Table of contents

The general distinction between optical absorption and photoemission experiments is elucidated. These are seen to be of considerable use when applied to studies of two or more occupied bands. Specific results are provided for two crystals, LiF and KF.

A calculation of the electron ground state associated with N in InGaP was performed, with a view to examining the validity of the impurity potential. It was found that the variation of the ground-state energy with composition was adequately described by a model using a screened ionic pseudopotential for the impurity and host. The effect of lattice distortion was also considered, and found to be small, but favourable as far as agreement with experiment was concerned.

The critical properties of d dimensional systems with a quadratic anisotropic term in the Hamiltonian are investigated with the aid of a renormalization group analysis based upon the Wilson perturbation expansion in epsilon =4-d. For anisotropic cubic systems with a nonzero four-spin coupling constant, u, it is found that the asymptotic critical behaviour is always one with vanishing quadratic anisotropy. In systems with lattice anisotropy a simple renormalization group argument leads to results in agreement with the universality hypothesis.

A generalization of Wilson's renormalization group equation is discussed. A large class of equivalent fixed points exists for each fixed point. The eigen perturbations fall into two classes: (i) scaling operators whose scaling exponents are independent of the fixed point within the class of equivalent fixed points, and (ii) redundant operators whose exponents depend on the choice of the renormalization group equation. The exponents of the redundant operators are spurious since the free energy depends only on the scaling fields of the scaling operators but not on the scaling fields of the redundant operators.

The elimination of the elastic degrees of freedom of a harmonic isotropic lattice transforms the magnetoelastic coupling into an effective magnetic interaction which consists of a short-range interaction recently discussed by Aharony and a long-range interaction due to the free surface of the systems. Within the renormalization group approach to critical phenomena it is shown that the critical behaviour of the system is described appropriately by the magnetothermomechanics provided that the additional short-range interaction does not change the critical behaviour.

For the hydrogen in palladium (PdH) system, the critical point has been located at T_c=566+or-1K, rho _c=0.29+or-0.01 atomic H/Pd ratio, P_c=19.89+or-0.05 atm (hydrogen pressure surrounding the palladium). Critical-point exponents delta , gamma and Delta have been determined for the critical isotherm, the isothermal compressibility of the hydrogen lattice gas (this being proportional to the relaxation strength of the elastic after-effect for the interstitial hydrogen in the palladium) and the relaxation time of the elastic after-effect, respectively. The experimental values of these exponents ( delta =3.2+or-0.3, gamma =1.01+or-0.01, Delta =1.01+or-0.1) and information from the specific heat measurements indicate that the critical-point behaviour of the PdH system is described by mean-field theory at least for epsilon =(T-T_c)/T_c approximately=10^-3. This behaviour is compatible with the interaction between the interstitial hydrogens being a long-range elastic type between lattice defects in the palladium.

For pt. I see ibid., vol.7, no.12, 2126 (1974). A temperature wave method has been used to measure the specific heat of the PdH system through the critical-point region. The specific heat at constant hydrogen concentration displays a simple discontinuity at the critical point, corresponding to the critical-point exponent, alpha , being equal to zero. In combination with other critical-point exponent data obtained from PdH this result leads to the conclusion that mean-field theory describes the critical-point behaviour of PdH.

The lattice parameters have been determined as a function of temperature for single crystals of the ferroelectric PbZr_0.9Ti_0.1O₃. By associating the difference in rhombohedral angle with the square of the order parameter, P_s, the critical index beta has been determined for the ferroelectric to paraelectric phase transition. This transition appears to be of second order with beta approximately=0.33 for (T₀-T)/T₀<or=0.06. This difference from the mean-field value ( beta =0.5) suggests the presence of critical fluctuations in the order parameter. Outside the critical region the order parameter deviates even further from mean-field behaviour. This is explained in terms of further fluctuations associated with a transition at a lower temperature.

Shows that, in general, the weak attractive tail in the interaction potential between an incident atom and a surface does not alter the qualitative results derived from the earlier model. In the particular case of a slowly moving incident atom which interacts strongly with the surface some account must be taken of the long-range part of the potential. It is also shown that correcting an error in the earlier analysis modifies the diagrams used with only a small change in the conclusions drawn.

A new technique for evaluating configurationally averaged properties of disordered systems due to Mookerjee (see abstr. A43969 of 1973) is examined. Attention is focused on the site-diagonal element of the single-particle Green function in the Anderson model of cellular disorder, and single-site coherent potential approximation (CPA) is shown to arise naturally within this new formalism. Generalizations to n site and cluster approximations then follow in a very direct and instructive fashion. Necessary analytic properties of the single-particle Green functions are an immediate corollary of the method. Numerical results are presented for the bimodally disordered tight-binding linear chain.

Positron lifetimes have been studied in CaO.P₂O₅ glasses doped with various transition-metal ions (Ti, V, Cr, Mn, Fe, Co, Ni, Cu and Ce). Present measurements show that all the transition-metal ions, except cerium, decrease I₂ while the change in tau ₂ is within experimental error. This is suggested to be due to 'spin-conversion' by which part of the o-Ps, by reacting with the transition-metal ion impurities in glass, are converted into p-Ps; the extent of conversion depends on the nature and the concentration of the impurity ions. Of all the transition-metal ions studied, vanadium(IV) is most effective and cerium(III) and cerium(IV) are least effective in quenching o-Ps; these have been explained as due to the unique nature of the vanadyl (VO²⁺) group and the shielded 4d electron of cerium respectively.

Numerical calculations of the small-signal characteristics of GaAs, InP, and n-type Ge have been carried out essentially by the method of Rees (1969). For GaAs and InP especially the imaginary part, that is the free-carrier contribution to the dielectric constant, is shown to depend strongly on the intervalley coupling strength. For Ge, good agreement with experiments is found at room temperature. At 77K the agreement is only semiquantitative.

The solutions for the model parameters appropriate to the bismuth Fermi surface have been obtained from the intermediate field (B=0.576T) polar magnetoresistivity measurements of Mase et al. at 20.4K (1962). The measured values for four different tensor components have been fitted to expressions recently derived for the magnetoconductivity in the classical range of magnetic fields. The results show that the theoretical expressions can correctly predict the magnitude and orientation dependence of the magnetoresistivity. The values obtained for the electron and hole mobility tensor components, the carrier density and the tilt angle of the valence-band Fermi ellipsoids are in good agreement with those calculated from the low-field magnetoresistivity measurements. The mobility components at 20.4K confirm the T^-2 variation above 8K obtained previously and hence provide further evidence that the scattering at these temperatures is between electrons in separate valleys.

The effect of the Cohen nonellipsoidal nonparabolic (NENP) band structure on the propagation of ultrasound in bismuth in the presence of a d.c. magnetic field is investigated by using a quantum-mechanical treatment which is valid at high frequencies and in strong magnetic fields. It is found that the absorption coefficient and sound velocity for ultrasound propagating parallel to the d.c. magnetic field depend upon the magnetic field and sound frequency. The dependence on magnetic field arises from the nonlinear effect of the energy bands owing to the NENP model for bismuth, while the dependence on sound frequency is due to the electron-phonon interaction in bismuth. Some oscillations and discontinuities in the absorption coefficient and change in the sound velocity appear in the region of strong magnetic fields and high frequencies. However, the oscillations will be diminished at sound frequencies above omega =2*10¹¹ rad s^-1. A brief discussion about the spin-splitting effect in bismuth is made. It shows that the spin-splitting energy cannot be neglected in the region of strong magnetic fields.

Using the method of Green functions, surface effects in a dense electron gas with fixed positive background are considered. The one-particle Green function of noninteracting electrons in an effective potential is represented in a form similar to the well known WKB approximation for the wavefunction. Friedel oscillations are shown to arise from discontinuities in the density of the positive background. An asymptotic expansion for the difference between the chemical potential and the effective potential is calculated yielding a value of about 1.2 eV for the work function of a dense electron gas.

Far infrared measurements on MgO doped with chromium and iron show the presence of lines at 12.5 and 15.3 cm^-1 attributable to Cr²⁺ ions. The Cr²⁺ ion concentration was monitored by measuring the low-temperature thermal conductivity and an improved estimate of the scattering cross section of Cr²⁺ ions to phonons is obtained.

The radiative efficiency of YAG:Cr³⁺ is known to increase rapidly with increasing temperature. This increase is larger than that expected purely on the basis of the increase with temperature of the R line sidebands. It is shown that this increase in radiative efficiency is mainly due to luminescence from the ⁴T₂ state which is about 1000 cm^-1 above ²E and which becomes populated during optical pumping at higher temperatures.