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By D. Turnbull, J. H. Hollomon

THERE is a large body of evidence'" indicating that solidification during the liquid-solid transition is usually induced by heterogeneities present in the liquid. By dispersing liquid metals into small droplets, the impurities responsible for catalyzing solidification are isolated within a small number of these droplets. The effect of the foreign body therefore is restricted to a single drop by this technique. Thus upon cooling below the melting temperature, solidification is initiated by homogeneous nucleation in the majority of the droplets that do not contain impurities. In the case of solidification of liquid metals, the activation energy for nucleation is so great that its rate changes by orders of magnitude for a change in temperature of only several degrees centigrade.' Effectively homogeneous nucleation occurs at a critical temperature upon continuous cooling. Thus by microscopic observation of single particles during cooling, a temperature at which the rate of homogeneous nucleation becomes sensible can be determined.3 since at the temperatures at which nucleation occurs in the absence of impurities the rate of crystal growth is extremely rapid, the temperature at which the entire particle solidifies is very nearly the temperature at which the nucleation of the solidification occurs. Thus for liquids that freeze at high temperatures the onset of nucleation can be established by simply observing the temperature at which the marked heat evolution and increase in brightness of the particle occur. For liquids that freeze at lower temperatures the onset of nucleation can be determined by a rumpling and change in shape of the particle resulting from its solidification. The microscopic technique for observing the solidification of small particles has already been described." In earlier papers the nucleation of solidification of pure metals 5,6 and of alloy systems7 showing complete liquid and solid solubility have been described. In the present paper, the observations are extended to a simple eutectic system (Pb-Sn) where the possibility of the formation of two solid phases exists. Metals for the investigation were obtained from the American Smelting and Refining Co. in the form of pure lead and pure tin, 99.8 and 99.9 pct purity, respectively. An ingot of each of the pure metals was made into shot by heating the metals at a temperature about 50 °C in excess of the melting point and pouring the liquid slowly into a container of water at 15°C. Samples of the shotted pure metals were weighed out to make alloys containing 5, 10, 15, 20, 25, 30, 40, 50, 60, 70, 80, and 90 atomic pct Pb. Samples of each alloy were then melted in separate beakers. Each melt was poured through a pyrex funnel into a cylindrical mold (% in. ID). The casting solidified in 10 to 20 sec. The inside of the mold as well as the funnel through which the metal was poured were coated with graphite to eliminate adherence of the metal. Analyses were performed on some of the compositions and are given in Table I. The compositions also were checked for these samples and for those that were not analyzed by determining the spread between the liquidus and the solidus upon melting the small metal particles. These measurements agreed as well with the nominal compositions as the analyses listed above. Results The results of the supercooling experiments for the several alloys are summarized in Table II and plotted on the constitution diagram in Fig. 1. Data for the pure lead and pure tin were taken from earlier investigations. The values for the maximum supercooling of the several alloys are the average of several determinations on a number of drops of each alloy. The maximum value in any determination was within about 2 pct of the average. For the alloys containing from 20 to 60 atomic pct Sn, inclusive, two marked changes of the surface structure were observed upon cooling. At the higher temperature, after the first appearance of the solid phase it continued to grow slowly at a constant temperature and then stopped. At the lower temperature the alteration of surface structure was abrupt. For the alloys containing from 70 to 95 atomic pct Sn, inclusive, an abrupt change in surface structure was observed at a single critical temperature.

Jan 1, 1952

By K. E. Beu

IN the measurement of retained austenite concentrations in steels using the integrated intensity method,1 Averbach has pointed out" that the absorption factor A(0) for a flat sample making a glancing angle 4 with the incident X-ray beam can be combined with his constant factor R to obtain our constant factor" G provided that "1—There is no preferred orientation in the sample, and 2—The geometric requirements [for the sample, film, and X-ray beam] have been met precisely."' If A(0) can be combined with R to give G according to the equation G = R . A(0) [14] then the possibility for making non-compensating errors in the austenite determination has been eliminated. This has been described previously in a technical note." Because of the brevity of the previous note,3 it was impossible to emphasize the fact that the two conditions on preferred orientation and geometry can be easily met experimentally, contrary to Aver-bach's statement that: ". . . the necessary conditions must be tested experimentally for each determination, and this is done most easily by observing whether the apparent absorption has the form of Eq. 2 [the theoretical equation for A(0)]."" he way in which these two conditions can be met experimentally will be discussed briefly to help clear up this point. In addition to these two conditions, other factors such as sample shape, homogeneity, and grain size which also affect A will be included in this discussion. A (0) depends on sample shape. The theoretical function for A was derived originally for a flat surface.' In general we have found that a flat sample surface is readily obtainable." If such a surface can * The effect of surfaces which are not flat on the measurement of retained austenite will be discussed later. be obtained, it has the following advantages: 1—it is easily reproducible from sample to sample, 2—it is the form required for metallurgical examination —this type of examination being frequently desirable for this work, and 3—it is an efficient shape for diffraction purposes. Perhaps the most important of these features is that a flat sample surface is easily reproducible; hence, this requirement on the repro-ducibility of A from sample to sample is met for all such samples. Fig. 1—Schematic diagram of the quartz crystal monochromator diffraction unit. The centerline of the main beam is at 6' to the target face. The tangent to the crystal face is at 16.8' to the moin beam. The centerline of the monochromatic beam is at 33.6 to the main beam. The sample surface can be rotated in its own plane. The angle of the sample surface and the monochromatic beam can be adjusted by rotating about the vertical axis, The film holder can also be rotated about B so that the film can be exposed over the desired angular range. For Fe K, X = 1.932A. 1011 planes of quartz have d = 3.35A. A(0) depends on homogeneity and grain size. If the sample is badly segregated or the grain size is large, the effect of micro-absorption and primary extinction1. ' must be considered. It has been shown, however, that for most plain carbon or low alloy hardened steels, neither micro-absorption nor primary extinction effects are present.' A (0) depends on camera geometry. For a given angle 0, A remains theoretically constant from a geometrical viewpoint only if the following factors are kept constant: 1—the angle of inclination .+ of the sample to the X-ray beam, and 2—the centering of the sample with respect to the film cylinder. These are mechanical problems which can be solved readily if the facilities of a good machine shop are available. The arrangement used to insure that the angle 4 remains constant and the centering of the sample is reproducible is indicated schematically in Fig. 1. The sample is clamped against a thin plate with a hole in it by means of a spring-loaded pres-

Jan 1, 1954

By Reynold Q. Shotts

CHEMICAL methods, based on the relative rates of oxidation of fusain, bright coal, and dull coal by nitric acid, have been devised to determine these coal components.1-4 Results obtained by oxidation methods for fusain have been checked against results obtained from microscopic methods5, 6on duplicate samples of the same coals, but to the author's knowledge this has not been done for bright and dull coal components. For this reason it is not certain that the two methods of analysis identify essentially the same chemical or physical units. It would be highly desirable to see results of the application of both methods to duplicate samples, but in the absence of any such data the author has attacked the problem indirectly. From the U. S. Bureau of Mines samples were obtained of three Alabama coals which the USBM had analyzed optically and reported on over the past 30 years. These samples were subjected to analyses by oxidation rate methods. Results of this work, and comparisons with the USBM analyses, have been published." This was the first indirect approach to the problem. The present report attempts a second indirect approach by way of internal validation. By nitric oxidation samples of two whole coals were carefully analyzed for fusain, bright coal, and dull coal. One coal was analyzed in duplicate. Duplicate portions of each of the coals were divided into three density fractions by means of heavy liquids. A duplicate portion of one of the coals was divided by sieving into three size fractions. Each fraction was analyzed by oxidation and its percentage composition calculated in terms of fusain, bright coal, and dull coal. Because the weight percent of each fraction was known, a material balance calculation for the whole coal was also made. The resulting reconstituted analysis of the whole coal could be compared to that determined by direct analysis. In addition, specific reaction rate constants were determined for each component and for each whole coal or fraction. Arbitrary reactivity indexes were calculated by dividing by 100 the sum of the products of the percent of each component in the coal and its specific reaction rate constant. The resulting figure was an average reactivity index for each coal or fraction. Weighting the reactivity indexes for each fraction by the percent of the fraction in the coal gave a reactivity index for each whole coal which could be compared to that calculated directly from the whole coal analysis. If oxidation analyses really delineate definite physical entities within the coal, or even definite groups of similar entities, reconstituted analyses calculated from fraction analyses should check closely those made of the whole coal. It probably is true that optical methods identify and describe a greater variety of components than do chemical methods and that variations are wide in the appearance and quantity of those components identified optically. Chemical methods based upon differences in oxidation reaction rates would of necessity be less discriminating, as between similar components, than would optical methods. The procedures followed for oxidizing the samples, analyzing the residues, plotting and calculating the percentage of each component, and calculating its specific reaction rate constant have been fully described.'-' In brief the method originally proposed by Fuchs et al.1 for the determination of fusain consists of the oxidation of small samples of coal in boiling 8N nitric acid in a condenser-fitted flask. After boiling for periods of 1/2 to 4 hr, the unoxidized residue is filtered and washed. The washed residue is treated with normal sodium hydroxide, diluted, and allowed to stand for several hours. The resulting brown liquor is removed, and the filtered residue dried, weighed, ignited, and weighed again. The ash-free residue is expressed as a percent of original dry, ash-free coal. The percent residue is plotted against time, and the extrapolation of this line to zero time gives the percentage of dry ash-free fusain present in the original sample. The shape of the resulting time plots has been explained' by the assumption that they are the result of two different types of reaction, the first part representing a first order reaction with rate a func-

Jan 1, 1956

By P. G. Winchell, M. Cohen, J. Woodilla

The kinetics of stabilization have been studied with respect to the isothermal component of the martensitic reaction in ivon-nickel alloys. Although the carbun (or nit-vogen) content may be very low in these alloys, it plays an important vole in the stabilization phenomenon. In fact, if these interstitial elements are removed by moist-hydrogen treatment, no evidence of stabilization is found. In the pvesence of 0.007 wt pct C, the activation energy for the stabilization process is comparable to that -for the diffusion of carbon (or nitrogen) in ferrite) rather than in austenitc. This suggests that the interstitial diffiision controlling the stabilization occurs within the martensitic embryos rather than in the matrix of the parent phase. The kinetics furthev indicate that the interstitial atoms tend to diffuse -from the embryos toward the suvroundings, thereby immobilizing the interface. This appears to be the origin of the stabilizing effect -found in these alloys. PHILIBERT' has shown recently that interstitial elements play an important role in the stabilization of martensitic transformations in iron-base alloys. However, determination of the temperature dependence for this stabilization process has produced values (- 11,000 cal per mol) that cannot be readily identified with the activation energy for diffusion of carbon (or nitrogen) in either ferrite or austenite. In the present work, the isothermal mode of the martensitic reaction was employed to derive the activation energy for stabilization, and this was found to agree fairly well with that for diffusion of carbon (or nitrogen) in ferrite. An iron-nickel alloy with 30.8 wt pct Ni and 0.007 wt pct C was used in these experiments, the specimens being in the form of rods 0.074 in. in diam and 2 1/2 in. long. The specimens were sealed in evacuated vycor tubes and austenitized at 1100°C for 1/2 hr prior to quenching in water. A second series of specimens was decarburized (and denitrogenized) prior to the above austenitizing treatment by annealing in moist hydrogen for 182 hr at 1215°C. In order to achieve a "standard" condition in the austenitic state, all the specimens were transformed to martensite by cooling to - 195°C before the final austenitizing. Both the 0.007 pct C and the decarburized series then had an Mi temperature of about - 30°C. The isothermal martensitic transformation was carried out at a reference temperature of -88"C, and was traced by means of electrical resistance measurements. Each resistance value was normalized by dividing by the resistance of the austenitic specimen at O°C, thus giving a resist- ance ratio R. The rate of decrease of the resistance ratio (-dR/dt) provided a measure of the transformation rate. It was found that a plot of R vs log t at the reference temperature resulted in a slightly curved line which could be closely approximated by two straight lines intersecting at a time of 10 min, as shown in Fig. 1. If G = dR/dlogt is the linear slope of either straight segment, the rate of transformation at any given time is: The ratio of G for 1 less than 10 min to that for t greater than 10 min was 1.19 for the 0.007 pct C series and 1.24 for the decarburized series. These ratios made it possible to compute the transformation rate at any time greater than 10 min, knowing the transformation kinetics prior to 10 min. The stabilization treatment was introduced by up-quenching from the reference temperature, usually after 10 min of isothermal transformation: to one of four stabilizing temperatures between 0" and 22"C. After holding for various times, the specimens were down-quenched to the reference temperature for additional isothermal transformation. In this way, it was possible to compare the transformation rate (- dR/dt), immediately after stabilization with the transformation rate (- dR/dt)U in the unstabilized condition. The degree of stabilization was defined as: Ordinarily, Gs and Gu would be measured after the same time of prim isothermal transformation.

Jan 1, 1960

By Cloyd M. Smith

A few years ago, the Ventilation Committee established the practice of resenting one topic each year for discussion at the annual meeting. The practice has met good response on the part of committee members and I suggest that it be continued. The topic chosen for this year, "Underground Anemometry," is a topic which has bothered me for more than 20 years. It seems to me that the coal industry is content to rely on slipshod methods for measuring the rate of flow of air underground, so I prefaced my discussional charge to committee members with the statement that I regard air measnrements made in the usual way, with hand held anemometer, as no good. Agreements and disagreements came in from more than a dozen engineers, some of whom are with operating companies, coal and metal; some with manufacturers; others with government agencies. The statement was accompanied by a questionnaire on the use of the rotating vane anemometer and by one describing two methods of using a mechanically held anemometer. The questionnaire will be considered first. The questionnaire and statement are as shown on pages 5 and 6, the committee members and respondents are given on page 4, and the general comments of the latter on page 5. Questionnaire 1. Has your company or agency issued written instructions for care and use of anemometers? If so, please enclose a copy with reply. Only one answer, McElroy's, was affirmative. It gave reference to Bureau of Mines publications1'5 which recom- mend the hand held anemometer for rough measurements and indicate that am accuracy of 5 pct can be had if calibration and method factors are used. Mathews said that instructions are principally oral while Maize reported that state inspectors of his department are well trained in use and care of anemometers. 2. Are your anemometers calibrated periodically? If so, by their manufacturer? or by? Are calibralion corrections applied to all observed mean velocity readings? Only one respondent, Lee, answered negatively as to calibration. This means that anemometers are generally calibrated but the questionnaire failed to ask how often this is done. As no one volunteered the information, we have no data on this point. In six cases the instruments are sent to their manufacturers for calibration. but Krickovic reports that his company limits manu-facturers' calibrations to anemometers which are used by operating personnel; those used by the engineering department being calibrated by U. S. Bureau of Standards. The Anaconda Copper Mining Co. has its ventilation engineers calibrate its anemometers. Most of the respondents say that a calibration correction is applied to each mean velocity reading, but Krickovic limits this to surveys made by the engineering department. Since Lee does not calibrate, he has no correction to apply. Maize reports that his department has its anemometers calibrated but does not apply corrections. 3. Do your men hold the anemometer by hand in measuring air flow? for 1 min? or traverse the section? for 1 min? or at? points for 5 sec each? Of 10 replies, 6 were "yes," 3 were "no," and one was "seldom" with respect to holding by hand. Among the six hand holders, four hold in a central position in the measuring section for a minute, except that two of them, Krickovic and Matthews, traverse the section by hand for survey or fan test. Their operating personnel hold by hand, centrally, for routine measurements. McElroy sometimes traverses with hand-held anemometer in rapid survey work. 4. If the anemometer is not held by hand, how is it supported? Augustadt supports the anemometer on an adjustable rod, Condon on "a rod of sufficient length to reach all points with observer standing in one position throughout traverse and at arm's length from plane of traverse." I presume that arm's length must be interpreted liberally enough to allow for arm movement, otherwise it would be impossible to manipulate the anemometer throughout the traverse section. Mancha upholds Condon in this method of traversing. Glanville hangs the anemometer on the end of a 4-ft staff by the hasp at the top of the anemometer frame. McElroy mounts it on the end of a rigid square shaft, 12 in. long, the staff being at right angles to the axis of the instrument. He traverses the section in two halves, holding the anemometer 3 feet from his body.

Jan 1, 1950

By R. G. Hawthorne

This report is concerned with fluid displacement in porous media, in those cases where viscous and gravitational forces control the displacement. Such a system would usually be found in a sand body of large physical dimensions such as an oil reservoir, although it is possible to create such a system in the laboratory. It is shown that the position of the fluid interface can be predicted by numerical calculations using a basic idea presented by Dietz. Fluid flow is considered in a vertical plane in a homogeneous, porous medium of sufficient thickness that the capillary transition zone is small in comparison with the total reservoir. A theory developed by Dietz' is used to make numerical calculations of the position of the fluid interface. The results for several conditions are compared with scaled model experiments. The results show that, for gas drive in a reservoir of steep dip, a relatively low flow rate can displace large volumes of oil before gas breakthrough. On the other hand, water injection at favorable mobility ratio and low dip may show best performance at high rates. Water tends to underride the oil and, given sufficient rime, will break through without much oil displacement. For certain conditions, which include relatively low flow rate, the interface is a straight line and its behavior is simple to calculate. At higher flow rates, the interface is unstable, and a numerical solution was programed for an automatic computer. In general, good agreement is shown between the fluid model and the computed results so long as gravitational forces have control. For a water drive at very unfavorable mobility ratio, many small water fingers appear. These viscous fingers are not controlled by the relatively small gravitational forces. When viscous fingering becomes the controlling factor, the mathematical model is oversimplified, and results do not check the fluid flow model. INTRODUCTION Present methods of reservoir analysis depend upon certain simplifying assumptions to obtain mathematical descriptions of practical use. Material-balance methods (Muskat2 or Tarner2) assume uniform fluid saturations in the entire reservoir, or in a few subdivisions of the reservoir. An unsteady-state flow calculation by West, er at considered pressure and saturation changes in flow to a well during solution gas drive, and neglected gravity effects. Results showed only a 4 per cent difference for ultimate oil recovery by the Muskat method, even though the case chosen for study was one in which unsteady-state effects should be high. The Buckley-Leverett5 method commonly assumes a one-dimensional flow system. It is applicable at high flow rates where viscous forces predominate over gravity forces. Simultaneous, parallel flow of the two fluids is assumed, and the concept of a fluid interface is not introduced. Permeabilities to each fluid for a given saturation must be known. The method is not applicable for a two-dimensional system where cross flow becomes possible. Less well known is the displacement equation derived by Dietz. This method is designed for two-dimensional flow systems and assumes a definable fluid interface within the porous medium. Dietz showed that, for a range of low flow rates, the interface would be stable. straight and at an angle of inclination which could be simply calculated. At a certain critical flow rate, the calculated interface tilt would equal the formation dip. For higher flow rates, a finger of displacing fluid would invade the displaced fluid. Dietz indicated that his method applied only to macroscopic reservoir behavior, while the Buckley-Leverett method applied to the small transition zone at the fluid interface. The examples worked out in this report are based on the fluid-displacement theory of Dietz. It is shown that the Dietz theory may be used to derive equations analogous to the Buckley-Leverett equations. In contrast to the Buckley-Leverett method, flow is considered in a plane rather than being limited to a line. Rather than a frontal advance, the movement of a fluid interface is followed. For flow rates substantially exceeding the critical rate and for high viscosity ratio, many fingers of invading fluid occur-—rather than the single finger assumed by Dietz. On the other hand, so long as some gravitational influence remains, the flow is not entirely parallel to the bedding planes as assumed by Buckley and Leverett; therefore, both methods fail to give an adequate descrip-

By N. S. Stoloff, R. C. Ku, R. G. Davies

The stress-strain behavior of Fe-Co and Fe- V alloys containing up to 25 pct solute have been studied in the temperature range 25° to - 196°C. The microyield stress is independent of temperature for all alloys studied, while the temperature dependence of the ordinary yield stress is large and comparable to that for unalloyed iron. An alloy-softening phenomenon is observed for many alloys relative to unalloyed iron, and appears to be a consequence of removal of inter-stitials from solution and their subsequent agglomeration. The ductile to brittle transition temperature is increased markedly by both cobalt and vanadium. Transmission electron microscopy observations reveal that cross slip and cell formation are restricted with increasing solute, which can account for many aspects of yielding and fracture behavior. IRON and other metals of bcc structure slip on many planes of the (111) zone at moderate and elevated temperatures, giving rise to wavy glide. At low temperatures, however, there is a tendency for slip to be restricted to planes of only one or two crystallographic types; in the case of Fe-Si alloys for example, (110) glide predominates, giving rise to planar slip bands."' Restriction of cross slip at low temperatures in iron has been linked by Brown and Ekvall3 to increased strain hardening in the preyield microstrain region, leading to an apparently large temperature dependence of the yield stress. Support for this view has been provided by Lawley and Gaigher4 from a transmission electron microscope study of molybdenum. They concluded that dislocations at lower temperatures, by virtue of their inability to change planes readily, are unable to interact and annihilate, leading to an increase in internal stress and work-hardening capacity. Restriction of cross slip at low temperatures has also been suggested to be an important factor in determining the ductile to brittle transition of single-phase solids, including metals of bcc structure.5 It is pertinent to note that most solute elements tend to raise the ductile to brittle transition temperature of poly crystalline ferrite,6,7 although in some cases, e.g., Fe-Cr7 and Fe-Al,8 the dilute alloys may actually yield at lower stresses than unalloyed iron. It appears, therefore, that solute elements may have an effect analogous to lowering the test temperature with regard to restricting cross glide. Such an effect has indeed been observed in the ionic alloy system KCl-KBr,9 in which bromine atoms, although causing little misfit and consequently little effect on the yield stress of KC1, have a pronounced effect in restricting wavy glide and inducing brittleness. The purpose of the present investigation was to determine the effects of selected solute atoms on the yield stress and fracture behavior of iron, and to elucidate in turn how the slip character was related to these properties. Since it is known that interstitial atoms exert a strong influence on the mechanical behavior of iron, the solute elements chosen for study were vanadium, which reacts strong with interstitials,10 and cobalt, which does not form highly stable interstitial compounds." EXPERIMENTAL PROCEDURE Four-pound ingots of each of the following alloys were vacuum-melted in zirconia crucibles: Fe-1, 5, 10, 25 at. pct Co, and Fe-1, 4, 10, 20 at. pct V. An ingot of unalloyed iron from the same original stock as that used for the alloy was remelted under similar conditions to eliminate variations in interstitial content arising from differing thermal histories. Chemical analyses of the iron, cobalt, and vanadium melt stock are listed in Table I. All ingots were rolled and swaged, commencing at 850°C, to 1/4-in.-diameter bar. The bars were then annealed at 850°C for 1 hr (except that the 10 and 20 pct V alloys were heated for 2 hr) to give a uniform equiaxed grain size of about 0.05 mm. Tensile samples of 0.125 in. diameter by 0.8 in. gage length were utilized for studies of the ductile to brittle transition. A second set of tensile samples were utilized for microstrain experiments in which strain sensitivity of 1 x 10"6 was achieved by a capacitance method.3 Cylindrical compression samples 0.250 in. diameter by 0.4 in. long also were prepared to study the influence of composition on the macroscopic yield stress, and for metallographic analyses of defor-

Jan 1, 1965

By Porter W. Shimer

The solution used in the following method for phosphorns-determination is the filtrate obtained in the nitric and sulphuric acid method for the determination of silicon (Transactions, vii., 346). This filtrate, being easily and quickly obtained, and always quite free from silica, is a desirable one for phosphorus-precipitation. IN order, however, to get all the phosphorus in a precipitable form the solution must be made under conditions more strongly oxidizing than simple solution in boiling nitric acid. In a solution thus

Jan 1, 1889

By J. M. Mutmansky, T. K. Greer

This paper takes a look at the optimal velocity to be used in coal mine entries and determines a statistical relationship for optimal velocity that can be applied under current mining conditions. This relationship provides the optimal velocity for coal mine airways under variations in power cost, mining cost differential, airway friction factor, time value of money, airway lifespan, and quantity of air carried. This enables the ventilation engineer to make an easy, rapid determination of the optimal velocity for planning purposes.

Jan 1, 1985

By G. H. K. Schenck, H. W. Robinson

Private weather forecasting services available on a contract basis can significantly reduce the uncertainty associated with weather-induced changes in mineral production and demand. Such services offer the mineral producer the opportunity for tactical and strategic response to weather conditions. There are at least 50 private meteorological consulting services as well as numerous individual meteorology consultants. Fees for services range from $150-$600 per day for one man to over $20,000 per month where a complex forecasting or modification program is undertaken.

Jan 1, 1971

By Sir Lowthian Bell

WITH the exception of air and water, it is open to question whether there is any form of matter which the human race could less easily spare than iron. Short of going the length of asserting that, without this metal for an anchor or steel for the compass, the adventurous navigator could never have crossed the wide Atlantic, we may credit the locomotive' and the steamer, and hence iron, for that sequence of events which has peopled North America with the

Jan 1, 1891

By J. Weertman

The paper of Gifkins and Snowden considers the interesting but difficult problem of determining the stress dependence of secondary (steady-state) creep at low stresses. These authors have concluded that at stresses below 250 psi (2 x 107 dynes per sq cm) the secondary creep rate of lead is proportional to the stress (viscous creep) and is not proportional to the stress raised to about a fifth power. The experimental data considered by them were obtained on tests conducted at room temperature and at 50°C. The lowest stress employed was 50 psi (3.5 X 106 dynes per sq cm). The authors pointed out the main difficulty in determining the stress dependence of creep at low stresses. The creep tests must be run for very long lengths of time. However they made no estimates of when an experimental creep rate determination must be rejected because it does not represent a true steady-state or minimum creep rate. In order to be certain that a creep curve is within the steady-state region, the total creep strain should be of the order of 0.1 to 0.2. For a creep test of a year's duration this requirement implies that a secondary creep rate smaller than about 10-3 per hr cannot be measured reliably. The corresponding creep rate for a 10-year test is 10-6 per hr. The creep rates of the tests that were considered by the authors to prove the existence of viscous creep were of the order of or less than 10-6 per hr. One can conclude reasonably that this data does not prove unambiguously that large strain steady-state creep rate of lead is proportional to the stress in the stress range of 50 to 250 psi (3.5 x 106 to 2 X 107 dynes per sq cm). Another technique can be used to obtain the stress dependence at low stress levels. The creep rate is a very sensitive function of temperature. The creep rate can be increased by very large amounts merely by increasing the temperature. We carried out steady-state creep tests on lead single crystals25 at temperatures up to 320°C. We were able to obtain creep rate data down to stresses as low as 35 psi (2.5 x 10' dynes per sq cm). Our smallest creep rate was 8 x 10-5 per hr. Thus we obtained large strain, steady-state creep rates to even lower stresses than were considered by Gifkins and Snowden. No evidence was seen for viscous creep. The creep rate was proportional to the stress raised to about a 4.5 power down to the lowest stresses. Since there is no reason to believe that changing the temperature should change the stress dependence of steady-state creep, we feel that large strain viscous creep does not occur in the stress range quoted by the authors for lead single crystals or large-grain polycrystalline samples of lead. This conclusion does not imply that viscous creep may nat occur in a lower stress range or in the same stress range for fine grain material or at creep strains very much smaller than 0.1. Support by the U.S. Office of Naval Research is acknowledged. Authors' Reply R. C. Gifkins and K. U. Snowden We thank Dr. Weertman for his discussion and although, as we hope to show, we do not agree with his reservations, we do concur in stressing the importance of ensuring that creep rates are reliably obtained. Dr. Weertman appears to be content to accept n = 1 for low stresses with fine-grained material but not for single crystals. We believe our results show that the former result cannot be accepted without also accepting the latter. We will also show that the probable errors in our minimum creep rates are insufficient to alter our conclusions, that the criterion proposed by Dr. Weertman is arbitrarily restrictive and his alternative experimental approach possibly invalid. 1) A principal result of our Fig. 1(a) is that n = 1 for polycrystalline specimens at room temperature and 50°C for stresses below -250 psi. There was evidence that crystal slip and grain boundary sliding contributed approximately equaily to the overall strain in this low-stress regime. This implies that either a) grain boundary sliding controls slip within the grains or b) both grain boundary sliding and crystal slip independently occur according to mechanisms which give n = 1. Alternative a does not seem acceptable, so we were forced to consider b. This led us to reexamine work on bicrystals by Strutt and Gifkins and plot curves Fig. l(b). Previously Strutt et al. (loc. cit.), had merged these points with others using the Zener-Holloman parameter and thus, we now believe, had been led to overlook the behavior where n = 1. Curves C and D in Fig. l(b) did appear to confirm the hypotheses that n = 1 for crystal slip at these low stresses and the sliding curve F was similarly of the expected form. It was comparatively easy to find a quantitative theory to account for n = 1 for sliding and the similarity of curves C and D to curve F (all obtained from the same set of specimens) led us to feel that the single-crystal curves were valid. 2) We believe the secondary creep rates for both the polycrystalline and single-crystal specimens to be in error by factors c2. In Fig. 6 creep curves for polycrystalline specimens of lead(1) and lead(II) are reproduced as curves a and b, respectively, and curve c is for a single crystal at 100 psi. It is clear that, although the attainment of secondary creep rate takes 2 years for a and 150 days for b, thereafter the curve is linear for periods of 7 and -1 year, respectively. The single crystal has a linear portion commencing after 20 and extending to 90 days. Creep extension was measured directly using a traveling microscope reading to 0.01 mm on gage lengths marked on the specimens; the gage lengths

Jan 1, 1968

By H. R. Joesting

Geophysical search for minerals is stepped up to meet requirements of expanded defense program - Seismic and electrical surveys become firmly established for ground-water and engineering investigations.

Jan 2, 1953

By Allen H. Rogers

THE need for coordinated effort on public problem by engineers has long been felt. Early in June there will assemble in Washington a conference composed of delegates from all the engineering organizations in the country. The call for this conference is issued by the Joint Conference , Committee of the four national societies as the completion of its work on the organization of a congress composed of delegates representing all the engineering organizations of the United States. The plan for this confederation was presented at a joint meeting of the administrative boards of the national founder societies on Jan. 23, 1920; and was unanimously approved in principle by that meeting. The work of the committee since that date has consisted in drafting a constitution of the organization to be presented at the conference for discussion and, after such amendments as may be adopted, acceptance.

Jan 1, 1920

By Sherwin F. Kelly

THE principal interest in the meeting sings arranged by the Geophysical Committee this year centered around the many papers dealing with the practical applications of geophysical methods to solving geological problems in many other parts of the world. The program Wednesday morning dealt with work in South Africa, Poland, and South America. Rudolph Krahmann's first paper gave a perspective of the geophysical investigations upon mineral deposits in South Africa. A striking point in his story was the tremendous increase in magnetic work during the last two or three years. This is largely accounted for by the intensive exploration for the extension of the Witwatersrand gold mining area. The author mentioned many surveys in which other methods were used for the search for ores of copper, lead, and zinc, and in the study of water-bearing and oil-bearing structures.

Jan 1, 1935

By D. E. Thomas, C. E. Birchenall

ALTHOUGH Eoltzmann gave a mathematical solution for the diffusion equation (for planar diffusion in infinite 01. semi-infinite systems only) in 1894 allowing for variation of the diffusion coefficient with a change in concentration, it was not until 1933 that this solution was applied to an experimentally investigated metallic system. The calculation was carried out by Matano' on the data obtained by Grube and Jedele3 for the Cu-Ni system. Since that time concentration dependence of the diffusion coefficient has been demonstrated for many pairs of metals. However, the nature of this dependence has never been fully elucidated. Many investigators have suspected that these variations could be related to the thermodynamic properties of the solutions, one of the earliest explicit statements being contained in a discussion of irreversible transport processes by Onsager' in 1931. Development along these lines has been greatly retarded by the lack of reliable data on the variation of tliffusivity with concentration, the paucity of the thermodynamic data for the same systems at the same temperatures and compositions, and an incomplete understanding of the relation of the thermodynamic properties of the activated state for diffusion to the bulk thermodynamic properties. The last factor has been discussed by Fisher, Hollomon, and Turnbull.5 In many instances where data exist, it is difficult to know which are acceptable. This problem probably applies more strongly to diffusion data than to activity measurements. For instance, four sets of observers"-" have reported self-diffusion coefficients for copper. The average spread between extreme results is a factor of about four, though the individual sets of data are self-consistent to about 20 pct. Thus one or more factors are out of control, at least in these experiments, making estimates of internal error unreliable. The most reliable diffusion data in most systems have resulted from the use of welded couples with a plane interface from which layers for analysis are machined parallel to the interface after diffusion. The layers are analyzed, and the result is a graphical relation between distance and concentration, usually called the penetration curve. Given the same set of analytical data and distances and following the same procedure in computation, different observers will generally produce diffusion coefficients which vary appreciably, especially at the extremes of the concentration range. Experiments must be carefully designed so that the precision is good enough to answer a particular question unequivocally. In the first calculation of the dependence of the diffusion coefficient on concentration in the metallic solid solution Cu-Ni, Matano found that the coefficient was insensitive to concentration from 0 to 70 pct Cu, after which it rose more and more steeply to some undetermined value as pure copper was approached.' The same behavior was reported for Au-Ni, Au-Pd, and Au-Pt.* The data used were those of Grube and Jedele which were very good at the time, but are not considered particularly good by present standards. Furthermore, the method of calculation makes the ends of the diffusion coefficient-concentration curve unreliable. For better reliability, the high copper end of the curve has been checked by incremental couples, where the concentration spread is 67.7 to 100 atomic pct Cu. The implication of the curves calculated by Matano was that diffusion is very concentration sensitive in one dilute range of this completely isomorphous system and hardly at all in the other. Matano's result is confirmed. Later Wells and Mehll0 published data on diffusion in Fe-Ni at 1300°C, which represent a thorough test of the shape of the concentration dependence curve. They ran couples with the following ranges of nickel concentration: 0-25 pct, 1.9-20.1 pct, 0-20.1 pct, 20.1-41.8 pct, 0-99.4 pct, and 79.3-99.4 pct. Although the trend of the data indicates an S-shaped concentration dependence, their curve was drawn to the pattern set by Matano. Their original data have been recalculated for the 0-99.4 and 79.3-99.4 pct couples. Wells and Mehl's points and two independent recalculations from the raw data are plotted in Fig. 1. What appears to be the best curve is drawn through them. This curve shows little sensitivity to composition in both dilute ranges with a strong dependence at intermediate composi-tions.? Similar experiments on the Cu-Pd system are reported here at temperatures where solubility is unlimited. These lead to the same type of concentration dependence for the diffusion coefficients as was found upon recalculation of the data for the Fe-Ni system. Experimental Procedure Cu-Pd: The concentration dependence of the diffusion coefficient may be determined by the use of

Jan 1, 1953

By Rodney P. Smith

The diffusivity of carbon (0.1 wt pct C) in Fe-Nz alloys (0 to 100 pct Ni) has been determined for the temperature range 860° to 1100°C. As a function of nickel content, the diffusivity has a maximum near 60 pct Ni (the maximum diffusivity being about 1.3 times that in the absence of nickel); the activation energy has a maximum between 40 and 50 pct Ni and a maximum between 80 and 90 pct Ni. The difference between the minimum activation energy and that in iron is about 3000 cal pev g-atom; Do has a minimum between 40 and 50 pct Ni and a maximum between 80 and 90 pct Ni. The results cannot be rationalized by an approximate thermodynamic treatment. THE diffusivity of carbon has been determined in a number of iron alloys over a limited concentration range. It seemed desirable to investigate a system which allows an extended range of alloy composition within a single-phase region. The Fe-Ni system is ideal in this respect, in that all alloys from 100 pct Fe to 100 pct Ni are fee in a convenient temperature range.&apos; The carbon diffusivity was determined by a decar-burization method. The experimental procedure was identical with that used to determine the diffusivity of carbon in y Fe-Co alloys.2 The experimental data are given in Table I. A small correction (order of a few percent) has been made to the measured carbon loss to correct for the carbon lost from the ends of the cylinders.&apos; Since the diffusivity of carbon varies with carbon content the measured diffusivity is an average value for a carbon content between zero (surface) and that at the center of the sample at the end of the decarburization periods. In making the correction in D to 0.1 wt pct C it is assumed that the measured D corresponds to the arithmetical mean of the carbon content at the surface and at the center of the sample at the end of the decarburization period.3 Since this correction is small (<4 pct in D) and since for our decarburization times the changes in carbon content at the center of the sample was small the mean carbon content could have been taken as half the initial value. It is further assumed that the change in D with carbon content for the alloys is the same as that for the diffusion of carbon in iron. From the data of Wells, Batz, and Mehl4 and of smith5 the correction of D from the mean carbon content to 0.1 wt pct C is 0.3 (0.1 - mean wt pct C). The results for iron are given in Ref. 2. Within the experimental error log Do.l%C for each alloy is a linear function of 1/T; the constants for the equation determined by the method of least squares are given in Table I. The deviations of the experimental points from the least-squares line are of the order of 2 pct in D. A comparison of our results for the diffusivity of carbon in nickel with those of other investigations is shown in Fig. 1. The lower curve in Fig. 1 is a linear extrapolation of values calculated* from the equation of Diamond6 for the relaxation time (temperature range 100° to 500°C). The results indicate a small increase in the activation energy over the temperature range 100° to 1400°C; however, it is difficult to say whether the change in Q is real or experimental error. Certainly the change in Q is less than the variation of 5 kcal per g-atom in the diffusivity of carbon in a iron.6 The experimental data for all the alloys are plotted in Fig. 2. As a function of nickel content the diffusivity has a maximum near 60 wt pct Ni at all temperatures investigated and possibly a minimum between 80 and 90 wt pct Ni for temperatures below 1000°C. The activation energy, Q, and log Do are plotted as a function of the nickel content in Fig. 3. Due to the limited temperature range of our experiments neither Q nor Do can be determined precisely; the activation energies appear to be consistent to ±0.3 kcal per g-atom; however the deviation from the absolute values may be considerably larger, see Table II. The Do values probably have little significance. The solid line for Do in Fig. 3 represents the values required to reproduce the experimental values for D when Q has values represented by the upper solid line The diffusivity of carbon may be expressed in terms of the mobility B22, the activity coefficient r2,

Jan 1, 1967

By A. J. Lena, M. F. Hawkes

Changes in hardness, tensile properties, microstructure, electrical resistance, and X-ray diffraction effects indicate that lattice strains are necessary for the embrittlement of ferritic stainless steels when heated for relatively short times at 475°C (885°F). It is suggested that 475°C (885°F) embrittlement is due to the accelerated formation of an intermediate stage in the formation of s under the influence of these strains. FERRITIC stainless steels (low carbon alloys of iron with more than 15 pct Cr) are subject to two forms of embrittlement when heated in the temperature range of 375° to 750°C. The embrittlement which occurs after long time heating between 565" and 750°C is well understood; it is caused by the precipitation of the hard, brittle s phase. Sigma is an intermetallic compound of approximate equi-atomic composition with an extended range of formation in Fe-Cr alloys. The maximum temperature at which this form of embrittlement can occur is dependent upon chromium content; and is approximately 620°C for a 17 pct Cr steel and 730°C for a 27 pct Cr steel. The other form of embrittlement occurs after relatively short heating periods in the range of 375" to 565°C; in the higher chromium steels, hours may be sufficient as compared to months for s embrittlement. This phenomenon is not at all well understood and several controversial theories have been proposed. The rate and intensity of embrittlement increase with increasing chromium content but the maximum rate occurs at 475°C re-gardless of chromium content. As a result of this, the phenomenon has been termed 475°C (885°F) embrittlement. The effect of 475°C embrittlement on the properties of ferritic stainless steels has been thoroughly reviewed by Heger.1 The embrittlement causes a pronounced decrease in room temperature impact strength and ductility, a large increase in hardness and tensile strength, and a decrease in electrical resistivity and corrosion resistance. Microstructural changes accompanying embrittlement are minor and difficult to interpret with a general grain darkening, appearance of a lamellar precipitate, grain boundary widening, and precipitation along ferrite veins having been reported at various times. With the exception of reported line broadening, X-ray diffraction studies by conventional Debye analysis of solid samples have been of little value. BY making use of electron diffraction methods, Fisher, Dulis, and Car-roll&apos; have recently shown the existence of a chromi-um-rich, body-centered cubic phase in 27 pct Cr steels which had been aged at 482°C (900°F) for as long as four years. Two types of theories have been advanced to account for the embrittlement. The first of these requires the precipitation of a phase not inherent in the Fe-Cr system with various investigators suggesting a carbide,3 nitride,3 phosphide,4 or oxide." Theories of this type have difficulty accounting for the influence of alloying elements on the embrittlement and for the facts that a minimum chromium content is necessary for embrittlement and the intensity of embrittlement increases with increasing chromium content. The second type of theory that has been proposed relates 475°C embrittlement to s phase formation which is inherent in the Fe-Cr system. An assumption of this kind can adequately explain the influence of alloying elements, for they exert an effect on 475°C embrittlement similar to that on s phase for-mation as can be seen in Table I. The minimum chromium content is essentially the same for both phenomena and it has been shown12,13 that s is a stable phase in the embrittling temperature range. In addition, it has been reported14,15 that pure alloys embrittle to the same extent as commercial type alloys. There are, however, several factors which have prevented complete acceptance of a s phase theory. Foremost of these is that the embrittlement can be removed by reheating for short time periods above 600°C, which in the higher chromium steels is within the stable s region. No s has ever been observed after one of these curing treatments, nor has any s been found as a result of embrittlement at 475°C. In addition, the simple precipitation of s cannot explain the time-temperature relationships for reactions between 350°and 750°C. This behavior is shown schematically in Fig. 1. Newell 16 and Ried-rich and Loib4 have shown that 475°C embrittlement follows a C-type curve as illustrated, while Short-

Jan 1, 1955

By E. T. Turkdogan, P. Grieveson

Experimental results are presented for the rate of solution of nitrogen in a iron in the temperature range 750° to 873°C and in 6 iron in the temperature range 1410° to 1470°C. It is shown that the rate controlling process is diffusion of nitrogen into the iron. The diffusiting of nitrogen in a and 6 iron is derived from the results, and the temperature dependence of the diffusivity is represented by the equation D = 7.8 x e- 18,900/RT sq cm per sec. The solubility of nitrogen in a and 6 iron, in equilibrium with 1 atm pressure of nitrogen, has been measured. Using these results and other available data, it is found that the variation of the logarithm of nitrogen solubility with the reciprocal of absolute temperature is nonlinear. In an Appendix, some results of Darken and Smith are presented for the rate of solution of nitrogen in iron using ammonia + hyidrogen mixtures. These data also support the view that diffudsion of nitrogen in iron is the rate-controlling process when ammonia + hydrogen mixtures are used. A considerable effort has been made to obtain data on the solubility1-5 and diffusivity of nitrogen in a iron6-l2 because an understanding of the effect of nitrogen on the properties of steel must be based on an accurate knowledge of the properties of nitrogen in pure iron. However, no information is available concerning the kinetics of solution of nitrogen in a and 6 iron. Recently the authors13 have investigated the rate-controlling mechanism operating in the kinetics of solution of nitrogen in y iron. This study was directed to determine the rate-controlling processes for similar reactions with a and 6 iron as well as to establish values for the solubility of nitrogen in equilibrium with nitrogen gas in a and a iron. EXPERIMENTAL The procedure used in experiments to determine the rate of solution in cylindrical iron rods was the same as that described in a previous communication.13 Ferrovac E grade iron used in all experiments contained the following impurities in weight percent: C, 0.005; Mn, 0.001; P, 0.002; S, 0.006; Si, 0.006; Ni, 0.025; Cr, 0.002; V, 0.004; W, 0.02; Mo, 0.01; Cu, 0.001; Co, 0.01; 0, 0.007. After cleaning the surface, the iron rods were treated in an atmosphere of purified hydrogen for 17 hr before the reacting gas was introduced for known experimental times. After quenching, the samples were sectioned radially and analyzed for nitrogen. In addition to experiments using rods, iron foils were used in the measurements of solution rates of nitrogen in a iron. The foils of two different thicknesses were prepared by cold rolling Ferrovac E grade iron cylindrical rod to 0.051 and 0.152 cm. Foil samples were used in a rectangular form 5 cm long and 1.25 cm wide. The specimens were thoroughly cleaned of surface oxide with fine emery cloth and degreased with carbon tetrachloride immediately before entry into the furnace. The experimental procedure was the same as that used in the study with rods. At the completion of an experiment, the foil samples of the nitrogenized iron were analyzed for nitrogen after discarding 0.3 cm from the perimeter of the specimen. Iron foils were nitrogenized and denitrogenized in the a and 6 range with a gas mixture of 95 pct N and 5 pct H for times varying from 5 min to 2 hr. Results obtained for the average composition of nitrogen in iron for these experiments are presented in Fig. 1. Prior to the denitrogenization experiments, the samples were saturated with nitrogen at 1000°C and 0.67 atm N, giving a uniform nitrogen concentration of 0.0204 pct. According to the known a-y phase boundary in the Fe-N system,14 this composition lies within the ferrite region at temperatures 750" to 850°C. Use of this initial nitrogen content insured that reaction occurred between the gas and a single solid phase, a iron. Examples of the results for the mean concentrations of nitrogen in cylindrical iron rods, 0.356 cm radius for both the a and 6 ranges are given in Fig. 2. Typical examples of the results obtained for the radial distributions of nitrogen in rods are presented in Fig. 3. It appears that the results for radial distributions can be extrapolated to constant surface compositions which agree with the equi-

Jan 1, 1964

By T. C. Boberg, R. B. Lantz

This paper presents a method for calculating the producing rate of a well as a function of time following steam stimulation. The calculations have proved valuable in both selecting wells for stimulation and in determining optimum treatment sizes. The heat transfer model accounts for cooling of the oil sand by both vertical and radial conduction. Heat losses for any number of productive sands separated by unproductive rock are calculated for the injection. shut-in and production phases of the cycle. The oil rate increase caused by viscosity reduction due to heating is calculated by steady-state radial flow equations. The response of successive cycles of steam injection can also be calculated with this method. Excellent agreement is shown between calculated and actual field results. Also included are the results of several reservoir and process variable studies. The method is best suited for wells producing from a multiplicity of thin sands where the bulk of the stimulated production comes from the unheated reservoir. The flow equations used neglect gravity drainage and saturation changes within the heated region. INTRODUCTION This paper presents a calculation method which can be used to predict the field performance of the cyclic steam stimulation process. The calculation method enables the engineer to select reservoirs that have favorable characteristics for steam stimulation and permits him to determine how much steam must be injected to achieve favorable stimulation. While the calculation represents a considerable simplification of physical reality and the results are subject to numerous assumptions which must be made about the reservoir, it has been found that realistic calculations can be made of individual well performance following steam injection. The duration of the stimulation effect will depend primarily on the rate at which the heated oil sand cools which, in turn, is determined by the rate at which energy is removed from the formation with the produced fluids and conducted from the heated oil sand to unproductive rock. A complete mathematical solution to this problem is a formidable task, and finite difference techniques would undoubtedly have to be used. The calculation method pre- sented here utilizes analytic solutions of simple related heat transfer and fluid flow problems. The method is sufficiently simplified that it can be used as a hand calculation, although the calculations are somewhat lengthy and laborious. For that reason, the analysis was programmed for an IBM 7044 digital computer. Well responses observed at the Quiriquire field in eastern Venezuela&apos; have been matched using this program after making suitable approximations for reservoir and wellbore conditions. One of the most valuable uses of this calculation method is to assess the effect of reservoir and proc-cess variables on the stimulation response. This paper contains results of several studies made of key reservoir and process parameters. Among the most important of these is the influence of prior wellbore permeability damage. If a well is severely damaged prior to stimulation, a higher stimulation response will be observed than if it is undamaged. If a portion of this damage is removed, a permanent rate improvement will occur. THEORY I)ES(:KJJ&apos;TION OF CALCULATION METHOD The process of cyclic steam stimulation is essentially one of reducing oil viscosity around the wellbore by heating for a limited distance out into the formation through the injection of steam. Suitable modifications of the calculation technique presented here can be made so that stimulation of wells by hot gas injection or in situ combustion can also be calculated. A schematic drawing of the heat transfer and fluid flow considerations included in the calculation method is shown in Fig. 1. In brief, the calculation assumes that the oil sand is uniformly and radially invaded by injected steam. For wells producing from several sands, each sand is assumed to be invaded to the same distance radially. In calculating the radius heated rn energy losses from the wellbore and conduction to impermeable rock adjacent to the producing sands are taken into account. After steam injection is stopped, heat conduction continues and oil sands with r < ra cool as previously unheated shale and oil sand at r > r, begin to warm. The effect of warming of oil sand out beyond r, has little effect on the oil production rate compared to the effect of cooling of the oil sand nearer the wellbore than ra. Thus, in computing the oil production rate, an idealized step function temperature distribution in the reservoir is assumed where the original temperature exists for r > rn and where an average elevated temperature exists for r < rn. The average temperature in the oil sand for the region r < rn is computed as a function of

Jan 1, 1967