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By Joyce A. Ober

Strontium occurs commonly in nature, averaging 0.034% of all igneous rock; however, only two minerals, celestite and strontianite, contain strontium in sufficient quantities to make its recovery practical, and these minerals are found in sedimentary rocks. Of the two, only celestite has been found to occur in deposits of sufficient size to make development of mining facilities currently attractive. Celestite, the most common strontium mineral, consists primarily of strontium sulfate (SrSO,). Strontianite, the second most common mineral, consists primarily of strontium carbonate (Sr CO3). Strontianite would be the more useful of the two common minerals because strontium is used most commonly in the carbonate form, but few deposits have been discovered that are suitable for development. The physical properties of strontium ores are listed in [Table 1].

Jan 1, 1994

By Michal Rehor, Vladimir Cablik, Peter Fecko, Tomas Lang

"1. Introduction The North-Bohemian Basin area is known for its largest Czech brown coal deposit. About 50% brown coal reserves have been exploited in the North-Bohemian Basin by the mining company of Severoceske doly, a.s. (North Bohemian Mines, j.s.c.) today. The opencast mining of brown coal naturally led to vast landscape damages. Therefore reclamation work has acquired great significance. The specific feature of Severoceske doly, a.s. mining is the fact that the mining has been realized in two geologically absolutely different localities. This fact demands even rather different methods of reclamations. The main problem at Doly Bilina localities is the occurrence of overburden rocks from the series of rocks of coal seams. These rocks are texturally light but large amounts of coal (cca 5 %) and sulphur (cca below 3 %) which makes the soil reaction extremely acid. If they appear on the surface of the dump, they create a phytotoxic area, reclamation of which requires special methods. Rocks from Doly Nastup Tusimice localities are more suitable to reclamation use, but texturally extremely heavy rocks with large fraction of physical clays appear there that can generate a sterile soil area. Their reclamation requirements are completely different from those on Doly Bilina phytotoxic areas. That is the reason of the application of some non – traditional restoration methods. This report briefly summarises the experience in application of fertilizable soils, power plant stabilizer, power plant ash and aerial sowing of charlock. The results are documented by the monitoring of the physical, mineralogical and pedological parameters of rocks in testing areas.2. Properties of Overburden Rocks in Opencast Mines Bilina and Libous The reclamation work methodology in the North Bohemian Basin is above all determined by the properties of overburden rocks which occur in the top horizon of the reclaimed sites. The research of the rocks reclamation properties dealt with four current mining localities in the central part of the basin. It concerned the Bilina and Libous mines. This chapter states the stratigraphic status properties of these sites with respect to reclamation availability. The total status of the area of interest is shown in the figure No. 1."

Jan 1, 2008

By M. L. Fenger

This report describes a study of the factors which affect medium voltage (661 - 1000 volts) and high voltage (1001 - 7500 volts) trailing cable couplers for use in underground coal mines to connect trailing rabies. Improvements in quality, dependability, and safety of medium and high voltage couplers are presented in the form of requirements for couplers. The results of an investigation of high voltage trailing cable coupler design and of whether trailing cable couplers must have a metallic shell as required by CFR 30 part 75.805 are presented. Conclusions and recommended research programs are included that describe the present situation and future development approaches.

Jan 1, 1978

By J. C. Engel

Recent innovations in mine safety include the use of mercury vapor lamps for mine vehicle illumination. Such lamps, however, extinguish whenever the line voltage at the machine momentarily sags or is interrupted. The lamps must then cool for several minutes before they will restart. By supplying reduced high frequency power to the lamps from an auxiliary source, it is possible to maintain ionization in the arc tubes preventing the lamps from extinguishing. Essentially an auxiliary high frequency supply, the keep alive system provides additional power to the lamps automatically whenever the lamps are in danger of dropping out. The system can also provide the operator with the ability to dim the lamps at will for periods of up to three minutes by simply interrupting the 60 Hz power to the conventional ballasts. Each unit, housed in a steel explosion proof enclosure with a volume of approximately 0.6 ft3, is capable of servicing up to six 175 watt H-39 mercury lamps and two 100 watt H-75 reflector flood lamps. A total of 16 units were produced for the USBM under this contract and its extension.

Jan 1, 1979

By Stephen Gerard Sawyer

This report presents a Fortran IV computer program for the structural analysis of space-frame protective canopies used in underground mines to protect equipment operators from falls of roof, face, or rib. This program entitled CANOPY permits rapid calculation of the elastic strength of a canopy for a variety of static loading conditions. Stresses in, and displacements of each structural member are computed and printed out. Additionally, identification of all members that have commenced yielding, weight of the canopy, total loads on the canopy, and maximum loads that the canopy can sustain elastically are output. Program description, input instructions, program listing, and two example problems are included.

Jan 1, 1972

By Ronald C. Koo

THE effect of grain size on the mechanical properties of the bcc metals has been a subject of intensive theoretical and experimental study.'-l5 Quantitative relationships have been established experimentally between yield stress and grain size and between the ductile-brittle transition temperature and grain size in a number of metals.6"15 Much significance has therefore been attached theoretically to the grain size dependence. In all these experiments, different grain sizes were always achieved by annealing specimens at various temperatures. The implicit assumption was that any change in the dislocation substructure or in the distribution of impurities which might occur simultaneously with the production of various grain sizes had only a negligible effect on the mechanical properties. The validity of this assumption, however, is questionable. transformation in iron-nickel alloys is actually an extraneous phenomenon due to inadvertent compositional changes in the martensite if the heating rate is not sufficiently rapid. This complication can be avoided by up-quenching for the reversal treatment,5 and then the stabilization does not appear. Clearly, the lattice imperfections and strengthening produced by the reverse transformation are not responsible for the marked stabilization which has been observed by other investigators in these alloys. Data will be presented in this note to show that, at least in recrystallized tungsten of commercial purity, the difference in the ductile-brittle transition temperature of specimens annealed at various temperatures is more a result of a variation in the distribution of impurities rather than of the difference in grain size produced by the anneal. Ductile-brittle transition temperatures in tension were determined on powder-metallurgy tungsten specimens recrystallized at various temperatures. Tensile specimens having a gage length of 1.50 in. and gage diam of 0.18 in. were recrystallized at 1450°, 2000°, 2350°, 2550°, 2750°, or 2800" for 30 min in a vacuum furnace at a pressure of 1 x 10"5 mm of Hg and then tested at a constant extension rate of 8 x 10 per sec in an argon atmosphere from 100" to 800". Typical quantitative analyses of impurities are given in the Table. These results show that, within the precision of the analyses, see Table, annealing did not result in any detectable change in the impurity contents of the specimens, nor was there any detectable difference in purity between specimens having large differences in grain size annealed at the same temperatures . The results of the tensile tests yielded three distinct ductile-brittle transition curves approximately 225' apart. As shown in Fig. 1, data of specimens annealed at 1450°C and those of specimens annealed at 2000°C (O) fell on Curve A. Data of specimens annealed at 2350" and 2550°C fell on Curve B, and those of specimens annealed at 2750" and 2800°C fell on Curve C. The decrease in ductility with increase in annealing temperature became so pronounced that one third of the specimens annealed at 2750" and two thirds of the specimens

Jan 1, 1963

By J. E. Bevan

Once mining compromises the stability of a rock mass, the dangerous task of roof bolting begins. Many attempts have been made to automate this process, but there are still many refinements that need to be made. In the past, roof bolting modules were designed around the abilities of a human operator. Currently, researchers are taking a new approach that focuses on designing modules that can utilize bolting methods that are easily automated. A non-rotating anchor that is locked into position by a linear force (as opposed to a rotational force) was designed by researchers at the U.S. Bureau of Mines. Once the bolt is secured in the bolt-hole by the anchor, the bolt is tensioned and a collet is used to secure the other end of the bolt. This process replaces the traditional bolt-nut fastening method. This program is part of an effort at the U.S. Bureau of Mines to automate the coal mining process.

Jan 1, 1994

Discussion of the paper of F. C. LANGENBERG and R. G. WEBBER, presented at the New York meeting, February, 1915, and printed in Bulletin No. 98, February, 1915, pp. 291 to 300. HENRY M. HOWE, Bedford Hills, N. Y.-The results here given are of great interest and are welcome as forming another rivet to increase the stability of our present theories of the constitution and properties of steel. The important discovery is that the hysteresis increases with the fineness of the structure, that is to say with the extent of contact between the particles of ferrite and cementite. All of the specimens except No. 4 consist of ferrite and cementite of different degrees of intimacy of admixture. If hysteresis represents something akin to surface friction, which retards the rotation of the ferrite on the application and release of the magnetizing force, then it is only natural that it should increase as it does with the intimacy of admixture, because it is at the surface of contact of a given particle of ferrite with the neighboring particles of cementite that this friction is to be expected, and of course the extent of surface must in¬crease with the intimacy of admixture. The somewhat greater hardness of specimen 4 than of the others may perhaps he referred to the principle discussed in my paper, Why Does Lag Increase with the Temperature from Which Cooling Starts?' The furnace-cooled specimens were cooled so slowly that the influence of the initial temperature of heating is effaced. But in the air-cooled specimens we have the suggestion that the high temperature, 1,000°, from which the cooling of No. 4 started has prevented the completion of the transformation, with the result that the metal is slightly harder than any of the others. The difference is not to be explained by difference in the fineness of structure, because the whole range of fineness from No. 1 to No. 6 is accompanied by no change in hardness, the only change being an appreciable increase of hardness following the air cooling from 1,000°.

Jan 5, 1915

By R. M. Brick, R. G. Treuting

DESPITE the basic importance of slip in the plastic deformation of metals, and the considerable experimental investigation, thought, and speculation that have been devoted to the fundamental nature of these processes, surprisingly few data have been reported regarding the microscopic appear- [ ] ance and distribution of slip lines,[$] the external manifestation of the slip process. Photographs hitherto reproduced in the literature are in general at low or unspecified magnifications with no correlation to the prior shear. A single-crystal cylindrical tensile specimen of alpha brass about ½ in. in diameter, one of many previously prepared by H. L. Burghoff,1 was available for study. A plane about 3/16 in. wide, parallel to the specimen axis and normal to the plane containing the slip direction and the specimen axis, was ground and metallographically polished along the entire 5-in. gauge length. Heavy etching produced a surface free of both scratches and flow. The specimen was strained in tension until slip markings first became visible on the polished surface (Figs. I and 2). Restressing the crystal caused additional markings to appear at an initially lower [ ] stress than previously was required. Stretching the specimen to produce a dense concentration of slip lines caused such variations in level in the polished surface (normal to the slip direction) that microscopic study at higher magnifications became impossible. After annealing 15 hr. at 850°C., the specimen recrystallized to form two grains with a boundary approximately normal to the specimen axis and about midway along its length. Each was X-rayed, and two planes were again polished along the length of the specimen, in this case each parallel to the slip direction in one of the two crystals. A light longitudinal scratch parallel to the specimen axis was drawn down the center of each plane. A Huggenberger extensometer was attached to the crystal A, whose slip plane would have the higher resolved shear stress of the two, and the specimen was again strained in tension.

Jan 1, 1941

By Richard L. Fowler

[Study and development of sensing techniques and sensors were performed to aid shuttle car drivers in detecting, obstacles and in guiding the car along the face haulage route. Microwave, acoustic, and optical sensing techniques were considered as part of the feasibility study for obstacle detection. Various guidance techniques, including wire-following and rib-ranging were investigated. Active optical sensing was selected for obstacle detection to obtain the bear overage and sharp angular cutoff characteristics required within the packaging limitations defined by the shuttle car configuration. Rib-ranging guidance was selected to achieve completely self-contained shuttle car system which responds to the mine geometry without need for wires, stripes, or other path defining devices. Extensive hybrid computer simulation runs were performed to valuate various guidance techniques during the feasibility study. Subsequent simulation rues were performed to establish parameter values for the rib-ranging guidance system. The obstacle detection and guidance system was designed, fabricated and installed on a standard shuttle car. The system satisfied all applicable permissibility requirements of Schedule 2G. An experimental permit was issued to Bendix for operation in an underground coal mine. System evaluation tests were performed first above ground at the Bendix Research Laboratories. The simulation model was validated by these runs. Final testing wan performed underground in an operating mine with an experienced shuttle car driver. All sensors successfully demonstrated Chi predicted performance capability during underground face haulage tests. Dust did not Impair system performance and lens cleaning was not required during working shifts. Further development is required to achieve the desired obstacle detection performance Closed loop steering control with manual override is recommended o: mended for the lateral guidance e system. The guidance system should be an invaluable aid to low-coal shuttle car drivers where continuous mining machines are utilized.]

Jan 1, 1973

By Sam Yao, Ali Naeem, Sara Barrett

Brooklyn Basin Project is a multi-billion-dollar development of the former Port of Oakland 9th Avenue Terminal located along the Oakland Estuary of California. A centerpiece of the development is the 10-acre shoreline park which will be built on a 1,200 ft long by 225 ft wide historic wharf. The wharf was built in the 1930’s on concrete and timber piles with a flat concrete slab. Prior to constructing the wharf, a rock dike was placed to protect the shoreline. The presence of the rock dike increased the hazards from lateral spreading of the underlying bay mud and non-ductile shear failure of piles driven through the dike. To open the park to the public, the wharf required a seismic retrofit in compliance with the California Building Code. The paper presents the results and conclusions of the following topics: • Structural condition assessment and repair strategies for the existing wharf deck, piles and jackets • Application of the California Building Code (CBC Ch31F) for the performance-based seismic evaluation of existing piers and wharves • Nonlinear pushover analysis of the wharf including the combination of inertial and kinematic effects • Impact of rock dike on lateral spreading and kinematic effects and the significance of existing piles in stabilizing the lateral spreading of the rock dike • Retrofit strategies for the wharf to meet the required seismic performance requirements per the California Building Code and reduce the demands on existing piles which were driven through the rock dike INTRODUCTION The 65-acre Brooklyn Basin Development project is located in Oakland, California. The project consists of 3,100 housing units, 200,000 sq. ft of retail and commercial space, along with various parks and public access improvements along the Oakland Estuary. A centerpiece of the development is the 10-acre Shoreline Park which will be built on a 1,200 ft long by 225 ft wide historic wharf. The wharf was built in the 1930’s on concrete and timber piles with a flat concrete slab. As shown in Figure 1, the wharf deck and piles support the 9th Avenue Terminal Building.

Jan 1, 2018

Corrosion affects the performance of rock support and reinforcement at various underground mines, including the George Fisher Mine, where recent studies showed that this risk to mining operations is generally not well understood. Corrosion reduces the capacity and life expectancy of ground support and generally is undetected unless the traditional destructive pull out test is employed to detect defect bolts. Where it is still acknowledged that the pull out test has still an important role to play in determining critical bond lengths for static and quasi static ground support designs, it does not provide an underground operation with any reassurance regarding its bolt's integrity, which has been compromised by in situ aggressive conditions. Non-destructive rock reinforcement calibration testing on single and twin strand cable bolts, rebar bolts and friction bolts at the George Fisher Mine enabled the testing team to detect bolts with compromised integrity in one area of the mine. The non-destructive rock reinforcement integrity testing conducted uses a complex 'Stress Wave Analysis' package based on the processing of clear seismic signals imparted into the rock reinforcement element that is being tested. The seismic signals are processed by 'Fourier Transform' into various criteria which can be used to produce models of the element such as mechanical admittance, frequency spectra and velocity which are all being used in the final modelling of the rock reinforcement element under analysis. This paper highlights the enormous potential to effectively manage the geotechnical risk that corrosion presents for an underground mining operation.

Nov 25, 2010

By Maxwell Adams

Considerable interest has recently been developed in sage-brush oil because of its possible utilization as a flotation agent in the mining industry. A list of some of its physical properties, together with the method used in its extraction, may prove of interest at this time. Something over a year ago, a study of the essential oils in desert plants was begun in the Chemical Laboratory of the University of Nevada. None of the oils so far studied possess properties of special interest to engineers, except the oil of sage, Artemisia tridentata, which has exceptional power as a flotation agent. This plant, known as common sage brush, also called black sage, is widely distributed over the semi-arid West, being found quite generally on most of the dry plains and mountains west of Missouri. The method of extracting the oil followed in these experiments is very simple. The leaves, twigs and small branches are placed in an airtight drum, having a capacity of about 27 cu. ft. Steam is admitted through a number of ,small openings at the bottom of the retort, and the pressure maintained at 20 to 25 lb. per sq. in. for 3 hr. The escape of the steam from the retort is regulated by allowing it to pass through a stop-cock into a condenser. The water in the receiver is drawn off from time to time and the oil, which is insoluble and floats upon the water, is thus collected. At the end of 2 hr. most of the oil has been driven out, though traces continue to come over for a much longer time. By raising the pressure, the time required could probably be shortened and the yield increased, but the lack of laboratory equipment has prevented the carrying out of this experiment. The stock wood, bark and branches contain no oil, the distribution of the oil being limited to the leaves and young shoots. There is a seasonal variation in the amount of oil contained. Samples collected on different dates gave the following amount of oil: May 1, 0.42 per cent.; May 27, 0.6 per cent.; June 30, 0.72 per cent.; Aug. 1, 0.9 per cent.; Sept. 10, 1.0 per cent. The increase appears fairly constant from early spring, when the leaves first appear, until light frosts occur in the autumn. When the plant is air-dried there is some loss of oil, as the following data will show: Two 100-lb. samples were collected at the same time. One was distilled when green; the other was air dried for

Jan 1, 1917

By D. Large, M. H. Davies, B. Driedrichs, U. Matzander

Synthesis report on a project carried out under the EC-funded BRITE-EURAM programme. A prototype high-resolution electromagnetic system, based on the theory of controlled-source magnetotellurics, was developed. The electrical source field is fed into the earth by dipoles at preselected frequencies and a multi-channel receiver measures five electric and three orthogonal magnetic fields. Suitable mapping algorithms and spatial filters are applied to the data and a new technique permits calibration during measurement. The system was field tested over a blind orebody, at 250-550 m depth, in the Aguas Tenidas area of the Iberian Pyrite Belt. Ten lines totalling 12 000 m of profile length were completed in seven days and the orebody was identified. Tests in the Irish Midlands suffered from strong electromagnetic interference of cultural origin

Jun 21, 1905

By Mick O'Meara

Metal Organic Chemical Vapour Deposition (MOCVD) is used in the production of computer circuit boards and metal shapes in nickel, gold, copper, cobalt, etc. All varieties of .MOCVD use the decomposition of a vapour of organometallic compounds to produce different forms of ultra-pure metals, or alloys. CVD Manufacturing's proprietary MOCVD process has been adapted and developed to produce commercially ultra-pure metal shapes, metal powders, and metal foams. Therefore, it is a purification process. The typical process has three steps. First, a volatile metal organic compound is produced from volumetrically contaminated metals, metal oxides, etc. Typical feed materials are metal powders, ores, concentrates, or a slurry of metals and contaminants. Secondly, the volatile. metal organic compound is purified by fractional distillation. Thirdly, the purified metal organic compound is decomposed into different forms of ultra-pure metals, such as net shapes, powders, or metal foams. A mixture of metals can be purified either by the selective production of volatile materials, or a separation can be achieved during the second step, in the fractional distillation stage. The purification and recycling of metals by the MOCVD process will be discussed, particularly with regard to nickel, aluminum, gold, the platinum group and other metals.

Jan 1, 2000

By P. Oliveira, A. Peres, A. Silva

"The decrease in iron content and increase in contaminants grade, associated with greater participation of compact and semi-compact materials, has impacted the recovery of a mechanical cells flotation circuit in the Iron Quadrangle, Brazil. The recovery decrease in the flotation stage motivated the current conventional flotation circuit reevaluation seeking alternatives to restore the recovery, without affecting the final concentrate quality parameters, with low investment. Sampling, chemical characterization of samples, bench scale flotation experiments, and mass balances were conducted. Analysis of the results showed opportunities to improve the circuit performance. The stages prior to the flotation circuit changes were: rougher, cleaner, recleaner and scavenger. In the previous configuration, recleaner was operated as cleaner scavenger and the iron grade in the scavenger concentrate was 23%, representing 38% of the new feed. After the circuit change, the circulating load was reduced from 38% to 15% and the iron content was upgraded to 42%, resulting in increased residence time. The iron content in the global tailings of the concentrator was decreased from 10.9% (year of 2013 average) to 10.2%, representing gains in both mass and metallurgical recoveries.INTRODUCTIONRegarding plant practice, the year 1972 represents a landmark for the concentration of iron ores in Brazil. VALE started up 28 units of WHIMS (wet high intensity magnetic separators) at the Cauê plant in Itabira, each one producing 1x106 t/year of concentrate. Later 17 WHIMS machines were commissioned at Conceição. During the 80’s decade of last century, changes in the ROM required the addition of a cleaner flotation stage to decrease the silica content in the pellet feed.The first company to use reverse cationic flotation as the only concentration operation of iron ore was SAMARCO (start up in 1977). Since 2015 flotation has been utilized at VALE in Itabira as major concentration process, magnetic separation acting as scavenger stage.The Jones matrix type WHIMS were manufactured for decades under patent by KHD Humboldt Wedag. After the expiration of the Jones patent, Eriez Magnetics took the world leadership regarding WHIMS manufacturing. The Brazilian branch of Eriez is Inbras. Based on plant practice experience at the Fabrica concentrator, the Brazilian company Gaustec was established (RIBEIRO and RIBEIRO, 2010) and is now present in different countries. The mega sized WHIMS GHX-1400 (18.000 Gauss, gaps smaller than 1.5 mm) were developed to face the challenge of huge throughput required by iron ore processing (Ribeiro et al, 2017)."

Jan 1, 2018

By Nathália M. Campelo, Alexandre P. Umpierre, Fabricio Machado

"The present work illustrates the reuse of macoporous anion exchange resins (employed for decolorization of solutions of organic substances such as sugar syrup and fruit juice concentrates in the soft-drink and beverages industries), based on crosslinked styrene-divinyl benzene copolymer (Sty-DVB) to the production of polymeric materials. Micro-sized particles of polystyrene and poly(styrene-ethyl acrylate) were obtained by mass-suspension sequential polymerization process. The proposed experimental technique was able to perform proper dispersion of the Sty-DVB in the thermoplastic matrix of polystyrene. The final material showed good thermal stability, showing degradation profile similar to that observed for the pure polystyrene. It was also noticed that polymer particles with spherical morphology can be obtained. In addition, the incorporation of ethyl acrylate monomer into the polystyrene chains minimizes the undesirable effect of fracture in polymeric particles, improving the mechanical and end-use properties of the final polymeric composite.IntroductionIn face of the industrial development, the development of techniques that are safer and less aggressive to the environment has become one of the main challenges in the industrial field. In this scenario, processes more efficient in terms of energy and raw materials can be regarded as an important requirement to minimize the production of waste. The reuse of waste becomes an attractive alternative for most industries engaged with sustainable and economic development.In this context, both the primary and the secondary mechanical recycling are potentially attractive because they allow for reuse of polymeric waste (post-industrial or post-consumer) as a source of raw material in the supply chain by using traditional methods of processing, so that the final materials can exhibit characteristics similar or superior to those observed in the virgins polymeric materials, considered as a starting product in the process of reuse of plastics [1-3]."

Jan 1, 2012

By P. H. Botha

An account is given of the procedures used by the South African Iron and Steel Industrial Corporation (Iscor) for tests on the flotation of coal fines, and some of the beneficiation problems encountered with coal from Durnacol, Grootegeluk, and the Soutpansberg area are discussed. These, and other South African coals differ from overseas coals in that they contain a high percentage of fixed ash, which means that they have to be crushed more finely for liberation and that they then contain more fine material (smaller than 0,84 mm). In addition, the coal from the three areas mentioned occurs in fine layers and seams, and contains many intergrown particles.

Jan 1, 1980

By B. Loveday, G. W. Delaney, S. Cummins

"Applying DEM to prediction of tumbling mill performance is challenging because several different modes of breakage are active in the process. As our knowledge of breakage and computational capacity improve, it is worth revisiting previous simulation tasks which did not produce a satisfactorily realistic description of a measured process. At SAG 2006, we reported the simulated and measured outcomes of treating a well characterised ore in a 1.2 m diameter mill. This well instrumented, pilot scale mill at the University of KwaZulu-Natal has been combined with some new approaches to ore testing to allow different modes of breakage to be tested. The mill design allows the rate of generation of fine material to be measured in close to real time for autogenous and SAG mill charges. The updated simulation model estimates mass loss with particle evolution and embeds the cumulative damage and breakage.The simulated results are compared with the measured results. Issues such as relating modelling inputs to particle breakage characterisation data and the accuracy of the predictions of the models are discussed."

Jan 1, 2012

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