Condensation of a chain polymer molecule

A new expression for the expansion coefficient of a flexible chain polymer molecule can be given in such a way that its first term corresponds to the case with only a hard-sphere repulsion and the other terms represent the effects of attraction between the segments. For low and high temperatures, more convenient expressions are used to find a possible condensation into a liquid-like condensed state from a gas-like state. It is found that in the condensed state, the square average end-to-end distance varies as N^?, where N is the number of segments and the exponent ? is around 0.6 in contrast to 1.2 for the high temperature case.     

Observations of glide and decomposition of a⟨101⟩ dislocations at high temperatures in Ni-Al single crystals deformed along the hard orientation

Ni-44 at.% Al and Ni-50 at.% Al single crystals were tested in compression in the hard d001 ¢orientation. The dislocation processes and deformation behaviour were studied as a function of temperature, strain and strain rate. A slip transition in NiAl occurs from a?111? slip to non-a?111? slip at intermediate temperatures. In Ni-50 at.% Al single crystals, only a?010? dislocations are observed above the slip transition temperature. In contrast, a a?101?{101} glide has been observed to control deformation beyond the slip transition temperature in Ni-44 at.% Al. a?101? dislocations are observed primarily along both ?111? directions in the glide plane. High-resolution transmission electron microscopy observations show that the core of the a?101? dislocations along these directions is decomposed into two a?010? dislocations, separated by a distance of approximately 2 nm. The temperature window of stability for these a?101? dislocations depends upon the strain rate. At a strain rate of 1.4 210^?4 s^?1, a?101? dislocations are observed between 800 and 1000 K. Complete decomposition of a?101? dislocations into a?010? dislocations occurs beyond 1000 K, leading to a?010? climb as the deformation mode at higher temperatures. At lower strain rates, decomposition of a?101? dislocations has been observed to occur along the edge orientation at temperatures below 1000 K. Embedded-atom method calculations and experimental results indicate that a?101? dislocations have a large Peierls stress at low temperatures. Based on the present microstructural observations and a survey of the literature with respect to vacancy content and diffusion in NiAl, a model is proposed for a?101?{101} glide in Ni-44 at.% Al, and for the observed yield strength versus temperature behaviour of Ni-Al alloys at intermediate and high temperatures.     

Dielectronic recombination of positive ions—II. Rate coeffecients for Mo38+

Dielectronic recombination rate coefficients for Mo³⁸⁺ recombining to Mo³⁷⁺ are given for electron temperatures of 1.4, 2.8, and 5.6 KeV. Non-relativistic results for various transitions were obtained in the resonance approximation by direct evaluation of Auger and radiative decay probabilities A_a and A_r, respectively, as discussed in the preceding paper. It is found that a large number of transitions contribute to the total rate. Tables of selected A_a, A_r, fluorescence yields, and rates are given. Excitation of n = 2 electrons to higher shells is found to be the dominant contribution at the temperature considered.     

Bianchi Type-IX Dust Filled Universe with Ideal Fluid Distribution in Creation Field

We have investigated Bianchi type-IX dust filled universe for ideal fluid distribution in creation field in which creation field is a function of time t only. To get deterministic cosmological model, we have assumed a supplementary condition a = b ⁿ , where a and b are metric potential and n is constant. Also, we have study the physical and geometrical parameters of the said cosmological model.     

Perturbation calculation of the distribution functions of mixtures of hard spheres

The distribution functions for a mixture of additive hard spheres of diameter σ_ii are calculated by means of an expansion in powers of σ _ij ⁿ - dⁿ , using an unperturbed single-component hard-sphere fluid of diameter d. Although the expansion converges only when the hard spheres in the mixture are nearly equal in size, it is useful because it is the only practical scheme available for obtaining the distribution functions of multicomponent hard-sphere mixtures.     

On exact equilibrium states in external gravitational fields of heated,self-gravitating gas clouds cooling by conducting and radiation

We present exact analytic solutions describing the equilibrium states available to a one-dimensional, self-gravitating cloud of gas subject to an external constant gravitational acceleration due to a plane of “stars”. The gas is taken to be heated at a rate proportional to the local gas density and is cooling by both radiation and conduction. The solutions are valid for a thermal conductivity which is an arbitrary function of gas temperature, T, and for radiative cooling which is proportional to the local gas density, ?, multiplied by an arbitrary function of gas pressure, ?. Illustrations of the general spatial dependence are given for the cases where the radiative cooling is proportional to ?²T, and in which the thermal conductivity is either constant, or proportional to T^a(a > 0) in the limits of T tending zero or infinity, respectively.We show that the phenomenon of density “inversion”, reported earlier, is indeed ameliorated by the radiative cooling term, as we had speculated it might be, but is not removed. This indicates that the phenomenon of density inversion is of rugged quality, persisting under a wide variety of conditions and, therefore, of general astrophysical import. We also show that, depending on the ratios of various parameters entering the problem, there is a new phenomenon possible in which the gas temperature has a local minimum at some non-central location so that a wedge of cool gas is in equilibrium surrounded by a hot medium.We have done these calculations as an aid to understanding the complicated behavior of interstellar gas clouds in particular, and the general physical interplay between force balance and energy balance in models of gas clouds more realistic than those heretofore available.     

Landau theory of the isotropic-nematic critical point

Landau theory is used to analyze the effect of an applied on nematics with positive dielectric (or diamagnetic) anisotropy. Analytic results are given for the phase boundary, stability limits, and location of the critical points in the field-temperature phase diagram. For biphenyl compounds having a dielectric anisotropy ?_a≈10, it is argued that the critical point should occur at E_c≈10² kV/cm, which is experimentally accessible.     

Phase structure and critical behavior of lattice Φ4 theory at different temperatures

The Variational-Cumulant Expansion method is applied to investigate the phase structure and the critical behavior of lattice ?⁴ theory at two different temperatures The phase diagrams, the external current J as a function of the expectation value of the field operator $«ngle ?i _L»ngle $ are calculated to the third order analytically. The critical behaviors of the expectation value $«ngle ?i _L»ngle $, the renormalized mass m_R and $m_R/«ngle ?i _L»ngle $ are given and compared with the mean-field scaling laws with logarithmic scaling corrections. It is shown that, at a fixed bare coupling, the broken phase at a lower temperature might be restored at a higher temperature and a bound on the Higgs-boson mass at definite temperature can exist.     

Thermodynamic perturbation theory for the (12-6-n) fluids

A perturbation method in which attractive forces are taken as perturbation of the repulsive (reference) forces is applied to calculate the thermodynamic properties of (12-6-n) fluids in terms of the properties of hard-sphere fluid. The numerical values of the thermodynamic properties (free energy per particle, compressibility and excess internal energy) for a range of temperature and density are given for (12-6-8) fluids. Further, two perturbation schemes are adopted to evaluate the total radial distribution function using the EXP version of the optimized cluster theory (OCT). The numerical results are reliable as reported at two states (T* = 1·036,ρ* = 0·65 andT* = 0·719ρ* = 0·85) for the (12-6-8) fluid and the Lennard-Jones (12-6) fluid as well.     

Isothermal reduction kinetics of nickel oxide using hydrogen: Conventional and Weibull kinetic analysis

The powder sample of nickel oxide was synthesized by sol-gel procedure. The isothermal reduction of nickel oxide using hydrogen was investigated by thermogravimetric analysis at five operating temperatures: 245, 255, 265, 275 and 300 °C. The kinetic triplet (E_a, A and f(α)) was determined using conventional and Weibull kinetic analysis. Both the kinetically procedures show that the reduction process considered can be explained with a two-step kinetic model. It is established that at lower temperatures (245 °C?T?255 °C), the reduction process considered is governed by two-parameter Šesták-Berggren autocatalytic model (first step) and at higher temperatures (T?265 °C), the reduction process is governed by Fn reaction model with different values of parameter n (second step). In this paper, the complex manner of dependence of the Weibull shape parameter (β) on temperature is established. With alterations of Weibull shape parameter from lower temperatures (β>1) to higher temperatures (β<1), it was concluded that isothermal reduction process of NiO using hydrogen can be described by a multistep reaction mechanism. These results are confirmed by the evaluated density distribution functions (ddf) of apparent activation energies (E_a), which show variations in basic characteristics at lower and higher operating temperature regions. Also, in this paper, it was shown that the shape parameter (β) of Weibull distribution function can represent the behaviour index, which indicates the kinetic pattern of the mechanism controlling the process studied.     

Courants critiques d'alliages supraconducteurs a concentration modulee spatialement II. — Effet de la temperature

The peak effect observed in the variation of the critical current as a function of the magnetic field H of periodically inhomogeneous films is observed only below a characteristic temperature T¹ given approximately by $\text{2ξ(T}{}^1\text{,}\text{C}\text{) = 2a}$ where 2a is the period of the modulation and C? the mean concentration. We describe the variation of the field values at peak J_c(H) as a function of temperature.     

The non-isotropic character of electric and dielectric properties of ammonium zinc chloride crystal

The dielectric constant, ε, and the d.c. conductivity, σ, were measured along the a-, b- and c-axes of (NH₄)₂ZnCl₄ (AZC) crystal in the 300-450 K temperature range. Crystals of AZC grown from aqueous solutions containing excess of ZnCl₂ were used. The value of the dielectric permittivity of AZC is extremely small compared to other ferroelectric crystals. Pronounced broad or step-like peaks at the phase transition temperatures were detected along the a- and b-axes, while ε along the c-axis is temperature independent up to the end of the measuring range. Reciprocal of the dielectric permittivity in the range of the commensurate to incommensurate phase transition obeys a relation similar to the Curie-Weiss law that is valid for second order ferroelectric/paraelectric phase transitions. The constants of the proposed relationship applied to the cooling run are given. The J-E characteristics along the three crystallographic axes were measured in the normal, incommensurate, commensurate and antiferroelectric phases. Hence, the type of conduction mechanism has been estimated. Parameters of Poole-Frenkel and Richardson-Schottky types of conduction mechanism have been determined. The effect of applied electric field on the conductivity measurement was also tested. Conductivity anomalies with different character were observed at the phase transition temperatures. The lnσ−1000/T dependence revealed thermal activation energy of conduction along the a-, b- and c-axes with different values in different phases of AZC.     

Dielectronic recombination of positive ions—III. Rate coefficients for Mo32+

Dielectronic recombination rate coefficients for Mo³²⁺ recombining to Mo³²⁺ are given for electron temperatures of 1.4, 2.8, and 5.6 keV. Nonrelativistic results in the resonance approximation were obtained and tables of selected Auger (A_a) and radiative (A_r) rates, fluorescence yields, and dielectronic recombination rates are given. Excitation of 2p electrons to higher shells is found to be dominant over other transitions including direct capture at the temperatures considered. The effect of the cascade transitions is estimated to be of the order of 30%. Different angular momentum averaging procedures change the results very significantly.     

Gell-Mann-Low function in the ϕ4 theory

An algorithm is proposed for the determination of the asymptotics of a sum of a perturbation series from the given values of its coefficients in the strong-coupling limit. When applied to the ?⁴ theory, the algorithm yields the β(g)∝g ^α behavior with α≈1 at large g for the Gell-Mann-Low function.     

Equilibrium vacancy concentration measurements on aluminum

Thermal expansion on high purity aluminum has been measured to study defects in thermal equilibrium by the (ΔL/L ₀?Δa/a ₀) method. Measurements of the changes in macroscopic length ΔL and lattice parameter Δa were made from room temperature to 637° C. Length changes were measured by a laser interferometer and lattice parameter changes by a X-ray diffractometer technique on the same crystal at identical temperatures. At temperatures above 400° C ΔL/L ₀ becomes greater than Δa/a ₀, indicating the generation of a noticeable amount of new lattice sites due to vacancy formation. Extrapolation gives a vacancy concentration ΔN/N ₀=9.8·10^?4 at the melting point (660° C). The experimental findings can be explained by assuming formation of monovacancies and divacancies. Values for the enthalpy and entropy of formation for mono- and divacancies are given.     

Coagulation equations with gelation

Smoluchowski's equation for rapid coagulation is used to describe the kinetics of gelation, in which the coagulation kernelK _ij models the bonding mechanism. For different classes of kernels we derive criteria for the occurrence of gelation, and obtain critical exponents in the pre- and postgelation stage in terms of the model parameters; we calculate bounds on the time of gelationt _c , and give an exact postgelation solution for the modelK _ij =(ij ^ω ) (ω>1/2) andK _ij =a ^i+j (a>1). For the modelK _ij =i ^ω +j ^ω (ω<1, without gelation) initial solutions are given. It is argued that the kernelK _ij ～ij ^ω with ω?1?1/d (d is dimensionality) effectively models the sol-gel transformation in polymerizing systems and approximately accounts for the effects of cross-linking and steric hindrance neglected in the classical theory of Flory and Stockmayer (Ω=1). For allΩ the exponents,t=Ω+3/2 andσ=Ω?1/2,γ=(3/2?Ω)/(Ω ? 1/2) andΒ=1, characterize the size distribution, at and slightly below the gel point, under the assumption that scaling is valid.     

Electron paramagnetic resonance and relaxation of amorphous silicon below 1 K

Amorphous silicon, generated within crystalline Si by ²⁸Si⁺ ion implantation, exhibits an electron spin relaxation rate which varies with temperature as T^2.37 between 0.3 and 4.2 K. These results exclude the current model of a phonon-limited, direct relaxation mechanism in a-Si. A relaxation process, consistent with the known temperature variation, is outlined. EPR signal strengths, relative to a known paramagnet at temperatures near 1.2 and 0.4 K, put limits on an antiferromagnetic Curie-Weiss temperature of 0?θ?0.06 K.     

Analytic solution of Percus-Yevick equation for fluid of hard spheres

A new method of analytic solution of the Percus-Yevick equation for the radial distribution functiong(r) of hard-sphere fluid is proposed. The original non-linear integral equation is reduced to non-homogeneous linear integral equation of Volterra's type of the second order. The kernel of this new equation has a polynomial form which allows to find analytic expression forg(r) itself without using the Laplace transformation. In addition, the first three moments of the total correlation function can be found.     

Effect of dose on irradiation-induced loop density and Burgers vector in ion-irradiated ferritic/martensitic steel HT9

Samples of F/M steel HT9 were irradiated to 20?dpa at 420°C, 440°C and 470°C in a transmission electron microscope with 1?MeV Kr ions so that the microstructure evolution could be followed in situ and characterised as a function of dose. Dynamic observations of irradiation-induced defect formation and evolution were made at the different temperatures. Irradiation-induced loops were characterised in terms of their Burgers vector, size and density as a function of dose and similar observations and trends were found at the three temperatures: (i) both a/2 <111> and a <100> loops are observed; (ii) in the early stage of irradiation, the density of irradiation-induced loops increases with dose (0–4?dpa) and then decreases at higher doses (above 4?dpa), (iii) the dislocation line density shows an inverse trend to the loop density with increasing dose: in the early stages of irradiation, the pre-existing dislocation lines are lost by climb to the surfaces while at higher doses (above 4?dpa), the build-up of new dislocation networks is observed along with the loss of the radiation-induced dislocation loops to dislocation networks; (iv) at higher doses, the decrease of number of loops affects more the a/2 <111> loop population; the possible loss mechanisms of the a/2 <111> loops are discussed. Also, the ratio of a <100> to a/2 <111> loops is found to be similar to cases of bulk irradiation of the same alloy using 5?MeV Fe²⁺ ions to similar doses of 20?dpa at similar temperatures.