Search Documents

By Benjamin C. Allen

The surface tensions of liquid chromium and manganese were determined by a modification of the dynamic drop-weight method and found to be, respectively, 1700 * 50 and 1100 * 50 dynes per cm at their melting points. Molten drops were formed LITTLE is known about the surface tension of liquid chromium and manganese, even though they are technologically important metals and widely used in steelmaking. In the past, direct determinations have been hampered by their high reactivity on the lower end of a vertically held rod inductively heated under argon. The technique essentially reproduced surface tensions reported for liquid nickel and zirconium using static drop-shape methods. and vapor pressure. In this work, surface tensions were measured by the drop-weight method, using induction heating under argon. EXPERIMENTAL WORK Chemical analyses of rods used are given in Table I. Chromium rods were prepared from iodide-process crystals which had been are-melted, hot-extruded, warm-swaged, and centerless-ground.'

Jan 1, 1964

THE metal iron has physical arid chemical properties which are some- what different from those of steels, but a knowledge of the pure metal is a useful starting point in studying the behavior of steels. Solid iron exists in two different crystalline forms, called alpha (a) and gamma (?) iron the former being the ordinary form at room temperature. When heated above the "A2 point," 769 C (1416 F), the metal becomes nonmagnetic, and at the "A3 point," 911 C (1672 F), it undergoes a change in crystalline form to become gamma iron. 111 the range 769 to 911 C, it is sometimes called beta (ß) iron to distinguish it from the magnetic alpha, but the two are identical in crystal structure. When gamma iron is further heated to 1392 C (2538 F), it changes into delta (d) iron, which is identical with beta or nonmagnetic alpha iron. Pure iron melts (in an inert atmosphere) at 1536 C (2797 F); the melting point is generally lowered by alloys or impurities. PHYSICAL AND THERMAL PROPERTIES OF IRON Many of the properties of iron undergo abrupt changes at the transition temperatures.1 For example, in heating through the A3 point, a sudden shrinkage in volume occurs. Similarly, melting is attended by sharp physical changes such as an increase in volume. Table 16-1 contains a summary of the measured physical properties of pure iron at several temperatures. Usually the properties change smoothly with the range of stability of a given form, but this is not always true. For ex- ample, the specific heat reaches a sharp maximum at the A2 point al- though no transformation occurs. (See Fig. 14-1.) Solvent Powers of Liquid Iron. Liquid iron is capable of dissolving most of the other metals and many nonmetallic elements as well. Of the metals that are liquid at the melting point of iron, only lead, silver, and bismuth refuse to dissolve to an appreciable extent. Table 16-2 contains a list of the common elements classified with respect to their solubility in liquid iron. Those which are very soluble or practically insoluble require no further discussion, but several of the nonmetals that are gases and exhibit limited solubility are of considerable importance to us and merit more detailed consideration.

Jan 1, 1964

By E. Gregory, C. G. Goetzel

The outstanding elevated temperature properties of materials made from sintered aluminum powder have been well established in recent years.1,2 and considerable investigation has been carried out on the structures which appear to be responsible for this type of strengthening.2,3 The maximum operating temperature of such materials is severely limited, however, by the low melting point of the aluminum matrix; and, therefore, considerable interest was aroused in methods of introducing the

Jan 1, 1959

By Charles H. Hopkins, J. M. Lohr

A COMMERCIAL development requiring a suitable alloy or alloys for sealing into various grades of glass made it desirable to have a more exact knowledge' of the expansion characteristics of the nickel-iron alloys than appeared in the published literature. The expansion of the more common [ ] types of glass under consideration varies from 2.7 to 10.4 X 10-s per degree Centigrade, over the range 20° to 400° C. For reference, the thermal expansion curves of several types of glass used for sealing by the lamp and tube industries are given (Figs. 1 and 2). This paper covers a detailed investigation of the thermal expansion of a series of nickel-iron alloys in which the nickel content varies from 30 to 70 per cent. Particular stress is laid on the alloys that contain between 40 and 55 per cent Ni.

Jan 1, 1938

By E. J. Roberts

F. C. Bond (Allis-Chalmers Mfg. Corp., Milwaukee) —This paper considers comminution as a first order process, with the reduction rate depending directly upon the amount of oversize material present. The data show that other factors should be taken into account, and it is possible that in time these may be evaluated as simultaneous or consecutive reactions: Development of the theory of comminution has been retarded for many years by the assumption that surface area measurements constitute the sine qua non of the work done in crushing and grinding, and it is encouraging to note the belated growth of other ideas. In the Abstract the term "net power" should be changed to "net energy." Throughout the paper the term "hp per ton" should be changed to "hp hrs per ton", or "hp hr t." The term "Probability Theory" in the title does not seem appropriate, since it is not clear how the probability theory is used in developing the ideas in the paper. There seems to be a contradiction between the large calculated advantages of closed circuit operation and the statement following that the closed circuit test results showed no significant change in grinding behavior, when compared with the batch grind curves. Tables I and II show that between 75 pct and 50 pct solids the energy input required decreases with increasing moisture content and may indicate the advisability of grinding at higher dilutions in certain cases. The calculation of the hp-hr per ton factor indicates an input in the laboratory mill of only 7.32 gross hp per ton of balls; this casts some doubt upon the accuracy of the factor used, since the power input in commercial mills at 80 pct critical speed is customarily much higher. The tests show that within fairly wide limits the amount of ore in the laboratory mill may be varied and a product of constant fineness obtained, provided that the grinding time is varied in the same proportion. This has often been assumed, and confirmation by actual testing is of value. The Cavg corrections for differences between the plant and laboratory size distributions do not seem very satisfactory, since in many cases the plant/laboratory ratio is farther from unity after correction than before. The following equation has been derived from the data in Table VI: Relative Energy (log new ball diam in in. + 0.410) Input = --------------—--------------- from which the relative energy inputs for balls of different sizes can be calculated and compared. The relative energy input is unity for balls of 2.715 in. diam. The equation indicates that the work accomplished by a ton of grinding balls per unit of energy input is roughly proportional to the square root of the total ball surface area; provided, of course, that the balls are sufficiently large to break the material. The data in support of this statement are admittedly meager, but are fairly consistent when plotted. The relative grindability values listed in Table VI for 200 mesh multiplied by 4/5 apparently correspond approximately to the A-C grindability at 200 mesh.' It would seem that for open circuit tests comparable accuracy could be obtained much more simply by the old method' of plotting the test grind, extending the mesh grinds to the left of zero time if necessary, and determining from the plot the equivalent time required to grind from the plant feed size to the plant product size, using the average of several mesh sizes. The en- ergy input value of one time interval could be determined by tests on materials of known grinding resistance, and this multiplied by the interval required should give the desired energy input value. The relative grindabilities would be the relative time intervals required for a specified feed and product size. When the plotted mesh size lines of a homogeneous material are extended to the left beyond zero time they meet at one point at zero pct passing. The horizontal distance of this point from zero time indicates the equivalent energy input required to prepare the mill feed. The author's results show that the closed circuit grinding tests give about the same K values as open circuit tests, from which he concludes that open circuit tests are satisfactory in many cases. The value of the closed circuit test is its ability accurately to predict energy requirements in closed circuit grinding for both homogeneous and heterogeneous materials. If the material is homogeneous, the open circuit test gives satisfactory results; but if the material contains appreciable fractions of hard and soft grinding ore, the open circuit tests will not be accurate because of the accumulation of hard grinding material in the circulating load. Since in most cases it is not possible to determine a priori whether the material contains hard and soft fractions, the closed circuit tests are preferable and more reliable. B. S. Crocker (Lake Shore Mines, Ontario)—Dr. Roberts probability theory of grinding is very similar to our log pct reduced vs. log tonnage method of plotting and evaluating grinding tests at Lake Shore. However, although we both seem to start at the same point we finish with different end results. Shortly after publishing our grinding paper (referred to by Dr. Roberts) in 1939, we did pursue the subject of the "constant pct reduction in the pct +28 micron material for each constant interval of time. We ran innumerable tonnage tests on the plant ball mills, rod mills, tube mills with 11/4 and 3/4 balls, and lastly pebble mills, with tonnage variations from 180 tons per day to 950 tons per day. We found that when we plotted the log of the tonnage against the log of the pct reduced of any reliable mesh, we had a straight line up until 90 pct of the mesh is reduced. We have also tested this in our 12-in. laboratory mill with the same results. We have used this method of evaluating grinds for the past 8 years and developed the recent four stage pebble plant on this basis. By pct reduced we mean the percentage of any given mesh that is reduced in one pass through a mill at a given tonnage (or time). For example, if the feed to a rod mill is 90 pct +35 mesh and the discharge at 500 tons per day is 54 pct +35, the pct reduced is 90 — 54/90 = 40 pct. If the feed had been 80 pct +35 the discharge would have been 48 pct +35 or pct re- duced 80-48/80 = 40 pct as long as the tonnage re- mained constant at 500 tons per day. Thus we can easily correct for normal variation of mill feeds. This log — log relationship derived from the tonnage tests of all our operating mills has proved of tremendous help in checking laboratory work and in designing alternate layouts or new plants. The difference between the log — log and the semi-log plot is only shown up when the extremes in tonnages are plotted. When the relationship between the pct reduced and the tonnage was first investigated, we used semilog

Jan 1, 1952

EXPLORATION U.S. 4,065,972 - Exploration for subsurface ore bodies of uranium. mercury or other inorganic or organic minerals having specific gases associated thereto Small gas sample containers are planted in a plurality of shallow holes in the surface of the earth in a predetermined pattern and left in place for a period of time sufficient to collect migrating gases. Each container includes a gas collection chamber and means for admitting gases at a predetermined flow rate. Strips of detector material which is sensitive to specific gases are mounted in the collection chamber. Recovered containers are subjected to qualitative and quantitative analysis. F. W Holub and H. W. Alter, assigned to Terradex Corp Jan. 3, 1978. 9 pp (73-421 5R) Filed 5-24-76 (689,710) Same. British 1,498,737, dated Jan. 25, 1978

Jan 1, 1979

By R. W. M. Lai

INTRODUCTION Manganese nodules were first discovered by the H.M.S. CHALLENGER expedition of 1873-76 and have engaged the interest of oceanographers and natural resources engineers ever since (1-4). Manganese nodules, some of them as large as grapefruit, cover vast stretches of the ocean floor throughout many parts of the world. In some areas the ocean floor is literally paved with nodules. The Pacific Ocean alone is estimated to contain 1.5 trillion tons of nodules which are forming at the rate of about 10 million tons per year (2). An analysis of the principal metal values for Pacific Ocean nodules is shown in Table I (5). [ ] The principal ingredients of the nodules are manganese and iron, but they also contain other important associated metal values such as copper, nickel, cobalt, and molybdenum. These associated metal values,

Jan 1, 1980

By J. B. Morrow, D. H. Davis

THERE are two general approaches to the problem of increasing profits from an operation. One is to lower expense; the other is to raise income. Mechanical preparation of coal may be used for either purpose but a prudent consideration of many details must precede any decision lest the results be negative instead of positive. It is quite possible that any net gain will result from a combination of the two. Since mechanically prepared coal invariably is a better product qualitatively than a hand-picked coal from the same mine, it is a reason- able expectation that the customer will be willing to increase the producer's income by paying a higher price. Or there may be the possibility that a combination of mechanical mining plus mechanical cleaning will give a lower over-all production cost for the coal in the railroad car. More likely, there will be found a combination of these two factors. From the customer's point of view, the competitive delivered cost per B.t.u. considered in relation to such incidental factors as dust nuisance, handling properties, ash disposal, and ash fusibility determines what he will pay. In a bulk tonnage product such as coal, freight is a very considerable part of the delivered fuel cost, and obviously freight paid on incombustible ash has no economic attractions. INCENTIVE FOR CLEANING Coal is prepared in four major ways: 1 (I) by screening or sizing, (a) by mixing or blending, (3) by cleaning, including hand picking and mechanical cleaning, (4) by dustless treatment. By a combination of any or all of these methods, coal can be prepared to standard specifications. It is easily possible to have good cleaning and still get a poor final product because of faulty screening or mixing,

Jan 1, 1943

By W. L. Falke, A. A. Cochran

Vast deposits of low-grade manganese ore exist in the United States, yet domestic production is insignificant compared to the more than 2 million tons of ore imported yearly into this country.1 A basic problem in connection with manganese is to find economical ways to utilize domestic resources.2 As a part of its program to conserve domestic mineral resources and to reduce dependence on foreign sources, the U.S. Bureau of Mines has conducted extensive research to broaden manganese technology and to find economical processes for recovering manganese from these low-grade resources. Although a great many processes have been proposed for treating domestic manganese resources, a failing of many of them is that too many steps are involved for economical operation.2 Some of the major processes that have been proposed were reviewed by Norman and Kirby.3,4

Jan 3, 1967

By P. Chiotti, R. J. Hecht

Vapov pressure data of solid and liquid alloys along with phase diagram data WERE employed in calculating the thermodynamic properties for the Ca-Zn system. The relative excess partial molal free energy for zinc in the liquid alloys was fitted to the relation wnvre i is we tvmpvrutiirc in ucgrees neivtu ana in is the tr~ole fvaction. Relations for the standard free energy of fortnation for the eight cornpounds were developed. ThE phase diagram for the Ca-Zn system as determined by Messing et a1.' is reproduced in Fig. 1. Earlier work on the phase diagram has been summarized by Hansen and Anderko2 and the very limited thermodynamic information for this system has been reviewed by Hultgren et a1.3 The heat of fusion for the compound CaZn2 has recently been determined to be 9260 cal per mole.4 Solubility data for calcium in zinc for the temperature range of 650" to 725°C were fitted by the relation and reported by Johnson and Dilloon5 In the present investigation zinc vapor pressure data were obtained by both the dewpoint and Knudsen methods in order to calculate the thermodynamic properties for liquid and solid alloys. The dewpoint method as employed in this work requires that only one of the components be significantly volatile, in this case zinc, and that the vapor pressure of pure zinc be known. For calculation purposes the vapor pressure data for pure zinc3 were fitted to the relations; for temperatures below 692.7K, the melting point of zinc. The corresponding free-energy relations for vaporization and sublimation of pure zinc are respectively. Some of the calculations also required knowledge of the free energy of fusion of zinc and calcium and the free energy for the 721°K allotropic transformation of calcium. The free energy of fusion of zinc was taken to be the difference between Eqs. [4] and [5], or The free energy of fusion and transition for calcium were based on the enthalpy values of 2040 and 222 cal per g-atom, respectively, as reported by Chiotti et al. 4 and the heat capacity data given by Hultgren et a1.3 and are represented by the relations, In the latter expression the difference in heat capacity between the a and 0 forms of calcium was neglected. MATERIALS AND EXPERIMENTAL PROCEDURES The metals used in preparing the alloys were Bunker Hill slab zinc, 99.99 pct pure, and Ames Laboratory calcium. The average impurities in the calcium in parts per million by weight, ppm, were N-17, H—77, Ba—216, Mg-15, Si—7, C—157, and Fe—9. The zinc was cleaned in dilute nitric acid and the calcium was used as received. The calcium was stored and handled in an argon-filled glove box and when removed from the dry box it was kept in an argon-filled desiccator. Tantalum was found to be a suitable alloy container. The alloy components were contained in a 1-in.-diam cylindri-

Jan 1, 1968

By J. W. Moody

The first Rodpeb mill ever built and placed in full scale successful operation went onstream in mid- 1960 at Marquette Cement Manufacturing Co.'s newly modernized portland cement production plant at Nashville, Tenn. It replaced a third stage of fine crushing and two 7x22-ft Compeb mills in the wet raw slurry grinding department. The Rodpeb mill at Nashville is similar in appearance to a Compeb mill but is larger. The mill, which operates in open circuit, is 9 ft in diameter and 38 ft long. The rod compartment is 12 ft long, with the rods being 11.5 ft in length and ranging in diameter from 4 in. down to about 1 in. The weight of the rod charge is 100,000 lb. The liners of the rod compartment are of the Lorain design.

Jan 4, 1963

By Roland Kammel, Takeo Oki

A suspension electrolysis method has been developed which enabled a direct anodic extraction of zinc from zinc sulfide concentrate and simultaneously oxidized sulfide sulfur to elemental sulfur. The investigation was performed in a laboratory-scale electrolytic cell, where the zinc sulfide concentrate particles (chemical composition in weight percent: 61.1% Zn, 2.3% Fe, 30.6% S, 3.4% SiO2 were suspended with or without graphite powder in a dilute sulfuric acid electrolyte. The main parts of the cylindrical electrolytic cell are shown in [Fig. 1]. The cathode (1), a rod of aluminum, is set at the center of the cell. The anode (2), which consists of four plates, is mounted on the inner face of the cell wall. Both PbO2(Pb) and graphite anodes were used. The cathode compartment (3) is separated from

Jan 1, 1976

Herbert Moore Harbach was born in Lebanon, Pa., Apr. 4, 1891, graduated from the Lebanon High School in 1911, and entered State College, from which he received his degree of Bachelor of Science in Metallurgical Engineering in 1915. He was employed by the Lackawanna Iron Co., at Buffalo, N. Y., and was later transferred 'to their Lebanon plant to start up the newly erected benzol plant. He was later made foreman of the coke ovens, which position he held after it was bought by the Bethlehem Steel Co., and until he enlisted in the service of his country in September, 1917. He was stationed at Camp Meade, Md., until the spring of 1918, when he was transferred to the C. W. S., at Niagara Falls, as an expert chemist. There he was engaged in perfecting the various kinds of gases,

Jan 2, 1919

BULLETIN 177. The decline and ultimate production of oil wells with notes on the valuation of oil properties, by C. H.- Beal. 1919. 84 pp., 4pls., 80 figs. BULLETIN 179. Abstracts of current decisions on mines and mining, reported from September to December, 1918, by J. W. Thompson. 1919. 166 pp. TECHNICAL PAPER 214. Motor gasoline; properties, laboratory methods of testing, and practical specifications, by E. W. Dean. 1919. 33 pp., 2 figs. TECHNICAL PAPER 219. Combustion and flue-gas analysis, by U. S. Fuel Administration. 1919. 12 pp., 5 figs. TECHNICAL PAPER 223. Cost-keeping for small metal mines, by J. C. Pickering. 1919. 46 pp. Only a limited supply of these publications is available for free distribution. Publications should be ordered by number and title. Applications should be addressed to the Director of the Bureau of Mines, Washington, D. C.

Jan 7, 1919

By Edward Ernst, Richard Runvik

AT the U. S. Gypsum Co. mine in Oakfield, N. Y., a flat-lying vein of rock gypsum is mined by the room and pillar method. Averaging only 4 ft thick, this vein is 1200 to 6000 ft in mineable width and many miles in length. Overlying the vein throughout the mine is a 2-ft thickness of distintegrated gypseous shale and fractured limestone which parts easily, falling with little or no warning. This shale, known as ash, varies in thickness from less than an inch to more than a foot. Small veinlets of selenite cut this shaley material, which breaks around timber props. The 18-in. limestone over-lying the ash is fractured vertically into blocks of varying size and will fail if any but the shortest unsupported spans are permitted. Above these two members is a thick layer of competent limestone.

Jan 6, 1957

By W. E. Keck, W. C. Lowry, G. C. Eggleston

The potential iron ores of Michigan can be classified from the stand-point of the predominant impurities into siliceous, sulphurous and phos-pllorous ores. Research on the flotation of each of these classes of ore was carried out in the following manner. The flotative properties of the valuable minerals of iron and of the worthless and deleterious ones were first determined under carefully controlled conditions. This information was then applied to synthetic mixtures of these minerals, which simulated the potential ores. Finally, data obtained during the two foregoing stages of the investigation were used in the flotation beneficiation of samples of the potential ores. Hematite is the most important mineral of iron in each of the above classes of iron ores. This paper deals with a study of that mineral in the very nearly pure state. There are two varieties of the mineral—specular hematite and massive hematite. The latter is the principal variety, but the former is an impor-tant' mineral of iron in some of the potential ores. Because of this condition, flotation research was performed with both varieties. This research consisted essentially of: (I) a survey of the literature on hematite flotation, (2) the preparation of pure massive hematite, (3) the preparation of pure specular hematite, (4) the development of a laboratory procedure and (5) flotation experimentation. For the purpose of this discussion, the results of previous work on the flotative properties of hematite can be summarized as follows: Specular hematite has been readily floated with terpineol and sodium oleate or heptylic acid1. Further, hematite has been likewise floated with a proprietary frother and oleic acid or other soluble oils2. Finally, lead nitrate, copper sulphate, silver nitrate, chromium nitrate, mercuric chloride, ferric

Jan 1, 1939

By G. C. Eggleston, W. E. Keck, W. C. Lowry

The potential iron ores of Michigan can be classified from the stand-point of the predominant impurities into siliceous, sulphurous and phos-pllorous ores. Research on the flotation of each of these classes of ore was carried out in the following manner. The flotative properties of the valuable minerals of iron and of the worthless and deleterious ones were first determined under carefully controlled conditions. This information was then applied to synthetic mixtures of these minerals, which simulated the potential ores. Finally, data obtained during the two foregoing stages of the investigation were used in the flotation beneficiation of samples of the potential ores. Hematite is the most important mineral of iron in each of the above classes of iron ores. This paper deals with a study of that mineral in the very nearly pure state. There are two varieties of the mineral—specular hematite and massive hematite. The latter is the principal variety, but the former is an impor-tant' mineral of iron in some of the potential ores. Because of this condition, flotation research was performed with both varieties. This research consisted essentially of: (I) a survey of the literature on hematite flotation, (2) the preparation of pure massive hematite, (3) the preparation of pure specular hematite, (4) the development of a laboratory procedure and (5) flotation experimentation. For the purpose of this discussion, the results of previous work on the flotative properties of hematite can be summarized as follows: Specular hematite has been readily floated with terpineol and sodium oleate or heptylic acid1. Further, hematite has been likewise floated with a proprietary frother and oleic acid or other soluble oils2. Finally, lead nitrate, copper sulphate, silver nitrate, chromium nitrate, mercuric chloride, ferric

Jan 1, 1939

By D. A. Martin, Laird Crocker, W. I. Nissen

The Federal Bureau of Mines has developed a process for removing SO2 from stack gases. The process comprises absorption of SO2 in an. aqueous solution of sodium citrate, citric acid, and sodium thiosulfate, followed by reaction of the absorbed SO2 with H2S to precipitate sulfur and regenerate the citrate solution for recycle. A pilot plant was operated at The Bunker Hill Co. lead smelter in Kellogg, Idaho, to assess the feasibility of using the process for flue gas desulfurization. Nominal capacity of the pilot plant, which treated .tail gas from the lead smelter sintering furnace, was 1699 standard meters cubed per hour (15 degrees celsius) of 0.3- to 0.7-percent-SO2 gas yielding about 272 net kilograms of sulfur per day. The pilot plant was operated for about 4500 hours and produced more than 45 net tonnes of sulfur. The operation demonstrated that (1) more than 95 percent of the SO2 could be removed from the lead smelter sintering furnace tail gases, (2) regeneration of the citrate solution with H2S and precipitation of sulfur in conventional stirred vessels was readily controlled and highly efficient, (3) the precipitated sulfur could be continuously recovered as a 99.5-percent-pure product by kerosine flotation and melting, and (4) the 77- to 79-percent-H2S gas used for sulfur precipitation could be readily produced from pilot plant product sulfur, natural gas, and steam. Projected operating costs, including capital charges, for a citrate plant, installed at a 118 000-tonne-per-year lead smelter and treating 49 271 standard meters cubed per hour of lead smelter sintering furnace tail gas, are estimated to be $384 per tonne of sulfur.

Jan 1, 1976

By A. W. Gauger

WITHOUT QUESTION the Commonwealth of Pennsylvania contains the most remarkable coal deposits of the whole world. Within its borders ,are to be found excellent coals ranging in rank from the high volatile bituminous of the western part of 'the state through the low volatile or semi-bituminous of central Pennsylvania to that aristocrat of solid fuels, anthracite, found in the East. . . . But while other states and even the Federa1 Government have recognized the needs of the coal industry, Pennsylvania has not. Though bituminous coal represents one of the most important industries in the state, far more important in annual productive wealth than agriculture, for example, hundreds, of thousands of dollars have been spent on agricultural research whereas little or nothing has been spent on coal investigation.

Jan 1, 1932

By L. A. Tarshis, H. E. Cline

A stability criterion for a lamellar eutectic interface was derived previously1 assuming that the wavelength, A,. of the perturbation which grows most rapidly is much larger than the lamellar spacing. A. This assumption was required to permit averaging of both the interface temperature and composition over the complicated geometry of a lamellae. If this assumption is invalid, as has been suggested.2,3 then the problem becomes too complicated to solve completely. The first of these analyses1 did not calculate the wavelength. A,. of the initially unstable perturbation. whereas the more recent analysis.' which led to a contradiction of this assumption. did not include one of the key factors for determining this wavelength. To rigorously determine the wavelength, the effect of the curvature of the perturbed interface (not considered by either of the above treatments) must be included. By omitting this term, one would be led to an incorrect conclusion regarding the magnitude of A,. but to an accurate criterion for stability as evidenced by the excellent agreement with experimental observations.' In the case of single-phase alloys. the critical wavelength. A,. for instability can be calculated from the Mullins and Sekerka4 (M.S.) analysis which includes the effects of capillarity. In the following discussion, the M.S. analysis is applied to lamellar eutectics and the critical wavelengths calculated for reasonable growth conditions in Pb-Sn eutectic alloys. In order to apply the M.S. analysis to eutectics. one may substitute i) the effective liquidus slope.1 m*. for the single-phase liquidus slope and ii) the ratio of the bulk alloy composition. C,. to the average interface composition in the liquid (Ci = CE where CE is the equilibrium eutectic composition) for the distribution coefficient to give:

Jan 1, 1970