Search Documents

By R. O. Burt

The paper examines the role of gravity concentration in both an historical contest and within the modern mineral processing industry. It discusses the principles of the process on both a theoretical and practical level. The importance of ore mineralogy and its effect on the choice of the wide range of equipment available is discussed. The paper concludes with a discussion on the relative merits of gravity concentration to other forms of processing and seeks to answer the classical question - "Quo Vadis?"

Jan 1, 1982

By Jarrod Bonsmann, Zachary T. Plitt

"A surge in mine related deaths in Middle Eastern conflicts over the past few years has prompted research into the mitigation of the impact on a blast loaded vehicle. In past military conflicts, it has been observed that blast loading can cause injury to the brain but the exact cause is unknown [1]. The recent rise in deaths due to Improvised Explosive Devices (IEDs) has led to research that has speculated that the high acceleration experienced by soldiers on a blast loaded vehicle leads to Traumatic Brain Injury (TBI) [2]. This research aims to investigate vehicle designs that can reducethe peak acceleration for passengers on board the vehicle, in the event that the vehicle is blast loaded by an IED."

Jan 1, 2016

By Robert Howard

With the rapid depletion of the Peerless Coal Co.'s mine in Spring Canyon, it was necessary, if the company was to remain in the coal-producing business, to look to the development of a new property or to acquire a mine already developed. After careful investigation of several operating properties it was decided by the officials of the company to take over the lease on an undeveloped acreage held by a private party in Price Canyon, about 3 miles north of Castle Gate, Utah.

Jan 1, 1930

By Ven Mercade

The flotation of calcite has been studied by many investigators, especially in terms of type of collector; pH; and metal ions that activate and, more importantly, depress the flotation of calcite (1)(2). Research was extended to the investigation of the effect of polyvalent metal salts and sodium silicate using these materials added separately or in mixtures (3)(4)(5)(6). Flotation of calcite was also studied with respect to its function as a carrier in the beneficiation of kaolin clays by Ultraflotation (7) (8) (9). The carrier used in Engelhard Minerals & Chemicals Corporation's industrial Ultraflotation operation is calcite. This fact, coupled with the continuing interest in Ultraflotation phenomena, led to a study to determine the effect of polyvalent metal-silicate hydrosols on the flotation of calcite.

Jan 1, 1978

By D. J. Reddish

The paper describes a case study where numerical modelling has been applied to predict potential risks associated with inflows of water in active mine workings from an overlying sandstone aquifer. The objective of the modelling was to predict the development of strata fractures and strains as the longwall panels were extracted and investigate their relationship to an sandstone aquifer. The numerical modelling study also included the investigation of the effect of mining on a fault that existed close to the start position of one of the panels. The potential effects of mining on the fault were undertaken by parametric studies adjusting properties for the fault and the relative position of extractions, which allowed the mine planner to position the panel layout accordingly.

May 1, 2003

By George Filz, Morales, Carlos, Bertero, Filippo Maria, Alessandro, Leoni

"The Deep Mixing Method (DMM) represents a viable solution to improve adverse geotechnical properties of foundation soils for many practical applications. A pre-construction soil investigation campaign is necessary to assess soil properties and to retrieve samples of different soil layers for a laboratory Bench Scale Testing program (BST). The BST has to be designed using various binder types, binder contents, and water/cement ratios in each of the soil types. Following the laboratory program, a full scale Field Test (FT) is typically necessary to verify the results of the BST. This paper will highlight the differences and the importance of performing both pre-construction laboratory tests and field tests to ascertain the proper mixing parameters in the different soil layers. Comparative analyses and interpretations between the lab and field stages, along with accumulated information about soil properties and quality control (QC) results, allow fine-tuning the production parameters throughout a project. Three Deep Mixing Method projects, where both laboratory and field tests were executed, are illustrated: (1) The LPV 111 Project (New Orleans, LA, USA): DMM was used for ground improvement/foundation strengthening to stabilize and support the burden of a new levee raise; (2) The Rio Puerto Nuevo Project (San Juan, PR, USA): DMM was applied to improve the soils adjacent to a 90"" forced sewer main relocation and to improve the soils for the base of a new drainage channel; and (3) State Road 83 (US 331) over Choctawhatchee Bay project (Walton County, FL, USA): DMM was applied to stabilize the causeway sections of the bridge enhancement project. Data recorded during laboratory and field tests for these projects were analyzed and interpreted to select the most appropriate construction parameters to provide a final high-quality product.INTRODUCTIONThe Deep Mixing Method (DMM) represents a viable solution to improve adverse geotechnical properties of foundation soils in many situations. The effectiveness of working parameters depends largely on the physical and mechanical properties of the soil to be treated. Therefore, well designed laboratory and field test programs, aimed to disclose the interaction between the site-specific soils and the mixing parameters, are essential to achieve the desired end product.Generally a pre-construction soil investigation campaign has to be performed to assess soil properties and to retrieve samples of different soil layers for the laboratory Bench Scale Testing programme (BST). The BST has to be designed using various binder types, binder contents (or cement factors - CF), and grout water/cement ratios (W/C) in each of the soil types; the selection of the different combinations and dosages for the BST is based on past extensive experiences on similar materials. Following the laboratory programme results, a full scale Field Test (FT) has to be designed and executed, installing several DMM elements to verify the results of the BST and fine tune the construction parameters, with the appropriate binder type and dosage and the most effective equipment and tool configuration."

Jan 1, 2015

By G. H. McKay

AT the Eagle mine, near Gilman, Colorado, where the Empire Zinc Company have installed an underground mill, transportation problems were comparatively simple. A railway siding on the Denver and Rio Grande railway is equipped with an unloading dock or platform at the portal of their service incline adit to the mill. This 18-degree incline is approximately 600 feet long from the unloading track to the head of the mill skipway. For the Big Missouri mill, upwards of 2,500 tons of material and equipment had to be trucked from tidewater at Stewart, B.C., a distance of 21 miles to the Big Missouri camp at elevation 2,800. From that point, this freight had to be moved either over or through the Big Missouri ridge, rising to elevation 3,450, to its final location 800 feet from the surface between elevations 2,150 and 2,350. Immediately after leaving the government dock at Stewart, the road crosses the International boundary line into Hyder, Alaska, and then follows a water grade for eleven miles along the lower stretches of the Salmon river. leaving the river, the road climbs for two miles before crossing back into British Columbia territory at Silver Heights, and then continues for another mile and a half to where the Big Missouri road branches off from the main road to the Premier mine. For a distance of four miles from the junction of the roads, the Missouri road is very narrow, with many sharp curves and with irregular up and down pitches and grades up to 25 per cent until it reaches the Summit. From there on, a fairly easy grade leads a mile and a half to the end of the road on Joker Plats. In winter, the last stretch of road is subject to heavy snow drifting, especially through a narrow funnel-shaped gulch, known as 'The Gap', where the snow may pile up to a depth of over twenty feet.

Jan 1, 1938

By A. Desbiens, A. Pomerleau

During the summer of 1994, a new PID-based control strategy was installed on line B of the grinding circuit at the Kidd Creek Division of Falconbridge Ltd. Part I of this paper described the methodology used to select the appropriate control strategy using a phenomenological dynamic simulator. Part II presents the implementation of the control strategy. Prior to the controller installation, it was necessary to solve various problems related to the process, such as a cyclic behaviour of the rod mill feed tonnage, a problem related to the mill water source and the calibration of the flowmeters. Once these problems were solved, the control strategy was accomplished in two steps. Step 1 corresponds to the installation of control loops to regulate the pump box level and the cyclone overflow density. Step 2 describes the implementation of a loop to control the cyclone feed density. According to Part I, a loop to control the circulating load is also part of the original design. However, reasons are given to explain the rejection of this loop. For both steps, technical procedures such as filtering, process identification and controller tuning are detailed. Finally, the operator’s interface is briefly described.

Jan 1, 1997

By William Gleason

"What will the mine of the future look like? Will it resemble the current operations that supply the world with the products it needs to function, or will it be something totally different? How will the demands from the communities that are most affected by mining operations shape the mine of the future? How will technology and innovation be used to help miners reach deposits that are getting harder to access, and what are the dangers of this new world? Who will work at the mine of the future, and what will that work look like?These are questions that do not yet have definitive answers, but they are questions that need to be asked for the mining industry to move into a future that is as filled with uncertainty and challenge as it is with promise and opportunity.On Feb. 16, the 2015 SME Annual Conference and Expo and the 117th CMA National Western Mining Association conference began with a keynote address, "The mine of the future: Forecasting opportunities and challenges for the global mining industry." Panelists from five sectors of the mining industry participated in the session, which was followed by the conference and expo, that in large part, were also trying to answer the question of what the mine of the future will look like.In coming months, Mining Engineering will continue the discussions and answer some of the questions submitted by members of the 2,000-person audience during the keynote address in a monthly feature called, "Predicting the Mine of the Future," and in Thought Leaders Podcasts with the panelists and other industry experts."

Jan 1, 2014

By D David

Amongst those whose task it is to design tumbling mills and other comminution machines there is an almost religious divide between devotees of the Bond method and devotees of other methods developed in more recent times. For a decade or so the issue was between the Bond power-based methods and the JKMRC (JK) simulation based approach. The newest method to challenge the status quo is power-based and was developed by Steve Morrell. As the title suggests, this paper will take some liberty at concluding that Fred Bond and Steve Morrell may be separated by history, but not by their approaches to their individual contributions to the science of comminution. Another driver for the paper is that although it is good to have diversity of thought, the existing divisions are problematic for those of us signing public disclosure documents. If alternative design methods produce materially different outcomes for the mill duty, then at least one of them is wrong or being used incorrectly. At some point the unsustainable argument may need to be put in a court of law that we metallurgists have two or more materially different design methods, each of which is correct! Therefore, perhaps a resolution is needed before this occurs?The works of both Fred Bond and Steve Morrell are each directly related to their contemporary grinding mill design and operational environments. Both their approaches are empirical, borne of observing and measuring real world situations. Both worked with theories that preceded them, gathered their own data and then each saw shortfalls in the status quo.Fred Bond was an escapee from revolution, a victim of The Great Depression, and had several near death experiences during his early site-based career. Perhaps he was fortuitously rescued from himself when asked by Allis Chalmers (A-C) to set up its rock testing laboratory in Milwaukie in 1930. Fred’s testing led him to conclude that neither the Kick nor the Von Rittinger theories explained his measurements. His writings on the failings of these old theories caused a divide between devotees of the old and new methods at that time. After many years, and much thought and plotting of data (the old way!), he came up with his now-famous equations (and his Third Theory) which have stood the test of time, certainly in the world of Bond-era machines.Coming from England via several African diamond mines, Steve Morrell immersed himself into the comminution world of the JK in Brisbane about a decade after Fred passed on. The JK had developed its semi-autogenous grinding (SAG) simulation framework using its own pendulum breakage tester, itself a derivative of the twin pendulum impact device invented by Bond decades earlier. At the JK Steve developed his authoritative Tumbling Mill Power equations and was involved in real world analysis of comminution problems on the global stage. Steve’s JK experience coincided with the demise of the rod mill, the rise of autogenous grinding (AG) and SAG milling and a rapid expansion in concentrator capacity.Morrell left the JK to pursue his own interests, which included ongoing consulting work, now demanded by the comminution world. He then turned to investigating a growing list of discrepancies between the opinions of designers and theoreticians, and the factual outcomes. The Morrell Method of design arose from this re-examination of ore testing, real world operating data and these glaring and expensive discrepancies between design and outcome. The elements necessary for a relook at the world of rock breakage were in place!CITATION:David, D, 2017. Steve and Fred would have been mates – a comminution design evolution story, in Proceedings MetPlant 2017, pp 2–11 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Sep 11, 2017

By James L. Hendrix

This paper is intended to give the reader an update on the work being done at the Mackay School of Mines about the fate of cyanide on precious metals mill tailings waste. During the last two years several tailings impoundments have been sampled and analyzed for total and free cyanides. From our sampling program we are beginning to learn valuable information concerning the fate of cyanides in precious metals mill wastes. Included in this paper is a detailed description of our sampling and analytical techniques. Also, some of the data obtained from five sites are given.

Jan 1, 1986

THE most successful and largest meeting of the Auxiliary to the A. I. M. E. was held this year. Great praise is due Mrs. Arthur S. Dwight, the acting chairman of the Ladies' Committee in the ab-sence of Mrs. Barron, and the other members of her committee for the able way in which they planned and carried out a varied and interesting program. Miss Margaret Callow, chairman of the Junior Committee, with her co-workers, made the days delightful for the Junior members, as well as visiting daughters. Under the leadership of Mrs. Jenkins, the registration of the ladies proceeded smoothly Monday morning. At the Mrs. Jenkins became ill with pneumonia on the second day of the meeting and was taken from the dinner to a hospital where she died the following Sunday. Born in Kansas City fifty years ago, she was an active and valued member of the Auxiliary in which she had long represented the Puget Sound Section. Mr. and Mrs. Jenkins, the latter treasurer of the Utah Consolidated Copper Co., had previously lived at McGill, Nev., where they are well known. She leaves a son and a daughter. luncheon on the fifth floor, Mrs. DeGolyer and Mrs. Church arranged a delightful hour, when greeting visit-ing friends proved more. interesting than food. Mrs. Bain efficiently ushered the ladies through the after-noon's program, seeing that they all found the buses on time. The first stop was at the Cloisters, where the quaint carvings and the faint odor of incense trans-ported all the visitors to the Middle Ages. That atmos-phere still clung, as we all looked at the marvelous collection of old Chinese jade, at the Metropolitan Museum, which was the next stop. The buses then took us to the MacDowell Club, where Mrs. Dwight gave a charming welcome, in the absence of the hostess, Mrs. Barron. The program, by Mr. and Mrs. Hardesty John¬son, was such a delight that repeated calls induced the artists to graciously respond with an encore. Then Mrs. Coster and Mrs. Sharpless assisted Mrs. Dwight in serving tea, about the glowing fireplace. In the evening the theater-goers guided by Mrs. Jordan were thrilled by "Interference.:" A detailed account of the annual meeting, in many ways the most interesting the Auxiliary has had, will be published later. This held the attention. of the mem-bers both morning and afternoon, on Tuesday. The absence of the President, Mrs. Barron, was much re-gretted, and the letter and the cablegram with her cor-dial greetings were much appreciated. Miss Stone ably presided in the place of Mrs. Barron, and graciously welcomed the incoming President, Mrs. Hoover. Her well-worded speech, accepting the office, was received with much enthusiasm. The visiting members were especially pleased with her description of herself as a "peripatetic-president." promising to visit the various sections as she crossed the continent on her frequent trips to California. An inspiring report was read from each section, and most particularly pleasing was a greet-ing brought by Mrs. Bateman of Toronto, from our sister organization in Canada. The sections are surely to be congratulated on their splendid work, not only for their own members, but also in sending clothing and other aids to the needy, as Mrs. Reynders directed, and in supporting libraries under the leadership of Mrs. Huntoon. The important work of the Educational Com-mittee, with its presentation of scholarships to various deserving young men, has been most efficiently carried on by Mrs. Jennings. Mrs. Jordan has inspired many to help in Braille, and Mrs. Eilers has extended the hos-pitality of the Auxiliary to many. The Washington Section is leading a movement to extend the privileges of Girl Scouting to the girls in lonely mining camps. The officers of the past year received flowers and grate-ful appreciation, and the incoming officers received a warm welcome. Very delightful features of the after-noon were the speech by the President of the A. I. M. E. for the coming year, Dr. George Otis Smith, and when a visiting member rose to say how much all the visiting members had enjoyed the Auxiliary's hospitality. The banquet and dance at the Waldorf were the most brilliant the Auxiliary has attended. Nearly twelve hundred were there to enjoy the festivity and to hear the speeches given, as Mr. Hoover and the other re-cipients accepted their medals and awards. The young people, the future supporters of the A. I. M. E. and the Auxiliary, enjoyed more hilarious tables in the bal-conies, and all enjoyed the dancing later.

Jan 3, 1928

By M. M. Wong, J. E. Klosterman

Scrap beryllium chips ( nominally 96 to 97 percent Be ) were electrore fined in a prototype cell with 408 lb of electrolyte composed of 52.4 mole - percent LiCl , 36.3 mole - percent KC1 , and 11.3 mole - percent BeCl2 . The cell temperature was 500 ° C. In a typical 10-3 /4 - hour deposition cycle , 0.415 pound of metal was produced ; the metal contained impurities in parts per million as follows : C , 700 ; 0 , 610 ; Al , 34 ; Ca , 32 ; Cu , 20 ; Fe , 25 ; Mg , 9 ; and Mn , 23 . Operation of the prototype cell for 2 years demonstrated that adapting the electrorefining process to an enlarged scale of operation presented few difficulties in mechanical functions , maintenance of optimum operating conditions , and control of product purity . After the spent anode feed was leached in a 5 - percent nitric acid solution and the fine - sized particles were removed , it was recycled in some tests . The metal produced was somewhat higher in impurities than metal from the fresh scrap chips .

Jan 1, 1964

By K. Svens, M. Lahtinen, L. Lehtinen

"Outotec's direct leaching process is an atmospheric leaching process for sulphidiczinc concentrates. The direct leaching process, based on special leaching reactors developed by Outokumpu and leaching know-how, is the most economical way to produce electrolytic zinc. The newest industrial-scale application of Outotec's direct leaching process will be started up in 2008 in China at Zhuzhou smelter. The process isintegrated to the existing production plant, replacing part of the old production facilities by modern technology and increasing the production capacity significantly. The process equipment supplied by Outotec includes also tailor-made reactors designed on the basisof the work and experience of Outotec Research Centre."

Jan 1, 2008

By J. T. Lapsley, I. I. Cornet, A. E. Flanigan, R. Hultgren, J. E. Dorn

With the greatly expanding use of magnesium during the war, it appeared necessary to the War Metallurgy Committee that procedures of heat treating common magnesium casting alloys be investigated systematically. Accordingly, the National Defense Research Committee of the Office of Scientific Research and Development placed a research contract with the University of California, supervised by the War Metallurgy Committee. Research on the solution heat treatment and aging of magnesium alloy AZg2, (formerly ASTM No. 17; also known as Dowmetal C or AM26o) which was done under "Restricted" Project NRC-2I, in 1942-1943, and reported in detail in a final report to the OSRD on September 3, 1943, is the basis of this paper, which has been released for publication by the OSRD. American experience with magnesium alloys prior to World War II was limited, although some of these alloys had been in commercial use since 1909. Requirements of the aircraft industry for light alloys made it imperative to understand and utilize the advantageous strength-weight properties of magnesium castings. Magnesium casting alloys are commonly solution heat- treated to increase their ultimate tensile strength and ductility; this treatment may be followed by an age hardening at elevated temperatures, which raises the tensile yield strength but diminishes the ductility. In the present investigation, AZp was studied to determine the effects on properties of various solution heat treatment and aging schedules. The principles of heat treatment of magnesium alloys are the same as for other non-ferrous alloys. The alloy studied, AZp, has a nominal composition of 9 pct aluminum, 2 pct zinc, and minor constituents. Fig I shows, by the projection of isothermal sections on the concentration plane, the solubility surface1 of the ternary magnesium-rich solid solutions as determined by X ray 'analysis. From this figure it may be seen that above approximately 375°C (707OF), AZp alloy is a single phase alloy at equilibrium; below this temperature the equilibrium condition is a two phase alloy. The beta constituent which precipitates from the solid solution exerts a hardening effect. Because the zinc concentration is only 2 pct, ancl because of its solubility relations, AZqz resembles a binary alloy of magnesium with aluminum. The solubility curve1 of Fig 2 shows how rapidly the solubility of the beta phase decreases with decreasing temperatures. Unlike many aluminum alloys, magnesium alloys do not age harden at room temperatures; precipitation hardening of AZ² alloy is performed at about 177°C (350°F). At this temperature about 3 pct aluminum

Jan 1, 1949

By R. Altındag, D. Akbay

The point load index is a simple, fast, and inexpensive method for determining rock strength and can be applied both in the field and in the laboratory. There are, however, some disadvantages and limitations to the method, and the test results can be affected by the person carrying out the test, the rock characteristics, or the test device. In this study we describe an investigation into how the point load index value is affected by the shape of the conical platens used in the test. Point load index tests were carried out using different devices fitted with conical platens of different spherical radii, and on a modified device which circumvented the limitations/disadvantages. It was seen that the point load index value increased as the platen radius increased, as expected. In the case of testing using non-standard conical platens, an equation is proposed to normalize the point load index value with respect to the standard spherical radius value.

Nov 1, 2021

By Joseph Cervik, Gerald L. Finfinger

This Bureau of Mines publication reviews underground methane drainage pro- grams being conducted in various coalbeds. Equipment used in drainage programs such as drills, underground pipelines, and methane monitoring systems is described.

Jan 1, 1980

By Neha Shukla, Nikhil Dhawan

The current study examines the extraction of rare-earth elements from trichromatic phosphor of discarded tube lights via baking processes. The Y2O3: Eu3+ (YOX) and BaMgAl10O17: Eu2+ (BAM) phases completely decomposed during acid and alkali baking with > 90% Eu and Y extraction. Prior, selective acid leaching of the YOX phase enhanced the acid baking process at a lower temperature (< 230 ℃). Feed acid baking showed a maximum 87% Tb, 36% La, and 17% Ce extraction at 500 °C, 0.5 h, 1 ml/g H2SO4, and alkali baking yielded 16.1% Tb, 86% La, and 73% Ce at 300 ℃, 0.5 h, 50 wt.% NaOH. The acid baking of the acid-leached phosphor yielded 72% Tb, 95% La, 63% Ce, ~ 95% Y, and Eu extraction at 300 °C, 0.5 h, 1.05 mL/g H2SO4. Lower Tb extraction during the acid baking of acid-leached phosphor can be attributed to the formation of Ba3Tb( PO4)3 and BaTbO3 phases. Insoluble Si3Tb5 phase formation and partial decomposition of CeMgAl11O19: Tb3+ (CMAT) phase in the alkali baking route leads to lower Tb extraction. The acid baking process is suitable for extracting Tb, Eu, and Y, whereas the alkali baking process is suitable for La and Ce. The thermal analysis of phosphor and flux interaction depicts that alkali baking is less energy-intensive than acid baking. In comparison, the one-step acid baking process and the two-step alkali baking process yielded desirable extraction results (87% Tb, total RE (rare earth) 78.5% and 50.4% Tb, total RE 59.3%). The product yield in the acid and alkali baking route of feed, acid-leach phosphor is 36%, 29%, and 39%, 28.2%, respectively, with ~ 98% mixed rare-earth oxide purity.

May 5, 2022

By A. C. Johnson, es Hol, E. O. Binyon

"INTRODUCTION AND SUMMARYThe tungsten properties of Lincoln Mines, Inc., and North Tem Flute Mining and Development Co. were first explored by the Bureau of Mines in 1942. Work on the project comprised trenching, sampling, a small amount of road and trail construction, and a small amount of core drilling. From April 13 to December 10, 1944, additional diamond drilling was done by the Bureau of Mines to test the lateral and downward extensions of the various tactite zones along the contact south of the Lincoln mine, including the property of the North Tem Piute Mining & Development Co.Claims leased by the Lincoln Mines, Inc., are in secs. 25 and 36, T. 3 S., R. 56 E.; secs. 30 and 31, T. 3 S., R. 57 E.: and sec. 1, T. 4 S., R 56 E., M. D. B. & M., in the Tem Piute Mining District, near the north end of the Timpahute Range in west central Lincoln County, Nev. D. B. Fegles is president of Lincoln Mines, Inc. and general offices are in the Wesley Temple Building, Minneapolis, Minn.In June 1945, the Atolia Mining Co. leased the property and purchased the mill and mining equipment from Lincoln Mines, Inc. P. R. Bradley is president of the Atolia Mining Co., whose offices are in the Crocker Building, San Francisco, Calif. This company surrendered the lease on the property on September 30, 1948. The property owners are continuing operations and are now engaged in building a 20-ton mill.The claims of the North Tern Flute Mining & Development Cc. are in sec. 1, T. 4 S., R. 56 E., M. D. B. & M. Merle F. Schofield is president of the company and maintains an office at Hike, Nev. These claims were leased by H. P. Laslett, of the Utah Nevada Mining Co., in 1945 and by the Atolia Mining Co. in 1946. The owners are now doing some exploratory work."

Jan 1, 1950

By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z&apos; the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z&apos; is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.&apos; For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7&apos;8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964