Lattice mechanical properties of alkaline earth metals in bcc and fcc phases

A model pseudopotential depending on an effective core radius treated as a parameter is used for alkaline earth metals in bcc and fcc phases to study the Binding energy, Interatomic interactions, phonon dispersion curves, Phonon density of states, Debye-Waller factor, mean square displacement, Debye-Waller temperature parameters, dynamical elastic constants (C₁₁, C₁₂ and C₄₄), bulk modulus (B), shear modulus (C′), deviation from Cauchy relation (C₁₂−C₄₄), Poisson's ratio (σ), Young's modulus (Y), behavior of phonon frequencies in the elastic limit independent of the direction (Y₁), limiting value in the [1 1 0] direction (Y₂), degree of elastic anisotropy (A) and propagation velocities of the elastic waves. The contribution of s-like electrons is incorporated through the second-order perturbation theory due to model potential. The theoretical results are compared with the existing experimental data. A good agreement between theoretical investigations and experimental findings has confirmed the ability of our potential to yield large numbers of lattice mechanical properties of certain alkaline earth metals.     

Orientation dependence of electrical properties of 0.96Na<Subscript>0.5</Subscript>Bi<Subscript>0.5</Subscript>TiO<Subscript>3</Subscript>-0.04BaTiO<Subscript>3</Subscript> lead-free piezoelectric single crystal

In this paper, a single crystal of 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ with dimensions of Φ 30×10 mm was grown by the top-seeded-solution growth method. X-ray powder diffraction results show that the as-grown crystal possesses the rhombohedral perovskite-type structure. The dielectric, piezoelectric and electrical conductivity properties were systematically investigated with 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples. The room-temperature dielectric constants for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal samples are found to be 650, 740 and 400 at 1 kHz. The (T _m, ε _m) values of the dielectric temperature spectra are almost independent of the crystal orientations; they are (306°C, 3718), (305°C, 3613) and (307°C, 3600) at 1 kHz for the 〈001〉, 〈110〉 and 〈111〉 oriented crystal. The optimum poling conditions were obtained by investigating the piezoelectric constants d ₃₃ as a function of poling temperature and poling electric field. For the 〈001〉 and 〈110〉 crystal samples, the maximum d ₃₃ values of 146 and 117 pC/N are obtained when a poling electric field of 3.5 kV/mm and a poling temperature of 80°C were applied during the poling process. The as-grown 0.96Na_0.5Bi_0.5TiO₃-0.04BaTiO₃ crystal possesses a relatively large dc electrical conductivity, especially at higher temperature, having a value of 1.98×10⁻¹¹ Ω⁻¹⋅m⁻¹ and 3.95×10⁻⁹ Ω⁻¹⋅m⁻¹ at 25°C and 150°C for the 〈001〉 oriented crystal sample.     

A new optical method for measuring the electron-phonon interaction parameter λ〈Ω2〉 using the spectral dependence of the relaxation rate

The spectral dependence of the electron-phonon relaxation rate γ_e−ph(ℏω) in metals is studied in pump-supercontinuum-probe (PSCP) experiments with femtosecond time resolution. Investigation of this spectral dependence, which exhibits a substantial slowing of the relaxation rate γ_e−ph(ℏω) near the Fermi level E _F , using the parametrization γ_e−ph(ℏω)∝λ〈Ω²〉 (ℏω−E _F )² makes it possible to determine directly the electron-phonon interaction parameter λ〈Ω²〉. The parameter λ〈Ω²〉 for YBa₂Cu₃O_7−δ is analyzed using this method. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 5, 329–332 (10 September 1999)     

Swelling of two-dimensional polymer rings by trapped particles

The mean area of a two-dimensional Gaussian ring of N monomers is known to diverge when the ring is subject to a critical pressure differential, p _c ∼ N ^-1. In a recent publication (Eur. Phys. J. E 19, 461 (2006)) we have shown that for an inextensible freely jointed ring this divergence turns into a second-order transition from a crumpled state, where the mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N ². In the current work we extend these two models to the case where the swelling of the ring is caused by trapped ideal-gas particles. The Gaussian model is solved exactly, and the freely jointed one is treated using a Flory argument, mean-field theory, and Monte Carlo simulations. For a fixed number Q of trapped particles the criticality disappears in both models through an unusual mechanism, arising from the absence of an area constraint. In the Gaussian case the ring swells to such a mean area, 〈A〉 ∼ NQ, that the pressure exerted by the particles is at p _c for any Q. In the freely jointed model the mean area is such that the particle pressure is always higher than p _c, and 〈A〉 consequently follows a single scaling law, 〈A〉 ∼ N ² f (Q/N), for any Q. By contrast, when the particles are in contact with a reservoir of fixed chemical potential, the criticality is retained. Thus, the two ensembles are manifestly inequivalent in these systems. An erratum to this article is available at .     

New results from the HAPPEX Experiments at Q<Superscript>2</Superscript> = 0.1GeV/c<Superscript>2</Superscript>

The nucleon's strange electric and magnetic form factors G _E ^s and G _M ^s can be probed via parity-violating electron scattering. The HAPPEX Collaboration has made new measurements of the parity-violating asymmetry A _PV in elastic scattering of 3GeV electrons off hydrogen and ⁴He targets with 〈θ_lab〉 ≈ 6.0^° . For ⁴He the preliminary result is A _PV = (+ 6.43±0.23(stat)±0.22(syst))×10^-6 . For hydrogen the preliminary result is A _PV = (- 1.60±0.12(stat)±0.05(syst))×10^-6 . From these values we extract G ^s _E = 0.004±0.014±0.013 at 〈Q ²〉 = 0.077 GeV/c^2 , and G ^s _E +0.09G ^s _M = 0.004±0.011±0.005 at 〈Q ²〉 = 0.109 GeV/c^2 , both consistent with zero, providing stringent new limits on the role of strange quarks in the vector structure of the nucleon.     

Temperature scaling of ferroelectric hysteresis in hard lead zirconate titanate bulk ceramic

The temperature scaling of the ferroelectric hysteresis was investigated in hard lead zirconate titanate (PZT) bulk ceramic. The power-law temperature scaling relations were obtained for hystersis area 〈A〉, remnant polarization P_r, and coercivity E_C in the forms of 〈A〉∝T^-0.9650, P_r∝T^-0.0261, and E_C∝T^-0.8823, respectively, which are mostly comparable to those of its soft counterpart. The observation that P_r decayed more slowly with temperature than in soft PZT was attributed to the presence of the complex defects in hard PZT. However, the product of P_r and E_C still provided the similar scaling law on the T dependence in comparison with 〈A〉. PACS 77.80.-e; 77.80.Fm; 77.84.-s; 77.84.Dy     

Wave mechanics of two hard core quantum particles in A 1-D box

The wave mechanics of two impenetrable hard core particles in a 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a macro-orbital (a kind of pair waveform). While the expectation value of their interaction, 〈 V _HC (x) 〉, vanishes for every state of two particles, the expectation value of their relative separation, 〈 x 〉, satisfies 〈 x 〉≥λ/2 (or q ≥ π/d, with 2d=L being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with 〈 x 〉= λ/2, phase position separation Δϕ = 2π and momentum |q _o| = π/d) and experience a mutual repulsive force (zero point repulsion) f _o =h ²/2md ³ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining a correct microscopic understanding of widely different many-body systems.     

Using the full Raman depolarisation in the determination of the order parameters in liquid crystal systems

The depolarisation ratio for the Raman-active phenyl stretching mode has been measured over the whole of the mesophase range, and the orientational order parameters deduced, in the uniaxial nematic liquid crystal octylcyanobiphenyl (8CB). Linearly polarised light was incident normally on a homogeneously aligned sample and a χ² minimisation routine performed on the 360^° depolarisation ratio profile. The order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 , together with the differential polarisability ratio, r , are used as fitting parameters and measured as a function of temperature. Interestingly, we show that the value for r , conventionally measured in the isotropic phase and assumed to remain constant, has a clear temperature dependence, ranging from -0.032±0.008 in the isotropic phase through to -0.245±0.015 at the nematic-to-smectic A phase transition. The measured order parameters 〈P ₂₀₀〉 and 〈P ₄₀₀〉 varied from 0.35- 0.55±0.02 and 0.180- 0.245±0.02 , respectively, across the 8 ^° C wide nematic phase range. The values of both 〈P ₂₀₀〉 and 〈P ₄₀₀〉 are in excellent agreement with theory, but it is noteworthy that 〈P ₄₀₀〉 shows a much better quantitative match than has been reported in previous work. Crucially the temperature dependence of r is shown to be a contributing factor in the low 〈P ₄₀₀〉 values that have been conventionally reported from Raman scattering measurements. The potential for fitting the entire angular depolarisation ratio distribution in liquid crystalline systems that are described by more order parameters, specifically biaxial materials, is discussed.     

Static and Vibrational Properties of Transition Metals

A model pseudopotential depending on an effective core radius but otherwise parameter free is proposed to study the equation of state by incorporating the s-d hybridization effects. Very recently proposed screening function due to Sarkar et al has been used to obtain the screened form factor. The equations of state for Cu, Ta, Mo, W and Pt have been studied up to the pressure of 1000 GPa. The vibrational properties such as phonon dispersion curves (in q and r space), phonon density of states, mode Grüneisen parameters, maximum frequency _max, mean frequency , ^21/2 = (/ ^-1)^1/2 and fundamental frequency ² and static properties such as dynamical elastic constants of rhodium and iridium are also calculated. The theoretical results are compared with experimental findings wherever possible. A good agreement between theoretical investigations and experimental findings has confirmed our formulation.     

Smoothening transition of a two-dimensional pressurized polymer ring

We revisit the problem of a two-dimensional polymer ring subject to an inflating pressure differential. The ring is modeled as a freely jointed closed chain of N monomers. Using a Flory argument, mean-field calculation and Monte Carlo simulations, we show that at a critical pressure, p_c ∼ N^-1, the ring undergoes a second-order phase transition from a crumpled, random-walk state, where its mean area scales as 〈A〉 ∼ N, to a smooth state with 〈A〉 ∼ N². The transition belongs to the mean-field universality class. At the critical point a new state of polymer statistics is found, in which 〈A〉 ∼ N^3/2. For p ≫ p_c we use a transfer-matrix calculation to derive exact expressions for the properties of the smooth state.     

Ultrasonic wave propagation in rare-earth monochalcogenides

The ultrasonic attenuation in thulium monochalcogenides TmX (X=S, Se and Te) has been studied theoretically with a modified Mason’s approach in the temperature and range 100 K to 300 K along 〈100〉, 〈110〉 〈111〉 crystallographic directions. The thulium monochalcogenides have attracted a lot of interest due to their complex physical and chemical characteristics. TmS, TmSe and TmTe are trivalent metal, mixed valence state, and divalent semiconductor, respectively. Coulomb and Born-Mayer potential is applied to evaluate the second- and third-order elastic constants. These elastic constants are used to compute ultrasonic parameters such as ultrasonic velocities, thermal relaxation time, and acoustic coupling constants that, in turn, are used to evaluate ultrasonic attenuation. A comparison of calculated ultrasonic parameters with available theoretical/experimental physical parameters gives information about classification of these materials.      

A QCD motivated model for soft interactions at high energies

In this paper we develop an approach to soft scattering processes at high energies which is based on two elements: the Good–Walker mechanism for low mass diffraction and multi-pomeron interactions for high mass diffraction. The principal idea, which allows us to specify the theory for pomeron interactions, is that the so called soft processes occur at rather short distances (r ² ∝1/〈p _t 〉² ∝ α′_ℙ≈0.01 GeV⁻²), where perturbative QCD is valid. The value of the pomeron slope α′_ℙ is obtained from a fit to the experimental data. Using this theoretical approach, we suggest a model that fits all soft data in the ISR-Tevatron energy range: total, elastic, single and double diffractive cross sections, as well as the t dependence of the differential elastic cross section, and the mass dependence of single diffraction. In this model we calculate the survival probability of diffractive Higgs production, and we obtain a value for this observable that is smaller than 1% at the LHC energy range.     

Dielectric parameterization of raman lineshapes for GaP with a plasma of charge carriers

We have studied the Raman lineshapes of several samples of GaP with appreciable carrier concentrations. There is no feature identifiable as a plasma resonance, but there are pronounced effects of interaction with the LO phonon resonance. For analysis we have developed a model along lines laid down by Barker and Loudon, employing Nyquist relations to calculate infrared fluctuations which scatter light. We introduce a response matrix α(ω) withseveral resonances; and we uncover some points which seem to be new, for coupled-mode scattering systems in general. In the GaP-plasma problem the data do not necessitate inclusion of the scattering amplitude from the plasma; we ascribe this to large plasma damping rates (ωτ≲1). This provides an account for the lack of any apparent plasma resonance in the scattering and for the modified appearance of the LO phonon, relative to the pure crystal. We emphasize that the following parameters suffice: Lorentz parameters measured in linear infrared experiments, the nonlinear parameterC from a visible-infrared mixing experiment, and the plasma frequency and damping fit to each sample. Beyond treatment of the plasma problem, the theory bears more generally on the conditions under which an LO Raman lineshape measures locally the shape of 〈E ²〉_ω. Also it bears upon the analysis of polariton linewidths to infer the variation of the phonon damping Γ(ω). This work was supported by the National Science Foundation Grant No. GH 32401. It is based on a major segment of the thesis of D.T. Hon, submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy (Physics) in the Faculty of the Graduate School of the University of Southern California.     

Double-beta decay: Present status

The present status of double-beta-decay experiments (including the search for 2β ⁺, ECβ ⁺, and ECEC processes) are reviewed. The results of the most sensitive experiments are discussed. Average and recommended half-life values for two-neutrino double-beta decay are presented. Conservative upper limits on effective Majorana neutrino mass and the coupling constant of the Majoron to the neutrino are established as 〈m _ν 〉 < 0.75 eV and 〈g _ee 〉 < 1.9 × 10⁻⁴, respectively. Proposals for future double-betadecay experiments with a sensitivity for the 〈m _ν 〉 at the level of 0.01–0.1 eV are considered.     

Comparison of the Seltzer Coefficient C 1 to Experimental Data

Experimental Coulomb isotope shifts δE _Coul from K _α transitions, and radius differences δ〈r ²〉 _eμ measured by electron scattering and muonic atom X-rays were used to derive ‘experimental’ coefficients C _1,exp for 54 isotope pairs of 18 elements from Mo to U. A χ²-analysis shows that these experimental coefficients are – on average – 3.5% lower than the theoretical C ₁ values calculated by Seltzer, or more precisely: C _1,exp=0.965(± 0.014)×C ₁. The need for more accurate theoretical calculations is stressed, and consequences of this deviation are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Nonadiabatic effects in the phonon spectra of superconductors

The nonadiabatic corrections to the self-energy part Σ_s(q, ω) of the phonon Green’s function are studied for various values of the phonon vectors q resulting from electron-phonon interactions. It is shown that the long-range electron-electron Coulomb interaction has no direct influence on these effects, aside from a possible renormalization of the corresponding constants. The electronic response functions and Σ_s(q, ω) are calculated for arbitrary vectors qand energy ω in the BCS approximation. The results obtained for q=0 agree with previously obtained results. It is shown that for large wave numbers q, vertex corrections are negligible and Σ_s(q, ω) possesses a logarithmic singularity at ω=2Δ, where Δ is the superconducting gap. It is also shown that in systems with nesting, Σ_s(Q, ω) (where Q is the nesting vector) possesses a square-root singularity at ω=2Δ, i.e., exactly of the same type as at q=0. The results are used to explain the recently published experimental data on phonon anomalies, observed in nickel borocarbides in the superconducting state, at large q. It is shown, specifically, that in these systems nesting must be taken into account in order to account for the emergence of a narrow additional line in the phonon spectral function S(q, ω)≈−π ⁻¹ Im D _s (q, ω), where D _s (q, ω) is the phonon Green’s function, at temperatures T<T _c . Zh. éksp. Teor. Fiz. 115, 1799–1817 (May 1999)     

“Quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen

We report the first observation of “quasi-Planck” spectra of capillary turbulence on the surface of liquid hydrogen in the dissipation domain. Capillary waves have been driven by low-frequency random force. We have observed that the frequency spectrum of surface elevation changes its dependence from power-like 〈|η_ω²|〉 ∼ ω^−2,8 at middle-frequency domain to “quasi-Planck” distribution ∼e ^ω/ω _d at higher frequencies. The frequency ω _d is proportional to the boundary frequency between inertial interval and dissipation domain and it is scaled up with the increase of driving force.     

Intervalley scattering in GaAs: ab initio calculation of the effective parameters for Monte Carlo simulations

Interactions between excited electrons and short-wavelength (intervalley) phonons in GaAs are studied using density functional theory for the conduction bands, and density functional perturbation theory for phonon frequencies and matrix elements of the electron–phonon interaction. We have calculated the deformation potentials (DPs) and the average intervalley scattering time 〈τ〉. The integration of the scattering probabilities over all possible final states in the Brillouin zone has been performed without any ad hoc assumption about the behavior of the electron–phonon matrix elements nor the topology of the conduction band. For transitions from the L point to Γ valley (within the first conduction band), we find 〈τ〉_L to be 1.5 ps at 300 K, in good agreement with time-resolved photoluminescence experiment. We discuss the difference between our calculated DPs, and effective parameters used in Monte Carlo simulations of optical and transport properties of semiconductors. The latter are based on Conwell’s model, in which electron–phonon interaction is described by one single constant and a parabolic model is used for conduction bands. We deduce the effective DP from our 〈τ〉, and compare it to our calculated DPs. We conclude that only effective DPs obtained from a full calculation of 〈τ〉 are relevant parameters for Monte Carlo simulations. PACS 71.10-w; 72.10.Di; 71.55.Eq     

Superparamagnetism in the 1D Ising model

The temperature dependence of the order parameter (〈M ²〉, the mean-square spin excess per spin) for a system with a finite number of spins of the 1D Ising model was investigated. It was shown that there is a nonzero temperature T _s below which 〈M ²〉 rapidly tends to unity. The analogy between the 1D ensemble of a finite number of spins and a system of superparamagnetic particles is discussed.     

Overall values of conventional discrepancy indices for crystals with heavy atoms. Part II. Results for monoclinic and orthorhombic crystals when the heavy-atom part alone constitutes the model

Theoretical expressions of 〈y _N〉, 〈|y _N − σ₁ y _P ^c |〉 and 〈|y _N ² −σ ₁ ² (y _P ^c )²|〉 (wherey _N andy _P ^c are the normalized structure amplitudes of the structure and the model respectively) are derived in terms of the heavy atom contributionσ ₁ ² for monoclinic and orthorhombic crystals containing a few (i.e., 1 or 2) heavy atoms of the same kind per asymmetric unit by taking the heavy atom part alone as the model. Results are obtained for both the related and unrelated cases. The local values of 〈y _N〉 and 〈|y _N ⁿ − σ ₁ ⁿ (y _P ^c ) ⁿ |〉, (n=1, 2) calculated from these expressions can be used to calculate the overall values of the conventionalR-indicesR(F) andR(I) for the related and unrelated cases. These overall values could be used to check the correctness of heavy atoms located in the structure. Contribution No. 550