Basics and Recent Advances in Two-dimensional X-ray Diffraction. Bob He, Bruker AXS April 15, 2014 Harvard University

Size: px

Start display at page:

Download "Basics and Recent Advances in Two-dimensional X-ray Diffraction. Bob He, Bruker AXS April 15, 2014 Harvard University"

Cameron Knight
6 years ago
Views:

1 Basics and Recent Advances in Two-dimensional X-ray Diffraction Bob He, Bruker AXS April 15, 2014 Harvard University

2 Basic Concept from XRD to XRD 2 12/4/2017 2

$Intensity Conventional X-ray Diffractometer Divergence slit Antiscatter slit Monochromator Bragg-Brentano Geometry. Point (0D) detector.$

3 Intensity Conventional X-ray Diffractometer Divergence slit Antiscatter slit Monochromator Bragg-Brentano Geometry. Point (0D) detector. Tube Sample Detectorslit Scanning over 2 range to collect XRD pattern. Corundum Powder Diffraction Two Theta

4 Diffraction Patterns vs. Atomic Arrangement

5 XRD 2 : Two-dimensional X-ray Diffraction

$2D diffraction pattern. Fig. B.$

6 XRD 2 : From 2D pattern to -2 image 2 Fig. A. 2D diffraction pattern. Fig. B. 2D pattern in rectangular -2 image. bob.he@bruker-axs.com 8

7 XRD 2 : 2D pattern in I on -2 coordinates Powder Texture bob.he@bruker-axs.com 9

8 XRD 2 : 2D pattern in I on -2 coordinates Stress Large grains bob.he@bruker-axs.com 10

9 12/4/ Geometry Convention and Diffraction Vector Approach

10 Single Crystals S S 0 Laue equation a b c ( s ( s ( s s s s ) ) ) h k l

11 XRD 2 : Debye cones from powders Bragg law n 2d sin

$XRD 2 : Diffraction pattern with both$ $Beam Sample Diffraction vector with H$

12 XRD 2 : Diffraction pattern with both and 2 information Debye Cone Incident Beam Sample Diffraction vector with H s s 0 cos sin 2 sin sin 2 cos

13 XRD 2 : Geometry Convention - Diffraction Space Diffraction rings (blue) in the laboratory axes (red).

$XRD 2 : Diffraction Vector & Unit Diffraction Vector The diffraction vector$ vector can be represented by its unit vector given by: cos sin 2 sin sin 2 1

vector can be represented by its unit vector given by: cos sin 2 sin sin 2 1

14 XRD 2 : Diffraction Vector & Unit Diffraction Vector The diffraction vector is given in laboratory coordinates by The direction of each diffraction vector can be represented by its unit vector given by: cos sin 2 sin sin 2 1 cos z z y y x x s s s s s s s s H cos cos sin cos sin L z y x h h h H H h

$from the diffraction space to the sample a11 a12 a13 space is: a21a22 a23 a 31 a 32 a 33 sin sin sin$

15 XRD 2 : Sample Space and Eulerian Geometry The angular relationships between X L Y L Z L and S 1 S 2 S 3 are: X Y Z L L L S a a a S a a a S a a a The transformation matrix from the diffraction space to the sample a11 a12 a13 space is: a21a22 a23 a 31 a 32 a 33 sin sin sin cos cos sin sin cos cos sin sin cos cos sin sin sin cos cos sin cos sin sin cos cos cos sin cos cos sin

$XRD 2 : Sample Space and Unit Diffraction Vector The components of the unit vector h S in the sample coordinates S 1 S 2 S 3 is then given by h1 a11 a12 a13h h 2 a 21a22 a23 h h3 a31a32 a33 h Or in$

16 XRD 2 : Sample Space and Unit Diffraction Vector The components of the unit vector h S in the sample coordinates S 1 S 2 S 3 is then given by h1 a11 a12 a13h h 2 a 21a22 a23 h h3 a31a32 a33 h Or in expanded form: x y z h h 1 2 sin (sin sin sin cos cos) cos cos sin cos cos sin (sin sin cos cos sin) sin (cos sin sin sin cos ) cos cos cos cos cos sin (cos sin cos sin sin) h 3 sin cos sin cos sin cos cos cos cos sin

17 Sources 12/4/

12/4/2017 21 Characteristic X-ray generation All present monochromatic home laboratory sources are based on characteristic radiation from a material anode The efficiency of this

18 12/4/ Characteristic X-ray generation All present monochromatic home laboratory sources are based on characteristic radiation from a material anode The efficiency of this process is very low Approximately 99% of the incident electron power is converted to heat, not X- rays Dissipation of this waste heat fundamentally limits the brightness of the source

12/4/2017 23 How to make brighter source I: Microfocus sources Brightness (B) is proportional to power loading (p) Power loading is higher for smaller spot focus p max 2 T m

19 12/4/ How to make brighter source I: Microfocus sources Brightness (B) is proportional to power loading (p) Power loading is higher for smaller spot focus p max 2 T m T0 r ln(2) Large spot Quasi-one dimensional heat flow limits power loading Small spot Two dimensional heat flow (more efficient cooling) Relative performance improved by 10 times

12/4/2017 24 ImS microfocus source Intensity 3x10 10 X- rays/mm 2 -sec (Cu Ka) 8 times higher than conventional 5.

20 12/4/ ImS microfocus source Intensity 3x10 10 X- rays/mm 2 -sec (Cu Ka) 8 times higher than conventional 5.4 kw rotating anode Typical lifetime >5 years High reliability 3 year warranty >300 installed Air-cooled Available in Cr, Cu, Mo, Ag

21 ImS & VÅNTEC-2000 vs. Classic Set-up Corundum Comparison Sealed Tube with Göbel Mirror 45kV, 40mA, (1800 W) 0.3mm collimator Microsource (ImS) TM 45kV, 0.650mA, (30 W) 0.3mm collimator total counts: 78K total counts: 1235K Intensity: 15.8x; Efficiency: 948x!

12/4/2017 26 How to make a brighter source II: Rotating anode sources Power loading can be increased by over an order of magnitude by rotating the anode surface to spread out the heat load Power

22 12/4/ How to make a brighter source II: Rotating anode sources Power loading can be increased by over an order of magnitude by rotating the anode surface to spread out the heat load Power load is also (modestly) increased by smaller spot In latest generation rotating anodes angular velocity is 10,000 rpm This improves performance by 50 times v T T w pmax m 0 w=beam width v=anode velocity

12/4/2017 27 TXS HB High brilliance rotating anode Highest intensity rotating anode 2x10 11 X-rays/mm 2 -sec Cu Ka 50 times the intensity of a 5.

23 12/4/ TXS HB High brilliance rotating anode Highest intensity rotating anode 2x10 11 X-rays/mm 2 -sec Cu Ka 50 times the intensity of a 5.4 kw classic RAG with multilayer optics Cu, Mo, Ag anodes Low maintenance Easy to align, highly stable mount No alignment base Precrystallized, prealigned filaments No realignment required after filament changes (2X per year) Precision aligned anode No realignment required after anode exchange (1X per year)

24 12/4/ What are the limits of rotating anode performance? Faster rotation () allows higher power loading p R max w However, faster rotation also increases mechanical stress 2 3 PR R 2 2 h R t 2t State-of-the-art rotating anodes are operated close to mechanical failure limits Little room for further improvement

25 12/4/ NEW: Liquid metal sources High-speed liquid-metal-jet anode Anode is regenerative No longer limited by melting >500 kw/mm 2 e-beam power density Rotating anode limited to maximum 50 kw/mm 2 E-beam Metal jet Interaction point

12/4/2017 30 Spot Size 5 µm 10 µm 20 µm Spot size [µm, FWHM] Voltage [kv] Power [W] Ga Kα Brightness [Photons/(s mm 2 mrad 2 line] 5 60 50 1.

26 12/4/ Spot Size 5 µm 10 µm 20 µm Spot size [µm, FWHM] Voltage [kv] Power [W] Ga Kα Brightness [Photons/(s mm 2 mrad 2 line] mm X-ray photon energy: Ga Ka 9.25 kev (=1.34 Å) Suitable replacement for Cu Ka 8.06 kev (=1.54 Å)

12/4/2017 32 So, is it possible to put a synchrotron beamline on a table top?

27 12/4/ So, is it possible to put a synchrotron beamline on a table top? Yes, at least the equivalent of a typical present generation bending magnet beamline

28 Detector 12/4/

29 Characteristics of area detectors: Sensitivity vs. Counting Rate MWPC MiKroGap CCD Image Plate Detective Quantum Efficiency (DQE): The DQE is a parameter defined as the square of the ratio of the output and input signal-to-nose ratios (SNR). ( S / N ) DQE ( S / N ) out The DQE of a real detector is less than 100% because not every incident x-ray photon is detected, and because there is always some detector noise. MiKroGap has the best overall performance. in 2 2D Workshop

30 XRD 2 : Choice of Detectors: Active Area and Pixel Size The angular coverage of 2D detectors with various active areas (D=150mm) 35 Bruker Confidential

31 XRD 2 : Choice of Detectors: Active Area and Pixel Size At D=150 mm, the angular resolution per pixel is for large detector, but 0.21 and 0.11 for two smaller 2D detectors. 36 Bruker Confidential

32 VÅNTEC-500 Outperforms all previous gaseous detectors. Large active area: 140 mm in dia. Frame size: 2048 x 2048 pixels 1024 x 1024 pixels 512 x 512 pixels Pixel size: 68 mm x 68 µm 136 mm x 136 µm 272 mm x 272 µm High sensitivity: 80% DQE for Cu High max linear count rate: 0.9 Mcps global; 160 kcps/reflection -local Low background noise: <10-5 cps/pix Maintenance-free: no re-gassing

33 Phase ID 12/4/

34 XRD 2 : Phase ID Measurement Geometry

35 XRD 2 : Single Frame Covering All Multilayer battery anode. 2 coverage: 70 at 8 cm detector distance A single frame showing information on phase, stress, texture and grain size 2D detector is essential for In-situ measurement

36 XRD 2 : Frame Merge and Integration 4 frames at 20 cm Merged frames 2 coverage: 100 Integrated profile for phase ID search/mat ch

37 Stress 12/4/

38 XRD: Sample Space & Unit Diffraction Vector The components of the unit vector h S in the sample coordinates S 1 S 2 S 3 is then given by h h h h cos sin sin sin cos which is a single value at each sample orientation.

39 The sin 2 - Method for Stress Measurements

40 The sin 2 - Method for Stress Measurements

41 Effects of Texture and Large Grain on e - sin 2 Functions

42 XRD & XRD 2 : Fundamental Equations for Strain As a second order tensor, the relationship between the measured strains and the strain tensor is given by: 0D/1D: 2D: e e ij h h i j Both equations are in the same form except the difference in h s e 2 2 e 2 e cos sin 12 sin2 sin e 22 sin sin 2 e cos sin2 e sin sin2 e cos e Introducing =90 or 270 (diffractometer plane), the above equation can be derived from the bottom equation e e (,,, ) { hkl} 2 2 (,,, ) h1 e11 h1h 2e12 h2e 22 2h1h 3e ij 23 h h 2 h h e h e i j

equation for stress measurement in XRD 2 : 2 S ( ) S ( h h 1 ( ) / S / 1 E 11 E

43 XRD 2 : Fundamental Equation for Stress Measurement Introducing the elasticity constants: E & or the macroscopic elastic constants: & 1 2 S2 1 the fundamental equation for stress measurement in XRD 2 : 2 S ( ) S ( h h 1 ( ) / S / 1 E 11 E h h h h h 33 2 h h 3 ) sin0 ln sin

$XRD 2 : Diffraction Rings Distortion Due to Stress The simulated diffraction ring distortion in radar$

44 XRD 2 : Diffraction Rings Distortion Due to Stress The simulated diffraction ring distortion in radar chart: (a) equibiaxial stress with scan; (b) uniaxial stress with ω scan for Fe (211) with Cr radiation.

45 The D8 DISCOVER with DAVINCI VÅNTEC-500 for stress measurement Almen strip (spring steel) (211) & (200) rings Ring distortion when sample rotates with and

46 XRD 2 : Stress Measurement Example Parameter setting Evaluate the data quality Results reporting: 11 = MPa 22 = MPa Principal stress and stress ellipse equibiaxial

47 Comparison of the sin 2 and 2D method for stress measurement With increasing data points, the new 2D method can measure stress with higher accuracy than the conventional sin 2 method for the same amount of data collection 59 Bruker Confidential 04/12/2017

48 XRD 2 : Stress Measurement with 2D method: Effect of Texture low intensity and poor profile due to texture tends to give larger 2θ shift error. Elastic anisotropy results in error in stress calculation

49 XRD 2 : Stress Measurement with 2D method: Effect of Large Grains Poor profile due to large grain size gives larger 2θ shift error. Diffraction profile of extreme large grain or substrate at a rocking angle brings error in 2θ.

$He, Two-dimensional X-ray Diffraction, John Wiley & Sons, 2009, pp 299-303.$

50 XRD 2 : Innovations to 2D method: Intensity Weighted Least Squares Regression low intensity and poor profile due to texture and large grain tends to give larger 2θ shift error. Ref: B. He, Two-dimensional X-ray Diffraction, John Wiley & Sons, 2009, pp S w i n i1 I w r i 2 i i 2 i n i1 w ( y i i yˆ maximum (or integrated) intensity the standard error of profile fitting of the i th data point i ) 2

Loading 60 58 56 54 (420) (331) 650 (331)+(420) Stress 52 50 600 (331) only stress 48 Improve the accuracy and reduce the

51 Standard error (MPa) Stress (MPa) XRD 2 : Innovations to 2D method: Stress Measurement from Multiple (hkl) Rings Regression Cu Film Stress vs. Loading (420) (331) 650 (331)+(420) Stress (331) only stress 48 Improve the accuracy and reduce the effect of anisotropy and texture (420) only stress Linear (331)+(420) Std.err (331) only std.err (420) only std.err Loading Strain (X 0.001)

52 12/4/ Texture, Orientation and Fiber

53 XRD 2 : Fundamental Equation for Texture Analysis The pole figure angles (a,) can be calculated from the unit vector components by the pole mapping equations: a sin 1 cos 1 h 3 h 2 1 h cos 1 h h 2 1 h if if h h

54 The D8 DISCOVER with DAVINCI VÅNTEC-500 for texture measurement Steel can (200) & (110) rings Intensity variation during scan

55 XRD 2 : Data Collection Speed vs. 2D or 0D 5 2D: 108 exposures (frames); 0D: 973 exposures (points) multiple pole-figures; single pole-figures 2D detector is 1~2 orders of magnitude faster than 0D detector.

$films Cu (311) (220) (200) (111) Four diffraction rings are observed$ at 10 cm detector distance.

56 Texture Measurement Using VANTEC-500: Magnetron sputter-deposited Cu films Cu (311) (220) (200) (111) Four diffraction rings are observed at 10 cm detector distance. Four pole figures can be measured simultaneously. Diffraction spots from Si wafer appear on some frames. Si (311)

57 Arts from XRD 2 : Pole-figure from Cu film and Si

58 XRD 2 : Miscut Angle O S2 S1 A D D B C A C B in degrees Two spots are produced by sample rotates during data collection 2theta integration shows the gamma angle between two spots 12/4/2017 Beijing Application Lab 70

59 XRD 2 : Miscut Angle The angle between two diffraction vector is given by the virtual oscillation angle The miscut angle a is from half of the 2arcsin[cosθ sin( γ / 2)] a 2arcsin[cos sin( / 4)] 12/4/2017 Beijing Application Lab 71

60 D8 Discover with VÅNTEC-500 PE Fiber: Orientation and Crystallinity 72 72

61 XRD 2 : Fiber with VÅNTEC-500

62 Crystal Size 12/4/

63 XRD 2 : Crystal Size by profile analysis: Organic glass for food & drugs *Courtesy of Prof. Lian Yu, U. of Wisconsin - Madison

$XRD 2 : Data Collection: Acetaminophen powder The spotty diffraction ring is due to the large crystallites compared to the sampling volume (beam size).$

64 XRD 2 : Data Collection: Acetaminophen powder The spotty diffraction ring is due to the large crystallites compared to the sampling volume (beam size). The number of spots on the ring is determined by crystallite size, instrumental window (-range), multiplicity of the crystal plane, and effective diffraction volume. The size of jelly beans and candy bin determines how many you can fill Bruker Confidential 76

65 XRD 2 : Particle size measurement by profile analysis: ss - o W s o s 1 2 For XRD 2, the instrumental window W is given by W 12 2 arcsin[cos sin( / 2)] Bruker Confidential 77

66 XRD 2 : Particle Size Analysis 2 profile analysis profile analysis 1 nm 10 nm 100 nm 1 m m 10 m m 100 m m 1 mm Scherrer equation: C t Bcos particle size range in pharmaceutical systems Gold nano-particle

67 12/4/ Thin film applications contributed by Jon Giencke

0.5 mm Collimator Knife Edge VÅNTEC 500 Ewald Sphere γ

68 Innovative XRD Techniques Rapid X-ray Reflectometry with XRD Instrument Setup ImS microfocus Cu Tube Montel Optic 0.5 mm Collimator Knife Edge VÅNTEC 500 Ewald Sphere γ Specular Reflection θ a = XRD coverage December 4,

69 Innovative XRD Techniques Rapid X-ray Reflectometry with XRD Layers of Various Thicknesses Superlattice with 4nm period Scan Mode One Frame nm nm nm nm Step Mode December 4,

$Diffraction with XRD Standard$ Plane Plane GID (Epitaxial

70 Innovative XRD Techniques In Plane Grazing Incidence Diffraction with XRD Standard GID (Polycrystalline Film) In Plane GID (Polycrystalline Film) In Plane GID (Epitaxial Film) December 4,

$Diffraction with$ XRD 10 nm

71 Innovative XRD Techniques In Plane Grazing Incidence Diffraction with XRD 10 nm Polycrystalline Film on Si Conventional GID GID In Plane GID 84 December 4, 2017

$Diffraction with XRD Comparison$

72 Innovative XRD Techniques In Plane Grazing Incidence Diffraction with XRD Comparison of Conventional and XRD 85 December 4, 2017

$Diffraction with XRD Ewald$ with Montel VÅNTEC 500 Ray

73 Innovative XRD Techniques In Plane Grazing Incidence Diffraction with XRD Ewald Sphere Construction Ψ IμS with Montel VÅNTEC 500 Ray Tracing Diagram Sample December 4,

$Grazing Incidence Diffraction with XRD Crystal$ Truncation Rod Measurement Raw Data What is a

74 Gamma Innovative XRD Techniques In Plane Grazing Incidence Diffraction with XRD Crystal Truncation Rod Measurement Raw Data What is a Crystal Truncation Rod? 2 Theta 0.05 Phi Step per frame

$Plane Grazing Incidence Diffraction with$ XRD Crystal Truncation Rod Measurement 25

75 Gamma Gamma Innovative XRD Techniques In Plane Grazing Incidence Diffraction with XRD Crystal Truncation Rod Measurement 25 nm Si / 50 nm SiGe / Si 20 nm STO on Si Phi Phi

$Innovative XRD Techniques In Plane Grazing Transmission Diffraction with XRD 8 nm Z is set slightly$

76 Innovative XRD Techniques In Plane Grazing Transmission Diffraction with XRD 8 nm Z is set slightly low, so only the edge is tilted into the beam 16 nm 40 nm STO 200 Si nm December 4,

77 Innovative XRD Techniques Reciprocal Space Mapping with XRD Comparison of RSM with XRD and 1D LynxEye 1D Detector 1D Detector Total Time for XRD 2 RSM (27 peaks): 15 minutes Total Time for 1D RSMs (4 peaks): 1.5 hours December 4,

78 Innovative XRD Techniques Lattice Parameter Refinement with DIFFRAC.TOPAS December 4,

79 12/4/ D Display Visualization of 3D Reciprocal Space with MAX3D Contributed by Jim Britten, Weiguang Guan, Victoria Jarvis McMaster University, Hamilton, Ontario, Canada

80 Example 1 Random Orientation GaAs NW on Carbon nanotube fabric Why bother with XRD 3? Sometimes there are surprises! Jim Britten, Bruker-NYU XRD Workshop June

81 Example 2 Multiple (8) Orientation GaAs NW s on Si Substrate 2D scan sequence Full scan in MAX3D Jim Britten, Bruker-NYU XRD Workshop June

More About XRD 2 1. Introduction. 2. Geometry Conventions. 3. X-Ray Source and Optics. 4. X-Ray Detectors. 5. Goniometer and Sample Stages. 6. Data Treatment. 7.

82 More About XRD 2 1. Introduction. 2. Geometry Conventions. 3. X-Ray Source and Optics. 4. X-Ray Detectors. 5. Goniometer and Sample Stages. 6. Data Treatment. 7. Phase Identification. 8. Texture Analysis. 9. Stress Measurement. 10. Small-Angle X-Ray Scattering. 11. Combinatorial Screening. 12. Quantitative Analysis. 13. Innovation and Future Development.

$diffraction will be published$

83 More About XRD 2 Volume H with a chapter on twodimensional X-ray diffraction will be published in 2014 and available at

84 XRD 2 Publications ICDD Most Downloaded AXA Papers

85 XRD 2 Publications Most Downloaded AXA Papers #2

86 XRD 2 Publications Most Downloaded AXA Papers #1

87 Fatal Bicycle Accident Collection of Evidence traces of car paint found on the bicycle Dr. W. Kugler Landeskriminalamt Baden-Württemberg Stuttgart, Germany

$2-dimensional diffraction pattern$

88 Fatal Bicycle Accident Mapping of Car Paint with GADDS video image (for documentation) 2-dimensional diffraction pattern integration of data: diffractogram for phase identification

Fatal Bicycle Accident The Car s Identification Lin (Counts) 5000 sequence of coatings is characteristic of car type 0 13 20 30 40 50 60 70 2-Theta - Scale New Frame - File: 2708_06.raw - Start: 12.

89 Fatal Bicycle Accident The Car s Identification Lin (Counts) 5000 sequence of coatings is characteristic of car type Theta - Scale New Frame - File: 2708_06.raw - Start: End: Step: New Frame - File: 2708_04.raw - Start: End: Step: New Frame - File: 2708_05.raw - Start: End: Step: New Frame - File: 2708_07.raw - Start: End: Step: 0.010

90 Police Officer s Pistol Exccessive Force? Death of a Bank Rober

91 Police Officer s Pistol Exccessive Force? Contact Trace on the Barrel

92 Police Officer s Pistol Exccessive Force? Contact Trace on the Projectile

Stress and Texture by XRD Bob He, Bruker AXS

Stress and Texture by XRD Bob He, Bruker AXS Intensity Conventional X-ray Diffractometer Divergence slit Antiscatter slit Monochromator Bragg-Brentano Geometry. Scanning over range to collect XRD pattern.