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By David E. Nicholas, Steven R. Dismuke, Paul F. Cicchini

The Buick mine, located 195 kilometers (120 miles) southwest of St. Louis in the Viburnum Trend, is owned and operated by Homestake Mining Company. The mine produces lead and zinc ore from a room and pillar mining method at a depth of approximately 335 m (1 100 ft). The Buick orebody typically averages 60 to 120 m (200 to 400 ft) in width with ore thicknesses ranging from 2.4 to 36.6 m (8 to 120 ft). The mine is divided in two; the halves are referred to as the North mine and South mine orebodies. The North mine orebody contains the higher grade ore; however, the developed reserves for the South mine orebody comprise about 60 percent of the total developed reserves for the Buick property. Existing pillars represent one-third of the total developed reserves.

Jan 1, 1986

By Kilmar Mine

The Kilmar dolomitic magnesite deposit~ in sourhwesr Quebec lie in Grenville Province sedimentary rocks that strike north and dip steeply west. The sediments comprise quartzitic, carbonate and argillaceous members. The middle or carbonate member hosts the magnesite and, like the two other members, has been intensely mewmorphosed. Magnesite occurs as lenticular shaped zones of altered limestone and is mixed with 5 to 30% dolomite crystals. Diopside, serpentine and mica are common accessory minerals. Magnesite appears to have formed from merasomarism of all or part of the carbonate member due to intrusion of hot magnesia-rich solutions. Magnesite is mined from a 490 m vertical shaf1 and is milled and burned into clinkers, which then are shipped 10 pyroprocessing industries around the world.

Jan 1, 1984

By Nóra Schreithofer, Zoltán Jávor, Kari Heiskanen

"One of the challenges the mineral processing industry is facing is caused by the fact that water resources in mining areas are becoming very limited and the cost of water is increasing. The water sources in arid regions often have high salt content. Environmental regulations are forcing plant operations towards completely closing the water cycles within plants. This means that impurities (salts, reagents, ions dissolved from minerals, etc.) accumulate within the circuit that will affect the flotation performance. Water purification can significantly increase the operating costs therefore it should be carefully considered weather the impurities need to be completely removed or is there a tolerable level of impurities that can still be left in the process water without significant deterioration of the flotation performance? Several additional questions arise: what are the tools that help identify what is a tolerable level of impurities? How do the different impurities interact and what is their effect on the process? The effect of frothers on the dynamic properties of air/liquid interface in different size-scales has been extensively studied by the authors in the past. Based on these studies a frother characterization framework was developed that systematically examines the dynamic surface properties of the air/liquid interface in relation to the bubble size. This work can be considered as tool that could be used for the above mentioned purpose. The present study investigates weather the same frother characterization framework can be applied for systems where both frother and different types of salts are present. Nasfroth 240 was used as a frother, in combination with structure-breaker KCl or structure-maker NaCl and CaCl2. Bubble size measurements in laboratory scale mechanical flotation cell and laboratory flotation column and dynamic surface property measurements (dynamic surface tension and dilatational elasticity) were performed. The results highlighted the addition of salt to the frother solutions significantly decrease the bubble size and increase the froth high. The coalescence behavior of bubbles showed correlation between the D32 and ionic strength of salts. The results highlighted that the studied structure maker and structure breaker salts effect the dynamic surface properties in different way."

Jan 1, 2014

By A. C. Halferdahl

DURING a study of reactions involving iron sulfides, it became desirable to know approxi-mately the heat of decomposition of pyrite. The values given for the heats of formation of pyrite and ferrous sulfide are 35,500 calories and 23,070 calories respectively. For the reaction 2FeS2= 2FeS+S:, the heat effect would be-24,860 calories. But pyrite gives sulfur and pyrrhotite upon heating and the latter is a solid solution of sulfur in ferrous sulfide. The only meas-urements of this decomposition are those of Allen and Lombard1 of the Geophysical Laboratory who have measured dissociation pressures of both covellite and pyrite and have carefully reviewed the literature. They give a table of values for covellite as determined by Preuner and Brockmoller2 and by Wasjuchnowa3 and compare these values with their own measurements. The conclusion is that the measurements of Preuner and Brockmoller are seriously in error, while Was-juchnowa's values fit in well with those of Allen and Lombard. Wasjuchnowa's measurements were made by a dynamic method, while Allen and Lombard em-plowed a static method on both covellite and pyrite. Tables I and II reproduce the measurements of Wasjuchnowa and of Lombard and Allen on covellite and pyrite.

Jan 11, 1927

By R. J. Schaefer, M. E. Glicksman

Direct, in situ observation of metallic alloys during solidification reveals that in some systems crystal multiplication occurs by means of a dendrite remelt-ing process, without the necessity of independent nu-cleation events. The solidification is observed on optically clean surfaces of supercooled molten alloys. In one system (Sn-3 wt pct Bi) , a fine-grained equi-axed structure is produced by the complete disintegration, via remelting, of transient initial dendrites. In contrast, several other metallic systems show little or no evidence of remelting activity. The behavior of these metallic systems is consistent with that expected on the basis of published observations of dendrite remelting in transparent organic alloy systems. It is concluded that dendrite remelting is an important crystal multiplication process in some metallic alloys, but is velatively unimportant in some other alloys. The detachment of dendrite branches from the primary stem by a remelting process has been observed by Jackson, Hunt, Uhlmann, and seward1 during the solidification of some transparent organic alloy systems. The branches released by this remelting process can drift free of the primary stem and serve as seeds for the formation of numerous independent crystals. This proliferation of new crystals does not require repeated independent nucleation events, but only modification of the initial solidification structure. The mechanism of dendrite remelting, as described by Jackson et a1.1 and by Tiller and O''Hara,2 is dependent on the transport of both heat and solute and is, therefore, expected to operate only in alloys, and not in pure substances. It was found in the transparent organic alloy systems that remelting occurred primarily in the constricted regions near the base of dendrite branches, where the branches had grown through the solute-rich liquid layer surrounding the primary dendrite stem. It was suggested that impure solid had formed in these constricted regions at a relatively low temperature and had later become unstable as further solidification of purer material raised the temperature. Jackson et al. proposed that the equiaxed zone of metal alloy castings originates from a similar remelting process, and they demonstrated the operation of this mechanism in "ingots" poured from saturated salt solutions. Although these substances were especially selected to show solidification behavior similar to that of metals,3 the remelting mechanism has, until now, been subject to the objection that its operation has not been directly observed in a metallic system. Considering the fact that thermal properties such as diffusivity may differ by as much as two or three orders of magnitude between metals and organic compounds, this objection was considered to be possibly serious. A method has now been developed by which it is possible to make direct optical observations of metals during solidification. This method has revealed transient solidification processes which would not be detected by metallographic examination of totally solidified specimens. In particular, a grain-refinement process in a metallic alloy has been observed to be a direct consequence of the total disintegration of an initial dendritic structure. The influence of an initial, transient solidification structure on the final solidification structure is demonstrated here for the first time in a metallic system. I) EXPERIMENTAL The technique of using a transparent flux to maintain an optically clean metal surface during solidification has been described by us elsewhere.* The

Jan 1, 1968

The fire started in the development section from methane released into the mine through a roof-bolt hole. The date was 8 May 1998. The flames spread quickly as the coal was ignited. After eight hours the Safety Department decided to seal the vertical ventilation shafts and the slopes. The quality of coal in the Esmeralda Mine is very high quality, and Minerales Monclova (MIMOSA) decided to recover the facilities, however, the Esmeralda Mine coals have a very high gas content of 12 m3/t. Immediately after the mine was sealed, MIMOSA staff implemented a plan to monitor the gas levels underground and contacted specialists for assistance in bringing the mine back on-line. During the next 2.5 months, MIMOSA staff and the specialists observed and analysed the gas behaviour supported by a chromatograph. With the results of the observations and analyses, MIMOSA in consultation with the specialists developed a recovery plan based on flooding the area in which fire might have propagated and in which rekindling was highly probable. Those results were analysed by the command centre (Mexican engineers responsible for mine recovery). At the same time MIMOSA trained rescue teams which included miners who had no previous experience in mine recovery operations. By 20 August 1998, the mine command centre had re-opened the slopes seal. Using a æStep-by-StepÆ system, the rescue team began the recovery process by employing cross-cuts and using an auxiliary fan to establish the ventilation circuit. The MIMOSA team advanced into the mine as far as allowed by the water level and was able to recover the main fan. The official mine recovery date was 30 November 1998.

Jan 1, 2005

By M. C. Udy, C. H. Lorig

THROUGH the years much interest has been centered in attempting to develop a direct method of iron-ore reduction, to replace or supplement the present indirect blast-furnace process. It would not be difficult to produce a list of more than 500 patents dealing with the direct production of iron and steel, but the few of this type of process that have proved successful do not produce in competition with the blast furnace; they produce special products. A survey of the literature reveals that the equilibrium conditions for the reduction reactions (iron oxides with carbon monoxide and with hydrogen) have been fairly well established but that data on the rate of reaction are discordant, although the general effects of the variables are known. This dissertation deals with the rate of reduction of a magnetite concentrate with hydrogen. The following variables have been studied: bed depth, gas velocity, particle size and temperature. The behavior of a single particle was also studied. LITERATURE Two general factors should be considered in a study of reduction of iron oxide: (I) equilibrium relations, and (2) rate of reaction. The first factor, equilibrium, has received the attention of many investigators and the equilibria Fe304-FeO-H2-H20, Fe3O4-FeO-CO-CO2, FeO-Fe-H2-H20, FeO¬Fe-CO-C02 are fairly well established. Of the second factor, the rate of reaction, much less is known. Data are comparatively scarce and there is very little concordance. The discordance probably results from the large number of variables influencing the reactions. However, the general effect of the variables is known. Among these variables are temperature, gas velocity, particle size, porosity, gas composition (distance from equilibrium), presence of impurities, greater or less prevalence of side reactions, and even design of the apparatus itself. Wetherill and Furnas1 published an excellent paper in 1934. They point out that any one or more of five processes (the chemical reaction, diffusion of the reactant through the gas film, diffusion of the reactant through the solid phase, diffusion of the reaction product through the solid phase, or diffusion of the reaction product through the gas film) may be the slow process, and thus the rate-controlling process. It is regretted that the work of these authors was limited to experiments at one temperature, and that the range of gas compositions was limited. Langmuir2 has shown that heterogeneous reactions take place at phase boundaries.

Jan 1, 1942

By D. Michael Holloway

The realignment of Interstate 880 replaces the double-decked (Cypress) viaduct collapsed in Oakland, California during the 1989 Loma Prieta Earthquake. The California Department of Transportation (CALTRANS) evaluated several pile foundation schemes for supporting the proposed structures. Structural support demands led to the selection of steel pipe piles (16-, 24-, and 42-inch-(406-, 610- and 1067-mm-)diameter), filled with concrete and steel reinforcement. Deep penetrations required through layers of very dense/cemented sands in some locations, caused serious drivability and pile integrity concerns. The need for large pile driving hammers and large diameter steel pipe piles pushed the engineers and prospective contractors well beyond the limits of local experience. Such questions as the feasibility of driving the pipes closed-ended through dense upper strata, and quantifying the effects of installation on the long-term capacities of the piles, led CALTRANS to develop a comprehensive pile test program to address the design and construction issues effectively. The results were furnished to prospective bidders on the production stages of the ensuing contracts.

Jan 1, 1996

Distinguished guests ladies and Gentlemen. As many of you know, before I became a Labour Member of Parliament, I had an unusual career path for a politician, in that I spent quite a few years working in the business community. In other words, I was mainstreamed before I was institutionalised. Given that some of this time was spent working for the then Macraes Mining Company Limited, now Gold and Resource Developments NL, I feel that I may have a perspective on how things are seen, on both sides of the fence. In terms of public perception and esteem I am not sure which career option was the step up and which was the step down. So far what I have found very familiar, is that in both roles there is a gulf between the reality and the perception of that reality - a gulf that is both huge and hard to bridge. I think it is a point worth making here amongst another busy industry cluster, that we can all too easily get so embroiled in the day to day activities, that we lose sight of how this might look to those running on a different treadmill. I can still remember scratching my head at the beginning of some days, as I worked to get new mining projects started that I knew were going to bring real jobs and economic benefit to New Zealand, but ending the day feeling like I may instead have been proposing bringing back both strip mining and slavery. If I learnt one valuable lesson out of that time it was this: .... mining has become so publicly demonised on the road to ecological nirvana, that even attempting a lucid dialogue on mining issues, with some, is incredibly difficult.

Jan 1, 2000

This paper describes the integration of the mineral resource management philosophy within strategic long term planning at Anglo Platinum Limited. Consideration is given to the philosophy, processes, techniques and supporting systems.

Jan 1, 2007

By Adrian Moore, Dominic Hooton, Alan Richards

Significant factors affecting airblast overpressure (AOP) emissions include charge mass per delay, distance from the blast site, burden, stemming height, and delay timing, topographic shielding, and meteorology. The effect of charge mass on the frequency of the airblast produced, and the delay timing required to control the level of airblast overpressure is explained by two case history examples which were not affected by topographical shielding and meteorology. One is a cast blast with a charge mass per hole of 1000 kg (2200 lb), and the other is a quarry blast with a charge mass per hole of 64 kg (141 lb), These examples show that the delay interval necessary to prevent an increase in AOP levels must be increased with an increase in charge mass per hole. The effect of a ‘soft-start’ technique where a reduction in AOP levels is achieved by decking only the initial front-row holes is also illustrated.

Jan 21, 2025

By Heidi Fauser

The aim of the project was the development of an electroforming process for the production of medical implants out of gold. To prove the applicability of this technology, tympanostomy tubes were chosen as demonstrators. These barbell-shaped tubes are usually produced mechanically; of silicone or, for higher therapeutic demands, of metal ? gilded silver or gilded stainless steel. Gold electroforming of the tubes as an alternative manufacturing process would reduce the expenditures for the mechanical preparation and lower the corrosion susceptibility significantly. To obtain electroformed gold tubes of the desired shape, the following steps are necessary: fabrication of a negative template by drilling holes with countersinks in an insulated aluminium sheet, electroforming process, removal of the aluminium by using a sodiumhydroxide solution. For the optimisation of the shape and surface quality of the tubes respectively the simplification of the manufacturing process, various parameters were tested, e.g. aluminium quality and sheet thickness, type of insulation layer, substrate processing, hydrodynamic conditions, type of electroforming electrolyte, electrodes position, etc. The manufactured tubes were characterised in view of thickness distribution, hardness, surface roughness and purity in comparison to mechanically produced reference tubes. From the results obtained during the project it can be concluded that electroforming processes can be easily adopted for the manufacture of medical implants. The time-consuming electroforming process is by far compensated by the simultaneous production of an arbitrary number of implants.

Oct 1, 2003

By hydrometamorphism is meant the alteration of rocks, ores and minerals by atmospheric waters. In its broadest sense, it includes the varied processes of weathering, oxidation, hydration, the leaching of rocks and ores, and the solution, migration and enrichment of metals. Rain water, as it strikes the earth, is practically pure water, except for small quantities of dissolved atmospheric gases; upon coming in contact with ore minerals, especially sulphides, however, it is transformed into solutions of great chemical activity, which attack, transform and rearrange the minerals of ore- bodies, and so effect enrichments of the greatest economic importance. Primary deposits so low in grade as to be without commercial value are frequently thus transformed into deposits of commercial importance. It is necessary in the examination of any orebody, therefore, to determine whether the valuable ore is of primary or of secondary origin; if primary, its value may be expected to continue indefinitely in depth to the zone of primary impoverishment; if secondary, the ore deposition is known to be controlled by surface agencies, and the valuable ore may be expected to continue to such depths only as have been reached by surface waters. The decomposition and weathering of rocks, unlike the changes undergone by orebodies, are accomplished by water carrying as dissolved constituents chiefly atmospheric oxygen and carbon dioxide, together with vegetable acids. The chemical changes wrought are principally hydration, oxidation and the formation of carbonates. The tendency is toward the solution of the more easily dissolved minerals, which is attended by the formation and a surface concentration of the more resistant minerals,

Jan 1, 1932

By Rudolph Emmel

THE mines operated by the South American Development Co. are located in the Zaruma mining district of southwestern Ecuador. They are near the old mining town of Zaruma, which is the only important city in the canton of the same name. The district is situated in the upper end of a valley lying between two spurs of the Cordillera, one of which may be considered the Coast Range and the other an intermediate range. The mining camp proper, known as Portovelo, and the plant are 2.4 km. south of Zaruma, on the north bank of the Amarillo River, a tributary of the Tumbes River, which flows southwestward through Peru to the Pacific. Portovelo is difficult of access; it is reached from Guayaquil by means of river steamers and muleback. Embarking at Guayaquil, the route is down the Guayas River, across the Jambeli Canal, and up the Santa Rosa River to Santa Rosa, a distance of 177 km. From Santa Rosa, the road or trail follows the Santa Rosa River, then across the summit of the Coast Range into Portovelo, a distance of 74 km.-a two-day trip on muleback. The mining property of the South American Development Co. comprises 297 lode claims and 142 placer claims. The combined lode claims cover an area, roughly rectangular in shape, 9000 m. long from north to south by 4000 m. wide; the northern edge of the rectangle is about 3000 m. north of the central plaza of Zaruma. Mineral lands in Ecuador are held by virtue of an annual tax per claim paid to the central government, no surface rights being included.

Jan 1, 1925

'T. C. MERRIMAN, New Haven, Conn. (written discussion *).-This most interesting paper gives much carefully obtained and valuable data. However, there are two points in connection with the commercial application of such data that might possibly be a source of trouble and mis-understanding. In the first place, the examination of thin sections of annealed brass, subjected to standard Brinell test.(500 kg. on a 10-mm. diameter ball) at thicknesses from 0.075 to 0.150 in. (1.9 to 3.8 mm.) indicates that cold work has been performed on the specimen during the application of the load sufficient to extend way through the section, and have the hardness of the metal affected by the backing. If the usual steel support is used, this effect is very evident. If a piece of soft brass is used as a support, there is an indentation in the surface of the support accompanied by a bulge on the under side of the tested specimen opposite the impression made by the 10-mm. ball. The result is that Brinell specifications (governmental or otherwise) on stock for a certain purpose may not be fair in all cases, since manufacturers, owing to differences in equipment, etc., may not all use precisely the thickness and conditions of stock on which the Brinell specifications were based. This would mean that the government Brinell specification might not give them the temper of stock best suited for their manufacturing methods. The concluding paragraph of this paper, stating that "the hardness of cartridge brass may be determined with greater accuracy by the Brinell hardness measurement than by attempting to judge it from the grain size" appears to be in line with the movement of the last year or so among brass manufacturers toward substitution of the Brinell test for microscopic examination as an acceptance test on cartridge brass. The statement may he strictly true that the Brinell test is the best test for hardness, but it is not, as the statement might readily be construed, a sufficient test of suitable condition. For instance, some cartridge brass might accidentally have been overheated to a point where it would be distinctly unsafe to use for the manufacture of small arms cases and then be so rolled (reduction 3 to 5 per cent.) as to pass perfectly proper Brinell specifications. Under such conditions the microscope would reveal its unsuitability where the Brinell test had failed so to do.

Jan 4, 1919

By B. W. Howlett, M. B. Bever, Somnath Misra

The heats of Formation of the compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2Te3 and the heats of solution of tellurium and selenium in liquid bismuth have been measured in a liquid metal solution calorimeter. The heat capacities near the melting point, the heats of fusion, and the melting points of the two tellurides have been measured in a constant temperature gradient calorimeter. The thermo-dynamic quantities are interpreted in relation to the stability of the compounds and the nature of the solid-liquid transition. THE selenides and tellurides of several elements of Group VB of the periodic system are of interest because of their electronic properties. The compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2Te3 are semi- conductors; they also have gained prominence in the fields of thermoelectricity and photoconductivity. However, little is known about their thermody-namic properties. As part of a research program on the thermo-dynamic properties of intermetallic compounds, the heats of formation of the compounds Sb2Se3, Bi2Se3, Sb2Te3, and Bi2Te3 were measured in a liquid metal solution calorimeter. The heat capacities near the melting point, the heats of fusion, and the melting points of the two tellurides were measured in a constant temperature gradient calorimeter. The results, in addition to their intrinsic interest as thermodynamic quantities, contribute to an understanding of the stability of the compounds and the nature of the solid-liquid transition. 1) EXPERIMENTAL 1.1) Materials. Samples of the compounds SbzSe3 and Bi2Se3 were prepared by melting the elements in stoichiometric proportions in evacuated Vycor capsules followed by quenchinn in water. They- were then annealed in vacuum for 12 hr at 550°C. A sample of Sb2Te3, consisting mainly of one large grain, supplied by the Lincoln Laboratory,

Jan 1, 1964

By E. M. Timoshenko

Autoclave technology can be effectively used for liberation of complex mineral raw materials to transfer valuable constituents into solution for their subsequent recovery or to refine feed material in order to remove deleterious impurities, e.g. arsenic. The high efficiency of autoclave processes is attributed to the fact that they are suitable for processing of refractory raw materials, have low capital costs, high productivity, ensure integrated utilization of the feed materials, produce innovative saleable products, completely eliminate any air emissions, provide low-waste or waste-less technology, mechanization and automation of production processes. In the immediate future, it might be expected that autoclave processes will find use on commercial scale for production of heavy non-ferrous metals in combination with other processes (hydrometallurgical, upgrading, sorption and solvent extraction, electrolytic, etc.) to ensure: - Integrated processing of refractory ores and concentrates (pyrrhotite, zinc, copper-zinc, lead-zinc, nickel-cobalt, copper, pyrite); - Production of metallic powders of base metals as commercial products (copper, cobalt, nickel, etc.), composites on their bases, final products and saleable salts. Processing technologies incorporating autoclave processes, especially at the stage of liberation (chemical upgrading) of raw materials are characterized generally by high overall recoveries of valuable constituents significantly exceeding recoveries common for conventional pyrometallurgical processes (for some elements by several tens of percent).

Jan 1, 2006

By H. S. Rathor

NTPC (National Thermal Power Corporation), a multi-unit organization, is generating 26% of India’s total power. This power is produced from its 14 coal based stations and 7 gas based stations. NTPC is entering into the business of power-distribution, power-trading, setting up of coal mines and diversification in non-conventional energy sector as well. For achieving the goal of the country “Power for All” NTPC has taken a giant stride by entering into Hydro Power generation which is also the cheapest and the cleanest renewable source of energy. In its pursuit for excellence, 800 MW Koldam Hydro Power Project is NTPC’s first venture in hydro sector. In Koldam, hydropower potential will be harnessed by constructing a 163m high earth and rock fill dam in a narrow gorge at upstream end of Bhakra reservoir. The river diversion is envisaged through two parallel, 14m finished diameter ‘horseshoe’ tunnels of length 901m and 934m at village Kian on the right bank, where the river forms a 180° loop. The diversion tunnels are designed to accommodate a flood of 6500m3/sec, taking into account the maximum probable discharge of 200 years return period. The tunnels pass through dolomite and limestone rock formations. The excavation of tunnels was done with drill and blast method. The excavation was attempted from both inlet and outlet faces. During geological investigation a rock fault was located at the outlet area. The location of the fault was such that it was passing through the edge of the Tunnel-1portal and around 30m away from the face of the Tunnel-2 portal. The quality of the rock at Inlet was also poor. To save the portals from slips, excavation of the tunnels was planned to start after the completion of the open excavation and its support system both at inlet and outlet. The tunnel excavation at inlet was envisaged by approaching the tunnels’ portal by constructing a road through 540EL bench and meeting the inlet portals on the upstream end, which would have been ready by mid2003, only after completion of the open excavation and its support system. To save time and cost, it was felt necessary to modify the planning by starting the tunnel excavation simultaneously along with open works both at inlet and outlet. The excavation at the inlet face of the tunnels started in December 2002 after rerouting the approach road to inlet portals through haulage road on the downstream and similarly Tunnel-1 at the outlet was started in the low cover area before completion of open area works. Thus the tunnel—heading excavation was started nearly 06 months early with the change of methodology.

Jan 1, 2005

By R. O. Williams

Analytical representation of the thermodynamics of solutions is highly desirable from the standpoint of accuracy, compactness, and numerical manipulations. In particular, computer calculations are greatly implemented. Mathematical considerations show that previous expressions have one or more serious defects. This investigation shows a Fourier series to be satisfactory but that it is also possible to derive a new series which fits certain additional conditions. Included examples show the value of analytical expressions in giving a simple characterization of each system using some two to five parameters, the elimination of the Gibbs-Duhem integration, and the es timation of the error for the experimental function as well as derived functions. It is further shown that the present characterization provides easy comparison between systems. IN the past, thermodynamic calculations have depended to a considerable extent on tabular and graphical methods. As the volume and precision of such data increase such methods become less satisfactory. Specifically, the selection of the optimum representation and the estimation of errors require statistical methods which in turn require analytical representation. The utilization of such data require further manipulations which are best done analytically for maximum precision. For example, phase equilibria are determined by common tangents to free-energy curves: a graphical determination is normally of low accuracy. As computers are increasingly used analytical representations become almost mandatory. Insufficient mathematical consideration has been given previously to the selection of empirical expressions. Those expressions having some theoretical justification are generally too inflexible and mathematically unattractive. We consider the problem in some detail and show that a Fourier series can be effectively used. Also a new series is defined which has certain advantages. ANALYSIS We wish to consider the analytical representation of the heat of mixing, AH, the excess free energy, ?Gxs, and the excess entropy, ?sXS, as a function of composition, X, for binary solutions relative to the pure components in the same state. When a distinction is not required, we use W to denote any one of the above functions. One may use a Taylor expansion around X = 0 to generate a power series. As the derivatives are un- known we represent the series as W = A + BX + CX2 + DX3 + EX4 + ... [l] where the constants A , B, C , ..- are to be selected to provide some optimum fit. For the extremes of composition W is necessarily zero so it follows that A = 0 [2a] B +C + D + E +••• = 0 [2b] Nonelectrolytes, which we are considering, appear to satisfy the condition that d3W/dx3 = 0 [3] in the terminal regions. This is the basis of the a, ß, and Q functions used by Hultgren et al.' and others. While this condition does not have a strong theoretical basis it does appear desirable that any analytical relation should satisfy this condition. Darken2 and Turk-dogan and Darken3 have shown that many systems exhibit this behavior over an extended range from each terminal region, departure being restricted to a limited intermediate region. Since we have no a priori knowledge as to where this transition occurs we can require that this condition be satisfied only as a limit at the extreme compositions as a general condition. We will show later how more restricted conditions can be included in specific solutions. Darken2 has called this behavior the quadratic formalism; we call our application the limiting quadratic formalism, LQF. This condition applied to the above power series requires that D = 0 [4a] 4-3-2E +5-4-3_F + 6 • 5 . 4G + ••• =0 [4b] The form of the power series normally used, due to Margules,4 is W=X(1-X)(A + BX + CX2 + DX3 + EX4 + •••) [5] where A, B, C, --. are a new set of constants. (Guggenheim5 has given a variation of this expression in a more desirable form. Since, however, it is contained in the above expression it does not require separate consideration.) This form is precisely what results by incorporating the conditions in Eq. [2] into the power series and regrouping the constants. The LQF requires that B =C [6a] and 4.3.2(D-C) +5-4-3(E-D) + ••• =0 [6b] Thus, the correct form of the Margules expression with two adjustable parameters is w =X(1-X)[A + B +X2-2/3x3)] 171 and the EX4 term must be included before three adjustable parameters are permitted.

Jan 1, 1970

By Walter B. Lenhart

This paper is one of a series on milling methods and costs being. published by the Bureau of Mines. The milling practices and special problems relating to grinding, tailings disposal, and choice of a treatment process at the Cardinal mill are discussed. The property of the Cardinal Gold Mining Co. is about 18 miles southwest of the town of Bishop, Inyo County, Calif., at an altitude of approximately 8,500 feet. The camp has been designated Bishop Creek by the postal authorities. The property comprises 33 mining claims, including fractions and millsite in sections 19, 20, 29, and 30, T. 8 S., R. 31 E. These claims are located in a general way along the strike of a band of quartzite.

Jan 1, 1938