PhD

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Figures

Below are all my illustrations and data plots that I've made for the thesis. In the caption for each, there are download links both to 900 dpi PNG images (and for some figures also an αPNG with transparent background), vector formats (SVG and PDF), and any alternative versions of the figures.

Most of the illustrations are created entirely in LaTeX using PSTricks, while most of the data plots were made in either MATLAB or using Python. Some of them were originally made for my master's thesis, though most have been extensively updated for the PhD thesis.

Superconductivity illustrations (chapter 2)

Figure 2.1: Mediation of a bosonic pair of electrons via phonons.
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Figure 2.2: Timeline for the history of superconducting compounds.
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Second version with the pressures shown as values: PNG•αPNG•SVG•PDF.

Figure 2.3: The magnetisation of a superconductor as a function of applied field.
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Figure 2.4: Magnetic field lines for a superconductor.
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Figure 2.5: Examples of typical cuprate unit cells.
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Figure 2.6: Typical phase diagram for a cuprate.
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Crystallography illustrations (chapter 3)

Figure 3.1: The lattice parameters in a standard crystal lattice.
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Figure 3.2: Simple examples of crystal planes in a standard crystal.
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Figure 3.3: The P, I, F, and C lattice centrings.
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Figure 3.4: Symmetries of orthorhombic crystals.
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Figure 3.5: Symmetries of tetragonal crystals.
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Figure 3.7: Examples of commensurate and incommensurate modulations.
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Figure A.1: Figures to help transform from tetragonal to orthorhombic.
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Figure A.2: Illustration for derivation of Bragg's law.
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Figure A.3: Illustration for proof of equivalence of Laue and Bragg conditions (version 1).
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Figure A.4: Illustration for proof of equivalence of Laue and Bragg conditions (version 2).
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Scattering illustrations (chapter 4)

Figure 4.1: Particle energies versus wavelengths for different scattering probes .
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Figure 4.2: A simple look at scattering vectors and angles.
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Figure 4.3: Requirements for constructive interference.
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Figure 4.4: Relating different energy units - X-rays.
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Figure 4.5: Relating different energy units - neutrons.
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Figure 4.6: X-ray and neutron scattering lengths compared.
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Figure 4.7: Examples of reciprocal space for twinned and modulated crystals.
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Figure 4.8: Indexing superstructures in reciprocal space.
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Figure 4.9: Projection of the fourth dimension reciprocal lattice vector.
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Figure 4.10: A displacement modulation along one axis using an AMF.
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Figure 4.11: Reconstructing the AMF of a displacement modulation.
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Figure 4.12: Construction of a t-plot from AMF's.
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La(2-x)Sr(x)CuO(4+y) illustrations (chapter 5)

Figure 5.1: The average Bmab crystal structure of La(2)CuO(4).
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Figure 5.2: Comparison of the tetragonal and orthorhombic unit cells .
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Figure 5.3: Phase diagrams following doping for La(2-x)Sr(x)CuO(4) and La(2)CuO(4+y).
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Figure 5.4: Two-dimensional phase diagrams following codoping for La(2-x)Sr(x)CuO(4+y).
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Figure 5.5: Lattice parameters - following Sr doping for La(2-x)Sr(x)CuO(4).
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Figure 5.6: Lattice parameters - following temperature for La(2)CuO(4+y).
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Figure 5.7: The twinning of La(2-x)Sr(x)CuO(4+y).
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Figure 5.8: Angular distance between twinning reflections.
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Figure 5.9: Phase diagram showing magnetic and superconducting phases.
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Figure 5.10: Stripes and antiferromagnetic spins in the plane.
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Figure 5.11: Doping dependence of the incommensurability δ in the stripe II phase.
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Figure 5.12: CuO(6) tilt structures and staging.
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Extra data illustrations (chapter 6)

Figure 6.1: Example of attempted detwinning.
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Figure 6.2: Example of neutron-Laue image of a La(2)CuO(4+y) sample.
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Staging illustrations (chapter 7)

Figure 7.1(a): Overview sketch of the BW5 instrument.
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Figure 7.1(b): Overview sketch of the RITA-II instrument.
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Figure 7.2: Reciprocal-space plane showing Bmab reflections splitting along l due to staging.
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Figure 7.3: Peak positions and integrated intensities for the x = 0.04 sample.
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DMC illustrations and data plots (chapter 8)

Figure 8.1: Overview sketch of the DMC instrument.
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Figure 8.2: Photo of the DMC instrument.
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Figure 8.3: Photos of three of the samples measured on at DMC.
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Figure 8.4: Example of (2θ,ω) plane for La(2)CuO(4+y).
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Figure 8.5: Example of a (0kl) reciprocal-space map for La(2)CuO(4+y).
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Figure 8.6: Types of annotation markers used in the DMC reciprocal-space planes.
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Figure 8.7(a): Low-temperature reciprocal-space (0kl) map for the La(2)CuO(4+y) sample.
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Figure 8.7(b): Low-temperature reciprocal-space (hk0) map for the La(2)CuO(4+y) sample.
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Figure 8.8(a): Room-temperature reciprocal-space (0kl) map for the La(2)CuO(4+y) sample.
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Figure 8.8(b): Room-temperature reciprocal-space (hk0) map for the La(2)CuO(4+y) sample.
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Figure 8.9(a): Low-temperature reciprocal-space (0kl) map for the La(1.94)Sr(0.06)CuO(4+y) sample.
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Figure 8.9(b): Low-temperature reciprocal-space (hk0) map for the La(1.94)Sr(0.06)CuO(4+y) sample.
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Figure 8.10(a): Room-temperature reciprocal-space (0kl) map for the La(1.94)Sr(0.06)CuO(4+y) sample.
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Figure 8.10(b): Room-temperature reciprocal-space (hk0) map for the La(1.94)Sr(0.06)CuO(4+y) sample.
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Figure 8.11(a): Mid-temperature reciprocal-space (0kl) map for the La(1.91)Sr(0.09)CuO(4+y) sample.
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Figure 8.11(b): Mid-temperature reciprocal-space (hk0) map for the La(1.91)Sr(0.09)CuO(4+y) sample.
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Figure 8.12: Room-temperature reciprocal-space (0kl) map for the La(1.91)Sr(0.09)CuO(4+y) sample.
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Figure 8.13: Overviews of naming for four of the superstructures discussed for La(2)CuO(4+y).
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Figure 8.14: Staging - data collapsed along k for the La(2)CuO(4+y) sample.
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Figure 8.15: Staging - data collapsed along k for the La(1.94)Sr(0.06)CuO(4+y) sample.
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Figure 8.16: Staging - data collapsed along k for the La(1.91)Sr(0.09)CuO(4+y) sample.
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Figure 8.17: Allowed reflections in the (0kl) and (hk0) planes.
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Figure 8.18: Chain data - for the La(2)CuO(4+y) sample collapsed along l.
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Figure 8.19: Crosses - example of collapsed data for La(2)CuO(4+y) at T = 10 K and 300 K.
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Figure 8.20: Flowers - example of collapsed data for La(2)CuO(4+y) at T = 10 K and 300 K.
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Figure 8.21: Flowers - example of collapsed data for La(1.94)Sr(0.06)CuO(4+y) at T = 2 K and 300 K.
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Figure 8.22: Flowers - example of collapsed data for La(1.91)Sr(0.09)CuO(4+y) at T = 100 K.
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Figure 8.23: Comparing two different La(2)CuO(4+y) sample (0kl) planes.
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Figure A.5: Coordinate system used for the calculation with DMC detector height.
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SXD illustrations and data plots (chapter 9)

Figure 9.1: Overview sketch of the SXD instrument.
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Figure 9.2: Photos of the SXD instrument.
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Figure 9.3: The La(2)CuO(4+y) sample measured on SXD.
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Figure 9.4: Example of a Laue view from the SXD instrument.
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Figure 9.5(a): Example of unwarped (0kl) planes from SXD at 10 K (non-symmetrised).
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Figure 9.5(b): Example of unwarped (0kl) planes from SXD at 10 K (symmetrised).
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Figure 9.6: Unwarped kl planes at varied h - showing volume on SXD.
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Figure 9.7(a): DMC comparison plots - unwarped (0kl) SXD plane at 10 K.
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Figure 9.7(b): DMC comparison plots - unwarped (hk0) SXD plane at 10 K.
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Figure 9.8(a): DMC comparison plots - unwarped (0kl) SXD plane at 290 K.
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Figure 9.8(b): DMC comparison plots - unwarped (hk0) SXD plane at 290 K.
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Figure 9.9: Staging - collapsed DMC-thickness data around eight different Bmab peaks.
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Figure 9.10: Zoomed in look at the 10 K (0kl) non-integrated plane.
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Figure 9.11: Staging - comparing collapses of DMC-thick. and non-int. maps at 10 K.
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Figure 9.12: Chains - comparing collapses of DMC-thick. and non-int. maps at 10 K and 290 K.
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Figure 9.13(a): A look at the (1kl) plane at 10 K.
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Figure 9.13(b): A look at the (1kl) plane at 290 K.
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Figure 9.14: SXD animation snapshots - kl planes at 10 K.
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Figure 9.15: SXD animation snapshots - hk planes at 10 K.
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Laboratory X-ray illustrations and data plots (chapter 10)

Figure 10.1: The Gemini and SuperNova instruments.
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Figure 10.2: Photos of the Gemini laboratory X-ray instrument setup.
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Figure 10.3: Mounting of the samples to kapton loops.
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Figure 10.4: Close-up photos of the samples measured on the laboratory X-ray instruments.
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Figure 10.5: Timeline of the laboratory X-ray measurements on the six main samples.
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Figure 10.6: Examples of raw laboratory X-ray frames.
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Figure 10.7: Overview of lattice constants found in X-ray source measurements.
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Figure 10.8: Unwarped (0kl) planes for some of the main data sets.
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Figure 10.9: Unwarped (0kl) plane of the LSCO_01_long scan (non-symmetrised and symmetrised).
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Figure 10.10: Unwarped (hk0) plane of the LSCO_01_long scan (non-symmetrised and symmetrised).
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Figure 10.11: Examples of Ewald3D views from the CrysAlis software.
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Figure 10.12: Unwarped kl planes at varied h - showing volume for LSCO_01_long scan.
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Figure 10.13: Unwarped (0kl) and (hk0) planes of the LSCO_01_long scan in full view.
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Figure 10.14: Examples of unwarped (0kl) planes exported directly from CrysAlis.
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Figure 10.15: Unwarped (0kl) planes for LSCO_01 and LSCO_07 - zoom around (0,-3,2).
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Figure 10.16: Unwarped (0kl) planes for LSCO_01 and LSCO_07 - zoom around (0,-2,4).
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Figure 10.17: Unwarped (0kl) planes for LSCO_01 and LSCO_07 - zoom around (0,0,-6).
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Figure 10.18: Unwarped (hk0), (hk1), (hk2), and (hk3) planes for two samples.
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Figure 10.19: DMC comparison plots - for the LSCO_01_long scan.
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TriCS illustrations and data plots (chapter 11)

Figure 11.1: Overview sketch of the TriCS instrument.
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Figure 11.2: A close-up of the TriCS instrument.
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Figure 11.3: The La(1.94)Sr(0.06)CuO(4+y) sample measured on TriCS.
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Figure 11.4: The (±4, ±4, 0) peaks measured at room temperature.
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Figure 11.5: Scans of three peaks using the 2D detector at room temperature.
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Figure 11.6: Measurement at Bmab peak location at 5 K and 300 K.
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Figure 11.7: Scans of four peaks using the 2D detector at low temperature.
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Figure 11.8: Measurements of (011), (101), (054), and (504) peaks as a function of temperature.
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Figure 11.9: Measurements of (200) and (220) peaks as a function of temperature.
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Figure 11.10: Zoom-in of (220) peak measured on DMC for La(1.94)Sr(0.06)CuO(4+y) at T = 2 K.
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Figure 11.11: Fobs versus Fcalc values for the 300 K data set refined in JANA2006.
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Discussion illustrations (chapter 12)

Figure 12.1: Comparing a standard unwarp with a background subtracted unwarp.
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Figure 12.2: Comparing different integration thicknesses for lab. X-ray data.
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Figure 12.3: Comparison of (0kl) and (h0l) planes.
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Figure 13.1: Example of ID11 data frames.
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Details on samples (appendix B)

Figure B.1: Overview of the sLCO_DTU_A and sLCO_DTU_B crystals after cutting.
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Figure B.2: The polished sLCO_DTU_B2 crystal.
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Figure B.3: Different batches of La(2-x)Sr(x)CuO(4) powders in progress.
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Figure B.4: Growing single crystals in a mirror furnace.
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Figure B.5(a): TGA measurements done on two pieces of a La(2)CuO(4+y) sample.
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Figure B.5(b): TGA measurements done on two pieces of a La(2)CuO(4+y) sample.
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Figure B.6: Susceptibility data for the sLCO_0B sample.
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Figure B.7: Susceptibility data for three different samples at different fields.
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Figure B.8: Finding critical temperature by linear fits.
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Figure B.9: Critical temperatures found in susceptibility data.
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Figure B.10: Effect of cooling and heating rates on susceptibility.
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Extra data figures (appendix D)

Figure D.1: Raw DMC reciprocal plane - (0kl) for La(2)CuO(4+y) at T = 10 K.
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Figure D.2: Raw DMC reciprocal plane - (0kl) for La(2)CuO(4+y) at T = 100 K.
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Figure D.3: Raw DMC reciprocal plane - (0kl) for La(2)CuO(4+y) at T = 300 K.
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Figure D.4: Raw DMC reciprocal plane - (hk0) for La(2)CuO(4+y) at T = 10 K.
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Figure D.5: Raw DMC reciprocal plane - (hk0) for La(2)CuO(4+y) at T = 300 K.
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Figure D.6: Raw DMC reciprocal plane - (0kl) for La(2)CuO(4+y) (other sample) at T = 5 K.
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Figure D.7: Raw DMC reciprocal plane - (0kl) for La(1.94)Sr(0.06)CuO(4+y) at T = 100–1.5 K.
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Figure D.8: Raw DMC reciprocal plane - (0kl) for La(1.94)Sr(0.06)CuO(4+y) at T = 100 K.
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Figure D.9: Raw DMC reciprocal plane - (0kl) for La(1.94)Sr(0.06)CuO(4+y) at T = 300 K.
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Figure D.10: Raw DMC reciprocal plane - (hk0) for La(1.94)Sr(0.06)CuO(4+y) at T = 2 K.
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Figure D.11: Raw DMC reciprocal plane - (hk0) for La(1.94)Sr(0.06)CuO(4+y) at T = 300 K.
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Figure D.12: Raw DMC reciprocal plane - (0kl) for La(1.91)Sr(0.09)CuO(4+y) at T = 100 K.
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Figure D.13: Raw DMC reciprocal plane - (0kl) for La(1.91)Sr(0.09)CuO(4+y) at T = 300 K.
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Figure D.14: Raw DMC reciprocal plane - (hk0) for La(1.91)Sr(0.09)CuO(4+y) at T = 100 K.
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Figure D.15(a): Choice of maximum intensity cut-off for DMC plots.
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Figure D.15(b): Choice of maximum intensity cut-off for DMC plots.
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Figure D.16: Staging - data collapsed narrower along k for the La(2)CuO(4+y) sample.
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Figure D.17: Staging - data collapsed narrower along k for the La(1.94)Sr(0.06)CuO(4+y) sample.
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Figure D.18: Staging - data collapsed narrower along k for the La(1.91)Sr(0.09)CuO(4+y) sample.
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Figure D.19: La(1.94)Sr(0.06)CuO(4+y) cooling run - temperature as a function of sample rotation.
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Figure D.20: La(1.94)Sr(0.06)CuO(4+y) cooling run - reciprocal-space map with markings.
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Figure D.21: Crosses - overview of collapsed cut-outs for La(2)CuO(4+y) at T = 10 K.
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Figure D.22: Crosses - overview of collapsed cut-outs for La(2)CuO(4+y) at T = 300 K.
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Figure D.23: Crosses - collapsed data around k = 2 for La(2)CuO(4+y) at T = 10 K.
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Figure D.24: Crosses - collapsed data around k = 0 for La(2)CuO(4+y) at T = 10 K.
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Figure D.25: Crosses - collapsed data around k = −2 for La(2)CuO(4+y) at T = 10 K.
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Figure D.26: Crosses - collapsed data around k = 2 for La(2)CuO(4+y) at T = 300 K.
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Figure D.27: Flowers - overview of collapsed cut-outs for La(2)CuO(4+y) at T = 10 K.
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Figure D.28: Flowers - overview of collapsed cut-outs for La(1.94)Sr(0.06)CuO(4+y) at T = 300 K.
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Figure D.29: Flowers - collapsed data for La(1.94)Sr(0.06)CuO(4+y) at T = 10 K and 300 K.
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Figure D.30: Flowers - overview of collapsed cut-outs for La(1.94)Sr(0.06)CuO(4+y) at T = 2 K.
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Figure D.31: Flowers - overview of collapsed cut-outs for La(1.94)Sr(0.06)CuO(4+y) at T = 300 K.
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Figure D.32: Flowers - collapsed data for La(1.94)Sr(0.06)CuO(4+y) at T = 2 K.
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Figure D.33: Flowers - collapsed data for La(1.94)Sr(0.06)CuO(4+y) at T = 300 K.
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Figure D.34: Flowers - overview of collapsed cut-outs for La(1.91)Sr(0.09)CuO(4+y) at T = 100 K.
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Figure D.35: Flowers - collapsed data for La(1.91)Sr(0.09)CuO(4+y) at T = 100 K.
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Figure D.36: Laue view from SXD - scans at low temperature.
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Figure D.37: Laue view from SXD - scans at room temperature.
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Figure D.38: Laue view from SXD - a background scan.
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Figure D.39: Temperature over time for two SXD data sets.
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Figure D.40: Examples of unwarped (hk0) planes from SXD at 10 K (non-symmetrised and symmetrised).
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Figure D.41: Examples of unwarped (0kl) and (hk0) planes from SXD measurements at 290 K.
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Figure D.42: Unwarped hk planes at varied l - showing volume on SXD.
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Figure D.43: Central map for each of the two 3D SXD overviews.
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Figure D.44: Raw SXD reciprocal planes - DMC comparable (0kl) and (hk0) at 10 K.
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Figure D.45: Raw SXD reciprocal planes - DMC comparable (0kl) and (hk0) at 290 K.
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Figure D.46: Raw SXD reciprocal planes - DMC comparable (0kl) and (hk0) at 10 K (no zoom).
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Figure D.47: Raw SXD reciprocal planes - DMC comparable (0kl) and (hk0) at 290 K (no zoom).
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Figure D.48: Zoomed in look at the 290 K (0kl) (non-integrated) plane.
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Figure D.49: Staging - collapsed non-integrated data around eight different Bmab peaks.
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Figure D.50: Unwarped (0kl) plane of the LSCO_01_110mm scan (non-symmetrised and symmetrised).
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Figure D.51: Unwarped (hk0) plane of the LSCO_01_110mm scan (non-symmetrised and symmetrised).
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Figure D.52: Unwarped (0kl) plane of the LSCO_07_long scan (non-symmetrised and symmetrised).
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Figure D.53: Unwarped (hk0) plane of the LSCO_07_long scan (non-symmetrised and symmetrised).
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Figure D.54: Unwarped (0kl) plane of the LSCO_07_longest scan (non-symmetrised and symmetrised).
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Figure D.55: Unwarped (hk0) plane of the LSCO_07_longest scan (non-symmetrised and symmetrised).
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Figure D.56: Unwarped hk planes at varied l - showing volume for LSCO_01_long scan.
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Figure D.57: Unwarped kl planes at varied h - showing volume for LSCO_01_110mm scan.
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Figure D.58: Unwarped hk planes at varied l - showing volume for LSCO_01_110mm scan.
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Figure D.59: Unwarped kl planes at varied h - showing volume for LSCO_07_long scan.
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Figure D.60: Unwarped hk planes at varied l - showing volume for LSCO_07_long scan.
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Figure D.61: Unwarped kl planes at varied h - showing volume for LSCO_07_longest scan.
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Figure D.62: Unwarped hk planes at varied l - showing volume for LSCO_07_longest scan.
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Figure D.63: Unwarped (0kl) planes for each of the main data sets.
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Figure D.64: Unwarped (1kl) planes for each of the main data sets.
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Figure D.65: Unwarped (2kl) planes for each of the main data sets.
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Figure D.66: Unwarped (3kl) planes for each of the main data sets.
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Figure D.67: Unwarped (hk0) planes for each of the main data sets.
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Figure D.68: Unwarped (hk1) planes for each of the main data sets.
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Figure D.69: Unwarped (hk2) planes for each of the main data sets.
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Figure D.70: Unwarped (hk3) planes for each of the main data sets.
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Figure D.71: DMC comparison plots - for the LSCO_01_long scan.
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Figure D.72: DMC comparison plots - for the LSCO_01_110mm scan.
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Figure D.73: DMC comparison plots - for the LSCO_07_long scan.
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Figure D.74: DMC comparison plots - for the LSCO_07_longest scan.
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