Abstract If the distance between atoms in a crystalline lattice is increased, an energy gap appears, which in a divalent material will separate occupied from unoccupied states of an electron. In a non-crystalline substance, a minimum is expected in the density of states (a ‘pseudogap’). An approximate theoretical estimate is given of the depth of the minimum at which the one-electron states become localized so that 〈σE(0)〉 vanishes; this turns out to be such that N(E F)/N(E F)free is about ⅓. The result depends rather sensitively on the parameters used; the value deduced from the experiments of Hensel and Franck (1966, 1968) on the resistivity of mercury at high temperatures gives for this ratio a value of ⅕. It is shown also that the localized states at the extremities of a valence or conduction band are of negligible importance if the wave functions are s-like on the atoms or ions, but may be of importance if they are not. A discussion is given of the electrical behaviour of chalcogenide glasses, amorph...

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Conduction in Non-Crystalline Materials

If the distance between atoms in a crystalline lattice is increased, an energy gap appears, which in a divalent material will separate occupied from unoccupied states of an electron. In a non-crystalline substance, a minimum is expected in the density of states (a ‘pseudogap’). An approximate theoretical estimate is given of the depth of the minimum at which the one-electron states become localized so that 〈σE(0)〉 vanishes; this turns out to be such that N(E F)/N(E F)free is about ⅓. The result depends rather sensitively on the parameters used; the value deduced from the experiments of Hensel and Franck (1966, 1968) on the resistivity of mercury at high temperatures gives for this ratio a value of ⅕. It is shown also that the localized states at the extremities of a valence or conduction band are of negligible importance if the wave functions are s-like on the atoms or ions, but may be of importance if they are not. A discussion is given of the electrical behaviour of chalcogenide glasses, amorph...

Conduction in non-crystalline materials

Microwave-Assisted Synthesis in Water as Solvent

“Hydrothermal synthesis” usually refers to heterogeneous reactions in aqueous media above 100°C and 1 bar. The previously common distinction between hydrothermal conditions below and pneumatolytic conditions above the critical point is no longer made, since no discontinuities are observed upon exceeding the critical conditions. Under hydrothermal conditions, reactants otherwise difficult to dissolve go into solution as complexes, in whose formation water itself or very soluble “mineralizers” can participate. Thus, one can obtain the conditions of chemical transport reactions,[1] of which hydrothermal syntheses can be considered a special case. During recent decades in the geological sciences—in which the method is also historically rooted—it has received a strong impulse, whose effect on preparative solid state chemistry is discussed here.

The Role of Hydrothermal Synthesis in Preparative Chemistry

Hot compressed water (HCW, here water above 200 °C) possesses very interesting properties This series of articles gives an overview of the state of the art as regards the understanding of reactions in HCW In the first part the macroscopic and microscopic properties of HCW will be described, followed by a summary of synthesis reactions published The impact of the unique properties shall be discussed in part II, with the thermal degradation of tert-butylbenzene and the oxidation of methanol being used as examples The studies reported will show that the microscopic properties are of more importance to understanding reactions in HCW than assumed in the past

Hot compressed water as reaction medium and reactant properties and synthesis reactions

Water is not restricted to moderate temperatures and low pressures, but can exist up to very high temperatures, far above its critical point at 647 K. In this supercritical regime, water can be gradually compressed from gas-like to liquid-like densities. The resulting dense supercritical states have extraordinary properties which can be tuned by temperature and pressure, and form the basis for innovative technologies. This Review covers the current knowledge of the major properties of supercritical water and its solutions with nonpolar, polar, and ionic compounds, and of the underlying molecular processes.

Supercritical water as a solvent.

The method of the Pendant Drop or Standing Bubble is applied to measure interfacial tensions between water and nonpolar fluids to high temperatures and pressures. The high pressure cell with two sapphire windows and the auxiliary equipment with several feed autoclaves is described. The shapes and sizes (about 2 mm) of drops and bubbles are recorded with microscope and video camera. A digital image processing procedure was developed which permits fast, objective and precise determination of the contour parameters.

The six gases helium, neon, argon, nitrogen, methane, and propane have been investigated to 473 K (with nitrogen to 573 K) and (in part) to 2800 bar. Gas densities came close to liquid density values. For comparison, water plus liquid n-hexane, n-decane, and toluene was investigated to 473 K and 3000 bar. For these liquid hydrocarbons, the interfacial tension γ always increases with pressure. At 373 K for water-n-hexane γ is 41.8 mN/m at 100 bar and 47.3 mN/m at 2600 bar, respectively. In the water-gas systems γ decreases with pressure and passes through a flat minimum around 1000 bar. For water-nitrogen at 373 K γ = 52.5, 46.5 and 48.3 mN/m at 200, 1400 and 2800 bar. Only with water-helium γ increases continuously with pressure.

Interfacial tension between water and non-polar fluids up to 473 K and 2800 bar

This article presents the results of conductivity and density measurements of liquid, gaseous, and supercritical mercury up to 1700\ifmmode^\circ\else\textdegree\fi{}C and 2100 bar. Beyond the critical temperature of 1490\ifmmode^\circ\else\textdegree\fi{}C the conductivity varies continuously from ${10}^{\ensuremath{-}4}$ to ${10}^{2}$ ${\mathrm{\ensuremath{\Omega}}}^{\ensuremath{-}1}$ ${\mathrm{cm}}^{\ensuremath{-}1}$ if the density is increased from 2 to 6 g/${\mathrm{cm}}^{3}$. This variation is an example of nonmetal-metal transition and is discussed accordingly. The activation energy of conductivity in the supercritical fluid decreases markedly with increasing density and approaches very small values around 5 g/${\mathrm{cm}}^{3}$. Conductivity data for dense gaseous mercurycesium mixtures are given.

Metal-Nonmetal Transition in Dense Mercury Vapor

A survey is given of recent results on properties of water and aqueous solutions at high pressures and high temperatures with emphasis on supercritical conditions. New PVT-data for water from static measurements are available to 1000°C and 10 kb. Dielectric constants and viscosity have been measured to 550°C and 5 kb. Infra-red and Raman spectra of OD-vibrations of HDO in F120 to 400°C and 5 kb give information about the extent of hydrogen bonded structure. Critical curves of binary aqueous systems with one inert component, for example argon, extending to 3 kb and 400°C are discussed. Absorption spectra of bivalent cobalt and nickel chlorides are measured to 500°C and 6 kb and conclusions about the stability of octahedral and tetrahedral complexes are drawn. Shock wave and static conductance measurements to 1000°C and more than 100 kb demonstrate the increase of the ion product of water by twelve orders of magnitude or more at these conditions.

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Water and aqueous solutions at high pressures and temperatures

Etudes de fluides supercritiques sous hautes pressions pour une large gamme de densite. On etudie en particulier les fluides avec des moleculaires polaires avec de fortes interactions (l'eau par exemple). Densite, constante dielectrique et auto-ionisation de l'eau

E. U. Franck

Papers

Supercritical water as a solvent.

Interfacial tension between water and non-polar fluids up to 473 K and 2800 bar

Metal-Nonmetal Transition in Dense Mercury Vapor

Water and aqueous solutions at high pressures and temperatures

Fluids at high pressures and temperatures