Table of contents

It is shown that a careful consideration of the Debye-Waller factor for atom-surface scattering explains the failure to observe diffracted scattering of He from most metal surfaces.

A broad high frequency depolarized peak has been observed in the light scattered from liquid helium I at an energy of approximately twice the maximum of the dispersion curve. Spectra are shown and a number of possible explanations of the phenomenon are discussed. The corresponding spectrum for ⁴He gas at 0.96 atm and 4.22 K has also been observed and shows no structure.

The Compton profile of polycrystalline LiCl is measured at Mo K alpha (17keV). The observed profile agrees, within the limits of experimental error, with that calculated from the local-orbital wavefunctions of Kunz (1970), but deviates at small values of electron momentum from the profile based on a superposition of Hartree-Fock free ions.

A reduced Green function, which is essentially the projection of the usual electronic Green function onto a finite-dimensional vector space, is defined for electrons in a finite system. This reduced Green function can be used in place of the usual Green function in formulae for the density of states and conductivity of the system, and can be calculated by any of the techniques used to calculate the usual Green function. Applications of the method to the theory of disordered and amorphous solids are discussed.

It is argued that in highly compensated n-type InSb in a magnetic field exceeding a critical value, both electron correlations and disorder are involved in an essential way. Wigner crystallization is then anticipated, and the electrical conductivity measurements of Somerford (1971) are interpreted as due to electrons diffusing via defects in the wigner electronic lattice, and in particular via vacant electronic sites. In view of the theoretical interest of such Wigner crystallization, further experiments are proposed on n-type InSb and other materials (though higher magnetic fields are then needed), including ac transport measurements and Bragg scattering of neutrons.

The electric field produced, under open circuit conditions, by momentum transfer from CO₂ laser radiation to mobile holes within p-type germanium need not be parallel to the laser direction. It is shown that the fourth rank tensor that describes this effect has only two independent terms. Measurements have been made for a number of propagation directions, and the results are consistent with the tensor description. For 2.5 Omega cm material, the maximum angle between the drag field and the propagation direction is 9 degrees 3'.

Reflectivity spectra of MoS₂ and NbSe₂ have been measured in the vacuum ultraviolet region between 1050 AA and 3000AA for near normal incidence of the basal plane. The results show a systematic trend in high energy interband transitions and in plasma resonances of these materials.

A method based on the anomalous scattering of either X-rays or neutrons has been suggested to separate the partial structure factors in a liquid or amorphous binary system.

The partial structure factors and radial distribution functions for molten CuCl at 713 K have been determined by the scattering of neutrons from samples of varied isotopic composition. A marked difference is observed between the Cu-Cu and Cl-Cl distributions. The data are discussed in terms of both a hard sphere model and an associated (covalent type) molecular model.

An analytical representation of the experimental data of Van Itterbeek et al. (1967) for argon and methane is carried out according to the Tait equation. This procedure is more accurate and covers a larger range than the complicated procedure of Van Itterbeek et al. Various thermodynamic functions of interest are calculated. Finally the validity of the principle of corresponding states for argon and methane is considered.

A simple form for the generalized density susceptibility for k approximately 0.5 AA^-1 and omega approximately 10¹³s^-1 is proposed for monatomic liquids which has the merit of satisfying certain sum rules and limits. It is shown to give a good description of the current correlation observed by Rahman (1968) in a molecular dynamics study of argon at 76 K. Moreover at small wavevectors a triple peak structure is obtained with the frequency of the collective excitation in good agreement with a molecular dynamics study of argon by Kurkijarvi, Levesque and Verlet (1968).

The applicability of the extended Huckel method for the calculation of the electronic properties of point defects in diamond-type crystals is discussed. A detailed study of the isolated vacancy in both the diamond and silicon lattice shows that the results obtained depend upon the size of the cluster chosen and the approximations made at the boundary of the system. Clusters with up to 47 host lattice atoms are considered. A cluster of 41 atoms, which includes all atoms directly bonded to the second neighbours from the point defect, is considered to be the most suitable system. On the basis of a comparison of ab initio and extended Huckel calculations for small molecules, it is argued that studies involving distortions are beyond the validity of the simple method used here. At best, the results from extended Huckel studies for point defects in diamond type crystal should be considered to be semiquantitative.

For pt. I see ibid., vol.4, 3065 (1971). The changes in the electronic structure of diamond and silicon crystals when a substitutional impurity atom is present are investigated within the framework of the one electron extended Huckel method. In most of the studies reported a cluster of 41 atoms is used to simulate the crystal. For diamond. the electronic properties associated with having a silicon, nitrogen, boron or aluminium substitutional impurity at the centre of the cluster are investigated. Similar calculations for silicon with a carbon, boron, aluminium, nitrogen, oxygen or sulphur substitutional impurity are also discussed. A more detailed study of the nitrogen donor in diamond shows that the position of the impurity level in the band gap depends upon the size of the cluster chosen and the approximations made at the surface. It is concluded that such a simple one-electron treatment is inadequate for the quantitative study of the electronic properties of impurity ions in covalent crystals.

The temperature dependence of the q approximately=0 infrared active phonons in CaF₂, SrF₂ and BaF₂ is reported in the range 5-500 K, and the pressure dependence of the long wave transverse optic phonons at 290 K, in the range 0-12 kbar. These measurements have been used to determine the variation of q approximately=0 transverse optic phonon frequencies at constant volume from 5 to 500 K and also the dependence on volume at 290 K. The results are discussed in terms of the complex selfenergies of this phonon and in terms of the volume dependence of the effective charges for these solids.

A careful analysis is made of the convergence of several perturbative techniques for calculating LEED intensities with the hope of finding a scheme that is both fast and accurate. Carefully calculated scattering factors are used in this analysis. Unfortunately divergence, or poor convergence of the relevant series holds for most theories. However a renormalization for the forward scattering (RFS) results in a highly convergent series (RFS perturbation theory) that is amenable to rapid calculations.

Bragg neutron diffraction studies have been carried out on fluorite solid solutions of YF₃ in CaF₂. The samples investigated were a single crystal containing 6 mol% YF₃ (studied at room temperature (RT)) and polycrystalline samples of compositions (Ca/Y)F_2.10 (500 degrees C), (Ca/YF)F_2.15 (RT and 900 degrees C), (Ca/Y)F_2.25 (RT) and (Ca/Y)F_2.32 (RT). The results in all cases indicate two types of interstitial site located along the (110) and (111) directions from the cubic, 1/2, 1/2, 1/2 positions (F, and F" respectively). Vacancies in the normal fluorine sites (Fⁿ) are also detected. Variations in the relative numbers of F', F" and Fⁿ atoms with excess fluoride content are observed. The clustering of defects has been considered and possible models which would account for the observed occupation numbers have been proposed. A revised neutron scattering length for calcium of 0.477+or-0.004*10^-12 cm is reported.

Excess electron and excess hole energy bands for beta -hydrogen phthalocyanine have been calculated using the tight binding approximation, omega technique LCAO-MO's as basis functions for constructing the Bloch functions and modified molecular potential. The energy bands are highly anisotropic. The mobilities of electrons and holes have been found to be independent of temperature in the range 200 K to 500 K. It has been suggested that the carrier scattering may be predominantly due to neutral molecules. An attempt has been made to explain some of the results of earlier workers.

Trial wavefunctions for the valence band in an amorphous semiconductor are constructed out of linear combinations of bond orbitals. In the absence of long range order, these functions are assumed to be statistically homogeneous and isotropic over extended regions of the material, yet satisfying the same strong local conditions for the bond coefficients as in the perfect crystal. The importance of topological restraints on the assignment of these coefficients is emphasized. In particular, it is shown that three mutually orthogonal extended states can always be found near the top of the band, analogous to the triple degeneracy at Gamma _25' in the crystal. Some observable characteristics of the electronic structure of these materials are conjectured.

The theory of multiple scattering by clusters of atoms is employed to analyse the electronic density of states in crystalline and amorphous materials. A study is made of different sizes of clusters, geometries, types of atoms and boundary conditions including the case when the use of periodic boundary conditions simplifies the problem by imposing 'translational symmetry' as in a superlattice of similar clusters. The results suggest that some combinations of scattering potentials in systems with appropriate short range order can be a sufficient condition for the existence of an energy gap in the electronic density of states above the muffin tin zero.

The muffin tin model of band structure and scattering theory can be modified to include a more general class of potential than the spherical kind usually employed in such models. It is shown how the generalization of the actual band structure calculations can be carried out once the solution of a set of coupled differential equations is known inside the muffin tin spheres. The importance of such generalizations to covalent materials is discussed.

Two general explanations for the Meyer-Neldel rule are described. The required correlation between the activation energy and pre-exponential factor for conductivity is shown to result by considering (i) a rectifying layer at the electrode-solid interface which produces a field dependent potential barrier through which charge carriers are transferred by the mechanism of thermally assisted tunnelling. In this case the characteristic temperature, T₀, is shown to depend on the temperature range over which data points are computed, (ii) a compensated wide band gap semiconductor with ohmic contacts which is subjected to a disturbance which affects the state of occupancy of its energy levels. Here, two results are of particular importance: (a) if the ratio of the two dominant state densities remains unaltered, the Meyer-Neldel rule with T₀ infinite is obtained and (b) if the concentration of the majority carrier band states of the solid tails exponentially with energy according to a parameter, T_c, the rule is obtained with T₀=T_c.

Characteristic plots of the real space densities are presented for diamond and zincblende semiconductors. A comparison is made between the valence distribution and the results of linear screening theory. The charge densities are decomposed into covalent and noncovalent contributions and the bond charges calculated. The charge transfer is investigated and it is found that the bonding in III-V compounds is between neutral and covalent. The Fourier components of the valence charge densities are tabulated.

A number of workers have reported that, at low amplitudes the response of pinned flux lines to a ripple field is linear and reversible, in contradiction to the Bean model. It is shown that this can be explained by the elastic movement of flux. The results allow the force exerted on the flux lines by the lattice to be calculated as a function of their displacement from equilibrium. It is found that unpinning first occurs for displacements of about 30 AA but that the full critical state is not built up until they have moved about 400 AA. One result is that the ac losses are less than would be calculated from the Bean model and this is confirmed by the experimental measurements.

The electrical conductivity of n-type GaS single crystals has been measured along the perpendicular to the c direction of the crystals. An excess of thermal activation energy and a frequency dependent conductivity in the direction parallel to the c axis of the crystal was observed. These effects were not observed in the p-type crystals. A hopping conduction in the n-type crystals along the c direction is inferred.

The behaviour of a classical Heisenberg chain of N spins with nearest neighbour interactions including a term quadratic in (S_k.S_k+1) which is multiplied by a random parameter is studied. The partition function for the system is found as an N-fold convolution of random integral kernels. Depending on the values of the random parameters in the interactions, the first and second largest eigenvalues of these integral kernels may or may not be degenerate at T=0. The connection between this degeneracy and the presence of absence of long range order in the system at T=0 is discussed.

Recently published curves of the magnon dispersion relations of Gd have been used in a calculation, based on Houston's method (1948), of the spin wave contribution to the specific heat of Gd at temperatures up to 60 K. The spin wave specific heat was found to be expressible as 2.09 T^1.56 mJ mol^-1 K^-1 below about 3 K and as 1.01 T^2.30 mJ mol^-1 K^-1 between 3 K and 14 K; no simple power law could be discerned in the results above 14 K. The results are compared with the experimental results of Lounasmaa and Sundstrom (1966) between 7 K and 25 K; it is suggested that some further experimental results below 7 K would be useful.

An approximate calculation to assess the behaviour of the short range order is carried out on an effective spin Hamiltonian obtained from a model of a compressible Ising system which includes the spin-phonon interaction only to first order in the ion displacements. As in the molecular field approximation a first order transition occurs for sufficiently large values of the spin-phonon coupling parameter.

The magnetic structure of DyAsO₄ has been determined by neutron diffraction on a powdered sample. DyAsO₄ undergoes a transition to a non-collinear antiferromagnetically ordered state at 2.5 K, with an inclination of the magnetic moments of phi _b=22 degrees relative to the b axis in the ab plane. The magnetic space group is P_I2₁2₁2₁ (orthorhombic symmetry). The magnetic moment is 8.6 mu _B at 2.2 K. The temperature behaviour of the magnetization is in agreement with an Ising magnet. The crystallographic parameters are determined and possible crystallographic phase transitions are discussed.

It is shown, by means of a series of calculations, that the generally accepted picture of configuration interaction causing the external electrostatic field to be screened is oversimplified. Overlap, charge penetration and correlation are all shown to be important and to modify this picture so much that it is no longer useful. An alternative model is discussed in which the same effective potential determines the configuration interaction contributions to both the one electron and two electron crystal fields for all excited states.

Vibrational absorption due to boron, carbon, nitrogen, silicon, aluminium and arsenic has been observed in gallium phosphide crystals. It is concluded that ¹¹B and ¹⁰B give gap modes with a separation of about 1.5 cm^-1. Previously reported absorption bands at 849 and 882 cm^-1 have only been detected in electron irradiated zinc doped crystals, and it would appear that they cannot be due to local+gap combinations. It has been confirmed that a line at 496 cm^-1 is due to ¹⁴N, and it has been shown unambiguously that another line at 465 cm^-1 is due to silicon as a result of observed isotopic splittings. Mass spectrographic and electrical measurements made on some of the samples examined has allowed estimates to be made of the apparent charges associated with the various impurities.

The authors have investigated the vibronic spectrum associated with the ²E to ⁴A₂ transition of YAG:Cr³⁺ in the temperature region 10-300 K. At low temperatures vibrational satellites corresponding to spontaneous phonon emission are observed only on the low energy side of the nophonon R lines which are located at 6863.2 and 6872.6 AA. At higher temperatures, vibronic emission appears also on the high energy side, corresponding to phonon absorption. With increasing temperature, the vibronic bands become more intense relative to the R lines, the peaks broaden, and a fluorescence continuum extends from 6500 to 8000 AA. The fluorescence lifetime of the ²E level which is 8.5 ms at 77 K decreases rapidly above 150 K at 1.6 ms at 300 K. The enhancement of the transition probability of the vibronic emission can account for the major temperature dependence of the fluorescence lifetime without requiring the contribution of purely nonradiative transitions. For this case a calculation of the purely radiative lifetimes can be made. The values are found to be tau _rad(R₁) approximately 0.07 s and tau _rad(R₂) approximately 0.09 s.

The 100 degrees C thermoluminescence (TL) sensitivity of fired quartz is increased greatly by beta irradiation and subsequent heating (eg by an order of magnitude following a 1 krad dose and heating to 500 degrees C). Its radioluminescence response increases similarly, implying that the increase of TL sensitivity arises from an increased probability of photon emission per thermally released charge. This implication is confirmed by the decrease of thermally stimulated exoelectron emission (TSEE) sensitivity which accompanies the increase of the TL sensitivity. Furthermore, the decrease of TSEE sensitivity shows that the increased TL sensitivity arises from an intrinsic change in the luminescence centres themselves, rather than from some cause external to the luminescence centres. The increase of TL sensitivity is reduced by uv irradiation, and restored by subsequent heating to 500 degrees C. These results indicate that the increase of TL sensitivity results primarily from an increase in the number of activated luminescence centres participating in TL emission, the centres being activated by charge capture.

Thermoluminescence (TL) and optical absorption measurements on LiF(TLD-100) show that the radiation- induced increase of TL sensitivity of this phosphor occurs in the luminescence process. New data are presented on thermally stimulated exoelectron emission (TSEE), photoluminescence (PL) and radioluminescence (RL). The TSEE results confirm that some of the TL traps in LiF(TLD-100) capture electrons. The PL behaviour suggests that the increased TL sensitivity does not arise from an increase in the number of luminescence centres which participate in the TL process, and that the most likely cause of the increased TL sensitivity is the removal of competitors with the luminescence centres. The RL data indicate that the TL traps are localized near the luminescence centres, especially those centres from which there is increased photon emission.

The epr spectrum of Mn²⁺ has been studied in single crystals of BaO at X and Q band frequencies. This spectrum is distinctly different from the spectra of Mn²⁺ in other alkaline earth oxides. In BaO the Mn²⁺ ion occupies a site with a (111) axis of symmetry, the spectrum fitting the spin Hamiltonian H_s= beta B.g.S+SDS+IAS with g/sub ///=2.0017, g_{perpendicular to} =2.0013, D=0,0778 cm^-1, E<0.005 cm^-1, A/sub ///=67.5*10^-4 cm^-1 and A_{perpendicular to} =68.5*10^-4 cm^-1.

The angular dependence of the spin-lattice relaxation time for the 1-3 low field transition of Fe³⁺ in a crystal of corundum doped with iron is investigated at 9.3, 9.4 and 9.5 GHz at 4.2 K. A minimum in T₁ is always observed when the frequencies of Fe³⁺ and Fe²⁺ are equal.

An analysis of the optical and magnetic properties of the (V(urea)₆)³⁺ ion is given on the basis of the ligand field model. The hexaurea vanadium ion occupies a D₃ site in the compound (V(urea)₆)ClO₄)₃, and the threefold axis coincides with the axis of the crystal. The trigonal crystal field and spin-orbit interaction matrices, calculated using the 'strong field' wavefunctions, were diagonalized simultaneously with the corresponding matrices of the electrostatic and octahedral crystal field. The energy levels calculated in this way were fitted with the absorption spectrum and the strengths of various interactions were determined. The effective Hamiltonian for the ground (octahedral) term t₂²³T₁ was used to obtain an analytical expression for the magnetic susceptibility. The theoretical values of the magnetic susceptibility were compared with the experimental values in the temperature range 80-300 K. Since the trigonal crystal field parameters and the spin-orbit interaction parameter appear in the expression for the magnetic susceptibility and they also affect the energy levels, their values were obtained by fitting the theoretical results simultaneously to the optical and magnetic data available.

The tensor formalism developed by Johnston (1969) for the elastic scattering of neutrons by magnetic salts is extended to several unfilled shells configurations. The case of two shells is investigated completely. Some examples of the crystals having this configuration are presented and a simple example of the U⁴⁺ ion is worked out. Finally, the method for the generalization of the theory to a configuration of N shells is given.

Detailed Zeeman studies of nuclear quadrupole resonance of the ³⁵Cl nucleus in a single crystal of 3,4-dichloronitrobenzene have been made. Two resonance frequencies corresponding to the two positions were observed. The crystal class was identified to be tetragonal. From the Zeeman analysis the field gradient directions, minimum number of molecules per unit cell, asymmetry parameter and hence C-Cl bond characters were determined. The equations for molecular planes were also derived using least squares analysis.