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By M. Barkhudarov

The results are presented of research aimed at validation and development of a general purpose CFD code FLOW-3D. FLOW-3D is a commercial code developed by FLOW SCIENCE, INC. A number of physical modeling experiments involving the filling of cavities of different geometries with coloured water have been performed in order to compare the measurements with the results of computer simulations. Other numerical calculations were also done to be compared with the known analytical solutions.

Jan 1, 1992

By Hapsari Rosa, Ross Cowie

Conventional blasting activities in the mining process use various types of explosives, with the primary raw materials being Ammonium Nitrate and diesel fuel. The quality and specifications of the two raw materials significantly affect the performance of explosives. One program from the Indonesian Ministry of Energy and Mineral Resources requires mixing 30% Bio Diesel 30 with 70% diesel fuel oil in several industrial sectors, including mining, to reduce greenhouse gas emissions and stabilize CPO prices. This program aims very well for environmental sustainability and the palm oil business. However, it turns out that this change impacts the performance and results of the blasting process in the mining industry, which is the appearance of fumes. This paper will discuss the tests carried out in the laboratory on Bio Diesel 30, the explosive products used, and rock samples were taken from a mine in East Java, Indonesia. The aim is to determine what factors can cause fumes utilizing a mixture of Bio Diesel 30 with pure diesel fuel. The parameters tested were visual differences, infrared spectrometry, density and viscosity, surface tension and contact angle for Bio Diesel 30, stability test for explosives, and the SEM-EDS method for rock samples.

Feb 6, 2023

By ALEX. S. THOMAS

HOWEVER good a furnace may be in regard to design, etc., or however excellent in the quality of the gas used, a suitable heat for the successful working of the metal cannot be obtained unless the melt be coated with a proper quantity of slag. This coating may be excessive or it may be deficient in quantity. The right degree of heat is the essential condition of successful working, for the quality of the steel made is never very good when the metal is allowed to simmer in the furnace for an excessive period, and this heat cannot be obtained if the metal is not protected by a proper covering of slag. This is not only to prevent the metal being over-oxidized and wasted, but also to prevent the metal being chilled when exposed with only a thin covering of slag. The slag may be obtained in either of two ways : 1, naturally, by the presence of sufficient silicon in the iron used, to unite with iron oxide to form a staple slag ; or, 2, by the addition of slag or free silica. In the first case the slag is formed naturally by the action of the oxygen in the flame - i.e., the oxidizing atmosphere of the furnace-on the silicon in the metal when melting. The charge then melts, as it is termed, "thick," and protects the banks from being cut. If too much silicon be present, however, and an excessive quantity of slag be formed, it will be found to be rather infusible, and unless care be taken to add the oxides quickly and follow the furnace up-thus rendering the slag more fusible by the extra iron oxide-the furnace bottom is liable to be pulled up. In such cases the author has frequently been able to warn

Nov 1, 1906

This Bureau of Hines report on underground mine communications addresses methods and equipment to meet the communication requirements of working sections and places of coal and metal-nonmetal mines. A review of the status of trapped miner detection is also presented.

Jan 1, 1977

By L. Roux

The initial evaluation of a coal deposit often raises uncertainty with regard to the accuracy of the reported Resources and Reserves. Reconciliation of results from mining and beneficiation with the original raw field data highlights deficiencies in original estimations. Credible Resource and Reserve estimation forms the basis on which an entire mining enterprise is motivated, initiated, funded, and established as a commercially viable proposition. This is required for sustainable extraction purposes and to support vital downstream industries such as power generation. Accurate determination of the density of the matrix of the material being evaluated is the key to credible values being obtained for Resources and Reserves. Losses between 15% and 20% of the Resource/Reserve can be realized if incorrect densities are applied to the tonnage derivation. Coal plies and particles have different relative densities, determined by the maceral composition, rank, and mineral and moisture content. These factors in turn contribute to the moisture, volatile matter, ash and carbon contents of a coal, which affect the overall density of the raw coal. More specifically, the relationship of ash to density and the effective matrix porosity were found to be critical in solving the greater majority of the problems in predictive calculations. A major deficiency identified is the inability to determine effective porosity, allowing absorption of adventitious moisture and altering the mass of the core sample. Although the volume of the raw material is altered through crushing, the change in mass after controlled air-drying, used with the original geometrical volume of the raw material, provides a credible air-dry density and allows the determination of the volumetric change related to effective porosity. This parameter can be validated through the evaluation of proximate ash using the ash-adjusted algorithm and a correction for the inherent moisture applied to also give a credible relative density value for an air-dried sample. A combination of theoretical, empirical, and reconciliatory evaluations of the available data, taken from the exploration phase through the mining process to final production, has shown that an integrated approach using the ash-adjusted density (AAD) methodology, in conjunction with other evaluative techniques, provides credible results with a considerably higher degree of accuracy than is currently possible.

May 1, 2021

By A. Gene Collins

Rapid, sensitive, and precise methods of determing major, minor and trace constituents of oilfield brines are needed. Several methods have been developed or adapted by the Federal Bureau of Mines at the Petroleum Research Center, Bartlesville, Okla. The following methods are described in this report: Spectrophotometric and volumetric for iodides and bromides; potentiometric for pH, alkalinity, acidity, borate boron, total boron, and organic boron; gravimetric for potassium; disodium ethylenediaminetetraacetate (EDTA) volumetric for total hardness, calcium, and magnesium; spectrophotometric for fluorides; and color comparison .for arsenic. Adequate sensitivity, precision, and accuracy were obtained for each method. The Bureau of Mines pioneered in research on the analysis of oilfield waters (2, 46, 47).6 However, several of these early procedures were quite time consuming. Also, they did not include methods for determining trace and minor constituents of brines.

Jan 1, 1961

By D. Bienstock

The use of alkalized alumina in removing sulfur dioxide from a coal-combustion flue gas at 625° F was investigated on a pilot plant scale. The absorber was 26 feet long and 1.6 inches ED. Counter-current gas-solids flow at gas velocities of 8 to 15 ft/sec in the presence and absence of baffles, as well as solids entrainment at gas velocities of 20 to 23 ft/sec with solids recycle, were employed. The spent absorbent as regenerated as fixed bed with the reducing gases--reformed natural .7.7d hydrogen. Of absorption-regeneration were successful completed using the alkalized alumina rolled into spherical granules 10 to 16 mesh. There was no loss in activity of absorbent toward SO2 with a modest attrition equivalent to 0.l percent of the solids feed. Supporting studies were conducted on the effect of the sodium content in the absorbent, the composition of the reducing gas, thermal treatment to increase absorbent hardness, and removal of absorbed chlorine from the absorbent. A mathematical model was formulated to describe the removal of SO2 by alkalized aluminum from fixed and falling beds.

Jan 1, 1967

By Ruth F. Brinkley

Principle activities of the Bureau of Mines Explosives Research Laboratory from July 1, 1960 to June 30, 1961 are reviewed briefly in Part 1. Part 1 also includes data obtained in connect ion with several minor investigations which are not sufficient to warrant separate publications. Part 2 gives brief abstracts of publications that appeared during fiscal year 1961; in general, the research reported in these publications antedates this period.

Jan 1, 1963

By Owen Matthews

THE property of Cochenour Willans Gold Mines, Limited, is in Dome township, Red Lake area, northwestern Ontario, a hundred miles north of Kenora and close to the Manitoba border. 'Planes of Canadian Pacific Air Lines, Limited, serve the district daily, except Sundays, from Kenora, Ontario, and Lac du Bonnet, Manitoba, passengers being trans-ported from Winnipeg to Lac du Bonnet by car. Freight is handled by the Patricia Transportation Company. It is brought in from Hudson, Ontario, on the Canadian National railway, in summer by water and in winter by tractor trains over the frozen lakes. The first staking on the property was done during the 'rush' of 1926 and 1927 by William M. Cochenour, and on April 30th, 1928, a syndicate was formed, taking in claims of W. M. Cochenour and Dan Willans and H. G. Young. Surface trenching was carried on almost continuously until 1934. In October, 1932, Ventures Limited took an option on the property, and in December of that year they carried out an extensive diamond drilling programme, but considering the results did not justify further work, they relinquished the option. In July, 1934, further surface work was carried out under the supervision of W. P. Mackle and, on the strength of his report, Noah Timmins Incorporated took an option on the property and agreed to make an initial expenditure of $100,000 on development work. This was carried out under the direction of Hollinger Consolidated Gold Mines and included the sinking of a shaft to a depth of 165 feet, establishment of a level at the 150-foot horizon, and some 1,900 lineal feet of drifting and cross-cutting. The results obtained from this work were not considered of sufficient promise and the option was terminated in August, 1935. Mr. Cochenour then approached Alex Mackenzie and associates, and the present Company, Cochenour Willans Gold Mines, Limited, was organized on April 9th, 1936, and sufficient money was raised to continue operations. Under the direction of W. P. Mackle, the shaft was deepened and a second level was established at the 275-foot horizon; but, due to several adverse reports by outside engineers, it was found impossible to raise sufficient money to carry on the work and operations were suspended in December, 1937. In January, 1939, an agreement was entered into with Gold Eagle Gold Mines for the milling in their plant of some Cochenour ore. A total of 4,959 tons was treated, and the results were so encouraging that further finances were raised by C. A. Gentles & Company, of Toronto. Following further development in the mine, it was decided to erect a mill. Construction was started on September 1st and the mill was turned over on November 29th. The first gold brick was poured on December 23rd.

Jan 1, 1942

On-stream determination of xanthate concentrations can be made by photometric measurements at 313 nm.A simple double-beam instrument was developed for this purpose. A mercury lamp is used as the light source and a composite filter of UGll glass and chromate solution is used to isolate the required spectral region. The light beam is split into two components of approximately equal intensity. One component is passed through a reference cell containing water to a photo detector; the other component is passed through the xanthate solution to a second photo detector. The reference signal controls amplifier gain to eliminate effects of lamp intensity changes and the amplified sample signal can then be used to measure xanthate concentration.Plant trials showed that provided a clear solution free of air bubbles was obtained from an on-stream filter, the instrument indicated the xanthate concentration and operated satisfactorily for long periods.

Jan 1, 1973

By Bryant Fitch

This paper will review thickening theory, from the ( ) of the practicing engineer, with particular emphasis on ( ) uncertainty or disagreement. It will attempt to outline broadly what we know and what we don't know. This should serve two purpose First, it will warn the process engineer where he might get into trouble. At least it will alert him to the risk involved in uncritically accepting any of the recommended design procedures. Second, it will identify for researchers some areas in which further work might be fruitful. Not too many years ago there would have been little to write on such a subject. We had been designing thickeners for decades, using the classic Coe and Clevenger procedure. As far as we were generally aware, they all turned out to be about the right size. And so if there was anything we didn't know, It certainly wasn't hurting us much. Today we know better. While it is true that in most cases units designed by the Coe and Clevenger procedure (1) will perform satisfactorily, we now know of cases in which they don't. And during the past few years there have been many developments and advances in basic thickening theory. So there is now a lot more room for disagreement, and a whole lot more to be uncertain about. What is "thickening" "Thickening" means different things to different people. For this paper we define it to mean sedimentation behavior characterized by line settling. Solids subside with a clear line of demarcation between settling solids and supernatant. Although the supernatant will usually be clear, in some cases it may be turbid. Line settling must entail that all particles just below the pulp-supernatant interface have the same subsidence rate, so that

Jan 1, 1971

By Neville Jordison

Indirect, gravity flow, heat exchangers have become a well established technology in mineral and metallurgical process plants. The technology is a conventional heat exchanger using high efficiency plates, with a free flowing bulk solid on one side of the exchanger and a fluid on the other side. This simple concept leads to many opportunities for achieving greater energy efficiencies in process plants. Indirect heat exchange is much more efficient than direct heat exchange using air such as in a fluid bed or rotary device. When air is used directly, large fans are required, it may also be necessary to chill the air, both high consumers of energy. By contrast, using water as the cooling medium requires only low horsepower pumps, typically only 10% of fan HP. Furthermore there are no stack emissions with the requirement for removal of dust or emissions. Indirect heat exchange also creates the opportunity to recover energy. This can work in two ways: energy can be recovered from a hot bulk solid, to heat pressurized hot water for steam generation or preheat air. Alternatively recovered energy from elsewhere in the plant in the form of hot water, steam, air or thermal oil can be used to preheat a bulk solid.

Jan 1, 2011

By T. N. Matveeva, L. B. Lantsova, N. K. Gromova

"Multimetal gold-antimony ores are complexed processing products, since they are characterized by veindisseminatedsulfide mineralization with fine-dispersed submicroscopic gold, low content and uneven distribution ofAu, which is concentrated together with iron sulfides (pyrite, arsenopyrite, pyrrhotite). Such ores are classified asrefractory ones and characterized by low gold recovery rates during cyanation. A particular feature of gold-antimonydeposits is the presence of antimony in industrial concentrations therein, along with gold that significantly increasesthe value of these deposits. The main antimony mineral is antimony sulfide - antimonite (stibnite). Gold-antimonyores undergo flotation concentration with producing collective gold-containing concentrates or gold sulfide andantimony concentrates. The purpose of the work is an experimental study of the flotation separation mechanism ofsulfide minerals of copper, antimony and arsenic using tannin-containing modifiers during processing of multimetalgold-bearing ores. During the research it was established that for the selective separation of antimony and arsenicsulfide minerals into concentrates of different kinds, it is possible to use vegetable reagents capable to be selectivelyadsorbed on the arsenopyrite surface. Using the laser KEYENCE VK-9700 and electronic LEO-1420 VP INCA-350microscopy methods, it has been established that the film of a vegetable modifier was not washed off with water andfixed firmly enough on the surface of the polished sections of arsenopyrite. In the X-ray spectrum there are C and Obands related to the reagent structure. The vegetative reagent is fixed both on the pre-adsorbed phase of the collectorand on the areas free from the collector. On the polished sections of antimonite before and after a contact with thetannin solution, only partial adsorbed tannin phases are detected, which disappear as a result of subsequent washingwith water.The reported study was funded by RFBR according to the research project ? 16-05-00646 ?."

Jan 1, 2018

By Hu Long

In this, the first systematic study of the oxidation of orpiment (As2S3) in sulfuric acid solution under oxygen pressure at temperatures above 170°C, the effects of retention time, temperature, particle size, oxygen partial pressure, the concentration of sulfuric acid and pulp density were evaluated. The effects of cupric and ferric ions on the oxidation rate of As(III) to As(V) were also examined. The products of oxidation are As(III), As(V), SO42- and elemental sulfur. At temperatures ranging from 170 to 230°C, most of the arsenic was found to be in the trivalent state, and oxidation to As(V) with oxygen was very slow. This was confirmed by attempting to oxidize a synthetic arsenious solution. However, the rate of oxidation of As(III) to As(V) is rapid in the presence of ferric ion. Elemental sulfur was found at all temperatures investigated, which can be further oxidized to sulfate at high temperature.

Jan 1, 1999

By Julian Malnic

Various natural, commercial, engineering and operational factors govern the evolution of approaches taken in the exploration for Seafloor Massive Sulphides (SMS) and in delineating the resource. These stages are prerequisites to the proposed mining of SMS deposits. This paper presents and analyses these factors from the view of an SMS exploration company that is pioneering the exploration of this rich alternative source of zinc, copper and gold. Current exploration practices developed by Marine Scientific Research (MSR) workers for SMS deposits are expected to give way to industry-generated methods as the SMS exploration industry gathers momentum. The exploration process falls into three phases that are described below: Prospecting (locating targets), Indicating Resources, and Measuring Mineral Resources Considerable streamlining of the SMS exploration process will accelerate the rate of discovery. The economics of SMS mining are projected to be superior to comparable terrestrial mining operations in both operating cash cost and capital terms.

Jan 1, 2001

By A. Anderko, V. G. Papangelakis, G. Moldoveanu, G. Azimi, M. Carlos

"OLI Analyzer is a software package that uses the powerful Mixed Solvent Electrolyte (MSE) model to simulate the behavior of multicomponent electrolyte solutions from infinite dilution to the limit of fused salt, and from temperatures below the freezing point up to near critical temperature of the mixture. The software also allows the creation of thermodynamic parameters for new chemical systems unavailable yet in public-domain or commercial software databanks. This communication reviews the basics of the model and provides some examples of modeling hydrometallurgical applications with emphasis on high temperature applications, including calcium sulfate scale formation in autoclaves, high temperature pH inference and iron control. INTRODUCTIONModeling of electrolyte systems has been of particular interest to various industrial processes, such as separation processes (e.g., solution crystallization, extractive distillation, seawater desalination or bio-separations), environmental applications (e.g., gas treatment, wastewater treatment or chemical waste disposal) and hydrometallurgy (e.g., pH control and neutralization, iron control, scaling and fouling of equipment). Using a chemical model, time-effective predictions of various properties of electrolytes can be obtained, which is beneficial not only during process monitoring, but also during process optimization and process scale up. As a result, pilot scale studies can sometimes be eliminated where budgetary constraints exist. Development of such a powerful model requires the use of a speciation-based model, in which solution chemistry is explicitly addressed (as compared with some models that treat electrolytes either as undissociated or fully dissociated systems), despite being computationally challenging. In addition, as a feature of electrolyte systems, speciation equilibria inherently influence the phase equilibria due to complex formation, ion pairing, and acid-base reactions. Therefore, how the electrolyte solutions behave at various conditions may differ significantly due to the non-ideality, which must be carefully addressed to obtain a model that is applicable to a wide range of conditions such as concentration, temperature, pressure and solvent system."

Jan 1, 2012

By Charles G. Maier

SCIENCE beginning in rational observation came of age, when its devotees first began to measure and count. It has been said that the most striking aspect, of science today is its growing abstraction, and its preoccupation with mathematical symbolism. Technology with specific and concrete objectives in the satisfaction of human wants, cannot conceivably achieve the abstract unification that science seeks, but .the utility of the' scientist's method has been too well proved to require bolstering. Metallurgy is in its scientific infancy.

Jan 1, 1931

By C. B. Scotty, E. F. Egan

INTRODUCTION The neutron-garnma log has been used for stratigraphic correlation by the oil industry for a number of years. In the past few years, the quantitative application of the log to provide information with respect to porosity has received considerable attention. The basic concept of quantitative interpretation has been pointed out in the literature.1 It shall be the purpose of this paper to develop by empirical means a method whereby the relationship of porosity to neu. tron-gamma deflection may be predicted for various bore hole diameters. This relationship is applicable to the present commercially available neutron-gamma log run in open hole. Data available at present are insufficient to establish similar correlations for cased holes. Through the development of such a correlation, the importance of the various factors which influence the log become evident. NEUTRON-GAMMA CURVE The logging tool conisists of a source of neutrons and a means of detecting and measuring gamma rays, the detector being shielded from the direct emission from the source. The gamma rays reaching the detector have three sources of origin: (1) the natural gamma radiation emitted by the formations, (211 induced gamma radiation resulting from neutron bombardment. (3) gamma rays emitted by the source and scattered by the formation. It has been found that a neutron derived porosity correlation is best for shale-free formations. Under this condition the natural gamma ray radiation is quite low, and therefore, will be neglected in this work. The induced gamma ray radiation resulting from neutron bombardment is predominantly a function of the hydrogen atom concentration of the substance penetrated. Due to the geometry of the presently used system, the neutron-gamma curve indicates low radioactivity opposite high hydrogen concentration and high radioactivity opposite low hydrogen concentration (Figs. 1 and 2). Having a curve which measures hydrogen atom concentration, it follows that if the matrix of the formation penetrated consists only of atoms other than hydrogen, and if the fluid filling the pores is either oil or water, the curve should be an indication of porosity (both oil and water have practically the same number of hydrogen atoms per unit volume'). The above criteria for a porosity (Correlation are fulfilled in clean sandztones and limestones in which the pore volume is completely filled with liquids (oil or water), but not in formations containing either free gas or shale or both. Free gas. even under pressure, contains considerably less hydrogen per unit volume than oil and water; therefore, a variation in response on the curve would be expected. Camp- bell and Winter,' indicate that this difference in hydrogen concentration is sufficient to distinguish between sands containing water or oil and those containing dry gas. Shale is a mineral that contains hydrogen in its molecular structure in addition to the hydrogen which is present in the water of hydration. Thus, in formations containing variable amounts of shale, the hydrogen concentration indicated by the curve is not a direct indication of porosity. Bush and Mardock' have indicated that a correction may be made by use of the gamma ray curve to provide a porosity correlation. Since the induced gamma rays are predominaiitly a function of hydrogen concentration, it would be anticipated that the fluid filled bore hole would materially influence the logs. It has been pointed out that the neutron-gamma curve response decreases with increase in hydrogen concentration, therefore, the response due to the induced gamma ray component decreases with increase in fluid filled hore hole diameter. The scattered gamma ray component of the log increases with increase in bore hole diameter. Although there is an

Jan 1, 1952

By Sue Sawyer

In October, November and December, teachers at the National Science Teachers' Association (NSTA) area conventions were lured to visit the Minerals Education Coalition (MEC) booth by the promise of free rocks, video tapes, and literature on earth science topics. Teachers were content to stand in lines that at times took as much as an hour and a half to progress through the exhibit. Adding to their interest was the opportunity to converse with people from the minerals industry who were staffing the booth. The MEC was formed by a group of associations and companies in the minerals industry. They felt the need to educate the public about the current-day minerals industry and how it affects everyone's life. The American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. (AIME) underwrote the major expenses of exhibit space and exhibitor services at all three conventions in 1997. SME members have been active in staffing and chairing the NSTA exhibit booth. But they represented only about one-third of the volunteers for the booth. Additional volunteers were drawn from local minerals companies, associations, interested teachers and other support groups. (See donors list on page 64.) In 1997, the conventions were held in Pittsburgh, PA, Denver, CO and Nashville, TN. The local SME GEM Committees chaired Pittsburgh and Denver and The Rogers Group Inc. supplied the chairperson in Nashville. Each exhibit relies on a local committee to plan and run the booth. Support is available from the GEM Projects Coordinator at SME headquarters. Usually the chair of the committee is drawn from the local SME membership. It is easy to see why the MEC booth is so popular. Free literature, videos, posters, workshop packets and rock specimens were handed out to about 5,500 science teachers at the three sites. Feedback from the attending teachers was overwhelmingly positive: "Who do we thank for these great materials?" Some of those great materials included Caterpillar's outstanding donation of Common Ground videos and teacher packets for Pittsburgh, Denver and Nashville for every teacher expected to attend. Placer Dome sent enough What's a Mine coloring books and It Comes from a Mine activity books for teachers at all three sites. Newmont supplied all teachers with an excellent poster describing gold processing. Women in Mining Education Foundation had plenty of its classroom activity handouts. The American Coal Foundation provided a list of its educational materials that are given out free to teachers who request them on school letterhead. The National Mining Association had its Facts About Minerals and Facts About Coal available. US Borax provided the funding to reproduce the NMA black and white posters that were published as inserts in Mining Voice magazine. In addition, each site had other materials chosen by the local committees to round out their selections. At each exhibit site, committees raise between $8,000 and $12,000 in cash donations from industry to support the high overhead of producing this exhibit. Usually, there are between 12 and 18 different rock specimens representing a range of mineral ores from aggregates to the metal ores. The committee arranged to have these donated (along with the freight charges to ship them to the site). Literature is also donated by the industry. It covers a diverse spectrum from basic information on rocks and minerals to posters, flow charts, videos and coloring books. Other donations include storage space before the event, haulage of items to the hall and door prizes. These exhibits could not have been staged without the network of SME Local Sections and the able chairs and committees at each site. At this time, credit should be given to their extensive donation of time and effort.

Jan 1, 1998

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