Dispersion relations and lattice thermal expansion of dysprosium

The lattice dynamics, second and third order elastic constants and the lattice thermal expansion of dysprosium have been calculated using Keating's approach. The ten third order elastic constants are calculated using four anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of dysprosium well. The low and high temperature limits γ?_I and γ?_H of the lattice thermal expansion are evaluated and the agreement between the calculated γ?_H and that obtained from the thermal expansion and specific heat data is satisfactory.     

Approach to Equilibrium for a Class of Random Quantum Models of Infinite Range

We consider random generalizations of a quantum model of infinite range introduced by Emch and Radin. The generalizations allow a neat extension from the class l ₁ of absolutely summable lattice potentials to the optimal class l ₂ of square summable potentials first considered by Khanin and Sinai and generalised by van Enter and van Hemmen. The approach to equilibrium in the case of a Gaussian distribution is proved to be faster than for a Bernoulli distribution for both short-range and long-range lattice potentials. While exponential decay to equilibrium is excluded in the nonrandom l ₁ case, it is proved to occur for both short and long range potentials for Gaussian distributions, and for potentials of class l ₂ in the Bernoulli case. Open problems are discussed.     

Contribution of structural order-disorder to the room-temperature photoluminescence of lead zirconate titanate powders

Intense and broad visible photoluminescent (PL) band was observed at room temperature in structurally disordered PbZr_0.53Ti_0.47O₃ powders. The lead zirconate titanate PbZr_0.53Ti_0.47O₃ powders prepared by the polymeric precursor method and heat treated at different temperatures were structurally characterized at long range by means of X-ray diffraction. The PL was measured at room temperature samples heat treated at different temperatures. Experimental measurements and quantum-mechanical calculations showed that the high structural order and the high structural disorder in PbZr_0.53Ti_0.47O₃ lattice are not favorable to the intense PL emission. Only samples containing simultaneous structural order and disorder in their lattice present the intense visible PL emission at room temperature.     

Lattice dynamics,third order elastic constants and thermal expansion of Cadmium

The lattice dynamics, second and third order elastic constants, pressure derivatives of the second order elastic constants and the temperature variation of the lattice thermal expansion of Cadmium have been worked out utilising Keating's approach. The ten TOE constants are calculated using four anharmonic parameters. The model used here reproduces the measured pressure derivatives of the SOE constants of Cadmium extremely well. The low temperature limit of the volume Gruneisen function γ_L is found to be nearer to the value of Andres. The high temperature limit γ_v(T) is in good agreement with the value calculated by Gschneidner Jr. from the Cv data for Cadmium. The lattice dynamics of Cadmium is found to be essentially similar to that of Zinc.     

Interatomic force constants studies of AMF3perovskite-type crystals (A = K,Rb; M = Mg,Ni, Co,Zn, Mn)

A simple model involving only three force constants allows us to evaluate the short range interactions in perovskite fluorides from the experimental values of the elastic constants and the lattice parameters of these compounds. The results indicate that the A-F bonds are quite central in character whereas the M-F bonds are axially symmetric; thus the short range A-F interactions are assumed to have the Born-Mayer form:ZZZZZBy studying the variations of the force constants with respect to the lattice parameter r, it is determined that ρ = 0·232 , λ = 2·8 × 10^?8 ergs for K⁺-F^?; ρ = 0·232 , λ = 4·1 × 10^?8 ergs for Rb⁺-F^?; λ₂, ρ₂ and ρ₂ are respectively 6·9 × 10^?10 ergs, 0·34 , 0·98for Co²⁺-F^? and 2·9 × 10^?10 ergs, 0·46 , 1·40for Mn²⁺-F^?. Taking into account both the short range repulsive potential and the long range electrostatic potential we can study the variations of the lattice energy as a function of r near the equilibrium position and deduce a theoretical value of the lattice distance. In spite of the simplicity of the model, the discrepancy between the experimental and the theoretical values is less than 10 per cent for all the compounds.     

Simulation studies of gas-liquid transitions in two dimensions via a subsystem-block-density distribution analysis

The finite-size scaling analysis of the density distribution function of subsystems of a system studied at constant total density is studied by a comparative investigation of two models: (i) the nearest-neighbor lattice gas model on the square lattice, choosing a total lattice size of 64×64 sites. (ii) The two-dimensional off-lattice Lennard-Jones system (truncated at a distance of 2.5 σ, σ being the range parameter of the interaction) withN=4096 particles, applying the NVT ensemble. In both models, the density distribution functionP _L (ρ) is obtained forL×L subsystems for a wide range of temperaturesT, subblock linear dimensionsL and average densities <ρ>. Particular attention is paid to the question whether accurate estimates of critical temperatureT _c and critical density ρ _c can be obtained. In the lattice gas model these critical parameters are known exactly and the limitations of the approach can thus be definitively asserted. The final estimates for the Lennard Jones problem areT _c =0.47±0.01 (in units of the Lennard Jones energy ε) and ρ _c (in units of σ²), a comparison with previous estimates is made.     

Lattice self-diffusion in plastic pivalic acid (acid 2.2 dimethyl propanoic)—III: Computer calculation of the correlation factor for various tracer self diffusion mechanisms. Discussion of these mechanisms

The correlation factors ? for lattice self-diffusion of tracers involving mono or divacancies have been calculated in “plastic” pivalic acid. The peculiarities of the crystalline structure have been taken into account. Dimers (molecules linked by 2 hydrogen bondings) induce short range order, but no long range order. The local order changes at the frequency ω_R with which hydrogen bondings break. ? has been obtained using the encounter model and the Monte Carlo method. It has been supposed that hydrogen bondings never break during an encounter. The calculation gives the upper limit of ? for ω_m = nω_R, where n ? 2 and ω_m is the frequency of migration of the defect. The asymptotic value of ? for n→∞ is also obtained. Two diffusion mechanisms for monovacancies as well as for divacancies have been considered. All these mechanisms are strongly correlated. In every case, dimers induce low values of ?. Other experimental data concerning point defects and diffusion in pivalic acid are discussed. Lattice self-diffusion should be due mainly to relaxed monovacancies migrating according to mechanism 1 (exchange of the monovacancy with one of the two molecules forming a dimer). This mechanism is characterised by 0.38 ? ? ? 0.57. Some contribution of divacancies, noticeable above 301K, is not incompatible with experimental data in the whole plastic range.     

Lattice dynamics,third order elastic constants and thermal expansion of gadolinium

A systematic investigation of the lattice dynamics, second and third order elastic constants and the temperature variation of the effective Grüneisen functions has been carried out in gadolinium using Keating's approach. The ten third order elastic constants are calculated using five anharmonic parameters. The present model reproduces the measured pressure derivatives of the second order elastic constants of gadolinium well. The low and high temperature limits gg_L and gg_H of the lattice thermal expansion are evaluated. The agreement between the calculated gg_H and that obtained from the thermal expansion and specific heat data of gadolinium is good.     

Surface diffusion and formation of ordered state

Surface diffusion and formation for an ordered phase is investigated using the lattice gas model in Monte-Carlo simulation. Interaction up to the second nearest neighbour between particles is considered. The coverage is calculated as a function of a normalized coordinate by the square root of the diffusion time, starting from the initial step coverage. When the temperature T is lower than T_c, a shoulder appears in the coverage curve at near half coverage. It is shown that this shoulder corresponds to the formation of a c(2 × 2) phase, in which the existence of long range order is confirmed. On the other hand, when T is higher than T_c, the shoulder in the coverage curve disappears, but the short range order of the first and second nearest neighbour correlation still remains and the formation of islands of c(2 × 2) pattern is locally observed. The microscopic growth mechanism of the c(2 × 2) phase is considered. The observed growth rate is explained phenomenologically through the diffusion coefficient which is concentration-dependent.     

The magnesium doping effect of the vanadate spinel MnV2O4

We investigate the structural, transport, and magnetic properties of Mn_1−xMg_xV₂O₄(0≤x≤0.8) to study the role of the A-site magnetism in vanadate spinels. With increasing Mg²⁺ concentration, the lattice parameters shrink and the hopping energy for electrons increases, whereas both the magnetic transition temperature and the structural transition temperature decrease gradually. The two temperatures become closer and eventually equal to each other at x=0.2. For x>0.2 the first order transition disappears and the magnetic ground state switches from a long range ordered ferrimagnetic state to a glassy state. The transition temperature of the glassy state continues to decrease with further increase of Mg content, which is attributed to the dilution in the magnetism on A sites.     

Anomalous states of the crystal structure of (Rb0.1(NH4)0.9)2SO4 solid solutions in the temperature range 4.2–300 K

Crystals of (Rb_0.1(NH₄)_0.9)₂SO₄ solid solutions are studied using x-ray diffractometry. It is revealed that the temperature dependence of the lattice parameter a exhibits an anomalous behavior, namely, the “invar effect” at temperatures above the ferroelectric phase transition point T _c and an anomalous increase in the temperature range from T _c to the liquid-helium temperature. An anomalous increase in the lattice parameter a and an increase in the intensity of Bragg reflections with a decrease in the temperature are interpreted within the model of the coexistence of two sublattices hypothetically responsible for the ferroelectric phase transition. A series of superstructure reflections observed along the basis axes corresponds to a sublattice formed in the matrix of the host structure. Analysis of the ratio between the lattice parameters of these structures allows the inference that, in the temperature range 4.2–300 K, the structure of the crystal under investigation can be considered an incommensurate single-crystal composite.     

Der Einfluß des elastischen Gitters auf den Orientierungsübergang von festem Ortho-Wasserstoff in Molekularfeldnäherung

We calculate the influence of the elastic lattice on the orientational order-disorder transition in fcc solid ortho-hydrogen. The angular momentaJ = 1 of the molecules are coupled by quadrupole-quadrupole interaction which we reduce within the space group Pa 3 to the Ising model approximation. Local mechanical equilibrium requires the lattice to adjust itself to the forces caused by the inhomogeneous fluctuations in the angular momentum configuration. Following Wagner [6] this results in a 4-angular-momentum interaction with long range and short range contributions depending on the one-phonon Green function of the lattice. We use a Debye phonon spectrum and the molecular field approximation in order to obtain numerical results. According to the first order nature of the phase transition we get a pressure drop at the critical pointT ^c of 9.7 bar. The experimental value is estimated to be 8 bar. Compared to the rigid lattice the phase transition on the elastic lattice is smoothed out by the short range contribution. This corresponds to a reduction of the discontinuity of the order parameter at the critical pointT ^c by about 13%. The phase transition will vanish completely if we increase the magnitude of the short range terms by a factor of three.     

Discontinuity in heat capacity of Fe0.5Co0.5(110) alloy thin films

In this work we calculate heat capacity of alloy thin films of FeCo on the surface of the plane (110), using three parameters, the concentration x(i), the lattice long range order parameter t(i) and the magnetic order parameter σ(i), being i the number of layers of the thin film. The formulations reported by Hill [1] in the context of small particles and Valenta's model [2] can be applied to the film structure when we treat a thin film as a system divided into subsystems equivalent to two-dimensional parallel layers. The FeCo bulk alloy is completely homogeneous while a thin film have spatial discontinuities in their surfaces. We consider three ferromagnetic thin films formed by 11, 15 and 19 layers in the Helmholtz's free energy, which is minimized applying their first partial derivatives with respect to chemical composition, long range order parameter and magnetic order parameter. We calculate internal energy and heat capacity as a function of temperature and we verify that have two jumps as are reported in literature for the bulk; there are many results of bulk or surface effects of FeCo, but no enough results about ferromagnetic FeCo thin films and this fact does this work interesting.     

Magnetic and structural properties of the metastable alloy Mn1.11Al0.89

Magnetic and structural properties of the metastable Mn_1.11Al_0.89 alloy have been studied by neutron and X-ray diffraction and by differential scanning calorimetry.A strong influence of the magnetic long range order on the crystalline unit cell was observed, particularly in the vicinity of 370°C.In the vicinity of the Curie temperature the structural transition of the crystalline lattice is followed by the critical exponent β_r = 0.5 ± 0.1 of the disorder parameter.     

Heat capacity and lattice dynamics of yttrium diboride in the temperature range 5–300 K

This paper reports an experimental study of the heat capacity and crystal lattice parameters of a polycrystalline sample of yttrium diboride prepared by high-temperature synthesis from elements. The electronic and lattice contributions to the heat capacity are isolated. The temperature dependences of the characteristic temperature, the linear thermal expansion coefficients α_a(T) and α _c (T), the bulk thermal expansion coefficient β(T), and the Grüneisen coefficient are calculated. A region of negative values of α _c (T) and β(T) is revealed. Anharmonicity is found to exert only a minor effect on the YB₂ lattice dynamics over a larger part of the temperature range covered.     

Electrical resistivity and magnetic properties of the Re1−xGdxAl2 laves phase (for Re: La,Lu, Y)

X-ray, magnetic, electrical resistivity and ESR studies of Re_1-xGd_xAl₂ type compounds (Re - La, Lu, Y) were performed. The transition temperatures, effective moments, effective mass, lattice constants, crystallographic parameters, thermal broadening of resonance linewidth and g-factors were obtained. It was found that the simple RKKY model applied to describing the electrical resistivity and magnetic susceptibility in a large range of concentrations x seems to be right.     

Special features of the structure and properties of La<Subscript>0.6</Subscript>Sr<Subscript>0.2</Subscript>Mn<Subscript>1.2−<Emphasis Type="Italic">y</Emphasis></Subscript>Cr<Subscript>y</Subscript>O<Subscript>3</Subscript> magnetoresisitive ceramics

Atomic order and magnetoresistive parameters are studied in La_0.6Sr_0.2Mn_1.2?yCr_yO₃ ceramics, in which Cr substituted for the above stoichiometric Mn content serves to enhance cluster formation in a solid solution. It is shown that in a range of 0.05<y<0.1, La_0.6Sr_0.2Mn_1.2?yCr_yO₃ experiences a phase transition from a partially disordered solid solution with a rhombohedral lattice \((R\bar 3c)\), in the form of planes possessing a long-range order and clusters of mesoscopic order, to a chemically microstratified solid solution, in the form of planes of an orthorhombic (Pnma) crystal lattice having a matrix structure and mesoscopic formations (clusters) coherently combined with a matrix of plane fragments peculiar to oxides of γ-MnO₂ type or, at y>0.1, of Cr₂O₃ type. It is shown that the structural phase transition is accompanied by maximum changes of the magnetoresistive parameters in the same range of Cr concentrations, i.e., 0.05<y<0.10.     

The bond bending model on triangular lattice and square lattice

The bond bending model is studied using the series expansion method on a triangular lattice and on a square lattice. The elastic splay susceptibility χ_SR and the elastic compressional susceptibility χ_el are calculated up to 11th order for the triangular lattice and up to 14th order for the square lattice. The elastic splay crossover exponent, ζ_SP, is found to be ζ_SP ≈ 1.26 ± 0.05 for the triangular lattice and ζ_SP = 1.30 ± 0.04 for the square lattice which is close to the conductivity exponent, ζ_Re, of the resistor network. From the scaling relation ? _B = dv + ζ_SP, we found that the bulk modulus exponent ? _B = 3.93 ± 0.05 for the triangular lattice and ? _B = 3.97 ± 0.04 for the square lattice which is in good agreement with the result ? _B = 3.96 ± 0.04, obtained by Zabolitzky et al. using a transfer matrix technique on a honeycomb lattice.     

Thermal evolution of the crystal structure of the correlated 4d post-perovskite CaRhO3

Thermal effect on the orthorhombic crystal structure (Cmcm) of the correlated 4d post-perovskite CaRhO₃ was investigated by an X-ray powder diffraction method between 60 K and 300 K. Anisotropic thermal evolution of the structure was observed over the temperature range, and in addition, an anomalous change of the lattice parameters was detected at the antiferromagnetic transition temperature of 90 K, indicating possible correlations between the lattice and the magnetic order.