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By Culver, Richard S.

In spite of the widespread interest in rock bolt research, relatively little is known about the critical region surrounding the bolt anchor. In analyzing the stress distribution around an opening resulting from rock bolt support, it is commonly assumed that the bolt is fixed at a point far enough from the surface so that the anchor does not influence the performance of the bolt. Furthermore, a bolt anchor is assumed to per- form satisfactorily if it will hold the design load with a minimum amount of load relaxation, commonly called bleedoff. From the standpoint of the design engineer both of these assumptions are reasonable, but they ignore the fact that the extremely high stresses in the region of the anchor are capable of generating fractures in the rock. Lang estimated the bearing stresses for a slot and wedge anchor on a one-inch-diameter bolt to be as high as 125,000 psi. This paper describes a more thorough analysis of the magnitude of the stresses around the anchor and the nature of the potential fractures that might result.

Jan 1, 1968

By G. A. Brady

Seven samples of Pennsylvania anthracite from the Bottom Ross bed were analyzed and tested to obtain data on cleaning characteristics, proximate and ultimate analyses, specific gravity, grindability, heating value, and ash softening temperature. Ash content of the samples varied irregularly from 9.0 to 34.4 percent, the range being narrowed to an upper limit of 14.8 percent ash by removing impurities dense enough to sink in a medium with a specific gravity of 1.90. Ash content of the sink material with specific gravity greater than 1.90 ranged from 56.4 to 80.4 percent; corresponding specific gravities were 2.095 to 2.534. Volatile matter contents were indicated to be higher for the ash-forming minerals than for the pure coal substance in the various specific gravity fractions of a given sample. Specific gravities of anthracites with compa¬rable ash contents but from different locations in the bed varied as much as 0.06. The grindability index increased significantly with increasing ash con¬tent of specific gravity fractions from all the samples.

Jan 1, 1968

By A. J. Strauss

The solubilily of lead in PbS as a funclion of lemperature has been investigated by means of Hall coej'icient (RH) measurentents OIL samples prepared by annealing and quenching Bridgman-grourz single crystals, which contain excess lead incorporated during /heir growth from the mell. For sufficiently long annealing times and sufficiently rapid quench rules, the samples obtained consist of n-lybe PbS snturated with In the semiconducting compounds PbS, PbSe, and PbTe, the point defects associated with the presence of lead in excess of the stoichio metric composition are shallow donors. The defects associated with the presence of excess nonmetal are shallow acceptors. lead at the annealing teuiperatiire, together luilh a dispersed second phase of lead microprecipitates. Due to the retrograde solubility of lead, the measured free carrier concentration (n = l/eR77) decreases with decreasing annealing tewperature (T) from- 2.4 X 10 em-3 for 1l85OK to 1.3 X 1018 cm-3 for 623°K. The dala are well-represented by the equation n =(1.08 x 102) exp[ - (0.37 ev.)/kT] cm-3 For most undoped samples of these compounds, the carrier concentration at room temperature and below is determined primarily by the stoichiometry, since the concentration of either excess lead or excess non-metal is large compared to the concentrations of intrinsic carriers and electrically active impurities. Therefore the dependence of composition in temperature and partial pressure can be investigated by means of Hall coefficient measurements, even though the deviations from stoichiometry do not exceed 0.03 at. Pct

Jan 1, 1968

By F. E. Rizzo, L. R. Bidwell, D. F. Frank

THE poor high-temperature oxidation resistance of the refractory metals becomes an important problem as higher operating temperatures are sought. A meaningful analysis of their oxidation behavior requires a knowledge of the phases that can appear during oxidation as well as their relative stability. Although several extensive investigations have been carried out to obtain this information for the W-0 system,1-10 serious inconsistencies still remain. First, the standard free energies of formation (AG°) determined in recent studies which used the solid electrolyte galvanic cell technique6,7,9 differ significantly from those obtained primarily from gas equilibration measurements.1,3,4,10 The disagreement is especially large for the highest oxides. These data have been used to predict the decomposition temperatures of WO2. 72 and WO2.90.1 A considerable extrapolation is required, resulting in a large uncertainty in the decomposition temperatures. Second, Bousquet and perachon3 have presented convincing evidence, ob- tained by gas equilibration measurements, in support of the long-contested existence of W30. Phillips and chang,ll on the other hand, were not able to observe this phase under similar experimental conditions. The purposes of this work, which is part of a continuing investigation of the W-Mo system, were to resolve the discrepancies between the AGO measured by gas equilibration and solid electrolyte galvanic cell techniques, to extend the latter measurements to lower temperatures, to redetermine the WO2.72 and WO2.90 decomposition temperatures, and to apply the more sensitive electromotive-force method to the question of the existence of W3O. I) EXPERIMENTAL PROCEDURE The measurement of ?G° of reaction by the use of calcia-stabilized zirconia solid electrolyte galvanic cells has been described previously.12 The method is based on the measurement of the difference in chemical potential of oxygen between an electrode containing the two oxides of interest and a reference electrode of known oxygen activity. Two different types of cell holders were used in this study. The first type of apparatus has been described earlier." It consisted of two solid electrodes separated by a disc of electrolyte. Both electrodes were exposed to the same stream of purified helium. With this design a gaseous transport of oxygen between the two electrodes is possible. The second type of apparatus, which has also been described earlier,14 effectively separated the two electrode atmospheres. It utilized a closed-end impervious, calcia-stabilized zirconia tube that was open to the atmosphere. The tube served as an electrolyte for the cell and provided a means for separating the anode compartment, which was held under a static vacuum, from an air reference cathode. The cells and reactions of interest are described in Table I. High-purity tungsten metal was obtained from the Fansteel Metallurgical Corp. and the Allied Chemical Corp. Table II contains an analysis of each material. WO3 was prepared by oxidizing the metal in air at approximately 600°C in high-purity recrystallized alumina boats and by the dehydration of reagent-grade tungstic acid in alundum boats. The two methods of preparing WO3 resulted in slightly different purities.

Jan 1, 1968

By Robert A. Bradburn

The Bureau of Mines has developed a miniature, portable two-level oxygen-deficiency alarm and produced three prototype models. Each operates from a 4.2-v dc power source, and the highest current drain of any model is 80 ma. An electrochemical cell, which produces an electrical output in proportion to the partial pressure of oxygen to which it is exposed, is used as an oxygen detector. The output of the cell is applied to an electronic circuit that detects two different levels of oxygen percentage below that of normal air, and produces distinct audible signals at these levels. The hazard alarm mode is activated when the oxygen percentage first drops below normal and produces a 500-cps "beep" tone with an intermittency of 1 cps. The danger mode produces a continuous 500-cps audible signal when the oxygen percentage drops still lower.

Jan 1, 1968

By David Kramer, Cecil G. Rhodes

Critical transport currents were measured as a function of perpendicular external magnetic field in Ti-22 at. pct Nb wire samples. These samples were heat-treated to yield w Phase precipitates at denslties ranging from 10 to 10 17cm-3. The Precipitates are ellipsoids of revolution with major axes of 50 to 1300A. Flux-Pinning by w precipitates is responsible for the high critical transport currents that were ob- ThE ability of a type II superconductor to sustain a zero-resistance transport current (Jc) in an external magnetic field (H) is due to the presence of micro-structural features which can impede the motion of magnetic flux penetrating the superconductor under the influence of a Lorentz force. Such features are referred to as pinning sites. The pinning strength is tained. A sample cooled from 800°C and annealed 1 hr at 450°C carried a critical tramport current of 10 amp per sq cm at 30 kG. Variations in the current-carrying ability of this alloy are due to changes in its pinning strength which is a function of precipitate density and composition and of the composition of the matrix. the reaction of the bulk superconductor to the Lorentz force and depends on the efficiency of the individual pinning sites and on their volume density. The super -current density increases with pinning strength, other things being equal. The above concepts are discussed in detail in a comprehensive review by Livingston and Schadler.' In Ti-Nb alloys, as in other binary titanium alloys, the metastable hexagonal w phase usually forms below the p/a + p phase boundary near the titanium side of the phase diagram. Stiegler et a1.' have summarized much of what is known about w phase in titanium and zirconium binary alloys. The present work deals with

Jan 1, 1968

By Sam Friedman

The Bureau of Mines conducted experiments using bench-scale apparatus to explore the effect of large changes in process variables on the yield and composition of the gases produced by passing 800° C steam through a fixed bed of Pittsburgh seam (hvab) coal. The total yield of combustible gases increased throughout the given range for the following variables: Superficial steam velocity increasing from 0.02 to 0.12 fps, pressure increasing from 1,000 to 6,000 psig, residence time increasing from 0 to 60 minutes, and temperature increasing from 800° to 900° C; however, a greater increase in the yield of hydrogen in comparison with the increase in yield of methane reduced the gross heating value of the gas to around 470 Btu per scf at conditions giving the maximum yield. Pressures of 1,000, 3,000, and 6,000 psig at 0.09 fps steam velocity, 800° C, and 60 minutes residence time, respectively, produced methane yields of 20, 24, and 22 percent, based on maf coal, with the gross heating value of the CO2-free gas decreasing from 552 to 520 and to 470 Btu per scf. Methane concentrations in the CO2-free gas were 26, 22, and 14 percent, respectively. Based on the gross heating value of the coal, the percentage of the heating value recovered in the gas was 60, 71, and 87 percent, respectively. The use of tungsten sulfide as a catalyst for converting carbon oxides and hydrogen into methane was explored briefly using both a sulfur-free gas rich in methane and a sulfur-bearing synthesis gas (3H2:1CO).

Jan 1, 1968

By P. R. Schmidt, N. J. Themelis

A study zvas made of the deoxidation of copper at 1170°C by injecting a jet of carbon monoxide vertically upwards into the melt. The effects of submersion depth (2 to 20 cm), orifice diameter (& to 5 in.), and gas velocity (100 to 3650 ft per sec) were examined. In the oxygen range 0.1 to 1.0 pct 0, the overall rate was conlrolled by gaseoLcs mass Lransfer. The results were interpreted in terms of a rate coefficient per unit depth which was found to be constant with distance along the jet axis and nearly proportional to the orifice Reynolds number in the range 1000 < NReo < 9100. AS the gas flow rate through an orifice submerged in a liquid is progressively increased, at least three regions of bubble formation may be distinguished. At very low rates, the formation of bubbles is practically a static phenomenon, depending on the orifice diameter, the liquid surface tension, and the densities of the two phases. In this region, the bubble size is constant while the frequency of bubble formation increases with gas flow rate.&apos;-3 At higher flows (500 < NR~, < 2100), the frequency of bubble formation reaches a steady value and the bubble size increases with gas flow rate; when the bubbles issuing from the orifice become so large that they start coalescing to form larger bubbles, the turbulence induced in the liquid by the passage of previous bubbles shatters them into small bubbles of varying size. Finally, for gas velocities in the intermediate and turbulent regions of flow (NR,, > 2100) a tangential separation surface is created around the jet and momentum transfer takes place between it and the surrounding liquid medium. The entrainment of liquid and the resulting deceleration of the gas-liquid dispersion causes the jet to expand forming a characteristic jet cone. The large velocity and density differences between the jet and the liquid result in a high degree of instability and the jet envelope fluctuates rapidly.The characteristic jet cone can be observed by means of time exposure photographs such as those shown in Fig. 1 for an air jet introduced vertically upwards in a water bath. High-speed photography has showns that the gas-liquid dispersion within the cone consists of small bubbles the size of which depends mainly on the jet orifice diameter and Reynolds number. In the laminar region of flow, the following correlation was obtained by Leibson: The results of Liebson et a1.&apos; are plotted in Fig. 2. It can be seen that the region 2000 < NReo c 10,000 is not well-defined experimentally. In the entrance to the fully turbulent region of flow (NR,, = 10,000), the mean bubble diameter decreased to about 0.4 cm and varied only slightly from there on according to the correlation:

Jan 1, 1968

By D. W. Fuerstenau, L. M. Berlioz

In 1957, Charles1 first presented an analysis of a relationship between the energy expended in comminution and the extent of size reduction achieved. Subsequently, Schuhmann extended and interpreted Charles&apos; approach to comminution. According to their analysis, the energy, E, expended in comminuting unit mass of fairly uniformly-sized material is related to the size modulus of the product, k, by where a is the distribution modulus (slope of the log-log cumulative size distribution plot) and C is a constant, which is primarily determined by properties of the solid. If there is any fundamental basis for the E vs k relationship, E must necessarily be concerned with the useful work for the size reduction process and not necessarily the work input, as discussed in detail by Harris.3 Charles and numerous other investigators tested this equation only by relating k to the grinding time, assuming expended energy to be directly proportional to time, but never directly measuring power. In our laboratories, we recently constructed a special batch ball mill with which the power could be accurately determined with torque measuring apparatus.4 With this device, a direct test of the Charles relationship could then be made for ball milling. 5 EXPERIMENTAL A stainless steel mill, 11.5 in. long and 10 in. in inside diam, lined with eight low-silhouette lifter bars, was used for these experiments. The grinding media consisted of 30 kg of single sized, 1-in. diam, stainless steel balls, which occupied about 50% of the total mill volume under static conditions. The void fraction of the static ball load was approximately 0.4, and for the dry grinding conditions used, the corresponding interstitial volume was filled when about 3300 g of the dolomite feed material was present. The 7x9 mesh dolomite used as feed was obtained as a natural, uncrushed product thus as- suring a random distribution of feed particle shapes. Charge weights of 660, 1320, 1980, 2480, 3300, 3960 and 5280 g, which correspond to 20%, 40%, 60%, 80%, l00%, 120%, and 160% of the interstitial load, respectively, were used. Grinding times of 20, 40, 60, 80, 100, 150, 200 and 300 revolutions were considered, with the mill operating at 54 rpm (approximately 60% of critical speed). The tests were made sequentially, in that the size distribution obtained after a certain grinding interval was utilized as the feed for the subsequent period of grinding. Agreement with control experiments where the mill ran continuously for the entire interval was excellent. Torque measurements were made utilizing a Baldwin-Lima-Hamilton SR-4 torque pickup in the manner that has been described previously.3 Standard wet (to obtain the -400 mesh material) and dry sieving procedures were followed using the Tyler full screen series. RESULTS The Gaudin-Schuhmann size distributions obtained in all of these experiments are characterized by distribution moduli (slopes), a, of about 0.66 and are representative of normal dry batch ball milling of a material like dolomite. As an illustration of typical

Jan 1, 1968

By I. R. Kramer

The stress associated with the surface layer was deter-minedfor iron and molybdcnum. These measurements show that the surface layer plays a very important role in the plastic deformation of bcc metals. From the relationship between strain arui the surface layer stress and the back stress imposed by the internal obstacles, it is Proposed that the term of of the Hall-Petch equation is related only THE large number of studies on plastic flow of bcc metals have failed to delineate clearly the nature of the obstacles influencing dislocation movement. Since there have been numerous articles which have reviewed the mechanisms proposed to explain various aspects of plastic flow of bcc metals (for example, conrad1 and Keh and weissmann2), no attempt will be made here to discuss their conclusions. However, it should be to the surface stress while the term Kfd is the stress required to move dislocations through internal obstacles. Further, it was possible to derive the well-known empirical equation C = , and it is shown that the terprz a is comprised of two terms: a term Cs associated with the surface layer stress and Ci related to internal dislocation obstacles. pointed out that in all of these publications it has been tacitly assumed that plastic flow occurred uniformly throughout the cross section of the specimen (except, of course, for the Luders band region), It has generally been further assumed that the nature and distribution of the obstacles opposing the motion of dislocations are of the same type throughout. The role of the surface layer in bcc metals has not, as yet, been considered even though its role in fcc metals has been shown clearly to be of primary importance.3-5 Investigations on fcc metals have shown that at the onset of plastic deformation a surface layer acts to

Jan 1, 1968

By F G. Cooke

"This paper describes a medium-sized copper mine's results in making innovations and changing operational practices to combat increasing expenditures due to higher labour and supply costs, extended workings, scarcity of experienced manpower and problems created by deteriorating ground conditions.OPEMISKA COPPER MINES (QUEBEC) LIMITED is located at Chapais in the Chibougamau area, in central eastern Quebec, approximately 300 miles north of Montreal and 150 miles north west of Lake St. John. The latter area, developed by lumbering and farming, has supplied the majority of the employees, who, with training and experience and a desire to work and improve themselves, have become the backbone of the Company's 600 personnel.Opemiska began production in 1954 at a rate of 400 tons per day, using diesel power and road transportation. The rate was progressively increased and, by 1959, with hydro-electric power and rail transportation, the mine had reached its present production rate of 2,000 tons per day. It has produced concentrates containing over 430 million lbs of copper."

Jan 1, 1968

By G. S. Crawford

Forecasts prepared by the B.C. Research Council for the National Harbours Board suggest that mineral shipments through B.C. Lower Mainland port facilities will increase more than four-fold, from 6 to about 25 million tons, during the decade 1965 to 1975. The longer term outlook is for a six-fold increase to about 35 million tons by 1985. In 1967, minerais accounted for more than one-third of the total deep-sea traffic tonnage, nearly as much as grain. By 1975, the minerals' share will be about half the total. The principal items are exports of potash from Saskatchewan, and of coal and sulphur from Alberta and British Columbia. Additional exports include copper and other mineral concentrates and propane. Imports are chiefly salt and phosphate rock. Coastal traffic in such items as cement, sand and grave!, and limestone totalled 3.3 mil-lion tons in 1967. They will continue to be of major importance, but do not have the spectacular growth potential of the deep-sea traffic.

Jan 1, 1968

By A. W. Henderson

Methods for converting WOCl4 to WCle were investigated in small-scale, laboratory apparatus to devise a method for preparing pure WCls suitable for conversion to tungsten metal. Chlorine, COCI2, and CCI4, alone and in combination with various forms of carbon, were tested as chlorinating agents at various temperatures. More than 95 percent conversion of WOCl4 to WCls was achieved with all reagents at 8000 C in the presence of activated carbon. Only CCl4 maintained its effectiveness in the absence of carbon at 800° C. The effectiveness of carbon was found to be related directly to its surface area.

Jan 1, 1968

By Herbert K. Kutter

This paper is concerned with the physical phenomena in the fracture process of presplitting and only indirectly with the establishment of the optimum presplitting parameters. Its nature is therefore qualitative, rather than quantitative. Before examining the problem of presplitting, it is first necessary to study the phenomena which occur when an explosive charge is detonated in a borehole. To do this it is desirable to consider the action of the explosion wave separately from that of the expanding gases.l In the theoretical analysis such a separation poses no problems. Experimentally this was accomplished by use of an underwater-spark discharge to generate the stress wave and by pressurized oil to simulate the pressure of the explosion products. The main role of the wave is to generate a densely radially fractured zone around the borehole. The subsequent gas pressure, exerted against the walls of a highly (radially) fractured cavity, generates a quasi-static stress field (henceforth referred to as static stress field). This stress field was found to be the same as that of a pressurized cylindrical "equivalent cavity" with a radius equal to that of the crack tips. Under these conditions the quasi-static stresses become appreciable and cause further extension of the radial cracks. It was further found that, under gas pressure, the longest of the radial cracks would extend first, and extension of two diametrically opposed radial cracks requires the least pressure. From these observations concerning the single shot the transition to a whole series of more or less simultaneous shots, as in presplitting, can readily be made. In the case of multiple shots, as in presplitting, exactly the same effects occur, but at numerous locations and sufficiently close in time that they interfere with

Jan 1, 1968

By R. B. Gavert, David J. Mack

ROOM- and elevated-temperature compression tests were made on the binary 3/2 electron compounds AuZn, CuAu, AgZn, AgMg, AuCd, and NiA1. These compounds possess either the B2 CsC1-type ordered structure or the A2 bee disordered structure represented commonly as ß and ß on equilibrium phase diagrams. In testing at room temperature, cylindrical specimens 0.508 cm by 0.330 cm diam were seated directly on an instron compression load cell (CF 0 to 10,000 lb). At elevated temperatures, testing included a special apparatus with a furnace heat source and a protective atmosphere.&apos; The specimens were strained at a rate of 1 pet per min. The compounds were prepared from 99.99 pet or better high-purity elements. Vacuum and/or argon cover gas was used throughout the mixing, melting, and specimen drawing processes. The generally equi-axed specimen grains varied in size from 0.5 to 1.5 mm for the five different compounds. The stress-strain curves in compression showed

Jan 1, 1968

By W. M. Gray

The determination of the state of stress existing at a point in any solid body requires the determination of the six components of the stress tensor relative to a convenient set of axes. One general method of doing this in rock is to make strain or deformation measurements associated with local relief of stress in a number of boreholes penetrating a limited volume in the vicinity of the point at which the stress is to be determined. The stress is assumed to be constant throughout this volume. Leeman1 has described a number of the instruments that have been developed for making deformation or strain measurements in boreholes. Panek2 has described the application of statistical methods to the determination of the average components of ground stress from sets of measurements made in boreholes by means of deformation meters of the type developed by the U.S. Bureau of Mines. In this paper attention is given initially to the strain cell developed for use on the flattened ends of boreholes by the Council for Scientific and Industrial Research (CSIR) , South Africa. The equations required for evaluating the average components of ground stress from measurements made by means of the CSIR strain cell are derived. These equations are similar in form to those applying to measurements made by the borehole deformation meter developed by the U.S. Bureau of Mines. The results of an investigation of the properties of the equations are described. These results are important in the practical use of both the instruments mentioned above and any instrument based on similar principles.

Jan 1, 1968

By William R. Barton

The domestic portland cement industry consumes more than 12 million tons annually of raw materials chemically similar to fly ash. How these materials are used and how fly ash can serve in their place are discussed. Factors influencing whether or not a particular plant will use fly ash in place of an alternate material are discussed.

Jan 1, 1968

The Bega granite at Whipstick, N.S.W., consists of a granite metasomatically altered to leucogranites and a spessartite-granite. The ore occurs in pipes controlled by jointing and shows evidence of post-depositional tectonic forces.The principal ore minerals are molybdenite and bismuthinite, with minor amounts of uraninite, pyrite, gold, bismuth, joseite A, joseite B, tetradymite, chalcopyrite, arsenopyrite, and skutterudite. The gangue minerals are microcline, albite, quartz, muscovite, and spessartite, with fluorite, chlorite, magnetite, and biotite as accessory minerals.The intrusion of granite was followed initially by ascending metasomatic fluids which penetrated along joints to be trapped in the domed roof of the intrusion to form the leucocratic granite. Iron-manganese-rich fluids metasomatically altered the granite to a spessartitegranite which is associated with the later deposited ore.Quartz veins and dykes of varying composition post date the ore deposition.

Jan 1, 1968

By D. E. Wolfson, H. J. Gluskoter, M. R. Geer, John A. Harrison, H. F. Yancey, I. S. Latimer

When this chapter was prepared for the kst edition in 1942, continuous mining machines virtually were unknown, and hand loading in underground mines, which gave an opportunity to discard impurities, accounted for 55 percent of the production of bituminous coal and lignite as compared with the 1965 figure of 11 percent. Only 24 percent of the total production was cleaned mechanically, compared with the present (1965) figure of 65 percent. The amount of refuse discarded during preparation for the same period increased from 13 to 21 percent. Changes in the equipment used in the cleaning process were as follows: [ ] Unclassified nearly 8 percent. Data on the amount cleaned by flotation was not collected until 1960 when 1.8 million net tons was so treated. In 1965 this figure increased to 6.9 million tons. Although the great increase in mechanization and full seam mining has resulted in substantial increases in the impurity content of the raw coal as well as in a finer size consist, some phases of face preparation are still important, particularly the variability of the distribution and thickness of the interbedded impurities and the changes in the character of the roof and floor from place to place in the mine. Knowledge of these factors in relation to all phases of the mining operation, particularly selective mining, are still of importance to the treatment of raw coal in the preparation plant. The major characteristics of coal and impurities from the standpoint of mechanical cleaning are particle size composition, generally called size consist, density differences, the relative friability of the coal and of its associated impurities, hardness, and strength. Some of the other factors related to preparation are petrographic composition and rank. COAL PROPERTIES Rank Perhaps 95 percent or more of the coal cleaned mechanically is of bituminous rank. Only a very small tonnage is subbituminous and prac-

Jan 1, 1968

By V. Koump, R. H. Tien, W. J. Kim

This paper presents an approximate solution of the problem of freezing of a binary alloy. he alloy is in the form of a one-dimensional slab of finite thickness. The surface temperature of the slab is assumed to be constant and lower than the solidus (or eutectic) temperature. The densities of the liquid and the solid are assumed to be equal. For a given binary alloy system, initial concentration of solute and surface temperature, the solution yields a) the temperature distribution in the solid skin, b) the temperature, concentration, and solid fraction distribution within the solid-liquid region, and c) the positions of the liquidus and the solidus (or eutectic) fronts as a function of time. The results of calculation for Fe-C and Fe-P systems are presented. In this investigation we are considering the problem of solidification of a binary alloy. The alloy is in the form of a one-dimensional slab of finite thickness. The molten alloy is initially at liquidus temperature. At time zero the surface of the slab is reduced to a temperature T, < Te,, where Te, is the solidus (or eutectic) temperature and T, is a constant. The densities of solid and liquid alloys are assumed to be equal and independent of temperature and composition. A qualitative picture of solidification of an alloy, under these conditions, is illustrated in Fig. 1. During the initial stage of solidification, before liquidus front reaches the center of the slab, freezing proceeds by propagation of two isothermal fronts, the liquidus front and the solidus (or eutectic) front. The fraction of solid at the liquidus front is zero; the fraction of solid at the solidus front is unity, The solid fraction and the temperature distribution between the two fronts and the width of the solid-liquid region change with time. During the later stage of freezing, after the liquidus front reaches the center of the slab, the liquidus front disappears. The solid fraction and the temperature at the center of the slab, as well as throughout the solid-liquid region, are now changing with time. The solidification is completed when the fraction of solid at the center of the slab reaches unity. In solution of this problem we seek to determine a) the temperature distribution in the solid, b) temperature, concentration,

Jan 1, 1968