In the last 30 days

• Open/close The statistical mechanics of polymers with excluded volume

  S F Edwards 1965 Proc. Phys. Soc. 85 613 Tag this article

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  The probability distribution of the configurations of a polymer consisting of freely hinged links of length l and excluded volume v is studied. It is shown that the interaction of the polymer with itself can be represented by considering the polymer under the influence of a self-consistent field which reduces the problem to an equation like the Hartree equation for an atom. This can be solved asymptotically, giving the probability of the nth link of the polymer passing through the point r to be ( L)exp[-27{ r-(5/3) ^3/5( v/3π l) ^1/5 L ^3/5} ²(1/20 Ll)] where L = nl is the length along the polymer and ( L) the normalization. Thus the mean square of r, r ², is (5/3) ^6/5( v/3π l) ^2/5 L ^6/5.

  The theory is extended to polymers of finite length, to the excluded random walk problem and to n dimensions.

• Open/close Energy Loss Processes in Ferroelectric Ceramics

  B Lewis 1959 Proc. Phys. Soc. 73 17 Tag this article

  Article References Full text PDF (436 KB)

  By a study of ageing effects in which permittivity, elastic compliance and the electrical and mechanical loss coefficients decrease with time, the principal ferroelectric loss process in low fields is identified as microhysteresis associated with small-amplitude domain boundary movement. Larger fields produce macrohysteresis effects due to large-scale boundary movement, and the permittivity, compliance and loss coefficients are increased. Although boundary movement is responsible for almost all the energy loss, its contribution to permittivity and compliance is usually small compared with induced effects within each domain. Thus a change in the magnitude of boundary movement alters the permittivity and compliance only slightly, but changes the loss coefficients considerably.

• Open/close The thermodynamic and optical properties of germanium, silicon, diamond and gallium arsenide

  G Dolling and R A Cowley 1966 Proc. Phys. Soc. 88 463 Tag this article

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  Measurements of the dispersion curves of the normal modes of vibration, by inelastic neutron scattering techniques, have been used to find the parameters of dipole approximation models to describe the lattice dynamics of germanium, silicon, diamond and gallium arsenide. The model for diamond, which has not previously been published, shows marked differences in the dispersion curves between this material and the other three and these give rise to characteristic differences in the physical properties. The models for all four materials give good agreement with the experimental results and enable other physical properties to be calculated with reasonable confidence in the frequencies of the normal modes computed from the models.

  Detailed calculations are made of the frequency distribution and its moments, and of the specific heat which is compared with experimental results. The agreement obtained is quite satisfactory for diamond but less so for the other materials. The negative thermal expansion coefficient of these materials at low temperatures is found to arise easily from these models, when they are extended in a simple way to include the central force part of the anharmonicity between nearest-neighbour ions.

  The infra-red absorption spectra are calculated both by assuming a joint density of states approximation, and also by assuming first- and second-nearest-neighbour interactions to describe the dipole moments. While none of these calculations is able to give a good account of the experimental results, the latter calculation suggests that second-nearest-neighbour interactions are necessary to explain the measured spectra. The calculations for diamond lead to an entirely different interpretation of the critical points in the spectra from that given previously.

  The Raman spectra of the elements have been calculated including the effects of anharmonicity on the one-phonon part of the spectra. Since the results depend on the orientation of the specimen and the geometry of the experiment a direct comparison with experiment is not possible. Nevertheless the results do suggest that this type of calculation may well be able to provide agreement with more detailed experiments. Critical points are frequently deduced from measurements of the infra-red and Raman spectra. The difficulties both in identifying and in assigning them to the appropriate normal modes are discussed.

• Open/close Specific Negative Resistance in Solids

  B K Ridley 1963 Proc. Phys. Soc. 82 954 Tag this article

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  The inherent instability associated with a specific differential negative resistance in a solid is discussed for the two cases voltage-controlled and current-controlled differential negative resistance. In the case of voltage-controlled differential negative resistance, it is shown that domains of high electric field occur. These domains are generally mobile and their movement is discussed. In the case, of current-controlled differential negative resistance, high current filaments form. The sizes of the domains and filaments are governed by the size of the specimen and by the principle of least entropy production. The effect of an external circuit is to inhibit stable filament formation in the case of current-controlled differential negative resistance and impose conditions under which stable domain formation can be observed in the case of voltage-controlled differential negative resistance.

• Open/close The Boltzmann Equation in the Theory of Electrical Conduction in Metals

  D A Greenwood 1958 Proc. Phys. Soc. 71 585 Tag this article

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  The motion of conduction electrons in a metal in an electric field, scattered by an irregular static potential, is considered; this model is applicable to the resistance due to lattice waves at high temperatures, and to imperfections at any temperature. In §2 the Boltzmann equation is re-derived without the customary perturbation theory, avoiding the usual necessity of averaging over phases of different electron states after repeated small time intervals. The assumption that the scattering centres are distributed at random in the crystal is alone sufficient. The theory is, however, still dependent on assuming that h/τ<< kT, where τ is the collision time, as is the usual perturbation theory. §3 gives a general formula for the conductivity of the model, not subject to any assumption. This helps to justify an argument by Landau according to which the usual theory is valid provided h/τ<<η, where η is the cut-off energy of the Fermi distribution. No direct evaluation of the formula has been achieved.

• Open/close The Electrical Conductivity and Thermoelectric Power of Bismuth Telluride

  H J Goldsmid 1958 Proc. Phys. Soc. 71 633 Tag this article

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  The electrical conductivity and thermoelectric power of the semiconductor Bi ₂Te ₃ have been measured between 150°K and 300°K. n-type and p-type samples with a wide range of carrier concentration have been included. Most samples have shown extrinsic conduction and have been partially degenerate over at least part of the temperature range, so it has been necessary to use Fermi-Dirac statistics in interpreting the results. A few samples have exhibited mixed and intrinsic conduction at the higher temperatures. It has been possible to determine the variation of carrier mobility with temperature and to estimate the energy dependence of the relaxation time, as well as a number of the semiconductor parameters.

• Open/close The second virial coefficient of carbon dioxide

  R S Dadson et al 1967 Proc. Phys. Soc. 92 1115 Tag this article

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  In an earlier paper some determinations of the virial coefficients of carbon dioxide and ethylene, planned as part of a continuing investigation of the ( p,v,t) properties of gases and gaseous mixtures, were described. These measurements utilized the `series-expansion' technique which it was intended to use consistently throughout the series. In view, however, of the aims of the work and the consequent demands on accuracy, it was decided, as a precaution against the possible intrusion of undetected systematic error, to carry out a limited series of measurements on one gas - carbon dioxide - by an independent method. For this the `piezometer' technique developed by Michels and his collaborators was chosen.

  This paper compares the values of the second virial coefficients obtained over the temperature range -10 to 200°C in the two series. These proved to be in very precise agreement, the discrepancies at corresponding temperatures being nowhere greater than 0.03 × 10 ^-3 amagat (0 7 cm ³ mole ^-1) and on the average of the order of only 0 01 × 10 ^-3 amagat (0.2 cm ³ mole ^-1). The significance of these results is discussed.

• Open/close The Lattice Constants of High Purity Alpha Titanium

  R M Wood 1962 Proc. Phys. Soc. 80 783 Tag this article

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  Lattice constants have been determined for a specimen of alpha titanium of greater purity than hitherto examined. Values of a ₀ = 2.95111 Å ± 6 × 10 ^-5 and c ₀ = 4.684 33 Å ± 10 × 10 ^-5 differ significantly from previous, accepted figures obtained by Clark in 1949. Comparative impurity contents for two grades of pure titanium are given.

• Open/close The Electrical Properties of Bismuth Telluride

  R Mansfield and W Williams 1958 Proc. Phys. Soc. 72 733 Tag this article

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  Measurements of the electrical conductivity, Hall coefficient, thermoelectric power and Nernst coefficient on specimens cut from zone melted Bi ₂ Te ₃ and on a single crystal are described. The current flow was parallel to the cleavage planes and the galvanomagnetic effects of the single crystal were measured with the magnetic field perpendicular and parallel to the cleavage planes. For the other specimens the Hall and Nernst coefficients were measured with the magnetic field perpendicular to the cleavage planes. The temperature range was 100°K to 600°K and specimens with a wide variation of impurity content were used. Analysis of the thermoelectric power and conductivity in the extrinsic range indicated that the specimens were partially degenerate, and when allowance is made for this, the temperature dependence of mobility is T ^-1.63 for electrons and T ^-1.94 for holes. In the high temperature range the conductivity measurements yield a value of the energy gap at 0°K of 0.21 eV. The temperature dependence of the Hall coefficient in the extrinsic range is anomalous and the explanation is not known. The Nernst coefficient Q exhibits the general behaviour expected for a semiconductor, and it is shown that it obeys a relation which can be derived from Moreau's relation, Q being proportional to TRσ d ² E/dT ² (thermoelectric power = dE/dT, Hall coefficient = R, conductivity = σ).

• Open/close Classical theory of charge transfer and ionization of hydrogen atoms by protons

  R Abrines and I C Percival 1966 Proc. Phys. Soc. 88 861 Tag this article

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  The theory is presented for obtaining, by a Monte Carlo method, the classical cross sections for charge transfer and ionization of hydrogen atoms by protons, in which the atoms are chosen initially from a microcanonical ensemble. With minor modifications the theory applies to any collisions between three charged particles which do not all have charges of the same sign. Scaling laws and an iterative solution of Kepler's equation are discussed.