Basics of XRD part I Dr. Peter G. Weidler Institute of Functional Interfaces IFG 1 KIT 10/31/17 The Research University in the Helmholtz Association Name of Institute, Faculty, Department www.kit.edu
Overview why XRD? Information inside XRD data Basics of crystallography Basics of X-ray scattering Sample preparation Basics of instrumentation Data evaluation (tutorials) -2- positions, phase identification lattice parameters quantitative XRD
Rietveld Refinement Basics Rietveld Refinement (different programs) hands-on -- tutorials -3-
Why XRD? Identification of material Quantification Solid state properties substitution, stress strain... changes upon heating, sorption,... So, what do we want... -4-
This!! -5- One method for all problems...
But before, we need the basics... sketch by clipart_zweten_animaatjes -6-
Information inside XRD -7-
Information inside XRD Ihkl = Io K M P L G A E T Fhkl ² Io = primary intensity K = scale-factor (cps, counts,...) M = multiplicity (planes of the same form {hkl} have the same scattering angle θ and therefore contribute to the same peak P = polarization-factor (angular dependency of dipole radiation) L = Lorentz-factor (single X-tal: time plane remains in diffraction position) G = geometry-factor ( e.g. powder: intensity on the cone circumference) A = absorption-factor (x-ray will be absorbed by the material) E = extinction-factor (decrease of intensity by secondary beams) T = temperature-factor (thermal movement of the atoms in the lattice) Fhkl ² = structure-factor -8-
for understanding...... it needs to know the basics:... in crystallography (ordering of the constituents)... in physics (radiation and its interaction with matter)... X-ray Diffraction ----> Understanding Structure-Refinement -9-
Basics of crystallography Crystal -> unit cell - 10 - crystal system --> symmetry
Basics of crystallography unit cell ----> translation ---> - 11 - crystal
crystal systems tetragonal a = b c, α = β = γ = 90 cubic a = b = c, α = β = γ = 90-12 -
crystal systems orthorombic a b c, α = β = γ = 90 rhomboedric a = b = c, α = β = γ 90 hexagonal a = b c, α = β = 90, γ = 120-13 -
crystal systems triclinic a b c, α β γ monoclinic a b c, α = γ = 90, β 90-14 -
lattice planes and Miller Index (hkl) (100) (010) (111) - 15 - (001) (311)
lattice planes and Miller Index (hkl) (0 0 1) plane Z but also direction [0 0 1] X Y orientation of a plane in space is defined by the surface normal, which is a vector - 16 -
lattice planes and Miller Index (hkl) Z (0 1 0) plane Y but also direction [0 1 0] X - 17 -
Orientation of crystals (111)-plane and looking down [111] direction (111) (100)-plane and looking down [100] direction [111] - 18 -
symmetry operations arrangement of atoms/molecules not random, follow precise rules : symmetry operations crystal symmetry physical properties - 19 -
symmetry operations symmetry operation act on unit cell --> reproducing the entire crystal rotational axis: 2-, 3-, 4- and 6-fold, and a mirror plane m - 20 -
symmetry operations 2-fold axis in combination with a mirror plane: 2/m handiness: object has own symmetry - 21 -
symmetry operations rotational axis in combination with a translation parallel to axis ---> screw-axis - 22 -
symmetry operations glide planes: mirror plane with translation oriented to the mirror plane - 23 -
making life easier...... one step back...... from 3D to...... 2 D; - 24 - (from space to plane)
from http://www.metafysica.nl/d2_lattice_1.html - 25 -
point group: 1-26 -
point group: 2-27 -
point group: 2-28 -
point group: m - 29 -
point group: 2mm - 30 -
point group: 4-31 -
point group: 4mm - 32 -
point group: 3-33 -
point group: 3m - 34 -
point group: 6-35 -
point group: 6m all examples from: http://en.wikipedia.org/wiki/wallpaper_group - 36 -
point group resp. space group --> 7 Crystal systems Triclinic (a), Monoclinic (m), Orthorhombic (o), Tetragonal (t) Trigonal (h), Hexagonal (h), Cubic (c) --> 32 Crystallographic point groups Triclinic (a) Monoclinic (m) Orthorhombic (o) Tetragonal (t) Trigonal (h) Hexagonal (h) Cubic (c) : 1, : 2, : 222, : 4, -4, : 3, -3, : 6, -6, : 23, -1 m, mm2, 4/m, 32, 6/m, m-3, 2/m mmm 422, 3m, 622, 432, 4mm, -3m 6mm, -43m, 42m, 4/mmm -62m, m-3m 6/mmm --> among 11 Laue groups ( Laue diagrams) ZnS, sphalerite - 37 -
point group resp. space group ===> 230 space groups P nma or C m or I 432 or... lattice type: P C F I... symmetry directions (orientations) --> primary secondary monoclinic : symmetry elements, crystal system tertiary unit axis b [010] orthorhombic: [100] [010] [001] cubic: {111} {110} {100} examples - 38 -
P primitive I Innenzentriert bcc base center cubic F Flächenzentriert fcc face center cubic - 39 -
point group resp. space group examples Goethite α-feooh orthorhombic P n m a #62 P n m a primitive lattice diagonal glide plane - - - - - - 1/2 along + 1/2 perpendicular to plane mirror plane axial glide plane - - - - - - - - - - - 1/2 along plane Magnetite Fe3O4 cubic F d -3 m - 40 - F d -3 m #227 face centered lattice diamond glide plane - - - -> - - - 1/4 along + 1/4 perpendicular inversion axis threefold screw axis with inversion mirror plane
point group resp. space group 3-fold inversion axis: - 41 -
symmetry operations 1 object --> 48 objects - 42 -
symmetry operations mirror plane - 43 -
symmetry operations 4/m 4-fold axis mirror plane - 44 -
symmetry operations _ 3m 3-fold inversion axis mirror plane - 45 -
Space Groups - 46 -
Space Groups - 47 -
Importance of symmetry considerations - 48 -
Importance of symmetry considerations Substitution e.g., Fe by Al or Si by Al... - 49 -
Importance of symmetry considerations - 50 -
Importance of symmetry considerations - 51 -
Importance of symmetry considerations magnetic properties: easy axis - 52 -
Importance of symmetry considerations crystal growth & crystal faces shapes - 53 -
Importance of symmetry considerations crystal growth & crystal faces shapes - 54 -
Importance of symmetry considerations crystal growth & crystal faces shapes - 55 -
Importance of symmetry considerations crystal growth & crystal faces shapes upper line after 3hrs 55' lower line beginning - 56 - Weidler et al. (1998) Geochim.Cosmochim.Acta
Importance of symmetry considerations 1669 Nicolaus Steno (* Copenhagen; DK; Schwerin, D) constancy of angles between crystal faces --> physical properties related with crystal directions example: birefringence --- double refraction http://www.chemgapedia.de - 57 - http://www.microscopyu.com
End of part 1 --> questions!!!!!!!!!!! Basics of instrumentation Data evaluation - 58 - positions, phase identification lattice parameters quantitative XRD part 2
Literature F. Donald Bloss Crystallography and Crystal Chemistry Mineralogical Society of America, 1994, pp.545 50-120 D.L. Bish & J.E. Post (Eds) Modern Powder Diffraction Reviews in Mineralogy Vol 20 Mineralogical Society of America, 1989, pp.369 30 190-450BRL 110BRL H.P. Klug & L.E. Alexander X-ray Diffraction Procedures Wiley, 1954, pp.716 (second hand bookstores 8-300 30-1130BRL) B.E. Warren X-ray Diffraction Dover Publications, 1969, 1990, pp.381 12 45BRL D.M. Moore &R.C. Reynolds X-ray Diffraction and the Identification and Analysis of Clay Minerals Oxford University Press, 1997, pp.378 50-60 190-230BRL C. Hammond The Basics of Crystallography and Diffraction (4th Ed.) IUCr; Oxford University Press, 2015, pp.519 40 150BRL - 59 -
Acknowledgment Bruker AXS Germany, Knielingen CEFET UMFG INCT-Acqua - 60 -