Table of contents

Observations are reported of the total intensity of light scattered by liquid ⁴He along isobars close to the lambda line. As expected, a peak in the intensity has been observed, and the shape of this peak is compared with that of the peak known to exist in the isothermal compressibility.

The energies of bound surface states both for atomic hydrogen and atomic deuterium on a (001) plane of LiF are determined by atomic scattering. Both level schemes are reproduced by only one Morse potential well. From this and other data an empirical rule relating the depth of the potential of an arbitrary gas on (001) LiF to the polarizability of the neutral gas atoms is established.

Using the surface Green function method for the same simplified model already described for Si (see Surface Sci., Vol.29, 540, 1972) the authors have been able to give a density of surface states for the (111) surface orientation of Ge, whose main features are in fair agreement with experimental results.

The s-d exchange interaction produces an anomalous renormalization of the conduction electron spectrum near the Fermi level. This leads to a resistivity formula which behaves like 1- alpha T² at T approximately=0.

In relation to previous work on T_c behaviour at high pressures (Jerome, 1971), the authors show that the anisotropy in resistivity of NbSe₂ decreases with pressure, reaching a value of about five at 45 kb. A crystallographic phase change occurs at a pressure of 33+or-3 kb.

The behaviour of magnetic excitons as a function of temperature is studied in cubic systems which have a ferromagnetic phase transition due to the exchange coupling between a singlet ground state and a triply degenerate excited state. The nature of the soft mode is discussed and found to be a zero-frequency electronic mode. It is shown that the singlet-triplet excitons do not exhibit full soft mode behaviour at T_c, and that the theory accounts qualitatively for the measurements of Birgeneau et al (1971) on Pr₃Tl and FCC Pr.

Effective pair potentials for liquid Na and liquid K have been calculated by combining previous X-ray structure data with the Born-Green, Percus- Yevick and hypernetted chain integral equations. It is concluded that reliable ion-ion potentials, in good overall agreement with recent pseudopotential calculations, can be obtained from the hypernetted chain equation. Contrary to earlier suggestions, the Born-Green theory does not appear to be applicable to liquid metals.

The longitudinal relaxation rate of the ¹¹⁵In nuclear spin in liquid In-Bi, Pb and Tl alloys is measured. The relaxation rate depends on both temperature and composition, and varies from 5200 s^-1 for pure liquid In to 6300 s^-1 for a 50 at% In-Bi alloy at 430K. The observations of Warren and Clark (1969) on In metal are used as a starting point from which deductions concerning the various contributions to the relaxation are made. It is found that the dependence on temperature may be accounted for by the presence of a contribution from the interaction of the nuclear quadrupole moments with the local electric field gradients which are themselves random functions of time due to the ionic motion. This contribution is found to be smaller than current theories predict, but the experimental observations are shown to support the proposal of the authors that there is a strong cancellation between the two and three atom contributions to the motion dependent quadrupolar relaxation rate in liquid metals.

Ultrahigh vacuum techniques have been used to measure the equilibrium pressure of hydrogen dissolved in niobium in dilute solutions over the pressure, concentration and temperature ranges, p_e=10^-7-10^-2 Torr, H/Nb=0-0.035, and T=351-487 K. Sievert's law which indicates ideal solution behaviour was observed for hydrogen concentrations below about H/Nb=0.023; the solubility data are described by the expression square root p_e=c(395.4+or-33.8)exp(-(4.345+or-0.161)*10³/T) where c=H/Nb*100. The standard partial molar entropy and enthalpy of solution are Delta s⁰=49.6+or-2.3 J K^-1 g-atom^-1 and Delta h⁰=-36.12+or-1.34 kJ g-atom^-1. The value of Delta s⁰ is compared with theoretical entropies calculated from configurational and vibrational contributions. The rate of evolution of hydrogen from a niobium filament has been studied over the pressure and temperature ranges 10^-7-10^-3 Torr and 465-553 K. The rate limiting process is identified as the recombination of hydrogen atoms on the metal surface rather than diffusion within the bulk provided the overall concentration is less than H/Nb approximately=0.02. The activation energy for the process is 67.56+or-1.26 kJ mol^-1.

Ultrahigh vacuum techniques have been used to investigate the equilibrium pressure-composition-temperature relationships of hydrogen-niobium solutions up to gas concentrations of H/Nb=0.5, and from these relationships the variations of the thermodynamic properties of the solution with composition have been determined. The variation of the entropy of solution indicates that gas concentrations in interstitial solutions of this type are limited to low nonstoichiometric ratios by the blocking of interstitial sites by neighbouring solute atoms rather than by any nonequivalence of the sites themselves. The measurements were made in the ranges: pressure p=10^-6-1 Torr, concentration H/Nb=0.017-0.502, temperature T=295-523 K.

Simple formulae, based on the rigid-ion model of lattice dynamical theory, have been obtained for mean square vibrational amplitudes in compound crystals in terms of the elastic constants and infrared or Raman frequencies. Results are obtained for cubic CaF₂, InP, ZnS, hexagonal ZnS, BeO and tetragonal BaTiO₃ for comparison with experiment and lattice dynamics calculations. The equivalent calculation based on the Debye approximation is found to contain two errors, each of about 25% even at low temperatures.

The phase transition in pure VO₂ is ascribed to softening, in the high temperature semimetallic phase, of an optical phonon at the R point of the Brillouin zone. This softening arises from an electron-phonon interaction the strength of which is a manifestation of the tightly bound character of the d electrons. The insulating nature of the low temperature phase is considered to be due to band splitting and uncrossing produced by the crystalline distortion. This change in the bands is the static, large amplitude, limit of the electron-phonon interaction responsible for the phonon entropy of the semimetal. Detailed numerical calculations are made for one dimensional chains along the c axis. Good quantitative agreement is obtained with known experimental data.

The dielectric response function is calculated exactly for transitions between a deep flat valence band and a conduction band with Lorentzian distribution of site levels (Lloyd's model). Site energies fluctuate independently of one another whereas the difference between the excited and the ground levels of each site is kept constant. Numerical examples are presented for three model densities of states. The effect of the fluctuations is to smear the edges and introduce small tails if the disorder is small. The absorption tail is much weaker than would be suggested by the tails in the densities of states. Large fluctuations of site energy levels reduce the density of states in the middle of the bands thus increasing the lifetime of the Wannier states, as a result the absorption band becomes narrower with increasing disorder.

The lowest order anharmonic contributions to the one-phonon Green functions for long wavelength phonons, and to the dielectric properties, have been calculated for sodium chloride. A breathing shell model was used to provide frequencies and eigenvectors. Coulomb contributions to the anharmonic matrix elements were included, and the volume dependence of all contributions was treated exactly. The phonon shifts and the static dielectric constant are in good agreement with experiment up to about three quarters of the melting temperature. The lowest order contribution to the width is about two thirds of the experimental value and, when the volume dependence is properly incorporated, varies with temperature as T^1.6 in good agreement with experiment.

The author obtains explicit formulae for the admixtures of the J=1 level of Sm²⁺ (4f)⁶⁷F into the J=0 level by exchange coupling to an adjacent Eu²⁺ (4f)⁷⁸S ion. The problem is formulated using states which are antisymmetric with respect to interchanges of electrons. An unperturbed Hamiltonian is defined which is symmetric with respect to interchanges, and the difference between it and the full Hamiltonian is treated by perturbation theory, taken to second order. It is found that the dominant processes are those in which, in the intermediate states, either two electrons, one from each 4f shell, have been excited into unoccupied orbitals, or two electrons from closed shells have been excited into the 4f shells, one electron to each rare earth ion. By the use of equivalent operator techniques, it is shown that the admixtures can be derived from an equivalent anisotropic exchange interaction, with the important feature that the spin operators which appear are defined in second quantized forms and are not identical with the commonly used spin operators. It is suggested that in phenomenological exchange spin Hamiltonians these new definitions should be used.

For Pt. I see abstr. A31606 of 1971. The author derives formal bounds for the critical concentration in a random system with interaction range r. A conjecture is made concerning the behaviour of a set of parameters associated with lower bound. A numerical lower bound resulting from this conjecture is then compared with the numerical estimates of Dalton et al. (1964).

The singularity of the static correlation function at the critical temperature in a ferromagnetic system is analysed by means of a set of coupled nonlinear integral equations which are obtained from the density field formalism of Sherrington (1966) and its extension to general order by Bhagavan and Lambert (1969). With the assumption of the onset of a phase transition, these equations yield a singular correlation function. Its singularity, which is determined in a selfconsistent way, shows a logarithmic deviation from the Ornstein-Zernike results. The singularity obtained is therefore fundamentally different from that given by the Orstein-Zernike theory.

A detailed investigation is undertaken of the relationship between the parameters characterizing the geometrical properties of self avoiding walks (Saw approximation) and those describing the critical behaviour of the Ising and classical vector models. There are strong indications that the statistical distribution of contacts is the same for chains and polygons, and this gives rise to the identity of critical temperature for specific heat and susceptibility. It is suggested that a particular set of configurations consisting of bridges across chains and polygons are sufficient to account for the critical exponents. Following a previous paper by Domb and Joyce (1972) on interactions in random walks a distinction is drawn between ladder and nonladder configurations. The difference in critical exponents for the different models is due to the difference in weighting of ladder and nonladder configurations. The same analysis applied to a dilute magnet leads to the conclusion that the critical exponents of specific heat and susceptibility are identical with those of an undiluted magnet. A series expansion is obtained for the Curie temperature of all the above models in terms of the statistics of contacts of various types in a self avoiding walk.

A simplified procedure is developed for calculating the weights of configurations which enter the high temperature expansions for the Ising and classical vector models. For ladder structures the weights can be derived from the partition function of a simple polygon by replacing a single interaction by a pair of parallel interactions successively along suitably chosen lengths of bonds. For nonladder structures a number of relations can be obtained by allowing chosen interactions to become infinite so that the nodes which they connect coalesce. The method can be used in d dimensions and results check with the calculations of Joyce (1967) for d=3 in terms of 3-j and 6-j symbols.

Using extended high-field series expansions and more precise estimates of the critical temperature the critical isotherm of the spin ¹/₂ Ising ferromagnet is re-analysed. The conjectures delta =15 (d=2) and delta =5 (d=3) are confirmed to within ¹/₂% and 1%, respectively. Good agreement is found, particularly in two dimensions, between series estimates of the critical amplitudes and the predictions of the lattice-lattice scaling hypothesis. Some tentative conclusions regarding the coincident and nonphysical singularities are drawn.

A simple theory for treating the magnon induced sidebands in optical transitions involving change of spin, taking place in antiferromagnetically ordered solids, is presented. The magnon excitation is considered as being caused by the 'hole' which is created in the spin system as a result of the transition. A formula is derived for lineshapes at 0K. A model calculation, along with a few computed lineshapes are also presented.

A theory is presented for two-magnon Raman scattering in a Heisenberg antiferromagnet at temperatures below T_N. The treatment makes use of a field theoretical perturbation expansion and a classification of terms with respect to a high-density parameter 1/z. The effects of magnon- magnon interactions are included by evaluating all contributions up to order (1/z)². In the zero temperature limit the results are very similar to those obtained by Elliott and Thorpe (1969) using a Green function equation of motion method. The calculations are applied to the antiferromagnets RbMnF₃ and NiO at various temperatures and a comparison is made with experimental work. The agreement is fairly good, particularly for the frequency and temperature variation of the Raman peak. However, the predicted resonance widths at elevated temperatures are found to be smaller than observed experimentally and the possibility of obtaining better agreement by inducing higher order effects in the theory is considered.

It is suggested that a broad absorption band which occurs in additively coloured CaF₂ at 521 nm and in additively coloured SrF₂ at 595 nm is a superposition of absorptions from two types of F₂ centre, one oriented along (100) and the other along (110). Broad emission bands of the two types of centre are also superimposed, peaking in CaF₂ at 585 nm and in SrF₂ at 644 nm. Under high resolution a zero phonon line of the (110) oriented F₂ centre is observed at 20K in both emission and absorption bands; it occurs in CaF₂ at 539.6 nm and in SrF₂ at 605.3 nm, The excitation spectra for both the zero phonon line emission and the broad band emission have been investigated and their polarization properties established. Both the zero phonon line and the broad absorption band may be made dichroic by bleaching with linearly polarized light at 77K; this treatment produces preferential alignment of the centres. The destruction of the dichroism by thermally induced disorientation has been studied. Optical pumping gives rise to a reduction of intensity of absorption of F₂ centres due to population of metastable excited states; the lifetimes of these states have been measured. Uniaxial stress measurements on the zero phonon lines show that the centres involved have orthorhombic I symmetry and that the dipole moment of the transition is along (100). The zero phonon lines also show a large linear Stark effect. From the combined stress and Stark measurement it follows that the point symmetry of the centres giving rise to the zero phonon lines is C_2v.

A number of prominent zero-phonon lines have been investigated in additively coloured CaF₂ and SrF₂ using uniaxial stress. Stark effect and magneto-optical techniques. It is tentatively suggested that a line at 598.8 nm in CaF₂ may be a transition of a square planar F₄ complex. There is a corresponding centre in SrF₂. Other lines investigated appear to be associated with impurities. A line at 553.7 nm in CaF₂ is a transition of a centre with cubic symmetry; a corresponding centre occurs in SrF₂. A line at 742.6 nm in CaF₂ also arises from a centre with cubic symmetry. A transition at 833.8 nm in CaF₂ is associated with a centre with C_2v symmetry. An E to A type transition in a centre with tetragonal symmetry occurs in CaF₂ at 524.7 nm A line at 591.0 nm in CaF₂ is an A-A type transition in a centre with trigonal symmetry. No lines have been found in SrF₂ corresponding to the 742.6, 833.8, 524.7 and 591.0 nm lines in CaF₂. Vibronic structure associated with the zero- phonon lines is described and problems of distinguishing between intrinsic F-aggregate centres and impurity associated centres are mentioned.

The low temperature Jahn-Teller induced phase transitions in TmAsO₄ at 6.0K and in TmVO₄ at 2.1.K have been investigated by means of Raman scattering. Phonon and electronic excitations have been observed in magnetic fields of up to 50kG. The results show that the Jahn-Teller distortion may be removed by application of a magnetic field and that the coupling of the Tm³⁺ ions to acoustic phonons is stronger than to optic phonons. The implications of this coupling are discussed.

The IR spectra of solution grown crystals of NaCl and KCl doped with Co(CN)₆^3- show a multiplet in the v₆ stretch frequency region of CN^-. Apparently the multiplet consists of four components in NaCl and three in KCl. However, a detailed examination of the results shows that the multiplet consists of several components due to different site symmetries in which Co(CN)₆^3- is present in the crystal. The most probable symmetries are D_2h and C₈. On x irradiation the multiplet characteristic of Co(CN)₆^3- appear on the low energy side. On heating the crystals, irreversible changes in the spectra occur. The spectra consist of many lines but only the line corresponding to NCO^- could be identified. The electronic spectra of the impurity show seven bands in the wavelength region 600 nm to 200 nm as compared with only three bands observed in the solution in this region. The bands are interpreted as being due to transitions of the split components of crystal field levels in O_h symmetry. Both peak positions and intensities are consistent with the assignment.

The stimulated emission cross section for Nd³⁺ in two sites within the lattice of single crystal CaO.2Al₂O₃ has been calculated from both fluorescent lifetime measurements and branching ratios and from absorption cross section studies. A comparison is made with values for other laser hosts.

Observation of the changes produced in donor-acceptor pair cathodiluminescence emission intensities of as-grown, cadmium fired and sulphur fired cadmium sulphide samples by electron radiation damage allows an estimate to be made of the initial donor concentration present and of the fraction of pairs excited. This analysis also shows that an increase in the donor or acceptor concentration need not necessarily result in an enhancement of the donor-acceptor pair luminescence emission intensity and, under certain circumstances, could lead to a reduction in emission intensity. The observations presented provide confirmation of the effect.

Measurements have been made of the lifetimes of the fast recombination luminescence transitions in alkali halides. The luminescence was excited by 2 MeV proton pulses about 2 ns wide and the lifetimes measured by the technique of single photon counting. All alkali halides in which fast luminescence occurs have been studied at 5K and 77K. The lifetimes of the major components lie in the range 1-4 ns, and in many cases a second component with a lifetime of about 10-20 ns is evident. The temperature dependence of luminescence in NaCl, KBr and KI has been measured and is compared with the behaviour of the slow luminescence in these crystals. A new model for the electronic structure of the excited states involved in recombination luminescence is proposed and compared with the model based on the inert gas molecule.