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By C. H. Mathewson, P. W. Bakararian

The greatcr part of the literature on the plastic behavior of magnesium dates back to that active period of research in crystal mechanics immediately following the widespread preparation of isolated metallic crystals large enough for the application of conventional methods of mechanical testing. These investigations, performed on single crystals, revealed an analogy between zinc and magnesium with respect to their fundamental mode of deformation. in the operation of glide and twinning, respectively, on crystallographically similar planes. Mathewson and Phillips (1928)' by geometrical analysis identified the plane in magnesium as the twinning plane. Schiebold and Siebel (1931) confirmed this twinning planc, established the basal plane as the plane of slip, and a digonal axis I as the slip direction. They also rcported twin formation in a secondary role on the {IOI} plane. Schmid (1931)³ summarized and discussed the earlier evidence and presented the results of his own experiments on the effect of temperature and small amounts of soluble elements. From X-ray studies on extended wire single crystals, he concluded that slip along the basal plane in the direction of the digonal axis I closest to the stress direction was the sole slip system operating at atmospheric temperature. This conclusion was based on experiments with crystals of many different orientations relative to the stress axis. Special attention was directed to the basal plane and the digonal axis I, as the plane and direction of greatest atomic density. Determinations of resolved shear stress at the onset of plastic yielding-—i.e., the critical resolved shear stress—were also made; the average of these calculations showing 82.9 grams per sq. mm. This value varied only slightly up to 300°C. at which temperature it was found to decrease to 70.5 grams per sq. mm. The extension of his crystals at temperatures above 225°C. further disclosed the presence of new slip systems. After the origince specimens of circular section had been

Jan 1, 1943

By A. W. Ruff

In the last ten years large gains have been made in the field of blasting. These gains have been both in the theoretical and in the practical application of explosives. One of the most publicized changes in the practical application of commercial explosives is the now-prevalent use of ammonium nitrate and fuel oil. The new water-compatible mixture of ammonium nitrate and TNT should also have a large field of application. Most of the theoretical gains have been concerned with the actual rock breakage obtained with explosives. In the last ten years, large gains have been made in the field of blasting. These gains have been both in the theoretical and in the practical application of explosives. One of the most publicized changes in the practical application of commercial explosives is the now prevalent use of ammonium nitrate and fuel oil. The new water-compatible mixture of ammonium nitrate and TNT should also have a large field of application. Most of the theoretical gains have been concerned with the actual rock breakage obtained with explosives. EXPANDING-GAS-BUBBLE THEORY There has been an outstanding change in the conception of how an explosive produces rock failure. The early theory which explained rock breakage was correct for some of the first force-producing agents such as quicklime. When a drillhole was filled with quicklime and water added, the material expanded and steam was generated. The expanding material and the steam exerted a slowly increasing pressure on the sides of the drillhole. The force broke the rock by splitting. Because a great quantity of gas was produced by the deflagration of gunpowder, the same process of the gas pressure splitting the rock was assumed to take place. Even after 80 years of use, the rock-breaking action of all high explosives was thought to be caused entirely by the expanding gas bubble which tore and split the rock. Fig. 1 shows a vertical section through an exploding spherical charge of high explosive. It illustrates the early theory which attributed the entire breakage to the expanding gas bubble. The basic idea of this theory is that the breakage started at the explosive charge and progressed toward the free face. REFLECTED-WAVE THEORY me expanding-gas- bubble theory has gradually been replaced by the reflected-wave theory. The reflected-wave theory explains rock failure by explosives in the following manner: The enormously high gas pressure in the drillhole produces fracturing of the rock on the sides of the drillhole. The fracturing around a 1 1/2-in. diam drillhole is usually confined to an area with about a 6-in. diam. In the fractured area, the pressure of the gas is reduced until the force on the walls is no longer capable of fracturing the rock. Although the gas pressure does not continue to fracture the rock, the pressure imposes a high impact stress on the wall rock. In addition, a pressure or seismic pulse is produced in the rock. The pulse is probably entirely a compression pulse when originally produced in the rock. But, with distance, part of the energy of the compression pulse is transformed into a tension pulse which follows the compression pulse. The explosive charges and burdens used in conventional mine blasting are such that the tension pulse of the original wave is probably too small to be considered in a practical evaluation of the theory. The compression pulse is transmitted through the rock with no associated fracturing.

Jan 1, 1961

By Gregory M. Dexter

Recent litigation in Pennsylvania between three coal-mining companies and a private water company resulted in the payment by the coal companies of the equivalent of about $500,000 to buy a new water supply to replace that which had been damaged by acid drainage from strip mining. An investigation of the relevant facts indicates that the water could have been treated by spending about $40,000 on equipment and $15,000 yearly for chemicals, labor, and power until the contarnination could be reduced about 80 pct. The water company's supply, furthermore, had deteriorated largely by reason of dry weather before stripping was begun by the coal companies. Payment to the water company should not have exceeded $300,000 and could have been as low as $100,000. Strip mining of coal is common in Pennsylvania. The most important objection to it in Pennsylvania is generally acid pollution of runoff water. An outline of the methods, therefore, that could be used to reduce such pollution, to compare acid-contaminated waters. and to treat such waters to make them satisfactory for public and industrial use is worth-while. The watershed of the West Penn Water Co. covers about 4.5 square miles, 20 miles west of Pittsburgh, and has two 90,000,000 gal reservoirs supplying about 1,300,000 gal daily for public and industrial use of which 450,000 gal daily are for two railroads. The pollution arises from weathered derivatives of typical'" Coal Measures"' rocks, the principal source being pyrite (and marcasite) in Pittsburgh and Rooster coals. Springs and seeps on hillsides issue from sandstone and limestone formations intersecting shale or clay land surfaces, or from perched water tables. The two reservoirs create an artificial permanent water table. Soap-hardness tests on three seepage samples taken in a dry summer ranged from 150 to 500 ppm. Water sampled came from aquifers above Pittsburgh and Rooster coals, obviating the possibility of contact with pyrite-containing coal. Since acid contamination of mine waters is the result of chemical reactions of oxygen and water with pyrite, it will be reduced by the exclusion of either air or water. The Sunnyhill Coal Co. has applied this principle in its "contouring" method of strip mining by burying contaminated coal-waste material under a compact, smoothed-up surface of top-soil, gravel, clay, and sand at a cost

Jan 1, 1950

By C. P. Heiner, C. S. Westerberg

Observation of the clinkering action of coal from the Castle Gate D seam in underfeed stokers over a period of years has given rise to the present investigation of the effect of bony coal on clinkering. Some very costly examples of slagging clinkers in particular cases have been of especial interest to the authors. In such cases coal analyses and ash-softening and fluid temperatures have been found of little value. In general, it was noted that slagging mas accompanied by a somewhat higher ash content of the stoker slack, and the suspicion naturally arose that foreign matter was the troublemaker. One would naturally suspect bony coal and rock impurities because of their occurrence and prevalence within the seam and the relative absence of sulphur or other impurities in the coal mined. The test results given herein indicate that the concentration of the bony coal and rock impurities in the coal determines the clinkering tendencies of the ash during combustion. Castle Gate D Seam Extending from the Utah-Colorado line near Grand Junction, Colo., westward to Greenriver, Utah, and thence in semicircular form north and westward to Castle Gate, and from there southward to Mt. Hilgard in central Utah, is a line of nearly perpendicular cliffs, composed of interbedded massive sandstone and shales, making up the coal-bearing horizon of the Mesaverde formation of Upper Cretaceous age. The cliffs face roughly concentrically toward the south and southeast and the strata, with conformably enclosed coal beds, gently dip away from the face of the cliffs and at right angles to their front line. Back of these cliffs the mountain masses rise to an altitude of from 8000 to 10,ooo ft. above sea level. Stretching away from their foot is a great shale plain, on which the towns are situated and over which the railroad lines and highways run. The Castle Gate mines enter the coal beds at their outcrop; the workings extending within a particular coal bed away from the outcrop and under the mountain mass back from the cliff line (Fig. I). Throughout the Mesaverde formation in the Castle Gate general area, there are from two to five workable coal beds. Usually not all of these are coincidentally of workable size and merchantable quality throughout any given large tract. In the Castle Gate mine area, the base of the Mesaverde horizon and coal measures is marked by a massive, cliffmaking, gray sandstone bed 60 to 80 ft. thick. Locally this is referred to as the "Castle Gate sandstone floor." Frank R. Clark, in U. S. Geol. Survey Bull. 793, designates it as the "Aberdeen sandstone." At Castle Gate the various coal beds are designated by the letters A, B, C, etc., commencing with the lowest bed.

Jan 1, 1942

By E. J. Roberts

The theory is developed that the tons ground through a given mesh per day in a wet ball mill is proportional to the percent plus that mesh in contact with the balls and the net power applied to the balls at this point. A grindability test is described. DURING the course of a study of the fundamentals of classification in 1937, the need for a more basic understanding of the action of a ball mill became acute. Unless one knows how classification affects grinding, one cannot hope to effectively improve on classification. The methods of evaluating grinding efficiency that depend on surface developed were studied but soon discarded for two reasons: 1. There was no apparent method which could be generally used to give a reliable figure for the actual new surface developed as a result of grinding. Subsequent papers have not changed this conclusion. 2. The practical evaluation of grinding in the main ore dressing applications was in terms of the percentage retained on a screen which passes 90 to 99 pct of the material and not in terms of surface area. The Probability Theory With the background of our experience in the field of closed-circuit grinding, together with the papers of Lennox,1 Gow,2 Gaudin,8 Fahrenwald,4 Coghill, and others, the approach of the theoretical physicist was then tried. The thought was somewhat as follows: When one grinds in a ball mill, a given expenditure of power leads either to a certain number of point to point blows per hp-hr or to a certain distance of line contact per hp-hr, depending on whether the action of the balls is considered to be cascading or rolling. It is also assumed that the balls actually come together on each blow or during the roll. Then a volume of slurry will be covered per minute which is some function of the size of the particle being considered (see fig. 1). All particles coarser than this size will be reduced through this size. This volume of slurry contains a certain weight of ore, depending on the percent solids and the density of the solids. If we fix the percent solids and the density of the solids and let w be this certain weight of ore in the volume covered, then, in mathematical terms, what we have just postulated is, w —— 8 hp (a) dt If W is the total weight of ore present in the mill, then we can write. W w/8 hp (b) W dt and if C is the cumulative percent plus the size chosen at the start of the time interval dt, w w c/dt W 8 hp x c (c) wc But wc/100 is the weight plus the size chosen which at 100 wc the close of time dt is finer than that size, and W is the decrease in the percent plus of the whole mass of ore or —dC. Then, —W dC/dt 8 hp x C. (d) In other words, the mesh tons ground through a given size per unit of time is proportional to the hp and the percent plus the mesh. A crude analogy would be to picture a 1-ft-wide steam roller going down the road at 1 ft per sec. If we place one egg on the road per square foot, one egg will be smashed per second. If we place a dozen eggs per square foot, a dozen eggs will be crushed per second. Similarly, if all the particles in w are plus the mesh, i.e., C=100, we should have a maximum rate of reduction. If only 10 pct of them are plus the mesh (C=10), we would have only one tenth the maximum rate; if only 1 pct are plus the mesh, the balls have a hard time finding anything to work on. This is where the term "probability theory" comes from. The chances of the balls crushing a particle through a given mesh depends directly on the concentration of particles coarser than this mesh in the general pulp in the mill. Giving W the units of tons and dividing equation (d) through by W, we obtain -dC hp ----- = k---— C [1] dt ton where k is a constant for any one size of particle, density of solid and moisture content of pulp. Eq 1 is the rate equation for a first order reaction and says that the rate of decrease of the percent plus a given mesh with time is directly proportional to the hp per ton applied to the body of ore and to the percent plus the mesh in the ore mass as a whole. Since it is a differential equation, it only

Jan 1, 1951

By William P. Jones

THE consumption of sulphuric acid, one of the most important commodities in our modern industrial world, is often used as a barometer for industrial activity. The economics of acid manufacture are largely dependent upon the location of the place of consumption and the availability of raw materials in that locality. Sulphuric acid is made from SO,, oxygen from the air and water. Therefore the sulphur dioxide is the only raw material to be considered in an economic study. SO, can be obtained from almost any material containing inorganic sulphur, such as elemental sulphur, pyrites, coal, sour gas and oil, metallurgical gases, waste gases, or gypsum and anhydrite. Many tons of acid can also be reclaimed by the recovery and concentration of spent acids. The aim of this paper is to present a guide to the economic aspects to be considered when the installation of an acid plant is contemplated. It must be remembered that 1 ton of elemental sulphur produces 3 tons of sulphuric acid and that the shipping of sulphuric acid by tank car is very costly. The size of the plant must also be given careful consideration. For instance, operation of a plant producing 5 tons of acid per day might be warranted in Brazil or Pakistan, whereas economics usually favor buying quantities up to 50 tons per day for use within the United States. Elemental sulphur, when available at the low price of 1M4 per lb delivered at an acid plant, has always been the raw material most frequently used for sulphuric acid. All conditions favor its use at this price. The so-called sulphur shortage has been the subject of so many technical papers, magazine articles, and newspaper items during the past y6ar that it hardly seems necessary to mention it again, but a very brief review of the matter will serve as a foundation for the discussion that follows. There is no shortage of sulphur. Only a shortage of low-cost Frasch-mined brimstone exists today. Other more expensive sulphur-bearing materials are plentiful, both in the United States and abroad. The low cost of Frasch-mined brimstone has discouraged the development of higher cost sources. However, the approaching depletion of Gulf Coast dome deposits and the greatly increased demand for sulphur here and abroad have made it necessary for industry to prepare for conversion to utilize sulphur in other forms. For future planning this situation must be considered permanent and not temporary. This conclusion is based on the fact that although sulphur demand will continue to rise, the production of Frasch-mined sulphur probably will not increase greatly beyond its present level of about 5,000,000 long tons per year. The International Materials Conference in Washington estimates 1952 requirements of the free world at nearly 7 million long tons; and the Defense Production Administration has recently set a new goal for 8,400,000 long tons annual domestic production by 1955. The total sulphur equivalent produced in this country in 1950 was 6 million tons. What, then, are the alternatives for the manufacture of the vital chemical, sulphuric acid? Today about 85 pct of this country's sulphur, and nearly 50 pct of the world supply, comes from our Gulf Coast salt domes and is extracted from the earth by Frasch's hot water process. The Gulf Coast salt dome deposits have been the most important known natural deposits in the world, producing 90 million tons of sulphur during the past 50 years. However, at the present rate of extraction these deposits cannot be expected to last indefinitely. Pyrites Pyrites are, and have been for many years, the source of more than 50 pct of the world's sulphur requirements. The principal use, of course, is in the manufacture of sulphuric acid. The use of pyrites in the United States has diminished greatly because of the availability of low cost native sulphur, but pyrites have continued a major source of sulphur in many other countries. The most available pyrites for use in this country are in the form of lump pyritic ore and in mill tailings from flotation of other minerals such as lead, zinc, copper, gold, and silver. An important factor, when the use of pyrites for acid manufacture is being considered, is the disposal of calcine. A ton of sulphuric acid requires approximately ton of high-grade pyrite and results in 1/2 ton of calcine. If the calcine is a fairly pure oxide, free of harmful impurities, it can be used, after sintering, in an iron blast furnace burden. Its value might be as high as 15d per unit of Fe at the blast furnace; or possibly $10.00 per ton of sinter, if it assays 65 pct Fe. This might result in a credit of $4.00 per ton of acid if the sintering plant and blast furnace are both located adjacent to the acid plant. On the other hand, several factors must be considered before this credit can be realized, i.e., freight to blast furnace, availability of sintering facilities, methods of eliminating impurities, and the removal of valuable metal values. In some locations it would be most economical to dump the calcines.

Jan 1, 1953

By Milton Williams

A comparison is made between the amount of interstitial water found by analysis in cores and that estimated from the resistivity curve of the electric log for the corresponding strata of producing reservoirs. It is shown that while the determined and the estimated water saturations are in good agreement in some cases, this agreement may be due to a fortuitous compensation of errors. Estimates of water saturations made from the electric 1og by use of existing relations should, therefore, be employed with caution. Also presented are data on the variation of salinity of interstitial waters in reservoir sands, and on the effect of variation of salinity and porosity on the validity of estimates of water content made from the electric log. INTRODUCTION Throughout the history of electric logging there have been recurrent cycles of optimism and pessimism as to the value of the electric log in the quantitative estimation of reservoir fluid content. The very early days of electric logging were an optimistic period, in which there was widespread faith in the ability of the resistivity curve to reflect fluid content, and in the ability of the potential curve to indicate textural characteristics. In time the accumulation of exceptions to this idealistic behavior brought about a general disillusionment, and caused the more pessimistic of those dealing with electric logs to believe that the sole importance of the log lay in stratigraphic correlation. Within the last several years optimism as to the quantitative use of the electric log has been revived, primarily as the result of the stimulating work of C. E. Archie' on the estimation of interstitial water in sands from resistivity data. Even though the general trend of thought on the quantitative value of the electric log reflects optimism, it is inevitable that there are some widely divergent opinions of the validity of quantitative estimates based on the electric log. A valid method of estimation of fluid content by means of the electric log and a general knowledge of the textural character of the reservoir rock would be of signal importance, not only in that it would save time and money in securing information on reservoirs now being drilled, but also because it would permit the evaluation of reserves in many fields drilled without adequate core data subsequent to the advent of electric logging. Because of this importance, Humble's Production Research Division, in cooperation with various other company divisions, initiated several years ago series of tests designed to evaluate the reliability of estimates of fluid content made from the electric log. The investigation was limited at the outset to sand reservoirs, since it was felt that the inclusion of limestone reservoirs would entail needless complications. In devising these tests it was immediately apparent that the chief difficulty in evaluating the worth of any method of estimation lay in establishing the true value of fluid content. The results of direct analyses of cores cut with ordinary mud were not sufficient, because of the probability of contamination of the fluids by filtrate from the drilling mud; the results of restored state tests on cores were deemed unsuitable because these results can hardly be said to furnish a primary standard. The method adopted was the direct analysis of cores cut with an oil-base drilling fluid. Such cores, when properly handled, are believed to afford the most precise determination of water content available at the present, and, in addition, lend themselves readily to the determination of various other properties which are pertinent to the estimation of fluid content from the electric log. Since it was desired to compare the fluid contents estimated from the electric log run in ordinary mud with cores cut in the same hole, the use of oil-base fluid necessitated the changing over, after all cores were cut, to a conventional mud. This procedure presented several advantages, one of which was that the use of oil-base fluid permitted

Jan 1, 1950

By T. O. Anderson, E. J. Stahl

Tests to increase knowledge concerning the process of hydraulic fracturing have been performed on three wells in the Allegheny field in western New York. The fracture orientation and its physical appearance at the well-bore was determined by impression packers run at appropriate times throughout the program. Fract~tre azi171uth and its dimensions thus determined were compared to the rock properties and treatment conditions. Logs to provide data concerning rock properties and to improve identification of vertical fractures were run before each step of the fracture treatment. Pressure osc~illu~iot~s were studied after each phase of tile treatments surface pressures during treatment. These measurements show that subsurface pressures exhibit many of the same characteristics as surface pressures during treatment of a well; however, transient pressures are dampened and deelayed in time at the bottom of the well when COmpared with surface pressures. Data obtained from this study provides a means to help locale and determine orientation of vertical fractures made in the open wellbore. Although these rests were performed in only one area, much of the information gained may be applied to fracturing programs in orher areas. INTRODUCTION In this study, various tests were made to provide data to better understand formation fracturing in situ. The reservoir studied is the Richburg oil sand which is a part of a series of predominantly grey sandstones and shales with occasional brown sandstone layers, known as the Caneadea unit of the Canadaway group of Upper Devonian age. Average physical characteristics of 12 cored wells in this area are 13-ft thick gross sand formation, 12-ft thick net sand. 1.7 md permeability, 11 percent porosity, 44 percent oil saturation (before secondary recovery) and 16 percent water saturation (before secondary recovery). This particular area of the Allegheny oil field was originally drilled prior to 1890. The first waterflood secondary recovery attempt was made in 1929. The present sustained waterflood development began in 1951 and is being carried out on a 4.5 to 5-acre spacing. Objectives of these tests were to (I) study fracture azimuth and dimension in relation to rock properties and treating conditions, (2) improve fracture identification techniques, (3) compare surface and subsurface pressure during all phases of treatment and (4) compare the periods of the fluid column oscillations occurring after each phase of treatment. Although the areas of investigation listed appear divergent in purpose, the program was designed primarily to increase knowledge of down-hole conditions leading to rock failure and extension of the fracture thus created. TEST PROCEDURES Wells upon which tests were conducted are designated as Wells 1 through 3. Well 2 was located 440 ft north of Well 1, and Well 3 was located approximately 880 ft west of Well 1. Wells 1 and 2 were completed with cable tools, while the producing interval of Well 3 was rotary cored using fresh water as the drilling fluid to obtain oriented cores. Tests were divided into separate phases on each well as the fracturing program progressed and consisted of measurements performed prior to treatment, during and after the formation breakdown operation. during fracture treatment and after treatment. To verify location and azimuth of the fracture created, and to obtain an impression of wellbore irregularities, a packer was used (Fig. 1). This packer was lowered on tubing into the wellbore opposite the interval under study and inflated in stages to allow the impression material to conform to the wall of the wellbore. A magnetic compass was attached to the tool for orientation reference. Impressions made prior to treatment showed no existing fractures in the wells under study. Impressions made after both formation breakdown and treatment pro-

By J. J. Jakosky

All electrical geophysical methods depend for their operation upon the effects produced by the flow of an electric current. By studying these effects it is possible to predict the general axis of current flow. The greater flow of current is in the path of greatest effective conductivity; and since the effective conductivity of a mineralized zone is different from that of its surrounding envelope (usually much greater), it is possible to locate such a mineralized zone by the distribution of current. Due consideration must be given, of course, to geological structure, to type of mineralization, and to other factors. A number of methods are used to cause this flow of current, and various methods arc available for detecting the presence of such current flow and for studying its effects. In a rather detailed way, this paper will discuss the theoretical and practical phases of the inductive methods of geophysical prospecting. Electromagnetic Generation of an Electeomotive Force The inductive method is so named because the current flowing in the conductor is obtained by electromagnetic induction, instead of by the use of ground electrodes through which a current is passed as in the applied potential systems, or by direct contact with the orebody. An alternating current flowing in a coil will create an electromagnetic field around the coil. This field will have the same frequency as the current and will radiate or travel outward from the coil in closed magnetic or flux circuits. These flux circuits (in air or a homogeneous medium) will be perpendicular to the plane of the coil and will extend or travel outward with uniform velocity in every direction. Maximum feld exists in the plane of the coil. Such a coil used for transmitting or as the "energizer" will exhibit similar figure-eight characteristics to those exhibited by the direction-finding coil which will be described in detail later.

Jan 1, 1929

By Wheeler Davey

WHEN metals are subjected to mechanical working, such as rolling, one of the phenomena that take place is a movement of the crystals of the metal into a system or systems of orientation which bear an angular relation to the direction of working. In rolled metal the crystals may orient themselves with respect to the rolling plane or the rolling direction, or both. Direct evidence of the existence of preferred orientations in rolled metal has been obtained by numerous investigators from X-ray patterns of the rolled metal. Most of these workers used a monochromatic pinhole method. Where the degree of preference for a single orientation is high the monochromatic pinhole pattern may be interpreted by a geometrical calculation based on the angular relationships of the planes in the crystal and the diffraction arcs on the X-ray pattern. This process may be aided by the geometrical construction of the locus sphere (Langenkugel), and reflection circles of Polanyi,1 Polanyi and Weissenberg,2 and Mark and Weissenberg,3 and of the plane polar figures (flachenpolfigur) of Franz Wever.4 R. M. Bozorth5 solves X-ray patterns from metals having a single preferred orientation by means of a series of charts which when placed over the X-ray pattern give directly certain angular relationships, between the crystal planes and the surface of the specimen.

Jan 1, 1929

By Louis Cates

AT THE annual meeting of the American Institute of Mining and Metallurgical Engineers in February, 1923, the Chairman of the Committee on Ground Movement and Subsidence appointed a subcommittee to work out a form of questionnaire and to collect data on subsidence and ground movement resulting from underground metal- and coal-mining operations, and on ground movement and safe slopes in connection with open-cut metal-mining operations. The author was requested to take charge of the collection of data and the preparation of a questionnaire in connection with the Committee's studies of open-cut metal-mining operations, this paper is a summary of the work carried on and information received therefrom up to February, 1924. The first approach to the problem of safe slopes is to gather all information that pertains to finished slopes; in other words, the steepest economic angle from the horizontal that will stand in order to uncover the ores to be mined and be safe while the extraction of the ore at the base of these slopes is in progress. Whether or not this angle is 35° or 45° depends on many factors. The number of benches maintained to take care of falling rock and their height and width are direct functions of this overall slope. The slope is here taken to mean the angle from the top edge of the pit through the edges of the respective lower benches to the bottom of the pit. If we accept this definition of the slope, it might save some confusion as there would be a difference if one took the line from the top edge of excavation to the toe of the bottom slope. This latter slope would not be constant, but would vary with the number of benches. The depth of the various ore faces will vary, of course, depending on the deposit; Table 1 shows this to range from 50 ft. to 1100 ft. The geology is an important factor, as are the climatic conditions under which one is operating. A saturated condition in some rock structure causes rock flows; in the Panama Canal excavation, slides have run on a ratio of as low as one on ten, which is a 10 per cent. grade, or a slope of less than 6° with the horizontal. Slopes as steep as 60° have been noted in the Utah Copper operations, so that a wide divergence will possibly be

Jan 8, 1924

By Paul G. Shewmon

The migration of slightly solzrhle spherical particles through a solid under the infllrence of a temperature gradient is analylzed for the cases of various transport mechanisms. It is shown that the variation of the velocity of the particles with radius, r, depends on the dominant mechanism of matter transport around or through the inclusion. Thus the velocity varies as r-1 jor surface-dijf1~sion controlled migratzon. is independent of r for volume diffusion in either phase, and varies as if the rate is determined by an interfacial reaction (n is the order of the interfacia1 reaction). These same results hold tor the migration of a cvlinder of length much greater than its radius. and .for other types of potential gradients, e.g., an electrical field. These equations are combined with recent electron-microscopic ohservations to show that the rate of migratzolz of small helium-silled bubbles through copper is determined by surface diffusion of the metal atoms. With these equations and the temperature gradients attainahle in an electron-microscope joil, the dominant transpar/ mechanism (or any migrating pnrtzclos can he determined. AS a result of fission, rare-gas atoms are created in the hot fuel element of a nuclear reactor. These insoluble atoms precipitate to form bubbles of the gas in the fuel. The subsequent migration and coalescence of these bubbles is thought to play a dominant role in the swelling of fuel elements which in turn can limit the fuel-element life. As a result of this practical problem and because of the relative simplicity of the system, workers in several laboratories have imbedded rare-gas atoms in metals with the aid of an accelerator and studied the formation and behavior of the bubbles that form on annealing. Recently Barnes and Mazey have studied the migration of such helium-filled bubbles in copper foils using the electron microscope and the temperature gradient that can be induced in the foil by the electron beam. They found that the smaller bubbles moved faster than the larger ones. It is shown below that, if this is true, the rate-controlling step in their migration is surface diffusion of metal atoms instead of volume diffusion, vapor transport, or an interfacial reaction. The analysis given is in no way limited to gaseous inclusions so the variation of velocity with particle size for any relatively insoluble precipitate particles could be used to obtain information about the relative importance of surface diffusion, volume diffusion, and interfacial reaction in such two-phase systems. VOID MIGRATION IN A TEMPERATURE-GRADIENT ANALYSIS Barnes' studies indicate that helium does not dissolve or diffuse in metals to a measurable extent, so that when the voids move they must do so through the movement of metal atoms from the leading to the trailing sides of the void.' Thus voids might move by surface diffusion, diffusion of vacancies in the surrounding lattice, or vapor transport. We consider first the case of flow by surface diffusion alone. We assume that there is a force, in the sense of irreversible thermodynamics, tending to move the atoms around the bubble in a given direction. We designate this direction as the x axis and the force per atom as Fa. The net rate of flow of atoms from one side of the bubble to the other, under the influence of this force, is the surface flux, Js, times the cross-sectional area available for flow, A,. A, is taken as the circumference times the thickness of the high-diffusivity surface layer 6. Thus where 51 is the atomic volume. For bubbles to advance a distance dx, a volume equal to nr : dx must flow around the void so that The minus sign enters because the bubble moves in the direction opposite to that of the force on the atoms. Equations for volume diffusion and diffusion through the vapor can be obtained in the same manner. For vapor transport we have Ag = and the ratio of the densities of metal atoms in the gas and the solid (pg/pl) enters so that

Jan 1, 1964

By R. N. Thurston, E. A. Nesbitt, G. Y. Chin

A general relalionship between the amount of glide shear (due to slip) and the macroscopic shape change has been developed. Since the deformation can be large, finite strain analysis is employed. In this treatnzent, the shape change is expressed by a deformation gradient matrix, F - [axi/aXj1, where X and x refer to the initial and final positions of a particle. This matrix is readily evaluated in terms of the amounl of glide shear, a , and the direction cosines of the slip-plane normal and the slip direction for a single active slip system. In the case of deformation from slip on several systems, the product F(a) of the several deformation gradient matrices is first calculated. Then, by assuming that the final configuration is reached by a long series of small shears of magnitude a, occurring more or less alternately in the several slip sys- IN problems of crystal plasticity, it is often necessary to relate the amount of glide in the operating slip systems to the macroscopic strain components. This relationship is relatively simple when only small strains are considered. In this case the separate strain contributions from several slip systems are additive. Such a procedure is incorrect in the case of large plastic deformation. To the authors' knowledge, no general treatment of the latter problem has appeared in the literature. In specific instances, Mark, Polanyi, and schmid3 have derived the relationship between glide and axial elongation during tensile pulling of a single crystal when only one slip system is active. A similar relationship for duplex slip was worked out by v. Goler and Sachs.4 Taylor and Elam5 have also studied in detail problems of large plastic deformation. Due to uncertainties as to the slip systems at the time, terns, the final deformation gradient matrix can be obtained. Mathematically, the problem is reduced to finding the limit of F(dN as N — m while a — 0 in such a way that the Product Na = 0, a ftnite conslant designatzng the accunzulated amount of shear. It turns out that this limit is simply , where F, is the matrix whose elements are the coefficients of a in the F(a) matix. Application is made of the present treatment to a fcc crystal of Perlrzalloy compressed on the (110) plane and contrained to elongate zn the [112] directzon. In addition, it is shown that one rnay readily obtain from the general analyszs the well-known formulas relating elongation, amount of glide shear, and amount of lattice rotation for crystals deforming by single and double slip under tension. however, they were mainly concerned with proving that slip occurs on {111}(110) systems in fcc metals. The present general treatment arose out of recent investigations of magnetic anisotropy in cold-worked Fe-Ni alloys6 as well as some related problems in strength anisotropy of single crystals.' Detailed application of the general analysis will be provided in the case of a Permalloy single crystal compressed on the (110) plane and constrained to elongate only in the [112] direction. It will be seen that, as expected, the small strain approximation leads to significant errors after moderate straining. It will also be shown that the present general treatment yields the formulas of Mark et al. and of v. Goler and Sachs in those specific cases. GENERAL CONSIDERATIONS Consider a homogeneous deformation in which a material point initially at moves to both positions being referred to the same set of Cartesian axes. Such a deformation can be

Jan 1, 1967

By B. M. Larsen, K. Heindlhofer

THIS paper describes a relatively simple electrical apparatus that, through the close analogy between the flow of heat and of electricity, enables one to solve quickly and with satisfactory accuracy many complex problems in heat flow. This device, developed in 1935, has proved especially useful in the solution of certain practical problems relating to the design and efficiency of regenerators for an open-hearth furnace or coke oven, yielding within a few hours information that would take weeks or even months to acquire by mathematical1.2 or experimental3 methods of comparable accuracy. Its description now is prompted by growing interest in such analogues, as shown by several recent papers.4.5 The analogy between flow of heat and of electricity appears to have been recognized first by Maxwell who, in his famous Treatise on Electricity and Magnetism (1881) says: The analogy between the theory of the conduction of electricity and that of the conduction of heat is at first sight almost complete. If we can take two systems geometrically similar, and such that the conductivity. for heat at any part of the first is proportional to the conductivity for electricity at-the corresponding part of the second, and if we also make the temperature of any part of the first proportional to the electric potential at the corresponding point of the second, then the flow of heat across any area of the first will be proportional to the flow of electricity across the corresponding area of the second. .. Thus, in the illustration we have given, in which flow of electricity corresponds to flow of heat, the electric potential to temperature, electricity tends to flow from places of high to places of low potential, exactly as heat tends to flow from places of high to places of low. temperature He noted, however, that this analogy is restricted: ... there is, however, one remarkable difference between the phenomena of electricity and those of heat. Suspend a conducting body within a closed conducting vessel by a silk thread, and charge the vessel with electricity. The potential of the vessel and of all within it will be instantly raised, but however long and however powerfully the vessel be electrified, and whether the body within be allowed to come in contact with the vessel, or not, no signs of electrification will appear within the vessel, nor will the body within show any electrical effect when taken out. But if the vessel is raised to a high temperature, the body within will rise to the same temperature, but only after a considerable time, and if it is then taken out it will be found hot, and will remain so till it has continued to emit heat for some time. The difference between the phenomena consists in the fact that bodies are capable of absorbing and emitting heat, whereas they have no corresponding property with respect to electricity. According to this statement the application of the analogy would be limited to problems of steady flow that do not involve heat-capacity effects. In spite of this

Jan 1, 1945

OF THE many categories into which scientific knowledge has been arbitrarily divided, the one which has proved most applicable in our attempts to gain an insight into the details of steelmaking processes is physical chemistry. To the young metallurgist who has only recently survived a college course in this subject, the application of its principles to reactions in liquid steel should not be difficult. To one who has had no such course or whose auld acquaintance with the subject has all but been forgot, such application is all too often thwarted by the abstruse presentations of the subject found in many of the available textbooks. AS a tool for the control of a complex process involving many chemical reactions, physical chemistry can become very valuable. The specialist who is using this tool for many purposes and perhaps contributing to its development will want to know a great deal more about it than can be included in this book. He will be interested in its history, its accomplishments and limitations, and its applications to many and varied problems. To the steelmaker or metallurgist, however, it is only one of a number of tools that he must use. He is willing to forego the detailed study of its inner workings in order to concentrate upon the development of skill in its application. It is the purpose of this chapter to present a simplified view of physical chemistry as a tool of great potential usefulness. This purpose and the desire for brevity have required the elimination of many of the gadgets with which the tool is usually adorned. It is hoped that this simplification will be conducive to clear understanding. The beginner is urged not to overlook the more extended treatments of the standard textbooks.* He is assured at the same time that the basic tool is sound and serviceable and is guaranteed to give satisfaction if regularly lubricated with common sense. Certain parts of physical chemistry require rather formidable mathematics for their complete development, but in the main those applications in which we are here interested can be expressed in fairly

Jan 1, 1944

By E. Miller, K. Komarek, W. Johnson

The activity of aluminum in solid Cr-A1 alloys has been measured by an isopiestic technique between Cr-A1890' and 1126" and 13 and 80 at. pct Al. The integral free energy of mixing has a minimum value of —5600 cal per g-atom at 59 at. pct Al. The maximum solid solubility of aluminum in chromium was determined to be 43 at. pct Al, and the composition limits of the compounds CrA14, Cr4A19, and Cr5Al, at 1000"~ were found to be 79 to 80, 66 to 70, and 59 to 63 at. pct Al, respectively. The thermodynamic properties of the Cr-A1 system have been investigated as part of a thermodynamic study of aluminum-transition metal systems.172 Little information is available on the equilibrium properties of the Cr-A1 system. The heats of formation of solid Cr-A1 alloys have been determined by Kubaschewski and Haymer at 600" and low-temperature specific heat data have also been obtained.~ More extensive work has been performed on the phase diagram, and a compilation has been provided by Hansen and Anderko,~ their phase diagram at elevated temperatures being essentially based on the work of Bradley and LU.~ The high-temperature portion of the phase diagram shows an intermediate phase CrA14 decomposing peritectically at 1018°C and existing at 82 at. pct A1 at 1000°C. They also identified the compounds with solubility limits of 72 to 75 at. pct A1 at 1000°C, and Cr5A1,, existing at 61 at. pct A1 at 1000°C. The maximum solid solubility of aluminum in chromium at 1000°C was found to be 46 at. pct Al. These elevated-temperature data were obtained by examination of quenched samples and were considered as less precise than the lower-temperature data. Koester, Wachtel, and Grube7 have revised the phase diagram as a result of their magnetic susceptibility and X-ray study. The results of this work differ appreciably from those of Bradley and Lu at temperatures above 800°C. The CrA1, compound is given as existing between 79 and 81 at. pct A1 at 1000°C, and they do not indicate the presence of a CrA13 phase reported by Bradley and Lu. They also report the compound Cr4Alg as having solubility limits of 66 to 70 at. pct A1 at 1000°C, while Bradley and Lu show this compound stable only up to 870°C. Koester et al. state that the high-temperature modification of the compound Cr5A18 is stable down to 1125"C, and not 980°C as stated by Bradley and Lu, and that the low-temperature modification of Cr5Al, has a range of homogeneity of 58 to 63 at. pct A1 at 1000°C. They also report that the maximum solid solubility of aluminum in chromium is 43 at. pct A1 at 1000°C. APPARATUS AND EXPERIMENTAL PROCEDURE An isopiestic method was employed which has been successfully applied to the determination of aluminum activities in solid ~e-All and Ni-Al alloys. Alloy specimens were held at different positions in a temperature gradient and were equilibrated with aluminum vapor from an aluminum reservoir kept at the temperature minimum of an impressed thermal gradient in a closed alumina system. Diffusion of aluminum into the specimens occurred until equilibrium was reached, at which the partial pressure of aluminum in each of the specimens was given by the vapor pressure of the pure aluminum reservoir. The activity of aluminum referred to liquid aluminum as the standard state in a given equilibrated sample at temperature T could therefore be expressed by: vapor pressure of pure aluminum at _ the temperature of the reservoir Vapor pressure of pure liquid aluminum, at specimen temperature T Since both the temperature of the aluminum reservoir and the specimen temperatures were determined experimentally, and the vapor pressure of pure aluminum is known as a function of temperature,' the activity of aluminum in a given aluminum alloy of known composition could be calculated. Initial runs were made with samples consisting of pure chromium chips placed in alumina crucibles. These runs exhibited large inconsistencies, indicating that equilibrium was not attained. High aluminum content Cr-A1 alloy powders were therefore substituted for the pure chromium specimens. The starting composition of the alloys was adjusted through experimentation until the concentration change necessary to attain equilibrium was small. In this manner, consistent results were obtained in reasonable times. SPECIMEN PREPARATION Alloy specimens were prepared from chromium of 99.997 pct minimum metallic purity: with 0.028 to 0.038 pct H, 0.0002 pct N, and 0.27 to 0.46 pct 0 (Aviquipo, Inc.). The aluminum had a purity of 99.99+ pct and the following impurities: 0.003 pct Cu; 0.002 pct S; 0.002 pct Fe; 0.001 pct Pb; 0.001 pct Ga (Aluminum Corp. of America). Alloy powders were prepared from weighed mixtures of chromium and aluminum by double-arc melt-

Jan 1, 1969

By H. W. Graham

[ ] Even though we have a small audience, I am sure there are some here who are interested in sponge iron. It is a large subject, with a lot of economic interest, and one that will continue to grow in importance as the years go by and as the conditions that urge action in that direction increase. The authors have chosen to deal in this paper with one particular narrow phase of a long program of work by the Bureau of Mines. Before asking for any general discussion, I would myself like to ask Mr. Buehl if he would tell us just a little bit about the mechanism of discharge and the form in which the material was discharged; that is, when dolomite is added, what happens to the dolomite? R. C. Buehl (author's reply)-You are interested in the equipment that was used? H. W. GRAHAM-No, just the product. R. C. Buehl-The product was in granular form, of a shape very similar to that of the ore used. Using minus 10-mesh ore, the product is essentially minus 10-mesh, mixed with the coal and dolomite. It is then passed through a belt type of magnetic separator, which picks up the magnetic iron and allows the dolomite and coal to fall off. If the coal is sufficiently valuable, it can be separated from the dolomite and, provided the coal has a sufficiently low ash content, it can be reused. For instance, if a low-ash reducing agent like petroleum coke is used, it can be reused until all the carbon is consumed. H. W. Graham-That clears the point for me. I was not quite sure whether the experi-

Jan 1, 1947

By R. F. Mehl, B. Lustman

THE formation of intermediate phase layers in cementation processes has been subjected to extensive qualitative investigation though to relatively little quantitative study; this work has recently been fully summarized by F. N. Rhines.1 It is necessary here only to enumerate the general conclusions drawn concerning the kinetic laws governing the growth of intermediate layers and to state what is known concerning the structural changes accompanying the generation of phase layers. I. When the intermediate phase is protective in type-i.e., when its density is less than that of the base metal, so that a continuous coating is formed and maintained-the isothermal growth of the phase follows a simple parabolic equation: [1 = ki [I]] where X is the thickness of the alloy layer, k the reaction rate constant, and [t] the time. The applicability of this equation to diffusion processes is tested by plotting the square of the thickness versus time, or by plotting the thickness versus the square root of time; the resultant achievement of a straight line in such a plot has been considered sufficient proof of the validity of this equation. Exceptions have been found where liquid phases are involved in the reaction, where the diffusion layer is cracked,2 and where thin semimetallic oxide and sulphide coatings are formed on metals.3 In the first two cases the thickness increases linearly with time, and in the latter it is a logarithmic function of time. 2. The rate of thickening varies with temperature according to the Arrhenius equation: [k = Ae-QIRT [2]] where k is the parabolic rate constant of Eq. I, or some other rate-descriptive function, A is the action constant, e the base of natural logarithms, Q the heat of activation, R the gas constant, and T absolute temperature. This equation has been found to be generally valid except when transformations occur during reaction in either the base metal or in the reaction layer; in such instances Eq. 2 is still applicable with different values for the constants A and Q above and below the transformation temperature. 3. All phases that are stable at the temperature at which diffusion occurs will appear in the interdiffusion of two components. In some cases certain of the phases may be too thin to be observed and identified easily. Nonequilibrium phases have never been noted in thick reaction layers; i.e., layers of a thickness that may be discerned microscopically. The relative thickness of each phase in a diffusion layer is proportional to the concentration gradient and to the rate of diffusion in that phase.4 The reaction layers tend to have a

Jan 1, 1942

By G. D. Just

INTRODUCTION Large scale underground mining involves the bulk handling of fragmented material. The cost and efficiency of the mining systems is there- fore significantly influenced by material flow characteristics. Flow problems may occur in the form of ore pass blockages which interrupt the free flow at extraction openings. The costs of such delays can be readily assessed and compared to the costs incurred in reducing blockages by improved fragmentation or larger ore passes. In practice the problem is more complex than this statement suggests because it is generally un- economic to design for zero ore blockages. Another major flow problem occurs in the form of relative movement of ore and waste as the fragmented material is extracted. This produces waste dilution in the recovered ore and influences total ore recovery. This flow problem is much more complex than the ore block- age phenomena. Many questions concerning the precise flow characteristics remain unanswered because of the variability of size distributions, particle shapes, material properties and the total extraction layout and design. Model studies can provide a visual and quantitative illustration of probable flow characteristics but full scale data collection is necessary to evaluate the precision of such information. The methods and types of data obtained must be carefully selected to recover the maximum volume of useful information for operational control and future design. It is essential that honest precision levels are assigned to the data and any subsequent analyses. Grade control data may give misleading short term information on flow characteristics because of the difficulty in knowing the true grade of the mass of material before extraction commences. However, in the long term control of extraction grades is vital to the profitable operation of the mining system. The most efficient extraction design and operational schedule can only be determined after all of the facts and variables are known. This is usually only possible after the orebody has been completely extracted. However, if design and operational personnel have a full appreciation of the nature and variability of material flow under different conditions the best possible results should be achieved. The most significant features of material flow are out- lined in this paper in order to provide mine planning and mine management personnel with some of the necessary information relating to material flow. Available facts and reliable figures from selected publications are noted in association with unbiased and hopefully accurate opinions of the relevance of the data to mine design and mine system control. Possible future developments and profitable areas for research into material flow problems are also detailed. MATERIAL FLOW AND MINING METHODS The effects of material flow on the design and operation of an integrated underground ore handling system is one factor which is common to most mining methods. Analysis of the system as detailed by Just, 1980, permits the identification of unit process objectives. For example, a typical underground ore handling system as illustrated in Figure 1, involves the following unit operations:- (i) Gravity flow of ore in stope (ii) Ore extraction at base of stope (iii) Ore haulage on the production level (iv) Dumping of ore into ore pass system (v) Gravity flow of ore in the ore pass (vi) Underground crushing of ore (vii) Haulage of crushed ore to shaft (viii) Hoisting of ore to the surface. Average flow rates in each of these unit operations can be misleading due to variability in incremental capacity caused by flow blockages and machine delays. Thus to effectively analyse the probable performance of the system, it is necessary to have a measure of the flow loading and haulage rate variability. Mechanical equipment performance specifications can be used to provide such information for loading, haulage and crushing; however, in the case of the gravity flow of material field measurements are required to relate the probability of "hang-ups" to the degree of fragmentation. Factors affecting the frequency of flow stoppages are, size, distribution and cohesiveness of broken material and the geometry and size of the flow channel. Ore pass channel design is relatively simple since regular cross-sectional shapes are used

Jan 1, 1981

By Robert D. Pike

In November 1939, on behalf of the Harbison-Walker Refractories Co., the author undertook the study of the problem of utilizing the dolomite of northwestern Ohio for the manufacture of calcined magnesia suitable for use in refractories. Grateful acknowledgment is made of the unfailing assistance and encouragement throughout this work from the executive and technical staff of Harbison-Walker Refractories Company. The dolomite of the Niagara formation that is exposed or near the surface of a wide area in northwestern Ohio1 constitutes a vast supply of almost pure dolomite. It offers a virtually unlimited supply of cheap raw material of uniform dependable analysis for the manufacture of magnesia. A typical analysis of dolomite from the vicinity of Luckey, Ohio, follows: Stone Completely Calcined CaO(Sro)a............. 30.35 57.806 Mgo................... 21.55 41.050 SiO2. ................... 0.30 0.572 R2O3................... 0.30 0.572 Ignition loss............. 47.50 a SrO about 0.06 pct. Brines containing magnesium chloride or sea water can be reacted with calcined dolomite to produce magnesia.2'3 In such reactions the MgCl2 of the brine supplies some of the magnesia and the amount of dolomite required is thereby reduced by an equivalent amount, but brines of commercial importance containing magnesium chloride are some distance away from the purest grades of the dolomite of northwestern Ohio. It was decided therefore to concentrate upon the development of a suitable process for separating the lime and magnesia of dolomite, depending upon the dolomite itself as the sole source of magnesia. This would make it possible to place a plant at the dolomite quarry, thus eliminating the cost of transporting the stone and also rendering the calcined magnesia available at a most convenient production point, considering the cost of delivery throughout the steel industry. The selection of a process depending solely upon the dolomite as a source of magnesia also necessarily entails production of the lime content of the dolomite as a by-product. It was recognized that if such a lime by-product could be produced in a suitable form, a plant location in northwestern Ohio would also be advantageous for marketing the lime. The problem, therefore, was the discovery and development of a low-cost process for separating the magnesia and lime of the dolomite of northwestern Ohio and producing each in a form relatively free from the other, and meeting the respective requirements of established markets. A satisfactory solution of this problem has been found, and it is the

Jan 1, 1948