The vibrational spectra of rectangular plates

The wire drive pulse-echo system has been extensively used to excite and measure modes of vibration of thin rectangular plates. The frequency spectra of different modes have been investigated as a function of the material elastic moduli and the plate geometry. Most of the work was carried out on isotropic materials. For square plates a wide selection of materials were used. These were made isotropic in their in-plane dimensions where the displacements are taking place. The range of rnaterials enabled the dependence on Poisson's ratio to be investigated. A method of determining the value of Poisson's ratio resulted from this investigation. Certain modes are controlled principally by the shear modulus. Of these the fundamental has two nodal lines across the plate surface. One of them, which has nodes at the corners, (the Lame mode) is uniquely a pure shear mode where the diagonal is a full wave length. One controlled by the Young's modulus has been found. The precise harmonic relationship of the Lame mode series in square and rectangular plates was established. Use of the Rayleigh-Lamb equation has extended the theoretical support. The low order modes were followed over a wide range of sides ratios. Two fundamental types of modes have been recognised; These are the longitudinal modes where the frequency is controlled by the length of the plate only and the 2~f product has an asymptotic value approaching the rod velocity. The other type is the in-plane flexural modes (in effect a flexurally vibrating bar where the -2/w is the geometrical parameter). Where possible the experimental work was related to theory. Other modes controlled by the width dimension of the plate were followed. Anisotropic materials having rolled sheet elastic symmetry were investigated in terms of the appropriate theory. The work has been extended to examine materials from welds in steel plates.

Vibrational methods applied to NDT testing and fluid density measurement

A system for the NDI' testing of the integrity of conposite materials and of adhesive bonds has been developed to meet industrial requirements. The vibration techniques used were found to be applicable to the development of fluid measuring transducers. The vibrational spectra of thin rectangular bars were used for the NDT work. A machined cut in a bar had a significant effect on the spectrum but a genuine crack gave an unambiguous response at high amplitudes. This was the generation of fretting crack noise at frequencies far above that of the drive. A specially designed vibrational decrement meter which, in effect, measures mechanical energy loss enabled a numerical classification of material adhesion to be obtained. This was used to study bars which had been flame or plasma sprayed with a variety of materials. It has become a useful tool in optimising coating methods. A direct industrial application was to classify piston rings of high performance I.C. engines. Each consists of a cast iron ring with a channel into which molybdenum, a good bearing surface, is sprayed. The NDT classification agreed quite well with the destructive test normally used. The techniques and equipment used for the NOT work were applied to the development of the tuning fork transducers investigated by Hassan into commercial density and viscosity devices. Using narrowly spaced, large area tines a thin lamina of fluid is trapped between them. It stores a large fraction of the vibrational energy which, acting as an inertia load reduces the frequency. Magnetostrictive and piezoelectric effects together or in combination enable the fork to be operated through a flange. This allows it to be used in pipeline or 'dipstick' applications. Using a different tine geometry the viscosity loading can be predoninant. This as well as the signal decrement of the density transducer makes a practical viscometer.

Organotellurium compounds for metal organic vapour phase epitaxy

The infra-red detector material cadmium mercury telluride can be grown by the technique of Metal Organic Vapour Phase Epitaxy using simple alkyl telluride compounds as the source of tellurium. New tellurium precursors are required in order to overcome handling and toxicity problems and to reduce the growth temperature in preparing the material. A range of diaryltellurium(IV) dicarboxylates and some 2-(2'-pyridyl)phenyl-tellurium(II) and tellurium(IV) monocarboxylates have been synthesised and characterised by infra-red, 13C N.M.R. and mass spectroscopy. Infra-red spectroscopy has been used to determine the mode of bonding of the carboxylate ligand to tellurium. Synthetic methods have been devised for the preparation of diorganotritellurides (R2Te3) and mixed diorganotetrachalcogenides (RTeSeSeTeR). A mechanism for the formation of the tritellurides based on aerobic conditions is proposed. The reaction of ArTe- with (ClCH2CH2)3N leads to tripod-like multidentate ligands (ArTeCH2CH2)3N which form complexes with the ions Hg(II), Cd(II), Cu(I), Pt(II) and Pd(II). Synthetic routes to aryltelluroalkylamines and arylselenoalkylamines are also reported. The crystal structure of 2-(2'-pyridyl)phenyltellurium(II) bromide has been solved in which there are six molecules present within the unit cell. There are no close intermolecular Te---Te interactions and the molecules are stabilised by short Te---N intramolecular contacts. The crystal structure of 2-(2'-pyridyl)phenylselenium(II)-tribromomercurate(II) is also presented. A study of the Raman vibrational spectra of some tellurated azobenzenes and 2-phenylpyridines shows spectra of remarkably far superior quality to those obtained using infra-red spectroscopy.

CO adsorption over Pd nanoparticles:a general framework for IR simulations on nanoparticles

CO vibrational spectra over catalytic nanoparticles under high coverages/pressures are discussed from a DFT perspective. Hybrid B3LYP and PBE DFT calculations of CO chemisorbed over Pd4 and Pd13 nanoclusters, and a 1.1 nm Pd38 nanoparticle, have been performed in order to simulate the corresponding coverage dependent infrared (IR) absorption spectra, and hence provide a quantitative foundation for the interpretation of experimental IR spectra of CO over Pd nanocatalysts. B3LYP simulated IR intensities are used to quantify site occupation numbers through comparison with experimental DRIFTS spectra, allowing an atomistic model of CO surface coverage to be created. DFT adsorption energetics for low CO coverage (θ → 0) suggest the CO binding strength follows the order hollow > bridge > linear, even for dispersion-corrected functionals for sub-nanometre Pd nanoclusters. For a Pd38 nanoparticle, hollow and bridge-bound are energetically similar (hollow ≈ bridge > atop). It is well known that this ordering has not been found at the high coverages used experimentally, wherein atop CO has a much higher population than observed over Pd(111), confirmed by our DRIFTS spectra for Pd nanoparticles supported on a KIT-6 silica, and hence site populations were calculated through a comparison of DFT and spectroscopic data. At high CO coverage (θ = 1), all three adsorbed CO species co-exist on Pd38, and their interdiffusion is thermally feasible at STP. Under such high surface coverages, DFT predicts that bridge-bound CO chains are thermodynamically stable and isoenergetic to an entirely hollow bound Pd/CO system. The Pd38 nanoparticle undergoes a linear (3.5%), isotropic expansion with increasing CO coverage, accompanied by 63 and 30 cm− 1 blue-shifts of hollow and linear bound CO respectively.

Real and imaginary parts of the vibrational relaxation of acetonitrile in its electrolyte solutions:new results for the dynamics of solvent molecules

Isotropic scattering Raman spectra of liquid acetonitrile (AN) solutions of LiBF4 and NaI at various temperatures and concentrations have been investigated. For the first time imaginary as well as real parts of the solvent vibrational correlation functions have been extracted from the spectra. Such imaginary parts are currently an important component of modern theories of vibrational relaxation in liquids. This investigation thus provides the first experimental data on imaginary parts of a correlation function in AN solutions. Using the fitting algorithm we recently developed, statistically confident models for the Raman spectra were deduced. The parameters of the band shapes, with an additional correction, of the ν2 AN vibration (CN stretching), together with their confidence intervals are also reported for the first time. It is shown that three distinct species, with lifetimes greater than ∼10−13 s, of the AN molecules can be detected in solutions containing Li+ and Na+. These species are attributed to AN molecules directly solvating cations; the single oriented and polarised molecules interleaving the cation and anion of a Solvent Shared Ion Pair (SShIP); and molecules solvating anions. These last are considered to be equivalent to the next layer of solvent molecules, because the CN end of the molecule is distant from the anion and thus less affected by the ionic charge compared with the anion situation. Calculations showed that at the concentrations employed, 1 and 0.3 M, there were essentially no other solvent molecules remaining that could be considered as bulk solvent. Calculations also showed that the internuclear distance in these solutions supported the proposal that the ionic entity dominating in solution was the SShIP, and other evidence was adduced that confirmed the absence of Contact Ion Pairs at these concentrations. The parameters of the shape of the vibrational correlation functions of all three species are reported. The parameters of intramolecular anharmonic coupling between the potential surfaces in AN and the dynamics of the intermolecular environment fluctuations and intermolecular energy transfer are presented. These results will assist investigations made at higher and lower concentrations, when additional species and interactions with AN molecules will be present.