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THE Mining Methods Committee during the past year has spent much of its time developing the interest of members of the Institute in the work that comes under its direction. The response on the part of the membership has been most encouraging and in order to give a concrete form to the program which it hopes to develop, an "Outline for Papers on Mining Methods" has been drawn up and is herewith submitted for consideration. This outline has slowly taken shape until it now represents ideas contributed by a great many men, and it is hoped that it will be suggestive and helpful in the preparation of papers. This program can be used for the preparation of papers covering single large operations or, preferably, as the basis for a description of methods and the presentation of results obtained either in different districts or in different branches of the industry. The Committee presents this outline for the consideration of the various Sections of the Institute with the request that they will endeavor to interest the members of the Sections in covering comprehensively the mining operations with which they are connected. It is not the plan of the Committee to publish a paper on every mine, giving all the details outlined, but rather that an engineer familiar with a district prepare the general information and engineers of each important mine in the district compile the specific information of the mine with which they are connected. The general information and the specific information shall be sent to the Committee, and with this information the Committee will prepare a paper on the results obtained under the various mining methods in the different districts. The Committee requests that all papers shall be compiled under the direction of the Chief Engineer of the company and then submitted to the General Manager before acceptance for publication or compilation and tabulation with other similar data. Where the study of this subject approaches the fields of other standing committees of the Institute, the

Jan 5, 1922

By John E. Conley

The production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.' The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnstonr2 Smyth and Adams,3 Ralston et al.,4 Furnas,6 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894" to 898' C. The dissociation of dolomite and magnesite, although studied by several investigators,4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (I) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1942

By John E. Conley

The production of lime by the burning or calcination of limestone, including all varieties from true dolomites and magnesian limestones to high-calcium types, continues as one of the essential basic industries. In 1937, a total of 4,124,165 tons of lime valued at approximately $30,091,000 was produced in the United States.' The importance of any contribution to our knowledge on the mechanism of the lime-burning process is, therefore, obvious. The burning of limestone has been practiced since the earliest days of our civilization, and the literature on the various phases of the industry is voluminous. Calcination of the various types of limestone has been studied by many previous investigators, but some points require additional research. Each occurrence of limestone provides an opportunity for specific investigation, because the characteristics of stones in different localities vary. Knibbs13 has given an excellent discussion of available data on the theory of lime and magnesia burning. The thermal dissociation of calcium carbonate has been studied more recently by Johnstonr2 Smyth and Adams,3 Ralston et al.,4 Furnas,6 Potapenko,6 and Southard and Royster.7 As a result of these investigations the dissociation temperature at atmospheric pressure has been established as 894" to 898' C. The dissociation of dolomite and magnesite, although studied by several investigators,4,6,8 still requires clarification by additional data. The calcination of limestone was studied for a twofold purpose: (I) to extend our information on the mechanism of the lime-burning process and (2) to standardize the conditions for calcination of high-calcium and dolomitic limestones for subsequent hydration tests on the lime.

Jan 1, 1942

By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7' has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers' requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant

By E. O. Fromm, R. I. Jaffee, R. M. Evans

IN connection with a research on gallium alloys, a method for the thermal analysis of very low melting alloys was developed, which appeared to be worthy of more than passing interest. As used, the method was suitable for work in the temperature range, — 72° to 250°C. However, with suitable adjustment, the method could be adapted for use over broader temperature ranges. The Rosenhain temperature gradient furnace,' adapted for low-temperature use, was the basis for the method. The gradient was set up in a stainless steel tube. The specimens were lowered through it at a constant rate while time-temperature or inverse rate data were taken. It was essential to maintain careful control of the top and bottom temperatures of the gradient. Also essential was good heat transfer from the walls to the specimen. This was accomplished by a liquid heat-transfer medium.

Jan 1, 1953

By Walter C. Labys

INTRODUCTION Interest in multicommodity stabilization schemes has increased recently for several reasons, a most important one being the experienced wide swings in primary commodity prices. These prices rose sharply between mid - 1972 and end - 1974 giving commodity exporting countries an opportunity to gain sizeable increases in export earnings. But since then, prices have tumbled and these countries are searching for a means to stabilize if not to increase their earnings. While this problem is particularly serious for developing countries, the developed countries are concerned about the impending upward price swing, which would increase inflation before recovery from the world recession is assured. As a direct consequence of the emergency meeting of the U.N. General Assembly devoted to commodity problems in April of 1974, interest has been renewed in the Keynesian (4) plan for an international multicommodity buffer stock program. In particular, UNCTAD (8) is designing an integrated commodity scheme to be discussed within that body. In terms of approaches that have appeared in designing such a program, none exist which relate to the interpretation of the independence and interdependence of prices of the commodities of interest. Typical criteria for selecting commodities for the scheme have included their importance in world trade, their particular origin from developing countries, and their feasibility for storage. But the financial management of a multicommodity buffer stock requires a consideration of commodity prices, yields, and risks as does as any portfolio of assets. The approach which we take in this study is that of application

Jan 1, 1977

By D. J. Carney, J. Chipman, N. J. Grant

An absolute calibration has been achieved for sampling and analyzing liquid steel for hydrogen based on Sieverts' values of hydrogen solubility in iron. Further checks were made in nickel, iron-nickel, and 18-8 stainless melts. The sampling method was successfully applied to a large number of commercial steel melts in various types of furnaces. The concurrent problem of sample storage was also solved. THE problem of sampling of liquid steel for hydrogen is more difficult than the problem of analysis. Hydrogen has a greater mobility than any other element; it is the only element that will diffuse out of steel at room temperature. In accordance with the known relation between temperature and diffusivity, the diffusion of hydrogen is extremely rapid at the temperature of liquid steel. Consequently, in the past, attempts to quench molten steel to retain the dissolved hydrogen have not been as successful as similar attempts with nitrogen or oxygen. The retention of hydrogen is especially difficult since it will continue to escape at room temperature even if the molten metal has been rapidly quenched. The hydrogen sampling methods may be classified broadly as (1) the rapid quenching techniques which attempt to preserve super saturation and (2) those methods which attempt to collect the gases evolved as the metal freezes and cools to room temperature. With all methods of sampling but especially with the rapid quenching methods, there is also a concurrent problem of storing the sample until analysis is undertaken. The two problems are interrelated and must be considered together when discussing liquid steel sampling techniques. The major obstacle in liquid steel sampling has been that there was no way of evaluating properly the various sampling and storage techniques which have been developed. It has not been possible to compare the accuracy of the various methods. For evaluation of sampling methods some known standard is required; this may be found in the published work on the equilibrium solubility of hydrogen in liquid iron which has been determined in three separate investigations.1,2,3 The data are shown in table I. Sieverts' original method of obtaining gas solubilities involved measurement of the volume of gas required to saturate the liquid metal contained in an evacuated bulb of known volume. This procedure, improved by introduction of high frequency induction heating, has yielded reproducible results which appear to be entirely dependable. Using Sieverts' method, it has been proved for iron and other metals and alloys that the hydrogen solubility is proportional to the square root of the pressure of the hydrogen gas above the liquid, so that one may work with various partial pressures of hydrogen to put different amounts of hydrogen in solution. From Sieverts' law it is possible to know accurately what amount of hydrogen is dissolved in the liquid metal at the time of sampling. The accuracy of a sampling method may be gauged by reference to this known solubility. It was the purpose of this investigation to develop a method for sampling liquid steel and for storing the sample so that the analytical result would represent the actual hydrogen content of the metal bath. For this purpose an induction furnace was

Jan 1, 1951

By E. Hoek

The stability of a rock structure depends primarily upon the extent to which fracture develops within the structure, The prediction of the extent of potential fracture, the first step in the study of fracture development, involves a knowledge of both the stress distribution in the structure and the criterion which governs rock fracture under various stress conditions. While a great deal of research effort has been devoted to the development of techniques for analyzing the stresses in mining and civil engineering structures1-3 and to the investigation of the fracture mechanism of rock 4-6 relatively little attention has been paid to the application of available knowledge to the solution of practical engineering problems. This paper describes a photoelastic technique for the determination of potential fracture zones in certain types of rock structures. A practical example, based upon a problem which might be encountered in designing the layout of deep-level mine excavations, is given as an illustration of the application of this technique. STRESS ANALYSIS AND ROCK FRACTURE In deciding upon the technique to be used for the solution of a problem involving the prediction of rock fracture it is necessary to consider: 1) What type of stress information is required to satisfy the fracture criterion for rock; anti 2) How this information can most conveniently be obtained. It has been established, both theoretically 4,7 and experimentally 5,6,8that the fracture of hard rock depends primarily upon the relationship between the algebraically greatest and the algebraically smallest of the

Jan 1, 1967

By M. I. Kabir, R. S. Schechter, L. W. Lake

This paper presents the development and application of a novel scaling technique that, when used with a streamline model, causes a "bundle" of one-dimensional (1-D) problems to reduce to a single 1-D calculation. The 1-D bundle is the streamline representation of a two-dimensional (2-D) problem. The 1-D calculation accounts for chemical-rock interactions and the streamline model for areal sweep. The scaling technique significantly reduces computation time, is readily modified to desktop calculations, and can be applied to both absorbing and reacting species. The work was sponsored by the US Bureau of Mines.

Jan 1, 1986

By E. F. Kingsbury

ONE of the well-known and important uses of the noble or precious metals has been for electrical contacts. In fact, the elements of this group, comprising gold, silver and the six platinum metals, have been called "noble" because of their ability to resist heat and corrosion, properties which were early found to be of importance in good contacts. Of these, platinum and its iridium alloys, palladium, and silver, have been extensively used. In recent years the electrical industry has been responsible for about one-eighth of the total consumption of the platinum metals in the United States. Information is not available as to what part of this one-eighth has been used for contacts but it is certainly an important one. SUBSTITUTES FOR PLATINUM During the past 20 years a considerable number of contact alloys have been proposed in the patent literature largely with the aim of more or less replacing platinum by gold or silver, and some of these alloys are finding increasingly widespread application as the reliability of their performance becomes established. From even the partial data-at hand it appears that this substitution by the less precious metals has replaced at least one-half of the amount of platinum that the entire electrical industry would otherwise be consuming at the present time. While the subject is of considerable interest to the metallurgist it is , even more so to the electrical engineer and it is surprising that the literature records no systematic and comprehensive investigation along these lines. Practically all the scattered work on noble metal contacts has centered around platinum as a Standard and has had two more or less distinct aims. One of these has been the replacement of platinum by cheaper materials, and the other, the development of materials of superior electrical performance. The merit of a contact metal has been assumed to be dependent on its infusibility, and since the more precious metals have the higher melting points there has naturally been an association of the two qualities in the sense that the more precious were

Jan 1, 1928

By C. G. Dunn, P. K. Koh

TWO recent review papers have considered the origin of primary and secondary recrystalliza-tion textures from the point of view of oriented nucleation and oriented growth theories."' Both theories require nuclei for primary recrystallization but provide no unequivocal answer to the question of what nuclei are. The answer to the same question regarding secondary recrystallization, however, often is that nuclei are certain primary recrystallization grains or primaries. The two theories differ, however, in specifying what the certain primaries are. In support of the oriented growth theory Beck and Hua originally stated "It may be assumed that in a re-crystallized material, even with a strong texture, there always are present some grains of practically any orientation. These may serve as nuclei for the coarse grains, provided that conditions are favorable for their growth." In commenting on this statement one would say that there are two restricting conditions: namely, that 1) the certain primaries (nuclei) are large enough to grow, and 2) their boundaries have high mobility. More recently Beck2 has con-

Jan 1, 1958

By I. A. Lange, A. M. Richardson

Although methods for determining shaft lining thickness are well documented, little attention has been given to the design of station breakouts and other related shaft ground support structures. This paper discusses design of selected shaft structures for the Cathedral Bluffs project, a planned 54-kt/d (60,000-stpd) oil shale mine in western Colorado. Design philosophy and construction sequences used in the three completed 520-m (1700 ft) deep, 4.6-m (15 ft) to 10.4-m (34-ft) diameter shafts are described.

Jan 1, 1984

By D. G. Westlake, U. F. Kocks

WHILE single crystals of most materials with cph lattice structure show essentially unlimited ductility, polycrystalline specimens of the same materials exhibit the entire range of ductilities. A difference between the ductility of single crystals and polycrystals may be associated with the special stress concentrations to be expected, for example, at the intersections of slip bands or twin lamellae with grain boundaries. Whether such stress concentrations prove catastrophic depends on the cleavage strength of the material, the size of the stress concentrations, and the speed with which they are formed. Thus, the ductility may vary in degree from material to material. Another possible reason for differences in ductility between single crystals and polycrystals is that a sufficient number of independent deformation modes must be available to insure compatibility between the macroscopic strains in neighboring grains.''2 This criterion is often taken to be a necessary condition for any polycrystal ductility whatsoever, not as one that determines different degrees of ductility; thus, a material with an insufficient number of independent deformation modes would have to be brittle as a polycrystal. The "sufficient number" is five if every grain is to accommodate arbitrary shape changes ("von Mises criterion "). We should like to argue that fewer than five independent modes may be sufficient to satisfy compatibility conditions; and that the internal stresses set up when the plastic strains are not compatible reach the theoretical fracture stress only after a significant amount of macroscopic strain has taken place which may vary in magnitude from case to case, allowing an influence on the degree of ductility. Experimental evidence for these statements is taken from the following review of the number of independent deformation modes observed in the various cph

Jan 1, 1968

By T. P. Meloy

In a recent paper, Gaudin and Meloy1 derived a size distribution function for single, impact fracture. Mular2 extended the use of this size distribution to describe the output of carefully controlled grinding experiments. As it stands, the function is difficult to compute. Consequently, a series of tables of the function are presented below: where M(x) is the cumulative fraction finer than size x when x is particle size. Weight percents are tabulated for the single parameter, r, in three different size ranges: from 0 to 1, from 1 to 10 and from 10 to 100. Tables I, II and III are cumulative percent finer and Tables IV, V and VI are for weight percent passing screen size x, retained on the screen below. A number of conditions from the table are plotted in Figs. 1 and 2. Fig. 1 is a plot of the cumulative percent finer vs. size, and Fig. 2 is the weight per-

Jan 1, 1963

By C. W. Gibbs, E. K. Parks

In 1929 the Standard Oil Company of California commenced the development of a device for obtaining temperatures and pressures in flowing and shut-in wells and of suitable running equipment for such a recorder. Although simple in principle, the recorder has required much experimental work in its development. The various problems have now been solved to such an extent that it is believed that the apparatus affords a sturdy and reliable means for obtaining information regarding depth pressures,—apparatus that may be turned over to a well gang for routine operation. As an example of the rough usage the device will withstand a recent incident may be cited. Owing to failure of the lowering line at the conclusion of a run a recorder was dropped some 6300 ft. through 2 1/2-in. tubing filled with gassy oil. The device was fished out undamaged and with the pressure record intact, although the instrument had been subjected to a pressure greater than 2300 lb. per sq. in. for some 24 hr. after impact at bottom. Description of Recorder The instrument is of the continuous recording loaded spring type (Fig. I). Temperature is not recorded continuously but is obtained by maximum recording thermometers in an auxiliary thermometer well. The entire instrument assembly, from bottom of the recorder to top of the socket, is 6 1/2 ft. long and weighs less than 25 lb. The maximum outside diameter of the recorder shell is 1 1/4in., and all attachments need be no larger. This permits lowering the device inside 2-in. tubing. The operating principle is simple. The well pressure acts upon a piston A resisted by the extension of spring B. The spring deflection is recorded by a stylus C upon paper within the recording drum D. Springs.—To improve accuracy at lower maximum well pressures five interchangeable spring assemblies are used. These have maximum pressure ranges of from 250 to 5000 lb. per sq. in. Piston diameter is the same in all cases, and each spring is designed for a deflection of about 5 in. for maximum pressure loading. A complete spring assembly there-

Jan 1, 1934

By Keith E. Robinson, Brian Stimpson

INTRODUCTION In inclined sedimentary strata slope failure may occur by sliding along bedding and along a discontinuity or weak zone, as illustrated in Fig. 1. This mode of failure may be called 'bi-linear', as the failure surface is comprised of two linear or approximately linear segments. This type of failure has been suggested for the famous Frank Slide, Alberta, Canada (Cruder and Krahn, 1973) in which an estimated 90 M 5 tons (8.97 x 10 MN) of rock separated from Turtle Mountain and buried the town of Frank. Also, with the increasing depth of open pits and the construction of highways through inclined sedimentary strata this mode of failure is of major concern to the rock slope stability engineer. A computer program for calculating factors of safety for this slope failure mode is provided and includes the ability to vary shear strengths of potential slide surfaces, ground water elevations and wedge geometry. LIMITING EQUILIBRIUM MODEL The simple limiting equilibrium model used in the analysis is shown in Fig. 2. It is assumed that jointing is orthogonal to bed- ding and that the interface between the upper and lower wedges there- fore corresponds to a joint plane or planes. No shear strength is attributed to the interface so that the resultant force, P, from the upper wedge acts normally across the interface. The normal loads

Jan 1, 1983

By THEODORE DWIGHT

Members of the Institute have already received a special pamphlet descriptive of the United Engineering Society building, and wilt doubtless be interested in the progress that has been made up to date-February 24th-in erecting this home for the engineering profession. The old buildings on lots Nos. 25 to 33 W. 39th St., New York, were,' removed many months ago, but final contracts for the new, building were not let until the summer of 1905. The size of the building is 115 ft. on 39th Street, and 88 ft. in, depth; the height from, the sidewalk to the top of the parapet is 220 feet. The cubic contents of the building from the. bottom of the basement floor, to the top of the roof, including the pent houses, is 2,290,000 cubic feet. The number of light's, in the building will be between 4,000 and 4,500. The air supply for Auditorium and Lecture. Halls will amount to nearly 10.0,000 cu. ft, per minute, and the exhaust. to 90,000 cu. ft. per minute. In excavating for cellar and foundations, the average depth where good rock was. found was 37 ft.-it varied, however,: from 27 to 65 ft., due to an old water-course having run through the center of the lot; this condition, and the presence of soft rock, which rapidly disintegrated when exposed to air and water, made the foundation-work very difficult. As two of the column-footings of the building have to sustain a weight of 3,000,000 11) each, the most substantial foundations are necessary; 13,000 cu. yd. of earth were excavated for the foundation and basement; and 1,600 cu. yd. of concrete were necessary, to build up the footings. In the completed building there will be about 3,500,000 bricks. Owing to the number of auditoriums, and their location, and the placing of the library on the top floor; where allowance will have to be made for the enormous weight of 300,000 books, the structural steel work has been unusually complicated in this building. For instance, over the auditorium there are two 60-ton plate-girders, made up

Mar 1, 1906

By Gen-Hua Shi, Richard E. Goodman

In hard, discontinuous rocks, failure modes and stability are controlled to a great extent by the intersection of discontinuities with the excavated surface. We have solved the general problem of finding the shape and size of all blocks formed through the inter- section of any number of joints and excavation surfaces and will demonstrate a simple graphical method for determining which of these is the "keyblock." An example will explain this methodology applied to a simple open pit. The effects of slope curvature in plan or section, will be demonstrated. Finally, we will show how to determine the optimum orientations for the cut slopes. The methodology is based upon a powerful topologic theorem concerning the finiteness of spatial intersections. This paper is a companion to another dealing with underground openings in the Proceedings of the 22nd Symposium on Rock Mechanics (MIT) , July 1981. This paper discusses the rock blocks created by the intersection of discontinuities and excavation surfaces in a rock mass. It establishes principles and procedures by means of which those blocks that are finite and critically located can be identified and described. The main assumptions are the following: 1. The rock itself is assumed to be strong so that the only concern for stability is the movement of rock blocks them- selves.

Jan 1, 1983

By T. S. Lundy, R. A. Padgett

The fact that cobalt diffuses in silver at a much slower rate in a region near a free surface than in bulk material has been demonstrated in a variety of experiments. Various possible mechanisms of this near-surface effect (NSE) are examined in light of experimental evidences. The tendency for surface segregation of some solute atoms appears to be a likely mechanism to explain the effect. UNIDIRECTIONAL and isothermal diffusion from a plane source of radioactive tracer into an isotropic, homogeneous medium follows the Gaussian solution to Fick's second law, or: where A(x,t) is the position and time-dependent concentration of the diffusing species, M is the quantity of diffusant per unit area initially at x = 0, and D is the diffusion coefficient. For a given time, say t = tl, one can easily see that: d In Aixji)_____1_ r2] d(x2) 4Dti Thus, if diffusion data obtained by serial sectioning are plotted as In A(x,tl) vs x2, the diffusion coefficient is obtained from Eq. [2]. The ideal behavior seldom is observed in real systems. Deviations from ideality generally occur either at small or large values of penetration distance. The overall picture is shown schematically in Fig. 1 where Regions I, 11, and 111 are due, respectively, to some near-surface effect or effects (NSE), volume diffusion, and short-circuiting effects. For different systems and conditions of specimen preparation and analysis, the relative importance of Regions I, 11, and I11 may be drastically different. Region I is completely absent in many systems and there is no NSE. In others, however, there may be considerable difficulty in determination of volume diffusion coefficients due to the overshadowing influences of Region I. Such is particularly true when indirect techniques such as the surface concentration decrease or the Gruzin method' are used to find D. In this paper several experiments which had as their goal a better understanding of near-surface effects are reported. Specifically, it is well-known that unusual penetration behavior results for the diffusion of several impurities in ilver- and that considerable controversy exists with regard to interpretation of the published diffusion data. We chose to examine those unusual results which occur for cobalt diffusion in monocrystalline silver395 primarily because knowledge of experimental procedures and materials were readily available. Both radioactive co60 and co5' could be utilized to offer a wide range of available concentration of the diffusing species. Experiments were also performed on the diffusion of AgnO in silver. They gave base-line data for the system—both for technique evaluation and for examination of the vacancy distribution near the surface. I) PROCEDURES Cylindrical-shaped specimens 1.25 cm diam and 1 to 1.25 cm long were cut from 99.999 pct Ag single crystals obtained from Monocrystals Co., Cleveland. One end surface of each specimen was polished flat and etched with a mixture of 20 ml saturated Cr03 solu-tion-20 ml H20-3 ml concentrated HC1. Radioactive tracer (co60 or co5' or Ag'lO, each having a radio-chemical purity of greater than 99 pct) was deposited onto the prepared surface either dropwise with evaporation to dryness of the solution containing the tracer (0.5 N HC1 solution for the co60 and co5' and 0.6 N HNO3 solution for the A"'), by electroplating, or by evaporation from a tantalum or tungsten filament in an evacuated bell jar. The amount of deposited cobalt was varied from many atomic layers of cobalt containing the co60 to approximately one co5' atom per lo6 surface atoms of silver. This large variation in amount of deposited cobalt yielded information about both the influence of a thick-source layer of tracer and solubility effects on the NSE. Such variations were possible because of the large differences in half-lives,

Jan 1, 1969

By Alan C. Noble

INTRODUCTION Forecasting of metal and mineral prices is a complex and hazardous undertaking. In order to accurately forecast prices, the complexities of both marketing and production must be modeled for each commodity. Even with the most detailed model, the economy may change unexpectedly, invalidating the forecast. Because of these factors, this chapter will not attempt to present specific methods for price estimation. It will, however, review the fundamentals of price forecasting as applied to planning and design of the final pit shell. Recognizing that no price estimate can be exact, sensitivity analysis will be reviewed as an approach to coping with these unknown variations.

Jan 1, 1979