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X-ray diffraction. Equipment Bruker D8 Analytical X-ray Systems.

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Presentation on theme: "X-ray diffraction. Equipment Bruker D8 Analytical X-ray Systems."— Presentation transcript:

1 X-ray diffraction

2 Equipment Bruker D8 Analytical X-ray Systems

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5 X-ray beam source  Bruker D8 ADVANCE uses an x-ray tube with a Cu anode as the primary x-ray beam source. In this component x-rays are generated when a focused electron beam accelerated across a high voltage field bombards a stationary solid Cu target. As electrons collide with atoms in the target and slow down, a continuous spectrum of x-rays is emitted, which is termed Bremsstrahlung radiation.  The high energy electrons also eject inner shell electrons in atoms through the ionization process. When a free electron fills the shell, an x-ray photon with energy characteristic of the target material is emitted.  Common targets used in x-ray tubes include Cu and Mo, that emit 8 keV and 14 keV x-rays with corresponding wavelengths of 1.54 Å and 0.8 Å, respectively.

6 Wavelengths for X-Ray source Copper Anodes Bearden (1967) Holzer et al. (1997) Cobalt Anodes Bearden (1967) Holzer et al. (1997) Cu K  Å Å Co K  Å Å Cu K  Å Å Co K  Å Å Cu K  Å Å Co K  Å Å Molybdenum Anodes Chromium Anodes Mo K  Å Å Cr K  Å Å Mo K  Å Å Cr K  Å Å Mo K  Å Å Cr K  Å Å  Often quoted values from Cullity (1956) and Bearden, Rev. Mod. Phys. 39 (1967) are incorrect. Values from Bearden (1967) are reprinted in international Tables for X- Ray Crystallography and most XRD textbooks. Values from Bearden (1967) are reprinted in international Tables for X- Ray Crystallography and most XRD textbooks.  Most recent values are from Hölzer et al. Phys. Rev. A 56 (1997)

7 BRAGG’s EQUATION d     dSin   The path difference between ray 1 and ray 2 = 2d Sin   For constructive interference: n = 2d Sin  Ray 1 Ray 2  Deviation = 2 

8 NanoLab/NSF NUE/Bumm θ - 2θ Scan The θ - 2θ scan maintains these angles with the sample, detector and X-ray source Normal to surface Only planes of atoms that share this normal will be seen in the θ - 2θ Scan

9  Powder diffraction data can be collected using either transmission or reflection geometry, as shown below. Because the particles in the powder sample are randomly oriented, these two methods will yield the same data ReflectionDiffraction Occurs from surfaceOccurs throughout the bulk Takes place at any angleTakes place only at Bragg angles ~100 % of the intensity may be reflected Small fraction of intensity is diffracted

10 Heat Incident X-rays SPECIMEN Transmitted beam Fluorescent X-rays Electrons Compton recoilPhotoelectrons Scattered X-rays Coherent From bound charges Incoherent (Compton modified) From loosely bound charges  X-rays can also be refracted (refractive index slightly less than 1) and reflected (at very small angles)  Refraction of X-rays is neglected for now.

11 How does it work? In powder XRD method, a sample is ground to a powder (±10µm) in order to expose all possible orientations to the X-ray beam of the crystal values of, d and  for diffraction are achieved as follows: 1. is kept constant by using filtered X- radiation that is approximately monochromatic. approximately monochromatic. 2. d may have value consistent with the crystal structure 3.  is the variable parameters, in terms of which the diffraction peaks are measured. diffraction peaks are measured.

12 How does XRD Works???  Every crystalline substance produce its own XRD pattern, which because it is dependent on the internal structure, is characteristic of that substance.  The XRD pattern is often spoken as the “FINGERPRINT” of a mineral or a crystalline substance, because it differs from pattern of every other mineral or crystalline substances.

13 Basic Component Of XRD Machine Therefore any XRD machine will consist of three basic component. Monochromatic X-ray source ( ) Sample-holder (goniometer). Data collector- such as film, strip chart or magnetic medium/storage. By varying the angle , the Bragg’s Law conditions are satisfied by different d-spacing in polycrystalline materials. Plotting the angular positions and intensities of the resultant diffraction peaks produces a pattern which is characterised of the sample

14 X-ray Components A typical X-ray instrument is built by combining high performance components such as X- ray tubes, X-ray optics, X-ray detectors, sample handling device etc. to meet the analytical requirements. A consequent modular design is the key to configure the best instrumentation.X- ray tubesX-ray opticsX-ray detectors.

15 Diffraction Pattern Collected Where A Ni Filter Is Used To Remove K β KK

16 Typical experimental data from Bruker XRD 2-thetaintensitas I 22 TiO Anatase 110 Rutile

17 101 Anatase 110 Rutile

18 Examples of 3D Reciprocal Lattices weighed in with scattering power (|F| 2 ) Figures NOT to Scale SC Lattice = SC Reciprocal Crystal = SC No missing reflections

19 Figures NOT to Scale BCC Lattice = BCC Reciprocal Crystal = FCC missing reflection (F = 0) Weighing factor for each point “motif”

20 Figures NOT to Scale FCC Lattice = FCC Reciprocal Crystal = BCC missing reflection (F = 0) 110 missing reflection (F = 0) Weighing factor for each point “motif”

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23 Sample preparation

24 Make a mine powder

25 Sample holder

26 Side Drift Mount Designed to reduce preferred orientation – great for clay samples, (and others with peaks at low 2-theta angles)

27 Film, pellets, crystals mineral specimens

28 Sample holder

29 Specimen Holders for X-ray Diffraction

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31  Match The Sample/Measurement Conditions With The Diffraction Pattern 1 2 3

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35  Misinterpreting X-Ray Diffraction Results

36 Why are peaks missing? The sample is made from Morton’s Salt JCPDF# is supposed to fit it ( Sodium Chloride Halite ) JCPDF#  Rock Salt

37 It’s a single crystal 22 At °2 , Bragg’s law fulfilled for the (111) planes, producing a diffraction peak. The (200) planes would diffract at °2  ; however, they are not properly aligned to produce a diffraction peak The (222) planes are parallel to the (111) planes

38 A random polycrystalline sample that contains thousands of crystallites should exhibit all possible diffraction peaks 22 22 22 For every set of planes, there will be a small percentage of crystallites that are properly oriented to diffract (the plane perpendicular bisects the incident and diffracted beams). Basic assumptions of powder diffraction are that for every set of planes there is an equal number of crystallites that will diffract and that there is a statistically relevant number of crystallites, not just one or two

39  (deg.) Intensity (a.u.)  Which of these diffraction patterns comes from a nanocrystalline material?  These diffraction patterns were produced from the exact same sample  The apparent peak broadening is due solely to the instrumentation ° slits vs. 1° slits optical cofigurations Scan speed ( stepsize) Hint: Why are the intensities different? o 1o1o

40  Crystallite Size Broadening  Peak Width B(2  ) varies inversely with crystallite size  The constant of proportionality, K (the Scherrer constant) depends on the how the width is determined, the shape of the crystal, and the size distribution the most common values for K are 0.94 (for FWHM of spherical crystals with cubic symmetry), 0.89 (for integral breadth of spherical crystals with cubic symmetry, and 1 (because 0.94 and 0.89 both round up to 1). the most common values for K are 0.94 (for FWHM of spherical crystals with cubic symmetry), 0.89 (for integral breadth of spherical crystals with cubic symmetry, and 1 (because 0.94 and 0.89 both round up to 1). K actually varies from 0.62 to 2.08 K actually varies from 0.62 to 2.08 For an excellent discussion of K, refer to JI Langford and AJC Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size,” J. Appl. Cryst. 11 (1978) p For an excellent discussion of K, refer to JI Langford and AJC Wilson, “Scherrer after sixty years: A survey and some new results in the determination of crystallite size,” J. Appl. Cryst. 11 (1978) p  Remember: Instrument contributions must be subtracted Instrument contributions must be subtracted Scherrer’s Formula

41 t = thickness of crystallite / crystallite size K = constant dependent on crystallite shape (0.89) = x-ray wavelength B = FWHM (full width at half max) or integral breadth  B = Bragg Angle Scherrer’s Formula

42 What is B? B = (2θ High) – (2θ Low) B is the difference in angles B is the difference in angles at half max 2θ high Noise 2θ low Peak

43 When to Use Scherrer’s Formula  Crystallite size <1000 Å  Peak broadening by other factors Causes of broadening Causes of broadening SizeSize StrainStrain InstrumentInstrument If breadth consistent for each peak then assured broadening due to crystallite size If breadth consistent for each peak then assured broadening due to crystallite size  K depends on definition of t and B  Within 20%-30% accuracy at best Sherrer’s Formula References Corman, D. Scherrer’s Formula: Using XRD to Determine Average Diameter of Nanocrystals.

44 Scherrer’s Example

45 t = 0.89*λ / (B Cos θ B )λ = 1.54 Ǻ = 0.89*1.54 Ǻ / ( * Cos (98.25/ 2 ) ) = 0.89*1.54 Ǻ / ( * Cos (98.25/ 2 ) ) = 1200 Ǻ B = ( )*π/180 = Simple Right! Target Metal Of K  radiation (Å) Mo0.71 Cu1.54 Co1.79 Fe1.94 Cr2.29

46  (deg.) Intensity (a.u.)  (deg.) Intensity (a.u.) Methods used to Define Peak Width  Full Width at Half Maximum (FWHM) the width of the diffraction peak, in radians, at a height half-way between background and the peak maximum the width of the diffraction peak, in radians, at a height half-way between background and the peak maximum  Integral Breadth the total area under the peak divided by the peak height the total area under the peak divided by the peak height the width of a rectangle having the same area and the same height as the peak the width of a rectangle having the same area and the same height as the peak requires very careful evaluation of the tails of the peak and the background requires very careful evaluation of the tails of the peak and the background FWHM

47 Remember, Crystallite Size is Different than Particle Size  A particle may be made up of several different crystallites  Crystallite size often matches grain size, but there are exceptions

48 Anistropic Size Broadening  The broadening of a single diffraction peak is the product of the crystallite dimensions in the direction perpendicular to the planes that produced the diffraction peak.

49 Instrumental Peak Profile  A large crystallite size, defect-free powder specimen will still produce diffraction peaks with a finite width  The peak widths from the instrument peak profile are a convolution of: X-ray Source Profile X-ray Source Profile Wavelength widths of K  1 and K  2 linesWavelength widths of K  1 and K  2 lines Size of the X-ray sourceSize of the X-ray source Superposition of K  1 and K  2 peaksSuperposition of K  1 and K  2 peaks Goniometer Optics Goniometer Optics Divergence and Receiving Slit widthsDivergence and Receiving Slit widths Imperfect focusingImperfect focusing Beam sizeBeam size Penetration into the samplePenetration into the sample  (deg.) Intensity (a.u.) Patterns collected from the same sample with different instruments and configurations at MIT

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51 What Instrument to Use?  The instrumental profile determines the upper limit of crystallite size that can be evaluated if the than the broadening due to crystallite size, then we cannot accurately determine crystallite size if the Instrumental peak width is much larger than the broadening due to crystallite size, then we cannot accurately determine crystallite size For analyzing larger nanocrystallites, it is important to use the instrument with For analyzing larger nanocrystallites, it is important to use the instrument with the smallest instrumental peak width   Very small nanocrystallites produce weak signals the specimen broadening will be significantly larger than the instrumental broadening the specimen broadening will be significantly larger than the instrumental broadening the signal:noise ratio is more important than the instrumental profile the signal:noise ratio is more important than the instrumental profile

52 Smaller Crystals Produce Broader XRD Peaks

53 Comparison of Peak Widths at Crystallite Sizes  Rigaku XRPD is better for very small nanocrystallites, <80 nm (upper limit 100 nm)  PANalytical X’Pert Pro is better for larger nanocrystallites, <150 nm Crystallite SizeFWHM (deg) 100 nm nm nm nm1.745

54 Decrease crystallite size A = anatase, R = rutile, B = brokite, (B)=TiO2(B) Wahyuningsih, S., 2009

55 CeO 2 19 nm  (deg.) Intensity (a.u.) ZrO 2 46nm Ce x Zr 1-x O 2 0

56  Many factors may contribute to the observed peak profile  Instrumental Peak Profile  Crystallite Size  Microstrain Non-uniform Lattice Distortions Non-uniform Lattice Distortions Faulting Faulting Dislocations Dislocations  Solid Solution Inhomogeneity  The peak profile is a convolution of the profiles from all of these contributions

57 Thank you for your attending! Workshop & Analysis Informations : Dr. Sayekti Wahyuningsih, M.Si Dr. Yoventina Iriani, M.Si Laboratorium MIPA Terpadu FMIPA Universitas Sebelas Maret Phone / fax : (0271)


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