Table of contents

Atomic vacancies and divacancies have been observed in computer-simulated liquid rubidium and the detailed size distribution of the holes has been measured by a computer technique. The results are compared with the predictions of the scaled particle and quasilattice theories of the liquid state. Good agreement is found between the calculated and observed self-diffusion coefficients using quasilattice theory.

The overlap integrals (2s mod 4f), (2p sigma mod 4f), and (2p pi mod 4f) have been calculated for the entire series of cubic lanthanide sesquioxides (C-Ln₂O₃) through analytical five-term (2s, 2p: O^2-) and four-term (4f:Ln³⁺) ground-state wavefunctions. The set of distances used for C₂ and C_3i cation sites is reported for the first time. It has been found that only pi -type electron delocalisation is feasible within the fragment Ln³⁺-O^2-; the respective overlap integrals vary from 0.12 to 0.03.

Thermally oxidised polyethylene is known to exhibit two low-temperature dielectric relaxations, each of which has been attributed to tunnelling transitions of dipolar groups containing hydrogen and oxygen. The authors examined these in the subkelvin range and deduced the following tunnel splittings: Vincett's relaxation with H in poly (C₂H₄), 7.8+or-0.8 mu eV; the same in poly (C₂D₄), 5.9+or-0.6 mu eV; Carson's relaxation with D in poly (C₂H₄), 3.4 mu eV (geometric mean). The latter implies an acoustic coupling constant of 35 meV. Moreover the time constant of Carson's relaxation is found to depend not only on the 'impurity' hydrogen isotope but also on the host hydrogen isotope. For different combinations of isotopes it obeys a multiplicative law. The results are related to the polaron-like 'dressing' of tunnelling impurities.

The authors have extended to lower temperatures and frequencies, a recent dielectric study of hydroxyl doped vitreous silica. At given frequency the dielectric constant has a minimum at a temperature proportional to f^1/3 while at given temperature the loss angle has a maximum proportional to T^0.28 at a frequency proportional to T³. The behaviour is attributed to a distribution of dipolar two-level systems having tunnel splittings comparable to the thermal energies kT of the experiments and relaxation rates comparable to the experimental frequencies.

A preliminary investigation is reported on the Raman spectra of hexammine cadmium (II) halides above and below their phase transition temperatures. The spectra indicate that both dynamic and static changes occur at the phase transitions. Critical effects of the light scattering intensity of internal modes involving NH₃ motion, which occur, provide direct evidence that ordering of the NH₃ groups begins at T_c is approached from above, and that these transitions are orientational in nature with an accompanying static distortion.

Magnetic anisotropy and the optical property have been examined in the temperature interval 77-300K in CoSiF₆.6D₂O. Results show a rise of 17K in the transition temperature in CoSiF₆.6D₂O with respect to CoSiF₆.6H₂O crystal.

The longitudinal magnetoconductivity of electrons in the presence of electron-hole droplets is calculated using the Born approximation. The magnetoconductivity has an oscillatory structure with period: Delta B^1/2= pi /_2a((m_ch(cross))/(2m_ze))^1/2 where m_c and m_z are the masses for cyclotron motion and for motion parallel to the magnetic field respectively. This analysis applied to recent experimental data on Ge at 2K gives a drop radius of 1.1 mu m.

For pt.I see Commun. Phys., vol.2, p.115 (1977). Presents numerical results for the ground-state properties of the simplest system showing the frustration effect, Ising spins on a square lattice with a variable concentration x of antiferromagnetic interactions. Ferromagnetism disappears at a concentration x_c approximately 0.09. The ground-state energy and degeneracy have markedly different behaviours below and above x_c. The authors compare the results with other calculations and stress the advantages of the frustration approach.

High-temperature series expansions for the nearest-neighbour Ising model of a spin glass are derived. The concentration dependence of the critical temperature is analysed by Pade methods, and no indication of a spin glass transition is observed. The analysis does not rule out cusplike behaviour.

Measurements of the 5-80 MHz dielectric response of KH₂PO₄ and CsH₂AsO₄ close to their transition temperature reveal a marked dielectric loss in the paraelectric phase of CsH₂AsO₄ and a pronounced Debye relaxation process in the ferroelectric phase of both materials.

The importance of phonon disorder on the angle resolved photoemission spectra of crystalline solids is estimated by employing a plane-wave final electron state. It is shown that while thermal disorder might not be important in the UPS regime, it nearly totally destroys k conservation in the XPS regime.

The author obtains low-density series expansions of the moments mu _n(p)(n=0,2,4) of the pair-connectedness for the acyclic directed square, triangular and honeycomb lattices. Lower bounds to the critical probability of each of the three lattices are also obtained.

A derivation of the Born-Green-Yvon (BGY) integral equation for two-dimensional systems is given. A form that is amenable to numerical solution for g(r) or inversion for phi (r) is obtained. To verify the result, the author shows that the integral equation for the case of rigid disks given before is derivable from the general expression. The two-dimensional forms of the Percus-Yevick (PY) and hypernetted chain (HNC) equations are also presented.

Cubic and quartic anharmonic contributions to the Helmholtz free energy of a diatomic crystal are derived as functions of temperature for a general force-constant model of the crystal. The corresponding cubic and quartic anharmonic contributions to the specific heat at constant volume for diamond, germanium, silicon, and grey-tin are evaluated in the high-temperature limit with central force interactions between the atoms up to second-nearest neighbours. The effect of thermal expansion of the lattice is taken into consideration. There is excellent agreement between the experimental and calculated values of anharmonic coefficient A, defined by C_v/3Nk=1+AT, for germanium and silicon. Values of A for diamond and grey-tin are predicted for which the experimental results are not available. It is concluded that the second-nearest neighbours' contribution is much smaller than that of the nearest neighbours in the calculations of anharmonic coefficients. A for diamond-structure crystals.

Some new experimental data (optical measurement and elastic constant determination) have shown discrepancies with model calculations, in LiH and LiD crystals. Using the classical shell model, the author has shown that second-neighbour H-H interactions are very important in this crystal. In order to correct the frequencies, particularly on the TO branches in the (1, 1, 1) direction, shell deformation effects have been introduced into the model and it has been shown that there exist no short-range forces able to improve the calculation. It is then necessary to introduce long-range three-body forces to explain all the dynamic properties of these two crystals.

The vibrational amplitude of the atoms in some simple alkali halide and metal crystals have been measured near their melting points by a Bragg diffraction technique. The results are found to be consistent with Lindemann's theory of vibrational melting.

Applying Landau's thermodynamical group theory, the permitted changes in the space structure of D₄ and C_4h class crystals, at the temperature of their structural second-order phase transition, are determined. Crystals with symmetry of all space groups of the classes D₄ and C_4h are considered except the C_4h⁶ group, the symmetry changes of which have been determined by Lyubarskii (1960). It is found that crystals of symmetry D₄ⁿ (n=1, 2, 3, 4, 5, 6, 7, 8, 9, 10) and C_4hⁿ (n=1, 2, 3, 4, 5), as the result of a structural second-order phase transition, can either undergo changes in symmetry within the tetragonal system (D₄ to D₄, C₄ and C_4h to C_4h, S₄, C₄) or change their symmetry from tetragonal to rhombic (D₄ to D₂, C₂ and C_4h to C_2h, C₂) or from tetragonal to triclinic (C_4h to C_i). The volume of the unit cell can remain unchanged, or can increase twice, three times or even eight times in the phase transition. The calculations do not take into account phenomena occurring in the critical region but deal only with the static properties of the crystals.

Raman scattering has been used to investigate the phonon spectrum of monoclinic K₃Fe(CN)₆ (KFC) and its isostructural analogue K₃Co(CN)₆ (KCoC), in the 12 to 295K temperature range, with the intention of understanding the nature of the (possibly) electronically induced phase transition at 130K, which occurs only in KFC. The quasi-soft mode behaviour of the energy and integrated intensity of the approximately 53 cm^-1 rotational phonon of largely B_g symmetry, suggests a re-orientational transition in both KFC and KCoC at about 120 and 60K respectively. In KFC, however, the anomalously temperature dependent intensity and linewidth associated with the Fe-CN asymmetric stretching and bending modes, which grow in intensity below 200K, are suggestive of a (possibly coupled) distortional process involving the Fe(CN)₆^3- octahedra. A Jahn-Teller mechanism which goes from a static to a dynamic regime in the characteristic time of the Raman experiment, at around 130K, has been tentatively invoked and shown to be essentially consistent with the Raman data and other known facts about the system. The Raman data clearly do not indicate a distortional process in KCoC, consistent with its quasi-molecular non-degenerate groundstate.

The effect of proton diffusion in transition metal hydrides on (i) the anisotropies of the nuclear spin relaxation times T₁, T₂, and T_{1 rho} in single crystals and (ii) on the width and shape of high-field T₁ and T_{1 rho} minima in powdered samples is investigated. To illustrate the basic ideas, the simplest case of unmagnetic FCC host metals (e.g., palladium), in which either tetrahedral or octahedral interstitial sites are assumed to be randomly occupied, is considered in detail. It is found that the anisotropies of T₁, T₂, and T_{1 rho} and of the dipolar local field in the rotating frame (the latter being proportional to the second moment of the absorption line) are extremely sensitive functions of the particular sublattice predominantly occupied by protons. It is shown that a vacancy mechanism (encountered perhaps for large proton concentrations) leads to narrower T₁ and T_{1 rho} minima than a random-walk mechanism of diffusion on the two sublattices considered.

Using optical and resistivity measurements the authors have investigated the metal-nonmetal transition for some metal-solid-noble-gas mixtures. They find evidence for heavy segregation in the samples giving a percolative character to the transition but the behaviour does not follow any existing percolation theory.

The EPR longitudinal and shear strain parameters for tetragonal Gd³⁺ in CaF₂ have been measured using the ultrasonic strain modulation technique (UMER). A comparison has been made with the results for the cubic Gd³⁺ site using the superposition model as a guide, but as the local elastic constants for the tetragonal defect are unknown, the conclusions are tentative.

Experimental results on InSb concerning the direct observation of the ionising transition from the donor ground level to the N=0 Landau level and concerning the first excited state transition are reported (T=4.2K). Results are obtained on samples doped in the melt as well as by nuclear transmutations (N₁=2*10¹⁴-5*10¹⁵ cm^-3). The observed shift of the energy of the ionising transition to higher values as the doping increases is explained on the basis of a level-broadening model (spatial fluctuations of the impurity potential); the energy of the first excited state transition remains unchanged with increasing doping as expected from the model. In the heavier doped samples (N₁ approximately 10¹⁵ cm^-3), the ionisation of the ground level can be observed at low enough magnetic fields where no magnetic freeze-out occurs. This shows that screening is not the predominant effect since in that case the energy of the ionising transition has to tend to zero.

The Anderson model of a magnetic impurity in a non-magnetic metallic host is investigated for cases in which the intra-atomic coulomb repulsion U is infinite. Using the (suitably defined) continuous group of renormalisation transformations the original Hamiltonian is transformed into a family of effective Hamiltonians by reducing the band edge cutoff D. Comparing problems which differ by an infinitesimal change in D leads directly to differential scaling equations for the energy of the localised level ( epsilon ) and the hybridisation interaction ( nu ₁). Extrapolating this trend beyond the limit where perturbation theory is expected to be reliable eventually leads to a ground manifold of base states in which the localised level is unoccupied and the impurity behaves as if it is non-magnetic giving rise to ordinary potential scattering. Similar scaling equations are derived for a periodic array of atoms with mixed valence, but there are extra terms in the effective Hamiltonian reflecting the interactions between localised electrons via conduction electrons.

For pt.I see ibid., vol.7, p.2023 (1974). Polycrystalline Tb_xS, Tb_xTe and Ho_xTe (0.85<or=x<or=1) with NaCl structure show antiferromagnetic FCC II order. The magnetic moments of Tb_xS and Ho_xTe are found to be oriented similarly to Tb_xSe, and equivalent monopnictides, and correspond to theoretical predictions based on exchange interactions and crystal-field effects. Corresponding to the orientation of the magnetic moments parallel to the direction (111), Tb_xS is trigonally distorted at 6K. The magnetic moments of Ho_xTe deviate 68 degrees from the (111) axis. In the case of Tb_xTe different angles of the magnetic moments (0 and 78 degrees ) with respect to the (111) direction were found for two investigated samples. Thus the magnetic order of rare earth monochalcogenides appears to be essentially modified by structure defects and non-stoichiometry.

The dynamics of a random ferromagnet with infinite-range exchange interactions and Gaussian distribution is studied. The Green function for the propagation of magnetic excitations is obtained in an exponential form which permits the use of techniques associated with problems involving random matrices. The magnetic properties of this system are obtained and compared with the ordered case.

The structural and magnetic properties of the system V_1-xAl_xO_2+or-y have been investigated by X-ray diffraction, NMR, magnetic susceptibility and EPR measurements. The existence of two insulating intermediate phases M₂ and T between the insulating M₁ and the metallic R is confirmed. The effect of oxygen non-stoichiometry is studied; it is shown that an excess of oxygen increases the stability of the M₂ phase. The susceptibility of the M₂ phase is that of a linear antiferromagnetic Heisenberg chain with J=-390K, due to the localised V⁴⁺ ions. The M₂ to T transition corresponds to the dimerisation of the chains. This article confirms the results obtained for the system V_1-xCr_xO₂ and their interpretation.

The dipolar-interaction induced crossover of a uniaxial ferromagnet (or ferroelectric) from Ising critical behaviour in the primary critical region to Gaussian critical behaviour in the secondary critical region is studied. The crossover scaling functions for the susceptibility and specific heat are calculated by renormalisation group methods at leading order in epsilon =4-d.

The dynamic spin Hamiltonian form for an Fe³⁺ ion in TiO₂ is given and its spin-lattice coefficients computed. On the basis of the change of resonance field with induced stress in an ESR experiment, the quadrupolar contributions SdS is found to exceed by two orders of magnitude the dipolar contribution beta HhS. A complete set of nine spin-lattice coefficients for SdS in orthorhombic symmetry is determined.

NMRON single-passage and full-modulation data for ⁵⁶Co, ⁵⁷Co and ⁶⁰Co in Fe are presented. The implications of these data are discussed in terms of the ensemble rotation concept. Using an analytical solution of the single passage problem for the pure magnetic interaction, the ensemble-rotation formalism is extended and compared with the predictions for an additional quadrupole-type mechanism. It is shown that the quadrupole-type mechanism may not account for the reduced full-modulation NMRON signal. Korringa constants for the Co isotopes are obtained using an ensemble rotation analysis of single passage data and these are compared.

A theory is presented for the temperature dependence of one-magnon light scattering in ferromagnets with single-ion anisotropy. A Green function method is employed, and the results obtained are applicable over a wide range of temperatures above and below T_c and they include both linear and quadratic magneto-optical coupling. The calculations are carried out for systems with spin S=1 and S=3/2. The theory is applied to obtain numerical results for FeCl₂ (in its ferromagnetic phase) and for CrBr₃.

Fine structure is reported in the luminescence spectrum associated with the two-phonon assisted decay of free excitons in intrinsic Si. The spectrum has been deconvoluted into eight components, and the major features can be identified with two-phonon processes in which a momentum-conserving phonon is emitted together with either a k=0 optical phonon O^Gamma or an intervalley scattering phonon connecting conduction band minima, but only by invoking 'forbidden' intervalley scattering phonons. It would appear that the complete insensitivity of the two-phonon luminescence to the symmetries of the phonons involved recently reported for Ge does not occur with Si, although there is some breakdown of the accepted symmetry selection rules.