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By Alexey T. Kovalev, Irina A. Khabarova, Valentine A. Chanturiya, Igor Zh. Bunin, Elizaveta V. Koporulina

"The paper presents new theoretical and experimental results about mechanisms of disintegration of mineral complexes and structural transformations of the sulfide surface under high-power nanosecond electromagnetic pulses (HPEMP). The heated gas outflow from nanosecond breakdown channels of sulfide minerals under HPEMP is considered. It is shown that the gas outflow from channels can be an additional destructive factor in the processes of the electric pulse discharge disintegration of mineral complexes. It is shown that the effect of HPEMP changes chemical surface composition and, respectively, technological properties of pyrrhotite and pentlandite. Morphology and elementary composition of new micro- and nanoformations on mineral surface of pentlandite and pyrrhotite have been investigated using up-to-date methods of SEM/EDX and Scanning Probe Microscopy. Preliminary electropulse effect on mineral products before flotation allows producing optimal conditions for flotation separation of pentlandite and pyrrhotite owing to forming the new nanophases and defects on the surface of sulfides.IntroductionThe effectiveness of High-Power Nanosecond Pulses in the disintegration and liberation of fine disseminated mineral complexes and the recovery of micro- and nanoparticles of precious metals from refractory ores was demonstrated in [1, 2]. Possible mechanisms of selective disintegration were considered in [1-3]. It has been shown both theoretically and experimentally that electric breakdowns can play an important role in the nanosecond pulsed treatment of milled minerals (e.g., semiconductor sulfides and quartz with particle sizes of 100 µm to 2-3 mm) that are carriers of finely disseminated gold and other valuable components. Electric discharges in such minerals are accompanied by a destruction of integrity in the form of breakdown channels and the formation of a system of cracks around these channels [3]. The development of the domains of induced cracks around the channels is determined by the pressure of evaporated material in the breakdown channel. Upon an instantaneous energy release in a channel (nanosecond discharges), the change in its transverse size and in the gas density and pressure in the channel is determined by (i) the radial motion of the evaporation wave, (ii) the radial expansion of the channel, and (iii) the heated gas outflow from the channel. The evaporation wave moves with a speed on the same order of magnitude as the speed of sound (or greater) and travels a distance of around the initial channel radius, i.e., a much smaller distance than the breakdown channel length."

Jan 1, 2011

By Nobumasa Kemori

Six kinds of copper '90ncentrates. were treated individually in a ,pilot scale. Outokumpu flsah smelting furnace ~n order to study their ?flash smelting behavior with respect to oxygen efficiency and dust generation. The copper concentrates tested were selected from the more than twenty sources which are treated at the Sumitomo Toyo copper smelter, so as to provide a wide range of chemical composition in terms .of Cu, S,Fe, Pb + Zn + As, and Si~ content. Oxygen efficiency 'and dust generation rates obtained in 'the experiments ranged from 80% ,to 108% and 11% to 20%, respectively. Relationships between these results and experhnental conditions such as chemical and mineral composition of the copper concentrates, flux ratio, fuel consumption and so on are also discussed quantitatively in this paper.

Jan 1, 1998

By Sne?ana Devi

Mineralogy is a significant scientific discipline, essential in establishing the nature and the character of raw materials, regardless of whether they are monomineral or polymineral. Mineralogical characterization is very important, because its results give valuable information on features and nature of examined materials. Information's on mineralogical nature of mineral raw materials influence directly the quality assessment of a raw material, and thus the possibility of its use. The possibility of use of mineralogy in different industrial branches confirms constant activity of this scientific discipline. By use of methods within mineralogical analysis (optical microscopy, x-ray diffraction and others) data on mineral raw materials can be obtained as support in mineral raw materials quality assessment. Short description of results of mineralogical analysis of some mineral materials (granodiorite, dolomites, clay, refractory materials, slags and casting powders) in this paper shows the importance of its support to quality assessment and determine the possibilities of their use.

Jan 1, 2009

By R. Hammen

Processes are needed to rapidly and cost-effectively produce highly pure lithium salts for the rechargeable battery sector. Lithium purification is a chemical engineering challenge, due to the low concentration of lithium compared to sodium, potassium, magnesium, calcium, and transition metal ions commonly occurring in lithium brine resources. We describe a Solid Phase Extraction (SPE) process that rejects sodium and potassium, while binding lithium and other higher valent ions. Lithium is then harvested by selective displacement from the SPE column. The rapid equilibration kinetics of SPE composites enables these ion separations to occur in a small SPE column and in one column stage. The chemical parameters of the process are described.

By Patrick R. Taylor

Sub-micron sized boron carbide powders have been synthesized in a non-transferred arc thermal plasma reactor. Precursors for this synthesis are boric acid or boron oxide powders and methane. The powders produced were characterized in terms of size, shape and purity. Methods to increase the purity of the product were evaluated and included hot water leaching to remove unreacted oxides and controlled temperature, air roasting to remove excess carbon. Theoretical results are also presented on the thermodynamics and mechanisms of the synthesis reactions.

Jan 1, 1994

By Claudio Parra De Lazzari

The determination of the governing step of the deoxidation rate and the effects of the hydrogen content of the mixtures (C), the diameter of the delivery orifice (4) and the Reynolds number of the orifice (Re.) on the product Av kjg were investigated. A,, is the total surface area of the interface between the bubbles and the melt and kjg is the mass transfer coefficient in the gas phase. The design of the experiments was based on a two level statistically fractionated, factorial planning. Oxygen in the melt was measured as a function of time. It was found that the governing step of the deoxidation rate was the transport of hydrogen in the gaseous phase and that {Ay kjg} increases with C, {o} and Reo.

Jan 1, 1997

By C. S. Simons

This paper presents a review of the extractive processes used in the production of nickel, with emphasis on developments since the beginning of the Second World War. Attention is given to the factors, many outside the nickel industry itself, which determined the direction of process research and strongly influenced the ultimate commitments to industrialize the resulting developments. An example of such a factor is the sudden surge in demand, far exceeding the then available nickel production capacity, that was caused by the advent of World War II; the result was the first serious consideration ever given to low- grade laterites as a viable source of primary nickel. Other factors discussed include such items as process development in the extraction of other metals - particularly copper; the availability of increasingly sophisticated materials of const- ruction; the advent of the "environmentalist" and related political developments; the massive escalation in the price of energy - particularly oil. The paper concludes with an attempt to forecast the nature of the most effective nickel process of the future, based on extrapolation from the economic and political situation that exists today.

Jan 1, 1988

By John Wallace

"Monitoring compound semiconductor crystal growth using multifrequency eddy currents for sensing illustrates some of the extreme problems of measurement and interpretation that are not often seen in metallic systems. Using sensor arrays and scanning sensors have produced a qualitative and quantitative understanding of some of the high temperature electrical conductivity mechanisms in several compound systems. A detailed review of the CdTe/CdZnTe data is presented showing some of the complexity in the data as opposed to what is found in elemental semiconductors.HistoryThe most common goal in the use of eddy current measurement in crystal growth is to deter-mine the curvature of the liquid solid interface during growth to test if the heat transfer estimates of the thermal design were adequate for single crystal growth[l]. This aim could be met but represented only a small fraction of the data that was produced observing a growth cycle. A secondary consideration was what could be discovered in the recorded data about the growth and subsequent heat treatment as the boule cooled. This is usually a more difficult task because a crystal growth process is not a controlled experiment so much as a process that continually sees modification. Using a sensor arrays or a scanning loop has produced a qualitative and quantitative basis for understanding some of the high temperature electrical conductivity mechanisms. The implication of the these measurements of electrical conductivity variations are important in that they reflect the complex defect states that will occur on cooling and heat treatment following crystal growth. In contrast to the complex behavior of the conductivity of these compound semiconductors in the solid and liquid state we have the very well characterized system silicon to compare. Initially the interest on using eddy currents to monitor compound semiconductors came from G. Westphal at the Texas; Instruments Company in 1987 to monitor aspects of growth and compounding of GaAs. This was followed by work on solution growth of HgCdTe with D. Witter. The initial interest in the use of eddy cur-rents for monitoring CdTe crystal growth came from Prof. Wilcox at Clarkson University in the practical interest to determine and control the crystal interface curvature during vertical brigdeman growth. The first actual work was done by one of his former students. G. Neuge-bauer at the II-VI Corporation which was carried on by G. Rosen at Clarkson and R. Shetty at II-VI Corporation and with A. Socha at Johnson-Matthey Electronics. The work on CdTe extends over four years and yielded sufficient data to allow one to evaluate the utility of the information produced as compared to what could be obtained from monitoring an elemental semiconductor such as silicon."

Jan 1, 1997

By Zhang Hanbo, Niu Liping, Zhang Zhiqi, He Jicheng, Dou Zhihe

"Rutile, ilmenite and Al-Ca complex reducer were used to prepare high titanium ferrous alloy by enhanced reduction-SHS method. The effects of the complex reducer compositions and slag types on the enhanced reduction-SHS process were investigated. The high titanium ferrous alloys were characterized by XRD and SEM. The results indicate that the high titanium ferrous alloys consist mainly of TiFe2, AlTi3 and Al2O3. The oxide inclusions exist resulting in directly the high oxygen content and micro-structural defects in the alloys. The titanium and oxygen contents decrease, but the aluminum content in the alloy increases while the mass ratio of calcium in the Al-Ca complex reducers increases. When the mass ratio of Al/Ca in the Al-Ca complex reducer is 6:1, titanium, oxygen and aluminum contents are 63.75%, 3.01% and 10.72% respectively. When the mass ratio of Al/Ca is 5:1 titanium content is 55.00% nearly and aluminum content is higher than 14.00%, but oxygen content is lower than 2.0%.1. IntroductionThe high titanium ferroalloys with 65%~75% titanium have the advantages of low melting point and high titanium content. They are widely used in special steel refining, while they are also a kind of very important quality orientation alloys in the rage of aviation and aerospace. At present, the methods of preparing high titanium ferroalloy include vacuum remelting and thermit reduction. The alloys prepared by the vacuum remelting method have good qualities and low oxygen content, so it is widely used in Russia, Western Europe and other developed countries. In China, there are abundant rutile resources, but waste titanium is lack, therefore, the preparation method is the thermit reduction. But there are many quality defects in the high ferrotitanium alloy, including high oxygen content, unstable quality and so on. In order to improve the qualities of the high titanium ferroalloy, especially to reduce oxygen content, the domestic and overseas have done a lot of further researches. For example, Sichuan E-mei ferroalloy plant and Beijing Nonferrous Metal Research Institute have prepared high titanium ferrous with 73.77% titanium with natural rutile, but the oxygen content is high. Through controlling the quality of raw material, they obtained the better qualities, but the oxygen content is still very high. South Africa Mintek company have prepared high titanium ferrous alloy with low nitrate by plasma heating under the isolation air conditions, but they couldn’t also remove effectively oxygen in the alloy. The oxygen exists in the form of Al2O3 and titanium protoxide. So it can be speculated that except TiO2 not being fully reduced, the no-sufficient alloy-slag separation is the direct reason resulting in high oxygen and poor microstructure. In view of present technical difficulties during preparing high titanium ferroalloy by thermit reduction, this paper proposed a new method of preparing high titanium ferrous with low oxygen by enhanced reduction-SHS with Al-Ca complex reducer. Ca in Al-Ca complex reducer has stronger reductive ability, it can effectively strengthen the reductive degree of TiO2. The slagging agent CaO CaF2 and MgO can effectively reduce the viscosity of Al2O3 slag to improve its liquidities to strengthen alloy-slag separation effects so that to remove inclusions and oxygen. In this paper, effects of slagging agent type on the reduction and the qualities of high-titanium ferroalloy were studied."

Jan 1, 2012

By Lawrence D. May, Harry Mudgett

"In the course of developing a new industrial process, information produced at the Research and Development (R&D) stage is critical to determining the technical and economic feasibility of the project. Understanding the fundamental operating parameters for each unit operation in a flowsheet typically comes from historical knowledge of similar systems or by technical development through a robust research program. This approach holds true for processes incorporating fluidized-bed technology. In this paper, the authors will present a practical approach for performing a research study that will allow a process owner to determine if the concept of using a fluidized-bed system can become a reality. Included are discussions of key steps required at each level of the R&D program, and the critical information required for advancing the project to the next stage.IntroductionThe conduct of a research and development program typically starts with a process owner identifying a new industrial need or modification to an existing operation. The owner can pursue this need through multiple routes, including initial in-house development, coordination through an engineering firm, contacting suppliers of key equipment envisioned for the process, or through direct contact with research and development organizations. Where and when the project is conducted is as variable as the number and types of owners who pursue them. Factors that can influence the decision of where to conduct a research program can include the type of process desired, the scale and scope of the project, the location of the project site relative to the R&D options, the experience, capability, and availability of the potential research sources, and the costs to conduct the program. Often, the owner may choose a combination of the available resources to achieve their objectives. In the end, the owner's choice should be based on a thorough understanding of their goals and objectives for the program, and a good understanding of how to measure success while achieving those objectives. Herein, the authors will describe the methods we have typically used to develop the information an owner needs to make an educated decision for investing in a new or modified process."

Jan 1, 2014

By Zhang Chuanfu, Tan Pengfu

"A thermodynamic model is developed to simulate nickel flash smelting process. In the nickel flash furnace, oxidation of concentrate occurs at one end, and reduction of slag occurs at the other. The model makes use two zones, namely the reaction shaft/settler zone and the appendage zone and accounts for 6 phases (matte, slag, silica, magnetite, Cu-Ni alloy and gaseous phase), 13 elements (Ni, Co, Cu, Fe, S, 0, N, C, H, Si, Al, Mg and Ca) and 33 chemical components in nickel flash smelting system. The compositions of matte, slag and gaseous phases in equilibrium are calculated by using the data of free energies of formation and activity coefficients of components. Two nickel sulfide species are used to allow for the modeling of sulfur-deficient mattes. The model predictions are compared with the known industrail data from Kalgoorlie Nickel Smelter, and excellent agreement is obtained. The model can be a very useful tool for monitoring and optimizing the actual industrial operations of nickel smelting process. The distribution behaviors of Ni, Co, Cu, Fe, S and 0 in the nickel smelting furnace depend on the process parameters such as smelting temperature, volumes of air, the content of the elements~ charge and oil.1. IntroductionThe nickel flash smelting furnace essentially consists of a reaction shaft where nickel sulfide concentrate is partially oxidized with air, a settle zone where matte and slag are allowed to separate, and a slag cleaning end where coke is added to provide for the reduction of the oxidized nickel from slag, and electrodes are used to provide heat.The theoretical model to consider a mass balance for copper flash furnace is developed by S. Goto and R. Shimpo[1][2J. However, this can not be true for nickel flash furnace as a whole since oxidation of concentrate occurs at one end (in the reaction shaft/settler), and reduction of slag occurs at the other (in the appendage). Despite these limitations, an acceptable pseudo-thermodynamic description of the furnace can be achieved using essentially two zones, namely the reaction shaft/settler zone and the appendage zone. Compositions of gas, slag and matte in two zones are calculated."

Jan 1, 1998

By Shoukun Wei, Cong Wang, Lin Cheng, Zhiyu Qiao, Jingkui Liang, Weidong Zhuang

"The subsolidus phase relations in the Sm2O3-CeO2-CuO ternary system sintered at 1000°C in air have been investigated by X-ray powder diffraction. The system can be divided into two ternary phase regions and three binary phase regions. Solid solution Sm2-xCexCuO4-y is the only ternary phase in the system. The maximum solid solubility was confirmed to be x = 0.2. The crystal structure, oxygen content and superconductivity of the solid solution Sm2-xCexCuO4-y have been investigated.I. INTRODUCTIONAfter the first discovery of the superconducting ceramic system La-Ba -Cu-O[l] with Tc = 30 to 40K, other families of cuprate-based ceramics have been synthesized with higher critical temperature. These oxides include the R-Ba-Cu-O (R: rare earth) systems (Tc=90K or so)[2,3], the Pb-Sr-(R,Ca)-Cu-O systems (T c = 50 to 100K), the Bi-Sr-Ca-Cu-O systems (Tc=80 to 105K)[4], the T1-Ba-Ca-Cu-O systems (Tc=85 to 125K)[5], the Hg-Ba-Ca-Cu-O systems (Tc=90 to 150K)[6,7], and some others. The improvement of Tc is very rapid. The measurement of the Hall and Seebeck coefficients shows that they all are p-type superconductors. In 1989, Tokura et al.[8] discovered the superconductors R2_XCexCU04_y(R = Nd, Pr, Sm) with Tc=20 to 24K (onset) and found that the charge carrier is electron in contrast to their hole doped counterparts. This discovery increases the fundamental understanding of the cuprate-based superconductors by comparing their characteristics and mechanisms to those of the p-type superconductors.One of the outstanding features of these n-type superconductors is the difficulty in obtaining samples in good charactors, such as the difficulty in obtaining zero resistivity state in single crystal or bulk samples; the semi-conductivity of bulk samples in ordinary state (opposite to the superconducting state) and a reducing reaction involved before the superconductivity has been found[9]. Therefore, it is necessary to optimize the sample preparation of the n-type superconductors. All the n-type superconductors have been found· considerable solid solubility. The compositional variations play a governing role in the carrier doping of the superconducting phases. Also, it is vital to the ceramic processing of superconductors to identify the compatible phases in the phase diagram. Finally, there is always the possibility of finding additional compounds, both superconducting and non-superconducting, in an unexplored system."

Jan 1, 1996

By J. E. Dutrizac

Fracture-exposed surfaces of sphalerite samples having five different solid solution iron contents ranging from 0.0 wt% to 14.8 wt% Fe were leached for 15 to 120 s at 100°C in 0.3 M Fe(S04)1.5 -0.3 M H2S04 media. The reacted samples were examined using X-ray photoelectron spectroscopy (XPS) which provides chemical state information on the first few nanometers of the solid surface. Surface compositions show that the leaching rate increases with increasing solid solution iron content of the sphalerite. Detailed evaluation of high resolution S2p spectra show that the leaching progresses via the formation of polysulphide species. Disulphide species were not detected in any of the experiments. Examination of the Zn2p and Fe2p spectra indicate little change in the chemical states of these elements over the duration of the experiments. Longer leaching times resulted in the generation of elemental sulphur. The ratios of elemental sulphur to dissolved ferrous ions and zinc suggest that less than 5% of the sulphide is oxidized to sulphate. Morphological studies showed that the elemental sulphur commonly formed at a few isolated sites, such as the grain boundaries. Furthermore, euhedral sulphur crystals were often identified. These observations suggest that at least part of the elemental sulphur forms via dissolved sulphide species which are oxidized in solution by ferric sulphate.

Jan 1, 2003

By Roberto Parra

The classic criteria of the preparation of the charge for the smelting of copper concentrates in a flash furnace considers the mass and energy balance from the chemical and mineralogy composition of the concentrates. The operation parameters fixed with this method don't assure the stability of the operation and the critical problems of the slag quality and dust formation occurs very often. This paper presents the results of a laboratory test that allows the predicition of the behavior of concentrates blends in the view of the minimization of the dust formation and the magnetite control in the slag. The combustion of different copper concentrates and blends were done in a drop tube furnace. The results show that the magnetite and dust formation don't have a linear behavior with the weight proportion of the blend and some optimal blends of 2 or 3 types of concentrates can be identified. From the reasonable hypothesis that the qualitative behavior of blends in the drop tube represents the real behavior in the burner, the preparation of the charge with this approach could help to solve those operational problems.

Jan 1, 2003

By Huimin Lu, Lian Zhou, Qiang Li

"A three-dimensional mathematical model is developed for the regenerative rotary hearth furnace with 40 meters medium diameter. The influence of combustion switchover and outlet pressure on the fluctuation and distribution of temperature and pressure is studied with numerical simulation method. The results showed that the temperature field and flow field is suitable for requirement of industrial production; the fluctuation of the temperature field and pressure is acceptable; the influence of outlet pressure on the furnace pressure is great.IntroduceRotary hearth furnace which is originally utilized as heat treating and reheating industrial furnace, now is also used for carbon based DRl production. With the need of market and the concern of resource recycling and environmental issues, the DRl production from ore or from waste material by rotary hearth furnace attracts more and more attentions from steel industry [1,2].When rotary hearth furnace works, the feed pellets are charged on the hearth and rotate within an annular furnace chamber with the process of reduction. For the sake of rapid reduction, usually the depth of the pellet is one or two layers, accounting for less than 90% of the volume of furnace. As result, the exhaust gases carry away a lot of heat, so that energy utilization efficient is low [3]. Currently, in order to reduce the consumption of energy and improve the production efficiency, many methods have been adopted. The regenerative combustion technology is one of the most promising."

Jan 1, 2013

By J. S. Becker

Technology developed and first implemented in the United Kingdom enables very low grade aluminum scraps containing oils, organics, plastics and ferrous metals to be directly charged, without pretreatment, into a unique melting furnace. The system has been in full scale production for over three years. The oxy-fuel-based furnace design incorporates internal afterburning in the furnace's hot zone, producing excellent thermal efficiency and very low emissions. The furnace is inherently low in NOx. This paper will provide both theoretical background and extensive operating results for this new melting concept. Applications describing both purpose built new furnaces and retrofits of existing reverberatory furnaces will be presented. Extensive operating emissions data will be presented.

Jan 1, 1996

By R. Padilla

The reaction of chalcopyrite with gaseous sulfur has been investigated in the range 350-450 °C in order to transform this mineral into a more acid soluble copper sulfide and insoluble iron sulfide. The results of thermodynamic analysis of this system as well as the X-ray diffraction analysis of the reaction products showed that in the temperature range 350 400°C the sulfidation reaction proceeded without formation of intermediate copper-iron sulfides according to: The effects of temperature and time on the conversion of chalcopyrite were studied. Conversion of chalcopyrite reached about 80% very rapidly with increase in temperature up to about 400°C. The recovery of copper from the sulfidized samples was determined by leaching in oxygenated 1.2M H2S04, 2M NaCI solution. Copper recoveries over 90 % were obtained from samples sulfidized for 30 min at temperatures lower than 400°C.

Jan 1, 2001

By W. L. Dalmijn

The processing of scrap and scrap cars starts with size reduction by a hammermill, or shredder. After the liberation the magnetic fraction is removed. The remaining non¬magnetic fraction mixed with other materials is screened and each fraction is processed separately. The increased use of plastic has a negative effect on the recovery of metals and waste production. At Huron Valley, Belleville Michigen, USA, the non-ferrous fraction from 5 million obsolete cars per year, containing 200,000 tons of non-ferrous metal, is processed. Aluminium Is recovered with a heavy medium separation process and concentrated with eddy current separators. The remaining heavy non-ferrous fraction is concentrated by a new combination of eddy current separation and image processing. After this separation process the zinc fraction is melted and refined and the copper, brass, stainless steel and other high-quality concentrates are sold to the secondary industries. The recycling of car scrap has become an important source of metals and materials for the secondary. materials processing industry.

Jan 1, 1995

By Garrett May

We present a periodic technique for measuring the thermal conductivity of thin, disk-shaped samples. In samples of this type, temperature measurements must be made across the sample faces and are therefore subject to large error due to the interface resistance between the temperature sensor and the sample. The technique uses measurements of the amplitude and phase of the periodic temperature across both a reference sample and the unknown material at several different frequencies. Modeling of the heat flow in the sample allows the simultaneous determination of the thermal parameters of the sample as well as the interface resistance. The technique is demonstrated on nanocomposite samples less than 1.0 mm thick.

Jan 1, 2008

By M. Oliazadeh

Spodumene [LiAl(Si2O6)] is the most common and desirable economic lithium-bearing mineral due to its high lithium content. In Canada, there are several spodumene deposits at the development stage that have the potential to help narrow the forecast lithium supply gap stemming from the widespread acceptance and increasing use of electric vehicles. Spodumene processing can be conducted using Dense Media Separation (DMS), flotation or combination of both. If spodumene liberation is sufficient at coarse particle sizes, DMS can be used for primary lithium concentrate production and silicate gangue minerals rejection. If liberation is not sufficient, flotation is then the main processing route for spodumene concentration. Even in cases where DMS is a viable beneficiation option, flotation may still be required to process the DMS middlings and/or the undersize fraction which is outside the particle size range for DMS. Considering flotation as a technique for spodumene beneficiation, there are several alternatives including the use of mechanical flotation cells, column flotation cells, coarse particle flotation cells, and/or Staged Flotation Reactors (SFR), either alone or in combination. Ore sorting can be incorporated at the start of the spodumene flowsheet to remove gangue minerals, particularly amphibole and pyroxene in the early stages. The main objective of flowsheet development for hard rock lithium deposits is to evaluate the ability of these options to produce a spodumene concentrate with a concentrate grade above 6% Li2O, lithium recovery of above 80%, and with the minimum operating and capital cost. This paper aims to describe the various processing options available for the beneficiation of spodumene from hard rock deposits and compare the associated operating and capital costs for each.