Phonon dispersion curves and atomic mean square displacement for several fcc and bcc materials

The atomic mean square displacement (MSD) and the phonon dispersion curves (PDC's) of a number of face-centred cubic (fcc) and body-centred cubic (bcc) materials have been calclllated from the quasiharmonic (QH) theory, the lowest order (A2 ) perturbation theory (PT) and a recently proposed Green's function (GF) method by Shukla and Hiibschle. The latter method includes certain anharmonic effects to all orders of anharmonicity. In order to determine the effect of the range of the interatomic interaction upon the anharmonic contributions to the MSD we have carried out our calculations for a Lennard-Jones (L-J) solid in the nearest-neighbour (NN) and next-nearest neighbour (NNN) approximations. These results can be presented in dimensionless units but if the NN and NNN results are to be compared with each other they must be converted to that of a real solid. When this is done for Xe, the QH MSD for the NN and NNN approximations are found to differ from each other by about 2%. For the A2 and GF results this difference amounts to 8% and 7% respectively. For the NN case we have also compared our PT results, which have been calculated exactly, with PT results calculated using a frequency-shift approximation. We conclude that this frequency-shift approximation is a poor approximation. We have calculated the MSD of five alkali metals, five bcc transition metals and seven fcc transition metals. The model potentials we have used include the Morse, modified Morse, and Rydberg potentials. In general the results obtained from the Green's function method are in the best agreement with experiment. However, this improvement is mostly qualitative and the values of MSD calculated from the Green's function method are not in much better agreement with the experimental data than those calculated from the QH theory. We have calculated the phonon dispersion curves (PDC's) of Na and Cu, using the 4 parameter modified Morse potential. In the case of Na, our results for the PDC's are in poor agreement with experiment. In the case of eu, the agreement between the tlleory and experiment is much better and in addition the results for the PDC's calclliated from the GF method are in better agreement with experiment that those obtained from the QH theory.

Molecular dynamics calculation of mean square displacement in alkali metals and rare gas solids and comparison with lattice dynamics

Molec ul ar dynamics calculations of the mean sq ua re displacement have been carried out for the alkali metals Na, K and Cs and for an fcc nearest neighbour Lennard-Jones model applicable to rare gas solids. The computations for the alkalis were done for several temperatures for temperature vol ume a swell as for the the ze r 0 pressure ze ro zero pressure volume corresponding to each temperature. In the fcc case, results were obtained for a wide range of both the temperature and density. Lattice dynamics calculations of the harmonic and the lowe s t order anharmonic (cubic and quartic) contributions to the mean square displacement were performed for the same potential models as in the molecular dynamics calculations. The Brillouin zone sums arising in the harmonic and the quartic terms were computed for very large numbers of points in q-space, and were extrapolated to obtain results ful converged with respect to the number of points in the Brillouin zone.An excellent agreement between the lattice dynamics results was observed molecular dynamics and in the case of all the alkali metals, e~ept for the zero pressure case of CSt where the difference is about 15 % near the melting temperature. It was concluded that for the alkalis, the lowest order perturbation theory works well even at temperat ures close to the melting temperat ure. For the fcc nearest neighbour model it was found that the number of particles (256) used for the molecular dynamics calculations, produces a result which is somewhere between 10 and 20 % smaller than the value converged with respect to the number of particles. However, the general temperature dependence of the mean square displacement is the same in molecular dynamics and lattice dynamics for all temperatures at the highest densities examined, while at higher volumes and high temperatures the results diverge. This indicates the importance of the higher order (eg. ~* ) perturbation theory contributions in these cases.

Letter to Mr. H.L.Vanderlip regarding a truck of cornices and other materials

Letter to Mr. H.L.Vanderlip regarding a truck of cornices and other materials. This is signed S.D. Woodruff, Aug. 17, 1876.

Receipt from James D. Tait of St. Catharines for curtain and drapery materials

Receipt from James D. Tait of St. Catharines for curtain and drapery materials, Sept. 21, 1886.

Tetrathiafulvalene and 2,2'-Bipyridine: Bridging both Worlds in the Pursuit of Novel Molecular Materials

The preparation and characterization of two families of building blocks for molecule-based magnetic and conducting materials are described in three projects. In the first project the synthesis and characterization of three bis-imine ligands LI - L3 is reported. Coordination of LI to a series of metal salts afforded the five novel coordination complexes Sn(L4)C4 (I), [Mn(L4)(u-CI)(CI)(EtOH)h (II), [CU(L4)(u-sal) h(CI04)2 (sal = salicylaldehyde anion) (III), [Fe(Ls)2]CI (IV) and [Fe(LI)h(u-O) (V). All complexes have been structurally and magnetically characterized. X-ray diffraction studies revealed that, upon coordination to Lewis acidic metal salts, the imine bonds of LI are susceptible to nucleophilic attack. As a consequence, the coordination complexes (I) - (IV) contain either the cyclised ligand L4 or hydrolysed ligand Ls. In contrast, the dimeric Fe3+ complex (V) comprises two intact ligand LI molecules. In. this complex, the ligand chelates two Fe(III) centres in a bis-bidentate manner through the lone pairs of a phenoxy oxygen and an imine nitrogen atom. Magnetic studies of complexes (II-V) indicate that the dominant interactions between neighbouring metal centres in all of the complexes are antiferromagnetic. In the second project the synthesis and characterization two families of TTF donors, namely the cyano aryl compounds (VI) - (XI) and the his-aryl TTF derivatives (XII) - (XIV) are reported. The crystal structures of compounds (VI), (VII), (IX) and (XII) exhibit regular stacks comprising of neutral donors. The UV -Vis spectra of compounds (VI) - (XIV) present an leT band, indicative of the transfer of electron density from the TTF donors to the aryl acceptor molecules. Chemical oxidation of donors (VI), (VII), (IX) and (XII) with iodine afforded a series of CT salts that where possible have been characterized by single crystal X -ray diffraction. Structural studies showed that the radical cations in these salts are organized in stacks comprising of dimers of oxidized TTF donors. All four salts behave as semiconductors, displaying room temperature conductivities ranging from 1.852 x 10-7 to 9.620 X 10-3 Scm-I. A second series of CT salts were successfully prepared via the technique of electrocrystallization. Following this methodology, single crystals of two CT salts were obtained. The single crystal X-ray structures of both salts are isostructural, displaying stacks formed by trimers of oxidized donors. Variable temperature conductivity measurements carried out on this series of CT salts reveal they also are semiconductors with conductivities ranging from 2.94 x 10-7 to 1.960 X 10-3 S em-I at room temperature. In the third project the synthesis and characterization of a series of MII(hfac)2 coordination complexes of donor ligand (XII) where M2+ = Co2+, Cu2+, Ni2+ and Zn2+ are reported. These complexes crystallize in a head-to-tail arrangement of TTF donor and bipyridine moieties, placing the metal centres and hfac ligands are located outside the stacks. Magnetic studies of the complexes (XV) - (XVIII) indicate that the bulky hfac ligands prevent neighbouring metal centres from assembling in close proximity, and thus they are magnetically isolated.