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By J. S. Marsh

TUESDAY, Feb. 16, was no day for strolling along the cold sidewalks of New York, and a large number of metallurgists sat down with pleasure to the warming task of wiping a few soldered joints. Presented by a joint-wiper of the modern school, G. M. Bouton, of the well-known team of Schumacher, Bouton, and Phipps, the initial paper brought into focus the theme of conservation of strategic metals and described the technique of making the fillet-type joint now employed by the Bell System. Using an over-all average of only 40 per cent of the solder formerly used by the conventional method. this important development bids fair to stick when the war is over. D. L. Martin and E. R. Parker then described the embrittling effect of hydrogen on silver previously heated in oxygen and the less serious but troublesome result obtained under the converse conditions. An interesting example of grain growth restriction created additional material for the lively discussion that ensued among those who have encountered one or another of these phenomena in silver and copper.

Jan 1, 1943

By Eugene H. Dawson

MICA is a mineral that once was a familiar sight as fireproof windows in stove and furnace doors and as lamp chimneys and shades. Since 1878, the beginning of the electrical age, the use of mica for such purposes has gradually declined and its use in electrical equipment and appliances has developed to such an extent that the known sources of supply are scarcely equal to the demand. With the increasing capacity of electric generating units, the size of mica sheets found in nature was inadequate. However, in 1894, a process was developed whereby thin films or splittings cemented with shellac or other binders could be pressed into large sheets. 18 The introduction of radio in the early 1920s created such a heavy demand for the smaller sizes of mica that on March 22, 1938, mica was included among 23 commodities on the list of strategic materials approved by the United States Army and Navy Munitions Board. To be included in this list, the material must be one whereof the domestic supply is not sufficient to meet the demand. COMPOSITION Mica is a complex mineral composed principally of the silicates of potassium, aluminum, and magnesium. Less prevalent species contain, as essential components, lithium, vanadium, and chromium. Iron usually is present either as an essential component or as an impurity. The mica group comprises some nine different species, five of which, muscovite, phlogopite, vermiculite, lepidolite, and biotite, are widely used in industry. Lepidolite and zinnwaldite (lithium micas) and roscoelite (vanadium mica) are sources of lithium and vanadium. Muscovite, "white mica," is potassium mica. Theoretical formulas H2KAl3(SiO4)3. There are two varieties, distinguished as to color, known in industry as ruby and green. In crystals or "books," the colors each range through varying shades of red and green. However, when split into thin films, all micas, except biotite and phlogopite, are colorless and transparent. Muscovite frequently is stained red or black by thin films of iron oxide between the laminae. The staining usually is derived from magnetite, which sometimes is found as unaltered crystals.

Jan 1, 1949

By D. P. Kedzie, R. A. Dodd

The fatigue strength, fatigue hardening, and effect of fatigue deformation on subsequent age hardening of supersaturated Al(Cu) solid solutions have been determined as functions of alloy composition and temperature. The fatigue strength/tensile strength ratios, determined at 150°, 25°, and -195°C, decreased with increase in alloy content for all temperatures, but the F.S./U.T.S. ratios at -195°C decreased much more rapidly than did the ratios for 150" and 25°C. This suggested that strain aging and/or age hardening occurred during tests at higher temperatures. Additionally, the F.S./U.T.S. ratios at 150°C exceeded those at 25°C for all compositions, indicating greater strengthening during fatigue at 150°C. The effect of fatigue or tensile deformation at 150°, 25°, and -195°C on subsequent age hardening showed that the deformatzon increased the rate of precipitation and indicated that mechanically produced vacancies were probably formed during deformation. Fatigue hardening was studied at 150°, 25°, and -195°C, and the effect of room-temperature rests after 10 and 100 cycles was examined. The results confirmed that strain aging occurred at the higher temperatures . DURING the last 15 years various mechanisms of fatigue crack nucleation and growth based on dislocation and vacancy interactions, operating singly or collectively, have been proposed. The probable consensus of present opinion is that the fatigue process in pure metals essentially involves dislocation interactions, and that vacancies formed by such interactions play a minor or inconsequential role. However, there is some evidence that age-hardened alloys tend to overage during fatigue, probably by local vacancy-enhanced diffusion, and strain aging also might be important in selected cases. Furthermore, it has been established that the behavior of quenched-in vacancies in Al(Cu) and other solid solutions is composition-sensitive. Therefore, it seemed worthwhile to investigate various aspects of the fatigue behavior of supersaturated Al(Cu) alloys and to examine the results in terms of vacancy-enhanced effects. EXPERIMENTAL The alloys used in this investigation were prepared from 99.994 wt pet A1 and OFHC copper, the latter containing 0.04 pet 0 as the principal impurity. Six alloys were made, containing, by actual analysis, 0.58, 0.96, 1.96, 2.85, 4.45, and 5.51 wt pet Cu. They were induction-melted in air in graphite crucibles, cast as 7-in. by 7/8-in.-diam rods in graphite molds, and hot-rolled to 5/8 in. diam. The experimental work was a three-part program involving the determination of a) 10' cycle fatigue stresses as a function of alloy composition and temperature; b) the effect of fatigue deformation on subsequent aging of the supersaturated alloys; and c) fatigue hardening as a function of alloy composition and temperature. For determining the 105 cycle fatigue stresses, a portion of the 5/8-in. stock was machined into Krouse rotating cantilever beam fatigue specimens, 2 in. in length by 1/4 in. minimum diameter. These were tested at +150°, 25°, and -195°C (liquid nitrogen) on a Krouse high-speed machine, with special weights to provide lower -than-normal loading ranges, this being necessitated by the small load requirements of those alloys of lower copper content. For the high-temperature tests a small resistance heater was designed to clear the collets and fit in between the chucks, while for the low-temperature tests a hollow nylon cylinder was used, having closed ends drilled to pass a fatigue specimen, and positioned similarly to the heater. A plexiglass container completely enclosed the fatigue machine; rubber gloves fixed to ports in the walls enabled the machine to be operated from outside the box. A tray of magnesium perchlorate dried the air in the container and prevented both atmospheric corrosion fatigue at room and elevated temperatures and troublesome ice build-up at low temperatures. A total of ten to fifteen specimens was used for each combination of alloy composition and temperature. The result of each test was plotted on a standard S-N diagram, and the next stress was selected on the basis of the trends indicated by previous specimens. In this manner a small portion of the S-N diagram was constructed, and the 105 cycle fatigue stress obtained. Small Krouse fatigue specimens were also used to study the effect of cyclic prestrain on subsequent

Jan 1, 1964

By F. William Bloecher, William B. Plank

CURRENTLY 12,892 students are enrolled in the mineral engineering schools of the United States and Canada, marking an all-time record high for these schools. It shows a remarkably rapid recovery from the effects of World War II. Enrollment in all the other engineering branches has also increased but not so rapidly as in the mineral engineering branch. Almost all the data in this report are from the eighth questionnaire study of the mineral engineering schools made, as formerly, under the auspices of the Mineral Industry Education Division of the AIME. Every school is represented in the data, for which the authors thank the deans and professors who supplied the information. For this reason, the data of all the studies are comparable, an achievement not always possible in endeavors of this kind. For comparison with the general engineering enrollment situation, data are included from the January 1947 issue of the Journal of Engineering Education.

Jan 1, 1947

By C. Kremer Bain

UNDER present economic conditions the necessity of mechanizing the mines of our country has become a very important problem. More and more mines are looking toward increased or complete mechanization of their operations, so in the writer's opinion it is quite pertinent that some of the associated problems that accompany such a program be pointed out. The following generalization on attempting a comparatively slight change in mining methods at the Southeast Missouri properties of the St. Joseph Lead Co. is an attempt to point out to anyone faced with a mechanization program that much time and C. KREMER BAIN, Member AIME, is Assistant to General Manager, St. Joseph Lead Co., Bonne Terre, Mo. AIME Sun Francisco Meeting, February 1949. TP 2743 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Manuscript received Dec. 27, 1948; revision received Oct. 13, 1949. effort can be saved, and many headaches avoided, if company policy can be established whereby everyone in the organization from the top down is desirous of improvement and is working towards the common objective. Any changes in mining methods, machinery, and so on, must entah coordination of all the other phases of mining as they all have to mesh as accurately as a smooth running chain of gears if satisfactory results are to be obtained. The purpose of this paper is to point out some of the problems which :have to be surmounted when any mechanization program is attempted, rather than to go into the mechanical details and actual operating data of the equipment employed. After all, machines have to be adapted to best suit the local conditions, so no general formula can be given that would apply to other properties. Although St. Josepll Lead Co. has been mechani-cally-minded for a number of years, as shown by the fact that over 110 million tons have been loaded mechanically since 1922, any further mechanization or changes always present a problem. When our ore bodies were of great height and area the breaking and loading were developed to a high degree of efficiency according to known standards. But in recent years, when our ore bodies became smaller and more scattered, the amount of tonnage we were able to break was not sufficient to supply our shovels with enough rock to keep them working to capacity. Our first step in attempting to rectify this situation was to develop a technique of moving the shovels to the broken ore in various stopes, which sometimes entailed a move each shift. A shovel is not producing when being moved, so within the last two years we have been endeavoring to devise some means of getting more rock broken in these smaller stopes and it was then that we became interested in jumbo drilling. To illustrate the fact that mechanization is a process of a chain of developments rather than a stroke of genius can best be shown by a general summary of conditions and obstacles which were encountered in our present attempt to establish template drilling of a standardized round. Our first jumbo was more or less the conventional type with two machines mounted on a crossbar. This arrangement proved to be impractical to duplicate satisfactorily the regular routine of slabbing in a more or less radial pattern as carried out by column drilling. One machine was either too close to or too far from the face and there was another disadvantage in that one drillman was frequently delayed while waiting for his partner to bottom a hole. Our next step was to eliminate the crossbar so the machines could operate independently of each other, but we still encountered the same objections mentioned above except that one drillman was free to drill three holes instead of one in a vertical plane independently of his partner. Time studies while trying to adapt the jumbo to the regular slabbing practice as accomplished by column drilling, revealed that twice as much time was spent in maneuvering the jumbo into position and aligning the holes as was consumed in drilling.

Jan 1, 1951

By C. Kremer Bain

UNDER present economic conditions the necessity of mechanizing the mines of our country has become a very important problem. More and more mines are looking toward increased or complete mechanization of their operations, so in the writer's opinion it is quite pertinent that some of the associated problems that accompany such a program be pointed out. The following generalization on attempting a comparatively slight change in mining methods at the Southeast Missouri properties of the St. Joseph Lead Co. is an attempt to point out to anyone faced with a mechanization program that much time and C. KREMER BAIN, Member AIME, is Assistant to General Manager, St. Joseph Lead Co., Bonne Terre, Mo. AIME Sun Francisco Meeting, February 1949. TP 2743 A. Discussion (2 copies) may be sent to Transactions AIME before March 31, 1950. Manuscript received Dec. 27, 1948; revision received Oct. 13, 1949. effort can be saved, and many headaches avoided, if company policy can be established whereby everyone in the organization from the top down is desirous of improvement and is working towards the common objective. Any changes in mining methods, machinery, and so on, must entah coordination of all the other phases of mining as they all have to mesh as accurately as a smooth running chain of gears if satisfactory results are to be obtained. The purpose of this paper is to point out some of the problems which :have to be surmounted when any mechanization program is attempted, rather than to go into the mechanical details and actual operating data of the equipment employed. After all, machines have to be adapted to best suit the local conditions, so no general formula can be given that would apply to other properties. Although St. Josepll Lead Co. has been mechani-cally-minded for a number of years, as shown by the fact that over 110 million tons have been loaded mechanically since 1922, any further mechanization or changes always present a problem. When our ore bodies were of great height and area the breaking and loading were developed to a high degree of efficiency according to known standards. But in recent years, when our ore bodies became smaller and more scattered, the amount of tonnage we were able to break was not sufficient to supply our shovels with enough rock to keep them working to capacity. Our first step in attempting to rectify this situation was to develop a technique of moving the shovels to the broken ore in various stopes, which sometimes entailed a move each shift. A shovel is not producing when being moved, so within the last two years we have been endeavoring to devise some means of getting more rock broken in these smaller stopes and it was then that we became interested in jumbo drilling. To illustrate the fact that mechanization is a process of a chain of developments rather than a stroke of genius can best be shown by a general summary of conditions and obstacles which were encountered in our present attempt to establish template drilling of a standardized round. Our first jumbo was more or less the conventional type with two machines mounted on a crossbar. This arrangement proved to be impractical to duplicate satisfactorily the regular routine of slabbing in a more or less radial pattern as carried out by column drilling. One machine was either too close to or too far from the face and there was another disadvantage in that one drillman was frequently delayed while waiting for his partner to bottom a hole. Our next step was to eliminate the crossbar so the machines could operate independently of each other, but we still encountered the same objections mentioned above except that one drillman was free to drill three holes instead of one in a vertical plane independently of his partner. Time studies while trying to adapt the jumbo to the regular slabbing practice as accomplished by column drilling, revealed that twice as much time was spent in maneuvering the jumbo into position and aligning the holes as was consumed in drilling.

Jan 1, 1951

By AIME AIME

WHETHER by the Mohawk Trail, Sound steamer, air plane, railroad or any other route or mode of locomotion, all roads will lead to Boston the week of National Metal Congress, Sept. 21-25. The Institute of Metals and Iron and Steel divisions of the Institute are then to meet jointly at the Hotel Statler, and the American Society for Steel Treating, the American Welding Society, the Society of Automotive Engineers and the Iron and Steel Division of the American Society of Mechanical Engineers present carefully planned programs at their respective sessions. The National Metal Exposition will be held on Commonwealth Pier.

Jan 1, 1931

By Walter Renton Ingalls

Vague references to tin-deposits in Mexico are scattered throughout technical literature, and that country has been looked to as a likely source of a part of the world's supply of till at no very distant date; but thus far nothing but occasional small lots have come forward, so that the notion has arisen that these mines are either mythical or unworkable. So far as I am aware, there has not yet been published any description of the tin-deposits of Mexico except a few brief references; and this paper, based on a study of them made in 1892, is therefore offered.

Jan 1, 1896

By C. R. Boyd

It would be a quite congenial task to attempt to describe all that extraordinary mineral wealth which is now giving such prominence to the region from the James River to the Tennessee line: adjacent to the great lines of the Shenandoah Valley and the Norfolk and Western railways; but such a task would be impossible within the limits of any ordinary paper. Hence, in advance of the fifth edition of my book and map on the Resources of Southwest Virginia, I must restrict myself to a limited but most interesting subdivision of this remarkable mineral belt.

Jan 1, 1884

By Roger E. Barthelemy

PRIMITIVE mining and metallurgy has today almost disappeared. Probably the only remaining tribal tin mining and smelting is practiced by the Laotian natives in one of the less known tin areas of the world. This district lies almost a thousand miles from the sea along the Mekong River, one of the longest rivers in the world, that marks the border between Siam and Laos, one of the five states forming French Indo-China. Less than twenty years ago it took more than two weeks' travel on elephant-back to reach the spot and today it still takes many days of travel, using all kinds of transportation from automobiles to native

Jan 1, 1938

By B. D. Saklatwalla

FOR the proper understanding of the inclusion of certain elements in this review it seems necessary to state the meaning of "rare metals." Certain elements occur in deposits limited in extent or concentration, so that the extraction of the element in relation to market conditions becomes uneconomical. Others may occur in extensive and rich deposits but the reduction of the metal may be difficult and costly. Both these conditions effect the same result, namely, make the metal rare and costly. As an example of the first kind may be mentioned radium and of the second, calcium.

Jan 1, 1939

By E. A. H. Tays

At the present time, the mine-owner has a number of patent crushers to choose from, when contemplating the erection of a mill; and a number of new ones are yearly brought to notice. We all know that the stamp-mill is the old standard; but several of the patent crushers, especially of the roller-type, are not without their merits. Having had a working experience, extending over a period of four years, with the " Bryan roller quartz-mill," working alongside of stamp-batteries, I take pleasure in giving to the members of the Institute the benefit of my experience with this mill.*

Jan 1, 1900

William Kent, New York City: I regard the paper of Professors Lord and Haas as the most important and valuable that has yet appeared on the subject of the calorific value of American coals. The close correspondence of the results they have obtained by the use of the bomb calorimeter with those calculated by the Dulong formula from the ultimate analyses, confirming the work done by Mahler in France some years before, is evidence of the extreme accuracy of their work, and gives us renewed confidence in Mahler's modification of the Berthelot calorimeter, and in Dulong's formula, which latter, until

Jan 1, 1898

By C. G. Dunn

With respect to theories of recrystalliza-tion in metals plastically deformed. it has been said that the present status of this subject is far from satisfactory.1 It may also be said that before any mechanism of recrystallization for metals and alloys can be set forth in a satisfactory manner, there must be made available considerable data on orientation changes that occur during the deformation and recrystallization processes. Although extensive data have been published on recrystallization in single crystals and in poly-crystalline specimens, more results of a type that can be classified according to simple orientation changes would be desirable in this complex field. It might even be said that before classifications are made according to types of orientation changes, it may be possible to classify a considerable amount of data into certain kinds of orientation states if groups of common or nearly common orientation occur. Methods for computing the probability of occurrence for various types of groups have been published2 and it has been pointed out in particular that it should be possible to analyze orientation data for high-order twin relationships between old and new grains even when agreement is not at all exact. In this connection, work on recrystallization in silicon ferrite reported in a paper concerned with complex groups of annealing twins3 indicated that some data were consistent with primary nucleation OCcurring according to a second-order or a third-order twin transformation. However, further work in this latter direction was definitely needed. It is, therefore, the purpose of the present paper to report data and analyses for primary nucleation in silicon ferrite following small deformations that have been carried Out at the Pittsfield Works' Laboratory of the General Electric Co. Analyses have been made with the aid of standard groups of twins that are reported elsewhere.4 PReparation oF Specimens and Experimental Procedure The material used in the present investigation was taken from the same heat of steel as that .used in a prior report.3 The finished strip in both cases was made by the Allegheny-Ludlum Steel Corporation according to methods that produce a high degree of preferred crystal orientation. Samples with large grains had the following composition: 3.45 per cent Si, 0.003 C, 0.008 P, 0.020 S, 0,075 Mn, 0.03I A1 and 0.072 Cu. Thickness of specimens was 0.012 inches. Plastic deformation was produced by cold-rolling the samples on a mill with 8-in. diameter rolls, the plane of the sample in each case coinciding with an XY plane (the plane of projection for the stereo-graphic plots) and the elongation occurring in the X direction. In general, elongations were held to about 3 or 4 per cent.

Jan 1, 1945

By D. A. Flanagan, B. L. Landrum, P. B. Crawford, B. C. Norwood

Herern is described a heat conduction model which has been developed to predict the pressure distribution within a reservoir being subjected to rrnsteady-state depletion. Although potentiometric models have been widely used to study reservoir pressure distribution, their application is limited to the study of steady-state cases. Electrical analyzers may be used to study unsteady-state phenomena, but their application and simulation have certain limitations. Much of the now accepted theory of unsteady-state fluid flow in porous media has evolved from previous heat conduction knowledge. An analogy between the flow of fluid in an unsymmetrical reservoir and con-duct ion of heat in a similarly shaped unsymmetrical metal plate is made to show adaptability of the hear conduction principle to transient reservoir cases. A description of the model and necessary instrumenrarion is included. Data show influence of well location on pressure distribution during unsteady-state deple[ion. Application of results is made to a hypothetical reservoir and to a reservoir located in an irregular aquifer. INTRODUCTION Development of methods for predicting behavior of petroleum reservoirs has resulted partially from adaptation of electrical and thermal flow concepts to the flow of fluids through porous media. Extensive investigation of electrical and thermal flow problems has resulted in mathematical solutions applicable to many reservoir problems. The relative ease of measuring electrical flow has brought wide acceptance of the use of the potentiometric model to study certain field problems. Potentiometric models are restricted to the study of steady-state conditions because of the instantaneous response of electrical flow to changes in the applied potential. The electrical reservoir analyzer has been one of our most useful instruments for studying certain phases of unsteady-state behavior1. Other than approximation techniques, no method exists for determining pressure distribution in an irregular reservoir during primary depletion. Heat flow, like fluid flow, is inherently transient. The model described here was developed to use this transient nature of heat flow, measurable in the laboratory, to simulate transient flow of fluids in the porous medium of the reservoir above the bubble point. A metal plate shaped like the reservoir to be studied was heated by a "well" source. Temperature increase in the plate is analogous to pressure decline in the field if the field is being depleted, or pressure increase if fluid is being injected. This study is intended to determine the feasibility of using the transient nature of the heat flow to study the transient behavior of fluid flow. It is hoped that this new technique will aid in the understanding of one of the more complex phases of reservoir engineering. THE FLUID FLOW-HEAT CONDUCTION ANALOGY The similarity of the equations which describe the flow of fluids through a porous medium and the conduction of heat through a solid is well known2. Rate of flow of fluids is given by Darcy's law3. while the rate of flow of heat is given by Fourier', (I,, - KA 4T........(2) Combining Eq. 1 with the equation of continuity for a compressible liquid", i.e.,results in Expressing y in terms of the compressibility, i.e., pr = peey ,..........(5) and by expanding the exponential and neglecting higher orders of cp one can obtain

By Walter Kauzman

ALL viscous or plastic flow of incompressible matter is the result of shear strain; the changing shape of any body that is being plastically deformed can be completely described in terms of the shear strain occurring at each point in the body.[t] Furthermore, the relative amounts of shear strain occurring in different parts of a body under stress depend upon the relative rates of shear strain at those different points, so that if the dependence of the shear rate of any material on the temperature, shear stress, previous history, etc., were understood, the principles of plastic deformation would be known, and we could calculate how a body made of a given material, having a given shape, and subject to a specified system of forces, would change its shape with time. It may be said, then, that the problem of plasticity resolves itself into, first, the problem of the rates of pure shear processes, and second, the application of what is known about pure shear to actual cases. It is the purpose of this work to investigate the former problem -i.e., the dependence of shear rates on temperature, stress, etc.-from the standpoint of recent developments in the field of chemical-rate theory and with particular reference to the phenomena occurring in the creep of metals and in the plastic flow of crystalline solids in general. It is left for the mechanical engineer, and perhaps the expert in hydrodynamics, to deal with the problem of applications.1 RESOLUTION OF MACROSCOPIC SHEAR INTO MICROSCOPIC MOVEMENTS; RESEMBLANCE TO CHEMICAL REACTIONS Just as any large body is made up of many small units, or atoms, so macroscopically observable shear is the result of many microscopic unit shear processes; just as the understanding of the behavior of large bodies demands the understanding of the atoms of which it is made, so the understanding of macroscopic shear demands the understanding of these fundamental unit processes. The study of shear from this "atomistic" point of view has made considerable progress. There has been fairly complete understanding of shear processes in gases for a long time, at least for nonturbulent flow, as a chapter on gaseous viscosity in any text on the kinetic theory of gases will prove. In recent years Andrade2 and Eyring3 have presented important theories for the flow of liquids and amorphous solids. Becker,4 Orowan,5 Taylor,6 Burgers,7 and Kanter8 have considered the

Jan 1, 1941

By Thomas Varley

IN THE congressional act establishing the Bureau of Mines one of the functions outlined was "to assist I the industry in the prevention of mineral waste." This had not only to do with the waste in mining but in milling and metallurgical practices, including smelting. The organization of the Bureau of 'Mines includes many divisions, each working in a particular field and charged with certain investigative work. The metallurgical division has the above duties under its immediate supervision, and the station located at Salt Lake City is directed by the chief of this division: There are ten experiment stations of the Bureau of Mines, located in various parts of the country, most of them being housed at state universities under cooperative agreements. Considerable care was exercised in locating the stations and in choosing the particular type of work to be investigated at each place. Inasmuch as the Bureau was designed to serve and cooperate with the industry it is only natural that the investigative work be of interest and importance to the territory immediately adjacent to the respective stations.

Jan 1, 1925

By A. W. Adamson

A model for transport processes in liquid mixtures is discussed which supposes that the elementary act involves a position exchange between two species and that the exchange is so confined by the solvent cage as to occur nearly isosterically. The rate-determining step, thus, is likened to a bi-molecular reaction and is so treated, using absolute rate theory. The cage model has been applied to diffusion, thermal diffusion, sedimentation and viscosity, but only the first and last of these phenomena are emphasized in the present paper. The model leads to semi-empirical relationships between the absolute value for a digusion coefficient and the activation energy for diffusion, between mutual and self-diffusion coefficients and for the variation of the viscosity of a binary mixture with composition. These are discussed in relation to experimental data for various systems, including hydrocarbon mixtures. It is shown that the proposed viscosity equation and seven other commonly used ones all may be regarded as special cases of a single general relationship; a brief critical analysis is made of the basis of selection of one or the other for data fitting or interpolation. INTRODUCTION AND GENERAL THEORY The present paper covers a brief discussion of a cage model for transport processes in liquid mixtures and how this model may be useful in treating the diffusional behavior and the viscosity of such systems. Since diffusion requires the more detailed treatment, it will be taken up first, and the model then applied to viscosity. There are two types of diffusion coefficients that may be measured experimentally, apart from thermal diffusion quantities. The first is the mutual or binary diffusion coefficient, D which may be defined in terms of Fick's first law. This states that the permeation, or flux P, is proportional to the concentration gradient. In the usual experiment, P is measured relative to a frame of reference fixed with respect to the medium (e.g., the diaphragm in a diffusion cell); as a consequence, the same value of D is obtained regardless of whether P and C refer to Component 1 or to Component 2; i.e., there is only one independent mutual diffusion coefficient for a binary system. In addition to D there will be various self-diffusion coefficients. defined in terms of the gradient in labelled species i and its permeation in an otherwise uniform medium. The thermodynamic approach to mutual diffusion supposes that the actual driving force is the gradient of the chemical potential, i.e., that In the case of a dilute solution of solute, Eqs. 1 and 3 lead to the Einstein equation, If the solution is ideal and the friction coefficient is taken to be then the familiar Stokes- Einstein equation results. Mutual and self-diffusion coefficients can not be related on general thermodynamic grounds; it is necessary to invoke some additional assumptions, i.e., a model; several such have been proposed. Hartley and Crank' supposed the existence of separate, intrinsic diffusion coefficients (Dl and D2) for each component, essentially corresponding to the two self-diffusion coefficients. The two flows can not be independent, however, but must be coupled through the usual restriction that there be no net volume flow. For an ideal solution. one then obtains' Glasstone, et al' treated diffusion in terms of absolute rate theory, but their approach otherwise resembled the previously mentioned one in that each species was considered to move with respect to the general medium in a manner determined by its individual jump distance and specific rate constant. For other than dilute solutions, a coupling of flows leading to an equation such as Eq. 6 would again be present. However, as required by Eq. 6, one does expect that the self-diffusion coefficient for the solute and the mutual-diffusion coefficient for the system become identical at infinite dilution. Lamm4 recognized that there should be three distinctive interactions in a two-component system-1-1, 1-2 and 2-2 — and, therefore, proposed three rather than two fundamental friction coefficients. Mutual diffusion resulted from 1-2 interactions only, and self-diffusion resulted from 1-2 plus either 1-1 or 2-2 interactions. Again, a collective coupling between all motions was imposed to meet the condition of no net volume flow. Laity' has shown how to convert the Onsager equations to a form very similar to Lamm's. Cage Model For Diffusion Work in this laboratory on diffusion in aqueous sucrose solutions made it apparent that three, rather than two, interactions were indeed needed," but considera-

By Alexander Anderson

TABLES showing the drift and inclination of wells surveyed in the years 1924 to 28' and in the year 1929' have already been published. Each of these tables included a little over 1,000,000 ft. of rotary hole. In the year 1930 the table -shown-in . Fig. 1, comprising, the results of surveys .of 1,030,344 ft. of hole and representing 11,642 individual survey readings, was compiled. For that purpose we selected 'I only wells that had been drilled in California during that year. The footage of Fig. 1 differs from the two earlier tables in that the wells were all drilled in the year 1930. In the earlier tables, the footage shown was surveyed in the years designated, but some of the wells were drilled in earlier years.

Jan 1, 1931

By R. W. Heckel, R. A. Tanzilli

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969