Diffusion of atoms and molecules in the solid hydrogens

The ‘‘motional averaging’’ of the NMR spectra has been used to determine the diffusion coefficient of molecules in HD, D-T, and ${\mathrm{T}}_2$ solids. The molecular hop frequency and diffusion coefficient are calculated from the measured spin-spin relaxation time and the rigid lattice second moment. Samples prepared by depositing streams of ${\mathrm{H}}_2$ or ${\mathrm{D}}_2$ gas, containing atoms produced by microwave discharge, onto cold substrates, held at 2 K or below are designated ‘‘amorphous’’ while those prepared by slow cooling from the liquid state are designated ‘‘crystalline.’’ We find that the diffusion in crystalline solids (c-${\mathrm{H}}_2$, etc.) is controlled by the number of vacancies in the lattice and have obtained values of the vacancy formation energy, ${\mathit{E}}_{\mathit{V}}$, the barrier height energy, ${\mathit{E}}_{\mathit{b}}$, and the energy of the first tunneling level in the hydrogen potential, ${\mathit{E}}_{\mathit{t}}$, for all the isotopes. The vacancy hopping rate, at the triple point, is approximately the same for all the isotopes. Data for the various isotopes can be compared by scaling the temperature by the quantum parameter. Measurements (by others) on both radiation damaged crystalline (c-${\mathrm{H}}_2$) and undamaged amorphous (a-${\mathrm{H}}_2$) solids at the atom recombination coefficients are used to extract the atom hop frequency. In c-${\mathrm{H}}_2$, we find that the atom and molecule hopping rates are almost identical. Other data on crystalline solids, taken by NMR techniques on ortho to para conversion in solid ${\mathrm{T}}_2$, yield model dependent atom hop rates. The atom and molecule hopping rates still agree even though the recombination coefficients no longer follow a simple thermally activated form. The recombination coefficients (and hence hopping rates) for crystalline solids differ from those of amorphous solids.