In the last 30 days

• Open/close On the General Theory of Surface States and Scattering of Electrons in Solids

  V Heine 1963 Proc. Phys. Soc. 81 300 Tag this article

  Article References Full text PDF (716 KB)

  In discussing the existence of surface states of electrons in solids or the scattering at a plane of discontinuity, it is necessary to match the wave function at the boundary plane, taken as the plane x = 0, using an infinite set of solutions of the Schrödinger equation in the solid. The solutions must all have the same energy E and the same k _y and k _z, but will have different values of k _x, which may be complex. The formal structure of the energy is therefore considered, when viewed as a complex function E of the complex variable k _x, and in particular the form of the lines along which E becomes real. This leads to some discussion about setting up approximate wave functions for surface states, differences between one, two and three dimensions, the energy of surface states relative to that of the Bloch bands, and the correction of a conclusion drawn by Goodwin in 1939.

• Open/close The Optical Properties of Bismuth Telluride

  I G Austin 1958 Proc. Phys. Soc. 72 545 Tag this article

  Article References Full text PDF (466 KB)

  The shape of the absorption edge in the semiconductor Bi ₂Te ₃ has been determined from transmission measurements on cleavage sections. The edge is of the form expected for indirect transitions, but an interpretation in terms of phonons characterized by a single energy is not applicable. A brief study of anisotropy effects is included.

  The energy gap at room temperature is close to 0.13 ev with a temperature coefficient of -0.95 × 10 ^-4 ev deg ^-1. The refractive index, determined from interference fringes, is 9.2 in the region 8-14 _μ.

  In degenerate samples the absorption edge is displaced towards higher energies. A simple quantitative discussion of this effect is given.

• Open/close The Origin of the `Invar' Effect

  R J Weiss 1963 Proc. Phys. Soc. 82 281 Tag this article

  Article References Full text PDF (414 KB)

  The idea that there are two electronic configurations of iron atoms in a face-centred cubic lattice is extended to the iron-nickel alloy system. With a reasonable variation of the energy difference of these two configurations with nickel concentration it is shown that the `invar' effect originates from the thermal excitation of the configuration with lower atomic volume in opposition to the normal anharmonic origin of expansion. The anomalous pressure dependence of the Curie temperature and the variation of Curie temperature with concentration for alloys containing 30-60% Ni are also shown to follow.

• Open/close Lens Designing by Electronic Digital Computer: II

  M Nunn and C G Wynne 1959 Proc. Phys. Soc. 74 316 Tag this article

  Article References Full text PDF (927 KB)

  The method of Successive Linear Approximation at Maximum Steps, described in the previous paper, has been applied to automatic lens designing on an electronic digital computer. A description is given of the form of programme used and the results of applying the method to three design problems are quoted.

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

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

  Article References Full text PDF (753 KB)

  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 Boltzmann Equation in the Theory of Electrical Conduction in Metals

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

  Article References Full text PDF (630 KB)

  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 Temperature Dependence of the Viscosity of Supercooled Water

  J Hallett 1963 Proc. Phys. Soc. 82 1046 Tag this article

  Article References Full text PDF (239 KB)

  The viscosity of supercooled water has been measured, using a capillary flow technique, down to -23.8 °C. The large supercooling was obtained by removing nearly all suspended particles from the water by an ion exchange column. These results agree with those obtained by White and Twining in 1914, who obtained results down to -9.3 °C.

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

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

  Article References Full text PDF (501 KB)

  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 The Infra-Red Emissivities of Indium Antimonide and Germanium

  T S Moss and T D H Hawkins 1958 Proc. Phys. Soc. 72 270 Tag this article

  Article References Full text PDF (224 KB)

• Open/close The Raman spectrum of calcium fluoride

  J P Russell 1965 Proc. Phys. Soc. 85 194 Tag this article

  Article References Full text PDF (201 KB)

  The first- and second-order Raman spectra of calcium fluoride have been measured. With the crystal at room temperature the structure observed is in good agreement with earlier measurements of infra-red absorption and vibronic satellites. Some additional structure observed in the second-order Raman spectrum is ascribed to overtones about k = 0 in the phonon spectrum.