Diffusion Monte Carlo Study of the Small Mixed 3He-4He Clusters

The ground state properties of helium mixed clusters ³He_2,3,4 ⁴He₂, ³He_2,3,4 ⁴He₃, ³He_2,3,4 ⁴He₄, ³He_2,3 ⁴He₅, consisting of up to eight helium atoms are studied using variational and diffusion Monte Carlo calculations. For clusters with three and four ³He atoms released-node diffusion Monte Carlo method is used. Our calculations show that, within errorbars, clusters ³He_3,4 ⁴He₂ have the same binding energy as the cluster ³He₂ ⁴He₂, and that ³He₃ ⁴He₃ has the same binding energy as ³He₂ ⁴He₃. The clusters ³He_3,4 ⁴He₂ and ³He₃ ⁴He₃ are in states in which one or two ³He atoms are far away from the rest of the system. Other considered clusters are bound. In particular, we have shown the stability of the cluster ³He₄ ⁴He₃, which was previously considered unstable. The calculations are performed using several different interatomic potentials and the conclusions concerning stability are insensitive to the particular form of the interaction potential. We compare our results with the recent experiment and other theoretical calculations.     

Rough model of a quantum liquid

As applied to condensed helium and hydrogen, a theory of quantum effects is suggested, one that is insensitive to the type of statistics of particles—the theory of quantum nondegenerate liquids. Evidently such a theory assumes that the mass of the atom and its polarization are small. For a zero-approximation, a system of hard spheres is chosen, and the attractive forces and the softness of the atom are considered to be small effects. The correlations between thermodynamic and kinetic characteristics of liquid He³ and He⁴ are obtained. On the basis of the experimental data for He⁴, and an isotropic law of the corresponding states for quantum systems with a large value of the de Boer parameter, all thermodynamic functions of liquid He³ are defined and tabulated in the regions of temperatures and molar volumes where they have not yet been measured. A rough model of a quantum liquid is suggested, based on the assumption of a dominating contribution by the diffusion excitations to the free energy of a dense condensed medium. The equation of state of the quantum liquid is derived. On the basis of the experimental data for He⁴, the equation of state of a quantum liquid consisting of hard spheres is compared with the similar equations obtained by a numeric computer simulation. The energy of the ground state of spin-oriented condensed hydrogen isotopes is defined.     

A technique for calibrating carbon resistor thermometers below 2 K

The usual method of calibrating carbon resistor thermometers against the vapour pressure of He³ and He⁴ is often inconvenient due to the nature of the experimental apparatus. Culbert and Sungaila have proposed a heat capacity technique in which the resistance-temperature relation is deduced by comparing the calculated internal energy-temperature function of a known sample to the measured internal-resistance function for the same sample. An improvement on their method utilizing holmium metal as a thermometric device is presented. The advantages, disadvantages, and reliability of this technique are discussed and a new carbon resistor thermometry equation of the form R = A + B/T + C/T² is proposed.     

Low-temperature heat capacity of helium films adsorbed on copper

Heat capacity measurements are described for films of pure⁴ He and a 12%He ³ mixture ofHe ³ andHe ⁴He adsorbed on copper, for 0.1<T<1.2 K.He ⁴ heat capacity isotherms show a step-type behavior as a function of coverage for the first two layers, while the mixture isotherms only show the first step. A comparison is made with recent multilayer data for helium films on Vycor published by other authors.Work supported by the National Science Foundation.     

Absorption Spectrum of Na Atoms Attached to Helium Nanodroplets

We present an analysis of the electronic 3p←3s excitation of Na atoms attached to ³He and ⁴He droplets. Once the ground state structure of the doped drops has been obtained within finite-range density functional theory, we determine the time-correlation function of the Na atom evolving in the full three-dimensional ²Π_1/2, ²Π_3/2 and ²Σ_1/2 potentials generated by its pairwise interaction with the helium atoms. The Fourier analysis of the time-correlation function determines the absorption spectrum of Na, which is compared with the experimental spectrum. We show that the existence of a redshifted shoulder in the absorption line of Na@⁴He _N , absent in Na@³He _N , is due to the wider vibrational motion of the dopant atom in the dimple it causes on the surface of the droplet.     

Adsorption of 4He N and 4He N 3He Clusters on Cesium

The ground-state properties of helium clusters ⁴He _N and ⁴He _N ³He, for N≤ 40, adsorbed on the surface of cesium are studied using variational and diffusion Monte Carlo calculations. Binding properties are determined using two different Cs–He interaction potentials. For the smallest clusters, self-binding on a Cs surface is stronger than in two or three dimensions. For N > 10 self-binding in three dimensions is stronger than on Cs for both types of Cs–He interaction potential considered. The obtained binding energies and structure are compared to results of recent density functional calculations. The emergence of edge states of ³He atom, localized along the contact line of ⁴He cluster with a cesium surface, is studied. First indication that ³He atom prefers to be close to the contact line appears already for the ⁴He₃ ³He cluster.     

A high-pressure mass spectrometric study of ion-molecule reactions in a mixture of CF4 and He

Gas phase ion-molecule reactions of positive He⁺ ions produced from helium with neutral carbon tetrafluoride have been studied. The measurements were made with a quadrupole mass spectrometer with a high-pressure ion source. The fractional abundance I_i/∑I_i of dominant ions CF₃⁺, CF₂⁺ and helium ions has been determined as a function of the (1% CF₄ and 99% He) gas mixture pressure (in the range 1.33-31.92 Pa) and of the repeller electrode potential (ranging from 3 to 10 V).     

Thermodynamic derivatives in3He-4He mixtures in the critical region of the superfluid transition

By assuming a phenomenological Ginzburg-Landau-Wilson free energy for³He-⁴He mixtures near the critical surface of the superfluid transition we can express thermodynamic derivatives of the form (?a/?b) _c,d in terms of a correlation function of ¦ψ¦², where Gy is the order parameter. Herea, b, c, and d are any four of the quantities entropys, number densityn, molar concentrationX, temperatureT, pressurep, and chemical potential difference Δ=μ₃?μ₄. Relationships among these thermodynamic derivatives are those of the Pippard-Buckingham-Fairbank approximation in the³He-⁴He case. Some combinations of the coefficients in the free energy are equal to derivatives on the critical surface and remain invariant with respect to renormalization group transformations. A general scheme is also developed to give correlation function expressions for thermodynamic derivatives.     

Critical curves in mixtures of carbon dioxide with ethane and ethylene based on a generalized fluctuation form of the van der waals equation of state

Critical curves of CO₂-C₂H₄ and CO₂-C₂H₄ mixtures are investigated using a new fluctuation equation of state. Particular attention is paid to the behavior of thermodynamic sensitives in the vicinity of the critical azeotropic points, at which the derivative of the molar volume with respect to the composition, which has no special features in the vicinity of the critical points of the pure components, becomes zero. Reliable agreement between the results of describing the critical curves of the mixtures and the known (including volumetric measurements) experiment is obtained. Possible intensification of supercritical extraction in using the CO₂-C₂H₆ mixture in the vicinity of the azeotropic point is predicted. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 73, No. 2, pp. 407–413, March–April, 2000.     

Deuterium and helium ion irradiation effects on TiB2 coatings

The surface damage and erosion of chemically vapor deposited TiB₂ coatings and commercial grade titanium, caused by 40, 60 and 120 keV D⁺ and ⁴He⁺ irradiation, have been studied for the as-deposited coatings and for coating surfaces that were mechanically polished prior to irradiation. Scanning electron microscopy analysis of polished TiB₂ samples irradiated with D⁺ and ⁴He⁺ to a dose of 3.1 × 10¹⁸ ions cm^-2 reveals significant surface damage due to blistering and flaking, whereas for identical irradiation conditions the as-deposited TiB₂ coatings show very little damage. For similar irradiation conditions the titanium metal samples showed blistering for the ⁴He⁺ irradiation case but no significant surface damage for the D⁺ case. Estimates of the erosion yields due to blister exfoliation in polished TiB₂ samples show an increase with increasing projectile energy for the total dose studied.     

Thermodynamic properties of the SnSb<Subscript>2</Subscript>Te<Subscript>4</Subscript> compound

The SnTe–Sb₂Te₃–Te system has been studied in the temperature range 300–430 K using emf measurements on reversible concentration cells of the type (–)SnTe(s) | liquid electrolyte, Sn²⁺ |(Sn–Sb–Te)(s)(+). The system has been shown to consist of two three-phase regions, separated by the SnSb₂Te₄–Te tie line. The best fit equation for the temperature-dependent emf data has been used to evaluate the partial thermodynamic functions of the SnTe and Sn in the alloys. Using these data, subsolidus phase diagram data for the SnTe–Sb₂Te₃–Te system, and relevant thermodynamic functions for SnTe and Sb₂Te₃, we calculated the standard Gibbs energy of formation, standard enthalpy of formation, and standard entropy of the SnSb₂Te₄ compound.     

The decay rate of critical fluctuations in3He-4He mixtures near the gas-liquid critical point

We have measured the critical light scattering intensity and the Rayleigh line shape for³He and for³He-⁴He mixtures with compositionX(³He)=0.95, 0.79, and 0.63 along their respective critical isochores near the plait point. The experimental linewidth of³He is compared with the calculated one from heat conductivity and equation of state measurements, and satisfactory agreement is obtained. For mixtures, gravity effects in our cell of finite height prevent us from reaching the critical point along a path at strictly constant composition and density. HenceT _c cannot be determined directly. Using the prediction that the scattered light intensity in the mixtures has the same diverging behavior as for the pure fluid, we determine the reduced temperaturet[T – T _c(X)]/T _c from the intensity. The measured Rayleigh line shape can be expressed by a single decay rate as a function oft for a given scattering angle of the light beam. Our experiments show that in the mixtures is only weakly dependent on composition. Our analysis leads to the determination of the mass diffusion coefficientD, which is found to be nearly independent of composition and nearly equal to the thermal diffusivityD _T measured for³He. The results are discussed in the light of the predictions from mode coupling theory.     

A diffusion model for the oxidation of hot pressed Si3N4-Y2O3-SiO2 materials

The parabolic oxidation behaviour of silicon nitride hot pressed from compositions of the Si₃N₄-Si₂N₂O-Y₂Si₂O₇ subsystem studied in 98 kPa air and 1273 to 1673 K has been discussed in terms of a diffusion model in which the most relevant parameters are the amount of the grain boundary phase, the width of the diffusion zone and the concentration gradient at the Si₃N₄/oxide reaction interface. The model accounts for both kinetic (oxidation rate constants) and thermodynamic (apparent activation energy for oxidation) variations with amount and composition of the grain boundary phase and proves suitable for the extension to other additive systems. The apparent activation energy for oxidation ranged from 260 to 623 kJ mol^–1 according to composition. It is suggested that a more appropriate evaluation of the thermodynamic parameters of the diffusion process must account for the variation of concentration profiles of the diffusing species with temperature.     

Growth and spectroscopic characteristics of Li2Mg2(MoO4)3 and Li2Mg2(MoO4)3:Co2+ crystals

We have determined the starting mixture composition and process parameters for the growth of bulk, uniform Li₂Mg₂(MoO₄)₃ and Li₂Mg₂(MoO₄)₃:Co²⁺ (1 at %) crystals by a modified Czochralski technique at low temperature gradients (<1°C/cm). The 1500-, 750-, and 600-nm bands observed in the optical absorption spectra of the Li₂Mg₂(MoO₄)₃:Co²⁺ crystals are due to the Co²⁺ ions, which have a 3d ₇ electron configuration and substitute for Mg²⁺.     

Transient phenomena initiating phase transition in dilution refrigerator

We have analysed the transient processes in a Dilution Refrigerator (DR) leading to phase separation of ³He–⁴He mixture into concentrated and dilute solutions using an extended SIDFO (Simulation of Integrated Dilution refrigerator For Optimisation) Pradhan et al. (2013) analysis tool. The evolution of the phase separation interface along the concentrated channel and its arrival in the mixing chamber for a given physical situation has been thoroughly examined. The significance of the ³He/⁴He composition in the mixer, the flow rate and the still power on the phase separation is presented here. The consequences of several relevant thermodynamic parameters and the composition of isotopic mixture for successful function of the DR is also discussed in this paper.     

An apparatus for preparing isotopically pure He4

A cryostat has been constructed for extracting pure He⁴ from He II of natural isotopic composition by means of a heat flush technique. It is shown that the method is in principle capable of yielding He⁴ which is entirely devoid of He³ isotopic impurities. A secondary heat flush, operated in conjunction with a conical heat exchanger of novel design, was used to place an experimental lower bound of 2 × 10¹⁵ on the $\text{He}{}^4\text{He}{}^3$ ratio of the product, a standard sufficient for all present or projected applications requiring isotopically pure He⁴. The apparatus produces 2 000 1 (at standard temperature and pressure) of He⁴ per thermal cycle. The design of future purifiers is discussed.     

Predicting the virial coefficients and thermodynamic properties of a multicomponent mixture with application to the ternary mixture of CH2F2+CF3CHF2+CF3CH2F

A model for estimating second and third virial coefficients, which has been used successfully to represent the behavior of pure gases and binary mixtures, was applied to a ternary mixture. An estimate for the ternary third virial coefficient.C ₁₂₃, was added to the model. Three experimentally determined binary interaction parameters were also used. The model has been applied to the ternary mixture CH₂F₂+CF₃CHF₂+CF₃CH₂F (R32+R125+R134a). The results are useful for calculating gas-phase densities, thermodynamic properties, and fugacities for phase equilibrium calculations. The use of such models leads to a considerable economy of effort in the case of multicomponent mixtures. Examples of the thermodynamic properties are given for the equimolar ternary mixture in the range from the dew-point temperature to 400 K at pressures of 0.5, 1, and 2 MPa. Calculated densities and speeds of sound are compared with new experimental values for a near-equimolar composition.     

On the chemical vapour deposition of Ti3SiC2 from TiCl4-SiCl4-CH4-H2 gas mixtures

An experimental study of the deposition of Ti₃SiC₂-based ceramics from TiCI₄-SiCI₄-CH₄-H₂ gaseous precursors is carried out under conditions chosen on the basis of a previous thermodynamic approach, i.e. a temperature of 1100°C, a total pressure of 1 7 kPa, various initial compositions and substrates of silicon or carbon. Ti₃SiC₂ is deposited within a narrow composition range and never as a pure phase. A two-step deposition process is observed, in agreement with the thermodynamic calculations. For a silicon substrate, TiSi₂ is formed as an intermediate phase from consumption of Si by TiCI₄ and then is carburized by CH₄ into Ti₃SiC₂. For a carbon substrate, the first step is the formation of TiC_x either from consumption of carbon by TiCI₄ or by reaction between TiCI₄ and CH₄ and then TiC_x reacts with the gaseous mixture to give rise to Ti₃SiC₂. In most cases, Ti₃SiC₂ is obtained as small hexagonal plates oriented perpendicular to the substrate surface. These nano- or micro-crystals are usually co-deposited with TiC_x and to a lesser extent SiC, and their size is increased by increasing the dilution of the gaseous mixture in hydrogen.