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By R. J. Blackwell, A. L. Pozzi

Scaled laboratory-model studies provide a powerful method for evaluation of a proposed oil-recovery process. In recent years, models have been used extensively to evaluate processes in which solvents displace oil, both for general cases and for specific reservoir conditions. Since the performance of a miscible flood in a horizontal reservoir can be significantly affected by transverse mixing between solvent and oil, this displacement mechanism must be accurately simulated in the scaled model studies. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long times for experiments. If scaling requirements for miscible displacements could be relaxed while accurate simulation of essential displacement mechanisms is maintained, the utility of model studies would be greatly enhanced. The purpose of the work reported herein was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascer tain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. These studies were performed with completely miscible systems in linear, horizontal models packed with unconsolidated media. From the experimental results, a set of relaxed scaling criteria was formulated which allows the requirements of geometric similarity and equality of the ratio of viscous to gravity forces to be omitted for specified conditions. The relaxed criteria are valid whether transverse mixing is by molecular diffusion or by convective dispersion. Correlations which permit prediction of vertical sweep efficiencies in linear, horizontal reservoirs were developed from the experimental data when transverse mixing is by molecular diffusion. These same correlations may be used when transverse mixing is by convective dispersion if an empirically defined, effective, transverse dispersion coefficient is used in the description of the mixing process. The effective transverse dispersion coefficient correlation essentially duplicates the dispersion coefficient correlation for equal-viscosity, equal-density fluid systems. Experimental values for the effective transverse dispersion coefficient can be measured readily. INTRODUCTION One of the most effective methods for evaluation of miscible-displacement oil-recovery processes is that of displacements in laboratory models scaled to simulate reservoir conditions. For these laboratory studies to be meaningful, however, the essential displacement mechanisms affecting reservoir performance must be accurately simulated. Since the performance of a miscible flood in horizontal reservoirs, or in dipping reservoirs at high rates, can be significantly affected by transverse mixing of solvent and oil, this mechanism must be considered in the design of laboratory experiments. Unfortunately, precise scaling of transverse dispersion coupled with the requirement of geometric similarity requires impractically large laboratory models and long experiment times. This difficulty seriously limits the utility of laboratory model studies. Craig,et al,1 demonstrated that geometric similarity is not required when mixing is unimportant. Their experimental data indicate, for the cases studied, that the displacement is sufficiently characterized by scaling the ratio of viscous-to-gravitational forces. This work suggests that relaxation of the requirement of geometric similarity and, possibly, other criteria might also be permissible when mixing is important, provided suitable groups describing the mixing process are scaled. The purpose of the work reported here was to evaluate the relative importance of various mechanisms affecting miscible displacement and to ascertain whether the essential features of the displacement process can be simulated even though some scaling groups are not satisfied. Consequently, laboratory investigations were made of the dependence of recovery on dispersion and other variables,

Jan 1, 1963

Climax Molybdenum Co. has contracted with the Government to operate its property at Climax, Colo. at maximum capacity for five years. Substitution of synthetic lubricants, polyalkylene glycols and their derivatives, for petroleum products in certain industrial applications is yielding substantial savings in production costs and improved operation of mechanical equipment.

Jan 1, 1951

By L. F. Mondolfo, B. E. Sundquist

The undercooling associated with the nucleation of the secondary phase from the liquid by the solid primary phase was studied in sixty binary alloys by means of a hot-stage microscope. It was found that in a system of a and ß, a usually nucleates ß at low undercoolings, but ß does not nucleate a, except possibly at undercoolings approaching homogeneous nucleation. This behavior can be explained in terms of relative interfacial energies and shows that crystallographic disregistry is only a minor factor in heterogeneous nucleation from metallic liquids. PREVIOUS experimental work1-6 on nucleation of solids from liquids has shown that normally nucleation is heterogeneous, and that small solid particles present in the liquid are responsible for the nucleation. These experiments and the theory that has evolved from them have made apparent that there is a "characteristic undercooling" associated with the nucleation of the solid from a given liquid by a given impurity. Little is known, however, about the chemical and structural relationships between the nucleating agent and nucleated solid that control the effectiveness of the nucleating agent in catalyzing the nucleation, as measured by the required undercooling. A review of the literature has yielded seventeen undercoolingsL-6 for the nucleation of solid from liquid metals by "known" nucleating agents. All values come from experiments in which the metal studied was divided into a number of particles (10 to 300 pin diam.) much larger than the number of extraneous impurity particles so as to obtain a large number of particles free of foreign nucleating catalysts. Known nucleating agents are then introduced by coating the droplets with particles or a thin film of the catalyst. Six of the seventeen undercooling values referred to cases where, for various reasons, the identity of the nucleating species was not at all certain. Another six cases involved nucleating agents with a crystal structure that was not known. Four other cases involved undercoolings listed as greater than or equal to undercoolings which were very likely those for homogeneous nucleation. One investigation3 involved adding to droplets powdered oxides, carbides, and so forth that were doubtlessly covered with adsorbed oxide or nitride films. The highly variable nature of these films resulted in highly variable undercooling (as was also found in preliminary work in this investigation). It is apparent that the information on heterogeneous nucleation in liquid metals is too limited to give rise to any definite conclusions on the nature of the catalytic process. With these problems in mind a new method was

Jan 1, 1962

By C. F. Wang

Manchuria in General Manchuria, called the "Three Eastern Provinces" in Chinese, forms the northeastern corner of China and is bordered by Siberia on the north and northeast, and by Korea on the east. It is a land famous in Chinese annals as the place of origin of the Ching dynasty, and in more recent times it has been an arena for diplomatic maneuvering and commercial competition between the Russians, advancing from the north, and the' Japanese from the southeast. It derives its name of "three eastern provinces" from the fact that it is divided into three provinces; Hei-

Jan 2, 1918

By R. E. Zimmerman

Wide attention is being placed upon various methods for cleaning the fine sizes of bituminous coals. The author describes and analyzes the results achieved on wet concentrating tables of modern design on unclassified feeds of —Vz in. particle sizes, including tests on high-sulphur coals. THE increased economic necessity of cleaning the small sizes of coal has forced wide attention upon various methods or processes being used. Although numerous cleaning plants in the past have been cleaning coal smaller than Vz or % in., the large quantities of higher ash fines being produced by mechanical mining and the need for cleaner coal under competitive market conditions have brought about many new installations of fine-coal cleaning plants. Of various methods used, one of the more popular types is the wet concentrating table. Approximately 525 tables have been installed in the United States in the past four years of which 320 have been installed in 20, large new plants. There are now probably 1600 tables of all types in existence in this country for cleaning coal. The purpose of this paper is to describe the cleaning of fine coal by wet concentrating tables. Its scope is confined to a discussion of the theory of tabling and some of the factors entering into tabling action, a description of the Deister SuperDuty diagonal-deck coal table and a discussion of the results of tabling various fine sizes of coals. Al- though tables have been used for cleaning coal as coarse as 2 in. and favorable results are reported, this paper is limited to reporting on the results of cleaning coal fines from 1/2 in. down. Also, although it is well known that the performance of tables is even superior under classified or closely sized feed conditions, this paper concerns itself with the results achieved by tabling unclassified feeds. History of Wet Concentrating Tables The wet concentration of minerals by some form of tabling is quite old, starting originally from fixed, smooth surfaced, tilted boards taking advantage of the laminar flow of liquid films and the separation of minerals according to specific gravity. This was followed by the development of rough deck surfaces

Jan 1, 1951

By R. E. Zimmerman

Wide attention is being placed upon various methods for cleaning the fine sizes of bituminous coals. The author describes and analyzes the results achieved on wet concentrating tables of modern design on unclassified feeds of —Vz in. particle sizes, including tests on high-sulphur coals. THE increased economic necessity of cleaning the small sizes of coal has forced wide attention upon various methods or processes being used. Although numerous cleaning plants in the past have been cleaning coal smaller than Vz or % in., the large quantities of higher ash fines being produced by mechanical mining and the need for cleaner coal under competitive market conditions have brought about many new installations of fine-coal cleaning plants. Of various methods used, one of the more popular types is the wet concentrating table. Approximately 525 tables have been installed in the United States in the past four years of which 320 have been installed in 20, large new plants. There are now probably 1600 tables of all types in existence in this country for cleaning coal. The purpose of this paper is to describe the cleaning of fine coal by wet concentrating tables. Its scope is confined to a discussion of the theory of tabling and some of the factors entering into tabling action, a description of the Deister SuperDuty diagonal-deck coal table and a discussion of the results of tabling various fine sizes of coals. Al- though tables have been used for cleaning coal as coarse as 2 in. and favorable results are reported, this paper is limited to reporting on the results of cleaning coal fines from 1/2 in. down. Also, although it is well known that the performance of tables is even superior under classified or closely sized feed conditions, this paper concerns itself with the results achieved by tabling unclassified feeds. History of Wet Concentrating Tables The wet concentration of minerals by some form of tabling is quite old, starting originally from fixed, smooth surfaced, tilted boards taking advantage of the laminar flow of liquid films and the separation of minerals according to specific gravity. This was followed by the development of rough deck surfaces

Jan 1, 1951

Discussion of the paper of N. V. Hansell, presented at the Cleveland Meeting, October, 1912, and published in Bulletin No. 72, December, 1912, pp. 1497 to 1,517. C. Q. PAYNE, New York (communication to the Secretary*) :-Mr. Hansell has presented in his paper a very interesting and valuable summary of the various methods of enriching iron-ores which have been developed during recent years. Particularly striking in this connection is the high degree of enrichment of the concentrates from magnetic iron-ores which is now commercially feasible. Magnetic concentrates containing from 6 7 to 139 per cent. of metallic iron, showing an efficiency of 90 and even 95 per cent. in. their separation, are not now uncommon. Such results exceed those obtained by gravity methods of treatment of all copper-, lead-, and zinc-ores, and are only equaled in the cyaniding of gold-ores and in the flotation treatment of certain copper-ores. It is of interest to note that the-type of magnetic field which is employed in securing these results, in the Gröndal (wet) and the Ball & Norton (dry) systems of treatment is the same in each case : viz., a field of alternating north and south poles. The credit for developing this simple and useful field, which has found so wide an application both in this country and abroad, is due to two American inventors and engineers, Clinton M. Ball and Sheldon Norton. At the same time, it should be noted that part of the improvement in the grade of the magnetic concentrates, especially in the case of the wet treatment of finely mineralized ores, is due to a well-devised scheme of mill-treatment, whereby a rough concentrate is usually obtained as an intermediate product, which is then recrushed and reseparated in obtaining final clean products.

Jan 3, 1913

By E. S. Greiner

Germanium and silicon have been plastically deformed in torsion at elevated temperatures. Slip took place on the four {Ill} planes. Dislocations, revealed by etch pits on a (111) face, occurred in rows that were traces of operative slip planes. THE plastic deformation of germanium and silicon by bending and tension at elevated temperatures has been reported by Gallagher.&apos; Transla-tional slip during plastic flow in these materials, according to Gallagher&apos; and Treuting,&apos; occurs on (111) planes. Recent work by Treuting&apos; indicates the direction of slip to be <1l0>. The present paper describes the plastic flow characteristics of germanium and silicon deformed by torsion. Torsional deformation was accomplished by twisting 1/4x1/4x2 in. specimens held in molybdenum grips and contained in an atmosphere of helium in a transparent quartz tube and heated by an external resistance furnace. The angular displacements were measured on a graduated circle with a pointer attached to the movable grip. Temperatures were measured with a chromel-alumel couple; the hot junction was within the quartz tube and in close proximity to the specimen. Photographs of samples of germanium and silicon twisted at 850" and 1180°C, respectively, are shown in Fig. 1. The germanium was twisted 230" per in. and the silicon 80" per in. These deformations are larger than those used in experiments to be described later and are presented only to emphasize the extensive plasticity of these materials. Germanium A single crystal specimen of germanium (n-type, 7 ohm-cm resistivity) with a (111) plane normal within 3" of the torsion axis, Fig. 2, was chemically polished with CP-4 solution" and then twisted 9" during the twisting of these specimens of germanium, the slip lines from the (lli) plane should have appeared in the four lateral faces instead of in only two. Perhaps the absence of rotational slip is brought about by the square cross-section. A cylindrical specimen would have a more uniform stress distribution in torsion than one with a square cross-section, and may deform by rotational slip. A specimen of germanium (n-type, 5 ohm-cm resistivity) twisted less than 8" per in. at 550°C, was cut to expose the (111) face 19" 28&apos; from the torsion axis, Fig. 4a. This face, after metallographic

Jan 1, 1956

Jan 1, 1961

By A. K. Mukherjee, John E. Dorn

The effects of strain rate and temperature on the critical resolved shear stress for (321)[111] slip were determined for the silver-rich CsCl type of intermetallic compound AgMg. The flow stress increased only slightly as the test temperature was first decreased below room temperature; a rapid increase in the flow stress was obtained with yet further decrease in temperature from about 250&apos; to 4OK. The effect of both the temperature and strain rate on the flow stress over the low-temperature range could be rationalized satisfactorily in terms of the Peiwls mechanism when the deformation was controlled by rate of nucleation of pairs of kinks. IN spite of the well-documented interest of metallurgists and engineers concerning the mechanical behavior of intermediate phases and intermetallic compounds, very little definitive information is available on this important subject. As recently summarized by westbrook,1 only limited and modest progress has been made thus far in elucidating the details of the mechanism of plastic deformation for the intermetallic compounds; the available information largely concerns phenom-enological descriptions of empirical observations and experimental facts, principally with reference to poly crystalline aggregates. The present report on the elucidation of the rate-controlling mechanism for slip in the bcc structure of AgMg is part of the comprehensive program of a systematic investigation on the mechanical behavior of intermetallic compounds. The intermetallic compound AgMg has a CsCl type of lattice structureZ and is completely ordered up to its melting point of 820c3 This material was selected for our present investigation because of its simple crystal structure, moderate and congruent melting point, ordered structure persisting up to the melting point, and some solubilities of the constituent elements, which could be expected to help in the growing of single-crystal specimens. Whereas previous investigations on the properties of AgMg include hardness,*"6 slip systems,7 tensile flow stress of polycrystalline specimens,&apos; and electrical resistivity,4 the current investigation will be directed principally at elucidating the rate-controlling dislocation mechanism responsible for slip in single crystals at low temperatures. It will be shown that the strain rate is consistent with a model involving the rate of nucleation of pairs of kinks by the Peierls mechanism for plastic deformation. EXPERIMENTAL TECHNIQUES Single-crystal specimens of the AgMg intermetallic compound were prepared and tested as follows: 1) A master alloy ingot of AgMg was produced by melting and chill casting the high-purity silver (99.995 wt pct) and high-purity magnesium (99.997 wt pct) in an induction furnace under a helium atmosphere. 2) Sections of the above-mentioned ingot were placed in a graphite mold containing a spherical cavity in which a single-crystal sphere of 1 in. diam was grown under helium by the Bridgman technique. 3) The operative slip systems were investigated at room temperature on a singlecrystal of AgMg, from measurements of the angles made by the slip traces on the two surfaces of the specimen, which were at 90 deg to each other. The investigation confirmed that the AgMg compound undergoes slip primarily in the (321) plane and in the [Ill] direction, but a small amount of secondary slip was also noticed in the (112) (111) system. No slip was observed in the (110) planes. 4) The single-crystal sphere, mentioned earlier, was oriented in a graphite mold containing a cylindrical cavity of 3/8 in. diam above the spherical receptable to give the angle xo = 45 deg between the axis of the cylindrical bar and the normal to the slip plane (321), and the angle AO = 45 deg between the slip direction [Ill] and the axis of the bar. Oriented single-crystal bar seeds were produced by melting, under a helium atmosphere, a polycrystalline bar in the cylindrical cavity above the oriented spherical seed and by growing an oriented single-crystal bar from the seed. 5) Finally, oriented single-crystal specimens were grown from these cylindrical seeds. 6) The cylindrical specimens were machined in a High-Tension Spark Cutting unit to give a 2-in. gage length. The spark-machined gage section was elec-tropolished in a bath containing 200 ml of H3PO4,

Jan 1, 1964

By Samuel M. Brock

Problems related to strip and auger coal mining have grown with the development of the industry and the economy. New technology has produced equipment that has made mining by surface methods not only highly productive, but potentially highly destructive of water resources and natural environments. On the other hand, growth of the economy has produced an increased demand for clean water and created new demands for amenity values that natural environments provide. Thus, opposing forces have created conflicts in resource use. And these conflicts have made surface mining highly controversial. Resolving the controversy will require the solving of complex economic and social problems. The essence of the economic problem created by surface mining is that, in the absence of proper regulation, substantial costs resulting from the process are borne by the public rather than the mine operator. The major goal for the regulation of the surface mining industry is to provide controls which will promote the attainment of maximum social welfare. Deciding upon the type of controls required, and how to apply them to attain a social optimum, however, poses some very difficult problems. In a comprehensive article on this subject, David B. Brooks defined the problem and suggested that benefit- cost analysis might be helpful in providing guidelines for making decisions about surface mining regulations.1

Jan 5, 1969

By F. P. Dewey

RICH HILL is situated in the famous car-wheel iron region of Southwestern Virginia, and although it contains many iron ores, this paper will be devoted chiefly to its car-wheel ore. Geologically, Rich Hill is somewhat difficult to describe, as the strata of the region are seriously folded and contorted. It lies at the base of one of the primordial spurs of the Blue Ridge, the ore appearing as a sedimentary deposit on the limestone No. 2, sometimes showing an imperfect stratification, but generally being an

Jan 1, 1882

By Maurice Rey, Victor Formanek, Paul Chataignon

IT is found when floating oxidized lead ores by sulphidization, that the presence of calcium salts in the water, is usually detrimental and lowers the recovery. This effect is particularly marked in dry countries such as North Africa, where the waters often carry large amounts of calcium sulphate and where the ore may even contain gypsum.

Jan 11, 1950

By P. F. Gnirk, J. B. Cheatham

The basic objective of this paper is to present a review of the state of knowledge concerning the fundamental mechanics of rock/bit-tooth interaction under downhole conditions. Of particular concern is the contributing significance of the various variables associated with the generation of rock chips by a single penetrating bit-tooth. The variables to be considered are fluid pressures which simulate borehole conditions, the mechanical properties of the rock, the shape and angle of attack of a bit-tooth, and the rate of load application on a bit-tooth. In addition, consideration is given to multiple bit-tooth penetration insofar as the effects of distance from and geometrical shape of adjacent penetration craters are concerned. Both experimental results and idealized theoretical models for single bit-tooth penetration are presented. Finally, the applicability of plasticity theory to drilling phenomena at depth, results of recent drag-bit studies, and several general theories of roller-bit drilling are briefly discussed. FUNDAMENTALS OF ROCK/BIT-TOOTH INTERACTION Drilling efficiency at depth in terms of penetration rate depends largely upon three essentially interdependent factors: 1) the bit, insofar as the mechanical motion, shape, and configuration of the bit-teeth are concerned; 2) the rock, as regards its mechanical behavior, or response to the penetrating action of the bit-teeth, when subjected to a state of stress induced by mud column, interstitial pore, and overburden pressure (and at great depths to high temperature) ; and

Jan 1, 1967

By Barry K. McMahon

The fundamental problem in rock mechanics is accounting for the discontinuous and anisotropic nature of the jointed rock mass. It is this problem that makes rock mechanics distinct from the mechanics of steel, glass, or concrete. Existing mathematical models explain much of the behavior of rock cores in the laboratory but, in civil engineering at least, the rocks that matter are the ones that are already broken. On the other hand, the basically descriptive methods now used in engineering geology do not lend themselves easily to mathematical analysis. A set of indices of geological properties related to the strength and deformation characteristics of jointed rock is needed. Like the index properties used in soil mechanics these will probably not have precise mathematical meaning, but once correlations are established with large scale tests they can form a basis for the transfer of test results, obtained in one area under one set of conditions, to the prediction of rock behavior in another area under another set of conditions. Indices of rock properties are even more important in rock mechanics than in soil mechanics as the cost of testing is much higher. To be useful, these indices must be easily and quickly measured and give reproducible results when measurements are made by different people. In this paper the word "joint" means all naturally occurring rock fractures with less than 3 in. of clay or other soft coating material. EXISTING INDICES OF ROCK PROPERTIES A comprehensive review of indices of rock properties for intact rock is given by Deere and Miller.&apos; They provide charts ". . . for estimating the strength or modulus properties for intact rock from the numerical indices obtained by either the Schmidt hammer, the Shore Scleroscope,

Jan 1, 1968

By R. S. Archibald

The subject of this paper is particularly appropriate, since Daniel C. Jackling was active in early exploitation of taconites on the Mesabi Range and contributed greatly to their later economic development. After his success in developing the low grade porphyries in the West he looked for more worlds to conquer, and so undertook the concentration of low grade taconites, from which he hoped to produce commercial ore. Mesabi Iron Co., organized in 1919, actually did produce merchantable sinter from taconites in 1922. The enterprise did not prove commercial at the time, as cost of production was high and the surplus of iron ore in the Lake Superior District already contributed to a low market price, but this same property has since been developed by Reserve Mining Co. The work done by Jackling had much to do with the success of this later venture. Iron ore was first discovered on the Marquette Range in Michigan in 1845. The first ore from this range came from the old Jackson mine in Negaunee in 1848. During these early years this property and others on the Marquette produced limited tonnages for transportation to Lower Lakes and for consumption by charcoal furnaces in the area, where a plentiful supply of hardwoods furnished the charcoal for iron smelting. The Marquette and other ranges tributary to Lake Superior did not produce much ore for transportation to Lower Lakes until the locks at Sault Ste. Marie were constructed, but from the time the first lock at the "Soo" was completed in 1855 these ores were transported through the locks to consumer centers in the East. The Marquette Range has a history of continuous production from 1848 to the present day.

Jan 5, 1959

By Jasper L. Stuckey

HISTORY IT is not known when kaolin mining was first begun in North Carolina. Evidence, in the form of excavations and primitive tools, indicates that some of the deposits were worked in prehistoric times. It has been suggested that the prehistoric mining was for mica, but the workings were all in altered or partly altered pegmatite material and the dumps do not represent the amount of material removed. Some of the early openings may have been made in search of kaolin or semi-kaolinized feldspar which was sold to English1 traders along the coast and used in some of the early English porcelains. In 1944,2 an application was made for an English patent to produce porcelain from an earthy mixture obtained from the Cherokee Nation in North America. It is well established, however, that the occurrence of kaolin in western North Carolina was known in England by 1767. In that year, Josiah Wedgewood sent T. Griffiths3,4 to what is now Macon County, North Carolina, to secure a supply of kaolin for use in England. Griffiths diary, now in Etruria Museum, Stokes-on-Trent, contains a most interesting account of his experience. Kaolin was discovered at St. Austell, England, shortly after the voyage of Griffiths, which probably accounts for the lack of further interest in American kaolin. Between 1767 and 1888, there are no records of kaolin mining in North Carolina. In the latter year, however, mining was begun near Webster, Jackson County, and, in the intervening period, has become an important industry. For some 20 years, kaolin mining was carried on chiefly in Jackson, Macon, and Swain Counties. About 1904, it was begun in the Spruce Pine district and for the past 20 years most of the kaolin mined in the State has come from Avery, Mitchell, and Yancey Counties. DISTRIBUTION The kaolins of North Carolina are limited in occurrence to the Piedmont Plateau and Appalachian Mountain area of the State. While kaolins are widespread in the Piedmont Plateau, having been prospected for in Rutherford, Cleveland, Gaston, Granville, Lincoln, Catawba, Iredell, Richmond, Moore, Randolph, and Montgomery Counties, the production from that area has never been important. The known deposits of commercial importance are limited entirely to the mountain area of the State. While kaolins occur widely distributed throughout the mountain area and have been prospected for in many counties of that area, commercial production has come chiefly from two districts. One of these includes Jackson, Macon, Swain, and Haywood Counties. The other includes Avery, Mitchell, and Yancey Counties. GEOLOGY With few exceptions, all the known kaolin deposits in North Carolina contain

Jan 1, 1947

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.&apos; 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.&apos; 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