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By W. H. Coghill, A. M. Gow, M. Guggenheim, A. B. Campbell

The object of this paper is to discuss the fundamental principles of ball milling and to present some observations which have been made in laboratory and plant investigations. The discussion will be limited to wet grinding of ores in cylindrical mills, but doubtless many of the principles involved will be equally applicable in the other fields of fine grinding in which mills of the same type are used. In the concentrators of the United States there are about 650 ball, rod, or pebble mills, operating or ready to operate, and these have about 100,000 connected horsepower. For grinding in cement plants there is about three times this connected horsepower, and other industries have an unestimated amount, all used for the general type of grinding that is to be discussed here. It is true that these figures do not represent stupendous amounts of power, but when one considers that ball milling is often the ((bottle neck" in a concentrator and that it often accounts for the largest single item in the cost sheet, the importance of a comprehensive understanding of the principles of ball milling can be appreciated. Much of the past literature devoted to the subject has been concerned with the Kick-Rittinger dispute over evaluating grinding, or with dissertations on ball paths and the closely allied impact versus attrition hypotheses, or with the exclusive consideration of certain specific variables, such as mill speed or circulating load, irrespective of the other factors in operation. Such subjects may be dismissed with but little discussion in what may be called, by comparison, a new philosophy in the study of ball milling. Briefly, this '(new philosophy" consists of using power as an index of the mill operation, and investigating grinding from the standpoint of set and induced varisbles, with emphasis on the latter.

Jan 1, 1935

By Alexander Gow

THE object of this paper is to discuss the fundamental principles of ball milling and to present some observations which have been made in laboratory and plant investigations. The discussion will be limited to wet grinding of ores in cylindrical mills, but doubtless many of the principles involved will be equally applicable in the other fields of fine grinding in which mills of the same type are used. In the concentrators of the United States there are about 650 ball, rod, or pebble mills, operating or ready to operate, and these have about 100,000 connected horsepower. For grinding in cement plants there is about three times this connected horsepower, and other industries have an unestimated amount, all used for the general type of grinding that is to be discussed here. It is true that these figures do not represent stupendous amounts of power, but when one considers that ball milling is often the "bottle neck" in a concentrator and that it often accounts for the largest single item in the cost sheet, the importance of a compre-hensive understanding of the principles of ball milling can be appreciated. Much of the past literature devoted to the subject has been concerned with the Kick-Rittinger dispute over evaluating grinding, or with dissertations on ball paths and the closely allied impact versus attrition hypotheses, or with the exclusive consideration of certain specific varia-bles, such as mill speed or circulating load, irrespective of the other factors in operation. Such subjects may be dismissed with but little discussion in what may be called, by comparison, a new philosophy in the study of ball milling. Briefly, this "new philosophy" consists of using power as an index of the mill operation, and investigating grind-ing from the standpoint of set and induced variables, with emphasis on the latter.

Jan 1, 1934

SUGGESTIONS that existing schools give instruction bearing on the mineral industry, or that schools for that purpose should be established in the United States, began to be made early, and it would require too much space to catalogue them all. Some of the more important may be mentioned to indicate their general character. In the "advertisement to such parents as have now (or expect to have) children prepared to be educated in the College of New York," which appeared in the New York Mercury of June 3, 1754, Samuel Johnson, the first president of King's College, the predecessor of Columbia, said that it was the "design of this college to instruct and perfect the youth," among other things, "in the arts of Numbering and Measuring of Surveying, and Navigation and Geography. . . . and in the Air, Water and Earth around us, and the various kinds of Meteors, Stones, Mines and Minerals, Plants and Animals; and in the knowledge of all Nature in the Heavens above us, and of everything useful for the Comfort, Convenience and the Elegance of Life . . . " Though the concept that natural science should be used to enlarge the bounds of human life was thus implicit at Columbia from the , very beginning (John Stevens graduated from it in 1768, James Renwick in 1807, Horatio Allen in 1833, and A. W. Craven in 1899), it was only during the period of Renwick's professorship of Natural and Experimental Philosophy and Chemistry (1830- 1853) that much attention was given to applied science.* Among the Austin papers, published by the American Historical Association,~ there is a draft in Stephen F. Austin's handwriting of a proposed memorial from the legislature of , Missouri to Congress, not only urging "the propriety and utility * See chapter 4 for early interest in this subject in Philadelphia.

Jan 1, 1941

By W. L. Maxson

GRINDING is one of the major problems in present-day milling practice, and in many cases, it represents one of the main items of expense. It becomes necessary from time to time, to compare grinding practice in one plant with that in another plant, and in making such comparisons, it would be very desirable were there available accepted standards of grinding resistance for the materials involved. Such a set of grinding constants would also be of considerable value in planning new grind-ing installations. There have been some tests published, notably those of Lennox,1 which have been generally cited as a basis for such comparisons. Most of the tests made have been based upon open-circuit grinding, in which a weighed sample of the ore was crushed to pass a certain mesh, and was .then ground under certain conditions, either wet or dry. Grinding was continued until a certain desired fineness was attained, and the compari-sons based on the grinding time, or the samples were all ground for a certain specified length of time and comparison based upon the screen analysis of the products. Such methods have been acceptable where the ore was to be ground in open circuit. However, in modern milling practice, many grinding problems involve closed circuits wherein the oversize returns to the mill and a large circulating, load builds up. A method of testing that does not take the circulating load into consideration might yield results quite different from those to he expected in practice, because the minerals in the ore that offer maximum resistance to grinding will accumulate in the circulating load up to an equilibrium value. Thus the nature of the ore charge in the mill at any instant may differ greatly from that of the new feed, with a consequent error in the rate of grinding determined by such a method.

Jan 1, 1933

By Reich G. Gaertner

Almost every mining engineer who has had charge of extensive underground workings will have observed how often directions as to course and levels, deduced from careful theodolite measurements, have been slighted or disregarded by mine-foremen and shift-bosses, and how often these tedious measurements had to be repeated, even for minor works, such as ventilation-drifts or winzes, in order to carry them on with the required or desirable regularity. Besides the time and care absorbed by theodolite surveys, there is still another inconvenience, namely, the interruption of transportation during the time of observation, and, in heavily producing mines, the loss consequent upon such interruption. In proposing a subsidiary instrument to the theodolite, it is my purpose not to present a new one, but simply to recommend to the consideration of American mining engineers one which has been in use in nearly all the prominent mines of Europe for many decades, and has there fulfilled its purpose admirably. I refer to the mining or hanging compass (Fig. 1). At my urgent request, the firm of Keuffel & Esser, of New York, have lately constructed this instrument in a form which adapts it better to use in this country. By the addition of the trigonometer, the banging compass becomes at once an instrument which will prove of value even in the hands of foremen and practical miners, who have little or no knowledge of trigonometrical calculations. Probably many will say that me have no use for needle-instruments ; that our modern theodolites are of such perfect description, and leave so little to be desired, that the introduction of a compass would look like a step backwards compared to the fine results obtained by angle-instruments. I concede all that, and do not pre-

Jan 1, 1886

By Carl S. Westerberg

Coal preparation practice and trends follow, among other factors, production trends in any given area. Considering an area the size of a state, some broad predictions may be made after a review of the annual production records. As this paper is concerned with coal cleaning in Utah, data on its production record are pertinent. Table 1 shows the percentage relation of coal production in Utah to the national total as a single figure up to 1935 which includes all recorded production. From 1935 through 1947 these data are presented by years. It is evident from these data that the production of Utah coal is ascending. The reason for this trend is industrial growth in the West resulting in a population shift which accounts for more people than the normal increase would supply together with Utah's relatively fortunate geographical location and its abundance of good-quality coal. Utah is also hopeful of supplying more coal in the future for West Coast power generation.I Utah is not unique among coal-producing states in anticipating greater production in the future. Coal Age states, " . . . it is now evident that a billion-ton yearly production of anthracite and bituminous by 1960 is not impossible." At present it is about 610,000,000 tons, the all-time high in 1947 was approximately 687,803,000 tons. In view of the trend outlined above, obviously more new mines will be required to produce the necessary tonnage. These in turn will require more mechanical cleaning capacity. Whether the required new plants will be built by present operators of mines and mechanical cleaning plants or by others now in the business of producing coal or expecting to enter it is of no consequence in this discussion. The fact is— they will be built.

Jan 1, 1950

By P. G. Shewmon, J. Y. Choi

The surface-diffusion coefficient for , has been measured on (111) and (100) surfaces of copper from 1000" to 620°C. D,(Ge) on the (111) is two to three times that on the (100) as was found earlier for copper and gold on copper. D, (Ge) on both (111) and (100) is about thirty times that found for gold or copper tracers on the same surfaces, while in the temperature range where both D,(Ge) and Ds(Au) have been measured the activation energy for germanium is the same as that for gold. The apparent activation energy for Ds(Ge) is not a constant, but decreases with temperature. In a recent paper we reported on the application of a new tracer technique to the determination of the surface-diffusion coefficient (D,) for gold and copper on (111) and (100) surfaces of copper.' In this paper, we shall give the results obtained when the same technique was used to measure Ds for germanium on the (111) and (100) surfaces of copper. In addition to providing data on D., for an additional element on copper, the longer half-life of germanium (275 days) meant that Ds could be measured down to a much lower temperature and thus over a much wider temperature range (1000" to 620°C) than was used in our gold-tracer work (1060" to 780°C) or copper mass-transport studies (1060" to 800). The apparent activation energy for D, (Ge) is essentially the same as that found for gold or copper in the same temperature range, though the values of D, (Ge) are thirty times greater than those found for gold or copper tracers. The most interesting new result found is that the apparent activation energy for Ds(Ge), and thus Do, definitely increases with temperature. Such a trend was much more apparent in Gjostein's mass-transport work on copper than in our own, though in an earlier paper we mentioned the difficulty of fitting all of our points with one straight line:= No real explanation of this is given though experiments done on grain boundary groove growth at various ambient pressures demonstrate unequivocally that vapor transport plays no part in the increase in activation energy with temperature.

Jan 1, 1964

By Herman Garlichs

The development of the extensive Southeast Missouri deposits greatly preceded that of the Iowa and Wisconsin deposits. It began about 1720 at Mine La Motte and other localities, and has continued uninterruptedly to the present time. It is estimated that this district produced about 184,000 tons of lead in the year 1916, having a value of approximately $25,000,000. This is a new high record. The Southwest Missouri orebodies were hardly known before 1845 and were not extensively developed until 1870. Lead production in Southwest Missouri for 1916 was 38,788 tons. Oklahoma produced 14,399 tons and Kansas 2,345 tons, making a total for Southwest Missouri, and the adjoining districts in Oklahoma and Kansas, of 55,532 tons of lead. The first metallurgists in Missouri were the Indian and the hunter. The early settler learned to procure his bullets either by melting ore in his camp fire or by throwing pieces of galena on an old stump and depending on the usual roasting and reaction method to obtain the metal. A little more refined method was to arrange two flat stones in the form of a, V. Wood and galena were placed in the furnace and ignited.. As heat developed, some of the metal was extracted and molded into bullets. The next step in utilizing the lead ores was the log hearth. All lead in Missouri was smelted in this crude affair before 1820. It was built on sloping ground, and consisted of a hearth of stone, surrounded on the front and two sides by a stone wall. The wall was 7 it. high in front. The top and rear end were left open and in front an arch or opening was made, forming the eye of the furnace. In front of this a pit was dug in the ground, to receive the molten metal. Large logs were rolled in at the back and made to rest upon ledges formed inside, to raise them from the hearth and to give a draft. These logs filled the entire width of the furnace. Small split logs were then set up around the two sides and the front, and the ore was piled on until the furnace was full. Finally, the mass was covered with logs and fuel until the ore was completely surrounded. A gentle heat was started, which was raised very gradually. After 12 hr. the heat was increased and continued for 12 hr. more, 24 hr. being required for each smelting. The furnace treated about 5,000 lb. per 24 hr. and the ore yielded about 50 per cent. of its metallic lead. A considerable quantity of the ore was not desulphurized, and fell between

Jan 1, 1918

By C. S. Matthews, H. C. Lefkovits

The performance of depletion-type reservoirs at the stage in which the gas is at such low pressure that gravity is essentially the sole driving force has been investigated both theoretically and by use of scaled models. A simple theory is developed which completely explains the scaled model experiments. It also agrees with some field data. When the range of production rates to be considered is less than 25, the theory predicts that the production rate decline curve for homogeneous reservoirs in which there is a free surface will be of the hyperbolic type with n = 2: The theory gives a physical significance to the parameter y. INTRODUCTION This investigation was undertaken to determine a method for prediction of performance of reservoirs where gravity is the sole driving agent. Depletion-type reservoirs fall into this category after the pressure has fallen to some low value. Some examples of this type are found at Healdton ('Oklahoma), Oklahoma City (Oklahoma), Midway-Sunset (California), and East Coalinga (California). Generally the production rate per unit thickness is quite low in such reservoirs, with the conse- quence that this stage is sometimes called the stripper stage. However, per well production rates may be of the order of 50 B/D because of the considerable sand thickness open in some of the reservoirs. In the past, predictions of behavior of such reservoirs have been based on empirical extrapolation of the rate of production to the economic limit. Difficulties arise when new wells are drilled in the field or when production is artificially curtailed, since in such cases the decline rate of individual wells or leases changes and no clear trend can be detected. It was hoped that the present study would lead to improved methods for evaluation of such reservoirs. The study was initiated by building a scaled model for a particular field and by running a number of experiments on this model. Later a simple theory was developed which explained the laboratory results completely. The theory led, as shown below, to a hyperbolic-type decline equation which had been used previously' in a completely empirical manner. THEORY The General Case The problem to be treated here is the following: We are given a homogeneous cylindrical porous reservoir with exterior radius r, wellbore radius r., and height h,, containing, from the bottom up to a height hit oil, some gas, and interstitial water (see Fig. 1 A). The portion of the reservoir between K, and h, is filled with gas at low pressure, with residual oil, and with interstitial water. If at a time t = 0, the level of the oil in the wellbore is lowered to a height h,, what is the production rate from the reservoir at a time to The configuration within the reservoir at some instant

Jan 1, 1957

By John N. Hobstetter

IT is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spontaneous diffusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow,' Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Becker1 in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r. beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration, The increase in free energy per mole accompanying the formation of a nucleus which is just stable, ?fe, is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. THE NATURE OF THE NUCLEUS It is necessary to have rather detailed knowledge of the nature of a nucleus if ?Fe is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown3

Jan 1, 1948

By B. N. Bose, M. F. Hawk

SINCE Davenport and Bain' introduced the isothermal transformation technique for the study of austenite decomposition in steels, a new field of investigation has opened up. Extensive research has been carried out on many different steels, but relatively little work has been done on eutectoid transformations in analogous alloy systems. The researches of Smith and Lindlief,² Mack,³ and Klier and Grymko²0 on the beta-phase transformation in copper-aluminum alloys, of Hibbard, Eichelrnan, and Saunders4 and Smith5 on the kappa-phase transformation in copper-silicon alloys, of Chaudron and Forester6 on the decomposition of "FeO," and of Wasserman7 on similarities between the iron-carbon, copper-aluminum, copper-tin, and copper-beryllium systems essentially comprise the field. The iron-nitrogen system, in view of its remarkable similarity to the iron-carbon system, is particularly attractive for the study of eutectoid decomposition. The present investigation is concerned with the study of isothermal transformation, proceeding by the familiar nucleation and growth processes, and of martensitic transformation characteristics of pure iron-nitrogen alloys. The kinetics of transformation and the morphology of the transformation products have been investigated, for these must be the factors determining the properties and behavior of the final product. The Iron-Nitrogen System he binary iron-nitrogen phase diagram has been a matter of considerable disagreement among vari01.1s investigators. However, the phase diagram according to Eisenhut and Kaupp8 and Lehrer10 is now considered essentially correct as reproduced in fig. 1. The important values, 2.35 pct nitrogen and 591°C, for the co-ordinates of the eutectoid point (obtained from this diagram and used in the re- search to be described) were confirmed in a concurrent study of Paranjpe, Cohen, Bever and Floe." The eutectoid decomposition involves the transformation of the ? face-centered cubic interstitial solid solution of nitrogen in iron to the a body-centered cubic interstitial solid solution of nitrogen in iron and the ?' nitride of iron. This nitride is essentially the compound Fe,N; it also possesses a face-centered cubic lattice but a considerably larger one than the ?; the nitrogen atoms in ?' are arranged in an ordered way in the centers of the unit cubes.8,10,11 A martensitic structure has also been reported8,12 in iron-nitrogen alloys and was studied in the research to be described here. Materials and Methods The specimens used in this investigation were prepared by nitriding "pure" iron. This iron was supplied by the Westinghouse Research Laboratories and is the product bearing their trade name "Puron"; it contains about 0.04 wt pct total impurities, the major portion of which is oxygen. Specimens were ribbons several inches long, a tenth of an inch wide, and 0.125 mm thick; this was the

Jan 1, 1951

By Frank Foote, E. R. Jette

In recent years the constitution of the high-silver aluminum-silver alloys has been extensively investigated. Hansenl has reviewed the literature to 1935. More recently, Obinata and Hagiya,2 Hofmann and Volk,3 Taziri4 and Tishchenko5 have confirmed the general features of the phase diagram in the region around 25 atomic per cent aluminum. In this paper we present the results of high-precision measurements of lattice constants of the silver-rich alpha solid solution in the homogeneous range and the neighboring two-phase regions. These results are used to establish the nature of the solid solution, the identity of directly measured densities with those calculated from lattice constants and the homogeneity limits of the alpha solid solution with respect to three different neighboring phases. A study of the earlier investigations indicated that the last two subjects in particular required new and accurate data. Experimental Procedure Preparation of the Alloys.—The alloys were made from high-purity silver and aluminum. The silver was "Proof Silver," 99.999 per cent pure, supplied by the U. S. Metals Refining Co. The aluminum was 99.97 per cent pure (contained Si, 0.009 per cent; Fe, 0.0016 per cent; Cu, 0.004 per cent) and was supplied by the Aluminum Company of America. The lattice constants of these two materials have been reported by Jette and Foote.6 Weighed amounts of the two metals were placed in alundum crucibles and melted in vacuo in a high-frequency induction furnace. The melts were allowed to cool in the crucible, the ingots thus obtained weighed about 10 grams. These ingots were then filed clean, hamered, again cleaned and given a homogenizing anneal in vacuo of from 6 to 15 days at temperatures ranging from 500" to 695°C. The ingots were air-cooled from the annealing temperature. Lattice-constant Measurements.—Carefully prepared filings for X-ray analysis were sealed into evacuated quartz or Pyrex tubes and annealed for various periods of time at suitable temperatures. The furnaces used were vertical, rapid-quenching furnaces, the samples being quenched by crushing the sample tube under water by means of a heavy plunger. The general X-ray technique has been previously described6 The cameras were of the symmetrical, back-reflection, focussing type. Ka, radiation from a cobait-nickel alloy target was used. The wave-length values were taken from the second edition of Siegbaum's book.7 A correction for the index of refraction was applied and the lattice constants were calculated by the method of Cohen.8, 6 The lattice constants were calculated to a common temperature of 25°C., using the value of the linear expansion coefficient of pure silver as 18.9 X 10-6. Presumably the expansion coefficient for

Jan 1, 1941

By Frank Foote, E. R. Jette

In recent years the constitution of the high-silver aluminum-silver alloys has been extensively investigated. Hansenl has reviewed the literature to 1935. More recently, Obinata and Hagiya,2 Hofmann and Volk,3 Taziri4 and Tishchenko5 have confirmed the general features of the phase diagram in the region around 25 atomic per cent aluminum. In this paper we present the results of high-precision measurements of lattice constants of the silver-rich alpha solid solution in the homogeneous range and the neighboring two-phase regions. These results are used to establish the nature of the solid solution, the identity of directly measured densities with those calculated from lattice constants and the homogeneity limits of the alpha solid solution with respect to three different neighboring phases. A study of the earlier investigations indicated that the last two subjects in particular required new and accurate data. Experimental Procedure Preparation of the Alloys.—The alloys were made from high-purity silver and aluminum. The silver was "Proof Silver," 99.999 per cent pure, supplied by the U. S. Metals Refining Co. The aluminum was 99.97 per cent pure (contained Si, 0.009 per cent; Fe, 0.0016 per cent; Cu, 0.004 per cent) and was supplied by the Aluminum Company of America. The lattice constants of these two materials have been reported by Jette and Foote.6 Weighed amounts of the two metals were placed in alundum crucibles and melted in vacuo in a high-frequency induction furnace. The melts were allowed to cool in the crucible, the ingots thus obtained weighed about 10 grams. These ingots were then filed clean, hamered, again cleaned and given a homogenizing anneal in vacuo of from 6 to 15 days at temperatures ranging from 500" to 695°C. The ingots were air-cooled from the annealing temperature. Lattice-constant Measurements.—Carefully prepared filings for X-ray analysis were sealed into evacuated quartz or Pyrex tubes and annealed for various periods of time at suitable temperatures. The furnaces used were vertical, rapid-quenching furnaces, the samples being quenched by crushing the sample tube under water by means of a heavy plunger. The general X-ray technique has been previously described6 The cameras were of the symmetrical, back-reflection, focussing type. Ka, radiation from a cobait-nickel alloy target was used. The wave-length values were taken from the second edition of Siegbaum's book.7 A correction for the index of refraction was applied and the lattice constants were calculated by the method of Cohen.8, 6 The lattice constants were calculated to a common temperature of 25°C., using the value of the linear expansion coefficient of pure silver as 18.9 X 10-6. Presumably the expansion coefficient for

Jan 1, 1941

By J. C. Landenberger

Freezeproofing waste dump cars during winter months has long been of concern at Kennecott's Utah Copper Div. open pit property. Waste mining operations at Bingham Canyon use trains of seven 40-cu yd side-dump railroad cars with electric locomotives to service stripping shovels. Waste is transported an average of nearly 3 miles from the mine benches to dumping areas. During winter months, usually beginning in late October or early November, intermittent and continued periods of freezing together with varying amounts of snow cause waste material to freeze or stick to the sides and bottoms of the cars. Because of the physical layout of the pit, it is not feasible to freezeproof all waste trains at one or even a limited number of locations. A waste haulage line usually serves one or two mine benches, so that freezeproofing facilities must be maintained at many locations. For example, at the time of writing 27 salting stations were in use.

Nov 1, 1955

By J. N. Hobstetter

It is widely believed that the nucleation of phase transformations in solid metals is accomplished by some type of local atomic fluctuations in the parent phase which arise from spoutaneous difiusion in the metal or alloy system. Under appropriate conditions, these fluctuations are believed to be stable in the sense that the free energy of the entire system is lowered if the fluctuations, or nuclei, grow. Under other conditions they are thought to be unstable in the sense that the free energy is lowered if they redissolve. The criterion for stability is usually taken as the size of the fluctuation. This view has been rationalized by Beckerl in terms of the free energy released by the volume of the nucleus and the free energy associated with the formation of a new surface surrounding the nucleus. The qualitative result of this reasoning is shown in Fig I where the changes in free energy for the surface and volume effects are plotted together with their sum against the radius of the nucleus. There is evidently always a critical size r, beyond which the release of free energy which is proportional to the volume always dominates the increase of free energy which is proportional to the surface area. Borelius2 has also attempted to rationalize the stability criterion for binary alloys, but in terms of the internal concentration of the fluctuations. He has found that, if surface energies are entirely ignored, the fluctuation must still reach a critical concentration if it is to become stable and avoid subsequent dilution. Although the Borelius theory fails to predict many observed nucleation phenomena such as the vanishing of the nucleation rate at the critical temperature, the major premise must certainly be valid. In this paper a reconciliation of the Becker and Borelius views is made by means of a search for nuclei which are at once stable with respect to both size and internal concentration. The increase in free energy per mole accompanying the formation of a nucleus which is just stable, AF., is independent of the path whereby the nucleus is brought into being. It is thus appropriate to seek critical nuclear attributes without reference to the fluctuation mechanism. The rate of nucleation, however, cannot be treated without a detailed understanding of the exact fluctuation process which produces stable nuclei. In this and succeeding papers the purpose will be to find the size, shape and internal concentration of the stable nucleus which is formed with a minimum increase in free energy in a wide variety of systems. The Nature of the Nucleus It is necessary ti have rather detailed knowledge of the nature of a nucleus if AF, is to be computed. Fortunately, enough facts are known or suspected about the nucleus to make possible a detailed analysis. X ray diffraction studies have shown

Jan 1, 1949

By Herman Garlichs

THE development of the extensive Southeast Missouri deposits greatly preceded that of the Iowa and Wisconsin deposits. It began about 1720 at Mine La Motte and other localities, and has continued uninterruptedly to the present time. It is estimated that this district produced about 184,000 tons of lead in the year 1916, having a value of approximately, $25,000,000. This is a new high record. The Southwest Missouri orebodies were hardly known before 1845 and were not extensively developed until 1870: Lead production in South-west Missouri for 1916 was 38,788 tons. Oklahoma produced 14,399 ,tons and Kansas 2,345 tons, making a total for Southwest Missouri, and the adjoining districts in Oklahoma and Kansas, of 55,532 tons of lead. The first metallurgists in Missouri were the Indian and the hunter. The early settler learned to procure his bullets either by melting ore in his camp fire or by throwing pieces of galena on an old stump and depending on the usual roasting and reaction method to obtain the metal. A little more refined method was to arrange two flat stones in the form of a V. Wood and galena were placed in the furnace and ignited. As heat developed, some of the metal was extracted and molded into bullets. The next step in utilizing the lead ores was the log hearth. All lead in Missouri was smelted in this crude affair before 1820. It was built on sloping ground, and consisted of a hearth of stone, surrounded on the front and two sides by a stone wall. The wall was 7 ft. high in front. The top and rear end were left open and in front an arch or opening was made, forming the eye of the furnace. In front of this a pit was dug in the ground, to receive the molten metal. Large logs were rolled in at the back and made to rest upon ledges formed inside, to raise them from the hearth and to give a draft. These logs filled the entire width of the furnace. Small split logs were then set up around the two sides and the front, and the ore was piled on until the furnace was full. Finally, the mass was covered with logs and fuel until the ore was completely surrounded. A gentle heat was started, which was raised very gradually. After 12 hr. the heat was increased and continued for 12 hr. more, 24 hr. being required, for each smelting. The furnace treated about 5,000 lb. per 24 hr. and the ore yielded about 50 per cent. of its metallic lead. A considerable quantity of the ore was not desulphurized, and fell between

Jan 7, 1917

SEVERAL distinctions can rightfully be accorded the Bagdad enterprise. For one thing, it has the most romantic name among the Porphyry Coppers and this is said with all due deference to Copper Queen and Inspiration! Bagdad was one of the richest and most magnificent cities of the glamorous world of the Arabian Nights. The record does not say who was responsible for applying the name Bagdad to the company that in 191 1 took over the property of the Arizona-Nevada Copper Company; but whoever it was must have had visions (or at least hopes) of a fabulously profitable mine. So far as I know, Bagdad is the only Porphyry whose owners, or officials, ran afoul of the law because of alleged sins of omission or commission in vending shares of the company's stock. E. B. Bronson, of New York, had been interested in Bagdad since 1909; and, during the lean period of the 1930's he had, as president of the corporation, endeavored to raise needed funds by the sale of 140,000 shares of treasury stock. Some legal questions arose as to the need for registration under the Securities and Exchange Act; but, when Mr. Bronson finally filed a registration statement, the New York office of the Securities and Exchange Commission found 155 "deficiencies" in the document. According to the judge who later heard the criminal case against Bronson, no evidence was introduced to show that he had personally benefited "to the extent of one dollar." However, it was charged that the setup was such that he was in position to profit if he had wanted to! A somewhat quixotic position, it would seem. In any event, he was convicted, on highly technical

Jan 1, 1957

By L. Guttman

LESTER GUTTMAN* The question of whether classical thermodynamics alone imposes any lower limit to solid solubilities was raised during a discussion among various members of the Institute for the Study of Metals. Although our conclusions are not new,1 they may be worth reiterating, since confusion on this subject seems to persist. In a binary system (A,B), the conditions for equilibrium, at constant pressure and temperature, between a solid solution and a liquid solution are µAs = µAl [la] µBs = µbl [lb] Here µ denotes the chemical potential either of component A or B, as shown by the subscripts, and the superscripts s and l refer to the solid and liquid solutions, respectively. These two conditions are just sufficient to determine the compositions of both phases. Suppose, however, that the solid phase is found experimentally not to contain any of component B; then we cannot evaluate µbs, which is defined by Here nAs and nBs are the number of mols of A and B, respectively, in the solid, whose free energy is Fs. Eq lb cannot be used, but it is no longer needed: we stated at the outset that the solid has the composition "pure A," and only the liquid composition need now be determined, from Eq la. All the equilibrium properties of the system can be derived from Eq la rigorously and simply. Hence there is no purely thermodynamic reason to exclude phase diagrams which show precisely zero solid solubility. Marsh2 has objected to such diagrams as implying that even the transformation of pure A begins at the eutectic temperature. In any case, the user of the diagram must have a certain minimum knowledge of how to interpret it, and it would seem simpler to remember the general rule that eutectic temperatures have no significance for pure components, rather than to show, say, by broken lines, on a scale which will often be exaggerated, a hypothetical solid-solubility about which we know only that it is less than a certain amount. The case of an intermetallic compound in equilibrium with a binary liquid solution does not require a separate treatment since nothing in the foregoing was dependent on the nature of the components. Therefore, thermodynamics alone does not exclude the possibility that (intermetallic) compounds may exist with compositions always precisely those given by their chemical formulas. With the aid of extra-thermodynamic methods, one may conclude that the solubility of one solid in another is never exactly zero. On the other hand, one would generally expect that the solubility will be small unless the components resemble one another (as do the metals), or form weakly-bound crystals. Therefore, it is useful to know that when there is no direct evidence for solid-solubility, one may neglect it without violating thermodynamic principles.

Jan 1, 1950

By J. Chipman, N. J. Grant, R. Rocca

D. E. Babcock (Republic Steel Corp., Youngstown, Ohio)—With reference to eqs 7 and 8, at what temperature do they apply John Chipman (authors' reply)—That was 1600°C. Dr. Babcock—You have l x 10-4 as the component for the lime and 1 or 4x10-. Now, is it by dividing one into the other you get the 400? That is assuming equivalent activity on the part of oxygen, sulphur, and magnesia. Dr. Chipman—Yes, they are calculated for 1600. Now, the first one for CaO was calculated before we had a glimpse of Dr. Rosenqvist's paper." If you take his calculation you get 14,000 cal which is very good agreement, but our calculation would be superseded by Dr. Rosenqvist's new data. Dr. Babcock—The state you assume those to be in is the liquid state, as near as you can measure? Dr. Chipman—Naturally it is based on the solid CaS, but if you add the effect of fusion on both sides it just about balances out, so the ratio would be about the same. B. M. Larsen (U. S. Steel Co., Kearny, N. J.)—If we knew the activity of sulphur in the slag instead of merely the percentage, we might be able to find some conflicting factors that balance one another out, and find that the FeO or oxygen pressure effect is really present over the whole range. Dr. Chipman—I am fairly sure we would. The activity of sulphur in the slag and the activity of CaO in the slag, if we just knew those quantities, would enable us to save a lot of this computation and assumption and all the approximations we are doing now. Mr. Larsen—Two other points perhaps should be included: 1—an independent effect of manganese in helping the desulphurization; and 2—the number of mols of constituents or number of mols of ions or whatever there is in the slag could vary with these compositions in such a way that you get dilution effects. Dr. Chipman—You can figure all that in if you want to and it might improve the degree of approximation a little bit. Maybe enough to justify the labor of calculation, inaybe not, but we did not do it. L. S. Darken (U. S. Steel Co., Kearny, N. J.)—The authors have tackled a very complicated problem in trying to tie together in one picture the desulphurizing problem over the wide range of basicity and oxidation level from that of the open hearth to that of the blast furnace. At the present state of our knowledge of slags such an ambitious undertaking necessarily involves the adoption of numerous hypotheses. Their formulation (eq 11) for the higher FeO range

Jan 1, 1952

By Alan Stanley

THE Maclntyre Development of National Lead Co. is located at Tahawus, N. Y., in the heart of the Adirondack Mountains. Operations involve the mining and concentrating of a titaniferous iron ore to produce ilmenite and magnetite concentrates. A general description of the operation and metallurgy has been given by Frank R. Milliken.1 Pigment plant production demands that the MacIntyre mill produce a 44.7 pct. TiO2 ilmenite concentrate. To achieve the required ilmenite grade and tonnage it is important that the table concentrate grade be closely controlled. Unfortunately, however, the titaniferous orebody which feeds the Maclntyre mill is not uniform. Ore dressing characteristics vary from one end of the orebody to the other, and from one level to the next.. The changeable nature of the mill feed precludes a single adjustment of the equipment for long periods of time. Thus the operators must constantly watch the equipment to insure a uniform concentrate from the fine and coarse tables and Wetherills, or dry magnetic separators. Chemical assaying of mill products requires about 4 hr from the time the sample is taken until assay results are obtained, and this is available only on a two-shift basis. The ore may change rapidly, even several times during a shift, so that assay results lose most of their control value by the time they are reported to the mill operating crew. Members of the crew have therefore tried to evaluate the table and Wetherill concentrate by visual inspection, since through long experience the shift operators, under most circumstances, can gage closely the grade of the mill products. However, there are times when the, physical nature of the ore is radically different from normal. Under these conditions visual inspection is of no value, and at such times final ilmenite as low as 43 pct TiO2 has been produced and shipped before the assay results have been received. The specific gravity method of assaying for TiO2 has been attempted to eliminate the shipping of ilmenite below normal grade as well as to help control day to day and hour to hour mill production. Table I shows the minerals found in the Maclntyre ore along with their average weight proportions and specific gravities. The first two products considered for the specific gravity method were fine and coarse table concentrates. It was reasoned that these products were essentially ilmenite with the higher specific gravity gangue minerals. Since they were always produced the same way, and the desired grade of TiO2 was always constant, the specific gravity of these materials would increase or decrease as the amount of ilmenite increased or decreased. Thus for table concentrates which assayed 40 pct TiO2 a constant gravity would invariably be obtained, and as the TiO2 value changed the specific gravity would change in direct proportion. The third product considered was Wetherill ilmenite. It was assumed that a desired grade of 44.7 pct TiO2 would also always contain the same amount and type of gangue minerals along with the ilmenite, and thus would always have the same specific gravity. As the TiO2 value of the ilmenite concentrate changed so would its specific gravity. Dr. Kenneth Vincent, chief metallurgist of the Baroid Division of National Lead Co. at Magnet Grove, Ark., ran specific gravity tests on 17 samples of the desired products. The lowest specific gravity reading assayed the lowest in TiO2 and as the specific gravity increased the trend was for the TiO2 assay to increase, see Fig. 1. Since these results warranted further investigation, a 500-g capacity Torsion balance and 250 ml Le Chatelier specific gravity bottles were obtained. [ ] Shift samples of fine table concentrate, coarse table concentrate, and final ilmenite were tested. Each sample was split and 85 g weighed on the Torsion balance. The Le Chatelier bottle was filled with water to a zero mark. To avoid wetting the neck of the bottle it was found necessary to do this

Jan 1, 1952