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By T. A. Rickard

Our Transactions contain two notable papers descriptive of the stamp-milling practice of the Black Hills and of Grass Valley, namely, the elaborate and complete treatise of Prof. H. 0. Hofman, on " Gold-Milling in the Black Hills,"" and the paper describing the North Star mill, by E. R. Abadie, its superintendent. Having visited and examined the stampmills of both localities, I venture to offer here such comment as more recent information or a different point of view has suggested.†

Jan 1, 1896

By John A. Ames

AMERICAN pioneers first discovered "commercial" salt in western New York State. Geologists gave the classically correct name of Salina to the salt bearing strata of New York. Rock salt occurs in rocks of approximately the same age and stratigraphic position as New York's Salina "group", to the south and southwest, in western Pennsylvania, eastern Ohio and northwestern West Virginia. Sodium chloride and associated salts occur in brines throughout much of the same area as the rock salt. Brines also are found in areas well beyond the margins of that under which the rock salt lies, especially to the west in Ohio and to the south in West Virginia. The occurrence of the brines in the same area as the rock salt is almost always coincidental rather than indicative of a physical association.

Jan 5, 1950

By A. W. Hahn

ALTHOUGH enormous tonnages of sulfide lead and lead-silver ores are treated by flotation, the products of flotation mills treating oxidized ores of lead and silver are almost negligible. However, each year there is a slight tonnage increase, and it is possible, should a sizeable oxidized lead ore tonnage be developed, the field will become an important one. In 1918, the Shattuck-Arizona Copper Co. erected a plant at Warren, Ariz., for the treatment of oxidized gold-silver-lead ores. Glenn L. Allen worked out the metallurgy for this plant, employing tabling, followed by flotation concentration. The Shattuck-Denn Mining Co., successors to the Shattuck-Arizona Co., now employs straight flotation in the same mill, treating about 200 tons daily. In 1922, the San Diego mill of the American Smelting & Refining Co., in the Parral district, Chihuahua, Mexico, started operating a 600-ton mill on a mixed sulfide-oxide gold-silver-lead ore. Tables and flotation are used here, and about 200 tons of oxidized slime treated by flotation. In 1923, the Eureka Holly Mining Co. started operating a 90-ton mill at Eureka, Nev., using tables and flotation, on an oxidized lead-silver ore. In 1924, the American Smelting & Refining Co. started a 250-ton mill in northern Peru, to treat a high grade oxidized gold-silver ore with very low lead values. In 1924, the Grand Central Mining Co. started a 200-ton flotation mill on old oxidized gold-silver-lead tailings at Fairbank, Ariz. In 1926, the Compania International Minera, a subsidiary of the Union Corporation of London, started a 250-ton flotation mill on oxidized lead-silver ores, and during April of this year, the Phelps-Dodge Corp. will probably start a 250-ton mill at Warren, Ariz., on oxidized lead-silver ores, similar to those being treated in the Shattuck-Denn mill.

Jan 1, 1927

By William A. West

One manifestation of anelastic properties in solids is the mechanical elastic aftereffect, which may be described briefly as follows: If a stress is applied to a solid body, a deformation or strain is produced. On removal of the stress, this deformation disappears, at least in part. As a first approximation, this appearance or disappearance of deformation usually has been considered instantaneous. Actually, however, for a very wide variety of substances, on application of stress the instantaneous deformation is followed by a further slow yielding, which continues, although at a rapidly diminishing rate, for as long as the stress is applied. Similarly, on removal of the stress, the instantaneous recovery from deformation is followed by a further slow recovery, which continues, although at a rapidly diminishing rate, often for a long time. This latter phenomenon has been called the "elastic after-effect." Experiments upon the elastic after-effect in metals, when properly designed and when properly interpreted, are capable of giving quite precise information regarding the relation between stress and strain in the various constituent parts of the metal. For example, if certain parts of the metal, such as grain boundaries or slip bands, behave in a viscous manner—that is, if therein—the relaxation spectrum will contain lines or bands associated with the relaxation of shear stress within these parts. No attempts have heretofore been made to utilize elastic after-effects for obtaining such detailed information. The purpose of the present paper is to explore the possibilities of properly designed and interpreted experiments on the elastic aftereffect in metals. Since new procedures and principles are employed in this study, an attempt has been made to record each step taken. Elastic after-effect observations are susceptible of simple interpretation only when the stress level employed is so low that all effects are linear with the stress. Just how low the stress level must be can he determined only by experiment. An advnntage, other than simple interpretation, is associated with low stress levels. When all effects are linear, derived quantities, such as the relaxation spectrum, are independent of the stress distribution. It is, furthermore, possible to employ the type of deformation that is most convenient from the experimental standpoint; for example torsion. It appears that in experiments involving both loading and unloading the following would be observed: I. Instantaneous deformation, recoverable instantaneously in whole, or in part. 2. Delayed deformation, recoverable slowly in whole, in part, or not at all. 3. Permanent deformation, the difference between total deformation and total recovery. In the work here described, unloading experiments only were made. Wires were

Jan 1, 1947

By William A. West

One manifestation of anelastic properties in solids is the mechanical elastic aftereffect, which may be described briefly as follows: If a stress is applied to a solid body, a deformation or strain is produced. On removal of the stress, this deformation disappears, at least in part. As a first approximation, this appearance or disappearance of deformation usually has been considered instantaneous. Actually, however, for a very wide variety of substances, on application of stress the instantaneous deformation is followed by a further slow yielding, which continues, although at a rapidly diminishing rate, for as long as the stress is applied. Similarly, on removal of the stress, the instantaneous recovery from deformation is followed by a further slow recovery, which continues, although at a rapidly diminishing rate, often for a long time. This latter phenomenon has been called the "elastic after-effect." Experiments upon the elastic after-effect in metals, when properly designed and when properly interpreted, are capable of giving quite precise information regarding the relation between stress and strain in the various constituent parts of the metal. For example, if certain parts of the metal, such as grain boundaries or slip bands, behave in a viscous manner—that is, if therein—the relaxation spectrum will contain lines or bands associated with the relaxation of shear stress within these parts. No attempts have heretofore been made to utilize elastic after-effects for obtaining such detailed information. The purpose of the present paper is to explore the possibilities of properly designed and interpreted experiments on the elastic aftereffect in metals. Since new procedures and principles are employed in this study, an attempt has been made to record each step taken. Elastic after-effect observations are susceptible of simple interpretation only when the stress level employed is so low that all effects are linear with the stress. Just how low the stress level must be can he determined only by experiment. An advnntage, other than simple interpretation, is associated with low stress levels. When all effects are linear, derived quantities, such as the relaxation spectrum, are independent of the stress distribution. It is, furthermore, possible to employ the type of deformation that is most convenient from the experimental standpoint; for example torsion. It appears that in experiments involving both loading and unloading the following would be observed: I. Instantaneous deformation, recoverable instantaneously in whole, or in part. 2. Delayed deformation, recoverable slowly in whole, in part, or not at all. 3. Permanent deformation, the difference between total deformation and total recovery. In the work here described, unloading experiments only were made. Wires were

Jan 1, 1947

By A. N. Winchell

In connection with law suits between mining companies at Bingham, Utah, a few years ago, the writer made petrographic studies of more than 1400 rock and mineral samples in thin sections, and also careful studies of their field relations. In petrographic studies, even when an area is studied intensively, attention is commonly centered very largely on the unusual features of special interest, so that the relative abundance of rock types (or minerals or textures) can only be determined by a study of map areas outlined largely by field methods, and cannot be based directly on microscopic work. It is very uncommon, and usually impossible, to take samples at regular short intervals along and across formations. It is precisely because such methods were used at Ringham that the work presents a rare opportunity for determining, on a microscopic basis, the relative abundance of rock types and the continuity of gradations between rock types. At the same time, a study was made of the alteration of sediments under the influence of igneous intrusions, with results that are believed to be of interest and importance. • Sandstone-limestone Gradation The sedimentary rocks of the Bingham district are chiefly sandstones, with some beds of limestone, all now lying with their strike nearly east and their dip nearly north at an angle of about 30°, near the surface. The limestone beds are remarkably irregular in thickness in some places, but usually change very slowly in composition along the strike. However, the most interesting results are obtained from a study of a section across the beds at right angles to the strike. In some places, such sections show the usual alternation of pure sandstone with nearly pure limestone, in the simple manner assumed in most geological discussions.

Jan 1, 1924

By A. M. Gaudin

THIS paper presents, with the help of colored photomicrographs, the new method of mineral identification termed "selective iridescent filming." This method pertains to the field of determinative mineralogy, which it provides with tools for: (1) phase identification, (2) solid solution analysis. The method should be particularly useful in the applied fields of: (1) paragenesis of ore deposits, (2) mineral dressing, (3) mineral synthesis and study of phase equilibria.

Jan 1, 1938

By H. A. Wheeler

. Page History.................................533 Location .........:.....................536 Geology...............................539 Description of the Eastern Field ... :..................543 Description of the Western Field .........,...........546 Quality of the Oil ................ ,........549 The Oil Sands .,.............................549 Drilling Features'........................., . 551 Well Density...........,.'...............:. 552 Plant Equipment.......................:.'., .554 Market Features..........................555 Production Prices.........,...................557 Royalties and Rentals.........................558 Cost of Oil Leases............................'.558 Operating Expenses..........................559 Operating 'Profits...........................559 Gas Developments ........................560 Gas-Gasoline production ... :....................561 Statistics.......562 History Illinois has SO recently attained the third place in the oil production of the United States that few realize its great importance, or are aware of its highly profitable character. Since 1907 Illinois has furnished about 15 per cent. of the United States output and about 10 per cent, of the world's production. The value of the output in 1913 is estimated at $307000,000, of which about $20,000,000 is profit. The present prosperity dates from 1905, but efforts have been made since 1865 to develop production and geologists have been very sanguine as to its future for over 25 years. Had the oil operators been as confident as the geologists, the field would have been opened at least 30 years earlier. For the rich Eastern Illinois oil field is located along the La Salle anticline, that was mapped 46 years ago by Professor Worthen in the

Jan 1, 1915

By S. F. Urban, G. Derge

At the time this investigation was initiated variations were observed in the quality of different heats of basic electric-furnace steels, although they had been made under purportedly similar conditions. This indicated that these variations were related to normally unobserved variations in the character of the bath, especially during the "refining" period. Although the slags used for this operation are commonly referred to as "reducing" slags, and are regarded as having a "deoxidizing" action on the bath, no reliable measurements of this action were available. It was decided, therefore, to study the behavior of oxygen in the metal for ' large enough number of heats to learn its normal variations and to relate these variations to regularly observed conditions of operation. The most important general conclusion reached was that the time a heat is held under a reducing 'lag should be reduced to a minimum, which was about an hour and a half under the conditions studied. Beyond this time no observable beneficial effects are obtained from the reducing slags, insofar as oxygen and sulphur content of the bath are concerned. It is likely that added time may increase hydrogen content as well as heat costs. The oxygen content of the bath is never reduced below the amount in equilibrium with the carbon. Concurrently with this work, J. S. Marsh1 presented data that supplement and support many of the results of this paper. Procedure The work was done in two different electric-furnace shops of the same plant. The selection of heats was made primarily with regard to the convenience of heat schedules. companion slag and metal samples were taken just prior to slag-ofi and throughout the refining period for an initial set of 17 heats, and before slag-off and near tap for an additional I3 heats. slag Sampling presented no particular problem; a spoonful of slag was poured onto a metal plate and when sufficiently cool was sealed in an airtight container. Sampling the metal for oxygen presented a more complex problem. Because of the lack of previous experience in sampling electric-furnace baths, a number of methods were compared. Chilled Wedge Samples2 An unkilled metal sample is removed from the furnace in a well-slagged car-bometer spoon and poured immediately into a heavy copper mold designed to provide rapid freezing. Three different types of molds were used to determine the optimum for electric-furnace hats. The Big wedge Mold (a) was a 4 by 4 by 4-in. split copper mold, yielding a wedge-shaped casting I in. wide, 1 1/2 in. long, and 34 in. maximum thickness, and was finally adopted as the most satisfactory design.

Jan 1, 1948

By S. F. Urban, G. Derge

At the time this investigation was initiated variations were observed in the quality of different heats of basic electric-furnace steels, although they had been made under purportedly similar conditions. This indicated that these variations were related to normally unobserved variations in the character of the bath, especially during the "refining" period. Although the slags used for this operation are commonly referred to as "reducing" slags, and are regarded as having a "deoxidizing" action on the bath, no reliable measurements of this action were available. It was decided, therefore, to study the behavior of oxygen in the metal for ' large enough number of heats to learn its normal variations and to relate these variations to regularly observed conditions of operation. The most important general conclusion reached was that the time a heat is held under a reducing 'lag should be reduced to a minimum, which was about an hour and a half under the conditions studied. Beyond this time no observable beneficial effects are obtained from the reducing slags, insofar as oxygen and sulphur content of the bath are concerned. It is likely that added time may increase hydrogen content as well as heat costs. The oxygen content of the bath is never reduced below the amount in equilibrium with the carbon. Concurrently with this work, J. S. Marsh1 presented data that supplement and support many of the results of this paper. Procedure The work was done in two different electric-furnace shops of the same plant. The selection of heats was made primarily with regard to the convenience of heat schedules. companion slag and metal samples were taken just prior to slag-ofi and throughout the refining period for an initial set of 17 heats, and before slag-off and near tap for an additional I3 heats. slag Sampling presented no particular problem; a spoonful of slag was poured onto a metal plate and when sufficiently cool was sealed in an airtight container. Sampling the metal for oxygen presented a more complex problem. Because of the lack of previous experience in sampling electric-furnace baths, a number of methods were compared. Chilled Wedge Samples2 An unkilled metal sample is removed from the furnace in a well-slagged car-bometer spoon and poured immediately into a heavy copper mold designed to provide rapid freezing. Three different types of molds were used to determine the optimum for electric-furnace hats. The Big wedge Mold (a) was a 4 by 4 by 4-in. split copper mold, yielding a wedge-shaped casting I in. wide, 1 1/2 in. long, and 34 in. maximum thickness, and was finally adopted as the most satisfactory design.

Jan 1, 1948

By Charles A. Ashburner

[The statistics contained in this paper were collected for the United States Geological Survey and communicated to the Institute, by permission, prior to their publication in the report on the Mineral Statistics of the United States for 1887.1 The total coal-production of Alabama in 1887 was about 1,950,000 short tons, the spot-value of which, at the mines, was $2,535,000. The coal-regions of the State lie in the extreme southern part of the Appalachian coal-field, the northern part of which lies along the western New York-Pennsylvania State line; between these limits, New York on the north and Alabama on the south, portions of the

Jan 1, 1889

By Elmars Ence, Harold Margolin

The partial isothermal section of the Ti-Cu-Zr system at 750°C has been studied. The crystal structure of Ti2Cu has been detevnlined as tetragonal and when expressed as face-centered tetragonal, a = 4.164, c = 3.611 A, and c/a = 0.867. TITANIUM systems in which ß-titanium decomposes eutectoidally into a and a compound rather readily are known as active eutectoid systems. Recently in active eutectoid alloys based on the Ti-Cu system, and containing additionally A1 and Zr, it has been found that zirconium may produce both moderate weakening and marked strengthening at elevated temperatures.' In order to obtain some insight into the behavior of zirconium, an attempt was made to determine whether compounds of the type Tix Zr and TixZryCu exist. Only results of the Ti-Zr-Cu studies are reported here since data on Ti-Zr alloys will be presented in a separate publication. EXPERIMENTAL PROCEDURE Alloys were nonconsumably arc melted in argon atmosphere as 15-g buttons, prepared from materials of the following purities: Bureau of Mines electrolytic Ti — Bhn 63 OFHC copper Reactor Grade Zirconium Bhn .C 150 Prior to alloy preparation the electrolytic titanium was premelted to avoid excessive spattering of the charges during melting. The weight losses during melting did not exceed 1 pct of the total weight of the charge. The alloys prepared are listed in Table I together with analyzed compositions. in cases where they were determined. Specimens for heat treatment were wrapped in molybdenum sheet, annealed in argon-filled quartz capsules, and quenched by breaking the capsules under iced brine. About 1 to 2 sec are required to remove the capsule from the furnace, drop it into the iced brine and break it. Because of the insulation effect of the quartz, this delay in quenching should not produce a large drop in temperature. In many instances, no difference or little difference has been detected between the same specimen quartz capsule quenched or directly quenched in vacuum by an impinging stream of water.' Ti-Cu-Zr alloys were homogenized for 48 hr at 825°C prior to annealing at 750°C. Annealing for 5 days at 750°C produced the same results as 11 days at temperature and it was therefore assumed that 5 days was sufficient to establish equilibrium. Titanium-copper alloys were homogenized for 40 hr at 900°C prior to heat treatment for 6 days at 750°C. Specimens for metallographic examination were electropolished and etched with the following solution:

Jan 1, 1962

By T. A. Ring

The bed filtration of colloidal particles has been modeled by performing a differential particle balance. The balance considered the localized particle deposition rate to be the sum of three rate resistances: mass transfer to a region near the surface, adhesion onto a partially filled surface, and resuspension from a partially filled surface. The differential particle balance equations, one for the free particles and one for the adhered particles, were solved by a finite difference algorithm. Results of this model are compared to experimental filter breakthrough curves.

Jan 1, 1985

By Charles A. Mitke

Discussion of the paper by CHARLES A. MITKE, presented at the San Francisco meeting, September, 1915, and printed in Bulletin No. 105, September, 1915, pp. 1941 to 1958. GERALD SHERMAN, Bisbee, Ariz.-Mr. Mitke justly might have made much stronger his claim for increase in efficiency of labor due to the introduction of forced ventilation. The product per man shift in stoping in the Gardner division has practically doubled. While it is true that improved methods have been responsible for a great part of this gain, and what is due to better ventilation cannot be definitely known, yet it is also true that the results could not have been obtained in that division as it was in 1912. . The paper discusses the two systems of ventilation in use, exhaust and pressure. In both the object is the same, to take foul air or gas out of the mine by the most direct course and replace it by fresh. In coal mines, the exhaust system is in almost universal use, and since the most advanced work in ventilation has been in that class of mines, it was naturally the first one to be considered. It has the advantage of leaving all adits, shafts, or other openings free for use. Doors are only needed to direct the course of the air, and not to confine it. Its disadvantages appear in case of fire, or if the ground over the mine is much broken by subsidence. The fan must work in gas in the case of a -fire, and may be. damaged or destroyed either by heat or by corrosive gas. At the time of the fire in the Lowell division of the Copper Queen, a small exhaust fan was placed over a ventilating raise, but the vanes and housing were destroyed by sulphurous gases within a few weeks. If the ground above the mined area is much broken, as is frequently the case when the ore deposit is thick vertically, a good deal of air is likely to pass through it, particularly if it is near the surface. Leakage from this source is a loss to the exhaust system by short circuiting, which is exaggerated by a contraction or block in the air course. It serves as an added outlet in the pressure system. This is strikingly shown at the United Verde, where many jets of steam may be seen coming up through the ground above the stoped country on a cold day.

Jan 12, 1915

By D. W. Smith

The beta solid solution phases of the systems copper-zinc, copper-aluminum, copper-tin and silver-zinc are structurally analogous.' R. F. Mehl and 0. T. Marzke2 have shown that the a phase upon segregating from the 6 phase in the system copper-zinc takes the form of needles lying parallel to a [Ill] direction or some similar direction, such as [556], of the parent solid solution, and that the a phase upon segregating from the ß phase in the system copper-aluminum also takes the form of needles. By analogy they assume that in this case also the segregate needles lie parallel to the [ill] or [556] direction in the ß lattice. The purpose of this investigation is to determine whether the structures resulting from segregation of the a phases from the respective ß phases of the systems copper-tin and silver-zinc are analogous to those obtained by Mehl and Marzke in the systems copper-zinc and copper-aluminum. Segregation of the a Phase from the ß Phase in the Copper-tin System Preparation of the Alloy.—An alloy containing 74.92 per cent (by weight) of copper and the balance tin was chosen for this investigation. This alloy, as can be seen from a portion of the constitutional diagram, Fig. 1, of the system copper-tin by Hamasumi and Nishigori,3 with the proper heat treatment should segregate the « phase out of the a parent, solid solution phase. The alloy was prepared from high purity cathode copper (analyzing 99.98 per cent Cu) and Straits tin (analyzing 99.94

Jan 1, 1933

By John A. Church

In May, 1878, I had the honor of presenting to the Institute, at the Chattanooga meeting, some observations upon the heat of the Comstock Lode, and since then the subject has attracted some attention and criticism, in the course of which, L have observed errors of apprehension which I beg leave to correct now. Mr. John Arthur Phillips discussed it before the Geological Society, his paper being printed in the Quarterly Journal for August, 1879." His criticism is based upon that part of my paper in which I quote a number of analyses of the mine waters, to illustrate the fact that the heat does not come from the oxidation of pyrite. I pointed out that these waters contain only an insignificant proportion of sulphuric acid, and not enough to account for even one per cent. Of

Jan 1, 1880

By A. R. Denison

This field in 1933 continued as in 1932, although to a much less extent, to dominate the drilling and production situation throughout the oil business. The 2466 producers completed in this field during the year are 28 per cent of such wells completed in the United States. The 2556 completions reported in the five counties within which the East Texas field lies are 21 per cent of all such wells reported in the United States. It follows that with such a command of the development situation, every other factor with regard to this field has an important bearing on the entire oil business. As a consequence, the important developments in the East Texas field are the important developments of the year. Very little new productive territory was added to the already known limits of this enormous field. On the other hand, drilling has shown that with a few very minor exceptions this field is a continuous productive area, with a regular outline and no "dry spots" other than that of a single well surrounded by producing wells. Drilling was confined to the already proven limits of the field. This consisted essentially of more adequate coverage of leases by wells, the meeting of required offsets and the drilling of a large number of small tracts which developed from subdivision of larger leases due to court action and other causes. The allowable throughout the year was, with minor variable factors, on a per-well basis. With the steady decline in per-well allowable after May, every operator was faced with declining

Jan 1, 1934

By A. J. Brown

I HEREWITH send to the Institute a sample of Pancake coal. It is rather early yet to make any estimate of the future value of the discovery; but it is certainly the most promising vein of coal yet discovered in the State of Nevada, and, I believe, the first true coal found west of the Rocky Mountains, or perhaps west of the Missouri River, unless some of the Utah coals belong to the coal measures of the Carboniferous age. The Pancake vein certainly belongs

Jan 1, 1875

By J. G. Savins

Analytical procedures are described for optimizing the selection of a rheological model when it is desired to express the functional relationship between true shearrate and shearing stress in analytical form. The procedures are extended to two principal model categories — "Generalized Newtonian" and "Viscoplastic" models. Graphical examples are presented to illustrate the utility of certain characteristic deriuative functions in distinguishing between these categories and in determining how well a particular model reflects the flow behavior of rheologically anomalous materials in simple shearing flows. INTRODUCTION Modern drilling fluids and fracturing fluids, being chemically complex, are frequently non-Newtonian — a peculiarity which complicates the solution of problems such as designing flowline and process equipment, and predicting laminar-turbulent behavior, solid-suspending ability and cutting-transport efficiency. Therefore, techniques of data analysis which accurately characterize the behavior of rheologically complex materials are needed for the accurate formulation of solutions of these and similar problems. It is the purpose of this paper to describe the application of a sensitive method of rheological data analysis — the dual differentiation-integration method of optimizing the selection of the functional relation between shear rate and shearing stress — to a variety of materials of interest in drilling and production practices. BASIC CONCEPTS THE DIFFERENTIATION METHOD To a first approximation, the viscosity function for a non-Newtonian system can be expressed in a form analogous to Newton's law of viscosity by the following generalization2.3 between the stress On introducing the restrictions that the system is incompressible and the motion is rectilinear, then l = 0 and l3 = 0 ; and with the further restriction that the flow is slip-free, the viscosity (an invariant) is then determined solely by 12. With this approach one can set up a suite of integral equations relating observed kinematical and dynamical parameters for certain types of flow experiments involving simple shearing motion, e.g., flow in a cylindrical tube, flow between rotating concentric cylinders, and flow between fixed parallel surfaces of large aspect ratio. Taken in the order cited, these integral equations are as follows.

By K. A. Jackson

An analysis of the conditiom fm the dendrite-eutec-tic transition is presented which takes into account a temperature gradient. The composition and temperature in the liquid ahead of a eutectic interface growing at a particular velocity are used to determine whether dendrites can grow faster than the eutectic interface in the liquid which exists ahead of it. If the dendrites grow faster, then a mixed structure with dendrites growing ahead of the eutectic interface is expected. If the dendrites do not grow faster, then only eutectic will be present. The analysis is presented for Sn-Pb system, for which sufficient experimental data to make the analysis are available. The transition from eutectic to dendrites-plus-eutectic derived by this analysis is in good agreement with the recent experimental observations of Mollard and Flemings on Sn-Pb alloys. In alloys which grow with a lamellar eutectic structure, the lamellar structure can be grown over some range of compositions close to the eutectic composition. When the composition is too far from the eutectic composition, dendrites of one or another of the primary phases grow ahead of the eutectic interface, producing a microstructure consisting of "primary phase" interspersed with a lamellar eutectic. Hunt and Jackson' have recently predicted the range of compositions over which the eutectic phase should grow in Sn-Pb alloys, and the composition-growth rate dependence of the transition from eutectic to dendrites-plus-eutectic. This prediction was based on work on organic eutectics. The model on which the prediction was based assumed that there was no temperature gradient in the system, a condition approximately satisfied in the study of organic eutectics2-5 but not in the growth of metallic alloys. Mollard and Flemings6,7 have recently reported experimental results for Sn-Pb alloys in which they have located the transition from eutectic to eutectic-plus-dendritic growth. The experiments were performed using large temperature gradients (65 to 515 deg per cm), so that the assumption of zero gradient on which the predictions of Hunt and Jackson' were based does not apply. It is not surprising therefore that the predictions' were not born out by the experiments.7 In the present work, a modification of the model used by Hunt and Jackson is presented which takes into account the temperature gradient. The modified form of the theory predicts the transition from eutectic to eutectic-plus-dendritic growth in terms of the composition, growth rate, and temperature gradient. Good agreement with the experimental data of Mollard and Flemings7 is obtained. THE HUNT-JACKSON MODEL The model used by Hunt and Jackson' to predict the transition from eutectic to eutectic-plus-dendritic growth was based on the assumption that dendrites grow ahead of a eutectic interface only if they grow faster than the eutectic interface. Analytic expressions for the growth rate of dendrites and the eutectic in Sn-Pb alloys were obtained by fitting experimental data with equations whose form was indicated by theory.

Jan 1, 1969