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By M. J. Richards, A. Szirmae, G. R. Speich

The formation of austenite from ferrite, ferrite plus retastable carbide, spheroidite, and pearlite has been studied in a series of irons, Fe-C alloys, and plain-carbon steels using fast heating techniques. In the absence of carbide, austenite nucleates at ferrite/ferrite grain boundaries; nucleation is followed by the rapid growth characteristic of a massive transfornation. The trarnsformation occurs at 950°C at heating rates of 106º C per sec and cannot be suppressed. Metastable carbide dissolves before austenite forms and does not influence the transformation kinetics. For spheroidite structures, austenite nucleates preferentially at the jinction between carbides and ferrite grain boundaries. Growth from these centers proceeds until the carbide is completely enveloped; subsequent growth occurs by carbon diffusion through the austenite envelope. For pearlite structures, austenite nucleates preferentially at pearlite colony intersections. Carbide la)?zellae dissolve at the advancing austenite interface but complete solution of carbide does not occur; the residtial carbide is eventually dissolvled or spheroid-ized depending on the carbon cuntent. The magnitude and temperature dependence of the austenite growth rate into Fe-C pearlite when incomplete carbide dissolution is assumed are satisfactorily explained by an approximate colume diffusion model. The impurities present in plain-carbon steel reduce the growth rate of austenite in comparison to that jound in an Fe-C alloy. The formation of austenite has been studied in much less detail than the decomposition of austenite. This is primarily a result of the importance of harden-ability in determining the mechanical properties of steel. Recently, more interest in the kinetics of austenite formation has resulted from the discovery by Grange1 that rapid heating techniques strengthen steel by refining the austenite grain size. Although the strengthening effect is not large, it is accompanied by no loss in ductility. In addition, interest continues in rapid heat treatment of low-carbon steel sheet for tin plate applications.2,3 Among the few systematic studies of austenite formation are the early work of Roberts and Mehl4 on formation of austenite from pearlite and recent work of Molinder5 and of Judd and paxton6 on formation of austenite from spheroidite. Also, Boedtker and Duwez7 and Haworth and paar8 have recently studied the formation of austenite from ferrite in relatively pure iron, Kidin et al.9,10 have studied the formation of austenite in 8 pct Cr steels, and Paxton has recently discussed various aspects of austenite formation in steels." The present work was undertaken to determine the kinetics of austenite formation for a variety of starting structures including ferrite, ferrite plus metastable carbide, ferrite plus spheroidal cementite, and ferrite plus pearlitic cementite. Emphasis was placed on determining the active sites for austenite nucleation, determining the temperature and time range of austenite formation, and in the case of pearlite a careful study of the growth rate of austenite was made in the absence and presence of impurities. By using a variety of heating techniques including laser-pulse heating, it has been possible to study austenite formation in an isothermal fashion over a wide range of temperatures. EXPERIMENTAL PROCEDURE The alloys studied in the present work are a zone-refined iron with 4 pprn C, an Fe-C alloy with 130 pprn C, 2 Fe-C alloys with 0.77 and 0.96 wt pct C, and a plain carbon steel with 0.96 wt pct C. The zone-refined iron and Fe-C alloys contained 60 pprn and 200 pprn total substitutional impurities, respectively. The plain carbon steel contained 2400 pprn Si, 2000 pprn Mn, and 900 pprn Cr. Various heat treatments were given to these alloys to produce different starting structures of equiaxed ferrite, ferrite plus metastable carbide, fine pearlite, and spheroidite. These heat treatments are given in Table I. A wide range of heating rates were employed in this work because many of the reactions occur so quickly at temperatures in the austenite range that they are completed during the initial heating cycle unless very fast heating rates are used. Essentially the same heating techniques employed by Speich et a1.12 and Speich and Fisher13 were used in this work. For time intervals of 2 sec to 20 hr, simple hand immersion of 0.010-in. thick specimens in a Pb-Bi bath was employed. These specimens were quenched in a 10 pct NaC1, 2 pct NaOH aqueous bath. For time intervals of 100 m-sec to 2 sec, an automatic dunking and quenching device was employed with 0.002-in. thick specimens. Again, liquid Pb-Bi baths were used for a heating medium but now helium gas quenching was employed. For time intervals of 2 to 100 m-sec a laser heating device was employed with 0.002-in. thick specimens; a helium plus fine water-droplet spray was now used for quenching. Additional information on heating times shorter than 2 m-sec was obtained by study of the zones around the centrally heated laser spot. Here diffusion of heat from the centrally heated zone raises the temperature of the specimen locally to all temperatures between ambient and the peak temperature, but for times of the order of microseconds. All the heat-treated specimens were examined by

Jan 1, 1970

Geologists in some underground gold mines collect grab samples from broken ore piles or trucks as a method of grade control. It is often known as muck sampling. Generally, the goal of grab sampling is to try and reconcile the mined grade at the ore source to the predicted grade and/or predict the mill feed grade. The mass of the sample collected is limited by health and safety issues, as well as by the capacity of the laboratory to process the samples within a given time frame. In general terms, grab sampling is known to be problematic because samplers tend to oversample the fines, and/or pick out high-grade fragments; surface sampling of piles does not test material within the pile; muck piles in development drives/faces are likely to be zoned due to the blasting sequence; high or low-grade material may preferentially segregate in the pile during mucking; the five per cent mass reject size of the material in muck piles is very large from underground blasting; some correlation usually exists whereby the larger fragments are enriched or depleted in the critical component of value; and the average error made in estimating the true stockpile grade is likely to be high. The method is prone to chronic fundamental sampling, grouping and segregation, delimitation, and extraction errors. Substantial warnings must be given about the use of grab sampling for grade control in gold mines. The method may appear to work sometimes, which can be attributed to a fine gold particle sizing and more disseminated distribution. As with all sampling methods, its appropriateness must be determined by ore characterization and heterogeneity testing to ensure the method suits the ore type.

Jan 1, 2010

By W. C. Phalen

SALT-MAKING PROCESSES THE production of salt in the United States divides itself at the outset into two distinct classes: (1) The mining of rock salt and its purification and separation into marketable sizes, and (2) the production of salt by evaporation from brines, bitterns, and other solutions. The processes employed at the present time in the manufacture of salt by evaporation may be outlined as follows: 1. Solar evaporation. 2. Direct-heat evaporation (a) in open kettles; (b) in open pans. 3. Steam evaporation, (a) in jacketed kettles, (b) in grainers. 4. Vacuum-pan evaporation. In this paper only the solar-evaporation processes practised in different parts of the United States will be described. SOLAR EVAPORATION Localities In the Eastern States the solar-evaporation process is not generally employed for climatic reasons. In the Western States, particularly in California and Utah, the great bulk of the salt produced originates in the solar-evaporation process. Of the Eastern States producing salt, this process, so far as the writer is aware, is employed in New York State only.

Jan 9, 1914

By John W. Finch

The Secretary of the Interior acting through the Bureau of Mines and the Geological Survey is authorized by the Strategic Materials (Public No. 117 - 76th Cong., Chapter 190 1st Sess.) to make investigation concerning essential minerals of which the quantities or grades obtainable from known domestic sources are inadequate. The Bureau of Mines, in carrying out its part of this program, may investigate deposits of such minerals in whatever manner may be necessary, in order to determine (1) the extent and quality of the are, (2) the most suitable method of mining and beneficiating it, and (3) the cost at which it may be produced. The essential objective in doing these things is to determine where and how supplies of minerals and metals of which domestic production is usually inadequate might be obtained in a national emergency, even though at higher cost than usual.

Jan 1, 1939

By Vahid Faghihi

SatraPM is a web-based software package, aiming to help project managers to easily handle their construction projects via internet. This software is capable of handling all projects of an organization, in which all projects can be defined in EPS the same as users in OBS. A 3D accessing module links EPS, OBS and inherent functions in order to provide a secure environment for the data to be processed throughout the system. This paper intends to take a deeper look at capabilities of SatraPM in helping project managers to keep track of and control their construction projects as well as its potential future features.

Aug 1, 2013

By Mariane Costalonga de Aguiar, Carlos Mauricio Fontes Vieira, Sergio Neves Monteiro

"This work evaluates the effect of incorporation of an ornamental rock waste into an industrial clayey body used for roofing tiles fabrication. Formulations with 0, 10, 20 and 30 wt.% of waste were prepared by replacing the sand in the industrial clayey body. The plasticity of the formulations was determined by the Atterberg limits. Specimens were fabricated by 18 MPa press-molding and then fired from 850, 950 and 1050°C. The specimens were tested to determine the water absorption, linear shrinkage and three points bending flexural strength. The results indicated that the waste improves the extrusion performance of the clayey body by decreasing its plasticity. The use of the waste was beneficial to the water absorption and mechanical strength of the fired clayey ceramic at 1050°C.IntroductionOrnamental rock is a natural resource available in the municipal area of Santo Antonio de Padua and located 150 km from the city of Campos dos Goytacazes, northe of state of Rio de Janeiro, Brazil. Intense industrial activity related to ornamental stones, especially gneisses, is traditionally occurring in the region. After mining, the flagstone is submitted to sawing to obtain blocks and then, after a manual operation, the final products are small flagstones [1,2]. During the sawing operation, a sludge composed of water and fine particles of rock is generated. A monthly production of 1000 tons of ornamental rock waste is estimated to be produced at Santo Antonio de Padua. The final disposal of this waste has brought serious environmental problems. Since most industries do not have an adequate sludge treatment, the waste is contaminating the soil and underground waters as well as obstructing rivers and lakes.Ceramic bodies industrially fabricated in the municipal area of Campos dos Goytacazes, 280 km from the city of Rio de Janeiro, are still empirically elaborated using a mixture of local clays. These clays are predominantly kaolinitic mineral, associated with high plasticity. Due to the excessive plasticity of the ceramic bodies, it is common to have dimensional defects in the final products after the drying and firing processes. Moreover, the kaolinitic structure and the presence of aluminum hydroxide confer a refractory behavior to the local clays. This impairs sintering during the firing operation. In the case of clay ceramics for civil construction, this results in greater porosity associated with elevated values of water absorption [3,4]. To avoid this problem, it is necessary to reformulate the ceramic body composition. The addition of both non-plastic materials to reduce plasticity and fluxes to condition the refractoriness is a possible alternative."

Jan 1, 2011

By H. R. McCabe

"The study of a detailed series of structure and isopach maps of the Palaeozoic strata of southwestern Manitoba indicates that the principal Palaeozoic tectonic elements -the Williston Basin and Elk Point Basin -have been modified to a considerable extent by major tectonic features of the Precambrian basement. The principal basement feature is the break between the Churchill and Superior provinces, which coincides roughly with the Manitoba-Saskatchewan border. East-west-trending orogenic belts within the Superior crustal block may also be reflected to some extent in later Palaeozoic movements. In addition, the Superior crustal block, as a whole, appears to have had a slightly different response to the tectonic forces, giving rise to both basin subsidence and basin uplift. During periods of deposition, especially during Ordovician time, the Manitoba portion of the basin appears to have undergone a relatively higher rate of subsidence, whereas during periods of erosion relatively greater amounts of uplift and truncation have occurred. As a result, the depositional and erosional patterns for most of the Palaeozoic formations in southwestern Manitoba are somewhat anomalous relative to the regional basin framework.Some prominent Palaeozoic structures probably are the result of salt solution and differential compaction caused directly or indirectly by relatively minor tectonic movements related to Precambrian basement features. In particular, the prominent hinge line at the edge of the Devonian Prairie Evaporite salt basin may be due, in large part, to salt solution. Numerous other small structural lows, structural highs and isopach thicks, probably resulting from salt solution, occur along the salt edge and have been important in modifying and controlling Mississippian oil accumulation in the Daly-Virden producing area."

Jan 1, 1967

By L. Adler

A fairly complex analysis is required to select, or evaluate a piece of excavating and bulk handling equipment and obtain its performance. At present there is little agreement as to what specific points should be considered, and even less on what procedure to follow. This paper provides both of these in a consistent and direct form. The analysis applies to all types and sizes of equipment from the bulldozer and the continuous miner, to the B.W.E. The importance of the equipment characteristics, job activities, and work conditions are stressed and separate analytical stems are established in a flow chart for these. They are combined using suitability tests in the following steps: 1) problem statement, 2) natural conditions, 3) suitability guidelines, 4) appropriate equipment types, 5) operational activities, 6) encumbered space, 7) geometric design, 8) equipment sizing, 9) failure and limits, 10) performance and consumption, 11) public policy checks, and 12) costs and profitability. Public policy and economics while considered throughout receive emphasis towards the end. The procedure is iterative, containing distinct feedback loops. Specifying the steps and sequence provides a necessary structure which has long been overdue.

Jan 1, 1983

By Karla Carolina Alves da Silvar

As ligas com memória de forma (LMFs) destacam-se por apresentar propriedades especiais, possibilitando seu emprego em diversas aplicações tecnológicas. Esses materiais podem ser integrados a uma matriz polimérica, agindo como um reforço, constituindo uma nova classe de matérias, chamada de Compósitos Inteligentes, que têm despertado interesse por sua versatilidade na criação de atuadores e/ou sensores. Nesse contexto, fios de nitinol, foram tratados termicamente para obter temperaturas de transformação próximas a ambiente. Em seguida, amostras desse material foram submetidas a calorimetria diferencial de varredura para verificação das temperaturas de transformação. Posteriormente, os fios tratados receberam um treinamento termomecânico para obtenção do efeito memória de forma reversível e assim executar o movimento similar a abertura e ao fechamento de uma garra, pretendido para o atuador a ser desenvolvido. Após essa etapa, os fios já treinados foram incorporados a matriz constituída por silicone e resina epóxi, dando origem a um compósito que ao ser ativado por uma corrente elétrica, reproduz o movimento do treinamento termomecânico dado aos fios. Esta pesquisa tem por finalidade, desenvolver um atuador constituído por um compósito inteligente, analisando características como: transformação martensítica e flexibilidade.

Aug 8, 2018

By J. R. Iwinski

Escanaba, Michigan, is located on the South¬ern shore of the Upper Peninsula on a sheltered area of Lake Michigan called Little Bay de Noquet. The Chicago and North Western Transportation Company has operated a rail-to-ship ore transfer facility at this location for well over 100-years. It is the only terminal of its type on Take Michigan and thus can offer a longer navigation season to lower lake markets than other upper lake ports. It all started in 1864 when the Peninsula Railroad of Michigan, now a part of the C&NW, completed a 100 km rail line from Little Bay de Noquet to the Jackson Mines at Negnauee, Michigan. During that first year of operation approximately 31 000t of ore were loaded onto ships at Escanaba from what was then called the Merchants Dock. By 1871 demand had already exceeded capacity and it was necessary to build a larger dock, which in turn was replaced with a still larger pocket dock in 1903. There are no plans or records available to indicate how the ore was handled from rail to ship prior to the construction of the pocket dock.

Jan 1, 1981

By F. Dai

Due to difficulties associated with gripping in direct tension, indirect methods are commonly used to measure rock tensile strength. In this work, we adopt an innovative indirect tensile test method: Semi-Circular Bend (SCB) to measure the tensile/flexural strength of Laurentian granite (LG). The static tests are carried out with a servo-controlled material testing machine and the dynamic tests are conduced with a Split Hopkinson Pressure Bar (SHPB) system. Pulse shaping technique is adopted to achieve dynamic force equilibrium in SHPB to facilitate data regression. Finite element method is used to relate the failure load to the tensile strength. Strong rate dependence of the tensile strength is observed. The flexural strength is higher than the tensile strength measured using Brazilian Disc (BD). This difference is rationalized using the non-local theory. To further validate the method, a coupled Finite element/Discrete element method (Fem/Dem) in conjunction with the smeared crack model is utilized to simulate the fracture process during dynamic SCB tests. The resulting fracture patterns are qualitatively consistent with those from recovered samples. Both the experimental and numerical methods have validated the results and this new method is readily to be used for other rocks and other brittle materials.

May 1, 2009

By Anderson, Burton E.

FOR several centuries diamond mining has been an adventurous, profitable and enticing industry in Brazil. Some of the world's most valuable diamonds have been found in this country. Two of the most famous stones are the "Estrella do Sul" (Southern Star), weighing 2541/ karats, and the "Branganca," weighing 1680 karats in the rough and 367 karats cut. For a great number of years the stones extracted and sold were mostly the white diamonds used for jewelry. Within the last thirty years black diamonds have been developed as an abrasive cutting material and in these black diamonds the State of Bahia, Brazil, has a monopoly of the world supply. Carbons, as they are commonly called, are being used for core-drilling, polishing, cutting, wire-drawing, and vari-ous other applications in which such a hard substance is required. Bernard Bandler & Sons, of New York City, have selected, graded and delivered these carbons to the United States markets.

Jan 1, 1932

By R. Kuhns

The western coast of South Africa hosts a significant diamond resource within gravels associated with paleo-shorelines, channels and transgressive lag deposits. Diamonds were transported from the Kaapvaal Craton to the coast largely during the late Cretaceous via the paleo-Orange river systems. On shore and near shore environments are underlain by Proterozoic metamorphic and granitic rocks which provide gully and pot hole-type traps associated with paleo-channels, basins, bays and beaches. Inner and mid-shelf environments are covered by diamondiferous, poorly lithified upper Cretaceous and Tertiary sediments. The upper Cretaceous gravels were reworked along the sediment-starved coast during much of the Tertiary. Reworking was mainly achieved during marine flooding events which produced lag gravels along the paleo-shorelines. This process reworked the diamonds from low-grade Cretaceous gravels and concentrated them in higher-grade Tertiary gravels.

Jan 1, 1995

By R. P. Vinson

The Bureau of Mines evaluated two real-time light-scattering dust monitors by measuring their response to Pittsburgh Seam coal dust and Arizona road dust (ARD). Both monitors, the model PDS-l, a personal dust sensor, and the model PCD-l, a digital dust indicator, are made in Japan by Sibata Scientific Ltd. Tests were conducted inside a laboratory aerosol chamber designed to maintain a uniform spatial distribution of the test dust. PDS-l and PCD-l measurements of concentrations for each test dust were averaged over 4-h test periods and compared with simultaneous gravimetric measurements. Both dust monitors responded linearly with mass concentration with both coal dust and ARD. However, the linear response of the PDS-l differed from that of the PCD-l for both dusts.

Jan 1, 1987

By Jacques Nantel

"The molybdenite property of Brynnor Mines Limited, Boss Mountain Division (wholly-owned subsidiary of Noranda Mines Limited), is situated approximately 360 miles northeast of Vancouver on the east slope of Takom-kane mountain in British Columbia's Cariboo District. Orebodies at the deposit fall into two categories; quartz breccia, and veins and stringers. The development of the breccia ore zone was started in June, 1964. The bulk of the ore is being mined from the stringer ore zone. The ore-body has been divided into 100-foot stopes and pillars. A sub-level blasthole method is used and the broken ore is handled in drawpoints and scram drifts. The development, drilling, blasting and handling of the ore are reviewed. The future pillar recovery operation is also analysed. The paper is also concerned with a scheduled shaft sinking program."

Jan 1, 1970

By Ana Clara Petrucelli

O estudo do sopro de oxigênio no EOF é muito complexo e envolve diferentes fenômenos, incluindo o desenvolvimento do jato supersônico, a interação do jato com o ambiente ao seu redor e o banho metálico, onde ocorrem importantes reações. No presente trabalho, diferentes alternativas de desenho de lança e bicos e arranjos desses no interior do EOF são desenvolvidos a interação do jato supersônico com o ambiente do banho metálico foi caracterizada. Para o EOF, o objetivo foi determinar a melhor combinação de variação de injetores e vazões para alcançar o menor tempo de mistura, estabelecendo um novo padrão operacional. Os injetores tiveram pouca relevância no tempo de mistura. Ventaneiras e lanças supersônicas apresentaram os menores tempos de mistura. A lanças supersônicas tem influência nos mecanismos de movimento do banho e projeção de material líquido no EOF, enquanto as ventaneiras afetam o movimento do banho.

Jul 29, 2018

By Alberto Eloy Anduze Nogueira

O lixo orgânico doméstico gera um problema de eliminação crescente, exigindo sistemas de processamento dispendiosos. É necessário encontrar novas aplicações para estes resíduos; uma poderia ser como matéria prima metalúrgica. Neste trabalho é estudado o desenvolvimento de pelotas auto-redutoras usando a pirólise de resíduos orgânicos, onde é gerado carbono e voláteis condensáveis e não condensáveis. O alcatrão resultante foi misturado com minério de ferro, pó de carvão e fluxante (CaO), para produzir as pelotas. O carvão fluidizado cria uma forte aderência dos elementos, mostrando uma boa viabilidade do presente processo.

Aug 16, 2017

By V. K. Gupta

"Effect of mill speed on grinding kinetics has been investigated with a view to using mill speed as a manipulated variable for control and optimization of the grinding circuit performance under variable ore hardness conditions. Dry and wet batch grinding tests were carried out for quartz, limestone and cement clinker in a 29 cm x 18 cm laboratory ball mill. Mill speed values selected were 55 and 70% critical. In the case of dry grinding operation, with an exception of quartz, for all materials studied the effect of mill speed on grinding rate was found to be insignificant for sizes finer than about 35 mesh. In the case of wet operation, grinding rates were found to be approximately proportional to the mill speed. The implications of these results are discussed.INTRODUCTIONIt is well known that mill speed has a considerable effect on the grinding rate of the ore particles l-3 For particles of a given size there is an optimum speed at which mill grinding efficiency is maximum (i.e. specific energy consumption is minimum) 3•4. Mill speed can, therefore, be effectively used as a manipulated variable to deal with the disturbances arising from changes in the size and hardness (grinding rate) of the ore being fed to the grinding circuit. Though, it has not been the case so far, with recent developments of ring motors2 and frequency inverters5 a continuous variation of mill speed has now become feasible, and it is expected that mill speed control will soon be a regular feature of plant operation2,6."

Jan 1, 1985

Fine Gravity Separation in the Reflux Classifier, Exploiting a High Shear Rate, Laminar Flow Mechanism The Reflux Classifier is used in the gravity separation of particles over a broad range of particle sizes. The device consists of a fluidised bed zone, with a system of parallel inclined channels above. The inclined channels provide a significant hydraulic advantage over conventional fluidised beds via the so-called Boycott Effect (Boycott, 1920). This paper describes a new advance in fine gravity separation based on the high shear rate and laminar flow profile that arises when closely spaced inclined channels are deployed. As reported recently (Galvin et al, 2009a), a powerful density based separation mechanism develops from this arrangement, suppressing the effects of particle size. In this paper we focus on two areas, firstly the application of the separator in the laboratory for batch fractionation of particles of varying size and density to determine the grade recovery curve and hence the liberation, and secondly the step change in separation performance achieved on a continuous steady state basis when closely spaced inclined channels are used. The variation in the separation density with particle size decreases significantly, and the Ecarte Probable Error (Ep) remains at low levels over a broad size range.

Sep 13, 2010

By Jingwei Lou, Bing Li, Suzhen Li, Miao Shen, Jianguo Yu

"As a main impurity in primary lithium metal, magnesium is difficult to remove because of the very close relative volatility of the two metals. Electrochemical refining provides a possibility to completely remove Mg in the LiCl-KCl melt prior to Li reduction. MgCl2 reduction processes in LiCl-KCl- MgCl2 melt were investigated by cyclic voltammetry (CV), square wave voltammetry (SWV), chronoamperometry and chronopotentiometry. Then potentiostatic electrolysis was carried out and Mg (II) ion was reduced onto a liquid lead cathode from the LiCl-KCl-MgCl2 melt at the Mg deposition potential. The results show that Mg ( II ) is reduced in one step with two-electron transfer. The reduction potential of Mg ( II ) was well defined. The reduction of Mg( II) results in Li ( I ) underpotential deposition at 0.2V more negative potential than that of Mg( II) reduction. Therefore, in order to prevent Li ( I ) from codeposition with Mg, accurately controlling Mg ( II) reduction potential during the potentiostatic electrolysis was necessary. Ninety three to 99 % removal rate of MgCl2 was achieved after 8-12 h electrolysis when liquid lead was used as cathode.IntroductionMetallic Li has been widely used in batteries, light weight alloys and in fusion reactors because of its excellent properties. Currently, the only way in industry to produce metallic Li is by electrowinning from molten LiCl-KCl at about 450 °C [l-5]. LiCl-KCl is the only electrolyte used, because they presents a lower eutectic temperature and KCl shows a slightly higher theoretical decomposition voltage than LiCl, as shown in Table l .The produced metallic Li generally contains 1-2 wt% impurities including Na, K, Al, Ca, Mg, Si, etc. [6l, which are derived from the corresponding metal chloride compounds or metal oxide compounds existing in the LiCl and/or KCl raw materials. These impurities have to be removed by subsequent vacuum distillation at high temperatures to meet the requirements for metal Li purity in the final products. Separation of Mg from Li by vacuum distillation is difficult because their relative volatilities are very close, as shown in Table 2."

Jan 1, 2011