Search Documents

By W P. Darcey

Jabiru Metals completed a feasibility study on the Jaguar Base Metal Project in July 2005. The study was based on conventional truck haulage via a decline. Conveyor haulage was considered but not in sufficient detail to provide a meaningful comparison. The current study investigates the cost and productivity of alternative ore transport systems for the Jaguar project. The options considered are conventional underground truck, conveyor, road train, rigid frame truck, monorail haulage and shaft hoisting. Shaft hoisting was not considered in detail due to the high capital outlay for such a relatively short mine life of less than six years. This study goes beyond the common approach of evaluating haulage systems in isolation; it includes development costs, timing of ore production and costs associated with mine services as well as administration and milling costs. The results of this study indicate that the best haulage option for the Jaguar project is conventional truck using the Hitachi AH400 trucks. The net present value (NPV) for this option is A$8.13 million higher than the next best option namely the Kiruna E635 electric truck. The conveyor option has the lowest operating cost per tonne of ore but the longer development time negatively impacts on its NPV. The monorail option is considered impractical due to the number and length of trains required to achieve production targets.

Mar 21, 2011

By Richard E. Sabaski

The demand placed on the mining industry in the past 15 years for increased production, coupled with lower grade ore and higher cost capital, has resulted in a noticeable increase in grinding mill sizes. The pressure to increase mill size continues. During the mid sixty's and early seventy's, ?larger? conventional ball mills were in the range of 13 - 16-1/2 f t. diameter (4 - 5 m) increasing by the mid 70's to 18 ft. (5.5 m) diameter. At the same time, autogenous mills expanded from 24 - 32 ft. (7.3 - 9.1 m) to the present 34 and 36 ft. (10.b and 11.0 m) diameters. These size pioneers of 16-1/2, 18, and 36 ft. diameter mills from Allis-Chalmers have been free from structural problems, because they were analyzed, modeled, designed, and field tested to meet the challenge.

Jan 1, 1981

By Ke Yang

"Drilled shafts are typically used to support structures subjected to large moments at the shaft head. The large moment can produce push and pull forces on the two sides of a drilled shaft. Consequently, the applied moment is partially resisted by the push-pull moment resistance induced from the vertical side shears. This type of push-pull resistance has not been fully recognized in most design and analysis methods. In this paper, a 30 finite element model for a drilled shaft subjected to lateral load and moment is presented and is validated against two field lateral load tests. Based on the 30 finite element model, a parametric study is carried out. It shows that the push-pull moment can resist 18-35% of the applied moment. The parametric study also shows that the push-pull resistance varies linearly with loading eccentricity when the eccentricity is less than the shaft embedment length. A method to estimate the push-pull resistance is proposed based on the results of the parametric study. Then, a new method for lateral capacity prediction is proposed to account for the push-pull resistance. The base shear resistance is significant for short drilled shafts; therefore it is also included in the proposed method. A case study on four lateral load field tests illustrates that the new method could improve the accuracy of lateral capacity prediction when compared with the traditional Broms method.INTRODUCTIONDrilled shafts are typically used to support a variety of structures subjected to large moments. Sound walls, highway signs, traffic signals, high-rise buildings, electrical transmission towers, and bridge piers are examples of cases where lateral loads with large eccentricity would result in high overturning moments on foundations.Current analysis methods for capacity predictions (Broms, 1964a and 1964b; Brinch Hansen, 1961) or deflection predictions (Reese, et al. 197 4) of laterally loaded drilled shafts are based on the lateral resistance of soils and rocks. However, O'Neill pointed out that moments can be partially resisted through the push-pull resistance provided by the vertical side shears due to the rotation of the pile (Reese, 1997)."

Jan 1, 2005

By G. M. Ritcey, A. W. Ashbrook, E. G. Joe

Solvent-in-pulp extraction of uranium from acid leach slurries of flotation concentrates is described. Solvent extraction was carried out in a 10 in. diam pulsed-plate column. The extractant was a 0.1 M tertiary amine (General Mills Alamine 336) in a kerosene diluent containing isodecanol as an emulsion suppressor and third phase inhibitor. In pilot plant operation at the Beaverlodge mill of Eldorado Mining and Refining, Ltd., slurry feeds containing up to 35% solids were processed at a throughput rate of 13.5 tpd of dry feed. Uranium extraction obtained was as high as 98%. Amine losses to the raffinate were approximately 0.07 lb amine per ton of original dry feed. The Beaverlodge Mill of Eldorado Mining and Refining employs a carbonate leach for the extraction of uranium from the ore.',' Prior to carbonate leaching sulphides are removed by flotation to reduce reagent consumption. This flotation concentrate containing some uranium is then leached with sulfuric acid, filtered, and the uranium precipitated with magnesium hydroxide. The precipitate is then returned to the carbonate leach circuit. Although the tonnage of flotation concentrate treated by acid leaching is low, reagent costs are relatively high. Also maintenance costs on the acid leach filtration circuit were beginning to show significant increases. The choice of solvent extraction-in-pulp as an alternative to the present circuit was influenced by the following factors: 1) elimination of acid pulp filtration, 2) increase in overall recovery because of soluble loss elimination, 3) reduction of reagent cost (mill sodium carbonate solutions are used as strip), and 4) production of higher purity precipitate at the mill site. Because a solvent-in-pulp process would be difficult to test on a bench-scale, the Eldorado experience in the use of pulse columns,3-5 mixer-settlers,6 and solvent-in-pulp operations in particular7 was applied directly to the initial pilot plant carried out during the summer of 1965 and followed by the second pilot plant in 1966. The latter work, which is presented in this paper, determined the following factors for anticipated scale-up to plant production: 1) overall uranium recovery by this process, 2) tonnage throughput expected, and 3) solvent losses anticipated for the full-scale plant. The equipment used consisted of a 10 in. diam extraction pulse column and three mixer-settlers for scrubbing, stripping, and acid equilibration. All equipment was designed by Eldorado and much of the pilot plant was built at the mill site. PROCESS CHEMISTRY Feed to the acid leach plant consists of a sulphide flotation1,2 concentrate containing mainly pyrite, uranium and graphite, with a particle size of 90%

Jan 1, 1968

By Nicholas Tabor, Norbert Fuegenschuh, Richard Taylor, Jean-Marc Wehrli

The Plymouth Tunnel forms part of the 16-mile long route of the Purple Line Light Rail Project promoted by the Maryland Transit Administration. The tunnel is approximately 1,220 feet in length with a shallow vertical alignment located beneath a residential area. Challenging mixed ground conditions included surficial soils, decomposed Saprolite, and highly weathered to fresh rock requiring the use of the Sequential Excavation Method (SEM) for construction. This paper discusses innovative approaches implemented during construction as well as challenges faced during planning and installation of a spray-applied permanent concrete liner.

Jun 13, 2021

By M. J. Russell, W. E. Stephens, D. B. Mohamad, A. B. MacKenzie

Redox front processes in rocks are important in the context of both radioactive waste disposal and the development of orebodies. Results are presented from a study of the distribution of uranium and thorium and the natural decay series equilibrium about redox fronts in a granite at the Criffel pluton and Craignair quarry, Dalbeattie in southwest Scotland. The results are considered in the context of large scale uranium aqueous transport in the region and compared with those from a previous study of highly developed redox fronts at Pocos de Caldas, Brazil. Results show that the Criffel pluton has experienced a recent and rapid removal of uranium from the uppermost section of the granite whereas thorium has remained relatively immobile. The radium and uranium distributions indicate that diffusion processes probably control the distribution of radionuclides about the front. These processes are similar to those observed at Pocos de Caldas. The trends of concentration and activity ratio about the Dalbeattie redox front are less pronounced than those at Pocos de Caldas owing to the shorter time available for the process and the lower intensity of weathering at Dalbeattie.

Jan 12, 1992

By D. Harrington

We Americans fondly believe that ours is the greatest , most progressive and most civilized country in the world , but the cold statistical facts reveal that we apparently have little appreciation for the lives of those whose efforts of various kinds give us whatever greatness we have . The latest available statistics indicate that the annual death rate per 100,000 persons , from accidents is nearly 80 , or far higher than that of any other country in the world ; it is more than double the rate in Denmark , Belgium, Netherlands , France , Sweden , Italy , Ireland , Germany , Norway, and Austria; it is practically double the rate in England and Wales and in Japan , and is from 25 to 60 per cent higher than the corresponding rate in Scotland , New Zealand , Australia, Switzerland , and Canada . And added to this is the fact that of the main industries of the United States mining has by far the worst accident record , viewed from either the frequency or the severity basis . The National Safety Council's latest figures for 27 of the country's main industries give mining the highest or worst accident frequency rate, 74.43 in 1929 ; meat packing comes next with 55.94 , and construction third with 50.41 . In accident severity in 1929 mining also was the worst offender , with a rate of 9.99 ; quarrying is second with 6.11 , and construction third with 4.62 . Metal mining's frequency rate in 1929 was 52.16 , as against 69.25 for bituminous coal mining ,99.68 for anthracite mining, and 74.43 for the entire mining industry ; accident severity for metal mining in 1929 was 5.99 , as against 11.69 for bituminous coal mining , 10.87 for anthracite mining , and 9.99 for the mining industry as a whole . Although this figure indicated that metal mining is on a much safer plane than either bituminous or anthracite coal mining, the frequency rate of 52.16 for metal mining was higher in 1929 than the frequency rate of all but one of the other 26 industries about which data are available ; the metal mining severity rate of 5.99 , while much better

Mar 1, 1932

By E Garbarino, P Molina, V Badino

Given the ever increasing quantity of construction and demolition waste (C&DW), one of the most challenging issues presently facing policymakers and public administrators in Italy concerns how to organise and manage collection and recycling and to understand whether and to what extent recycled aggregate can complement natural building aggregates in a sustainable supply mix (SSM). The paper presents the results of a research aimed at analysing energy and environmental implications of the C&DW recycling chain in the administrative territory of Provincia di Torino in northern Italy. In respect of a population of about 2.25 million inhabitants, the annual production of C&DW in the area under study is 1.8 Mt. A combined geographical information system (GIS) and Life Cycle Assessment (LCA) model was developed, paying attention to the geographical location, land use, transportation network and avoided landfill: crucial issues for sustainable planning and management. Around 90 recycling plants were classified according to the size, typology (stationary, semi-mobile and mobile) and physical- mechanical characteristics of the recycled aggregate. Under different assumptions relevant to the delivery distance, and considering the typology and grade of recycled aggregate, as well as local availability of natural aggregates, it was possible to evaluate the geographical coverage of aggregates demand and to use LCA in order to identify and quantify energy and environmental indicators.

Jan 1, 2009

By B Mennie, R Poedjono, G Coad

PT Freeport Indonesia operates a large copper and gold mining operation near Tembagapura, Papua (formerly, Irian Jaya), Indonesia. This is a remote location with its own set of unique operational characteristics. The mining and concentrating operations typically produce a concentrate containing 2500 tpd of copper and 6000 oz of gold per day from the combined mining of a 45 000 tpd (ore) block cave operation (DOZ Mine) and a 190 000 tpd (ore) open pit mining operation (Grasberg Open Pit). The Grasberg Open Pit mine will be exhausted in 2015 at which time FreeportÆs operations will entirely underground mining methods. The Common Infrastructure Project (CIP) incorporates the elements required for the shift to underground mining at a production rate approaching 200 000 tpd. The AB Adit portion of the CIP will provide deep level access to the Grasberg Block Cave (below the Open Pit), Kucing Liar, Big Gossan, and the Mill Level Zone orebodies. Commencement of the project was September 2003. The Grasberg Block Cave is planned to start production in 2014. This paper provides details on the project scope, innovative contractual framework, advancement of mining methods throughout the life of the operation, equipment selection, manpower selection, training, geological, and socio-political conditions related to the project.

Jan 1, 2005

This publication summarizes, for potential contractors and all other interested parties, the research and development of in-house and contract projects programmed by the Bureau of Mines for fiscal year 1983 (October 1, 1982-September 30, 1983) under its Health and Safety Technology program. The objective of these projects is to provide an ordered and sequenced series of advance toward the Bureau's overall goal of providing the systems technology required to create a more healthful and safer working environment for the Nation's mining and minerals processing workers.

Jan 1, 1982

By W. A. Haley

This paper discusses how a large wheel loader should be equipped, with particular attention paid to tires and tread life, and describes the several steps that can be taken to provide favorable working conditions and reduce over-all costs. A comparison is then made of wheel loader production and costs vs those of power shovels, and the present and possible future applications of the wheel loader are outlined.

Jan 1, 1969

By D. K. DeForest

The olfactory system (sense of smell) is crucial to the ability of fish to avoid predators, recognize kin, and synchronize reproduction (Baldwin et al. 2003). Copper (Cu) has been shown to impair olfaction in juvenile freshwater life stages of salmonids (including Pacific salmon and trout) in some laboratory experiments; and in the United States, public concerns have been expressed that current regulatory criteria for Cu in fresh water are not adequately protective of olfactory function in salmonids (e.g., OSU 2007; Pearson 2007). These concerns have largely been raised because some Cu concentrations that have caused olfactory impairment in salmonids in the laboratory are less than Cu concentrations that have been shown to reduce salmonid survival, growth, or reproduction (the effects endpoints that are typically considered in deriving ambient water quality criteria). However, two important and interrelated points that must be considered: (1) freshwater Cu criteria are "driven" by the sensitivities of several invertebrate species that are more sensitive than the olfactory impairment threshold in salmonids when (2) the influence of water chemistry on Cu bioavailability is properly considered in deriving Cu criteria. Bioavailability refers to the ability of various chemical forms of Cu to interact with receptors on the surface(s) of organisms and thus directly cause toxicity or uptake by the organisms. The toxicity of Cu and other metals to aquatic organisms is a function of water chemistry. For example, acute Cu toxicity in fresh water generally decreases as pH, water hardness (Ca2+ and Mg2+), alkalinity, and dissolved organic carbon (DOC) concentrations increase (Meyer et al. 2007). The U.S. Environmental Protection Agency (USEPA) has recommended hardness-based freshwater aquatic life criteria for Cu and other metals since the 1980s (e.g., USEPA 1985); and hardness-based metals criteria decrease (i.e., become more restrictive) as water hardness decreases. More recently, the USEPA has recommended freshwater aquatic life criteria for Cu based on the biotic ligand model (BLM; USEPA 2007), which accounts for the influence of multiple water chemistry parameters, including DOC, pH, alkalinity, Ca2+, Mg2+, and several other cations and anions. The BLM-based Cu criteria generally decrease as DOC concentration, pH, alkalinity, and water hardness decrease. Because DOC has a stronger influence on Cu bioavailability than water hardness, hardness-based and BLM-based Cu criteria can differ considerably. For example, in water that has low DOC and high hardness, the hardness-based Cu criterion would be relatively high (because it is driven by the high hardness) but the BLM-based Cu criterion would be relatively low (because it is driven by the low DOC). Thus, any evaluation of the protectiveness of Cu criteria against a given effect, such as olfactory impairment, must properly account for the chemistry of the exposure water. Meyer et al. (2013) compiled data on Cu-induced olfactory impairment and olfactory-induced behavioral effects from tests in which BLM parameters were measured. They demonstrated that the USEPA's BLM-based freshwater life criteria for Cu are protective against olfactory impairment, because it adequately accounts for water chemistry (whereas the USEPA's hardness-based Cu criteria are not consistently protective). Olfactory impairment by Cu is now receiving increased attention in Canada and Europe (e.g., Wall 2013; Stang 2013). Accordingly, in this paper we have expanded the analysis of Meyer et al. (2013) to consider copper guidelines from various other countries and whether these guidelines are protective against olfactory impairment.

Feb 23, 2014

By Konner Horton, Adam L. Bedell, Don Del Nero, Brian Jones

"The City of Atlanta’s Water Supply Program Tunnel project includes a 7,315-m (24,000-ft) long, 4-m (13-ft) diameter, hard rock tunnel. A complex aspect of the project involves connecting five, blind bore shafts to the tunnel in a location close to current drinking water reservoirs. During the supplemental geotechnical investigation following the initial contract award, results from additional borehole geophysics were reviewed. Unfavorably oriented fracture sets forced a change in the original pre-excavation grouting program designed for that site. Real-time grout monitoring and geophysical data were compared to provide assurance that the program, as designed, correlated with the in situ ground conditions. Following grouting, results were modeled, and all grouting data were reviewed to determine if grouting was complete.Project backgroundThe current water supply system operated by the city of Atlanta’s Department of Watershed Management (DWM) consists of four, aged, raw-water pipelines, one of which dates back to 1893. Based on previous assessments completed by the DWM, the entire water supply system is at, or will soon reach, its recommended useful life. As such, the city acquired the Bellwood Quarry in 2006 with the intention to create a water storage facility with a volume of approximately 9.1 billion L (2.4 billion gal) to serve approximately 1.2 million people.The project location is shown in Fig. 1, which is generally in the northwest part of downtown Atlanta, GA. The overall project has been divided into two phases. The Phase 1 project connects the quarry and the Hemphill Water Treatment Plant (HWTP), and the Phase 1 Extension project connects the HWTP to the Chattahoochee Water Treatment Plant (CWTP) and the Chattahoochee River. A 7,315- m (24,000-ft) tunnel with a finished diameter of 3 m (10 ft) connects all three elements. The HWTP location is also where the city’s two most proximate drinking water reservoirs are located."

Jan 9, 2018

By I. Iwasaki

Platinum group elements (PGE) are often found in arsenide and sulfarsenide minerals as inclusions in copper-nickel bearing gabbroic rocks. Major losses of platinum in flotation have been attributed to the poor recoveries of the arsenic minerals. Flotation characteristics of a synthetic nickel arsenide and arsenopyrite were studied through rest potential and oxidation rate determinations, surface analyses, and micro-and batch-flotation tests. The use of nitrogen during grinding and flotation together with copper activation improved the PGE recoveries from Duluth Complex ores. The flotation behaviors of the sulfarsenide minerals are still unresolved. The role that electrochemical interactions play among arsenides, sulfarsenides, sulfides and grinding media on their f10atabilities is discussed.

Jan 1, 1988

By M. L. Apel

A conceptual approach to the bioremediation of uranium mill tailings (UMT) is presented., This approach focuses on, biosorption to remediate the. effluent solution and bioleaching remediate the. solid fraction. Comparative biosorption studies were performed with synthetic single metal solutions using a commercially available biopolymer. The maximum rate of metal sorption by calcium alginate was found to be 5.43, 6,39, 6.48, and 9.74 mg dm-3 min-1 for U022*, Ba2+, Cd2+ and Zn2+, respectively. Activation energy (AEa) for barium uptake by calcium alginate beads was determined to be 11.5 kJ, indicating a diffusion controlled reaction mechanism. Thermodynamic values (AG+ AH+ and ASt) of the metal-alginate activated complex, as reported in the literature, were found to be in agreement with those calculated from this research. Results show that this biopolymer can be effectively applied in the removal of select metals prevalent in uranium mill tailing effluents and associated waste streams.

Jan 1, 1991

Since it was first introduced, the Coal Mine Roof Rating (CMRR) has been widely accepted as a tool for geologic characterization and mine planning. This paper discusses the application of the CMRR to another practical ground control problem. Extended cuts (cuts greater than 6 m (20 ft) in length) are commonly used with remote control continuous miners. Extended cuts can greatly increase productivity, but they have been associated with a number of fatal roof fall accidents. When extended cuts are attempted in weak roof, the roof may collapse before it can be bolted, causing hazardous conditions. Until now, it has not been possible to predict where conditions may not be suitable for extended cuts. In this study, data on the CMRR and extended cut experience were collected at 36 mines in 7 states. It was found that when the CMRR was greater than 55, deep cuts were routine in nearly every case. When the CMRR was less than 37, extended cuts were almost never taken. Between 38 and 55, extended cuts were feasible sometimes but not others. The data also shows that extended cuts are less likely to be stable if either the entry span or the depth of cover increases.

Jan 1, 1998

By Henry J. Schwellenbach

The New York Trap Rock Corporation has four plants located along the Hudson River, all within 70 miles of New York City. The company produces crushed stone for use as construction aggregate, with a total annual production amounting to 6 million tons. The crushed stone is moved to markets in metropolitan New York, New Jersey and Long island areas by water transportation. There are daily deliveries of approximately 35 scowloads to the market area. Its customers are contractors with ready-mixed concrete and asphalt plants located on the water, where the aggregate is unloaded for its ultimate use. For a number of years capital equipment was replaced only when the current operating machinery was no longer serviceable, or when' a need was apparent for a different type of equipment. There was no particular regard for efficiency or for operating and maintenance costs. Such lack of system often resulted in the emergency purchase of equipment which was later found to be unsuitable for the job. A few years ago it became apparent that a systematic procedure was necessary. After evaluation of several systems, an individualized plan was evolved from the basic pattern developed by the Machinery and Allied Products Institute. The system adopted by New York Trap Rock has proved wholly satisfactory.

Jan 1, 1959

By O. C. Ralston

Natural or artificial manganese dioxide of a grade pure enough to be satisfactory as depolarizer for dry cells has never been available in large supply simultaneously with being available in desired quality . The Second World War called for more of it than ever . A supply of natural material from the Gold Coast was ample for the war and was not completely exhausted . Whereas the crystal form of the manganese oxide was not recognized as a matter of importance until the war came , it is now known that gamma MnO2 is a desirable form and that pyrolusite , once thought acceptable , is not the best mineral . The following paper is a translation of an internal company report filed at the Bitterfeld office of the I. G. Farbenindustrie A.G. by Dr. Peter Marx in 1933 , just a year after G. W. Nichols had published in the Transactions of the American Electrochemical Society a study of making anodic manganese dioxide from solutions of manganous sulfate . The I. G. experiments were made to confirm the American work and were also extended to a larger scale . Only chemical purity was considered , and no mention is made of crystal form . The report adds to the knowledge submitted by Nichols but has not been previously available to the general public . Believing it of value to the United States industry , a translation has been made .

May 1, 1948

By J. A. Finch

For base metal sulphides, iron rejection starts in mineral processing. This review focuses on the changes in plant practice specifically to improve iron sulphide rejection by controlling contaminant ion effects and discusses selected innovations in mineral processing that can be expected to play a role in iron control. One change to control contaminant ions is size reduction (the use of stage grinding and inert stirred milling) and another is system chemistry (order of reagent addition and exploitation of the flexibility of sulphoxy species). Plant examples illustrate the successes, and indicate that there are several options available. The general innovations consider the new tools for measuring gas dispersion properties and quantifying froth characteristics from images. Examples of their application to improve concentrate quality illustrate the potential. Other innovations adapt geostatistics to model variations in ore flotation response to provide feed forward control and rigorously apply the statistical experimental methodology in plant test work. An example from one concentrator shows that significant improvements to reduce the iron content of concentrates can be achieved by applying these basic principles.

Jan 1, 2006

By H. E. Cook

The Ising model for the internal energy of a binary alloy has been used to obtain a general equation for the critical resolved shear stress of partially ordered crystals. The equation expresses the stress in terms of the Warren "alphas " and can be used to estimate the variation in strength with order without the assumption, present in the original formulation of this problem in terms of domain size, that order is complete within each domain and that the domains are of ungorm size and shape. In addition, it is the general equation, according to the Ising model, for strengthening by short-range order. Two applications of the equation are considered: One is an estimate of the variation in strength of CkAu with long-range order. The other is an estimate of the variation in strength of FeCo with quench temperature. Reasonable agreement is found with the variations reported in the literature. When the internal energy of an alloy crystal depends upon the distribution of solute, the strength of the crystal will also depend upon it because a portion of the applied stress for plastic deformation will be: where V is the volume of the crystal and E(E) is the energy change associated with the solute redistribution caused by the plastic strain, E. We expect T to equal zero for a crystal having a random arrangement of solute because the arrangement would remain random after plastic deformation. Likewise, we expect it to equal zero when the crystal is perfectly ordered because the motion of paired dislocations found in such crystals does not disrupt order. However, when short-range order exists or when long-range order is incomplete, plastic deformation will decrease the amount of order and additional work, proportional to the ordering energy, will be expended. Fisher' estimated T for crystals having short-range order by assuming an interaction energy between neighboring atoms and estimating the change in the number of unlike neighbors as a dislocation moved through the crystal. (His analysis was limited and several workers2"6 have since given more complete ones.) Fisher minimized the importance of a strengthening mechanism of this type for paired dislocations in a structure having long-range order. ~ottrell,' however, pointed out that T could be appreciable for ordered crystals having antiphase domains. He attributed the strengthening to the increase in surface energy of the domains as they were cut by paired dislocations. Ardley,' in his test of Cottrell's theory, found that r for Cu3Au crystals obeyed the equation: for 1 > t where 1 is the domain size, t is the domain wall thickness, and y is the surface energy of an antiphase boundary. His experiments represent the classic confirmation of the strengthening mechanism proposed by Cottrell. However, the assumptions involved in using Cottrell's theory are valid only for large domain size in CU~AU,~"~ i.e., when Eq. [2] reduces to: For small domains, ~linn~ has questioned Ardley's assumption that order was complete, and, indeed, Stoloff and ~avies" fpnd it incomplete until a size of approximately lOOA was reached. Even when the order within a domain is complete, it is not obvious how one determines the appropriate value for I in a structure where domains vary in size and are irregularly shaped. The purpose of this paper is to estimate T without restrictions upon the degree of order and domain shape. Our major assumption will be the use of a generalization of the model proposed by Bethe" (the Ising model) for the internal energy. This will in fact allow us to combine the theories for strengthening by short-range order and by antiphase domains into a single, general formalism. We will use the results to estimate the variation in strength of Cu3Au crystals with long-range order8 and the variation in flow stress of FeCo crystals with quench temperature.12'13 INTERNAL ENERGY For simplicity, we restrict our considerations to those binary solid solutions which can be described as an arrangement of atoms on a Bravais lattice. An atom site will be indexed by three numbers (PI, pz, p3) determined by the vector: from the origin fixed at atom (0, 0, 0) to the atom site where a', an, and a, are the lattice translation vectors. We write: For the energy of the crystal where pi(p) is the probability (either zero or one) of finding an atom of type i (i = 1, 2) at site (p), which is shorthand for (pl, pz, p3) and pj(p + r) is that for an atom of type j (j = 1, 2) at the site (p + r), which is shorthand for (pl + rl, The coupling parameter, resents the energy associated with the pair Pi(p), Pj(p + r). The crystal is assumed large enough so that surface effects can be neglected; therefore, trans-lational and inversion symmetry require the coupling parameters to obey the relations

Jan 1, 1969