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By L. Eaton, A. W. Last, J. L. Stevens

COPPER ore from Kennecott Copper's Ray mine, about 60 miles southeast of Phoenix, Ariz., is concentrated at the company's mill at Hayden, some 18 miles south of the mine. The Hayden mill is currently treating 16,000 tons of ore per day by flotation, using raconite, a crude butyl xanthate, as a collector for the sulfide copper minerals and lime as a pyrite depressant.1 The ore contains significant amounts of nonsulfide copper minerals, but recovery of these values has been low. The Hayden mill is now being modified to provide for treatment of future ores by leach- precipitation-flotation (L-P-F). This modification, costing about $5 million, is expected to reduce the loss of nonsulfide copper values and improve overall copper recovery by an additional 2 lb per ton of ore.

Jan 11, 1957

By G. A. Baird

With the exception of eight wildcat completions, which were unsuccessful and abandoned, all of the 1935 new drilling was performed in the proven fields. As of Dec. 31, 1935, 22 drilling rigs were in operation, of which 9 were at wildcat locations and the remainder were being used in new drilling in proven fields; in addition, 25 workover rigs (exclusive of cleanout rigs) were operating, all in the major fields. Production of Crude Oil.—Notwithstanding the considerable decrease in new completions during 1935 as compared with 1934, crude production mounted to a new high of 148,893,225 bbl., clean oil at 60' F., representing an increase of 12,532,579 bbl. over the previous record year, 1934, total of 136,360,646 bbl. This increase was due: (1) to the flush production

Jan 1, 1936

By G. A. Baird

With the exception of eight wildcat completions, which were unsuccessful and abandoned, all of the 1935 new drilling was performed in the proven fields. As of Dec. 31, 1935, 22 drilling rigs were in operation, of which 9 were at wildcat locations and the remainder were being used in new drilling in proven fields; in addition, 25 workover rigs (exclusive of cleanout rigs) were operating, all in the major fields. Production of Crude Oil.—Notwithstanding the considerable decrease in new completions during 1935 as compared with 1934, crude production mounted to a new high of 148,893,225 bbl., clean oil at 60' F., representing an increase of 12,532,579 bbl. over the previous record year, 1934, total of 136,360,646 bbl. This increase was due: (1) to the flush production

Jan 1, 1936

By Richard D. Call

Data obtained from development drilling provide the basic input for open pit mine planning and design. Development drilling is defined as delineation of the size, mineral content, and disposition of an ore body by drilling boreholes (Thrush, 1968). The objectives of development drilling are: ( 1 ) determining the geometry of the mineralization, ( 2 ) determining the grade and tonnage, , ( 3 ) obtaining samples for metallurgical testing, and ( 4 ) obtaining geotechnical data for mine design. To accomplish these objectives, an appropriate drilling plan must include the number of holes, the spacing and orientation of the holes, and a suitable data collection program. The data collection program covers sample collection, hole logging, and data presentation. This chapter will present some guidelines for development drilling and data collection techniques. The operational aspects of drilling will be covered in an- other chapter.

Jan 1, 1979

By A. J. Naldrett, N. T. Arndt

In Archean greenstone belts, ultramafic lavas occur interbanded with basalts, commonly at the base of volcanic-sedimentary cycles. The lavas form part of a recently recognized extrusive rock series, the magnesian series, in which liquid compositions range from peridotitic (33 wt-% MgO) to basaltic (8 wt-% MgO). Rocks of this series occur as peridote, pyroxenite and magnesian basalt flows, and intrusive/extrusive bodies of dunite (49 wt-% MgO) grading outwards into a peridotitic marginal zone. The nickel sulfide deposits are of two main types: (1) basal accumulations of massive and disseminated pyrrhotite + pentlandite associated with some of the thickest and most magnesian (<40 wt-% MgO) of the peridotite flows, and (2) widespread zones of disseminated sulfides in the dunite lenses. Massive sulfide segregations may occasionally occur within the dunites.

Jan 1, 1977

By T. S. Maio, J. G. Mansanti

In 1978, Ozark Lead Co. made the decision to expand the capacity of its mine/mill complex by 33%. The objectives of the expansion were to increase mine production capacity by 1.8 kt/d (2000 stpd), increase lead metal production by 21.8 kt/a (24,000 stpy), and to construct new facilities and modify existing equipment to accommodate increased production. This paper gives a brief explanation of the equipment installed and the overall production and metallurgical benefits realized from this expansion. The expansion was completed in the second half of 1980 with all equipment debugging and fine tuning completed by the first quarter of 1981. Concentrator modifications and improvements were basically restricted to four areas: materials handling, automation of the mill grinding circuit, increased flotation capacity, and concentrate dewatering.

Jan 1, 1985

By W. C. Winegard, C. J. Simpson, C. J. Beingessner

VARIOUS organic compounds, such as borneol, carbon tetr a bromide, and hexachloroethane, solidify as transparent plastics with a fcc structure. Each of these substances undergoes a solid-state transformation from the plastic phase to a brittle phase at temperatures slightly above 20°C. Since it was known that these plastic crystals solidified like metals,1 it was decided to investigate the possibility that solid-state grain growth would occur in the same way as it does in metals. Two-dimensional grain growth in thin films of plastic organic compounds has been studied with the aid of cinemicrophotography. Samples varying in thickness between 250 and 1000 @ were prepared by subliming a thin layer of the compound onto a microscope slide plate which was then covered with a second slide plate.

Jan 1, 1968

By Thomas M. Drown

At the meeting of the Istitote in New York, in February, 1880," I described a process of determining sulphur iu metallic allphides, with especial reference to the determination of pyrites in coal. The procem, as then described, is as follows: A solution of sodium hydrate, of 1.25 specific gravity, is saturated with bromine. If an excess of bromiue is used it must be neutralized by the addition of a little more sodium hydrate. The pulverized mineral or coal is moistened with 25 c.e. of this solution autl heated, then hydrochloric acid is added cautiously to just acid reaction. This operation is repeated with another 25 c.c. of the alkaline solution, and again rendered acid. The mixture should be kept hot. The contents of the beaker or dish are then

Jan 1, 1881

By Jerry M. Thornton, Richard W. Cannon, Don C. Rotherham

This paper attempts to show the role of induced polarization (IP) and resistivity surveys in the discovery of the ore bodies of Gibraltar Mines Ltd. (N.P.L.) and the importance of conducting large enough surveys to properly evaluate the results. The first IP survey was conducted in the area in 1963. This survey was extended and other IP surveys were added to it for the next seven years. The data from these surveys was finally combined to produce four large scale plan maps of resistivity and percent frequency effect (PFE) results (N = 1 and 3). A halo-type anomalous zone 6000 ft wide and 14,000 ft long was thus outlined in the PFE maps. The four ore bodies of Gibraltar Mines were found to occur along the inside rim of this IP halo.

Jan 1, 1973

By Marvin P. Barnes

The Sacaton open pit copper mine has recently been placed into production. Some problems have been encountered in maintaining grade control due to differences between early block estimates and actual production grade. A study was made using three methods for computing grade for 50&apos; x 50&apos; x 40&apos; size blocks from exploration and development drill holes; 1) The polygonal method, 2) The inverse distance squared method, and 3) The geostatistical kriging method. The results of each were compared against a control block file created by using the assay results of all blast holes drilled in the ore over three benches of the new pit. Results indicate that the kriging technique gave better estimates for grade of individual blocks than did the other two methods for this particular deposit.

Jan 1, 1977

By Thomas M. Plouf

Getting optimal performance from flotation cells can, in many cases, be critical to a project&apos;s economic viability. Simple testing procedures can sound early warning signals as well as maintain optimum recoveries from the flotation cycle. The materials required for a simple testing laboratory include: (1) pH meter or pH paper, (2) bottles of reagents used in plant flotation, (3) stop watch, (4) calibrated eye droppers. (5) laboratory flotation machine (1000-g tank, open impeller), (6) froth collection pans, (7) magnifying glass, (8) sizing screen sufficient to retain 10% of the flotation feed coarse fraction, (9) sizing screen for the size particles at which desliming of the plant flotation feed is to take place, and (10) a set of screens covering the complete range of feed particle size.

Jan 4, 1978

By D. W. Frommer, M. M. Fine

Early in 1957 St. Joseph Lead Co. announced discovery of three new centers of iron ore deposition in east central Missouri.1 The discovery resulted from exploratory drilling in the vicinity of a magnetic anomaly or high. A deep hole, drilled into the Pre-Cambrian porphyry to determine the cause of anomaly, penetrated a magnetite-rich deposit.2 The magnetic surveys that revealed the anomalies were begun by the Missouri Geological Survey in 1929 and were continued into the 1930&apos;s 3. At that time an area in Crawford County known as the Bourbon magnetic high was located. A second anomaly, similar in size and intensity, was discovered about six miles to the northeast in Franklin County in the vicinity of Sullivan. This area was not studied in detail until the early 1940&apos;s.

Jan 3, 1959

Mar. 3-7, ASTM, spring meeting and commitee week, Hotel Statler, Cleveland. Mar. 4, AIME, Morenci Sub-Section, Longfellow Inn, Morenci, Ariz. Mar. 5, AIME, Chicago Section, Ladies Night, Chicago. Mar. 10-13, National Electrical Mfrs. Assn., spring meeting, Chicago. Mar. 10-14, National Assn. of Corrosion En-Engineers, annual convention, Galveston. Mar. 11, Society for Applied Spectroscopy, 6 pm, supper, Tosca&apos;s; S pro, meeting, Socony-Vacuum Training Center, 63 Park Row, New York. Mar. 16-19, American Institute of. Chemical Engineers, Atlanta Biltmore Hotel, Atlanta. &apos;Mar. 17-21, ASTE, annual meeting, Chicago. Mar. 20, AIME, Philadelphia Section, Engineering Bldg., University of Pennsylvania, Philadelphia. Mar. 22-Apr. 6, Chicago International Trade Fair, Navy Pier, Chicago. Apr. 1, Society for Applied Spectroscopy, Socony-Vacuum Training Center, 63 Park Row, New York.

Jan 1, 1952

By L. M. Clarebrough, A. K. Head, G. W. West, M. E. Hargreaves

RECENTLY Welber and Webelerl reported that during the annealing of fatigued copper no energy was released, but that energy was absorbed in the range of temperature 250" to 400°C. In view of the fact that strain hardening occurs during the fatigue of copper, this result was surprising and it seemed desirable to check the measurements. This note describes measurements made by a different technique which indicates that energy is stored during the fatigue of copper. Two test bars with gage length ¾ in. in diameter and 6 in. long were machined from OFHC copper and annealed in vacuum for 1 hr at 600°C. These were fatigued to fracture in an Avery pulsator at a frequency of 2000 cycles per min. The first specimen fractured after 0.25x10 cycles under a push-pull

Jan 1, 1956

By N. Arbiter, J. Steininger, C. C. Harris

Power consumption and operating variables in air-liquid systems for a wide range of operating conditions in the turbulent region have been correlated by two dimensionless groups involving the power ratio and the flow number. The form of the correlation was developed by considering flow balances related to the air-liquid composite density in the impeller zone. Data for two phase air-liquid systems, both from literature and from the present investigation, has been correlated with high statistical significance. Two phase solid-liquid and three phase gas-liquid-solid systems have also been correlated. The quantification of power requirements in the agitation of liquids is well established.1 Rushton, Costich and Everett have shown that, for mixers operating in the fully turbulent region with no vortex, the power number

Jan 1, 1964

By D. Cox, M. J. Duggin, L. Zwell

The carbides of approximate composition and Mn have been studied using X-ray diffraction techniques. Those carbides of the type (Fe,Aln)zC ave isostructural with cementite. The cell pararmeters a and c have minimum values at approximately 10 at. pd substitution of manganese for iron; no satisfactory explanation has yet been found for this phenomenon. The carbide fFeMn4)C has a monoclinic unit cell whose dimensions are close to those of ,11,15Cz A neu-troip-dij~ractiot~ study of (F&apos;eAlrz4)C~ reveals that, like MnsCZ, it is isostructural with Pd5Bz. The iron and manganese atoms occupy the palladium atom sites, while the carbon atoms were found to have the same atomic coordinates as the hovon atoms. A neutrorr-diffraction study of indicates that the carbon-atom positions are very close to those occupied in (Fez.,ll/lr~,.3)C. In both carbides studied, tlre iron and manganese atomzs were found to be essentially randomly distributed, although, in the case of (Fe,.811fn1.2)C, it is possible that there may be a slight preference of manganese atoms for- the general (d) positions and a corresponding slight preference of iron atoms for the special (c) positions. It has been found that a complete range of solid solution exists between Fe3C and Mn3C at 1050°C,I although Mn3C becomes unstable when the temperature is reduced to 95O0C,&apos; and can only be retained by rapid quenching. It is also known that a complete range of solid solution exists from Fe5Cz to M~SC~,~ although the stability range of carbides of the type (Fe,Mn)sCz as a function of the relative proportions of iron and manganese is not known. X-ray examinations of Oh-man&apos;s carbide3 and Spiegeleisenkristall,~ which have the approximate compositions (Fe3.67Mnl.33)C2 and (Fe3-,Mn,)C, where x lies between 0.4 and 1, respectively, have been made. The following carbides have also been studied: ] The lattice parameters determined during these investigations are listed in Table I. It is seen that carbides of the type (Fe,Mn)sCz have a monoclinic unit cell while carbides of the type (Fe,Mn)3C have an orthorhombic unit cell. It is evident that the variation of lattice parameters with manganese content is not linear for carbides of the type (Fe,Mn)3C. The coordinates of the atoms in (Fe2.7Mno.3)C have recently been determined by single-crystal analysis., The fractional atomic coordinates have been shown by Fasiska and jeffrey to be in good agreement withj those deduced from an earlier analysis of Fe3C by Lipson and etch.&apos; However, it was impossible to determine whether iron and manganese atoms occupied ordered positions because of the small difference between the atomic scattering factors of iron and manganese. The atomic positions in Mn5Cz (Refs. 8 and 9) and Fe5C2 (Refs. 7 and 8) have been obtained only by comparisons made with the isostructural compounds P~SB~.&apos; Since X-ray diffraction techniques were used in these investigations, accurate positioning of the carbon atoms, which have a low atomic scattering factor, was difficult. No attempt has been made to determine the atomic positions in the other carbides previously studied. It was felt that an investigation of the lattice parameters of a number of intermediate carbides of the types (Fe,Mn)sCZ and (Fe,Mn)& would be of interest. It seemed likely that a neutron-diffract ion study of such carbides would indicate whether ordering occurred between the iron and manganese atoms because of the large difference between the neutron-scattering cross sections of iron and manganese. It also seemed probable that such an investigation would provide a determination of the atomic coordinates of the carbon atoms. I) EXPERIMENTAL DETAILS Specimens, each weighing approximately 20 g, were carefully prepared according to the following proportions: The components were 500-mesh powders of 99.995 pct purity iron and spectroscopically pure carbon and a 200-mesh powder of 99.995 pct purity manganese. The component powders were intimately mixed by prolonged shaking, then each specimen was inserted into a spot-welded cylindrical container of tantalum foil, whose end was closed but not sealed. Each specimen in its envelope was then sintered at 1050° C for 24 hr in a thin-walled evacuated quartz capsule, such a time having been previously found sufficient for equilibrium to be attained.&apos; Each specimen was then quenched in order to attempt to retain the high-temperature phase, as the literature indicates that transformations may occur on cooling. Debye-Scherrer X-ray photographs were taken of each specimen using a 114.6-mm-diam camera, Fig. 1, patterns 2 to 6. The exposure time was 6 hr using filtered iron radiation at a tube voltage of 40 kv and a tube current of 12 ma.

Jan 1, 1967

By M. L. Leonardi

THE Searles Lake orebody is located in the north- west corner of San Bernardlno County. It is a dry lake bed with an exposed salt surface covering an area of 12 square miles. Recoverable mineral values are contained in the mother liquor below the surface of the lake. Stratification in the lake bed has separated the brine into two bodies which dlffer in composition. Although liquor is processed from both bodies, this paper will discuss only the upper structure brine. Fig. 1 illustrates a typical cross-section of the two commercial orebodies. The orebody is composed of a porous salt deposit 70 to 90 ft deep. The upper structure is separated from the lower orebody by a 12 to 16-ft thick impervious mud seam, as shown in Fig. 1. These salt structures are composed of 55 pct solid-phase salts and 45 pct voids which are filled with the original mother liquor. The brine wells are drilled to the separating mud seam and cased to wlthin 10 ft of the bottom. This is done to draw the brine horizontally from the bottom of the structure. It is pumped with multistage centrifugal pumps Into the plant at the rate of 3 milllon gal per day. The first process that was successful was developed by Charles P. Grimwood for the recovery of potash. The first evaporator unit was built in 1916. In the early twenties, Dr. Morse worked out a process for the recovery of borax. This made the cycle more efficient, as the end liquor could be sent back to the evaporators rather than being sewered. In 1926 the American Potash & Chemical Corp. was formed as a new company, and the entire plant was remodeled. The plant at that time produced only potash, borax, and boric acid. Since then the American Potash & Chemical Corp. has added processes for the production of USP boric acid, refined potash, sulphate of potash, soda ash, salt cake, lithium concentrates, Pyrobor (Na2B4O7) bromine, phosphoric acid, and lithium carbonate. The main plant cycle may be depicted as a closed cycle, see Fig. 2. The raw material, brine, enters the cycle to be mixed with the end liquor, known as ML2, from the pentahydrate borax crystallizers. The mixture of these two forms evaporator feed. Evaporator feed is pumped to the evaporators where it is concentrated, with respect to potash and borax. In the same operation water vapor, sodium chloride, salt trap salt, and clarifier salt are removed from the cycle, see Fig. 3 for potash plant product. The evaporators produce a concentrated liquor which contains approximately 19.5 pct KCI. This liquor is diluted as it enters the potash plant to keep all salts, except potash (KCI, 97.0 pct) in solution. Here the moist potash leaves the cycle at 100°F. The end liquor, known as ML1, is pumped to the borax pentahydrate crystallizers, where crude borax pentahydrate is crystallized and removed as solid phase. The ML2 is sent back to pan feed to be reconcen-trated, see page 207. Note that the only water to leave the cycle is in the form of vapor and moisture in the solid phase products crystallized. Thus there is a constantly cycling volume of liquor to which brine is added. Since the volume of liquor cycled does not increase, the brine is, in effect, evaporated to dryness. This would be true if there were no liquor losses. But, as in all processes, there are always unavoidable and accidental losses which reduce the volume of cycling liquors. The losses must be made up with brine. The concentration process is the beginning and the end of the cycling liquors. In this process there are three evaporator units of the triple effect counter-current type, that is, there are three pans in each unit and the heat flows in one direction while the liquor flows the other way through the evaporator pans, see Fig. 4. During the evaporation process a great deal of sodium chloride, burkeite, some sodium carbonate monohydrate, and a little lithium-sodium phosphate are crystallized. The volume of these salts is so great that they must be removed as they are formed or the process would come to a standstill. Brine and recycled mother liquor No. 2 enter the third effect evaporator pan from the evaporator feed storage tanks, see Fig. 5. A steady flow of liquor is removed from the bottom of the No. 3 pan and is pumped through the No. 3 cone of the salt trap, a clear liquor being returned to the NO. 3 pan. A portion of this clear liquor is pumped to the second effect pan. This process is repeated in each pan. The liquor from the No. 2 pan is pumped through the No. 2 salt trap cone and returned to the No. 2 pan.

Jan 1, 1955

By K. J. Rosengren

INTRODUCTION Mount Isa Mines Limited operates a major mining complex at Mount Isa in northwest Queensland, Australia. The location is arid and remote, some 600 miles distant from the nearest port of Townsville on the eastern coast (Fig. I). Current mine production is 6 million long tons per annum comprising 3.8 million tons of copper ore and 2.2 million tons of silver-lead-zinc ore. Copper ore production is scheduled to increase to 5.8 million long tons per annum by 1973 and a new silver-lead-zinc mine is being developed at Hilton, 13 miles north of Mount Isa. The Mount Isa and Hilton orebodies occur in a single stratigraphic member, termed the Urquhart Shale. This shale is conformable with several other sedimentary formations striking north-south and dipping approximately 65º west. The silver-lead-zinc orebodies occur in bands conformable with the shale bedding and tend to be of tabular shape, varying in width from a few feet to nearly 200 ft. The copper orebodies occur in breccia bodies, locally known as "silica-dolomite", within the Urquhart Shale and tend to be more irregular and massive with widths up to several hundred feet. The detailed geology is described by Bennett (1 2). At present, production comes almost entirely from underground operations with only about 25,000 tons per year of carbonate ore from open pit operations. The mining method used in the copper orebodies is sublevel open stoping with pillar recovery by pillar blast before stope filling or by sublevel caving after stope filling. A large primary sublevel caving operation was also carried out until recently in one of the orebodies. The wider lead orebodies are mined by sublevel open stoping, with or without pillar recovery, while cut and fill stoping is used in the narrower orebodies. Details of the mining methods are given by Davies (3). The company&apos;s interest in open pit mining stems from a large open pit which was mined out in 1965 and a further large open pit planned for future production. In addition, the company is currently evaluating several large ore deposits in Australia and New Guinea. All of these orebodies would be mined by open pit methods and rock mechanics studies of slope stability are now a standard feature of all open pit evaluations.

Jan 1, 1972

By G. Ansel, J. P. Doan

THE important literature concerning zirconium in magnesium-base alloys is predominantly contained in patent references. Sauerwald, Eisenreich, and Holub1-4 discovered the profound grain-refining influence of small amounts of zirconium on cast magnesium and the attendant increases in strength, and ductility. They extended their work to reveal that limited amounts of certain other elements, including zinc, could be added for further improvement in strength and hardness. British. Patent 5111376 relates to the parent discoveries of Sauerwald, Eisen¬reich, and Holub. All of these references deal primarily with casting characteristics and properties in the cast state. Minor mention is made of desirable tensile strength, ductility, and toughness of wrought Mg-Zr alloys* modified by one or more additional elements. No extensive reference in the literature" has been found to the particular characteristics of wrought Mg-Zn-Zr alloys, with which the present paper is concerned. - The work to be discussed represents essentially an extrusion study of the Mg-Zn-Zr alloys and indicates that this system is highly interesting in the wrought state both academically and commercially. Accordingly, an important aim of this paper is to describe the hot-workability, tension and compression properties, metal¬lography, and toughness of these alloys. Compositional variations are limited to the ranges o to 7 per cent Zn and o to I per cent Zr. EXPERIMENTAL PROCEDURE Alloying and Casting Alloying ingredients were cell mag¬nesium, commercial zinc (intermediate grade), and a chloride salt containing approximately 50 per cent ZrCl2 and 50 per cent alkali chlorides. This salt is produced by Titanium Alloy Manu¬facturing Company. Melting, alloying, and pouring procedure essentially followed the crucible process as described by Nelson.6 The magnesium was melted using Dow No. 310 flux, and the temperature raised to 1350° to 1400°F for the alloying operations. After alloying of the zinc, the zirconium containing salt was added in small portions with vigorous stirring. This is an adaptation of the method described in British Patent 533264.7 The alloying efficiency of zir¬conium was approximately 30 per cent. During the alloying of zirconium, fluorspar was added in amount required as a flux¬inspissating agent. Next the melt was refined with Dow No. 310 flux and held quietly for 15 min. Finally billets were cast in a book-type permanent mold

Jan 1, 1946

By Merton C. Flemings, Harold D. Brody

Analyses that include diffusion of solute in the solid phase are formulated to describe solute redistribution in dendritic solidification of metallic alloys. The analyses are based on conditions that include negligible undercooling before nucleation of solid phases, negligible increase of solute in advance of the tips of growing dendrites, complete diffusion within the liquid over distances the order of dendrite spacings, and a plate-like dendrite morphology. The classical nonequilibrium freezing equation, Cs = kCo(I - fS)k-l accurately describes solute redistribution between dendrite arms for the solidification processes considered, provided diffusion in the solid is negligible. To account for the effect of diffusion in the solid, an analytic expression is given which is similar inform to the classical expression. 172 addition, a numerical-analysis procedure is etnployed to examine in more detail the effect of diffusion both during and after solidification. The analyses are intended for application to solidification of castings and ingots to describe a) final solute distribution after solidification and cooling to room temperature (microsegregation) and b) local fraction solid as a function of ternperatcre within the solidifying casting or ingol. SOLUTE redistribution in cellular and dendritic solidification has been discussed quantitatively in recent papers&apos;-3 and in a series of earlier work.4-6 However, none of the analyses developed have permitted close correlation of theory with final solute distribution (microsegregation) observed in castings and ingots. In this paper, discussion is given of approximations which may reasonably be made in mathematical treatment of microsegregation, and analyses are presented based on these approximations. Numerical results are given for Al-Cu alloys. In a second paper the analyses will be compared with exeriment.7 CLASSICAL ANALYSIS The classical quantitative treatment of solute redistribution within a closed "volume element" has been derived repeatedly, for example by Gulliver,4 Scheil,&apos; and Pfann.&apos; This "classical nonequilibrium solidification equation" is written for constant partition ratio: where Cs = interface composition of the solid when the weight-fraction solid within the "volume element" is fs (weight fraction, wt pct); k = equilibrium partition ratio; Co = initial alloy composition within the volume element (weight fraction, wt pct). Assumptions of Eq. [11 are: 1) There is negligible undercooling before nuclea-tion, or from curvature or kinetic effects. 2) There is no mass flow in or out of the volume

Jan 1, 1967