Table of contents

The authors transform a two-dimensional model of Ising spins with pure three-spin interactions and a special magnetic field into a spin model which is equivalent to the Baxter model. This shows that the original model exhibits a phase transition which is induced by the field h and whose critical exponents depend continuously on the strength of h.

The authors have made calculations comparing the energy of various atomic and molecular halogen defects in NaCl. We have found that it is energetically possible for the H centres produced by irradiation to form a defect comprising a Cl₂ molecule in a divacancy if the adjacent ions are removed to a surface or dislocation. The observed perfect interstitial loops may thus form exothermically from H centres.

The authors have investigated the dielectric response of carriers in inversion layers in a MISFET. Particular attention has been paid to the Anderson-localized regime (where the carriers are localized by disorder) and the possible Wigner lattice. In the Anderson-localized regime, it is found that the long-wavelength dielectric function is given by a Thomas-Fermi function. The most interesting feature of the dielectric response of the two-dimensional Wigner lattice is that its static dielectric constant omega (Q to 0,0) to - infinity .

A one-dimensional gas of hard rods each having a spin mu =+or-1 with nearest neighbour interactions only is studied. Results are presented for the zero-temperature behaviour for a constant, linear and stepped nearest-neighbour potential, where in certain cases more than one singularity is possible. The extension of the singular behaviour to finite temperatures with the aid of a Kac potential is briefly discussed.

For pt.I see abstr. A36337 of 1973. The formation of cation and anion vacancies has been studied in high purity CaO and SrO powders after irradiation by 20 MeV protons. The rate of formation of cation vacancies fits a model of interstitial-vacancy recombination. Isochronal annealing curves show that the isolated vacancy concentration is enhanced by thermal treatment at temperatures just below those at which the isolated vacancy begins to disappear. This is interpreted in terms of the decomposition of a vacancy-vacancy or vacancy-impurity aggregate. At slightly higher temperatures (640K for CaO) the isolated vacancy is converted to the vacancy-hydroxyl ion complex and isothermal data indicates close to 100% conversion. At higher temperatures the vacancy-hydroxyl ion complex is destroyed. The probable mechanism of the first process is vacancy diffusion with an activation energy of 1.8 eV, to a hydroxyl ion where the vacancy is trapped and partial charge compensation occurs. At higher temperatures it seems likely that diffusion of interstitial cations to the vacancy occurs with an activation energy of 3.1 eV. The efficiency of vacancy production is an order of magnitude less than that predicted for primary displacements confirming the importance of recombination between vacancies and those interstitials formed within a critical volume around the vacancy.

The adiabatic elastic constants c₁₁, c₁₂ and c₄₄ of TlCl have been obtained from measurements of ultrasonic wave transit times through a specimen of TlCl over the range 150-300K. The isothermal elastic constants, the heat capacity at constant volume and the Gruneisen parameter have been calculated from the elastic constants and associated data. The Gruneisen parameter is found to increase with decreasing temperature. The Debye characteristic temperature of 0K is found to be 141K. The anisotropy factor 2c₄₄^T/(c₁₁^T-c₁₂^T) is found to increase with decreasing temperature in accord with other CsCl-type ionic crystals.

A two-dimensional model system exhibiting antiferrodistortive structural phase transitions is considered. It covers the displacive and order-disorder regime. Using a molecular-dynamics technique, various spectral densities were calculated and new excitation branches were found close to the transition temperature and close to the displacive limit. These new branches appear in addition to the expected phonon resonances. One branch is traced back to the cluster dynamics and the other one to a two-phonon process. At the appropriate wavevectors they collapse into a central peak.

A detailed description of a newly developed experimental technique for measuring the angular distribution of phonons radiated from the surface of a solid, heated to a few K, into liquid helium 4 at T<or approximately=0.1K is given. The relevance of such measurements to the Kapitza boundary conductance problem is discussed and examples of measured angular distributions from cleaved (100) faces of sodium fluoride crystals and from gold films evaporated on glass substrates are presented to illustrate the possibilities of the technique.

For pt.I see ibid., vol.8, 289 (1975). Detailed measurements of the angular distribution of phonons radiated from the cleaved (100) faces of sodium fluoride crystals pulse heated to 0.9K<or approximately=T₁<or approximately=3.2K into ⁴He at T approximately 0.1K are presented for the first time. The angular distributions can be resolved into two components, a narrow central peak and a broad background, the shape of the central peak being explicable on a modified acoustic mismatch theory where surface damping in the solid is taken into account. The background component accounts for the majority (>or approximately=85%) of the energy flux across the interface at all source temperatures, and its variation with source temperature T₁ corresponds well to the temperature dependence of the excess Kapitza conductance observed in steady heat flow experiments for a wide variety of materials. This temperature dependence is consistent with a threshold energy for transmission into the background of approximately 5K.

The magnetic susceptibility of a T_g ion coupled to E_g lattice displacements is calculated exactly. Symmetry-adapted phonon operators are used, by which means previous work is clarified. Attention is drawn to the behaviour of different lattice models, and the cluster model is found to give more realistic results than a non-dispersive Debye lattice.

The method of high-temperature series expansions is used to study the dependence of T_c on the concentration p of interactions in a randomly diluted S=¹/₂ Heisenberg model. It is found that, for all three cubic lattices, the interval of p over which the Pade approximants to the series converge extends further towards the critical probability for percolation than for the corresponding site diluted model. In this interval the critical curve is linear and extrapolates to intersect the T=0 boundary at a value of p marginally above the critical probability for bond percolation. The anomalous dependence of the susceptibility exponent gamma on p which has recently been reported for the site diluted model is not observed for the model studied here.

The authors have re-examined the high-temperature susceptibility series (through tenth order) for the classical isotropic n=2 (X-Y and planar Heisenberg) and n=3 (Heisenberg) models, following suggestions by Kosterlitz and Thouless (see abstr. A36398 of 1973) that the (n=2) phase transition may be understood in terms of 'topological' order in a dilute vortex gas. Evidence is found (most conclusive for n=2, X-Y) supporting Kosterlitz' suggestion (see abstr. A41169 of 1974) that the susceptibility behaves as X₀ exp(A epsilon ^{- nu} ), where epsilon =1-K/K_c. For the X-Y case, the authors obtain an apparent exponent of nu approximately=0.75-0.77. For the planar and (n=3) Heisenberg models the evidence is weaker but indicative of nu approximately=0.7 in the former case and nu approximately=0.8 in the latter.

A theory of the temperature dependence of the nuclear magnetic relaxation in the paramagnetic phase is presented. The relaxation rate is expressed as a product of the wavevector-dependent susceptibility and the wavevector-frequency-dependent relaxation-shape function for which a semi-phenomenological representation, based on the method of moments, is used. The temperature dependence, which is contained in the susceptibility and the moments of the relaxation-shape function, is estimated on the basis of a spherical model. The theory is applied to the ¹⁹F resonance in RbMnF₃ and comparison with the experimental measurements of Hess and Hunt (see abstr. A48113 of 1972) is made.

ENDOR of Yb³⁺ in ThO₂ has given similar results to those in CaF₂. The measurements have allowed us to determine the energies of the excited states of the lowest J=⁷/₂ manifold of Yb³⁺ showing that the crystal field in ThO₂ is almost identical to that in CaF₂. This is in excellent agreement with the predictions of the superposition model of Newman (1971), where the crystal field is dominated by covalent contributions from the ligands. In particular the energy of the Gamma ₈ state is 605(3) cm^-1, which becomes 650 cm^-1 if a similar correction is applied to that necessary in CaF₂. The ENDOR linewidth of approximately 60 kHz is significantly narrower than that in CaF₂, which has allowed the determination of a somewhat more precise value of the hyperfine structure anomaly, Delta =-0.007(8)%. This leads to a ratio of s to f electron contributions to the hyperfine structure, A_s/A_f=+1.9+or-2.2%.

The Mossbauer spectra of the cubic spinel FeV₂O₄ at 298 and 193K in the paramagnetic state have been resolved into a pair of two quadrupole split sub-spectra of unequal intensities. The results have been interpreted as evidence of a partially inverse cation distribution in FeV₂O₄ and not as arising from a mixture of a normal and a completely inverse spinel as suggested by du Plessis (1971). The degree of inversion has been determined from the relative areas under the two sub-spectra to be 10+or-3% at 298K. This is in good agreement with the value of 8% determined from the intensities of the X-ray diffraction pattern.

The temperature dependence of vibrational modes polarized parallel to the polar axis of potassium strontium niobate, a 'tungsten-bronze'-type ferroelectric, is investigated using polarized Raman techniques. The low-frequency Rayleigh component of the spectrum may be fitted to a Debye relaxation spectral function, the relaxation time appearing to increase towards the ferroelectric-paraelectric phase transition as is observed in some hydrogen-bonded ferroelectrics. Dielectric dispersion measurements are presented which are consistent with a Debye relaxation over a comparable frequency regime. Measurements of the integrated intensity of the A₁ (TO) modes as a function of temperature are discussed in terms of the static dielectric properties of the material.

For pt.I see abstr. A24692 of 1973. Following a previous paper on the Raman spectrum of copper formate tetrahydrate, the authors have made detailed observations of the modes in the vicinity of the antiferroelectric transition at 235.5K. It is found that whereas all copper formate modes are practically unaffected and the external water modes show some variation over the range 90-250K, the external water modes exhibit pronounced spectral changes in the neighbourhood of T_c which may be attributed to the onset of disorder which accompanies the transition to the paraelectric phase. In addition, a search has been made without success, for angular dispersion to distinguish between the previously suggested structures P2₁/n and P2₁ below T_c. The absence of angular dispersion favours the P2₁/n space group.

X-ray K emission spectra of niobium selenides and tellurides have been investigated using a 400 mm bent crystal (mica) spectrograph. The position of the K alpha _1.2 and K beta ₁ lines of niobium in Nb₃Se₄ and Nb₃Te₄ lie on the lower-energy side, while in NbSe₂ and NbTe₄, these lines shift towards the higher-energy side with respect to the niobium metal. On the other hand, the trend of the shift in the K alpha _1.2 and K beta ₁ lines of selenium in these niobium selenides is the opposite to that observed for the K alpha _1.2 and K beta ₁ lines of niobium with respect to their respective metals.