Reacción de estado sólido en compuestos polimorfos tipo RE2(MoO4)3 monitorizados por termodifractrometría en un sincrotrón

Abstract

This work is focuses on the study of the solid-state synthesis and phase transitions of rare-earth molybdates with formula 𝑅𝐸2 (𝑀𝑜𝑂4 )3 by X-Ray thermodiffraction, with powder samples. This family of compounds is interesting because it consists of up to 10 different polymorphs. Thus, their structural variety gives them important physical properties with interesting applications. The stoichiometric mixture of the oxides 𝑀𝑜𝑂3 and 𝑅𝐸2𝑂3 where 𝑅𝐸 ≡ 𝑁𝑑, 𝑆𝑚, 𝐸𝑢 𝑦 𝐺𝑑 were used as initial samples. Since this work is not completely experimental, we decided to introduce this family of compounds, in detail, by plotting and describing the different crystal structures of the two main polytypes: modulated scheelites, and ferroic phases. For this purpose, we made a bibliographic tour from the fundamental to modern crystallography, defining concepts such as polytypes, crystalline symmetry, space and superspace groups, modulated structures, among others. The experiment was performed at the ESRF synchrotron (Grenoble, France); specifically, with the Spanish beamline BM25-A, six year ago. The collected data have never been fully analysed, so, it has been necessary to retrieve and review the experimental conditions and explain them in detail. While we are reviewing the experimental data, we have decided to explain how a synchrotron works and its advantages over a conventional X-ray tube. In addition, we also review some basic concepts of diffraction for describing the diffraction by crystalline powder. Regarding the experimental conditions, we distinguish between the first heating, in which the compounds with stoichiometry RE2Mo3O12 were formed (from room temperature up to 900ºC), and the other cooling and heating cycles, to study the phase transitions. The schedule followed for the Nd and Sm samples was similar and it consisted of more cycles than for the Eu and Gd samples, as time in these experiments is limited. The heating and cooling cycles were carefully plotted for each sample. There were more than 100 diffractograms, so my role was to help identify and refine some of these diffractograms, in particular the pure phases and the last cycles of the refinements. Before that, I had to explain and distinguish between the phase identification and Le Bail refinement. To achieve the phase identification, we had to plot most of the diffractograms and compare them with the simulated diffractogram for each phase, whose crystal structure was obtained with the help of the ICSD database. In addition, we obtained more quantitative results, such as the lattice parameters, with Le Bail refinements of some selected phases identified at different temperatures. The most difficult work was the identification and refinement of, we believe, all the non-stoichiometric crystalline phases (including starting oxides) before the formation of the α-phase. Afterwards, it was easier to observe the α ⇔ β transition at high temperature. As we progressed in this work, we completed a phase diagram within this family of rare-earth molybdates, studying the sequence and reversibility of the phase transitions. To do so, we have taken into account the temperatures of each cycle and the ionic radii of the rare earths. Some of the phases and transitions found had not been studied before, for example, the non-reversible transitions from the β’ phase, obtained at room temperature by quenching (very fast cooling to freeze the crystalline structure at ambient conditions), to the α-phase or the 𝐿𝑎2 (𝑀𝑜𝑂4 )3 phase, normally obtained by cooling. Along the way we have found a possible phase mixture or an incommensurable phase for the 𝑁𝑑2 (𝑀𝑜𝑂4 )3, during the heating cycle, also from the β’ phase. In contrast, we have not studied the better known β’ ⇔ β’ (ferroelectric-paraelectric) phase transition. From the conclusions obtained we can carry out further refinements and evaluate the thermal dependence of the lattice parameters, as well as publish a scientific paper based on this work. The work has been divided into three chapters: The first chapter was entitled: Introduction to molybdates with 𝑅𝐸2 (𝑀𝑜𝑂4 )3 stoichiometry, crystal structures, polymorphisms and phase transitions. It reviews the state of the art, motivations, aims and objectives of the work and explains the organisation of the work. The second section was devoted to basic explanations of symmetry and direct lattice, crystal systems and crystal classes, space groups and the reciprocal lattice. In the third section we described the different crystals with formula 𝑅𝑒2 (𝑀𝑜𝑂4 )3 divided into modulated scheelites (including the 𝐿𝑎2 (𝑀𝑜𝑂4 )3- and the α-phase) and the ferroelectric-ferroelastic phase and paraelectric-paraelastic phase (i.e. the ferroic phases β and β’). Finally, we described other possible molybdates with different RE/Mo ratios. In the second chapter entitled: Diffraction techniques and experimental conditions. We focused on synchrotron radiation: storage rings and synchrotron radiation sources, the properties of synchrotron radiation and, in particular, the BM25 - X-Ray 'Beamline' from the Spanish CRG. Following sections were dedicated to the X-ray diffraction and polycrystalline samples. From a schematic diagram of a powder diffractometer, we give the experimental conditions of thermodiffraction including heating-cooling schedules. The third chapter is devoted to the analysis of the results and discussion. First, we explain how the different phases can be identified from the experimental diffractograms. For this purpose, we modelled the complete profile with the structural data obtained from the ICSD database and compare them with experimental ones. Second, we explain the Le Bail least-squares refinement and the particular strategies. We presented and discussed the results of the first heating cycle (𝑅𝑒2 (𝑀𝑜𝑂4 )3-phases formation) and the subsequent cooling and heating cycles (thermal evolution and phase transitions). We end this chapter with conclusions and possible future work. Due to the very large and varied literature reviewed (more than fifty articles) and in order not to lose the work done, we added an important part in the supplementary material. Here we include the most complex descriptions, mathematical developments and some very specific definitions.