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We present a model equation of states for expanded metals, which contains a pressure term due to a screened-Coulomb potential with a screening parameter reflecting the Mott-Anderson metal-to-nonmetal transition. As anticipated almost 80 years ago by Zel'dovich and Landau, this term gives rise to a second coexistence line in the phase diagram, indicating a phase separation between a metallic and a nonmetallic liquid., 6 pages, 3 figures

The demarcation of the chemical elements into metals and non-metals dates back to the dawn of Dmitri Mendeleev's construction of the periodic table; it still represents the cornerstone of our view of modern chemistry. In this contribution, a particular emphasis will be attached to the question ‘Why do the chemical elements of the periodic table exist either as metals or non-metals under ambient conditions?’ This is perhaps most apparent in the p-block of the periodic table where one sees an almost-diagonal line separating metals and non-metals. The first searching, quantum-mechanical considerations of this question were put forward by Hund in 1934. Interestingly, the very first discussion of the problem—in fact, a pre-quantum-mechanical approach—was made earlier, by Goldhammer in 1913 and Herzfeld in 1927. Their simple rationalization, in terms of atomic properties which confer metallic or non-metallic status to elements across the periodic table, leads to what is commonly called the Goldhammer–Herzfeld criterion for metallization. For a variety of undoubtedly complex reasons, the Goldhammer–Herzfeld theory lay dormant for close to half a century. However, since that time the criterion has been repeatedly applied, with great success, to many systems and materials exhibiting non-metal to metal transitions in order to predict, and understand, the precise conditions for metallization. Here, we review the application of Goldhammer–Herzfeld theory to the question of the metallic versus non-metallic status of chemical elements within the periodic system. A link between that theory and the work of Sir Nevill Mott on the metal-non-metal transition is also highlighted. The application of the ‘simple’, but highly effective Goldhammer–Herzfeld and Mott criteria, reveal when a chemical element of the periodic table will behave as a metal, and when it will behave as a non-metal. The success of these different, but converging approaches, lends weight to the idea of a simple, universal criterion for rationalizing the instantly-recognizable structure of the periodic table where … the metals are here, the non-metals are there … The challenge of the metallic and non-metallic states of oxides is also briefly introduced. This article is part of the theme issue ‘Mendeleev and the periodic table’.

The reverse Monte Carlo (RMC) and Voronoi-Delaunay (VD) void analyses were applied to study the modification of chain geometries near the semiconductor (SC) to metal (M) transition in expanded liquid Se along the isochore of d = 3.4 g/cm3 .Fluctuations of dihedral angles with increasing temperature and pressure cause modification of the helical (H) chain to the planar zigzag (Z) chain conformations. The distribution of voids size (rV ) supported by chain segments and distances to the 4th ~ 6th neighbor atoms on the chain segments provide information on the stacking of planar zigzag chains compensated by empty space (L-voids, rV ~ 3.6 A) which leads to the formation of metallic domains. Near SC-M transition region the number fraction NZ /NH for Z and H chain segments increases.

The paper attempts to analyze the implications for the liquid-vapor transition of the recent finding of the coexistence of metallic- and non-metallic domains in liquid mercury. In particular, it is shown that liquid mercury forms a “pseudo-binary” mixture, for which the liquid-vapor two phase region in the pressure-temperature plane is no longer a single line but a two dimensional domain.

We examine the density-dependent metal-non-metal transition (MNMT) for the Group 1 elements hydrogen, rubidium and caesium. Remarkably, the experimentally observed metallization densities agree closely with those predicted from the 1927 classical theory of K. F. Herzfeld, which outlines the critical conditions necessary for the metallization of any element of the periodic system. The metallization densities of the alkali metal elements are also consistent with the quantum mechanical theory of the MNMT, as first set out by Sir Nevill Mott. © VCH Verlagsgesellschaft mbH, 1996.

Theoretical studies have long predicted that hydrogen will become a metal when subjected to intense pressure, but experimental studies have provided only indirect glimpses of this possibility. In their Perspective, Hensel and Edwards describe results from Lawrence Livermore National Laboratory in which the crucial quantity—electrical conductivity—has been measured as a shock wave passes through liquid hydrogen. As discussed in a news story by Kerr (p. 1667), the results have important implications for Jupiter, a planet consisting of hydrogen and helium under high pressure.

The small-angle X-ray scattering data of expanded fluid mercury published in the literature were evaluated using a modified form of the Teubner–Strey equation for microemulsions together with the general treatment of two-phase systems according to Porod. The parameters obtained in the critical region and the metal–nonmetal (M–NM) transition are evidence of a nanoemulsion composed of M and NM domains. The structure of this emulsion is characterized by density, volume fraction and size parameters (average chord length, polydispersity) of the domains. On the basis of these parameters, a structural model for fluid mercury in the liquid–vapour critical region and the M–NM transition is developed. Analysis of the relationship between the volume fraction of the M domains and the electrical conductivity reveals that a percolation transition occurs, with a threshold located near the liquid–vapour critical density. This observation is consistent with recent theoretical developments.

The classification of a chemical element as either ‘metal’ or ‘non-metal’ continues to form the basis of an instantly recognizable, universal representation of the periodic table (Mendeleeff D. 1905 The principles of chemistry , vol. II, p. 23; Poliakoff M. & Tang S. 2015 Phil. Trans. R. Soc. A 373 , 20140211). Here, we review major, pre-quantum-mechanical innovations (Goldhammer DA. 1913 Dispersion und Absorption des Lichtes ; Herzfeld KF. 1927 Phys. Rev. 29 , 701–705) that allow an understanding of the metallic or non-metallic status of the chemical elements under both ambient and extreme conditions. A special emphasis will be placed on recent experimental advances that investigate how the electronic properties of chemical elements vary with temperature and density, and how this invariably relates to a changing status of the chemical elements. Thus, the prototypical non-metals, hydrogen and helium, becomes metallic at high densities; and the acknowledged metals, mercury, rubidium and caesium, transform into their non-metallic forms at low elemental densities. This reflects the fundamental fact that, at temperatures above the absolute zero of temperature, there is therefore no clear dividing line between metals and non-metals. Our conventional demarcation of chemical elements as metals or non-metals within the periodic table is of course governed by our experience of the nature of the elements under ambient conditions. Examination of these other situations helps us to examine the exact divisions of the chemical elements into metals and non-metals (Mendeleeff D. 1905 The principles of chemistry , vol. II, p. 23).

We have performed quantum molecular dynamics simulations for expanded fluid Rb and Cs. We compare the pair correlation functions with results derived from neutron and x-ray scattering experiments. The experimentally observed structural changes with the density and temperature variation are reproduced. The density of states and the electronic charge density extracted from the simulations indicate a crossover from metallic to nonmetallic behaviour near the critical point due to a localization of electrons at nuclei.

Experimental results in the liquid vapour critical region of metals show that the metal-nonmetal transition noticeably influences, the electronic, thermodynamic, structural, dynamic and interfacial features of fluid metals. The main emphasis of the paper is on the intimate interplay between the changes in interparticle forces and the changes in the electronic structure associated with the pressure ionization.

Short wavelength collective excitations in liquid Hg at room temperature have been investigated by high-resolution inelastic X-ray scattering. Clear evidence for the existence of propagating modes was found from the S ( Q , ω ) at constant Q up to about 17 nm −1 . A positive dispersion in the Q – ω relation for these excitations was identified. This behavior is described in a simplified viscoelastic view.

Looking back on the 35 years that have passed between the first LM-conference in Brookhaven and LAM 11 in Yokohama it is clear that the field of liquid metals has gained in certainty, in depth and in width. It is impossible to try to summarize within the scope of a lecture all of the important developments that had happened in between, and it is even more futile to try to define emerging areas of opportunities. But it may be interesting to compare the topics of the 1966-conference in Brookhaven with their counterparts of the 2001-conference in Yokohama, and to see briefly the effects of 35 years of active development on the field.

Liquid Te just above the melting point is a poor metal. Its structure is assumed to consist of short chains of covalently bound atoms, with strong chain–chain interaction causing metallic like properties. To study the temperature dependence of this structural arrangement, energy dispersive X-ray diffraction measurements were carried out on liquid Te in a temperature range between 500 and 1700 °C and an applied pressure of 50 bar. It is found that the position of the first peak in the structure factor is located around 2.1 A −1 at 500 °C and shifts to 2.25 A −1 for temperatures above 1300 °C. Additionally, an increase in the scattering intensity is observed around 1.4 A −1 with rising temperature. The structural variations also influence the corresponding pair distribution functions. With increasing temperature, the first co-ordination shell shifts to larger distances but remains at a constant position above 1100 °C, suggesting a structural transition in this temperature range. This view is supported by temperature induced changes which are observed in the second coordination shell.

Anomalous X-ray scattering experiments have been performed for glassy (g-) As 2 Se 3 at room temperature and for liquid (l–) As 2 Se 3 at 400 °C in order to clarify the role of each constituent for the short- and intermediate-range order (SRO and IRO). The differential structure factors Δ i S ( Q )s close to the As and Se K edges have been obtained from a detailed analysis. The first nearest neighbour distances around both As and Se are about 0.24±0.02 nm for both g- and l-As 2 Se 3 , which would support the SRO model that g- and l-As 2 Se 3 have an SRO similar to the corresponding crystal. The prepeak in S ( Q ) for g-As 2 Se 3 seems to be dominated by a partial structure factor S AsAs ( Q ), which reveals the existence of the As–As IRO with a correlation length of about 0.52 nm. In l-As 2 Se 3 , however, the substitution of Se atoms into some As sites would cause a contribution in Δ se S ( Q ) at the prepeak position.

Interesting results were obtained in the initial investigation of the nucleation behavior of supersaturated sulfur vapor up to temperatures above the λ transition. This is a second-order phase transition in liquid sulfur characterized by a change in molecular structure from closed sulfur rings to open radical chains within a narrow temperature range. Although the temperature dependence of the constant rate supersaturation is not correctly represented, it is surprising again how well classical nucleation theory describes experimental results even for such a complex substance. For homogeneous nucleation, there are indications that the λ transition influences the nucleation behavior as a consequence of the changing thermophysical properties density and surface tension of the liquid sulfur. Photoinduced nucleation shows a striking effect directly correlated with the transition. Below the λ temperature, the vapor is extremely sensitive to irradiation with light in the range 260−360 nm that decreases the cons...

It is shown that many useful concepts and theoretical methods developed for description of transport and relaxation of charge carriers in disordered inorganic solids can be successfully applied to the description of such phenomena in disordered organic solids. While for 3D systems analytical calculations are semi-quantitative, the theoretical results for 1D systems are exact. The latter predict pronounced mesoscopic effects for rather large samples calling for caution in the treatment of experimental data.

An analytic theoretical description of transport processes based on the concept of transport energy is suggested for disordered organic solids. It gives not only the natural explanation of experimental data but also accounts for the results of computer simulations considered so far puzzling. In particular, this approach accounts for the strong difference between the temperature dependence of the carrier drift mobility and that of the relaxation time. Experimental data for the low-field drift mobility display the temperature dependence in the form $\ensuremath{\mu}\ensuremath{\propto}\mathrm{exp}{\ensuremath{-}{(T}_{0}{/T)}^{2}}.$ It is believed that the characteristic temperature ${T}_{0}$ is determined solely by the scale of the energy distribution of localized states, and such a temperature dependence of \ensuremath{\mu} is widely used to determine this energy scale from experimental data for various materials. We show that this temperature dependence is not universal and that parameter ${T}_{0}$ depends also on the concentration of localized states and on the decay length of the carrier wave function in the localized states. The suggested theory provides a general basis for the treatment of transport processes in disordered organic media.

The first experimental study of the spectral dependence of the nucleation of cesium vapor caused by light absorption is carried out in a diffusion cloud chamber. The spectral dependence of the nucleation rate is compared with the absorption and ionization spectra of cesium vapor. The results evidence that the observed structure in the nucleation spectrum at photon energies above the ionization threshold is correlated to the light-induced ionization of cesium dimers Cs2+. At lower photon energies light-induced nucleation can be either due to generation of ions by direct ionization of cesium clusters, to various two-step ionization processes, or to optical excitation of cesium atoms. The spectral dependence of the nucleation rate provides a new and powerful tool to study ionization spectra of metal vapors. In addition to results obtained by conventional methods a more consolidated insight into energy levels of atoms and clusters under equilibrium conditions is possible.

An investigation of the density dependence of the structure in liquid rubidium was performed along the liquid vapour coexistence line up to temperatures of 1573 K and 50 bar, and corresponding densities between 1.45 and 0.87 g/cm 3 . All experiments were carried out at the beamline ID30 of the European Synchrotron Radiation Facility (ESRF) in Grenoble. The diffraction pattern could be measured using the combination of a newly developed high-temperature high-pressure scattering setup and monochromatized X-rays of about 50 keV with an imaging plate detector. Although the duration of a single experiment took only approximately 20 s, an extreme improvement in scattering statistics and an extended Q-range could be achieved compared with a previous neutron scattering result on the same system.

The properties of metallic hydrogen–nonmetallic helium mixtures are of considerable interest for planetary modelling. In the light of the unfavourable outlook for reliable measurements under the extraordinarily high temperatures and pressures prevailing in the planet’s interiors it becomes interesting to study the phases of fluid mercury–helium mixtures which might serve as a model for the hydrogen–helium-system. At sufficiently high density, nonmetallic expanded mercury experiences a transition to a conducting state not unlike that recently observed in hydrogen. The experimental results for mercury–helium, which extend to pressures of 4000 bar and temperatures to 1800 K, show that two distinct fluid phases exist at supercritical temperatures and high pressures.

Knowledge of the properties of hydrogen and helium and their mixtures, at temperatures and pressures prevailing in the giant planets is of considerable interest for planetary modelling. In the light of the unfavourable outlook for reliable measurements under these extreme conditions effort has been spent investigating the high-temperature high-pressure properties of fluid metals which are experimentally accessible in the laboratory and which might serve as models for compressed fluid hydrogen. The main emphasis of the paper is on the density dependence of the dynamic structure factor of liquid rubidium which reveals that a monoatomic-molecular transition occurs in the metal-non-metal transition region of the expanded liquid analogous to that suggested to occur in shock compressed hydrogen. Additional emphasis is on new results of the phase behaviour of dilute mixtures of helium in the near critical metal mercury.

We have studied the adsorption of mercury on sapphire at temperatures and pressures close to the liquid-vapour critical point (Tc= 1478°C, pc= 1673 bar, pc = 5.8 g/cm3) of mercury. The mercury film undergoes a first-order phase transition known as prewetting. At low temperatures, the prewetting line meets the bulk coexistence curve tangentially at the wetting temperatures Tw = 1310°C. At high temperatures the prewetting line terminates at the prewetting critical point Tcpw = 1468°C and the prewetting pressure pcpw = 1586 bar lying close to the bulk critical point. In analogy with the line of compressibility maxima extending above the liquid-vapor critical point, we can identify an extension of the prewetting phase line for T>Tcpw which marks the maximum in the two-dimensional compressibility of the prewetting supercritical phase.

A new theory of thermostimulated currents at low temperatures has been recently suggested. We use this theory to study the effect of defect concentration on thermostimulated conductivity in hydrogenated amorphous silicon.

Transport properties of disordered semiconductors at low temperatures are determined by hopping of electrons via localized band tail states. Much attention has been paid recently in both experimental and theoretical studies to the relation between the diffusion coefficient of carriers, D, and their mobility, μ, in the hopping regime. Rather controversial results have been reported. In particular, some computer simulations have been claimed to show that the conventional Einstein relation μ=eD/kT is violated in the hopping regime even in the case of thermal equilibrium. We study the relation between μ and D by a computer simulation and show that such statements were based on a wrong interpretation of the simulation results. In thermal equilibrium, the Einstein relation between μ and D must hold, although in a nonequilibrium system this relation can be violated.

The metal-insulator transition, a quantum phase transition signifying the natural transformation of a metallic conductor to an insulator, continues to be the focus of intense inquiry and debate. The first discussion of the heuristic differences between metals and insulators, and implicitly the critical conditions for the transition between these canonical electronic regimes, dates back to the dawn of the twentieth century. As we approach the end of the century, the precise nature of the metal-insulator transition remains one of the major intellectual challenges in condensed matter science. In this article we present a brief introduction to just some of the key underlying features of this enduring physical phenomenon. The following articles and discussion present a detailed current account of the many facets of the science of the metal-insulator transition.

Fluid metals are typical examples of materials whose electronic structures depend strongly on the thermodynamic state of the system. The most striking manifestation of this state dependence is the metal–non–metal transition which occurs when the dense liquid evaporates to the dilute vapour or when the fluid is expanded by heating to its liquid–vapour critical point. The main emphasis of the paper is on the intimate interplay between the changes in interparticle forces and the changes in the electronic structure associated with the metal–non–metal transition. The most significant experiments relevant to this question are those on the liquid–vapour coexistence curves, the static– and dynamic–structure factors S ( Q ) and S ( Q,ω ), the electrical properties and interfacial features in the liquid vapour–critical region. For example, reflectivity experiments on mercury against sapphire reveal clearly the existence of a prewetting transition. The transition line starts at the wetting transition temperature T w . T w lies in the metal–non–metal transition region.

Theoretical interpretation of the thermally stimulated conductivity (TSC) is suggested for the temperatures at which transport is via hopping of carriers through localized bandtail states. The description is not based on specific assumptions used in the most of the previous TSC theories, such as, e.g., neglect of the retrapping of mobile carriers, etc. Our approach is based on the general concept of the transport energy according to which the transport path of hopping electrons in the bandtail is temperature dependent. This theory allows for a natural extension to higher temperatures and accounts for all existing experimentally observed trends in the TSC including the puzzling so far pinning of the low-temperature maximum on the TSC curves at different initial temperatures. Experimental results for the low-temperature TSC are presented, which are consistent with the theoretical predictions.

S(Q,{omega}) for liquid rubidium measured along the liquid vapor coexistence line exhibits monatomic behavior from normal density down to twice the critical density. At this density we observe excitations characteristic of a harmonic oscillator. We interpret this as evidence for the passage of the fluid from a monatomic to a molecular state. First principle total energy calculations for lattices of ribidium at 0K predict that expansion favors spin pairing and leads to a lattice of dimers with an increase in vibron energy with decreasing density. The excellent agreement of the calculated vibron energy with the experimental result provides theoretical support for the appearance of molecules. {copyright} {ital 1997} {ital The American Physical Society}

Optical reflectivity data are reported for expanded liquid caesium over the range (density, ) to (density, ) for photon energies . Optical effective mass ratios obtained from the plasma frequency are compared with mass ratios extracted from analysis of the magnetic susceptibility. Both masses exhibit enhancements for liquid densities less than about , suggesting that expanded caesium gradually transforms to a highly correlated metal below this density.

It is known that in disordered semiconductors with purely exponential energy distribution of localized band-tail states, as in amorphous semiconductors, all transport phenomena at low temperatures are determined by hopping of electrons in the vicinity of a particular energy level, called the transport energy. We analyse whether such a transport level exists also in materials with densities of localized states (DOSs) different from the purely exponential one. We consider two DOS functions with , typical for polymers, heavily doped semiconductors, and, probably, liquid semiconductors and , typical for mixed crystals. It is shown that in both cases the transport energy exists, implying that it also exists for all intermediate forms of the DOS. Special attention is paid to the dependences of the transport level and of its width on the DOS parameters and temperature.

Reflectivity experiments on fluid mercury against an optically transparent sapphire window at high temperatures and high pressures close to the liquid - vapour critical point reveal clearly the existence of a prewetting transition of mercury on the sapphire substrate. The prewetting line intersects the coexistence curve at the wetting temperature , and terminates at the prewetting critical temperature and prewetting critical pressure lying close to the bulk critical point.

The static electric polarizability α of Si N , Ga N As M and Ge N Te M clusters in a molecular beam, with nozzle temperatures ranging from 38 to 300 K, were investigated from their deflections in an inhomogeneous electric field. A striking size dependence is observed for small Ga N As M and Si N clusters. Specifically, for Ga N As M clusters with up to 15 atoms, the polarizability oscillates strongly between low values for even numbers of atoms N + M and high values for odd numbers of atoms N + M. This behavior of α as a function of size can be understood by a widening of the band gap and additional occurrence of defect-like electronic states. The temperature dependence of the polarizability of most Ge N Te M clusters indicates the importance of vibronic (ionic) contributions to α. This may be related to the ferroelectric behavior of bulk GeTe.

This paper discusses recent experimental results in the liquid-vapour critical region of mercury. These results show that the existence of the metal-non-metal transition noticeably influences electronic, thermodynamic, structural and interfacial features. Optical reflectivity experiments were conducted for mercury in contact with an optically transparent sapphire substrate. The experiments were carried out with the mercury close to the vapour-liquid coexistence curve. The temperature and density dependence of the reflectivity reveal clearly the existence of a prewetting transition of mercury on the sapphire substrate. At high temperature, the transition line terminates at a surface critical temperature T sc lying below the bulk critical temperature T c . At low temperature, it terminates at the wetting transition temperature T w . Furthermore, the transition lies close to the bulk vapour-liquid coexistence curve and occurs when the bulk vapour pressure is within a few percent of its saturation value.

The phase behaviour of dilute mixtures of the He in near-critical fluid Hg has been studied within the ranges 69 MPa to 332.5 MPa, 1433 K to 1882 K and amount-of-substance fractions x (He) within the values 0.0018 and 0.1020. A high pressure and high-temperature vessel was filled with known amounts of He and Hg (synthetic method) and heated; an isochoric record of p and T was made while the temperature was gently decreased and the transition from homogeneous to two-phase systems was indicated by abrupt slope changes in the p -against- T isochores. Two distinct fluid phases are shown to exist in (helium + mercury) at temperatures and pressures higher than those corresponding to the critical point of pure mercury (“fluid–fluid equilibrium of the first type”) and the system's critical line, beginning at the critical point of pure Hg, runs steeply to higher pressures and temperatures. Solubility values as high as 0.28 mol·dm −3 were measured for He in near-critical fluid Hg, in contrast to the much lower values estimated for He dissolved in metallic liquid Hg at sub-critical temperatures. The isobaric solubility of He in Hg increases with temperature for super-critical pressures so that (helium + mercury) shows a positive enthalpy and entropy of dissolution under these conditions. At sufficiently high density, non-metallic near-critical Hg experiences a transition to a metallic state, resulting in a strong repulsive interaction between dissolved He and the surrounding conduction electrons, and hence the isothermal solubility of He decreases.

Some recent theoretical approaches to the hopping of electrons through localized band-tail states are discussed. Particular attention is given to the approximation in which energy relaxation of non-equilibrium electrons is treated as diffusion in energy space and to the approximation based on the averaging of hopping rates. It is shown that both approaches lead to results different from those based on Mott's semiquantitative technique with averaging hopping distances, not the rates. Detailed analysis shows that both diffusion approximation and averaging of hopping rates are inapplicable to hopping relaxation and transport of carriers in band tails.

Photoconductivity in amorphous semiconductors at very low temperatures is temperature-independent, being determined by the energy-loss hopping of carriers through localized band-tail states. In such a hopping relaxation, neither diffusion coefficient, D , nor mobility of carriers, μ, depend on temperature and the conventional form of the Einstein's relationship μ = eD kT is not valid. The relationship between μ and D for the hopping relaxation of electrons in the exponential band tail is calculated and it is shown that it has the form μ ∝ eD ϵ 0 , where ϵ 0 is the energy scale of the exponential band tail.

Most elements are metals. These elements remain metallic when they are heated through their melting point at normal pressure. Perhaps more surprisingly, two elements that are non-metallic in their solid form, silicon and germanium, also become metallic on melting. Indeed, if we consider the extremes of temperature and pressure found in many geophysical and astrophysical settings – some of which are now accessible in terrestrial laboratories – even more non-metallic elements become metallic in the fluid state. This includes fluid hydrogen, which has recently been shown to be metallic at high enough temperatures and pressures.

Recent measurements for expanded Hg, Cs and Rb have shown that the liquid - vapour coexistence curves for these metals do not obey the `law of rectilinear diameters'. It is shown here that a two-state Van der Waals equation with a density-dependent cohesive energy will lead to compositional fluctuations that result in a breakdown of the `law'. Calculations predict that Hg and the alkali metals will exhibit similar behaviour near the critical point. However, in the case of Hg the 6p - 6s band-gap closure, which occurs at higher than critical densities, leads to an anomalous behaviour not observed in the alkali metals. The influence of this transition on the rectilinear behaviour is treated by introducing a further modification of the two-state model.

Magnetization curves of stabilized cobalt-cluster dispersions in tetrahydrofuran with a narrow size distribution have been studied by SQUID and Gouy balance measurements. The cobalt colloids are generated by a newly developed electrochemical method which allows one to generate clusters with mean cluster sizes of about 1000 atoms. The final size distribution of the clusters is examined by small-angle x-ray scattering (SAXS) and high-resolution transmission electron microscopy (HRTEM) measurements. The magnetization curves have been measured with special emphasis on changes at the freezing point of the solution. The liquid phase shows typical superparamagnetism whereas strong deviations from Langevin behavior occur in the solid dispersion which can be understood in terms of magnetic anisotropy effects. These observations are discussed with regard to recent Stern-Gerlach experiments on isolated ferromagnetic clusters in molecular beams. It is shown that cluster size and susceptibility of the dispersions are related. This permits the control of the growth of the clusters during the electrolysis by measuring the susceptibility as a function of the charge that is converted in the cell.

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A system of nanometer sized cobalt clusters surrounded by dielectric shells has been investigated by electrical dc conductivity measurements. The cobalt clusters have a diameter of 36 A and are surrounded by an approximately 12‐A‐thick layer of tetra‐octyl‐ammonium bromide surfactant molecules and poly(phenyl‐p‐phenylenevinylene). The conductivity σ shows a temperature dependence ln(σ)∝(T0/T)1/2 in the range 100

Calculations are carried out to solve the thus far puzzling problem of the long‐time trends in the photoinduced condensation of supersaturated vapors observed in thermal diffusion cloud chambers. These trends are the long‐time delay of the condensation after switching the light on and the long‐time decay after terminating the light. The calculations show that the supersaturation level which governs the condensation process cannot be affected significantly by irradiation under conventional experimental circumstances, and hence its change cannot be the cause of the long‐time transients. These trends are attributed to the slow diffusion‐limited growth of liquid droplets before they achieve the observable size of 10−3–10−2 cm. The predictions are in good agreement with experimental data.

Recent measurements of the electron and hole drift mobilities and the optical absorption in hydrogenated amorphous silicon have strongly supported the presence of long-range potential fluctuations (LRPF) in a-Si:H. Independently, such fluctuations were suggested as the cause of the exponential energy distribution of localized tail states in amorphous semiconductors. These two problems are analyzed theoretically, and it is shown that the experimental results on the optical absorption can, indeed, be well accounted for, even quantitatively, by the classical theory of LRPF. However, this theory does not predict a purely exponential dependence for the density of states. Such a dependence could only appear in the transition range from a Gaussian shape, which for shallow states is caused by typical classical fluctuations, to a weaker dependence caused by quantum mechanical fluctuations for deeper localization energies.

Binary oxygen potassium clusters were generated by seeded supersonic expansion of a gaseous mixture of potassium, argon and molecular oxygen. Clusters of composition K x O ( x = 5, 7, 9) and K x O 2 ( x = 5–7, 9) were detected for the first time. Their ionization potentials are smaller than 3.67 eV. Scattering experiments with H 2 O as target molecules indicate that K 3 O and K 4 have much more compact ground state structures than the planar aggregates K 3 and K 4 .

The static electric polarizabilities a of silicon clusters with up to 60 atoms have been measured employing a mass selective molecular beam deflection method. The polarizability per atom αN = α/N of the SiN-clusters has been investigated for Si11 and the size ranges N = 14-28, 22-34, 28-44, 34-50, 41 -58, and 42-68. The results show that the polarizability per atom decreases from N = 11 until a minimum at N≥28 is reached. The polarizability per atom increases for N > 28, passes through a maximum at N≈36 and finally converges between N≈50-70 against the value αN =1.9Å3. If the model of a homogeneous dielectric sphere is applied to the larger clusters one calculates that the value αN =1.9Å3 corresponds to a dielectric constant of ε = 3.2. This value is significantly smaller than the dielectric constant of bulk silicon εb = 11.8. The present paper focuses on the maximum in the polarizability at N≈36. This effect is discussed with special emphasis to recent Car-Parinello calculations which have predicted cage-like silicon structures that enclose a core of several highly coordinated atoms. This structure suggests an improved dielectric sphere model where the core is represented by a smaller sphere with its own dielectric constant εc. It is shown within this model that the observed maximum in polarizability is due to a significant enhancement of the core dielectric constant to a value of εc ≈50. This enhancement is related by means of a simple model to the effect that silicon becomes metallic under high pressure