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The effect of change in slag composition upon metal losses to the slag and the relationship between slag composition and slag matte separation was investigated at 1400°C. The synthetic slags containing CaO, MgO, SiO2,, A1,0, and FeO were similar to those employed in the electric furnace smelting of sulphide Cu-Ni concentrates containing PGM (Precious Group Metals) from the Merensky Reef of South Africa. The matte with a grade of 9.3% Cu and 16.0% Ni was a typical electric furnace product. The results indicated that the Cu and Ni solubility in the slag increases with the increase of the basicity ratio and CaO and MgO contents of the slag. At constant CaO/MgO ratios the rise in basicity decreases the metal losses. When FeO and SiO2 contents of the slag are kept constant, the substitution of MgO with CaO decreases the metal losses. The relationship between slag composition and matte-slag separation was found to depend primarily on the basicity ratio and the FeO content of the slag. The net effect comes from a strong interaction of the two in such a way that increasing basicity and decreasing FeO contents deteriorate the clean separation of the two phases.

Jan 1, 1994

By Ralph H. Nafziger

The feasibility of smelting a Ni-Co-Cr-bearing laterite ore from southern Oregon was evaluated by the Bureau of Mines. The objective was to prepare a master alloy for subsequent stainless steel production. A mixture of the ore with suitable reductants and fluxes was smelted in a 50-lb-capacity single-phase ac electric furnace under sub- merged arc conditions. The smelting tests produced a metal in which most of the nickel was concentrated. High-chromium recoveries required an excess of carbon. The resulting metal alloys contain sufficient nickel for some stainless steels. Ferrochromium additions would be required to attain suitable chromium levels. This research was conducted under the Oregon Metals Initiative in cooperation with Walter B. Freeman.

Jan 1, 1993

By Junzo Hino

Most of the waste that contains a small portion of copper is landfilled. The recycling process of copper from the waste, such as shredder residue, should be developed in order to save mineral resources and prevent environmental pollution. Shredder residue, generated from disposed automobiles and electric appliances, consists of many types of plastics, glasses and metals. The combustion heat of plastics is efficiently used for smelting in the recycling process that consists of melting and reduction. Because the waste contains numerous components the knowledge of the distribution behaviors of the main components is necessary to develop the recycling process. The distribution behaviors in the recycling process are evaluated by using the thermodynamic calculation program, HSC Chemistry. The calculation results are compared with the practical operation data of the recycling process and discussed.

Jan 1, 2003

By Vinod K. Sikka, René Cooper

"Cohoes, New York 12047 Intermetallics are an attractive class of advanced materials. The aluminide intermetallics offer advantages including: (1) lower density, (2) oxidation resistance, (3) carburization resistance, and (4) interesting mechanical properties because of their ordered crystal structure. Even though the attractive properties of the aluminides and other intermetallics have been known for nearly four decades, their practical applications have not been developed for two reasons: (1) the poor ductility (in some cases, both ambient and high temperatures) and (2) the lack of processability into meaningful components. Recent advances such as ductilization of Ni3Al by small additions of boron and the knowledge that environmental effects are the major cause of poor ductility in Fe3Al and FeAl systems have brought the intelmetallics into the forefront of research and their commercial applications. This paper has described a method for melting Ni3AI-based alloys that successfully utilize the exotherrn for the formation of NiAl from the elemental materials. The reaction-synthesis method has also been utilized for the production of NiAI and NiAI-based alloy powders from the elemental powders. The reaction-synthesized powders of NiAI and NiAI-based alloys were consolidated by hot extrusion and evaluated for tensile properties over a temperature range from room temperature to 1050ºC. The powder-processing conditions have been found to have more influence on the ductile-to-brittle transition temperature of NiAI than the powder-production method.IntroductionIntermetallics are an attractive class of advanced materials [1-11]. The alum in ide interrnetallics offer advantages including: (1) lower density, (2) oxidation resistance, (3) carburization resistance, and (4) interesting mechanical properties because of their ordered crystal structure. Even though the attractive properties of the aluminides and other interrnetallics have been known for nearly four decades, their practical applications have not been developed for two reasons: (I) the poor ductility (in some cases, both ambient and high temperatures) and (2) the lack of processability into meaningful components. Recent advances such as ductilization of Ni3Al by small additions of boron and the knowledge that environmental effects are the major cause of poor ductility in Fe3Al and FeAl systems have brought the intermetallics into the forefront of research and their commercial applications. The paper will briefly review the processing techniques being pursued for the commercial applications of Ni3Al-based intermetallics. The major emphasis of the paper will deal with synthesis of Ni3Al and NiAI intelmetallics."

Jan 1, 1994

By Yasuhiro Konishi, Norizoh Saitoh

"We have developed new recycling technologies, based upon an eco-friendly biotechnology, in order to extract precious and rare metals sourced from post-consumer products. Recently we have been focusing on the metal ion-reducing bacteria, Shewanella algae and Shewanella oneidensis, which are able to reduce and deposit the precious metal ions (gold (III), platinum (IV), palladium (II), and rhodium (Ill)) into metal nanoparticles at room temperature within 120 min. When targeting the leachates from printed circuit boards, the Shewanella bacteria were able to allow selective reduction and deposition of gold (III) ions under acidic conditions in the presence of heavy metal ions, proposing a new bio-recovery system for gold. We also found that the Shewanella bacteria can separate and concentrate soluble rare metal ions (dysprosium (III), indium (Ill), and gallium (Ill)) from dilute solutions. Using this biomass adsorbent, the effectiveness of system for the novel recovery of indium from the leachate of used LCD (liquid crystal display) panels has been demonstrated.IntroductionMany high-tech manufacturing industries are highly dependent upon the use of critical raw materials that are the rare metals (e.g. rare earth elements/indium) and precious metals (e.g. gold/platinum group metals). There are now serious global concerns over the short term and long term availability of critical raw materials for high-tech manufacturing. This highlights the paramount importance of sustainable component reuse and material recycling technologies for recovery of critical raw materials. We believe that the most important domestic source of precious metals is through more recycling, and this will require more research and further development for the recycling of precious and rare metals. In general, chemical/thermal recycling is deemed to be the most appropriate means to extract the precious and rare metals from postconsumer products. However, there are issues related to the heavy use of toxic and hazardous chemicals, and the release of toxic emissions.Biological recovery methods provide an attractive alternative strategy and use microorganisms to separate and concentrate soluble precious and rare metals from dilute solutions into microbial cells via biosorption [1-3] and biomineralization [ 4, 5]. Biological systems generally operate at ambient temperature and near-neutral pH. Consequently, microbial recovery of metals would be an environmentally friendly method for recycling precious and rare metals from end-of-use products."

Jan 1, 2014

By Marco Zurco, Claudia M. Mendez, Alicia E. Ares, Carlos E. Schvezov, Carlos M. Rodriguez

"Zinc-Tin alloys were solidified in horizontal form and the obtained results were analyzed. During solidification the distribution of temperatures were measured by using thermocouples located strategically along the length of the samples. From the measured temperatures the following parameters were derived; the local temperature gradient, the cooling rate and the velocities of the liquid and solids fronts. Comparing the structure of the samples and the values of these parameters it was found that the temperature gradient reaches minimum values of as low as - 0.6 °C/cm, and velocities of the fronts of around 0.1 cm/s. In addition, the grain size was measured along the samples. The results are presented and discussed in the frame of the results previously obtained for other alloys.IntroductionGenerally solidification leads to two types of grain morphologies: columnar and equiaxed. The origin of each one has been the subject of numerous theoretical and experimental researches in the field of metallurgy for many years [1-7]. The columnar-to-equiaxed transition, CET, is considered as an object of high technological relevance with respect to the directional solidification of metallic alloys. This structure transition may be sharp or gradual and it has been reported to be dependent on thermal conditions associated with the casting process, including melt convection, heat transfer coefficients at the metal-mold interface, growth rates, thermal gradients, cooling rates, transport of solute, alloy composition, melt superheat, mold temperature, mold design, casting size, casting geometry, and the concentration of nucleating particles. As a consequence, it is critical for industrial applications to understand the physical mechanisms which control this transition during solidification. Many studies highlight the importance of the relative growth of the equiaxed and columnar grains and develop expressions or numerical procedures to describe a criterion for the CET. A number of experimental investigations reported in the literature suggest that the CET occurs when GL in the melt reaches a minimum critical value [5-7]."

Jan 1, 2012

By Takahiko Okura

Most non-ferrous raw materials are associated with sulphur. To extract the metals, the sulphur is recovered typically as Sulphuric acid or liquid S02. On the other hand, natural gas may contain over 20% of hydrogen sulphide (H2S) and a huge quantity of elemental sulphur is produced through oil and gas refining processes in the world. A large fraction of the sulphur mined from natural sources is eventually returned to the earth as fertilizers, by-products of desulphurisation and neutralisation processes, or as fugitives to the atmosphere. However, the supply and demand for sulphur are in imbalance. Such situation urges to develop a new smelting process without sulphuric acid production. This paper briefly reviews the global sulphur balance and the technologies for recovering elemental sulphur. The core of this paper is a proposal to convert S02 gas to elemental sulphur by using organic materials. Some results of thermodynamic calculations and experiments are presented.

Jan 1, 2003

By Masanori Abe, Yoshitaka Kitamoto, Kazuhiro Nishimura

"Ferrite plating is a chemical processing which utilizes Fe2+ - Fe3+ oxidation to synthesizing polycrystalline films of ferromagnetic spinels (MFe20 4, M = Fe, Co, Ni, Zn, Al, Cr, TI, etc:) directly from an aqueous solution at 24 - 100°C. This low temperature process allows us to fabricate new ferrite film devices on · substrates of such non-heat-resistant materials as plastics, GaAs integrated circuits, and biomaterials. Synthesized from an aqueous solution the ferrite plated ·films are highly biocompatible. Thus various magnetic device and biomedical applications have been proposed and realized using ferrite-plated films. Ferrite-encapsulated polymer microspheres are applied to antibody carries for enzyme immunoassay, and also to toners/carriers for photocopying. Perpendicular magnetic recording media utilizing plated CoNi ferrite films are proposed. The low-temperature synthesized films of NiZn and Co ferrites are potentially used as soft-magnetic and/or insulating layers, respectively at high/microwave frequencies.IntroductionFerrite plating is a processing which facilitates the formation of crystalline spinel ferrite films with various compositions, (Fe, M)30 4 (M = Fe, Co, Ni, Zn, Al, Cr, TI, etc.), directly from an aqueous solution at 60 - 100°C [1]. This opened the door to fabricating novel ferrite-film devices using substrates of such non-heat-resistant materials as plastics and GaAs integrated circuits [2-4]; conventional ferrite film preparation techniques such as sputtering, vacuum evaporation, MBE, LPE, etc., require high temperatures(> -600°C) for crystallization of ferrites, which deteriorates the non-heat-resistant substrates. Recently we extended ferrite plating to be preformed at room temperature [5, 6]. This enables us to use as substrates such organic materials as biomaterials (e.g. enzymes) having very low heat-resistance."

Jan 1, 2000

By Jianguo Yin, Wenqiang Yang, Xiaoli Yuan, Juan An, Wentang Xia

Low grade iron ore with phosphorus (LGIOWP), a raw and wasted industrial solid material was used as an adsorbent to remove Pb(II) from wastewater. The effects of initial pH value, adsorptive time, initial Pb(II) concentration, adsorptive temperature and LGIOWP dosage on the Pb(II) removal efficiency were studied. The results show that the Pb(II) removal efficiencies exceed 99.4% and Pb(II) concentrations are less than 0.30 mg/L under the conditions of pH value 7.0, adsorptive temperature 50 oC, adsorptive time 30 min, initial Pb(II) concentration 100 mg/L, particle size <0.25 mm, adsorbent dosage 5 g/L and stirring speed 260 r/min. After Pb(II) removal reaction, the Pb(II) concentrations of wastewater completely accord with the requirement of national discharge standards of pollutants from lead and zinc industries (GB 25466-2010) (TPb= 0.5 mg/L) in China. Therefore, it can be concluded that LGIOWP is a new low-cost adsorbent which is suitable for the adsorption of Pb(II) from wastewater.

Jan 1, 2015

By Åke Saudström

An EAF dust sample generated in a scrap based steel mill was treated by a combination of hydro- and pyrometallurgial techniques. The EAF dust contained mainly ferritic spinels forming solid solution phases according to the general chemical formula (MnxZnyFe1-x-y)Fe2O4 and other oxide phases such as ZuO. CaO and Ca2Fe2O5. The EAF dust was first treated by hydrochloric acid leaching at p8=3 which dissolved 63% of the zinc. The pyrometallurgical treatment of the leaching residue was studied using an induction heating system to simulate some important operations of EAF smelting of the residue in combination with steelmaking. The leaching residue was mixed with carbon powder to obtain a mixture with 52.1% ZnFe2O4 and 175% carbon. The mixture, scrap, and slag former were charged together in a crucible and heated to attain a melt temperature around 1650°C. The effects of different amounts of mixture on the zinc balance and iron recovery were examined. Based on the test results, suggestions are made for the EAF recycling procedure of the leaching residue.

Jan 1, 2003

By A. E. Isaacson

Bureau of Mines researchers developed and tested equipment to measure corrosion rates on a commercial-scale mill as an aid in predicting the effect of corrosion on minerals and how this effect relates to downstream processing. Bench-scale experiments were designed for duplicating ore grinding conditions closely enough that realistic rate determinations can be made in laboratory tests. Rates measured in a laboratory system compared favorably with those measured in the field. Cast steel was found to have corrosion rates in a copper mill and laboratory test cell of 22 and 21 mpy, respectively. Corrosion was found to account for less than 5% of the total grinding media wear in the operations studied.

Jan 1, 1987

By Carlos A. Nunes

V-AI alloys have been used commercially to produce pure vanadium by Electron Beam Melting (EBM), as well as to obtain Ti-based alloys (ex. Ti-6AI-4V). The aluminothermic reduction of vanadium pentoxide (V205) is the primary method to obtain these alloys. Concerning the obtention of pure vanadium, earlier studies have indicated alloys presenting Al content between 10 and 15wt% as the most suitable alloys for direct EBM. In the present work we investigated the aluminothermic reduction of V205 in order to define process parameters for the obtention of V-AI alloys with composition in the previously mentioned range. It was studied basically the effect of excess AI, CaO addition and reaction atmosphere (air, argon) on the alloy composition (AI, 0, N). In addition, microstructural analysis of selected alloys by SEM (BSE images) and EPMA (WDX) were also performed.

Jan 1, 1996

By Raj P. Singh

Applications of cementation in the recovery of metal ions from process solutions have been known for a long time. Cementation reactions involve electrochemical precipitation of a noble metal from solutions of its salts on a more electropositive metal which, in tum, progressively dissolves. For example, addition of zinc metal powder in a solution containing zinc and cobalt ions would allow for the precipitation (separation) of cobalt according to the following chemical reaction. This paper pertains to the recovery of cobalt from cobalt process solutions via a cementation reaction on aluminum shavings (metal scraps from cans etc). Specifically, we report on the characterization of cobalt process solutions, a by-product obtained from cobalt chemicals, and the kinetics of cobalt, nickel and manganese cementation from process solutions on aluminum shavings.

Jan 1, 2000

By Claudio Toro, Alex Moyano, Jonkion Font, Carlos Caballero, Pedro Morales

"Codelco-Chile in the last decade has carried out industrially-oriented research as an alternative to the traditional batch-type converting process. In a first stage carried out preliminary evaluations in a rearranged Peirce Smith (PS) converter, and then an exploratory test in a “Convertidor Teniente” (Teniente converter, TC) for the Codelco-Chile Continuous Converting Process. However, the validation test for this process in the TC was delayed up to the second quarter of 2007 where the validation studies were done satisfactorily.Thus, the objective of this paper is to present the results of the campaign tests validating the Codelco-Chile Continuous Converting Process in the TC1 of the Codelco Norte smelter.The results of charging the solid or liquid matte or high grade matte (“white metal”) by Garrgun, or by mouth of the 22 m x 5 m TC1 are presented. Some features of the industrially validated process are discussed, and the pilot test results of the matte injection are also presented."

Jan 1, 2009

By Daniel K. Kim

The charge for the copper refinery is a mixture of anodes produced at San Manuel from BHP source concentrate and copper purchased from external sources. Control of unwanted impurities in the tankhouse - is very important and beneficial. Currently available removal/recovery technologies were reviewed for the control of bismuth and antimony levels in the electrolyte. Recent studies have focused on solvent extraction (SX) technology and generated successful results for the removal and subsequent recovery of bismuth and antimony. The SX system employs the reagent, ACORGA SBX-50, in conjunction with a patented high chloride stripping system. The latter enables recycle of the eluant, avoiding the high costs associated with conventional systems, such as regeneration of resin. Concerns over potential transfer of organics and chloride ion to the electrolyte were readily addressed, solved and demonstrated using conventional, established technology. This paper describes the benefits of electrolyte purification, the flexibility afforded by the SX system, the operational practices necessary for maintaining adequate control of bismuth and antimony impurities in the electrorefining environment and possibilities for future development /exploitation of the Zeneca SX system at the San Manuel refinery.

Jan 1, 1998

By A. Treverrow, G. A. Brooks, H. K. Worner

"The work by H.K Worner and co-workers at CRA in the 1960s, and early 1970s, established that molten metals could be refined continuously utilising counter current flow of metal and slag. Womer also demonstrated that counter current refining could produce highly refined metal products. These developments coincided with the advent of high intensity metallurgical reactors in both the ferrous and non-ferrous industries (e.g. BOS, Q-BOP and later Sirosmelt) that utilised high levels of gas injection to produce rapid stirring and very fast reaction. These new generation of high intensity metallurgical reactors allowed high tonnage rates through relatively small volume vessels.Whilst, it is well known that the counter current flow of reacting phases offers the potential of efficient mass transfer and high purity products, the application of counter current reactors to molten metal/slag systems has been criticized on the basis that they suffer from either low intensity or, alternately, from poor refining due to excessive dispersion. These criticisms relate to the balance between intensity and the refining capacity of a reactor. That is, whilst high levels of mixing transversely to the direction of flow promotes high mass transfer, longitudinal mixing (dispersion) is detrimental to refining. Of course, mixing in one direction invariably leads to mixing in other directions, thus creating a playoff between high mass transfer and excessive dispersion.This balance between intensity and refining has been the subject of recent studies overseas, and at"" the University of Wollongong, using cold modelling techniques to evaluate the effect of mixing on dispersion in a counter current refining launder. These studies have shown that for a given geometry and mixing regime, dispersion decreases with increasing flow of liquid phases. This means that whilst high mass transfer cannot be achieved in a refining launder without sacrificing the degree of refinement, there is no impediment to achieving high productivity through such a system, in fact, high through puts may favour good refining. Thus, it may be possible to match a high productivity smelting operation with a equally productive counter current refining stage."

Jan 1, 1996

By Zemin Ma

A novel chromate [Cr(VI)] reducing bacterium was isolated from chromite ore processing residue disposal site of China and identified as a Leucobacter sp. by 16S rRNA gene sequence homology. The minimum inhibitory concentration of strain CRB1 was 820 mg l-1 of Cr(VI). The reduction of Cr(VI) occurred only under aerobic conditions. With an initial concentration of 2.5×108 cells ml-1, 1800 mg l-1 of Cr(VI) was reduced entirely within 38 h under the optimum conditions, at 30 °C and pH 9.0. Increasing Cr(VI) concentrations prolonged reduction process and higher cell densities meant quicker reduction. A blue precipitate was produced during chromate reduction of strain CRB1, which was binding to the surface of bacterial cells and determined as trivalent chromium with electron paramagnetic resonance (EPR) spectrometry. The conspicuous chromate reduction ability of Leucobacter sp. CRB1 suggested a potential for bioremediation of Cr(VI) containing wastes.

Jan 1, 2008

By Zhongning Shi, Ramana G. Reddy

"By cyclic voltammetry and potentiostat electrodeposition using Potentiostat/Galvanstat, electrochemical behavior on Ag electrode in electrolyte 0.2M NaOH+0.01MPb(NO3)2-0.01M TeO2 -0.01M TlNO3 solution were also carried out at 298K. The processes of electrodeposition of Tl2Te3 and PbTl4Te3, a thermoelectric material, are reported along with analysis of the composition of the obtained deposits. The results showed that two different underlying processes are occurring depending on deposition potential. One process involves the reduction of TeO3 2- and Tl+ to Tl2Te3 in a potential interval of -0.70V < E < - 0.89V (vs. Hg/HgO). A second process at more negative reduction potentials involves reduction of TeO3 2-, Pb2+ and Tl+ to PbTl4Te3 in a potential interval of -1.02V < E < - 1.19V. The crystalline Tl2Te3 and PbTl2Te3 were deposited electrochemically on Ag substrates at -0.84V and -1.10V respectively. Thermoelectric (TE) material can form a temperature gradient across the material to make electric voltage, which is popular in waste heat utilization and recovery industry. Lead telluride, PbTe, is a small band gap semiconductor of 0.32eV at 300K. PbTe can change its n-type semiconductors with Pb-rich to p-type semiconductors with Te-rich[1]. And it is one of the best TE materials used in thermoelectric generators working between 500K and 600K, or even at a higher temperature of 800K.Three facto,rs play a role in the performance of a thermoelectric material: electrical conductivity (s), thermal conductivity(?), and the Seebeck coefficient (S). These can be combined with absolute temperature (T) to give a figure of merit (ZT) for the material, ZT = s2sT/?. By increasing the electrical conductivity and decreasing the thermal conductivity, which can enhance the ZT value, many efforts, such as alloying with other elements and making the materials nano-sized, have been done to improve its properties recently. Hsu et al. reported that the ZT value of Cubic AgPbmSbTe2+m is increased to 2.2 by doping Ag-Sb to PbTe.[2]."

Jan 1, 2011

By Joseph Bloch

The hydriding of bulk metals and alloys is a gas-solid reaction in which a hydride product layer is initially nucleated adjacent to the gas-solid interface and continues to grow until a complete transformation of the parent (a) phase into the hydride phase. The combination of measurements of the overall hydriding kinetics of samples having defined shapes and dimensions, together with examinations of partially hydrided samples, enables the presentation of the reaction rate in terms of an appropriate reaction model. A common and important type of topochemical development of the hydride in bulk metals and alloys involves a hydride layer formed on the metallic surface. The continuity of the layer can affect the reaction rate. The rate of hydrogen absorption in a sample, in the presence of a hydride layer, is usually analyzed using a model combining several sequential steps in which the hydrogen is transferred from the gas phase into the reaction site. Coupling the flux equations across the layer under proper steady state conditions, results in a complex rate equation in which the steady state rate of hydrogen absorption (proportional to the hydride layer velocity) is expressed in terms of the pressure, temperature, the rate constants of the sequential steps and the critical concentrations of hydrogen in the hydride. Generally, the rate constants of the individual microscopic processes are comparable in magnitude, so that the overall rate is not controlled by any of the specific sequential steps. However, there are two limit cases related to the first stage, the adsorption, for which the general rate equation is much simpler, namely, the fast and the slow adsorption approximations. Using this limit cases, equations are derived for the steady state hydriding rate of a given system. These equations provide means to anticipate the pressure dependence of the steady state absorption rate under low pressures, close to Peq and under very high pressures. At the low pressure regime both the fast and slow absorption cases yield linear pressure dependence. For the very high pressure range, it is found that the rate become independent of the applied pressure. The rate is given then by a combination of the individual rate constants of the system and the critical hydrogen concentrations. The model is shown to apply in several real cases, such as ZrCo, LaNi5 and titanium.

Jan 1, 2002

By A. Kar, J. Mazumder

"Laser ablation is a process that can be used to synthesize novel nanoscale particles as well as to deposit thin films of various materials. Usually, nanoscale particles and thin films are formed at relatively high and low pressures, respectively, inside the ablation chamber. This paper presents a mathematical model to predict the particle size distribution in the plasma generated during laser ablation. The model is developed by considering the effects of the laser-matter and laser-plasma interactions, the Stefan condition, and the discontinuity across the Knudsen layer. The nanoscale particles are found to be located at the central region of the plasma near the target. The particles have very high velocity and temperature. A good qualitative agreement is observed between the results of this model and experimental data. IntroductionRapid solidification produces novel microstructures whose atomic arrangements and/or chemical compositions are different from those of conventional materials. The conventional materials are either crystalline or amorphous. The crystalline materials have both short- and long-range orders, whereas the amorphous materials have only the shortrange order. The nanocrystalline materials have neither short- nor long-range orders, and for this reason, they exhibit novel properties which are important for synthesizing new materials. The atoms of a nanocrystal can be classified as ""crystal atoms"" and ""boundary atoms"", where the ""crystal atoms"" have the nearest-neighbor configurations similar to the lattice configuration, whereas the nearest-neighbor configurations of the ""boundary atoms"" differ from the lattice configurations 1. Various aspects of the nanoscale materials have been discussed in Refs. [1-7]."

Jan 1, 1994