Characterisation of amorphous and nanocrystalline molecular materials by total scattering

The use of high-energy X-ray total scattering coupled with pair distribution function analysis produces unique structural fingerprints from amorphous and nanostructured phases of the pharmaceuticals carbamazepine and indomethacin. The advantages of such facility-based experiments over laboratory-based ones are discussed and the technique is illustrated with the characterisation of a melt-quenched sample of carbamazepine as a nanocrystalline (4.5 nm domain diameter) version of form III.

Dihydrogen in cation-substituted zeolites X - an inelastic neutron scattering study

An inelastic neutron scattering (INS) study of the rotational - vibrational spectrum of dihydrogen sorbed by zeolite X having substituted sodium, calcium and zinc cations is reported. The rotational - vibrational spectrum of H-2 was observed at low energy transfer ( below ca. 25 meV, 202 cm(-1)); the vibration was that of the H-2 molecule against the binding site (H-2 - X, not H - H). The vibration frequency was proportional to the polarising power of the cation (Na+ < Ca2+ < Zn2+). Polarisation of the H-2 molecule dominated the interaction of H-2 with this binding site. The total scattering intensity was proportional to the dihydrogen dose. However the vibrational intensities became constant at ca. 0.3 wt% showing that the H-2 binding sites had saturated. Additional dihydrogen appeared as unbound or weakly bound dihydrogen exhibiting recoil.

Aperiodicity, structure, and dynamics in Ni(CN)(2)

By combining the results of both x-ray diffraction and neutron total-scattering experiments, we show that Ni(CN)(2) exhibits long-range structural order only in two dimensions, with no true periodicity perpendicular to its gridlike layers. Reverse Monte Carlo analysis gives an experimental distinction between M-C and M-N bond lengths in a homometallic cyanide framework and identifies the vibrational modes responsible for anomalous positive and negative thermal expansion in the title compound.

Spectrally invariant approximation within atmospheric radiative transfer

Certain algebraic combinations of single scattering albedo and solar radiation reflected from, or transmitted through, vegetation canopies do not vary with wavelength. These ‘‘spectrally invariant relationships’’ are the consequence of wavelength independence of the extinction coefficient and scattering phase function in veg- etation. In general, this wavelength independence does not hold in the atmosphere, but in cloud-dominated atmospheres the total extinction and total scattering phase function vary only weakly with wavelength. This paper identifies the atmospheric conditions under which the spectrally invariant approximation can accu- rately describe the extinction and scattering properties of cloudy atmospheres. The validity of the as- sumptions and the accuracy of the approximation are tested with 1D radiative transfer calculations using publicly available radiative transfer models: Discrete Ordinate Radiative Transfer (DISORT) and Santa Barbara DISORT Atmospheric Radiative Transfer (SBDART). It is shown for cloudy atmospheres with cloud optical depth above 3, and for spectral intervals that exclude strong water vapor absorption, that the spectrally invariant relationships found in vegetation canopy radiative transfer are valid to better than 5%. The physics behind this phenomenon, its mathematical basis, and possible applications to remote sensing and climate are discussed.

A wavenumber independent boundary element method for an acoustic scattering problem

In this paper we consider the impedance boundary value problem for the Helmholtz equation in a half-plane with piecewise constant boundary data, a problem which models, for example, outdoor sound propagation over inhomogeneous. at terrain. To achieve good approximation at high frequencies with a relatively low number of degrees of freedom, we propose a novel Galerkin boundary element method, using a graded mesh with smaller elements adjacent to discontinuities in impedance and a special set of basis functions so that, on each element, the approximation space contains polynomials ( of degree.) multiplied by traces of plane waves on the boundary. We prove stability and convergence and show that the error in computing the total acoustic field is O( N-(v+1) log(1/2) N), where the number of degrees of freedom is proportional to N logN. This error estimate is independent of the wavenumber, and thus the number of degrees of freedom required to achieve a prescribed level of accuracy does not increase as the wavenumber tends to infinity.

On integral equation and least squares methods for scattering by diffraction gratings

In this paper we consider the scattering of a plane acoustic or electromagnetic wave by a one-dimensional, periodic rough surface. We restrict the discussion to the case when the boundary is sound soft in the acoustic case, perfectly reflecting with TE polarization in the EM case, so that the total field vanishes on the boundary. We propose a uniquely solvable first kind integral equation formulation of the problem, which amounts to a requirement that the normal derivative of the Green's representation formula for the total field vanish on a horizontal line below the scattering surface. We then discuss the numerical solution by Galerkin's method of this (ill-posed) integral equation. We point out that, with two particular choices of the trial and test spaces, we recover the so-called SC (spectral-coordinate) and SS (spectral-spectral) numerical schemes of DeSanto et al., Waves Random Media, 8, 315-414 1998. We next propose a new Galerkin scheme, a modification of the SS method that we term the SS* method, which is an instance of the well-known dual least squares Galerkin method. We show that the SS* method is always well-defined and is optimally convergent as the size of the approximation space increases. Moreover, we make a connection with the classical least squares method, in which the coefficients in the Rayleigh expansion of the solution are determined by enforcing the boundary condition in a least squares sense, pointing out that the linear system to be solved in the SS* method is identical to that in the least squares method. Using this connection we show that (reflecting the ill-posed nature of the integral equation solved) the condition number of the linear system in the SS* and least squares methods approaches infinity as the approximation space increases in size. We also provide theoretical error bounds on the condition number and on the errors induced in the numerical solution computed as a result of ill-conditioning. Numerical results confirm the convergence of the SS* method and illustrate the ill-conditioning that arises.

Hydrogen adsorption in a copper ZSM5 zeolite: an inelastic neutron scattering study

Currently microporous oxidic materials including zeolites are attracting interest as potential hydrogen storage materials. Understanding how molecular hydrogen interacts with these materials is important in the rational development of hydrogen storage materials and is also challenging theoretically. In this paper, we present an incoherent inelastic neutron scattering (INS) study of the adsorption of molecular hydrogen and hydrogen deuteride (HD) in a copper substituted ZSM5 zeolite varying the hydrogen dosage and temperature. We have demonstrated how inelastic neutron scattering can help us understand the interaction of H-2 molecules with a binding site in a particular microporous material, Cu ZSM5, and by implication of other similar materials. The H-2 molecule is bound as a single species lying parallel with the surface. As H-2 dosing increases, lateral interactions between the adsorbed H-2 molecules become apparent. With rising temperature of measurement up to 70 K (the limit of our experiments), H-2 molecules remain bound to the surface equivalent to a liquid or solid H-2 phase. The implication is that hydrogen is bound rather strongly in Cu ZSM5. Using the simple model for the anisotropic interaction to calculate the energy levels splitting, we found that the measured rotational constant of the hydrogen molecule is reduced as a consequence of adsorption by the Cu ZSM5. From the decrease in total signal intensity with increasing temperature, we were able to observe the conversion of para-hydrogen into ortho-hydrogen at paramagnetic centres and so determine the fraction of paramagnetic sites occupied by hydrogen molecules, ca. 60%. (c) 2006 Elsevier B.V. All rights reserved.

Relationship between phonons and thermal expansion in Zn(CN)2 and Ni(CN)2 from inelastic neutron scattering and ab initio calculations

Zn(CN)2 and Ni(CN)2 are known for exhibiting anomalous thermal expansion over a wide temperature range. The volume thermal expansion coefficient for the cubic, three dimensionally connected material, Zn(CN)2, is negative (alpha(V) = −51  10(-6) K-1) while for Ni(CN)2, a tetragonal material, the thermal expansion coefficient is negative in the two dimensionally connected sheets (alpha(a) = −7  10(-6) K-1), but the overall thermal expansion coefficient is positive (alpha(V) = 48  10(-6) K-1). We have measured the temperature dependence of phonon spectra in these compounds and analyzed them using ab initio calculations. The spectra of the two compounds show large differences that cannot be explained by simple mass renormalization of the modes involving Zn (65.38 amu) and Ni (58.69 amu) atoms. This reflects the fact that the structure and bonding are quite different in the two compounds. The calculated pressure dependence of the phonon modes and of the thermal expansion coefficient, alpha(V), are used to understand the anomalous behavior in these compounds. Our ab initio calculations indicate that phonon modes of energy approx. 2 meV are major contributors to negative thermal expansion (NTE) in both the compounds. The low-energy modes of approx.8 and 13 meV in Zn(CN)2 also contribute significantly to the NTE in Zn(CN)2 and Ni(CN)2, respectively. The measured temperature dependence of the phonon spectra has been used to estimate the total anharmonicity of both compounds. For Zn(CN)2, the temperature-dependent measurements (total anharmonicity), along with our previously reported pressure dependence of the phonon spectra (quasiharmonic), is used to separate the explicit temperature effect at constant volume (intrinsic anharmonicity).