A high-pressure and high-temperature synthesis of platinum carbide

High-pressure synthesis is a powerful method for the preparation of novel materials with high elastic moduli and hardness. Additionally, such materials may exhibit interesting thermal, optoelectronic, semiconducting, magnetic, or superconducting properties. We report on the new high-pressure, high-temperature synthesis of platinum carbide. The experiments were performed in a laser-heated diamond anvil cell and data were collected using the synchrotron X-ray diffraction method at pressures >75 GPa at high-temperatures. The new platinum carbide has a rock-salt type structure, with space group Fm3m and cubic symmetry. It was confirmed to remain stable to at least 120 GPa. This structure is the same as that of other metal carbides reported in previous studies. After decompression, the new high-pressure phase was recoverable at ambient pressure. The Birch-Murnaghan equation of state for this new phase was determined from the experimental unit cell parameters, with K₀=301 (±15) GPa, and K′₀=5.2 (±0.4).     

Structural property of CsCl-type sodium chloride under pressure

The structure and equation of state of CsCl-type sodium chloride have been determined using high-pressure powder X-ray diffraction from 32 to 134 GPa. The CsCl-type phase remains stable over this entire pressure range. Pressure-volume data can be fitted with a Vinet equation of state with K_30 GPa=135.1 GPa, K′_30 GPa=3.9, and V_30 GPa=27.70 Å³. The nearest-neighbour distance between sodium and chlorine atoms decreased as pressure increased. Significant discrepancies of nearest-neighbour distance between previous theoretical predictions and this study were observed at pressures higher than 70 GPa.     

Renormalization group analysis of a confined, interacting Bose gas

The renormalization group is not only a powerful method for describing universal properties of phase transitions, but it is also useful for evaluating non-universal thermodynamic properties beyond mean-field theory. In this contribution we concentrate on these latter aspects of the renormalization group approach. We introduce its main underlying ideas in the familiar context of the ideal Bose gas and then apply them to the case of an interacting, confined Bose gas within the framework of the random phase approximation. We model confinement by periodic boundary conditions and demonstrate how confinement modifies the flow equations of the renormalization group, thus changing the thermodynamic properties of the gas. Received: 20 July 2001 / Revised version: 20 August 2001 / Published online: 23 November 2001     

Prediction and Refinement of High-Order Virial Coefficients for a Hard-Sphere System

The n^th virialcoefficient for a hard-sphere system is expressed as the sum of n^2 and a remainder. When n ≥ 3, the remainders of the viriaJs can be accurately expressed with Pade-type functions of n. The maximum deviations are only 0.039-0.053%, which are much better than the existing approaches. By using the predicted virials, the compressibility factors of the hard-sphere system can be predicted very accurately in the whole stable fluid region, and those in the metastable fluid region can also be well predicted up to a packing fraction of 0.545. The simulated B7 and Bl0 are found to be inconsistent with the other known virials, and thus they are refined to be 53.2467 and 105.042, respectively.     

Phase diagram of the three states Potts model with next nearest neighbour interactions on the Bethe lattice

We have found an exact phase diagram of the Potts model with competing nearest neighbor and next nearest neighbor interactions on the Bethe lattice of order two. The diagram consists of five phases: ferromagnetic, paramagnetic, modulated, antiphase and paramodulated, all meeting at the multicritical point . We report on a new phase which we denote as paramodulated, found at low temperatures and characterized by zero average magnetization lying inside the modulated phase. Such a phase, inherent in the Potts model has no analogues in the Ising setting.     

Ultrafast all-optical polarization switching based on “virtual excitation” of InGaAs(P) MQWs

All-optical polarization switches based on near-resonant excitation have been demonstrated recently, which operate without significant real carriers excited in MQWs so as to avoid carriers accumulation. In this paper, we focus our investigation on the switch adopting InGaAsP MQWs because it could be compatible with the optical communication system. Our theoretical analysis is restricted to χ³ regime (i.e., the lowest-order nonlinear regime) and based on the dynamics-controlled truncation (DCT) scheme which provides a formalism for studying the coherent dynamics in weakly-nonlinear coherent optics of semiconductors. By using the theoretical model based on DCT theory, the switching action was simulated. With this theoretical model, we study the respective contributions of phase space filling and Hartree-Fock mean field as main terms of the optical Stark effect to the switching process, then exhibit the influence of delay time and control intensity for the switching response.     

Impossibility to describe repulsion with contact interaction

Contact interactions always lead to attractive behavior. Arguments are presented to show why a repulsive interacting system, e.g. Bose gases, cannot be described by contact interactions and corresponding treatments are possibly obscured by the appearance of bound states. The usually used cut-offs are identified as finite range parameters.     

The chemical potential for the inhomogeneous electron liquid in terms of its kinetic and potential parts with special consideration of the surface potential step and BCS-BEC crossover

The chemical potential μ of a many-body system is valuable since it carries fingerprints of phase changes. Here, we summarize results for μ for a three-dimensional electron liquid in terms of average kinetic and potential energies per particle. The difference between μ and the energy per particle is found to be exactly the electrostatic potential step at the surface. We also present calculations for an integrable one-dimensional many-body system with delta function interactions, exhibiting a BCS-BEC crossover. It is shown that in the BCS regime the chemical potential can be expressed solely in terms of the ground-state energy per particle. A brief discussion is also included of the strong coupling BEC limit.     

Phase-retrieval in hard x-ray diffraction imaging: Can we quantitatively reconstruct a “real” transmission function?

X-ray phase-retrieval algorithms are widely exploited in contemporary hard x-ray diffraction techniques to image at the nanoscale, less than 10-20 nm. Often reconstruction of the sample shape (image) suffices for the purpose of experiment. Identification of specimen composition requires a quantitative profiling of the complex refractive index. This Letter shows that, although such quantitative analysis is possible in many cases, there is a lower limit to variations in optical density, which can be quantitatively reconstructed using the common phase-retrieval methods.     

Dynamic critical phenomena in two-dimensional fully frustrated Coulomb gas model with disorder

The dynamic critical phenomena near depinning transition in two-dimensional fully frustrated square lattice Coulomb gas model with disorders was studied using Monte Carlo technique. The ground state of the model system with disorder σ=0.3 is a disordered state. The dependence of charge current density J on electric field E was investigated at low temperatures. The nonlinear J-E behavior near critical depinning field can be described by a scaling function proposed for three-dimensional flux line system [M.B. Luo, X. Hu, Phys. Rev. Lett. 98 (2007) 267002]. We evaluated critical exponents and found an Arrhenius creep motion for field region Ec/2<E<Ec. The scaling law of the depinning transition is also obtained from the scaling function.     

Fractional vector calculus and fractional Maxwell’s equations

The theory of derivatives and integrals of non-integer order goes back to Leibniz, Liouville, Grunwald, Letnikov and Riemann. The history of fractional vector calculus (FVC) has only 10 years. The main approaches to formulate a FVC, which are used in the physics during the past few years, will be briefly described in this paper. We solve some problems of consistent formulations of FVC by using a fractional generalization of the Fundamental Theorem of Calculus. We define the differential and integral vector operations. The fractional Green’s, Stokes’ and Gauss’s theorems are formulated. The proofs of these theorems are realized for simplest regions. A fractional generalization of exterior differential calculus of differential forms is discussed. Fractional nonlocal Maxwell’s equations and the corresponding fractional wave equations are considered.     

Non-equilibrium phase transition of the fully frustrated square lattice Coulomb gas model

The non-equilibrium phase transitions of the fullyfrustrated (f = 1/2) square lattice Coulomb gas (CG) modeldriven by external electrical fields are studied in the frameworkof the short-time dynamic scaling approach. The criticaltemperature T_c, the static and dynamic critical exponents2β/ν, ν, and z are obtained for several smalldriving fields. The results show that T_c decreases with theincrease of electric field, and 2β/ν and z arestrongly dependent on the external electric field. Interestingly,contrary to the equilibrium case, in the presence of smallelectric field, the calculated exponent ν is close to that inpure 2D Ising model, which provides numerical evidence thatexternal electric field may change the universality class of thef = 1/2 CG system.     

Gain mechanisms in field‐free InGaN layers grown on sapphire and bulk GaN substrate

The gain mechanisms and recombination dynamics of InGaN layers strongly depend on the structural properties of the substrate material. The 4.5 nm and 9.5 nm thick layers were grown by metal organic chemical vapor deposition on two different substrates (sapphire and GaN) with different dislocation densities. Time‐resolved photoluminescence spectroscopy at high excitation densities identifies the saturation of nonradiative recombination centers through excited carriers as a major gain mechanism. The prime argument is an unusual nonexponential luminescence decay. This was confirmed by a lower threshold of the optical gain for the structures grown on GaN with lower dislocation densities. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Femtosecond laser-induced dynamic alignment in Coulomb explosion of CO: Roles of laser wavelength, intensity and pulse duration

Dependences of dynamic alignment of CO molecules induced by intense femtosecond laser fields on laser wavelength, intensity and pulse duration are investigated by numerical simulations. A counting approach and a fourth-order Runge-Kutta algorithm are used to calculate the angular distribution and the time evolution of molecules. A two-step Coulomb explosion model of diatomic molecules in intense laser fields is used to determine the instant that CO molecular dynamic alignment is over. Our calculating results show that the linear polarizability and the damping force play an important role in the angular rotation of CO molecule in conditions of 800 nm laser wavelength and 10¹⁵ W/cm² laser intensity. The contributions of the second-order field-induced dipole moment and the higher-order correction term to molecular rotation acceleration comparing to the linear polarizability and damping force are negligible. The extent of dynamic alignment of CO molecules reduces with the increasing of laser intensity. The dynamic alignment time of CO molecules is tightly connected to the laser pulse duration. The angular distributions of CO molecules as the laser pulse length varied from 50 to 250 fs at laser intensity of 3×10¹⁴ W/cm² are shown and discussed.     

First law of thermodynamics and Friedmann-like equations in braneworld cosmology

We derive the Friedmann-like equations in braneworld cosmology by imposing the first law of thermodynamics and Bekenstein's area-entropy formula on the apparent horizon of a Friedmann–Robertson–Walker universe in both Randall–Sundrum II gravity and Dvali–Gabadadze–Porrati gravity models. Israel's boundary condition plays an important role in our calculations in both cases, besides the first law of thermodynamics and Bekenstein's area-entropy formula. The results indicate that thermodynamics on the brane world knows the behaviors of gravity.     

Renormalization group treatment of the scaling properties of finite systems with subleading long-range interaction

The finite size behavior of the susceptibility, Binder cumulant and some even moments of the magnetization of a fully finite O(n) cubic system of size L are analyzed and the corresponding scaling functions are derived within a field-theoretic ɛ-expansion scheme under periodic boundary conditions. We suppose a van der Waals type long-range interaction falling apart with the distance r as r ^{- (d + σ)}, where 2 < σ < 4, which does not change the short-range critical exponents of the system. Despite that the system belongs to the short-range universality class it is shown that above the bulk critical temperature T _c the finite-size corrections decay in a power-in-L, and not in an exponential-in-L law, which is normally believed to be a characteristic feature for such systems. Received 8 August 2001     

Stabilization of the extra dimensions in brane gas cosmology with bulk flux

We consider the anisotropic evolution of spatial dimensions and the stabilization of internal dimensions in the framework of brane gas cosmology. We observe that the bulk RR field can give an effective potential which prevents the internal subvolume from collapsing. For a combination of (D−3)$(D-3)$-brane gas wrapping the extra dimensions and 4-form RR flux in the unwrapped dimensions, it is possible that the wrapped subvolume has an oscillating solution around the minimum of the effective potential while the unwrapped subvolume expands monotonically. The flux gives a logarithmic bounce to the effective potential of the internal dimensions.     

Synthesis and physical properties of negative thermal expansion materials Zr1−xMxW2O8−y (M=Sc, In, Y) substituted for Zr(IV) sites by M(III) ions

Zr_1−xM_xW₂O_8−y (M=Sc, In and Y) solid solutions substituted up to x=0.04 for Zr(IV) sites by M(III) ions were synthesized by a solid-state reaction. X-ray diffraction experiments from 90 to 560 K revealed that all solid solutions had a cubic crystal structure and showed negative thermal expansion coefficients. The lattice parameters of Zr_1−xM_xW₂O_8−y were smaller than that of ZrW₂O₈ probably due to oxygen defects, though the ionic radii of substituted M³⁺ ions were larger than that of Zr⁴⁺. Order-disorder phase transition temperatures of the substituted samples drastically decreased in the order of Y, In and Sc compared to the percolation theory, and decreased with increasing M content.     

X-ray emission in the ‘water window’ from a nitrogen gas puff target irradiated with a nanosecond Nd:glass laser pulse

Received: 20 April 1998/Revised version: 19 June 1998     

Renormalization in theories with modified dispersion relations: Weak gravitational fields

We consider a free quantum scalar field satisfying modified dispersion relations in curved spacetimes, within the framework of Einstein–Aether theory. Using a power counting analysis, we study the divergences in the adiabatic expansion of 〈?²〉$〈{?}^2〉$ and 〈T_μν〉$〈T_{\mu \nu }〉$, working in the weak field approximation. We show that for dispersion relations containing up to 2s powers of the spatial momentum, the subtraction necessary to renormalize these two quantities on general backgrounds depends on s   in a qualitatively different way: while 〈?²〉$〈{?}^2〉$ becomes convergent for a sufficiently large value of s  , the number of divergent terms in the adiabatic expansion of 〈T_μν〉$〈T_{\mu \nu }〉$ increases with s. This property was not apparent in previous results for spatially homogeneous backgrounds.