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By R. W. Fountain, John Chipman

The solubility of nitrogen in Fe-B alloys (0.001 to 0.91 pet B) is determined by the Sieverts' technique for temperatures of 950° to 1150°C. The activity coefficient of nitrogen is decreased by boron. The three-phase equilibrium between ? iron, BN, and gas is established and also the four-phase equilibrium between iron, BN, Fe2B, and gas. The above equilibria are calculated for a iron. The relation of these data to hardenability and strain aging of boron-treated steels is discussed. BORON additions are known to enhanbe the hardenability of heat-treatable steels and to assist in the control of strain aging in sheet steel for deep drawing. The increase in hardenability is explained by the theory that adsorption of boron on austenite grain boundaries reduces their free energy and thus retards ferrite and upper bainite nucleation.l,2 Digges and Reinhart3 have shown that the full effectiveness of boron in commercial steels is achieved only when strong nitride formers such as titanium and zirconium are also present. The influence of nitrogen on eliminating the boron contribution to hardenability was also demonstrated by Shyne and Morgan.4 These workers prepared Ni-Mo steels containing either nitrogen or boron or nitrogen plus boron. The nitrogen-plus-boron steels showed the lowest hardenability which was attributed to the presence of stable nucleating particles, presumably nitride. Morgan and Shyne5-7 have shown that boron in the amount of 0.007 pet will completely eliminate strain aging due to nitrogen in low-carbon, open-hearth steels. In addition, by proper control of the boron additions, a rimming steel can be produced. Since the effectiveness of boron on hardenability and eliminating strain aging is influenced by the amount and distribution of the nitrogen in the steel, the present study was. undertaken to determine the influence of boron on the solubility of nitrogen in iron. EXPERIMENTAL PROCEDURE The solubility of nitrogen in Fe-B alloys was measured by the method of Sieverts, which consists of determining the amount of gas dissolved by the metal in a constant volume system. The apparatus employed in this investigation and the experimental details have beendescribed previously.B AMcLeodgage was added to the apparatus to allow measurements at very low pressures. The alloys were melted at reduced pressure in a basic-lined induction furnace using electrolytic iron and ferroboron. Ferroboron was added after the primary deoxidation of the iron with carbon. Since it was difficult to attain a constant low level of oxygen by this procedure, silicon was added after the carbon deoxidation and prior to the ferr obor on addition. The alloys were castas 2-in. sq ingots, heated in argon at 1050loC, and forged to 1/4-in. plate. After forging, 1116 in. was machined from each side of the plate to remove any possible contamination, and it was then cold-rolled to 0.010-in. sheet. The sheet was cut into approximately 1/4-in. squares and pickled in an inhibited H2SO4 solution to ensure a clean surface. In the case of the boron alloys, a hydrogen treatment could not be used for surface cleaning because boron losses resulted. The composition of the alloys is given in Table I. For a solubility determination, a 75-g sample was inserted in a quartz tube and sealed in place in the apparatus. The entire system was evacuated at room temperature and leak tested for 24 hr. If no leaks were observed, the system was heated to the temperature of measurement and again leak tested for 24 hr. If no leaks were detected, the hot volume and solubility determinations were begun. The hot volume was determined at a constant temperature for each run by admitting successive amounts of argon and recording pressure vs volume, which, in all cases, resulted in a straightline relationship. The argon was then removed and the procedure repeated with nitrogen. Successive additions were made until the desired nitrogen content of the metal and equilibrium pressure of the system were obtained. The

Jan 1, 1962

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.'-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.' Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By L. M. Pidgeon, K. T. Aust

There has been considerable interest in the possible use of titanium in magnesium alloys.' Zirconium has shown some promise in this connection2 and its general similarity with titanium suggests that the latter might act in a similar manner. A literature survey revealed that quantitative data on the Mg-Ti system was unavailable. Several patents3 have claimed that titanium additions from 0.2 to 4 pct to magnesium alloys were possible, but no mention was made as to the form in which the titanium existed in the alloy. Kro114 succeeded in introducing only traces of titanium into magnesium by bubbling TiCl4 through the metal under argon or by reacting it with sodium titanium fluoride. The application of theoretical data given by Carapella5 based on Hume-Rothery's principles, involving atomic size factor, crystal structure, valency and the electro-chemical factor, suggests that a Mg-Ti alloy is a favorable case, and the system appeared to warrant experimental examination. Experimental Procedure and Results THERMAL ANALYSIS If titanium is appreciably soluble in magnesium, a change in the melting point of the magnesium might be detectable using standard cooling curve methods. Magnesium was melted in graphite crucibles under an argon atmosphere, the assembly being enclosed in a silica tube. Graphite thermocouple protection tubes served also to stir the melts. The apparatus was very similar to Fig 1, with the addition of a refractory and baffle system to prevent undue heat losses from the top of the crucible. Chromel-alumel thermocouples were calibrated using Al of 99.97 pct purity. Dominion Magnesium Limited sup- plied redistilled high purity magnesium of the analysis given above. Titanium was added in three different forms: 1. Titanium powder —100 mesh, from the Titanium Alloy Manufacturing Co., Niagara Falls, N. Y. 2. Sheet titanium from the U.S. Bureau of Mines, produced by Mg reduction of TiCl4. 3. Magnesium —50 pct titanium master alloy from Metal Hydrides Inc., Beverly, Mass. The melting point of the high purity magnesium used was measured experimentally as 651.0°C. More than a dozen tests were conducted using titanium from the three sources referred to above, in calculated additions up to 20 pct titanium, at temperatures between the melting point and 1000°C and holding periods up to 6 hr. In no case was evidence obtained of solubility of titanium in magnesium, using inverse-rate and time-temperature curves. The melting point of the magnesium was unchanged within the accuracy of measurement, namely -+0.5°C; and no other thermal arrests were detected. Metallographic investigation of the thermal analysis billets indicated that the titanium additions were apparently mechanically entrapped in the magnesium in segregated areas. Consequently, these samples were not analyzed for titanium. The master alloy proved to be a mechanical mixture of titanium particles in a magne- sium matrix. These results indicated that the titanium solubility, if such existed, could not be obtained by the usual thermal methods. X RAY DIFFRACTION INVESTIGATION In an effort to detect solubility of titanium in magnesium, samples were investigated using both the Debye-Scherrer and the Focusing Back-Reflection methods. Filings from samples of the thermal analysis billets and from pure magnesium were annealed in argon one hour at 350°C to relieve mechanical strain. Measurements made of the interplanar spacings showed no difference between the Mg-Ti samples and pure magnesium. The interplanar spacings could be measured to within 0.0002A, and the greatest variation found was 0.0004A, in the back-reflection method. The diffraction lines for magnesium were not shifted by the titanium additions indicating that the solid solubility of titanium in magnesium is of a very low order—less than 0.5 pct. From both diffraction methods, a d or interplanar spacing of 0.817A was obtained for the redistilled high purity magnesium. This latter value is not given in the standard X ray diffraction cards for magnesium metal or vacuum distilled magnesium. Theoretical calculations for a close-packed hexagonal space lattice for magnesium indicate that the planes {2134) should give a line which was found. The relative intensity for this reflection at 0.817A is slightly less than that at 0.870k for magnesium. SOLUBILITY OF TITANIUM IN LIQUID MAGNESIUM The Mg-Mn system was examined by Grogan and Haughton6 who were

Jan 1, 1950

By J. J. Gilman

Examination showed that characteristic cleavage step patterns are observed on the cleavage surfaces of undeformed, slipped, bent, twinned, compressed, and indented zinc crystals; and the effect of temperature is discussed. Dimples were seen to produce cleavage steps in a treelike pattern in otherwise undeformed crystals. The steps seem to originate when cracks intersect screw dislocations. IT has been known for a long time that the path of fracture in polycrystals may be discontinuous (see Jaffe, Reed, and Mannl for review). Recently, Kies, Sullivan, and Irwin2 have proposed, and given evidence, that crack propagation is discontinuous within individual crystals as well. Other evidence has been given by Low.' When discontinuous cracks within a crystal join together to make a macrocrack, the lamellae between each set of two cracks are torn somewhere, forming small cliffs. These cliffs appear as lines when the cleavage surface is observed microscopically.4,5 The lines have been called vein, tree, and riverlike markings by various authors, and they have sometimes been mistaken for fissures. The descriptive term cleavage steps is used in this paper. Cleavage steps vary in height over a wide range of values, from molecular dimensionsG to lor. and larger. Kies, Sullivan, and Irwin,2 as well as George,' have shown that the gross cleavage step patterns for plastics, polycrystalline metals, and for mono-crystals are sometimes similar. Thus, they depend mostly on the mechanical variables that prevail during cleavage and are relatively insensitive to the structure of the material. For example, parabolic markings2,7,8 sometimes result when cracks open up ahead of, and not coplanar with, the main crack front. If the advance crack has the same velocity as the main crack, their intersection line is a parabola, otherwise it is a hyperbola or an ellipse. The patterns are strongly affected by differences in crack velocities. This results in chevron patterns which point to the place of origin of the main crack. It is the purpose of this paper to demonstrate the existence of a mechanism of cleavage step formation which is a continuous rather than a discontinuous process. Also, certain characteristic step patterns are described, and the strong effect of temperature is shown. The specimens were zinc monocrystals (grown from 99.999+ pct pure metal). These were cleaved at room temperature and at — 196°C. Results and Discussion Cleavage step patterns are highly variable from point to point on a given specimen, as well as from one specimen to another. Although the patterns shown in the photographs are typical, they have been selected for graphic illustration. Figs. la and lb compare undeformed crystals that were cleaved at —196 °C and room temperature, respectively. Cleavage at room temperature (Fig. lb) resulted in a higher density of high steps (dark black lines) and enhanced the visibility of the fine background markings. Deformation by simple slip caused no marked change in the step patterns until the glide strain reached about 1.0. But, as Fig. lc shows, the density of high cleavage steps was greatly increased by large glide strains. Corrugations lying perpendicular to the slip direction may also be seen in Fig. lc. These are caused by deformation bands. The cleavage resistance of the crystal of Fig. lc was very high compared to undeformed crystals (estimated by the force on a needle required for cleavage). Striking and varied cleavage step patterns were observed on bent crystals. Two characteristic patterns that were observed on crystals bent at 25°C, and cleaved by reverse bending at —196°C, are shown in Figs. 2a and 2b. The first, Fig. 2a, consists of V-shaped lines similar to the parabolas of other materials2,7 Fig. 2b shows a pattern that is the equivalent of Fig. la, consisting of faint background lines with a few higher step markings. Cleavage of bent crystals at room temperature resulted in Figs. 2c and 2d. Now, the cleavage step lines show a strong tendency to follow one of two perpendicular paths. In Fig. 2c (bent once), many of the cleavage step components that lie parallel to the bend axis are assembled into irregular lines. In Fig. 2d (bent twice), the cleavage steps again tend to consist of two perpendicular components, but neither of the components is assembled into lines. Also, the step density is higher.

Jan 1, 1956

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 Eugene A. Thiers, William V. Morris

INTRODUCTION Direct reduction processes reduce the various commercial forms of iron oxide (pellets, concentrate, fines, etc.) to metallic iron at temperatures lower than that of molten iron. Thus, this technology includes practically, all iron reduction processes other than blast furnaces and electric pig iron furnaces (whose output in terms of world production is negligible). The product of these processes which is known as direct reduced iron (DRI), or sponge iron, is primarily used as a source of metallic iron in steel-making operations. Interest in DRI, which has been significant since the early 1960s, increased significantly in recent years with the rapid growth of DRI installed capacity throughout the world. The importance of the subject for the Circum-Pacific region stems directly from the influence that DRI has on iron ore consumption and on future steel development for this region. Although there is widespread agreement that electric furnaces will continue to increase their share of global steel output, and especially so in the countries of the Pacific Steel community, some doubts exist about future scrap supplies being adequate to support growth at past rates. The authors believe that such doubts are soundly based. As this paper points out, the total supply of all metallics used in electric furnaces may not be adequate to support the extrapolated rapid growth in electric furnace steel production. This paper seeks to provide perspective on the global and Circum-Pacific prospects for DRI in light of recent energy price developments and the current recession. In this regard, the demand for DRI within the context of recent evolutionary patterns in steel-making, the outlook of DRI supply in terms of prevailing production costs, and the prospects of new technology are discussed. THE DEMAND FOR DRI Although several reports published in the last 10 years predict high rates of growth in DRI, the subject remains a controversial one. Significant growth has indeed occurred, but not to the extent anticipated in the studies summarized in Table 1. The substantial difference between previous expectations and present reality can be ascribed primarily to: (1) lower growth in steel production than formerly anticipated; (2) numerous cancellations of DRI facilities that were previously announced; and (3) a fundamental and probably irreversible change in the economics of DRI production. Note that DRI capacity at the end of 1980 was about 16 million tonnes, a significantly lower figure than any of the projections above. In addition, DRI production was only about half of capacity, reflecting the abnormally low rates of capacity utilization in this industry. [ ] Before examining the current outlook in steel, it is pertinent to note that the market for DRI is usually different in the industrialized countries of the West from that in developing countries. In the former, the available infrastructure and industry's diversification extends DRI's potential markets to numerous steelmaking, foundry, and other industrial applications, although competition from scrap and other forms of metallic iron is constant. Scrap is generally available in these countries and, therefore, DRI competes with it in electric furnace steelmaking, basic oxygen steelmaking (as a coolant), cupola foundry operations, or as an additive in the metallic charge for open hearth and blast furnaces. On the other hand, DRI in developing countries is often allocated exclusively to domestic electric furnace steelmaking or, when capacity exceeds domestic captive requirements, to export. Notwithstanding quality considerations, DRI is being and is likely to continue to be used predominantly as a source of metallics in iron and steel-making. Other uses of DRI, such as in copper cementation represent a marginal market in terms of overall tonnage and can be ignored at this point. Therefore, DRI demand is-determined by the overall availability of metallic scrap in its various forms--a function of steel production and its probable evolution. The Global Steel Outlook Given the present recession, an objective appraisal of the long-term outlook for steel is particularly difficult. On the one hand, historical trends and, especially, the inertial forces associated with such a basic industry as steel must be recognized; such trends suggest that the current stagnation with

Jan 1, 1982

By C. Law McCabe, R. G. Hudson

The Knudsen cell has been employed to determine the free energy of formation of Mn7Cs in the temperature range 800" to 950°C. A value of 66,440 cal was found for hH°o for a-manganese. Measurements of the pressure of manganese over a mixed carbide, (Fe,Mn),C, points to a power relationship between aun7cs and N.4,. RECENTLY Kuo and Perssonl have reported that the carbide of manganese which is in equilibrium with graphite at temperatures up to 1100° C is Mn7Ca. There are no published data on the thermo-dynamic properties of this compound. In order to determine the stability of Mn7Ca, it appeared that, by obtaining the pressure of manganese above 8-manganese and also above Mn,C, in equilibrium with graphite, the free energy of formation of Mn7Ca from 8-manganese and graphite could be obtained. In addition, the vapor pressure of manganese, reported by Kelley From data of Bauer and Brunner,' is subject to some uncertainty and further determinations of the vapor pressure of manganese seemed warranted. In this investigation of the pressure of manganese vapor above pure manganese and also above the carbide of manganese in equilibrium with graphite the apparatus used is the Knudsen orifice cell. The same apparatus, experimental procedure, and method of calculating the pressure was used in this investigation as in one previously reported.~ Care was taken to insure that the cells were at constant weight before using them in a run. The manganese charged in the cell was CP grade powder, carbon free, obtained from the Fisher Scientific Co. A spectroscopic analysis of the manganese after appreciable amounts of it had vaporized from the Knudsen cell showed that no element was present in sufficient quantities to contribute to a weighable weight loss or to decrease the vapor pressure of manganese to any appreciable extent. The spectro-graphic analysis was 0.002 pct Cu, 0.05 pct Fe, 0.002 pct Pb, and 0.002 pct Ni. 8-manganesea is the allo-tropic form of manganese which was present in the cell at temperatures used in this investigation. The manganese carbide, Mn,Ca, was made in the following way: In a closed graphite cell manganese powder was added to graphite powder, which was made from graphite rods for spectrographic use. The manganese powder was the same as that described previously; 5 pct excess graphite was added over that required for the formation of Mn7C,. The mixture was heated in a closed graphite cell for approximately 20 hr at 1350°K under vacuum. X-ray analysis revealed that there was no manganese present after this treatment, but that the lines due to Mn,C, were present. In order to prove that there was no volatile carbide of manganese which was effusing out of the cell, the following experiment was performed: A graphite effusion cell containing graphite power, in excess of that to form Mn,C, of a desired amount, was brought to constant weight on heating at 1228°K. The required amount of manganese was accurately weighed and then added to the graphite effusion cell. The cell was placed in a vacuum at 1228°K for one week, which was the time calculated for the manganese to have effused completely, assuming instantaneous formation of Mn,C8. The cell was then weighed again. This experiment was carried out on two different occasions and both times the weight loss of the cell came within 1 pct of the weight of manganese originally charged minus the weight of manganese left in the cell, as determined by chemical analysis. These data are summarized in Table I. This agreement is considered to be within experimental error and is taken as proof that no carbide of manganese is volatile in this temperature range. It was established, by X-ray analysis, that Mn,C, formed before appreciable amounts of manganese vaporized from the metal powder which was charged. The identification of the carbide of manganese which was present in the Knudsen cell in equilibrium with graphite and manganese vapor was carried out by Kehsin Kuo at the University of Uppsala. He established that the authors' sample, which was submitted to him for analysis, contained the phase

Jan 1, 1958

By G. Pizzi, G. M. Ciucci, G. L. Chierici

The use of the material balance equation to estimate the volume of hydrocarbons originally present in a reservoir, whose producing mechanism is partly due to water drive, has been discussed in the literature by several authors. There is no general agreement upon the possibility of obtaining reliable results by this method. Gas reservoirs in contact with an active aquifer are considered in this paper. Theoretical considerations based on the cybernetic principle of uncertainty (which states that the internal structure of a system cannot be uniquely determined from its observed external behavior) lead to the conclusion that the volume of gas originally present in a reservoir of this type cannot be uniquely determined from its past history. The range of values which encompasses the actual value of the reserves varies from case to case and must be determined by either numerical or analogical methods. Results obtained for six gas fields are reported. All these fields were produced with small fluctuations in their production rates, as is common practice for gas reservoirs; no gas storage fields were considered. Results obtained show that reserves values in a range of 1 to 2, associated with appropriate aquifers, allow the matching of the reservoir past history with mean-square deviations less than the experimental errors involved in pressure and produclion measurements. Similar results have been found in several other partial water drive gas reservoirs. From these results it is concluded that gas reserves cannot be uniquely determined from the past performance of partial water drive reservoirs, at least in cases where the reservoir has been submitted to small fluctuations in the production rates, and pressure data of normal accuracy are available. INTRODUCTION A number of authors have analyzed the problem of estimating the reserves originally present in a partial water drive reservoir from its past pressure-production performance. Literature which deals with this subject can be grouped, according to their conclusions, as follows. 1. A reliable value for the reserves can be obtained even if reservoir data (pressure and cumulative production) are affected by errors within the normal range.'-' 2. A reliable value for the reserves can be obtained only if reservoir data are very accurate'- or if past production performance has been subjected to abrupt variations in the production rate."' 3. No unique value for the reserves can be obtained from reservoir past production performance. This conclusion has been based upon theoretical considerations" and verified in several field cases. The purpose of this paper, which deals only with partial water drive gas reservoirs, is to test the above conclusions against actual field cases. Some theoretical considerations on this problem are also presented. THEORETICAL CONSIDERATIONS As the behavior of a gas reservoir communicating with an aquifer depends on both the aquifer and the reservoir characteristics, the physical system to be studied is the combined gas reservoir plus aquifer. The information which is available for studying the performance of such a system is the well production rates and bottom-hole pressures, all given as functions of time. The external behavior of the reservoir-aquifer system is therefore described by 2n input variables (Gp, Wp,) and n output variables (p,), n being the number of wells in the reservoir. In reservoir engineering it is common practice to consider the reservoir as a whole, disregarding the internal distribution of pressures and of producing wells. This practice is equivalent to substituting the above multi-variable system with a single-variable system, where the average reservoir pressure is the only output variable and the cumulative production G,(t) and W,(t) are the input variables. The internal structure of such a system, defined by initial gas reserves G, aquifer shape and dimensions, boundary conditions and petrophysical parameters distribution throughout the aquifer, is unknown. Therefore, from a cybernetic point of view the system is a "black-box It has been demonstrated" that for a blackbox the indetermination principle holds. Accordingly, the number of different internal structures (or set of parameters) which can account for the observed external behavior is infinite. As a consequence, the initial reserves cannot be uniquely determined from the reservoir past performance. When W,(t) is known, the determination of G from

By W. G. Pfann

The simultaneous segregation of two solutes during the directional solidification of an ingot is treated mathematically on the basis of simplifying assumptions. Expressions are derived for the difference in concentration of two solutes, and for the location and concentration gradient of a pn barrier formed in a semiconductor by the segregation of a donor and an acceptor. THE problem of normal segregation of a single solute during the freezing of an alloy has been treated mathematically by a number of investigators. Gulliver' showed that coring increases the quantity of eutectic above that to be expected at equilibrium, for a system having limited solid solubility and, on the basis of simplifying assumptions, calculated the fraction of eutectic to be expected. Scheuer2 expressed composition of solid solution in terms of a distribution coefficient and the fraction solidified and compared experiment with calculation for the systems A1-Cu, Al-Zn, Cu-Sn, Cu-Zn. Hayes and Chipman,3 in a detailed study of segregation in a low carbon, rimming steel ingot, calculated distribution coefficients for a number of solutes in iron, compared calculated and experimental segregation curves, and discussed the effects of process variables such as rate of solidification and stirring. In the present paper a mathematical analysis is made of the simultaneous segregation of two solutes during the orderly freezing of a solid solution system, with particular emphasis on the difference in solute concentrations. Although the analysis is quite general and can be applied to the segregation of minor elements in alloys, it is directed in particular at the solidification of a semiconductor containing a donor and an acceptor. Normal segregation has unique aspects in a semiconductor, because of the ways in which donors and acceptors affect the electrical properties. The difference between two solute concentrations becomes of importance, as does also the gradient of the difference where the difference goes through zero, this being the concentration gradient of excess carriers at a pn barrier. A primary object of this paper is to extend the mathematical treatment of segregation to include these newer aspects which are of particular significance for semiconductors. One property of interest is the electrical conduc- tivity, which arises from the presence of donors 'or acceptors in solid solution. The conductivity may be either n-type or p-type depending on whether donors or acceptors, respectively, are in atomic excess. For both germanium and silicon, elements of Group V of the Periodic System, such as P, As, and Sb, are donors and elements of Group 111, as B, Al, In, and Ga, are acceptors.4-6 If a donor or acceptor is present alone in solid solution, the conductivity is proportional to its concentration." If both a donor and an acceptor are present, then the conductivity is proportional to the difference in their atomic concentrations. If the donor and acceptor segregate at different rates then a pn barrier in certain circumstances may form at some point in the ingot. Accordingly, equations are derived and illustrated which express the effect of segregation on: 1—the concentration of a single solute with a discussion of the assumptions; 2—the difference between two solute concentrations and means for minimizing its variation in an ingot; and 3—the location and concentration gradient of a pn barrier. The analysis is applicable to processes in which the entire charge is melted and then progressively frozen from one end. The method in which an ingot is solidified in a crucible7 and that in which a solidifying rod is pulled from the melt8 both fall into this category. Segregation of One Solute If a cylinder of molten alloy is caused to freeze slowly from one end, a normal segregation of solutes will usually occur, producing a lengthwise concentration gradient in the ingot. Depending on whether a solute raises or lowers the melting point of the solvent, it will become concentrated in the first or last regions, respectively, to freeze. If it is assumed that freezing is such that there is no diffusion of solute in the solid, complete diffusion in the liquid, and that k, the distribution coefficient, defined as the ratio of solute concentration in the just-freezing solid to that in the liquid, is constant, then the

Jan 1, 1953

By P. R. Gage, R. W. Bartlett

At high temperatues and reduced oxygen pressuves, molybdenum silicicles oxidize to form SiO(g) vathev than a passivating SiO2 film. This is a sevious problem for low-pressure applications of sili-cide-coated rejvactory tnetals. As oxiclalion pvoceeds, the higher oxidntion potential of silicon initially suppresses oxidation of molybdenum and silicon is depleted near the surface. Eventually, silicon depletion causes secondary passivation (SiO2) mid an active to passiue transition in oxidntion behavior at moderately low pressures. At very low pressures, silicon depletion continues until steady-state oxidation of both silicon and rnolyhdenum can proceed at rates propovtional to their initial stoicliiorrzetvies. Ohsel-vations of 'oxidatiou-rate belzcriliov at temperatures from 1101° to 1700°C and oxygen pressures from 10-7 to 1 at in were made using thermogravimetn'c, X-ray diffraction, and elect?*on-rtric?ro/,vobe techniqrres. The experimental results are in good agreement with calculated lirnits for the various types of behavior that were based on tlievtnochernicnl atzd dffusion rate data for the Mo-Si system. A protective oxide film normally forms during the oxidation of elemental silicon. However, at elevated temperatures and reduced pressures this film is not present and oxidation is rapid. wagnerl has shown that this behavior occurs because SiO(g) is more stable than SiO2. The behavior of the silicides at high temperatures is similar but more complicated. Molybdenum and several silicide compounds are involved and the chemical activity of silicon, or the equivalent silicon vapor pressure, can vary considerably in these phases. Also, diffusion in the silicides resulting from reactions in which a higher silicide is reduced to a lower silicide, or molybdenum containing dissolved silicon, must be considered. EXPERIMENTAL AND ANALYTICAL METHODS Isothermal oxidation experiments were conducted using hot-pressed MoSi2 and Mo5Si3 wafers. Each experiment was conducted at a fixed oxygen pressure by controlling the flow of oxygen in and out of the furnace chamber. Most of the experiments were conducted in a molybdenum-wound tube furnace. Special construction features, including use of a high-purity dense A12O3 refractory tube, permitted operation in high vacuum to 1500°C. Higher temperatures could be obtained at higher working pressures and with a sacrifice of tube lifetime. Temperature was measured with three Pt 6 pct Rh/Pt 30 pct Rh thermocouples and controlled with a proportional controller. Weight changes were monitored with a quartz spring balance. The few experiments, at higher temperatures and low pressures, were conducted in a cold wall vacuum chamber using induction heating with direct susceptance of the sample. Because of the variable levitation effect of the induction coil on the sample, weight changes could not be monitored continuously in these experiments. All samples representing both experimental methods were weighed before and after oxidiation and examined with a microscope and analyzed by X-ray diffraction. The analytical treatment assumes equilibrium at interfaces and uses existing thermodynamic data. For convenience, equilibria are expressed as chemical potentials or as vapor pressures of the gases involved. The resulting differences in equilibrium vapor pressure between adjacent interfaces and between the surface and external atmosphere drive diffusion processes in the solid and gas boundary film, respectively. These diffusion processes govern the rate of oxidation. A bibliography of the sources of thermochemical data for the reactions pertinent to the Mo-Si-O system is given in Table I. Reactions are listed with the sources of free-energy data referenced. Since all of these reactions involve one or more gas species, usually oxygen, a plot of the product-gas chemical potential, -RT In Pg, vs absolute temperature for each reaction is given in Fig. 1. These curves can be used to determine equilibrium vapor pressures or to compare the stability of different compounds in the various gases: O2, Si, SiO, and Moo3,. The data of Table I and Fig. 1 were used to determine the analytical results presented in this paper. EXPERIMENTAL RESULTS The weight changes for three MoSi, samples oxidized at 1500°C are plotted against time in Fig. 2. The treatments were identical except for the indicated variance of oxygen pressure and each curve represents one of three characteristic types of behavior that were observed. The upper curve is an example of passive oxidation, which is defined as

Jan 1, 1965

By J. M. Uys, T. B. King

The solubility of water in silicate melts of various compositions was measured. The basicity of the silicate did not appreciably affect the water solu-bulity at low-base content (acid compositions). Near the orthosilicate composition the solubility increased with basicity for silicates in which the cation displayed a weak ion-oxygen attraction and apparently decreased for those in which the cation showed a strong ion-oxygen attraction; metasilicates of the former class dissolved more water than those of the latter. Temperature had little effect on water solubility. The experimental results are interpreted on the basis of two modes of solution, the contribution of one decreasing, and that of the other increas -ing, with increased melt basicity. In the former, solution occurs through interaction with doubly-bonded oxygen atoms and in the latter, through interaction with singly-bonded oxygen atoms, or, in very basic melts, through reaction with free oxygen ions. THE hydrogen content of a steel melt is in a large measure determined by water dissolved in the slag. In some glasses water may be a major cause of "seeds". Water vapor in the furnace atmosphere is the primary source in both instances. A knowledge of the mechanism of water solution in silicate melts should help in assessment of practical methods for its control in steelmaking and glass refining. Walsh et a1.l measured the water content, expressed as hydrogen, of 40 pct lime-20 pct alumina-40 pct silica and 62 pct manganese oxide-38 pct silica melts as a function of the steam partial pressure, in equilibrium with the melt. Tomlinson 2 and, also, Russell3 investigated this relationship for a molten 30 pct soda-70 pct silica glass. In all three investigations, the solubility of water was found to be proportional to the square root of the partial pressure of steam. Moulson and Roberts 4 confirmed this relationship for a silica glass. On the basis of the square root relationship, Tomlinson2 and Russell3 interpreted the solution reaction as "network-breaking", similar to that expected on the addition of metal oxides to silica. Walsh et al.' postulated two possible modes of solution, one the mechanism suggested by Tomlinson and Russell and the other the reaction of the water molecule with an oxygen ion to form hydroxyl ions. These two modes of solution suggest opposite effects of melt basicity on water solubility. However, little appears to be known about the effect of melt basicity on water solubility. Walsh et a1.l found, in the lime-silica system, that the water content increased slightly with increased basicity. As these authors pointed out, this does not appear to be in accord with their further observation that slags containing little or no silica dissolve very little water. Kurkjian and Russell5 measured the effect of basicity on water solubility in alkali silicates in the composition range 15 to 45 mole pct alkali oxide. They found a minimum in the water content at about 25 mole pct alkali. This was interpreted on the basis of two concurrent solution reacZions; one in which solubility was proportional to the activity of doubly-bonded oxygen and, in the other, proportional to the activity of singly-bonded oxygen. The present work was aimed at establishing the effect of basicity on water solubility in silicate melts over as wide a range of compositions as practical. APPARATUS AND EXPERIMENTAL PROCEDURE The silicate melt was equilibrated with a "carrier-gas" of accurately known water content, quenched, and analyzed for water by a vacuum fusion technique. Some pertinent details of the equilibration procedure, analysis technique, preparation, and handling of the silicates are given below. Gas-Silicate Equilibration. The apparatus used to equilibrate the melt with the gas mixture was similar to that used by Walsh et al.' but with some important modifications.6 Purification trains were provided for nitrogen and hydrogen; whenever air or oxygen was used as carrier gas the nitrogen purifiCation train was used with the copper furnace at room temperature. Gas flow rates were measured with capillary flow meters; bleeders filled with a mixture of dibromo and tribromo ethyl benzene (density about 2 g per cc) were used for convenience in controlling flow rates.

Jan 1, 1963

By E. S. Machlin

An extension of the thermodynamic theory has been made for the case of irreversible growth processes occurring by the motion of an interface. The theory is applicable to such diverse phenomena as diffusion, growth in recrystallization, continuous grain growth, growth of carbides, etc., growth of eutectoid products, growth in solidification, recovery, "slipless" flow, etc. THE publication of a recent book1 has served to focus attention on a very powerful means of treating certain irreversible processes. This method which has been formally described as the thermodynamic theory of irreversible processes is applicable to processes which involve an approach to equilibrium and for which the deviations from equilibrium are small. The irreversible processes can be classified into three groups: chemical reactions, transport processes (diffusion, heat and electrical flows), and relaxation phenomena involving a degradation of internal energy to more stable states. The limits of applicability of the theory can be precisely defined1,2 for each type of irreversible process. For example, in a chemical reaction at constant temperature and pressure, the Gibbs free energy released per mol in the process should be less than the thermal energy, RT. Another type of irreversible process, which sometimes involves a combination of the first two of the above-mentioned groups, is treated in this paper. This process is one characterized by the motion of an interface separating two regions having different values of free energy and may be briefly described as a growth process. Prigogine2 and Herring3 have treated special cases of this type of process. Previous conscious applications of the theory in metallurgy have been limited to the field of diffusion, one of the transport processes. Darken,4 Bardeen,5 Prigogine2 and others have made significant contributions in this respect. Some other applications of the theory are described in this paper. The Theory The thermodynamic theory of irreversible processes is based on the work of Onsager,6 DeDonder,7 Prigogine2 and others. A resume of the theory has been given by Prigogine2 and DeGroot.1 A brief description of the theory follows, although for a complete understanding the reader is urged to read the references. It is first assumed that the change in entropy, even for a system removed from equilibrium, is given by dS = [dU + pdV - Si µi, dn, - Sk Pk dxk]T-1 Using this expression, the irreversible entropy production in the system is calculated by subtracting the contribution to the change in entropy of the system by transfer of heat, work, or matter from the surroundings. Thus, for example, the irreversible entropy production of a system at constant temperature and pressure is given by dtS = — — dG (DeDonder7) Now it has been shown by Prigogine,2 DeDonder,7 and DeGroot1 that the rate of irreversible entropy production diS/dt, when calculated in the manner suggested, can be written as a sum of products of conjugate forces XK and fluxes Jk, i.e., d,s/ = Sk Jk Xk [I-1] dt The assumption is next made that a linear relation exists between a given flux and the forces, obtained from Eq. I-1, i.e., Ji = Sk Lik Xk (i = 1, 2, . . . n) [I-2] Generally, there is a degree of freedom in choice of the fluxes and forces. However, for all the choices consistent with Eq. I-1 the Onsager8 relations, based on the principle of microscopic reversibility, namely, Lik = Lki, are valid. The coefficients Lik, depending upon the choice of the conjugate fluxes and forces, may be more or less dependent upon the parameters defining the state of the system. In general, the proper choice of fluxes and forces utilizing Eq. I-1, makes the coefficients Lik independent of time. Also, because many of the three classes of irreversible phenomena have already been treated,1,2 a proper choice can be made by analogy. In any case, the validity of Eq. 1-2, from whatever choice made using Eq. I-1, must be tested by experimentation. The theory, thus, comprises the following steps: 1—The irreversible entropy production is calculated to yield Eq. I-1. 2—The terms in Eq. I-1 are grouped

Jan 1, 1954

By T. K. Perkins, L. R. Kern

A study of fluid mechanics, rupture of brittle materials and the theory of elastic deformation of rocks shows that, for a given formation, crack width is essentially controlled by fluid pressure drop in the fracture. Operating conditions which cause high pressure drop along the crack (such as high injection rate and viscous fluids) will result in relatively wide cracks. Conversely, operating conditions which cause low pressure drop (low injection rates and thin fluids) will result in relatively narrow cracks. Charts and equations have been derived which permit the estimation of fracture widths for a variety of flow conditions and for both horizontal and vertical fractures. INTRODUCTION There has been considerable speculation concerning the geometry of hydraulically created fractures in the earth's crust. One of the questions of practical importance is the width of fractures under dynamic conditions, i.e., while the fracture is being created and extended. Such width information could be used, for instance, to help estimate the area of a fracture generated under various conditions. Also, there has been a recent trend toward the use of large propping partiles.13, 15 Therefore is is desirable to know what factors can be varied in order to assure entry of the large particles into the fracture. There has been some work on fracture widths reported in the literature. In particular, there have been several Russian publications dealing with this sub-jeCt.1.31,3 These papers have dealt principally with the elastic theory and the application of this theory to hydraulic fractures. These studies have not led to an engineering method for estimating fracture widths under dynamic conditions. A recent paper3 has reviewed and summarized the Russian concepts. An earlier paper- from our laboratories also discussed the application of the elastic theory to hydraulic fractures. This first approach, based largely on photoelastic studies, has proved to be too simplified to accurately describe the fracturing process. However, these early thoughts have served as a guide during the development of more exact concepts. We would like to present in this paper our current concepts regarding fracture widths and some estimates of hydraulic fracture widths for several conditions. We believe that it is now possible to predict with fair accuracy the factors influencing fracture widths. Furthermore, the method of prediction has been reduced to a simple and convenient graphical or numerical calculation. CRACKS IN A BRITTLE, ELASTIC MATERIAL Many investigators2, 4, 30 have shown that competent rocks behave elastically over some range of stresses. Of course, if the tensile stress imposed upon a rock exceeds some limiting value, then the rock will fail in tension. In similar manner, there are some limiting shear stresses that can be imposed upon rocks. Hubbert and Willis11 have discussed the shear conditions which will lead to failure. Under moderate stress conditions (such as those likely to be encountered when hydraulically fracturing) and when stresses are rapidly applied, relatively, most rocks will fail in a brittle manner. Hence, for this discussion of hydraulic fractures in the earth's crust, we assume the rocks behave as brittle, elastic materials. Let us develop the discussion in the following way. (The following thoughts are applicable only to brittle materials.) 1. First we consider a brittle, elastic system. An energy balance will show the minimum pressure necessary to fracture rock, and from this pressure we calculate the minimum crack width resulting from extension of a hydraulic fracture. 2. Then we will show that, under ordinary fracturing conditions, fracture widths are appreciably greater than the minimum widths of extending fractures. In fact, we will find that crack width is controlled by fluid pressure drop in the fracture. 3. We will discuss pressure drops in fractures and resulting crack widths for various operating conditions and both vertical and horizontal fractures. 4. Finally, we will discuss the significance of these concepts, their relationship to fracturing pressures, etc. First, consider minimum fracture extension pressures. We can shed some light on this question by considering the theory proposed by Griffith7, 8 Yo explain the rupture of brittle, elastic materials. Griffith recognized that solid materials exhibit a surface energy8 (similar to surface tension in a liquid). The fundamental concept of the Griffith theory is that, when cracks spread without the application of external work (in the interior of an elastic medium which is stressed

By R. G. Wheeler, J. W. Goffard

The Larson-Miller parameter was used to correlate time, temperature, and indentation creep of magnesium, aluminum, and some of their alloys. In the temperature range 300" to 450°C, the short-time Meyer hardness of pure magnesium was less than that of the magnesium alloys tested, but for long times the pure magnesium has greater indentation creep resistance. Aluminum (1100 alloy) had 1.5 to 2.5 times more indentation creep resistance than magnesium at 300" and 450oC, respectively. Hardening of aluminum with a dispersion of Al2O3 was effective in the time and temperature ranges studied. New technologies have required the development of new materials and the utilization of the more familiar materials for new and unusual applications. The use of magnesium and aluminum and some of their alloys, because of their desirable nuclear characteristics, light weight, low cost, and ready availability, has been extended to the 300" to 450°C temperature range. In this temperature range the basic consideration of these materials must be their rate of plastic flow rather than offset yield strengths. The indentation testing reported here arose from a need for design data for the load-holding ability of supports made of these materials. Test Procedure—Hardness indents were made with a 0.275-in.-diam quartz indentor and a 10.65-lb load. The indentor was made by fire-polishing a spherical surface on the end of a fused quartz rod. The samples were held at temperature in a graphite crucible controlled to ±2°C. A thermocouple was attached to the sample and test temperatures were recorded. The diameter of the spherical indentation was measured at the end of a test period and the compression stress (Meyer Hardness) was determined by: H___________load__________ m = projected area of indent Samples were 1 in. in diam and at least 1/4 in. thick. It was observed that at the higher temperatures and longer times, the quartz indentor would stick to the magnesium sample. The quartz indentor was, therefore, frequently inspected and fire-polishing repeated when necessary. The area of sticking was always a small fraction of the area of indent and was therefore considered to have an insignificant effect on results. Correlation of Hot-Indentation Test Data with Time-Temperature Parameter—Sherby and Dorn' have correlated creep or tensile data of a' solid solutions of aluminum with a temperature and strain-rate parameter suggested by Zener and Holloman. underwood2 used this parameter to correlate creep properties of some steels with hot hardness, and upon the basis of this correlation a means of obtaining creep properties from short-time (and inexpensive) hot hardness tests has been demonstrated. Since the validity of the correlation of creep properties with a time-temperature parameter and the correlation of creep properties with hot hardness have been shown, it follows that hot hardness may correlate with the time-temperature parameter. The hot-indentation data obtained was expressed as Meyer hardness, and was shown to be time and temperature dependent. Correlation of Meyer hardness, time, and temperature with the parameter was made using the relationship: Hm = Meyer hardness t = time, hours T = absolute temperature, OK K = constant A value for the constant K was calculated by equating In l/t + K/T at different temperatures and times but at the same hardness. The correlation was tested by plotting Hm vs the parameter, In 1/t +K/T. Since materials are being sought which have high hardness at low indentation creep, i.e., a high Meyer hardness for long time at high temperatures, low values of the parameter are ofthe most interest. TEST RESULTS Magnesium—Pure magnesium (99.98 pct) cut from extruded rod was indentation tested perpendicular to the rod axis at temperatures of 300°, 350°, 400°, and 450°C for times ranging from 6 sec to 112 hr. Fig. 1 shows the time dependency of Meyer hardness at the four constant temperatures. Fig. 2 shows the correlation of the Meyer hardness of pure magnesium with the time-temperature parameter using a K of 22,720 in Eq. [I]. At the bottom of Fig. 2, the effect of doubling the time of indentation t2 = 2(t1), on the abscissa for any time is shown graphically. This effect is of constant magnitude. Also shown graphically are the magnitudes of the effects on the

Jan 1, 1960

By Paul G. Shewmon

The migration of slightly solzrhle spherical particles through a solid under the infllrence of a temperature gradient is analylzed for the cases of various transport mechanisms. It is shown that the variation of the velocity of the particles with radius, r, depends on the dominant mechanism of matter transport around or through the inclusion. Thus the velocity varies as r-1 jor surface-dijf1~sion controlled migratzon. is independent of r for volume diffusion in either phase, and varies as if the rate is determined by an interfacial reaction (n is the order of the interfacia1 reaction). These same results hold tor the migration of a cvlinder of length much greater than its radius. and .for other types of potential gradients, e.g., an electrical field. These equations are combined with recent electron-microscopic ohservations to show that the rate of migratzolz of small helium-silled bubbles through copper is determined by surface diffusion of the metal atoms. With these equations and the temperature gradients attainahle in an electron-microscope joil, the dominant transpar/ mechanism (or any migrating pnrtzclos can he determined. AS a result of fission, rare-gas atoms are created in the hot fuel element of a nuclear reactor. These insoluble atoms precipitate to form bubbles of the gas in the fuel. The subsequent migration and coalescence of these bubbles is thought to play a dominant role in the swelling of fuel elements which in turn can limit the fuel-element life. As a result of this practical problem and because of the relative simplicity of the system, workers in several laboratories have imbedded rare-gas atoms in metals with the aid of an accelerator and studied the formation and behavior of the bubbles that form on annealing. Recently Barnes and Mazey have studied the migration of such helium-filled bubbles in copper foils using the electron microscope and the temperature gradient that can be induced in the foil by the electron beam. They found that the smaller bubbles moved faster than the larger ones. It is shown below that, if this is true, the rate-controlling step in their migration is surface diffusion of metal atoms instead of volume diffusion, vapor transport, or an interfacial reaction. The analysis given is in no way limited to gaseous inclusions so the variation of velocity with particle size for any relatively insoluble precipitate particles could be used to obtain information about the relative importance of surface diffusion, volume diffusion, and interfacial reaction in such two-phase systems. VOID MIGRATION IN A TEMPERATURE-GRADIENT ANALYSIS Barnes' studies indicate that helium does not dissolve or diffuse in metals to a measurable extent, so that when the voids move they must do so through the movement of metal atoms from the leading to the trailing sides of the void.' Thus voids might move by surface diffusion, diffusion of vacancies in the surrounding lattice, or vapor transport. We consider first the case of flow by surface diffusion alone. We assume that there is a force, in the sense of irreversible thermodynamics, tending to move the atoms around the bubble in a given direction. We designate this direction as the x axis and the force per atom as Fa. The net rate of flow of atoms from one side of the bubble to the other, under the influence of this force, is the surface flux, Js, times the cross-sectional area available for flow, A,. A, is taken as the circumference times the thickness of the high-diffusivity surface layer 6. Thus where 51 is the atomic volume. For bubbles to advance a distance dx, a volume equal to nr : dx must flow around the void so that The minus sign enters because the bubble moves in the direction opposite to that of the force on the atoms. Equations for volume diffusion and diffusion through the vapor can be obtained in the same manner. For vapor transport we have Ag = and the ratio of the densities of metal atoms in the gas and the solid (pg/pl) enters so that

Jan 1, 1964

By H. S. Thomsen, W. C. Duesterhoeft, R. E. Hartline

The attenuation and phase shift which formations produce in the electromagnetic field of an induction-type electrical well-logging instrument are great enough to substantially affect the response of the tool to formation conductivity under normal logging conditions. The application of the general equations for the propagation of an electromagnetic field in a conductive medium to the transmitter-receiver coil pair of an induction-logging-tool coil system gives an expression for the response which properly takes the propagation effects into account. A comparison of a calculation of this type with the response computed from the commonly used geometric factor concept, which does not include the propagation effect, leads to a factor Go representing the ratio of the responses computed by the two methods. The value of Go decreases not only with increasing formation conductivity, but also with increasing transmitter-to-detector coil spacing. For a single coil pair with a 40-in. spacing, the value of Go is 0.972 in a 20-millimho/m formation. The value is reduced to 0.915 and 0.812 for conductivities of 200 and 1,000 millimhos/m. As a result, the basic signal generated by the induction-logging coil system is not linearly related to formation conductivity as expected from the geometric factor concept. A uniform conductivity scale can be obtained only by adding a suitable nonlinear element to the recording system. The addition of auxiliary coils, having spacings less than the main-coil span, to achieve focusing results in an even greater departure of the basic signal from linearity with conductivity. The solution of the field equations near the interface between two formations of different conductivity gives the curve shape on an induction logging tool in crossing the interface. The addition of auxiliary coils to achieve focusing can add anomalous character to the curve shape in crossing the interface, which might be mistaken for lithological detail. Preliminary calculations which include the propagation effects in the determination of the conductivity correction for thin beds lead to correction factors which are substantially smaller than those obtained from geometric factor considerations. It is apparent that thin-bed corrections derived from geometric factor calculations are of doubtful validity. INTRODUCTION Although the electromagnetic induction type of electrical well log has been used for a number of years and has gained general acceptance in quantitative well-log interpretation, no technically complete investigation of the mechanism and of its operation has been published. The studies which have been presented are based upon the premise that neither the shape nor the intensity of the induction field of the logging tool is in any way affected by the electrical characteristics of the formation. From the inception of induction logging it has been recognized that under some formation conditions the performance of the instrument could be expected to be substantially different from that predicted by the simplified analysis. This anomalous performance has been called "skin effect" since it is the result of the same phenomenon which causes high-frequency alternating currents to flow only near the surface of metallic conductors. In the range of conductivities encountered in the sediments, the formation actually does not exhibit the sharply defined conducting "skin" shown by metals. The gradual modification of the distribution of the currents in the formation, produced by the induction field of the logging tool, is the direct result of phenomena associated with the propagation of the electromagnetic field through the formation. Therefore, it can be much more appropriately described as the "propagation effect". One purpose of this paper is to review the results of a solution of the equations for the performance of a single transmitter-receiver coil pair induction-logging system which takes into account the propagation effect, showing the manner in which the tool performance established by this analysis differs from that derived from the less comprehensive analyses currently in use. PRINCIPLE OF OPERATION OF THE INDUCTION LOGGING INSTRUMENT The high-frequency alternating current which is maintained at a constant value in the transmitter coil

By A. E. Dwight

Lattice parameters were determined for eighteen equiatornic alloys of the CsCl-type structure, ten of which were previously un-reported. It was found that fomation of the CsCl-type structure in binary alloys of the transition elements is largely dependent on position of the elements in the periodic table. The relative size of the two elements was not found to be a controlling factor. A recent paper by Beck, Darby, and Arora1 corre-lates the occurrence of CsC1-type ordered structures with the position of the constituent elements in the periodic table for the first long period. It was also suggested that a definite increase in relative bond strength between unlike atoms occurred when, in binary alloys of iron-group elements, the other component is changed from a chromium-group element, to a vanadium-group element, to titanium. A later paper by Philip and Beck2 noted that the lattice contraction increased in the order CrFe, VFe, and TiFe. It was also noted by Philip and Beck2 that the lattice contractions of CsC1-type alloys decreased in the order: TiFe, TiCo, and TiNi, which is an apparent reversal of the contractions expected from the position in the periodic table. It was suggested that the increasing lattice contraction is an indication of increased stability, i.e., greater A-Bbond strength. The present investigation was carried out to determine whether the relation of the position in the periodic table to the formation of the CsC1-type structure was also correct for alloys involving the second and third long-period elements. A systematic search was made for CsC1-type structures among equiatomic alloys and for those found, the lattice contraction was determined. EXPERIMENTAL TECHNIQUE The elements Y, Gd, Ti, Zr, Hf, V, and Cb are designated the A group and the elements Mn, Re, Fe, Ru, Os, Co, Rh, Ir, Ni, Pd, Pt, Cu, Ag, and Au are designated the B group. Equiatomic alloys were prepared for 57 AB combinations. The alloys were arc melted in a multicrucible furnace3 in buttons ranging from 5 to 20 g. Chemical analyses were not made, as the charge weights agreed closely with those of the buttons after melting. The alloy buttons were homogenized at 800° to 900°C. Metal log raphic and X-ray specimens were prepared and heat treated at temperatures from 600° to 1200°C. Specimens for X-ray diffraction were usually ground to a powder in an agate mortar; however, needle-shaped solid specimens were used when the alloy was sufficiently ductile to permit their preparation. Diffraction patterns were taken with a Straumanistype Debye-Scherrer camera using filtered Cu or Co radiation. The lattice parameters were obtained in A by plotting the calculated a0 values against the cos29/sin 0 + cos2?/? function and extrapolating linearly to ?= 900. Metallographic control specimens were polished on cloth wheels with diamond paste and etched with various phosphoric and nitric acid reagents. RESULTS The eighteen equiatomic alloys listed in Table I gave evidence of a cubic structure with two atoms in the unit cell, although two of these cubic structures exist only at elevated temperatures and transform to a tetragonal structure on quenching. Nine of these eighteen alloys gave diffraction patterns with super-lattice lines showing that the structure is of the CsC1-type. The lack of superlattice lines in patterns of the other nine alloys may be attributed to the small difference in atomic scattering power of the components. Metallographic study indicates the occurrence of nine narrow single-phase fields at the AB composition. Any or all of these nine may also have a CsC1-type structure. The VFe alloy was found to have a CsCl-type structure by Philip and Beck2 through the use of CrKa radiation (for which the scattering factor of V is anomalously low), whereas the Cu radiation used

Jan 1, 1960

J. Chipman (Massachusetts Institute of Technology, Cambridge, Mass.)—The fact that the experimental work has been applied to copper rather than iron and that the paper is presented to the Iron and Steel Division, I regard as rather significant. It shows the unity of metallurgy and the fallacy of trying to cut it up by metals. This result for the solubility of sulphur in molten copper correlates with Professor Schuhmann's finding that the published data on the other side of the copper-sulphur miscibility gap are also in error. I should like to ask the author to say a little bit more about the sulphur capacity of the slag. T. Rosenqvist (author's reply)-—I hope that Dr. Chipman will find the derivation of the expression for sulphur capacity more clearly explained in the printed version of the paper than in the oral discussion at the meeting. I feel that this quantity, which actually is the ratio of two activities, can be measured more easily than the individual activities. Even if the ratio CaO/CaS is chosen as the standard state, the expression can be used for any slag, even for slags completely free of lime, and it represents a way to put the desulphurizing power of all slag constituents into one bag. Some doubt has been expressed as to whether oxygen ions really exist in calcium oxide and in molten slags. From a thermodynamic view point that question is of minor importance. The term oxygen ion activity, or any activity for that matter, is defined rigorously by the equation: activity = exp u/RT, where u is the change in free energy connected with the transfer of one mol of ions from the standard state into the slag. Whatever happens to the ion in the slag is of no concern to the thermodynamicist. Regardless of whether the ion is "free" in the slag or not, or whether it is present in a very small amount, its activity can always be expressed, and for a thermo- dynamic calculation that is all we need. However, ionic activities will only be of some real value if they are simple functions of the slag composition, or can be measured easily. Concerning the real nature of the oxygen in the slag, my feeling is that the oxygen atom has a rather multiplex nature depending on how strongly it is tied by covalent forces or polarized by the other atoms or ions present. The oxides of iron, cobalt, and nickel differ from calcium oxide and blast furnace slags as to the amount of free electrons that can give rise to electronic conductivity. In slags we know that the conductivity is mostly ionic. The fact that reversible emf's can be obtained with oxygen electrodes in certain salt melts, indicates a significant amount of oxygen ions in these melts. But extended work, e.g. polaragraphic studies and measurements of transference number; are needed to obtain quantitative information about the real structure of the slags. D. E. Babcock (Republic Steel Corp., Youngstown, Ohio)—-With reference to the ion, it might be well to remember Dr. Moses Gomberg. All of his life he had no use for the ionization theory and he contributed greatly to the field of chemistry on the assumption there was no such thing as ions. I do not think we have to worry about whether the oxygen is ionic or not. I think one thing specifically should be brought to your attention and this I think is one of the important contributions of Dr. Rosenqvist. He pointed out what we know as oxygen potentials or what is described as oxygen potentials. I have used this concept for a long period of time and I want to state that if this concept is properly applied, it vitiates much of what we have in the literature, or makes our usual ideas regarding oxidation seem primitive. That one thing is more valuable than almost all the rest of the discussion as a fundamental basis on which to build a reasonable in-

Jan 1, 1952

By R. McNeill, D. E. Weiss, E. A. Swinton

In a continuous countercurrent exchange process, an alteration in any one of the operating conditions has a complex effect on the others, which can only be predicted by employing the transfer unit or the theoretical stage theory on a basis of trial and error. A simple method is described for illustrating diagrammatically the behavior of a counter-current system, the equations being simplified by means of a concept the maximum hypothetical exchange performance. An example based on a typical metallurgical system is given, in which a divalent metal is recovered from a dilute solution, the resin being regenerated continuously by a monovalent ion. Useful conclusions are drawn from a study of the theory. Practical methods for performing continuous ion exchange are discussed, and the development of equipment based on modified ore dressing jigs is described. A swinging sieve jig contactor is evaluated experimentally. DURING the last decade, the new synthetic ion exchange resins have been applied extensively in industries outside the field of water treatment, but there is no record of a continuous counter-current process operating on an industrial scale. Attempts have been made to devise a satisfactory process but many problems remain to be solved. The basic principles of continuous processes will be outlined, as well as the major problems in their operation and the progress made in the CSIRO laboratories toward the development of satisfactory industrial techniques. In the metallurgical field ion exchange resins can be used for various applications such as the recovery and concentration of valuable metals from mine waters,' the regeneration of pickling and plating liquors," the prevention of pollution by waste effluents and the recovery of the constituents from them," and the purification of valuable metals such as the rare earths by chromatographic fractionation on columns of ion exchange resins.7,8 . Turther applications undoubtedly will be found in the field of hydrometallurgy where the use of ion exchange resins would enable direct extraction of the desired metal ion from the filtered leach liquor or the leach pulp. For example, an ion exchange process has been described recently for the extraction of gold from a cyanide leach pulp." A continuous process would have advantages in many applications over the usual process employing a fixed bed and intermittent cycle. In a recovery process, it would yield a product stream of steady purity and concentration, it would waste less water in rinsing, and if the contacting apparatus were efficient less resin would be used, since each portion of the resin would be cycled as soon as it was loaded instead of lying idle until the whole bed was ready for regeneration. A very major advantage is that it would be simpler to control automatically. It is probable that continuous operation will be the key for really large scale applications of ion exchange. The flow sheet of a continuous ion exchange recovery-concentration process is illustrated diagrammatically in Fig. 1. Dilute liquor containing the valuable ion flows through the stripping section countercurrently to a moving bed of resin and leaves after a final contact with freshly regenerated resin. The resin leaves the unit almost in equilibrium with the incoming liquor and then flows to the regenerating unit where it is treated by a slow countercurrent flow of concentrated regenerant solution. The adsorbed ion is displaced from the resin and appears in the concentrated product stream. The resin then must pass through a rinse unit or section where regenerant entrained by the resin is washed back into the regeneration section by water. The regenerated and washed resin is then recycled back to the stripping section. I. Theoretical Operating Behavior of Continuous Ion Exchange Stripping System The simple theory of continuous ion exchange is analogous to that of solvent extraction and other diffusional transfer operations and is governed by the equilibrium relationship, the mass balance, the rates of mass transfer, and the contacting efficiency of the unit. Equilibrium Relationship—The relative affinity of two ions A and B, for a particular resin immersed in their solution, can be expressed by plotting compositions of the solution against compositions which exist in resin in equilibrium with those solutions, i.e. C/Co vs q/a where C, is the total normality of the solution, C is the normality of ion A in the solution, a is the total exchange capacity of the resin in gram equivalents

Jan 1, 1956

By H. W. Schadler

The superplastic behavior of low carbon and manganese bearing steels has been evaluated. The results of elevated-temperature stress-strain rate and elongation tests are reported which indicate that high strain rate sensitivity (>0.5) and adequate elongations are achievable in ultrafine-grained steels 1 to 2 p, but at strain rates which are not commercially attractive. It has been demonstrated that the fine grain size is retained after long times and high strains if the temperature is kept within the range of the two-phase (a + ?) field. INTEREST in superplasticity has been stimulated by the desire to: 1) understand the origin of, and mechanisms responsible for, the large uniform elongations observed, and 2) exploit this property for commercial advantage in metal forming operations. Although the Zn-22 wt pct Al alloy presently being studied as a model material1-5 may find application in sheet forming and extrusion, the potential of super-plasticity should best be realized in large tonnage materials, such as steel and aluminum alloys. The degree of superplasticity in low-carbon and manganese-bearing steels has been evaluated. The results of elevated-temperature stress-strain rate and elongation tests on ultrafine grain size material are reported. Avery and Backofen6 and Hart7 have shown that geometrically stable flow leading to extensive uniform elongation in the tension test is associated with high values of the strain rate sensitivity, m, defined: Lozinsky had reported that titanium and zirconium experience permanent deformation if subjected to a constant load and cyclic heating through the temperature range of the phase transformation. Although strain rate sensitivities in excess of about 0.2 had not been reported previously for steel, permanent deformation had been observed11-13 in a wide variety of steels subjected to a constant load and cyclic heating through the temperature range of the a-? phase transformation. Thus by analogy, steel could be expected to exhibit high strain rate sensitivity but only in the a + ? condition. High strain rate sensitivity has been observed at 650°C (a + Fe3C), but not reported as such, by Bailey, Dickenson, and pearson14 in 1931 at a strain rate of about 10-9 per min. It then remained to determine whether high tensile elongations would be observed in a rate-controlled test at constant temperature and at what strain rate strain rate sensitivity values greater than 0.5 would be observed. Since previous experience8 had indicated the importance of fine grain size to realizing high m at reasonable strain rates, it was first necessary to produce an ultrafine grain size and then keep the grains from growing during the test. The results of this investigation show that fine grain size can be readily produced16 and maintained by restricting the temperature of testing to below the ? transus. Further, superplasticity (high m and large uniform elongation) is observed. However, the strain rate range is only marginally useful for commercial forming operations with the finest grain size produced. MATERIAL The material investigated initially was a 1.9 wt pct Mn, 0.42 wt pct C, hot-rolled bar previously used by Low and Turka1015 and available in the laboratory. The 0.500-in. round was cold-rolled to a 0.090-in. flat, annealed for 4 hr at 850°C in argon, air-cooled, and cold-finished to 0.050 in. Subsequently, four additional steels of the compositions given in Table I were investigated to explore the effects of manganese, carbon, and test temperature on the observed stress-strain rate behavior. These steels were melted under argon, cast to 0.75 by 2 by 5 in. slabs, hot-rolled at 850°C, surface-finished to 0.13 in., and cold-finished to 0.050 in. Sheet tensile specimens 0.200 in. x thickness with 1- or 2-in. gage length were cut parallel to the rolling direction. Table I also includes the nominal transformation temperatures for the AISI 1340 and the four experimental steels. EXPERIMENTAL PROCEDURE Production of Fine Grain Size. Ultrafine grain size (1 to 5 p) was considered essential for this studv. Grange16 has described two techniques for producing

Jan 1, 1969