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The icosahedral quasicrystal (i-QC), an aperiodic crystal, exhibits non-crystallographic symmetry in three-dimensional space. Its unique structural properties continue to draw significant attention in Condensed Matter Physics. Tsai-type i-QCs for example, have been the focus of extensive research since 2000. However, due to challenges in determining the structure of i-QCs, their exact crystal chemistry and the relationship between their structure and physical properties remains unclear. So-called quasicrystal approximants (ACs) share similar atomic arrangements and chemical compositions with their aperiodic siblings. The exploration of the correlation between structural and physical properties in periodic ACs thus permits to gain deeper insights into local structures that resemble those of QCs, and thus on the crystal chemistry of QCs.

This thesis deepens our understanding of the Tsai-type ACs and QCs, focusing on optimizing synthesis methods and using single-crystal X-ray diffraction (SCXRD) to elucidate the crystal chemistry of ACs. Structural evaluations of various ACs employ elemental tuning and substitution in binary and ternary Tsai-type systems such as Gd-Cd and Gd-Au-Al; the results are connected to the observed magnetic properties.

Chapter 1 provides an overview of QCs and ACs, covering their history, structure, and physical properties to give readers a solid background on the topic. Chapter 2 outlines the synthesis methods and sample characterization techniques used in this research. Chapter 3 presents the key findings, including a detailed structural evaluation of ACs, AC-related superstructures, and more complex AC structures. This analysis clarifies the structural mechanisms associated with phase stability and connect them to their physical (magnetic) properties. Finally, a summary of the thesis main contribution to the research community, and concluding remarks on the chemical insights into the structural and physical properties of ACs and QCs are given in Chapter 4.

Magnetic materials play a vital role in modern society, with applications ranging from data storage and electric power generation to magnetic refrigeration and gas liquefaction. This thesis explores structure-magnetism relationships in selected magnetic intermetallics, with particular emphasis on magnetic structure determination using neutron diffraction as the primary tool. Intermetallics, formed by combining two or more metals or metalloids, offer a unique platform where physical properties can be tuned through structural modifications. Understanding these relationships is essential not only for applications but also for deepening our knowledge of how structure and magnetism intertwine in complex systems.  

This work is broadly divided into two parts. The first focuses on Tsai-type quasicrystal approximants in the RE-Au-E systems (RE = Sm, Ho, Tb; E = Al, Si). Large single crystals were grown and studied using single-crystal neutron diffraction, enabling detailed and unambiguous determination of their spin structures. Ho-Au-Al was found to exhibit a non-coplanar, non-collinear ferrimagnetic arrangement with a whirling spin order along the crystallographic [111] direction. In Tb-Au-Si, where an additional RE atom modifies the Tsai phase (pseudo-Tsai phase), a similar spin arrangement was observed, but with partial disorder induced by the extra RE site.  

The second part studies magnetocaloric materials, specifically Fe₂P-based and RE₂In (RE = Nd, Pr, Tb, Ce) compounds, which are among the most promising candidates for energy-efficient cooling technologies. In Fe₂P substituted with Mn and Si, compositions near Fe₂ P showed incommensurate antiferromagnetic ordering as revealed from neutron powder diffraction, highlighting the extreme sensitivity to Mn substitution. For RE₂In compounds, distinct magnetic phase transitions were observed depending on the RE element, in which Nd₂In adopts a commensurate modulated structure below its magnetic phase transition (TC ≈ 110 K), while Pr₂In evolves from a simple ferromagnetic structure at 45 K to a modulated phase at lower temperatures. Mixed RE substitutions in RE₂In were further explored as a strategy to tune their magnetic properties.