Search Documents

By H. E. T. Haultain

The study of rock crushing or grinding in tube-mills is difficult on account of the large size of the units employed in the field and the large number of variables entering into the problem. Three or four years ago, in the laboratory of the Department of Mining Engineering of the University of Toronto, a serious effort was commenced to study the matter under laboratory conditions. Experiments were carried on in a cylindrical tube-mill 18 in. long and 12 in. in diameter, inside measurements,

Jan 1, 1923

By H. E. T. Haultain

The study of rock crushing or grinding in tube-mills is difficult on account of the large size of the units employed in the field and the large number of variables entering into the problem. Three or four years ago, in the laboratory of the Department of Mining Engineering of the University of Toronto, a serious effort was commenced to study the matter under laboratory conditions. Experiments were carried on in a cylindrical tube-mill 18 in. long and 12 in. in diameter, inside measurements,

Jan 1, 1923

By L. K. Eigenbrod, F. Notaro

Enactment of Public Law 91-173 (Federal Coal Mine Health and Safety Act of 1969) has placed new responsibilities on the mining industry. The new law, aimed at eventually solving the problem of pneumoconiosis, sets new respirable dust standards at 2 mg per cu m. Techniques employed to date have been shown to lack total effectiveness in meeting the prescribed standards. Since it is possible that even the new standards will eventually have to be lowered to effectively attack the medical problem, the need for new and more reliable methods of assuring clean respirable air will intensity. This paper presents, in a preliminary manner, both the present technical capability and growth potential of cryogenic technology for supplying miners with clean breathing air. Work with two sizes of prototype supplied-air (cryogenic-liquid) respiratiors in Union Carbide's Fawn Coal mine, will be described. Other potentially fabricable systems will be discussed and a preliminary assessment made of the potential cost of introducing cryogenic air breathing systems in coal mine service.

Jan 1, 1972

By R. G. McQueen, E. G. Zukas

THE production of isotropic fine-grained ingot iron would be most useful since physical measurements associated with the elastic properties of iron are influenced by the size and orientation of the individual grains. This can be accomplished at present for small samples by established metallurgical procedures, but for large samples (in excess of 2 in. diam by 1 in. thick) it is virtually impossible to produce reasonably small uniform grains with random orientation. Such pieces can, however, be produced by impulsive loading followed by a suitable recrystallization treatment. The shock loading system employed is diagrammed in Fig. l. Here the 3/8-in. iron plate is accelerated by the plane-wave initiated high explosive charge through a 1 5/8-in. air space. Collision of this plate and the specimen of interest generates a shock wave in excess of 300 kbars which passes through the specimen. For this type of work it is not necessary to use machined parts: for example, the ingot iron pieces are saw cut from the billet so that they can be inserted in short sections of iron pipe. The recovered specimens are less distorted, however, if the air gap between the iron sample and pipe is filled with Woods metal. The dimensional changes resulting from this type of loading technique are minor, usually less than a 10 pct reduction in thickness. Compressive yield

Jan 1, 1962

By James C. Fisher

Traditional uranium exploration techniques were utilized and comparatively evaluated in the Front Range, Colorado uranium province. Intense surficial leaching and thick colluvial cover render traditional airborne and ground radioactivity reconnaissance prospecting useless. Radon gas emanometry and sulfur gas emanometry were slightly more effective but the long and short term variations In soil gas emanation rates make it extremely difficult to gain useful information from these systems. The technique judged most useful was Track Etch radon prospecting. The excellent definition of the technique, as well as its repeatability, indicate that it is an ideal prospecting tool for narrow vein-type deposits similar to those of the Front Range, Colorado.

Jan 1, 1976

By E. G. Leonardon

The object of this paper is to describe briefly the practical results obtained in several problems of civil engineering by resistivity measurements of the underground. It is intended for the mining engineer, as well as for the construction engineer; the stratigraphical problems discussed are general and frequently are encountered in mining exploration. Resistivity measurements have been used in mining and oil exploration for a number of years.' Their introduction in the field of civil engineering, on the contrary, is rather recent. It was applied for the first time in the spring of 1928 near Littleton, N. H., in the survey of two dam sites for the New England Power Assn.2 Since then, the geophysical firm with which the author is connected has had an opportunity to develop this field of activity, and more than 20 investigations at dam and tunnel sites have been carried out in the United States and Canada. A part of this work has been verified by underground or drilling exploration. This paper deals with but a few of the results, which we are permitted to make public now. The theoretical and technical sides of the processes employed will not be discussed; they have already been described in various technical publications. A few general points will be mentioned, to make clear the practical examples given. Resistivities OF the Rocks The surveys are based on the measurement of the specific resistance of the rocks. This resistivity is the electrical resistance of a cylinder of

Jan 1, 1932

By Paul D. Merica, W. A. Mudge

ONE of the most prominent features of our present-day industrial development is the ever-increasing demand put upon materials of construction Engineering ingenuity, within the past 25 years, has been unusually active, and in some fields at least engineers frankly say that engineering design has progressed as far as the limitations imposed by the properties of the present materials of construction will permit. Consequently, they are today demanding improvement in their working materials and seeking new ones, through the aid of which the present limitations of design may be overcome The activity of this search is evident in all fields, but it is particularly so in that of structural materials required to be resistant to corrosion The corrosion resistance of metals and alloys is never absolute and all-inclusive, a particular alloy will withstand some corrosive conditions well and fall utterly under others Furthermore, other properties, physical and mechanical, required in conjunction with corrosion resistance vary considerably for different commercial applications One wants a soft, ductile sheet metal resistant to atmospheric corrosion, another, a high-strength alloy resistant to sulfuric acid The last decade has witnessed active and definite progress in the development of high-strength, corrosion-resisting alloys In June, 1924, a symposium by the American Society for Testing Materials, on Corrosion-Resistant, Heat-resistant and Electrical-resistance Alloys, disclosed no less. than 60 commercial alloys the properties of which were described as being suitable for industrial service where corrosion resistance

Jan 1, 1935

By M. Vallée

This case study compares the actual production figures for the No. I and No. 2 copper orebodies of the Société Miniére Louvem, Val d'Or, Quebec, with the preproduction estimates and a postmortem geostatistical estimation using kriging techniques. The deposits considered are small subvertical sulphide orebodies which were mined from August 1970 to April 1973, producing 648,000 tons at 2.04% Cu versus the 1968 computed reserves of 671,000 tons at 2.51% Cu (with 20% dilution), thus showing a 25% overestimation of the copper contained. The postmortem geostatistical estimation based on the same 44 D.D.H. intersections available in 1968, shows 2.24% Cu (no dilution), compared to 3.23% Cu (no dilution) given by the conventional section method. Block by block kriging techniques were used, but within the ore contours as determined by the geologist. In this case, Characterized like many sulphide deposits by highly dispersed sample values, geostatistical kriging techniques permit a more realistic estimation of the metal contained within a given volume, than the conventional methods which overestimate it. This study has been conducted by the Mineral Exploration Research institute (IREM-MERI) for SOQUEM, and is one of the few case studies released with all pertinent data. More postmortem of this kind are required for geologists and geostatisticians to improve their methods and their "batting average".

Jan 1, 1977

By Fred D. DeVaney

W. O. Philbrook (Carnegie Institute of Technology, Phila.)—Mr. DeVaney's paper is a valuable addition to the growing technology of the magnetic roasting of lean iron ores. His furnace is ingeniously designed to permit close control of the process and to achieve high thermal efficiency by counter-current heat exchange and the withdrawal of both solid and gaseous products at relatively low temperatures. The principle of using a lean reducing gas to avoid over-reduction of the ore even at high operating temperatures (for rapid re-action rate) is thoroughly sound. The gas analyses and flow rates reported, however, are internally incon- sistent and render suspect any details of a heat balance based upon them. While it is entirely proper to consider the entrant gas as a reagent and to account only for the heat evolved by consuming a portion of the gas, many operators are accustomed to a heat balance using the total calorific value of the reagent supplied; and comparison of heat balances made with different bases of calculation can be quite misleading. Since Mr. DeVaney's paper is likely to be cited frequently in future discussions of magnetic roasting processes, it seems worth while to point out the internal discrepancies and to give alternate values of heat requirements for different bases of calculation.

Jan 1, 1954

By David A. Martin

Resource based companies have been inundated with changes in government tax legislation during the past few years. To cope, capital investment planning analysts have turned almost completely to computer simulation modeling to react quickly enough to determine the effect on their companies' major investment projects and on the projected financial picture of the companies. This paper will examine various royalty and tax structures as applied to coal, oil and gas, and minerals in the U.S. and Canada with particular emphasis on recent changes in the Canadian tax scene and their implications to capital project economic evaluation in other parts of the world.

Jan 1, 1977

By David G. Chedgy, Wen L. Chen, Bill S. Taylor

Theoretically the heavy medium cyclone is capable of cleaning raw coal from a top size of about 38 mm (1 1/2 in.) to a bottom size of about 200 mesh. With this idea, plants have been built recently using the heavy medium cyclone without desliming. The full size range down to zero is fed into the cyclone. Products + 28 mesh are removed in the normal manner on drain and rinse screens. The 28 x 200 mesh products are recovered separately from the magnetic separator tailings. Simplicity of flowsheet and plant operation coupled with the high efficiency of the heavy medium cyclone makes this a very attractive approach.

Jan 1, 1980

By Cyril S. Taylor, Junius D. Edwards

Magnesium is the lightest metal used for structural purposes, for which reason perhaps more than usual interest is attached to measurements of its density. Although the density of solid magnesium has been det,ermined frequently, no measurements of the density of the liquid metal are available. Because of unusual experimental difficulties in measuring the density of the liquid, only a limited number of measurements of good precision were secured. The results, especially the value for the crystallization shrinkage, are of great interest in connection with the casting of the metal. A number of samples for these measurements were made available through the courtesy of the American Magnesium Corp. They were in the form of extruded bars 3/8 in- in diameter and several were of exceptional purity, as indicated by careful analyses. Table 1 gives the density values (at 20" C.) for magnesium of varying degrees of purity. The density was measured at room temperature by comparison of the weight in air, and when immersed in distilled water. The necessary buoyancy corrections were applied, so that the density could be expressed in absolute measure—grams per milliliter. The effect of the buoyancy of the immersed suspension and the surface-tension pull of the water upon the suspension were eliminated from the results by a preliminary weighing of the suspension immersed to the working depth. Great care was necessary to prevent the introduction of a significant error by the formation of gas bubbles upon the clean magnesium surfaces; these are sometimes very minute and easily escape observation. They may be detached by raising the specimen from the water and again immersing; this should be done just prior to completing the weighing. Their formation may be almost entirely prevented during a measurement by previously immersing the specimen in a solution of paraffin in petroleum ether. The thin film of paraffin remaining after the evaporation of the solvent prevents wetting of the magnesium surface by the water. In one such determination, the paraffin coating on a 22-gm. Specimen

Jan 1, 1923

By Junius D. Edwards, Cyril S. Taylor

Magnesium is the lightest metal used for structural purposes, for which reason perhaps more than usual interest is attached to measurements of its density. Although the density of solid magnesium has been det,ermined frequently, no measurements of the density of the liquid metal are available. Because of unusual experimental difficulties in measuring the density of the liquid, only a limited number of measurements of good precision were secured. The results, especially the value for the crystallization shrinkage, are of great interest in connection with the casting of the metal. A number of samples for these measurements were made available through the courtesy of the American Magnesium Corp. They were in the form of extruded bars 3/8 in- in diameter and several were of exceptional purity, as indicated by careful analyses. Table 1 gives the density values (at 20" C.) for magnesium of varying degrees of purity. The density was measured at room temperature by comparison of the weight in air, and when immersed in distilled water. The necessary buoyancy corrections were applied, so that the density could be expressed in absolute measure—grams per milliliter. The effect of the buoyancy of the immersed suspension and the surface-tension pull of the water upon the suspension were eliminated from the results by a preliminary weighing of the suspension immersed to the working depth. Great care was necessary to prevent the introduction of a significant error by the formation of gas bubbles upon the clean magnesium surfaces; these are sometimes very minute and easily escape observation. They may be detached by raising the specimen from the water and again immersing; this should be done just prior to completing the weighing. Their formation may be almost entirely prevented during a measurement by previously immersing the specimen in a solution of paraffin in petroleum ether. The thin film of paraffin remaining after the evaporation of the solvent prevents wetting of the magnesium surface by the water. In one such determination, the paraffin coating on a 22-gm. Specimen

Jan 1, 1923

By Donald W. Frommer

For many years the Bureau of Mines has been con- ducting comprehensive iron ore research programs with the objective of increasing domestic supplies and divising techniques that would enable profitable exploitation of low-grade and complex domestic iron-mineral deposits. Since 1962, much of the Bureau's flotation research at Minneapolis has been concerned with studies on the treatment of low-grade hematitic-goethitic jaspers of the Marquette range, Mich. Ores from Michigan require grinding to substantially minus 400-mesh for liberation that will permit production of quality concentrates. With such fine grinding, diminished flotation effectiveness can be expected because of slime interference. The word "slime" is an ambiguous term. Taggart states "Slimes in an ore pulp are loosely defined as the fine fraction that overflows a desanding separator. . ."

Jan 4, 1964

By Paul Hett

The much-heralded Deep Ruth operation of Kennecott Copper Corp., at Ruth, Nev., is scheduled to become a producer by 1957. Inaugurated as a project in 1951, production was originally scheduled to start in 1953, but excessive water hindered shaft sinking. A revised schedule called for output by 1955, but again plans had to be changed. This time the change was to permit mining of an orebody that would have otherwise been lost because of block caving methods planned for the main deposit. The new ore is within the cave limits of the larger orebody, above the first production level. Ore will start coming from this new source in 1956, a year ahead of the principal operation. (See NEWS, page 344.) There is little doubt that current economic conditions and unforeseen expenditures for early shaft development will make the Deep Ruth a high-cost producer. Yet, some of the drawbacks of the Kennecott operation may be mitigated by the possibility that additional exploration will increase the already assured 25 million tons of 0.83 pet copper ore. While Kennecott is missing out on the current high copper market and is thus left with a potentially narrowed profit, the predicted demand for copper has created an optimistic feeling. Its development is certain to enlarge known U. S. copper reserves and significantly extend the life of Kennecott's Nevada operations.

Jan 4, 1955

By A. E. Bibb, F. W. Kunz

A platelet form of zirconium hydride was found in zirconium and ZY-1 wt pct U single crystals containing hydvogen in the range of 50 to 100 ppm. The habit planes for the hydride plateletg in the zirconium crystals were found to be {1012}, {1121}, and (1122) while the habit planes in the ZY-1 wt pct U crystals were {1121), {1123}, and (1.231). With the exception of the {1231} plane, these have been identified as the twin planes in zirconium. The different effect of hydridc on the mechanical puoperlies of zirconium at high and low strain rates has been explained in terms of the defornzation mechanism and the habit planes of the hydride. ZIRCONIUM and zirconium-base alloys are considered for many nuclear reactor applications, where the pick-up of hydrogen is a distinct possibility, if not an unavoidable occurrence. An excellent example of this is the absorption of hydrogen by zirconium and its alloys during aqueous corrosion, where as much as 30 pct of the hydrogen produced by the corrosion reaction is picked up by the metal. Under the proper conditions, the absorbed hydrogen would precipitate as zirconium hydride and consequently alter the mechanical and physical properties of the zirconium-base alloys. The knowledge obtained from a study of the crystallographic aspects of the hydride precipitation is necessary for the interpretation of the observed changes in the mechanical and physical properties. The deleterious effect of hydrogen on zirconium-base materials is not always observed in normal slow tensile loadings at or above room temperature, but becomes immediately obvious under impact loading, where the energy absorbed decreases with increasing hydrogen content,' and in notched specimens where triaxial loadings are attained.2 This effect is of serious consequence in the applications of Zr where shock loads or high strain rates are experienced. The purpose of this investigation was to determine the crystallographic planes of the Zr and Zr-1 wt pct U matrices upon which zirconium hydride will precipitate and to correlate these with the observed mechanical property data. PROCEDURE Crystal Growth—Single crystals of Zr and Zr-1 wt pct U alloy were used in this investigation. The Zr crystals were made from sponge that had a typical analysis as shown in Table I. Large grains were grown in this material by rapid cooling an arc-melted charge in a button furnace. This operation undoubtedly lowered the volatile impurity concentration below those listed in Table I. Back-reflection Laue patterns of these large grains showed the presence of considerable substructure and lattice distortion within each grain. It was found that an 18-day anneal in an argon atmosphere at 840°C (a high a heat-treatment) followed by furnace cooling, resulted in the further growth of the large grains and removed the detectable substructure ana lattice distortion. Equiaxed crystals with a cube edge of approximately 1/4 in. were produced in this manner. Large crystals of Zircaloy-2 (1.5 wt pct Sn, 0.15 wt pct Fe, 0.1 wt pct Cr, 0.05 wt pct Ni) also were produced by this technique but the large amount of substructure formed could not be removed by annealing. The Zr-1 wt pct U solid solution crystals were produced from an alloy rod consisting of Westing-house-Foote hafnium-free crystal bar zirconium and depleted uranium. The chemical analysis of the alloy is also given in Table I. Three-inch sections were cut from an 0.120-in.-diameter alloy rod and tapered to a fine point on each end. The samples were sealed in evacuated Vycor tubes, homogenized for 5 hr at 1000°C in the ß-phase field, and slowly lowered in a gradient furnace into the a phase (800°C), annealed for 60 hr at this temperature to produce grain growth and furnace cooled. This technique produced large grains approximately 1/2 to 3/4 in. long over the entire cross section of the rod, which were free of observable substructure. Metallographic examination up to X1000 did not show the existence of any second phase in these grains. Crystal Orientation—All crystals were abraded on fine emery paper to produce two flat surfaces 90 deg to each other. The crystals were analyzed by the standard Back-Reflection Laue technique to obtain the crystal orientation with respect to the abraded surfaces. The Back-Reflection Laue Photograms of all crystals used were clear and sharp indicating that the crystals were free from any substructure that could be detected by these means. Hydriding—Only samples containing four to five grains were used for hydriding. Samples that exhibited fine grained patches were discarded. The samples were hydrided using the following technique. After etching in 48 vol. pct HNO3, 48 vol. pct H2O, and 4 vol. pct HF (48 pct) solution, the specimens

Jan 1, 1961

By S. J. Shale

Recent changes at Cornwall are highlighted by development of a panel caving method, with slushing drifts, for underground practice as open pit operation nears close. Metallurgy keeps the pace with high recovery from increasing amounts of harder to liberate, higher sulphide content, underground ore.

Jan 7, 1953

H. W. Turner, San Francisco, Cal. (communication to the Secretary*): This excellent paper apparently represents the results of extensive observation and experience among the mines of the Mother-Lode, but I strongly question its relegation of the dioritic intrusions to the period of fissuring and ore-deposition. The dioritic rocks referred to are evidently those areas represented by Ransome in the Mother-Lode folio1 as meta-diorites, and, as he says, are merely basic facies of the great granodiorite batholite of the Sierra Nevada. If followed downward I venture to predict that these meta-diorite areas would be found to connect with the great batholite, and to be in fact mere apophyses of it. I see no reason for supposing that these apophyses were intruded into the Mother-Lode slates at a period later than the intrusion of the granodiorite in general. The period of fissuring was subsequent to this intrusion; the basic granodiorite or quartz-diorite areas of the foot-hill region are themselves fissured extensively; and the fissures were filled with quartz, apparently during the same general period of the formation of the Mother-Lode veins. Prichard and Ransome2 both refer to the deposition of quartz in the same lode at different periods resulting from a reopening of the fissures. Some time since, I saw in the stopes of the

Jan 1, 1904

By D. de Fontaine

A convolution procedure is described for obtaining an analytical expression for the composition profiles of solute concentration:; in binary solid solutions. The free energy of solutions containing such compositional inhomogeneities can then be evaluated and the stability of spherically symmetric clusters (G.P. zones, for short) us a function of their radii and central compositions can be studied accordingly. Two characteristic zone radii are defined: the minimum radius (RM) corresponding to the smallest zone for which growth is energetically favored over dissolution, and the critical radius RK) corresponding to zones associated with the minimum work of formation. The values of RM and RK coincide at the two classical limits of nucleation and growth and spinodal decomposition. As the spinodal is approached, however, RM and RK diverge increasingly and it is proposed that the initial] decomposition morphology is governed more closely by the minimum, rather than by the critical radius since the former possesses no singularity within the m eta stable phase boundary. Reversion is briefly discussed in the light of the foregoing and it is shown that a set of reversion temperatures located between the coherent miscibility gap and the coherent spinodal must correspond to a given distribution of low temperature zones. SINCE the early works of Guinier1 and preston,2 the kinetics and morphology of GP zones have been studied extensively, see Ref. 3, for example, for a recent review. Nevertheless, a completely satisfying theoretical treatment of the decomposition of meta-stable or unstable binary solid solutions is still lacking due to the almost unsurmountable mathematical difficulties that one encounters in attempting to solve the pertinent diffusion equation which, in principle, describes the whole process. This equation, first derived by Cahn for the initial stages of spinodal decomposition,4 is a nonlinear partial differential equation of the fourth order in anisotropic space, a general analytical solution of which is completely out of the question. From this equation, some prediction can be made, however, concerning the later stages of spinodal decomposition5 and a recent numerical solution6 of the equation in the case of one- and two-dimensional composition modulations of a solid solution inside the spinodal has led to the following considerations: the sinusoidal morphology7 is to be expected only for solutions of average composition c, located near the center of the coherent miscibility gap.8 For solutions with co closer to the spinodal decomposition, depleted shell zones9 should constitute the first recognizable decomposition product, later evolving to iso- lated, enriched preprecipitates in a uniformly depleted matrix as this must, in all cases, constitute the final metastable morphology, barring, of course, loss of coherency and change in crystal structure. In agreement with the qualitative description of Bonfiglioli and Guinier,l0 it thus appears that the various models discussed by previous authors are, in fact, idealized successive stages of the general decomposition process. Unfortunately, corresponding calculations for a solid solution outside the spinodal are not yet available because of two additional difficulties: it is essential that the diffusion equation be solved in three-dimensional space, and furthermore, one must include in the equation an appropriate "source term" describing the statistics of the creation of composition fluctuations required to trigger the nucleation events. At present, a general treatment of this problem does not appear to be tractable. Nevertheless, by using a modelistic approach, i.e., by selecting a priori certain composition variation profiles and by evaluating their associated free energies, one can draw certain conclusions relative to the stability of these isolated composition modulations or "zones", both outside and inside the spinodal. This is the object of the present investigation. THEORY We shall now describe a standard four-parameter spherically symmetric GP zone, evaluate its free energy according to the Cahn and Hilliard11 formula (Eq. [5], below), and plot the corresponding energy surfaces as a function of zone amplitude and radius as

Jan 1, 1970

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' 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'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,' 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"' 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' 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.'' 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'

Jan 1, 1961