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By K. Vanbroekhoven

An industrial site near the centre of a historical town in Flanders is characterized by chromium(VI) contamination of the groundwater. Since the potential for natural attenuation was not sufficient to control the groundwater plume as observed from different analyses like pH, Eh, soil oxidation and reduction capacity, the feasibility of site remediation based on in-situ bioprecipitation of chromium was examined in lab microcosm studies. By creating reducing conditions by addition of a carbon source in the groundwater, chromium(VI) can be biologically reduced to chromium(III), which can form an insoluble precipitate of chromium(III) hydroxide. Microcosms contained contaminated groundwater and aquifer samples that were collected and manipulated under anaerobic conditions. Three different carbon sources were screened for their effectiveness: molasses from sugar beet production, molasses form starch production (protamylasses) based on potato juice and lactate. The different concentrations of sugar molasses were used to determine the optimal conditions. A range of parameters was monitored at regular time intervals for a period of six months such as chromium(VI) and chromium(III), DOC, methane, pH, Eh. A rapid conversion of chromium(VI) to chromium(III) was observed for all conditions tested. However, extensive removal of chromium from the groundwater by precipitation was only achieved for a limited number of conditions. In general, lactate was found to be the most effective carbon source, slightly better than the lowest concentration of sugar molasses that was tested, which itself was more effective than molasses based on potato. Higher concentrations of molasses, although causing a steeper decline in redox potential, resulted in less effective Cr removal. Typically, the fermentation of molasses results in acidification and this drop in pH may hinder the formation of insoluble chromium(III)hydroxides. It may also be possible that certain components of the molasses form soluble complexes with chromium(III). For lactate, no significant drop in pH was observed. Following the laboratory microcosm tests, the stability of the chromium precipitates was examined by performing a sequential extraction on the microcosm materials. These were performed under redox conditions which were similar to the ones observed in the field. Since the outcome of these tests was positive, a pilot scale test was implemented in the field in April 2005. Two different substrates, the cheap waste product sugar molasses and lactate are being injected creating two different impact zones and typical parameters are monitored. Frequent re-injections were important to maintain reduced conditions and are carried out three-weekly up to now. To study the stability of precipitates formed, mesocosm socks containing aquifer material were installed in the monitoring wells and harvested at regular intervals. Results of this pilot test will be presented and compared to the laboratory results. Based on the success of this field test, a full scale process will be designed and implemented as remediation strategy.

Jan 1, 2006

By W. S. Landers

This report presents a detailed study of low temperature, entrained-bed carbonization of an Australian coking coal. The coal studied was high-volatile B bituminous from the Foybrook mine, an open-cut operation in the Liddell seam, New South Wales, Australia. Carbonization was conducted in an 8-inch diameter, continuous vertical reactor at several temperatures from 960° to 1,300° F. It was demonstrated that this bituminous coal can be carbonized within this temperature range to produce tar and a nonagglomerated char, without prior oxidation or char recirculation. Carbonization rates from 138 to 287 lb/hr (as-carbonized basis) were investigated. It was found that the carbonization temperature and the air-to-coal ratio must exceed minimum values to insure continuous operation. At the higher air-to-coal ratios employed, all or most of the carbonization heat was provided by internal combustion with air in the reactor. At the lower air-to-coa1 ratios, part of the heat for carbonization was supplied externally. On the moisture-and ash-free basis, the yield of tar plus light oil ranged from about 26 to 44 gallons per ton, and the char yield ranged from approximately 1,160 to 1,370 pounds per ton. The heat in the gas ranged from about 900 to 3,000 Btu/lb of moisture-and ash-free coal. Carbonization product yields correlated well with air-to-coal ratio and carbonization temperatures. The volatile matter in the char was found to be temperature dependent. At 1,300° F carbonization, the volatile matter in the char was 8.7 percent (dry basis), whereas at 9600 F carbonization, the residual volatile matter was about 16 to 18 percent (dry basis).

Jan 1, 1965

By J. A. Bakken, G. Sævarsdóttir, H. Pálsson, M. Þ. Jónsson

The role of the electric arc in the consumption of electrodes in submerged arc furnaces has long been debated. The hostile environment in the furnace does not make direct measurement feasible, so simulation has been used to evaluate the arcs contribution to the erosion. Magnetofluiddynamic (MFD) electric arc simulations and a cathode / anode sub-model developed in order to provide boundary condition to the arc model have been used for this purpose. The cathode / anode sub-model provides current distributions and cathode / anode fall voltages for the arc and temperature distribution for the electrode surface, which is paramount to the erosion rate which in turn is calculated from the Clausius Clapeyron equation and the Hertz Knudsen formula for the vapour transport. In the case of high-current industrial AC arcs, arc currents are typically ~100 kA, phase voltages ~100 V and total furnace power ~10 ? 60 MW. The results show that although enormous amounts of material is evaporated, much of it recondenses on the surface. Furthermore the results show that the arc erosion increases strongly with the arc current. If a single arc is present its contribution to erosion is close to the actual total erosion in the furnace. Results from this analysis indicate that there are possibly more than one arc present in the crater, in which case less than 40% of the total erosion would be due to the arc, the rest is chemical erosion.

Jan 1, 2007

By K. Holmberg, D. Herriot

This paper by Mr Mclvor is yet another contribution to the eternal controversy surrounding the benefits, or otherwise, of high circulating loads in closed circuit grinding. Throughout the paper it is difficult to establish whether the author is referring to effects relating to the mill, classifier, or to the overall circuit. Table 1 is put forward as indicating the advantage of operating at high circulating loads. From the two (it would be interesting to see more) product sizing points provided in each case, the conclusions to be drawn are that cases one and two have very similar size analyses. The third case, however, indicates a much flatter curve, that is to say, higher fines production and a very wide spread of size ranges. If the objective of this circuit is to provide a closely sized product with minimum overground slimes to the downstream process, then it would appear to be the less "efficient" by far. No data is given for product pulp densities either. The term "efficiency" should never be used without a careful and clear definition. In this case, "efficiency" is used to express an apparent percentage reduction in operating work index (Bond) from the measured "standard" at 250% circulat¬ing load operation. The Bond calculation is itself based upon

Jan 1, 1989

The ore is very 'refractory. It consists essentially of arsenical pyrites, iron pyrites, zinc blende, galena, antimony as sulphide and probably, in combination with galena, as Jamesonite, magnesium, and aluminium silicates with quartz. Some of the oxidized ore, of which there is very little, has a very interesting composition. A specimen shown to me by the ,general.manager, Mr. F. B. Stephens, consisted of hydrated arseniate of iron, orpiment, pyromorphite, lead oxide, with magnesium silicates and quartz. The ore found in the mine with a composition similar to this specimen was valued for gold contents at 60 oz. per ton. This ore is found as a small leader, which runs parallel to the main ore body, at intervals cutting through it.The ore is conveyed from the mine to the reduction works by means of a double road tram line. The mine is situated about rooo feet above the plant on a hill. The grade is so great (about I in 2) that the loaded trucks coming down are able to pullthe empty ones up, thus obviating the necessity of motive power for haulage. All that is necessary is two large grooved pulleys, fixed at the summit of the hilI, and provided with a rope-break for steadying the speed of the trucks down the hilI.

Jan 1, 1903

By R. W. Fedors, S. T. Green, F. T. Dodge, D. B. Walter

Spatial and temporal temperature variations in a high-level radioactive waste repository drift can give rise to moisture transport within the drift. Knowledge of this moisture transport may be important to assessing the potential for corrosion of all metallic components in the drift. The model presented here shows one approach to simulating evaporation, transport, and condensation of water in large underground openings using a framework based on computational fluid dynamics. Simulation results that explicitly model water and latent heat transport are presented.

Jan 1, 2004

By I M. Platten, S C. Dominy

The evaluation of historical goldfields is currently topical, reflecting a high gold price, improvements in knowledge and technology. and lack of greenfield sites. Many goldfields comprise narrow gold-quartz veins which are structurally complex with an irregular distribution of gold; variable geometry and architecture; and display late deformational effects. The study of historical mine records can be an important tool during early and advanced project evaluation since it contributes to understanding the orebody, exploration target size and setting expectations. The historic Engineer Mine property is located 32 km west of Atlin, British Columbia on the east side of Tagish Lake. The economically important Engineer and Double Decker veins belong to a NNE-SSW vein set. These are narrow, commonly <2 m dilational veins with a minor sinistral strike component and of an epithermal type. Documented ore production between 1910 - 1952 is recorded as approximately 14 263 t at 39.4 g/t Au and 19.5 g/t Ag (for 18 000 oz Au and 8950 oz Ag). The underground workings consist of about 5500 m of tunnels, shafts, raises and stopes over eight levels. The mine is currently being re-evaluated. In 2011, an Inferred Mineral Resource of 41 000 t at 19 g/t Au for 25 000 oz Au (at a 5 g/t Au cut-off) was defined from historical data supported by modern drilling into the Engineer and Double Decker veins. A surface and underground bulk sampling and milling program was undertaken in 2011.CITATION:Dominy, S C and Platten, I M, 2012. Application of historical data to estimate a mineral resource at the Engineer gold mine, British Columbia, Canada, in Proceedings Narrow Vein Mining 2012 , pp 81-100 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Mar 26, 2012

The objective of this study was two-fold: 1. To perform a world literature search pertinent to the analysis, selection and design of hoisting systems and their components and to codify the search into a literature compendium. The search resulted in a technical data file of over 1500 hard copy items. The compendium index was also suitable for establishing a comprehensive computer-loaded data base on the subject. 2. To develop a comprehensive system of guidelines to cover salient aspects of analysis, selection and design of electrical, mechanical and structural components of a hoisting system with a view to establish parameters for maximum safety and efficiency of operation, installation and revision of the system. 3. (a) In-shaft equipment design and specification criteria are considered as they influence guideline preparation. (b) A comprehensive review of hoist electric drives and controls as applied to mine hoists is set forth with special reference to duty cycle calculations and their effect on electrical component selection.

Jan 1, 1988

By Michael Amick

Over the last few years as the coal industry has seen an increase in the price of coal, a renewed interest in the additional mining of pre-law highwall sites has occurred. Much premium coal and property remains behind these pre-law highwalls but access to mining is limited because prior mining used auger machines to remove coal from under the highwall. Older augers seldom reached more than 200 feet and often no more than 100 feet but this zone of auger holes destabilizes the highwall to where additional mining is often unsafe. If the reserve is large enough, the highwall can be stabilized with common flyash and cement grouts to form a face-up for an underground mine but this expensive method is usually not practical for continuous use with a highwall mining machine. It is estimated there are hundreds of miles of highwall riddled with auger holes where the coal reserve available is ill-suited for deep mining for a variety of reasons. However, these same properties are ideal for additional mining with state-of-the-art highwall mining machines that have a reach up to 1200 feet, except to the relatively thin auger mined de-stabilized zone. The renewed interest in highwall mining these properties has driven research into finding an economical way to stabilize the highwall so the highwall mining machine can recover additional coal. This research discovered and fine-tuned a process that is economical and is successfully supporting the highwall at a highwall mining operation. This paper discusses the research involved in determining the strengths need, the methodology used to place any grouts, the effect on mining plans and the increased recoveries. ARMPS-HWM is used extensively in this research. The failure of the highwall, when not grouting, and the success, when grouting using the new materials and equipment utilized, confirmed the ARMPS-HWM method.

Jan 1, 2007

One Hundred Sixteenth Meeting of the Institute, Monday, Feb. 18, to Thursday, Feb. 21, inclusive, 1918. Committee on Arrangements J. E. JOHNSON, JR., Chairman BRADLEY STOUGHTON, Vice-Chairman A. R. LEDOUX J. V. N. DORR L. W. FRANCIS F. T. RUBIDGE G. D. VAN ARSDALE MRS. S. J. JENNINGS E. M. SHIPP RALPH W. DEACON ARTHUR L. WALKER The program for the New York Meeting, in February, 1918, as planned by the Committee on Arrangements at meetings in the middle of December, and therefore subject to slight alteration in detail, is as follows: MONDAY, FEBRUARY 18 9 a. m. to 5 p. m. Registration at Institute Headquarters. 10 a. In. Technical Sessions. 12.30 p. in. Luncheon at Engineering Societies' Building. 2 p. m. : Technical Sessions. 8.30 p. m. War Smoker or Patriotic Meeting. TUESDAY, FEBRUARY 19 10 a.m. Annual Business Meeting, followed by Technical Sessions.

Jan 1, 1918

By Yoginder P.

ACKNOWLEDGEMENTS Authors sincerely appreciate the interest, cooperation and technical support of the coal company management and staff in conducting the study. Without their assistance this study would not have been possible. INTRODUCTION AND SPECIFIC OBJECTIVES An area in the midwest overlying abandoned room-and-pillar mine workings at, shallow depth has been experiencing subsidence movements with associated damage to surface structures. Other coal companies in the area have also been having similar experience. A 16 - month cooperative study between a mining company and the Department of Mining Engineering at SIUC was developed with the following objectives. 1) Determine the extent to which surface and subsurface movements were complete in the area, 2) Identify the mechanism(s) of subsidence in the area, 3) Determine the influence of geology and hydrology of the area on subsidence movements, 4) Observe the conditions of abandoned underground workings with a borehole TV camera, 5) Characterize the extent of damage and monitor possible progressive damage to selected surface structures, and 6) Make recommendations to a) minimize further damage to surface structures in the area, b) identify future areas that may be affected by these movements and c) modify mining systems to minimize these movements.

Jan 1, 1986

By P. Massi

"Wholly owned by the Coniagas Mining Company, the oldest continuously listed mining company on the Toronto Stock Exchange, St. Andrew Goldfields is located on Hwy. 101 approximately 30 miles east of downtown Timmins, Ontario. Geographically situated on the Porcupine-Destor Fault, the mine and mill in Stock township is positioned in the heart of Northeastern Ontario's goldmining communities.In July 1988, a 600 ft. shaft, hoist, and compressors were already in place when construction started on a 500 T.P.D. capacity C.I.P. mill and crushing plant.By June 15, 1989 the mill was commissioned and attained the design capacity by August of that same year. Since then, changes to the circuit have increased throughput to 900 T.P.D. from two significantly different ore sources.Meeting the Ministry of the Environment's guidelines is an ongoing commitment utilizing the Inca S02 process in line between the tailings pond and secondary polishing pond.INTRODUCTIONExploration on what is now known as St Andrew Goldfields' Stock Township Mine was carried out ln the early l960 1 s by Hollinger Mines Ltd. The property was acquired by Quebec Sturgeon River Mines 1n 1973 and the main shaft was started ill 1979.When St Andrew Goldfields was incorporated 1n 1983, exploration and development commenced to identify the ore body. The company decided 1n 1987 to bring the Stock township property into production after an extensive feasibility study and testwork at Lakefield Research in Toronto. Leslie Engineering was contracted to design, engineer and procure al 1. equipment from the coarse ore bin to the tailings distribution system and backfill plant"

Jan 1, 1992

By L. K. Weaver

The Bureau of Mines has started an engineering study of oil recovery by miscible-phase displacement. As a preliminary part of the investigation a literature and patent study was made to prevent duplication of work already done, to become acquainted with those actively engaged in research of this type, and to learn where the recovery method has been attempted. This bibliography gives results of this study. The bibliography includes 254 references to U.S. and foreign patents and published literature relating to miscible-phase displacement processes of oil recovery. It is divided into the following sections: (1) U.S. patents, (2) foreign patents, (3) literature references, (4) author index, and (5) publication and source reference. The patents and literature references are listed alphabetically by author by intervals of years. References to February 1963 are included.

Jan 1, 1963

By J. Visman

"SummaryThis paper is presented as part of a programme to show the steps taken by industry and others interested in supplying a solid fuel of constant quality to 'satisfy a consuming market. The paper deals with the general principles underlying quality control in coal preparation plants, namely, constant quality and close adherance to acceptance limits. It also describes how control of ash content is ""generally hampered by the problem of coal sampling .and the long duration of the ash analysis and how these difficulties may be overcome.Quality control can be effected in several ways. Thorough blending wll reduce variations appreciably, except those of long trend. The latter can be detected by automatic sampling and quick ash analysis. At present, under favourable conditions, a system of half-hourly ash determinations with an accuracy of 0.5 to 1.0 per cent can be realized, to the effect that trends with a 'wave length' of more than two hours cu be eliminated within the limits of accuracy of the ash figures. The general solution of the problem is a combination of blending, accurate sampling, quick ash determination, and statistical analysis of the pattern of ash distribution.The use of statistical methods of analysis, such as the t test and F test, is •discussed at some length in order to emphasize the importance of the correct evaluation of observational data if there is to be confidence in the validity of test results.General ConsiderationsCOAL, as a fuel, is too cheap for a long haul across the country. The limiting distance depends on the price of the local competitive fuels, and, as the price depends to a great extent on quality, so does quality, to the same extent, command the market."

Jan 1, 1952

By A. T. Shurick

THE NRA Administrator's casual reference to the coal code as the next "pineapple" to be fixed was a conservative estimate of his job. This thorny and adamantine morsel now looms as a critical test of NRA. A failure in coal supplies would have the gravest potentialities in the Administration's program at this time. And the loss of prestige from a breakdown of the enforcement machinery in this initial large-scale test of strength would accentuate the incipient indications of insurrection in other directions. General Johnson has had a difficult task. It involves problems festering for a quarter of a century. A succes¬sion of Presidents have been glad to tide over their respective regimens with inconclusive expedients; they have been baffled by the complexities of the technical angles and hopelessly irreconcilable concepts of powerful conflicting interests with large issues at stake.

Jan 1, 1933

By Mohammad Irshad, Klaus Mussger, Harald Wagner

Despite the fact that the New Austrian Tunneling Method; NATM, has been used in the United States for the past 23 years or so, still considerable misconceptions exist in the industry about the nature of the method and its implementation. In the authors’ view its implications are usually not well understood. The paper provides an overview of the highlights of NATM usage over the past two decades to illustrate the point that NATM is now a well-established tunneling method in the U.S.A. Accordingly the thrust of this paper is on the more pragmatic aspects of the NATM technology usage as it concerns the Owners, Designers and the Contractors. Prior to examining the implications of NATM usage from the viewpoints of various stakeholders, it should be helpful to first briefly provide an overview of the history of the method as it was introduced and implemented on several key tunneling projects in the US, over the last 2 plus decades.

Jan 1, 2005

By Roger J. Morrell

Bureau of Mines laboratory experiments with reduced scale cutter and cutter forces were performed to (1) define the fundamental relationships governing disk cutter performance and (2) to develop a method of predicting disk cutter performance in soft, medium, and hard rocks. The rock cutting experiments were performed in four igneous and metamorphic rocks that ranged in compressive strength from 38,000 to 67,000 psi. A special testing machine called a linear cutter apparatus (LCA) was used to load and traverse a free rolling disk cutter across a smooth rock surface. Each pass of the disk produced a single crater, and runs were spaced to avoid breakage between craters. During each run the normal and tangential cutter forces were measured and recorded. The soft and medium rock data were obtained from previous Bureau experiments with disk cutters. Crater depth, tangential cutter force, crater volume, specific energy versus normal cutter force, and crater width versus depth are defined within this study. With the use of standard physical properties, performance prediction equations were developed using stepwise linear regression analysis techniques. A method of using these prediction equations to calculate the boring rate, the cutter spacing, and the torque and energy requirements of a full-scale boring machine was also developed.

Jan 1, 1974

By Jim Sarvinis, Mark Berkley, David Clarry, Jason Berzansky

"Technologies developed to sequester CO2 or use CO2 for enhanced fossil fuel recovery are currently being utilized across the globe. Taxation regimes and CO2 credit trading are becoming drivers for a number of projects. Some mining companies have also identified ancillary opportunity to sequester CO2 in their by-products; recent work in the alumina industry is a prime example. In addition to process plant emissions, mining companies are becoming increasingly aware of their overall carbon footprint, including CO2 generated during the production of utility power. New power plant designs, in various stages of development, include CO2 separation and sequestration techniques. This paper summarizes the state-of-the-art for these technologies; including integrated gasification combined cycle (IGCC) power plants. A concept to use the gasification products as reductant in metallurgical processes is also described. The relevance of technology from power plant designs with post-combustion capture to the processing of off-gas generated in metallurgical facilities is also reviewed.IntroductionGlobalization and international economic growth have led to an increase in energy demand worldwide, and a corresponding increase in greenhouse gas (GHG) emissions. In 2005, 81% of global energy supply came from fossil fuels [1]; and while alternative energy technologies are emerging, it will require many decades to curb society’s fossil fuel dependence. Given the global concern of climate change and its scientific relationship with anthropogenic carbon dioxide (CO2), there is at present great interest in the development of techniques to reduce emissions of CO2. While most of these efforts are related to power generation and energy efficiency, the development of technologies for CO2 capture may offer opportunities in reducing emissions from industrial processes."

Jan 1, 2008

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall's statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949