Search Documents

By Edward F. Fitzhugh

Quantitative appraisal of the chances of finding various tonnages and grades of ore clarifies any exploratory development proposal. Ways are discussed of appraising chances in conformance with probability principles, and graphs are suggested to show tonnages, grades and the corresponding judged expectancies. Introduction When exploratory development of a mineral deposit is contemplated, three interrelated questions normally must be answered before a sound decision can be reached. How much will the program cost? How much will the anticipated ore add to the immediate value of the mine? And what is the chance of developing this ore? To justify development, the deposit should present a favorable disparity between the three factors, cost, chance and return. If, for example, there is a 50-50 chance of success, the ore that is sought should have an immediate worth (after deducting all subsequent charges that it must bear) of more than twice the cost of the development. Likewise, if the chance of finding the ore is but one in five, that ore should enhance the immediate value of the mine by more than five times the cost of developing it- With sound economic and operating assumptions, the cost of exploratory development and a present value of anticipated ore may be estimated within reasonable limits. Less general attention has been given to appraising ore chances in comparable terms. The exploratory experience of the mining industry is broad enough that knowledge, vision and judgment may be combined to yield more tangible evaluations of Ore expectancy than are now customary' A way of making such appraisals is suggested herein. The mathematics of probabilities cannot be applied directly to the search for ore. By coupling applicable principles of probability, however, with pertinent experience gained in mineral exploration, an estimate often can be made of the chance of finding a certain tonnage and grade of Ore in a specific location. Such estimated, or judged, expectancies for the several blocks of ground in a deposit may be combined in a simple chart to show the relationship of the various exploratory possibilities and the potential magnitude of the deposit' An engineer or geologist may find that the quantitative thinking required for an appraisal of this type is an aid in clarifying and coordinating his views and recommendations. For a person wishing to understand these views, an ore-expectancy

Jan 1, 1949

By Edward F. Fitzhugh

Quantitative appraisal of the chances of finding various tonnages and grades of ore clarifies any exploratory development proposal. Ways are discussed of appraising chances in conformance with probability principles, and graphs are suggested to show tonnages, grades and the corresponding judged expectancies. Introduction When exploratory development of a mineral deposit is contemplated, three interrelated questions normally must be answered before a sound decision can be reached. How much will the program cost? How much will the anticipated ore add to the immediate value of the mine? And what is the chance of developing this ore? To justify development, the deposit should present a favorable disparity between the three factors, cost, chance and return. If, for example, there is a 50-50 chance of success, the ore that is sought should have an immediate worth (after deducting all subsequent charges that it must bear) of more than twice the cost of the development. Likewise, if the chance of finding the ore is but one in five, that ore should enhance the immediate value of the mine by more than five times the cost of developing it- With sound economic and operating assumptions, the cost of exploratory development and a present value of anticipated ore may be estimated within reasonable limits. Less general attention has been given to appraising ore chances in comparable terms. The exploratory experience of the mining industry is broad enough that knowledge, vision and judgment may be combined to yield more tangible evaluations of Ore expectancy than are now customary' A way of making such appraisals is suggested herein. The mathematics of probabilities cannot be applied directly to the search for ore. By coupling applicable principles of probability, however, with pertinent experience gained in mineral exploration, an estimate often can be made of the chance of finding a certain tonnage and grade of Ore in a specific location. Such estimated, or judged, expectancies for the several blocks of ground in a deposit may be combined in a simple chart to show the relationship of the various exploratory possibilities and the potential magnitude of the deposit' An engineer or geologist may find that the quantitative thinking required for an appraisal of this type is an aid in clarifying and coordinating his views and recommendations. For a person wishing to understand these views, an ore-expectancy

Jan 1, 1949

By H. A. Tobelmann

age Introduction ............................. 22 Crushing............................... 25 Leaching............................... 28 .Reduction.............................. 47 Electrolytic Deposition..............a.......... 51 Discard for Purification of Electrolyte.................. 60 Recovery of Copper from Discard Solution .............. 62 Resolution of Cement Copper...................... 64 Summary............................... 64 Appendix............................... 66 Discussion............................... 69 Introduction The location, mode of occurrence of ore, and preliminary tests leading to the development of the present leaching process and the building of the present plant on the property of the New Cornelia Copper Co. at Ajo, have been described in previous papers presented to the Institute and in the discussions thereof.l It is sufficient to say that these tests began early in July, 1912, and were continued to the close of January, 1916; that small tests at Douglas were followed by the construction of a 1-ton plant at the mine; and this was followed by the operation of a 40-ton plant for 11 mo. In all about 15,000 T. of ore were treated experiment-

Jan 1, 1919

By C. Laird, C. E. Feltner

IN previous workif2 we have shown that the steady state cyclic stress response of pure copper tested in the low cycle fatigue range was determined only by the plastic strain amplitude and the test temperature. hus, copper, at any given temperature, has a unique cyclic stress-strain curve independent of prior history. Cu-7.5 wt pct Al, however, showed a stress response for a given plastic strain amplitude and temperature which depended sensitively on prior history. From this work we predicted that all wavy slip mode materials, typified by copper, would have a unique cyclic stress-strain curve; whereas all planar slip mode materials, typified by Cu-7.5 pct Al, would not. This prediction has now been tested for a number of materials of widely varying crystal structure and slip character. Wavy slip mode materials studied include: Fe. Al, Cd, disordered FeCo-V, and Cu-3 pct Co (quenched and aged). Planar slip mode materials investigated include: Fe-3 pct Si, ordered FeCo-V, disordered Ni3Mn, ordered Ni3Mn, and Zn. The treatment and properties of these materials are listed in Table I. Cyclic stress-strain curves were determined by controlled plastic strain tests (see Ref. 1 for details) at room temperature for all materials in both the initially annealed and cold worked conditions. The results obtained for iron and Fe-3 pct Si are typical of wavy and planar slip mode materials, respectively. The cyclic stress-strain curves for these materials are shown in Fig. 1 and it can be seen that iron has a unique cyclic stress strain curve while Fe-3 pct Si does not. Aluminum, Cu-3 pct Co, and disordered FeCo-V showed a behavior like that for iron, while Ni3Mn in both the disordered and ordered condition behaved in the same manner as Fe-3 pct Si. These results therefore support the general conclusion drawn in Refs. 1 and 2 that. for wavy slip mode materials, a cyclic mechanical equation of slate it =t.(hcp, i. T) is approximated in which the satura-

Jan 1, 1970

By H. F. Yancey, M. R. Geer, C. L. Allyn, R. H. Eckhouse

W. M. Bertholf—This is an excellent report of a well-conducted investigation, of sufficient scope to provide generally useful information. Some years ago we had occasion to test the Humphreys spiral on the middling from our table plant. The conclusions reached in this investigation come as no surprise to us. In certain applications it is virtually impossible to improve on the spiral from the monetary returns point of view even though its "efficiency" may be low. We have noted that in all successful applications of the spiral the feed is "classified," hence we were somewhat disappointed in the showing the spiral made on the Poplar Ridge coal, the only one of the four which could really be considered the equivalent of a classified feed. As was noted in the paper, however, this coal contained a considerable amount of middle and high-gravity material, apparently more than enough to make up for the theoretical advantage of small particles in these categories. A comparison of particle size in the various specific gravity classes of the four coals is given in table XXV. Table XXV. Comparison of Particle Size in Various Specific Gravity Classes. (Unit size, 150 m to 0.105 mm) Black Eagle Clements Poplar Ridge Rosly,n 1.3 Float 7.47 10.60 8.68 9.66 1.3 x 1.4 7.89 7.96 7.58 8.20 1.4x1.6 7.24 8.36 5.58 6.85 1.6 x 1.8 7.98 8.31 3.42 7.33 Sink 1.8 7.85 7.13 5.09 7.41 Avg 7.69 10.08 7.15 8.38 This tabulation indicates that there was very little difference in the size of the various gravity fractions for three of the coals, Poplar Ridge varying the most. Examination of figs. 3, 6, 7, and 8 reveals a general similarity of behavior for all coals except Black Eagle. Would the authors care to speculate on the reasons for the difference in the distribution curve for the sink 1.60 material in the washed coal of fig. 3 as compared to the others? This difference is particularly noticeable in the 8xl4-mesh size. Was there a "shape effect"? J. D. Price and W. M. Bertholf—The performance data on three of the coals studied appear to be typical, but there are certain departures from the general pattern in the case of the Poplar Ridge coal which are large enough to deserve special consideration. For example: 1. Despite the high proportion of sink 1.60 material in the feed, it was not possible to make a corresponding proportion of high-ash reject. (See table XVI.) 2. Even though approximately 70 pct of the feed was 1.40 float with an ash content of 6.6 pct, and this

Jan 1, 1951

By R. H. Eckhouse, M. R. Geer, H. F. Yancey, C. L. Allyn

W. M. Bertholf—This is an excellent report of a well-conducted investigation, of sufficient scope to provide generally useful information. Some years ago we had occasion to test the Humphreys spiral on the middling from our table plant. The conclusions reached in this investigation come as no surprise to us. In certain applications it is virtually impossible to improve on the spiral from the monetary returns point of view even though its "efficiency" may be low. We have noted that in all successful applications of the spiral the feed is "classified," hence we were somewhat disappointed in the showing the spiral made on the Poplar Ridge coal, the only one of the four which could really be considered the equivalent of a classified feed. As was noted in the paper, however, this coal contained a considerable amount of middle and high-gravity material, apparently more than enough to make up for the theoretical advantage of small particles in these categories. A comparison of particle size in the various specific gravity classes of the four coals is given in table XXV. Table XXV. Comparison of Particle Size in Various Specific Gravity Classes. (Unit size, 150 m to 0.105 mm) Black Eagle Clements Poplar Ridge Rosly,n 1.3 Float 7.47 10.60 8.68 9.66 1.3 x 1.4 7.89 7.96 7.58 8.20 1.4x1.6 7.24 8.36 5.58 6.85 1.6 x 1.8 7.98 8.31 3.42 7.33 Sink 1.8 7.85 7.13 5.09 7.41 Avg 7.69 10.08 7.15 8.38 This tabulation indicates that there was very little difference in the size of the various gravity fractions for three of the coals, Poplar Ridge varying the most. Examination of figs. 3, 6, 7, and 8 reveals a general similarity of behavior for all coals except Black Eagle. Would the authors care to speculate on the reasons for the difference in the distribution curve for the sink 1.60 material in the washed coal of fig. 3 as compared to the others? This difference is particularly noticeable in the 8xl4-mesh size. Was there a "shape effect"? J. D. Price and W. M. Bertholf—The performance data on three of the coals studied appear to be typical, but there are certain departures from the general pattern in the case of the Poplar Ridge coal which are large enough to deserve special consideration. For example: 1. Despite the high proportion of sink 1.60 material in the feed, it was not possible to make a corresponding proportion of high-ash reject. (See table XVI.) 2. Even though approximately 70 pct of the feed was 1.40 float with an ash content of 6.6 pct, and this

Jan 1, 1951

By T. M. Geffen, F. F. Craig

Laboratory model flow tests have been made to simulate field conditions of partial pressure rnaintenance by dispersed gas drive on rocks having sandstone-type porosity. In this production method there is a significant saturation gradient between injection and production wells. A means of calculating relative permeability characteristics. from partial pressure rnaintenance flow tests has been developed. This method takes into account the saturation gradient. These kg/ko characteristics are identical to those for solution and external gas drives. This method of calculation, which has been proved experimentally, has limitations; however, it is valid for cases likely to be encountered in field prediction of partial pressure maintenance performance. The production performance of a hypothetical reservoir has been calculated for several different injection programs, involving both full and partial pressure maintenance. Results indicate that the maxinum oil recovery by these gas injection programs is obtained by full pressure mainte- nance at the original bubble point. Correspondingly lower oil recoveries are obtained by postponing gas injection and/or by reducing the degree of pressure maintenance. INTRODUCTION Dispersed gas injection is an important method of recovering additional oil beyond that obtainable by pressure depletion alone. The injected gas acts as a source of additional energy to displace oil from the rock formation as well as to retard oil shrinkage in the reservoir. In practice, gas injection is usually started after the reservoir pressure has fallen below the original bubble point. For various reasons sufficient gas is generally not injected to completely maintain the pressure in the reservoir. So, injecting gas at a declining reservoir pressure results in a combined external and solution gas drive. These two oil displacement processes are characterized by different gross saturation distributions in the reservoir. The external gas drive, like all frontal drive processes, inherently results in an oil saturation which increases from the injection wells to the producing wells. In the solution gas drive there is essentially a uniform oil saturation throughout the reservoir, provided the field is being depleted uniformly. It has been customary to predict oil recovery performance under partial pressure maintenance by a method which does not take into account the saturation gradient1. It has been shown2 that neglecting the presence of a saturation gradient can cause considerable error. It is the purpose of this paper to develop and present an improved method of predicting partial pressure maintenance performance of reservoirs including, where necessary. the effects of well arrangement. From the laboratory standpoint, this problem involves the measurement of the basic flow behavior (relative permeability characteristics) under partial pressure maintenance conditions. Recent research- as shown that for rocks having sandstone-type porosity, the relative permeability characteristics are identical for solution gas drive and complete pressure maintenance external gas drives. Since both solution and external drives have the same basic flow behavior, it was speculated that partial pressure maintenance, being a combination of the two, would also

Jan 1, 1957

By J. G. Faller, L. P. Skolnick

The distribution of cobalt and vanadium over non-equivalent crystallographic sites in C14-type Zr(VCo), alloys has been investigated. An anomalous X-ray scattering technique developed by Skolnick, Kondo. and lavine7 by which the separation in the scattering factors of two similar atoms can be enhanced was employed. Six alloys spanning the pseudobinary section ZrV1.6Co0.4-ZrVO.6CO1.4 at 10pct steps showed a nonrandom compositionally dependent distribution. Specifically, at high vanadium content cobalt preferentially occupied sites of type (6h) and vanadium, sites of type (2a; at low vanadium content the reverse was observed. In addition to the distribution fraction the structural parameters x and z were obtained. There was no significant deviation of these parameters from those obtained in the ideal C14 structure. Certain suggestions are made to account for the observed nonrandomness in the distribution of atoms on the two types of sites. INTERMETALLIC compounds of formula AB2 iso-morphous with MgCu2, MgZn2, and MgNi2 are known as Laves phases. Because Laves phases exhibit high symmetry and coordination numbers, the highest possible for an AB2-type compound,1 they are among the most frequently observed compounds in nature. In recent years interest has centered about the purely transition metal Laves phases2-' in efforts to understand the function of atomic size and electronic structure in the formation of these compounds. It has been observed that pseudobinary Laves phase systems often show a variation of structure across the phase diagram. Such a system is the ZrV2-ZrCo2 in which the structure varies from cubic MgCu2 to hexagonal MgZn2 to cubic MgCu2.4 Some understanding about the conditions under which the second modification is stable can perhaps be gained by studying the distribution of cobalt and vanadium atoms on lattice sites in the MgZn2 modification of the system ZrV2-ZrCo2. In both the MgZn2 and MgNi2-types there exist nonequivalent positions open to occupancy by the B element, whereas in the MgCu2 prototype all sites are equivalent. Skolnick, Kondo, and La-vine7 have developed an anomalous scattering technique suitable for this type of investigation. Whereas the influence of size on the formation of a Laves phase is well recognized, no substantial evidence has been put forth in support of the size ratio dependence of a particular prototype. Berry and Raynor8 suggested that RA /RB ratio does indeed affect the type of structure that is chosen, MgZn2 compounds tending to cluster about 1.225 while MgCu2 compounds were found at larger deviations from this ratio. Dwight,3 however, from a study of 164 Laves phases does not believe this generalization to be justified. Electronic effects are certain to play a part in the stability of Laves phases in general and in the choice of a structure type in particular. For example, size along would favor the formation of Laves compounds of Ti, Zr, Hf, Ta, or Nb as the A element with nickel or copper as the B element. The absence of such is attributed to an unfavorable electron : atom ratio by Elliott and rostoker.4 Early experiments of Laves and witte9 with pseudobinary and pseudoternary systems of the three prototypes established the dependence of crystal structure upon electron: atom ratios. They observed that the MgCu2 structure dissolved elements of higher valency until the electron: atom ratio of =1.8 was reached; the MgZn2 likewise dissolved elements of lower valency replacing zinc. witte,6 from calculations of the electron : atom volumes of Brillouin Zones, obtained limits of stability for the prototypes MgCu2 and MgZn2. Elliott and Rostoker4 used these limits with considerable success in the all-transition element Laves phases they investigated. According to witte,6 compounds between the electron :atom ratios of 1.80 and 2.32 were of the MgZn2 type; those above and below exhibited the MgCu2-type structure. On the basis of these limits and an assumed valency of zirconium based upon the near tetra-valence of titanium, Elliott and Rostoker obtained valencies for the first transition series elements. For the Laves phases with which this investigation is concerned, ZrV2 and ZrCo2, the authors calculated electron :atom ratios of 2.54 and 1.56, respectively. These ratios are for the MgCu2-type structure and straddle the stability band of the MgZn2 modification. One could, therefore, predict that a pseudobinary system ZrV2-ZrCo2 should pass through the MgZn2 modification in traversing the composition diagram from one end to the other. Implicit in this assumption is a smooth change of the electron: atom ratio from 2'54 to 1.56. MOSS10 states that his finding the low temperature structure of ZrCr2 to be C15 instead of C14 alters greatly Elliott's valency of zirconium and hence the assumed valencies of the other metals. Such a quantitative correlation of structure with electron : atom

Jan 1, 1963

By John Henry Harden

It appears that in the earlier days of anthracite coal mining, 1824-25, the Lehigh region mined 76 per cent. of all the coal sent to market. During the same period Wyoming sent 12 and 5 per cent. respectively, whilst the Schuylkill sent 11 and 18 per cent., the number of tons marketed being in those days very small indeed. In the year 1828 the Schuylkill region mined over one-half of all the coal sent to market, and continued to do so for thirty years (with the exception of the year 1831), until 1858 ; since that date the production has declined very steadily in comparison with the other regions, until, in 1876, it was only 34 per cent. Wyoming, in the year 1820, was mining 40 per cent., but the production of all the regions was very small; in six years it declined to 5 per cent., increased to 34 per cent. in 1831, declined to 10 per cent. in 1838. Since which time the increase has been gradual, until 1873-75 Wyoming produced over 50 per cent. of all the anthracite coal sent to market. In 1867 the production exceeded that of Schuylkill, and has continued to do so since that time. In the year 1876, during the existence of the "coal combination," Wyoming lost 9 per cent.; during the same time Lehigh gained 7 and Schuylkill 2 per cent. over their relative production of the preceding year, the decrease of Wyoming being two and a half million tons, the increase of the Lehigh one million, the decrease of the Schuylkill nearly three-quarters of a million. The extraordinary production of the Lehigh region at a time of decreased demand and in opposition to an agreement with the other regions to limit the supply to the supposed demand mas the cause of the disagreement which ultimately broke up the combination of the great coal-producing and carrying companies. The Lehigh region produced very steadily, from 1829 to 1854, an average of about 22 per cent. of the whole production. From 1854

By C. W. Kempton

If New England were located in some distant and almost inaccessible region, there is no doubt that its mineral resources would have been ere this well developed and generally acknowledged, but laboring under the disadvantage of nearness, it has been neglected. Its surface, moreover, is not cut up by mountains and canons, and the remnants of many of the old ridges are extensively covered by glacial drift. Having for the past ten months been engaged in the development of a mineral district in Southeastern Maine, 1 would take this opportunity to lay before the Institute sketches of results, and try to give some idea of the formations as found. The Sullivan Mining District extends from the town of Franklin, through Hancock, Sullivan, and Gouldsborough, from northwest to southeast, about sixteen miles. A general idea of this locality may be gathered from the map accompanying. (Fig. 1). Sullivan is situated at the head of Frenchman's Bay, ten miles north from Bar Harbor, Mount Desert, twelve miles from Ellsworth,

Jan 1, 1879

By W. G. Matteson

The Gulf Coastal plain of the southern United States is that area bordering for a large part, the Gulf of Mexico and extending inland and northward to the main interior highland region. It is more or less V-shaped and includes the States of Florida, extreme southern Alabama, all .of Mississippi and Louisiana, the eastern and southern half of Arkansas, and the eastern, southeastern, and southern portions of Texas. While the contents of this paper apply to. the Gulf Coastal plain in general, they are intended to refer more specifically to that portion of the plain included between the 90th and 97th meridians, and the 29th and 33d parallels, an area that may be described geographically as comprising western Mississippi, all of Louisiana, part of eastern and all of south-eastern Texas. It is within this area that numerous and prolific oil pools have been developed during the last 17 years.

Jan 2, 1918

By Fred D. DeVaney

MINNESOTA taconites are extremely hard, and fine grinding is required to produce an acceptable concentrate. To reduce grinding costs, waste material is rejected by magnetic separators as soon as it is liberated. Cyclones are now used in all Minnesota taconite plants to close the grinding circuits. Erie Mining Co. installed its first grinding section at Aurora, Minn., in 1948-a 9 ½ x12-ft. mill and a fine grinding section consisting of a 10 ½ x12-ft ball mill in closed circuit with a duplex 60-in. spiral classifier. Concentrates from the magnetic cobbers treating the rod mill discharge passed directly into the classifier; the ball mill discharge was also treated in magnetic separators and the concentrate from these machines also went to the spiral classifier. Both concentrates passed through ac demagnetizing coils. It is axiomatic that for proper classification the material in suspension must be well dispersed, and it follows that magnetic concentrate must be almost completely depolarized if classification is to be successful.

Jan 8, 1957

By Peter J. Lean

The introduction oE computer control in the grinding circuit of the New Broken Hill Consolidated Limited concentrator in the early 1970's gave smoother operation at optimum performance. The ore feedrate and water additions to the grinding circuit were controlled to operate each of the ball mill/ rake classifier grinding units at the upper limit of the circulating load while classifier overflow density was maintained to give a product size and pulp density suitable for flotation. An incremental expansion of the concentrator in 1981-82 included the installation of hydrocyclones in closed circuit with three of the four ball mills. Without the rake classifiers in circuit the previous control strategy could not be used and the complex interaction of hydrocyclone performance characteristics when classifying coarse grained sulphide ore resulted in the over-grinding of the lead mineral galena. Testwork aimed at optimising grinding circuit performance recognised the enhanced tendency of higher specific gravity minerals to report to the cyclone underflow. The data has been evaluated on an individual mineral basis and then used to develop a model For grinding circuit control. The development of the model which uses inputs of ore feedrate, metal content of the Feed and slurry density of the cyclone overflow to predict the size of the minerals in the grinding circuit product is described and model predictions are compared with plant performance.

Jan 1, 1984

By R. Clare Coffin

The production of petroleum in the Rocky Mountain district increased from 27,104,436 bbl. in 1929 to 33,048,630 bbl. in 1930. This increase was due to the development in southeastern New Mexico; which is in reality a portion .of the West Texas province. Disregarding production in southeastern New Mexico, the Rocky Mountain district produced 25,799,027 bbl. in 1929 and 23,164,988 bbl. in 1930, a decrease of 2,634,039 bbl. for the period. The daily production in January, 1930, averaged 70,839 bbl. for the entire district and in December, 1930, the daily production was 98,995 bbl. Total production by states is given in Table 1. Three important discoveries of oil and one of gas occurred in the district during 1930 in structures not, previously known to contain oil or gas. Oil was discovered in Dry Creek structure, Carbon County, Mont.; in the Midway structure, Natrona County, near Casper, Wyo.; and in the Greasewood structure, Weld County, Colo., northwest of Fort Morgan. Gas was discovered in the Bell Rock structure in Moffat County, western Colorado. Seven deep tests in as many different fields encountered oil in lower horizons than those already exploited. All of these discoveries were in the state of Wyoming. They occurred in the Salt Creek field, Natrona

Jan 1, 1931

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 D. A Dahlstrom

THE necessity for slime elimination from valuable mineral and coal products has become increasingly significant within the past 5 years.' , Most of the mechanized mining and present beneficiation methods have resulted in larger tonnages of extreme fines, silts, and clay, commonly called slimes, processed by the preparation plant. Economics in turn have forced the plant operator constantly to lower the bottom size of effective beneficiation, necessitating an almost complete recovery of valuable solids regardless of particle size. When these important factors are considered, the need for an efficient slime removal method for fine solids becomes self-evident. Ordinarily slimes have been classified as ranging from 75 microns, or 200 mesh, down to colloidal dimensions of less than one micron. At the same time there is general agreement that the most troublesome slimes are primarily clays, silts and extreme fines, so that the actual top size may be placed at approximately 30 to 40 microns. This immediately restricts any desliming operation to classification, as screening or other methods would be both uneconomical and grossly inefficient at such dimensions. The liquid-solid cyclone has been recognized as one of the most efficient fine size classifiers available to the mining industry. Applications of cyclones to thickening, high efficiency solid recovery, degritting,

Jan 1, 1953

By D. A. Dahlstrom

THE necessity for slime elimination from valuable mineral and coal products has become increasingly significant within the past 5 years.' , Most of the mechanized mining and present beneficiation methods have resulted in larger tonnages of extreme fines, silts, and clay, commonly called slimes, processed by the preparation plant. Economics in turn have forced the plant operator constantly to lower the bottom size of effective beneficiation, necessitating an almost complete recovery of valuable solids regardless of particle size. When these important factors are considered, the need for an efficient slime removal method for fine solids becomes self-evident. Ordinarily slimes have been classified as ranging from 75 microns, or 200 mesh, down to colloidal dimensions of less than one micron. At the same time there is general agreement that the most troublesome slimes are primarily clays, silts and extreme fines, so that the actual top size may be placed at approximately 30 to 40 microns. This immediately restricts any desliming operation to classification, as screening or other methods would be both uneconomical and grossly inefficient at such dimensions. The liquid-solid cyclone has been recognized as one of the most efficient fine size classifiers available to the mining industry. Applications of cyclones to thickening, high efficiency solid recovery, degritting,

Jan 1, 1953

By W. A. Tiller

The conventional techniques1 for determining the liquidus and solidus surfaces of an alloy system containing more than two components are extremely tedious to use and do not provide a complete picture of the equilibrium relations between solid and liquid alloys. These techniques are unable to yield "tie-line" information concerning solid and liquid phase equilibrium, a very important parameter in the solidification description of the liquid alloy and a very necessary parameter in the preparation of "zone-levelled" alloy crystals. The tie-line in a polycomponent system is analogous to the partition coefficient, k, in a binary system, it gives the composition of the solid, Cs, in equilibrium with a liquid of composition CL. That is, CS = kCL, where CL = [CO, c1,...Cn] denotes the concentrations of the n + 1 constituents, and k = [ko, kb ,...kon] denotes the gross partition coefficient for the elements between the two phases; thus, k is the tie-line in this system. To provide complete information concerning the two-phase equilibrium in a polycomponent system it is necessary to know both the liquidus surface and the gross partition coefficient. From these two the solidus surface is obtainable. The conventional techniques are unable to provide this information in other than a binary system so we must look elsewhere. In recent years considerable insight has been gained into the correct description of the liquid-solid transformation, 2,3 and controlled solidification experiments may now be designed to both facilitate and enhance equilibrium diagram studies. In the present paper consideration is given to two methods for obtaining the liquidus surface and the tie-lines in polycomponent systems. The methods to be described below deal with the solidification of an n + 1 constituent liquid alloy of initial composition [co, Co ,...Con], where the superscripts refer to the elements present and the Oth element is considered as the solvent in which the n solutes are dissolved. The general assumptions made in the treatment are the following: (i) the solid and the liquid at their interface are in equilibrium during the growth of the solid phase, (ii) there is no diffusion in the solid phase, and (iii) the liquid phase is completely mixed and is therefore homogeneous in concentration. METHOD I In this section a general experimental method will be described which, in principle, is capable of giving an exact description of the liquidus surface and tie-lines. Consider the unidirectional solidification of the liquid alloy specimens L cm in length (freezing either horizontally or vertically). Allow the sample to be frozen very slowly from one end, as indicated in Fig. 1, with complete mixing in the liquid, and then analyze the solid bar to determine its chemical constitution as a function of position, x, along the bar. Let Fig. 2 represent a possible distribution of the ith constituent along the bar. At the point x' the concentration of the ith constituent is C1/5(x'), and the average concentration of the rest of the bar between x' and L is given by C:(X' - L) where [ A(x) c1s(x)dx c1/s(x'-L) = f A(x) dx x * and A(X) is the cross-sectional area at x. In a similar manner. all the Cf(x' - L) may be determined. Thus, the gross artition coefficient k for liquid of composition [Cs(x - L),...Cs(X' - L)] is given by -ko= CUs')/Cos(x' - L)" k0 = csn{x')/cs(x'- L) During the freezing of a charge of length L, the liquid composition may vary over a wide segment of the phase diagram and the gross partition coefficient over this segment of the phase diagram may be determined from one, bar. Fig. 3 illustrates the magnitude of Cs(g)/C,' as a function of the fraction g of the bar which has Solidified.2 We can see that the concentration in the bar will vary over a range of about 15 wt pct for C,' = 10 wt pct and k0 = 0.5. It appears that 4 or 5 specimens would be adequate to study a simple binary eutectic phase diagram.

Jan 1, 1960

By C. G. Dunn, F. Lionetti

The energy associated with grain boundaries in polycrystalline aggregates is believed to play a major role in grain growth processes and, when growth ceases, to determine the final equilibrium grain boundary angles. Further, the energy of grain boundaries of recrystallization nuclei is a factor in nucleation processes. It is important to know, therefore, how the energy per unit area of a grain boundary, that is, the grain boundary surface tension y, depends on the difference in orientation of the two lattices of the grains producing the boundary. Although the problem is important, surprisingly little has been done toward a quantitative evaluation of the effect of orientation difference on grain boundary energies. C. S. Smith1 recently has discussed this problem and in addition to showing effects of orientation difference on equilibrium angles has shown a variety of interesting effects of surface tension on the appearance of microstructures. Fig 1 and the following relations expressed in Eq 1, which connect equilibrium grain boundary angles and surface tensions, illustrate equilibrium conditions which are believed to hold true in metals. ?l2 _ ?23 _ ?l3 [1] sin ?3 sin ?1 sin ?2 Clearly any two of these surface tensions can be expressed in terms of the third when the equilibrium angles ?1, ?2, and ?3 are known. Applied to the present problem for solid state equilibrium of three grains, the angles ?1,?2 and ?3 must be measured in a plane perpendicular to the line of junction of the three grains. Normally a direct determination of these angles from random microsections is impossible. Consequently Harker and Parker2 and Smith1 (except for some measurements on flat specimens) resorted to a statistical method to determine equilibrium grain boundary angles. Smith reported that grain boundaries meet the surface of a piece of metal nearly perpendicularly. He reported also, in connection with direct angle measurements on flat specimens with grains extending through the thickness, that angles varied appreciably from 120" and concluded that there was a measurable effect of orientation difference on surface tension. Another direct way of determining equilibrium angles and a method adaptable to studying particular configurations, recently suggested by Dunn,³ is to use a three-grain flat specimen with orientations of grains so chosen that the junction line of the three grains will be straight throughout the thickness and perpendicular to the surface of the specimen. Choice of orientations is possible when individual grains of each group can be grown to predetermined orientations through the reorienting and growth of " seed crystals " as described.³ Not only is it possible, for example, to have grains with the same crystallographic plane in the plane of the specimen, but a given orientation difference between two grains can be made a common factor to an unlimited number of three-grain groups while a series of orientation differences is investigated. Any effect of anisotropy of gas-solid surface tension due to grain orientation should be minimized by having all gains oriented the same with regard to crystallographic plane in the plane of the specimen. Another feature of the three-grain group is the notched grain boundaries as shown in Fig 2 for one specimen (S4). The notches serve to anchor the end positions of the grain boundaries (especially at high temperatures) while the central and junction point of the grains moves toward an equilibrium position. Final equilibrium should produce straight grain boundaries if the notches are very narrow and if changes in orientation* of the grain boundary do not alter the surface tension.† If one assumes the straight line condition and no change of surface tension with small changes in grain boundary orientation and finds the equilibrium configuration by a minimization of the grain boundary energy, one obtains the relations given in Eq 1. The approach to straight line boundaries or to minimum energy configurations in specimens containing large grains, such as those used in the present investigation, may be very slow compared with the approach to equilibrium conditions for the grain boundary angles. It may be desirable, as proved to be the case in the present investiga-

Jan 1, 1950

By P. H. Royster

On the Continent, ferromanganese has been produced in the blast furnace almost continuously since 1876, but little definite information concerning the practice is to be found in technical literature, and almost nothing in the way of a theory of the manganese furnace. In this country, prior to 1904, but one company had attempted its production in a serious way, and none of the operating data or other information from this company has been, or is, available to the public..In the last 5 years, as a result of the restriction of imports, a number of furnaces have been blown in on this alloy, with the result that in 1918 as many as 18 furnaces were in blast. The majority of the men in charge of these furnaces had had little previous experience in such operations; so the Bureau of Mines, in the summer of 1918, undertook the collection of data from ferromanganese furnaces. Operating data were collected by the Bureau from eleven ferromangahese furnaces, which will be referred to throughout this paper as furnaces A, B, C, F, G, I, J, K, L, M, and P; the dimensions of seven of the furnaces are given in Table 1. The companies from whom this information was obtained, and to whom should go the credit for whatever value this information may possess, are the Bethlehem Steel CO.,

Jan 1, 1920