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By A. M. Rowe

A considerable quantity of experimental hydrocarbon K-factor data has been correlated as a function of component identity, temperature, pressure and convergence pressure. To utilize these correlations effectively, convergence pressure must be determined accurately, particularly for volatile mixtures near their critical states. This paper presents phase diagrams that illustrate physically the meaning of convergence pressure. A new method, referred to hereafter as the "critical composition method", will be outlined for calculating convergence pressure. An example calculation has been included to illustrate how to use this new technique. INTRODUCTION The principle of hydrocarbon phase composition calculations as applied to such diverse problems as optimizing separator performance or predicting fluid compositions at various stages of reservoir depletion is the same. Usually, temperature, pressure and the numbers of moles of the various components of the fluid contained in a given volume are known. Questions answered by the phase calculation are what fraction of the total mass of fluid exists in each of the equilibrium phases, and what are the mole fractions of the various components in the two phases? To answer these questions the Natural Gasoline Supplymen's Assoc. (NGSMA) has correlated a considerable quantity of K-factor data as a function of temperature, pressure, component identity and convergence pressure.l To use these correlations to obtain the best answers possible, one must be able to calculate the convergence pressure. This is particularly true for over-all fluid compositions in the neighborhood of the critical state. STATEMENT OF THEORY Use of convergence pressure as a correlating parameter is based on a postulate similar to the law of corresponding states used in correlating PVT data of hydrocarbon gases. This postulate, which proposes convergence pressure as a correlating parameter, has been stated as follows: "The equilibrium vaporization constant for one component in a complex system is the same as the equilibrium constant at the same temperature and pressure for the same number or kind of components, providing only that the convergence pressures of the two systems are exactly the same at the same temperature and that the components are of the same homologous series".2 This law, as with all laws of physics, cannot be proven theoretically. It can only be justified by experimental data supporting its premises. Arguments have been made that this law violates Gibb's phase rule. For example, consider a four-component system. By Gibb's phase rule, which is thermodynamically rigorous, f = c — P + 2 =4, for a four-component, two-phase system. Thus, four independent intensive variables must be specified to establish completely all the intensive variables of the equilibrium phases. On the other hand, according to convergence pressure theory, only three variables need be specified for any mixture containing four different components. These variables are temperature, pressure and convergence pressure. Thus, the two laws appear to be in conflict. However, the convergence pressure postulate is more restrictive than Gibb's phase rule. It applies only to mixtures of the same homologous series. Hence, these two concepts are not in disagreement. PHASE DIAGRAMS DESCRIBING CONVERGENCE PRESSURE This paper presents phase diagrams grading from the simple two-component system to the more complex four-component system to illustrate convergence pressure. A less abstract definition of convergence pressure will be stated that is

By J. E. Pogue

That the domestic consumption of gasoline displays a marked seasonal variation, with a low in the winter and a high in the summer, is well known. It is logical to expect that the nature of the variation has itself been undergoing a change as a result of improvement in roads, general employment of closed cars, and growth of mass haulage; but so far as I am aware the change in seasonal variation has never been investigated and measured. It is the purpose of this paper to present the method and results of such an investigation, undertaken as a contribution to the technique of planning operating schedules now so prominent in connection with the functioning of the industry under a Federal quota system. For the method employed I am indebted to the suggestions and help of Frederick R. Macaulay,1 who kindly looked over the work sheets; and

Jan 1, 1934

By Paul Weir

DURING the past decade, methods of producing bituminous coal in the State of Illinois, which ranks third in production among the states in which bituminous coal is mined, have undergone great changes. From less than one million tons in 1923, the strip-mine production has gradually increased to a high of 11,725,870 tons in 1937. From a negligible amount prior to 1927, the amount of coal mechanically loaded underground had increased to a high of 28,374,362 tons in 1937. The amount manually loaded in 1937 reached a low of 12,332,023 tons. In this same year, this state ranked first in strip-mine production, also in mechanically loaded production. For this reason a study of the influence of mechanization on location of production in Illinois may be helpful in anticipating what may happen in other producing states. The reason for the changes in methods lies in the differences in costs of production. The Bureau of Research and Statistics of the National Bituminous Coal Commission has made public the following costs of pro-duction by various methods in the State of Illinois (district 10) for the last nine months of 1937: all mines, $1.7602 per ton; strip mines, $1.4319; mechanical loading mines, $1.7457; hand loading mines, $2.1793; all underground mines, $1.8703. These are weighted averages for the entire district. Inasmuch as production in 1937 was reported from 58 counties scattered over two-thirds of the area of the state and from five different seams varying in thickness from less than 3 ft. to as much as 12 ft., it is apparent that the location of production must be influenced by the extent of mechanization possible in the various producing counties.

Jan 1, 1939

HAVING taught you to make aqua fortis and to cleanse and reduce it to perfection, before I teach you the work of parting on a large scale, I wish now to teach you how to make an assay of the amount of gold present in a quantity of silver, so that you may proceed to your work with open eyes in order to become aware of mistakes when you have erred yourself or have been deceived by someone else. Therefore it is necessary to know very exactly, before you take it out, how much gold should be in your cucurbits from the weight of the silver that you put in. Thus you may see the gain or loss, if you had to deliver it to someone else or if you had bought it. If you did not do this you would proceed blindly in your work.

Jan 1, 1942

The resolution drafted by J. W. Richards, J. V. N. Dorr, and Allen H. Rogers on the death of J. E. Johnson, Jr., and adopted by the Board of Directors, is as follows: "The Boards of Directors of the American Institute of Mining and Metallurgical Engineers wishes to place on record its great personal loss in the sudden death of Mr. J. E. Johnson, Jr., our fellow Director of the activities of the Institute, a member our Executive Committee, Chairman of the Institute's Committee on Admissions, and Vice-chairman of its Iron and Steel Committee. "A mere recital of these positions of trust and responsibility, which he filled with conscientious efficiency and marked ability, shows how greatly the Institute has lost by his death. No one else of the Institute's officers could have been so illy spared. We, his colleagues, take up his tasks with a sense of our inability to discharge them as well as he, and this with a doubled sense of our loss. "Others have written and spoken of the blow which his death has been to the furtherance of the metallurgy of iron and steel. His pre-eminence in this line is one of the facts of which the Institute is justly proud. Here his personality, originality, courageousness in advocating new principles, clearness of writing and forcible presentation of facts, are irreplaceable. His two great treatises on the blast furnace are his literary and scientific memorial.

Jan 7, 1919

By H. E. Howe, A. A. Smith

E. Schumacher.*—Mr. Smith has shown us once again how variable lead alloys can be. I have studied lead alloys for a good many years and know from experience that their behavior cannot be predicted by analogy with other alloys. I have always been interested in observing how the creep resistance of lead may be improved by the addition of as little as 0.03 per cent Ca. Without the presence of calcium the grains of extruded lead pipe are fairly equiaxed and motion can take place easily at the boundaries. The calcium addition of 0.03 per cent causes the grain boundaries to become very irregular and jagged, and results in creep resistance many times greater than that of pure lead. Mr. Smith showed that in the one per cent antimony-lead alloy creep is occasionally excessive even where low stresses are involved. We have observed this phenomenon many

Jan 1, 1945

The Institute makes liberal provision for inclusion of engineering students through individual Student Associate membership. Such members pay $2 per year, receive MINING AND METALLURGY, may purchase Technical Publications at reduced rates, have the privilege of attending all meetings and are furnished a distinctive badge in the form of a watch fob. Provision is also made for the affiliation of organized student societies in recognized schools of engineering chemistry, geology and related sciences. In order to qualify for affiliation it is not necessary that all members of the society become Student Associates since the individual members of the society are not listed as members of the Institute However, a large majority of the members of many of the societies are also Student Associate Members of the Institute. Among the things that the Institute does for the affiliated societies are the following: (a) A copy of each issue of MINING AND METALLURGY is furnished to the society; (b) Reports of the meetings and activities of the society are reported in MINING AND METALLURGY; (c) Assistance is given by the Institute in obtaining speakers for the meetings of the society; (d) The name of the society and of its officers is listed in the annual Directory and other publications of the Institute; and (e) Members of the society are given the use of the Engineering Societies Employment Service. Student organizations, desiring to be recognized as affiliated student societies of the Institute, should make application to the Secretary, giving particulars as to the nature of their organization, of their membership, and their officers. The accom¬panying list on page 24 gives the names of the affiliated student societies, their presi¬dents and their secretaries, as of April 17, 1931.

Jan 1, 1923

By A. D. McMaster, M. L. Gimpl, N. Fuschillo

There is interest in the use of rhenium metal films as resistive elements in thin-film circcits, and already some zvork has been done using er)aporated rhenium films. It has been found that rheniim films protected from the atmosphere by an evaporated layer of silicon monoxide show excellent electrical stability. Unprotected films, however, are subject to aging- effects, notably the increase in electrical resistivity as a function of time. This phenomenon can be understood as primarily one of oxidation of the thin films. This paper is concerned with the study of the oxidation and crystallization behavior of such unprotected films. It has been found that the oxidation rates are a function of the substrate temperatures used during the deposition of Lhe metal films. The strictures observed in the films are correlated with the film resistivities and some data are presented to establish the existence of the various types of oxides of rhenium. ThERE is some interest in the use of thin films of rhenium metal as resistive elements in monolithic, thin-film integrated circuits. Some work has been done using evaporated films and it has been found that such films, if protected from the atmosphere by an evaporated layer of silicon monoxide, show excellent electrical stability up to temperatures of 500"." Rhenium films unprotected from the atmosphere tend to age and the electrical resistivity of the films increases as a function of time. Rhenium films, of the order of <100A thick, prepared by electron-beam evaporation techniques are found to oxidize very readily when exposed to dry air at room temperature. It would seem, therefore, that this aging phenomenon could be attributed to the oxidation of the metal films. In this investigation, the oxidation and crystallization behavior of thin films of rhenium evaporated onto silicon monoxide substrates were studied as a function of the substrate temperatures used during the evaporation. The films were examined using electron-microscopy and electron-diffraction techniques. EXPERIMENTAL RESULTS Rhenium metal was evaporated onto suitable prepared substrates which were heated to various temperatures. The evaporations were performed in a vacuum of approximately 5 x 1CT5 torr. The evaporation was carried out at a rate of approximately 10A per omin. The final film thickness was approximately lOOA and the resistance ranged from 5000 to 10,000 ohms per square. The substrates used for supporting the metal films were made by evaporating 75A of silicon monoxide onto freshly cleaved mica. The silicon monoxide film was then floated off the mica by immersing the composite in water. The film could then be picked up on a clean nickel grid. Silicon monoxide substrates were chosen because of their similarity to quartz and glass substrates commonly used for making thin-film resistors. Fuschillo, Gimpl, and McMas-ter have also shown that silicon monoxide films have only minor structural changes at temperatures up to 800°C. This fact simplified the interpretation of any changes observed in the electron micrographs or electron-diffraction patterns obtained from the deposited rhenium films. After the evaporations were completed, the substrates were cooled to room temperature, except where noted differently, before the coated substrates were removed from the vacuum system. All aging of the deposited films was done in a desiccator. The evaporated films were examined in an electron microscope equipped with a hot stage that would permit continuous observations of the samples up to temperatures of 1000°C. RESULTS A series of electron micrographs of the rhenium films deposited on the silicon monoxide substrates are shown to Figs. 1 to 3. In all cases, the metal films are approximately 100A thick and the micrographs were taken 1 hr after the deposition was completed. here was no apparent structure in the films deposited on the substrates held at the higher temperatures. The

Jan 1, 1967

The Institute makes liberal provision for inclusion of engineering students through individual Student Associate membership. Such members pay $2 per year, receive MINING AND METALLURGY, may purchase Technical Publications at reduced rates, have the privilege of attending all meetings and are furnished a distinctive badge in the form of a watch fob. Provision is also made for the affiliation of organized student societies in recognized schools of engineering, chemistry, geology and related sciences. In order to qualify for affiliation it is not necessary that all members of the society become Student Associates since the individual members of the society are not listed as members of the Institute. However, a large majority of the members of many of the societies are also Student Associate Members of the Institute. Among the things that the Institute does for the affiliated societies are the following: (a) A copy of each issue of MINING AND METALLURGY is furnished to the society; (b) Reports of the meetings and activities of the society are reported in MINING AND METALLURGY; (c) Assistance is given by the Institute in obtaining speakers for the meetings of the society; (d) The name of the society and of its officers is listed in the annual Directory and other publications of the Institute; and (e) Members of the society are given the use of the Engineering Societies Employment Service. Student organizations, desiring to be recognized as affiliated student societies of the Institute, should make application to the Secretary, giving particulars as to the nature of their organization, of their membership, and their officers. The accompanying list on page 21 gives the names of the affiliated student societies, their presidents and their secretaries, as of April 16, 1933.

Jan 1, 1932

On Apr. 21, the Victory Liberty Loan was offered to the public. This Loan is made necessary by the expenditures incident to closing of the war. As in preceding Liberty Loans, an intensive campaign is being conducted, and this Committee is to obtain and record subscriptions from the Industry of which you are a part. I am sure you feel as I do in wishing the Mining Committee to make as good a showing as possible. By placing or recording your subscription through us will help your Committee to make its proper showing, and, as heretofore, your transaction can he carried out with any bank or trust company you may prefer to designate. Payment may be made in full or in six instalments. In either case, 10 per cent. will be required on or before May 10. Subscription blanks will be mailed to you as soon as available. CHARLES HAYDEN, Chairman.

Jan 5, 1919

A High-speed Dilatometer and the Transformational Behavior of Six Steels in Cooling. By Arthur L. Christenson, Edward C. Nelson and Clarence E. Jackson. (With discussion).................................606 Dilatometric Studies of the Graphitization of Cast Iron. By N. A. Ziegler. With discussion) 627 An Interferometer Type of Dilatometer and Some Typical Results. By- L. &apos;4. WIlley and W. L. Fink. (With discussion).........................642 The meeting was held in the Pine Room of the Statler Hotel, Cleveland, Ohio, on Tuesday afternoon, October 17, 1944. The chairmen were F. M. Walters, Jr. and Howard Scott. Introduction F. M. Walters, Jr.—The principal advantages of the dilatometric method perhaps are two, as compared with the method of thermal analysis. One is that the dilatometric method can be applied with a large variety of rates of heating and cooling, whereas thermal analysis—that is, the study of the transformational characteristics by means of heat evolution—is limited to the rates of heating and cooling that reveal the evolution of heat. The dilatometer can be used for the study Of reactions at zero rates of heating and cooling; that is, isothermal reactions. As you will hear this afternoon, the rates have been pushed up as far as 500°C. a second. The other advantage is that the dilatometric method shows that a two-phase region is a two-phase region, whereas the thermal analysis merely reveals the temperature at which the rates of heat evolution are greatest.

Jan 1, 1945

Jan 1, 1949

By W. J. Reagan

Mr. Caine, members and friends of the AIME Electric Furnace Conference, as Chairman of the Executive Committee it is my pleasure to welcome you to this our fifth annual conference. I can assure you that the conference chairman and his committee have prepared a program of unusual and timely interest. Mr. Caine has spoken of the educational session. This part of our program was of unusual interest last year and I am sure that the subject of this year&apos;s discussion will prove to be just as interesting. The wide variety of subjects cover both the basic and the acid electric furnace and are in keeping with the usual high quality maintained on our programs in past years. As the papers and discussions will be published in the PROCEEDINS, you will in a short time be able to add another volume to the present series.

Jan 1, 1947

By Thomas E. Garnar

Zirconium and hafnium are curious elements because they are almost always found together in nature. Zirconium was discovered by Klaproth in 1789 and isolated 35 years later by Berzelius. Because hafnium&apos;s chemical properties are so close to those of zirconium, it was not discovered until 1923 when Coster and Von-Heresey detected it using x-ray spectrographic analysis. These elements occur most commonly in nature as the mineral zircon (ZrSiO4) and less commonly as the oxide baddeleyite (ZrO2). They also are found as a variety of other silicates. Zircon was identified as a component in alluvial and beach sands in 1895, but it was not produced in any quantity until 20 years later. Zircon is always a coproduct from TiO2 mining and processing. During World War I it was produced as a coproduct of beach sand mining for titanium minerals just south of Jacksonville Beach, FL, and was patented as a refractory. It was not until the 1930s when Zircon Rutile, Ltd. began mining at Byron Bay on the east coast of Australia that zircon was first used as a foundry sand. Later in the 1940s, NL Industries, Humphreys Gold Corp., and E. I. du Pont de Nemours & Co., Inc. began production of zircon sands from fossil beaches in northeast and northcentral Florida. Baddeleyite first became available as a commercial product in 1916, but never in the quantity of zircon. Zircon holds a unique position as an industrial mineral because it is used for both its physical and chemical properties as well as an ore of zirconium and hafnium metals. Australia is the major zircon producer followed by South Africa and the US. Zircon is also produced in India, Sierra Leone, Sri Lanka, Malaysia, China, Thailand, and Brazil. Undeveloped heavy mineral beach sand reserves containing zircon are known to occur in Egypt, Malawi, Senegal, and Tanzania. Locations are shown in Fig. 1. Mineralogy Zirconium and hafnium are always present together in naturally occurring compounds. Most commonly they form as the silicate sometimes containing iron, calcium, sodium, manganese, and other elements. Less commonly they are found as oxides in combination with titanium, thorium, calcium, and iron. Zircon is the most common form. It is extremely resistant to weathering, therefore, often it is present in ancient beach sands and placer deposits. Although resistant to alteration from external sources, it is vulnerable to internal alteration as the result of thorium and uranium substituting for zirconium either in the zircon lattice or in solid solution. Alteration to the metamict state takes place as radioactive emanations from these elements disorder the crystal lattice, accompanied by hydration, reduction in specific gravity, and changes in color. The mineralogy of zircon and baddeleyite and variation of physical and chemical properties are shown in Table 1. The effects of zircon&apos;s internal alteration and darkened color can be corrected by heating to 1000°C for 30 min or so. A certain time-temperature relationship makes it possible for decolorization and reordering of the crystal lattice to take place when heating at higher temperatures for shorter periods or at lower temperatures for longer periods. After heating, x-ray diffraction patterns are sharper, the grains may be harder, and except for particles of malacon, the grains will be white or colorless in the absence of grain surface coatings. The color change is only temporary and the particles slowly darken with time. Zircon fluoresces light yellow in shortwave ultraviolet light. If exposed to ultraviolet light for extended periods of time, white (calcined) zircon turns purple. With time the induced color begins to fade and eventually disappears (e.g., calcined Florida zircon exposed to ultraviolet light for 24 hr still retains faint, but discernible, purple color after six months).

Jan 1, 1983

By C. R. Boyd

In 1874 I received an appointment in the corps organized by Col. William P. Craighill, U. S. Engineers, to survey the New or Upper Kanawha river for the purpose of ascertaining the practicability and

Jan 1, 1895

By C. B. Manula, H. Gezik

In planning modem-day mining operations, management needs to pass from the area of subjective decision-making to an area of objective decision-makirlg. Planning procedures currently being practiced by many mine managers depend primarily on common sense and trial-and-error methods which oftentimes never reach optimum solutions. For this reason, an attempt is made to provide an understanding of linear programming to solve production planning problems. More specifically, a linear programming model is proposed to solve the production scheduling problem as it was found to exist in the crushed stone industry. Optimal production scheduling is of prime concern here, since the industry has to cope with seasonal demands for its products. The solution, as determined through the application of the model, provides management not only with an optimal production schedule but also with the following information regarding the improvement of existing facilities: (I) the location of bottlenecks which limit production and profit; (2) the directions in which the company i fixed equipment should be expanded or modified; and (3) the evaluation of unused resources. Future trends in stone production will quite likely parallel those in the construction industry. Continued record expenditures for structures such as dams, highways, and buildings are the reasons for this accelerated growth. Production forecasts for the next decade are predicted to be around one billion tons with an approximate 7% annual increase. The problem of increasing production from 570 million tons in 1966 to 1 billion tons by 1976 offers no small challenge. This situation is further compounded by other problems and economic factors. Population expansion, government regulation, labor agreement, and changes in technology wd cause managers and operators to be confronted by many more complexities than characterize present-day operations. Some of these. problems and economic factors are: (1) In some metropolitan and other urban areas, easily accessible sources of stone are almost depleted. Transportation costs will be a prime concern of the industry. (2) Population growth has forced residential expansion to a point where many quarry operators must conform to urban and suburban regulations. (3) Government regulation in regard to air and water pollution, noise, and reclamation as well as zoning developments necessitate that crushed stone producers keep abreast of changing conditions and requirements. (4) The crushed stone industry operates under pressure of a highly competitive situation. Every company&apos;s objective is to retain a favorable marketing position by exercising great attention to production and marketing costs. This is rather difficult, since the crushed stone industry is one segment of modern mining which has to cope with a seasonal demand for its products. Among the problems posed here, the one of exercising great attention to production and marketing costs is of current interest to management. Under seasonal demand conditions, this problem creates further difficulties for managers who need to plan and forecast. STATEMENT OF THE PROBLEM Various methods of Operations Research have been developed to handle a problem whose genesis is explained above. It is very seldom, however, that these quantitative means are used in practice by the mining industry. This paper describes the use of Operations Research methods to solve a production planning problem when demand is seasonal. The seasonal production planning problem is an important one because of the substantial costs associated with changing production, employment, and inventory levels to adjust to seasonal sales patterns. Most companies try to operate within reasonable levels of employment changes and hold inventories within storage capacities. In general, little or no attempts were made to develop minimum cosl schedules or to provide objective means to compare various production policies. When demand varies within a fixed time period, 11:-oduction requirements may be met by following one

Jan 1, 1970

By Robert Glass Cleland

[Incorporated under the laws of the State of New York OFFICE, 41) WALL STREET, NEW YORK 5, N. Y. Authorized4,000,000 shares $150,000,000.00 Outstanding-5,071,260 shares 126,781,500.00]

Jan 1, 1952

The President was authorized to appoint. a liaison committee to cooperate with the American Mining Congress in respect to the establishment of a Secretary of Mines and Mining in the President&apos;s Cabinet. He appointed Edwin Ludlow, Chairman; Mark L. Requa, and J. E. Johnson, Jr. It was resolved to accept the invitation from the Chicago Section to hold the. 120th meeting of the Institute in Chicago during the week of Sept. 15, 1919. The action of the Executive Committee in appointing Past President E. Gybbon Spilsbury as representative of this Institute to visit France upon the invitation of the Société des Ingénieurs Civils de France was approved. The final budget for 1918 was approved. Tile President was authorized to appoint a committee, of three members, on the Development of Activities of the Institute. The committee was requested to report at the February meeting of the Institute, and the Secretary was requested to invite each local section to have a member present to discuss the subject. The President appointed J. W. Richards, Chairman; P. N. Moore, and Allen H. Rogers. Thirty-six members, ten associates, and five junior associates were elected; one change of status from associate to member was granted; two members were reinstated; and eight resignations were accepted. An extension of time was granted to nine members. The dues of eight members were suspended on account of their being in active service.

Jan 2, 1919

By Amos Bowman

In the last two years I have had an opportunity to study the conditions of gold-mining in the far northwest of the Pacific coast —in Cariboo district, British Columbia. That country joins Alaska

Jan 1, 1887

By K. A. Jackson, J. D. Hunt

The discussion by Tammann and Botschwar of the transition from eutectie grouth to denrdritic plus eu-tectic growth is reviewed and applied to metallic eutectic systems. Using expevimental data on the geowth rate of the Pb-Sn eutectic, and an extrapolalion of dendritic growth rate in tin and Sn-Pb alloys , qlcantitatice prerlictiotls of the extent of the eutectic region in tin-vich Sn-Pb alloys are made. There are no experimenta1 measuvements available for detailed comparison with these predictions. EUTECTIC structures form over a small range of compositions. The theory of lamellar growth presented by Jackson and Hunt&apos; indicates that it is in principle possible to have eutectic growth over almost the complete range of compositions between the two solidus lines. This does not occur in practice. Alloys far from the eutectic composition grow dendritically followed by a eutectic as shown in Fig. I. The transition from a eutectic to a dendritic plus eutectic interface cannot be predicted from constitutional undercooling arguments because constitutional undercooling always exists ahead of the eutectic interface.&apos; Reasonable predictions can, however, be made using arguments originally put forward by Tammanl. and Botschwar.3 These and later workers&apos;"*6 carried out extensive experimental investigations of the extent of the eutectic range in organic materials. They concluded that the structure formed, eutectic or dendrites plus eutectic, depended on which structure grew faster at the given undercooling. This is, of course, equivalent to the structure which grows with the smallest undercooling at a given growth rate. In this paper, we will discuss these ideas briefly and then apply them to predict quantitatively the range of eutectic growth in tin-rich Pb-Sn alloys. The temperature dependence of the growth rates of dendrites and eutectic for a typical metal alloy of eutectic composition is shown schematically in Fig. 2(a). The growth rate for the eutectic increases more rapidly with undercooling than those of the dendrites because of the short diffusion path maintained in the eutectic, see Fig. 1. For an alloy off the eutectic composition on the A-rich side, the growth rates shift as shown in Fig. 2(b). The liquidus temperature of the a phase increases, that of the 3 phase decreases, and the temperature of zero growth rate for the eutectic does not change. The curves, particularly the dendritic ones, change shape as well, but for our purposes the principal effects occur because of the change in liquidus temperatures.3-6 In an isothermal system, only a dendrites will grow above TE, Fig. 2(b). If the temperature is below TE, and both phases have nucleated, a dendrites will grow ahead of the eutectic at

Jan 1, 1968