Abstract
Superconductivity at room temperature and near-ambient pressures is a highly sought-after phenomenon in physics and materials science. A recent study reported the presence of this phenomenon in N-doped lutetium hydride [Nature 615, 244 (2023)], however, subsequent experimental and theoretical investigations have yielded inconsistent results. This study undertakes a systematic examination of synthesis methods involving high temperatures and pressures, leading to insights into the impact of the reaction path on the products and the construction of a phase diagram for lutetium hydrides. Notably, the high-pressure phase of face-centered cubic LuH(3) (fcc-LuH(3)) is maintained to ambient conditions through a high-temperature and high-pressure method. Based on temperature and anharmonic effects corrections, the lattice dynamic calculations demonstrate the stability of fcc-LuH(3) at ambient conditions. However, no superconductivity is observed above 2 K in resistance and magnetization measurements in fcc-LuH(3) at ambient pressure. This work establishes a comprehensive synthesis approach for lutetium hydrides, thereby enhancing the understanding of the high-temperature and high-pressure method employed in hydrides with superconductivity deeply.