Search Documents

By R. D. Nelson, J. C. Shyne

The ß and a ß transformations in plutonium were studied with particular emphasis on the transformation kinetics and microstructure. Significant observations are: 1) The kinetic data show conclusively that the ß — a transformation in high-purity plutonium can proceed isothermally with no athermal component. 2) Plastic deformation of the stable (3 phase retards the subsequent (3 — a transformation. 3) Plastic deformation of the stable a phase accelerates the a — ß transformation; the acceleration is attributed only to residual stresses. 4) The a and a?a volume changes occur anisotroPically in textured plutonium. 5) An apparent crystallogvaphic relationship exists between the parent and the product phases of the and (3 — a transformations. 6) Both applied uniaxial compressive stresses and uniaxial tensile stresses raise the starting temperature for the ß — a transformation. 7) A given uniaxial tensile stress favors the a — ß transformation more than an equivalent applied uniaxial compressive stress opposes the transformation. These observations of the (ß —a and a — ß phase changes in plutonium are consistent with known mar-tensitic transformations. ThIS paper elucidates some of the characteristics of the a— ß and ß —a transformations in plutonium. Because considerable conjecture exists about the mechanisms by which the phase transformations occur in plutonium, experiments have been performed to provide indirect information concerning the mechanisms responsible for the a —ß and ß -a transformations. Indirect information is of particular value in the study of plutonium because of the experimental difficulties presented by the metal. Single crystals have not been produced in any of the allotropes. The large density results in high X-ray and electron-absorption factors and consequently complicating X-ray and electron diffraction. The kinetics of ß — a and a — ß transformations of plutonium and the behavior of the transformations under a variety of conditions have been investigated in detail. Information about the mechanisms of the allo-tropic transformations of plutonium was obtained indirectly from three sources: 1) the effect of plastic deformation of the stable parent phase upon the transformation kinetics; 2) the behavior of the metal transforming under applied stresses; and 3) the microstruc-tural and crystallographic features between parent and product phases. PHASE-TRANSFORMATION CHARACTERISTICS In characterizing solid-state phase transformations in metals and alloys, it is useful to define several types of transformations. An aim of the present work was to identify the low-temperature transformations in plutonium by type, i.e., as martensitic or nonmar-tensitic. Practical definitions for these terms follow. The terms commonly used to categorize phase transformations lack universally accepted definitions. This confusion arises doubtlessly because some terms specify crystallographic or morphological character while other words have a kinetic or a thermodynamic connotation. For example, martensitic specifies certain definite crystallographic restrictions. Unfortunately, martensitic is sometimes used in an ill-defined way to imply kinetic characteristics. Further confusion attends the use of such expressions as nucleation and growth, diffusional, and massive. From time to time new systems of phase-transformation nomenclature are suggested; unfortunately none of these has gained general acceptance.1,2 The authors of the present paper have no intention of entering the controversy. We recognize that some readers may object to the nomencliture used here. For exampie, the terms military and civilian have recently been used in much the same way as martensitic and non-martensitic are used in this paper. This paper is intended to describe several specific details of the low-temperature phase transformations in plutonium. The authors have found it useful to identify these transformations as martensitic; the term was chosen as the best available to describe the experimentally observed features of the transformations studied. A martensitic transformation is one that occurs by the cooperative movement of many atoms; the rearrangement of atoms from parent to product crystal structure occurs by the passage of a mobile semico-herent growth interface. The geometric features characteristic of a martensitic transformation are a specific orientation relationship between the product and parent phase lattices, a specific habit-plane orientation for the growth interface, and a shape change with a specifically oriented shear component. There is no alloy partition between the parent and product phases in a martensitic transformation. Martensitic transformations may display either athermal kinetic behavior or thermally activated isothermal kinetic behavior. Some martensitic transformations occur isothermally, although more commonly martensitic transformations are athermal. Isothermal martensitic transformations are suppressible by rapid cooling. In athermal martensitic transformations, nucleation and growth are not thermally activated and the transformations are essentially time-independent. Nucleation, growth, or both can be thermally activated in isothermal martensitic reactions. Transformation of the parent phase into a marten-

Jan 1, 1967

By F. G. Loper

Simulation as a mathematical technique is not new. However, recent increases in digital computer speeds and the ease of programming with languages such as Fortran have centered a good deal of attention around simulation in the last few years. By ignoring all but the relevant characteristics of a process, a mathematical simulator may be constructed which, when fed operating data, should react as the process would. The output becomes numbers, instead of tons, however. Thus, a trial-and-error operation of such a simulator will permit management to study a major system change at little cost.

Jan 1, 1967

By A. H. Larson, L. G. Twidwell

DURING the roasting of zinc sulfide concentrates and by-product recovery from flue dusts, the zinc sul-fate phase may occur in various stages of the processes. In addition to zinc sulfide, other sulfide phases are usually present such as CdS, PbS, CuzS, and FeS. Consequently, the effect of these sulfides on the thermal decomposition of ZnS04 was investigated. Merck high-purity, anhydrous zinc sulfate was used as the starting material. The sulfate was heated under an argon atmosphere, at a rate of 10°C per min. With the first slight indication of decomposition as determined by gas analysis, the sample was removed from the furnace and allowed to cool. X-ray patterns showed no other phase present. It is estimated that less than 0.05 pct of the ZnS04 decomposed. The metal sulfides were also heated under an argon atmosphere to drive off any adsorbed water. The materials were then sized (-200 to +270 mesh), mixed in predetermined mole ratios, and pressed into pellets. The experimental measurement of the reaction rate consisted of purifying the argon carrier gas, continuous flushing of the heated reacting mixture with argon, and collection and analysis of the SOn product gas. The reaction system was heated to 600°C and al-

Jan 1, 1967

By Harry Perry

By 1980, the free world's need for economic sources of energy is expected to double. As a result, there will be a tremendous potential for all energy sources working together to supply the demand. For coal to continue its dominant role as a low-cost energy source, means must be found for it to meet the challenge of nuclear power and to overcome obstacles placed on its use by air and water pollution regulations. As the more limited reserves of gas and oil diminish, economic ways are also required for converting coal to synthetic liquid and gaseous fuels, and to chemicals, thus resulting in optimum utility of the most abundant low-cost fuel resource. The means for accomplishing these ends can only come about by a vigorous research and development program. Successful efforts by industry and government working together, both in America and abroad, will assure the continued use of coal to meet the world's energy demands. This paper discusses the emerging patterns of energy sources throughout the world and the role that research and development on coal will play in supplying future energy requirements.

Jan 1, 1967

By H. J. Gerritsen

From presently available components a portable, rugged, reliable apparatus can be built which will be able to detect methane concentrations of 0.1% and lower in air. Sensitivity and design considerations of the apparatus are given. Ways to build even simpler and cheaper apparatus in the future are indicated. Traditionally the problem of detecting and monitoring the presence of dangerous gases present in small concentrations in air has been a difficult one. Whether canaries,' or sophisticated chemical or thermal conductivity methods are used, they seem to be either slow, cumbersome, or otherwise not completely satis factory. A seemingly natural way of gas detection is to measure the strength of absorption undergone by light of a wavelength that the gas to be detected absorbs. This method has been difficult to apply in view of the low power output over a narrow wavelength range in the infrared from traditional glow bar light sources. Besides, the apparatus to select such a narrow band of wavelengths is quite costly and complex. The use of a laser solves these problems simultaneously. Although a variety of lasers are available to detect a variety of gases (such as carbon monoxide or methane) whose early detection would be desirable, this paper deals exclusively with the use of lasers for methane detection. ABSORPTION SPECTRUM OF METHANE IN AIR The absorption spectrum of pure methane is very well known.2-4 There are four fundamental vibrations, all occurring in the infrared of which only two absorb strongly. They occur at 3.3 µ and 7.7 µ. The absorption spectrum is quite complicated due to the fact that the methane molecule can rotate in a variety of rotational quantum states. These rotational states are furthermore split by anharmonic forces such as the Coriolis force.4 When methane is present in air at atmospheric pressure, much of the very fine structure due to the anharmonic force is washed out since the pressure broadening is of the same magnitude as the splitting due to anharmonicity. For most of the spectrum at 3.3 µ, the rotational lines are typically separated by 0.01µ while the individual linewidth is 0.0001 µ. It is thus very important that the laser emit at a wavelength that coincides with one of these rotational lines. Before elaborating on the point that such a laser exists and how it performs, it is necessary for later discussion to point out that in the

Jan 1, 1967

By T. H. Alden

BaCKOFEN, Avery, and Turner have shown"2 that the large tensile elongation in superplastic metals is correlated with a high strain-rate sensitivity of the flow stress. At present, the reported superplastic materials are complex eutectic or eutectoid systems with a large solubility range in at least one of the terminal phases. This note describes the behavior of a solid-solution alloy (at 22°C)5,= Sn-1 wt pct Bi, which has been processed in order to produce a fine grain size.2,3,6 The chill-cast, 1/2-in.-diam ingot was homogenized for 1 week at 130°C, extruded at O°C to 0.083 in. diam, quenched within 15 sec, and stored at -196°C. Samples were warmed to room temperature 16 hr prior to mechanical testing or metallography. During tension testing at room temperature, it was found that the flow stress reached a steady-state value which depended on the imposed elongation rate and was independent of strain to an error of about ±5 pct. In Fig. 1 is plotted log a vs log e where a is the measured steady-state flow stress and i the imposed strain rate. These quantities were calculated using "instantaneous" area and length to an accuracy in the sample diameter of ±5 x 10-4 in. The log a-log 1 curve is sigmoidal. The strain-rate sensitivity, which may be given by d log old log 6,' has a maximum value of about 0.48 between i = 5 x 10-4 and 5 x 10-3 per min. The value is well above frequently measured values for metals at creep temperatures (0.1 to 0.3) and comparable to the rate sensitivity for Pb-Sn solder: which has been shown to be superplastic.2,3 Note, however, that below or above the strain rate of 10-3 per min the rate sensitivity of Sn-1 pct Bi decreases and at high rates is more nearly like that of conventional metals. The grain size of this material is relatively uniform, Fig. 2, and may be specified by an average linear intercept i.' Grain growth occurs at room temperature but after 16 hr, L = 5. Tensile elongation was measured on finer-grain-size specimens, which had been at room temperature 15 min prior to testing. After 15 min, the samples are fully recrystallized. Three strain rates, 5 x 10-3, 10-2, and 2.5 x 10-2 per min, were employed for which the measured elongations varied from 425 to 500 pct. These results would seem to justify the term superplastic, applied to this alloy, although the ductility is inferior to that of the Sn-Bi eutectic.3 The Sn-1 pct Bi alloy, which is a single-phase material with equiaxed, fine grains, is an excellent one on which to make an estimate of the Nabarro-Herring9 creep rate. According to the model of Avery and Backofen2 a substantial part of the deformation must be accomplished by N-H creep in the strain rate-temperature regime in which d log a/d log 1 = 0.5. The maximum N-H creep rate is given by9 L2kT where v is the atomic volume and D the self-diffusion coefficient. For this test v = 3.O x 10-23 cu cm, D = 1.4 e-23,300/RT = 2.5 x 10-l7 sq cm per sec,7 L = 5x 10+4 cm, T = 295°K, and a = 2000 lb per sq in. = 1.38 x 10' dyne per sq cm. The calculated creep rate is E= 4 x 10-11 per sec which may be compared with the measured creep rate at this stress, Fig. 1, of 6.7 x 10-5 per sec. The N-H creep rate is seen to be negligible. Earlier consideration2 of this question was in error because incorrect diffusion coefficients were used. The assistance of R. R. Russell in metallography is acknowledged gratefully.

Jan 1, 1967

By R. M. Jorda

The mechanism of parafin deposition and prevention has been studied in the laboratory using an apparatus which provides a quantitative means of studying parafin deposition on metal and plastic surfaces. The amount, hardness, adhesion, per cent wax and mean molecular weight of parafin deposits appear to be governed by surface roughness alone, all other conditions being constant. Tests of various plastic coatings indicate that most smooth, nonparafinic plastics are capable of reducing parafin deposits in oil wells, but flexible, highly polar, nonparafinic plastics are more suitable for providing long term resistance to parafin deposition in oil wells if the flow stream contains abrasive materials. INTRODUCTION The problem of paraffin deposition is one of long standing in the oil industry.' Crude oils often contain paraffins which precipitate and adhere to the liner, tubing, sucker rods and surface equipment as the temperature of the producing stream decreases in the normal course of flowing, gas lifting or pumping. Heavy paraffin deposits are undesirable because they reduce the effective size of the flow conduits and restrict the production rate from the well. Where severe paraffin deposition occurs, removal of the deposits by mechanical, thermal or other means is required, resulting in costly down time and increased operating costs. The troublesome paraffins are normal hydrocarbons ranging from approximately C15H38 to C38H78 mixed with small amounts of branched paraffins, monocyclic paraffins, polycyclic paraffins and aromatics.' The amount of paraffins found in crude oils varies from less than 1 to more than 30 per cent. Many publications are available which deal with this problem, and perhaps the most significant findings in recent literature are contained in a publication by Hunt3 ho developed the "cold spot tester", a really useful means of investigating paraffin deposition. Hunt's observations led to many generalized conclusions concerning the effect of surface roughness on paraffin deposits. He ascertained that there was an observable qualitative correlation between the severity of paraffin deposition and the roughness of the surfaces which he tested (cold rolled steel, stainless steel and several plastics). Because of the number of meaningful observations made by Hunt, his cold spot tester was modified somewhat and extensive tests were per- formed to study the quantitative relationship between surface roughness and the physical and chemical nature of paraffin deposits. LABORATORY TEST PROCEDURES The cold spot test apparatus consists of a flat circular plate mounted on a curved tube and positioned in a vessel containing a wax-oil solution (Fig. 1). The apparatus is arranged so that the temperature of the central portion of the circular plate can be varied by means of a circulating liquid stream; the test equipment includes provisions for maintaining a constant wax-oil solution temperature and stirring speed. In the paraffin deposition studies, the modified cold spot tester was used as follows. The cold spot probe consisted of a flat circular plat 2 in. in diameter and 1/8-in. thick positioned in the wax-oil solution kept at constant temperature. As in Hunt's earlier experiments," a cold liquid was circulated through a tube connected to the circular plate so that the liquid impinged on one side of the plate cooling the plate from the center outward, causing paraffin to deposit on the side of the plate exposed to the wax-oil solution.

Jan 1, 1967

By E. A. Kaarsberg

The electron photomicrographs shown in this paper are of samples of the A.P.I. Reference Clay Minerals Montmorillonite No. 27 and Kaolinite No. 4 and of a shale from Spraberry Oilfield in Texas. These samples are part of a larger collection whose physical properties, composition and internal structure were previously studied by ultra-sonic and X-ray methods. ' Elastic anistropy was indicated in the montmorillonite and shale samples by sound velocity measurements parallel and perpendicular to the bedding. In the montmorillonite the velocities parallel and perpendicular to the bedding were 2.12 and 1.92 km/sec respectively, a difference of about 11%; in the shale the same velocity measurements were 4.18 and 3.75 km/sec, a difference again of about 11%. Within the bedding plane the sound velocity was also found to be independent of direction. The electron photomicrographs of the montmorillonite sample, which are shown in Fig. l(a) and (b), clearly indicate the preferred orientation of the mica-like clay particles parallel to the bedding. In Fig. 2(a) and (b) similar orientation in the shale sample can be seen although not quite as clearly. This is probably because, in addition to the clays illite and chlorite, the shale sample contains grains of quartz, calcite and dolomite which do not as readily show an alignment pattern as the clays do. This suggests that the elastic anisotropy of these two samples is derived from a preferred alignment of component mineral grains which are themselves elastically anisotropic. The bulk elastic properties of these two samples therefore appear to be much like those of mica. Velocity measurements were made on the kaolinite sample in three directions at right angles because no bedding could be discerned in it. The values ob-

Jan 1, 1967

By William H. Lehr

A 4200 ton-per- hour marine transfer terminal, where river and oceangoing vessels simultaneously exchange cargos of coal and phosphate rock, is now in operation near the mouth of the Mississippi. Its materials handling machinery includes a bucket ladder barge unloader; a rope operated clamshell bucket unloader; a coal loader; and a rail mounted bucket wheel machine. The design and operation of this equipment is described as are the docks and conveying, breasting and barge-haul systems in use at the facility. Design considerations imposed by soil and river conditions, geography, operating needs and investment requirements are discussed. The economic significance of design and shipping innovations introduced by this facility is noted.

Jan 1, 1967

By R. Stauffer, S. Lindsay

"Sherritt Gordon Mines Limited utilizes pressure hydro-metallurgical techniques to recover nickel, copper and cobalt from su1phidic concentrates, mattes and various other metal-bearing materials.A brief description of the nickel refinery operation is given. In the nickel refinery process, an ammonia pressure leach is employed to treat the feed materials to dissolve the non-ferrous metals as their respective ammine complexes. The resulting leach solution goes through a series of steps which removes copper as copper sulphide and further purifies the solution prior to nickel precipitation by hydrogen reduction. The reduction end solution, containing the cobalt which was originally present in the leach solution as well as residual nickel, is treated with hydrogen sulphide. The resulting nickel-cobalt sulphide precipitate feeds the soluble cobaltic ammine process, which separates the nickel and cobalt and recovers the cobalt as a pure powder.A detailed description of the cobalt recovery process is given. Included are the various steps, comprising: acid leaching of the mixed sulphides, solution purification, ammine complex formation and cobaltous oxidation, two-stage nickel precipitation, cobalt conversion and reduction. A brief description of cobalt powder handling is included, along with typical physical properties and chemical analyses of the cobalt product. In general, the purpose of this paper is to describe the present plant practices employed in the recovery of cobalt as a by-product of the nickel refinery operations."

Jan 1, 1967

By Robert E. Barieau

General expressions for evaluating various thermodynamic properties applicable to the van der Waals equation of state have been derived. These formulas were subsequently used to evaluate various thermodynamic functions in the two-phase region. The results indicate that, for a van der Waals fluid, there is a finite discontinuity in the second derivative of the vapor pressure curve, in the second derivative of the chemical potential or Gibbs free energy at the critical point, and in the heat capacity at constant volume measured at the critical density. Numerical values are tabulated and graphs are presented for all functions calculated.

Jan 1, 1967

By Robert E. Barieau

This report gives the principles of the method used by the Helium Research Center of the Bureau of Mines when solving nonlinear-regression problems and contains the mathematical equations necessary to accomplish the following objectives: the evaluation of the parameters in such a way that the sum of the weighted squares of the residuals of an experimental observable is a true minimum, regardless of the functional relationship between the variables and these parameters; and the evaluation of all variances and covariances of the parameters by means of the usual approximation of the law for the propagation of errors.

Jan 1, 1967

By E. W. Geist

This paper is presented from the viewpoint of the mill operator and maintenance supervisor. Its purpose is to highlight the things that have been accomplished by the mill designers to lighten the load for the maintenance superintendent and to reduce the overall costs for the plant operator. The complexity of plant design, the civil and structural engineering problems encountered when the satisfactory maintenance layout is accomplished are appreciated, and the writer is fully aware of the complexities of these problems. However, it is not the purpose of this particular paper to dwell upon these problems, nor to emphasize or de-emphasize the problems of the civil, mechanical and electrical engineers. It is simply that the paper will attempt to review what these people have accomplished in spite of the many technical problems. This paper then is prepared with the operator and maintenance people?s viewpoint. What is their definition of design for maintenance? It is the writer's interpretation that the various design concepts which mean improved maintenance are such items as (I) maintenance areas, (2) laydown space for maintenance materials in specific maintenance jobs, (3) the inclusion of bridge cranes in the plant and specific design of the craneways to accomplish flexibilities for the cranes, and (4) the location of the piece of equipment to allow maintenance people to work around the equipment - - - this specifically includes the orientation of the particular piece of equipment.

Jan 1, 1967

By R. W. Smith, R. W. Lai

Very recently there has been a quickening of research effort in the field of silicate mineral flotation, particularly as regards the flotation of beryl.' These studies have already contributed much to the understanding of both anionic and cat-ionic flotation of silicates. Of particular interest concerning anionic flotation has been the work done on heavy metal activation of silicates by M. C. Fuerstenau and co-workers.4,7 In addition. in the paper by Fuerstenau, Rice, Somasundaran and Fuerstenau7 attention was paid to low pH anionic flotation of beryl in the absence of activators. This subject was also covered in the papers by Avotins,3

Jan 1, 1967

By R. Kossowsky

In the course of a study concerned with structural stability of precipitation hardening nickel base super -alloys after exposures to elevated temperatures, some interesting effects of hydrostatic pressure treatment on Rene were observed. The evidence presented below suggests that hydrostatic pressure treatment of the solution heat-treated alloy can affect the dispersion of the y' (Ni3Al) phase upon subsequent precipitation heat treatment and long time aging. Rene 41 alloy has the following nominal weight percent composition: Al B C Co Cr Fe Mn Mo Ti Ni 1.4 0.006 0.7 11.3 19.2 1.0 0.05 9.4 3.3 balance The effect of successive pressure, precipitation heat treatment, and long time aging on the microstructure of this alloy was determined by subjecting a number of alloy buttons to five different thermopressure treatments. Pressure and precipitation heat-treatment parameters are listed in Table I. Fig. 1 shows y' morphology* of specimens in groups I and 11. The treatment results in a fine dispersion with particle size on the order of 950 and 1350A, respectively, see Table I. Fig. 2 shows the morphology of y' precipitate in

Jan 1, 1967

By J. D. Campbell

"Coal is one of Alberta's major fuel resources, but its distribution, especially in the flat plains region, has been somewhat obscured by surficial deposits. After a period of neglect, easily strippable plains coal is presently approaching a position of dominance in electrical power production, a position it is likely to retain for a number of decades in the face of strong competition from hydro and nuclear power. Accordingly, the Research Council of Alberta has undertaken an inventory survey of the province's supplies of this resource.In the southern part of the province and in the north-central forest-fringe area, some strippable coal is found in the Belly River Formation and its equivalents, but major strippable coal reserves in large areas of central Alberta occur within the Edmonton Formation. The survey is planned on a reconnaissance scale, drilling test holes at 2-mile intervals in selected large areas. It appears to show that, in well-settled regions, large reserves of strippable coal are only to be expected where they have long been known; major presently unknown bodies of coal must be sought in unsettled regions or at depths too great for strip mining. However, such bodies might still be economically competitive with hydro and nuclear power in the production of electric power for some time to come."

Jan 1, 1967

By H. R. Cooper

Beginning from the point of view that process control of ore flotation can be approached by on-line analysis of processing behavior, an equation was developed which has characteristics useful for a multi-variable feedback loop. The application of this equation to optimizing control with a data acquisition system will be discussed in Part 11. OBJECTIVE OF CONTROL The purpose of developing a feedback method for concentrator control is to provide a means for determining ore processing behavior in order that data describing the ore can be used to make appropriate changes in control conditions while the ore continues to flow through the flotation circuit. In absence of simple linear relationships between pairs of variables in the flotation process, attention is directed to the need for a generalized relationship which possibly would incorporate all pertinent variables. It would be possible to apply such an equation to the control of variables in a concentrator in real time according to operational requirements as ore gradually changes in quality and processing behavior. To meet this objective, it is necessary to define relationships describing flotation performance in terms of performance variables capable of being measured on-line, either with on-line instruments and analyzers or with manual methods lending themselves to quick determination of meaningful information. Relationships derived to meet this objective form a model for the flotation process. The evaluation of flotation parameters of the ore and the execution of control on the basis of the derived information while the ore is continuing through the process would constitute a feedback control system. Data for the following control and performance variables can be made available: 1) ore feed rate, 2) collector addition rate, 3) lime addition rate, 4) pulp density, 5) assay or multiple assays in feed, tails, or concentrate sufficient for material balancing, 6) particle size distribution in flotation feed, 7) froth height, and 8) frother addition rate. Other process variables, such as flotation air input and mechanical agitation intensity, are usually not considered as control variables and were not taken into account in this analysis. Other data, such as that describing the ore, would be useful for concentrator process control. However, information of this type (such as ore hardness, grain size of the mineral, chemical species of the mineral, and ore surface properties) being not presently measurable in the on-line sense, has the effect of causing disturbances in the system which can be detected only indirectly. The process control system being sought must recognize disturbances by their effect on measured performance followed by determining control changes to compensate for them in meeting the objectives of improved performance (perhaps higher throughput, maximum return, etc.). A suitable model for the process having capability of recognizing the effects of ore disturbances should provide the means for introducing proper compensation through control changes. This would be done by processing on-line data with the model to calculate coefficients reflecting ore characteristics. This procedure can only be applied in a typical flotation system when on-line data can be processed at faster rates than the usual rate at which the ore in flotation feed takes on significantly different characteristics. For example, material balance data can be accumulated in approximately 5-min intervals using on-line X-ray fluorescence analysis. The flotation system time constant might be 15 min including grinding. Ore changes having time constants longer than 1 hr could be accommodated using on-line feedback control by this procedure. FORM OF A FLOTATION MODEL A suitable form for mathematical expression of the flotation process is an equation involving rates, when each of the components entering into the separation can be treated independently by a rate equation. A first-order, kinetic rate equation can be written on

Jan 1, 1967

Jan 1, 1967

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'-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,' and Pfann.' 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

By D. R. Uhlmann, T. P. Seward, K. A. Jackson, J. D. Hunt

microscopic ohservations on alloys of organic trzaterials show that dendrite arms can melt off under normal conditiorzs of growth. This occurs because of the interactiorz of' heat and matter fluxes during dendritic growth. The re melting occurs where the den-drite arms are joined onto the main deizclrite sterrz. Many detached crystals can be produced in this fashion. It is postulated that this remelting phenornenon occurs in metal alloys, giving rise to the equi-axed region in castings. Experiments peyformed orr castings of transparent materials support remelting as a primary source of detached crystals. Ob~ervations an equiaxed tones in metal castings are discussed in terms of this and other mechanisms. It is concluded that the partial remelting of dendrites is on important mechanisnl for producing the equiaxed regions in castings. THE freezing of a casting can be divided into three regions: a chill zone formed near the mold wall, a columnar region, and a third region, at the center of the casting, which is called the equiaxed zone. The origin of the grains that comprise the equiaxed region is the subject of this paper. We will first outline the mechanisms which have been proposed to account for the origin of the equiaxed region and discuss some recent experiments which cannot be explained by these theories. We will then present some microscopic observations of dendritic growth which have led us to conclude that the equiaxed zone in castings can arise from partial remelting of dendrites. This proposal is supported by observations on transparent castings. Finally, we will discuss several observations on metal castings which could not be explained previously, and which can be accounted for by the present proposal. Previous Mechanisms. Winegard and Chalmers3 pointed out that the molten central region of an ingot could be constitutionally supercooled, because of the solute layer at the growing interface. In this supercooled region, nucleation on particles could occur, giving rise to the equiaxed crystals. Another mechanism has also been suggested,4y5 that the nuclei originate in the chill zone then float or are carried by convection to the center of the casting, where they grow to produce equiaxed crystals. In this case, all the crystals nucleate immediately on casting, so this mechanism will be termed "big-bang" nucleation. Walker's Experiments. J. L. Walker has made observations on the solidification of nickel and Ni-Cu alloys which cannot be accounted for by either of the above mechanisms. In studying the grain size resulting from freezing of nickel at various undercoolings, walker6 found that at large undercoolings the grain size was small, due to mechanical nucleation, as discussed by walker7 and Horvay.' At small undercoolings, the grain size was large, and the growth dendritic. In Ni-Cu alloys, however, for initial undercoolings starting from just below the melting point and extending for a hundred or so degrees of undercooling, fine grains were also observed. Samples were undercooled 200 Centigrade degrees without nucleating, and were then heated 130 Centigrade degrees so that the undercooling was 70 Centigrade degrees, and nucleated. The samples had a small grain size, indicating multiple nucleation. There were no heterogeneous nuclei in the liquid which could operate at the temperature of growth. Constitutional supercooling could not have been greater than the supercooling of the initial melt, since the temperature rose as the freezing continued. walker -as also shown that a Ni-Cu alloy which can be undercooled to below its solidus will produce typical columnar and equiaxed regions when cast into a cold mold. This alloy could not reach a temperature below its solidus by constitutional supercooling. It could not, therefore, have nucleated heterogeneously. Neither the big-bang mechanism nor the Winegard-Chalmers mechanism can account for the fine grain

Jan 1, 1967