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During the year terminating at the date for the third annual meeting of Engineering Foundation, the Board completed, its undertaking to sustain the National Research Council for one year. Assistance given in the organization of the National Research Council has been amply justified by the results. The Council is now well established in a 4¬story building at 1023 16th Street, N. W., Washington, and has recently secured another similar building near by in order to house its increasing force. The breadth, importance and volume of work done have steadily grown. Foreign offices have recently been established in London and Paris, Dr. H. A. Bumstead being in charge of the former and Dr. William F. Durand of the latter. The total expenditure by Engineering Foundation for the National Research Council was $9,036, derived partly from income of the endowment fund and partly from special gifts from Ambrose Swasey and Edward D. Adams. In May, Walter M. Gilbert was appointed Assistant Secretary of Engineering. Foundation, with headquarters in Washington, his services being contributed by the Carnegie Institution. He also became and has remained to date Assistant Secretary of the National Research Council. In September, resolutions were exchanged between the Engineering Foundation Board and the National Research Council, setting forth a policy of continuing reciprocal relationship, and a conference committee, Chairman M. I. Pupin, Dr. Charles Warren Hunt, and Gano Dunn, was appointed to inform the National Research Council of the readiness of Engineering Foundation to work upon definite problems sug-gested by the Council. No problems have yet been suggested.

Jan 5, 1918

By R. W. Raymond

WISH to call the attention of the Institute to a curious subject, brought to my notice last summer by Mr. Begger, the accomplished metallurgist of the smelting-works of the Boston and Colorado Company at Black Hawk, near Central City, Colorado. At these works, the richest auriferous sulphhrets of Colorado (particularly copper pyrites) are smelted in reverberatories, together with roasted tailings (iron pyrites), and the gold and silver are concentrated into a new, artificial sulphide, or copper matte, containing $1500 and upwards of the precious metals per ton, and this is shipped to Swansea. I will say in passing, that this shipment of an unrefined product, like the similar shipments from Utah and Nevada to San Francisco, Chi¬cago, St. Louis, Newark, New York, and Europe, of crude argentiferous lead or "base bullion," is not a sign of incomplete metallurgy here, but has a sound business reason. The separation of the precious metals in the West would be more expensive, to begin with ; and then it would necessitate the movement of these metals by express, at high rates and risk, to commercial centres or coining mints, while the base metals having no home market, must be shipped and sold at little or no profit. At present, the gold and silver, safely packed, as it were, in the base metals, are transported with safety as ordinary freight; and the base metals probably more than pay cost of shipment and separation. To return to the Black Hawk reverberatories. On a recent occa-

Jan 1, 1873

IT is intended herein: to make some brief comments on geophysical 'work in general and on the various methods, and then to refer to that branch which, perhaps, is of the greatest importance and interest to the metalliferous mining engineer, i.e., the variousmethods of electrical prospecting.The term geophysics was originally applied to those larger physical and geodetic studies and methods concerned with such purely scientific subjects as the investigation of the true figure of the earth and the determination of the stability relations resultingtherefrom. Applied geophysics and geophysical methods of prospecting are concerned primarily with the search for, and investigation of, useful mineral deposits concealed within the earth's crust and not readily detectable by the normal methods employed bythe mining geologist and prospector. The methods employed have been devised as a result of co-operation between mining men, geologists, and physicists, and, although steady progress has been made during the past 20 years or so, it is within the last four orfive years that the importance of these methods has been acknowledged by the mining world in general. Although many of these methods are still in, or have barely emerged from, the experimental stages, a steadily increasing list of important discoveries is attributable to their employment-more particularly in Europe and America than elsewhere. The various methods have each their own limitations regarding the class of work they can undertake, and no one method is capable of general application. The greatest care should be exercised in selecting the method, or methods, to be employed in any particular area, the...

Jan 1, 1928

By Menne DM

The carbon-in-pulp (CIp)process has become well accepted and firmly established in the gold industry of South Africa and, at this stage, six large CIP plants are treating close to I million metric tons of material per month. Many small operators are also using CIP and additional large plants are either nearing completion, are on the drawing boards,. or are being considered. The programme of testwork that preceded the acceptance of the CIP process in South Africa was conducted over some eight years and has been previously described'-7. With the start-up of the President Brand CIP plant on 'calcine' in July 1980 and that of the Western Areas CIP plant on repulped filter residues in September 1980, the emphasis on the CIP process switched from pilot plants to these large plants - and has largely remained there. As it has started up, each new CIP plant benefited from the experience gained and the developments made, on earlier plants but, since so few plants have so far been established in South Africa, each new plant and each new design has revealed a further set of conditions to be met and problems to be overcome. However, in the highly collaborative atmosphere of the South African gold-mining industry, the results and observations from the operation of these first plants were shared by all mining groups. This paper will attempt to describe typical developments on, and results obtained from, these new large plants, and will incorporate significant results from the earlier laboratory and pilot-plant investigations.,

Jan 1, 1982

By B. Stas, L. Siska, L. Dlouhy, A. Skrabis

The basic research program of the Scientific Coal Research Institute at Ostrava - Radvanice into the problem of geophysics has been influenced by the specific nature of present urgent geo- physical problems in mines and directed to attain higher grade of effectiveness, safety, and overall economy in mining activity. The research has been divided into two basic trends: Seismoaccoustic research deals with questions pertaining to safety in mining especially when work is in coal seams under "heavy roofs", i-e., thick beds of sandstone prone to rock bumps and characterized by caving. Methods have been developed with the definite aim to determine the time and space prognosis of critical states of tension in the rock mass when stability is disturbed as a result of mining activity. Seismic research is directed towards the determination of detailed structural and tectonic elements of the internal geological formation of the Carboniferous rocks, the establishment of continuity or tectonic faulting of coal seams, and the evaluation of magnitude, shape, and time changes in the rock mass surrounding the mine workings. The measurements have been applied either from the surface or in the underground workings according to the specific nature of individual problems. Satisfactory results have been obtained in some branches of this research, other branches being still in the stage of development. Remarkable results have been achieved in the development of seismoaccoustic methods designed to establish the time prognosis of dangerous dynamic phenomena accompanying the process of strata deterioration above the worked longwall face. One of the most

Jan 1, 1971

By Donald T. Robertson, Kurt Hecht, Michael K. Muchard

"This paper presents case histories of driven concrete pile damage detected with dynamic testing methods utilizing strain gages and accelerometers embedded in the pile at the prestressing yard during pile construction. Data from the embedded instrumentation is compared with data taken with external bolt on instrumentation and other test methods such as low strain testing on the same pile. In the most severe cases, the piles were extracted revealing and corroborating the embedded data collector results.INTRODUCTIONDynamic testing of driven pile foundations was originally developed in the late 1960’s and commercialized in the early 1970’s. While the methods of analyzing dynamic test data have improved with the advancement of computer technology, the test method and the sensors used to acquire the data have changed little. In 1998, under a research grant provided by the Florida Department of Transportation, (McVay et al, 2002) an Embedded Data Collector system (EDC) was developed. The collector utilizes two sensor packs, each consisting of one strain gage and one accelerometer, embedded near the pile toe and pile top. Utilizing the toe sensor pack, the system provides reliable real time pile end bearing capacity measurements. This end bearing capacity is combined with a Case Method Solution augmented with an automatic damping calculation to provide the overall pile capacity, pile skin friction capacity and pile end bearing capacity. Also, since the gages are embedded, they have the ability to track all changes from the casting yard (i.e. prestress), driving, and subsequent setup (freeze, relaxation, etc) at both the top and bottom of the pile."

Jan 1, 2017

By AIME AIME

I N JUNE, 1918, at a meeting of the American Society of Mechanical Engineers in Worcester, Mass;, a resolution was adopted for a committee to investigate the aims and organization of that society. This was followed subsequently by similar independent action on the part of the Society of Civil Engineers. The other two Founder Societies were approached and requested to appoint similar committees, the four committees to combine as a .Joint Development Committee, later called the Joint Conference Committee, to investigate what might be done in the way of coordinating those activities of the Founder Societies which ape of common interest, and which were then being pursued separately. The Joint Conference committee worked diligently -for almost. two years and. brought forth a tentative as outlined in its report which was published in full in MINING AND. METALLURGY, December, 1919. It recommended the formation of a nation-wide organization to be composed of representatives' of all of -the engineering societies, local, state, regional, or national, the object to be to further the interest of the public through the use of technical knowledge and engineering experience, and to consider and act upon matters common to the engineering and allied technical professions. Whereas the technical societies have large fields of endeavor in welfare work, and their prime. efforts are 'still in technical lines, this new organization was to be devoted entirely to service, looking to the welfare of the nation and the engineering profession, and to service for the public in local and state affairs.

Jan 1, 1920

By J. E. Hilliard, H. E. Cook

It is shown that for systems having a miscibility gap the spinodal composition (c,) in the vicinity of the critical temperature (Tc) is related to the equilibrium composition (c,) by where cc is the critical composition. This expression is exart for the limit T — Tc and is a good approximation down to (T/Tc) - 0.9. If the miscibility gap meets the composition of the pure components THE recent theoretical treatment by cahn1,2 on spinodal decomposition of solid solutions has revived interest in methods of estimating the chemical spinodal, * i.e., the locus on a binary phase By use of the appropriate expression, the spinodal can be drawn on the Phase diagram almost by inspection with an accuracy comparable to that of lengthy calculations in which a free-energy function is fitted to the phase diagram. Satisfactory agveemenf is also obtained with spinodals comPuted from experimental free-energy curves. where G is the Gibbs free energy of the homogeneous solution and c the atomic fraction of component 2, the derivative being evaluated at constant temperature (T) and pressure (P). (These subscripts will hereafter be omitted from the partial derivatives.) If experimental measurements of G as a function of c and T are available in a single-phase region above the spinodal, then these can be extrapolated to obtain a series of metastable free-energy isotherms in the two-phase region, and from these isotherms a series of spinodal compositions can be calculated. Because the value of is very sensitive to experimental errors, an elaborate analytic procedure is required for

Jan 1, 1965

By H. B. Charmbury, D. R. Mitchell

Recovery of fine coal from solids reporting to wash water has become increasingly important. These solids range from about 28 mesh to 0 and constitute 3 to 7 pct by weight of the feed tonnage to a coal preparation plant. In the past they were usually wasted to streams, but present clean stream legislation makes it necessary to remove them from the wash water and, if economically possible, recover the associated coal as a saleable product. Where these solids are not wasted to streams or to slime ponds they are recovered by thickeners and filters. Since filter cake is often high in ash or sulfur, or both, it is not readily marketed or used. Common practice is to mix it with other plant products, generally slack or cleaned run-of-mine. Uniform blending is difficult, not only because the impurity is usually high, but also because during certain operating periods it is possible to get a concentration of this filter cake in a railroad or barge. At some plants filter cake has been derived from the froth flotation clean-up of Dorr thickener underflow. The operating circuits required for a froth flotation plant make this a comparatively high-cost treatment, and in the last few years experiments have been carried out with bulk oil methods. These also are quite expensive and lend themselves only to special situations. Table I gives some characteristics of thickener underflows for plants in the Pittsburgh area treating Pittsburgh seam coal. It will be noted that there is a concentration of impurities in the -200 mesh sizes.

Jan 1, 1960

By Henry M. Howe

This paper gives the results of an investigation of the beha vior of the argentiferous cobalt-nickel arsenides of Temiskam-ing, Ontario, in roasting, made in the metallurgical laboratories of the School of Mines of Columbia University in the City of New York. The ore was kindly given by the owners of the La Rose and Trethewey properties at Cobalt, Ontario, and Mr E. J. Hall, Tutor in Assaying in Columbia University, has helped us much. I. Object of the Investigation. The object of the investigation was to learn: 1. The temperature at which the arsenic is most rapidly expelled ; 2. The thoroughness with which it is expelled by prolonged roasting at this temperature; 3. The effect of adding charcoal (a) near the end of the roast and (b) at. the beginning of the roast. II. Nature of the ORe. The important ores mined in the Temiskaming deposits are: native silver—with small amounts of dyscrasite (Ag,Sb), ar-gentite (Ag,S), pyrargyrite (Ag,SbS,)—smaltite (CoAs,), chlo-anthite (NiAs,) and niccolite (NiAs). Mispickel (FeAsS) and cobaltite (CoAsS) also occur in smaller quantities. The average composition of the ore shipped from this district for the first six months of 1905 was: silver, from 4.1 to 4.8 per cent.; cobalt, from 6.9 to 8.2 per cent.; nickel, from 3 to 4.7 per cent.; and arsenic, from 30.9 to 34.6 per cent. The ore which we treated consists chiefly of smaltite. In our 1aboratory-work

Jan 1, 1908

By George Grandy

Kvaerner experience is being used to develop software to design or simulate crushing and screening plants. The model techniques discussed are presently being used for open-circuit plants and are being extended to closed circuit plants. The program contains a library of routines, each representing a piece of equipment or unit operation, which are assembled into one of several open-circuit plant configurations. Routines include gyratory primary crushers; standard secondary and shorthead tertiary cone crushers; single, double or triple deck screens; and stockpiles, feed bins and belt conveyors. The program uses steady-state models to simulate the performance of crushers and screens that have small residence times and quickly reach equilibrium when operating conditions and/or parameters are changed. The dynamic aspect of the total circuit model concerns the storage units within the circuit, i.e. stockpiles and bins, and, in the closed circuit configuration, circulating loads and size distributions. In many cases, just vendor's catalog data are necessary for a pre-feasibility simulation; in other cases, actual plant test data are required to obtain more accurate simulations. The entire plant is shown in a single graphic screen so the user can see all the relevant information he might want, and soft-keys are provided for the user to make on- line parameter changes and observe the effects on storage elements, equipment feed rates and the final product size distributions. The model also reports equipment utilization in percentage, power consumption, and other related operating information, and soon, will be able to report estimated capital and operating costs.

Jan 1, 1999

By Raimo Matikainen

Sublevel stoping has been used in Finland since the 1930's and today more than ten under- ground mines have adopted it as their main stoping method (Fig. I). Approximately 80% of the total underground tonnage is mined by sub- level stoping (Table 1) The first mines to introduce the sublevel stoping method in Finland were limestone mines. The development of sublevel stoping was very slow up to the mid 1960's when the switch to trackless mining started and the increase of mechanization lead to higher capacity and productivity. The method itself has been almost the same since the 1950's when long hole drilling was introduced. According to a future prognosis sublevel caving will give way to sub- level stoping; on the other hand, open pit mining will at the same time grow rapidly with some new mineral orebodies, which will he brought into production. Most Finnish orebodies are, however, only marginal ores and they could not support mining with more expensive methods than open pit mining or sublevel stoping. The future of sublevel stoping seems relatively bright. GEOLOGICAL AND ROCK MECHANICAL BACKGROUND The rock mechanical conditions in Finland are in general relatively good and the rocks firm. The compressive strength is normally 40 - 150 Mpa and modulus of elasticity 40 - 200 Gpa. Low values are common in altered and fractured rocks and near the ore contact Rock stress measurements have been carried out already for 20 years for mine design and monitoring purposes. The results of these measurements show that relatively high horizontal stresses seem to be common (Fig. 2).

Jan 1, 1981

By P. Somasundaran, I. J. Lin

There are several methods described in the literature for the determination of the order and the rate constant for the flotation of minerals. These often involve some type of computational or graphical procedures. A relatively simpler method developed on the basis of a technique used by Chang" in chemical kinetics is described in this paper. Chang's technique, like most others in chemical kinetics," is based on the law of mass action which states that the rate of a chemical reaction is proportional to the active masses of the reacting substances at any given time. Application of this law to the flotation of minerals would involve the adaptation of the terms "flotation" for "chemical reaction" and "floatable amount of the minerals" for "the active masses of the chemical reactants." There are indeed a large number of physical processes controlling the actual flotation rate. The most inefficient one of these could be considered equivalent to the slowest reaction in a series of chemical reactions. If variables such as aeration rate and agitation are kept at constant levels, the rate of flotation under free flotation conditions (i.e., conditions under which the suspension is dilute) will be given by the following equation: where C is the concentration of the floatable minerals in the pulp at any given time t, K is the rate constant, and n is the order of the reaction. If we represent the floated fraction of the floatable mineral at time t as m (0 m - 1) and C at t = 0 as Ca, integration of Eq. 1 yields

Jan 1, 1974

By S. M. Spottiswoode

Rock mechanics benefits of stope support in deep-level mining originate principally from the ability of the support to resist relative movements between the hangingwall and the footwall. While the role of stabilizing pillars and backfill on reducing the energy release rate (ERR) at the face is well understood on the basis of elastic behaviour of the rock mass, the effect of support on controlling movement of fractured ground around deep-level stopes has not yet been thoroughly studied. As part of a programme of studying the behaviour of this fractured ground, geophones were placed 10 m from the face on the roof and floor of a longwall stope in which packs were used as supports. It was found that differential movement between the roof and floor generally exceeds average stope movement during a seismic event. Conventional support therefore transmits very little seismic energy; this is expected to remain true until complete convergence occurs. In backfilled stopes, backfill can become at least as stiff as the fractured wall rock. This will have the effect of reducing the length of the hanging- wall beam. Amongst other rock mechanics considerations, a shorter hanging- wall beam should: (i) increase the resonance frequency of the hangingwall and thereby decrease the levels of vibration for seismic events with M > 1,0; (ii) reduce absolute vibration levels by increasing the mass of rock immediately adjacent to the stope which is shaken by seismic waves; and (iii) reduce differential movement between the roof and floor and thereby reduce cyclic strain on the backfill and on gully support.

Jan 1, 1988

By Eric K. Albert, J. Kiusalaas

The paper presents an overview of SPASID (Kiusalaas and Albert, 1983), a new computer program developed under U.S. Bureau of Mines funding for the prediction of surface subsidence caused by under- ground mining operations. The presentation, which is illustrated with two case studies, also re-evaluates the influence function method as a tool of subsidence prediction, arriving at some rather unconventional recommendations. SPASID consists of four modules that communicate through common data bases: (1) Preprocessor. This module prepares and maintains the database for the entire site. The database contains all the information about the site and the mine operation that is necessary for the computation of subsidence. (2) Subsidence Predictor. The influence function method is used to predict the surface displacements that occur in any portion of the site that occur between two given dates. The computations take into account the time lag between extraction and displacement, and the effects of pitching seams and incomplete compaction at the edges of panels. The program contains i not he's influence function and the Green's function of transversely isotropic elasticity theory. (3) System Identification. The purpose of System Identification is to determine the optimal values of the various parameters associated with the influence functions in the Subsidence Module. System Identification requires measurements of subsidence from a site with a sirnilar overburden structure. The values of the subsidence parameters are obtained by minimizing the discrepancy between the measured and computed surface displacements. (4) Postprocessor. The Postprocessor is a graphics facility for displaying the data generated by the other program modules.

Jan 1, 1984

By Thomas H. Leggett

In speaking of the mining and economic conditions prevailing at the present time on the Rand, it is not my intention to go into the details of the mining practice, since this has been already well described both in the Transactions' and elsewhere,2 but rather to take a more comprehensive view of the industry and its surroundings as a whole, marking its general development and the lines of its future progress. In a paper entitled Deep-Level Shafts on the Witwaters-rand, with Remarks on a Method of Working the Greatest Number of Deep-Level Mines with the Fewest Possible Shafts,' presented to this Institute in August, 1900, I drew attention to the great cost of sinking the very deep vertical shafts that were then being seriously proposed as necessary for the development of the deeper areas, pointing out the strong advisability of working this ground by means of inclines to be sunk from the existing shafts of from 3,000 to 4,000 ft. in vertical depth. In this paper it is stated (p. 975): '" In short, practice upon the Rand now tends towards fewer vertical shafts and more underground inclines, especially for the very deep mining about to be undertaken." In consequence, the 6,000-ft. vertical shafts, at one time so much discuesed, have never been started, and they do not now seem likely ever to be. The necessity of placing all deep shafts further apart in order to make them control and exhaust larger areas was also dwelt upon. This economy wae vitally necessary for both

Jan 1, 1909

By Al Cropp, Julie Hunt, Will Goodall, Ron Berry, Dee Bradshaw

Geometallurgy aids the understanding of ore body variability but has the most value if the data is easily available along the entire mining value chain. This requires cross-discipline communication and collaboration across traditional silos, and an organizational culture that encourages that to flourish. Data that are collected by the numerous groups (i.e. mining, geology, milling, processing, refining, smelting, marketing, environmental etc.) involved in the mining process may have relevance to other stakeholders; mineralogical and textural data for example has value to all these groups. Data required for modeling comminution or identifying acid potential from waste rock may already exist, however it needs to be made available to all the relevant stakeholders in the right format at the right time. As part of the GeM (AMIRA P843 & P843A) project the opportunity has been taken during the sponsor meetings, short courses, case studies etc. to ask the question: ‚What information do you want from further up the chain?? For example, to metallurgists ‚What information would you like from the geology group before the ore enters the mill?? The geology group may already have information important to mineral processing but not know it is of interest. This could, for example, be in the form of a geometallurgical drill core log that contains quantitative measured values. This paper focuses on the interaction between the mining, geology, mineral processing and environmental groups, using ore properties resulting from geological alteration to identify potential impacts throughout the mining process and discusses how a cross discipline approach can benefit all.

Jan 1, 2014

By S. J. Rothman, A. L. Harkness, L. T. Lloyd

Self-diffusion in Y uranium has been measured using U235 as the tracer isotope. The diffusion coefficient fits an Arrhenius-type equation D = 2.33 x 10 -3 exp (- 28,5000/RT) cm2/sec The values of Do and Q are unusually low and are not consistent with the values expected from theories based on a simple vacancy mechanism of diffusion. CYLINDRICAL samples, 1 cm in diam and 1/2 to 1 cm long, were prepared from high-purity uranium containing 0.0343 pct u235, Table I. The samples were water quenched from 690°C (the a-ß transformation is at 668°C) to remove preferred orientation, and annealed at 450 "C to minimize residual stresses. One end of each cylinder was polished on a 1-µ diamond lap and electropolished in a phosphoric acid solution. After a final cleaning by cathodic sputtering, a 1- to 3-µ thick layer of the tracer isotope, uranium containing 93 pct u235, was sputtered onto the sample.' To prevent contamination during the diffusion anneal, the diffusion couples were placed in a tantalum cup and covered with another piece of uranium, and the whole assembly was sealed off in an evacuated quartz tube. Annealing temperatures were constant within +2.0°C. The samples were heated and cooled slowly between room temperature and the ß-? transformation (774°C) in order to minimize distortion of the sample surface that might arise from aniso-tropic thermal expansion and density changes during phase transformations. After machining off 1/16 in. from the radius to

Jan 1, 1961

By R. V. Ramani, R. Bhaskar

The results of an experimental and theoretical research study into the spatial and temporal behavior of dust in mine airways is summarized. Experiments were performed in mine airways under both controlled and normal operating conditions. The controlled experiments included the documentation of the concentration and deposition patterns for two types of dust under three different velocities. Real-time dust concentration data were obtained using real-time aero- sol monitors (RAM-I) to determine the dispersion coefficient in a mine airway. On the theoretical font, a convection diffusion model of the dust flow phenomenon in mine airways was developed considering dominant mechanisms affecting dust transport and deposition in mine airways. Mechanisms modeled include turbulent and gravitational deposition, coagulation, and dispersion. In this paper, comparative analyses of results (8 the controlled experiments with the predictions of the mathematical model are presented. In addition to the overall validity, the adequacy of the individual components of the model, such as deposition in the total and respirable range, and dispersion are examined in light of the experimental observations. The experimental data from controlled experiments compared more favorably with model predicted results for similar conditions as opposed to the comparative analysis results for in-mine experiments. Specifically, the model predictions for an 800-m stretch of a mine airway reveal some significant differences from the behavior noticed in the mine. The deposition was lower than that predicted by the model. Consequently, concentrations were higher than those predicted by the model. The implications of these and other findings for further investigations are discussed in the paper.

Jan 1, 1987

By V. Koump, R. H. Tien

An approximate mathematical solution is found for the problem of unidimensional solidification of a slab of a binary alloy with time-dependent surface temperature. For the model considered, the solid skin does not form until the liquidus front has moved a certain distance. This distance depends on the rate of cooling and can be as large as half the thickness of the slab when the cooling rate is small. Assuming that the THE process of unidirectional solidification of binary alloys with constant surface temperature was analyzed by the present authors in a recent paper.' In the previous analyses, the surface temperature was considered to be lowered instantaneously, at the beginning of solidification, from its initial value to some surface temperature decreases linearly with time and that the solidus and the liquidus lines are straight, calculations are made of the temperature and concentration distributions, movements of the liquidus and the solidus fronts, as well as changes of temperature, solid fraction, and solute concentration of the liquid at the center of the slab. arbitrary temperature, lower than the solidus temperature. Although the solution of the problem for the case of constant surface temperature has some practical applications, instantaneous changes of temperature are physically impossible. Present theoretical study of the unidirectional solidification of a binary alloy is based on a more realistic model, i.e., in this case, the surface temperature of the slab decreases from its initial value continuously with solidification time. The model of solidification within the solid-liquid region is the same as the one described in the

Jan 1, 1969