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Showing papers in "Il Nuovo Cimento D in 1990"


Journal ArticleDOI
TL;DR: In this article, free energy diagrams of amorphous alloys are constructed using Miedema's semi-empirical model of heats of formation, which accounts for the experimental glass-forming concentration range in binary alloys of transition metals.
Abstract: Free-energy diagrams of amorphous alloys are constructed using Miedema's semiempirical model of heats of formation. These diagrams account for the experimental glass-forming concentration range in binary alloys of transition metals. One of the main factors controlling glass formation is the elastic contribution to the heat of mixing of the solid solution phase. Free-energy diagrams of this kind are also useful for interpreting some characteristic processes occurring in amorphous systems, such as the spontaneous vitrification observed by Von Allmen and coworkers in several Ti-based and Nb-based alloys.

83 citations


Journal ArticleDOI
TL;DR: In this paper, the authors show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material, and they find two types of polaritons depending on the values of the in-plane wavevectork II: those atkII ω/v cannot be coupled to waves in the barrier.
Abstract: We show how the breaking of the translational invariance in a quantum well modifies the concept of polariton with respect to that defined for bulk material. Polaritons in quantum wells result from the combination of the exciton states with the radiation field. They are here obtained as the solutions of Maxwell equations with retardation, provided an appropriate nonlocal response function is used for the electric susceptibility, and Maxwell boundary conditions are imposed. We find two types of polaritons depending on the values of the in-plane wavevectorkII: those atkII ω/v cannot be coupled to waves in the barrier. In both cases explicit expressions are given for radiative shifts and radiative broadenings as functions ofkII. Numerical results are obtained for GaAs-Ga1−xAlxAs and for CuCl quantum wells and new experiments are suggested. The existence of resonant and surface polaritons justifies an interpretation of the temperature dependence of the radiative lifetime suggested by the same authors. It also decreases the radiative efficiency in the direction perpendicular to the planes and increases the radiative efficiency parallel to the planes with increasing temperature.

57 citations


Journal ArticleDOI
TL;DR: The existence of parity-breaking phase transition between untwisted and twisted bipolar structures of the tangentially anchored spherical nematic drops has been shown experimentally as mentioned in this paper, and temperature dependences of the order parameter (twist angle) have been determined for the drops of 8 CB and 8 OCB.
Abstract: The existence of the parity-breaking phase transition between untwisted and twisted bipolar structures of the tangentially anchored spherical nematic drops has been shown experimentally. Twisted structures behave like the optically active objects in spite of the nonactivity of nematic and isotropic matrix themselves. Temperature dependences of the order parameter (twist angle) have been determined for the drops of 8 CB and 8 OCB. It has been shown that these dependences are very similar to that observed in usual second-order phase transition.

41 citations


Journal ArticleDOI
TL;DR: In this paper, a phenomenological approach was used to show that the mixed splay-bend elastic constant of nematic liquid crystals must be considered zero unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the first order derivatives times the second order derivatives, and with the fourth powers of the first-order derivative, such contributions just reduce to one in the presence of a threshold.
Abstract: By means of a phenomenological approach, we demonstrate that the mixed splay-bend elastic constantK 13 in the free energy density of nematic liquid crystals must be considered zero, unless the bulk contributions of the squares of the distortion second-order derivatives are taken into account, together with the squares of the first-order derivatives times the second-order derivatives, and with the fourth powers of the first-order derivatives. Such contributions just reduce to one in the presence of—and close to—a threshold. Furthermore, the saddle-splayK 24-term instead is shown always to play an essential role, as the bulk first-order elasticity, in determining the distortion free energy of nematics with weak anchoring subjected to spatial deformations. Finally, the new surfacelike elastic constants are shown to have a nilpotent character: thus they behave as well asK 24 from the point of view of the variational calculus.

35 citations


Journal ArticleDOI
TL;DR: In this paper, it is argued that both of these effects can lead to more attractive pair interactions and possibly to effects much larger than Friedel oscillations, and that these contributions are state-dependent and their presence might be expected on the basis of clustering behavior seen for some systems in theirvapour phases.
Abstract: Interactions controlling ionic motion and structure in liquid metals can be systematically developed beginning with the ultimate view of such systems as neutral assemblies of nuclei and electrons, and proceeding to standard reduced Hamiltonians reflecting assemblies ofions and electrons. The assumption of electronically rigid ion leads via response methods and pseudopotentials to statically screened ion-ion potentials and beyond. Fluctuations are introduced into this otherwise common viewpoint by relaxing the assumption of electronically rigid ion cores and also by treating electronic response beyond linear order. It is argued that both effects can lead to more attractive pair interactions and possibly to effects much larger than, for example, Friedel oscillations. These contributions are state (i.e. density) dependent and their presence might be expected on the basis of clustering behavior seen for some systems in theirvapour phases. This leads to two limiting viewpoints on the liquid-state structure of such systems, the first as an entirely monoatomic phase but with a pair interaction that is unusual, the second as a system supporting transient clusters whose presence reflects the complexities argued on the basis of a more extended treatment of the electron problem.

33 citations


Journal ArticleDOI
TL;DR: In this paper, the complex impedance of a water-filled cell has been measured in the frequency range between 0.01 Hz and 100 kHz at temperatures ranging between 5°C and 80°C.
Abstract: The complex impedance of a water-filled cell has been measured in the frequency range between 0.01 Hz and 100 kHz at temperatures ranging between 5°C and 80°C. The obtained results have been interpreted according to the Gouy, Chapmann and Stern model describing the water behaviour in the presence of electrode interfaces. The deconvolution of the measured complex impedance allowed to separate the contribution arising from the «bulk» water from those due to the Helmholtz layer and to the diffuse charge layer occurring at the electrode interface. The capacitance and resistance of the three layers are reported and their frequency and temperature dependences are briefly discussed. The use of this method as a tool to investigate the low-frequency dielectric properties of water is suggested.

20 citations


Journal ArticleDOI
TL;DR: In this article, the existence of lyomesophases in the water systems of disklike molecules without the laterally surrounded longitudinal chains (carboxyderivatives of phtalocyanine and their metallocomplexes) is shown.
Abstract: The existence of lyomesophases in the water systems of disklike molecules without the laterally surrounded longitudinal chains—carboxyderivatives of phtalocyanine and their metallocomplexes—is shown. The dependence in displaying of lyomesomorphism on the metal nature and the arrangement of carboxyl groups in molecule is defined. The structures of lyomesophases are determined.

20 citations


Journal ArticleDOI
TL;DR: In this article, the structural properties of liquid group-V elements (and a compound InSb) and their differences with their room temperature crystalline phases are analyzed using short-wavelength neutrons (0.7 A).
Abstract: In this paper, we study the structural properties of liquid group-V elements (and a compound InSb) and we analyse the differences with their room temperature crystalline phases. Neutron diffraction experiments are performed using short-wavelength neutrons (0.7 A). We show different melting behaviours of a light element (As) and a heavy element (Sb) under study. Whereas As keeps its coordination three upon melting, Sb is six-coordinated in the melt. Similarly, InSb has a coordination number increasing from 4 to about 6 upon melting. Large entropies of melting are related to important structural variations.

19 citations


Journal ArticleDOI
TL;DR: A review of the history of the Fraunhofer approximation can be found in this paper, where the authors examine the historical evolution of this approximation which essentially started in optics when Bruns introduced the term eikonal in 1895.
Abstract: Certain problems in optical scattering are best understood when the more complicated exact scattering theory is replaced by an approximation. The Fraunhofer approximation is a well-known example. In the past ten years a considerable amount of work has been done in various disciplines towards assessing the usefulness of a new approximation referred to in the literature either as the eikonal approximation or as the high-energy approximation. The purpose of this paper is to provide a much needed review of this work and in addition to examine the historical evolution of this approximation which essentially started in optics when Bruns introduced the term eikonal in 1895.

19 citations


Journal ArticleDOI
TL;DR: In this article, the surface mechanism of deuterium reactions in palladium and titanium (clod fusion or neutron swapping) leading to strong tritium production and isotope shifts in Palladium was introduced.
Abstract: For explaining the surface mechanism of deuterium reactions in palladium and titanium (clod fusion or neutron swapping) leading to strong tritium production and isotope shifts in palladium, the mechanism of an exotic deuterium plasma with possible short nuclear distance by thermal motion was introduced. Using a new model of the surface tension of metals, resulting in a «swimming electron layer», the increase of the concentration of deuterons and the decrease of their distance cause a higher cold fusion in the surface layer by orders of magnitudes compared with the bulk material.

17 citations


Journal ArticleDOI
TL;DR: In this paper, an attempt is made to study effective electron mass in quantum well wires of ternary chalcopyrite semiconductors by formulating a new 1D dispersion relation, within the framework of the k·p formalism considering the anisotropies in the band parameters.
Abstract: An attempt is made to study effective electron mass in quantum well wires of ternary chalcopyrite semiconductors by formulating a new 1D dispersion relation, within the framework of thek·p formalism considering the anisotropies in the band parameters. It is found, taking quantum well wires ofn-CdGeAs2 as an example, that the effective Fermi level mass depends on the subband index due to the combined influence of crystal-field splitting parameter and the anisotropic spinorbit splitting parameters, respectively. The masses increase with increasing carrier degeneracy and decreasing film thickness, respectively. In addition, the well-known results for the corresponding parabolic energy bands have been derived as special cases of the generalized formulations.

Journal ArticleDOI
TL;DR: In this article, the results arising from a systematic X-ray analysis carried out on a homologous series of N-(4-alkoxysalicylidene)-4′-alkyl-aniline, either as uncomplexed ligands or as copper (II) complexes, are reported.
Abstract: The results arising from a systematic X-ray analysis carried out on a homologous series ofN-(4-alkoxysalicylidene)-4′-alkyl-aniline, either as uncomplexed ligands or as copper (II) complexes, are reported. Such an investigation, performed in order to elucidate the role played by both the metal centre and the length of the aliphatic chain, suggests a molecular packing which accounts for the increased order induced by the metallic core, the strong interdigitation of the molecules, the solid-phase features and the structural properties of the smectic mesophases.

Journal ArticleDOI
TL;DR: In this article, the authors review the description of dynamical processes in dense classical fluids by means of effective eigenmodes, which effectively represent the (microscopic) dynamical behaviour of the fluid on the molecular scale as far as time correlation functions or dynamic structure factors are concerned, that are observed in light, neutron or computer experiments.
Abstract: We review the description of dynamical processes in dense classical fluids by means of effective eigenmodes. These eigenmodes effectively represent the (microscopic) dynamical behaviour of the fluid on the molecular scale as far as time correlation functions or dynamic structure factors are concerned, that are observed in light, neutron or computer experiments. These effective eigenmodes can be determined either theoretically from hydrodynamic or kinetic theory or experimentally from an exponential or Lorentzian fit to observed correlation functions. We also consider the relevance of these modes for fluid mixtures and colloidal suspensions.

Journal ArticleDOI
TL;DR: Langmuir-Blodgett films of a number of native proteins have been prepared and their activities confirmed as mentioned in this paper, and the possibility of exploiting these layers in immunosensing structures is also reported.
Abstract: Langmuir-Blodgett films of a number of native proteins have been prepared and their activities confirmed. The possibility of exploiting these layers in immunosensing structures is also reported.

Journal ArticleDOI
TL;DR: In this paper, the rotational diffusion of a rodlike molecule in a nematic and smectic liquid crystal is considered in the molecular-field approximation, and the microscopic friction constant, which determines the molecular rotation drag, possesses an exponential temperature dependence with the activation energy determined by the isotropic part of the intermolecular interaction energy.
Abstract: The rotational diffusion of a rodlike molecule in a nematic and smecticC liquid crystal is considered in the molecular-field approximation The microscopic friction constant, which determines the molecular rotation drag, possesses an exponential temperature dependence with the activation energy determined by the isotropic part of the intermolecular interaction energy The rotational viscous coefficients,γ 1 andγ ⊥ are obtained by averaging of the corresponding microscopic stress tensor with the nonequilibrium distribution function The additional activation energy, proportional to the corresponding order parameter, appears in the expressions for the rotational viscosity coefficients both in nematics andC smectics

Journal ArticleDOI
TL;DR: In this paper, it was shown that the diffusion coefficient perpendicular to the electric field in Ar is the only quantity which, in practice, requires to have recourse to multiterm approaches and that the low values ofE/N permit to neglect inelastic collisions and have a large fraction of electrons in the energy regions where the cross-sections are strongly dependent on the electron energy.
Abstract: SummaryAccurate calculations of energy distributions and transport coefficients have been made in Ar and Hg by solutions of the Boltzmann equation for atoms at rest. The low values ofE/N permit to neglect inelastic collisions and have a large fraction of electrons in the energy regions where the cross-sections are strongly dependent on the electron energy. Comparisons between different techniques of solution with various approximation orders have shown that the diffusion coefficient perpendicular to the electric field in Ar is the only quantity which, in practice, requires to have recourse to multiterm approaches.RiassuntoSono state eseguite accurate soluzioni dell’equazione di Boltzmann per distribuzioni energetiche e coefficienti del trasporto in Ar e Hg nell’ipotesi di atomi a riposo. I bassi valori diE/N utilizzati permettono di trascurare le collisioni anelastiche ed avere una elevata frazione di elettroni nelle regioni energetiche dove la sezione d’urto dipende fortemente dall’energia elettronica. Confronti tra diverse tecniche di soluzione e vari gradi di approssimazione hanno mostrato che il coefficiente di diffusione perpendicolare al campo elettrico in Ar è l’unica quantità che, in pratica, richieda l’uso di soluzioni «multiterm».РезюмеИспользуя решения уравнения Больцмана для покоящихся атомов, аккуратно вычисляются энергетические распределения и транспортные коэффициенты в Ar и Hg. Малые значенияE/N позволяют пренебречь неупргими соударениями и получить большую долю электронов в энергетических областях, где поперечные сечения сильно зависят от энергии электронов. Сравнения между различными методами решения с использованием различных порядков приближений показывают, что коэффициент диффузии перпендикулярно электрическму полю в Ar является единственной величиной, которая на практике требует использования «многочленных» решений.

Journal ArticleDOI
A. Gordon1
TL;DR: In this article, it is shown that the solitonic mechanism may be responsible for the diffusion of ionic defects in some hydrogen-bonded solids, and a good agreement with experiments is obtained for H3O+ in ice crystals.
Abstract: It is shown that the solitonic mechanism may be responsible for the diffusion of ionic defects in some hydrogen-bonded solids. A good agreement with experiments is obtained for H3O+ in ice crystals.

Journal ArticleDOI
TL;DR: It is able to demonstrate that, merely by choosing the two fundamental constants of differential geometry to be complex numbers, standard «clockspring” curves adequately describe and explain these geometries though one small improvement is possible.
Abstract: Our earlier foundation paper for the new science ofTheoretical Conchology presented a general theoryexplaining seashell growth trajectories in terms of optimal, energy-efficient, tensile «clockspring» curves satisfying Hamilton's «least-action» principle. Meanwhile, working in isolation and publishing in Japanese, after the tradition of Wasan, Takashi Okamoto presented precise measurements and uncannily accurate 3D curveguesses which provide a finedescription of several bizarre, and previously little understood, «free-coiling» heteromorphic ammonites. One of these,Nipponites mirabilis, is so bizarre and wild that it provides the first good test of our new general theory. We are able to demonstrate that, merely by choosing the two fundamental constants of differential geometry to be complex numbers, our standard «clockspring” curves adequatelydescribe andexplain these geometries though one small improvement is possible. Even more surprising, considering the sheer wildness of the geometries, is the fact that Okamoto's guessed 3D «spheroidal» shapes agree with our correct, more general, «Lissajous» counterparts to several significant figures … a remarkable feat of precise measurement and intuition, on Okamoto's part, perhaps in its own way comparable to the achievements of Tycho Brahae and Johannes Keppler.

Journal ArticleDOI
TL;DR: In this paper, a new high-powered ultraviolet laser system is proposed, which can have a far-reaching impact in basic research and even more so in a great many industrial applications.
Abstract: A new high-powered ultraviolet laser system is proposed. The system doubles the infrared light from a Nd-Yag laser mode-locked at 100 MHz, injects this light into a storage-ring cavity to accumulate a high power in the visible and then doubles this into the ultraviolet at 2600 A. The power levels anticipated at this wavelength are much larger than those of commercially available c.w. lasers. The new system can have a far-reaching impact in basic research and, even more so, in a great many industrial applications.

Journal ArticleDOI
TL;DR: Using the monolayer model, a thermodynamic approach is suggested in this paper to compare the surface reactivity to the volume reactivity under both equilibrium and nonequilibrium conditions (sorption and chemical processes).
Abstract: Using the monolayer model, a thermodynamic approach is suggested in order to compare the surface reactivity to the volume reactivity under both equilibrium and nonequilibrium conditions (sorption and chemical processes). Capillary parameters, such as surface tension and surface dilation, have a direct influence on the efficiency of chemical reactions and on their stability.

Journal ArticleDOI
TL;DR: In this article, a method for recording spectrally resolved thermally stimulated luminescence is presented, which utilizes a continuous rotating interferential filter controlled by a PC and allows for noise filtering, spectral deconvolution and interpolation.
Abstract: A method is presented for recording spectrally resolved thermally stimulated luminescence. It utilizes a continuous rotating interferential filter controlled by a PC. Data processing allows for noise filtering, spectral deconvolution, interpolation and various fittings for a clear presentation of results.

Journal ArticleDOI
TL;DR: In this article, a generalized valence is defined for an atomic group; it reduces to the known expressions for the case of an atom in a molecule, and it is the sum of the correlations between the fluctuations of the atomic charges.
Abstract: In this work, a generalized valence is defined for an atomic group; it reduces to the known expressions for the case of an atom in a molecule. It is the sum of the correlations between the fluctuations of the atomic chargesq C andq D (C belongs to the group andD does not) around their average values. Numerical results agree with chemical expectation.

Journal ArticleDOI
TL;DR: In this paper, the real impact of a gas temperature different from zero is also studied by specific calculations of transport coefficients and energy distributions in Ar and Hg at very low values of the field.
Abstract: Multiterm calculations of energy distributions and transport coefficients of electrons in real and model gases acted upon by d.c. electric fields have recently been done by the authors with a new theory, developed to overcome known limitations of the conventional approach. In all of our previous calculations, gas temperature has always been neglected, for analytical and numerical simplicity. In this paper it is shown how this unphysical limitation can be removed. The real impact of a gas temperature different from zero is also studied by specific calculations of transport coefficients and energy distributions in Ar and Hg at very low values of the field.

Journal ArticleDOI
TL;DR: In this article, the binding energy of a two-dimensional exciton for a set of states labelled by the quantum numberm associated to the angular momentum in the direction perpendicular to the surface was calculated.
Abstract: We calculate the binding energy of a two-dimensional exciton for a set of states labelled by the quantum numberm associated to the angular momentum in the direction perpendicular to the surface. The Frohlich electron-phonon and hole-phonon interactions are taken into account. The statem=0 is more bound with respect to that obtained by the Wannier exciton theory with the screening given by the static dielectric constant and the reduced mass calculated by the electron and hole polaronic masses. The opposite effect is found for the statem=1,2,... Whenm becomes large, the hydrogenic series is recovered with the screening and reduced mass defined above. Our results are compared with the experimental data concerning exciton luminescence GaAs/Al x Ga1−x As, CuCl/CaF2 and CdTe/Cd1−x Zn x Te quantum wells.

Journal ArticleDOI
TL;DR: The dispersion of collective density fluctuations (extended sound modes) has been measured in mixtures of liquid alkali metals and the corresponding molten alkali-halide salts as mentioned in this paper.
Abstract: The dispersion of collective density fluctuations (extended sound modes) has been measured in mixtures of liquid alkali metals and the corresponding molten alkali-halide salts. Mixtures with salt concentrations from 10 to 40% were investigated for momentum transfersQ between 4 and 14 nm−1. ForQ-values larger than 11 nm−1 the collective modes could even in the most favourable case no longer be separated from the quasi-elastic peak, the width of which increases roughly ∼Q 2 in this region of momentum transfers. At a concentration of 10% RbCl in Rb we find a dispersion which would correspond to expanded liquid Rb at the temperature of the mixture (∼1000 K), demonstrating the dominant metallic character of the mixture (screening by nearly free electrons) at this salt concentration. At higher concentrations of salt, where influences from different partial dynamic structure factors interplay, the dispersions deviate from this simple structured dispersion curve, most likely due to the influence of an early onset of some ionic type of screening in the liquid.

Journal ArticleDOI
TL;DR: In this paper, the positron spin relaxation in a longitudinal magnetic field was investigated in some solids where Ps formation occurs, and the experimental results indicated that this relaxation manifests itself in those organic compounds where the POS can excite low-lying triplet states.
Abstract: The positron spin relaxation in a longitudinal magnetic field was investigated in some solids where Ps formation occurs. The experimental results indicate that this relaxation manifests itself in those organic compounds where the positron can excite low-lying triplet states. The values of positron slowing-down time, obtained by adopting a schematic model, range from 13 to 28 ps.

Journal ArticleDOI
TL;DR: In this article, a statistical thermodynamic model for ligand binding to giant respiratory macromolecules, such as molluscan hemocyanins, is proposed, which complies with the fundamental structural organization of this class of proteins.
Abstract: A statistical thermodynamic model for ligand binding to giant respiratory macromolecules, such as molluscan hemocyanins, is proposed. The model complies with the fundamental structural organization of this class of proteins. It assumes that each morphological unit functions as the element of a one-dimensional Ising lattice, so that conformational transitions occurring upon ligand binding may be propagated to the whole macromolecule through nearest-neighbour interactions. An application of the model to the analysis of oxygen equilibria of the β-hemocyanin ofHelix pomatia is presented and its general properties are discussed in connection with other models.

Journal ArticleDOI
TL;DR: In this article, a new derivation of the mode-coupling theory of liquid dynamics is presented which is applicable to both quantum and classical systems and a clear distinction between the basic underlying hyphotheses and the more technical approximations has been attempted.
Abstract: A new derivation of the mode-coupling theory of liquid dynamics is presented which is applicable to both quantum and classical systems. A clear distinction between the basic underlying hyphotheses and the more technical approximations has been attempted. Asymptotic corrections to the dynamics of modes due to mode-coupling effects and selfconsistent mode-coupling theories emerge from the original idea as two markedly different branches of application.

Journal ArticleDOI
TL;DR: In this paper, the authors studied the thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field, including the effects of Hall currents, and found that the Hall currents are stabilizing for T 1>M(1+x)2.
Abstract: The thermosolutal instability of a rotating plasma in the presence of a uniform vertical magnetic field is studied to include the effects of Hall current. When the instability sets in as stationary convection for the case of no rotation, the Hall effects are found to be destabilizing. The stable solute gradient and rotation are found to have stabilizing effects. In the presence of rotation the Hall currents are found to be stabilizing forT1>M(1+x)2. the case of overstability is also considered and it is shown that such solutions exist. The variation of the frequency with respect to the wave number at the neutral state is graphically shown.

Journal ArticleDOI
TL;DR: In this paper, a review of liquid dynamics studies on liquid metals is reported, particularly the case of liquid lead, which was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities.
Abstract: In the present review of liquid dynamics studies on liquid metals are reported. Particularly the case of liquid lead is reviewed because this case was carefully studied by neutron scattering technique,S(Q,ω) being determined at two widely different temperaturesT=623 K andT=1170 K and therefore different densities. In addition extensive supplementary MD simulations were made using a 16 384-particle system. The simulations ranged from a determination of an effective pair potential for lead to simulation of the density correlation functionsF(Q,t) andFs(Q,t), as well as the longitudinal and transversal current correlation functionsJ1(Q,t) andJT(Q,t). The MD simulation «calibrated» via the experimentalS(Q) andS(Q,ω) was used to prolong the range of neutron data to draw conclusions regarding such quantities as dispersion relations for the current correlationsJ1(Q,t) andJT(Q,t), the generalized viscosity functions ν1(Q,t), ν1(Q) and νs(Q). Information regarding bulk viscosity νB(Q) is also gained. Conclusions are drawn regarding the relative importance of the derived pair potential form by comparison to corresponding hard-sphere data. The general framework of linearized hydrodynamic equations for the macroscopic situation transforming to visco-elastic equations of motion for finite wave-length and high frequency works well also for the case of a continuous potential. The region of transition from simple visco-elastic to hydrodynamic behaviour is occurring at wavelengths in the range (12÷20) A for the cases studied. The spatial properties of the viscosity functions ν1(r), νs(r) and νB(r) are found to correlate well with the range of the radial distribution function for the liquid. The general results for liquid lead probably have wide range of applicability to other simple liquids with similarS(Q) andg(r) properties.