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By Brahm Prakash, R. Schuhmann

Chemical conditions for flotation and nonflotation of quartz with oleic acid as collector and barium, calcium, aluminum, iron, and tin as activators were studied using a simple vacuum-flotation technique in glass-stoppered graduates. The detailed study of barium activation led to an interpretation based on ideal Langmuirian chemisorption.

Jan 5, 1950

By Walter S. McKee

When mixed with common cast steel in quantities ranging from 11 to 131/2 per cent. and properly treated, manganese increases the ductility of the metal and adds greatly to its toughness and resistance to abrasive action, which properties comprise the distinctive characteristics that make manganese steel so valuable for many purposes at the present time.. * At present the manganese-steel foundries of this country have an annual capacity of about 60,000 tons and most of the growth has occurred within the past 10 years. In the early days of the industry it was impracticable to make manganese castings weighing over a few thousand pounds, but at present crusher heads, rolling-mill pinions, and similar castings weighing up to 30,000 Ib. each are produced, and it does not appear that the limit of weight has been reached by a considerable margin. Manganese steel is similar in analysis to ordinary first-class converter metal except that it is high in carbon and contains from 11 to 13.5 per cent. of manganese. From one standpoint manganese steel is similar to malleable iron in that the casting as it comes out of the sand is hard and brittle and must be made ductile by a heat-treating process. The heat treatment is an essential part of the process of making manganese-steel castings and must be properly carried out to secure satisfactory results. The necessity for heat treatment limits the thickness of sections which may be made of manganese steel. Originally the annealing depth was comparatively small, but researches carried on during the past few years have resulted in an increase in the thickness of section up to 51/2 in., which it is possible to treat successfully. Large castings are cored out to a minimum thickness of 51/2 in., thus not only eliminating some of the internal stresses which are invariably set up in a very thick casting, but also reducing the weight and inertia of the piece, an important consideration if the casting is to be a moving part in a machine. At the same time, the thickness of 51/2 in. is sufficient to permit the use of manganese steel for the heaviest classes of machinery.

Jan 1, 1916

By C. B. Foraker

THE Magma mine, of the Magma Copper Co., at Superior, Pinal County, Arizona, is 68 miles east of Phoenix and 21 miles west of Miami, Arizona, on highway U. S. 180. TEMPERATURES AND UNDERGROUND WATERS Surface Temperatures.-The average surface dry-bulb temperature at Superior is 72.4°; wet-bulb, 57.4°; with an indicated relative humidity of 38 per cent. The average yearly rainfall from 1921 to 1936, inclusive, was 18.74 in. The maximum condition of the atmosphere is in June, July and August, and the minimum is in January and February. The surface temperatures, of course, influence the temperatures of the down-cast shafts; however, the variation between winter and summer causes a difference of only 2° to 3° in the stopes and working places that are not close to the intake shafts. Average atmospheric conditions are shown in Fig. 1. Rock Temperatures.-Rock temperatures on the deeper levels of tile mine are as follows: LEVEL DEGREES LEVEL DEGREES 2000 109 3200 127 2250 112.5 3400 130 2550 116 3600 134 2800 120 3800 137 3000 124 4000 140 There appears to be no difference in rock temperature for any particu-lar horizon of the various formations or in the vein. Water encountered is always the same temperature as the rock from which it flows, and for this reason it is thought that the water is heated by the rock; not the rock by the water. The country rock apparently has been heated by the various intrusions, perhaps the vein itself, and has not yet had time to cool off. The geothermal gradient (Fig. 2) as indicated by the rock tem-peratures given above is 1 1/2 ° per 100 feet.

Jan 1, 1938

By C. H. Mathewson

ABOUT fifty pages of Henry M. Howe's profound treatise, "The Metallography of Steel and Cast Iron," are devoted to twinning with special reference to the origin, nature and general significance of the Neu-mann bands in ferrite. Howe believed with Osmond and Cartaud1 that the Neumanns are mechanical twins and his careful observations leave no doubt that these straight-sided narrow bands habitually occur parallel to trapezohedral planes of form {211}. Attempts to develop the structure of the bands by various methods so that their identity could be established beyond question have not been conspicuously successful. Howe thought that they deflected slip bands. Some of the etching figures which have been developed within and adjacent to Neumann bands support the contention that they are twins. A good example of this effect in ferrite containing 0.6 per cent. of nickel and 1.3 per cent. of phosphorus, originally due to Harnecker and Rassow,2. was reproduced in the 1928 lecture before the Institute of Metals Division on twinning in metals.3 In this case, the sides of the figures might represent the traces of cubic planes laid bare by etching a properly oriented grain of ferrite, twinned along a plane of form 12111. Our own observations in this direction may be represented by Fig. 1 which shows in a deeply etched cavity in the boundary region between a Neumann band and the original crystal two small crystal surfaces which resemble the faces meeting at a reentrant angle in the simple cube twinned along a bisecting plane of form {211} as sketched in Fig. 2. Rosenhain and McMinn4 in 1925, after a careful study of slip bands in ferrite containing Neumanns previously produced by shock, concluded

Jan 1, 1928

By Thomas Harris

This paper. was written in conjunction with the work being undertaken by the Technical Committees on Classification of Coal, and an effort has been made to compile information relative to the use of coal for stationary steam generation in order to use this information to assist the Committee on Classification of Coal for the ultimate purpose of elimination of losses both by the' reduction of indivi-dual effort and waste in the consumption of material. Under the auspices of the National Association of Purchasing Agents, a questionnaire was drawn up to develop this information from stationary steam plants throughout the United States. in order to consolidate the information de-veloped from the many hundreds of boiler tests on coals consumed by various coal¬burning equipment. These questionnaires covered: 1. The company reporting, location and method of delivery to the plant. 2. Complete coal date, including description of coals used (with. sufficient space to- include first, second and third, preference) on--source of coal used,- complete-analysis and factors affecting choice of, coal used. 3. Plant data, divided into - A. Hand fired, B. Overfeed stokers,. . C. Underfeed stokers, D. Traveling grate stokers, E. Pulverized coal, and included complete description of furnace data, draft data, coal-burning rate, type of stoker, type of pulverizer, efficiency date and remarks.

Jan 1, 1933

By H. L. Stone, A. O. Garder

A numerical method of solving the partial differential equations which describe the one-dimensional displacement of oil by gas has been presented. Possible extension of the method to treat multidimensional flow is discussed, and the limitations of this extension are indicated. Using this method, it is possible to allow for the existence of a gas cap, the presence of any number of gas-injection or oil-production wells and the evolution of dissolved gas from the oil. It is also possible to allow for variation in the cross-sectional area, elevation, porosity and permeability of the reservoir. The influence of relative permeability and the force of gravity in the direction of flow upon the displacement is considered. The influence of capillary pressure upon the flow and the effect of gravity in the direction perpendicular to flow are neglected. The physical properties 01 the fluids are considered to be Junctions of pressure only, and equilibrium between contiguous phases is assumed. The numerical calculations can be readily carried out by the use of a digital computer. Several example analyses have been performed using the IBM 704 computer, and about one-third of an hour of computing time was required per case. Reservoir behavior predicted by use of this numerical method was compared to data obtained by other methods for three cases — complete pressure maintenance, dissolved-gas drive and gas-cap drive. The independent solutions to these problems were obtained by analytical solution, laboratory experiment and field data, respectively. Agreement of the numerical solution with data from these sources was good; this agreement establishes the convergence and accuracy of the numerical method. INTRODUCTION Most petroleum reservoirs can be produced by any one of several alternative programs. When a reservoir is produced by primary methods, production economics can be influenced by controlling the number and location of wells and the flow rate of each well. An even greater influence may be achieved by augmenting the recovery of oil obtainable by primary methods. This can be accomplished by injection of fluids such as water, natural or enriched gas or a bank of light liquid hydrocarbons. Selection of the most desirable operation requires a means of predicting the reservoir behavior which will result from each of the several alternative programs. The purpose of this paper is to present a mathematical method for predicting the behavior of reservoirs produced by gas-cap drive, dissolved-gas drive or pressure maintenance by gas injection. The method described herein takes cognizance of phase changes caused by a decline or an increase (due to gas injection) in reservoir pressure, of the presence of a gas cap and of the effect of gravity on the flow of gas and oil. Relative permeability relationships are used to define the flow properties of the rock. Allowance is made for variation in cross-sectional area, elevation, permeability and porosity of the reservoir. Both the influence of capillary pressure upon the flow and pressure gradients in the gas cap are neglected. Whenever a liquid phase and a gas phase are in contact, they are assumed to be in equilibrium. The physical properties of the fluids are considered to be functions of pressure only. Therefore, if the method is to be used to predict the effects of a gas-injection program, mixtures of the injected gas and formation crude should-have the same physical properties as mixtures of formation gas and crude. The equations to be presented in this paper apply only to a one-dimensional case; therefore, they neglect the influence of gravity in the direction transverse to the flow. As is well known, this gravitational influence may lead to overriding of oil by gas. Consequently, this procedure as presented is most applicable to long, thin reservoirs for which gravity overriding is not important. On the other hand, the equations presented can be generalized to treat multidimensional flow and, hence, to consider gravity overriding, if desired. A word of caution on two points is advisable here, however. First, the authors have not demonstrated the accuracy of the numerical technique for multidimensional flow. Second, and more important, capillary pressure will often be of importance in multidimensional problems. Obviously, in such cases a generalization of the

C. N. FEnner, New York City (communication to the Secretary) : A possible explanation of some of the' phenomena of amalgamation cited by Mr. Bayliss and others has occurred to me. We know that if, to a quantity of mercury, gold and silver are added until a putty-like paste is formed, and if this mass is spread on a flat surface and pressure is applied, a more fluid portion of the mercury will be squeezed out from the rest, carrying gold and silver with it. The proportion of gold to silver will depend, I think, upon various causes and conditions—the relative chemical affinity which gold and silver have for mercury; the amount of pressure used; the presence of other metals:

Jan 1, 1898

By John V. Beall

There was optimism on 14th Street on April 22, Earth Day. We only have the report second hand because the demonstration conflicted with another appointment. Fifth Avenue was closed to vehicular traffic from 14th Street to the Park for a few hours and the crowd that showed up to promenade rivaled anything that can be imagined, even one at a country fair in Merry Old England. Certainly the domestic animals were there and the costumes were wild-as they are almost any day on 5th Avenue. However, the mood was friendly, happy and optimistic according to one of our neighbors who filmed and taped interviews with some of the characters. People think the air is going to be clean, and the water pure in the future. Land is going to be treated with respect. Even if the demonstration temporarily fouled the streets with litter, it served the purpose of dramatizing awareness. In talking to our friend about his experiences we didn't miss the opportunity to sound out his impression of whether or not people recognize that no group of people nor industry has a monopoly on pollution.

Jan 1, 1970

By Stanley J. LeFond

Jan 1, 1985

By Bahrein Petroleum Company

In Comodoro Rivadavia, well 8. 132, drilled in zone No. 2, has discovered between 5205 and 5297 ft., the dcepest pool yct found in this field. The oil production in Bahrein for the year 1939 totaled 7,588,554 bbl., a decline of 709,444 bbl. from the 1939 production of 8,297,998 bbl. The production for the first seven months of 1939 remained fairly constant, the daily average by months during this period ranging between 20,000 and 22,000 bbl. per day. The daily average rose in August to the year's high of 23,800 bbl. per day, then dropped gradually to the year's low of 18,787 bbl. per day for November. The daily average for the year was 20,791 bbl. At the end of 1939 there were 59 wells producing and 8 wells drilling.

Jan 1, 1940

By Bahrein Petroleum Company

In Comodoro Rivadavia, well 8. 132, drilled in zone No. 2, has discovered between 5205 and 5297 ft., the dcepest pool yct found in this field. The oil production in Bahrein for the year 1939 totaled 7,588,554 bbl., a decline of 709,444 bbl. from the 1939 production of 8,297,998 bbl. The production for the first seven months of 1939 remained fairly constant, the daily average by months during this period ranging between 20,000 and 22,000 bbl. per day. The daily average rose in August to the year's high of 23,800 bbl. per day, then dropped gradually to the year's low of 18,787 bbl. per day for November. The daily average for the year was 20,791 bbl. At the end of 1939 there were 59 wells producing and 8 wells drilling.

Jan 1, 1940

By A. G. Starliper, H. Kenworthy, A. Ollar

Vapor pressure determinations were made on synthesized germanium sulfides. Germanium and cadmium were removed from sphalerite concentrates by fuming. The fume was retreated to separate some of the cadmium from the germanium and, at the same time, upgrade the germanium to more than 5 pet content. MANY sphalerite concentrates contain certain impurities which have economic value as byproducts. These may include the volatile sulfides of germanium, cadmium, and lead. The objectives of the research reported in this paper were to study the fundamental volatility characteristics of germanium sulfides, to increase the recoveries of ger-

Jan 1, 1957

By H. F. A. Hergt, K. L. Sutherland, J. Rogers

In 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group — SO4- or — SO3- are excellent collectors for cassiterite and promise to be selective. The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000-gram Denver cell. Experimental Methods Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously de- scribed.5,10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these the determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver SUbmachines,—Melboume tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By J. Rogers, H. F. A. Hergt, K. L. Sutherland

In 1938 Ralston4 reviewed the many attempts to find a satisfactory collector for the separation of cassiterite from its ores and in 1944 Dean and Ambrose2 summarized some further attempts. Generally, soaps and amines are effective but nonselective collectors. We have discovered that reagents containing either the polar group — SO4- or — SO3- are excellent collectors for cassiterite and promise to be selective. The response to these reagents of cassiterite and of minerals commonly associated with it was studied, using the captive-bubble technique. Using these fundamental data, the practicability of separation and concentration of tin was investigated by flotation tests in a 2000-gram Denver cell. Experimental Methods Reagents All inorganic reagents were of Analar grade. The preparation and purification of sodium cetyl sulphate, cetyl trimethyl-ammonium bromide, laurylamine and cetylamine have been previously described.5 The other collectors were commercial surface-active agents, which were used without purification. Tests Captive-bubble Tests and Cylinder Flotation Tests have been previously de- scribed.5,10 The full lines shown in the figures relating solution composition to contact (flotation) distinguish solutions in which contact (flotation) is possible from those in which it is not. The curve is derived by successive approximation and the accuracy is ±0.2 pH units and ± 5 mg. per liter of collector or depressant. Solution compositions for which it was shown experimentally that contact or flotation is possible are marked by a circle, those for which it is not possible, by a cross, and those for which it is doubtful by a cross within a circle. It is assumed that at all other solution compositions within (without) the curve, contact or flotation is possible (not possible). After testing in the collector solution, the mineral was removed, washed, and tested by the captive-bubble method in water, or floated in a cylinder with frother only. In this way the composition of solutions in which a mineral was conditioned but in which properties of the collector solution prevented contact or flotation can be defined. The composition of solutions in which conditioning was possible lie between the full and broken curve, and the experimental results are indicated by a square. The curves show the limits of composition of solutions in which flotation in a cell would be possible but many factors other than those considered in these the determine recovery and grade of a given mineral in practice. Flotation Tests in 500 and 2000-gram Denver SUbmachines,—Melboume tap water, containing 12 parts calcium, 6 parts

Jan 1, 1947

By V. A. Josendal, J. W. Wilson, B. B. Sandiford

Two radioactive tracers have been tested as a means of determining core saturation in multiphase flow studies. Cesium chloride was tried as a water-phase tracer, but complications in its use in low permeability cores resulted from sorption of cesium by the core or water-wet pads. IodoI3'ben-zene proved very satisfactory as an oil-phase tracer. The synthesis of iodobenzene from the sodium iodide as received from Oak Ridge is simple and direct. The tracer is insoluble in water and there was no evidence of sorption by any of the core materials used. use of the method to determine saturation profiles during capillary and dynamic desaturations and relative permeability measurements on oil-water and oil-gas systems is described. Comparisons of the dynamic and capillary methods of relative permeability determination were made using the tracer to check core saturation and saturation distribution. Other experiments are also described in which mobility of the oil phase at various saturations was measured by displacing labeled oil by flowing inactive oil. Similar experiments were made using water labeled with cesium 134. INTRODUCTION To be fundamentally sound. any laboratory method of determining relative permeability must meet, among others, the following requirements: (1) the core saturation between the pressure taps must be uniform, and (2) there must be uniform pressure difference between the phases in the region between the pressure taps. In practice it may eventually be shown that appreciable departure from either or both of these conditions may be permitted without introducing sensible error. but the magnitude of such error remains to be established. There is need then for methods of saturation determina- tion which will determine the saturation profile in a core as well as the overall average saturation given by the gravimetric or material balance methods usually employed. Methods which have received consideration include resistivity, X-ray absorption, gamma ray absorption, neutron diffraction, and radioactive tracers. The resistivity method has use in the determination of profile, but needs checking by independent means.' The X-ray method has been used successfully, but requires elaborate equipment and calibration.23 4 At present gamma ray absorption is practical only for very large cores. The neutron methodo does not appear adaptable to measurement of saturation variations in short cores since it is a scattering method. Russell, Morgan and Muskat' employed radiovanadium in a study of the mobility of interstitial water. Coomber and Tiratsook used radioiodine as an oil-phase tracer and measured profiles in unconsolidated sand packs. ADVANTAGES OF RADIOACTIVITY METHOD A thorough discussion of the theory of radioactive tracers and the technique of using them to study the movement of fluids in sands is given by Coomber and Tiratsoos and need not be detailed here. The method requires less equipment than the X-ray method; the counting problem is similar, but the generation and regulation of the radiation, which is a major problem in the X-ray method, is not required in the radioactivity method. In the X-ray method it is customary to add up to 20 per cent of absorber, usually an iodine compound, to the phase to be labeled. while in the radioactivity method a mere trace is sufficient. A possible disadvantage of the radioactivity method is that a disproportionate amount of the activity comes from the portion of the core nearest the counter, whereas the X-ray gives a true average saturation in the region traversed by the beam. 011 the other hand, this characteristic of the radioactivity method renders it peculiarly adaptable to study of certain types of radial variations in saturation. As with the X-ray method, a tracer may be added to either the oil or water-phase. An oil-phase tracer is more generally useful. however. since it permits work on oil and gas in the

Jan 1, 1952

By J. A. Church

I. Early Furnaces,......423 11. Experiments with the HIgh-Shaft FURnace,..... 426 III. ExperMents wIth the Wide FURnace,..429 IV. ExperEentS with Extreme BOSH,... 43.2 V. Survival of the 56 by 180 IN. Furnace,.434 VI. Recent ExpeEiments,.....436 VII. SUMMary,........438 I. Early Furnaces. Copper blast-furnace construction in America has long recognized a general standard in the rectangular water-jacketed shaft with separate forehearth. The details, however, and especially those relating to shaft dimensions, have had to meet a great variety of conditions, and show no uniformity whatever. Selecting a few of the present day Western plants, we find furnace lengths varying from 12.5 to 87 ft., widths at tuyere level from 42 to 84 in., and heights above tuyeres from 5 ft. 4 in. to 22 ft. 4 in.; and comparing present designs with those of the past, we meet contrasts no less striking. Unlike its transverse section, the length of a furnace has come to depend rather on the size of unit desired than on the requirements of smelting; and if the question of length be ignored, several of the various existing designs can be grouped together on the basis of a common transverse section. This section, having a width at tuyere level of 56 in. and a height above tuyeres of 18 ft., was developed at Great Falls, and the story of its development contains some interesting features. Ground was broken for the Great Falls works in the spring of 1891. About a year later, the concentrator was able to begin operation, followed within the next few months by the Brueckner, reverberatory, and converter departments, and in April, 1893, by the first blast fur-

Jan 1, 1914

By J. L. Huiatt, D. G. Foot

The Bureau of Mines, U.S. Department of the Interior, investigated methods of recovering potash values from process and waste brines. Laboratory pan evaporation of four chloride brines produced crude salts containing predominantly sylvite, halite and carnallite. Six sulfate- chloride brines produced crude salts containing primarily schoenite, kainite, leonite, sylvite, carnallite, and halite. Potash grades ranged from 7.2% to 22.2% K20, and recoveries by crystallization ranged from 85% to 99%. Sylvite flotation from chloride evaporites with amine collector, recovered 90% to 97% of the potash in a concentrate containing 54.3% to 60.3% K20. Fatty acid flotation of the high sulfate evaporite recovered 78% of the sulfate minerals in a 28%-K20 concentrate. Flotation of the remaining chloride minerals with amine collector recovered 80% of the potash in a 59.7%-K20 concentrate. Solar evaporation of 37 854 L (10,000 gal.) of brine recovered 99% of the potash in a crude evaporite containing 24.5% schoenite and 20% sylvite. Flotation in a 45-kglh (100-lblh) continuous flotation unit recovered over 95% of the potash in schoenite and sylvite concentrates, containing 28% and 62.3% K20, respectively. An economic evaluation is included.

Jan 1, 1985

NEW MEMBERS The following list comprises the names of those persons who became members during the period Dec. 10, 1915 to Jan. 10, 1916. ANDERSON, FRANK BASIL, Min. Engr., Sampler, Copper Queen Cons. Min. Co., Bisbee, Ariz. BAILEY, LEWIS NEWTON, Min. -Engr 4227 St. James Place, Sail Diego, Cal. BELL, JAMES E., Min. Engr., Care Chile Exploration Co., Chuquicamata, Chile, South America. BONILLAS, YGNACIO SAFFORD, Min. Geol., Copper Queen Cons. Min. Co., Bisbee, Ariz. BRADLEY, GEORGE OLIVER, Mech. Engr Hobart Bldg., San Francisco, Cal. CLARK, GEORGE L., Min. Engr Vipond Mine, Schumacher, Ont., Canada. CONKLING, RICHARD A., Geol., Roxana Petroleum Co. of Oklahoma, Tulsa, Okla. GOHRING, W. B.. Geol., Supt. of Mines, Calumet and Arizona Min. Co., Warren, Ariz.

Jan 2, 1916

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

THE primary interest in the subject of this chapter lies in the fact that various heats of steel made to the same chemical specification do not always have the same properties. The properties considered here, of course, are those inherent in the ingot immediately after solidification and not qualities imparted by variations in subsequent mechanical or thermal treatment. The expression "made to the same chemical specification" is used because some of the variations in properties are due to variations in chemical analysis within the specified ranges of those elements commonly specified and determined. Other variations in properties are due to variations in those constituents of steel (elements or compounds) that are not ordinarily included among the elements specified, thus not a part of the specified "composition." The term "constitution" is used to include not only the specified composition but also the nature and distribution of every element or compound contained in the steel entering the ingot mold ; also included are items such as aluminum oxides and nitrides, presence of soluble gases, and dispersion of nonmetallic particles. When it is considered that the constitution of steel is determined by the addition or absorption into the bath of all such constituents from whatever source, it follows that constitution is of necessity the final result of steelmaking practice. It is the agency through which steelmaking practice operates to control the properties of the steel. The term steelmaking practice is here used in the broad sense, meaning the control of all the materials entering the steel and of the conditions under which the process is carried out. Steelmaking practice, thus defined, establishes the chemical system within which the reactions between components must proceed in obedience to the laws of chemistry. Thus the chemical constitution of the steel is established and, through constitution, the properties of the metal are established. In the preceding chapters it has been shown how the constitu-

Jan 1, 1964