Asymptotic Behavior of the t Expansion

The asymptotic behavior of a system's ground-state energy from the t expansion of Horn and Weinstein has been suggested to have the form E ₁(t)=E ₁+exp(–a _n t+b _n ). In the limit of very large t, this becomes E ₁(t)=E ₁+exp(–a ₁ t+b ₁). A simple analysis shows that the parameters are a ₁=E ₂–E ₁ and b ₁=ln[(E ₂–E ₁)|c ₂|²/|c ₁|²]. Functions are introduced which allow determination of a ₁, b ₁ and lower bounds to E ₁.     

Product analysis and mechanism of toluene degradation by low temperature plasma with single dielectric barrier discharge

A single dielectric barrier discharge (DBD) low-temperature plasma reactor was set up, and toluene was selected as the representative substance for volatile organic compounds (VOCs), to study the reaction products and degradation mechanism of VOCs degradation by low-temperature plasma. Different parameters effect on the concentration of O₃ and NO_x during the degradation of toluene were studied. The exhaust in the process of toluene degradation was continuously detected and analyzed, and the degradation mechanism of toluene was explored. The results showed that the concentration of O₃ increased with the increase of the power density and discharge voltage of the plasma device. However, as the initial concentration of toluene increased, the concentration of O₃ basically keep steady. The concentration of NO_x in the by-products increased with the discharge voltage, power density, and initial concentration of toluene in the plasma device, and the concentration of NO₂ was much higher than the concentration of NO. The degradation process of toluene was detected and analyzed. The results showed that the degradation mechanism of toluene by plasma includes high energy electron bombardment reaction, active radical reaction and ion molecule reaction. Among them, the effect of high-energy electrons on toluene degradation is the largest, followed by the effect of free radicals, in which oxygen radicals participated in the reaction mainly through the formation of C–O bond, CO bond, (CO)–O– bond and –OH radical, while nitrogen radicals participate in the reaction mainly through the formation of C–NH₂, (CNH)- bond, CN bond and C–NO₂ bond. The results can provide some data supports for the study of low-temperature plasma degradation of VOCs.     

Synthesis of PbTiO3 ceramics using mechanical alloying and solid state sintering

The pressure-less sintering behavior of PbTiO₃ powders synthesized by mechanical alloying TiO₂ and PbO was investigated using dilatometry and Rietveld refinements of X-ray diffraction patterns. As-synthesized, the powders are nanocrystalline with a mean particle size of 20 nm. Pressure-less sintering in the range 500-1050°C gives single phase ceramics with densities of 85-90% and crystallite sizes in the range 80-400 nm. Cracking due to the paraelectric-ferroelectric phase transition was not observed in samples sintered below 700°C due to the small crystallite size whereas macroscopic cracks formed in samples sintered above 700°C. Rietveld analysis indicates the formation of Pb vacancies in samples sintered and held for 24 h at intermediate temperatures (600-1000°C) which gives some insight into the mechanism of Pb loss and second phase formation in this system.     

Phase transitions in ternary caesium lead bromide

Phase transitions in ternary caesium lead bromide (CsPbBr₃) were studied by means of DSC, TMA and high temperature X-ray diffraction. The samples were prepared from the solution by water evaporation and from the melt. on the DSC curves as well as on the temperature dependence of the lattice constants of CsPbBr₃ only two effects were found belonging to the earlier published phase transitions at 88 and 130°C and no further effects. Linear thermal expansion coefficient α of individual CsPbBr₃ modifications were calculated from both TMA and high temperature X-ray diffraction. The structural parameters of the room temperature orthorhombic phase were refined and the results are presented. CsPbBr₃ prepared from the solution contained about 10% of CsPb₂Br₅ and so the DSC curve of pure CsPb₂Br₅ was also measured and an effect at a temperature of 68.5°C was found. This revised version was published online in July 2006 with corrections to the Cover Date.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Field-theoretic approach to second-order phase transitions in two- and three-dimensional systems

We review the physical principles which are at the basis of recent field-theoretic computations of the critical exponents in two- and three-dimensional systems. We concentrate on those points that do not show up explicitly in the more standard-expansion: they must be discussed with care if one uses a perturbative approach at fixed space dimensions (the loop expansion). We present in detail simple computations of the critical exponents, while we summarize the results of longer and more accurate computations.     

Position-space renormalization for systems with weak long-range interactions and the breakdown of hyperscaling

Exact renormalization group equations are derived for a position-space renormalization of spin systems with weak long-range forces. It is shown how an apparent dependence of the critical exponents on the choice of the renormalization group can be resolved via the mechanism of dangerous irrelevant variables and that this same mechanism is responsible for the breakdown of hyperscaling. The dimensiond=4 can be seen to be a borderline dimension above which classical critical exponents are expected.     

OUH体系的结构和分析势能函数

采用密度泛涵B3LYP方法优化出了OUH分子的各种结构，确定了最稳定构型和离解能，以及它们的谐性力常数，并导出双原子分子UH,UO的Murrell-Sorbie势能函数及其光谱数据。采用多体项展式方法，导出OUH(X^4A')基态分子的分析势能函数，获得OUH(X^4A')体系的势能面，考察了这个势能函数的基本性质，正确地复现出OUH分子的平衡结构特征，结果表明：U+OH,O+UH,H+UO的反应均为无阈能的放热能反应。为进一步探讨OUH体系的反应动力学过程打下了基础。     

Structure and Phase Transitions of SnP2O7

SnP₂O₇ is a member of the ZrP₂O₇ family of materials, several of which show unusual thermal expansion behavior over certain temperature ranges and which show a number of displacive phase transitions on cooling from high temperature. Here we describe the structural properties of SnP₂O₇ from 100 to 1243 K as determined by X-ray and neutron powder diffraction. These studies reveal that SnP₂O₇ shows two phase transitions in this temperature range. At room temperature the material has a pseudo-cubic 3×3×3× superstructure. Electron diffraction studies show that the symmetry of this structure is P2₁3 or lower. On warming to ∼560 K it undergoes a phase transition to a structure in which the subcell reflections show a triclinic distortion; above 830 K the subcell reflections show a rhombohedral distortion. Significant hysteresis in cell parameters is observed between heating and cooling. The structure of SnP₂O₇ is discussed with references to other members of the AM₂O₇ family of materials.     

V(Ⅴ)促进SO_4~(2-)/ZrO_2固体超强酸的制备及催化反应

用低温陈化的方法制得V(Ⅴ)促进型SO42-/ZrO2固体超强酸(SZV),用流动指示剂法测定其酸强度,用IR,XRD和XPS进行结构表征,并将制得的催化剂用于催化乙酸和丙三醇的酯化反应.结果表明,低温陈化样品比常温陈化有更强的酸性和更高的催化活性,IR谱图中S O键的伸缩振动峰显著增强,在600~650℃的焙烧温度下,低温陈化样品的晶体结构为ZrO2四方相,XPS图中Zr3d峰位出现较大的化学位移,表明低温陈化使SZV样品具有较高的酸性.