Logo: to the web site of Uppsala University

This work will begin with an introduction to quasicrystals (QCs) and their structure, defining the unit cell-equivalent for icosahedral quasiperiodicity: a 3D tiling based on the golden ratio and aperiodic in all three dimensions. We briefly present the cut-and-project method used to generate QCs from a higher dimension hypercrystal, and how to build the 3D Penrose tilings, composed of the two golden rhombohedra. We introduce the atomic elementary units used to understand Tsai-type icosahedral QCs and their related approximant crystals (ACs). Approximants are conventional periodic crystals with local atomic environments very similar to their QC counterparts. Two methods for synthesis of Tsai-type QCs and approximants are introduced, the self-flux method as well as a rapid quench method. We describe briefly the differences between the two methods and aspect about phase stability for QCs and ACs obtained in binary and ternary systems. Various types of structural modulations can be induced in ACs which are absent from QCs. We present a new criterion discovered during the doctoral studies, which links the structure of existing ACs to the existence of stable QC counterparts. Basic concepts of magnetism relevant to Tsai systems are then introduced, with a description of the 4f shell magnetism in lanthanide elements, how it differs from transition metal magnetism, with localized (and relatively large) magnetic moments. In intermetallic systems such as Tsai-type QCs and ACs, the main type of magnetic interaction is of RKKY type. We link their structure to the magnetic behavior and phase transition that can occur in frustrated systems: spin glass, reentrant spin glass, spin ice, etc. and how they can be related to various Tsai systems.