The electron transport properties of pure liquid metals

Progress in the theory of the electrical conductivity and other ordinary transport properties of liquid metals since 1961 is reviewed. After a brief account of the basic nearly-free-electron diffraction formula, the quantitative comparison of this formula with experiment is discussed.

For the alkali metals, the agreement is adequate, given the uncertainty of the pseudopotentials, although there is controversy about the calculation of the temperature coefficient of ρ _L. To explain the observed volume dependence of ρ _L, and the thermoelectric power, it also seems necessary to allow for the variation of the pseudopotential with the positions of the Fermi level and the core levels relative to the bottom of the conduction band.

Quantitative results for the noble and polyvalent metals are meagre, and although calculations of ρ _L for Al and Zn are in excellent agreement with experiment there may be other cases where the basic formula is not adequate. The general question of the structure and convergence of the perturbation series for ρ _L is discussed, and it is suggested that corrections for higher order terms can be minimized by making the pseudopotential as near as possible to the t-matrix of an ion.

The anomalous properties of Hg are then discussed, in the light of the work of Mott (1966). In this connection it is shown that Edwards' formula (1962) for ρ _L, in which the Fermi velocity, v _F, is taken to be that of a free electron, ?k _F/m, despite deviations from the free-electron curve for ?(k), can be derived by using the expectation value of the current operator in place of e v _F in the Boltzmann equation. This modification of the elementary theory allows the Hall constant of a liquid metal to deviate from 1/nec, as found experimentally.     

The thermodynamics of symmetric two centre Lennard-Jones liquids

We have carried out molecular dynamic simulations for the thermodynamic properties of two centre Lennard-Jones fluids at lower densities and higher temperatures than have been studied previously, and have also made simulations for one additional shape. The results, together with results already given in the literature, are presented in a parameterized form which is very convenient to use in testing the simulation results against data for real liquids. Tables of second virial coefficients are also provided. We illustrate the use of our results by an analysis of pure liquid ethane, which is found to be well represented by such a model with L* = 0·67, ε/k = 137·5 K and σ = 3·506 Å. We also suggest that the experimental thermodynamic properties of suitable liquid mixtures can, with the aid of a theory for the equivalent pure liquid parameters (L _x *, ε _x , σ _x ), be satisfactorily interpreted using the general results given in this paper.     

About Some Structural Differences of Certain Inorganic Salt Solutions in Natural and Heavy Water

Based on viscosity measurements of seven electrolyte soultions (KCl, K Br, KI, LiCl, Na₂CO₃, Li₂SO₄, and MnSO₄) in heavy water and the viscosity data of four electrolyte solutions (KCl, KBr, Kl, and Na₂CO₃) in ordinary water the activation energies of viscosity have been determined from the Pantchenkov equation. The dtermination were made at 25°, 35°, 45°, 60°, 75°, and 90°, at various concentrations up to near saturation. The activation energies of viscosity for pure heavy and ordinary water have been determined, too. The results allowed conclusions on the various influences of the investigated salts on the structure of heavy and ordinary water solutions.     

Intervalley electron scattering by phonons in (GaAs)<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript>(AlAs)<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>(001) ultrathin superlattices

The electron scattering by short-wavelength and long-wavelength phonons in (GaAs) _m (AlAs) _n (001) superlattices with ultrathin layers (n, m = 1, 2, 3) has been investigated using the pseudopotential method and the phenomenological model of bonding forces. The deformation potentials have been found for intervalley electron transitions in the conduction bands of the superlattices and solid solutions of the corresponding compositions. It has been shown that, owing to the localization of the wave functions in the quantum wells Γ, L, and X, the intensity of intervalley electron transitions in the superlattices, as a whole, is higher than that of similar transitions in the solid solutions. As the content of light Al atoms in the superlattices increases, the deformation potentials monotonically increase for the X-X transitions and decrease for the L-L and X-L transitions. The potentials of the Γ-X and Γ-L transitions change nonmonotonically depending on the layer thickness due to the pronounced quantum-well effects in the deep Γ quantum wells of GaAs. The deformation potentials averaged over phonons and related valleys in the superlattices are close to the corresponding potentials in the solid solutions.     

Heterodiffusion of chromium and cobalt in liquid iron

The heterodiffusion has been studied by the method of stationary diffusion source. In that method the saturated radioactive vapour of the diffusing element comes into contact with the liquid in which diffusion is being studied. Two variants of that method were applied and the diffusion coefficients of chromium and cobalt in liquid iron were determined, i.e.D _{(Cr→Fe, 1860K)}= =4·9×10^?5cm²/s andD _{(Co→Fe, 1820K)}=5×10^?5cm²/s, respectively. The values of maximum concentration of chromium in Fe-samples after diffusion were of the order of 10^?1 to 10^?2 wt-%, those of cobalt of 10^?4 wt-%. This experimental method is rather simple and the results obtained are in good conformity with other measurements.     

Noise map validation by continuous noise monitoring

This paper presents a comparison of two noise assessments in the Gdansk agglomeration in Poland. One is based on the noise map produced by computational method for the city in 2007, the second one is based on real data from continuous measurements acquired by a noise monitoring network operating in the city since 2008. Differences are shown and analyzed. Additionally, seasonal and weekday influence on noise indicators (L_DEN, L_D, L_E and L_N) is analyzed and discussed in this paper.     

Thermal diffusion and the approach to the steady state in gases: II

The theory of the rate of approach to the steady state in themal diffusion is tested experimentally on the systems He-Ar, He-CO₂, H₂-CO₂, and D₂-CO₂ over a temperature range of about -78°c to 325°c. The course of the diffusion has been followed by means of the radioactive tracers ³⁷Ar and ¹⁴CO₂. The theory appears to be verified, and the results are used to calculate ordinary diffusion coefficients, which are in reasonable accord with previous measurements by other techniques. The thermal diffusion factors, which are obtained from the same measurements, also appear to have reasonable accuracy. The experimental method therefore appears to have promise as a sensitive method for the determination of forces between unlike molecules.     

Response of fcc metals and L12 and D022 type trialuminides to uniaxial loading along [100] and [001]: ab initio DFT calculations

Ab initio density-functional calculations have been used to investigate the response of the face-centred cubic (fcc) metals Al and Cu, and of the L1₂- and D0₂₂-type trialuminides Al₃(Sc,Ti,V) to uniaxial loading along the [100] and [001] directions. The results obtained under uniaxial strains are compared to the response to biaxial (epitaxial) strains. The ideal tensile and compressive strengths and their limitation by shear instabilities along these deformation paths have been calculated. Although the response of both pure fcc metals could be expected to be very similar, our results show a fundamental difference: whereas for Cu a special invariant state with C ₂₂?=?C ₂₃, leading to a bifurcation from the tetragonal to an orthorhombic deformation path, is reached at a strain of 10%, for Al this state is reached only at a strain of 33% close to the critical strain defining the ideal tensile strength. The reaction of the L1₂-type trialuminides is comparable to the response of Al; no bifurcation to an orthorhombic deformation path is predicted. The response of the D0₂₂-type trialuminides is different from that of the L1₂-type phases because of the difference in the stacking of the atomic planes along the [001] direction. For D0₂₂-type trialuminides, the uniaxial compression along this direction or epitaxial tension in the (001) plane leads to the formation of a stress-free D0₃ structure, in complete analogy to the fcc???bcc transformations observed for the pure metals. Under uniaxial [100] loading the guiding symmetry along the deformation path is orthorhombic and leads to the formation of special structures under both tension and compression parts, which are related to the D0₃ structure in the same way as the parent D0₂₂-lattice is related to the L1₂ structure.     

Rotational relaxation of symmetric tops CH3D and CD3H in some inert liquids

Infra-red spectra of CH₃D and CD₃H dissolved in liquid Ar, Kr, Xe, N₂, O₂ and CH₄ or CF₄ have been recorded. From the band shapes, rotational correlation functions, band moments and intermolecular mean square torques have been calculated. To describe the tumbling motion, involved in the parallel band profiles, we have computed the theoretical correlation functions in the m or j diffusion limits. The validity of these Gordon models is discussed. In an attempt to obtain some information on the rotational diffusion tensor, experimental correlation times have been estimated from A₁ and E bands of CD₃H.     

Rotational diffusion of carbon monoxide in various simple liquids

Infra-red spectra of CO dissolved in liquid N₂, O₂, Ar, Xe and CH₄ have been recorded both in the fundamental and the first overtone. From the band profiles, rotational correlation functions, band moments and intermolecular mean-square torques have been calculated. With the help of Gordon's rotational diffusion model [1] we computed the theoretical correlation functions in the ‘M-diffusion’ (including or not a distribution of angular momentum correlation times) and ‘J-diffusion’ limits. The validity of the Gordon and Debye diffusion models in the various dense gases is discussed.     

Self diffusion in liquid Na-K alloy

Self diffusion coefficients,D _i, in liquid Na-K alloy at 373 K have been computed in the linear trajectory approximation of Helfand, with square well as an attractive tail. From the computedD _Na andD _K, the mutual diffusion coefficient,D _NaK has also been determined.D _Na,D _K andD _NaK all increase with increase of concentration of potassium, while the ratio,D _Na/D _K remains constant (1.45 ± 0.01) over the entire concentration range.     

Convergence to diffusion waves of solutions for viscous conservation laws

We study the large-time behavior of solutions of viscous conservation laws. It is shown that solutions tend to diffusion waves, which are constructed based on the heat equation and Burgers equation. The convergence is in theL _p , 1p sense and is obtained as a consequence of theL ₂ decay of the difference between the solution and its asymptotic state of diffusion waves.Supported by the National Sciences Council of the Republic of China under the contract NSC-76-0208-M-001-09Supported by NSF under Grant No. DMS-84-01355     

Physical processes of current gain in InAs bipolar junction transistors

InAs bipolar junction transistors (BJTs), grown by molecular beam epitaxy, are reported with common emitter current gains (β's) as large as 400. The factors affecting the common emitter current gain have been studied by estimating the magnitudes of the base transport factor (α_T) and emitter injection efficiency (γ). This has been accomplished by studying a sequence of InAs BJTs with varying emitter doping densities, N_E. Minority carrier diffusion length in the base (L_B), α_T, and γ have been extracted from measured electrical characteristics. The results of the study of these InAs BJTs are as follows: L_B≈0.4 μm, α_T≈98% and γ ranges from 92% to nearly 100% depending on N_E. This knowledge of the magnitudes of the injection efficiencies suggests when it would be useful to move from the simple BJT structure to the more advanced heterojunction bipolar transistor (HBT) structure. Lower γ BJTs would be improved, however high-γ BJTs would benefit little, by the use of the widegap emitters of HBTs. The method developed here to estimate γ, α_T and L_B is not specific to InAs BJTs, but should be useful for study of BJTs and HBTs in any material system.     

Surface tension measurement of metastable liquid Ti–Al–Nb alloys

Thermophysical properties of liquid alloys are usually difficult to measure, especially for high melting point and reactive alloys. In this work, the surface tensions of superheated and undercooled liquid Ti₅₅Al₄₅, Ti₅₀Al₄₅Nb₅ and Ti₄₅Al₄₅Nb₁₀ alloys are determined by using oscillating drop method under electromagnetic levitation state. The experimental results of Ti–Al and Ti–Al–Nb alloys display linear temperature dependence. The maximum undercoolings of 259 (0.143T _L), 268 (0.146T _L) and 275 K (0.147T _L) are respectively achieved for these three alloys. Furthermore, the viscosities of liquid Ti_55−x Al₄₅Nb _x alloys are also derived from the experimental results.     

On generalized Lax equations of the Lax triple of the BKP and CKP hierarchies

Based on the Lax triple (B_m, B_n, L) of the BKP and CKP hierarchies, we derive the nonlinear evolution equations from the generalized Lax equation. The solutions of some evolution equations are presented, such as soliton and rational solutions.     

Carrier diffusion in InGaAs/GaAs quantum wells grown on vicinal GaAs(0 0 1) substrates

We have investigated the influence of vicinal GaAs substrates on the optical and electronic properties of InGaAs/GaAs quantum wells (QWs). A single In_0.10Ga_0.90As QW was grown by molecular-beam epitaxy on a vicinal GaAs(0 0 1) substrate with a miscut angle of 0° (nominal), 2°, 4° and 6° towards [1 1 0]. The carrier diffusion was obtained by a micro-photoluminescence scan technique that permits to observe the effective diffusion length characterized by the lateral spread of carriers in the QW followed by radiative recombination. The carrier diffusion length was obtained parallel (L_||) and perpendicular (L) to the atomic steps. The diffusion length decreases as the temperature increases up to 100 K. Above this temperature we found different behaviours that depend on the sample miscut angle.     

Determination ofL-shell X-ray production cross-sections in holmium by 10–40 keV photons

In an effort to resolve the existing discrepancy between experiment and theory, the cross-sections for the production ofL _l,L _α ,L _β andL _γ groups ofL-shell X-rays of Ho by photons of nine energies in the range 10–40 keV have been measured using an improved version of annular source double reflection geometrical set-up. Contrary to the earlier findings of Garget al that the measured values of the cross-sections are consistently higher than those calculated theoretically, the present results do not confirm this. The plausible deficiencies in the experiments of Garget al are pointed out and possible remedies to overcome them are suggested. It is concluded that the higher values obtained by Garget al are probably due to systematic errors in their method of measurement.     

Quantitative study of diffusion jumps in atomistic simulations of model gas–polymer systems

Microscopic mechanisms underlying the diffusion of particles in polymeric and other systems include ‘jumps’ that are said to provide for a substantial contribution to the overall particle displacement. Such jumps have been observed in molecular simulations and experimentally, leading to important qualitative conclusions. An efficient method has been proposed for the identification and quantitative processing of jumps, and successfully employed in simulations of gas–liquid alkane systems. In the present work, the same method is applied in equilibrium Molecular Dynamics simulations of methane-like molecules dispersed in polymer-like alkanes, at atmospheric pressure and temperature well above the polymer melting point. The systems studied were prepared and equilibrated and a linear diffusion regime was confirmed by means of various criteria. The occurrence of distinct jump events was clearly revealed and their average length and frequency were calculated. In this way, a random-walk-type diffusion coefficient, D _s,?jumps, of the penetrants, was obtained and found to be lower than the overall diffusion coefficient D _s,?MSD calculated by the mean square displacement method. This is a strong indication that the overall diffusion is a combination of longer jumps with other microscopic mechanisms such as smoother and more gradual displacements effected upon the diffusing particle by its surroundings.     

Measurement of diffusion coefficients of thallium ion in H2O and D2O systems at different concentrations

Sliding cell method, developed in our laboratory, has been used to measure the inter diffusion coefficient of thallium ion in thallous sulphate solution over a wide concentration range using both water and heavy water as solvent at 35°C. The results have been analysed from the point of view of both ion-ion and ion-solvent interactions. The comparison of the diffusivities of the same ion in D₂O and H₂O electrolyte solutions at the same temperature indicate that the addition of salt affects the two solvents differently.     

LES/PDF for premixed combustion in the DNS limit

We investigated the behaviour of the composition probability density function (PDF) model equations used in a large-eddy simulation (LES) of turbulent combustion in the direct numerical simulation (DNS) limit; that is, in the limit of the LES resolution length scale Δ (and the numerical mesh spacing h) being small compared to the smallest flow length scale, so that the resolution is sufficient to perform a DNS. The correct behaviour of a PDF model in the DNS limit is that the resolved composition fields satisfy the DNS equations, and there are no residual fluctuations (i.e. the PDF is everywhere a delta function). In the DNS limit, the treatment of molecular diffusion in the PDF equations is crucial, and both the ‘random-walk’ and ‘mean-drift’ models for molecular diffusion are investigated. Two test cases are considered, both of premixed laminar flames (of thickness δ_L). We examine the solutions of the model PDF equations for these test cases as functions of Δ/δ_L and h/δ_L. Each of the two PDF models has advantages and disadvantages. The mean-drift model behaves correctly in the DNS limit, but it is more difficult to implement and computationally more expensive. The random-walk model does not have the correct behaviour in the DNS limit in that it produces non-zero residual fluctuations. However, if the specified mixing rate Ω normalised by the reaction timescale τ_c is sufficiently large (Ωτ_c ? 1), then the residual fluctuations are less than 10% and the observed flame speed and thickness are close to their laminar values. Away from the DNS limit (i.e. h/δ_L ? 1), the observed flame thickness scales with the mesh spacing h, and the flame speed scales with Ωh. For this case it is possible to construct a non-general specification of the mixing rate Ω such that the flame speed matches the laminar flame speed.