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By D. C. Van Aken, O. J. Rajtora

A research effort sponsored by the Department of Energy (DOE) and several steel producers, is investigating the benefits of coating steelcasting nozzles with various materials. Coatings were applied to casting simulation nozzles made from industrial tundish nozzles (primarily of magnesia) and industrial submerged entry nozzles (SEN's) (primarily of alumina-graphite) in order to extend casting time prior to nozzle clogging. Nozzles were coated by air plasma spray (APS) using a 9M series APS system from Sulzer-Metco. The ability of these coatings to provide protection from clogging was evaluated using a steel casting simulation. Substrate-coating compatibility was characterized using optical and SEM microscopy.

Jan 1, 2004

By R. A. Guereca

The Bureau of Mines conducted an analysis to determine criteria for steady-state, laminar flow boundary conditions for a coiled-tube gas viscosimeter by comparing experimental data from a thick-walled, stainless steel capillary in a horizontal, straight-tube condition, with similar data taken after the same capillary was formed into a helix. Overlapping volumetric f10wrates and pressure drops are covered for both configurations at pressure levels of 28, 225, and 1,000 psia at 3000 K. Friction factor, Reynolds number, and Dean number correlation plots show conditions where the coi1ed-tube flow deviates from straight-tube flow. The coiled-tube data indicate departure from Poiseui11e steady-state laminar flow at a Reynolds number close to 390 and a Dean number of about 15. Below these conditions and consistent with the data reported, Dean's circulation appears negligible. For the particular coil used, a conservative upper limit of 10 is chosen for the Dean number corresponding to an upper limit of about 250 for the Reynolds number.

Jan 1, 1967

By R. J. Charles

Previous study of simple impact systems indicated that energy required for fracture and size reduction of brittle materials is greatly dependent on the type of loading that is employed. In this regard it was postulated that fracture and size reduction of a brittle specimen might be accomplished by a high velocity impact at an energy level at which a low velocity impact would leave the specimen relatively undamaged. The finite time required to propagate energy away from the point of loading of an impacted object to other parts of the object and to its supports may permit a concentration of energy at the point of impact if the rate of loading is high. Localizing of energy at the point of impact could quickly initiate fractures that would propagate through the impacted material along with the traveling stress waves. As the cracks form, the initially absorbed strain energy would be released and portions of it travel ahead of the crack tips as stress waves. These secondary stress waves, combined with the initial stress waves derived from the impact, would produce high localized strain conditions in front of the fracture zone. The fracture zone would propagate and the specimen shatter. High rates of loading are brought about by short impact times, in turn obtained by employing high velocity projectiles that are of small mass compared to the impacted object.

Oct 1, 1956

By J. C. Gathje

Newmont&apos;s Phoenix Project is located near Battle Mountain, Nevada and is scheduled to produce copper concentrates containing high precious metal values. High temperature pressure oxidation (PDX) of the concentrates was considered as a treatment option during process development. The metals content in Phoenix concentrates range from: 15-25% for Cu, 1-10% for Zn, 0-2% for Pb and ?27% Fe. The precious metals content of the Phoenix concentrates can range up to ?300 g/t Au and >3,000 g/t Ag. As a consequence it was necessary that any process for consideration should have the capability of recovering both the copper and precious metal values. Typically, gold can easily be leached from the autoclave discharge solids, but silver is chemically bound with the jarosite formed and cannot be directly leached. Laboratory investigations led to the development of a patented PDX process that minimizes the formation of jarosite so that the silver can be leached easily along with the gold. The process was confirmed with extensive pilot plant testing. Excellent solution extraction of copper and zinc was achieved, and both iron and lead were precipitated in the PDX residue. The process produces clean PDX discharge liquors with very low iron concentrations. As an example, conventional PDX techniques resulted in pregnant liquors containing ?5 g/L Fe. However, the Newmont process, which controls the iron and sulfate species, achieved high iron precipitation in the PDX solids and pregnant liquors containing <0.5 g/L Fe. High gold and silver recoveries were achieved by direct cyanidation of the PDX solids. This process has the added benefit of producing PDX solids that demonstrate superior settling and filtration characteristics.

Jan 1, 2006

By M. A. Marois

This paper proposes an improved temporal stability condition for the implementation of an inverse heat transfer method for predicting the time-varying bank thickness of the phase change protective bank inside a high temperature furnace. The direct problem is handled with the enthalpy method. The inverse method rests on the Adjoint Problem and the Conjugate Gradient Method. It is shown that the temporal stability condition for the inverse phase change problem relies on the time delay of the temperature measurements. Results indicate that this time delay is proportional to the heat diffusion time including heat diffusion through the mushy zone.

Jan 1, 2011

By A. Karadogan

Decision making can be defined as the selection process of the best routes from the alternatives in order to achieve a goal, and mostly involves uncertainty. Additionally, mostly qualitative variables (weak rock, massive ore deposit, etc.) are in question. Mine planning engineers often use their intuition and experience indecision making. As fuzzy set theory has been used since 1970, these uncertainties are easily evaluated in the decision-making process. Real world study is decision making under vague constraints of different importance, involving uncertain data (qualitative variables), where compromises between antagonistic criteria are allowed. This paper presents a new approach in the selection of an underground mining method based on fuzzy set theory for the Ciftalan Lignite Site located close to Istanbul in Turkey. The physical parameters such as geology and the geotechnical properties of ore, hanging and foot wall, economic effects, environmental effects, are established with field and laboratory tests together with the determination of other qualitative variables. Meanwhile, some qualitative variables dealing with the matter was described according to the view of a number of experts. Then fuzzy set theory is applied to these parameters, considering the available underground methods in order to choose the proper method. At the end of the evaluations, the room and pillar method with filling was determined as the most suitable method for the test site. Keywords: Decision making, fuzzy set theory, underground, mining, method selection

Jan 1, 2008

Direct smelting of copper in a single vessel has long been the extractive metallurgist&apos;s dream. Such a process offers the important alvantage. of (i) maximum use of the energy available from oxidizing the sulphur and iron of the concentrate: (ii) restriction of SO2 emissions to a single constant-strength source; (iii) minimum materials handling and (iv) elim-ination of at least one process step. Extensive developmental work was carried out in the 1960&apos;s and 1970&apos;s to implement such single-step processes. Some of the processes reached the prototype stage and it appeared that copper smelting technology was on the thresthold of a new, efficient, minimum-pollution era. Since that time, however, the forward thrust has slowed and single-step copper smelting is still a process of the future.The paper describes the potential advan-tages of single-step smelting; its history and current status; and the reasons why it has not been adopted industrially. It concludes that the potential benefits of single-step smelting are powerful and that many of the difficulties encountered in the 1970&apos;s will be overcome in the 1980&apos;s.

Jan 1, 1985

By P. M. Robinson, M. B. Bever

The heats oj formation at 273°K of the compounds CdTe, I)z2Te, InTe, In2Te3. In2Te5, SrzTe, and PbTe have been rleasrred in a liquid metal solutiotz caloritrete? 1.t1itlz bismuth as solvent. The?, are iterpretecl in yelation to tlze stability and bonding of the cott/pozltzds. Tile heats of fusion atzd the melting- points of tlze cotlzpounds InTe and Itzz,Te3 1lcti.e been measured in a cotrslant-temperature gradient calorimeter. The entropies of fusion are disc,ztssecl in YIIIS 01. the degree of order in the solid at the melting point. THE heats of formation of the tellurides of cadmium, indium, tin, and lead have been measured as a continuation of research on the thermodynamic properties of compounds of tellurim.&apos; The tellurides of these metals were selected with a view to examining the relation between the heat of formation and the position of the metal in the periodic system. The elements cadmium, indium, and tin are in the same period and tin and lead are in the same group of the periodic system. The tellurides of indium are of special interest because four compounds, In2Te, InTe, In2Te3, and InzTe5, occur in this system. The available information on the heats of formation of the compounds investigated consists of values for CdTe, SnTe, and PbTe derived from electromotive-force measurements,J a value for CdTe obtained by tin solution alorimetr, and values for InTe and In2Te3 determined by combustion calorimetry.5 These values, however, refer to various temperatures ranging from 273&apos; to 673°K and some of the reported error limits are large. Liquid metal solution calorime-try may be expected to yield more accurate values for the heats of formation than electromotive-force measurements or combustion calorimetry. The heats of fusion and the melting points of the compounds InTe and In,Te3 were determined in a constant-temperature gradient calorimeter. No published information appears to be available on the heat of fusion of these compounds. The results reported here give an indication of the degree of order in the solid compounds at the melting point. 1) MATERIALS AND EXPERIMENTAL PROCEDURE Materials. Samples of the compounds SnTe and PbTe were obtained from the Westinghouse Research Laboratories and samples of the compound InTe from Lincoln Laboratory, Massachusetts Institute of Tech- nology. Additional samples of the compounds InTe, SnTe, and PbTe and samples of CdTe, In2Te, In2Te3, and In,Tes were prepared from 99.995 pct Cd (Baker Chemical CO.), 99.999+ pct In (American Smelting and Refining Co.), 99.99 pct Sn (Baker Chemical Co.), 99.999+ pct Pb (Fisher Scientific Co.), and 99.999+ pct Te (American Smelting and Refining Co.). Stoichiometric amounts of the component elements were melted in sealed, evacuated Vycor tubes. The melts were held at approximately 100°C above the liquidus for about 16 hr and shaken repeatedly. The melts of the compounds In2Te and InzTe5, which form by peritectic reactions, were quenched into iced water. The melts of the other compounds, which have congruent melting points, were slowly cooled to room temperature. The samples were then annealed for 5 days at approximately 50°C below their respective solidus temperatures. Metallographic examination did not reveal any evidence of second phases or segregation. At least two batches of each compound were prepared. Samples from each batch were used in determining the heats of formation and, in the cases of InTe and In,Te3, the heats of fusion. The Heats of Formation. The heats of formation at 273°K of the compounds were measured by metal solution calorimetry with liquid bismuth at 623" as solvent. In this technique, the heat of formation is determined from the measured heat effects on dissolution of the compound and of a mechanical mixture of the component elements. The difference between these heat effects adjusted for changes in the composition of the bath gives the heat of formation at the temperature from which the samples are added to the bath (273°K). The experimental technique and method of calculation have been described in detail elsewhere.= It should be emphasized that the reported heats of formation depend on the thermodynamic data used in calculating the heat effects for the calibration additions. In the present investigation, the calorimeter was calibrated by adding pure bismuth at 273°K to the bismuth bath at 623°K. The reported heats of formation are based on a value of 4.96 kcal per g-atom for the difference in the heat contents of bismuth at 623" and 273". If a new value for this quantity becomes available, the reported results may be adjusted in direct proportion. The concentration of solute in the bath at the end of a calorimetric run did not exceed 1.7 at. pct and was usually less. In this range, the heat effect on dissolution of the solute was a linear function of the concentration of solute. In determining the heats of formation of the compounds in the system In-Te, a few runs were carried out in which two neighboring compounds such as InTe and In,Te3 and the corresponding mechanical mixtures of the components were added to the calorimeter. The

Jan 1, 1967

By Matthew Spedding

The complex nature of the carboniferous measures prevailing in the U.K. has dictated the types of mining required to exploit the coal seams. Most mines in Britain are referred to as deep mines in the sense that they operate at depths of 1800 - 3000 feet. The main system of coal transport to the surface is by vertical shafts which intersect the workable seams which at times number between 4 and 5. As mining has been practiced in most of the major coalfields in the U.K. for well over 100 years, with the initial extraction of the shallower and more profitable seams, the present management have been left a legacy of indiscriminate extraction which severely hampers their efforts to maximise the mine layouts. There is no single standard design of mining layout capable of meeting the wide variety of conditions which exist in the British coalfields. Mining layouts are subject to fixed and variable parameters. In discussing multi-seam working, the main parameter must be the effect of old workings above and below the seam to be extracted. There is a distinct lack of reliable information which would enable layouts to be designed to completely avoid or control these destructive forces. The guidelines are, therefore, mostly empirical.

Jan 1, 1977

By C. R. Stephan, N. B. Greninger, S. J. Luzik

The U.S. Bureau of Mines conducted explosion tests on various full-scale cementitious bulkheads used in abandoned mine areas to evaluate the ability of the bulkheads to withstand gas explosion over-pressures of 20 psig. Tests were performed on 120-ft2 solid-concrete-block seals of varying thicknesses and designs. Of the seven solid-concrete-block seals tested, only the standard-type seal, having a 16-in thickness, keyed at the floor and ribs, all joints mortared, wedged at the roof, and a center pilaster, maintained its integrity when subjected to a 20-psig pressure wave. After being subjected to repeated explosions, the standard seal only showed a small hairline crack and had an air leakage of 87 ft3/min at a pressure differential of 1 in H2O. Tests were performed on cementitious foam seals of varying thicknesses and compressive strengths. Explosion tests have shown that 200-psi strength, 4- and 8-ft-thick seals can withstand a 20-psig pressure wave. At a pressure differential of 1 in H20, no air leakage was detected through the 200-psi, 8-ft-thick foam seal.

Jan 1, 1991

By A. J. Kraemer

This paper is the second and concluding report of the results of the Bureau of Mines&apos; twenty-second semiannual survey of motor fuel marketed in the United States. The first paper Was published as Report of Investigations 30634 and reported data relating to gravity, vapor pressure, and distillation range of the samples. The present paper deals particularly with results of the determination of copper strip corrosion (method 530.22),5 color (method 10.11),6 sulphur content by the lamp method, 7 copper dish evaporation residue (method 530.1),8 and "gum" content as given by the steam-oven method as developed by the Bureau of Mines. 9 The price at the time the sample was taken and the tax are also stated for each sample. The sample numbers used throughout this report are identical with those used in Report of Investigations 306310; ?for example, No. 225 of this report is the same sample as No. 225 of Report of Investigations 3063.

Jan 1, 1931

By D. D. Young

During the 1970&apos;s a number of covered storage facilities were constructed in North America to store and handle large quantities of bulk, solid materials. This trend, away from outdoor storage piles, will probably continue at a stronger pace in the 1980&apos;s. This paper attempts to answer some of the questions often raised about the economics of large covered storage facilities. The paper is in four parts: 1. Why Build a Storage Facility? 2. 2. Common Components of Storage Systems With Details of Six Storage Facilities 3. Results of a Study for 50,000 Mg Clinker Storage 4. Guidelines for Conducting a Study to Select a Storage System.

Jan 1, 1980

By R. O. Williams

It is shown that Ni3Al precipitates homogeneously from nickel-rich alwminum alloys as plates on the (100) planes. Prior to actual precipitation a process occurs which is believed to be one of increasing short-range order. After precipitating the Ni3Al plates enlarge through competitive growth. Discontinuous precipitation can occur simultaneously with the above processes. Recent ideas of the origin of precipitation strengthening appear adequate to explain the hardness changes. REMARKABLY little appears to be known about the precipitation process in Ni-Al alloys in spite of their technical importance. This investigation originated to supply additional information about precipitation in general, this system in particular. Information on the structures and kinetics have been obtained through the use of hardness, X-rays, microscopy, calorimetry, and resistivity on high-purity alloys. PROCEDURES Six alloys, Table I, were prepared by melting carbonyl nickel and high-purity aluminum in alumina crucibles in vacuum and casting into 1-in. graphite molds. All rods were homogenized at least once at 1300°C for 24 hr prior to swaging and this was repeated on the first three alloys after 75 pct reduction. Alloy 4 could be reduced only 10 pct at 1000°C (probably in two-phase field) prior to fracture but 1/4-in. samples quenched from 1100°C were readily reduced cold. Alloy 5 was reduced 15 pct cold but failed on the next pass while alloy 6 of essentially the same aluminum content failed inter-granularly without apparent flow up to 1000°C. The alloys were heated in hydrogen at the elevated temperatures and formed thin, coherent aluminum oxide coatings which provided excellent oxidation resistance at lower temperatures. However, freshly prepared surfaces showed considerably less resistance at 500"to 700°C in air and apparently resulted in internal oxidation. As a consequence, low-temperature agings were carried out in evacuated tubes. RESULTS The isothermal hardening behavior of these alloys at 500"and 565C is given in Figs. 1 and 2. These results were obtained from samples cold worked 75 pct, recrystallized at 1000°C (1100°C for the 7.8 pct Al) and quenched in water. This recrystallization was used to give smaller grain sizes so as to obtain more uniform hardness values and the points represent an average of five readings. The electrical resistivity was measured on 1/16-in. wires quenched from 1000°C during aging at 495°C to give Fig. 3. The energy release and its rate are given in Fig. 4 for the 6.9 pct Al alloy during aging around 500°C. Inasmuch as this was a single run, its accuracy is not known but certainly the general shape and magnitudes are correct. The method used to obtain these results is described elsewhere.&apos; Data for the aging at 600°, 700°, and 800°C of these alloys cold worked 50 pct are given in Fig. 5. Supplementary information from microscopy and X-ray diffraction have been included to indicate recrystallization, discontinuous precipitation and the appearance of superlattice lines from the Ni3Al. The hardness of these alloys as annealed, aged, cold worked, and cold worked and aged is given vs composition in Fig. 6. Those samples which were isothermally aged, Figs. 1 and 2, were reaged at 532°C and at successively higher temperatures for the indicated times to give the data of Fig. 7. These results as well as certain others, support the idea that the level of hardness reached for temperatures above 600°C are equilibrium values more or less independent of path. This being the case, the breaks in the curves would be the complete solution of the Ni,Al. The electrical resistivity versus temperatures for some of these alloys, both aged and unaged, is given in Fig. 8 along with those data from heating slowly (10 deg per day) to high temperatures. Interesting points include the lowering of the Curie temperature (the change in slope), the lack of any indications of a solubility limit and the large temperature coefficient for the Ni3Al. A slight break for Ni3Al around 100C shows up but this is not a Curie temperature as Ni3Al is not ferromagnetic down to -190°C. Metallographically both the nickel-rich solid solution and the Ni3Al appear very much like pure nickel. Profuse twin boundaries are present both

Jan 1, 1960

By T. M. Broderick

InveStIgations into the possibilities of economically mining and concentrating low-grade iron ores of the Lake Superior region are attracting increasing attention. Among the organizations that are carrying on the work are the United States Bureau of Mines, the State of Minnesota (which spends about $80,000 annually on problems of the iron and ferroalloy ores of Minnesota), and the State of Michigan (which spends about $10,000 annually of its iron-ore research). Several of the mining companies are also financing research. Of the states in the Lake Superior district, Minnesota has done most in iron-ore concentration. In 1930, thirty-seven concentrating plants were in operation on the Mesabi Range, beneficiating about one-third of the total ore shipped. About one-half of these plants reduced silica; the others reduced moisture or improved the structure of the ore.&apos; Research into the possibilities of magnetic concentration of the Eastern Mesabi magnetite ores indicates that vast tonnages of that ore may be utilized at a profit in the not distant future. Magnetic concentration has also been tried at Sellwood, Ontario, on the Moose Mountain deposit, and at the Berkshire mine in Wisconsin on the magnetic ores of the Western Gogebic Range. There have been few attempts to concentrate Michigan iron ores. In order to determine the possibilities of such concentration, iron-ore research has been carried on at the Michigan College of Mining and Technology for the past few years. After a general survey of the iron ores of the state, a program of more detailed experimentation was outlined, starting with work on the Ironwood formation of the Gogebic Range. The results of this research led to the belief that gravity methods will produce fairly satisfactory concentrates from the parts of the iron formation that are made up of comparatively thick alternating beds of rather high-grade ore and lean chert. About 85 per cent of the iron and steel produced in the United States comes from ores of the Lake Superior district. The reserves of direct

Jan 1, 1935

By T. M. Broderick

InveStIgations into the possibilities of economically mining and concentrating low-grade iron ores of the Lake Superior region are attracting increasing attention. Among the organizations that are carrying on the work are the United States Bureau of Mines, the State of Minnesota (which spends about $80,000 annually on problems of the iron and ferroalloy ores of Minnesota), and the State of Michigan (which spends about $10,000 annually of its iron-ore research). Several of the mining companies are also financing research. Of the states in the Lake Superior district, Minnesota has done most in iron-ore concentration. In 1930, thirty-seven concentrating plants were in operation on the Mesabi Range, beneficiating about one-third of the total ore shipped. About one-half of these plants reduced silica; the others reduced moisture or improved the structure of the ore.&apos; Research into the possibilities of magnetic concentration of the Eastern Mesabi magnetite ores indicates that vast tonnages of that ore may be utilized at a profit in the not distant future. Magnetic concentration has also been tried at Sellwood, Ontario, on the Moose Mountain deposit, and at the Berkshire mine in Wisconsin on the magnetic ores of the Western Gogebic Range. There have been few attempts to concentrate Michigan iron ores. In order to determine the possibilities of such concentration, iron-ore research has been carried on at the Michigan College of Mining and Technology for the past few years. After a general survey of the iron ores of the state, a program of more detailed experimentation was outlined, starting with work on the Ironwood formation of the Gogebic Range. The results of this research led to the belief that gravity methods will produce fairly satisfactory concentrates from the parts of the iron formation that are made up of comparatively thick alternating beds of rather high-grade ore and lean chert. About 85 per cent of the iron and steel produced in the United States comes from ores of the Lake Superior district. The reserves of direct

Jan 1, 1935

In a state-of-the-an review of predictive methods for longwall support load calculation, special respect is paid to those techniques which enable actual roof conditions and local lithology of strata to be involved. Principal systems of roof examination include the borehole perforation test and seismic velocity measurements. Roof strata stability is related to caveability classifications and roof inclination due to subsidence. The critical analysis of both load resistance prediction methods and roof stability classifications shows that each has its own value of reliability level. The present research opportunities analysed underline the significance of developing fully reliable prediction techniques as needed by the coal industry.

Jan 1, 1991

By John C. LaScola

The Bureau of Mines repeatedly surveyed a grid of monuments over an active longwall mine panel in southwestern Pennsylvania during a 1-year period. Both conventional ground surveying techniques and photogrammetry were used. The objective of this investigation was to compare elevation measurements of subsidence obtained from aerial and ground survey methods under dynamic ground conditions. The results of a statistical analysis of the survey data show that the mean of the differences between 372 matched pairs of elevation measurements was 0.20 ft (61 mm) with a 95-pct-confidence interval of 0.05 ft (15 mm). The mean of the absolute values of the differences was 0.38 ft (116 mm) with a 95-pct-con-fidence interval of 0.04 ft (12 mm). Ninety-five percent of the absolute values of the differences were less than 1.11 ft (338 mm).

Jan 1, 1988

By A. M. Gaudin

THIS paper presents, with the help of colored photomicrographs, the new method of mineral identification termed "selective iridescent filming." This method pertains to the field of determinative mineralogy, which it provides with tools for: (1) phase identification, (2) solid solution analysis. The method should be particularly useful in the applied fields of: (1) paragenesis of ore deposits, (2) mineral dressing, (3) mineral synthesis and study of phase equilibria.

Jan 1, 1938

By P. J. Remington

Field measurements utilizing a seat pad accelerometer were made on 61 surface coal mining machines in order to quantify the vibration levels experienced by the operators. Those data were combined with information on the statistics of the operating times of those machines in order to compare the operator&apos;s vibration exposure to the criteria in ISO 2631, ?A Guide for the Evaluation of Human Exposure to Whole Body Vibration.? The comparison showed that about ha]f of all surface coal mining machine operators can be expected to be exposed to vibration exceeding the fatigue decreased proficiency criterion, whereas only on the order of 15% would be expected to experience vibration exceeding the exposure limit. Detailed exposure statistics are presented and the implications of the results are discussed.

Jan 1, 1983

By R. W. Heckel, H. W. Paxton

The growth of grain boundary films and Widmanstiitten plates of proeutectoid cementite in hypereutectoid steels ulas considered quantitatively in three plain carbon steels and one "pure" iron-carbon alloy. Growth was found to take place at a slower rate than would be predicted on the basis of a model invoking rate control by long range diffusion of carbon. The films in the pure alloy grew faster than those in the plain carbon steels. A possible explanation is suggested. In 1904, Nernsst&apos; and Brunner2 postulated that ionic crystals growing in supersaturated aqueous solutions grew at rates determined by diffusion through the solution to the growing crystal interface. The gradient down which the diffusion took place was assumed to be fixed by the supersaturated bulk solution concentration, the concentration dt the crystal surface and some arbitrary distance. The flux of material to the crystal was described as Flux where D is the diffusion coefficient, A the crystal surface area, Ci the bulk solution concentration, Co the saturated solution concentration, and 6 the thickness of the diffusion zone. It is obvious that the expression is an adaptation of F+ick&apos;s3 first law of diffusion (steady state). This was the initial formulation of what will be defined here as "diffusion controlled growth," i.e., growth limited by the long range diffusion of a component either to or from the advancing interface assuming both phases at the interface to be in equilibrium. This idea of equilibrium interface concentration implies an infinite reaction rate at the interface. Volmer, Zener,&apos; and 11schner6 have derived expressions for the diffusion controlled growth of spherical precipitates in metallic systems. These analyses agree that the growth in a given direction should be parabolic with time. Brown and Hawkes7 observed that graphite, formed both from the decomposition of cementite and from the decomposition of eutectoid austenite in cast irons, grew according to a parabolic relationship and, therefore, concluded that the laws of diffusion controlled growth, as defined above, were obeyed. They, among others, failed to consider, however, that parabolic growth is a necessary, but not sufficient, condition for diffusion controlled growth. Mehl and Dube"&apos; have pointed out that equilibrium may not be realized because the concentration at the interface cannot change instantaneously from that of the bulk to the saturation value. Furthermore, they propose that an equilibrium solute concentration in the parent phase adjacent to the precipitate would remove the thermodynamic activity gradient across the interface and, thus, stop the growth process. Frisch" has also emphasized the importance of interface concentrations that vary throughout the growth of a new phase. The variation in activity across an interface, as discussed by Onol&apos; and Cahn and Hilliard,12 is of fundamental importance to this question. Ham13 considered the data of Turnbull14 on the growth of barium sulfate in aqueous solutions. He concluded that the data could be analyzed in terms of a radiation-type boundary condition. Flux across interface = K (c, - C,) [21 where C, is the concentration in the solution at the interface, Co the saturated solution concentration, and K the proportionality constant. The edgewise growth of Widmanstlitten plates, frequently referred to as the rate of lengthening, was first considered by Zener.&apos;&apos; Basing a mathematical analysis on steady-state (constant velocity) growth he concluded that where G is the growth rate, D the solute diffusivity, Ci the concentration in the bulk, Co the equilibrium interface concentration, C, the concentration in the precipitate, a a constant, Y the radius of curvature of the edge of the plate, and rC the critical radius, i.e., the radius which would increase the activity of solute at the interface at equilibrium under the influence of capillarity to that of the bulk. Zener1&apos;

Jan 1, 1961