1. The Muppet’s Guide to: The Structure and Dynamics of Solids Single Crystal Diffraction

2. ∂ In single crystals the sample and detector need to aligned to the diffraction condition. q ω 2θ2θ Symmetric Scan Asymmetric Scan Grazing Incidence (-) q ω 2θ2θ To get a precise and robust lattice parameter need to fit many peaks and refine – move sample each time

3. ∂ Single Crystal Diffraction  -  0 (  rad) Angular acceptance is very high. Only accepts parallel beams and gives energy discrimination. Removes height errors Double Axis Triple Axis

4. ∂ Single Crystal Diffraction What one sees in reciprocal space depends on the detector resolution Double axis Triple axis

5. ∂ Tilts and Mosaic WARNING: Cannot distinguish in a Double axis rocking curve A mosaic crystal broadens the peak which should be constant in  In-plane periodicities within the coherence length (a couple of microns) will also cause a broadening of the peak in q x (c.f. particle size) but will be constant in q x

6. ∂ Epitaxial Layers J. Aldous et al J. Cryst. Growth 357 (2012) 1-8 NiSb(~50nm)/GaAs

7. ∂ Single Crystal Diffraction In single crystals the sample and detector need to aligned to the diffraction condition. q ω 2θ2θ Symmetric ScanAsymmetric Scan Grazing Incidence (-) q ω 2θ2θ qzqz qxqx Si

8. ∂ Asymmetric reciprocal space map around GaAs(422) A weekend of counting….

9. ∂ Reciprocal space maps Reciprocal space is very very big and there can be many many reflections. Symmetric scan

10. ∂ MnSb on a Virtual Substrate Ge Si MnSb Comparing growth modes on different substrates. Compare MnSb on GaAs (111) with Ge (111). C. Burrows et al. J. Cryst. Growth Des. (2013) 13, 4923

11. ∂ Ho Thin Films XRD measured as a function of temperature

12. ∂ Ho Thin Films Substrate and Ho film follow have different behaviour

13. ∂ Whole film refinement

14. ∂ Electric & Magnetic Fields Woodridge et al. J. Sync. Rad. 19 710-716 (2012 ) Single Crystals of Pb[Mn 1/3 Nb 1/3 ]O 3 -0.32PbTiO 3 (PMN-0.32PT) 002 +3kV Rhombohedral-3kV Orthorhombic

15. ∂ In-situ Electrical Measurements

16. ∂ Nanostrain project (WP1) X-rays measure the atomic strain, but also need to correlate this with changes in macroscopic size.

17. ∂ Cubic-Tetragonal Distortions CUBIC TETRAGONAL

18. ∂ High Temperature Powder XRD 0.4BiSCO 3 - 0.6PbTiO 3 (K. Datta) Tetragonal → Cubic phase transition Courtesy, D. Walker and K. Datta University of Warwick

19. ∂ CsCoPO 4 Phase Transitions Dr. Mark T. Weller, Department of Chemistry, University of Southampton, www.rsc.org/ej/dt/2000/b003800h/www.rsc.org/ej/dt/2000/b003800h/ Variable temperature powder X-ray diffraction data show a marked change in the pattern at 170 °C.

20. ∂ Eutectics

21. ∂ wt% Ni 20 1200 1300 304050 1100 L (liquid)  (solid) L +  L +  T(°C) A 35 C o L: 35wt%Ni Cu-Ni system Consider Cu/Ni with 35 wt.% Ni Following Structural Changes 43 32  :43 wt% Ni L: 32 wt% Ni L: 24 wt% Ni  :36 wt% Ni B  : 46 wt% Ni L: 35 wt% Ni C D E 24 36 Figure adapted from Callister, Materials science and engineering, 7 th Ed. A.Liquid B.Mixed Phase C. D. E. Solid

22. ∂ Cored Samples Issues: Lattice Parameter Particle Size Strain Dispersion

23. ∂ NiCr Follow structue Fcc: hkl are either all odd or all even. Bcc: sum of hkl must be even.

24. ∂ Thin films How do we measure really thin samples? As layer thickness reduce, diffraction peaks broaden until they are no-longer recognisable. Realistic limit for HR-XRD: 5 nm in the lab and maybe 2 nm at a synchrotron. Lattice parameter precision.

25. ∂ In-plane XRD Thin Ge on Si (110). Clear relaxation along the in- plane directions but remaining strained along the directions.

26. ∂ Diamond in-plane maps vs rotational azimuth

27. ∂ XRD from ultra-thin MnSb films In-plane Out of plane