Anisotropic Mean-square Displacements Research Articles

Disorder of (NH4)3H(SO4)2 in the high-temperature phase I

The highly disordered crystal structure of triammonium hydrogen disulfate, (NH(4))(3)H(SO(4))(2), in the high-temperature phase I was studied using single-crystal neutron diffraction. It is known that the O atom involved in hydrogen bonding between neighbouring SO(4) tetrahedra is disordered and takes a split-atom position, building a two-dimensional hydrogen-bond network in the (001) plane. The H atoms in these SO(4)-H-SO(4) hydrogen bonds are disordered and hence refined with a split-atom model. Moreover, from the much larger anisotropic mean-square displacements of ammonium protons the NH(4)(+) groups were refined with a reasonable split-atom model, and their motional behaviour was also analysed by rigid-body treatment. Finally, careful consideration was given to show possible supplementary proton migration between the ammonium protons and those of the hydrogen bonds in this high-temperature phase.

Dynamic proton disorder and the II–I structural phase transition in (NH4)3H(SO4)2

X-ray powder diffraction, differential scanning calorimetry (DSC)/thermogravimetry (TG) and single-crystal neutron diffraction methods were used to investigate triammonium hydrogen disulfate (NH(4))(3)H(SO(4))(2) (TAHS) in the temperature range between 293 and 493 K. The temperature-dependent X-ray powder diffraction measurements show a clear hysteresis of the I <-->II phase transition of TAHS with transition temperatures of T(up) = 412.9 (1) K on heating and of T(down) = 402.6 (1) K on cooling. From the existence of hysteresis and from the jump-like changes of the lattice parameters, the I <--> II phase transition of TAHS is considered to be first order. With DSC/TG measurements we confirmed that there is only one phase transition between 293 and 493 K. Through careful investigation on single crystals of TAHS using neutron diffraction, the correct space group (C2/c) of room-temperature TAHS-II phase was confirmed. Crystal structure analysis by single-crystal neutron diffraction showed a strongly elongated displacement ellipsoid of the proton which lies in the middle of the (SO(4))H(SO(4)) dimer with \bar 1 local symmetry. The protons of the NH(4) groups also show strongly enlarged anisotropic mean-square displacements. These findings are interpreted in terms of a characteristic proton disorder in the TAHS-II phase.

Anisotropic mean-square displacements in two-dimensional colloidal crystals of tilted dipoles

Superparamagnetic colloidal particles confined to a flat horizontal air-water interface in an external magnetic field, which is tilted relative to the interface, form anisotropic two-dimensional crystals resulting from their mutual dipole-dipole interactions. Using real-space experiments and harmonic lattice theory we explore the mean-square displacements of the particles in the directions parallel and perpendicular to the in-plane component of the external magnetic field as a function of the tilt angle. We find that the anisotropy of the mean-square displacement behaves nonmonotonically as a function of the tilt angle and does not correlate with the structural anisotropy of the crystal.

A quantum-mechanical calculation of the dynamic structure factors of magnesium difluoride

Ab initio calculations of dynamic structure factors are performed with a methodology that requires the crystalline density matrix determined by the periodic Hartree-Fock CRYSTAL code. Amplitudes and orientations of the atomic vibrations are fixed by the mean-square displacements available in the literature. This method, which is here upgraded so as to satisfy normalization conditions, gives rise, for any temperature T, to a “dynamic” density matrix different from the static one. An application to the calculation of the dynamic structure factors of magnesium difluoride (MgF2), which has anisotropic mean-square displacement tensors, is proposed and compared with experiments at 298 K. © 1996 John Wiley & Sons, Inc.

On the differences between X-ray and neutron thermal vibration parameters.

For crystal structures analyzed by both X-ray and neutron diffraction, the anisotropic mean-square displacement parameters of the non-H atoms are sometimes found to differ significantly. The differences can usually be adjusted by either: (1) an isotropic factor q, defined by UijX = qUijN, to correct for a temperature difference between the two experiments; (2) anisotropic factors qij, defined by UijX = qijUijN, to correct for a temperature difference and different anisotropic diffraction effects of absorption, extinction, thermal diffuse scattering, multiple reflection, or systematic measuring errors in the two experiments; (3) anisotropic diffraction correction terms delta Uij, defined by UijX = UijN + delta Uij; (4) the sum of an isotropic temperature correction and anisotropic diffraction corrections, defined by UijX = qUijN + delta Uij. Correction parameters q, qij and delta Uij are easily calculated by linear least-squares fit, and the corrections from (3) or (4) seem to be the most reliable. Corrections calculated from X-ray and neutron Uij's of the non-H atoms of a crystal can be useful for adjusting the neutron Uij's of the H atoms for adoption, along with the neutron coordinates of the H atoms, as fixed parameters in an X-ray analysis of the electron density distribution.

Restrained structure-factor least-squares refinement of protein structures using a vector processing computer

A least-squares refinement program RESTRAIN has been developed, which is capable of refining macromolecular structures using structure amplitudes, phases from isomorphous replacement or anomalous scattering and pseudo-energy restraints. In addition to positional parameters and isotropic temperature factors, anisotropic mean-square displacements may be refined either as individual atomic U tensors or as TLS tensors applied to groups of atoms. Anharmonic effects may be handled by coupling together occupancies to enable the electron density of an atomic group to be distributed over more than one subsite. A novel way of restraining groups of atoms to be planar has been developed that does not require dummy atoms and does not restrain the plane to lie in its current orientation.

Anisotropic mean-square displacements (MSD) in single-crystals of 2H- and 3R-MoS2

Anisotropic mean-square displacements (MSD) in single-crystals of 2<i>H</i>- and 3<i>R</i>-MoS₂