Crystal Chemistry and Phonon Heat Capacity in Quaternary Honeycomb Delafossites: Cu[Li_(1/3)Sn_(2/3)]O)2 and Cu[Na_(1/3)Sn_(2/3)]O_2

This work presents an integrated approach to study the crystal chemistry and phonon heat capacity of complex layered oxides. Two quaternary delafossites are synthesized from ternary parent compounds and copper monohalides via a topochemical exchange reaction that preserves the honeycomb ordering of the parent structures. For each compound, Rietveld refinement of the powder X-ray diffraction patterns is examined in both monoclinic C2/c and rhombohedral R3̅m space groups. Honeycomb ordering occurs only in the monoclinic space group. Bragg peaks associated with honeycomb ordering acquire an asymmetric broadening known as the Warren line shape that is commonly observed in layered structures with stacking disorder. Detailed TEM analysis confirms honeycomb ordering within each layer in both title compounds and establishes a twinning between the adjacent layers instead of the more conventional shifting or skipping stacking faults. The structural model is then used to calculate phonon dispersions and heat capacity from first principles. In both compounds, the calculated heat capacity accurately describes the experimental data. The integrated approach presented here offers a platform to carefully analyze the phonon heat capacity in complex oxides where the crystal structure can produce magnetic frustration. Isolating phonon contribution from total heat capacity is a necessary and challenging step toward a quantitative study of spin liquid materials with exotic magnetic excitations such as spinons and Majorana fermions. A quantitative understanding of phonon density of states based on crystal chemistry as presented here also paves the way toward higher efficiency thermoelectric materials