Table of contents

Room-temperature measurements of the frequencies of normal modes propagating along the c-direction in LiNbO₃ have been carried out by inelastic scattering of neutrons. Altogether eight branches of the phonon dispersion relation, covering a frequency range of up to approximately 10 THz, have been determined.

Recently Hernandez and Ziman (abstr. A52796 of 1973) claimed to have found internal inconsistencies in Eggarter and Cohen's semiclassical approach to electron transport in gaseous He. It is shown here that their objections are unfounded.

The Nth-order response, effected by an external scalar field coupled to a system initially in thermodynamic equilibrium, is expressed with the help of imaginary-time correlation function using the spectral representation of its Fourier coefficients.

The partition functions and the two-body correlation functions are obtained for a class of one-dimensional models. Extensive use of the theory of group representations makes is possible to determine straightforwardly the spectral decomposition for the transfer operator. Explicit calculations are performed for some simple models with and without external field. In particular a lattice version for a nematic liquid crystal is obtained. One also shows how the formalism introduced can be used to study the influence of boundary conditions. One finally discusses some possible generalizations to higher-dimensional systems.

The critical properties of the xy model with nearest-neighbour interactions on a two-dimensional square lattice are studied by a renormalization group technique. The mean magnetization is zero for all temperatures, and the transition is from a state of finite to one of infinite susceptibility. The correlation length is found to diverge faster than any power of the deviation from the critical temperature. Analogues of the strong scaling laws are derived and the critical exponents, eta , and delta , are the same as for the two-dimensional Ising model.

A simple model undergoing a structural phase transition is studied using diagrammatic methods. In the limit of an infinite number of displacement components the critical dynamics are discussed for potential range sigma and dimensionality d satisfying d/2< sigma <d.

A simple method is developed for computing the electrostatic potential in ionic crystals of orthorhombic structures where tetragonal and cubic structures are special cases. The method essentially consists of direct summation of Coulomb terms due to the point charges. A very short computer program is devised and presented, which enables the reader to computer the potential at any point inside any orthorhombic structure. With is program, the self potential (the potential than an ion experiences) of a simple orthorhombic lattice neutralized by a uniform charge density was computed as a function of the lattice spacings. It was found that there are certain values of the lattice spacings where the self potential (and therefore the crystal energy) is minimum. The curve of the self potential is a potential well which is infinite at small values and large values of each of the lattice spacings.

A generalization of the Augmented Plane Wave Method (APW), for band structure calculations, where continuity is not imposed on the trial wave functions is considered. Attention is called to trial functions psi which have the combination psi + lambda R² delta _n psi , of the function and its normal derivative, continuous at the surface of the APW sphere. It is shown that a study of the calculated eigenvalue as a function of the parameter lambda is very revealing because it establishes an upper and a lower bound to the true eigenvalue. It is shown that there is an ideal value of lambda for which the convergence is best.

Clusters and (both disordered and periodic) ensembles of generalized muffin-tin potentials, nonzero only within arbitrary non-overlapping volumes, are considered, assuming the scattering states of each of these single muffin-tin potentials are known. Generalizations of the equations for the cluster scattering states, of the Lloyd-formula for the density of states and of the KKR equations for the band structure are obtained. The usual separation into potential and structure appears only if the muffin-tin potentials can be enveloped with non-overlapping spheres. Otherwise, near field properties must be taken into account.

A one-band model of a random binary alloy A_xB_1-x is analysed in terms of a two-sites coherent potential approximation. In the tight-binding hamiltonian, the off-diagonal randomness is introduced via the composition-dependent hopping energies between nearest-neighbour sites. The inclusion of the off-diagonal randomness correlates the scattering from a given site to that from its nearest neighbours. Such a correlation is incorporated in the handling of diagonal randomness (arising from the composition dependence of the atomic potentials) by treating the diagonal randomness in the pair approximation. The theory leads to the wavevector-dependent coherent potentials and previous approximations used in this problem are easily obtained in appropriate limits.

The integrals are estimated, considering the following contributions. (i) Deviations from the muffin-tin potential assumed in Mattheiss' APW calculation, both outside and inside the muffin-tin spheres. (ii) Lack of selfconsistency. Changes in the populations of the various sub-bands of the 3d band cause changes of these integrals. (iii) Different approximations for the exchange interaction, such as the Slater or Kohn-Sham rho ^1/3 approximations are shown to have only small effect. (iv) The effect of screening by the vanadium 4s band is estimated. (v) The effect of covalency with the gallium 4p band is estimated and shown to be small. A comparison of the crystal-field integrals estimated this way, with those guessed empirically, shows differences of the order of 20-40 mRyd. A proper selfconsistent calculation is probably required to get a still better accuracy.

The features of the screening of an ionized impurity of a semi-conductor have been calculated for fields sufficiently strong that the n=0 Landau level approaches the Fermi level at very low temperatures. The variation of the strength of the screened potential and its range along and perpendicular to the fields have been studied as a function of field strength. The scattering amplitude of n=0 electrons has been analyzed in the regime in question, and it is shown that the potential may to a reasonable approximation be taken to be of zero range in the field direction but not in the transverse one. The results are illustrated with numerical calculations for GaAs with 4*10¹⁶ carriers.

Hole trapping in anthracene is studied by analysing space-charge limited and thermally stimulated currents against applied voltage V and temperature T. The two methods are used for thin crystals, with continuous hole injection from a copper iodide electrode. The use of the two techniques allows a quantitative determination of the characteristics of deep and shallow traps. It is shown that, even in the range where deep traps control i(V) curves, an influence of shallow traps is still noticed. Variation of the quasi-Fermi level is stated precisely as a function of V and T. For the crystals studied, in dry air, the main level of shallow traps is about 0.65 eV above the valence band, but levels between 0.75 and 0.9 eV have been obtained by thermocurrents; the total density of deep traps, which have an exponential distribution in energy, is about 10²² m^-3.

The acoustic domain formation in semiconducting CdS crystals with with their c axis parallel to the applied electric field is discussed. For the first time the Brillouin scattering technique is used not only for on-axis phonons but for the whole spatial distribution, and reveals a continuous variation of the tilt angle between the off-axis domain and the c axis during the acoustic build-up. The results are interpreted in terms of the small signal linear theory of sound amplification in off-axis directions. The agreement between experiments and calculated prediction is very good if one takes into account the high value of the electric field inside the domain and the associated decrease in conductivity by carrier trapping.

Radiative capture of electrons from a Gamma ₁ conduction band to an impurity state which possess atomic s-like or d-like characteristics is forbidden at k=0. Allowed transitions occur with increasing probability as k increases, owing to the increasing admixture of p states according to k.p perturbation theory applied to III-V and II-VI compounds. The capture rate of hot electrons can be so sufficiently enhanced over the capture rate of thermal electrons that a negative differential resistance appears in photoconductive materials. It is suggested that this effect may account for the properties of slow domains in GaAs.

In the systems considered the lattice is divided into sub-lattices of N_a and N_b sites occupied by spins of magnetic moment mu _a and mu _b respectively such that N_a mu _a not=N_b mu _b. The exchange interactions tend to line up the a and b spins in opposite directions. The susceptibility of a linear lattice with sites arranged...abbabbabb...is obtained for general values of the exchange energies and of the ratio mu ₃/ mu _b. The division of the (T,H) plane into regions of ferrimagnetic and ferromagnetic behaviour is investigated. The spontaneous magnetization of the ferrimagnet is proportional to that of the ferromagnet and the susceptibility critical index gamma is found to be the same. The susceptibility of a 'loose-packed' ferrimagnet with N_a=N_b but mu _a not= mu _b is expressed in terms of the susceptibilities of the ferromagnet and of the antiferromagnet.

For pt. I, see ibid., vol.7, 1174 (1974). If, in the triangular 1:3 ferrimagnet of part I, the exchange energy between sites of the larger (b) sub-lattice is put equal to zero, then the b sites 'decorate' the bonds between the sites of the other (a) sub-lattice. At any temperature T and external field H the properties of a decorated model are derivable from those of a ferromagnet on the a sites of an effective temperature and field which are functions of T and H. An expression for the zero-field susceptibility is found and illustrated by that of the 1:3 model at various values of the magnetic moment ratio mu _a/ mu _b. It is found that where compensation point exists, a curve of discontinuity in the (T,H) plane intersects the T axis there. If a direct a-a interaction is introduced the curves of discontinuity are found to start from the H axis. The critical temperature of the triangular 1:2 ferrimagnet with no b-b interactions is found by a star-triangle transformation.

Inelastic neutron scattering experiments and susceptibility measurements have been carried out on polycrystalline Er_cY_1-cAl₂. A least-squares fitting procedure has been applied to the neutron data which favours four sets of crystal-field parameters. The results are compared with the measured susceptibility and other bulk magnetic properties. From this it is concluded that the crystal-field parameters x=-0.54 and W=-0.018 meV are the most probable ones.

Optical pumping of additively coloured SrF₂ at 77 K or lower temperatures produces an observable metastable EPR spectrum. The EPR line arise from two excited S=1 levels characteristic of M-type centres aligned along (110).

Absorption spectrum of lithium fluoride doped with manganese is investigated in the wavelength region 6000 AA-1400 AA. The observed bands in the visible and ultraviolet region are attributed to d-d transitions and those observed in the vacuum ultraviolet region are assigned to charge transfer transitions.