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A flux growth method for the high-yield synthesis of Pb10(PO4)6O single crystals was developed. This optimized synthesis method was utilized for the systematic doping of copper into the lead apatite structure, where the availability of single crystals allowed for a detailed structural analysis via single crystal X-ray diffraction. Our developed synthesis method resulted in a different type of copper doping in lead apatite where instead of Cu(II) doping onto the lead sites, doping occurred via Cu(I) doping into the disordered channels at the center of the Pb(1)/Pb(2) columns in the form of CuO2 linear units. The presence of Cu(I) as opposed to Cu(II) in the structure was shown via magnetic susceptibility data which also indicated a lack of superconductivity in the modified lead apatite at all achieved doping levels. The knowledge gained from this study enabled a reanalysis of the initial diffraction data reported for LK-99. While this work further supports the lack of superconductivity in the modified lead apatites, it does allow us to suggest a more accurate formula for LK-99: Pb10(PO4)6(CuO)2O1-1.5x. 

Geometric magnetic frustration arises when the geometry of a structure prevents the simultaneous fulfillment of nearest-neighbor antiferromagnetic interactions and is commonly observed in lattices that exhibit a triangular topology, such as those found in the pyrochlore structure. Via a mild hydrothermal route, we have synthesized seven quaternary β-pyrochlore related fluorides AxM2+xM3+(2–x)F6, (A = Cs and Rb; M2+ = Co2+, Ni2+ and Zn2+; and M3+ = V3+ and Fe3+). Crystal structures and compositions were determined using a combination of single-crystal X-ray diffraction and energy-dispersive spectroscopy. After adjusting the reaction conditions, phase pure products of AxM2+xM3+(2–x)F6 were obtained. The magnetic susceptibility and isothermal magnetization data for all seven compounds were collected to interpret the magnetic behavior, which ranged from paramagnetic to antiferromagnetic with and without a ferromagnetic component. We found that the magnetic behavior of the AxM2+xV3+(2–x)F6 pyrochlore structures strongly depends on the presence or absence of unpaired electrons on the M2+ position. The titled pyrochlore compounds, with the exception of the Zn-analog, can be considered frustrated materials, with frustration indices in the range of 6 –13. 

Single crystals of A₃MF₆(A = Rb, Cs; M = Al, Ga) were grown from mixed alkali chloride/fluoride fluxes. The polymorphism of each compound was studiedviaTGA/DSC and high temperature X-ray diffraction.