Isotopic dependence of the frequency of optical vibrations in molybdenum monohydride

It is currently known that three hydrides – PdH_x, MoH_x, and TiH_x – exhibit an inverse isotope effect in superconductivity. Namely, the phase with a heavier hydrogen isotope, deuterium, has a higher critical temperature. Hydrides and deuterides of palladium have intensively been studied both experimentally and theoretically, but the origin of the isotope effect has not been established with certainty. The commonly accepted explanation is that the effect is likely to be due to the strong anharmonicity of the optical hydrogen vibrations, which was considered to be responsible for the large deviation of the ratio of the fundamental optical frequencies ω_H/ω_D = 1.51 from the harmonic value 2 ≈ 1.41. In the present paper, powder samples of MoH_1.1(1) and MoD_1.07(3) were synthesized under a hydrogen / deuterium pressure of several gigapascals and studied by inelastic neutron scattering (INS) at ambient pressure and T = 10 K. The INS study demonstrated that optical vibrations of H atoms in MoH_1.1 and D atoms in MoD_1.07 are harmonic and the ratio of fundamental optical frequencies ω_H/ω_D = 1.44 is close to the harmonic value 2 ≈ 1.41. This shows that anharmonicity is not a necessary condition for the presence of the inverse isotope effect. The MoD_1.07 sample was additionally studied by neutron diffraction (ND) at ambient pressure and T = 100 K. In agreement with previous ND results for MoH_1.2, the ND study of MoD_1.07 showed that deuterium atoms occupied almost all octahedral interstitial sites in its hexagonal close-packed metal lattice and formed a NiAs-type crystal structure with the composition close to MoD. The overstoichiometric composition MoD_1.07 of the deuteride is likely to result from a small fraction D/Mo ~ 0.07 of deuterium atoms partially occupying the tetrahedral interstices.