Thermal diffusion in binary mixtures containing molecular gases. III. The temperature dependence of αT

A recent expression for the thermal diffusion factor α_T for binary atom-molecule mixtures, which includes a full range of inelastic collisional contributions [McCourt, F. R. W., 2003, Molec. Phys., 101, 2181] has been utilized to calculate its temperature dependence for equimolar N₂-He, Ne, Ar mixtures and for an equimolar CO₂-Ar mixture. Accurate classical trajectory values for the effective cross-sections entering into the expression for α_T, obtained for the most reliable potential energy surfaces available, have been employed in the calculations. Good agreement has been attained with experiment for all four binary mixtures, including the decrease of α_T with increase in temperature observed for CO₂-Ar mixtures, heretofore considered to be anomalous.     

Thermal diffusion factors of hydrogenic trace mixtures with helium by column calibration factor

Using column calibration factor (CCF)F _s for a given column, the temperature dependence of experimental thermal diffusion factors α_T of hydrogenic trace mixtures in helium are accurately determined. This study, however, observes the inelastic collision effect in these trace mixtures when α_T by our CCF method are compared with those by the existing methods and theoretical ones respectively.     

Isotopic thermal diffusion factors of the noble gases

A new set of isotopic thermal diffusion factors for Ar, Kr and Xe is reported. The data have been obtained from thermal diffusion column measurements in a column previously calibrated with Ne gas, and complete the α_T data for the binary mixtures of noble gases given previously. The results lead to the conclusion that the thermal diffusion properties of the noble gases and their mixtures are well described by the law of corresponding states first proposed by Kestin, Ro and Wakeham. It is also concluded that the calibration technique used makes the thermal diffusion column a valuable instrument for the determination of the thermal diffusion factors of isotopic and non-isotopic dilute gas mixtures.     

Low-temperature x-ray diffraction studies of the crystallographic parameters and thermal expansion of (CH3)2NH2Al(SO4)2 · 6H2O crystals

The a, b, c, and β crystallographic parameters of the (CH₃)₂NH₂Al(SO₄)₂ · 6H₂O crystal (DMAAS) have been measured by x-ray diffraction in the 90–300-K temperature range. The thermal expansion coefficients along the principal crystallographic axes α_a, α_b, and α_c have been determined. It was shown that, as the temperature is increased, the parameter α decreases and b increases, whereas c decreases for T<T _c (where T _c is the transition temperature) and increases for T>T _c, so that one observes a minimum in the c=f(T) curve in the region of the phase transition (PT) temperature T _c ～ 152 K. The thermal expansion coefficients α_a, α_b, and α_c vary in a complicated manner with increasing temperature, more specifically, α_a and α_c assume negative values at low temperatures, and the α_a=f(T), α_b=f(T), and α_c=f(T) curves exhibit anomalies at the PT point. The crystal has been found to be substantially anisotropic in thermal expansion.     

Long-wavelength magnetic excitations in the Zn0.55Mn0.45Fe2O4 ferrite

The small-angle neutron scattering energy spectra of the Zn_0.55Mn_0.45Fe₂O₄ ferrite are analyzed at different temperatures (both below and above T _C ? 390 K) and scattering angles. The thermal expansion coefficient α(T) is measured in the temperature range 80–600 K. It is revealed that inelastic neutron scattering is governed not only by spin waves of the Holstein-Primakoff type but also by the substantial contribution of additional long-wavelength magnetic excitations. The physical nature of these low-energy magnetic excitations is discussed.     

Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/ poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D_T) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D_T is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D_T^0, = - 1.69×10^-7cm²(sK)^-1. The Soret coefficient S_T of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).     

Law of corresponding states and thermal-diffusion factor of Ne---Kr and Ar---Kr mixtures

New data of the thermal diffusion factor, α_T, for five Ne---Kr and four Ar---Kr mixtures in the low temperature range are given. It is shown that the dependence of α_T on the composition of these mixtures together with the thermodynamic and first-order transport properties of the noble gases can be interpreted consistently using the law of corresponding states proposed by Kestin, Ro and Wakeham. Moreover it is suggested that the thermal diffusion factor of these mixtures could also be interpreted by this law.     

Thermal diffusion in binary mixtures containing molecular gases II: mixtures of N2 with He,Ne, Ar,and Kr and of CO2 with He and Ar

Expressions developed for the thermal diffusion factor, αT, for binary mixtures containing molecular species have been tested for six different atom-molecule interactions. Specifically, the interactions between N₂ and He, Ne, Ar and Kr, plus the interactions between CO₂ and He, Ar, have been examined, in each case using at least two competing modern potential energy surfaces. Detailed expressions in both the ‘total-energy-flux’ and the ‘two-flux’ representations have been developed, and the importance of the anisotropic components of the intermolecular potential energy surfaces in determining the thermal diffusion factor for such mixtures has been determined.     

Transport properties of a binary mixture of CO2ben N2 from the pair potential energy functions based on a semi-empirical inversion method

The potential energy surface of a CO₂-N₂ mixture is determined by using an inversion method, together with a new collision integral correlation [J. Phys. Chem. Ref. Data 19 1179 (1990)]. With the new invert potential, the transport properties of CO₂-N₂ mixture are presented in a temperature range from 273.15 K to 3273.15 K at low density by employing the Chapman-Enskog scheme and the Wang Chang-Uhlenbeck-de Boer theory, consisting of a viscosity coefficient, a thermal conductivity coefficient, a binary diffusion coefficient, and a thermal diffusion factor. The accuracy of the predicted results is estimated to be 2% for viscosity, 5% for thermal conductivity, and 10% for binary diffusion coefficient.     

1H NMR study of the α phase of Mg2NiHx system

Hydrogen behavior in the α phase of Mg₂NiH_x system was studied by ¹H NMR. ¹H NMR spectra and spin-lattice relaxation times, T₁ and T_1ρ, of Mg₂NiH_0.22 were measured in the temperature range between 100 and 480 K. The drastic change in the linewidth is observed between 170 and 340 K, and ¹H rigid lattice is observed below 170 K, from which it is deduced that the hydrogen atoms are randomly distributed in α-Mg₂NiH_x. The relaxation mechanism for t₁ is the paramagnetic one, while the T_1ρ value is determined partially by hydrogen diffusion. The hydrogen diffusion rate has been determined from the linewidth and the T_1ρ value. The paramagnetic relaxations observed in T₁ and T_1ρ have been discussed relating to the hydrogen diffusion.     

Low temperature electrical conductivity and magnetoconductivity of Fe39Ni39Mo4Si6B12 and Co58Ni10Fe5Si11B16 metallic glass alloys

A detailed study on the weak localization phenomenon vis-a-vis electron-electron interaction effects in magnetic metallic glasses has been carried out. We measured the electrical conductivity and magnetoconductivity within the temperature range 1.8≤T≤300K. A maximum on the conductivity versus temperature curve exists atT=T _m. The conductivity was observed to follow aT ^1/2 law forT<T _m andT ² law forT>T _m. Magnetoconductivity data of these alloys indicate the prominence of electron-electron interaction at low temperatures. The authors have determined the inelastic scattering field and spin-orbit scattering field from the magnetoconductivity data. The inelastic scattering field obeys aT ^p law (p=2) at low temperatures.     

Concerning free volume quantities and the glass temperature

Free volume quantities proposed earlier by Boyer and Simha in connection with the glass transition are reformulated by taking into account the temperature dependence of the thermal expansivities α _l and α_g for the liquid and the glass, respectively. This necessitates an extrapolation of the liquid to temperatures below Tg which is performed by means of the reduced volume-temperature function established and given a theoretical foundation previously. For the glass, low temperature experimental data, encompassing all relaxations occuring below T_g, are required.

Two polymer series are examined in detail, namely, poly(methacrylates) and poly(vinyl) alkyl ethers, where α_g has been measured between at least 30°K and T_g. Results for poly(methylacrylate) and poly(styrene) are also given. The systematic decrease in the product (αl - αg) · T|_T=Tg with increasing length of the side chain noted previously is considerably reduced but not eliminated when the appropriately corrected expression is substituted instead. However, the free volume fraction related to the quantity αlT|_T=Tg remains more nearly invariant in the polymers analyzed.

An alternative treatment is discussed which considers an occupied volume expanding below T_g by a mechanism of thermal vibrations solely. Experimental and theoretical means of obtaining this quantity arc suggested.     

Heat capacity and lattice dynamics of yttrium diboride in the temperature range 5–300 K

This paper reports an experimental study of the heat capacity and crystal lattice parameters of a polycrystalline sample of yttrium diboride prepared by high-temperature synthesis from elements. The electronic and lattice contributions to the heat capacity are isolated. The temperature dependences of the characteristic temperature, the linear thermal expansion coefficients α_a(T) and α _c (T), the bulk thermal expansion coefficient β(T), and the Grüneisen coefficient are calculated. A region of negative values of α _c (T) and β(T) is revealed. Anharmonicity is found to exert only a minor effect on the YB₂ lattice dynamics over a larger part of the temperature range covered.     

Collision cross sections and swarm coefficients of water vapour ion clusters (H2O)nH+ with n = 1, 2 and 3 in N2, O2 and air

The ion swarm transport coefficients such as reduced mobility, diffusion coefficients and reaction rates of three water vapour ion clusters (H₂O) _n H⁺ (with n = 1, 2 and 3) in N₂ and O₂ have been determined from a Monte Carlo simulation using calculated and measured elastic and inelastic collision cross sections. The elastic momentum transfer cross sections have been determined from a semi-classical JWKB approximation based on a rigid core interaction potential model. The inelastic cross sections have been deduced from the measured ones in the case of similar ion cluster. Then, the cross sections sets are fitted using either the measured reduced mobility at low electric field in the case of (H₂O) _n H⁺ in N₂ or the zero-field mobility calculated from the Satoh's relation and the measured ones in N₂. From the sets of elastic and inelastic collision cross sections thus obtained in pure N₂ and O₂, the ion transport and reaction coefficients for (H₂O) _n H⁺ are then calculated in dry air and also extended over a wide range of reduced electric field in N₂ and O₂. These ion data are very useful for modelling and simulation of non-equilibrium electrical discharges more particularly in humid gases at atmospheric pressure.     

The thermal expansion of axial metals

The thermal expansion of axial metals is surveyed with particular reference to recent very low temperature data for zinc, cadmium, magnesium, β-tin, indium, bismuth and antimony. For a given solid, the independent thermal expansion coefficients α_⊥ and α_‖ are conveniently compared at low temperatures by plotting α_⊥/T ³ and α_‖/T ³ against T. The plots show clearly how contraction in one principal symmetry direction ensues from rapid expansion in the other direction. The Grüneisen functions γ_⊥ and γ_‖ are discussed for each solid using data from lattice-dynamical models and neutron-diffraction measurements. They show how features of the individual thermal expansions arise from a combination of vibrational, elastic and electronic effects. For these solids and for zirconium, titanium, yttrium and thallium the larger of γ_⊥ and γ_‖ at high temperatures is that referring to strains in the direction of the stronger forces (judged from the axial ratio). At lower temperatures the inequality reverses, except for tin, implying that the highest normal-mode frequencies depend most strongly on strain in the direction of the stronger forces. More experimental studies of thermal expansion at the lowest temperatures are desirable, as well as more second and third-order elastic constant data. Theoretical work is needed on realistic lattice models applicable to non-cubic metals.     

Phase relations for SrF2 TO 50 Kbars and 1900°C and its compression to 40Kbars at 25°C

The phase diagram of SrF₂ to 50 Kbars and 1900°C, obtained primarily by differential thermal analysis (d.t.a.), is presented. In analogy to the isostructural compound CaF₂, three solid phases, α, β, γ-SrF₂, as well as the liquid field, have been located. Thermochemical data (dT/dP, ΔV, ΔS) of the α-β and α-γ boundaries, and the melting curve are given. A tentative phase diagram for the isostructural compound BaF₂ is proposed. In addition, the first compression data for SrF₂ to 40 Kbars are reported. The bulk modulus, its pressure derivative, and the Grüneisen constant of SrF₂, CaF₂ and BaF₂ are compared.     

Restoration of kT factorization for low pT hadron hadroproduction

We discuss the applicability of the k _T factorization theorem to low-p _T hadron production in hadron–hadron collision in a simple toy model, which involves only scalar particles and gluons. It has been shown that the k _T factorization for high-p _T hadron hadroproduction is broken by soft gluons in the Glauber region, which are exchanged among a transverse-momentum-dependent (TMD) parton density and other subprocesses of the collision. We explain that the contour of a loop momentum can be deformed away from the Glauber region at low p _T , so the above residual infrared divergence is factorized by means of the standard eikonal approximation. The k _T factorization is then restored in the sense that a TMD parton density maintains its universality. Because the resultant Glauber factor is independent of hadron flavors, experimental constraints on its behavior are possible. The k _T factorization can also be restored for the transverse single-spin asymmetry in hadron–hadron collision at low p _T in a similar way, with the residual infrared divergence being factorized into the same Glauber factor.     

Law of corresponding states and thermal-diffusion factor of He-Ar mixtures from two-bulb measurements

Experimental data of the thermal diffusion factor for low density He-Ar mixtures are given. The measurement apparatus is a two-bulb operated at T_H = 308 K and T_C = 77.6 K, the mean temperature being T = 148 K. It is concluded that the extended law of corresponding states proposed by Kestin, Ro and Wakeham is able to predict in a correct way the obtained results.