Figure 1.1 · structure-drawing · Thesis 4 · Orayech 2015The schematic representation of the cubic simple perovskite structure $A B O_{3}$. The $A$ and $B$ cations are shown as yellow and blue sphe… Figure 1.2 · other · Thesis 4 · Orayech 2015Cation ordering schemes in perovskites. From left to the right: rock salt, layered and columnar ordering are shown for $B$-site ordering in… Figure 1.3 · structure-drawing · Thesis 4 · Orayech 2015Types of ordering in perovskites with two different $B$-site cations. (a) Ideal rock-salt ordering; (b) partial rock-salt ordering with loca… Figure p1-9 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure 3.1 · other · Thesis 4 · Orayech 2015Geometrical illustration of the Braggs' law. Figure 3.2 · other · Thesis 4 · Orayech 2015The schematic of the powder diffraction cones produced by a polycrystalline sample while its interaction with an incident-beam. Figure 4.1 · group-subgroup-tree · Thesis 4 · Orayech 2015Graph of maximal subgroups relating the $F m \overline{3} m$ and the $P 2_{1} / c$ space groups of room temperature $\mathrm{Sr}_{2} M \mathrm{SbO}_{6}(M=L n, Y$… Figure 4.2 · group-subgroup-tree · Thesis 4 · Orayech 2015Graph of maximal subgroups relating the $P m \overline{3} m$ and the $A m m 2$ space groups of room temperature $\mathrm{Na}_{0.5} \mathrm{K}_{0.5} \mathrm{O}_{3}$… Figure 5.1 · tem · Thesis 4 · Orayech 2015a shows the general aspect of the powder sample. Two different types of particles can be observed: large particles of about $2-8 \mu m$ and… Figure 5.2 · rietveld-plot · Thesis 4 · Orayech 2015Experimental (symbols) and calculated (line) a) neutron and b) X-ray profiles for the Rietveld refinement of $\mathrm{Na}_{0.5} \mathrm{K}_{0.5} \mathrm{NbO}_{3}$… Figure 5.3 · structure-drawing · Thesis 4 · Orayech 2015To the left, chain of maximal sub-groups of $P m \overline{3} m$ space group down-to the experimentally observed room-temperature $A m m 2$… Figure 5.4 · tem · Thesis 4 · Orayech 2015a) Bright field TEM micrograph of a typical particle in the sample. b), d) and e) SAD patterns acquired along the [011], [2-11] and [110] zo… Figure 5.5 · pattern · Thesis 4 · Orayech 2015Thermal evolution at low-temperatures from NPD measurements (to the left) of the 101 rhombohedral reflection, and at high-temperatures from… Figure 5.6 · other · Thesis 4 · Orayech 2015Results of the refinements, in the $75^{\circ}-82^{\circ} 2 \theta$ and $98^{\circ}-106^{\circ} 2 \theta$ intervals, in $\mathrm{Na}_{0.5} \mathrm{K}_{0.5} \mathrm{NbO}_{3}$… Figure 5.7 · pattern · Thesis 4 · Orayech 2015Portion of (a) NPD and (b) XRPD profiles for $\mathrm{Na}_{0.5} \mathrm{K}_{0.5} \mathrm{NbO}_{3}$ showing, at selected temperatures $70,150,350,550$… Figure 5.8 · structure-drawing · Thesis 4 · Orayech 2015To the left, chain of maximal sub-groups of $P m \overline{3} m$ parent phase space group down-to the experimentally observed low-temperatur… Figure 5.9 · rietveld-plot · Thesis 4 · Orayech 2015Experimental (symbols) and calculated (line) neutron profiles for the Rietveld refinement of $\mathrm{Na}_{0.5} \mathrm{K}_{0.5} \mathrm{NbO}_{3}$… Figure 5.10 · cell-vs-t · Thesis 4 · Orayech 2015Thermal evolution of the lattice parameters of $\mathrm{Na}_{0.5} \mathrm{K}_{0.5} \mathrm{NbO}_{3}$, as obtained from XRPD and NPD measurem… Figure 5.11 · mode-drawing · Thesis 4 · Orayech 2015(a) Relative atomic displacements with respect to the cubic structure, in the P4mm phase: those define polar distortion mode. (b) The four b… Figure 5.12 · amplitude-vs-t · Thesis 4 · Orayech 2015(a) Results from the conventional symmetry adapted modes' amplitude refinements. See the text for details. (b) The structures obtained after… Figure 5.13 · amplitude-vs-t · Thesis 4 · Orayech 2015Results of the parameterized refinement. For further discussion, see the text. The dimmed symbols show the results obtained for the first pa… Figure 5.14 · amplitude-vs-t · Thesis 4 · Orayech 2015Evolution with temperature of the tetra-vector, but split in two parts: amplitudes of the modes $\mathrm{Na} / \mathrm{K}(x)$ versus those o… Figure 5.15 · structure-drawing · Thesis 4 · Orayech 2015Calculated SP (see the text for further details). Different colours represent the points of the SP resulting from the data of different sour… Figure 6.1 · tem · Thesis 4 · Orayech 2015(a) Secondary electron image showing the overall appearance of the powder sample. The inset shows an enlargement of a particle. (b) Back-sca… Figure 6.2 · tem · Thesis 4 · Orayech 2015(a) Bright field image of electron transparent area of one particle. (b) Selected area electron diffraction pattern acquired along the [001]… Figure 6.3 · amplitude-vs-t · Thesis 4 · Orayech 2015Amplitudes of $\mathrm{GM}_{4}^{+}$(spheres), $\mathrm{X}_{3}^{+}$(stars), the global amplitude-value for the tri-dimensional $\mathrm{X}_{5}^{+}$… Figure 6.4 · rietveld-plot · Thesis 4 · Orayech 2015Experimental (symbols) and calculated (line) (a) X-ray profiles and (b) neutron profiles from the Rietveld refinements of $\mathrm{La}_{2} \mathrm{CoMnO}_{6}$… Figure 6.5 · amplitude-vs-t · Thesis 4 · Orayech 2015Two dimensional sections showing the mode-amplitudes of the three dimensional space transforming according to the $\mathrm{X}_{5}^{+}$irrep.… Figure 6.6 · cell-vs-t · Thesis 4 · Orayech 2015Evolution, at room temperature, of the cell parameters along the analyzed structures in the families: $\mathrm{Ln}_{2} \mathrm{CoMnO}_{6}$ (… Figure 6.7 · pattern · Thesis 4 · Orayech 2015Thermal evolution of selected ranges in $2 \theta$, obtained from the XRPD experiment: (a) $24.5-27^{\circ}$, corresponding to the (111) pri… Figure 6.8 · rietveld-plot · Thesis 4 · Orayech 2015Temperature evolution of the amplitudes of the modes breaking the symmetry from the cubic to the $P 2_{1} / n$ and $R \overline{3}$ symmetri… Figure 6.9 · cell-vs-t · Thesis 4 · Orayech 2015Variation with temperature of the lattice parameters for $\mathrm{La}_{2} \mathrm{CoMnO}_{6}$, as obtained from the NPD (2-300 K)(dimmed bla… Figure 7.1 · amplitude-vs-t · Thesis 4 · Orayech 2015Energy projections, in the $\mathrm{X} 5+$ two-dimensional space (A10, A11), for a fixed value of $\mathrm{X}_{3}^{+}$as indicated and for t… Figure 7.2 · amplitude-vs-t · Thesis 4 · Orayech 2015(a) Evolution with the tolerance factor of the partial distortion of the $\mathrm{Sr}_{2} \mathrm{MM}^{\prime} \mathrm{O}_{6}$ given by the… Figure 7.3 · amplitude-vs-t · Thesis 4 · Orayech 2015(a) Representation of the $\mathrm{X}_{5}^{+}$direction given by the components $c 1$ et $c 2$ for the $\mathrm{Sr}_{2} \mathrm{MM}^{\prime} \mathrm{O}_{6}$… Figure 8.1 · pattern · Thesis 4 · Orayech 2015(a) Evolution of the synchrotron X-ray powder diffraction patterns at room temperature of the $\mathrm{Sr}_{2} \mathrm{MSbO}_{6}(\mathrm{M}=\mathrm{Ln}, \mathrm{Y})$… Figure 8.2 · rietveld-plot · Thesis 4 · Orayech 2015Graph of maximal subgroups relating the space groups of the parent phase (highlighted in blue) and distorted phase (highlighted in green) of… Figure 8.3 · rietveld-plot · Thesis 4 · Orayech 2015Experimental and calculated powder diffraction profiles for the Rietveld refinement of $\mathrm{Sr}_{2} \mathrm{NdSbO}_{6}$ (a) and $\mathrm{Sr}_{2} \mathrm{YbSbO}_{6}$… Figure 8.4 · amplitude-vs-t · Thesis 4 · Orayech 2015a): Amplitudes of $\mathrm{GM}_{4}^{+}, \mathrm{X}_{3}^{+}$and $\mathrm{X}_{5}^{+}$irreps consolidating the RT phases of $\mathrm{Sr}_{2} \mathrm{MSbO}_{6} \mathrm{M}=\mathrm{Ln}$… Figure 8.5 · cell-vs-t · Thesis 4 · Orayech 2015Evolution, as a function of the tolerance factor increasing of the unit-cell parameters (a), the unit-cell volume (b) and the monoclinic ang… Figure 8.6 · pattern · Thesis 4 · Orayech 2015Thermal evolution of the $22-26^{\circ} 2 \theta$ interval, corresponding to the monoclinic primitive reflections (-111) and (111) (top) whi… Figure 8.7 · amplitude-vs-t · Thesis 4 · Orayech 2015Temperature evolution of the amplitudes of some of the symmetry adapted modes in $P 2_{1} / n$ and $R \overline{3}$, as obtained from the XR… Figure 8.8 · cell-vs-t · Thesis 4 · Orayech 2015Temperature evolution of the lattice parameters of $\mathrm{Sr}_{2} \mathrm{MSbO}_{6}$. The cell parameters of the trigonal phase are shown… Figure 8.9 · phase-diagram · Thesis 4 · Orayech 2015Phase diagram (phase transition temperatures versus tolerance factors) for the $\mathrm{Sr}_{2} \mathrm{MSbO}_{6}$ ( $\mathrm{M}=\mathrm{Ln}, \mathrm{Y}$… Figure 9.1 · pattern · Thesis 4 · Orayech 2015Splitting of the singlet cubic reflection (444) ${ }_{\mathrm{c}}$ into a triplet: (404), (-404) and (044) reflections. The plot shows a fit… Figure 9.2 · pattern · Thesis 4 · Orayech 2015Selected $2 \theta$ intervals for the four compositions of the $\mathrm{Sr}_{2} \mathrm{Co}_{1-x} \mathrm{Mg}_{x} \mathrm{TeO}_{6}$ series.… Figure 9.3 · rietveld-plot · Thesis 4 · Orayech 2015Experimental (symbols) and calculated (line) X-ray profiles and neutron profiles for the Rietveld refinement of the $\mathrm{Sr}_{2} \mathrm{Co}_{1-x} \mathrm{Mg}_{x} \mathrm{TeO}_{6}$… Figure 9.4 · amplitude-vs-t · Thesis 4 · Orayech 2015Variation, as function of the tolerance factor, of the three distortion irrep amplitudes $\mathrm{GM}_{4}^{+}$ (black), $\mathrm{X}_{3}^{+}$… Figure 9.5 · pattern · Thesis 4 · Orayech 2015Disappearance, as temperature increases, of the primitive reflections (311), (-311), (131) and (-131) of the $\mathrm{Sr}_{2} \mathrm{Co}_{0.9} \mathrm{Mg}_{0.1} \mathrm{TeO}_{6}$… Figure 9.6 · pattern · Thesis 4 · Orayech 2015Thermal evolution of the (444) cubic reflection splitting located in the interval ( $82^{\circ}<2 \theta<{ }^{\circ} 86$) for the $\mathrm{Sr}_{2} \mathrm{Co}_{1-x} \mathrm{Mg}_{x} \mathrm{TeO}_{6}$… Figure 9.7 · amplitude-vs-t · Thesis 4 · Orayech 2015Temperature dependence of (a-c) the amplitudes of the modes related to the $P 2_{1} / n, I 2 / m$ and $I 4 / m$ symmetries and (d-f) their c… Figure 10.1 · rietveld-plot · Thesis 4 · Orayech 2015Experimental (symbols) and calculated (line) X-ray profiles and neutron profiles for the Rietveld refinement of the $\mathrm{Sr}_{2} \mathrm{Ni}_{1-x} \mathrm{Mg}_{x} \mathrm{TeO}_{6}$… Figure 10.2 · amplitude-vs-t · Thesis 4 · Orayech 2015(a): Variation, as function of the tolerance factor, of the distortion-amplitude transforming according to the $\mathrm{GM}_{4}^{+}$irrep an… Figure 10.3 · amplitude-vs-t · Thesis 4 · Orayech 2015Temperature dependence of the mode-amplitudes refined in the $P 2_{1} / n, I 2 / m$ and $I 4 / m$ space groups for the $\mathrm{Sr}_{2} \mathrm{Ni}_{1-x} \mathrm{Mg}_{x} \mathrm{TeO}_{6}$… Figure 10.4 · pattern · Thesis 4 · Orayech 2015Thermal evolution of different splitted reflections for the $\mathrm{Sr}_{2} \mathrm{NiTeO}_{6}$ compound. Figure 10.5 · pattern · Thesis 4 · Orayech 2015Thermal evolution of different splitted reflections located in the interval ( $75^{\circ}<2 \theta<^{\circ} 77$) for the $\mathrm{Sr}_{2} \mathrm{Co}_{1-x} \mathrm{Mg}_{x} \mathrm{TeO}_{6}$… Figure 10.6 · phase-diagram · Thesis 4 · Orayech 2015Tolerance factor and temperature dependence phase diagram of $\mathrm{Sr}_{2} \mathrm{MSbO}_{6}$ and $\mathrm{Sr}_{2} \mathrm{MTeO}_{6}$. Th… Figure 10.7 · pattern · Thesis 4 · Orayech 2015(a) Evolution of the laboratory X-ray powder diffraction patterns of $\mathrm{Ca}_{2} \mathrm{MSbO}_{6}(\mathrm{M}=\mathrm{Nd}, \mathrm{Eu}$… Figure 10.8 · rietveld-plot · Thesis 4 · Orayech 2015Experimental (symbols) and calculated (line) X-ray powder diffraction profiles for the Rietveld refinement of $\mathrm{Ca}_{2} \mathrm{EuSbO}_{6}$… Figure 10.9 · amplitude-vs-t · Thesis 4 · Orayech 2015Variation of the $\mathrm{GM}_{4}^{+}, \mathrm{X}_{3}^{+}$and $\mathrm{X}_{5}^{+}$distortion irreps in the monoclinic symmetry $P 2_{1} / n$… Figure 10.10 · amplitude-vs-t · Thesis 4 · Orayech 2015Two dimensional section showing the obtained amplitudes of the irreps (Blue) $\mathrm{GM}_{4}^{+}$, (Red) $\mathrm{X}_{3}^{+}$and the two co… Figure 10.11 · cell-vs-t · Thesis 4 · Orayech 2015Evolution, as a function of the tolerance factor increasing of the unit-cell parameters (a), the unit-cell volume (b) and the monoclinic ang… Figure 10.12 · other · Thesis 4 · Orayech 2015Evolution of the occupancy x (which is the fraction of the Calcium in the B-site occupying by the $\mathrm{M}^{3+}$ element in the formula $\left.\left[\mathrm{Ca}_{1+x} \mathrm{M}_{1-x}\right]\left[\mathrm{M}_{x} \mathrm{Ca}_{1-x}\right] \mathrm{SbO}_{6}\right)$… Figure 10.13 · group-subgroup-tree · Thesis 4 · Orayech 2015Group-subgroup tree connecting the paraelectric $P 4 / n m m$ phase to the ferroelectric $P 2_{1}$ phase Figure 10.14 · structure-drawing · Thesis 4 · Orayech 2015Images in the real space and in the reciprocal space, showing clearly the Nano-Chessboard structure. Figure 10.15 · structure-drawing · Thesis 4 · Orayech 2015Theoretical models describing the Nano-Chessboards structure. Figure 10.16 · raman · Thesis 4 · Orayech 2015Raman spectra of the monoclinic $\mathrm{Sr}_{2} \mathrm{MSbO}_{6}(\mathrm{M}=\mathrm{La}, \mathrm{Nd}, \mathrm{Sm}$ and Eu$)$ measured at r… Figure p62-842 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p130-1662 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p218-2566 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p219-2573 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p220-2580 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p221-2587 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p222-2615 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p224-2665 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p226-2703 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p254-3554 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p254-3557 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p255-3560 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p255-3563 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p256-3578 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p257-3592 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p258-3609 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p259-3625 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p260-3643 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p261-3674 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p262-3703 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p263-3724 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p264-3729 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image) Figure p264-3734 · other · Thesis 4 · Orayech 2015(no caption found; uncaptioned image)