Table of contents

The melting behaviour for finite size clusters is calculated in the framework of positional disorder theory. It is shown that the 'melting anomalies' observed in a variety of absorbate systems, such as H₂O in porous Al₂O and N₂ or Ar on TiO₂, are consistent with the melting characteristics of small clusters. In particular, the specific heat of small clusters exhibits a broadened peak centred at temperatures below the bulk melting point T_m. As the cluster size increases, the peak tends to sharpen and shift closer to T_m. Furthermore, the theory predicts a characteristic size for the onset of bulk first-order melting transition behaviour.

Four distinct peaks are observed at 140, -26, -132 and -140 degrees C in the sigma _x* against T^-1 plot between 200 and -196 degrees C for (NH₄)₃H(SO₄)₂, corresponding to four different phase transitions of which the one at -26 degrees C is reported here for the first time. Data on doped samples reveal the charge transport mechanism in the crystal.

Studies of magnetic viscosity in (Fe_0.68Mn_0.32)₇₅P₁₆B₆Al₃ are presented. The magnetisation in a constant field H is described by M=M₁+S ln t. The coefficient S(T) peaks at T_m(H). The authors show that s and the susceptibility chi scale similarly and deduce the ferromagnetic/spin glass transition temperature T_fg approximately=35K, in agreement with their previous results.

CdS has been known to exist in both a hexagonal (wurtzite) and cubic (zincblende) phase. In both cases the electronic structure has been reasonably well defined. Recently, by means of pressurisation and quenching, a metastable cubic (sodium chloride) phase has been shown to exist as well as 77K and standard pressure. In addition, several groups have reported both diamagnetic and paramagnetic anomalies in CdS. It seems reasonable to assign these anomalies partly to extrinsic influences. Nonetheless, recent evidence indicates the NaCl phase of CdS is host to the diamagnetic anomaly. In this letter, the authors present band structure results for both cubic phases of CdS.

A numerical calculation is made of the critical percolation probability p_c on a branching network in which the number of bonds emanating from a site decreases by unity for each step away from the origin. When the coordination number N of the origin is large the authors find that Np_c=1.5. This result is at variance with the value of e suggested by a recent study of hopping conductivity in which the above lattice structure is assumed.

The Kadanoff-Migdal treatment of the dilute q state Potts model is shown to yield a zero temperature crossover exponent phi =1 for all q and d (lattice dimensionality) in agreement with a recently proposed exact result.

The Ising spin gauge theory along its line of vanishing unit Wilson loop has been proposed as a model for spin glasses. The authors have performed Monte Carlo simulations to determine the phase diagram of this theory in six dimensions, the upper marginal dimensionality attributed to true spin glasses. As in three and four dimensions, the contour of vanishing Wilson loops does not meet a transition line for finite values of either the gauge or spin-spin coupling constant. It is concluded that either the gauge theory analogy is incorrect or the upper marginal dimension of spin glasses is not six.

The magnetic phase diagrams of the mixed metamagnets Fe_1-pMn_pCl₂ have been studied by magnetically induced light scattering, Faraday rotation and neutron diffraction. The Neel temperatures T_N(p) and temperature dependence of sublattice magnetisation were determined from the (1,0,1) magnetic reflection intensity. Tricritical temperatures T_t(p) and fields H_t(p) were found by tracing isotherms of the field-induced light scattering in the mixed-phase region. Magnetisation isotherms were plotted using Faraday rotation. T_t(p) tends to zero at p_c approximately=0.3, near the two-dimensional percolation limit for a triangular lattice while H_t(p) tends to about 0.7 H_t(0). A comparison is made with Fe_1-pM_pCl₂ (M=Mg, Co). T_n(p) falls with increasing p with a slope of -1.74.

The generalised phonon density of states G( omega ) has been determined by means of inelastic neutron scattering from powder samples of Bi₂Se₃, Bi₂Te₃, Sb₂Te₃ and the solid solutions Bi₂(Te_0.5Se_0.5)₃ and (Bi_0.5Sb_0.5)₂Te₃ at 77K. The purpose of this investigation is to obtain more insight into the lattice dynamics and the binding of these semiconducting layer compounds of the V₂VI₃ type. The experimental data obtained for the compounds investigated show that the most pronounced peak of G( omega ) at rather high frequencies shifts according to the square root of the mass ratio to higher frequencies if the group VI element Te is replaced by Se. This peak does not shift perceptibly if the group V element Bi is replaced by Sb. Thus the results indicate that the corresponding lattice modes consist predominantly of group VI element motion. At lower frequencies, the results show a considerable influence of the group V element on the generalised density of states.

The screening length xi and the singular part of the free energy of the two-dimensional Coulomb gas are calculated for small fugacity, y, in the vicinity of the transition temperature, T=¹/₄, from Kosterlitz's renormalisation-group equations. The results are expressed in terms of a single 'scaling function'. As special cases the authors recover known behaviour in (i) the critical region and (ii) the low-density, high-temperature limit where xi approximately A(T)y^{- nu} with nu =2T/(4T-1). They also obtain the new result that, as T to ¹/₄, A(T) has the singular form A(T) approximately (T-¹/₄)^v.

At low vacancy concentrations in crystals the motion of an atom due to the vacancy mechanism is a correlated walk during the sequence of atomic jumps arising from an encounter of a specific atom and a specific vacancy. It is shown that the diffusion correlation factor and the atomic displacement probability of the correlated walk of an atom in a cubic crystal may be simply obtained from some well known functions of random walk theory.

From the study of the temperature dependence of quadrupole coupling constants and linewidths a detailed insight into the diffusion of Li in Li₃N has been achieved. In accordance with the strong anisotropy of the ionic conductivity the authors found two vacancy-induced diffusion mechanisms for Li ions, one within the Li₂N layers and another one perpendicular to them. The second one involves both types of Li position. The jump frequency for the diffusion within the Li₂N layers increases strongly with the concentration of hydrogen in the samples.

The authors give a brief outline of a 'poor man's' scaling approach as applied to locally coupled electron-phonon systems. For these systems they show that the retardation of the effective interactions have to be taken into account. The approach is extended to the calculation of one-electron Green functions and applied to the spinless Anderson model coupled to phonons. A general expression is obtained for the renormalisation of the resonance width due to phonons. This gives the results of Hewson and Newns (1979, 1980) in the appropriate limits but is more general in being applicable to a continuum spectrum of local phonons and for all values of the coupling strength.

A discrete basis set consisting of occupied and excited states has been used in conjunction with many-body perturbation theory to calculate the crystal-field shielding parameters sigma _k(k=2,4,6) in Pr³⁺. The shielding-antishielding parameter sigma _k measures the modification due to core electrons in the crystal potential at the location of the 4f shell in the rare-earth ions. Obtained values of sigma ₂ and sigma ₄ correspond to shielding, while that of sigma ₆ corresponds to antishielding. Comparison with existing results is made. Contributions to sigma ₂ due to the electron-electron correlation effects are also calculated and found to be important (about 17% of the lowest-order contribution, but of opposite sign). Correlation contributions to other parameters reported in earlier work were found to be of similar magnitudes, but of varying signs.

Electronic structure of disordered two-band systems is investigated by both the direct diagonalisation and the real-space renormalisation method with an emphasis on the interplay of disordered bands connected by the inter-band mixing. The nature of the Anderson-localised states is clarified for the cases of a direct-gap intrinsic semiconductor and a hybridised s-d system. It is shown that, in the case of a semiconductor, there exists a significant correlation in the two-band components of localised states in the pseudo-gap region. In the case of the s-d model, the s band drastically affects the structure of d band, giving rise to eigenstates with characteristic hybridisation.

The authors study the time-dependent correlations of the free-ends isotropic XY model in a transverse field. The boundary effects on the longitudinal correlation, namely (S_j^z(t)S_l^z(0)), and bulk dynamic properties are considered at the temperature limits T= infinity and T=0- (for h>or= mod J mod ) where the results are known in closed form. The transverse correlation namely (S_j^x(t)S_l^x(0)) is calculated exactly at T=0 (for h>or= mod J mod ), and the boundary effects discussed. At T= infinity the known result for the bulk correlation is rederived by using a new combination of fermion operators.

The magneto-volume effects of ferromagnetic and antiferromagnetic metals are discussed by using the spin-fluctuation theory for finite-temperature magnetism developed by the present author with the use of the functional-integral method. The authors calculate the temperature-dependent magnetic pressure, from which the spontaneous volume magnetostriction is obtained, by taking account of the volume dependences of the electron-electron interaction and of the band structure. The theory is shown to yield an interpolating description covering the weak- and strong-coupling limits and to reduce to the Hartree-Fock theory at T=0K. Numerical calculations are performed for GCC Fe and FCC NiFe alloys. Attention is paid to the Invar alloy, whose anomaly is well accounted for by the present calculation.

Resonant (RCR) and non-resonant (NCR) cross-relaxation measurements are reported for ruby crystals containing Cr⁴⁺ as an additional impurity. From the RCR measurements, values for g/sub /// and the zero-field splitting D are found for the Cr⁴⁺ ion. D is also determined from NCR and is in agreement with that obtained using RCR. As the values of g/sub /// and D are both different from those deduced previously by high-field EPR, a detailed theoretical calculation of the effects of random strain is given. Differences between the values of D are satisfactorily explained.

An account is given of results obtained from thermally detected EPR experiments on doped rubies under conditions favourable for resonant cross-relaxation effects. From measurements of the signal intensity, known (Cr⁴⁺, Fe²⁺ and V³⁺) impurities and unknown impurities have been studied. The results obtained from Cr⁴⁺ are used to explain the apparent shift of the Cr⁴⁺ resonance observed in previous direct relaxation measurements. A comparison of these results with those from Fe²⁺ and V³⁺ show that the resonant cross-relaxation probability is dependent upon random internal strain. The use of the relaxation properties in this technique is also discussed as an aid in the identification of strongly coupled ions present in very low concentrations.

Scandium has been known as coactivator of the luminescence of the ZnS crystals but is role in the photoluminescence and the thermoluminescence processes has not been well understood. The authors have used the EPR of chromium, which can act as both an electron and hole trap, and also ODMR, to investigate these processes. In particular, the measurements of the change of the chromium Cr⁺ EPR signal intensity in thermal or light-induced processes enable them to determine the energy depths of the important centres in ZnS:Cr,Sc. The ODMR experiments correlated the luminescence transitions with specific defects such as Sc²⁺ donors and (V_Zn-Sc) A-centres.

The behaviour of Cu in ZnO contrasts strongly with that of Cu in other II-VI compound semiconductors. Internal relaxation between the crystal-field-split states of Cu²⁺, 3d⁹, is essentially non-radiative in ZnO. However, a strong near-infrared luminescence is consistently observed in Cu-doped ZnO, some 0.14 eV above that which would correspond to the absorption seen for Cu²⁺. The form of the excitation spectrum of the green luminescence associated with a charge transfer state contrasts strongly with that of the Cu near-infrared luminescence, and contains three no-phonon lines alpha , beta and gamma previously reported by Broser and co-workers (1978). Detailed magneto-optical properties of these lines are compared with this previous work and lead to the first satisfying attribution of them given in another paper (see ibid., vol.14, p.2859, 1981). Finally, it is noted that a 14.4 meV splitting in the infrared optical absorption probably does not arise from an unexpectedly small spin-orbit splitting in the ²T₂ ground state of Cu_Zn²⁺, but may be due to phonon coupling.

The first satisfactory assignment is given for the three closely spaced zero-phonon lines which appear near 2.86 eV in the absorption and photoluminescence excitation spectra of Cu-doped ZnO crystals. The zero-phonon lines, designed alpha , beta , gamma , represent charge-transfer type transitions in which a hole is excited from the Cu 3d shell to form a bound state with a neutral deep-acceptor-like configuration, i.e. Cu_zn²⁺(3d⁹) to (Cu_Zn¹⁺(3d¹⁰))h. The three transitions terminate on different excited hole states which derive from the special nature of thMe wurtzite valence band structure. A qualitative description of these excited hole wave-functions, consistent with the magneto-optical data, is obtained using a Wannier-function basis for the upper valence bands of ZnO and including a small admixture of Cu impurity 3d orbital character in the bound state. It is shown that the energies of the bound hole states in the excited configuration (Cu¹⁺)h are determined by the Wannier-function energies and by spin-orbit interaction with the heavy Cu impurity core, whereas the hole g-factors and the polarisations of the alpha , beta , gamma , lines reflect mainly the symmetry properties of the lattice Wannier functions.

A new approach is presented for a single-site theory of binary alloys with environmental disorder and arbitrary forms of off-diagonal disorder. The method involves rederiving the off-diagonal disorder theory of Blackman et al. (1971) using the cumulant diagram approach and extending it to include the fluctuations in the diagonal elements due solely to the atomic environments. The theory differs from that of Kaplan et al. (1980), but has correct limiting behaviour, including the independent band limit. Some numerical results are given. The technique also allows the inclusion of short-range order in the atomic distribution for arbitrary forms of off-diagonal disorder. As an example, the self-consistent quasi-crystalline approximation is applied to a phonon system.