Showing papers by "National Physical Laboratory published in 1972"

The Vibrational Properties of Disordered Systems: Numerical Studies

Abstract: A review is presented of the direct numerical approach to the study of the atomic vibrational properties of disordered systems. The basis and details of the numerical methods employed are first described. This is followed by a review of applications of the approach to two-component disordered lattices, glasses, mixed-crystal systems, orientationally disordered crystals, and random polymers.

Quasi-Newton Methods for Unconstrained Optimization

Abstract: Many techniques for solving general nonlinear unconstrained optimization problems involve iteratively minimizing a model function that satisfies certain interpolation conditions. These conditions provide a model that behaves like the objective function in the neighborhood of the current iterate. The model functions often involve second-order derivatives of the objective function, which can be expensive to calculate. The fundamental idea behind quasi-Newton methods is to maintain an approximation to the Hessian matrix. The practical success of quasi-Newton methods has spurred a great deal of interest and research that has resulted in a considerable number of variations of this idea. The analytical difficulties associated with characterizing the performance of these algorithms means there is a real need for practical testing to support theoretical claims. The goal of this project is to describe, implement, and test these methods in a way that is uniform, systematic, and consistent. In the first part of the paper, we derive several classical quasi-Newton methods, discuss their relative benefits, and show how to implement them. In the second part, we investigate more recent variations, explain their motivation and theory, and analyze their performance.

Displacement Measurement from Double-exposure Laser Photographs

Abstract: Surface displacement can be measured by recording a double-exposure photograph of the laser-illuminated object, followed by optical processing of the recorded speckle-pattern image. The analysis can either be on a point-by-point basis, or by a spatial filtering technique which resolves the motion in any desired direction orthogonal to the line of sight. The limits within which the technique may be used to measure lateral translations and rotations of the surface are examined theoretically and experimentally, and the effect of lens aberrations and surface scattering properties are discussed. Surface tilt may also be measured by recording a defocused double exposure image and analysing its optical transform. The photographic techniques described can be extended to measuring surface vibration, by recording a single ‘time-averaged’ exposure and examining the modified optical transform fringe pattern.

Mossbauer studies of the high-spin-low-spin equilibria and the localized-collective electron transition in LaCoO 3

Abstract: M\"ossbauer studies combined with magnetic-susceptibility data on well-characterized LaCo${\mathrm{O}}_{3}$ in the 4.2-1200-K region show that cobalt ions exist predominantly in the low-spin ${\mathrm{Co}}^{\mathrm{III}}$ state at low temperatures which transform partially to high-spin ${\mathrm{Co}}^{3+}$ ions up to 200 K. Above 200 K, ${\mathrm{Co}}^{3+}$ and ${\mathrm{Co}}^{\mathrm{III}}$ ion pairs transform to ${\mathrm{Co}}^{\mathrm{II}}$ and ${\mathrm{Co}}^{4+}$ pairs. At high temperatures, the population of ${\mathrm{Co}}^{3+}$ decreases significantly and completely disappears at the localized-electron-collective-electron transition temperature at 1210 K. The variations of the Lamb-M\"ossbauer factor and the center shift with temperature provide valuable information on the high-spin-low-spin equilibria, as well as on the nature of the phase transitions and symmetry changes in LaCo${\mathrm{O}}_{3}$. All these changes are reflected in the transport properties of LaCo${\mathrm{O}}_{3}$. There appears to be little doubt that the first-order localized-electron-collective-electron transition in LaCo${\mathrm{O}}_{3}$ is caused essentially by the change in entropy of the $d$ electrons.

Creep of Discontinuous Fibre Composites. II. Theory for the Steady-State

Abstract: A simple theory is developed to explain the results of paper I, for the steady-state creep of a fibre composite containing alined discontinuous fibres. Rigid and creeping fibres are considered and also the effect of sliding at the interface. The physical basis of the theory is that due to the presence of the fibres the rate of shearing of the matrix is increased. An assumption is made that this increase is inversely proportional to the fibre separation. It is shown that the assumption is not critical for large values of the exponent relating strain rate and stress of the matrix. The theory accounts for the experimental results in paper I, predicts how the strain rate sensitivity of the composite will depend on those of fibre and matrix and reduces to a known form for a Newtonian fluid.

Note on matrices with a very ill-conditioned eigenproblem

Abstract: Gives a bound for the distance of a matrix having an ill-conditioned eigenvalue problem from a matrix having a multiple eigenvalue which is generally sharper than that which has been published hitherto.

High Resolution Observations of the Submillimetre Stratospheric Emission Spectrum

Abstract: THIS letter reports the preliminary results of some recent measurements of the thermal emission spectrum of the stratosphere in the submillimetre region. This follows analysis of previous measurements from aircraft1–3 using Fourier spectroscopic techniques which snowed how, using a Michelson interferometer with a Golay cell detector, spectra may be obtained to a maximum resolution of about 0.2 cm−1. From such results, the mixing ratios of H2O and O3 may be determined relative to O2. Several emission lines due to H2O, O2 and O3 were also observed for the first time in the atmosphere, which raised the possibility that other much weaker lines due to minor atmospheric gases might be observed.

Multiple fracture in a steel reinforced epoxy resin composite

Abstract: Specimens of an epoxy resin reinforced by steel wires have been made to fail by a process which involves extensive cracking of the matrix before the UTS of the composite is reached. Such behaviour can result in energy being absorbed by the composite under constant or rising load conditions even when the composite is composed of two brittle phases. The influence of fibre size and volume fraction on the cracking process have been examined, and it has been shown that for low fibre volume fractions and large fibre sizes, the cracking process is governed by a simple relationship. When the fibre size becomes small, or the volume fraction becomes large, the cracking process is hindered, and this relationship breaks down. Under extreme conditions, cracking of the matrix can be completely suppressed and the matrix can be forced to exhibit properties markedly better than it would have shown when tested by itself. The design of materials which behave in this way may provide an important means for producing ceramic-matrix compositions with very good mechanical properties.

The formation and microstructure of dental silicate cements

Abstract: The chemistry of the cement-forming reaction between phosphoric acid solutions and fluorine-containing aluminosilicate glasses has been studied using a variety of physicochemical methods. These materials are the dental silicate cements and the microstructures of a number of these cements have been examined by optical, electron and scanning electron microscopy. The element distribution between partially reacted glass particles and the gel matrix which binds them has been determined by electron probe microanalysis.

Viscous flow of aligned composites

Abstract: The case is considered of an aligned composite subjected to tensile creep in the direction of the fibres. A geometrical argument shows that shear strain in the composite is amplified l/2s times compared with unsupported matrix, where l/2s ∼ aspect ratio of the inter-fibre spaces. The shear stress is amplified (l/2s)1/n times, where n is the exponent in the matrix creep law. Consequently the rate of energy expenditure is amplified Vm(1/2s)1+1/n times, as is therefore the tensile flow resistance of the composite (Vm is the volume fraction of matrix). The potential increase in flow resistance is thus enormous. However, the fibre end-stress, which is calculated, ∝ fibre diameter, and may be large enough to initiate rupture unless the fibres are very thin (e.g. 1 μm diameter). The tensile load is roughly equally divided between matrix and fibres irrespective of volume fractions.

Creep of discontinuous fibre composites I. Experimental behaviour of lead-phosphor bronze

Abstract: Measurements of the creep rate of specimens of lead containing alined rods of phosphor bronze of constant length (either 4.5 cm or 2.25 cm) and diameter (0.45 mm) are described. The rate of steady-state creep has been measured for composites in which the fibres creep, and for those in which they do not, and these are compaied with the rates of creep measured for the fibres and matrix alone. The deformation is very non-uniform due to small variations in volume fraction or arrangement of the wires. Voids form early in the creep test but do not immediately lead to fracture. The rate of creep is not sensitive to surface preparation of the wires. The rate of creep is compared with that predicted by a simple theory developed in paper II + + , which appears to be in accord with experiment.

Mössbauer Effect for Fe 57 in Ferroelectric Lead Titanate

Abstract: M\"ossbauer effect for ${\mathrm{Fe}}^{57}$ in ferroelectric PbTi${\mathrm{O}}_{3}$ has been investigated over the temperature range 300-1100\ifmmode^\circ\else\textdegree\fi{}K. The quadrupole interaction in the ferroelectric phase remains nearly saturated up to 320\ifmmode^\circ\else\textdegree\fi{}C, beyond which it decreases gradually to disappear at and above the transition temperature ${T}_{C}=(480\ifmmode\pm\else\textpm\fi{}2)$ \ifmmode^\circ\else\textdegree\fi{}C. The ratio of the quadrupole interaction sensed by the $\frac{3}{2}$ state of ${\mathrm{Fe}}^{57}$ nucleus in PbTi${\mathrm{O}}_{3}$ to that in BaTi${\mathrm{O}}_{3}$ at room temperature is 1.41 \ifmmode\pm\else\textpm\fi{} 0.04, in good agreement with the value 1.46 \ifmmode\pm\else\textpm\fi{} 0.07 obtained through perturbed ${\mathrm{Sc}}^{44}$ $\ensuremath{\gamma}\ensuremath{-}\ensuremath{\gamma}$ angular-correlation studies by Hass and Glass. The numerical value of the electric field gradient, as also that of isomer shift at room temperature, indicates that this lattice is more covalent than BaTi${\mathrm{O}}_{3}$. Both the center shift and the area under resonance show anomalous temperature variation in the vicinity of the transition temperature. Analysis of the temperature variation of these parameters suggests that the Debye temperature of the lattice decreases considerably on crossing the transition temperature. Analytical form of the Lamb-M\"ossbauer factor in the presence of the Cochran type of soft mode has been derived. Computer fitting of the theoretical value of the Lamb-M\"ossbauer factor at various temperatures normalized to that at ${T}_{C}$, with the corressponding normalized areas under resonance, has brought out the essential validity of the suggested temperature variation of the soft mode.

High Accuracy Spectrophotometry at the National Physical Laboratory.

Abstract: The techniques and equipment used at the National Physical Laboratory (NPL) to achieve high accuracy spectrophotometric measurements are described and discussed. The emphasis at NPL has always been on the determination of systematic components of error and their elimination or correction rather than on the attainment of mere precision, which is largely a matter of variance and resolution. The scales of regular transmittance, diffuse transmittance, total transmittance of scattering samples, regular reflectance, diffuse reflectance, total reflectance and radiance factor are determined, maintained, and made available in practical form to industry by combined use of a reference NPL manual spectrophotometer and commercial recording spectrophotometers. The presentation will concentrate on transmittance measurements made with the reference instrument, which is designed specifically to allow separate investigation of the various possible sources of systematic error, processes that are not practicable with commercial spectrophotometers. The investigation of the linearity of the complete photoelectronic system has always been a key factor, and double-aperture devices have been used consistently at NPL for over 40 years to monitor the performance of this instrument and its predecessors. Besides instrumentation, the procurement of material standards of suitable quality is a major limitation of the art, and the types in use at NPL are described, including the recently developed Ceramic Colour Standards.

The mechanical properties of perfect crystals I. The ideal strength

Abstract: In this paper we present computer calculations of the ideal strength of crystals of sodium chloride and argon, for a variety of modes of homogeneous deformation. As models of the interatomic binding we employ the simple, two-body, central-force Born-Mayer and Lennard-Jones potentials respectively. The calculations for argon are appropriate to absolute zero, those for sodium chloride to room temperature. The results indicate a very marked anisotropy of the ideal tensile strength for sodium chloride, with a pronounced minimum at , which is consistent with the observed cleavage on this plane. The ideal tensile strength of argon is shown to be much less dependent on orientation, which accords with the lack of any obvious cleavage plane in this material. We also make some estimates of the ideal shear strength, and find this to be a minimum for {1 114 shear for both argon and sodium chloride.

Precision differential calorimetry and the heat of fusion of polyethylene

Abstract: A procedure is described for the analysis by computer of the output from a differential scanning calorimeter. Enthalpy calibration with a variety of materials confirms that alumina is excellent for this purpose. Both the crystallinity, xT, and the heat of fusion of polyethylene, ΔHT, vary with temperature and it is important that both are measured. The use of a room-temperature crystallinity with a high-temperature heat of fusion can be very misleading. Interfacial effects are shown to be negligible in most cases and the heat of fusion of perfectly crystalline polyethylene is given by ΔHT/xT. It is 309 Jg−1 at the melting point.