Alfred Hüller

Torsional ground state splitting for tetrahedral molecules

With improved neutron scattering and nuclear magnetic resonance techniques it has been possible to observe the splitting of the torsional ground state—commonly referred to as tunnel splitting—of a number of high symmetry molecules in various crystal fields. The tunnel splitting depends nearly exponentially on the strength of the potential experienced by a molecule as it rotates in the crystal. Tunneling spectroscopy may thus be developed into a sensitive probe for measuring rotational potentials once the relation between the potentials and the tunnel splitting is known. We have used the pocket state formalism to calculate the splitting for tetrahedral molecules in tetrahedral fields. With increasing potentials the wave function becomes smaller in the overlap region making an accurate prediction of the tunnel splittings more difficult. Our calculation provides reliable results for splittings from 200 μeV down to about 1 μeV. Detailed predictions are made for the isotope effect in solid methane and for the ...

Electrostatic model for the rotational potential in ammonium halides

An electrostatic model for the rotational potential of an ammonium tetrahedron in a cubic field is proposed. The rotational potential can be written as a rapidly converging series of kubic rotator functions. The NX4 ion, where X is hydrogen or deuterium, performs small angular motions about the minimum of the potential in both the ordered and disordered states, giving rise to librational energy levels. The anharmonic portion of the energy levels, both from the kinetic and potential energies, accounts for good agreement with infrared absorption data in NH4Cl, ND4Cl, NH4Br, and ND4Br. We use a one parameter fit to these data and then compute the potential barriers for rotations about threefold and fourfold axes of the tetrahedron. The difference between the transition temperatures for ND4Cl and NH4Cl is also explained.

Tricritical points for competing interactions

Competing interactions, responsible for two differently ordered phases in the ammonium halides, also cause the coexistence of different short range correlations in the disordered state. Correlations of the nonordering density may be the reason for tricritical behavior or even a discontinuity of the transition. Molecular field theory neglects all correlations and thus is unable to provide an appropriate description of NH4Cl under pressure and of NH4Cl-NH4Br mixtures. In this paper a phase diagram is obtained for the ammonium halides in first Bethe approximation from a simplified model Hamiltonian with competing interactions. A tricritical point is found for the order-disorder transition into the uniform or “ferromagnetic” phase as well as for the transition into the “antiferromagnetic” phase.

The isotope effect and orientational potentials of methane molecules in gas hydrates

We report an inelastic neutron scattering experiment at T=2 K of a fully deuterated methane hydrate CD4⋅5.75 D2O. In the experiment the J=0→J=1 rotational transition of an almost free quantum CD4 rotor at an energy transfer of 0.4 meV has been found. No line splitting due to the two different kinds of cages, which are occupied by the methane molecules in the host lattice, has been found. Using a simple electrostatic model of the orientational interaction between the methane molecules and the water molecules in the host lattice we are able to explain the measured spectra of both the deuterated and protonated samples. The intrinsic linewidth found for the rotational transition in deuterated and protonated samples can be attributed to the frozen in disorder of the water dipole moments in the cages. The contribution of the van der Waals interaction has also been calculated on the basis of empirical atom–atom interaction parameters and has been found to be one order of magnitude smaller than the electrostatic ...

Competing interactions in the ammonium halides

The indirect interaction of two ammonium tetrahedra via the polarizable halide ions in between is investigated. It tends to order the tetrahedra in an antiferromagnetic way, whereas the direct interaction favors the ferromagnetic state. A mechanism is suggested that reduces the antiferromagnetic interaction and thus can account for the ferromagnetic order in NH4Cl. Strong fluctuations are expected along the [1,1,0]-directions in reciprocal space.

Many body forces and elastic constants of rare gas crystals

The effect of many body Van der Waals forces on the elastic constants of solid rare gases is calculated. These results are combined with contributions from the two body potential and zero point energy. The violation of the Cauchy relation is studied.