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By H. C. Miller

The success of any project in which gas is injected into oil-producing sands to increase the current rate or the economic ultimate production of oil or in which surplus gas from oil producing operations is stored temporarily in reservoir sands that have been wholly or partly depleted of their producible oil depends mainly upon an understanding of the underground movements of oil, water, and injected gas and the ability to control their speed and direction of migration through the reservoir sands. Many operators believe that injected gas always travels up the structure and drives oil to wells structurally higher than the injection wells, because the specific gravity of the injected gas is less than that of the fluid substances in the formation. Consequently, many injection wells are located on the flanks of oil-bearing structures with the idea of utilizing the energy of the injected gas to drive the oil to producing wells higher on the structure. It is true, under certain conditions of pressure and fluid depletion of the reservoir sands, that injected gas will move in an up-structure direction, but the theory that injected gas always moves up the structure is based on an erroneous conception of the laws that pertain to the expansion of gases. By definition, "a gas is distinguished by its property of infinite expansion and is limited in volume only by the walls of the vessel which contains it."3 The expansion of gas that is injected into reservoir sands also is limited by "walls" that surround the space influenced by the injected gas. The walls of the majority of undrilled or virgin oil-bearing reservoirs in California are the impervious shales overlying and underlying the productive strata and the "dams" or effective barriers of edge water around the rims of the reservoirs. When gas is injected into the sands of a producing reservoir, regardless of the location of the injection well on the structure or the degree of depletion of oil from the sands, one of the walls which confine the gas in the structure about the injection well is fluid. This wall will be edge water in a nearly depleted reservoir, where the drainage cones or regions of reduced pressure about injection and producing wells intersect; and, where there is no interference of drainage cones and the injection well is structurally above the edge water, the wall will be oil. In some producing reservoirs bottom water may be the lower wall of the space that confines the gas about injection wells, but the effect of bottom water on limiting the expansion of gas is the same as if the water was not present and impervious formation separated the producing from the underlying nonproducing strata. Therefore, since compressed gas always seeks regions of reduced pressure and its final volume is limited only by formation and fluid barriers and since the force exerted by the gas under pressure is equal in all directions, the course of migration of injected gas in reservoir sands in California and the

Jan 1, 1932

By S. H. Ash

Tunnel driving is recognized as one of the most hazardous of occupations; this is a reflection of the high accident severity rates and resultant high compensation and similar costs in this industry. Most tunnels are driven by contractors who bid for the jobs, taking into consideration the prevailing industrial insurance rates at the time the bids are placed. After the bid is secured the contractor then attempts to complete the job at the minimum cost to himself. In a sense the accident-cost item is fixed for at least one year when a policy is secured. Time is generally an important factor not only for the contractor, but also for the insurance carrier and the assured. If the assured represents a private interest, the cost burden usually is ultimately placed on the general public which avails itself of the service contemplated; if the project is a governmental enterprise the cost burden unquestionably falls upon the general public involved and on the general tax payer. For these reasons it is of vital interest to the public that accidents not only be kept at a minimum as a humanitarian objective, but also because the accident-cost burden, too frequently not even realized and considered to the degree that it should be, can assume proportions that materially affect the cost of the enterprise. The basic industrial insurance rate for tunneling in California in 1932 contemplated an earned premium of 12.12 percent of the labor pay roll. The State has been particularly engaged in large construction enterprises, some of which involve high accident cost rates, notably structural-steel bridge building, which contemplates an earned premium of 19.65 percent of the labor pay roll. When this figure is compared with the much lower rates that apply to other industries it is apparent that a heavy toll in human wreckage is taken by such engineering projects, which must be viewed as monuments to human suffering as veil as to human achievement.

Jan 1, 1933

By M. Lonoff

G. Campbell The paper by M. Lonoff looks at the importance of byproduct prices on copper production. The paper develops several interesting points on this topic, but there are some points in the theoretical discussion that could use further development. A couple of these theoretical topics will be considered here using the paper's framework of assumptions without concern about how realistic the assumptions are for the copper industry. Lonoff's theoretical model is based on a static, homogenous world where all copper/byproduct deposits are identical, and these deposits are the main source of these metals. Due to the importance of the byproducts to the production decision, the term coproducts will be substituted for the term byproducts to reflect more accurately this condition. The conclusion is drawn that a rise in coproduct prices necessitates a decrease in copper prices because copper production is increased as a consequence of increased coproduct production. The observation that real world behavior does not always follow this pattern is dismissed as "speculation." However, it can be easily shown that within this simple framework market forces might create the observed behavior. The key question to be answered is what causes coproduct prices to rise. Three possible cases will be used as illustrations. The first case is the one implicity assumed by Lonoff. Here, the demand for coproducts increases at all prices (an outward parallel shift of the demand curve) with the demand for copper remaining constant. As reported in the paper, the results are higher coproduct prices, an increase in coproduct production, and lower copper prices due to the resulting increase in copper production. The second case is when the supply of coproducts are constrained-leading to higher market prices. Copper production, as required by the simple model, is also reduced which Reply by M. Lonoff Campbell's comments give me an opportunity to clarify a few points in "Copper and Its Byproducts." That paper examined the affect of byproducts on the copper market and considered the relative riskiness of multi-metal deposits from an investment standpoint. That brief note made no attempt to be exhaustive. Nevertheless, Campbell's comments miss the point of the paper and necessitate a response. My "theoretical model" was static and I freely conceded after introducing the assumption of identical deposits that "none of the assumptions hold." These simplifying assumptions allowed me to bound the possible effects of higher byproduct prices on the copper price by assuming identical deposits and computing average price effects. I took great pains to subsequently explain that since deposits are not identical the identity of the marginal deposit might change due to byproduct price changes. In this case, average price affects will overstate the affect of byproducts on copper prices. According to Campbell, I dismiss as speculation any "real world behavior that does not always follow this pattern" (of metals prices moving in opposite directions). In the byproducts paper I noted that gold, copper, and silver price movements often parallel each other on an intra-day or day-to-day basis. Such movements are largely due to market anticipation of or reaction to changes in interest rates that affect carrying costs of metals stocks. Other movements may be due to anticipated changes in available supply or physical requirements. I loosely grouped these effects as speculative. To distinguish this statement from the main thrust of the paper, I contined "In the long run if gold and silver prices remain high the equilibrium copper price will be lower." The paper set out long run equilibrium conditions rather than attempting to explain price movements on a daily basis or on a year-to-year basis.

Jan 11, 1983

By Robert D. Coale

This paper will describe the copper concentrate slurry pipeline and pumping system between the concentrator and the port at Bougainville Copper Ltd. The operations of Bougainville Copper Ltd. are located on the island of Bougainville in the South Pacific. Geographically, it is the northernmost island of the Solomon Group but, politically, it is part of Papua New Guinea. Papua New Guinea is a United Nations Trust territory administered by Australia, having recently been given self-government, with independence scheduled for December 1974. (Fig. 1). The island is approximately 130 miles long by 30 miles wide, with the Crown Prince mountain range forming a spine along its length. The mountains in place are over 8,000 feet high with the mine located on the western flank at an elevation of 2,200 feet. Exploration on Bougainville for copper by Conzinc Riotinto of Australia (CRA) began in 1963 and by 1968, through geophysical, geochemical and diamond drilling methods, an orebody containing nearly one billion tons of ore grading approximately 0.48% Cu. and sane gold had been outlined. Bougainville Copper Ltd., the company operating the mine, is 53.6% wined by CRA, 20% mined by the government of Papua New Guinea with the public Folding the remainder of the shares. The first copper concentrate was produced in early 1972, with production for the first full year, 1973 being:

Jan 1, 1974

By K. Nielsen

The paper presents a brief overview of the mineral industry in Norway, followed by a description of the mineral policy and relevant legislation including the roles of the Norwegian Directorate of Mining and Geological Survey of Norway in this context. The discussion then proceeds to describe the land use planning framework on a national, regional and local level, the interaction between land use planning and the Directorate of Mining and the Geological Survey respectively, and how this impacts on the mineral industry and the exploitation of mineral resources. Some recent Norwegian examples of land use planning conflicts are also presented.

Jan 1, 2005

By R. Burger, M. Masukawa

Cato Ridge Alloys (CRA) is a joint venture company between Assmang of South Africa, Mizushima Ferro Alloy Company (MZK) and Sumitomo Corporation from Japan. Negotiations for the formation of the company started in 1992 with the joint venture agreement signed on the 19th September 1996. MZK was to supply the technical know how for the production of Medium and Low Carbon FeMn while Assmang was to manage the day to day activities of the company. Sumitomo Corporation was to act as facilitator between Assmang and MZK and, together with Ore and Metal are responsible for the marketing of the refined products. The conceptual design of the plant started in December 1996 and the first charge of molten high carbon ferromanganese metal was charged on the 19th January 1998. Problems experienced during the initial startup period were addressed resulting in substantial operational improvements. A build-up in the stock of fine metal was addressed through the development of a process to remelt the fine metal, the development of a market for fine metal and the upgrading of the crushing and screening plant to reduce the generation of fine metal. The mass yield from High Carbon Ferromanganese to Refined Ferromanganese was increased through the implementation of statistical process control, changes to the blowing patterns and the development of a sampling device for taking samples during the process. Converter refractory consumption was reduced. This was achieved on the converter by improving the cooling of the converters with the installation of cooling fans and cooling fins. The heating schedule of the converters was changed for improved refractory life. Production schedules were modified to allow cooling of the refractory between low carbon erromanganese charges. Additional changes made to improve operations were: ? Changing from mehanite casting trays to metal fines beds. ? Installation of sonic horns in the baghouse to prevent the bridging of dust. ? Improved welding on the lance tips.

Jan 1, 2004

By M. Ahrens

The paper describes the main drive systems of an iron ore pelletizing plant and related important design aspects. It is shown how today?s drive systems provide the desired flexibility for the process and lead to high energy efficiency and system reliability. With respect to electric drives expansion projects have many technical issues in common with green-field installations. However, there are aspects where important, distinct differences occur. It is shown which considerations for selecting and sizing drive systems for such a plant as well as for integrating them into an overall plant control concept need to be taken into account. Besides the design of the drive systems a key aspect for such an expansion project is the network interaction. Harmonics levels at different points in the plant network need to be checked carefully with simulations during the design phase to avoid problems later-on during operation. The power factor compensation and the harmonic filtering of the new production line cannot be designed independently of the already existing plant. The paper highlights areas where problems could occur and which points need to be paid attention to when a plant is expanded.

Jan 1, 2008

By J. Ling, L. Racine, P. Cousin, A. R. Laplante

"The problem of gold recovery by gravity from high density gangues is first discussed from a fundamental perspective. Three potential difficulties are presented: poor liberation and fine gold particle size, concentrate bed erosion by coarse dense particles, and slow percolation of gold particle through the high density gangue bed. Two case studies are presented to illustrate the impact of these three problems on circuit performance and the feasibility of gravity recovery. It is concluded that careful testing can determine the scope of the first problem and feed preparation can limit the extent of the second. The third problem is clearly the most serious and results in lower gravity recoverable gold recoveries than would be achieved with the same recovery effort on a low density gangue application.IntroductionSince the commercialisation of the Knelson Concentrator in 1980, gold gravity recovery has experienced a surge in interest, in Canada and the United States first, then Australia, Zimbabwe and Russia, and finally worldwide. Table I details number of units sold in various countries, which corresponds approximately to their importance as gold producers 1. Exceptions. such as the low rank of South Africa or the importance of Zimbabwe, despite the much higher gold throughput of the former, are generally the result of differences in the effectiveness of the local marketing strategies, as well as a reflection of the ""philosophy of recovery"" prevalent in the country.The impact of the Knelson has not been felt equally in all plants. Typically, a highly successful application falls into the following categories: (a) alluvial or hard rock recovery for which gravity is the sole recovery method, (b) hard-rock free gold milling with ores which have a very high gravity-recoverable gold (GRG) content, (c) low grade sulphide copper-gold ores which include flotation ahead of cyanidation and (d) free-milling gold ores ahead of Other applications can be successful, but are not as common. The ""explosion"" of centrifuge concentration, of which the Knelson is the most successful but by no means the sole model, has created a certain euphoria which can be summarized as ""gravity recovery will improve the profitability of gold milling, no matter what."" This presentation is about applications that are not so successful, or even downright unsuccessful. The rationale is not to down-play gold gravity recovery, but to set it in its rightful position: metallurgically, it is not appropriate all of the times; it can become inappropriate if poorly designed; and it can be metallurgically possible but economically unjustifiable. In this paper, this will be illustrated and explained rather than demonstrated, with the use of both industrial plant surveys and laboratory test work. Alternate gravity approaches will be suggested."

Jan 1, 1997

The University of New South Wales (UNSW Australia) has been a world leader in the development of innovative virtual reality technologies over the last 15 years. AVIE (Advanced Visualisation and Interactive Environment) was developed by iCinema as a collaborative venture between UNSW?s Faculties of Engineering and the College of Fine Arts. This is the world?s first 360°-surround, virtual reality (VR) stereo projection theatre system. The School of Mining Engineering at UNSW Australia has developed 18 different virtual reality modules aimed at mine safety training and mining engineering education. These modules are being regularly used in both the mining industry and the university. The School of Mining Engineering is continuously involved in the development of different modules. Research is also currently being conducted on the implementation of other technologies into this environment. Artificial intelligence (AI) and fuzzy logic are tools that the authors would like to consider implementing in future module development. This paper will review current research in both these areas and consider options for applying these technologies.

Jan 1, 2014

By Charles Henrique Xavier Morais Magalhães

Os Aços Inoxidáveis Duplex possuem uma estrutura constituída basicamente por ferrita e austenita na proporção aproximada de 50%. Este trabalho estudou a influência da temperatura de um tratamento térmico na morfologia e fração de ferrita e austenita no aço UNS S32304. Os tratamentos térmicos realizados consistiram no aquecimento das amostras, desde a temperatura ambiente até a temperatura de 1250°C, seguido de um resfriamento lento em um segundo forno estável em uma determinada temperatura. As amostras permaneceram neste segundo forno por um intervalo de tempo necessário para que suas temperaturas atingissem exatamente um valor desejado, sendo então imediatamente retiradas e resfriadas em água a 20°C para preservar a estrutura resultante do ciclo térmico aplicado. As amostras foram metalograficamente preparadas, atacadas e analisadas com o auxílio de um microscópio ótico. As frações de fases medidas por MO se aproximaram dos resultados obtidos por simulação utilizando o software Thermo-Calc. A morfologia das fases variou significativamente com a diminuição da temperatura de tratamento, uma vez que a austenita se mostrou mais fragmentada nas temperaturas mais baixas, porém o bandeamento não deixou de existir na estrutura.A transformação da ferrita em austenita se mostrou fortemente dependente do tempo.

Aug 16, 2017

By N. Som

The pile capacity in cohesive and granular soils depends on a number of parameters. The values of these parameters as recommended by Indian Standard Code of Practice vary over wide ranges. A designer often finds it difficult to select appropriate values of these parameters for realistic estimate of a pile capacity. The present paper makes a critical review of the values of the parameters given in Indian Standard Code of Practice and suggests a realistic approach to selecting them in the light of recent research.

Jan 1, 1996

By Fred S. Karn

Inhibitors are used in coal mines as a precaution against accidental dust explosions. Although rock dust is the usual inhibitor many others have been tested. To facilitate testing a screening process using laser irradiation was proposed. The procedure includes irradiation of a coal-dust mixture followed by mass-spectrometric analysis of the evolved gases and an evaluation of the flammability characteristics of the gases. Carbonate-type inhibitors decreased the percentage of combustibles in the gases generated and inhibitors like NaCI (thermally stable salts) decreased the total gas generated. A suitable test procedure did not result from the investigation, demonstrating the inadequacy of fast heating, non-combustive techniques in rating inhibitors of coal dust explosions.

Jan 1, 1973

By B Xiao, J Yang, H Chen

"An EXTENDED ABSTRACT is available for download. A full-length paper was not prepared for this presentation. The Tuwu-Yandong Cu deposit, located in the East Tianshan mountains in the eastern section of the Central Asian Orogenic Belt, is the largest and economically most important porphyry Cu deposit in Xinjiang, China. It contains ~3 Mt of copper at an average grade of 0.46 per cent Cu and 0.2 g/t Au, with significant amounts of Mo and Ag. The deposit is mainly hosted in the Carboniferous Qi’eshan Group and plagiogranite porphyry, and is controlled by faults that are east–west-, north-west- and north-east-trending. Ore minerals in the Tuwu-Yandong deposit are dominated by pyrite, chalcopyrite and molybdenite, with minor bornite, chalcocite, magnetite, sphalerite and galena. Gangue minerals are mainly composed of quartz, sericite, chlorite, epidote, anhydrite, gypsum, muscovite, biotite, phosphorite, sphene, dolomite, actinolite, barite, albite and calcite. Based on the megascopic and microscopic textural relationships and mineral assemblages, five stages of hydrothermal alteration and hypogene mineralisation are recognized in the Tuwu-Yandong Cu deposit: the potassic stage, propylitic stage, phyllic stage, late veins stage and supergene stage. Most of the copper was deposited during the phyllic stage, along with less molybdenite.CITATION:Xiao, B, Chen, H, Wang, Y and Yang, J, 2015. Geology, mineralisation and alteration of the Tuwu-Yandong porphyry Cu deposit, north-west China, in Proceedings PACRIM 2015 Congress, pp 641–644 (The Australasian Institute of Mining and Metallurgy: Melbourne)."

Mar 18, 2015

By D. F. Smith

The thermodynamic data presented in the literature for zirconium compounds are incomplete. Among the compounds for which adequate data are Zacking are zirconium fluoride and sulfate. This paper reports experimental heat-content values determined by the Bureau of Mines for these two zirconium salts throughout the temperature range of 273° to 1,200° K. No crystalline transformations were found in the two compounds investigated, and neither of the compounds melted over the temperature range studied. MATERIALS TESTED The Oak Ridge National Laboratories, Oak Ridge, Tenn., supplied the two zirconium salts used in this investigation. The zirconium fluoride was high- purity reactor grade material. The zirconium sulfate contained between 0.01 and 0.10 percent hafnium and calcium, and other elements in concentrations below 0.01 percent, A spectrographic analysis of the two compounds is given in table 1. Before use the compounds were dried at 400° C. for several hours to removed adsorbed moisture.

Jan 1, 1962

By Andrzej Walentek

This paper presents the results of numerical modeling of the fractured zone around longwall gateroads. The numerical computations have been based on the results of underground measurements of the fractured zone around longwall gateroads, which were performed for various geological and mining conditions and measured with the use of the endoscopic method with a digital camera. Having results of the underground investigations, trials of duplicating them by the Finite Element Method using software PHASE and the Hoek-Brown failure criterion were performed. In order that the fractured zone predicted by the model-based computations closely simulate that measured underground, some selected parameters in the Hoek-Brown failure criterion were modified based on the earlier determined relations used for prediction of the roof-to-floor convergence in longwall gateroads. As a result, the model-based computations produce results very close to those obtained from the underground measurements. Determination of the fractured-rock zone around the mine roads is of great importance to mining practice, especially in planning and designing supports for longwall gateroads. The influence of the front abutment pressure causes the fractured rock zone around the roads to increase and results in an increase of support load. Moreover, proper determination of the fractured rock zone is one of basic elements in the process of planning roof bolting for mine workings.

Jan 1, 2009

By Zhou Lu-Jian

The Port of Shekou is situated at Shenzhen Bay on the east bank of Lingding Ocean. Its coastline is about 6 km long and the water depth near the shore is Favourable. Across the bay is the ' New Territories " of Hong Kong. The port is at a distance of 22-23 seamilesaway from center of Hong Kong and 80 seamiles to Huangpu Harbour of Guangzhou, its highway links with Shen-Guang Highay. Since 19 79 China Merchants Group of the Transportation Department, began to set up Shekou Industrial Zone, the port has been developing and flouri­shing in business. With 15 large or small berths in all, the present portline is 2600 m, and the annual cargo throughout is over 3,000,000 tons and the annual passenger traffic is about 2,000,000 persons. Equalling a medium-scale seaport, it has been officially approved as an oceangoing transit port by the ministry of Transportation. The construction of Shekou port is chara-terized by the self-collected funds and the short construction period. In view of this, the optional plan of the port structure must serve the requirements of simplicity in struture, economy in mate­rial and speed in construction. That accounts for the most application of the sheet piling type to the port in Shekou. Once the project was approved, the cons­truction started. Only within an average period of 7-8 months, a deep water pier was completed and put into operation, which covered series of processes from exploration, designing, tender for con­struction to completion.

Jan 1, 1991

By M. R. Geer, H. F. Yancey

"INTRODUCTION With the advent of war in 1941, military operations in Alaska were enlarged on such a scale that the demand for coal in the Territory more than doubled. Coal was needed urgently for heating forts and other military establishments, for use on large construction projects, and for handling the greatly increased volume of traffic on the Alaska Railroad. -The additional tonnage required, estimated at perhaps 250,000 tons per year, probably could have been supplied by the United States, but shipping space between Pacific Coast ports and Alaska was already overburdened with military supplies and construction materials. Moreover, although of only secondary importance in wartime, the cost of coal shipped into the Territory is reported to have been as high as $40 per ton. The alternative to importing coal was, of course, to increase the Production of the Alaska mines.Production of coal in Alaska reached, 350,000 tons in 1944, or more than double the prewar' output. The responsibility for increasing coal production was assumed largely by the Army, A Coal Commission attached to the Alaska Department arranged financial assistance for some mining operations, aided the operators in producing equipment for mechanization, and provided most of the labor necessary to operate the mines. The Bureau of Mines contributed to the program in several ways. First, exploration by the Bureau in the Moose Creek district revealed a substantial tonnage of coal of better grade than any currently mined in the Territory, 4/ and drilling in the Broad Pass district, where a mine to supply coal for the army had been started, revealed that the reserves were far less than had been supposed; this operation was abandoned. Second, coal-preparation practices were studied, and recommendations for improvements made, at two of the operating mines at which the quality of the coal makes preparation a factor of vital importance. Some of the information obtained in these studies forms the basis for the present report."

Jan 1, 1946

By R. Heath Forbes

The route of a new, 4-mile long, electrical transmission line passed through residential neighborhoods and commercial areas of a small town in the South Carolina Coastal Plain. The new line consisted of 54 new poles and a one-mile underground section. Most of the new poles were constructed within 50 ft of existing structures, and in some cases, within 8 ft to 20 ft. A widely-space subsurface exploration consisting of 20 cone penetration test soundings indicated the subsurface conditions along the alignment generally consisted of saturated, loose to medium dense, fine slightly silty to silty sand. The pole foundations consisted of 20 to 30 ft long, prefabricated ?caissons? (essentially an open-end pipe pile with a prefabricated connection system at the top) with diameters of 28 to 56 inches. The steel caissons were installed with vibratory pile hammers. To help prevent damage and defend against possible allegations from nearby property owners, vibration and settlement monitoring was performed during all foundation installation activities. Limited structural condition assessments were also performed before and after foundation installation. For 53 of the 54 foundations, the ground vibrations recorded at distances coincident with the nearest structure locations ranged from 0.05 inches per second to 1.46 inches per second. With consideration of the dominant frequency, the majority of these values were below the commonly used USBM vibration limits. For a foundation installation that was only 8 ft from the nearest structure, a peak particle velocity of 3.06 inches per second was recorded, which exceeded the USBM limits. For all cases, the measured ground surface settlement was negligible (i.e., less than ¾ inch). Several spurious claims alleging vibration-induced damage were made, but the monitoring program provided an adequate defense. One claim involving artwork that fell to the floor during foundation installation at a distance of 8 ft from the house was deemed legitimate.

Jan 1, 2011

By C. Thiart

Kriging is an interpolation technique for predicting unobserved responses at target locations from observed responses at specified locations. Kriging predictors are best linear unbiased predictors (BLUPs) and the precision of the BLUP is assessed by the mean square prediction error (MSPE), commonly known as the kriging variance. Both the BLUP and the MSPE depend on the covariance function describing the spatial correlation between locations and on specific parameters. The parameters are usually treated as known, whereas in practice they invariably have to be estimated and the empirical BLUP (that is, the EBLUP) so obtained. The empirical or estimated mean square prediction error (EMSPE), or the so called ?plug-in? kriging variance estimator, underestimates the true kriging variance of the EBLUP, at least in general. In this paper five estimators for the kriging variance of the EBLUP are considered and compared by means of a simulation study in which a Gaussian distribution for the responses, an exponential structure for the covariance function, and three levels of spatial correlation ? weak, moderate, and strong ? are adopted. The Prasad-Rao estimator obtained using restricted or residual maximum likelihood (REML) is recommended for moderate and strong spatial correlation and the Kacker-Harville estimator for weak correlation in the random fields.

Jan 1, 2014

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.'-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann's constant, and the vacancy formation entropy, respectively. After applying Stirling's approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling's approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling's approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967