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By N. A. McLeod

BALL wear in wet grinding mills has been the subject of considerable discussion in the last few years. Its importance to millmen is obvious in view of the fact that ball wear may cost from 2 to 4¢ per ton of ore for the more fortunate operators and many times this cost when a refractory ore must be reduced to a fine state of comminution. Consequently, any factual information that may be obtained on the nature of ball wear may be applied to introduce changes leading to lower ball consumption and therefore also to lower costs. In 1940, while employed with the Britannia Mining and Smelting Co., Britannia Beach, B.C., I had occasion to investigate factors that might affect ball consumption. We performed a number of tests, which will be briefly described. These tests originated as a result of changing from a 3 1/2-in. ball to a 2-in. ball of different type of manufacture and were motivated by the desire to obtain the best possible type of 2-in. ball. Our testing was helped by the fact that the company operated a one-ton electric furnace, so that it was quite easy to make steel changes. It should be emphasized at the beginning that these tests produced results that in their general application to milling should be interpreted qualitatively rather than quantitatively. As will be evident in the description of the method used in testing, the balls were subjected to an intermittent batch grinding treatment, which may have produced results in rate of steel wear that may not have an accurate correlation with steel consumption in full-scale mill operation. However, with this fixed and rather arbitrary method of testing, results were obtained that may be of some interest and may stimulate further work on this subject. Unfortunately, owing to pressure of war work, our tests, which we had intended to repeat on a continuous grinding operation, had to be discontinued. METHOD OF TESTING Tests were made in a small cylindrical mill, rotating at 72 r.p.m. Internal dimensions of the mill were 10 1/2-in. dia. by 9 in. The cylindrical inner surface was lined with rubber and the two ends were formed by steel plates. A charge of 2000 grams dry feed and 2000 c.c. of water was added every 2 hr., the mill being drained of pulp before the addition of each charge, by tilting and sluicing with water. The mill was run on afternoon and night shift for daily periods of about 15 hr. total grinding time, and each test lasted from 60 to 150 hr. This batch method of testing involved a higher average pulp temperature in the mill, which undoubtedly affected comparative results in some of the tests. HARDNESS OF BALL VS. WEAR In these tests, special "eutectoid" steel balls were used, some of which were chill-cast and quenched, some sand-cast and quenched, and some sand-cast and annealed to a dead soft condition. The results obtained, using as mill feed an ore containing considerable free quartz and

Jan 1, 1945

By Leandro Brunholi Ramos

Foi estudado o efeito da temperatura no comportamento à corrosão sob tensão do aço inoxidável dúplex AISI 318 em solução contendo 115.000 ppm de cloreto, pH4 a temperatura ambiente e a 70°C. Ensaios de tração com baixa de taxa de deformação foram realizados. Foi avaliada a susceptibilidade do aço inoxidável dúplex AISI 318 à corrosão sob tensão no potencial de circuito aberto e em vários potenciais anódicos e catódicos. Os resultados mostraram que a redução do alongamento variou com o potencial aplicado. Os resultados experimentais mostraram que o aço AISI 318 ficou imune à corrosão sob tensão em potencial entre -750 mVECS e 1.000 mVECS na temperatura ambiente e entre -650 e -100mVECS para a temperatura de 70°C. Em potenciais maiores que o potencial de pite observou-se uma redução drástica no alongamento em ambas as temperaturas. No entanto, quando os potenciais aplicados foram abaixo de -650 mVECS para a temperatura de 70°C e -750mVECS para a temperatura ambiente, houve uma redução no alongamento final até a ruptura, provavelmente através do processo de fragilização por hidrogênio.

Aug 8, 2018

By Roach C

Exploration on the Callide Coalfield by Thiess Bros. Pty. Limited had reached the stage in mid 1976 where there was a need for a comprehensive appraisal of the coalfield geology. Exploration strategy in 1977 - 1978 was defined by the selection of the most attractive targets. All available literature, reports and plans were reviewed and borehole records assessed. The geology of the coalfield was placed in its regional setting and the genesis of the Callide Coal Measures described in a structural and sedimentological context. Their general form and extent was then examined by the technique of stratigraphic analysis through the interpolation and extrapolation of the available data. A "localized" reserve classification was drawn up and reasonable estimates of the various geological reserves produced, in terms of their reliability and depth of overburden. Quality trend maps were also produced. The resultant "base map" was virtually a summation of all the information to June, 1977, and the basis for the exploration programme in the 1977 - 1978 financial year. The technique allowed for "base maps" to be produced at almost any stage, each one a refinement of its Predecessor.

Jan 1, 1978

By T. Glen Heslop, Dennis H. Laubscher

INTRODUCTION In all cave mining operations waste is drawn mixed in the ore, hauled, hoisted and milled. This waste usually contains some mineral which partly covers some of the costs of mining and milling it, but it still re- presents a loss of profits as the production rate from the mine is matched to the mill capacity - every tonne of waste milled replaces a tonne of profitable ore. Draw control aims to reduce the amount of waste drawn and to increase the amount of ore recovered. It is also used to regulate the grade of ore flowing to the mill and in block cave blocks to prevent potential stress build- up on the major apexes above grizzly drifts. This paper summarises what has been learnt about draw control in the forty years that cave mining methods have been used in the three largest underground chrysotile asbestos mines in the southern hemisphere. The four mining methods to which draw control has been applied are: a. Block caving. b. Shrinkage with overburden caving. c. Sublevel caving. d. Open stoping. Open stoping has been included because on a number of occasions severe falls from the back and side of these open stopes have occurred. Without full records of where and when ore is blasted, when and how much ore has been drawn from each of the drawpoints, it would be impossible to analyse the migration of ore and fallen waste in the stope. Several problems peculiar to chrysotile asbestos ore bodies affect the practice of draw control. Heterogeneous fragmentation, cavities, side pressures and the interaction of stresses in the caved ore affect the migration of ore under draw. Fibre is normally not developed uniformly throughout the ore bodies, values vary from place to place but there is usually a general decrease upwards and the hangingwall contact is an economic limit. The immediate hangingwall rock frequently looks like the ore body hostrock and is difficult to recognise in a drawpoint, and cannot be used as the marker for stopping draw. During caving or shrinkage, a large proportion of fibre becomes detached from the host rock and re- ports in the fines, which migrate differently to the larger rocks. The fines are not sticky, and flow easily if loose and dry, but compacted, the fibre and rock fines con- solidate the ore. During draw the proportion of fines in the ore varies considerably, as fines either flow relatively freely between the large rocks or become trapped and compacted above large rocks or hangups. This creates a large sampling error in drawpoint grade assessments, whether done visually or by bulk sampling, unless the assessments are done frequently. The method of draw control used is to regulate the draw rate in an attempt to lower the ore-waste interface as evenly as possible, and to finally stop working the drawpoint when a calculated tonnage has been drawn.

Jan 1, 1981

By Harry E. Krumlauf

The year 1957 was one of declining metal price and production. Many lead-zinc-copper mines were forced to close, and the remaining mines limited production to stay more in line with demand. High cost of labor, supplies, and equipment and high taxes aggravated the situation. Some operators postponed or abandoned expansion programs because of uncertain economic conditions. Output was curtailed by elimination of over- time employment and reduction of the working force. The number of employes laid off was small- reduction in the labor force was accomplished by not replacing those who left a company's employ.

Jan 2, 1958

W. 0. HOTCHKISS,* Madison, Wis.-When we began to do geological field work in the Lake Superior region, we found a correlation in existence, and, as youngsters, accepted all that as settled. Both Mr. Allen and I, since that time, have seen a great many things that were not apparent nor visible to Van Hise, and those who worked with him; we realize now that the correlation was not final and that much remains to be determined concerning geology of the Lake Superior region. My attitude on this matter is that we should not publish an amended correlation as a final thing. We should avoid, in every way possible, foreclosing the minds of those who follow us in working in the geology of this region. As a matter of fact, no correlation can be final at present, because facts and data are accumulating so rapidly that every classification must be immediately modified to fit further observation. Consequently, my attitude in this matter would be, instead of saying that the iron formations of the Lake Superior region are all Middle Huronian, to say that there may be three Huronians-or four or five- we do not know. I believe it is better policy to hold to our present correlation. I do not believe there is any economic benefit to the mining man or the geologist working on problems relating to explorations for iron ore, that cannot be just as well solved by maintaining our present correlation, with a. wholesome idea of our lack of knowledge and the necessity for further detailed work. Then, if any new horizons are discovered in any particular range, the minds of the investigators will not be foreclosed because some one has said that all the iron formation is in the Middle so that there is no use looking elsewhere for it. There is use looking elsewhere, in many cases, as the ore deposits become exhausted.

Jan 1, 1920

By E. J. Kloos

Two self-contained breathing apparatus of the closed-circuit compressed-oxygen type were evaluated for performance at 32° to -25° F. Low-temperature effects of oxygen and carbon dioxide concentration, visual properties of the facepiece, and mechanical operation of the apparatus were studied. Although operation varied with the wearer, his breathing rate, the apparatus precooling time, and the temperature, results suggest that general use of currently approved compressed-oxygen closed-circuit breathing apparatus be limited to temperatures above 32° F.

Jan 1, 1968

By José Arango

El presente texto describe la aplicación del sistema MIMS en las estadísticas de producción de la Sociedad Minera Cerro Verde S.A. El sistema fue instalado inicialmente para el control de mantenimiento de los equipos, movimiento logístico, y contable. Posteriormente, se realiza el cambio del sistema de información manual a un sistema computarizado, donde se analiza los problemas cotidianos del sistema de información antiguo y se los compara con los cambios experimentados. En ese sentido, el objetivo de este sistema es facilitar el alcance de sus metas a la organización mediante el uso eficiente de todos sus recursos disponibles: personas, información, equipos, tecnología, y materiales diversos. La eficiencia de la utilización del recurso de información es medida por la relación del costo para obtenerla y el valor del beneficio derivado de su uso.

May 25, 1998

By S. H. Ash

Mass production methods, although increasingly important for economic reasons, create new hazards, remove many hazards, and improve health and safety by reducing exposure and obtaining better supervision. Such methods must be efficient or be discarded. Skilled workmen are required who must be trained to utilize equipment that replaces picks, shovels, and explosives. The effects of working conditions on the health of workmen have long been evaluated in noncoal mines. Studies and action programs relating to environmental health hazards in the mineral industry have placed particular emphasis on dusts. The anthracite industry is conducting an action program on the problem of dust. Segments of the bituminous industry are now conducting similar investigations. An industrial hygiene survey of coal mining in the State of Washington has been conducted and the results published in 1949. (State of Washington, Department of Health, I. H. Bul letin 4.) Chest X rays were obtained from miners in the six major coal-producing counties. State Health Department mobile X-ray equipment was set up at most large mines. Participation was on a voluntary basis, and response was obtained from 70 percent. Important in successful mining safety programs are training programs for supervisors and workmen alike. These programs recognize that the employe is the focal point in injury prevention and are planned and function around him. During the war, industries had to compete with each other for workers and to obtain and hold good workers, working conditions had to be made attractive. The average age of the mine worker increased, and, contrary to what many expected, mining injury rates decreased rather than increased. To attract competent workers, risks to life and limb, as well as laborious tasks, have to be reduced, and an experienced worker is indispensable for safety. Young men are returning to modernized mines. Mass production methods and equipment are more to their liking; jobs are more remunerative, demand action, and require special training and skill that give them the mark of a craftsman. Such workmen can be taught safe methods.

Jan 1, 1950

By C. K. Eilerts, J. D. Ham

Laboratory research has been conducted to evaluate the characteristic effects of condensate saturation on the mobility of gas in typical reservoir rocks. A pump with two pistons provided phases in equilibrium at controlled flow rates and constant liquid-vapor volume ratios. Core samples were tested in a holder that permitted sealing steady-state phases in the pore spaces under flow test pressures for weighing with sufficient precision to give an accurate measure of the attained saturations. Parameters of the study were pressure, apparent velocity, flowing liquid-vapor volume ratio, fluid composition, core material and length-to-diameter ratio. Tests were conducted at 515 and 1,515 psia to determine the effect of pressure on the mobility-saturation relationship. Influence of the apparent velocities 0.30, 0.15 and 0.07 cm/sec and of five liquid-vapor volume ratios from 0.0001 to 0.01 was determined at 515 psia The principal fluid system was nitrogen and and separator liquid from a Gulf Coast condensate, but the effect of a condensate of different viscosity was also determined. The significance of a possible concentration of liquid near the outlet end of the test cores was investigated. Core materials included a consolidated sandstone and a low-permeability limestone. Relative mobility and liquid-vapor volume ratio relationships are concluded to be dependent on pressure, saturation and, to a lesser extent, on velocity. For each porous medium and fluid there is a minimum saturation essential to two-phase flow, and high velocities of flow have only limited effect on saturations in this range. INTRODUCTION It is now recognized that knowledge of the availability of a reservoir gas — the period that gas may be recovered from a reservoir at a given rate — is as important as the estimate of gas in place. When reservoir conditions are such that pressure decline owing to production will result in retrograde condensation, liquid saturation can increase in the structure around the production well in a way that may restrict flow capacity, and hence future availability. l Based on a numerical solution of transient radial flow of single-phase gas-condensate fluids, 2 a program for computing the accumulation of condensate in a reservoir and the effect of this condensate on deliverability has been developed. During this development a need evolved for data that described the influence of pressure, velocity of flow and condensed liquid on mobility as recovery progressed. This paper presents the results of experimental investigation to obtain insight into the mobility relationship at reservoir pressures of gas-condensate fluids. A core holder for flow tests at reservoir pressure was developed to weigh the core and its fluid contents under pressure to determine saturation. A specially constructed pump was used to drive a two-phase fluid through the core until a steady state prevailed. The core was used as a differential device, and properties measured were intensive rather than extensive. APPARATUS Fig. 1 shows a schematic representation of the major pieces of equipment used in the mobility determination. The weighable core holder is connected to a two-piston, constant-displacement pump. Attainment of steady-state flow is indicated by stability of the flow differential read from the high-pressure manometer. WEIGHABLE CORE HOLDER An important part of the data needed was the mobility-saturation relationship. This required that mobilities and saturations be measured at pressures, flow velocities and liquid-vapor volume ratios characteristic of condensate reservoirs.

By A. K. Bakshi, K. J. Shoop, Komar S. Kawatra, T. C. Eisele

Slurry rheology can have significant impact on the performance of autogenous grinding circuits. A viscous slurry can act as a cushion and retard impact forces between the media and the ore, which reduces grinding efficiency. On the other hand, a dilute slurry will not be viscous enough to hold slurry in the impact zone of the media, which will lead to inefficient use of impact energy. An unfavorable rheology can also lead to overgrinding or centrifuging of the slurry inside the mill. Slurry rheology also affect classification, with higher viscosity increasing the cut size. In this article, the causes of the rheological effects on autogenous grinding and hydrocyclone classification have been discussed. Both plant and pilot scale data from autogenous grinding have been provided to show the effects of viscosity on specific energy con- sumption and other breakage characteristics of the ore. It is shown that: (1) high viscosity, produced by low temperature and high fines content, significantly increases the specific energy consumption and the production of critical size material in an autogenous mill; (2) In hydrocyclone operation, increasing the viscosity causes the d50(c) size to become coarser.

Jan 1, 1998

The known coal resources of South Australia are either of poor quality, or expensive to extract, or both. Export quality coal occurs only at great depth in the remote north of the State; the balance of the State's coal resources are suitable only for local electricity generation. Currently there is only one coal mine in the State, at Leigh Creek. This provides fuel for approximately 34% of the State's electricity generation, the balance being fuelled by natural gas. In the near future, new fuel sources must be developed to augment diminishing supplies of natural gas, and to cater for increasing demands for electricity. The South Australian Government has determined that future electricity generation will be based on the combustion of local coals. The geological and geographical environment of the known coal deposits and the quality of these coals are such that the most up to date and innovative technology must be applied to both extraction and combustion processes. The Government, the Electricity Trust of South Australia, and several Australian and overseas companies have embarked on an extensive research and development programme to ensure that these otherwise useless resources can be developed to the benefit of the State.

Jan 1, 1987

By Steven W. Schmauch

A mineral survey by the U.S. Bureau of Mines and U.S. Geological Survey indicate the Blanco Mountain RARE II area has low potential. Lode deposits consist of small, mineralized quartz or quartz-gossan veins. The veins are sparse and widely separated and lead, silver and gold content is restricted in amount and concentration. No gold or other potentially economic minerals were found in a placer deposit. There is no evidence of industrial mineral, geothermal, or energy resource potential in the study area. INTRODUCTION A mineral resource survey of the Blanco Mountain RARE II area (No. 5059), Inyo and Mono Counties, California was conducted in July 1981. This report summarizes the results and interpretations of the Bureau of Mines investigation.

Jan 1, 1982

By Jan Svoboda, Atsushi Shibayama, Toyohisa Fujita, Toshio Miyazaki, Kenji Murata

"The electrical disintegration (ED) method and disintegration by underwater explosion were investigated as new fragmentation techniques for the kimberlite ore and tungsten scrap of superalloy (carbide bit). The results of various breakage tests demonstrated that both fragmentation methods as new disintegration techniques for recycling were able to liberate various components of materials of different resistivity and elastic impedance.SUMMARYThe breakage of the kimberlite ore from South Africa (sample size: 15 mm x 15 mm x 6 mm) was achieved by the ED method. A relationship between the sample size, voltage, the electrical current and the energy needed for the disintegration was found from the experimental results. Kimberlite exhibited a high degree of breakage, when the high voltage of 60 kV and the pulse current of approximately 5000 A were applied to the sample by the generator during 0.2 microseconds (Fig. 1)."

Jan 1, 2003

By R. Y. Wan, S. L. Chryssoulis

"Gold associations were established in a·biooxidized, chlorinated CIL residue assaying 0.02 oz Ault and in a biooxidized thiosulfate leach residue assaying 0.01 oz Au/t. A detailed mineralogical study involved: assays of screened fractions; light microscopy; ion probe microanalysis to quantify 'invisible' gold in sulfide minerals; proton probe microanalysis to detect and quantify preg-robbed gold. In the CIL residue, most of the gold is preg-robbed (71 %). In the thiosulfate leach residue, gold occurs mainly as submicroscopic disseminations in microcrystalline quartz (chert). In both residues, the 'invisible' gold in pyrite accounts for a minor fraction of the gold assay. Quantitative determination of the gold occurrence in the two residue samples established conclusively that gold adsorption on carbonaceous matter in the thiosulfate leach is of minor importance.Acknowledgement: published with permission of Newmont Gold Company."

Jan 1, 1997

By W. Joseph Schlitt

The types of copper leaching and recovery operations in the United States are reviewed, along with characteristics and trends in the industry. The contribution of the various leach operations to total mine output is discussed in order to provide a perspective on the relative importance of copper leaching as a method of production.

Jan 1, 1980

By J. H. Soulé

"The Copper King copper-gold-silver deposit was discovered about 1880. Various individuals and companies have been interested in the deposit and considerable work has been done, although production, if any, has been small. The deposit is located in the western part of Laramie County Wyo., and is favorably nituated with respect to rail and truck transportation and high-tension power facilities.Mild summers and cold winters characterize the climate. Precipitation averages between 16 and 17 inches annually, with considerable snowfall in the winter. Permanent streams are small and most available water in being stored for use by Cheyenne, Wyo. Range grasses comprise the bulk of the vegetation, with small treed and shrubs common in the most rugged areas.The deposits lie upon land owned by Wyoming, now leased by a group of Wyoming and Colorado businessman constituting the Copper King Mining Co.Primary copper-gold mineralization seems largely confined to an equigranular, relatively fine grained gneiss that is part of a pre-Cambrian complex of metamorphic rocks ranging from schists to pegmatites. The copper minerals are oxidized to a depth of from 100 to 150 feet, with the occasional occurrence of secondary minerals at greater depths. The copper minerals chalcopyrite, malachite, chalcocite, bornite, cuprite(?), and some native copper were observed in Le deposit.In addition to the 4,030 feet of diamond-core drilling in 11 holes done on the deposit by private companies, the Bureau of Mines drilled 3 holes for a total of 2,630 feet. The sample results of this drilling plus available data from previous drilling and sampling are appended to this report."

Jun 1, 1955

By C. H. Fulton

Page Introduction........................... 280 Distillation Products from Reduction of Zinc Ore........... 281 Preliminary Investigations..................... 290 Equilibrium of Reaction Zn + CO2 + ZnO + CO in Temperature Range of Condensation........................ 293 Requisites for Successful Condensation................ 299 Discussion............................ 300 Introduction The study of the condensation of zinc from its vapor was undertaken to shed light on certain problems encountered in large-scale electric zine-furnace work. recently conducted. It is a matter of common knowledge that one of the disadvantages of the arc type, electric zinc furnace, is the production of a large amount of blue powder and proportionately little liquid spelter, for, as stated by Stansfield,l "A notable defect in the electric smelting of zinc ores is the difficulty experienced in obtaining the distilled zinc in the liquid state; ...... when zinc ores are smelted electrically, very little liquid metal is commonly obtained, nearly all of the zinc being in the state of powder." This difficulty was not encountered in the electric furnace used12 the main difficulty being the destruction of the fire-brick lining of the large condenser, in certain parts, and the formation of .some oxide and dross coatings on the condensing surfaces. The reason for these difficulties could readily be explained by the infiltration of air whenever the condenser was changed from one retort base to the other, the zinc absorbed in the fire-brick forming oxide and causing rupture by its expending volume. Two facts, however, tended to disprove this theory for the rupture of the fire-brick lining: first, the large distilling retort, lined with fire-brick, which was shifted from charge to charge on alternate bases at temperatures between 1200 and 1300 C., fully exposed to the air, showed no signs of disintegration whatever; second, marked disintegration in the condenser occurred .only in places that were at tempera-

Jan 1, 1919

By S. Fairis Samuelson

Boling Dome. a piercement salt dome in the Texas Gulf Coast basin is (was) the single largest deposit of native sulfur in the Western world. Total sulfur production has been over 81.000,000 long tons and the mine is still in production. Data from over 60 years of operation and 8.000+ wells reveal a salt dome rich in history as well as minerals. Sulfur mineralization and production correlate well with caprock structure and morphology. The occurrence of Mississippi Valley-type deposits in fracture zones is notable in some areas and may warrant additional study. DISCOVERY AND PRODUCTION HISTORY Boling Dome is located in the south- east corner of Wharton County, Texas, 60 miles south-west of Houston. It is a piercement type dome in the Houston diapir province. It was discovered in 1922 when the county surveyor noticed sour gas seeps along the San Bernard River (Haynes. 1942). Several companies including Gulf Production Company. Humble, Texas Company, Sun and others quickly began drilling for oil and gas. Traces of native sulfur were reported in cuttings from many wells penetrating the caprock, but the first commercial quantities of sulfur were not found until Gulf Production's E.M. Chase 3 and 4 wells were drilled in 1927. Texas Gulf Sulphur, then mining sulfur at Gulf Dome in Matagorda County, secured the sulfur rights from Gulf for $3 million in cash and half of the profits after expenses for development and construction of plant and townsite were met (Haynes, 1942). The drilling results from 200 or so Wells revealed a massive deposit destined to become the largest single source of native sulfur in North America. Original reserves were estimated at just over 46 million long tons and were increased in later years. Production by the Frasch method was begun by Union Sulphur in 1928, and continued by Texas Gulf Sulphur Co. in 1929, and Duval Sulphur Co. and the Baker Williams Co. in 1935. Union produced 8,009 long tons, Duval produced 571,123 long tons, and Baker Williams produced 1,453 long tons. Through its deal with Gulf, Texasgulf acquired the largest and best mineralized portion of the dome and has produced 88,544,466 long tons through 1990, and production is planned for several more years. That amount of sulfur is equivalent to a cube measuring 1,152 feet on each side, or a sulfur highway 1 foot thick, 20 feet wide and 14,479 miles long. Peak production averaged 8,376 ltpd in 1948. A price war between North American sulfur producers and Mexican sulfur producers in 1956, followed by the recession of 1957 and 1958 (Haynes, 1959) coupled with a rapid increase in mining depth to below 700 feet began a gradual production decline that was never reversed (Figures 1 and 2).

Jan 1, 1992

By Rex O. McLellan

The formation of a monovacancy in a metal is simulated in an elastic model by the displacement of the surface of a small spherical cavity in a large elastic continuum. The application of linear elasticity to this distortion results in a well- known formula for the energy and an expression for the concomitant entropy change due both to the shear strain in the continuum and also to the dilation of the solid resulting from the boundary conditions at the surface of the solid. Elastic data (the sliear modulus and its temperature coelficient) are used to calculate the entropy and energy of formation for many metals. Despite the simplicity of the assumptions involved, the agreement between the calculated entropies and energies and experimental values is remarkably good. In recent years there has been a large increase in measurements of the absolute concentration of mono-vacancies in metals as a function of temperature. Hence new data for both the energy and the noncon-figurational entropy of formation of monovacancies has become available. Recent measurements&apos; of the anomalous (non-Arrhenius) self-diffusion in many bcc metals has also focused interest on the prediction of the thermodynamic parameters of mono- and multi-vacancies in those metals for which no data are available. Damask and Dienes&apos; have discussed the various theoretical calculations of the energy of formation EL, of a monovacancy. These include simple models involving the breaking of atomic bonds on moving atoms from the interior of a crystal to the surface, models combining elastic calculations with surface-energy terms and detailed quantum mechanical calculations. The simler models give the correct order of magnitude of &, but tend to overestimate it by a factor of about two. The quantum mechanical calculations4"7 have been carried out for the noble and alkali metals with generally reasonably good agreement with the available Ef data. The calculation of entropy of formation Sfv14 lnvolves a fundamental calculation of the perturbation of the phonon spectrum caused by the creation of a vacancy. Huntington, Shirn. and wajda8 have given an approximate evaluation of sJV by considering an Einstein model for the localized vibrations in the immediate neighborhood of the defect and then using elastic theory to calculate the entropy associated with the shear stress field in the distorted crystal (as originally proposed by Zenerg). They also included a term due to the dilation of the crystal. They obtained a value of 1.47k for copper, in good agreement with the experimental value (1.50k). However, Nardelli and Tetta- manzi1° have recently shown that neglecting the coupling between atoms (Einstein Model) may lead to a serious error so the agreement may be somewhat fortuitous. In this work simple linear elastic theory is used to calculate the entropy and energy of formation of mono-vacancies. Despite the simplicity of some of the assumptions involved, the agreement with the available experimental data is remarkable. However. the reasonable degree of success in the application of linear elastic calculations to the excess entropy of a solute atom in a dilute solid solution1&apos; indicates that the application of elastic theory to vacancies. where the interaction of different atomic species is not involved, may not be inappropriate. THE ELASTIC MODEL The metal is assumed to be a spherical elastic continuum. A small spherical cavity of volume V = 4i;v:&apos;/3 is cut from the center. removed. and dissolved rever-sibly in the bulk of the material. TO a good approximation no net atomic bonds are broken and the material does not undergo a volume change although the externally measured volume of the body would increase by V. The radius of the sphere of metal is much larger than r Next a negative pressure is applied to the cavity causing its surface to be displaced inward by an amount simulating the relaxation of the lattice around a monovacancy. In this model the energy and entropy accompanying the distortion are taken as 4, and <. As a first approximation the equation of state for the solid is taken as: r = ro(i + *~D LiJ where K is the bulk modulus. P the hydrostatic pressure. Vo the volume of the material at 0°K and zero pressure. and d+/dT = 30. where 0 is the linear thermal expansion coefficient. The variation of entropy with hydrostatic pressure is given by the Maxwell equation: These equations give the entropy change resulting from increasing the hydrostatic pressure from 0 to P as: and since • we have: This is the entropy arising from the dilation resulting

Jan 1, 1970