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By L. M. Barker, E. G. Lewis

THE literature of milling is replete with papers devoted to the subject of ball milling, all of which no doubt have contributed in one way or another to progress in that art. In this paper reference will be made to only a few of the many authors, but the value of the contributions of all who have written on that subject is hereby acknowledged. With a few exceptions the efforts of most students of the subject have been devoted to laboratory investigations of principles. Davis1 was one of the first to report on plant-scale investigations and to present to mill men certain criteria for the guidance of ball-milling practices. His conclusions with respect to the significance of sizing analyses of classifier sands in their relation to the factors of mill speed and ball sizing are particularly referred to. Those conclusions were: I. If the balls are large or the speed of the mill is high, crowding will appear at the finer sizes in the classifier sands. 2. If the balls are small or the speed is low, crowding will appear at the coarser sizes in the classifier sands. 3. The indications are that best efficiency is obtained when the screen analysis of the sands show a minimum crowding at any size. The last conclusion was qualified by the statement that it had not been proved conclusively. It is surprising, however, that the literature of later years reveals little evidence that millmen have made any serious attempt to apply those criteria. This may, perhaps, be explained by the fact that the average plant-scale ball-milling problem presents so many variables that an investigation of any one of them encounters the problem of control of the others-a problem that often is unsurmountable in a small plant. In a large plant, in which there is a duplication of grinding units in parallel operation, opportunity may be afforded for determining the value of such criteria. Nevertheless, a study of published data from grinding circuits of both large and small plants suggests that either Davis' criteria have been tried and found inapplicable or have never been given consideration. For the purpose of testing Davis' conclusions and with improvement of ballmilling efficiency as the final objective, a test program was initiated in the concentrator of the New Cornelia branch of the Phelps Dodge Corporation early in 1938. The practices of that plant have already been described.2 The fine-grinding units are arranged so that any one of eight units may be operated as a test unit and its results compared with those of the remaining units. All units receive similar feed from a common storage bin, in which the product of the fine-crushing plant is bedded by traveling tripper. The ball mills are all similar in size and operated at the same speeds, and are individually metered. The feeder conveyors of each unit are equipped with Merrick weightometers. The test program as initially outlined proposed investigation of the following:

Jan 1, 1941

By Wallace W. Key

Chalk is a natural calcium carbonate occurring as the remains of soft, friable, minute marine organisms. Whiting can be either finely ground calcium carbonate prepared from chalk, marble, or limestone or the product obtained by chemical precipitation from a solution or suspension containing lime. Until relatively recently, whiting made from limestone was termed "whiting substitute," but it is now usually designated as limestone whiting. Precipitated calcium carbonate, sometimes called "precipitated whiting" or "precipitated chalk," is a finely divided calcium carbonate product obtained by chemical precipitation from a solution or suspension containing lime. Considerable quantities of precipitated calcium carbonates are produced from many chemical processes. Naturally occurring calcium carbonate in a variety of crystalline forms and in all degrees of chemical purity forms a substantial part of the earth's crust. Exactly where a chalk grades into a marl or calcareous shale through increase of clay or silt or into a hard limestone through consolidation and crystallization is difficult to determine because no rigid specifications have been promulgated for classifying them. Composition and Properties Once considered to be amorphous, chalk was later found to be cryptocrystalline. In the pure state it consists entirely of CaCO3, but many deposits are impure. When impurities are removed and the material is reduced to a finely divided state, it is known as chalk whiting. Much confusion attends the use of the term "chalk" as well as the classification of whiting materials. For instance, blackboard chalk is not necessarily chalk but is sometimes plaster of paris or a form of talc. Colored "chalks" may be true chalk colored and compressed with a binder but are probably such materials as hematite, clays, or carbonaceous matter. The term whiting was applied exclusively to the product derived from true chalk before World War I. Chalk imports were difficult to acquire during World War I, and whiting substitutes, a term applied to the products derived from natural rock deposits and precipitated calcium carbonate, were introduced. Substitute whitings were not acceptable at first, but it was found that blending true chalk with substitutes often created an improved product; eventually by selection of limestone and finer grinding, products not only acceptable, but for some uses superior to chalk whiting, were developed. Gradually the term "substitute" was dropped because chalk whiting had lost its importance, being largely supplanted in the United States by other whiting materials. Whiting is now made in ever-increasing quantities from limestone, marble, dolomite, marls, vein calcite, oyster-shell, as well as primary and byproduct precipitated calcium carbonates. Distribution of Chalk Europe-In England, France, Belgium, Denmark, and other European countries highpurity chalk occurs in extensive beds. The Cretaceous period, or the "age of chalk," in geologic history receives its name from the great deposits of chalk exposed on either side of the English Channel. It has been estimated that oceans in which chalk and allied deposits were formed covered more than 500,000 square

Jan 1, 1960

By L. M. Barker, E. G. Lewis

THE literature of milling is replete with papers devoted to the subject of ball milling, all of which no doubt have contributed in one way or another to progress in that art. In this paper reference will be made to only a few of the many authors, but the value of the contributions of all who have written on that subject is hereby acknowledged. With a few exceptions the efforts of most students of the subject have been devoted to laboratory investigations of principles. Davis1 was one of the first to report on plant-scale investigations and to present to mill men certain criteria for the guidance of ball-milling practices. His conclusions with respect to the significance of sizing analyses of classifier sands in their relation to the factors of mill speed and ball sizing are particularly referred to. Those conclusions were: I. If the balls are large or the speed of the mill is high, crowding will appear at the finer sizes in the classifier sands. 2. If the balls are small or the speed is low, crowding will appear at the coarser sizes in the classifier sands. 3. The indications are that best efficiency is obtained when the screen analysis of the sands show a minimum crowding at any size. The last conclusion was qualified by the statement that it had not been proved conclusively. It is surprising, however, that the literature of later years reveals little evidence that millmen have made any serious attempt to apply those criteria. This may, perhaps, be explained by the fact that the average plant-scale ball-milling problem presents so many variables that an investigation of any one of them encounters the problem of control of the others-a problem that often is unsurmountable in a small plant. In a large plant, in which there is a duplication of grinding units in parallel operation, opportunity may be afforded for determining the value of such criteria. Nevertheless, a study of published data from grinding circuits of both large and small plants suggests that either Davis' criteria have been tried and found inapplicable or have never been given consideration. For the purpose of testing Davis' conclusions and with improvement of ball-milling efficiency as the final objective, a test program was initiated in the concentrator of the New Cornelia branch of the Phelps Dodge Corporation early in 1938. The practices of that plant have already been described .2 The fine-grinding units are arranged so that any one of eight units may be operated as a test unite and its results compared with those of the remaining units. All units receive similar feed from a common storage bin, in which the product of the fine-crushing plant is bedded by traveling tripper. The ball mills are all similar in size and operated at the same speeds, and are individually metered. The feeder conveyors of each unit are equipped with Merrick weightometers. The test program as initially outlined proposed investigation of the following:

Jan 1, 1941

By J. B. Patton

No academic program of reasonable duration can provide a geologist with all the skills that may be needed for applied work in industrial minerals. However, any curriculum that does not provide background in such basis subdisciplines as mineralogy-petrology, stratigraphy, sedimentology, structure, and geomorphology will leave the practitioner handicapped. Enough geochemistry to understand materials requirements, and sufficient geophysics to use geophysical data, are essential. In addition to purely scientific considerations, the industrial minerals geologist must be able to evaluate economic factors. He may also be faced with legal, social, and political problems in land use, zoning, envil.onmenta1 protection, and reclamation.

Jan 1, 1985

By William Kent

More than twelve years were spent by Wöhler at the instance of the Prussian Government in experimenting upon the resistance of iron and steel to repeated stresses. The results of his experiments are expressed in what is known as Wöhler's law, which is given in the following words in Du Bois's translation of Weyrauch:* " Rupture may be caused not only by a steady load which exceeds the carrying strength, but also by repeated applications of stresses, none of which are equal to the carrying strength. The differences of these stresses are measures of the disturbance of continuity, in so far as by their increase the minimum stress which is still necessary for rupture diminishes." A practical illustration of the meaning of the first portion of this law may be given thus: If 50,000 pounds once applied will just break a bar of iron or steel, a stress very much less than 50,000 pounds will break it if sufficiently often repeated. This is fully confirmed by the experiments of Fairbairn and Spangenberg, as well as by those of Wöhler; and, as is remarked by Weyrauch, it may be considered as a long-known result of common experience. It partially accounts for what Mr. Holley has called the " intrinsically ridiculous factor of safety of six." Another "long-known result of experience"—although this has not, as the writer believes, been investigated by scientific experimenters—is the fact that rupture may be caused by a succession of shocks or impacts, none of which alone would be sufficient to cause it. Wrought iron will crystallize by repeated blows in service and become weaker than cast iron. Iron axles, the piston-rods of steamhammers, and other pieces of metal subject to continuously repeated shocks invariably break after a certain length of service. They have a "life" which is limited. Iron rods in bridges sometimes crystallize and break, although the rods in most of our iron bridges

Jan 1, 1880

President H. M. Howe, Boston, Mass. (communication to the Secretary): Le Chatelier's pyrometer is certainly a most convenient and accurate instrument for the laboratory, and one that may be used under some conditions in the mill. I have used it for several years and with great satisfaction. Like Prof. Roberts-Austen and unlike Herr Blass, I have always found that its indications remain constant over long periods. Like Prof. Roberts-Austen, also, I find it possible, in a quiet place, to read with extreme accuracy ; and, by the use of a telescope, I can read temperatures to within a degree, for some delicate determinations which I have in hand. Variations in the temperature of the room affect the readings of the instrument far less than one would expect. When the current is cut off, the mirror does not always return exactly to the same place; in other words, the zero shifts appreciably, and must be determined often, indeed every few hours if accuracy be desired. In some cases I have had it determined within a very few minutes of every important reading. To this end a switch should he introduced, so that the circuit may be broken readily. With this arrangement we can determine accurately the position of the zero within a very few seconds of the time of taking any especially important reading. The chief causes of the variation of the zero which I have noticed are as follows: a. The suspension may not be tight enough, so that the momentum of the galvanometer frame as it swings makes its supporting wires slip in their bearings. b. Changes in the position of neighboring iron objects may deflect the mirror. c. Changes in the temperature of the room may, perhaps, change the torsion of the suspension wires, and so shift the mirror. d. Dust may attach itself to the galvanometer frame, and by friction against the surrounding fixed parts of the galvanometer, may

Jan 1, 1895

By G. R. St. Pierre, A. Ghosh

In the Si-C-0 system at temperatures of interest in process metallurgy there are four stable condensed phases—silicon, carbon, silica, and silicon carbide (Sic). Silicon melts at 1683oK1 and shows negligible solubility for carbon and oxygen at 1700°K. However, silicon dissolves approximately 1.5 at. pct C at 2500oK.2 Carbon in the form of graphite remains pure and dissolves negligible amount of silicon.' Silica (crysto-balite) melts at 2001°K' and is essentially a stoichio-metric compound. Silicon carbide is a solid and shows negligible deviation from stoichiometry up to approximately 2800oK.2 Besides the condensed phases there is a gas phase

Jan 1, 1970

By C. G. Black

The purpose of this paper is to present data obtained from an investigation conducted on the grindability of coal by the American Society for Testing Materials Tentative Standard ball-mill method. This investigation has been conducted over a period of a year, during which time several hundred tests were run on a wide selection of different coals coming from Pennsylvania, Ohio, West Virginia and Kentucky. The data herewith presented tend to show that the tentative standard ball-mill method might give results that are misleading and that a volume measure might be more indicative of the true grindability of materials of varying specific gravity. A means whereby the time element might be reduced has been studied and other phases of this work such as preparation of samples, mechanical screening, reporting results and duplicating tests have been investigated. It is hoped that all criticism offered in this paper will be taken as constructive, with the purpose ill mind of perfecting the method now tentative to show the true conditions 2nd of making optional the manner in which certain parts of the test might be conducted to meet diversified laboratory conditions. Weight and Volume The results of grindability on extraneous material from the coal scam obtained with the present tentative standard ball mill method indicate easier grinding of these materials as compared to most coals. Varying amounts of these impurities in the coal therefore may cause a raising of the grindability index and may lead to the erroneous conclusion that coals containing large amounts of these foreign materials are easier to grind. For a true comparison of grindability, it would seem necessary to grind to the same particle weight. If material were sized in a commercial mill by means of an air current set at a velocity to remove 1.60 sp. gr. float coal ground to 80 per cent minus 200 mesh, any 1.60 sink particles would be left behind, and in order to remove this 1.60 sink material by the same current it would be necessary to grind finer and produce a

Jan 1, 1936

By C. G. Black

The purpose of this paper is to present data obtained from an investigation conducted on the grindability of coal by the American Society for Testing Materials Tentative Standard ball-mill method. This investigation has been conducted over a period of a year, during which time several hundred tests were run on a wide selection of different coals coming from Pennsylvania, Ohio, West Virginia and Kentucky. The data herewith presented tend to show that the tentative standard ball-mill method might give results that are misleading and that a volume measure might be more indicative of the true grindability of materials of varying specific gravity. A means whereby the time element might be reduced has been studied and other phases of this work such as preparation of samples, mechanical screening, reporting results and duplicating tests have been investigated. It is hoped that all criticism offered in this paper will be taken as constructive, with the purpose ill mind of perfecting the method now tentative to show the true conditions 2nd of making optional the manner in which certain parts of the test might be conducted to meet diversified laboratory conditions. Weight and Volume The results of grindability on extraneous material from the coal scam obtained with the present tentative standard ball mill method indicate easier grinding of these materials as compared to most coals. Varying amounts of these impurities in the coal therefore may cause a raising of the grindability index and may lead to the erroneous conclusion that coals containing large amounts of these foreign materials are easier to grind. For a true comparison of grindability, it would seem necessary to grind to the same particle weight. If material were sized in a commercial mill by means of an air current set at a velocity to remove 1.60 sp. gr. float coal ground to 80 per cent minus 200 mesh, any 1.60 sink particles would be left behind, and in order to remove this 1.60 sink material by the same current it would be necessary to grind finer and produce a

Jan 1, 1936

By G. R. Fritterer

INVESTIGATORS in the field of temperature measurement have long sought a thermoelectric couple fulfilling the following requirements: 1. It should be useful up to and including high industrial tempera-tures; i. e., 1000° to 1800° C. 2. Its thermoelectric variation with temperature should be linear and be maintained after heating to high temperatures for long periods of time. 3. It should be reproducible; i. e., different couples of the same elements should have similar calibration curves. 4. Its thermoelectric power should be large so as to allow the industrial use of rugged recording instruments. 5. Chemical reactions with, and physical changes within the elements of the couple should not alter its calibration. No thermocouple proposed to date exhibits simultaneously all of these characteristics, whereas the couple about to be described fulfills all requirements to a satisfactory degree.

Jan 1, 1933

By A. Kenneth Schellinger

THE terms surface tension .and surface energy are well known when applied to liquids and are generally described by referring to the excess energy of the air: liquid interface as a result of unsaturated molecular forces surrounding the surface molecules of the liquid due to the presence of the air phase on one side. Such unbalanced forces produce the familiar water droplet of spherical form and are generally summed up as a surface tension measured in dynes per centimeter which can be shown mathematically to be equal numerically to a corresponding surface energy expressed in ergs per square centimeter. A specific surface energy, however, is best thought of as the energy necessary to produce one unit of new surface on a substance. Hence, in producing a bubble in a flotation cell the impeller must supply surface energy corresponding to the air: liquid interfacial area on the interior of the bubble. Inasmuch as it is relatively easy to extend or contract the surface of a liquid, there are a number of successful methods for liquid surface tension, or energy, measurement based upon surface deformation. This happy state of affairs does not, however, extend to solids, which are considered to possess surface energies for the same reasons as do liquids, i.e. because of unsaturated ionic bonds at the solid gas interface. As in the case of the flotation cell producing surface on liquids as new bubbles, it takes energy to produce new surface on solids as new particles. As every mill man knows, this surface is produced on mineral solids in a grinding mill by the action of a tumbling mass of iron balls. But here so much energy usually is wasted by the inefficient action of these balls that a large amount of heat is generated, and the surface energy production may be easily confused with the energy necessary to produce this ineffective heat. The tumbling balls and fracturing minerals ultimately take their energy from a rather large electric motor. It has been variously estimated that from 10 to 20 pct" only of this energy from the motor does not appear as heat and may be presumed to appear as surface energy on the minerals present.. Such a production of new surface on the mineral phases is accompanied, of course, by a size reduction that is inevitable as more and more mineral interior molecules become surface molecules by the fracture exposure. This size reduction of mineral particles, although the most obvious feature and perhaps the sole object of the milling operation, is from this energy viewpoint the outward manifestation of the production of surface energy only. Measurement of the characteristic surface energies of pure minerals and their various mixtures in ores would be a step towards understanding of the energetics of the commercial grinding operation. In addition, the characteristic surface energy of a mineral is probably a physical property specific for that mineral, and therefore, from a scientific standpoint, should be measured. It is interesting to note that, in contrast to the large body of work on the surface tensions of liquid systems and biological systems, the field of solid surface energies has been neglected. Prior to. 1920 it is difficult to find more than one or two references to work on solid surface energies in Chemical Abstracts. Since 1920 such references number somewhat less than 100, while those on liquid systems are numbered in the thousands. Much of this apparent neglect of the field of solid surface energies (the term is intended to be somewhat inclusive at this point and refers both to the solid: gas, and the solid: liquid interface) is because of the lack of a reliable method of measurement rather than any lack of scientific curiosity. It was, and still is, difficult to produce new surface on a solid without the simultaneous production of interior changes in the same solid which may consume part of the energy used. The extension in the surface area can be measured, but the interior crystal-

Jan 1, 1952

By Albert Sauveur

The instrument about to be described meets so perfectly the special needs of the metal microscopist that there eeeme to be little doubt but its merits must be readily appreciated by those who have had any experience in the microscopical examination of metals. The Microscope-Stand.—The microscope-stand proper, Fig. 1, consists of a microscope-tube, provided with both coarse and fine adjustments of the best construction, and with a draw-tube, rigidly mounted on a bar supported at both ends on substantial and firm cast-iron legs. The height between the table and the under side of the supporting bar is 5 in. and the distance between the supporting legs 12 inches. This arrangement affords free space below the objective for the examination of large epecimens of metals, such as full rail-sections, without detracting in the least from the value of the

Jan 1, 1912

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 Robert J. De Angelis, James H. Barker

An improved method for solving dynawzical dislocation problems using a digital computer is described in this paper. Interactions between two distinct types of dislocations were studied: attractive screw dislocations; and Lomer lock forming dislocations. One dislocation is positioned in the lattice and is initially at rest, while the other dislocation is moved through the lattice on an intersecting slip plane at a constant velocity in the range 0.5 to 0.999C. (C is the transverse velocity of sound.) The results obtained from these computations indicate that screw dislocations account for a small fraction of the total strain over a wide portion of the range of velocities studied. They further indicate that mixed dislocations mainly repel other dislocations in the neighborhood of the active glide plane. From this a possible explanation for cell formation is put forth. The density of Lomer locks expected to exist after a strain of 0.2 was found to be 1.4 x 106 cm-2 which is in good agreement with indirect experimental estimates. IN the past, predictions of favorable or nonfavorable dislocation reactions were based on the associated changes in elastic strain energy. Such considerations take no account of the probability of the two dislocations coming into contact to react. Venables1 was the first to approach these probabilities by considering the interactions between two moving screw dislocations on perpendicular glide planes. Because of the restrictive types of dislocations and glide plane geometry employed, his results have limited application to metallic crystals. The work to be presented here develops a general approach to solving dynamical dislocation problems; either dislocation-dislocation interactions, presented here in detail, or dislocation interactions with any other suitably defined stress field. Two types of dislocation-dislocation interactions common to face centered cubic (fee) materials are considered: those between pure screw dislocations of opposite sign on intersecting slip planes and those between mixed dislocations on intersecting slip planes, that can react to form a perfect dislocation. This latter reaction, referred to as the Lomer reaction, produces a locked product dislocation that finds it energitical favorable to disassociate into two Shockley partials and a stair-rod dislocation. This partial configuration known as a Lomer-Cottrell (L-C) lock plays a major role in work hardening of fee crystals. seeger2 names the L-C lock as the prime contributor to Stage II hardening while Kuhlmann-wilsdorf3 and Meakin and Wils- dorf4 also state that it is a significant contributor to work hardening. However, with a few notable exceptions,5-7 direct observations of the Lomer lock and the L-C lock by electron transmission microscopy are scanty, and even these are subject to other interpretations.5,6 In a study of partial dislocations present in austenitic stainless steel, whelan8 did not observe any L-C locks at the head of pile-up groups. This result contradicted existing work hardening theories and led him to postulate an alternate theory based on the stress required to break away dislocations intersecting a pile-up group, from their stacking fault nodes. Due to the importance of the Lomer reaction in producing L-C locks which are an essential feature in current work hardening theories and because there exist no data giving direct quantitative values for the density of locks, and because there has even been some doubt expressed as to whether this important reaction occurs at all, a study of the dynamic behavior of the mixed dislocations which form the Lomer lock was undertaken. Due to their ability to cross-slip with relative ease, screw dislocations play an important role in the deformation of fee crystals. For this reason, the second type of reaction considered here is between screw dislocations of opposite sign. In addition, computations in volving screw dislocation interactions are relatively simple, thus providing a convenient check on the cornputational scheme employed. DEFINITION OF PROBLEM The force exerted on a dislocation due to a generalized stress field is given by the Peach and Koehler9 equation: Here t2 and b2 are respectively the tangent and Burgers vectors of the dislocation, and T1 is the stress dyadic defining the local stress field. The stress field may be externally applied or generated internally by the presence of a lattice defect, such as a second dislocation, as is the case in this work. Frank10 has shown that an equivalent momentum, P, of a screw dislocation can be defined by: Here, EST is the total energy of a screw dislocation and ESo is its rest energy. The left side of Eq. [2] is the time derivative of momentum and the right side is the position derivative of the energy due to the dynamical nature of the dislocation. The total energy of a dislocation is the sum of the potential and kinetic energies. Weertman11 has developed the expressions which were used here; these give the potential and kinetic energies of uniformly moving edge and screw dislocations in an isotropic medium.

Jan 1, 1969

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 Andrew Mayer

Early in 1942 National Lead Co. was requested by the War Production Board to construct and operate a plant for the Government to produce magnesium by the ferrosilicon process which had been developed by Dr. E. M. Pidgeon in the laboratories of the Canadian National Research Council. A contract with the Defense PlantCorporation was concluded in May 1942 and Magnesium Reduction Co., a wholly owned subsidiary of National Lead Co., was formed to carry out this project. The capacity of the plant was rated at I0,000,000 lb. of magnesium per year, equivalent to an average production of about 14 tons per day. The Process The process, in brief, is as follows: The raw materials are dolomite and ferro-silicon, 75 per cent grade. The dolomite is calcined, the calcine and ferrosilicon are ground and mixed and the mixture is briquetted. The briquets are charged into tubular retorts of chrome-nickel steel set horizontally in a furnace with the open ends projecting outside the front wall. The retorts are then closed and evacuated. Magnesium is liberated according to then reaction 2(MgOl CaO) + Si = 2Mg + zCaO, Si% It is distilled from the charge and con- densed on a removable sleeve in the throat of the retort. Sodium and potassium, if present, are also liberated, distilled and condensed on a "sodium condenser" in the end of the retort. At the expiration of the distillation period the retorts are discharged and the cycle of operations is repeated. For the rated daily capacity of 14 tons of magnesium there are required approximately 170 tons of dolomite, equivalent to about 85 tons of calcine, and 16.5 tons of ferrosilicon. The retort residue, a bulky powder which at present is waste, amounts to about 87 tons. Choosing the Site The investigation to select the location of the plant was conducted by the Research Laboratories of National Lead Co. This work included geologic and economic surveys of a number of districts, examination of dolomite samples by chemical, spectrographic and petrographic methods and large-scale tests of dolomite from several of the more promising localities. in the last-named tests 2-ton samples were put through the ferrosilicon process in the pilot plant of the Canadian National Research Council, under the guidance of Dr. Pidgeon. The conclusions drawn from the investigation, in regard to the quality of dolomite to be used in the ferrosilicon process, were: First, the dolomite should contain not less than 21 per cent MgO and not more than 2 per cent acid-insoluble material. Second, the dolomite should

Jan 1, 1944

By Thomas D. Henderson, Donald E. Crowell

INTRODUCTION This paper presents a "case history" of the steps taken to estimate capital and operating costs for a typical porphyry copper concentrator of ±9,070 metric tons (10,000 short tons) per day capacity. The concentrator described herein is hypothetical, but is based on experience and is, in effect, a composite of several actual projects. The numbers used are illustrative only and do not represent actual costs at any particular concentrator. These numbers are, however, representative of typical milling costs at one point in time, and. are sufficiently accurate to illustrate the cost estimating procedures described in this paper. It is not possible to publish actual, current milling costs and, in any event, actual cost figures quickly become meaningless in today's economic situation with various costs all rising at different rates. The paper is divided into three parts: (1) order-of-magnitude estimate, (2) feasibility study estimate, and (3) discussion of differences between estimated and actual costs.

Jan 1, 1978

By R. H. King

This paper describes the results of an underground coal mine trial installation of a shielded trailing cable. The cable was a three conductor, round, type SHC-GC and was installed on a shuttle car in a conventional room-and-pillar mining section. The purpose of the study was to evaluate proposed legislation that would require shielding on low-voltage trailing cables. Such legislation would require machine modifications to cable reels, packing glands, and couplers; increase cable splicing complexity; and necessitate additional splicing materials and training. Furthermore, fault location might be more difficult. Even though shielding will cause some problems for the mine operator, it can reduce electrical shock hazard to mine workers. This paper presents information that mine operators can use to solve most of the problems encountered if they are required to install shielded cables. The in-mine evaluation was funded by the US Bureau of Mines; however, the views and conclusions in this paper are those of the author and should not be interpreted as necessarily representing official policies of the US government.

Jan 1, 1982

By S. P. Goplen, M. Henriksen, T. F. Barron

In the past decade, numerous large scale drilling projects have made use of reverse circulation air lift methods. Reverse air lift pumping can be established by injecting gas into a column of liquid; the subsequently decreased density of the gas-liquid mixture allows atmospheric pressure outside the lift conduit to establish flow. The rate of flow can be controlled by varying the gas to liquid ratio. A typical reverse circulation air lift system is depicted in [Fig. 1]. Allen 1 has described a number of reverse air lift drilling projects. Although cited examples are generally related to large diameter holes, the method has seen use in other applications such as sand dredging, chemical pumping, water well pumping. and continuous coring. One particular benefit obtained with enclosed reverse circulation drilling is elimination of lost circulation. The required air/water ratio for pumping at a given submergence and lift has been established experimentally by Gibbs.2 His data, however, do not reflect sensitivity of flow rate to air/water ratio. Further, in Gibbs' work, air apparently is injec-

Jan 1, 1980

By R. G. Mallon, R. L. Braun

Primary copper-sulfide ore deposits that are well below the water table can be chemically mined by in-situ high-pressure leaching. The leaching is accomplished by pumping oxygen gas into the bottom of a large underground flooded column of rubblized ore. Part of the injected oxygen dissolves under the high hydrostatic pressure in the column. With a high enough injection rate, the excess oxygen gas induces a convective circulation of oxygenated solution within the rubble column, which transports dissolved oxygen throughout the system. At elevated temperatures, this results in a relatively rapid dissolution of the copper minerals. A method of calculating the leaching rates is presented. The calculation is done by means of a finite-difference computer code that couples all of the processes relating to copper leaching, convective circulation, and the injection, dissolution, and consumption of oxygen. Results of the calculation for a typical case show that over 70% of the copper can be extracted in less than six years with good efficiency in oxygen utilization.

Jan 1, 1976