Introduction to Powder Diffraction/Practical Data Collection

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1 Durham University Chemistry Department Introduction to Powder Diffraction/Practical Data Collection Dr Ivana Evans Durham, January 2007 Durham Outline Information in a powder pattern What is diffraction How to collect (laboratory) data Lab vs synchrotron vs neutron What is Rietveld refinement 1

2 Session 2 Introduction 1. Peak positions determined by size, shape, symmetry of unit cell internal structure 3. Peak widths influenced by size/strain of crystallites - microstructure. 2θ 2. Peak Intensities determined by where atoms sit in unit cell internal structure 45,000 40,000 Counts 35,000 30,000 25,000 20,000 15, ,000 5, θ - degrees Historical background 1895: Röntgen discovers X-rays (Nobel Prize 1901) 1912: von Laue discovers X-ray diffraction on crystals (Nobel Prize1914) 1913: Bragg & Bragg discover structure analysis by XRD, NaCl (Nobel Prize 1915) 1916: Debye & Scherrer discover powder X-ray diffraction, LiF 1963: Zachariasen solves the structure of β-pu from PXRD by direct methods 1969: Rietveld method 1990: direct space approaches to structure solution 2000: work on 100+ atom structures, proteins 2

3 Diffraction: physical phenomenon Crystalline state of matter long-range 3D order Diffraction scattering on periodic arrays Crystallography 2d hkl sinθ = λ F hkl = Σf j e 2πi(hx j +ky j +lz j ) Samples (a) (b) Single crystal Four differently oriented single crystals Polycrystalline material (c) I (d) 2-theta 3

4 Experiment data compressed into one dimension 2θ 2θ Powder diffraction can give you Thermal expansion Structure determination Kinetics studies Particle size Particle strain In-situ chemistry Powder Diffraction Crystallization/ amorphization Phase transitions Ionic migration Polymorphism 4

5 Laboratory Configurations 2 1 (a) 3 θ θ (b) 2 3 Reflection geometry Transmission geometry Laboratory Bragg Brentano 5

6 Laboratory Bragg Brentano Detector Tube Monochromator Divergence Slits/ Sollers Receiving Slit Antiscatter Slits/ Sollers Sample PSD for Speed 6

7 Capillary Transmission Mode Sample Preparation Dependent on experiment Bulk holders Single crystal Si wafers for low background See examples on guided tour 7

8 Data Collection Machine dependent Make sure statistics are good enough for information you need Consider spending longer counting at higher 2θ to compensate for intensity fall off in diffraction Make sure you have sufficient points to define a peak (e.g. 10 across fwhm) can rebin later but can t create extra points Consider optical set up and whether it s suited for your sample (see later tutorials) First guess on a normal lab instrument 5-90º 0.02º step, 1 second per step ~ 1 hr Common Crimes Sample Prep Surface roughness Intensities affected as f(2θ) Negative temperature factors 8

9 Common Crimes Sample Prep Sample height 2θ offset = zero - 2* height*cos(θ)/radius; Common Crimes Sample Prep Infinite thickness e.g. organic sample sprinkled on substrate may not be infinitely thick Intensities affected as f(2θ) 9

10 Common Problems Sample Prep Preferred orientation e.g. platelets with c-axis perpendicular to sheets will give strong 00l reflections Might be able to correct Common Problems Sample Prep Texture Much harder to correct Certain unrelated hkl reflections wrong intensity 10

11 Avoiding Preferred Orientation Capillary measurements Flat plate reflection & transmission Side/back mounting Spray drying Sieving Neutron diffraction Common Crimes Data Collection Beam overspill Intensities affected as f(2θ) High background at low 2θ due to sample holder High 2θ Low 2θ 11

12 Common Crimes Data Analysis LP Factors don t ignore the geometry of the instrument you re using Different configurations require different corrections e.g. Bragg-Brentano, incident monochromator 1+ cos 2θ mono cos LP = 2 sin θ cosθ 2 2 2θ Common Crimes Data Analysis Think about errors! Poisson statistics sig(i)=i 0.5 normally assumed No longer true if you scale data No longer true for psd s where some parts of pattern measured for longer Use 2θ, I, sig(i) format error propagation! 12

13 Synchrotron vs Lab Pros Far higher intensities Choice of wavelength Much sharper peak widths Grenoble/Didcot/Japan/etc Cons Sample damage Must apply for beam time Limited access Grenoble/Didcot/Japan/etc Neutrons vs X-rays Pros Distinguish e.g. Mn/Fe Information on O in metal oxides Penetrating so can use complex sample environment Grenoble/Didcot/Japan/etc Cons Flux generally much weaker than X-rays Large samples Must apply for beam time Limited access Grenoble/Didcot/Japan/etc 13

14 Refinement: pre Rietveld Integrated intensity refinement State of the art until late 60 s early 70 s Poor observation-to-parameter ratio Problems due to overlap Limited applicability Suitable for high symmetry systems Used extensively for high T nonstoichiometric phases 12 observations 4 variables Scale factor Uiso(Fe) Uiso(O) Occ(O) Cheetham et al., Refinement: the Rietveld method Rietveld, 1969: diffraction pattern analysis by a curve fitting procedure First proposed for constant wavelength neutron data The difference between the observed and calculated profiles is minimized typical Rietveld plot: Parameters refined: structural parameters (atomic positions, displacement parameters, occupancies, unit cell parameters) instrumental parameters (zero point, background parameters) peak shape function parameters 14

15 Conclusions Overview/intro to diffraction/rietveld Many specific details will be covered in later lectures/tutorials Tour of instruments if you want 15