Fig. 1. (a) Ternary phase diagram (convex hull) of the Lu–N–H system at 1 GPa. The values of the enthalpy from the convex hull are shown next to the colored circles. The circles with black solid boundaries denote the stable phases. (b) Comparison of the XRD pattern from reported experimental data²² (lower black curve) and the pattern calculated for P3̄m1-Lu₂H₂N at ambient pressure (upper red curve). The inset shows the crystal structure of P3̄m1-Lu₂H₂N, with green, gray, and pink spheres depicting Lu, N, and H atoms, respectively.

Fig. 2. (a) Crystal structure of Fm3̄m-LuH₃ with different types of H occupancy sites. Green spheres depict Lu atoms; pink and red spheres depict H occupancy of O and T sites, respectively. (b)–(d) Calculated enthalpy of formation of Lu₄H_mN_12−m as a function of T-site occupancy at 1, 10, and 50 GPa, respectively. n(T) is the number of nitrogen atoms in each stoichiometry occupying T sites.

Fig. 3. (a) Phonon spectra, Eliashberg phonon spectral function α²F(ω), and electron–phonon integral λ for R3m-Lu₂H₅N at 50 GPa. The magnitudes of the phonon linewidths are represented by the sizes of the blue circles. (b) and (c) Crystal structures of R3m-Lu₂H₅N in the framework of Fm3̄m-LuH₃ and the conventional cell, respectively. Green, gray, and pink spheres depict Lu, N, and H atoms, respectively.

Fig. 4. (a) Dependence of minimum dynamically stable pressure on N-doping concentration. (b) Dependence of T_c on N-doping concentration at 50 GPa. The Coulomb pseudopotential uses μ* = 0.10.

Fig. 5. (a) Electronic band structure and DOS (states eV⁻¹ f.u.⁻¹) of LuH₃ (solid black curves) and LuH_2.97N_0.03 (solid red curves) at 50 GPa. The grey solid horizontal line indicates the Fermi energy. (b) and (c) Phonon spectra, Eliashberg phonon spectral function α²F(ω), and electron–phonon integral λ for LuH₃ and LuH_2.97N_0.03, respectively, at 50 GPa. The magnitudes of the phonon linewidths are represented by the sizes of the blue circles.