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By Richard C. Banting

Excessive vibration is known to have an adverse affect on soft body tissue and operators of heavy mining equipment can be exposed to vibration that exceeds levels recommended in international guidelines (ISO 2631-1, for example). Research has found that many of the seat and suspension systems currently used in mine haul trucks and load haul dump vehicles are actually amplifying the vibration. This overview presentation will outline the current research being conducted at Laurentian University and the University of Western Ontario, and the roles of partners in rating the ability of a number of commonly used mine vehicle seats to isolate harmful vibration.

Oct 1, 2010

By Louis J. Cabri, Donald Hoy

"Samples with contrasting gold mineralization were studied quantitatively prior to metallurgical tests. The AD samples are coarser-grained and characterized by abundant Sb minerals (jamesonite, berthierite, stibnite). The finer-grained MW sample has abundant pyrite and pyrrhotite, with arsenopyrite and galena next in abundance. A large number of gold mineral particles were determined by SEM investigation of hydroseparation concentrates, ranging from 150 to 597 per sample. The grain-size distribution of the gold minerals shows evidence of bimodal grain-size distributions (volume %), with the coarse fraction being most significant in sample MW-1 (maximum ECD=308µm). The coarsest gold minerals in the AD samples range from 139µm to 281µm ECD.The deportment of gold minerals is as electrum, aurostibite, native gold, and a possible new mineral (AuNiSb4). Gold also occurs in nisbite. The gold minerals are dominated by electrum in three samples and aurostibite is next in abundance. The major gold minerals are probably representative of three stages of gold mineralization. The first stage is represented by electrum, which is partly to completely replaced by Sb-rich mineralization forming aurostibite, and the last stage is native gold, often occurring as rims on one or the other earlier gold mineral. The gold minerals are strongly associated with sulphides in the AD samples (55 to 60 vol.%). At the grind used for the hydroseparation the liberated gold mineral quantity (volume %) is also significant, ranging from 65% for sample MW-1 to 30 to 37% for the AD samples.INTRODUCTIONThe Clarence Stream deposit is located 70 km south-southwest of Fredericton and 25 km northnorthwest of St. George, south-western New Brunswick, near the international boundary with Maine (Fig. 1)."

Jan 1, 2007

By Richard Klimpel

"Over the last 15 years, there has been a number of plant scale sulfide mineral flotation tests organized by this author specifically aimed at understanding how flotation rate varies with reagent type and dosage. With regard to the Interaction of collector dosage, particle size, and frother type, the eight specific trends listed in the paper (Illustrated with data from two specific case studies) are qualitatively the same for almost all plants studied in some depth. The Interaction of flotation rate K and equilibrium (Infinite time) recovery R in the plant has been denoted as the R/K trade-off. The effect of collector dosage on the rate of flotation of specific particle size intervals is particularly interesting and once understood, is quite useful In understanding how industrial flotation plants respond to changing reagent type and dosage. The location and magnitude of the R/K trade-off can be different for various ores and various plant configurations, but the RIK trade-off is almost always present. The purpose of this paper is to clearly describe and illustrate the nature of this very Important flotation system Interaction so that operating engineers have a starting reference point for beginning successful plant Improvement studiesIntroductionIt is well recognized by industrial froth flotation plant operators that improving existing sulfide circuit performance is often difficult due to the self-compensating systems nature of the froth flotation system, e.g. Klimpel (1988, 1989, 1995). Extensive plant testing with existing and new reagents by this author throughout the world has clearly shown that one of the more important self-compensating mechanisms is the Interaction between collector dosage, frother type, and particle size. The term self-compensation in flotation simply means that as the plant operator consistently changes one parameter in the same direction, the nature of the froth flotation system Is such that the circuit will eventually begin to resist this controlled parameter change by automatic (uncontrolled) changes In other parameters and the overall circuit performance will go through a maximum or minimum (hence causing the operator to stop the parameter change)."

Jan 1, 1997

By Laxman (Lucky) Amaratunga, Hisham Madi

Final disposal of mine wastewater neutralization sludge continues to be one of more pressing problems in the mining industry. The disposal of mining and metallurgical waste products into underground reduces the environment impact and improves the safety of the mining operation and the economics of the enterprise. This current research focuses on an investigation of utilization of mine wastewater neutralization sludge obtained from Kidd Creek Mine site, as a supplementary material for their proposed deep mine pastefill system. Their proposed pastefill consist of combination of rock aggregate in a matrix of imported sand and tailings with binder (Portland cement + Slag cement). Pastefill mixes containing various percentages of the waste sludge 0 (control mix), 1, 2, 3, and 5% by weight as replacement to the fine sand were prepared and tested with different percentages of binder. Hypothesis behind this approach is to study the behavior of sludge as replacement of sand in matrix as well as its ability to act as a binder. Compressive strength, percentage of sludge, binder dosage, slump, water to cement ratio, percentage of solid, and curing time are being observed. The results indicated that sludge can be incorporated into the pastefill and enhance its strength without compromising the pastefill quality and integrity.

Jan 1, 2004

By R. J. Visintainer, W. L. Whitlock

"Difficulties with the sizing and operation of centrifugal froth pumps are common and the underlying fluid dynamics are complex. Design and selection often relies on previous experience, offering unreliable guidance for novel applications or unexpected problems. The current paper describes a program of extensive laboratory testing on froth handling centrifugal pumps, covering a range of flows, heads, speeds, viscosity, air content and froth stability. Variations in impeller vane design and the effectiveness of an airlock venting apparatus were also examined. The program resulted in a better understanding of centrifugal froth pump dynamics and insight for the troubleshooting of field applications.INTRODUCTION The Challenge of Pumping Froth In pumping mineral processing froth, the handling of large quantities of air within the fluid is often unavoidable. Efforts to reduce the amount of air present at the pump suction, while always recommended for improving pump performance, may have limitations. Some strategies may also carry an economic penalty, such as unwanted process dilution (e.g. due to water spray or injection), or increased capital cost of equipment due to oversized pumps, sumps and/or piping. Froth pumping losses fall into several categories, as described below and represented graphically in Figure 1. • Density effects: Entrained air reduces the pressure created by the centrifugal pump in direct proportion to the reduction in bulk density. This is not a true “loss”, since the head produced by the pump (in meters of froth), may remain unaffected. However, the reduction in pressure often leads to a corresponding increase in pump speed required to drive the system, which itself leads to increased NPSH required by the pump (NPSHR). Furthermore, by adding a gas phase, the overall volumetric flowrate is increased, assuming a fixed quantity of de-aerated liquid being handled. This leads to increased suction velocity which further reduces the NPSH margin by simultaneously increasing pump NPSHR and decreasing system NPSH available at the pump suction (NPSHA). • Viscosity effects: Increased viscosity introduces an additional factor in some froth pumping applications, such as oil sands bitumen froth. Losses result from increased shear stress within the fluid flow, which increase with flowrate. Viscosity also facilitates the formation of airlock by reducing turbulence and allowing individual bubbles to coalesce more easily within the flow stream. Finally, it increases pump NPSHR by increasing local pressure drop in the vicinity of the vane inlet edges. • Airlock effects: Also known as air binding, it occurs when air or gas coalesces within the pump suction or impeller passages and begins to collect there, held by buoyancy forces within the rotating flow field. In essence, the liquid “floats upwards” towards the pump suction against the outward directed centrifugal forces. The airlock acts as a blockage, with corresponding reductions in flow, head and efficiency. NPSHR also increases, due to increased velocity and distorted streamlines in the flow circumventing the blockage."

Jan 1, 2012

"This paper reviews the chemistry involved in the recovery of gold from cyanide solution with anion-exchange resins, and also discusses the most critical aspects of the engineering of an effective resin-in-pulp (RIP) process. As far as the chemistry is concerned, the conclusions reached by a great many researchers, as well as the performance of the only operating RIP plant in the Western World, at the Golden Jubilee Mine in South Africa, support the view that the process is technically viable and, in many cases, could prove to be more attractive economically than alternative processes such as zinc cementation and carbon-in-pulp (CIP). On the engineering side, there is still a need for further development before larger scale ( > 50,000 tpm) RIP plants can be designed, built and operated with confidence. However, the experiences gained during nearly 3 years of operation of the Golden Jublee RIP plant indicate that the process can be engineered with confidence for smaller operations ( < 50,000 tpm), and this will probably be the scope of application of the first-generation RIP plants. INTRODUCTIONThe use of anion-exchange resins in gold processing has, for a number of years, been proposed as an alternative to more conventional processes such as zinc cementation and carbon adsorption, and detailed research programs that have been carried out at a number of laboratories have demonstrated the technical viability of the process. (Burstall et al, 1953, Davison et al., 1960, Tataru, 1973, Laskorin et al. 1978, Hosking, 1984, Riveros and Cooper, 1987 and Palmer et al., 1988)The main incentive for this work was the fact that resins have several characteristics that are quite different from carbon, which make them potentially more attractive substrates for the recovery of gold. The following are examples: -"

Jan 1, 1991

By S. Kelebek, B. Nanthakumar

ABSTRACT The sensitivity of sulphide minerals towards oxidation depends on the mineralogical makeup and nature of sulphide ores. This paper focuses on chalcopyrite behaviour in a nickel-copper sulphide- ore matrix that was aged in the mine-site stockpiles. Results of collectorless, collector-induced flotation and recovery by size are presented following a discussion of XPS analysis that was used to gain insight into oxidative alteration of chalcopyrite’s surface chemistry. Chalcopyrite maintains its high flotation activity despite exposure to weeks of oxidative conditions. It is concluded that chalcopyrite is quite tolerant to stockpile oxidation due to various factors related to alteration of its surface chemistry.

Jan 1, 2012

By H. Miki, S. Wheatley

The addition of precipitated silica greatly enhances chalcopyrite leaching in the presence of sodium chloride at moderate temperatures (65-90°C) in acid media with ferric ions as the oxidant. The beneficial effect increases with the increase in chloride concentration and temperature. The addition of sodium silicate and silica sand has no significant influence. The analysis of solubility data in acid/salt solutions indicates that the solubility of silica as Si(OH)4 as the dissolved species is controlled by the activity of water, as expected from the hydration theory. Kinetic analysis shows the trends that copper dissolution from chalcopyrite in the presence of precipitated silica with sodium chloride follows a shrinking sphere model indicating a chemically controlled surface reaction. The effect of temperature on copper dissolution in the presence of both precipitated silica and sodium chloride was also larger compared to the results in sodium chloride alone. The SEM analysis shows that chloride and silica facilitates the precipitation of sulfur on the surface of the silica particles rather than the chalcopyrite particles which avoids the blockage of the mineral surface and thus improves the leaching kinetics.

Jan 1, 2014

By R. Holmwood, M. Faris, P. Holloway, M. Collins

Sulphuric acid addition is a major driver of the economics in the processing of nickel laterite ores by high pressure acid leaching (HPAL). Understanding the optimal acid addition rate is essential for the success of any HPAL operation, and this is especially true at Ambatovy, where the composition of the feed tends to vary significantly on a day-to-day basis. Most studies on the effect of acid on nickel extraction in HPAL have used laboratory testwork as their basis. Although these studies are invaluable in assessing the economics of a new project, they are limited by the range of ore composition that can be tested and the differences between the operation of the laboratory equipment and the commercial plant. To enable optimization of the acid addition at Ambatovy, operating data from the HPAL operation were obtained using OSISoft’s PI system and the data from several periods were examined to develop relationships between acid addition and nickel extraction. The initial relationships from 2014 focused on the acid required to achieve a target nickel extraction of 95%, with aluminum and magnesium in ore and feed slurry solids content as the major variables. As Ambatovy ramped up through 2015 and 2016, the calculated acid requirement was further refined to address the effects of HPAL temperature and retention time, and the oxidizing/reducing characteristics of the ore, and to generate acid requirement relationships as a function of ranges of nickel extraction. These relationships supported raising the target nickel extraction to 96% and enabled the development of an economic model between acid addition and nickel extraction.

Jan 1, 2017

By Rowena Anderson

Mining companies are now looking for more effective ways to engage the community in public participation. Consensus-based approaches are becoming the most popularly applied way of achieving meaningful public participation. This paper introduces the principles surrounding consensus-building approaches and the processes for getting them started. The Healthy Communities Movement is one such consensus-based approach that offers a well-established holistic model for conceptualizing a healthy sustainable community. It also highlights the importance of public participation as an essential component of achieving a sustainable community. The paper concludes by illustrating how current company-community relations programs can utilize these models.

May 1, 2002

By Zetti Gavelán

Lack of skilled workforce in mining industry during the current decade has been a serious concern for most mining organization globally. At the beginning of this decade the major envisioned difficulty was related to generational breach of mining professionals. By 2003, mining industry recover from a low metal prices cycle following by a worldwide mining investment boom in 2005 that triggers a talent war among mining companies that was not only limited to professional level but skilled operators as well. Despite world?s economy collapse in October 2008, impact on mining industry was small comparing to other industries and appears to show evidence of healing. Under this context, fundamentals that have been driven lack of skilled workforce for the mining industry in previous years still valid. Starting in 2007, Minera Argentina Gold SA - Barrick Veladero, subsidiary of Barrick Gold, initiated an innovative selection and training program for candidates without exposure to mining. Following our corporate social responsibility mandates, Barrick Veladero decided to change its hiring process entirely, concentrating on selection and training of local people with no experience rather than hire experienced mining operators. This paper shares Barrick Veladero experiences on its hiring program, challenges faced, and current results.

May 1, 2010

By M. S. King

"A simple method is proposed for determining the long-term deformation behaviour of evaporites. The theory developed can be tested by measuring the change in diameter as a function of time of a vertical mine shaft opposite evaporite strata. Ultimate shaft closures predicted by the theory agree well with those calculated with the very much more complex theory of Serata (1968), provided that sufficiently high octahedral shear strengths are used in the former.An analysis of measurements made in an isolated opening in a Saskatchewan potash mine shows that the octahedral shear strength of the surrounding potash and halite was approximately 500 psi several years after the opening was mined. This value is less than that deter-mined experimentally for halite by Serata. The same data indicate, furthermore, that the in-situ octahedral shear strength is decreasing slowly with time.The current controversy regarding the actual deformation of evaporites will only be resolved by the cooperation of potash producing companies in releasing data on the long-term deformation of their mine shafts."

Jan 1, 1971

By Marty Hudyma

Large seismic events have been reported in mines in the Sudbury mining camp for more than 70 years. Nevertheless, no detailed record of the events has been compiled. In 2008, the Sudbury Regional Seismic Network (SRSN) research project was initiated to collect more accurate data with regard to the magnitude and locations of mining-induced seismic events in and near the mines in the Sudbury Basin. The data is used to better understand the mechanisms of the events and cause-effect relations between mining and seismic events. Through the collection of a central database of large seismic events, new insight is being be gained into why some mines are much more prone to large events than others. Fifteen low cost seismic stations have been distributed throughout the Sudbury basin. The data from each seismic station is uploaded to a central server using the internet. Data recorded on the SRSN is processed on a daily basis, and a weekly summary of blasts and events is issued to project sponsors. Seismic events smaller than local magnitude +1.0 have been identified and located. Event location accuracy is less than 2 kilometres, however, many events have been located less than 1 km from a mine. The SRSN fills a seismic monitoring gap between the in-mine microseismic monitoring systems and the earthquake monitoring system operated by the Geological Survey of Canada. Since July 2008, more than 600 mine blasts and more than 450 mining-induced seismic events have been recorded in the Sudbury basin. This paper primarily discusses the technical aspects of the design and operation of the SRSN. The SRSN is a Canadian Mining Industry Research Organisation (CAMIRO) research project, with industry sponsorship and support from FNX Mining, Itasca Canada, Vale Inco and Xstrata Nickel.

Oct 1, 2010

By Yi Yang, Mark Zoback

"We report laboratory studies of the time-dependent deformation of core samples from four different formations in the Williston Basin - the Lodgepole formation, the Middle and Lower Bakken formations and Three Forks formation. The laboratory tests reveal varying amounts of viscoplastic deformation in response to applied differential stress. The time-dependent deformation is generally greater in rocks with higher clay and organic content, and can be described by a power-law function. Because the magnitude of the creep strain is linearly proportional to the applied differential stress, we can utilize viscoelastic theory and geophysical logs to estimate the degree to which tectonic stress is affected by viscoplastic stress relaxation. We suggest that viscoplastic stress relaxation results in the Upper and Lower Bakken Formations act as frac barriers during hydraulic fracture stimulation in the Middle Bakken, but the Lodgepole and the Three Forks Formations are not frac barriers.INTRODUCTIONHorizontal drilling and multi-stage hydraulic fracturing in shale reservoirs are critical for successful exploitation of ultra-low permeability shale gas, tight gas and shale oil reservoirs. Characterization of the mechanical properties of the reservoir rocks is essential to understanding the behavior of rocks during drilling and completion. Previous laboratory studies have shown that the timedependent deformation in clay-rich shales can be characterized as linear/viscoelastic deformation (Chang et al., 1997; Hagin and Zoback, 2004a, b; Sone and Zoback, 2013b, 2013c). Sone and Zoback (2013c) showed that laboratory measurements of time-dependent deformation in various gas shale reservoir rocks, and demonstrated that the viscoplastic deformation of these rocks can be characterized by a power-law function. They interpreted the results in the framework of linear viscoelastic theory to quantitatively assess the geomechanical effect of viscous time-dependent deformation over engineering and geological time scales. (Sone and Zoback, 2014) further extended the theory and proposed a viscous relaxation model that can be applied to predict the continuous differential stress magnitude using the geophysical logs. They tested the validity of their model by comparing the stress prediction with the occurrence of drilling induced tensile fractures (DITFs) and the vertical hydraulic fracture penetration observed from microseismicity."

Jan 1, 2015

By N. Giguère

Until recently, the heat treatment of pressure die cast parts has always been considered unpractical because the solution heat treatment resulted in unacceptable blistered parts. This was due to the presence of massive porosity associated with the die casting process where the inflow of metal inside the mold cavity is extremely turbulent. With the steady improvement of foundry practices and the generalization of vacuum die casting, porosity defects have been reduced to the point that a partial solutionizing heat treatment can be applied without any damage to the casting. However the solutionizing temperature must be lower than that applied to macroporosity free castings and for much shorter time. The object of the present study was to determine the optimum solutionizing temperature that can be applied to aluminum 383 die cast brackets along with the optimal temperature and time of aging resulting in the highest improvement in mechanical properties (both strength and ductility). This was done by testing strength and deformation on the casting itself using a specially designed jig; the crushing force to deformation curve was analyzed so as to quantify the improvement in both strength and ductility gained with the partial precipitation hardening heat treatment.

Jan 1, 2011

By Boyd Davis, Vladimiros Papangelakis, Douglass Duffy, Michael Carlos

"The processing of lateritic saprolite in hyper-concentrated magnesium chloride brines offers several potential advantages for the hydrometallurgical production of nickel. An aggressive HCl-MgCl2 leach at atmospheric pressure can significantly reduce magnesium dissolution, and offers the ability to recover HCl and MgO by a less energy intensive process than conventional techniques via the formation of magnesium hydroxychlorides. Inevitably, the high chloride concentration renders iron fully soluble during leaching and thus requires subsequent iron control and disposal steps. Experimental measurements coupled with OLITM modeling were conducted to investigate the behaviour of iron in concentrated magnesium chloride brines, in terms of chemistry (nature of iron species) and solubility limits. The solubility of ferric chloride in magnesium chloride solutions of concentrations and temperatures relevant to this process was controlled by a previously unreported solid phase: 2.5FeCl3·MgCl2·7.5H2O. Iron precipitation tests on synthetic leach solutions without seeding indicate a metastable akaganeite precipitate which transitions to hematite upon equilibration. Magnesium chloride solubility in ferric chloride solutions was also investigated to allow the simulation of a ternary phase diagram for the MgCl2-FeCl3-H2O system, in order to determine process conditions that avoid unwanted chloride precipitation.INTRODUCTION In the search for more economical processes to treat lateritic saprolite for nickel production, chloride hydrometallurgy has been increasingly investigated. While High Pressure Acid Leaching (HPAL) can frequently economically treat lateritic limonite, the presence of saprolite negatively affects process economics. The higher magnesium content of saprolite increases acid consumption, because magnesium sulphate, unlike iron and aluminum sulphates, does not hydrolyze in HPAL. This soluble magnesium decreases the sulphuric acid strength by an amount greater than the amount of acid stoichiometrically required to leach magnesium, which must also be disposed of or recovered (Jankovic, Papangelakis, & Lvov, 2009). Due to these issues, pyrometallurgy is most commonly employed to treat lateritic saprolite, via the Rotary Kiln-Electric Furnace (RKEF) process; this process uses a rotary kiln to dry and partially reduce nickel and iron oxides before sending the calcine to an electric furnace for smelting to produce a ferronickel product for the stainless steel market. Although the problems encountered during hydrometallurgical processing are avoided and nickel recoveries are high, high capital and energy costs prevent the application of this process to lower grade lateritic saprolite deposits (De Bakker, 2011)."

Jan 1, 2016

By B. D. Pandey, M. S. Kim, B. S. Kim

The recovery of Sn from used Pb-free solder (Sn, 3~4 % Ag, < 0.9 % Cu, < 1.2 % Pb) has been investigated by electrorefining in sulfuric acid solutions containing small amount of hydrochloric acid. This involved preparation of the anode material by melting and casting the used solder followed by refining. During electrorefining, dendritic tin was deposited on stainless steel cathode. Increasing the amount of hydrochloric acid up to 0.3 mol /L in the electrolyte enhanced the current efficiency to 92.2 % and the enrichment ratio of silver to 94.3 % in the anode slime which was otherwise 84.7% and 81.6 % in absence of HCl, respectively. The electrolyte containing hydrochloric acid has also prevented the precipitation of tin oxide in the bath. In the scale-up experiment using 1.6 kg anodes, 84.3 % current efficiency and close to 100 % Ag enrichment ratio were obtained, while the purity of electro-refined tin was over 99.9 %. The energy consumption of the winning process was found to be 0.151 kWh /kg-Sn which is competitive as compared to commercial tin electrorefining processes.

Jan 1, 2014

By P. Czaja

The paper presents a patented and copyright protected concept of constructing a shaft lining that goes through rock masses having strong rheological properties and being susceptible to leaching. In the case of salt layers, especially at significant depths (over 900 m) the relative convergence of the heading contour may amount to 40 ?/year. That results in the fact that any other method of securing the shaft lining, e.g. by making it flexible, will not be sufficient to ensure the stability of the shaft reinforcement geometry. In the new shaft lining concept the excessive rock creep into the outbreak inside the shaft diameter will be removed by local and controlled leaching of the shaft cheeks by means of fresh water directed through a porous medium at the contact layer behind the watertight tubing lining. The paper presents the structure of such a lining and an outline of the construction technology. In order to implement such a lining, a typical tubing will be applied. Separate design and manufacturing will be required for the technological rings used to control the leaching process behind the lining.

Aug 1, 2013

By Vincent Roy

Numerous on going activities at the Daniel-Johnson Dam : ? Surveillance / monitoring ; ? Structural investigations & evaluation ; ? Injection work ; ? Crack mapping ; ? Instrumentation management (drawings & inventory) ; ? Drainage system state ; ? Foundation evaluation

Aug 1, 2013

By P. Walford, C. Mealin, D. Good

"The geology of the Ore Fault Ni-Cu deposit has been reinterpreted in the light of recent studies of the geology of the Neoarchean Bird River Sill Complex and the occurrence of economic Ni-Cu and Zn-Cu-Ag mineralization. The Ni-Cu sulfides are hosted by the lower of two parallel NNW-trending and moderately W-dipping mafic-ultramafic intrusions related to the Bird River Sill Complex. The bod¬ies intruded a bimodal volcanic suite consisting of weakly deformed mafic flows and felsic pyroclastic rocks. The mafic volcanic rocks are geochemically related to the MORB-type rocks of the Lamprey Falls Formation, and the felsic volcanic rocks are related to arc-type rocks of the Peterson Creek Formation. The original pyroxene- and olivine-dominated mineralogy of the sills has been replaced by variable ser¬pentine-amphibole-talc-carbonate assemblages.The Ni-Cu sulfide assemblage exhibits textures and geochemical signatures typical of orthomagmatic sulfide mineralization. The sulfide minerals are associated with cumulate layers of magnetic ferrochromite that range in thickness from a few to tens of centimeters. A later event of Zn-Cu-Ag sulfide mineralization associated with quartz veining and garnet-chlorite alteration along a fault that strikes north, dips vertically, and cuts all rock types. The mineralized fault is cut by the NE-trending Peterson Creek shear zone. Where the Ni-Cu and Zn-Cu-Ag mineralized zones intersect, remnant magmatic features such as amphibolite or cumulate ferrochromite bands occur within quartz veins or local chlorite alteration. The mixed zones contain a very unusual polymetallic assemblage of Ni, Cu, Zn, Ag, and platinum group elements (PGE)."

Jan 1, 2009