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By Arthur A. F, MacKenzie I. H

Copper in zinc/lead sinter charged to the Imperial Smelting Furnace operated by Sulphide Corporation Pty Limited at Cockle Creek, New South Wales, concentrates in a complex lead dross which forms as the bullion is cooled to around 400°C. The 0.35 mm portion of this dross, containing approximatelY 67 per cent of the total copper, is treated via a hydrometallurgical route to produce 5000 tonne/yr of CuSO4 5H2O crystal.Around 3000 tonne/yr of copper-lead dross containing 49 per cent copper is leached at 55°C in continuous leach reactors with ammoniacal ammonium carbonate leach liquors to convert copper to soluble copper amine complexes. Leach ettlciencies of 80-85 per cent are obtained. Leach residues are repulped with ammoniacal liquid diluents from the plant and heated in a four stage steam distillation unit to reduce ammonia levels to between 0.5 and 1.0 g/Iitre. The resultant slurry is directed to an effluent treatment plant for final treatment, and separation and return of solids to the sinter plant.Copper is extracted from leach liquor by solvent extraction techniques based on the use of L1X 54 diluted 3:1 with Shellsol 2046 to give a nominal copper loading of 30 g/litre. The loaded organic is contacted with a sulfuric acid solution of pH 5 to remove the bulk of ammonia and zinc, then stripped at 55°C with a 60 g/Iitre H2SO4 95 g/Iitre copper solution to yield a 15 g/Iitre H2SO4 125 g/Iitre copper solution.This liquor is fed to an adiabatic vacuum crvstalliser operating at 35°C and 5 kPa vacuum where crystals of CuSO4 5H2O are formed. Crystals are separated from mother liquor and washed in a two stage pusher centrifuge, then dried in a hot air rotary drier. The crystal product obtained is of a high chemical purity and readily conforms to both Australian and overseas standards.

Jan 1, 1983

By R. E. Mitchell

Environmental Impact Assessment (EIA) is the accepted method for evaluating proposed mining and other industrial projects to obtain regulatory approval and to help companies plan for responsible development. Another evaluation system becoming increasingly more common for proposed projects is the Environmental, Social and Health Impact Assessment (ESHIA). An ESHIA differs from an EIA for its more comprehensive and inclusive approach to evaluate potential impacts on public health, and its ecosystem services approach to assessing biodiversity impacts. An ESHIA may also be required by certain lenders for financing major projects. Conducting an ESHIA for a proposed mining development is not without its challenges, with costs, scheduling, regulatory concordance and other constraints to be considered. This paper examines some benefits and challenges of ESHIAs and summarizes lessons learned using a case study approach.

Jan 1, 2012

By Nicholas J. Grant, William H. Ferguson, Bill C. Giessen

Ta-lr alloys have been examined over the complete range of compositions using metallographic and X-ray techniques. The terminal solid-solubility limits, solidus temperatures, and intermediate phases were determined. There are four inter-mediate phases: o, tetragonal, analogous to a (Fe-Cr); 0,. orthorhombic; az, tetragonal; and a TaZr,, cubic, AuCu, structure. Of these, o and a, melt peritecticaLly, a, decomposes peritectoidally, and a TaIrs has a congruent melting point. Three peri-tectic and one eutectic reactions occur. 1 HE Ta-Ir phase diagram has not been treated in the literature. Intermetallic phases and terminal solid solubilities have been described and estimated.'-4 The previous findings have been confirmed in this work. A complete diagram with additional phases and solidus curves is presented. EXPERIMENTAL METHODS Starting materials were tantalum powder of 99.8 pct purity, supplied by the National Research Corp., Cambridge, Mass., and iridium powder of 99.9 pct purity, supplied by the Bishop Co., Malvern, Pa. Both powders were -200 mesh. Table I lists the analyses as given by the suppliers. A standard procedure was employed in making the alloy buttons, which was described in detail in Refs. 5 and 6, and which included repeated arc-melting of powder compacts and determination of the composition by the weight-balance method. This is especially justifiable due to the similar vapor pressures of tantalum and iridium. In the critical parts of the diagram, a spacing of 1/2 at. pct was used, based on premelted master alloy material. The observed structures and X-ray spectra were consistent with the composition sequence of the alloys. Table II lists the final alloy atomic percentages with the calculated percent error of composition. Cross sections representative in grain size and composition were selected for the study, as described in Ref. 5. Based on prior experience, no contamination from the tungsten electrode was considered. Temperature measurements were obtained using a Leeds and Northrup optical pyrometer and have been described extensively in Refs. 5 and 6. All heat treatments were made in the high-vacuum tantalum tube furnace mentioned in Ref. 5. Samples annealed in tantalum containers cooled from 1800" to 1000"~ in 5 sec; those annealed in ceramic crucibles cooled over the same range in 15 to 30 sec. The thermal treatments are listed in Table 111. All specimens were homogenized at 1735°C for 24 hr. Tantalum-rich compositions were treated in tantalum buckets. Iridium-rich compositions were annealed in tantalum buckets below the eutectic temperature of 1950°C; up to 2200°C, tungsten-lined tantalum baskets were used; and above 2200°C thoria crucibles were used. It was found that refractory oxides (in early stages of the investigation alumina crucibles were used up to 1800°C and thoria crucibles were used to 2400"~) give off minute amounts of oxygen and thereby influence the microstructure considerably, or react directly with the alloys.

Jan 1, 1963

By W. G. Miller, J. D. Scott, D. C. Sego

ABSTRACT The influence of using different extraction processes (caustic versus non-caustic) on thethixotropic strength of oil sands fine tailings is examined, as is the influence of adding a coagulant tocaustic fine tailings. The thixotropic strength of fine tailings at large void ratios manifests itself as a bonding or gel strength that has been widely noted both in the laboratory and in the field. This gel strength has a significant influence on preventing the initial consolidation or settlement of fine tailings. Differences between the fine tailings’ thixotropic strength development are explained based on their physical and chemical characteristics.

Jan 1, 2010

By C. P. Miller

In a study of the usefulness of geochemical and biogeochemical prospecting for nickel made about two years ago, approximately ten localities, representing several different types of nickel occurrences were sample, and about 1500 samples of plant and soil were collected. This report will briefly cover the data and results for two areas, and s summary of guides for prospecting.

Jan 1, 1959

By Ihsan Berk Tulu, Haochen Zhao, Deniz Tuncay

This paper proposes a new method to estimate the percentage of load carried by the gob in underground coal mines using a new parameter that introduces the site-specific overburden geology. The new parameter was defined as the total strong layer thickness (tstr) that represents the strength and stiffness of the overburden with a single value. Twelve field measurement case studies from 11 different U.S. longwall mines with different overburden geologies were used to develop the new methodology. 2D numerical models of these case studies (and additional parametric runs with different panel widths) were verified against field measurements such as surface subsidence and stress. Statistical analyses using the model results were conducted for a loading model with the new tstr parameter as one of the variables. The new methodology was found to have a coefficient of determination (R2) of 85% when compared to the field measurements and the parametric models. The method was then tested for practical implementation for pillar design. The percentages of load carried by the gob as estimated by the new method were implemented into the LaModel program, that is commonly used in the coal industry. The results obtained from LaModel were compared to the available field stress measurements, and the new method implemented into LaModel was found to give successful results.

Jul 18, 2022

By Jean Dupere

Mr. Chairman, Ladies and Gentlemen, I'd like to take just a moment of your time before we examine the current position of the asbestos industry and its market outlook to take a searching look at the product itself. I feel that if we are to understand the problems that beset this basic mining and manufacturing industry and, more important, if we are to appreciate the solutions to these problems that I plan to put forward in a few moments' time, then we had better look at asbestos from the proper perspective. Asbestos has a unique combination of properties - properties not found in any other natural substance or man-made material. This has resulted in asbestos finding its way - in fact, being welcomed - into literally hundreds of applications.

Jan 1, 1984

By Paul T. Allsman

The guiding principle in developing this plan resulted from evaluating potential future markets for oil, the quantity of mineable oil shale and the optimum rate of production comensurate with market demand on the available oil from shale. In addition, the rate of production may depend upon a solution to the problems of scarcity of resources other than oil shale. The rate of production finally will tend to establish the choice of technologies with these limits. The principle components discussed will be: 1) The place of oil shale among the various energy sources and its relative adaptability for use in the area of major consumptive demand. 2) A recalculation of the reserves and their classification on the basis of quantity, grade - gallons per ton, - and physical characteristics principally thickness, overburden and depth.

Jan 1, 1982

By W. Wallace, T. Ong, M. Gautam, M. Keane, S. Xing, J. Harrison

"Diesel exhaust soots were assayed in the Ames Salmonella typhimurium histidine reversion assay system using TA 98, the soots being applied as the following preparations: dispersion in dipaimitoyl glycerophosphoryl choline (DPL), dispersion in dipalmitoyl phosphatidylethanolamine (DPP!), and dispersion in dipalmitoyl phosphatidic acid (DPPA) in physiological saline, and in physiological saline without added surfactant. The extracts of soots by dichloromethane / dimethylsulfoxide (DCM/BHSO) were also assayed. Studies were performed both with and without :IQ microsomal activation of the soot preparations. The DPP! and DPPA surfactants were chosen as phospholiridz with two palmitic acid moieties esterified to a glycerol as is the case with DPL, but with hydrophilic groups having different electrophilic characters. The soots, without S9 activation, showed mutegenic activity when extracted in the conventional procedure with DCM/DMSO. The mutagenic activity of soots dispersed in DPL was quantitatively comparable to, and in some cases greater than, the activity expressed by an equal mass of soot extracted by DCM/DMSO. Soots in other surfactantpreparations, DPP! and DPPA, also expressed positive mutagenic activity. Praincubation with S9 microsomal enzyme fraction reduced the activity of solvent extracted soots, and greatly diminished the activity of DPL dispersed soots. Initial sister chromatid exchange (SCE) assays using the Chinese hamster V79 cell line indicated DPL dispersed soot also can cause SCR in mammalian cells. Results thus far suggest that surfactant suspended or ""solubilized"" respirable soot particles could provide a mechanism for transport and expression of mutagens in the lung."

Jan 1, 1989

By Scott Turner

PRESIDENT SCOTT TURNER officiated as chairman of the opening session on mining methods, Monday morning, Feb. 15. The first paper was that of Max H. Barber on open-pit mining in the Lake Superior district, read by C. F. Jackson. W. L. Taylor stated that liquid-oxygen explosive had been tried but that the operators are satisfied with the explosives used; lb. of dynamite breaks one ton of rock. Although black powder is considered the most effective explosive, the factor of safety has decided in favor of high explosives. Lucien Eaton told of the Michigan Lime and Chemical Co.'s large L. 0. X. plant at Rogers City, Mich. Mr. Turner referred to this plant, also said that the Bureau of Mines is shortly to issue Bulletin 349 completely covering the use of L. 0. X. from its inception. W. D. B. Motter, Jr., gave some items concerning Chuquicamata, Chile. Twelve years ago the blasts moved 850,000 to 1,000,000 tons, but average shots now move 250,000 to 300,000 tons. One pound of L. 0. X. breaks 3.7 tons, against 3.1 tons by dynamite. Another speaker told of some large dynamite blasts in open pits, one of 360,000 Ib. in March, 1931, and another of 430,000 lb. to be shot in 1932. Tests have been made to determine the effect of large shots on the surrounding country. Mr. Taylor said that 4- and 5-yd. shovels were preferable to those of 8 yd.; their performance is better and cost is lower.

Jan 1, 1932

By David G. Borg

"Although researchers have realized varying degrees of success in numerics modeling, computer blast simulations and small scale in-situ testing, most will agree that the greatest uncertainty in total success stems from the uncontrollable field variables. Given the diverse nature of field conditiorencountered, no reliable and proven method of evaluating fragmentation quantitatively, and the lack of adequate field controls found in many operations, it is unlikely that a universal plug-in model will be developed for all blasting in the imediate future. This does not imply that all research devoted to modeling should cease, for it is precisely here where more research efforts are desperately needed."

Jan 1, 1989

By M. Cai

"It is well known that Peak Particle Velocity (PPV) plays a critical role in triggering rockburst damage in burst-prone underground mines. To estimate the PPV distribution around excavations, advanced numerical modeling can be used. In wave propagation numerical modeling, velocity field is often assumed to be uniform around an excavation. However, it is observed that wave velocities near mine openings are not constant, but rather non-uniform. Wave velocity in a rock mass depends on many factors such as rock quality and confinement. In particular, confinement has a large influence on wave velocity. The confinement around an excavation is low at the wall boundary and increases gradually and reaches a constant value far away from the excavation boundary. Hence, stress redistribution due to excavation will have a profound influence on wave propagation in underground mines. A better understanding of the influence of excavation effect on wave propagation helps to interpret the field observation of rockburst damage and improve mine safety. For this purpose, a non-uniform velocity model need to be constructed and the influence excavation effect should be taken into account in numerical wave propagation modeling.In the present study, a non-linear velocity model is developed firstly by considering the influence of confinement on wave velocity. This model links wave velocity to confinement explicitly. A coupled numerical method is then developed and used to study the seismic wave pattern around excavations in underground mines. Two codes, FLAC and SPECFEM2D, are coupled in the analysis. The motivation of developing the FLAC/SPECFEM2D coupled approach is to take merit of each code, such as the stress analysis capability in FLAC and the powerful wave propagation analysis capability in SPECFEM2D. The coupling process is realized through three steps: (1) static stress redistribution around an excavation is analyzed in FLAC; (2) data for coupling analysis, such as non-uniform velocity field (based on the new developed velocity model), mesh, absorbing boundaries, etc., are generated by FISH functions in FLAC and passed to SPECFEM2D; and (3) wave propagation modeling is performed in the SPECFEM2D considering a fault-slip seismic source. Because stress redistribution around the excavation is considered, non-uniform velocity field for the SPECFEM2D model can be obtained and this is a notable feature of this study. Very large difference in the S-wave response in these two modeling approaches with uniform and non-uniform velocity fields can be seen from the modeling results.Using the FLAC/SPECFEM2D coupled modeling approach, accurate velocity models can be constructed and this in turn will help to produce accurate PPV distribution around the excavations. Accurate PPV contours can be used to identify high rockburst risk zones for improved dynamic ground support strategy."

Jan 1, 2015

By D. J. M. Grodzian

Polymorphic transformations taking place in grinding processes, of massicot to litharge in PbO system, and of y to a in Fe203 system, were re-investigated. Grinding was carried-on in a steeel rotation mill charged with WC balls, under inert atmosphere. The kinetics of transformation in PbO was established by means of quantitative X-ray diffraction analysis. The resulting data fit a modified logistic growth function up to about 75% of transformed volume fraction, when a mixture at steady-state equilibrium is formed. The reasoning for the use of a modified logistic function is discussed. A sigmoidal growth function can be used if resulting data fit also an empirical power relationship between transformed volume fraction and time. However, it lacks the significance expressed by a modified logistic function. Assuming, the loss in magnetism is directly related to the amount of transformation in Fe 203, a quantitative analysis was performed using a magnetic balance method. The results fit only the modified logistic growth function, and transformation proceeds almost to completion. A wide literature survey of the subject is given. Available data from literature is compared with the results of the present study, and is shown also to fit a modified logistic grown function, with surprisingly similar slpes in a linear plot, independently of the material. The instrumentation effect on kinetics parameters, and the establishment of equilibrium mixture values, are discussed.

Jan 1, 1975

By M. A. Selim, W. H. Somerton

Thermal expansions and heats of reaction of three typical sandstones were measured in the temperature range of 25°to 1,000°C. The significance of these data in subsurface heat-transfer calculations is discussed. Linear thermal expansions were measured both parallel and perpendicular to the bedding planes. Volume expansions are reported as the perpendicular expansion plus two times the parallel expansion. Expansion behavior of the sandstones was found to be controlled by the expansion characteristics of the quartz content. Differential expansion of the quartz grains and other minerals included in the sandstones caused permanent deformation of the heated samples after they were cooled to room temperature. Structural damage resulting from heating is probably an important cause of the reduction of thermal conductivity of heated samples. Measurements of heats of reaction were based on the known heat required for a- quartz inversion. Thermal reactions, which probably include deby-droxylation of clay minerals and decomposition of carbonate minerals contained within the samples, were found to require more than one-fourth of the amount of heat necessary to raise the temperature of the rock alone. In shales and limestones, the reaction heat could be substantially greater than that required from specific heat considerations alone. INTRODUCTION In earlier work, l-3 methods of measuring thermal properties were developed and thermal data for several sedimentary-rock types were reported. Data included thermal conductivity, specific heat and thermal diffusivity. In addition, calculations of heat transfer in subsurface formations may require data on the thermal-expansion characteristics of rock and the heats of reaction of mineral constituents. Thermal expansion of rocks is relatively small in magnitucle and, from the standpoint of change in bulk density, has only minor effects on heat-transfer cliaracteristics. Thermal-expansion behavior, however, may have significant effects on the structure of rocks. Differential expansion of different minerals and along different crystal-lographic axes may result in structural damage which could effectively reduce the thermal conductivity of the rock. Many mineral constituents of sedimentary rocks undergo phase or related changes when heated to sufficiently high temperatures. Although some of these reactions (such as the a-ß quartz inversion) are reversible and the heat absorbed is returned to the system upon cooling, many of the major reactions are irreversible. Through certain temperature ranges, the additional heat energy required to complete the reactions may be nearly as great as that necessary to raise the temperature of the rock in the absence of thermal reactions. If the heat requirements for these reactions are not considered, serious errors in heat-transfer calculations may result. Thermal-tzxpansion and thermal-reaction data have been obtained for three typical sandstones. Methods of measurement and results obtained are reported and discussed in the following. THERMAL EXPANSION OF SANDSTONES The linear expansions of three outcrop sandstones (Bandera, Berea and Boise) have been measured in the temptbratue range of 25° to 1,000° C. Expansion measurements were made in the directions parallel and perpendicular to the bedding. The differential expansion apparatus used is that described by Mitoff and Pask.4 The test sample is heated in an electric furnace with a temperature rise of 6°C/minute. The lengthening of the samples upon heating is compared with the small and known expansion of a fused silica rod. The change in length is transmitted to an X-Y recorder by means of a Statham transducer. A maximum error of ± 1.5 per cent has been obtained with this apparatus

By Arthur A. Center

WAR demand- motivated developments in the zinc industry during 1942. Stocks of Prime Western were built up and High-Grade remained tight. The Prince The Prime Western stocks are expected to be cut down and the demand for High-Grade more easily filled as the Depue reflux plant of the New Jersery Zinc Co. increases - production. Subistition of steel for brass in artillery shell cases will have a considerable effect on the zinc situation of the country one estimate of the saving in zinc in 1943 by this substitution being a little under 100,000 ton, of metal. The metal saved will, of course be High-Grade. If the substitution occurs, the present tight situation in High-Grade may be entirely relieved as new production comes on the market and zinc may find itself approaching a situation as comfortable as that of lead provided the supply of zinc-hearing raw materials is sufficient to keep all reduction plants tip to capacity production. The premium price of the per pound of zinc over set quotas which went into effect early in 1942, helped to bring about the new lead-slag-fuming plant and other new sources of raw materials.

Jan 1, 1943

By G. M. Bond

Reduction of the emissions of greenhouse gases, such as CO,, is currently the subject of extensive research. A novel strategy is put forward here, based on a biomimetic approach providing accelerated deposition into carbonate form for long-term sequestration. It offers the advantages of a process that: does not require concentration of CO, from flue gases; could potentially be used in an on-site scrubber to provide a plant-by-plant solution to reducing CO, emissions; is an environmentally benign procss with an environmentally benign product; and is based on readily available, low-cost reagents (except perhaps the catalyst).

Jan 1, 1999

By Gihan E. Abdelraham, Youssef G. Youssef, Mohamed M. Kamel

"Previous studies defined Narrow Mechanically Stabilized Earth, NMSE, walls as a retaining wall with aspect ratio (wall width to its height, L/H) less than 0.70 as in traditional walls. Some studies investigated its behavior and its failure planes compared to those of traditional walls. In this paper, parametric study using finite element analysis PLAXIS, 8.2 has been introduced to discuss global factor of safety, FS, maximum horizontal displacement, Ds, maximum tension force of reinforcement element, Tmax, and active earth pressure coefficient, ka, as a function of different aspect ratio of NMSE wall, L/H, reinforcing elements spacing, S, elastic axial stiffness of reinforcement element, EA, wall batter, 1/m, soil friction angle, f, and wall height, H. The results indicated that increasing aspect ratio increases the factor of safety, maximum horizontal displacement, maximum tensile force and active earth pressure. Increasing elastic axial stiffness increases factor of safety, maximum tension force of reinforcement element while decreasing the maximum horizontal displacement.IntroductionReinforced earth is a composite geoconstruction material, which embodies two basic components; namely engineering fill and reinforcing elements. The latter one is responsible for improving the tensile and shear resistance of the soil. The soil-reinforcement technique has been in use for many geotechnical applications especially MSE walls.A narrow wall system is referred to as a MSE wall with an aspect ratio, L/H, below 0.70 that is placed in front of a stabilized wall. An example of a narrow wall system with its dimensions is illustrated in Fig. 1."

Jan 1, 2017

By E. Cetin

Orebodies that contain more than one economically important mineral are generally evaluated by parametric cut-off grades. This approach often leads to mis-valuation of mineral deposits because cut-off grades are not based on the grades of each individual mineral and, because of the parametric formulation, are only indirectly related to the individual grade distributions. The only realistic approach is a formulation that accounts separately for each component mineral. The grid search method can be used as a means of multi-mineral cut-off grade optimization in this context. This paper describes the use of the grid search method in cut-off grade optimization for multi-mineral deposits. The authors introduce the general concepts of the method and formulate its application to cut-off grade optimization; they describe a software implementation of the method that can accommodate cut-off grade optimization for mineral deposits that contain up to three economic minerals. Keywords cut-off grade, optimization, grid search, multi-mineral deposits.

Aug 1, 2013

By William R. Chedsey

ALTHOUGH few changes can be reported in educational methods at the mineral technology schools during 1940, other events have taken place of direct interest to, and that will have a profound effect upon, mineral industry education on the United States. In the erection of new buildings, some notable changes have been made on the campus, The U.S. Bureau of Mines Experiment Station at the University of Utah, Salt Lake City, was dedicated on May 20. The construction and equipment of this building cost between $300,000 and $400,000. It will be the general headquarters for the metallurgical division of the Bureau and will have a pronounced effect upon the mineral industries research program at the University.

Jan 1, 1941

By M. Lak, M. Asghari, M. Saghaeian, R. Hejazi, A. Haratian

"Magnetic separation techniques are used extensively in mineral processing operations. Magnetic separators are robust and relatively easy to operate. As the ore get hard and low grade, fine grinding must be required mostly to allow for a high degree of mineral liberation. These processes encounter the magnetic separation process difficulty due to a significant change in the separation behavior of particles. This study investigates the effectiveness of a novel proven wet magnetic separator for the beneficiation of Lebedinsky (Russia) iron ore achieved through developing pole arrangement and tank design. Basis on the results of multiphasic simulation of a medium intensity magnetic separator (MIMS) and dense media tank using Magnetic Design Software, a new model of the MIMS separator was developed. The main of the new MIMS separator was focused on improving separation and the decreasing the number of separators in cobber stage of the plant. The new MIMS separator was tested into a pilot plant on the received samples from Lebedinsky iron ore plant. In addition to the basis on the results of the modeling, promising results of test work and previous experiences, it was claimed the unit capacity of new separator is 33.33% more than the existing separator that could decrease the number of separators. In addition, the significant energy saving in the same operational condition could be obtained without any important adverse effect on the final concentrate quality.INTRODUCTION Magnetic separation is a long-established method for the purification and removal of substances from fluids (Augusto et al., 1999; Buck et al., 2015; Hoffmann et al., 2002; Lauda et al., 2016; Lindner et al., 2010; Podoynitsyn et al., 2016; Rashidi et al., 2016), mainly in mining processing industries ranging from steel production to coal desulfurization as commercial technology (Andres, 1994; Augusto, 2002; Svoboda, 1987). High gradient magnetic separation as an effective method for recovering of weak and fine magnetic particles separation has undergone dramatic developments, and has also achieved extensive application during this time (Svoboda and Jujita, 1987). Magnetic separation operations can be categorized into high intensity as electrical (up to 20,000 gauss), Medium intensity (2000-5000 gauss) and low intensity (less than 2000 gauss) techniques. Magnetic separators offer a simple, clean and economic way to sort magnetizable ores and minerals. After pulverization, the material is run through an inhomogeneous magnetic field, where particles of different susceptibility experience different magnetic forces. The force increases with susceptibility, magnetic field and field gradient (Jongst et al., 1984).In magnetic separation, the difference in the susceptibilities of the various particulate materials is used to separate the material flow into two or more products (Wasmuth and Unkelbach, 1991). The magnetic force acting on a particle can be calculated using the following equation:"

Jan 1, 2018