Table of contents

An exact solution is given for the conductivity sigma (p) of branching networks with all but a fraction p of conducting links removed. The conductivity is related to the percolation probability P(p) of the branching model by sigma (p)= mu (p)P(p) where mu (p) is an effective mobility determined by the shape of the infinite cluster, mu (p) is proportional to p-p_c⁽⁰⁾ for p near the critical concentration p_c⁽⁰⁾ where the most probable infinite clusters are predominantly chain-like. The model reproduces the qualitative features of experiments by Kirkpatrick on disordered square and simple cubic networks of resistors, giving the conductivity vanishing for p less than p_c⁽⁰⁾ and otherwise almost linear in p except near p_c⁽⁰⁾ where sigma (p) varies as (p-p_c⁽⁰⁾².

Using the diffraction theory of random wavefunctions, it is argued that recent interference electron microscopy of thin amorphous films cannot be employed to distinguish between the crystallite and random network models.

In a recent paper (abstr. A74234 od 1972) Robinson and March gave a discussion of the correction factor due to many-particle interactions to the van der Waals interaction between two atoms of a dense rare gas fluid. A central role in their treatment is played by the volume integral of a quantity involving the pair distribution function. By taking various numerical examples for this function it appeared that the value of the integral is almost independent of the structure of the fluid and depends mainly on the density. In this comment it is shown that this conclusion is rigorously valid and can be proved analytically without numerical work.

It is shown, that for any monatomic, Born-von Karman model of lattice dynamics, there exists the shell model with isotropic shell-core coupling, having the same elastic properties. Phonon frequencies and frequency spectra of the shell model are easily expressible in terms of the corresponding quantities for the first model.

A method for finding the electron states in a thin crystalline layer with realistic surface potential is given. The method gives good agreement with the computer calculations of Schulte and Bross (1972). In many realistic cases the eigenvalues of mod k mod (k=crystal momentum) in a layer of thickness Na(a=length of unit cell are close to mod k mod = pi n/(N+1)a(n=1,2,...,N). The results are applied to the spectra of InSb films and of linear organic dye molecules.

A formula for the averaged moment per site in amorphous (or liquid) ferromagnets is derived by using a molecular field model, taking into account exactly the structure fluctuations which could exist in amorphous (or liquid) materials.

Measurements of the quadrupolar relaxation rate of the Ga spins in liquid Ga-In alloys are reported. The rate is an increasing function of composition and a decreasing function of temperature. The dependence on temperature leads to an interpretation of the data in terms of a contribution from each of two separate mechanisms. One is the coupling to the time dependent field gradients associated with the diffusive motion of the ions and the other is characteristic of the relaxation in pure liquid Ga metal.

Since no workers have yet succeeded in repeating the reported observations of optical modulation of electron beams, experiments are proposed which investigate the processes involved without demanding the high electron-beam coherence which has proved the main source of difficulty.

The middle infrared absorption spectrum of DyVO₄ has been investigated at 1.7K and 90K. For the lower temperature the positions of all the levels in the ⁶H_13/2 and ⁶H_11/2 manifolds are given but no fine structure due to magnetic interactions was found. At 90K, broad absorption bands were seen.

Photoelectron emission studies indicate that the upper valence band in MoTe₂ and NbSe₂ is formed from the transition metal non-bonding d_z2 orbital, in accordance with recent theory. Comparison of work function and photothreshold for MoTe₂ leads to a band gap of the order of 1 eV.

Photoemission spectra using incident photon energies of 40.8 eV have been recorded for several dichalcogenides of metals of groups IV, V, and VI, with layer structures. The valence band densities of states so measured show the progressive development of d bands in these materials. These results are compared with the predictions of available band models for these compounds.

The factors affecting the formation of B32 Zintl phases are examined. Evidence is presented that the pseudopotential effects discussed by others have not been shown to be essential, and that the structures must still be accounted for largely by geometric factors.

Undoped alkaline earth fluorides are strongly resistant to coloration at room temperature by X-rays. However, the crystals colour fairly readily at 77 K and lower temperatures. The present paper shows that the colourability of SrF₂ at 4 K is comparable with that of K Br. However, the colourability falls sharply by a factor of about 5 at 34 K and a further fall occurs at 67 K. X irradiation of SrF₂ at 77 K and lower temperatures produces F centres and V_K centres; the number of H centres formed is always more than two orders of magnitude smaller than that of V_K centres. The F band shows partly resolved structure and this is more extended for irradiation below 34 K than above.

X irradiation of SrCl₂ at 77 K produces V_K centres and F centres; H centres are not produced in observable concentration. A study of the effects of polarized bleaching light on the optical and EPR spectra shows that a ² Sigma -² Sigma type transition of the V_K centres occurs at 397 nm. The V_K centres decay at 105 K with an activation energy of 0.251 eV. Some of the moving holes are trapped at lattice defect sites forming V_KA centres. Only perturbed F centres are observed in appreciable concentration in the irradiated crystals. These centres have been investigated by EPR and magneto-optical methods. The F band shows partly resolved structure with peaks at 580 and 667 nm.

Dislocation studies in Bi-Sb crystals were made by etch pit techniques on the cleavage plane. A new reagent capable of revealing dislocations inclined to the cleavage plane is reported. Dislocation spirals and loops on the quenched specimens have been observed.

An attempt is made to reconcile the suggestion of Fisher (1967) that the partition function of a condensing gas has a singularity at the phase boundary with the numerical calculations of Gaunt and Baker (1970) for the metastable state.

The Dingle temperatures (Landau state lifetimes) have been determined from the Shubnikov-de Haas Effect at 1.2 K for three specimens of graphite as a function of the angle theta between H and c. For a single crystal which contains negative scattering centres, the lifetimes are almost independent of theta (<64 degrees ), whereas in a single crystal which contains positive scattering centres, the electron lifetime becomes much shorter than the hole lifetime for theta >40 degrees . In pyrolytic graphite, both lifetimes decrease steadily as theta is increased. These dependences are interpreted in terms of a trigonal fluting of the Fermi surfaces, which affects electrons more than holes. A preliminary estimate of stacking fault spacing in good quality pyrolytic graphite is given as approximately 1370 AA, and the influence of the mosaic structure of pyrolytic graphite on the measurements is briefly discussed.

For pt. I, see abstr. A47799 of 1972. Two conclusions are obtained for the three dimensional Anderson's model. The first is that the ratio G_i1,if/G_i'1if between the values of the Green function at two different sites is equal to the corresponding state ratio u_i1^beta /u_i'1^beta provided that the energy parameter E is equal to an energy eigenvalue E_beta . The second is that the fall-off rate lambda _beta of the eigenstate with the energy E_beta , which was introduced by Thouless (1972) for the one dimensional case, can be defined also in the three dimensional case, and can be identified with the degree of localization defined by an average of the logarithm of the ratio mod G_ij/G_i+1,j mod .

The thermoelectric power of two crystals of AgCl doped with Mn²⁺ ions has been measured over a range of temperatures from 97 to 414 degrees C using Ag electrodes. These data, and also earlier data for pure AgCl and for AgCl doped with Cd²⁺ ions have been shown to be fully consistent with the assumption that the heats of transport, and also another related parameter, are independent of temperature. The value of the heat transport for Ag⁺ ions migrating on the cation sublattice by a vacancy mechanism (Q_M) is 0.311 eV, while the values for the collinear (Q_ic) and noncollinear (Q_inc) mechanisms are -0.180 eV and -1.20 eV respectively. These numerical values are consistent with elementary theories of the heat of transport.

A method is described for iteratively solving the Boltzmann equation with the angular dependence of the distribution function expanded in Legendre polynomials. Compared with earlier integral equation methods this approach is shown to have a number of advantages which can lead to an increase in computing efficiency by as much as two orders of magnitude. Numerical results for p-Ge and n-GaAs have been calculated to show the convergence properties of the present approach.

The dynamic properties of paramagnets are investigated within a continued fraction representation of the relaxation shape function. The approach seeks to isolate the dominant frequency dependence and requires an estimation of the temperature dependence of static spin correlation functions. A three-pole approximation is shown on the basis of comparison with computer calculation and neutron scattering measurements on RbMnF₃ to provide a good description of the dynamic properties of one and three dimensional paramagnets over a wide range of wavevectors and temperature.

The Jahn-Teller coupling is known to lead to the reduction of single parameters such as the spin-orbit coupling (the Ham effect). An important question is what it does to exchange interactions. This problem is studied for what is probably the simplest case, direct exchange between two Tg ions coupled to the Eg types of distortions of a cubic lattice. It is found that the exchange interaction has a complicated form, that in general it is quenched, and that it may become temperature dependent. The method used is a combination of the transformation method for Jahn-Teller problems and a new formulation of the exchange problem, in terms of second quantization.

A theory of the 'bottleneck' which restricts relaxation by the Orbach mechanism when too few phonons of the appropriate frequencies are available is developed for the case of a spin doublet relaxing via a single excited level. The extent to which the relaxation disturbs the distribution of phonons is found on the assumption that the only broadening of the two bands of lattice modes concerned is that associated with the finite lifetime of the excited spin level. The relaxation is hindered most when the splitting of the doublet in an applied magnetic field H is such that the bands are well separated. Otherwise overlap between them reduces the effect of the bottleneck, so that it disappears as H approaches zero.

The dielectric properties of crystals are studied on the basis of the weakly anharmonic crystal model. Particular emphasis is placed on the low frequency behaviour of the dielectric susceptibility and on the possibility of a coupling between the dielectric properties and the fluctuations in the phonon density distribution. These fluctuations cannot be treated by low-order perturbation theory but can be discussed by solving the appropriate transport equation. The approximate solution to this equation is obtained following the techniques developed for ultrasonic attenuation.

For pt. I, see ibid., vol. 6, 121 (1973). The response of a crystal in the neighbourhood of a structural phase transition is discussed. It is shown that the behaviour of the scattering cross section is very dependent upon the symmetry of the two phases. The weakly anharmonic crystal model is used within the framework of the Landau theory of phase transitions to discuss nonpiezoelectric/ ferroelectric, piezoelectric/ferroelectric and transitions involving an increase in the size of the unit cell both of the improper ferroelectric kind and otherwise. In every case it is shown that the theory gives rise to the possibility of quasi-elastic as well as inelastic scattering below T_c, but above T_c quasi-elastic scattering is expected in the piezoelectric/ferroelectric and improper ferroelectric phase transitions.

A general method is presented for determining physical boundary conditions for the normal excitation modes of a finite crystalline array of identical units having a dipole-allowed transition to the excited state. Progressive polarization waves are produced during continuous irradiation, giving an internal electric field, part of which shields the crystal interior from the externally applied field as required by the Oseen-Ewald theorem, the remainder determining the refractive index. On removing the applied radiation, quasi-stationary states are established, the amplitude of the shielding fields being set equal to zero to give complex wavevectors and eigenfrequencies.

The infrared response of alkali halide crystals is investigated through a detailed analysis of the frequency dependent self energy of the transverse optic mode. Particular effort is made to understand the magnitude and temperature dependence of the width of the infrared absorption peak, given by the imaginary part of this self energy. The effects of intra-ionic nonlinearity are considered, and calculations are presented for KBr at 300 K indicating that these are small. The modification of the effective two-phonon density of states by phonon-phonon interaction is investigated, and calculations show that these can alter the self energy by up to 20%.

The IR absorption spectrum of KBr crystals doped with BO₃^3- ions in the region 2000-700 cm^-1 is reported. The splitting of the v₃(E') mode indicates that the site symmetry of the ion is lower than C_3v. The observed overtones and combination bands fix the position of v₄(E') as 584 cm^-1.

Ten absorption bands are observed in the electronic spectra of NaCl and KCl crystals doped with Fe(CN)₆^3- ions in the range 50000-20000 cm^-1. Six of these bands are assigned to the ligand to metal charge transfer transitions (t_1u⁶t_2g⁵ to t_1u⁵t_2g⁶ and t_1u⁵t_2g⁵e_g¹ and a_1g²t_2g⁵ to a_1g¹t_2g⁶). The positions of these bands agree with those calculated using Dq=1944 cm^-1, B=623 cm^-1 and C=3270 cm^-1 for d⁶ configuration. The remaining four bands are assigned to crystal field transitions for d⁵ configuration and agree with the calculated peak positions for Dq=3450 cm^-1, B=700 cm^-1 and C=2400 cm^-1. Vibration spectrum in the (C identical to N) stretch region shows that the Fe(CN)₆^3- ion is present predominantly in the C_s site symmetry.