An analytical equation of state for mercury

This paper presents a procedure for predicting the equation of state of mercury, by including mercury in the scope of a new statistical mechanical equation of state that is known for normal fluids. The scaling constants are the latent heat of vaporization and the density at the melting temperature, which are related to the cohesive energy density. Since experimental data for the second virial coefficient of mercury are scarce, a corresponding-states correlation of normal fluids is used to calculate theB(T) of mercury. The free parameter of the ISM equation, λ, compensates for the uncertainties inB(T). Also, we can predict the values of two temperature-dependent parameters, α(T) andb(T), with satisfactory accuracy from a knowledge of ΔH _vap andp _m, without knowing any details of the intermolecular potentials. While the values ofB(T) are scarce for mercury and the vapor pressure of this metal at low temperatures is very small, an equation of state for mercury from two scaling parameters (ΔH _vap,p _m) predicts the density of Hg from the melting point up to 100° above the boiling temperature to within 5%.     

Initial sintering stage of thoria powder investigated by emanation thermal analysis

The initial stage of free sintering of thoria (ThO₂) has been investigated by means of emanation thermal analysis. Thoria powder (having surface area of 18 m² g^–1) was prepared from thorium oxalate (homogeneously labelled by²²⁸Th) by heating to 500 ° C. The release of²²⁰Rn was studied at various temperatures. The curves of radon diffusion release measured during isothermal heating of thoria powder at four temperatures (705, 735, 780 and 825 ° C) have been used for investigating the kinetics of the surface changes of thoria powder during the initial stage of sintering. The experimental data evaluated obey the kinetic law E _p S _eff = const ×t ⁿ , whereE _p is the emanating power due to the diffusion of radon in intergranular space and open pores,S _eff is the effective surface area,t is time andn equals 0.64. The effective surface areaS _eff has been proposed as a new parameter characterizing the active surface of powdered solid and its changes during sintering.     

Similarity analysis of axisymmetric free convection on a horizontal infinite plate subjected to a mixed thermal boundary condition

Summary Similarity analysis of the problem of axisymmetric free convection on a horizontal infinite plate is considered assuming that the plate is subjected to a mixed thermal boundary condition. It is shown that the thermal boundary condition is characterized by a nonnegative parameterm and the two cases ofm=0 andm=1 correspond to prescribed plate temperature and prescribed surface heat flux respectively. If one has to compute the heat transfer coefficient for various values ofm, there is no need to solve the boundary value problem everytime; it is enough to solve a certain polynomial equation provided the solution is known for any particular value ofm.Notation a ₀(r),a ₁(r),a ₂(r) coefficients in Eq. (1) - A transition parameter used in Eq. (22) - C function ofr defined in Eq. (8.1) - f dimensionless stream function - F dimensionless pressure - g acceleration due to gravity - G function ofr defined in Eq. (8.2) - m mixed thermal boundary condition parameter - N normalized heat transfer coefficient in Eq. (26) - Nu _r Nusselt number - p fluid pressure - p _e ambient pressure - P normalized pressure drop at the plate - Pr Prandtl number - r radial coordinate - S normalized stress at the plate - T temperature - T _e ambient temperature - u velocity in the radial direction - w velocity in the axial direction - z axial coordinate - coefficient of thermal expansion - dimensionless similarity variable - dimensionless temperature - exponent inC - kinematic viscosity - ambient fluid density - stream function     

Kinetics of non-isothermal crystallization process and activation energy for crystal growth in amorphous materials

An equation expressing the volume fraction,x, of crystals precipitating in a glass heated at a constant rate, α, was derived. When crystal particles grow m-dimensionally,x is expressed as In [- ln(1 -x)] = -n (nα - 1.052mE/RT + Constant whereE is the activation energy for crystal growth andn is a numerical factor depending on the nucleation process. When the nuclei formed during the heating at the constant rate,α, are dominant,n is equal tom + 1, and when the nuclei formed in the previous heat-treatment before thermal analysis run are dominant,n is equal tom. The validity and usefulness of this equation was ascertained by applying it to a Li₂O·2SiO₂ glass. A method for determining the values ofn andm from DSC curves was proposed and it was concluded that the modified Ozawa-type plot is very useful and convenient to obtain the activation energy for crystal growth.     

Open pore description of mechanical properties of ceramics

A dependence of Young's modulus of elasticity on open porosity in ceramics is derived from an open-porosity model, which in the literature, is applied to salinity conductivity and fluid permeability in rocks. A random distribution of grain and pore size is assumed. The relation developed,E(p)=E _o(1–"p)^m, whereE is the modulus of elasticity of the porous ceramic,E _o is the theoretical elastic modulus,p is the porosity andm is an exponent dependent on the tortuosity of the structure of the ceramic, adequately describes the dependence of the modulus of elasticity on porosity. The model is applied to the experimental data from several ceramics such as alumina, silicon nitride, silicon carbide, uranium oxide, rare-earth oxides, and YBa₂Cu₃O_7– superconductor, and the value ofm is obtained for each case. We have shown thatm has a value of nearly 2 for sintered ceramics, unless sintering aids or hot pressing have been used during fabrication of the ceramic. Such additional procedures approximately double the magnitude ofm. On joint appointment with: Materials Laboratory, Physics Department, University of the West Indies, Mona, Kingston 7, Jamaica,     

Decomposition of algebras overF q (X 1,...,X m )

LetA be a finite dimensional associative algebra over the fieldF whereF is a finite (algebraic) extension of the function fieldF _q(X ₁,...,X _m). Here F_q denotes the finite field ofq elements (q=p^l for a primep). We address the problem of computing the Jacobson radical Rad (A) ofA and the problem of computing the minimal ideals of the radical-free part (Wedderburn decomposition). The algebraA is given by structure constants overF andF is given by structure constants overF _q(X ₁,...,X _m). We give algorithms to find these structural components ofA. Our methods run in polynomial time ifm is constant, in particular in the casem=1. The radical algorithm is deterministic. Our method for computing the Wedderburn decomposition ofA uses randomization (for factoring univariate polynomials overF _q).Research partially supported by Hungarian National Foundation for Scientific Research (OTKA), Grants 2581, F4116 and EC Cooperative Action IC 1000 (ALTEC).     

Fermi surface changes and electron scattering anisotropy in the potassium-rubidium alloy system

The de Haas-van Alphen effect has been used to study the changes in Fermi surface (FS) dimensions and the electron scattering in dilute K(Rb) and Rb(K) alloys. Small discrepancies, around 10%, have been found between the observed FS cross-section changes and those calculated from a linear interpolation of the lattice constant between the two host values, the cross-section changing more rapidly than expected in each case: these discrepancies appear to reflect rather accurately a real nonlinearity in the lattice constant change with solute concentration. There are also measurable changes in the FS anisotropy, which are described well by a combination ofs andp phase shifts in K(Rb) and bys andd in Rb(K). The electron scattering has a significant forward-scattering component, the ratiox _ρ/x ₀ between the resistivity temperature and the average Dingle temperature being 0.63 and 0.59 for K(Rb) and Rb(K), respectively. The scattering rate anisotropy in Rb(K) is about 7%, with the maximum rate at 〈110〉: this can be fitted rather well by a combination ofs andp phase shifts.     

The analysis and synthesis of probability transformers

Summary A logical network withn inputs andm outputs ((n, m)-network) supplied by a binary random vector may be considered as a device transforming the input probability distribution into the output one. In this paper a method of analysis of such a network is presented. The approach is based on the orthogonal expansions of the logical functions and the corresponding distributions into the Walsh-Rademacher series. On the basis of the results obtained the synthesis problem has been formulated in terms of the spectral approach.     

Helium adsorption on exfoliated graphite

High precision adsorption isotherms of³He and⁴He on bare Grafoil and on Grafoil coated with a monolayer of argon have been measured in the temperature range 4–20 K, using a high resolution, pressure-sensitive capacitance gauge located at 4.2 K close to the sample chamber. This gauge obviated thermomolecular pressure effects and corrections. The isotherms yielded the following resultant data: The monolayer coverage V_m for⁴He on bare Grafoil was 0.42 cm³ (STP)/m² and for³He on bare Grafoil was 0.395 cm³ (STP)/m²: the isosteric heat of adsorptionQ _st/R of the second layer of³He on bare Grafoil was 23.5 K andQ _st/R for³He on argon-coated Grafoil for the first layers was 47.5 K. Also, the data for³He and⁴He on bare Grafoil at and just aboveV _m have been used by Novaco (see subsequent paper) for determination of the virial coefficients of the gas phase occuring in the early formation of the second layer.     

Kinetic study of selenium used as optical data storage and holographic recording materials

A kinetic study has been performed on selenium for isothermal and continuous heating processes. The activation energy (E _a) and Avrami exponent (n) have been evaluated in the range 414 to 449 K for the isothermal process and at a heating rate of 5 to 40 K min^–1 for continuous heating. A new iterative calculation to give exact values ofE _a andn for a continuous heating process is also presented.     

Thermophysical properties of quinoline as a function of temperature (303–503 K) and pressure (0.1–400 MPa)

Measured and derived thermophysical properties of quinoline are reported for pressures up to 400 MPa at temperatures from 303 to 503 K. The specific volume at 353 K was determined from the specific volume at atmospheric pressure measured b) pycnometry and from isothermal compressibilities measured as a function of pressure up to 400 M Pa. Specific volumes, isothermal compressibilities, thermal coellicients of pressure, and isobaric and isochoric heat capacities at pressures up to 4011 MPa are derived at several temperatures. The effects of pressure on the isobaric heat capacity of quinoline, a weakly self-associated liquid. are discussed and compared with the pressure effects on heat capacities ofn-hexane andm-cresol.     

A branch & bound method for the general-shop problem with sequence dependent setup-times

A branch & bound algorithm is presented for a very general scheduling problem withn jobs andm machines. Each job consists of a set of operations. Each operation has to be processed on a dedicated machine. There may be arbitrary precedence relations between the operations. The set of all operations is partitioned into groups. If on a machine an operation belonging to groupG _g is processed immediately after an operation belonging to groupG _f there is a setup ofs _fg time units. We assume thats _fg=0 iff=g and that thes _fg satisfy the triangle inequality. Computational results for this general problem as well as for special cases like the job-shop problem and the open-shop problem are reported.Supported by the Deutsche Forschungsgemeinschaft (Project JoPTAG) and by INTAS (Project 93–257)     

Nuclear magnetic resonance studies of isotopic impurity tunneling in solid hcp4He

Nuclear magnetic relaxation studies of isotopically impure solid⁴He have been made in the temperature-independent region of the relaxation spectrum, below 0.7 K. The Torrey theory for nuclear relaxation has been applied to measurements ofT ₁ andT ₂ to calculate the characteristic fluctuation time of the³He atoms due to the zero-point motion of³He and⁴He atoms. The fluctuation rates have been determined as a function of molar volume and Larmor frequency in samples where the mole fractions of³He in the gaseous mixtures used to form the solids were 0.02, 0.01, 0.005, and 0.002. The volume dependence of the fluctuation rate has been found to be far greater than that of the exchange rate of a³He-³He pair.T ₁ has been found to vary as ₀ ² , and bothT ₁ andT ₂ increased as the concentration decreased, in agreement with the Torrey theory. Preliminary investigations of the solid isotopic phase separation have also been carried out.Research supported in part by the National Science Foundation through Grant No. GP-29682 and the Advanced Research Projects Agency through the Materials Science Center at Cornell University, MSC Report # 1675.     

Transform domain characterization of cyclic codes overZ m

Cyclic codes with symbols from a residue class integer ringZ _m are characterized in terms of the discrete Fourier transform (DFT) of codewords defined over an appropriate extension ring ofZ _m . It is shown that a cyclic code of length n overZ _m ,n relatively prime tom, consists ofn-tuples overZ _m having a specified set of DFT coefficients from the elements of an ideal of a subring of the extension ring. Whenm is equal to a product of distinct primes every cyclic code overZ _m has an idempotent generator and it is shown that the idempotent generators can be easily identified in the transform domain. The dual code pairs overZ _m are characterized in the transform domain for cyclic codes. Necessary and sufficient conditions for the existence of self-dual codes overZ _m are obtained and nonexistence of self-dual codes for certain values ofm is proved.     

Low temperature preparation ofβ-alumina by an alkoxide route

β-alumina has been prepared by the thermal decomposition of a mixture of sodium and aluminium isopropoxides followed by heating up to 1000°C. It has been found necessary to use sodium isopropoxide in excess (25–30%) for the complete formation ofβ-alumina at 1000°C. On the other hand one obtains a mixture ofβ-alumina andα-alumina when the starting materials are taken in the stoichiometric ratio Na₂O:11Al₂O₃. DTA, TG and DTG studies of a mixture of sodium and aluminium isopropoxide showedβ-alumina formation at 1000°C. NCL Communication No. 4446.     

Bayesian approach to parameter estimation of the generalized pareto distribution

Several methods have been used for estimating the parameters of the generalized Pareto distribution (GPD), namely maximum likelihood (ML), the method of moments (MOM) and the probability-weighted moments (PWM). It is known that for these estimators to exist, certain constraints have to be imposed on the range of the shape parameter,k, of the GPD. For instance, PWM and ML estimators only exist fork>−0.5 andk≤1, respectively. Moreover, and particularly for small sample sizes, the most efficient method to apply in any practical situation highly depends on a previous knowledge of the most likely values ofk. This clearly suggests the use of Bayesian techniques as a way of using prior information onk. In the present work, we address the issue of estimating the parameters of the GPD from a Bayesian point of view. The proposed approach is compared via a simulation study with ML, PWM and also with the elemental percentile method (EPM) which was developed by Castillo and Hadi (1997). The estimation procedure is then applied to two real data sets.     

Superfluid Phase Transition of 3He-4He Mixture Films Adsorbed on Alumina Powder

The superfluid phase transition of ³ He- ⁴ He mixture films adsorbed on 500 Å alumina powder has been studied for mixture films whose superfluid thickness is less than a monolayer. The transitions are found to be controlled by the Kosterlitz-Thouless critical line, but a strong broadening of the transition is observed as the ³ He concentration is increased. Analyzing the broadening in terms of a KT vortex-pair theory modified for the the finite powder size yields a vortex core parameter which increases nearly linearly with added ³ He. Also observed in these measurements is a temperature-dependent and ³ He-dependent depletion of the superfluid density at low temperatures, which is thought to arise from the high-frequency ripplon/third sound excitations of the film.     

New formula for lattice dimension of an oxide spinel with cubic structure

An empirical relation between lattice parameter and cationic radii for cubic spinels has been established by considering the packing of anions in non-ideal situation and ionic displacement parameter (δ =u−3/8). This relation gives the value ofa, the lattice parameter, which is much closer to the observed value.     

Material and geometry effects on crack shape in double torsion testing

Previous work has established a model for expressing the curved crack front shape observed in a Double Torsion test in a single parameter, the shape factorS. This paper demonstrates the ability of this model to account for crack shape effects on measured toughness against crack speed data, using a direct measurement ofS, in tests on polymethyl methyacrylate (PMMA) of various molecular weights. The analysis is then extended to enableS to be predicted without reference to the material crack front size parameter referred to in earlier work: only specimen geometry significantly influences the crack front shape in a wide variety of materials.     

Concentration dependence of the anomalous thermoelectric power of dilute magnetic alloys

It has been pointed out recently by one of us (M.S.R.C.) that the variation of the Kondo slopesd (of the /c vs. lnT curves) of dilute magnetic alloys containing a finite solute concentrationc bears a close resemblance to the variation of the functionf (=cos⁶ cos2) with the phase shift for ordinary spin-independent scattering. Sinced is itself primarily determined byf the inference is that is a function ofc when the criterion of infinite dilution is violated. For infinite dilutions theory expects the anomalous thermoelectric power in such alloys to be independent ofc as well as ofT. Taking the experimentally observed extremum in the TEP (S _m) as an approximation to such a TEP, we report, for finite solute concentrations, the variation ofS _m withc, to correspond with the variation off(=cos ⁶ sin2) with . This substantiates the above inference. In fact, one can predict the sign and the variation (withc) ofd, knowing that ofS _m, and vice versa, for a given dilute magnetic alloy system.