X-ray Diffraction (XRD) Technique Presentation
- 1. Undergraduate Course Environmental Engineering Materials (SEE-613) Theory Course Instructor: Engr. Shahbaz Hussain Department of Structures and Environmental Engineering University of Agriculture, Faisalabad-Pakistan
- 2. 2 Environmental Engineering Materials; SEE-613 11/19/2023 X-ray Diffraction (XRD) Sample
- 3. Contents Environmental Engineering Materials; SEE-613 3 11/19/2023 ❖ Introduction ❖ Background ❖ Why to select XRD? ❖ Production of X-rays ❖ Crystallography ❖ XRD Working Principle ❖ Sample Preparation ❖ Constructive Interference ❖ Bragg´s Law ❖ The Bragg-Brentano Geometry ❖ X-ray Diffraction Animation ❖ Worked Example ❖ Fraunhofer diffraction ❖ Destructive Interference ❖ XRD Setup ❖ Experimental Diffraction Methods ❖ The Seven Crystal Systems ❖ Diffraction Peaks in Cubic Systems ❖ Information obtained/derived from XRD ❖ Applications of XRD Methods
- 4. Introduction Environmental Engineering Materials; SEE-613 4 11/19/2023 • It is a novel & non-destructive method of chemical analysis, and a variety of x-ray techniques are available in practice. These are ➢X-ray absorption ➢X-ray diffraction ➢X-ray fluorescence • “Every crystalline substance gives a pattern; the same substance always gives the same pattern; and in a mixture of substances each produces its pattern independently of the others“. • The X-ray diffraction pattern of a pure substance is, therefore, like a "fingerprint of the substance". It is based on the scattering of X-rays by crystals. • When X-rays interact with a solid material, the scattered beams causes diffraction. Definition: The atomic planes of a crystal cause an incident beam of X- rays to interfere with one another as they leave the crystal. The phenomenon is called X-ray diffraction.
- 5. Introduction Environmental Engineering Materials; SEE-613 5 11/19/2023 • X-rays are electro-magnetic radiation with wavelengths in the range 0.1 to 100 A0. • X-rays used in diffraction experiments have typical wavelengths of 0.5 to 1.8 A0. What is XRD?
- 6. Background Environmental Engineering Materials; SEE-613 6 11/19/2023 • X- rays were discovered by Wilhelm Conrad Roentgen in 1895 who called them "X-rays" and it is also called as "Roentgen Rays". In 1901, he was honored by the Noble prize for physics. In 1995 the German Post edited a stamp, dedicated to W.C. Röntgen. • Gordon Darwin, grandson of C. Robert Darwin developed 1912 dynamic theory of scattering of X- rays at crystal lattice • X- ray diffraction was discovered by Max Von Laue in 1912. Wilhelm Conrad Roentgen Post Stamp Gordon Darwin Max Von Laue
- 7. Why to select XRD? Environmental Engineering Materials; SEE-613 7 11/19/2023 ➢ Measure the average spacing's between layers of atoms. ➢ Determine the orientation of a single crystal. ➢ Find the crystal structure of an unknown material. ➢ Measure the size, shape and internal stress of small crystalline regions.
- 8. Production of X-rays Environmental Engineering Materials; SEE-613 8 11/19/2023 Cross section of sealed-off filament X-ray tube ➢ X-rays are produced whenever high-speed electrons collide with a metal target. ➢ A source of electrons — hot Tungsten (W) filament, a high accelerating voltage between the cathode (W) and the anode and a metal target, Cu, Al, MO, Mg. ➢ The anode is a water-cooled block of Cu containing desired target metal.
- 9. Crystallography Environmental Engineering Materials; SEE-613 9 11/19/2023 Crystalline materials are characterized by the orderly periodic arrangements of atoms. ➢ The unit cell is the basic repeating unit that defines a crystal. ➢Parallel planes of atoms intersecting the unit cell are used to define directions and distances in the crystal. ➢These crystallographic planes are identified by Miller indices. ➢Miller indices are reflections of X-ray diffraction from the planes of crystals and are represented by (hkl) values. Determining the Miller indices (hkl) for the diffraction lines: 𝑑(ℎ𝑘𝑙) = 𝑎 ℎ2+ 𝑘2+ 𝑙2
- 10. XRD Working Principle Environmental Engineering Materials; SEE-613 10 11/19/2023 ➢ When X-rays fall on the sample, they interact with atoms and change their direction (diffract from the original direction) causing either constructive or destructive interference. This can be used to gather different information about the sample. • The angle between incident beam and the lattice planes is called θ. • The angle between incident and scattered beam is 2θ . • The angle 2θ of maximum intensity is called the Bragg angle.
- 11. XRD Working Principle Environmental Engineering Materials; SEE-613 11 11/19/2023
- 12. Sample Preparation Environmental Engineering Materials; SEE-613 12 11/19/2023
- 13. Constructive Interference Environmental Engineering Materials; SEE-613 13 11/19/2023 ➢ When two X-rays are in phase (their crests and troughs occur at the same time). ➢ Resultant wave has a higher amplitude. ➢Occurs when total path difference between two X-rays (2d sin ) is n where n is the order of reflection. W.H. Bragg (father) and William Lawrence. Bragg (son) developed a simple relation for scattering angles, now call Bragg’s law. n = 2dsin
- 14. Constructive Interference Bragg's Law of X-ray Diffraction From fig. 1, we can write . n = AB + BC -------(1) AB = BC So, n = AB + AB n = 2AB ------------(2) Where, n = 1, 2, 3 ,… for 1st , 2nd , 3rd ….order of reflection respectively. and =path difference between two X-rays. From fig. 2, According to trigonometric ratios, we can write Sin = AB d AB = dSin ………(3) By putting value of “AB” in equation (2), we obtained: n = 2dsin This is known as Bragg's law of X-ray diffraction 11/19/2023 Environmental Engineering Materials; SEE- 613 14 Atomic Plane Ray 1 Ray 2 Fig 1 Fig 2
- 15. Another View of Bragg´s Law Environmental Engineering Materials; SEE-613 15 11/19/2023 n = 2d Sin
- 16. The Bragg-Brentano Geometry Environmental Engineering Materials; SEE-613 16 11/19/2023
- 17. X-ray Diffraction Animation Environmental Engineering Materials; SEE-613 17 11/19/2023
- 18. Worked Example Environmental Engineering Materials; SEE-613 18 11/19/2023
- 19. Worked Example Environmental Engineering Materials; SEE-613 19 11/19/2023
- 20. Fraunhofer diffraction Environmental Engineering Materials; SEE-613 20 11/19/2023
- 21. Destructive Interference Environmental Engineering Materials; SEE-613 21 11/19/2023 • When two X-rays are out of phase (their crests and troughs do not occur at the same time). • Amplitude of resultant wave will be less than incident waves. • Occurs when total path difference between two X- rays (2d sin) is not equal to n where n is the order of reflection. Destructive Interference: n 2d sin
- 22. XRD Setup Environmental Engineering Materials; SEE-613 22 11/19/2023
- 23. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 23
- 24. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 24 1. LAUE'S METHOD • In this method a single crystal is held stationary in the path of radiation of continuous wavelength. While is kept constant, the wavelength , is varied. • A plane film receives the diffracted beams. A developed film after its exposure shows a diffraction pattern that consists of series of spots.
- 25. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 25 Laue’s method is divided into two types: a) Transmission Method b) Black Reflection Method a) Transmission Method A beam of x-ray is passed through the crystal, after passing through the crystal, x-rays are diffracted and recorded on a photographic plate.
- 26. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 26 Transmission Method
- 27. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 27 b) Back Reflection Method This method provides similar information as the transmission method.
- 28. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 28 2. Rotating Crystal Method
- 29. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 29 2. Rotating Crystal Method In this method , a single crystal is rotated about the fixed axis in a beam of monochromatic. The angle is variable while the wavelength is kept constant. The variation of angle due to rotation of the crystal brings different atomic planes in the crystal into position. To record such reflections a film is mounted on a cylindrical holder that is concentric with a rotating spindle.
- 30. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 30 2. Powder Method • This method is useful for samples that are difficult to obtain in single crystal form. • The powder method is used to determine the value of the lattice parameters accurately.
- 31. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 31 2. Powder Method • A sample of hundreds of powdered crystals show that the diffracted beams form continuous cones. • A circle of film is used to record the diffraction pattern. • Each cone intersects the film giving diffraction lines. • The lines are seen as arcs on the film.
- 32. Experimental Diffraction Methods 11/19/2023 Environmental Engineering Materials; SEE-613 32 Powder Diffraction Diffractogram
- 33. The Seven Crystal Systems 11/19/2023 Environmental Engineering Materials; SEE-613 33
- 34. Diffraction Peaks in Cubic Systems 11/19/2023 Environmental Engineering Materials; SEE-613 34
- 35. Worked Example 11/19/2023 Environmental Engineering Materials; SEE-613 35
- 36. Cont.. 11/19/2023 Environmental Engineering Materials; SEE-613 36
- 37. Cont.. 11/19/2023 Environmental Engineering Materials; SEE-613 37
- 38. Information obtained/derived from XRD 11/19/2023 Environmental Engineering Materials; SEE-613 38 ▪ Particle size and shape ▪ Crystal structure ▪ Element/Phase identification and quantification ▪ Lattice parameter ▪ X-ray tomography (imaging) ▪ Residual stress measurements
- 39. APPLICATIONS OF XRD METHODS 11/19/2023 Environmental Engineering Materials; SEE-613 39 ➢Determination of crystal size ,shape and orientation of the given crystal compound. ➢Particle size determination by spot counting methods. ➢Crystallographic structural analysis. ➢Identification of single and multi phase materials ➢The powder XRD pattern may be thought of as fingerprint of the single crystal structure, and it may be used conduct qualitative and quantitative analysis.
- 40. APPLICATIONS OF XRD METHODS 11/19/2023 Environmental Engineering Materials; SEE-613 40 ➢Unit cell calculations for crystalline materials. ➢Obtain XRD pattern are used to measure d- spacings of the given compound. ➢To measure thickness of thin films and multi- layers. ➢To determine atomic arrangement.