14. DIFFRACTION IN TERMS OF THE RECIPROCAL LATTICE: EWALD’S CONSTRUCTION (2) As the lattice rotates about (000) various reciprocal lattice points (hkl) pass through the surface of the sphere. P (1/dhkl) (1) The origin of the reciprocal lattice (000) is fixed at the point where X-rays exit the sphere. Draw a sphere with radius = 1/ as shown on the left B O sin OBP = sin  = OP/OB = OP/(2 /) sin  = d*/(2/) = d* /2 Since P is a reciprocal lattice point, the length of OP is by definition d* (i.e.1/ dhkl) (3) Whenever that happens, conditions are met which satisfy Bragg's Law: From the above diagram, sin  = d*/(2/) = d* /2, and because P is a reciprocal lattice point by definition, d* =1/d, the expression is identical to the form: 2d sin  = .

15. EWALD’S SPHERE AND DIFFRACTION

16. The EWALD SPHERE of reflection relates crystal space with diffraction space (or reciprocal space)

18. EWALD’S CONSTRUCTION (2) As the lattice rotates about (000) various reciprocal lattice points (hkl) pass through the surface of the sphere. (1) The origin of the reciprocal lattice (000) is fixed at the point where X-rays exit the sphere. (3) Whenever that happens, conditions are met which satisfy Bragg's Law: From the above diagram, sin  = d*/(2/) = d* /2, and because d* =1/d, the expression is identical to the form: 2d sin  = .

19. THE END (FOR THE MOMENT)

20. REAL AND RECIPROCAL LATTICE

21. DIFFRACTION IS CENTROSYMMETRIC

22. RECIPROCAL LATTICE (100)

23. POLYCHROMATIC OR LAUE DIFFRACTION