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

∂ 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

∂ 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

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

∂ 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

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

∂ 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

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

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

∂ 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

∂ Ho Thin Films XRD measured as a function of temperature

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

∂ Whole film refinement

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

∂ In-situ Electrical Measurements

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

∂ Cubic-Tetragonal Distortions CUBIC TETRAGONAL

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

∂ CsCoPO 4 Phase Transitions Dr. Mark T. Weller, Department of Chemistry, University of Southampton, Variable temperature powder X-ray diffraction data show a marked change in the pattern at 170 °C.

∂ Eutectics

∂ wt% Ni 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 wt% Ni L: 32 wt% Ni L: 24 wt% Ni  :36 wt% Ni B  : 46 wt% Ni L: 35 wt% Ni C D E Figure adapted from Callister, Materials science and engineering, 7 th Ed. A.Liquid B.Mixed Phase C. D. E. Solid

∂ Cored Samples Issues: Lattice Parameter Particle Size Strain Dispersion

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

∂ 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.

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

∂ Diamond in-plane maps vs rotational azimuth

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