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R. Smoluchowski

Bio: R. Smoluchowski is an academic researcher from Princeton University. The author has contributed to research in topics: Work function & Order of magnitude. The author has an hindex of 9, co-authored 14 publications receiving 1424 citations.

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TL;DR: In this paper, the authors used the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal.
Abstract: Work function is experimentally known to be different for different faces of a crystal by amounts ranging from one-tenth to half a volt. For tungsten the faces can be arranged according to decreasing work function as follows: 110, 211, 100 and finally 111. The explanations so far suggested for the differences of the work function are discussed and shown to give either an incorrect sequence or a wrong order of magnitude of the observed differences. The author uses the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal. The origin of the latter can be described in the following manner. With every atom one can associate a polyhedron ("$s$-polyhedron") with the atom at its center, such that it contains all points nearer to the atom under consideration than to any other atom. If the distribution of the electron density within these polyhedra of the surface atoms was the same as for the inside atoms then there would be no double layer on the surface. However, this is not the case since the total energy is lowered by a redistribution of the electron cloud on the surface. There are two effects: the first is a partial spread of the charge out of the $s$-polyhedra and the second is a tendency to smooth out the surface of the polyhedra. In consequence of the second effect the surfaces of equal charge density are more nearly plane than in the original picture. The two effects have opposite influences and since they are comparable in magnitude, it is not possible to predict the sign of the total double layer without numerical computations. Some general formulae for the double layers are derived and discussed more fully in the case of a simple cubic and a body-centered cubic lattice. The minimum problem of the surface energy is solved for four faces of a body-centered crystal and the results are applied to the case of tungsten. One obtains the differences between the work functions for different directions. The results agree satisfactorily with the experimental data: assuming a reasonable density of the free electrons, one obtains the correct sequence of faces and the correct differences of the work function. The surface energies are calculated an d found in agreement with the observed stability of certain crystal faces.

1,117 citations

Journal ArticleDOI
22 Mar 1968-Science
TL;DR: The presence of subsurface ice may explain the higher radar reflectivity of the dark areas than of the bright areas, and observation of its seasonal variations is suggested.
Abstract: Water in the form of ice can exist on Mars as permafrost that is either in equilibrium with the water content of the atmosphere or gradually evaporating through a protective layer of soil. The latter situation is evaluated quantitatively, and the required thicknesses of the protective layers are estimated. The presence of subsurface ice may explain the higher radar reflectivity of the dark areas than of the bright areas. Observation of its seasonal variations is suggested.

93 citations

Journal Article
TL;DR: In this article, the authors used the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal.
Abstract: Work function is experimentally known to be different for different faces of a crystal by amounts ranging from one-tenth to half a volt. For tungsten the faces can be arranged according to decreasing work function as follows: 110, 211, 100 and finally 111. The explanations so far suggested for the differences of the work function are discussed and shown to give either an incorrect sequence or a wrong order of magnitude of the observed differences. The author uses the picture of Wigner and Bardeen according to which the work function is a sum of a volume contribution and a contribution due to a double layer on the surface of the metal. The origin of the latter can be described in the following manner. With every atom one can associate a polyhedron ("$s$-polyhedron") with the atom at its center, such that it contains all points nearer to the atom under consideration than to any other atom. If the distribution of the electron density within these polyhedra of the surface atoms was the same as for the inside atoms then there would be no double layer on the surface. However, this is not the case since the total energy is lowered by a redistribution of the electron cloud on the surface. There are two effects: the first is a partial spread of the charge out of the $s$-polyhedra and the second is a tendency to smooth out the surface of the polyhedra. In consequence of the second effect the surfaces of equal charge density are more nearly plane than in the original picture. The two effects have opposite influences and since they are comparable in magnitude, it is not possible to predict the sign of the total double layer without numerical computations. Some general formulae for the double layers are derived and discussed more fully in the case of a simple cubic and a body-centered cubic lattice. The minimum problem of the surface energy is solved for four faces of a body-centered crystal and the results are applied to the case of tungsten. One obtains the differences between the work functions for different directions. The results agree satisfactorily with the experimental data: assuming a reasonable density of the free electrons, one obtains the correct sequence of faces and the correct differences of the work function. The surface energies are calculated an d found in agreement with the observed stability of certain crystal faces.

84 citations

Journal ArticleDOI
TL;DR: In this article, the thermal annealing of KBr x rayed at temperatures below 20 ifmmode^\circ\else\textdegree\fi{}K was analyzed.
Abstract: Measurements and a detailed analysis were made of the thermal annealing of the $\ensuremath{\alpha}$ band in KBr x rayed at temperatures below 20\ifmmode^\circ\else\textdegree\fi{}K. Four distinct annealing stages at 11, 17, 19, and 21\ifmmode^\circ\else\textdegree\fi{}K were resolved, the first three stages corresponding to first order reactions and the fourth stage to a second order reaction. The activation energies for the annealing stages were about 0.015, 0.03, 0.04, and 0.06 eV, respectively. The first three stages were interpreted as a correlated recombination of close pairs of bromide vacancies and interstitials, and the fourth stage as the recombination of more distant defect pairs through a free migration of an interstitialcy. The activation energy 0.06 eV is interpreted as the free migration energy of a bromide-ion interstitialcy. Interaction energies between a vacancy and an interstitial ion in several configurations were calculated and possible annealing sequences for the first three annealing stages are proposed. The observed low pre-exponential factor for the first stage is also discussed.

59 citations

Journal ArticleDOI
01 Sep 1978-Science
TL;DR: Saturnian rings and icy satellites may be covered with amorphous rather than crystalline ice, which may be stable, and its presence could be deduced from the rate of temperature drop in a shadow.
Abstract: Saturnian rings and icy satellites may be covered with amorphous rather than crystalline ice. Its likely source is water molecules sputtered by particles in the radiation belts, it may be stable, and its presence could be deduced from the rate of temperature drop in a shadow. Observation of this effect is, however, difficult, especially for the rings. A possible relation to the brightness anisotropy of ring A is pointed out.

33 citations


Cited by
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Journal ArticleDOI
TL;DR: A review of the fundamental interactions of water with solid surfaces can be found in this paper, where the authors assimilated the results of the TM review with those covered by the authors to provide a current picture of water interactions on solid surfaces, such as how water adsorbs, what are the chemical and electrostatic forces that constitute the adsorbed layer, how is water thermally or non-thermally activated and how do coadsorbates influence these properties of water.

2,022 citations

Journal ArticleDOI
TL;DR: In this paper, the surface diffusion of tungsten adatoms on several smooth, low-index planes of the Tungsten lattice has been followed by direct observation of individual atoms in the field-ion microscope.
Abstract: Surface diffusion of tungsten adatoms on several smooth, low‐index planes of the tungsten lattice has for the first time been followed by direct observation of individual atoms in the field‐ion microscope. Contrary to expectation, the mobility at room temperature is found to increase in the order (211) > (321) ∼ (110) > (310) ∼ (111). Migrating atoms are reflected at the boundaries of the (110), (211), and (321) planes; on the latter two, motion along atomic rows is favored over diffusion across lattice steps. From quantitative determinations of the rate of change of the mean‐square displacement, diffusion coefficients are obtained as follows: (110), D=3×10−2exp(−22 000/RT)cm2/sec; (321), 1×10−3exp(−20 000/RT); (211), 2×10−7exp(−13 000/RT). Differences in diffusion on the (211) and (321), planes of very similar structure, suggest a weakening of interatomic forces at lattice edges.

1,376 citations

Journal ArticleDOI
TL;DR: In this article, the authors developed a surface-enhanced Raman scattering (SERS) model of adsorbates on metal surfaces, where the long-range enhancement by resonances of the macroscopic laser and Stokes field is separated quantitatively from the metal electron-mediated resonance Raman effect.
Abstract: On the basis of different types of experiments, the authors develop implicitly the model of surface-enhanced Raman scattering (SERS) of adsorbates on metal surfaces. The long-range enhancement by resonances of the macroscopic laser and Stokes field is separated quantitatively from the metal electron-mediated resonance Raman effect. The latter mechanism proceeds by increased electron-photon coupling at an atomically rough surface and by temporary charge transfer to orbitals of the adsorbates. This model can account for the chemical specificity and vibrational selectivity of SERS and (partly) for the SERS specificity of the various metals.

1,312 citations

Journal ArticleDOI
TL;DR: A comprehensive understanding of phenomena at interfaces with organic materials will improve the rational design of highly functional organic electronic devices.
Abstract: A most appealing feature of the development of (opto)electronic devices based on conjugated organic materials is the highly visible link between fundamental research and technological advances. Improved understanding of organic material properties can often instantly be implemented in novel device architectures, which results in rapid progress in the performance and functionality of devices. An essential ingredient for this success is the strong interdisciplinary nature of the field of organic electronics, which brings together experts in chemistry, physics, and engineering, thus softening or even removing traditional boundaries between the disciplines. Naturally, a thorough comprehension of all properties of organic insulators, semiconductors, and conductors is the goal of current efforts. Furthermore, interfaces between dissimilar materials-organic/organic and organic/inorganic-are inherent in organic electronic devices. It has been recognized that these interfaces are a key for device function and efficiency, and detailed investigations of interface physics and chemistry are at the focus of research. Ultimately, a comprehensive understanding of phenomena at interfaces with organic materials will improve the rational design of highly functional organic electronic devices.

749 citations

Journal ArticleDOI
TL;DR: In this paper, an analysis of the hydrologic response of a water-rich Mars to climate change and to the physical and thermal evolution of its crust is carried out, with particular attention given to the potential role of the subsurface transport, assuming that the current models of insolation-driven change describe reasonably the atmospheric leg of the planet's long-term hydrological cycle.
Abstract: An analysis is carried out of the hydrologic response of a water-rich Mars to climate change and to the physical and thermal evolution of its crust, with particular attention given to the potential role of the subsurface transport, assuming that the current models of insolation-driven change describe reasonably the atmospheric leg of the planet's long-term hydrologic cycle. Among the items considered are the thermal and hydrologic properties of the crust, the potential distribution of ground ice and ground water, the stability and replenishment of equatorial ground ice, basal melting and the polar mass balance, the thermal evolution of the early cryosphere, the recharge of the valley networks and outflow, and several processes that are likely to drive the large-scale vertical and horizontal transport of H2O within the crust. The results lead to the conclusion that subsurface transport has likely played an important role in the geomorphic evolution of the Martian surface and the long-term cycling of H2O between the atmosphere, polar caps, and near-surface crust.

731 citations