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By Roy T. Southin*

The finding of Wojciechowski and Chalmers that columnar crystal growth can be stopped by an already existing network of equiaxed crystals is supported by other recently reported work on both static and mechanically stirred ingots.27,28 Support for the dendrite arm fragmentation mechanism, too, can be obtained by comparing the effects of spinning on ingots cast in a material which has a dendritic solid/liquid interface during solidification with one which has a cellular interface, since no evidence of change at the interface, other than a change in growth direction, can be found in the cellular material. But there are alternative ways of producing an equiaxed zone in materials which characteristically solidify with a cellular interface. For example, interrupted spinning of a normally cast ingot can do it. In this case it has been shown28 that the equiaxed zone is caused by the showing of dendritic particles from the top surface of the ingot to nucleate a network of equiaxed crystals which forms a barrier to the continued growth of the columnar grains. This showering has also been shown to be a major effect in materials solidifying with dendritic interfaces. It has also been proposed28,29 that, for an equiaxed zone to form, not only must nuclei be present ahead of the interface but also these nuclei must grow to sufficient size to be a barrier to the further growth of the columnar grains. A further requirement is that a network of these grains continually be produced ahead of the growing interface; otherwise there is a reversion to columnar growth as found by Wojciechowski and Chalmers. In normally cast ingots it is possible for nuclei ahead of the interface to grow since during a large portion of the solidification time there is no temperature gradient ahead of the interface,30 and, in fact, the liquid may be slightly undercooled.29 This then is the major difference between the work under discussion and normal industrial solidification conditions, since Wojciechowski and Chalmers imposed a considerable temperature gradient in the liquid. The statement in the Wojcieshowski and Chalmers paper that one needs to lower the temperature gradient

Jan 1, 1969

By T. O. Massalski, J. D. Ayers

A massive transformation, 0 —am, takes place in a number of copper-based systems where the ß phase field at high temperatures extends to compositions that are slightly less solute-rich than the limits of the a phase field that exists at lower temperatures. Consequently a solid-state transformation becomes possible that does not involve a change of composition. Within this narrow range of composition the massive am phase can be usually produced in two ways: by a fast quench from the ß phase through the a phase field, or by pulse heating into the a phase field of an undecomposed ß phase retained at room temperature by a prior quench. In the Cu-Ga system the occurrence of a massive am phase has been also observed in alloys whose composition falls outside the equilibrium a phase field1 but not in the Cu-Zn system.2 We have recently observed the occurrence of the ß — am transformation also in two silver-based systems, Ag-Zn and Ag-Cd. The a and 0 phase fields in these systems again slightly "overlap" in a narrow composition range. In the Ag-Zn system this range falls between 36.7 and 40.2 at. pct Zn, and in the Ag-Cd system between approximately 41 and 42.5 at. pct Cd. Alloys were prepared from high-purity materials and cast in quartz tubes under inert atmosphere. No significant change of composition occurred during casting. After homogenizing in the 0 phase field, small pieces of each alloy were reheated at the homogenizing temperatures for a few minutes and quenched into various media. There were examined metallographic-ally after removal of surface layers that may have suffered from contamination or from the loss of the solute element. In the Ag-Zn system extensive areas of the am phase (identified by selective etching, observation of the slip trace variants, and occurrence of twinning) were observed in a comparatively low-zinc alloy (37.8 at. pct Zn) for all quenching media employed: iced

Jan 1, 1969

By George A. Moore

A recent survey of existing analytical results, and an attempt to correlate them with each other and with the known history and behavior of the samples, indicated that none of the commonly applied methods could be considered established as intrinsically reliable. It was. therefore, desired to attempt to establish the reliahility of some one method by external evidence. If this were to be accomplished, other methods could then be evaluated in terms of the method establibhed. The correct method was accordingly to be chosen without regard for cost, speed, or convenience; with the requirements for routine application to be reserved for 1ater consideration. The method of total combustion was chosen and submitted to a limited number of tests against primary standard samples. Considerable experimental difficulty was encountered, indicating that additional work on the experimental arrangements is desirable. While the work to (late by no means represents a completed investigation, it is helieved that the combustion method is basically sound and that its development should be continued. Choice of Method Of the several available methods, mechanical disintegration. electrochemical methods'2'3 modifications of the Sieverts experiment,% and vacuum fusion, were all judged to contain one or more factors of un- certainty not at present completely cvaluated or suhject to complete control. These methods, therefore, were considered currently unsuitable for referee purposes. Solid evolution was considered to be of doubtful significance when conducted in the alpha range. A reasonable chance for a true analysis was found for evolution in the gamma range. Preliminary tests have indicated a very slow rate for evolutioll from gamma iron. indicating a running time of possibly 100 hr. for a one-centimeter sample. Difliculty in distinguishing such slow. evolution from blank gas was anticipated, hence the method was not consitlerctl the most suitable for the present purpose. The combustion method was evaluated as being most sound on fundamental principles. The only important unknown would be to determine that the iron oxide formed did not occlude water at the tcmperaturv of the combustion.with the odvious precautions of using a sound and clean specimen, providing a system sufficiently tight to give acceptable blanks in longtime runs, and providing a suficicntly sensitive measuring system, reasonable, precise, and truthful analytical results could be logically expected. Apparatus The equipment as originally operated is shown in Fig. I, and the glassw-are in its latest modification in Fig. 2. The sulphuric acid drier and small safety tube in the upper right of Fig. I were replaced by a KOH drier and combined manometer safety tube, to permit operation at reduced

Jan 1, 1945

By J. W. Cunningham, M. J. Stultzman

THE demand for improved materials for high-temperature service has increased during the last few years. Iron,- nickel,- and cobalt-base alloys have been investigated extensively and many alloys with outs'tanding high-temperature strength have been developed. Considerable research has been directed toward improved methods of processing these alloys. The vacuum furnace as a tool for the purification and improved control of high-temperature alloys has been studied extensively and production units are in operation. The research covered by this paper studied the effects of casting in air, vacuum, or argon upon the elevated-temperature properties of two nickel- and two cobalt-base alloys. The alloys investigated were Stellite 31, He 1049, Udimet 500, and Guy Alloy. MELTING AND CASTING PROCEDURES Two heats of each of the four alloys under investigation were melted and investment cast under the following conditions: 1) Stellite 31 was melted and investment cast in air and in vacuum, with an argon atmosphere for pouring. 2) He 1049 was melted and investment cast in air and in vacuum, with an argon atmosphere for pouring. 3) Udimet 500 was melted and investment cast in vacuum with and without additions of zirconium and boron. 4) Guy Alloy was melted and investment cast in vacuum and in argon. The heats were all melted in induction furnaces equipped with preformed magnesia crucibles of 50-lb capacity. The air-melting furnace was powered by a spark-gap converter of 40 kw capacity. The vacuum-melting furnace was powered by a motor-generator set of 100 kw capacity. The argon heat of Guy alloy was melted in the vacuum melting furnace under an argon atmosphere. Virgin materials were used for preparing all heats except the air heats of Stellite 31 and He 1049. The charge for the air heat of Stellite 31 was a commercial blend of shot. The charge for the air heat of He 1049 was Stellite 6 shot plus those virgin materials necessary to give the desired composition. All of the materials used were of the same grade used com-

Jan 1, 1960

By Arch. B. Johnston, Carle R. Hayward

The effect of copper on steel has been studied by numerous investigators. Before modern testing methods had been developed, blacksmiths noted red shortness in iron, the cause for which was ascribed to the presence of copper. Numerous papers have been published on the corrosion of steels containing various amounts of copper, and a few writers have discussed the effect of copper on the mechanical properties of steel. The purpose of the investigation described in the following paper was to obtain additional data on the mechanical properties of medium-carbon steel containing small quantities of copper. Among those who have published results of mechanical tests on copper steels are Ball,' who states that copper increases the tensile strength and hardness but lowers the elongation. Stead2 states that copper steels closely resemble nickel steels containing equivalent percentages of nickel, as regards tensile strength, resistance to shock, corrosion and hardness. Wigham3 found that copper in small amounts had no injurious effect on steel. Breui14 found that with 1 per cent. carbon, copper lessened the brittleness of steel and in low-carbon steel it increased the tensile strength and lowered the ductility slightly. H. H. Campbell5 states that copper up to 0.25 per cent. slightly raises the elastic limit, elongation and reduction of area.

Jan 1, 1918

By K. Huessener

This paper attempts a survey of the principles involved in the combustion of blast-furnace gas in boilers and stoves. I do not expect to be able to give much information which is actually new, since the laws and methods of calculation pertaining to this problem are contained in a number of handbooks; but, so far as I am aware, they have nowhere been treated exclusively with reference to this one problem of gas economy. The road which I follow is less that of strictly scientific research than that of the practical engineer, faced by operation problems which require a quick solution by easily accessible means without a prolonged search in scientific handbooks. For this purpose I give a number of tables and diagrams, as well as the results of many years1 practical working experience as combustion engineer, which I trust will prove useful to my readers. HlSTORICAL Considering the tremendous efforts made during the last 15 years to increase the efficiency of all kinds of power plants, it is highly surprising that until a comparatively very recent period, progress in the economical combustion of blast-furnace gas has been so slow, The explanation generally put forth, that fuel has been so cheap that it was hardly worth while to bother about this economy, will not hold good, for the greatest trouble was taken to improve the combustion of coal and to reduce the consumption of steam, The most plausible explanation appears to be the general impression, held as an accepted fact, that gas, especially hot, uncleaned, blast-furnace gas, was not a good boiler fuel. Many managers of high repute had tried unsuccessfully to improve the conditions of its use, and the dictum went forth that efficiencies of over 60 per cent., particularly with high loads, were impossible. This was the situation not only in the United States, with very cheap fuel, but also in Europe, where fuel prices are twice and three times as high.

Jan 1, 1916

By P. S. Katval

It is interesting to note that an attempt has been made to rationalize the effect of prestrain on the strength of Hastelloy X-280 after various aging treatments. However, two points raised by the authors seem to be somewhat unclear. 1) Concerning their Fig. l(a), the authors state: "Extensive dislocation networks are still in evidence. The 24-hr aging at 1500°F and the 15-min soak at 1350°F did not eliminate the dislocations introduced by the 20 pct cold reduction." This is, of course, to be expected since complete "elimination" of dislocations would require recrystallization which does not occur at 1500°F in Hastelloy X. However, recovery

Jan 1, 1969

By N. F. Neumann, A. W. Schlechten

Metal chlorides were formed by reacting metal oxides and calcium chloride; the effect of additions to the reaction mixture was studied. It was found that by use of proper additions, metal chlorides could be prepared from mixtures that were not reactive under ordinary conditions. ManY recent metallurgical developments involve the use of chlorine or chlorides as primary reagents; good examples are found in the production of ductile zirconium and titanium by reduction of their chlorides with magnesium. Various methods of preparing metal chlorides are used and many others have been proposed. Some chlorides are formed by the direct combination of a metal or alloy with chlorine. Other processes react chlorine and metallic oxides; carbon or other reducing agents are usually employed to reduce the metal oxides and so promote chlorination. Metallic chlorides have also been produced by the exchange of chlorine between metal oxides and a chloride, such as sodium chloride. This type of reaction was the basis for the old process of chloride roasting in which metal ores were roasted in the presence of salt. Soluble chlorides thus formed

Jan 1, 1959

By Persifor Frazer

In his " Final Report," Vol. 11, part second, p. 763, Prof. Rogers sums up the metalliferous veins of the mesozoic sandstone by remarking that these are not associated with dykes or trap-rock, but are independent metalliferous injections. But singularly enough, in enumerating the different kinds of ores, no mention is made of

Adolph Thies, Haile Gold-Mine, S. C.: I have little to add to what my friends Messrs. Nitze and Wilkens have said on this subject. What I have done in mining during the last fortyone years, partly in this country and partly in South Africa (though not, as to Africa, in the diamond- or the gold-fields,

Jan 1, 1896

By John Dodd

This paper reviews advances in the technology of abrasion resistant iron and steels, which could help combat abrasion and wear in mining operations. With the recent progress in high chromium alloy iron development, high temperature heat treatment of massive castings can be eliminated, aloy cost reduced, and cracking problems avoided. Data on erosion-corrosion resistance of these irons; trends in the development of improved cast steels; and factors influencing toughness and abrasion resistance of manganese steels are all considered. The 7% Mn. 1% Mo manganese steels are shown to combine toughness and abrasion resistance, and composite castings are a means of combating abrasion in applications involving severe impact. A brief appraisal is given of recently developed martensitic wrought steels with improved weldability.

Jan 1, 1982

By A. W. Schlechten, R. P. Abendroth

Jan 1, 1960

By S. E. Bretherton

This title introduces the subject I wish to describe to my fellow members, very few of whom, I 'hope, have ever had as much trouble with the smelting of ore containing much zinc, either in the lead blast furnace or the matting furnace, as circumstances have forced upon me: First, for several years in Leadville, Colo., after the sulphide ores containing zinc had been developed with greater depth and were sold to the intereats with which I was connected for smelt-ing in the blast furnace for the recovery of the lead, silver, and gold; then, in New Mexico and Arizona, where the principal source of ore supply for our custom smelter was from miners who sent most of their product in the form of concentrates, which we briquetted and smelted in the blast furnace, producing a matte containing copper, silver, and gold, for which we were paid; together with some zinc and lead, which was penalized if in excess of a maximum base set by the refinery to which we sold our copper matte; last, but not least, my experience in Shasta county, Gal., where for the sake of recovering $13 per ton value in copper, silver, and gold, I have smelted ore containing as high as 40 per cent. zinc (the last 18,951 tons smelted averaged 15 3/10 per cent. zinc) which we not only lost, but which it cost us money to lose. After such an experience, and knowing that, instead of being worth only $13 per ton, such 15 per cent. zinc ore should be worth about $30, including zinc at the present market value, the question of recovering the zinc in a profitable manner from such ore became very interesting to me. During several years' time I sent samples, of from 5 to 1,200 lb. each, to be tested by the different best-known zinc-recovery plants, and experimented with several processes proposed by others for the treatment of such ore, with but little encouragement, until I

Jan 1, 1914

COMMITTEES. Precious and Base Metals. Charles W. Goodale, Chairman.. L. D. Ricketts, Vice-Chairman Darsie C. Bard, Secretary, Montana State School of Mines, Butte, Mont. Leonard S. Austin, Thomas J. Grier, Willet G. Miller, David W. Brunton, Hennen Jennings, Albert F. Schneider, Theodore B. Comstock, Edmund B. Kirby, George C. Stone, Stanley A. Easton, Charles W. Merrill, Benjamin B. Thayer. Samuel S. Fowler,

Jan 11, 1913

By S. K. Tarby, W. O. Philbrook

The rate of FeO and MnO reduction from silicate and aluminate slags by carbon-saturated iron is dependent on both slag composition and temperature. Owing to variable stirring rules during- the course of reaction, the reduction processes occur in two stages in stationary graphite crucibles. In the first stage the slirring caused by CO evolution results in forced convection conditions in the slag. As the boiling action subsides during reduction, the flow conditions within the system become those defined by natural convection. Analysis of the data by an unsteady-state penetration model indicates that the rate of reduction is controlled by the rate of cocur-rent flow of' cations and anions from the bulk slag to the interface during both stages of reduction. The hearth reactions of the blast furnace have been extensively investigated from the viewpoint of equilibrium by deductions from controlled laboratory experiments. However, the literature contains relatively few studies that have been directed toward the area of slag-metal reaction kinetics, and the majority of these have been concerned with the rate and mechanism of sulfur transfer between iron and slag. More recently, attention has turned to the kinetic factors in the reduction of oxides from liquid slags. One of the first investigations in this field was conducted by Dancy1 on the reduction of pure liquid FeO and pure liquid Fe3O4 by carbon-saturated iron. The integrated form of the rate equation indicated that the reduction of FeO was of the first order up to 80 pct reduction. Over the initial 30 pct of reduction, the magnetite reaction was also interpreted as a first-order process. The rates of reaction were extremely rapid as indicated by a 30 pct reduction of the liquid magnetite in a time interval of about 1 to 2 sec. Phil-brook and irkbbride' studied the reduction of FeO from a lime-alumina-silica slag by carbon-saturated iron and solid graphite in stationary crucible assemblies. With the use of the differential form of the rate equation, the rate of the reduction reaction was found to be proportional to the second power of the concentration of the reactant FeO for both the slag-metal and slag-graphite reactions. These authors presented a number of comments in an effort to explain the difference between the molecularity of the above reaction and the observed second-order relation. One such argument, recently extended by Wagner,3 was that the rate-limiting step may well be one of transport control. A complete discussion of the proposed mass-transport control mechanism of this reduction reaction will be presented in a later section of this paper. Kinetic studies of the reduction of other oxide species, namely chromous oxide, titania, and silica, have also been reported. McCoy and philbrook4 used rotating crucible assemblies to investigate chromium reduction from Ca0-SiO2-A12O3 slags. First-order kinetic law was obeyed for the slag-metal reduction reaction as determined by the integration method of data analysis. Due to scatter of the data, any dependence of the rate constant on temperature or slag composition was obscured. Concentration-time data for the reduction of titania from blast-furnace type slags under reducing conditions were obtained by Delve, Meyer, and Lander.' The data were too few, however, for a formal kinetic interpretation. Kinetic data for the very slow reaction of silica reduction have been observed by McCoy and Philbrook6 and Fulton and chipman.7 The former experimenters found the reaction-rate constant for silica reduction by carbon-saturated iron to be 20 to 60 times less than the rate constant for chromium reduction. In their work on the reduction of SiO2 in mechanically stirred systems, Fulton and Chipman also found small values for the specific reaction rate and derived a high value for the energy of activation for the reaction. In both of these investigations, the reduction process was assumed to follow first-order behavior. schuhmann8 proposed that the rate-limiting step in this reaction is the diffusion of oxygen from the interface through a boundary-layer film to the bulk metal phase, and Rawling and Elliott9 have reported experimental confirmation of this hypothesis for temperatures below 1600°C. Turkdogan et a1.10 have also concluded that the rate of reduction of silica is a slow process and controlled by the diffusion of oxygen in the metal, but only in the absence of carbon monoxide bubbles at the slag-metal interface. In the presence of bubbles, achieved either by injecting carbon monoxide at the slag-metal interface or by blowing it through the metal and slag, these investigators found a rather rapid reduction of silica which appeared to be controlled by an interfacial reaction involving the de-sorption of silicate ions from the slag-metal interface to the metal phase as silicon and oxygen atoms. In view of the unresolved nature of the kinetics of FeO reduction and the lack of kinetic data for the manganese reaction,

Jan 1, 1968

By T. C. Poulter, B. M. Caldwell, D. E. Brink

The flash X-ray has been used more than a decade to study the configuration of the jet from a shaped charge. The high-speed, rotating-mirror smear camera has provided time-distance graphs of detonations and shock fronts in transparent materials, and the high-speed framing camera has given pictorial representations of the progress of explosive phenomena. Adequate means for measuring the paths and velocities of all parts of the shaped-charge cavity Iiner during the collapse phase have not existed heretofore. A technique enabling the single-lens framing camera to make stereoscopic photographs of the cavity liner while it is collapsing has been developed. Analysis of this photographic record gives the directions and velocities of various parts of the Iiner surface, permitting direct quantitative measurement where this has previously been impossible. Significant improvements in shnped-clrarge design are expected to result. INTRODUCTION The familiar oilwell jet perforating charge, generally referred to as a "shaped charge", is related to the Mun-roe charge first described by C. E. Munroe in 1888 and later by Neumann in 1910. It differs in construction from the Munroe charge in that its cavity is lined with some inert material (usually metal)', and it differs in performance by projecting a fast jet of dense liner material against the target instead of a stream of expanding detonation products. Fig. 1 represents a typical shaped charge in axial cross section. The charge is circularly symmetrical about its longitudinal axis. The cavity at the right is lined with metal, usually copper; and, with the exception of air, the liner is otherwise completely empty. High-explosive material is intimately in contact with the convex surface of the liner and extends in the other direction to the booster. This is a pellet of high explosive having somewhat different characteristics and serves to couple the detonator to the main charge. When the detonator is fired, a small hemispherical reaction zone of very high temperature and pressure occurs at its output end. The booster responds, adding its own latent energy to the reaction, thereby initiating the main charge. The reaction progresses throughout the main charge at a velocity of 7 to 8 mm/microsecond until all the explosive material has reacted. With a reaction pressure of about 160,000 atm, the surrounding material is moved rapidly away from the high-pressure zone. As the detonation proceeds along the cavity liner, moving from apex to edge, the liner is collapsed toward the axis of the cavity, where liner material from all parts of the concave surface converges. A zone of extraordinarily high pressure results. with only one escape path—outward along the axis. The particles from the liner, thus, become a jet of very high velocity, with a density characteristic of the material from which the liner was made. The kinetic energy of the jet, concentrated in a small area of the target, has great penetrating power. It overcomes the strength of any target, and the target material crumbles or deforms plastically to escape from the path of the jet. An unlined cavity charge, on the other hand, projects a turbulent body of hot gaseous material against a target and erodes the exposed surface. With equal quantities of explosive, the penetration effectiveness of an unlined charge is a small fraction of that of a lined charge. Given an explosive charge with a detonator at one end and an axially symmetrical metal-lined cavity at the other, one has a perforator of considerable potency. To maximize the penetrating and other desirable effects,

By L. C. Uren, E. J. Bradshaw

This paper presents the results of a group effort by a number of University of California students and faculty members, and the authors attach their names primarily in the capacity of editors and interpreters of the data thus assembled. In addition to the writers, the following individuals have made substantial contributions in time and effort in the conduct of this research: Dr. A. J. Carlson, Associate Professor of Petroleum Engineering; J. E. Gosline, University Research Assistant; C. F. Bedford, G. W. Mikulasek and H. S. Conder, senior and graduate petroleum engineering students; H. Bachman, G. Spencer and G. W. Gard, mechanicians in the Department of Mining and Metallurgy. Acknowledgment is also due the Research Board of the University, the Department of Mining and Metallurgy, and Prof. F. H. Probert, Dean of the College of Mining, for continued cooperation in securing mechanical assistance and funds for the purchase and assembly of apparatus. Significance of the Pressure Gradient The expulsion of petroleum from its reservoir sand doubtless is due to expanding natural gas intimately associated with the oil, to the hydrostatic pressure of encroaching edge waters, and to gravitational influences. These forces may operate independently or collectively. In any case they subject the fluids stored within the reservoir sands to elevated pressures, thus causing movement of oil and gas through the productive formations toward the lower pressure of the well outlets. This movement is opposed by pore friction, capillarity and adhesion: resisting influences brought to bear by the reservoir sand on the moving fluids. The magnitude of the resisting force is influenced directly by the viscosity, surface tension and density of the oil, as well as by the properties of the gas. The more rapid the rate of flow, the greater will be the resistance offered, and the greater will be the energy consumed.

Jan 1, 1932

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By Paul A. Flinn, Jean-Marie Robert Genin

The MCssbauer effect was used to study the distribution of carbon in Fe-C alloys of high carbon content during room-temperature aging. In freshly formed rnartensite the carbon distribution is approximately random; carbon clustering occurs dun&apos;ng aging. In the retained austete the carbon atoms are isolated, suggesting an efiective repulsion; and no rearrangement during room-temperature aging is evident. The kinetics of the carbon clustering in martensite has been studied in detail at 0" . 10". and 20°C. The time and temperature dependence observed is sinzilar to that reported for a variety of other aging effects, such as resistance change, hardness increase, and recovery of internal friction. The stabilization of the martensite kransformation also appears to be related to the clustering effect. DESPITE extensive efforts since the early days of Reaumur, the mechanism which provides the strengthening of steel remains controversial in many cases for several reasons: 1) The structure of as-quenched martensite is not well-determined. 2) Experimental methods capable of distinguishing between various hardening mechanisms are not well-developed. 3) The temperature of formation of many low-alloy martensites is so high that the martensite formed during quenching may be already tempered to some extent before any observation. Among all the hardening phenomena, the most puzzling one occurs at room temperature, where no structural changes have been detected by the usual methods of X-ray diffraction or electron microscopy. However, a new and more sensitive technique became available with the discovery of the MBssbauer effect. This effect makes possible the detection of changes in the local environment of iron atoms in solid solution. It has been extensively used in the study of substitutional alloy systems, for example, Fe-Al,1 Fe-Si,2,3 Fe-Rh,4 and Fe-Ni.5 Making use of the possibility of obtaining new structural information, we undertook an investigation of the aging of high-carbon Fe-C martensite to follow the structural changes involved in the aging at room temperature. Preliminary results6 showed that a clustering of the carbon atoms occurs with time. A systematic study of the kinetics of the process showed a striking similarity to the kinetics of stabilization of the marten-sitic transformation, thus suggesting further investigation of the relationship. EXPERIMENTAL TECHNIQUE To eliminate difficulties with the aging of martensite prior to the first experimental measurements, we needed an alloy with an M, temperature not above room temperature. Other investigators7 were misled by results obtained on alloys which transformed above room temperature and underwent structural changes prior to the first Mossbauer measurements. Winchell and cohen8 dealt with this difficulty by using a third element, nickel, to depress the MS below room temperature. The presence of nickel did not seriously interfere with hardness or resistivity measurements, but it would complicate the interpretation of the Mossbauer data by increasing the variety of iron environments. We chose, therefore, to obtain the necessary lowering of the M, simply by increasing the carbon content. After the first quench to room temperature, our specimens are retained austenite, which we later quench into liquid nitrogen. The martensitic transformation takes place suddenly, so that the as-quenched condition of the samples is retained, since the temperature is low enough to prevent any carbon diffusion. A Massbauer spectrum at 77°K can be taken and analyzed; after an appropriate up-quenching to the aging temperature, a new Mossbauer measurement at 77°K can be made. Fig. 1 shows a typical cycle of experiments. The samples were foils 25 p thick of high-purity

Jan 1, 1969

By C. E. Sims

The carbon-oxygen reaction without doubt is the basic reaction in steelmaking. It is important on several counts: In the first place, carbon is the element that distinguishes steel from iron. It is the principal element controlling properties, and its control is of prime concern. Although the principal objective of the carbon-oxygen reaction is to oxidize excess carbon, the accompanying boil should not be underrated. The mechanical agitation, stirring, and mixing resulting from the boil are so useful in the distribution of heat and in promoting uniformity of composition in the bath that, were it not a natural accompaniment of the carbon-oxygen reaction, it is probable that something would have to be invented to replace it. The open-hearth operation, for example, with the bath heated from above by radiation, would be impracticable without the carbon boil. The electric-arc furnace is somewhat less dependent on it, but every melter knows how much easier it is to gain temperature with minimum damage to refractories during the boil than with a dead bath The motor action of the induced current of the induction furnace makes the carbon boil unnecessary but even there a severe oxidation has been found useful in giving greater freedom from porosity in certain steels. The quantitative aspects of the carbon-oxygen reaction have been given considerable attention by a large number of investigators, and the principles of physical chemistry have played an important part in these studies. Physical chemistry is the science of the mechanics and mathematics of chemical reactions. It is possible to study the mechanisms of reactions in a qualitative manner writhout reference to mathematics and thus obtain valuable concepts as to the manner in which the wheels go around. When it is desired to express quantitative relations in these reactions, however, resort to mathematics is not only convenient but necessary. Mathematics may also be regarded as the shorthand language of physical chemistry. A basic relation whose description requires numerous words may be expressed very simply by a mathematical formula or equation. A good example of this is the equilibrium constant for a chemical reaction. Expressed verbally, it is: When a chemical reaction has reached a condition of equilibrium, the Product of the concentration of the reacting substances on one side of the equation, divided by the product of the concentration of the reacting substances on the other side, gives a quotient that is a constant at constant temperature For the carbon-oxygen reaction C + O ^ CO this is expressed simply as % C X % O -%co where K (from the German Konstant) is the equilibrium constant for the reaction. Although mathematics is such a necessary and useful tool, it is also a potential pitfall. Mathematics in itself is an abstract science, which is not inhibited by consideration of mechanisms or materials.

Jan 1, 1948