The study of magnetism on a triangular lattice has intrigued physicists for some years, as this special arrangement allows the probing of new electronic phenomena by frustrating the dominant nearest-neighbor couplings. Every project presented here bears importance to geometric frustration. Three chapters present research on compounds in previously known crystal structure families that exhibit signs of geometric frustration: pyrochlores (ch. 2), anhydrous alums (ch. 3) and yavapaiites (ch. 4). The last two chapters (5 and 6) present the discovery of two previously unknown crystal structures, both possessing triangles within their structures, and which may lead to future discoveries within the field of geometric frustration.;In addition to the magnetic properties of triangular lattice materials, each project presents important progress in the crystallography of these materials. It was shown that the pyrochlores could soak up oxygen into the normally vacant 8a site forming a metastable material with excess oxygen. The anhydrous alums were shown to exhibit an inherent disorder along one crystallographic axis. The discovery of this feature led to the reassignment of the crystal structure of anhydrous alum itself, KAl(SO4)2. A comparison of the known anhydrous alums and the related yavapaiite structures has shown a non-systematic correlation of cation radius and electron count to specific crystallographic features such as unit cell size and bond angles. The discovery of two crystal structures in the Pb-Mn-SO4 phase diagram revealed novel crystallographic features. The first, PbMn5(SO4) 6, has unique Mn2+2O9 dimers of face sharing octahedra and two complementary triangular layers of magnetic cations that resemble regular polygon tilings. The second material, PbMn(SO 4)2, forms a rare chiral structure in which the Pb and Mn atoms spiral around each other along one axis to form a double helix.;Overall, the work provides insight into the interplay of magnetism, magnetic interactions and crystal structure by probing materials that were previously reported, and by expanding horizons through the discovery of novel crystal structures. It is of particular importance that the new crystal structures are made with readily available materials under relatively simple conditions. This implies that many chemically simple systems may remain to be found. In addition, it highlights the wonderful complexity of solid state chemistry that prevents the researcher from knowing a priori what crystal structures will form with a particular stoichiometry.
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