A detailed study of the mechanical and electrical aspects of microparticle impact phenomena

An experimental and theoretical study of the impact behaviour of charged microparticles in a high voltage vacuum gap has been carried out to investigate under controlled conditions the role of low velocity microparticles (ζ 500 ms-1) in initiating electrical breakdown in such gaps. This has involved developing a unique (UHV) low-velocity source of micron-sized charged particles to study the underlying mechanical and electrical aspects of micro-particle impact on a range of target materials e.g. Pb, Ti, C, stainless-steel and mica etc., having atomically clean or oxidised surfaces. Argon-ion etching and electron-beam heating has been used for in-situ surface treatment and ellipsometry for characterising the target surfaces. An associated sphere/plane theoretical model has been developed for detailed analysis of the many complex electrical (in-flight in-field emission, M.I.M. tunnelling and ohmic conduction) and mechanical (impact dynamics, deformation and heating) phenomena that are involved when a microparticle closely approaches and impacts on a plane target. In each instance the influence of parameters such as particle radius, particle/target impact velocity, surface field, surface condition and material has been determined.

A comparison of the growth curves of the foliose lichen Parmelia conspersa determined by a cross-sectional study and by direct measurement

Changes in the radial growth rate (RGR mm/yr) through life were studied in thalli of the foliose lichen Parmelia conspersa by two methods: (1) a cross-sectional study (Study A) in which the RGR was measured in 60 thalli from 0.2 to 13 cm in diameter, and (2) by radial growth measurements over 4.5 years of fragments, consisting of a single major lobe, which were removed from large thalli and glued to pieces of slate (Study B). Both studies suggested there was a phase of increasing RGR in small thalli followed by a more constant phase, the latter beginning at approximately a thallus radius of 6-8 mm. However, in Study B significantly increased RGR was observed during the second 6-month growth period. This phase of growth was more likely to be due to an increase in lobe width than to an effect of climate. In addition, a lobe in a large thallus with both adjacent lobes removed significantly increased in width over 1 year compared with control lobes. These results suggest that (1) mean lobe width in a thallus may be determined by the intensity of marginal competition between adjacent lobes, and (2) changes in lobe width during the life of a lichen thallus may be a factor determining the establishment of the linear phase of growth in foliose lichens. © 1992.

Sedimentology, palaeontology and diagenesis of the Much Wenlock limestone formation

Lithofacies distribution indicates that the Much Wenlock Limestone Formation of England and South Wales was desposited on a shelf which was flat and gently subsiding in the north, but topographically variable in the south. Limestone deposition in the north began with 12m of alga-rich limestone, which formed an upward shoaling sequence. Deepening then led to deposition of calcareous silty mudstones on the northern shelf. The remainder of the formation in this area formed during a shelf-wide regression, culminating in the production of an E to W younging sandbody. Lithofacies distribution on the southern shelf was primarily controlled by local subsidence. Six bedded lithofacies are recognised which contain 14 brachiopod/bryozoan dominated assemblages, of which 11 are in situ and three consist of reworked fossils. Microfacies analysis is necessary to distinguish assemblages which reflect original communities from those which reflect sedimentary processes. Turbulence, substrate-type, ease of feeding and other organisms in the environment controlled faunal distribution. Reefs were built dominantly by corals, stromatoporoids, algae and crinoids. Coral/stromatoporoid (Type A) reefs are common, particularly on the northern shelf, where they formed in response to shallowing, ultimately growing in front of the advancing carbonate sandbody. Algae dominate Type B and Type C reefs, reflecting growth in areas of poor water circulation. Lithification of the formation began in the marine-phreatic environment with precipitation of aragonite and high Mg calcite, which was subsequently altered to turbid low Mg calcite. Younger clear spars post-date secondary void formation. The pre-compactional clear spars have features which resemble the products of meteoric water diagenesis, but freshwater did not enter the formation at this time. The pre-compactional spars were precipitated by waters forced from the surrounding silty mudstones at shallow burial depths. Late diagenetic products are stylolites, compaction fractures and burial cements.

A structural investigation of the alkali metal site distribution within bioactive glass using neutron diffraction and multinuclear solid state NMR

The atomic-scale structure of Bioglass and the effect of substituting lithium for sodium within these glasses have been investigated using neutron diffraction and solid state magic angle spinning (MAS) NMR. Applying an effective isomorphic substitution difference function to the neutron diffraction data has enabled the Na-O and Li-O nearest-neighbour correlations to be isolated from the overlapping Ca-O, O-(P)-O and O-(Si)-O correlations. These results reveal that Na and Li behave in a similar manner within the glassy matrix and do not disrupt the short range order of the network former. Residual differences are attributed solely to the variation in ionic radius between the two species. Successful simplification of the 2 the difference method has enabled all the nearest neighbour correlations to be deconvolved. The diffraction data provides the first direct experimental evidence of split Na-O nearest-neighbour correlations in these melt quench bioactive glasses, and an analogous splitting of the Li-O correlations. The observed correlations are attributed to the metal ions bonded either to bridging or to non-bridging oxygen atoms. 23Na triple quantum MAS (3QMAS) NMR data corroborates the split Na-O correlations. The structural sites present will be intimately related to the release properties of the glass system in physiological fluids such as plasma and saliva, and hence to the bioactivity of the material. Detailed structural knowledge is therefore a prerequisite for optimizing material design.

An examination of the calcium and strontium site distribution in bioactive glasses through isomorphic neutron diffraction, X-ray diffraction, EXAFS and multinuclear solid state NMR.

Strontium has been substituted for calcium in the glass series (SiO2)49.46(Na2O)26.38(P2O5)1.07(CaO)23.08x(SrO)x (where x = 0, 11.54, 23.08) to elucidate their underlying atomic-scale structural characteristics as a basis for understanding features related to the bioactivity. These bioactive glasses have been investigated using isomorphic neutron and X-ray diffraction, Sr K-edge EXAFS and solid state 17O, 23Na, 29Si, 31P and 43Ca magic-angle-spinning (MAS) NMR. An effective isomorphic substitution first-order difference function has been applied to the neutron diffraction data, confirming that Ca and Sr behave in a similar manner within the glass network, with residual differences attributed to solely the variation in ionic radius between the two species. The diffraction data provides the first direct experimental evidence of split Ca–O nearest-neighbour correlations in these melt quench bioactive glasses, together with an analogous splitting of the Sr–O correlations; the correlations are attributed to the metal ions correlated either to bridging or to non-bridging oxygen atoms. Triple quantum (3Q) 43Ca MAS NMR corroborates the split Ca–O correlations. Successful simplification of the 2 < r (A) < 3 region via the difference method has also revealed two distinct Na environments. These environments are attributed to sodium correlated either to bridging or to nonbridging oxygen atoms. Complementary multinuclear MAS NMR, Sr K-edge EXAFS and X-ray diffraction data supports the structural model presented. The structural sites present will be intimately related to their release properties in physiological fluids such as plasma and saliva, and hence the bioactivity of the material. Detailed structural knowledge is therefore a prerequisite for optimising material design.

Quasi-separation of the biharmonic partial differential equation

In this paper, we consider analytical and numerical solutions to the Dirichlet boundary-value problem for the biharmonic partial differential equation on a disc of finite radius in the plane. The physical interpretation of these solutions is that of the harmonic oscillations of a thin, clamped plate. For the linear, fourth-order, biharmonic partial differential equation in the plane, it is well known that the solution method of separation in polar coordinates is not possible, in general. However, in this paper, for circular domains in the plane, it is shown that a method, here called quasi-separation of variables, does lead to solutions of the partial differential equation. These solutions are products of solutions of two ordinary linear differential equations: a fourth-order radial equation and a second-order angular differential equation. To be expected, without complete separation of the polar variables, there is some restriction on the range of these solutions in comparison with the corresponding separated solutions of the second-order harmonic differential equation in the plane. Notwithstanding these restrictions, the quasi-separation method leads to solutions of the Dirichlet boundary-value problem on a disc with centre at the origin, with boundary conditions determined by the solution and its inward drawn normal taking the value 0 on the edge of the disc. One significant feature for these biharmonic boundary-value problems, in general, follows from the form of the biharmonic differential expression when represented in polar coordinates. In this form, the differential expression has a singularity at the origin, in the radial variable. This singularity translates to a singularity at the origin of the fourth-order radial separated equation; this singularity necessitates the application of a third boundary condition in order to determine a self-adjoint solution to the Dirichlet boundary-value problem. The penultimate section of the paper reports on numerical solutions to the Dirichlet boundary-value problem; these results are also presented graphically. Two specific cases are studied in detail and numerical values of the eigenvalues are compared with the results obtained in earlier studies.

The correlation of the indentation size effect measured with indenters of various shapes

Experimental results are presented which show that the indentation size effect for pyramidal and spherical indenters can be correlated. For a pyramidal indenter, the hardness measured in crystalline materials usually increases with decreasing depth of penetration, which is known as the indentation size effect. Spherical indentation also shows an indentation size effect. However, for a spherical indenter, hardness is not affected by depth, but increases with decreasing sphere radius. The correlation for pyramidal and spherical indenter shapes is based on geometrically necessary dislocations and work-hardening. The Nix and Gao indentation size effect model (J. Mech. Phys. Solids 46 (1998) 411) for conical indenters is extended to indenters of various shapes and compared to the experimental results. © 2002 Elsevier Science Ltd. All rights reserved.