Search Documents

Current mine production planning, scheduling, and allocation of resources are based on mathematical programming models. In practice, the optimized solution cannot be attained without examining all possible combinations and permutations of the extraction sequence. Operations research methods have limited applications in large-scale surface mining operations because the number of variables becomes too large. The primary objective of this study is to develop and implement a hybrid simulation framework for the open pit scheduling problem. The paper investigates the dynamics of open pit geometry and the subsequent material movement as a continuous system described by time-dependent differential equations. The continuous open pit simulator (COPS) implemented in MATLAB, based on modified elliptical frustum is used to model the evolution of open pit geometry in time and space. Discrete open pit simulator (DOPS) mimics the periodic expansion of the open pit layouts. Function approximation of the discrete simulated push-backs provides the means to convert the set of partial differential equations (PDEs), capturing the dynamics of open pit layouts, to a system of ordinary differential equations (ODEs). Numerical integration with the Runge-Kutta scheme yields the trajectory of the pit geometry over time with the respective volume of materials and the net present value (NPV) of the mining operation. A case study of an iron ore mine with 114 000 blocks was carried out to verify and validate the model. The optimized pit limit was designed using Lerchs-Grossman?s algorithm. The best-case annual schedule, generated by the shells node in Whittle Four-X yielded an NPV of $449 million over a 21-year mine life at a discount rate of 10% per annum. DOPS best scenario out of 2 500 simulation iterations resulted in an NPV of $443 million and COPS yielded an NPV of $440 million over the same time span. The hybrid simulation model is the basis for future research using reinforcement learning based on goal-directed intelligent agents.

Jan 1, 2008

By Robert G. Nisle

The classic theory of pressure build-up in shut-in oil wells as developed by Horner and van Everdingen is based on two-dimensional radial symmetry in the well-reservoir system. Such symmetry does not exist in the case of a well which parfiially penetrates the producing formation. As a result of this lack of symmetry the use of the classic theory in such cases become questionable. In this paper the mathematical theory has been extended to include the case of partially penetrating wells. Numerical solutions illustrating the up-dication of the equations are presented. The effect of partial penetration on pressure build-up is shown by a comparison of synthetic pressure build-up curves derived from the numerical solution of the equation for partially penetrating wells for various degrees of penetration. It is shown that partial penetration is detectable from the characteristic shape of the pressure build-up curve and that formation productivity may be calculated from the pressure buildup data in a manner identical to that described by the classic theory. INTRO DUCTION The use of pressure build-up data on shut-in oil wells is a well-established technique for the measurement of reservoir productivity. The work of Homer' and van Everdingen' is well known. Since the publication of their pioneering work, others"' have elaborated and extended the technique. These authors have dealt exclusively with the case of wells that completely penetrate he producing formation. Two-dimensional radial symmetry is achieved, thereby, and the problem is greatly simplified. This ideal situation is seldom encountered in practice. But, in spite of this, the technique is often employed anyway. The question, therefore, arises: how much confidence can be placed in the results of such calculations when the data are taken on wells that only partially penetrate the producing formation? It is the purpose of this work to answer this question. Only the single-phase fluid case will be considered. van Everdigen' has presented a rigorous solution of the two-dimensional case, but because of mathematical complexity, this solution has not proved to be particularly useful. Horner' utilized Kelvin's point source solution in two dimensions and showed that it is a sufficiently good approximation for oil reservoir studies. The geometry of the well and the producing formation is illustrated in Fig. l. Geometrically the formation may be described as an infinite slab. The infinite slab is defined as the solid (the porous medium in this case) bounded by two parallel planes. Thus, the slab extends to very great distances in both the positive and negative directions of two of the coordinate axes, but is finite in

By Tapan Goswami

The main objective of the blasting phase in a coal mining operation is to maximise the coal recovery. However, coal loss due to blasting is a serious problem. The Australian Coal Association Research Programme (ACARP) reported in 2011 that in Australia one in every ten coal mines is completely wasted due to such losses. Coal is either lost in the spoil, largely due to the blasting operation or becomes diluted and cannot be recovered entirely. The major coal loss mechanisms include losses from the coal seam roof, the floor, the front edge and from dilution. Coal damage and loss mechanisms during cast blasting that have been observed by various authors include: •Excessive cast dragging the coal edge in the cast direction. Movements of this nature are oftenassociated with the formation of trenches. •Spatial movement of overburden where rock shears and moves in a plane above the coal seam,which damages and dilutes the coal. •Rock falling over the coal during the blast often producing indentations in the exposed coal. •The inappropriate use of bulk and initiating explosives that often results in coal damage. •Insufficient stand-off distances from the coal. The Australian coal mining industry has gone a long way towards addressing the coal loss issues since 2011: almost all operations now deploy touch-coal drilling and sporadically use gamma logging for loading overburden. A study was conducted to compare the effectiveness of touch-coal information in which some touch-coal blastholes were drilled on a fixed or random pattern. In another study, some blastholes were drilled to the touch-coal, gamma-logged and mapped to determine stand-off distances. It was found that the coal roof surface created by gamma-logged holes was the most effective option for minimising coal loss. As a result, a variable stand-off distance was found to be the key to minimising losses. This paper discusses the importance of coal mapping, the rock properties of the roof and floor interface of the coal seam, and the significance of loading and initiating designs in minimising coal damage. Furthermore, the importance of using electronic initiators cannot be emphasised enough. This paper also discusses how a cast blast can be initiated from many locations by mitigating geological abnormalities and thereby avoiding spatial movement of rock shearing in a plane above the coal seam.

By L. Gilbert

Recent changes to environmental legislation and trends in the environmental regulation of mining in the Northern Territory are being driven by (among other factors) Federal Government policies and international agreements on the environment. These trends are discussed and the expected application of the NT Water Quality Management Strategy (based on the National Water Quality Objectives) over the next few years is examined with respect to mine environmental management practices. Some of the potential conflicts and changes in approach which may develop are identified and examples discussed. Proactive means of integrating trends in environmental legislation with mine planning and waste management are discussed.

Jan 1, 1994

By Alvin Schallis

The. problem of supplying enough magnesia for the American war effort has become highly important. Before hostilities began, only about two-thirds of our, require vents came from domestic sources; now they must supply almost all the magnesia we need. A further burden is placed upon our own supply by the fact that more and more magnesia is being required, not alone to pace the war tempo of general industrial activity, but also to replace chrome ore in refractories and to make magnesium metal. The domestic magnesite and brucite industry is equipping itself to satisfy much of this greater demand for magnesia, but the remainder must be obtained elsewhere. The principal sources of magnesia are magnesite, brucite, dolomite or high-magnesium limestone, natural brines, sea water, salt-works bitterns, magnesium silicates, and magnesium salts. Although dolomite is tae subject of this paper, it should be considered in perspective with all these highly competitive sources of magnesia.

Jan 1, 1943

By J. H. Clemes

The process of leaching silver ores with sodium hyposulphite is comparatively new, and published accounts of the details and losses of the process are as yet very few. The following account of a careful series of experiments to determine the actual loss in this process may therefore be acceptable to members of the Institute. The ore treated was highly calcareous, and the principal sulphide present was iron pyrites. Following is an analysis by Professor Price, of San Francisco, of the ore treated : Per cent. Silica,..........15.13 Sulphur,.........13.31 Arsenic,.......... 9.82 Iron............ 17.33 Alumina,..........1.35 Zinc,...........4.92 Lead,..........1.78 Carbonate of lime,..33.78 Magnesia,.......... 2.58 100.00 Ten tons were crushed dry with a 30 X 30 screen = 900 holes per square inch. In order to feel our way with this ore, two experimental or "pilot" charges were roasted. Pilot Charge No. 1. Treated 1000 pounds in a four-hearth reverberatory. 8.30 p.m.—Entered fourth hearth, remaining there one and onehalf hours; sulphur began to burn. 10 p.m.—Changed to third hearth; ore became red-hot half an hour after entering; the fireplace was kept almost destitute of fuel. 2.30 A.M.—Changed to second hearth. Charge continued, giving off a large quantity of sulphurous fume; the fireplace was kept dark.

Jan 1, 1884

By G. H. Kuhnhausen

The Bear Creek Uranium Mill was designed in 1975 to process 909 tonnes per day (1000 STPD) of low-grade uranium ore from the Powder River Basin in Wyoming. The mill was expanded to 1818 tonnes per day (2000 STPD) in 1979. The Bear Creek Uranium Project is owned by the Bear Creek Uranium Company, a partnership of Rocky Mountain Energy Company and Mono Power Company. The original mill design contemplated processing ores from Bear Creek Uranium Company properties exclusively. The expanded capacity has been utilized for tolling ores from Kerr McGee Nuclear Corp. and other mining companies in the region. This paper describes the process of designing the original mill, the lessons learned from operation, and the design of the process modifications required for expansion. The project background, design philosophy, design basis, design criteria, actual flowsheet, special design considerations, and a comparison of assumed operating conditions and actual operating results will be presented. Bear Creek Uranium Company wishes to thank and acknowledge the help granted by the many operating companies who provided invaluable information, insight, and critique of the Bear Creek design through all the various stages and were instrumental in the successful completion and start-up of the mill. Without their contributions, the design philosophy used at Bear Creek would not have been possible and the results obtained would surely have been less satisfactory.

Jan 1, 1979

By German Zambrana

The solution of the problem of beneficiation of cassiterite from its primary ore deposits is of fundamental importance to Bolivia. The process today involves a gravimetric treatment of the ore followed by sulphide flotation. During the last year, a cassiterite flotation stage has been added in several plants to treat the slime tailings. Although cassiterite flotation is already economical for the slime tailings and the mechanism of the process are understood, it is felt that further research could improve the results. In the past, considerable amount of research and test ark has been performed to select appropriate collectors to improve recovery, to increa¬se the grade of tin in the concentrate, to minimize the effect of metallic ions like Ca+2, Fe+2 and Fe+3 which prevent flotation, and to increase the pH of the pulp which now it can not be higher than 3.0. It has been reported that the halogen salts (1) like NaCl exhibit special surface affinity for cassiterite but none for quartz. These effect seems to be favourable for the selective flotation of cassiterite from silica minerals. In view of these preliminary results it was decided to follow the research accordingly: OBJECTIVES The objectives of the present investigation are: 1. 0 evaluate the influence of NaCl salts in quartz and cassiterite flotation.

Jan 1, 1971

Shortly after Denny, Robson, and Irwin published their first paper in 1937, on the prevention of silicosis by metallic aluminium, experiments were begun on the practical application of the discovery.It was thought at that time that aluminium powder, to be effective in aluminium therapy, would have to be intimately admixed with siliceous dust at the latter's source. There followed several years of experimental work underground, during which the application of aluminium powder was tested in:(1) Speakers on machine columns, vibrated by drills.(2) Vials placed in drill holes to be blasted.(3) Both homogeneous and heterogeneous mixture with explosives.(4) Packages with tamping.(5) Compressed-air lines.(6) Special compressed-air ejectors for use while drilling and after blasting.(7) The discharge of ventilation fans.(8) The filters of respirators.It was concluded from this research that any adequate method of introducing aluminium powder into a mine atmosphere would require too much extra gear, supervision, and aluminium p;wder, and would interfere unduly with underground routine.Later, animal experiments by Denny, Robson, and Irwin2 showed that aluminium powder provided effective therapy when inhaled independent of silica dust. Therefore, some means of surface treatment was deemed more practical.APPARATUS USED IN THE DEVELOPMENT OF ALUMINIUM PROPHYLAXIS SAMPLINGA basic requirement was a method of sampling to assess accurately the particle-size concentrations of dispersed aluminium powder. Konimetry, though regularly practised at McIrityre, was inadequate for the research in mind. On the other hand, the efficiency of the thermal precipitator was recognized as being very high. Accordingly, the latter instrument was chosen as best suited to our needs. Through the courtesy of the Ontario...

Jan 1, 1945

There are two main areas of application of geology in quarrying: (i) In regional planning for industrial mineral requirements.(ii) In direct quarry management. The regional planning requirement has recently become more evident because of greatly increased land demand conflicts around cities. The direct quarry involvement is a reflection of both the economy and the greatly increased sophistication of the quarry industry. Here, professional planning and development expertise by a geologist is required, to ensure continued supply of raw materials at the best price to the consumer with sufficient profit to the producer. Today, geological insurance safeguards capital investment in plant and assures economical development plans.

Jan 1, 1978

By John Johnston

WHEN I was honored by being invited to give the Howe Memorial Lecture, I decided to read Howe's book, "The Metallography of Steel and Cast Iron," published in 1916-that is, about 25 years ago-in search of a text. I found the book written in fine, clear, attractive, yet precise style, as I expected, knowing that his father ¬Dr. Samuel Gridley Howe, his mother-Julia Ward Howe, and all of his four brothers and sisters had lived in a New England literary atmosphere and had written books. This leads me to suggest that many authors of metallurgical papers and books could well study Howe's writings with a view to the improvement of their own. I failed to find a specific text, but did find a subject, for in reading his book I was struck by the few instances in which time is considered explicitly as a factor in the phenomena examined, and by the fact that many of the hottest arguments would have been settled had time been taken properly into account. Indeed, Howe hardly mentions time except in a rather incidental way, as in a few references to lag; for instance: The lowering of temperature at which the transformation occurs by rapid cooling . . . is a phenomenon of undercooling or lag. It is in part explained by the fact that the transformation itself is a time-consuming reaction which, setting in during a rapid fall of temperature. is naturally protracted till the temperature has sunk far below that at which it is due. He does discuss, quite fully, the iron-carbon equilibrium diagram, as known at that time, introducing it by stating: As he is a reasonable man who is not deterred from using a hand truck for moving his trunk by the consideration that he has thus to move a trunk plus a truck, so am I reasonable in putting into your hands this useful, indeed indispensable, tool for mastering the ABC of iron metallurgy. Somewhat later, in introducing a discussion of the phase rule, which "it would be hardly proper to pass . . . by without an attempt to outline its meaning," for "a clear exposition of its applicability or jurisdiction is needed to restrain the half-initiated from misusing it and the uninitiated from being misled by these misuses," he writes-and I quote his statement because we cannot properly discuss the influence of time on a process until we know the state of equilibrium which would ultimately be reached by the system under consideration It is a most remarkable and valuable generalization, its conceptions help greatly toward getting a broad outlook on metallography, but its misconception has brought out a flood of obscuring writings. It tells us about the constitution towards which alloys tend, that which they reach when equilibrium is complete, when all tendencies have corrected themselves and have been complied with completely. Its application, in absence of true equilibrium, is like determining density with a telescope or even with a tuning fork; it is like the mad tea party at which the butter put into the works "f the watch was the best butter. If the reader learns no more than to beware of attempts to decipher the conditions of inequilibrium by a law which touches only the conditions of exact

Jan 1, 1942

By Oliver Bowles

"Asbestos" is not the name of a distinct mineral species but is rather a commercial term applied to fibrous varieties of several minerals. The origin and significance of names applied to asbestos by early writers are discussed in the section devoted to sources of supply and terms employed in ancient times. VARIETIES The most useful variety of asbestos is chrysotile, a fibrous serpentine the composition of which is expressed by the formula H4Mg3Si209. Chrysotile is characterized by a strength and flexibility that permit the use of the longer fibers for spinning. The bulk of the world production of both long and short fibers, is of this variety.

Jan 1, 1935

By T Sparks

The Collie River catchment, located approximately 200 km south of Perth, covers an area of around 2830 km2 and is the source of run-off to the Wellington Dam, an important irrigation water resource for the Collie Irrigation District. The salinity of the Wellington Dam has increased due to historical clearing and irrigators currently use water with salinity levels approximately twice that of the Murray River in South Australia (Water and Rivers Commission, 2001). The Collie River Salinity Situation Statement (2001), released by the Water and Rivers Commission (now the Department of Water), identified realistic actions that could achieve the salinity reduction target. Subsequent benefit-cost analyses and prefeasibility studies recommended the diversion of the most saline flows in the Collie River away from the dam as an immediate intervention (URS, 2003). The East Branch of the Collie River above the locality of Buckingham (20 km east of Collie) contributes around half of the salt that flows into the Wellington Dam and the diversion and storage of the saltiest flows from the East Branch at Buckingham was identified as a viable option for reducing salinity in Wellington Dam. The proposal had one problem û the water could not be disposed of as quickly as it was diverted. However, in the vicinity of the diversion site were a number of coal mine voids and after preliminary discussions, the Government/Griffin Coal alliance was formed and from this the opportunities have continued. Diverted water would be stored temporarily in an adjacent mine void (Chicken Creek 4 void) and then disposed of to the sea. The disposal options included Western Power CorporationÆs saline discharge pipeline from Collie Power Station, or a new pipeline. The diverted water was also identified as a potential raw source for treatment and use in industry. This has opened up opportunities including desalination, water efficiencies in the power stations, increased reliability of water supply for the power stations, water for new industries, wastewater disposal options and extra water for PerthÆs water supply. In the process of solving the water storage problems the project introduced a range of mine water quality problems û heavy metals and pH û and the Department of Water (DoW) is now working with the mining industry and the Centre for Sustainable Mine Lakes (CSML) to develop treatment and management technologies. The project has received support and funding through the National Action Plan for Salinity and Water Quality (NAP) and it has been possible to accelerate and enhance this project as a result of NAP. The DoW has developed the proposal to an advanced stage and gained approvals for the capital diversion program to go ahead. The partnerships have expanded to include the second mining company, Premier Coal, the Water Corporation, Western Power and the Harvey Irrigation Cooperative. The proposal could feasibly result in a $90 million integrated water management initiative for Collie using the latest technology, mining operations and providing water for value adding industries in the local area. The DoW is not a mining company; however, our experience in managing water in times of shortage, environmental water quality criteria, competition for water and managing community expectations will have the same success factors:consultation and knowing your community and stakeholders, sharing issues and working in partnership can provide results far greater than the initial issue, even brackish water has value, every sector is in competition with each other and has to have a share of the water, an integrated approach can provide opportunities for development in areas of water shortage, and never think of water as wastewater.

Jan 1, 2006

By Milka Madahana, John Ekoru

Particulate matter is one of the leading pollutants in the mines and in the communities in the areas near or surrounding the mines. The availability of large Clinical and environmental data sets obtained from the mines has brought about the need to use better approaches to analyze the collected data. Prediction and control of particulate matter concentration in the mining environment is essential in minimizing air pollution and protecting the respiratory health of mine workers. The main objective of this research work is to analyze datasets obtained from a mining area using machine learning techniques which will then be followed by the real-time estimation of dust particulate in the mines. Datasets collected over 8 years in an hourly sampling rate from an open cast mine is cleaned and analyzed for trends and patterns. Artificial Neural Networks (ANNs), Support Vector Machines and decision trees techniques are applied to analyze and predict the particulate concentrate. The estimation of particulate concentration using Artificial Intelligence will significantly contribute toward the development of quantitative tools to be used in correlating of cause and effect of dust concentration in mines. The results obtained in this work will form a sub-unit of a respiratory health monitoring system for mine workers. The system is essential in the collection, analysis, and tracking of mine workers’ respiratory health, thus it forms part of an early intervention system for mine workers. From the existing theory, we expect the Artificial Neural Network will perform much better than previously used classical models.

Jun 25, 2023

By J. P. Capp

The Bureau of Mines conducted field-scale experiments in underground gasification of coal with oxygen-enriched air. A path about 140 feet long was linked at the rate of LO feet per day through a coalbed hydraulically fractured with a mixture of starch gel and sand. During the best gasification period, which extended for 2-1/2 days, 785,000 std. c.f. per day of 124-B.t.u. gas was produced. In other periods the heating value at times was almost 300 B.t.u. per std, c.f,, but sustained production of such gas was not achieved. During gasification, a total of 50 tons of coal was gasified and 114 tons of coal was carbonized. Approximately 12 million B, t .u. per foot of nominal path was recovered at the surface.

Jan 1, 1962

By T J. Sprott, Associates

A number of people have expressed concern, understandably, that if mining operations take place in the Coromandel, the flows of mineralised ground water which exist will be intercepted. This water in many cases contains toxic metals including mercury, arsenic and lead and it is thought that if this water is allowed to enter streams or the waters of the Hauraki Gulf, it could endanger natural marine life and possibly established fisheries. This paper seeks to explain in simple terms the geology and the process of deposition of the various mineral deposits in the ground, the chemistry of the reactions between these minerals and the rain water falling on the ground, the hydrology and behaviour of this mineralised groundwater as it moves through the ground until it eventually enters the sea.

Jan 1, 1981

"Chairman: Professor J. Elbrond Rapporteur: Miss V. E. MartingPapers.Aids to planning production in coal mines by F. H. Deist and M. P. RobertsCapacity calculations, investment allocation and long-range production scheduling in German coal mines by F. L. WilkeOre reserve evaluation and open pit planning by J. M. Marino and J. P. SlamaThis session was devoted to the economic aspects of planning and scheduling. After Dr F. H. Deist had introduced the paper Aids to planning production in coal mines, Dr T. V. Falkie summarized the following formal contribution prepared jointly with Dr R. V. Ramani, describing the work that has been done at the Pennsylvania State University in the development of simulation programs for mine planning over the past 15 years:During the late 50's and early 60's, Monte Carlo simulators were developed to model continuous miner-shuttle car transport systems, track haulage systems, belt conveyor networks, etc. In the mid-60's attention was directed towards deterministic simulation of equipment performance, given the equipment characteristics and the system profile. In the late (10's all these systems (miners, shuttle cars, belts and trains) were integrated together to form a complete coal mine simulator and the program could predict the output potential of the system, given the mining dimensions, method and equipment employed. The actual sequence of coal-cutting operations is entered into the computer through the use of a special programming language which permits any type of mining configuration to be simulated. The simulator is hybrid in nature in that the shuttle cars, trains and belts are simulated deterministically, whereas rate functions with delay frequencies are entered for the continuous mining operations of sumping, shearing, fleeting, cleaning, etc. With suitable manipulation of the data, the program may be applied to all belt or conventional mining sections. Most of these simulators were developed through the assistance of grants from the Department of Mines and Mineral Industries of the Commonwealth of Pennsylvania and are available from the Coal Research Board of the Commonwealth,"

Jan 1, 2014

By A. Bauer, P. Katsabanis, M. Baker

The principal results from a previous paper presented at the Mine Accident Prevention Association of Ontario in 1987 (1) are summarized here. It is concluded that the selection of explosives in mines experiencing sulphide ignitions is important and that aluminized explosives should be avoided because of their high explosion temperatures and their detonation products. The duration of the blast is also critical and secondary blasts should not occur simultaneously with nearby priroa:ty blasts.

May 11, 1988

By S. P. Chong, N. C. Shih, G. A. Turner

Fine powders, with the bulk of the particle diameters Jess than 10 microns, were aerated so that each particle was, on the average, separated from its neighbours by 1.3 to 2 mean diameters. In this state, measurements were made of the viscosity and settling rate of the powder, and the interfacial tension between it and a moist pellet. From the viscosity measurements, qualitative analogies are drawn between the behaviour of the aerated powder and that of a dense gas near its critical point.

Jan 1, 1970

By Ralph Hultgren

IN solid solutions atoms of differing sizes occupy the same crystalline lattice, requiring that some of them be compressed and others expanded. The energy involved has been called misfit strain energy and is an important concept of crystal chemistry. If the atomic sizes and elastic constants of interatomic bonds are known, the misfit energy may be calculated,' provided certain simplifying assumptions are allowable. Usually, isotropic crystals are assumed and interatomic distances are taken to be the statistical average determined from X-ray diffraction. Such calculations yield values of the misfit energy of the order of 1 or 2 kcal per atom in alloys such as Au-Cu at compositions of 50 atomic pct. However, evidence has accumulated in recent times that atoms change their sizes with composition of alloys, implying electronic rearrangement of the bonds. The size changes have been found particularly by application of the X-ray method developed by Warren, Averbach, and Roberts.' Thus, Averbach, Flinn, and Cohen3 determined radii in Au-Cu alloys. Oriani4 showed that these new radii led to a calculated misfit energy in disordered AuCu, which was decreased from the values calculated by the usual theory more than twenty-fold, to only 80 cal per g atom. Thermodynamic calculations from the phase diagram5 also show misfit energy to be no more than a few hundred calories per g atom in this alloy. The question of what electronic rearrangements are possible therefore becomes compelling in estimating misfit energy. In the following pages the results of certain calculations on the AuCu tetragonal superlattice are submitted. Conclusions drawn from these should be applicable in large degree to disordered solid solutions. As in all ordered states, bonding distances in the superlattice are individually known, rather than being merely average distances as found from lattice constants of disordered states. Moreover, only the Au-Au and Cu-Cu distances are strained; the elastic constants of these are known in the elementary state. In the usual calculation it is necessary to assume elastic constants for Au-Cu bonds. Misfit energy has thus been calculable without the need of many simplifying assumptions usually made. It is still assumed that equilibrium bond lengths and elastic properties of the bonds are the same in the alloy as in the pure metals. As previously discussed, this is probably not correct. Also assumed is that the bonds are not affected by strain of neighboring bonds. A calculation of Young's modulus from compressibility data shows this to be far from true; extensive electronic rearrangements take place. It would seem that misfit energy cannot be calculated from elasticity data for the elements. The usual methods may, however, give an upper limit which is often much higher than the true value. The question of electronic rearrangement is, of course, a complex one. Pauling's theory gives a simple, approximate treatment of the relation between type of bond and bond distance. This has been applied with some success to the Au-Cu system, as will be shown in a later section. Misfit Energy in Au-Cu Alloys Hume-Rothery and Raynor6 discuss the Au-CU system as a type example of strain energy. The gold atom is 12.8 pct larger in diameter than the copper atom, near the size factor limit beyond which solid solubility is severely restricted. They therefore consider the misfit energy to be large, a conclusion for which they believe they find evidence in the phase diagram. Gold and copper are completely miscible in the solid state, but the alloy has a minimum melting point at an intermediate composition. From this Hume-Rothery and Raynor conclude that the strain energy is nearly large enough to prevent miscibility; the phase diagram tends toward a eutec-tic type. In Ag-Cu, which has almost identical size relationships, solid miscibility is quite limited; whereas in Au-Ag, where atomic sizes are nearly the same, there is complete miscibility without a minimum in the melting point. From their arguments the heat of formation of Au-Cu would be expected to be endothermic or only slightly exothermic, that of Ag-Cu to be endothermic, and that of Au-Ag to be exothermic. Deviations, from Ve-gard's law of additivity of atomic radii support these conclusions, since Au-Cu and Ag-Cu both have pronounced positive deviations, and Au-Ag has a negative deviation. Nevertheless, Au-Cu alloys form exothermically; indeed, considerably more exothermically than Au-Ag, Table I. Hence, strain energy must be much less important in this case than Hume-Rothery and Raynor have supposed.

Jan 1, 1958