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By T. A. Rickard

The notion prevails that writing is a knack, that the skilful use of the pen is a gift of nature. This is an error. Dogberry may be responsible for it; he said: "To be a well-informed man is the gift of fortune, but to write and read comes by nature". Because Dogberry said it, we may be sure that Shakespeare thought otherwise. Ability of any sort may be partly innate, but my own observation and experience lead me to conclude that most of the easy writers have become so by constant practice. As I recall the names of men successful with the pen, I remember that most of them have written a great deal and have taken particular pains to improve their style. The suggestion that proficiency in the difficult art is a happy accident provokes a sardonic smile. The larger part of the great writing in our literature is the result of persistent effort. An easy fluency has been the undoing of many; their flamboyant and fantastic scribbling has proved as perishable as froth. This criticism applies to technical writing also; in order that a technical description or discussion may hold the interest of the reader, at least long enough to cause him to read it to the end, the writing must be done carefully and systematically; otherwise it will fail in its purpose of conveying information. Clearness is absolutely essential. "It is not enough to use language that may be understood; it is necessary to use language that must be understood."* The purpose of writing, at least of that which is meant to be read by others, is not only to express ideas but to communicate them. Lack of perspicuity may prove as %ad as

Jan 1, 1931

C. P. SANDBERG, LONDON, ENG : † I think we should all be grateful to the Pennsylvania Railroad Company, and to their chemist, Dr., Dudley, for spending so much time and money in order to solve an important question ; nor are we less indebted to the public spirit which leads them to impart the experience thus gained. In Europe nothing similar has hitherto been done, either by a company or by any private individual. In England the great railway companies employ their engineers in other ways, and do not keep a chemist or specialist to study rails; but even if they did they would probably not publish the results. The chief professional engineers are so occupied with their private practice of railroad construction generally, that they cannot be expected to devote their time and energies to so special a question. The German Railway Union has, in my opinion, missed the real object of its elaborate researches by falling into the error of specifying costly, impracticable tests for rails-tests at the same time which do not infallibly expose the impurities that may be in the rails under examination. There has, therefore, been nothing done on this side of the Atlantic in the way of exhaustive study to determine the best composition for steel rails. America should consequently have full credit for the enlightened example which she has set. I wish, however, to make a few remarks on Dr. Dudley's second paper, a paper which follows very much upon the same lines of argument as the first read three years ago, upon which I have previously touched in my paper on the same subject read at the meeting in August last. If Dr. Dudley had discovered a new metal he could hardly, I think, have taken more pains to prove that he was correct in his first formula for the best chemical composition of steel rails. But I have seen so much done in the way of proof by experiment that I am inclined to think that almost anything can be proved by experiments and by samples. If Dr. Dudley would only give up his formula, which would not suit any country-not even America- * For the convenience of members it has bees thought best to insert the continuation of this discussion at the Virginia meeting in tide place, rather than to delay its permanent publication until the issue of Volume X, Transactions, where it would properly belong. T. M. D., Sec'y, † Sent to the secretary in manuscript.

Jan 1, 1881

Jan 1, 1938

Jan 1, 1938

By William Hurst

THE content of this paper is a presentation of the diffusivity theory for the calculation of the water drive on an oil reservoir in which b the history of reservoir pressure with time are the essential parameters for the determination of the rate and cumulative water encroachment into a field. The paper is divided into two parts-the main portion and appendix. The main body is essentially the application of the principles underlined here to actual field data. It consists of the work plots of the radial-flow case, and includes a discussion of an illustrated problem for which the water-drive calculations are treated in conjunction with the volumetric-balance equation. The appendix is a mathematical treatment of the linear, radial, and spherical cases of water influx into a reservoir.

Jan 1, 1942

ALABAMA. Aldrich, Aldrich, W. F. Anniston, Noble, A. E Bessemer, Abbott, C. E., Fer¬gusson, V. Birmingham, Aldrich, T. H., Jr., Bowron, C. E., Bowron, J., Collord, G. L, Crockard, F. H., Davis, F. H, Dimmick, F. D., Hillman, Ludwig, C. P., McCarthy, M. E., McCormack, G B., McCrery, Ramsay, E., Shook, A. M. Car¬bon Hill, Pill, J. R. Coal City, Lydecker, I. S. Gannts Quarry, Hiller, E. Helena, Squire, J. Holt, Shook, J. \V. Huntsmlle, Moss. Lehigh, Toulmin. Oxmoor, Green¬amyer, A. G. Rock Run, Garvin, J. M. Sheffield, Miller, D. I. Woodward, Lodge, J., Woodward, A. H. ALASKA. Ellannar, Stevens, B. Fairbanks, Hamilton, A. L, Robe, L S. Hadley, John¬son, P. Jualin, Hoggatt, W. B. Juneau, Denby, Thane, B. L., Whipple, J. R. Katalla, Hampton, W. H. Ketchihan, Barber, J. C., Geiger, A. \V., Parker, J. L. Niblack, Finck, W. N., Niedling, B. B. Nome, Garfield, C. D. Tin Oity, Fay, A. H. Treadwell City, Kinzie, Stow, H. P. Valdez, Esterly, G. M., Hazelet.

Jan 1, 1910

By J. R. Long, T. R. Graham, R. S. Dean

FOLLOWING the development of elec¬trolytic manganese production by the Bureau of Mines, an extensive program was planned to study the character of this high-purity product and its possible utilization in various alloy combinations. Previous work reported in the literature concerning alloys containing substantial amounts of manganese dealt largely with material prepared from relatively impure grades of the metal, and in many instances the impurities thus introduced did not permit true evaluation of manganese as an alloying element. One phase of the Bureau's program included a general review of the system and the establishment of the physical properties of copper-manganese-zinc alloys, using electrolytic manganese, and with particular emphasis directed to com¬positions within the alpha solid solution area. A number of reports of the work on alloys in this system, giving specific data concerning the equilibrium system and some of its alloys, have already been published. One study1 established the alpha solid solution area at various temperature levels and composition ranges up to 50 pct manganese. Other investigation reports presented the properties of selected alloys; namely, a 65 pct copper, 10 pct manganese, 25 pct zinc alloys' a sensibly white manganese brass composed of 70 pct copper, 20 pct manganese, 10 pct zinc,3 and a series of alloys with a constant copper content of 60 pct and 5 to 25 pct manganese, balance zinc.4 In these reports tensile properties as influenced by cold-working and subsequent annealing were given in detail. Additional data are now available on other alloys of the alpha region up to 50 pct manganese, and these, together with previously published information, are sufficiently complete to establish the relationship between properties and composition for this portion of the ternary system. The present report is a summary of the tensile properties of wrought alloys in the form of sheet and rod stock. The summary is necessarily limited to data for only one condition of cold-work and a single annealing temperature, since a complete exposition of all the data available would be too extensive for this presentation. Nevertheless, it is possible to make a reasonable approximation of the tensile properties in other conditions of cold-working and annealing by a correlation of the data previously presented on specific alloys and the data given here.

Jan 1, 1947

By R. J. Murphy, N. J. Grant, J. W. Dowding

A large number of blast furnace slag-metal tests were examined to determine if the manganese reduction could be used as a primary indicator of the degree of oxidation or reduction of the slag and of its desulphurizing power. Slag basicity and temperature were also evaluated. Two laboratory heats were made and sampled prior to reaching equilibrium to check blast furnace data. IN a recent investigation of the factors affecting desulphurization in the blast furnace, is was evident that manganese reduction appeared to parallel the course of desulphurization. Grant, Kalling, and Chipman1 pointed this out in a series of time studies utilizing closely controlled laboratory melts. Fig. 1 is a composite plot of sulphur removal and manganese reduction as a function of time under two slags of different basicity. Manganese reduction appears to approach equilibrium at approximately the same rate as does sulphur. It was also demonstrated that the addition of oxygen to the slag, as manganese oxide, caused a sharp reversal of sulphur from the slag to the metal.' It has been shown that "Excess CaO" was a primary factor in measuring the degree of desulphurization under ideal reducing conditions,1,2 the following reaction being representative of the process: CaO (slag) + S + C (solid) = CaS(slag) + CO (gas) It was also evident that a second reaction could drive the sulphur from the slag into the metal. A suggested reaction was' CaS (slag) + 0 = CaO (slag) + S Any change in the oxidizing power of the system would thus affect both the sulphur and the manganese without causing any change in the calculated basicity of the slag. "Excess CaO," "Excess Base," and other similar basicity values, under such oxidizing conditions, would therefore not be the best measure of desulphurizing power; instead, as was shown by and Chipman" he oxygen content of the slag at low oxygen levels would be the controlling factor. Unfortunately, the extent to which FeO is reduced in the blast furnace makes it difficult to utilize slag FeO as an accurate indicator of the degree of oxidation. By comparison, manganese reduction in the blast furnace proceeds more slowly and is generally only about 40 to 70 pct complete. manganese, which is present in significant amounts and is readily analyzed, offers an opportun-

Jan 1, 1954

By Jan M. Mutmansky, Gordon H. Walrod, Y. J. Wang

The selection of a shaft size for ventilation purposes is a classic problem of concern to mining engineers. This presentation is concerned with the sizing of conventionally-sunk circular shafts with concrete or shotcrete linings. Costs of sinking shafts of three different depths, from 150 m to 300 m (500 ft to l000ft), and six different diameters, from 4.27 m to 7.32 m (14 ft to 24 ft), were obtained through questionnaires to shaft contractors. The primary objective of the economic model presented is the balancing of detailed annual capital and operating costs to achieve the minimum overall cost of the shaft installation over its life. The economic model is similar to previous analyses but treats several of the individual cost categories in an updated fashion. Included in the paper is a detailed analysis of the effects of varying power costs on optimal shaft size. Also included are a statistical analysis of current shaft costs and comments on the choice between shotcrete and concrete linings.

Jan 1, 1980

Jan 1, 1969

By G. H. Walrod, J. M. Mutmansky, Y. J. Wang

The selection of a shaft size for ventilation purposes is a classic problem of concern to mining engineers. This presentation is concerned with the sizing of conventionally-sunk circular shafts with concrete or shotcrete linings. Costs of sinking shafts of three different depths, from 150 m to 300 m (500 ft to 1000 ft), and six different diameters, from 4.27 m to 7.32 m (14 ft to 24 ft), were obtained through questionnaires to shaft contractors. The primary objective of the economic model presented is the balancing of detailed annual capital and operating costs to achieve the minimum overall cost of the shaft installation over its life. The economic model is similar to previous analyses but treats several of the individual cost categories in an updated fashion. Included in the paper is a detailed analysis of the effects of varying power costs on optimal shaft size. Also included are a statistical analysis of current shaft costs and comments on the choice between shotcrete and concrete linings.

Jan 1, 1979

By J. C. Kerkering, P. M. Daling

This paper discusses a study performed to evaluate the feasibility of transferring formal system safety assessment technology to the mining industry. A representative listing of formal techniques was evaluated to select the most useful methods for the mining industry to implement. Criteria for selecting methods included the interests, needs, and requirements of mine safety officials. This paper describes one of the selected methods, preliminary hazards analysis (PHA), and illustrates the analysis procedure for a mining example. This study also includes an assessment of the adaptability of selected methods to a user-interactive computer system for use by mine safety personnel. This paper includes a description of a conceptual computerized PHA-type safety program that facilitates performance of the safety analysis and can accommodate updates and revisions as necessary.

Jan 1, 1983

By William R. Webster

I have continued the investigation of the Pottstown Iron Com pany's basic Bessemer keel plates on the line referred to in my paper of last October (Trans., xxi., 766)) and have added a study of the hardening effects of sulphur, which were not taken into account at that time. The results are so encouraging that I now give them in full. For some months we have graded all the steel at these works by the table given in my former paper, and checked the grading by the forging-tests as described in the paper of Mr. Joseph Hartshorne, read at the same meeting (Trans., xxi., 748). The steel thus graded was bloomed for the plate orders. Then one slab was rolled into a plate for the order, and a tension-test was made of this plate. By the result of this tension-test we were guided in rolling the balance of the heat. Out of several hundred heats graded in this manner, 95 per cent. met the requirements of the orders in every respect, and were accepted; but these results will no doubt be improved upon, when the influence of sulphur is also considered.. The hardening effect of sulphur seems to be about 500 pounds per each .01 per cent. of increase. In the table accompanying the pres ent paper, the ultimate strength with .06.5 per cent. sulphur agrees with the old table where sulphur was not considered; that is, for all steels with less than .065 per cent. sulphur we now get lower re sults, and for those with more sulphur, higher results. Making this allowance for sulphur, the assumed ultimate strength of a 3/8-inch plate of pure iron is reduced from 38,000 pounds per square inch to 34,750 pounds. With this as a basis, I have constructed my new table, giving each of the elements, carbon, phosphorus and manganese the same hardening effect as before, to wit : Carbon is credited with a constant effect of 800 pounds per each, 0.01 per cent. Phosphorus shows greater effect in high-carbon than in low-carbon steels. For 0.07 and 0.08 C, it has about the same effect as carbon, that is, 800 pounds for each .01 P. This increases to 1500 pounds per .01 P in 0.15 C steel, or nearly twice the effect of carbon. This

Jan 1, 1894

By H. A. Baumann

Experimental data are presented showing the influence of size consist and firing rate upon the performance of bituminous coal-fired, single-retort, industrial underfeed stokers. Size segregation, degradation, and distributor data are also included. The conclusion is reached that size consist of the fuel as fired, is a critical factor in its performance on this class of equipment.

Jan 1, 1950

By H. L. Gilbert, W. W. Stephens

Production of anhydrous zirconium tetrachloride by direct chlor- ination of a zirconium oxide carbon mixture in a silica-brick-lined chlorinator is described. Theory and thermodynamics of reactions are discussed. A pilot-model chlorinator and full-scale production equipment are described and operating data are included. ANHYDROUS zirconium tetrachloride required as a starting material in the Kroll process for production of ductile zirconium has been produced in this country principally by chlorination of the carbide or "carbonitride" made by reduction of zircon sand concentrates with carbon in the arc furnace. This process and the equipment used have been fully described.'.' It is well known that zircon or badde-leyite ores may be chlorinated directly with chlorine in the presence of carbon, and this one-step approach would seem at first glance to be preferable to the two steps involved in the carbide-chloride operation. As previously discussed1 considerations leading to adoption of the longer process were: 1—Chlorination of the carbide proceeds rapidly at temperatures below 500°C, whereas temperatures above 900°C were considered necessary for chlorination of zircon-carbon mixtures. 2—The highly exothermic nature of the carbide-chlorine reaction makes it self-sustaining, while heat must be supplied continuously in direct chlorination of the ore. 3—Silicon was thought to be chlorinated along with zirconium in the direct chlorination of zircon, leading to high chlorine consumption. In production of carbide in the arc furnace, silicon is driven off as silicon monoxide and does not enter the chlorinator. 4—For efficient direct chlorination, the ore must be finely ground and intimately mixed with carbon, and the mixture briquetted. 5—Direct chlorination requires a much larger chlorinator for a given production capacity than chlorination of carbide. Recently it has become necessary to produce large quantities of zirconium metal from a chemically purified zirconium oxide. Since the cost of the latter is high, the relatively high losses encountered in production of carbide in the arc furnace could not be tolerated, and a graphite resistor furnace5 was developed for production of carbide, which was then chlorinated in equipment previously used for chlorinating arc-furnace carbide. This method of operation was quite satisfactory, and losses in the carbid-ing step were minimized. However, operating costs were relatively high, and the process did not lend itself particularly well to large-scale operation because of the multiplicity of small units required and the hand labor needed to load, unload, and maintain the furnaces. To chlorinate the carbide, a vertical-shaft chlorinator was used in which the charge was heated with a central split graphite-rod resistor.' Operation of this chlorinator was somewhat less satisfactory with the resistor furnace carbide than it had been with the arc-furnace carbide due, principally, to the differences in physical properties of the carbide. The arc-furnace carbide is obtained as a fused metallic-appearing mass which can be crushed to -1/4 in. with production of a minimum of fines, whereas the resistor-furnace product is lightly sintered and produces a large proportion of fines in crushing and handling. These fines tend to pack in the chlorinator and promote channeling. which results in poor chlorine efficiency and low capacity. Data based on production of 22,000 lb of chloride from resistor-furnace carbide in this equipment are shown in Table I. Necessity for increasing production of chloride from about 2,000 to 15,000 lb per week led to further investigation of possible methods for direct chlorination of the oxide or oxide-carbon mixtures. Direct chlorination of the pure oxide presents much less difficulty than chlorination of zircon sand or oxide ores. The oxide is easily ground to —200 mesh, and no silica is present to cause excessive consumption of chlorine or contamination of the product. Theoretical Considerations The principal chemical reactions involved in chlorination of mixtures of zirconium oxide and carbon may be written as follows: ½ ZrO2 (c) + C(c) + Cl2(g) = ½ ZrCl,(g) + CO(g) [I] 1/2 ZrO, (c) + CO(g) + Cl2(g) = ½ ZrCl,(g) + CO2(g) 121 ½ ZrO2 (c) + ½ C(C) + Cl2(g) = 1/2 ZrCl4(g) + ½ CO2(g) [3]

Jan 1, 1953

By L. R. van Wert

CAREFUL research into the nature of the metallic state has yet to discover, with any certainty, its essential quality. We do riot yet know, for sure, what it is that makes the metallic elements different from, if not actually unique among, all created things. We do know, of course, that metals have certain more or less characteristic properties-they are hard, strong, and tough, and good conductors of heat and electricity, and these so-called metallic properties provide a definition of a sort. How- ever, it is the structure rather than the behavior of the metals which gives the really fundamental information necessary to the understanding of metallicity. But this information is not easily obtained. Nature has a way of keeping secrets. But happily we do possess some knowledge of how a metal is built up, and it is this matter, rather than the presentation of a formal definition, that will be discussed here.

Jan 1, 1937

By John H. Schemel

Large Zircaloy-2 hammer or press forged bars did not exhibit the uniform excellent corrosion resistance to steam normally expected of the alloy in wrought form. Weight gains of coupons cut from forged bars were 40 to 60 mg per sq dm compared to the 28 mg per sq dm obtained on hot rolled sheet and strip. The mechanism of this corrosion and its relation to microstructure is discussed. After these observations, a solution heat treatment followed by rapid cooling was tried on coupons from eight heats of forged bars. The basket-weave structure resulting from the quench did not show agglomeration of intermetallic compounds. These coupons showed uniformly good corrosion resistance with weight gains very close to the 28 mg per sq dm expected of Zircaloy-2 after the 14-day steam test. A large forging was solution heat-treated and tested for structure, mechanical properties, and corrosion resistance. Corrosion resistance was excellent and uniform throughout the section. The normally anisotropic mechanical properties were changed to completely iso-tropic. Strength levels were raised while there was a small loss in ductility at the service temperature. Tempering of the quenched structure below the ß transus did not improve the ductility at the test temperature of 600°F. ZIRCALOY-2 end caps for nuclear fuel elements Zircaloy-2 is an alloy of 1.5 pct Sn, 0.1 pct Fe, 0.1 pct Cr, and 0.05 pct Ni, balance hafnium-free zirconium patented by Westing-house Electric Co. used in pressurized water reactors are machined from large hammer-finished forged bars. The bars forged for this application range from 3 1/2 in. to 7 1/2 in. squares. One of the tests used to evaluate Zircaloy-2 for this service is a 14-day exposure to very high-purity steam at 75oF and 1500 psi pressure. Normally wrought products will exhibit a black lustrous film of zirconium oxide after the test and show a weight gain of approximately 28 mg per sq dm. Coupons representing the forged bars exhibited a wide variety of corrosion results ranging from acceptable black coupons to some covered with white crystals of zirconium oxide that had weight gains of nearly 100 mg per sq dm. One of the most common effects was a white corrosion product that looked like a stain to some observers and the outline of massive metal grains to others. Very careful specimen preparation prior to the corrosion test did not affect the result and metallographic examination did not reveal a structural feature of a size and shape that would correlate with the corrosion product. In addition to the relatively poor corrosion resistance, the forged product was not as ductile as desired. The problem of obtaining uniform and more acceptable properties in these heavy-forged sections seemed to be a function of the microstructure of the metal and, in particular, the distribution of the intermetallic compounds. None of the four alloying elements however are appreciably soluble in a zirconium and are present as compounds which usually appear scattered randomly throughout the structure. Moudryl showed that the distribution of these intermetallic compounds in Zircaloy could be related to a ostringero corrosion failure. Grozier et al. discussed another structural defect that causes a similar corrosion effect. In this case, an elongated gas-void was determined to be the cause. M. L. Picklesimer held in his discussion of the Grozier paper that at least a part of the observed =stringersn were caused by the distribution of the intermetallic compounds. He proposed a

Jan 1, 1962

By J. E. 214-000-000-010 Warren, M. R. J. Wyllie, T. Meidav, L. Scharon, R. Uhley, A. J. deWitte

By considering the stoichiometry of the underground combustion process, an equrztion was derived relating the point velocity of the combustion front as a function of the air flux, fuel content, efficiency' of oxygen uitilization, hydrogen:carbon ratio, and ratio of carbon dioxide In carbon monoxide produced. In addition, an equation for cnlcrllating the amount of injected air necessary 10 produce the oil from I Cu. ft of reservoir space was derived. This equation has a direct bearing on evaluating compression costs for the process. Values calculated from these equations are in good agreement with experimentnlly obscrvcd values obtained from laborator) tube runs reported in the literature. The equations are also u\eful for atlcrlyzinf: experinlental data for inconsistencie.r.. I NTRODUCTION The injection of energy in the form of heat into an oil-bearing formation as a means of increasing the recovery of oil has been the subject of much discussion and experimentation as far back as 1920. The ideas have ranged from the injection of steam to the direct use of electricity as a means of getting thermal energy into a formation. However, most laboratory and field studies have been confined to the process whereby a portion of the crude in the reservoir is burned to generate the necessary heat to increase the mobility of the oil by reducing its viscosity. A recent paper by W. L. Martin, et al.', described the results of a number of laboratory experiments in which the combustion process was studied in a sandpack. Studies such as this indicate that with the temperatures involved, the oil is partially coked in this process and it is this coke which provides the fuel for combustion. The combustion of this residual coke can be analyzed theoretically by applying simple stoich-iometric principles to the combustion process. It is the purpose of this paper to compare the results reported in these experiments with those obtained from theoretical considerations. The variables studied by Martin, et al, among others, include combustion front velocity, air flux, oxygen utilization, fuel concentration, ratio of carbon dioxide and carbon monoxide in combustion gases, and the hydrogen:carbon ratio of the residual fuel. All these variables come into consideration when the stoichiometry of the combustion process is studied. The experimental conditions and results are tabulated in Tables 3 and 4 of Ref. 1. For purposes of comparison with calculated results, it was necessary to change the units of a number of the variables. UNDERGROUND COMBUSTION STOICHIOMETRY The combustion or oxidation of the carbonaceous residue or "coke" on the sand can be described in terms of the equation: where n is atomic ratio of hydrogen to carbon, m is ratio of moles of CO2 to CO produced, and CH. is taken as the unit molecular weight, realizing that actually the coke has a large range of high molecular weights. Assuming that all the fuel laid down in the sand is burned, the ratio of moles of oxygen consumed to moles of coke can be written as follows. Moles 0MolesMolescoke In terms of moles O2 per pound of coke, where 12 + n is the molecular weight in pounds per mole. If the 0, consumed is measured in standard cubic feet (60°F and 1 atm) and the coke in pounds per cubic foot of formation, 2, then:

By J. Kucera, J. Vreštál

DIFFERENT authors1 ' have been engaged in meas-uring the vapor pressure of pure cobalt. The results of their measurements satisfy the expected temperature dependence of vapor pressure and are in mutual agreement, with the exception of the results by De Dyk Man and ~esmejanov.~ The latter authors, by using the effusion method, have achieved considerably higher values than other workers. By using the isotope exchange method they obtained much lower values than other authors. The determination of thermodynamic functions of the binary Ni-Co system was carried out, as far as we know, only by De Dyk Man and Nesmejanov.4 This determination was based on extremely low values of vapor pressure over pure cobalt obtained by the isotope exchange method. Therefore we considered it useful to repeat these measurements. Furthermore, the reliable values of thermodynamic functions should complement the migration characteristics, the inner magnetic field data obtained by Miissbauer effect measurements, specific heat data, and the K effect and positron annihilation characteristics that have been achieved for the Ni-Co system in the Institute of Metallurgy of the Czechoslovak Academy of Sciences in Brno.5-9 The measurements in this paper were performed by the isotope exchange method. In this method, as has been shown by analysis,10-'3 the vaporization rate, w, can be calculated from the relation w = k/1oSw [1] i0Sw) [1] where L, is the activity per unit mass of the source, S is the area of evaporation, k is the tangent at the point t = 0 to the curve giving the radioactivity de-pendence of the target vs annealing time, t, and wis the probability for the tracer atom condensation on the target surface. The value for cc. can be obtained from the equation w = a + 2P(l-a) [2] where P is Clausing's coefficient and a is the condensation coefficient. In the present work the cylinder shaped containers for annealing the samples were used, characterized by the ratio 1:d = 1.06. Here 1 is the length and d the diameter of the container. For this ratio P = 0.514 and w =0.5, and w is independent of the condensation coefficient. The vaporization rate is related to the vapor pressure p by the relation where R is the gas constant, T is the absolute temperature, and M is the molecular weight of the component investigated. Measurements of the vapor pressure of the i component over the pure metal, p!, and the alloy, pi, at the given temperature and composition enable one to calculate the thermodynamic activity of this component from the equation ai=pi/pi [4] is and the activity coefficient ri=ai/xi [5] xi where xi is the molar fraction of the investigated alloy component. EXPERIMENTAL Evaporization rate measurements were carried out with pure cobalt and eight different Ni-Co alloys, which were kindly delivered by the Centre National de Recherches Me'tallurgiques Liege, Belgium. The composition of the alloys is given in Table I. The cobalt used in these alloys contained the following impurities: 0.016 wt pct Fe, 0.014 wt pct Cu, 0.01 wt pct Mn. Other elements were present in much lower concentrations. From the melts, samples in the form of small cylinders of 12 mm in diam were ma-chined. The thickness of the targets and sources was 2.5 and 1.2 mm, respectively. The lower thickness of the sources was chosen to make their over-all ac-tivity as low as possible. Sources were activated in

Jan 1, 1970

By W. O. Philbrook, R. H. Spitzer, F. S. Manning

A generalized mathematical model has been developed to describe the kinetics of gas-solid reactions with special attention given to the hydrogen reduction oj dense spheres of hematite. This reduction process must pvoceed through a sequence of transport and chemical .reaction steps acting in series. Under typical experimental conditions, none oj the individual transport and reaction resistances may be neglected in the development of a physically significant model. A linear vate of thickening oj the product layer, usually taken as evidence of interface-controlled .reuction, may be observed even though transport resistances play a dominant role in the over-all kinetics. The temperature and pressure dependencies of all terms have been carefully evaluated in order to .make fill use oj arailable expe-inzental data in evaluation oj the model. FOR obvious technological reasons, the kinetics of reduction of iron oxides has become the subject of intensive experimental and theoretical investigation during recent years. Continuing efforts to construct mathematical models to describe the kinetics of reaction between a gas stream and a granular bed of solid particles have demonstrated the necessity of a thorough understanding of the reaction kinetics of a single particle within the system as a prerequisite to the construction of physically significant models of complex, reacting systems. This paper presents a critical examination of the transport and chemical-reaction processes involved in single-particle oxide reduction and develops the mathematical expressions necessary to evaluate their importance. Comparison of theoretical predictions with experimental results contributes important new understanding of the complex nature of this process. The reduction process has been studied under a wide range of experimental variables, and it is not surprising that apparent conflicts in observation and interpretation appear in the literature. The interested reader is referred to the reviews of Themelis and auvin"? and Manning and philbrook3 for a description of much of this work. The course of reaction commonly has been followed by measuring the oxygen weight loss from the particle as a function of time. A number of authors have suc- cessfully correlated their data in terms of a model which assumes that the reduction process is controlled by the rate of reaction at a single, sharply defined, advancing interface. According to this model, the interface will advance linearly with time. A mathematical model for gaseous reduction in a packed bed developed by the present authors in an earlier paper4 recognized that reduction must proceed through the series hematite (Fe203), magnetite (Fe30,), wiistite (Fe,O), and finally metallic iron. The reduction scheme permitted a stepwise topochemical reduction of the individual particles to metal or to the lowest oxide thermodynamically possible for the local gas composition in the bed. The limiting situations of theoretically dense and very porous oxide structures were considered. On the basis of available experimental evidence, the simplifying assumption was made in each case that all product layers would thicken linearly with time. A generalized single-particle model has now been developed to determine the significance of transport resistances in the product layers and in the gas film surrounding the particle. The analysis shows that the interplay of transport and chemical resistances is such that an apparently linearly advancing interface may be observed despite the fact that the reaction may be under significant transport control. Attention thus far has been focused on the development of a model for the topochemical behavior of dense spheres of hematite in atmospheres capable of reducing them completely to metal. The formation of successive product layers of iron, Fe,O, and Fe304 is assumed to follow the mechanism originally described by dstrijm.' All oxygen removal from the core occurs at the iron/Fe,O interface, intermediate oxide layers being propagated by sol id-state diffusion without change in the oxygen density of the core. Since fractional reduction is operationally defined in terms of oxygen weight loss, the kinetics of the over-all reduction of FeZ03 to iron is properly studied in terms of the gas-solid reaction occurring at the iron-wiistite interface. The fractional reduction of a partially reduced oxide sphere is given by: here refers to the radial position of the iron/Fe,O interface. This model is not universally applicable because, as explained in the earlier paper,4 a consideration of porous particles or of dense particles in atmospheres not capable of reducing wiistite must allow for the possibility of gaseous reduction at interfaces other than the one between iron and Fe,O. However, evidence that certain hematite specimens actually do follow the dense-pellet mechanism developed here is provided by the data of cewan' and of Bogdandy and

Jan 1, 1967