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By G. Dodbiba, A. Otsuki, T. Fujita, J. Ponou, A. Shibayama

"The different types of nano to submicron particles, which are well-dispersed nano particles, coagulated nano particles or settled submicron particles, have been measured by the interactive force apparatus (IFA). The information is very useful for mineral processing treatment. The IFA can measure the particle size distribution in low to high concentration of particles in liquids and non-light transparent liquids. Here, mainly the emulsion and bubble size measurements are described.Emulsion (w/o type) is prepared with oil and water mixture. The nano to micro emulsion particle size is usually measured by light scattering method. The particle size distribution of emulsion of light oil measured by IFA agreed well with the one by the dynamic light scattering (DLS) method. The water size distribution in emulsions of gasoline is difficult for the small reflection index and C heavy oil is difficult for the black color by DLS method. The IFA can measure both emulsions.There are many methods to measure fine air bubbles, however, the finer nano size measurement apparatuses are DLS method and IFA. A “ghost” peak appeared in the large particle micron meter size in DLS method. The mean diameter in IFA is similar with DLS for the nano meter size. INTRODUCTIONParticle size distribution measurement of nano to submicron particle, emulsion and bubble size distribution are very useful for ultrafine particle separation and characterization of fine particles by the necessity of recent fine minerals separation (For example, Li et al.2016, Mikhlin et al.2016, Wang et al.2013). As for the size measurement of solid particles in liquids, three different types of nano to submicron particles, that are well-dispersed nano particles, coagulated nano particles or settled submicron particles, have been measured by the interactive force apparatus (IFA). The particle size distributions are compared with the one of dried particles measured by TEM or SEM. The well-dispersed nano particle size distribution by IFA is influenced by the nano size surfactant micelles and becomes smaller, when compared with the TEM result. The size distribution of nano size of magnetite particles in water is influenced by the isoelectric point and the mean diameter of coagulation becomes larger. The particle coagulation in diluted suspension is about 2nm smaller when compared with the higher concentration. The submicron nickel particle size distribution is well agreed the result by SEM. The coagulation effect is small in the submicron size of nickel powder in water (Fujita et al., 2013). In this paper, the emulsion and bubble size measurements are mainly described."

Jan 1, 2016

By H. Dundar

The first application of High Pressure Grinding Rolls was in 1985 at a cement plant, for the purpose of capacity improvement. Then various circuit configurations were derived to achieve a reduction in overall specific energy consumption, by transferring more of the grinding required to the HPGR. In most circuit configurations, the recycle of fines is required for effective breakage between the rollers. By increasing the fines amount in the feed material to a specific level within the recycling load, a uniform material bed is created and a higher pressure gradient along the roller width is obtained, resulting in compact flakes, including more fines. The fines recycle results in enhancement of the interparticle breakage. This paper will discuss the effect of the feed size distribution on HPGR performance.

Jan 1, 2012

By Marcel Laflamme, N. R. Rillette

"In 1982, a study was initiated to investigate relationships between bonus and accidents in Quebec underground mines. In 1983, the study was expanded to include the impact of age and experience on accidents.The paper will describe the methodology followed in gathering information at ten mines from three mining camps in the Province of Quebec, and its transfer to data banks for subsequent treatment. Multifactorial analysis of nine variable files for the ten mines has shown: that age, experience and seniority are linked; that total working hours are tied with overtime; that bonus is linked to the main activity of the miner, and not to accidents. The most tangible factors affecting accidents seem to be the introductory training and subsequent retraining at regular intervals."

Jan 1, 1989

By M. E. Sirkka

"INTRODUCTIONInco Ltd. has ten operating mines in the Sudbury district. Over the last ten years mining methods have changed at Inco with special emphasis on the introduction of bulk mining replacing conventional mechanized cut-and-f ill and undercut-and-fill methods. At the same time, the technology and size of LH D equipment has also progressed to meet the demands of bulk mining. This paper will concentrate on various aspects of the introduction and operation of electric LHD equipment a t Inco Limited, Ontario Division. BackgroundInco Limited received its first electric 2 cu. yd capacity LHD in July 1975 at Creighton Mine. The unit was tested pulling shrinkage stope muck and then was moved to a mechanized cut and- fill complex on 6600 Level. The electric scooptram received quick acceptance from the operators, due to its quiet operation and low heat generation, in a relatively hot operating environment. Although there are only two of these units operating a t present, this initial favourable experience, both in cost and efficiency, led to the development and purchase of electric scooptrams of the 5 cu. yd size. There are currently eleven 5 cu . yd electric LHDs in operation.The most recent development a t Inco is the move to yet larger electric LHDs in the 8 cu. yd size. The first electric ""Eight"" has now been in operation at Copper Cliff South Mine for over a year. This unit has the distinction of being the first one of its kind in service in North America. At the time of writing, there were ten 8 cu. yd electric ma chines operating in Inco's Ontario Division Mines, with three on order."

Jan 1, 1989

By Charles Tkaczuk

Key issues ? No business tool has greater potential to effect change and enhance profitability than process control. ? Successful businesses see process control as an integrated engineered system, designed and built into their business models from day one. ? The integration and use of process control sets the stage for years of compounded returns. ? Has been used for years to optimizing recoveries and minimizing waste. ? However, the mining/ore extraction sector has been slow to adopt integrated process control. What is the problem? ? Most executives and engineers do not clearly understand process control when applied to mining/extraction activities. ? Common approach has been to apply generic process control strategies as a blanket cure all and wait for it to pay off. ? No central focus which results in multiple group involvement, overlap and inconsistent application of questionable technology. ? Considered a low priority until production activities commence. ? Comfort in using brute force mining methods. ? An off-the-shelf integrated under ground mining process control architecture has not until recently been available.

May 1, 2004

By H. Dundar

The first application of High Pressure Grinding Rolls was in 1985 at a cement plant, for the purpose of capacity improvement. Then various circuit configurations were derived to achieve a reduction in overall specific energy consumption, by transferring more of the grinding required to the HPGR. In most circuit configurations, the recycle of fines is required for effective breakage between the rollers. By increasing the fines amount in the feed material to a specific level within the recycling load, a uniform material bed is created and a higher pressure gradient along the roller width is obtained, resulting in compact flakes, including more fines. The fines recycle results in enhancement of the interparticle breakage. This paper will discuss the effect of the feed size distribution on HPGR performance.

Jan 1, 2012

By D. M. Cruden

"When two discontinuities form a tetrahedral wedge in a rock slope, a factor of safety for the wedge can be simply calculated (if motion is driven only by gravity and resisted only by friction) from plots of the normals to discontinuities on an overlay of a polar, equal-area spherical projection to which the great circles of a similar equatorial projection have been added.IntroductionThe stability of slopes in rock masses is often controlled by the discontinuities that exist in the masses. In particular, the geometry of the discontinuities constrains the ways in which the mass may fail. Displaying the orientation of the discontinuities on a spherical projection has been found to be a useful way of identifying possible failure modes. The most concise display shows the orientation of the normals (or poles) to the discontinuities that compose the fabric of the rock mass. Computer processing of large samples of discontinuity orientations is necessary if the sampling biases identified by Terzaghi (1965) are to be routinely corrected. Fortunately, displays of the poles to discontinuities (or pi diagrams) are relatively easily produced on the line printer of a computer or by a computer plotter (Cruden , 1978; Ramsden and Cruden, 1979). Unfortunately, further analysis of the stability of a rock mass has tended to use traces of typical discontinuities on a spherical projection rather than pi diagrams; examples may be seen in Hoek and Bray's book (1981)."

Jan 1, 1990

By Rodrigo A. Marinho

Erratic high grade values are as common in Nature as they are a source of problems for resource estimators. In some highly erratic metal deposits, less than 2% of the drilling samples can represent more than 10% of the total metal in the blocks and they are associated with a high risk level. There is a risk of local overestimation but also of global overestimation, with the high grades being projected over too large a volume. Capping or restriction of these outliers control is being widely used in the industry and commonly applied in resource estimation for the last three decades. The primary purpose of this paper is to present and describe the most applied methodologies for restricting the extrapolation of high grade samples and discuss the results based on a theoretical simulated model. Additionally, this paper demonstrates the economical impact associated with the high-grade and the project risk profile associated with each method.

Oct 1, 2009

By Pierre Boulanger

This paper describes a generic technology for modeling in real time the various operations of surface mines. Based on various sensor fusion techniques and high-speed network, a virtual reality model of a mine capable of representing not only static infrastructures but also mobile equipment such as trucks and excavators is created. The modeling technique deal with a wide range of sensors such as survey data, satellite pictures, ore concentration, machine condition indicators, video, sound, real-time GPS locator, range sensor, etc. The model created allows for every piece of information to be displayed in context allowing for a better temporal and spatial correlation of events by mine operators, planners, and supervisors. Syncrude, a Canadian mining company located in northern Alberta, is planning to use this technology, not only to understand oil sands mining processes better, but also to give decision-makers better access to the timely, accurate information from the field that they need to make informed decisions.

May 1, 2001

By M. McKim

"Due to the fact that there were no formal papers submitted for this session we can only print the discussions of the papers. a) Maqnetic Mill Liners : M. MckimE. MarcotteFalconbridge LimitedReplyIn looking at the slides on magnetic mill liners a question comes to mind, particularly in the case of a large diameter mill using large grinding media, concerning the potential hazzards which may exist from large chuncks of steel hanging in the mill. Would you comment.The magnetism was sufficiently strong from liner to liner to hold ........................ .(We are sorry but we could not transcribe the full reply to this question as no microphone was used by the speaker and i't was impossible for us to complete the rest).·"

Jan 1, 1984

By D. E. Ayres, J. Farstad

"The Midwest uranium deposit is located within the Athabasca Basin near its eastern margin and displays many of the features seen in a number of other similar deposits in this area. The mineralization occurs in the vicinity of a tectonically disrupted portion of the unconformity separating the clastic sedimentary rocks of the Helikian Athabasca Group from Aphebian pelitic meta-sediments which are equivalent to the basal pelitic meta-sediments of the Wollaston Group. The orebody consists of pods of massive pitchblende and sulphur-arsenides within an elongate and tablular envelope of disseminated and fracture controlled mineralization. The massive pods are intimately associated with overbank mudstones of the lowermost Athabasca Group. Both structure and lithology have played major roles in localizing the deposit as follows:1. The basement lithology influenced the mineralogy of the regolith produced on the pre-Athabasca unconformity.2. The style of clastic deposition and the character of the regolith on this unconformity favoured local preservation of mudstones.3. The basement lithology influenced the location of zones of post-Athabasca faulting.4. The proximity of these fault zones to mudstones provided for the coincidence of circulatory channels for fluids bearing uranium, with a good precipitant for the metal.IntroductionA brief summary of the geology of the Midwest uranium deposit was presented by J. Farstad (1979) to the attendees of the Saskatchewan Potash and Athabasca Basin uranium deposits field trip organized by the Canadian Institute of Mining and Metallurgy (May 28 to June 1, 1979). Since that time a substantial amount of data has been collected and studied. This paper is a precis of a report by J. Farstad (1981) which summarizes the geology of the deposit as inferred by visual examination of diamond drill core, augmented by information obtained from detailed examination of selected cores by D.E. Ayres."

Jan 1, 1986

By T. E. Newkirk

In the past few years there has been considerable controversy on the most suitable material to be used in ventilation doors which will have to serve also as fire doors. For this reason it was thought useful at Mclntyre to find out to what extent our zinc chloride treated spruce doors were fire resistant and what protection we could expect in case of an underground fire. The doors to be tested were constructed of the same material as that used in our regular ventilation doors underground, namely, 2-inch tongue-and-groove well seasoned spuce. It is to be noted, however, that whereas the dimensions of the ventilation doors are 5 ft. by 6 ft., those of the test doors were only 14 in. by 17½ in. The treated doors were made up from lumber that l1ad been treated with chromated zinc chloride, as described in Mr. Keeley's paper. Two kinds of tests were carried out: a heat test and a flame test. An electric muffle furnace for assaying, equipped with a pyrometer, was used for the beat test, the furnace door being replaced by the wooden door to be tested. In the flame test, the door to be tested formed one end of a rectangular steel box in which was placed a large blow-torch. Air was admitted at the rear of the box. A pyrometer recorded the temperature at the inside surface of the door where flame impinged. The results of the tests are presented in the accompanying table, in which the word 'failed' is to be interpreted as meaning that the door had been damaged to the extent that smoke, but not necessarily flame, issued from its outside surface.

Jan 1, 1949

By Peter N. Calder, Louise H. Michaud

"An interactive mine planning package has been developed to aid with the tasks involved in generating dragline mine plans. This package employs recent advances in PC-based,3D computer graphics and 3D geologic modelling. A Gridded Seam Model (GSM), capable of modelling rugged topography and multiple coal seams, including folding and faulting, is used to generate the geologic database This model is then integrated with an interactive graphics mine planning system in order to develop one model and one database for the generation of the mine design, the depletion of the coal reserves and the removal of waste material.As well as offering large potential saving in the time required to carry out the planning tasks, the system offers immediate visual feedback to the planning engineer. This can greatly aid in the conceptual understanding of complex geology and mine plans and can allow for the evaluation of a number of mining options within a reasonable time frame.IntroductionThere are a large number of variables that must be taken into account during the development of a dragline mine plan. This is especially true when developing a mine in mountainous terrain, where there is a lack of continuity of the geology and topography over the mine site. Until recently, the complexity of dragline mine plans has prohibited the development of a universal mine planning package that is applicable to all geologic and topographic situations. The majority of the commercial programs that are presently available to facilitate dragline mine planning have been developed for specific mine properties or are limited in the coal geology and mining methods that they can simulate (Brown and Clifford, 1983; White 1983; White and Jones, 1984; Sadri and Lee, 1982; Dagdelen, 1979)."

Jan 1, 1993

By D. Lauzon, H. de Ruiter

"In 1988a decision was taken to design and install a computerized mine monitoring and control system. This system had to monitor and control all pumping and ventilation underground. The operation of the mine air heating, using waste heat from the mine water and compressors, was to be part of the system. It ultimately also had to interface with the four existing Canadian General Electric Series 3 PLC's which controlled the No .3 shaft loading pockets. Beside operational control and trouble shooting, the system is a valuable tool in energy management and ultimate savings are estimated at $50,000 per year.The final equipment selection was a General Electric Series Six PLC on surface with a total of 17 Series One Plus and Juniors PLC located underground. Data is transferred through a two-pair shielded cable using modems. Both analog and digital functions are being utilized.The basic monitoring and control system was commissioned during 1989and, due to a higher level of technology today, further improvements have been planned for the future. The system was designed by Walter Dow together with Gordon Champion of D.G. Champion Engineering Ltd. of Toronto. Advice for the ventilation part of the project was obtained from Maurice White, Independent Ventilation Consultant.The Ministry of Energy, Mines and Resources and the Ministry of Energy of Ontario approved this project together with the waste heat recovery project to qualify for a grant of$135,000 under the Enerdemo-Canada program.IntroductionThe Macassa mine is a narrow vein gold mine situated about 2 km west of the town of Kirkland Lake in northeast Ontario. The mine has been in continuous operation since 1933 and a total of about 3.0 million ounces have been recovered out of 6.6 million tons of ore ."

Jan 1, 1991

By C. -M. Katsari, G. N. Anastassakis

"Copper is considered one of the most important industrial metals because of its properties (conductivity, malleability) and variety of uses. Approximately 70% of the global copper is used for various electrical applications, with a significant part of copper originating from recycling, since copper can be recycled and re-used countless times, without any loss of performance and difference in the quality of recycled copper in comparison to that from ore. Copper recycling significantly contributes to natural resources conservation, waste minimization, energy saving, and overall cost reduction. Approximately, 35% of the globally produced copper originates from recycled copper.The objective of the current work is to investigate the recovery of copper from electric wire scraps using wet shaking table as an alternative to air separation methods that prevail over the wet ones in recycling processes. The tests were carried out using feed of correspondingly high- and low-grade in copper. In the first case, the wire scraps had been subjected to shredding only, prior to tabling separation; in the later, the low-content tailing of prior air separation was used as feed ?n table separation.In regard to testing, the following factors were examined: table tilt, water flow-rate, and reciprocating speed. The results of the tests clearly denote that copper wire separation from plastic polymer is feasible, as in most cases, table separation resulted in heavy products of high purity in copper and high recovery, and tailings of very low copper grade. The results of the current work clearly denote that wet tabling can be applied efficiently for the separation of recycled copper wire from plastic, as an alternative to air separation methods, as well as for the recovery of copper from the low-grade tailings derived from air separation methods."

Jan 1, 2016

By D. Kao, J. Gogal, S. Humphrey, T. Byrne, M. Davoodi

"High total and dissolved uranium values were noted in the process water at the Cigar Lake Operation (CLO) during early production start-up period, whereas significant levels of dissolved uranium had not been observed previously at similar operations. The excess dissolved uranium resulted in higher demands on the water treatment plant, along with higher operating costs, environmental risks and some unrealized revenue potential. A species balance indicated that uranium was leaching into solution in the grinding, dewatering, and storage circuits under normal operating conditions. Jet boring, water recycle, ball milling, and the use of Pachuca tanks for ore storage results in a highly oxidative environment, which is favourable to leaching.This paper will outline the testwork performed to identify the conditions under which the uranium leaches into solution and to determine required conditions for uranium precipitation. Maximum uranium leaching was found to occur under normal operating conditions (pH ranging from 7.0 to 8.5); testwork indicated that both lowering and raising the pH can significantly reduce the uranium leaching. Analytical results combined with the batch scale testwork indicate that the uranium solubility is associated with carbonate species in the ore. Uranium precipitation was maximized at pH values greater than 10.5 or less than 6, corresponding well to carbonate leaching and precipitation values from literature. Higher precipitation efficiencies were noted at high pH ranges.As a result of this work, a pH control system has been implemented in the Pachuca storage vessels and thickener prior to water treatment plant on a trial basis. Caustic soda is recommended for pH control due to ease of operation, economic viability and material requirements and downstream constraints."

Jan 1, 2016

By A. J. Sinclair

Abstract-Exploratory data evaluation is an essential part of every high quality, mineral inventory estimate. Efficient analysis involves a thorough organization of available quantitative data that are the basis of the estimate and perhaps the formation of composite grades. Data organization and evaluation can involve more than 50% of the time necessary to conduct a mineral inventory estimation. The principal purpose of exploratory data evaluation in mineral inventory work is to improve the quality of estimation by providing insight into characteristics of the variables under investigation. Specific aims include: (1) to recognize and eliminate errors; (2) to provide a comprehensive knowledge of the statistical characteristics of all variables of interest for resource/reserve estimation; (3) to document and understand the interrelationships among the variables of interest; (4) to recognize systematic spatial variation of variables such as grade and thickness of mineralized zones; (5) to recognize and define distinctive geological domains that require independent estimation of mineral inventory; (6) to identify and characterize outliers; and (7) to evaluate similarity/dissimilarity of various types of raw data, especially samples of different supports. These aims are not mutually exclusive but they can all have their own impact on resource/reserve estimation. Error must be minimized. Individual variables can have characteristics that lead to different decisions in the course of estimation. Similarly, interrelations of variables might contribute to the ease (or difficulty) with which estimates of several variables can be obtained. Trends can impose the need for two or more domains, each of which might be estimated independent of the others. Outliers, a perennial problem, require detailed evaluations because they impact on reserves much out of proportion to their abundance. Data, of widely different supports, generally must be standardized if all are to be used for purposes of estimation.

Jan 1, 1998

"Line Creek Resources Ltd. produces three million clean tonnes per year of metallurgical and thermal coals for the international market. The mining operation, which is located in the mountains of southeastern British Columbia, produces coal from four pits by conventional truck and shovel methods.The South Pit, which has been in operation since J982, has a benched highwall 490 m in height. Shallow dipping coal seams at the base of the syncline formation will be exposed in the highwall over the next four years of pit life. The first of these seams, which will measure 500 m in final highwall length, was exposed in J994. An auger, powered by a 1250 hp engine capable of cutting 2.2 m diameter holes, was brought on site in J994 and has proven to be a successful means of recovering coal from the J3 m thick seam.This paper covers the background to the selection of an auger mining method to recover highwall reserves together with the geotechnical and methane considerations for this approach.IntroductionLine Creek Resources Ltd., a wholly owned subsidiary of Manalta Coal Ltd., owns and operates the Line Creek mine. The operation which consists of four active pits, a processing plant, and rail loadout is located in the southeastern coal fields of British Columbia. Figure 1 shows the general area.The coal bearing sequence at the mine is preserved on the east and west limbs of a major syncline. Up to twelve mineable coal seams, ranging in thickness from 2 m to 15 m are contained in the formation. Within the pits the seams are stratigraphically consistent and structurally undisturbed, except for small-scale thrust faults that create multiple repeats of the seams."

Jan 1, 1995

By A. Mular, T. Bond, G. D. Farnell, J. F. Kingston

"ABSTRACT:-A 60—cm semiautogenous grinding-(SAG) mill was designed -for continuous wet operation in closed circuit with a vibrating screen. The circuit is fully instrumented and automated. Part of the control system incorporates Foxboro SPEC 200 controllers around the pump box to maintain level. The rest of the control system involves an ACTION model BC2 basic direct digital controller that handles all other inputs/outputs and contact closure sensing:·The success of the control system is attributed to the uniqueness of specially designed mass flow metering systems. Various control strategies are possible. Employed to date has been control of a mill load set-point by cascading the deviation from load set-point as the set-point to the fresh feed rate ""controller"". Mill feed water is ratioed to total flow rate of solids fed to the mill. The performance of the circuit is being correlated with the performance of full scale SAG circuits in British Columbia to develop models, to assess the feasibility of scale up and to investigate the effects of design variables on responses such as circuit throughput. 1 INTRODUCTIONWhere ore types are appropriate, semiautogenous grinding and/or autogenous grinding (AG) has replaced conventional grinding. Secondary/Tertiary crushing plants are thereby eliminated so that capital expenditures are less and overall comminution costs can be lower (Barratt 1982). To establish the suitability of an ore for SAG circuits, pilot scale tests with 1.7 to 1.8 M diameter mills are often conducted. At least one test per ore type in a deposit has been necessary. Often, each test involves a large amount (up to 50 tonne) of sample, so that the testwork can be expensive and may discourage the use of SAG or AG circuits. However, MacPherson (1977) has employed a continuous 45 cm dry Aerofall mill circuit closed with screens and an air classifier to determine whether ores are suitable for SAG milling. The amount of sample per ore type is of the order of 60 kg or less. Thus an established SAG mill scale up procedure that employs small circuits is highly desirable.The purpose of this paper is to describe a small 60 cm wet continuous SAG/ AG mill pilot circuit assembled at the University of British Columbia to study the feasibility of scale up, to assess the influence of design variables, to develop mathematical models and to evaluate the effects of alternative control strategies on circuit performance"

Jan 1, 1988

By N. Moelans, I. Bellemans, K. Verbeken

In this work, we present a phase field model to simulate the facetted crystallization of Fe3O4 in a quaternary FeO-Fe2O3-Cu2O-SiO2 melt under different partial pressures of oxygen. An important focus in creating more realistic phase field models is the incorporation of the thermodynamic driving forces in multicomponent multiphase-field models by coupling to thermodynamic databases. The diffusion of FeO, Fe2O3 and Cu2O is considered. The ratio of FeO/Fe2O3 at the upper boundary is in equilibrium with the oxygen fugacity of the atmosphere, while conserving Fe. Two-dimensional simulations are performed with different varying oxygen fugacity in the atmosphere. For the considered composition range, the growth velocities of the spinel crystals increase with decreasing oxygen fugacity. INTRODUCTION Crystallization of silicate melts has its applications in geology, pyrometallurgy and glass making. In pyrometallurgy, the solidification of slags influences the freeze lining behaviour (Campforts et al., 2007) and the cooling of slag after tapping (Durinck, Jones, Blanpain, & Wollants, 2008). Modeling of silicate melt crystallization is frequently done on the macroscopic level, using thermodynamic equilibrium calculations to determine the fractions of all phases as a function of temperature. The Factsage software and database package (Bale et al., 2016, 2009, 2002) already proved its usefulness in pyrometallurgical applications, for example to model the phase mixture after solidification of a stainless steel slag (Durinck et al., 2008). Crystallization of phases typically results in complex morphologies on the mesoscale, e.g. dendrites or facetted growth. On this mesoscale, the phase field concept has proved to be a very powerful tool (Moelans, Blanpain, & Wollants, 2008) for modeling crystallizing microstructures, because it can treat arbitrarily complex interface shapes with minimal mathematical complexity. In contrast to macroscopic models, the diffusion profiles and crystallization kinetics can be described as well as the morphology of individual crystals. First, Kobayashi (Kobayashi, 1993) simulated a growing dendrite in a pure undercooled metallic liquid. Then, Warren and Boettinger (1995) simulated a dendrite in an isothermal system considering a binary alloy. The extension to multi-phase systems was done by Steinbach et al. (1996). This was further extended by Tiaden, Nestler, Diepers, and Steinbach (1998) to a framework with coupled diffusion and phase field equations in multi-component systems.

Jan 1, 2019