Basics of XRD part I. 1 KIT 10/31/17. Name of Institute, Faculty, Department. The Research University in the Helmholtz Association

Transcription

1 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

2 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

3 Rietveld Refinement Basics Rietveld Refinement (different programs) hands-on -- tutorials -3-

4 Why XRD? Identification of material Quantification Solid state properties substitution, stress strain... changes upon heating, sorption,... So, what do we want

5 This!! -5- One method for all problems...

6 But before, we need the basics... sketch by clipart_zweten_animaatjes -6-

7 Information inside XRD -7-

8 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-

9 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-

10 Basics of crystallography Crystal -> unit cell crystal system --> symmetry

11 Basics of crystallography unit cell ----> translation ---> crystal

12 crystal systems tetragonal a = b c, α = β = γ = 90 cubic a = b = c, α = β = γ =

13 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 =

14 crystal systems triclinic a b c, α β γ monoclinic a b c, α = γ = 90, β

15 lattice planes and Miller Index (hkl) (100) (010) (111) (001) (311)

16 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

17 lattice planes and Miller Index (hkl) Z (0 1 0) plane Y but also direction [0 1 0] X

18 Orientation of crystals (111)-plane and looking down [111] direction (111) (100)-plane and looking down [100] direction [111]

19 symmetry operations arrangement of atoms/molecules not random, follow precise rules : symmetry operations crystal symmetry physical properties

20 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

21 symmetry operations 2-fold axis in combination with a mirror plane: 2/m handiness: object has own symmetry

22 symmetry operations rotational axis in combination with a translation parallel to axis ---> screw-axis

23 symmetry operations glide planes: mirror plane with translation oriented to the mirror plane

24 making life easier one step back from 3D to D; (from space to plane)

25 from

26 point group:

27 point group:

28 point group:

29 point group: m

30 point group: 2mm

31 point group:

32 point group: 4mm

33 point group:

34 point group: 3m

35 point group:

36 point group: 6m all examples from:

37 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

38 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

39 P primitive I Innenzentriert bcc base center cubic F Flächenzentriert fcc face center cubic

40 point group resp. space group examples Goethite α-feooh orthorhombic P n m a #62 P n m a primitive lattice diagonal glide plane /2 along + 1/2 perpendicular to plane mirror plane axial glide plane /2 along plane Magnetite Fe3O4 cubic F d -3 m F d -3 m #227 face centered lattice diamond glide plane > /4 along + 1/4 perpendicular inversion axis threefold screw axis with inversion mirror plane

41 point group resp. space group 3-fold inversion axis:

42 symmetry operations 1 object --> 48 objects

43 symmetry operations mirror plane

44 symmetry operations 4/m 4-fold axis mirror plane

45 symmetry operations _ 3m 3-fold inversion axis mirror plane

46 Space Groups

47 Space Groups

48 Importance of symmetry considerations

49 Importance of symmetry considerations Substitution e.g., Fe by Al or Si by Al

50 Importance of symmetry considerations

51 Importance of symmetry considerations

52 Importance of symmetry considerations magnetic properties: easy axis

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

56 Importance of symmetry considerations crystal growth & crystal faces shapes upper line after 3hrs 55' lower line beginning Weidler et al. (1998) Geochim.Cosmochim.Acta

57 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

58 End of part 1 --> questions!!!!!!!!!!! Basics of instrumentation Data evaluation positions, phase identification lattice parameters quantitative XRD part 2

59 Literature F. Donald Bloss Crystallography and Crystal Chemistry Mineralogical Society of America, 1994, pp D.L. Bish & J.E. Post (Eds) Modern Powder Diffraction Reviews in Mineralogy Vol 20 Mineralogical Society of America, 1989, pp BRL 110BRL H.P. Klug & L.E. Alexander X-ray Diffraction Procedures Wiley, 1954, pp.716 (second hand bookstores BRL) B.E. Warren X-ray Diffraction Dover Publications, 1969, 1990, pp BRL D.M. Moore &R.C. Reynolds X-ray Diffraction and the Identification and Analysis of Clay Minerals Oxford University Press, 1997, pp BRL C. Hammond The Basics of Crystallography and Diffraction (4th Ed.) IUCr; Oxford University Press, 2015, pp BRL

60 Acknowledgment Bruker AXS Germany, Knielingen CEFET UMFG INCT-Acqua