X- ray crystallography

This presentation contains the introduction, generation of x- rays, Bragg's law of diffraction and the types of crystals.

1. Submitted to : Dr. Prema Kumari . K. B. Assistant Professor, Department of Pharmaceutics, COPS, DSU Banglore . Presented by: Arpitha B M M Pharm (I SEM), Department of Pharmaceutics, COPS, DSU Banglore . X- RAY CRYSTALLOGRAPHY

2. Contents Introduction Production of x- ray Bragg’s law Types of crystal Reference COPS DSU Department of Pharmaceutics 2

3. Introduction X-rays were discovered in 1895 by the German physicist W. C Roentgen He was awarded the Nobel prize for physics in 1901 . COPS DSU Department of Pharmaceutics 3 Wilhelm Conrad Röntgen (1845-1923)

4. X-RAY PROPERTIES X – ray invisible, highly penetrating ER of much shorter wavelength (higher frequency) than visible light. The wavelength range for x rays is from about 10 -8 m to about 10 -11 m, the corresponding frequency range is from about 3 × 10 16 Hz to about 3 × 10 19 Hz . COPS DSU Department of Pharmaceutics 4

5. GENERA TION OF X-RAYS X- rays are generated by following methods : By bombarding target element with a beam of high energy electrons. By irradiating metal target with primary beam of x- rays. By using a radioactive source whose decay causes emission of x rays. COPS DSU Department of Pharmaceutics 5

6. Absorption of X-rays A larger atom is more likely to absorb an X-ray photon , because larger atoms have greater energy differences between orbitals -- the energy level more closely matches the energy of the photon . Smaller atoms, where the electron orbitals are separated by relatively low jumps in energy, are less likely to absorb X-ray photons. The soft tissue in our body is composed of smaller atoms, and so does not absorb X-ray photons particularly well. The calcium atoms that make up our bones are much larger , so they are better at absorbing X-ray photons . COPS DSU Department of Pharmaceutics 6

7. X-RAY CRYSTALLOGRAPHY X -ray crystallography is a technique in crystallography in which the pattern produced by the diffraction of x-rays through the closely spaced lattice of atoms in a crystal is recorded and then analyzed to reveal the nature of that lattice . The wavelength of X-rays is typically 1 A ° , comparable to the interatomic spacing (d istance between atoms or ions ) in solids. We need X-rays: COPS DSU Department of Pharmaceutics 7

8. Crystal Structure Determination A crystal behaves as a 3-D diffraction grating for x-rays The , measurement of the separation of the X-ray diffraction maxima from a crystal allows us to determine the size of the unit cell and from the intensities of diffracted beams one can obtain information about the arrangement of atoms within the cell. COPS DSU Department of Pharmaceutics 8

9. Bragg’s law COPS DSU Department of Pharmaceutics 9 English physicists Sir W.H. Bragg and his son Sir W.L. Bragg developed a relationship in 1913. To explain why the cleavage faces of crystals appear to reflect X-ray beams at certain angles of incidence (theta, θ ). This observation is an example of X-ray wave interference . 9 Sir William Henry  Bragg (1862-1942) , William Lawrence  Bragg (1890-1971) In 1915, the father and son were awarded the Nobel prize for physics "for their services in the analysis of crystal structure by means of Xrays ".

10. Bragg’s Law Theory When a beam of x- ray is incident upon the crystal, it gets scattered by the electrons constituiting the crystal atoms. If the scattered x rays undergo constructive interference, they are said to be diffracted by the crystal plane. Each crystalline matterial scatters the x- rays in a specific diffraction pattern and thus produce a fingerprint of its internal structure. The diffracted beams are called reflection. X- rays are difffracted only if Bragg’s law is satisfied which is given by the equation. Sin θ = n λ /2d Where n= integer θ =angle of incidence λ = wavelength d= the interplanar distance of the crystal COPS DSU Department of Pharmaceutics 10

11. Bragg’s equation COPS DSU Department of Pharmaceutics 11 When an x ray beam strikes a crystal surface at an angle θ , electrons constituiting the atoms of crystal surface to oscillate at the same frequency as that of incident x ray beam and emits fraction of ER. Rest of the rays penetrate to the second layer. Again in second layer some of the rays gets scattered while rest of them penetrate to the third layer and so on. Every crystalline substance scatters the rays in a unique diffraction pattern thus producing finger prints which is characteristic to its atomic and molecular structure.

12. The scattered rays may give constructive and destructive interference. Constructive interference are obtained only if the pathlength or distance between two planes is equal to a whole number of wavelength. Basic requirements for the x- ray diffraction are, A) path lengths or difference between layers of atoms should be same as that of wavelength of radiation. B) scattering centers should be spatially distributed. COPS DSU Department of Pharmaceutics 12

13. Bragg’s law governs the condition for diffraction and the diffracted beam reffered to as reflection, obeys bragg’s equation When an x- ray beam strikes the crystal surface making an angle θ , fraction of the incident radiation gets scattered owing to the interaction with atoms located at O,P and R as shown in the figure below. COPS DSU Department of Pharmaceutics 13

14. As mentioned above, pathlengths or distance between the planes l,m,n is identical and represented as ‘d’. When an x- ray beam strikes the top crystal plane at O and the x-ray strikes the second crystal plane at P, pathlength between the parallel x rays is equal to AP+PC . COPS DSU Department of Pharmaceutics 14

15. But for constructive interference, AP + PC = n λ --------(1) When n= integer λ = wavelength of scattered radiation COPS DSU Department of Pharmaceutics 15

16. Now consider the two triangle OAP &OCP shown in the figure. From the two triangles ΔAOP=ΔCOP ΔOAP=ΔOCP=90⁰ According to ASA( angle side angle) rule, ΔOAP are similar because two angles and one of their sides are equal COPS DSU Department of Pharmaceutics 16

17. Therefore ΔOAP= ΔOCP Since side AP=PC substituting AP=PC in eq 1 we get, PC+ PC= n λ 2PC= n λ PC= n λ /2-------(3) Now consider the Δ OPC In ΔOPC, Sin θ = PC/OP PC=OP Sin θ PC= d Sin θ (distance between two parallel lines l and m is d) COPS DSU Department of Pharmaceutics 17

18. Therefore PC=d Sin θ But from eq 3 PC= n λ /2-----(4) Therefore by substituting eq 3 in eq 4 n λ /2= dSin θ ----Bragg’s equation By rearranging , we get Sin θ = n λ /2d (to get constructive interference) COPS DSU Department of Pharmaceutics 18

19. COPS DSU Department of Pharmaceutics 19 Constructive & Destructive Waves Constructive interference is the result of synchronized light waves that add together to increase the light intensity. Destructive İnterference . results when two out-of-phase light waves cancel each other out, resulting in darkness. 19

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21. Reference Textbook of pharmacetical analysis vol 2 Instrumental methods of chemical analsis , Dr. G. R. Chatwal and Sham Anand COPS DSU Department of Pharmaceutics 21

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