Analytical representation of the density derivative of the Percus–Yevick hard-sphere radial distribution function

ABSTRACT

Explicit analytical expressions are presented for the density derivative, ?g_HS(R; ρ)/?ρ, of the Percus–Yevick approximation to the hard-sphere radial distribution function for R ≤ 6σ, where σ is the hard-sphere diameter and ρ = (N/V)σ³ is the reduced density, where N is the number of particles and V is the volume. A FORTRAN program is provided for the implementation of these for R ≤ 6σ, which includes code for the calculation of g_HS(R; ρ) itself over this range. We also present and incorporate within the program code convenient analytical expressions for the numerical extrapolation of both quantities past R = 6σ. Our expressions are numerically tested against exact results.     

Is the Pauli exclusion principle the origin of electron localisation?

ABSTRACT

In this work, we inquire into the origins of the electron localisation as obtained from the information content of the same-spin pair density, γ^{σ, σ}(r₂∣r₁). To this end, we consider systems of non-interacting and interacting identical Fermions contained in two simple 1D potential models: (1) an infinite potential well and (2) the Kronig–Penney periodic potential. The interparticle interaction is considered through the Hartree–Fock approximation as well as the configuration interaction expansion. Morover, the electron localisation is described through the Kullback–Leibler divergence between γ^{σ, σ}(r₂∣r₁) and its associated marginal probability. The results show that, as long as the adopted method properly includes the Pauli principle, the electronic localisation depends only modestly on the interparticle interaction. In view of the latter, one may conclude that the Pauli principle is the main responsible for the electron localisation.     

The determination of hopping rates and carrier concentrations in ionic conductors by a new analysis of ac conductivity

The a.c. conductivity σ(ω) of ionic materials takes the form, σ(ω) = σ(0) + Aωⁿ. The carrier hopping rate, ω_p, is obtained from the new expression σ(0) = A ω_pⁿ and the carrier concentration is estimated from σ(0). The contribution of creation and migration terms to the activation energy for conduction may be determined from the thermal activation of σ(0) and ω_p and the corresponding entropy terms quantified. Data have been analyzed for four widely different ionic materials: single crystal Na β-alumina, polycrystalline Li₄SiO₄, Ag₇l₄AsO₄ glass and Ca(NO₃)₂/KNO₃ glass and melt. For each, the carrier concentration and hopping rates have been obtained.     

Conductivity of a periodic two-component system of rhombic type

The conductivity and the distribution of electric field, current, and charge density in a periodic two-component system composed of rhombs with an arbitrary vertex angle of 2α are investigated. The effective conductivity of such a medium is represented by a tensor with components σ _eff ¹¹ (α) and σ _eff ²² (α) in the principal axes that satisfy the Dykhne relation σ _eff ¹¹ (α) σ _eff ²² (α)=σ ₁σ₂, where σ₁, σ₂ are the isotropic conductivities of media 1 and 2. In addition, the relation σ _eff ²² (α)=σ _eff ¹¹ (π/2?α) is satisfied. The principal axes are directed along the diagonals of the rhombs. It is shown that there are three lines in the rectangle 0<α ≤π/2,?1<Z<1((Z=σ₁?σ₂)/(σ ₁+σ₂)) on which the charge density is expressed in terms elliptic functions. An explicit expression is obtained for all physical quantities on these lines.     

Second-order ferroic properties of a Pb5Ge3O11 uniaxial ferroelectric

The ferrobielastic properties (ferroic properties of the second order) earlier theoretically predicted for lead germanate uniaxial ferroelectric crystals are justified experimentally. It is demonstrated that single-domain samples are formed upon cooling to temperatures below the Curie point under uniaxial mechanical stresses corresponding to a combination of mechanical stresses σ₁₁σ₁₃ or σ₂₂σ₂₃. The macroscopic mechanism of this phenomenon is considered.     

Heterodyne coincidence spectroscopy

A new type of light-scattering experiment, which should measure directly the triple static structure factor S ⁽³⁾ (k, q) of a fluid, is proposed. S ⁽³⁾(k, q) is the full spatial Fourier transform of the equilibrium triplet distribution function g ⁽³⁾(r ₁, r ₂, r ₃). The experiment may also be used to study dynamic correlation functions of the form <a_k (t)a_q (t′)a_k_q(t″)> (where a_k () is the kth spatial Fourier component of the density), thereby giving new information on mode-mode coupling. The method obtains its information from triple correlations in the arrival of scattered photons at three detectors. The detectors must be operated in the heterodyne mode (i.e. with a local oscillator); the scattering volume must be much larger than the volume over which molecular positions are correlated. Comparison is made with previous analyses of other multi-detector experiments.     

Relaxationserscheinungen im 63 P 2-Zustand des Quecksilber-Isotops199Hg bei Stößen mit Quecksilberatomen im Grundzustand

The decay ofrf resonance signals (Δm _F =± 1, ΔF=0) in the hfs-states (F=3/2, 5/2) of the 6³ P ₂-state of¹⁹⁹Hg has been observed by means of a sampling method. By comparing the relaxation times to those of the even isotopes, the cross section σ₂(F) for the destruction of an alignment in the hfs-states by collisions with ground state Hg-atoms could be measured. The following ratios were obtained: σ₂(F=3/2)/σ₂=1.04±0.06 and σ₂(F=5/2)/σ₂=0.90± 0.03. The cross section σ₂ for the even isotopes was found to be (2.620±0.265) 10^?14cm². Assuming total decoupling of nuclear spinI and electronic angular momentumJ during the collision, the cross sections for the destruction of an orientation (σ₁) and an “octupolarisation” (σ₃) could be calculated. For the even isotopes the following ratios were derived: σ₁/σ₂=0.76 ± 0.07 and σ₃/σ₂=1.08 ± 0.09.     

Zum Kernphotoeffekt am Ar40 und Ar38

Liquid Argon was irradiated with bremsstrahlung from 18 to 31 MeV endpoint energy in steps of 2 MeV. The yields of the reactions Ar⁴⁰(γ, n)+(γ, p) and Ar³⁸(γ, n) were measured by detecting the 269a and the 35d rest activity with a low-level-counter. Cross section curves for the (γ, n)-processes could be found from the yield values, and they allowed together withσ _N, σ(γ, p) andσ(γ, np) a determination ofσ(γ, 2n) and σ_γabs for Ar⁴⁰. The integrated cross section forσ(γ, n) from threshold to 33 MeV yields (200±40) MeVmb for Ar⁴⁰ and (210±40) MeVmb for Ar³⁸, the corresponding value for σ_γabs being (450±60) MeVmb for Ar⁴⁰.     

Multiscale model of deformed polycrystals. Hall-Petch problem

The paper puts forward a multiscale model of deformed polycrystals according to which the basis for self-consistent deformation of grains is rotational wave flows of planar structural transformations at their boundaries. Computer-aided engineering of grain boundaries reveals two types of rotational wave flows defined by the misorientation angle of adjacent grains. Grain boundary flows of the first type develop at low-angle boundaries and feature low curvature. These flows generate dislocations in the grain bulk and the Hall-Petch equation for them has the form σ=σ₀+kd^?1/2. Grain boundary flows of the second type develop at high-angle boundaries and feature high curvature. These flows generate curvature bands in near-boundary zones and inject them into the grain bulk, resulting in fragmentation of grains and breakdown of translation invariance. For such self-consistency of grains in a polycrystal, the Hall-Petch equation has the form σ=σ₀+kd^?1. Experimental data in support of the proposed multiscale model are presented.     

Change in the size dependences of the surface properties of nanodiamond upon variation in the isotope composition

The isothermal-isomorphic dependences of the specific surface energy (σ), its isochoric temperature derivative (σ′), and surface pressure (P _sf) on the size of nanodiamonds ¹²C and ¹³C at 100 and 4300 K are calculated. It is shown that the ratio σ(¹²C)/σ(¹³C) decreases with decreasing size along both isotherms, and σ′(¹²C)/σ′(¹³C) increases with decreasing size, and this effect is higher at lower temperatures. The ratio P _sf(¹²C)/P _sf(¹³C) increases with decreasing size. The effect is stronger at higher temperatures.     

Distribution function for large velocities of a two-dimensional gas under shear flow

The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degreek⩾4 diverge for shear rates larger than a critical valuea _c ^(k) , which behaves for largek asa _c ^(k) ∼k ⁻¹. This divergence is consistent with an algebraic tail of the formf(V) ∼V ^−4-σ(a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann equation far from equilibrium.     

New mechanism of impurity conduction in lightly doped crystalline noncompensated silicon

It is found that the plastic deformation of lightly doped crystalline silicon samples (N<6×10¹⁶ cm^?3) with a low compensation (K～3×10^?2) gives rise to nonohmic conduction σ_M in electric fields that differs radically from conventional hopping conduction via the ground states of impurities (σ₃). The values of σ_M can exceed values of σ₃ by a factor of 10³?10⁵. The value of σ_M and its dependence on the electric (E) and magnetic (H) fields can be controlled by varying the density of dislocations and the mode of thermal sample treatment. A strong anisotropy of σ_M is observed in samples with oriented dislocations: the conductivities along and across dislocations can differ by a factor of 10⁴. The results are explained by the occurrence of conduction via the H^?-like states of impurities concentrated in the vicinity of dislocations. The levels of these states lie between the upper and the lower impurity Hubbard bands.     

Effect of carbon ion bombardment and surface oxidation on the twinning rate of single-crystal bismuth

A study is made of the change in the dependences of the normal velocity of twinning boundaries on the magnitude of shear stresses in the twinning plane v _n =v _n (τ) in bismuth crystals owing to ion-cluster doping and oxidation of the irradiated surface. Irradiation was by 25 keV carbonions at a dose of 10¹⁷ ion/cm². Twinning of the crystals took place under pulsed loading conditions with pulse durations of 10⁻⁵−10⁻⁴ s and stress amplitudes of (0.2–2.0)×10³ g/mm³. Carbon ion bombardment of single-crystal bismuth causes a shift in the v _n =v _n (τ) curve toward lower stresses. An oxide film slows down the motion of twinning dislocations. Zh. Tekh. Fiz. 69, 130–131 (May 1999)     

Li2Mo2O6多晶材料的结构与电性能的研究

本文用固相反应烧结制备出Li₂Mo₂O₆多晶材料。经X射线分析、红外光谱和电子顺磁共振谱(EPR)的研究,确定了它的结构是Li₂Mo₂O₄和MoO₂两个晶相组成的烧结体。钼离子以四价状态存在于MoO₂晶相结构中。采用交流阻抗谱分析了晶界与温度变化的相关性。测得了样品的ln(σ_总T)-1/T 曲线是由两段直线和一段曲线所组成;总电导率化能σ_27℃=1.36×10^-3(Ω·cm)^-1,σ_115℃=1.49×10^-3(Ω·cm)^-1,σ_300℃=9.71×10^-3(Ω·cm)^-1,σ_370℃=2.42×10^-3(Ω·cm)^-1;电导活化能E₁=0.043eV,E₂=0.235eV,E_平均=0.76eV。采用维格纳极化电池法测得电子电导率σ_e,σ_e27℃=2.240×10^-5(Ω·cm)^-1,σ_e300℃=4.476×10^-3(Ω·cm)^-1。实验证明,室温下材料为固体电解质,300℃附近为良好的离子与电子混合导体。 关键词：     

Transmission of electrons through ferromagnetic material and applications to detection of electron spin polarization

The salient features of the total low energy inelastic electron scattering cross section in transition metals are described by a constant term σ₀ plus a term σ_d that is proportional to the number of unoccupied d-orbitals. This simple model predicts that low energy electrons transmitted through a ferromagnetic ultrathin film acquire a transport spin polarization a(χ). Using the ratio σ₀/σ_d as the only adjustable parameter, the model predicts the enhancement of the spin polarization of the low energy cascade electrons as well as a(χ) in reasonable agreement with the existing observations on Fe, Co and Ni. A detector for electron spin polarization P based on the spin dependent transmission of electrons through ferromagnetic material is proposed which should be superior to existing P-detectors by 1–2 orders of magnitude.     

Stereodynamics of the reactions Ne+H2+/Ne+D2+/Ne+T2

The vector correlations between products and reagents for the reactions Ne+H + 2 , Ne+D + 2 , and Ne+T + 2 are calculated by means of the quasi-classical trajectory method on a new potential energy surface constructed by Lü et al. [J. Chem. Phys. 2010 132, 014303]. The polarization-dependent differential cross-sections (2π/σ)(dσ 00 /dω t ), (2π/σ)(dσ 20 /dω t ), (2π/σ)(dσ 22+ /dω t ), and (2π/σ)(dσ 21 /dω t ), and the distributions of P (θ r ), P (φ r ), and P (θ r ,φ r ) are calculated. The isotopic effect, which is associated with the difference in mass factor among the three reactions, is revealed.     

High-temperature phase transitions in the improper ferroelectric KIO3

The ac conductivity (σ_ac) and dielectric permittivity (?) are determined in the temperature range 300?K?T3 compound. The results indicated that the compound behaves as an improper ferroelectric and undergoes a ferroelectric phase transition from a high temperature rhombohedral phase I to a low temperature monoclinic phase II at T _c?=?(486?±?1)?K. A second structural phase transition was observed around 345?K. The conductivity varies with temperature range and for T?>?428?K intrinsic conduction prevails. Different activation energies in the different temperature regions were calculated. The frequency dependence of σ(ω) was found to follow the universal dynamic response [σ(ω)∝(ω) ^s(T)]. The thermal behaviour of the frequency exponent s(T) suggests the hopping over the barrier model rather than the quantum mechanical tunneling model for the conduction mechanism.     

Probability diffusion in non-Markhovian,non-Gaussian molecular ensembles: A theoretical analysis and computer simulation

A theoretical generalisation of the Fokker/Planck equation for atomic and molecular diffusion is compared with the results of a molecular dynamics simulation of a triatomic molecule ofC _2v symmetry. The molecular dynamics results are non-Markhovian and non-Gaussian in nature, markedly so in the case of the centre of mass linear velocityV. This may be ascertained by simulating the long-time limit of the three dimensional kinetic energy autocorrelation function <V ²(t)V ²(0)>/<V ²(0)V ²(0)>, which falls well below the theoretical Gaussian value of 3/5. By expressing the Mori continued fraction as a multidimensional Markhovian chain of differential equations and expressing this in turn as a non-Gaussian probability-diffusion equation of the Kramers/Moyal type it is possible to account for the simulation results in a qualitative fashion.     

Detection of (<Emphasis Type="Italic">C</Emphasis> + <Emphasis Type="Italic">A</Emphasis>)-type dislocation self-blocking in magnesium

The self-blocking effect predicted theoretically and then observed in intermetallides is established for a pure metal, namely, for magnesium. This effect can be observed only for magnesium single crystals whose axis is parallel to the c axis and whose yield stress behavior σ _y (T) has a temperature anomaly. For such single crystals, the self-blocking of the (c + a)-type edge dislocations is established during pyramidal slip of type II. The self-blocking is proved by dislocation extension along the preferred direction without external stress. In this case, the á 1[`1]00 ñ \left\langle {1\bar{1}00} \right\rangle directions appear preferred. TEM images of (c + a) dislocations extended along the preferred directions are presented. It is demonstrated that two effects – temperature anomaly of σ _y (T) and dislocation self-blocking – have the common nature: a two-valley potential relief of the dislocation. A model of two-valley relief of the (c + a) dislocations in Mg is proposed.