Visualization of 3D Diffraction:MAX3D

Jim Britten, Weiguang Guan, Vicky Jarvis

McMaster University, Hamilton, ON, Canada

britten@mcmaster.ca

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Abstract

MAX3D is a program for the visualization of 3Ddiffraction data. This includes everything seen by thearea detector – not just harvested Bragg spots. The inputmay be transmission data from a single crystal, reflectiondata from a textured solid, or diffraction from a thinnanoparticle film on a substrate. Tools have beendeveloped for probing, imaging and exporting selectedareas of reciprocal space in terms of 2Theta or HKL. Ithelps you understand your sample, recognize diffusescattering and troubleshoot difficult problems. It is apowerful tool for generating teaching materials from realsamples. MAX3D is available at no charge for Academicresearchers.

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Quick X-ray Review

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From Pecharsky & Zavalij

Reciprocal Space

SCD - 2D image + scan –> 3D Int vs 2θXRD2 - 2D image –> 1D Int vs 2θ

From Bob He’s book: Two-Dimensional X-Ray Diffraction

nλ=2d(sinθ)

Single Crystal

Powder or polycrystalline solid

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Visualisation of 1D Reciprocal Space

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CdTea=6.4827F-43m

ZnTea=6.1034F-43m

Rotate the sample in the beam and collect 2D frames.

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The 2D images can be mapped into reciprocal space – onto the surface of Ewald’s Sphere

From Pecharsky and Zavalij

Detector

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Single Crystal Structure Determination

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Rotate 200µm crystal in X-ray beam

Every 0.5° store CCD image of diffraction.

Identify unit cell and Space Group

Collect full diffraction pattern

Phase and Fourier Transform to see structure

Al70Pd21Mn9 - Geetha Balakrishnan, University of Warwick

Nathan Armstrong, Tom Timusk, McMaster

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Visualisation of 3D Reciprocal SpaceQuasicrystal

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Diffuse Scattering

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Hexanapthylbenzene. Laura Harrington, Mike McGlincheyCPDW13 CLS 9

Diffuse Scattering

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Hexanapthylbenzene. Laura Harrington, Mike McGlincheyCPDW13 CLS 10

GdPb2Cu3Se4 1200ᵒC for 4 hrs (Plates)XRD pattern from Panalytical X’Pert Pro

Diffractometer, Cu Kα1 - Forbes, Mozharivskyj

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Canadian Macromolecular Crystallography Facility, 08B1-1 (CMCF-BM) Beamline

GdPb2Cu3Se4

Phone a friend –Pawel Grochulski. Look at a single grain of the powder on a protein beamline.

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Protein SC Diffraction Pattern

Alba GuarneTamiza Nanji

Rigaku R-Axis4++Image Plate

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Follow Phase Changes

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Zheng, Preston, McMaster U

Residual Stress – Sampling 3D RS

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(Image from Bob He’s book)

Looking for subtle changes in 2θposition of line/arc/shell to indicate orientation dependent residual stresses. Hard to see visually – need mathematical analysis.

High angle snapshots of diffraction shell segments in four series of φsteps at different ψ tilt angles. Looking for elliptical deviation from spheres where r = 1/d0

220Ferrite

From Bob He’s book: Two-Dimensional X-Ray Diffraction

nλ=2d(sinθ)

Single Crystal

Powder or polycrystalline solid

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SCD - 2D image + scan –> 3D Int vs 2θXRD3 - 2D image + scan –> 3D Int vs 2θ

A ‘pole’ is a unit vector along a diffraction vector representing one grain. For a random powder the number of poles is normalized to 1. Textured samples show a variation in normalized pole density with orientation.

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From Bob He

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Mo diffraction from surface of tab of an Aluminum weighing dish

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Mo diffraction from Al foil (ALCAN)

φ-scan, 2θ=-40, ω=168, χ=54.74, 2s φ-scan, 2θ=-40, ω=175, χ=54.74, 2s

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Mo diffraction from Al foil (ALCAN)

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1 1 1

2 0 0

2 2 03 1 1

XRD3 of Al foil showing rolling texture

Pole figures from Al foil on Mo CCD

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111

220

200

311

Rolling Direction

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Al Foil Pole Figures calculated from ODF (MTEX in Matlab)

. . . from GADDS User Guide

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Texture Example: Au nanoparticle film grown on MgAl2O4 substrate

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200 nm

Majdi, Preston, McMaster U

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Pole Figures from Au filmStereographic projections of individual 2θ hemispheres

Recent Modifications to MAX3D

• Update VTK and QT libraries

• Merge frame readers into a Unified Reader

• 3D shells of Δ2θ thickness for pole figures

• 3D Clipping

• 2D and 1D projection output

• 3D pointer to identify diffraction features in terms of (fractional) hkl

• Linux version

• Supercomputer cluster version

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Mn5Ni6Si4 ; Marek Niewczas, Sheikh Ahmed

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Mn5Ni6Si4 ; Marek Niewczas, Sheikh Ahmed

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3D Clipping, Reloading at Higher Res

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2D and 1D Projections of the VOI

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Example: 2D Projection Output

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Slice View

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HK0 > HK8

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Electron Diffraction of Mn5Ni6Si4

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Current MAX3D project

• Reader for 3D Electron Diffraction Data• EMPAD detector

• Jo Etheridge, Monash University

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Funding Acknowledgements

• SHARCNet Dedicated Programming Awards • Ranil Sonnadara

• Mark Hollingsworth, KSU

• Joe Ferrara, Rigaku

• Thank You• . . . and for the tutorial . . .

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InAsSb Pillars for Multispectral Long-wavelength Infrared AbsorptionCurtis J. Goosney, Victoria M. Jarvis, James F. Britten, Ray R. LaPierre

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311 Pole Figure

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