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By James P. Kimball

AMONG the curious results of the recent advance of prices in the iron trade of the United States, one of them at least is to be regarded as of great importance. I allude to the utilization of mill cinder as a cheap and almost costless substitute for high-priced iron ores in many blast furnaces, situated within easy reach of such raw material. It has been, with but few exceptions, the practice in this country, based upon tradition rather than upon authority or European precedents, to waste this material on 'account of its high proportion of silicic and phosphoric acids, although known to contain more iron than most ores, and although also known to be sometimes applied to the blast furnace in greater or less quantities without serious detriment to the iron for specific purposes. While in use to a limited extent in the Hocking Valley and Hanging Rock iron regions of Ohio for several years, its use in Western Pennsylvania has only become general of late, under the exigencies of high prices and a short supply of ore. Especially has mill cinder largely entered into the stock of furnaces attached to rolling mills in and about Pittsburgh. Under such circumstances the cinder pig has been paddled on the premises, and the malleable iron produced has been unexpectedly good. Cautiously as at first mill cinder has been applied, it is evident that the temptation to use it freely is a strong one whenever the commercial rates for high-class ores are out of proportion to the general conditions of the iron trade, as sometimes happens in this country, especially as the free use of it is apparently justified by the quality of the iron produced from this cheap and abundant material. Indeed the consumption of cinder pig has., not been wholly confined to mills using up the production of furnaces belonging to the same plant. One furnace at least on the Ohio, at Covington, for several' months has been making foundry pig from "all cinder." The iron has gone into the general trade. It is probable that malleable iron of good quality can he made from the poorest cinder pig, but with what degree of economy will

Jan 1, 1881

By J. R. Stone, J. T. Roy

ASARC09s continuous tapper for lead blast furnace is described. Its use throughout the company's plants has resulted in higher production rates, lower labor costs, and better working conditions. It has also permitted wide latitude in blast pressures, as well as in charge and slag compositions. The practice of tapping a lead blast furnace has remained essentially unchanged for many years. In principle, it is a batch operation discharging the products from the continuous smelting of lead-bearing materials. As such, it imposes certain restrictions on the proper functioning of the smelting operation. First, it calls for a highly developed sense of timing, and a considerable amount of physical effort on the part of the operator. Dirty and hot working conditions, as well as the hazards of flying metal and slag, usually prevail. These conditions have resulted in higher labor costs, both in rate and in amount. Labor turnover has also been high. Secondly, rigid control of mechanical and metallurgical factors must be maintained. Frequent oxygen lancing of the tap hole is needed to permit tapping, thereby increasing operating costs. Rapid increases in smelting rate, plugged tap holes, or forgetfulness on the part of the operator may permit the molten material to rise above the tuyeies and freeze the furnace. Also, the operator will often blow out the tap hole after draining, filling the area with fume. Composition of charge also vitally affects the tapping. The type of lead-bearing material being smelted will naturally affect the smelting rate, and thus the frequency of tapping. The amounts and types of fluxing materials, which determine the ultimate fluidity of the slag, must be regidly controlled. Finally, the batch tapping of a continuous smelting operation of this type appears to be wrong in principle. The molten material drains into the crucible at the bottom of the furnace where it starts cooling immediately and continues to cool until tapped out. While keeping the lead molten is no particular problem, maintaining a fluid slag at all times is often difficult, and sometimes impossible. These factors all point to the desirability of a method for the continuous tapping of a lead blast furnace. The expected advantages would be more desirable working conditions, lower labor costs, increased production, and a much wider latitude in both blast pressure and charge composition. CONTINUOUS TAPPING Historical. A number of devices, e.g., mechanical tappers, siphons, and lead wells, have been tried in the past in attempting to effect continuous tapping. None proved to be entirely satisfactory for tapping lead and slag simultaneously. It was not until 1955, however, that ASARCO designed and put into operation a successful tapping unit at its East Helena, Mont. lead smelter. This unit is described in detail in U.S. Patent NO. 2,890,951. Continuous Tapping Unit—See Figs. 1 and 2. Fig. 1 is a schematic drawing of the unit in place, showing front and side views. The component parts are identified in the caption. Fig. 2 is an actual photograph, front view, of the tapping unit attached to the base of the blast furnace. Operation. The operation of the tapping unit is quite simple. Essentially it consists of a narrow tapping bay surrounding the furnace tap hole, with a deep notch in the front wall. When the blast furnace is started this notch is open down to the level of the tap hole. Starting the furnace may be accomplished in several ways but the most satisfactory method is to plug the tap hole with clay, permitting metal and slag to build up inside the furnace. Before the liquid reaches the tuyeres, the plug is removed and the furnace is drained to the settler. The blast is then stopped momentarily while the notch in the front wall of the tapping bay is dammed with chrome brick and plastic chrome ore. The blast is again started, and the height of the dam is adjusted so that the liquid in the bay will counterbalance the internal pressure of the furnace. When the desired level is reached the slag and metal will overflow to the settler. It should be noted that the molten material ,is not siphoned from the furnace and that the metal 'acts as a liquid valve controlling the flow of slag through the tap hole. During normal operations the tapping bay is filled primarily with lead, covered with a thin layer of slag. Thus, the heavier lead plays the major role in compensating for variations in furnace pressures. Due to the high specific gravity of lead, changes in the liquid level in the tapping bay will never exceed a few inches. For this reason it is seldom necessary to change the height of the dam due to minor variations in operating conditions. Some turbulence of the liquid in the bay is essential at all times. This indicates that the level of the

Jan 1, 1963

By H. S. Price, J. C. Cavendish, R. S. Varga

A numerical formulation of bigh-order accuracy, based on variational methods, is proposed for the solution of multidimensional diffusion-convection-type equations. Accurate solutions are obtained without the difficulties that standard finite difference approximations present. In addition, tests show that accurate solutions of a one-dimensional problem can be obtained in the neighborhood of a sharp front without the need for a large number of calculations for the entire region of interest. Results using these variational methods are compared with several standard finite difference approximations and with a technique based on the method of characteristics. The variational methods are shown to yield higher accuracies in less computer time. Finally, it is indicated how one can use these attractive features of the variational methods for solving miscible displacement problems in two dimensions. INTRODUCTION The problem of finding suitable numerical approximations for equations describing the transport of heat or mass by diffusion and convection simultaneously has been of interest for some time. Equations of this type, which will be called diffusionconvection equations, arise in describing many diverse physical processes. Of particular interest here is the equation describing the process by which one miscible liquid displaces another liquid in a one-dimensional porous medium. The behavior of such a system is described by the following parabolic partial differential equation:

Jan 1, 1969

By K. H. Coats, M. H. Terhune

Analysis and example applications have been performed to compare the accuracy and computing speed of alternating-direction explicit and implicit procedures (ADEP and ADIP) in numerical solution of reservoir fluid flow problems. ADIP yields significantly greater accuracy and requires about 60 per cent more computing time than ADEP, not 300 or 500 per cent more as reported elsewhere. l,2 INTRODUCTION Several recent papers 1-3 discuss an alternating-direction explicit difference approximation (ADEP) to the diffusion equation. Example applications of ADEP and ADIP4 were reported to support conclusions that ADEP is comparable in accuracy to ADIP and requires one-fifth to one-third the computing time of ADIP. Applications of ADEP in calculation of two-phase flow in reservoirs was also proposed. 3 This study was performed to compare further the relative merits of ADEP and ADIP in simulation of two-dimensional flow of one and two fluid phases in reservoirs. Since two-phase flow equations are often essentially elliptic rather than parabolic, the efficiency of ADEP in solving the elliptic equation was also examined.

Jan 1, 1967

By J. F. Myers, F. M. Lewis

The paper reports the development of a large, slow speed ball mill closed circuited with a hydroscillator. This increased grinding efficiency 28 pct over conventional units.

Jan 1, 1950

By H. W. Gillett

Unlike most previous Howe lecturers, I had not the good fortune to be associated with Henry Marion Howe, nor to be directly one of his students. Yet, through his writings, he has been my teacher, as he has of all American metallurgists. Instructive as his writings are—I use the present tense because Howe thought so keenly and reasoned so surely, seeing clearly, as if by intuition, what was hazy to lesser minds, that his writings are still vital—it is not those books and papers, nor even the minds he trained in his classes, that were his most outstanding service. It was the spirit of Howe in his approach to the problems of metallurgy, his broad-mindedness and fairness, his recognition of the need for theories and hypotheses to explain metallurgical phenomena, his willingness to use them as servants, as well as his questioning attitude—his refusal to accept them as masters—that comprise his greatest service. This most thoroughly warrants the honor the Institute pays each year to his memory. These traits I so respect and honor in any man that I glory in this opportunity to do reverence to him in whom they were so notably united. Howe's Discussion of a Creep Problem I have often wished that Howe were still with us to turn his keen insight upon the problems of the use of metals at high temperatures, a field much studied but still very hazy. Indeed, 53 years ago, in a paper1 before this Institute, Howe stated a problem closely allied to some that still perplex metallurgists and engineers dealing with the high-temperature field. Howe was intrigued by a report2 from another old master, Robert Henry Thurston, on the behavior of annealed vs. cold-drawn iron wire, and in order to broaden the foundation for metallurgical generalization, Howe made experiments of his own on copper and silver. In these tests by Thurston and by Howe, the wires were rapidly loaded to determine the

Jan 1, 1939

By R. L. Manegold

IN RECENT years there has been a decided trend toward bringing ores and coal out of open-pit and underground mines by long, sloping single-stage belt conveyors. Because the high investment cost of haulage conveyors dictates maximum speed and full loading for economy, conveyor belts are running faster than ever before, with a greater burden on the belts. In addition, larger blocks of ore are being mined and conveyed. Rougher use of large mining equipment generates more tramp iron; mechanical loading rejects nothing. Therefore the extraction of tramp iron and other deleterious materials for the protection of haulage conveyors at transfer points, chutes, and idlers is becoming an increasingly difficult job. In our experience, the best method of protecting long haulage conveyor belts is to extract the tramp iron, at least the large tramp iron, ahead of the main haulage conveyor or series of conveyors. It is most practical to collect the tramp iron at the earliest source -possible, usually directly after the primary car unloading dump or after the primary crushers, which are ordinarily not affected by tramp iron, see Fig. 1. The coal or ore from its primary source is fed by chutes or feeders onto a buffer or shock belt conveyor, a short, ruggedly built conveyor system that can be considered somewhat expendable. Its primary function is to bring the ore up to speed for transmission to the haulage conveyor. There is no assured method of protecting this conveyor from tramp iron damage at its feed end. Likewise, there is a possibility, although remote if the magnet applied to this belt is installed correctly, that the tramp iron extraction process will damage the shock belt, which is, however, short and comparatively inexpensive. Magnetic head pulleys with their maximum effective range of about 8 or 10. in. cannot be considered for large installations, even though they are desirable because of the continuous and, automatic tramp, iron removal feature. Further, the most dangerous form of tramp iron with respect to potential damage to a haulage conveyor is the long rod, roof bolt, or rail segment, which is not extracted satisfactorily because of the limited tangential contact of such an iron shape with the magnet. Magnetic head pulleys are also undesirable because the dribble or fines from the head pulley discharge at the same point as the tramp iron. Screens must be used to separate the fines from the magnetics, resulting in additional expense and loss of head room. Magnetic detectors have been used with success, but they only indicate the, presence of iron, and the conveyor belt must be stopped for its manual removal. The, stoppage of any conveyor means that all preceding equipment must be stopped or a cascade of material on the idle conveyor will result. Occasionally combinations of detectors and magnetic, head pulleys are used. The detector precedes the magnetic head pulley and detects only large pieces of tramp iron, while the magnetic pulley subsequently takes out the smaller ferrous metals. Suspended magnets overcome the disadvantages of magnetic head pulleys, detectors or a combination of both. There are several magnetic extraction problems involved in applying a suspended magnet at this

Jan 1, 1952

By P. Sanchez-Mejorada

GEOLOGISTS who are acquainted with the mines of northeastern Mexico realize that the most important lead-silver replacement deposits of the province are confined to a single formation. But since the formation is several hundred meters thick, the author has determined the relative position of the lead mantos in the belief that this information will prove useful in the search for new mines. This article describes the stratigraphic location of lead-silver replacement deposits known in several mines situated in a region comprising part of the states of Coahuila and Nuevo Leon. The area studied extends for 200 km* (125 miles) from east to west and 70 km (45 miles) north to south. Metallogenic Province: The most important metallic deposits of the region have the following common characteristics: 1) The orebodies occur as manto replacements of calcareous sediments. 2) The horizons that have contributed large tonnages of ore are in similar positions in the corresponding stratigraphic columns (as it will be shown later on). 3) Lead is the most important metal in the ores. Silver is commonly present in small amounts. Occurrence of zinc is dependent on the degree of oxidation of the primary sulfides. 4) A large proportion of the total production has been in the form of oxidized ores. 5) The deposits are located on anticlines. Rocks of Cretaceous age crop out over large areas of the states of Nuevo Leon and Coahuila. forming part of a belt that extends to the south along the eastern Sierra Madre. The sediments are cut by a small number of intrusive stocks ranging in characteristics from rhyolite to diorite. The most prominent structural feature of the region is a series of folds trending northwest-southeast. Faulting is not conspicuous in the region, although a major fault zone is found farther East.' The physiography closely reflects structural features, with mountains formed by anticlines and valleys conforming with intermediate synclines. Narrow valleys have also been developed along the axes of many anticlines, where solution of limy sedi- ments and erosion have proceeded along axial tension fractures. Stratigraphy: Rocks of the Upper Cretaceous are exposed in only a small percentage of the total area. Generally they have been eroded away from the mountains and are covered by recent talus and alluvium in the valleys. Humphrey' has published an excellent paper describing the Cretaceous formations of the Sierra de los Muertos, a short distance west of Monterrey. A brief summary of these formations is given below to convey an overall picture of the stratigraphic sequence that prevails just south of the area under consideration. Upper Cretaceous Indidura: Essentially thin shaly sediments. Cuesta del Cura: Limestone in thin wavy beds

Jan 1, 1959

By John H. Hollomon

A REVIEW of the steps which have been made to increase knowledge in the field of ferrous physical metallurgy during the closing period of World War II brings both pleasure and disappointment. Contributions of great value have been made, to be sure. However, due partly to the stress of the times, researchers in this field have been in the main directing their attention toward the short-range problems involved in the development and production of materiel for war. Furthermore, publication of the results of a great number of studies has had to be delayed. Much of the German work may, indeed, be lost entirely, owing to the efficiency of our bombers, which managed to account for most of the famous Kaiser Wilhelm Institut of Dusseldorf, not to mention the other large laboratories and manufacturing plants throughout that country. It would seem safe to assume, however, that fundamental research in Germany had been forced to give way to the shallow, but more pressing, engineering problems of a country trying to avoid defeat. In Russia the picture has been clouded by the limitations imposed upon comunication; but this much does seem clear: Russia alone among the great nations of the world has maintained her long-range view and has continued to foster research of the most fundamental type. English workers; on the other hand, appear to have been able only to meet the demands of the pressing problems of war, and their studies have been of the short-range variety. That metallurgical research of any sort should have continued in France during this chaotic period in her history would seem impossible, but, amazingly, a small handful of scientists did manage to carry on their work, and it is to be hoped that more will be heard from them in the future.

Jan 1, 1946

By D. N. Dietz

Jan 1, 1969

By P. D. White, J. T. Moss, J. S. McNiel

Results of experimental work on the in situ combustion process were first published in this country in 1953' when Kuhn and Koch described results of a three-well test in Jefferson County, Okla. Shortly there-after Grant and Szasz2 described field studies in Nowata County, Okla., in which several modifications of the basic combustion process were investigated by injection of various oxidizing gas mixtures other than air. In the past five years speculation concerning this method of oil recovery has continued, with a number of interesting papers on various aspects of in situ combustion appearing in the literature3,4,5,6,7. However, only one of these' provided actual engineering information on pattern-type field experiments. The primary objectives of the Oklahoma three-well test were to check operation of specially designed electrical ignition equipment and evaluate problems associated with initiation of combustion in a natural oil sand reservoir. Immediately following successful completion of this test in the Pontotoc sand, plans were activated for a second field experiment to be conducted in the same sand a short distance away. The objective of this second field test1 as to establish a relationship between field observations and information derived from laboratory experimentation and computations. Secondary objectives of the test were to develop operating tech- niques and define operating problems, and to obtain information that would assist in the economic and engineering appraisals of the process. Careful planning was required since this test was designed with the hope of providing basic information on the characteristics and operation of a combustion drive. It was necessary to include test facilities which would not only permit precise control and measurement of the process variables but would also provide sufficient flexibility of control to insure that variables in the combustion process could be studied during the course of the test under a wide range of conditions. In order to accomplish these objectives elaborate instrumentation and several control wells were included in the design of the test installation. This type installation was felt to be well suited for an experimental study, but was in no respect intended as a counterpart of a commercial-scale operation. PRELIMINARY LABORATORY WORK An important objective of the field experiment, as stated previously, has been to obtain reliable data on operating variables which might be compared with similar data obtained in laboratory combustion tests. The value of successful correlations between quantities that can be measured in the laboratory and those obtained in a full-scale commercial venture has been well established for other industrial processes. The difficulty of following a process underground should make such correlations even more essential here. Also. approaching the field test phase of development of in situ combustion, it was considered desirable to precede design of test equipment with laboratory combustion studies under a variety of conditions to establish likely ranges of variables. These included temperature, air injection rate, frontal advance rate and produced gas composition.

By Emil-Paul Lorenz

Considered as a whole, the mineral resources of the Turkish Republic (Anatolia) are in their untapped virgin state, and the little development shown is not the result of modern systematic geologic exploration but the continuation of the ancient open-pit mining methods of the Orient. When I came to Turkey in 1924, I found myself confronted by a formidable task because of the lack of preliminary geologic mapping. Today this condition has not essentially changed; less than one per cent of the country is covered by topographic mapping adequate for modern requirements. However, I was able to bring a semblance of order in a presentation of the mineral deposits of this country, by tracing the story of the mineral deposits that showed surface evidence of their existence. At present only the easily discovered mineral deposits of coal, copper, and lead-silver ores are being exploited. In the case of coal, of 3,000,000,000 metric tons available, only 100,000,000 have been mined. The same is also true for copper, lead-silver, and other ores, as shown in Table 1.

Jan 1, 1948

By Richard Miller

RECENT studies of creep have made it apparent that plastic deforma-tion may occur in metals under stresses less than the elastic limit as deter-mined from short-time tests. In summarizing conclusions drawn from creep tests by various investigators, Tapsell1 said: "It is evident that if a material has a true elastic range, the elastic limit must represent the maximum stress for no creep." The presence of a. definite elastic limit, represented in single crystals by a critical or threshold shearing stress, is claimed by Schmid2, Elam3 and others who have investigated the plastic deformation of single crystals. However, this "law of critical shearing stress" was deter-mined2 from short-time tests, and the measurement of the deformation was made with apparatus primarily designed to observe large amounts of plastic deformation, not to detect elastic changes. Experimental data recently obtained with highly sensitive instru-ments by A. W. Hanson4 on zinc and by Podaschowsky5 on rock salt indicate that the elastic range in single crystals is considerably narrower than formerly was supposed. Moreover, a theoretical possibility of permanent deformation, under the influence of even the smallest shear stress in single crystals above a certain temperature (Td), has been developed by G. I. Taylor6. This evidence seemed to warrant an examination of the elastic limit in large single crystals by means of creep tests. The first metal chosen for examination was zinc.

Jan 1, 1936

By Persifor Frazer

INTRODUCTION For various reasons I have not specified the locality where the research indicated in the following pages was undertaken. It will suffice to say that it was on the grounds of a villa once remote from, but now completely surrounded by, its neighboring city, and in close proximity to an industrial establishment of great extent and importance manufacturing many kinds of steel articles and employing upwards of thirty chimney-stacks for power and process work. The problem was to discover the cause or causes of the mortality to trees and plants on the place, and to trace these causes to their origin. Before undertaking this experimental work, the bibliography accompanying this paper was compiled and studied. It appears from an examination of the careful scientific work performed by the ablest French, German, and English chemists during the last 25 years that they are unanimous in assigning the principal-in fact, the overwhelmingly predominant-cause of the destruction of vegetation to sulphur oxides, resulting either from direct- oxidation of sulphur in oil of vitriol works, etc., or from the oxidation of the sulphur from the minerals associated with commercial coal. Schröder and Schertel showed in 1884 that the sulphates deposited upon the leaves are not injurious to the plants; and Freytag proved that free sulphuric acid could not be found

May 1, 1907

By A. T. Miesch, L. B. Riley

Distribution of minor elements in sandstone-type uranium deposits of the Colorado Plateau is being studied by the USGS on behalf of the A EC. A primary objective has been to provide basic data which could be useful in geo-chemical exploration for new deposits. The basic statistical measures — similar to those used in sedimentary petrology—are described. The underlying principle is that the frequency distributions fit or approach the log-normal form. Since 1952 the U. S. Geological Survey on behalf of the U. S. Atomic Energy Commission has conducted a study of the distribution of minor elements in sands tone-type uranium deposits of the Colorado Plateau. A primary objective in this study has been to provide basic data which could be useful in geo-chemical exploration for new deposits. Among the basic data considered important are estimates of the abundance and habit of each element in the ore and in the host rocks. It has been found that a few basic statistical techniques, and variations of these techniques, are useful in this type of study. Some of the basic techniques have been used to advantage by researchers in geochemistry and in other fields of geology, especially sedimentary petrology; others have been used to only a limited extent. Among the latter is the linear correlation coefficient, which has proved useful in assessing the element associations in a particular rock type without analysing individual mineral separates. In computing the basic statistical measures a scale has been used which is, in some ways, similar to the phi ($) scale used by sedimentary petrol-ogists in grain-size studies.' FREQUENCY DISTRIBUTIONS It has been recognized for some time that the results of analyses for a given minor element in a suite of samples of rocks or ores yield frequency distribution curves which are approximately normal when the curves are plotted on logarithmic or geometric scales. In other words, the analytical results give an approximate lognormal frequency distribution. A classical example is given by D. G. Krige2 in the study of the distribution of gold values from a mine on the Witwatersrand. Another example is shown in Fig. 1, the distribution of barium concentrations in samples of uranium ore from the Chinle formation. The geochemical data are analogous to grain-size data gathered by the sedimentary petrologist. Both types of data, after simple logarithmic transformations, may be treated by conventional statistical methods based on the normal distribution. This is not to say that other types of transformations may not serve equally well or better for particular element distributions.3 Spectrographers and other analysts are quite aware of the dependence of their precision on the concentration of the element present.4 For example, in the part per million range the variation may

Jan 1, 1961

By Walter W. Bradley

FOR a number of years up to the economic setback of the 1929-1931 period, the greatest proportional advances in the mineral industries in California were made among the substances in the nonmetallic groupings, particularly among the so-called industrial minerals and the salines. During the past year or two, although these have not regained the stride that marked their progress in the preceding decade, we can still record, -some new developments. California produces annually between 55 and' 60 different minerals on a commercial scale. Of these, some 40 to 45 comprise the "structural," "industrial," and "salines" materials as grouped in the reports of the State's Division of Mines. Barite-The barite deposits of California were described in Report

Jan 1, 1935

"Butte originated as a placer mining camp. The first gold discovery was made in the year 1864, near what is now Main Street. Placer mining was vigorously prosecuted along Silver Bow Creek and in Missoula, Buffalo, Town and Parrot gulches for a period of five years, at the end of which time, in 1870, the camp was practically deserted. In the meantime, the quartz veins so prominently traceable over the hillsides were located, the first location being made by W. L. Farlin and called the Black Chief claim, and later restaked as the Travona. Reasoning from the presence of the gold placers, free-milling gold ores were eagerly looked for by the early prospectors. Claims covering the great Rainbow and other silver lodes were located in the sixties. The presence of valuable silver ores in these veins caused the staking out of many claims, believed to be valuable only for silver, but which later proved to be enormous copper producers.Treatment of these early discovered rich ores was first attempted in arrastres. Later, stamp mills were built. The Centennial dropping 10 stamps, was the first, and in 1875 Mr. Farlin built the Dexter 10-stamp mill, intro¬ducing chloridizing-roasting. More successful processes were soon introduced and several large mills built, among which were the Alice, Lexington, Silver Bow, Moulton and Bluebird, in all representing a total of 290 stamps. The silver mining industry reached its zenith in 1887 and declined rapidly in the early nineties, following the sudden drop in the price of silver in 1892.During this period of silver mining activity the business of copper mining was making rapid strides. Development of the veins, located as silver veins, had uncovered copper ore in many instances. There was great activity in ""claim staking'' in the years from 1871 to 1879, during which period most of the claims covering the present productive copper area were located."

Jan 1, 1913

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.'-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann's constant, and the vacancy formation entropy, respectively. After applying Stirling's approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling's approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling's approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By L. E. Lynd

Ilmenite concentrates prepared from beach and dune sands of Florida, India, Australia, and other localities deviate to varying degrees from the theoretical composition of pure ilmenite, and generally contain more TiO2 than the formula FeTi03 would indicate, and some Fe2O3. This variation in composition is due to different amounts of altered ilmenite in the concentrates. (') The alteration has been shown to take place by oxidation and leaching of the iron in ilmenite, to yield residual products consisting of amaphous or very finely crystalline titanium dioxide and ferric oxide. Other studies(2) have stressed that ilmenite may alter first to an amorphous titanium-iron oxide, or to an amorphous mixture of titanium and iron oxides, with later alteration to crystalline titanium dioxide. There has been some speculation as to whether alteration of ilmenite is usually caused by weathering or by hydrothermal pr0cesses.(3,4,5 Three main methods of approach were used to study the mechanism and rate of ilmenite weathering. (1) Etch tests were used to learn the relationship between crystallographic orientation and the rate of chemical attack on ilmenite. (2) Altered ilmenites in New Jersey sands were compared with ilmenite in rocks of the area from which the sands were probably derived. (3) Experiments were carried out to determine at what rate, and by what agents, originally fresh ilmenite could be altered in the laboratory under simulated weathering conditions. ETCH FIGURES ON ILMENITE CRYSTAL PLANES A rather large ilmenite crystal from Sannidal, Norway, about 11/2 x 11/2 x 2 inches, bearing a few natural faces with imperfect surfaces, was prepared for etching by grinding and polishing crystal planes whose Bravais-Miller indices (referred to hexagonal axes) had been determined by X-ray methods to be 00.1, 10.0, and 10.2. Metallographic examination showed that the crystal was homogeneous, and uniform in orientation, except for the presence of twin lamellae which were oriented with their broadest surfaces parallel to the 00.1 planes of the large crystal. Since ilmenite is rather inert to standard etch reagents, strong solutions of hot sulfuric acid and cold hydrofluoric acid were used. Preliminary tests established that better etch figures were obtained using HF than with H2So4 solutions. The etch figures produced on 00.1 and 01.0 planes of ilmenite by etching 3 to 5 minutes in cold concentrated HF solution are shown in Figures 1, 2, and 3. The figures on 00.1 are "etch hillocks", rather than pits, and according to Honess(6), this phenomenon

Jan 1, 1961