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By George R. Cowan

A number of studies hare been reported of the effects produced in metals subjected to deformation by shock waves with maximum pressures ranging from tens to hundreds of kilobars. On the basis of the equations for the flow of mass, momentum, and energy through a stationary shock front, the macroscopic stress-strain curve for the resulting shock deformation can be calculated within narrow limits from the experimentally determined Hugoniol curve. In relatively weak shocks which are preceded by an elastic wave, the stress rises above the clastic limit only as plastic deformation proceeds cold thus the shock has a long toe. In strong shocks that override the elastic wave a high stress is applied without prior plastic deformation. A more important effect of increasing the shock pressure is the generation of shear stresses, called supercrilical shear stresses, that exceed the strength of the perfect lattice. A change in the mechanism of deformation is expected to result from the onset of supercritical shear. The shock disordering of ordered Cu3Au in strong shocks appears to be an example of such a change. It is suggested that the formation of fine twins in copper and nickel and the formation of structures which enable visible twins to be formed in the rarefaction ware, observed in copper and presumably in disordered Cu3 Au, are related to the occurrence of supercritical shear in shock dcformation. In recent years several studies1,2 have been made of the changes in structural and mechanical properties of metals produced by the passage through the metals of strong shock-compression waves ranging from about 50 to 800 kbar pressure. Recent work involving dynamic measurements of the shock compression "Hugoniot" curves 3-8 of many metals has developed techniques and provided data required to obtain the shock pressure and the (transient! plastic deformation produced in the shock-conlpression experirnents.9 Shock deformation has been found to be much more effective than slow deformation in changing the mechanical properties of metals, when the two are compared on the basis of equal plasti strain, Holtzman and Cowan9 made quantitative estimates of the shearing stress occurring in a shock front in a metal by assuming that the shearing stress is similar to that occurring in a shock front in a viscous, heat-conducting fluid, with the addition of a yield stress. Taylor's solution9 for a weak shock was used to estimate pairs of values of shearing stress and thickness of the shock front obtained by assumed choices of the ratio of effective kinetic viscosity to thermal diffusivity. It was noted from these values that. unless the shock front is extremely thin. heat conduction has slight effect, and the shearing stress is nearly independent of the mechanism of deformation. This mechanism does, however, determine the thickness of the shock front and the rate of strain. Furthermore, since the maximum possible shearing stress occurring in shocks of moderate strength does not greatly exceed the shear stress occurring in conventional slow deformation, the mechanism of deformation is not expected to be qualitatively different. The greater effectiveness of shock deformation in changing the mechanical properties of metals can be attributed partly to the fact that dislocations, when driven by near-conventional stresses, cannot keep up with the shock front, thus necessitating a higher dislocation density than required for an equivalent slow strain. The fast uni-axial strain occurring in the thin shock front would also be expected to cause a larger number of dislocation intersections to occur. In the upper range of shock pressures that have been studied the estimated values of the shearing stress exceeded the estimated shear strength of a perfect crystal. Under these circumstances it is reasonable to expect that the mechanism of deformation might be considerably different from that involved in slow deformation. Except for the observation by smith1 of twins in shocked copper, the effects of shock waves on metals did not show any obvious or large changes in properties that would indicate the onset of a change in the mechanism of deformation. The recent investigation of the effect of shock waves on ordered and disordered specimens of Cu3Au by Beardmore, Holtzman, and ever" showed a spectacular decrease in the amount of long-range order retained by initially ordered Cu3Au when the shock pressure was raised from 290 to 370 kbar. Since Dr. Holtzman and I suspected that this behavior probably was due to the onset of a shearing stress in the shock front in Cu3Au which exceeded the limiting shear strength of the perfect crystal. it was considered appropriate to examine directly the shock-front equations for a solid. and to obtain a sound estimate of the shearing stress occurring in the front using equation of state data obtained from shock studies. In this paper an estimate is made of the

Jan 1, 1965

By Robert G. Johnson, Richard J. Prosen

THE present work was done in connection with a program for investigating metal-to-ceramic braze techniques using the well-known reactivity of titanium with certain ceramic oxides. The investigation extended over the range of 0 to 30 pct Ti. The indium was obtained from the Indium Corp. of America and was specified to be 99.97 pct pure. The titanium was supplied by Metals Disintegrating Co. and was stated to be 99.5 pct pure. Each 2 to 4 g quantity of the alloy compositions studied was prepared using a mixture of 300 mesh powders pressed into pellet form. The pellets were heated in thin-walled molybdenum crucibles using a resistance-wound furnace in a vacuum less than 10-4 mm of Hg. Little reaction occurred between the molten alloy and the crucibles at the temperatures and short time intervals used. Only slight spectroscopic traces of molybdenum were found in the melt after a typical period of heating. The points shown on the phase diagram of Fig. 1 represent thermal arrest measurements. The phase boundaries shown are consistent with the thermal arrest and X-ray data obtained. The temperatures were determined using a Pt-Pt 10 pct Rh thermocouple with the junction spot-welded to a short molybdenum rod. The rod was almost completely immersed in the liquid metal, so that good thermal contact with the melt was achieved. The small mass of the crucible and its contents made it possible to obtain many heating and cooling curves in a few minutes time, an advantage which helped to minimize the effects of indium evaporation at the higher temperatures. A Brown strip chart recorder was used to display the thermal arrest curves. To check the technique, the melting point of 99.999 pure Al was measured and found to be within 1 of 660.2c, the accepted melting point. The upper limit of temperature with this technique was about 900°C beyond which the evaporation rate of indium became great enough to alter appreciably the alloy composition during the runs. A peritectic transition was found at 796°+ 5°C from 1.5 to 30 wt pct Ti. It was not found at 0.5 or 1.0 pct. A small super-cooling effect was observed. The melting-point transition to the B + L phase was found up to 20 pct Ti but not at 25 pct. Within the 1 deg accuracy of the measurement, the transition temperature was that of pure indium, 156°C. The liquidus line to the left of the 1.5 titanium point was located only approximately. The two crossed circle points at 1.0 and 0.5 pct Ti place a lower limit on the liquidus line and were determined by observing visually the cessation of vibrations in the melt caused by the damping effect as B-phase crystals were formed during cooling. The B-phase boundary was found at 23.8 pct Ti by X-ray analyses of small single crystals of the B phase isolated from 2 pct Ti melts. The compound was found to be Jetragonal with lattice dimensions of c = 3.052A and a = 10.094W. From the unit cell dimensions and the measured density of 6.42 i 0.05 g per cc, the compound was determined to be In4Ti3 which has 23.8 pct Ti. The calculated density of 6.44 g per cc is obtained assuming 2 mol

Jan 1, 1962

By H. D. Kessler, M. Hansen, R. J. Van Thyne

The phase diagram of the titanium-rich portion of the system Ti-Cr-Fe to 70 pct Ti was established by means of isothermal sections at 900°, 800°, 750°, 700°, 650°, 600°, and 550°C, using arc-cast alloys. An isotherm at 800°C was determined for the section bounded by Ti, TiFe2, and TiCr2. Micrographic analysis was employed as the principal method of investigation, supplemented by X-ray diffraction and incipient melting studies. A ternary eutectoid, ß ? a+ TiCr2 + TiFe, occurs at approximately 8 wt pct Cr, 13 wt pct Fe, and about 540°C. AMONG the first titanium-base alloys in commercial production were the Ti-Cr-Fe alloys. For this reason, the Materials Laboratory, Wright Air Development Center, sponsored an investigation of the system. No information on the constitution of the titanium-rich corner was available. Vogel and Wenderott studied titanium-poor ternary alloys.' As part of this program, the binary systems Ti-Cr and Ti-Fe have been determined previously by the authors.' Other investigators have also studied the binary systems Ti-Cr,3-7' Ti-Fe.³,8-10 Both of the binary systems are characterized by the eutectoid decomposition of the ß phase. Most of the effort of the present work has been concentrated on the titanium-rich corner with compositions of less than 30 pct total chromium and iron content. The determination of isothermal sections was the experimental approach used to obtain the ternary phase diagram. Vertical sections were used to check the consistency of the isothermal sections. While this investigation was in progress, a study of the Ti-Mo-Cr system at Armour Research Foundation disclosed the existence of a high temperature modification of TiCr2 above 1300 °C.11 This allotrope has a hexagonal structure of the MgZn2 type, iso-morphous with TiFe2, whereas the low temperature modification of TiCr2 is cubic," of the MgCu2 type. The existence of allotropy in TiCr2 of course means a more complicated set of phase relationships in this general region than if the phase were monomorphic, as was first assumed. Additional studies were made late in the investigation in order to clarify the part that the hexagonal TiCr2 phase plays in the ternary phase relationships. These will be discussed in a separate section. Because they are of greatest practical significance, the phase relationships in the titanium-rich corner will be presented first, omitting the equilibria involving the hexagonal modification of TiCr2 in an effort to simplify the presentation somewhat. Experimental Procedure Materials: The titanium used in the preparation of the alloys was iodide crystal bar (99.9 pct pure) produced by the New Jersey Zinc Co. High purity chromium and iron were obtained from the National Research Corp. Table I gives the analyses of these materials. Melting Practice: Over 100 alloy ingots weighing 10 to 20 g were melted in a nonconsumable electrode arc-melting furnace. As the techniques are identical to those reported previously,12,13 they will not be detailed here. The ingots were melted in the cavity of a copper melting block insert under a slight positive pressure of helium. No measurable hardness

Jan 1, 1954

By L. R. Shoenberger

Boron has been used to produce nonaging low-carbon sheet steel. Retention of the necessary minimum amount of about 0.006 pet partially killed the steel. Amounts exceeding about 0.012 pet increased the degree of deoxidotion, piping tendencies, and possibility of hot tearing in primary rolling. Semikilled practice resulted in good ingot yields and satisfactory surface quality. Aluminum added with the boron provided a protective de-oxidizer. Good drawobility was indicated by performances of the steel in a limited number of deep-drawing trials. Some problems with hot-tearing and boron-analysis procedures were overcome. Metal lographically, the boron semikilled steels revealed some structures not usually found in plain low-carbon steels. IN 1943 Low and Gensamer1 reported that strain aging, which hardens and embrittles ordinary low-carbon rimmed steel, was due to nitrogen and carbon, and that oxygen played a relatively unimportant role. Since then, many investigators have substantiated their findings and indicated that nitrogen is particularly potent. Commercially, today's most widely produced non-aging sheet steels for deep drawing are either aluminum killed or vanadium rimmed types. The difference in deoxidation practice, alone, is evidence that oxygen is apparently not an important consideration in control of strain aging. The fact that nitrogen is important is apparent in the consideration that has been given, knowingly or unknowingly, to the amount combined with aluminum and vanadium. Patents were granted to Hayes and Griffis2 for the processing of aluminum-killed steel, and to Epstein" for the manufacture of vanadium rimmed material. Certain prescribed steps in producing these steels can be correlated with the formation of the respective nitrides within certain temperature ranges below the usual hot-finishing temperatures. The potential nonaging properties of either type can be reduced or suppressed by cooling too rapidly to permit the aluminum or vanadium to combine with nitrogen. Subsequent suberitical annealing of the cold-rolled strip, however, normally forms the nitrides and produces the resistance to strain aging. Titanium-killed nonaging steel, described by Comstock,1 forms a nitride in the molten state and is essentially nonaging throughout its processing. Zirconium-killed steel, which was investigated briefly by the author,* appeared to have similar nitride- forming characteristics. It is known" that chromium can produce nonaging rimmed steel, but relatively little is known of the potentialities of some of the other nitride-forming elements such as boron, silicon, columbium, and cerium. In attempting to develop a new nonaging cold-rolled sheet steel with good drawability, the following factors were considered pertinent. Such a steel would necessarily have a low carbon content and therefore have a relatively high degree of oxidation when made in a basic open-hearth furnace. If the denitriding element were also a deoxidizer, a part of the addition would be lost as oxide. The degree of deoxidation would determine whether the steel is rimmed, semikilled or killed, and also could be expected to have an important bearing on ingot yields and ultimate surface quality. Assuming that the pattern for the production of cold-rolled sheets would not be changed to any great extent, the nitride must form in the molten steel, in hot rolling, in subsequent cooling, or in annealing. The nitride, once formed, should resist dissociation and be stable in the final product. Usually an excess of the nitride-forming element is required to combine with sufficient nitrogen. If the element used is a strong ferrite strengthener, a small excess may markedly decrease drawability. With aluminum and vanadium, about 0.03 to 0.05 pct in the steel is preferred. Epstein has said" that about 0.30 pct chromium is required. Titanium nonaging steels are hard unless a sufficient amount (about 0.30 pct) is added also to combine with the carbon. The cost of the necessary amounts of these latter two elements discourages commercial acceptance. Silicon was considered as a possible nitride former, but since amounts up to 0.10 pct in rimmed and semikilled steels do not induce marked resistance to strain aging, larger amounts are apparently required, which would tend to harden and strengthen the ferrite. Of the other elements mentioned, all but boron are expensive heavy-metal elements. Stoichi-ometrically, almost an equal weight of boron would be required to combine with the nitrogen—-ordinarily about 0.003 to 0.006 pct in scrap-practice open-hearth steels. Boron is a slightly stronger deoxidizer than carbon but is less powerful than zirconium, aluminum, or titanium. Thus a rimmed-steel practice might be possible. There is much in the technical literature concerning the hardenability effects of minute amounts of boron in killed steels but very little about its behavior in low-carbon material—particularly as a ferrite strengthener. The available data indicated a need for better information concerning the effects of boron in low-carbon strip steels. Experimental Work Development of a Boron-Treated Nonaging Strip Steel—Initial attempts to produce a boron-rimmed strip steel employed 3-ton basic open-hearth heats which could be teemed into molds large enough to sustain a normal rimming action. Boron as ferro-boron was added to the ladle in small amounts because of the reported hot-short character of aluminum-killed heat-treating grades containing more than about 0.005 pct boron. Actually, the amounts used, i.e., 1/8 and 1/4 lb per ton, would be large for

Jan 1, 1959

By R. Al-Hussainy, P. B. Crawford, H. J. Ramey

The effect of variations of pressure-dependent viscosity and gas law deviation factor on the flow of real gases through porous media has been considered. A rigorous gas flow equation was developed which is a second order, non-linear partial differential equation with variable coeficients. This equation was reduced by a change of variable to a form similar to the diffusivity equation, but with potential-dependent diffusivity. The change of variable can be used as a new pseudo-pressure for gas flow which replaces pressure or pressure-squared as currently applied to gas flow. Substitution of the real gas pseudo-pressure has a nrtmber of important consequences. First, second degree pressure gradient terms which have commonly been neglected under the assumption that the pressure gradient is small everywhere in the flow system, are rigorously handled. Omission of second degree terms leads to verious errors in estimated pressure distributions for tight formations. Second, flow equations in terms of the real gas pseudo-pressure do not contain viscosity or gas law deviation factors, and thus avoid the need for selection of an average pressure to evaluate physical properties. Third, the real gas pseudo-pressure can be determined numerically in term of pseudo-reduced pressures and temperatures from existing physical property correlations to provide generally useful information. The real gas pseudo-pressure was determined by numerical integration and is presented in both tabular and graphical form in this paper. Finally, production of real gas can be correlated in terms of the real gas pseudo-pressure and shown to be similar to liquid flow as described by diffusivity equation solutions. Applications of the real gas pseudo-pressnre to radial flow systems under transient, steady-state or approximate pseudo-steady-state injection or production have been considered. Superposition of the linearized real gas flow solutions to generate variable rate performance was investigated and found satisfactory. This provides justification for pressure build-up testing. It is believed that the concept of the real gas pseudo-pressure will lead to improved interpretation of results of current gas well testing procedures, both steady and unsteady-state in nature, and improved forecasting of gas production. INTRODUCTION In recent years a considerable effort has been directed to the theory of isothermal flow of gases through porous media. The present state of knowledge is far from being fully developed. The difficulty lies in the non-linearity of partial differential equations which describe both real and ideal gas flow. Solutions which are available are approximate analytical solutions, graphical solutions, analogue solutions and numerical solutions. The earliest attempt to solve this problem involved the method of successions of steady states proposed by Muskat.' Approximate analytical solutions' were obtained by linearizing the flow equation for ideal gas to yield a diffusivity-type equation. Such solutions, though widely used and easy to apply to engineering problems, are of limited value bemuse of idealized assumptions and restrictions imposed upon the flow equation. The validity of linearized equations and the conditions under which their solutions apply have not been fully discussed in the literature. Approximate solutions are those of Heatherington et al.. MacRobertsl and Janicek and Katz.' A graphical solution of the linearized equation was given by Cornell and Katz. Also, by using the mean value of the time derivative in the flow equation, Rowan and Clegg' gave several simple approximate solutions. All the solutions were obtained assuming small pressure gradients and constant gas properties. Variation of gas properties with pressure has been neglected because of analytic difficulties. even in approximate analytic solutions. Green and Wilts8 used an electrical network for simulating one-dimensional flow of an ideal gas. Numerical methods using finite difference equations and digital computing techniques have been used extensively for solving both ideal and real gas equations. Aronofsky and Jenkins"I " and Bruce et al.11 gave numerical solutions for linear and radial gas flow. Douglas et al." gave a solution for a square drainage area. Aronofsky 13 included the effect of slippage on ideal gas flow. The most important contribution to the theory of flow of ideal gases through porous media was the conclusion reached by Aronofsky and Jenkins" that solutions for the liquid flow case'" could be used to generate approximate solutions for constant rate production of ideal gases. An equation describing the flow of real gases has been solved for special cases by a number of investigators using numerical methods. Aronofsky and Ferris 10 onsidered linear flow, while Aronofsky and Porter 17 considered radial gas flow. Gas properties were permitted to vary as linear functions of pressure. Recently, CarteP 18 proposed an empirical correlation by which gas well behavior can be estimated from solutions of the diffusivity equation using instantaneour values of pressure-dependent gas

Jan 1, 1967

By J. B. Cohen, B. W. Howlett, M. B. Bever

The partial molar heats of solution at infinite dilution in tin of aluminum at 300° and 350°C and of gallium, indium, and thallium at 240°, 300°, and 350°C have been measured by tin solution calori-metry. Aluminum, gallium, and thallium are endo-thermic on solution; indium is exothermic. Any temperature dependence of the heats of solution lies within the experimental scatter. Over the dilute ranges investigated, only aluminum has a measurable change in its heat of solution with composition. HEATS of solution of one element in another reflect the interaction between them. The investigation of partial molar heats of solution in dilute alloys is of particular interest as the properties of the solvent are altered to only a limited extent by the presence of the solute and also as the interaction between solute atoms is small. When the heats of solution of a related series of elements in a solvent are known, a systematic comparison may be made. In the investigation reported here, the partial molar heats of solution of the Group III elements aluminum, gallium, indium, and thallium in dilute solution in tin were measured. This work follows an investigation of the heats of solution in tin of the Group IB elements.' EXPERIMENTAL PROCEDURES Materials. Samples of gallium, indium, and thallium were obtained from Johnson, Mathey and Co., Ltd. Indium and thallium were supplied as wire, 1.6 mm in diam; gallium was in the form of irregular pieces. The supplier reported the following minimum purities: gallium—99.95 pct; indium—99.99 pct; thallium—99.99 pct. The aluminum, obtained from Alcoa Research Laboratories, was reported to be 99.995 pct pure. The tin was supplied by Baker and Co., Inc.; the reported analysis indicated a tin content of at least 99.96 pct with lead as principal impurity. Calorimeter. this description will cover only the essential features of the calorimeter with special attention to modifications made since an earlier description was published.' A Dewar flask containing the tin bath was held in a constant-temperature bath of a near-eutectic mixture of lithium, sodium, and potassium nitrates. This bath, which was stirred vigorously, was heated by a primary resistance winding in the container wall and by a secondary winding immersed in the salt. The voltage supplied to both windings was stabilized. The temperature of the salt bath was controlled by means of a platinum resistance thermometer in one arm of a Wheatstone bridge. The light from a mirror galvanometer in the bridge circuit fell on a photocell which controlled the current in a saturable reactor in series with the secondary winding. In this manner, the temperature of the salt bath was controlled to ±0.003°C and that of the tin bath to at least ±0.002°C. Each of these temperatures was measured by two iron-constantan thermocouples in series, coiled in a helix to minimize heat loss and immersed in the salt and tin baths in protective sheaths. The temperature of the laboratory was kept constant to ± 1°C during a run. Specimens were dropped into the tin bath from an addition arm held at O°C which was part of the cal-orimetric system. The system was evacuated to about 0.02 1 to minimize oxidation and to reduce transfer of heat. The bath was stirred by a glass stirrer introduced through a double Wilson seal. The samples were scraped clean before weighing, which was carried out as rapidly as possible. Each sample was immediately placed in the evacuated addition arm to minimize contamination. These precautions were especially necessary with aluminum. After the runs with gallium and thallium at all temperatures and with indium at 240° and 350°C (Series I) were completed and before the runs with indium at 300°C and aluminum at 300° and 350°C (Series 11) were begun the following changes were made. The shape of the Dewar flask was changed so as to result in a lower surface to volume ratio of the bath and at the same time the amount of tin was reduced from 500 to 400 g. The paddle type stirrer was replaced by a helical screw and the rate of stirring was increased to about 150 to 200 rpm.

Jan 1, 1962

By R. E. Ogilvie, A. R. Kaufmann, S. H. Gelles

The solid-solubility limits of iron in beryllium were determined between 850o and 1200oC by analysis of differential type multiphase diffusion couples, using an X-ray absorption technique. The maximum value of the solubility limit was found to be 0.92 ± 0.02 at. pct (5.46 wt pet) at the eutectic temperature 1225°C. The solubilities of nickel and beryllium were determined between 900°and 1200°C by the same technique and the maximum solubility was found to be 4.93 + 0.01 at. pct (25.2 wt pet) at the eutectoid temperature, 1065°C. A previously unreported high-temperature phase which decomposes eutectoidally at 1065 °C was found to exist in the beryllium-nickel system at a composition of approximately 8 at. pct Ni (36 wt pet) by diffision-couple analysis. The presence of this phase was confirmed by thermal analysis and metallo-graphic analysis of the structure resulting from the eutectoid decomposition. G. V. Raynor1 has treated the solid solubilities of some of the elements in beryllium on the basis of the "Hume-Rothery" rules2 which have been modified to include ionic size and ionic distortion effects. It was predicted that the solubility of iron and nickel in beryllium should be slightly less than that of copper. The lowering of the solubility, according to Raynor, is due to a more unfavorable relative valency effect and an ionic size effect. Kaufmann and corzine3 have compiled data on the solubilities of elements in beryllium and have discussed them in the light of the Raynor paper. These authors feel that, because the elements having the greatest solubility in beryllium systematically fall in the Group VIII and IB Columns of the periodic table, the electronic structure greatly influences the maximum solid solubility of elements in beryllium. The solubility of iron in beryllium was determined by Teitel and cohen4 as part of the study of the beryllium-iron phase diagram. The determination was carried out by X-ray and thermal analysis and according to the phase diagram presented, the maximum solubility of iron in beryllium is 0.41 at. pct (2.5 wt pct) at 1225oC. However, it is estimated that the uncertainty in the position of the a-beryllium primary solid-solution boundary is about 0.5 at. pct (3wtpct). Losana and Goria3 in studying the beryllium-nickel phase diagram, determined the solid solubility of nickel in beryllium by thermal analysis. They found the maximum solubility to be between 1.65 and 2.65 at. pct (10 to 15 wt pct) at 1240°C. This value decreased rapidly with decreasing temperature. In determining approximate ranges of solubilities for different elements in beryllium, Kaufmann, et al,8 reported a value of between 1.3 and 1.7 at. pct (7.9 to 10.1 wt pct) for the solubility of nickel in beryllium. The value was obtained by metallographic examination of quenched alloys and lattice-parameter measurements. However, the authors also noted a single-phase structure for a 1.7 at. pct Ni alloy (10 wt pct) on cooling from the liquid. This would indicate a higher solubility range than was reported. ~isch,' in his X-ray studies of beryllium-copper, beryllium-nickel, and beryllium-iron intermetallic compounds, reports the disappearance of a second phase (Ni,Be2) in the beryllium primary solid solution at approximately 4 at. pct (20 wt pct). THEORY The analysis of concentration gradients in diffusion couples has proven to be a useful tool in determining phase equilibria.8-14 In this particular study the diffusion couples were chosen to straddle the expected composition range of the phase boundary, then heat treated at a given temperature and the concentration gradient evaluated. The composition of the phase boundary for a given temperature appears at a point of discontinuity of the composition gradient. Examples of typical phase diagrams and the concentration gradients which should be found in such systems are shown in Fig. 1. In the present work, gradients of the form of Fig. l(c) were obtained in diffusion couples made of pure beryllium and two-phase alloys of beryllium with either iron or nickel. The composition at the point where the gradient becomes discontinuous, Cs, corresponds to the solubility limit of either iron or nickel in beryllium. The analysis of the concentration gradients was carried out by an X-ra absorption method developed and applied by Ogilvie and later used by Moll13 and Hilliard.l4 It depends on the fact that the absorption of X-rays by matter is determined by the concentration and type of the various atomic species present. The relationship for the intensity, I, of a monochro-

Jan 1, 1960

By W. M. Wojcik, R. F. Kowal

Oxygen and sulfur distributions in commercial, 5-ton ingots of killed, medium carbon steel are described. Oxygen distribution is found to vary with deoxidation practice. Irregular distribution of oxygen within ingots makes necessary special precautions in sampling of rolled products for analysis of oxygen. Oxygen distribution is discussed in terms of recently published solidification concepts which had been successfully applied to simpler cases of segregation. These concepts have been found inadequate to explain observed oxygen distributions. Convective movements of the liquid metal, as determined by tracer elements, are shown to be capable of accounting for the observed distributions of oxygen. IN an effort to explore the origin of surface and subsurface imperfections in pierced steel products, a study of oxygen and sulfur segregation was made on ingots cast in open-top and hot-top molds. The results of our previous investigations1"3 have indicated the importance of the location and amount of oxide inclusions in an ingot. Inclusions close to the surface of the ingot have been found to contribute greatly to the formation of imperfections in the surface of finished products. This study of the effects of deoxidation and casting practice on segregation and the resulting oxygen distribution in ingots was initiated to determine the parameters controlling the location of inclusions in an ingot. Segregation of solute elements during solidification of low-melting binary alloys has been studied in the past.1, 5 Formation and growth of inclusions in iron melts have been studied under specific conditions."- In spite of these and other recent studies,10-12 segregation during solidification of commercial, killed steel ingots is not well understood. Consideration of solidification rates, of segregation during solidification of the chill, dendritic, and central zones, and of material balances for the segregated elements has indicated that a simplified theoretical solidification model is not adequate. However, the observed high oxygen contents in localized volumes of the dendritic zone can be rationalized if additional effects of convection currents in the ingots, precipitation, and rapid growth of new phases are considered. EXPERIMENTAL PROCEDURE Steelmaking and Processing. A group of nine killed. medium carbon steel heats having compositions listed in Table I have been studied. The deoxidation and mold practices used were varied to give a wide range of steel oxygen contents. The amounts of aluminum added to the ladle and the ingot casting practices (hot top and open top) were the main variables. The steel was made by a duplex practice in 160-ton tilting basic open-hearth furnaces. All nine heats were top-cast into 24 by 24 in. big end down, fluted molds, to a height between 60 and 76 in., using both open tops and exothermic hot tops. The deoxidation practice and the tapping and teeming details for each heat and ingot studied are given in Tables II and III, respectively. Hot-top practice is indicated by the letter H following the heat designation. Furnace and ladle temperatures were measured by standard disposable-tip, Pt/10 pet PtRh thermocouples. Teeming-stream temperatures were obtained as described by Samways et al.,13 by immersing a Pt/10 pet PtRh thermocouple, covered by a silica sheath, into the teeming stream under the nozzle. The output of this thermocouple was recorded with Leeds & Northrup Speedomax potentiometer. Calibration of the latter thermocouples was based on the freezing point of a pure iron/oxygen alloy (2795°F). The accumulated errors of measurements were within ±10°F. The thermocouple measurements were supplemented in this investigation by continuous recording of a ratioing, two-color pyrometer (Shawmeter), protected from smoke by a blast of clean air within the sighting tube, and calibrated to read with better than ±10°F accuracy. Following teeming of three heats, P, R, and T, tracer elements were added to the steel in the molds to obtain a record of the progress of solidification. As soon as the teeming stream was shut off, a 0.010-in.-thick steel can containing a mixture of crushed standard ferro-titanium and ferro-vanadium (0.05 pet of each alloy element) was plunged into the middle of the steel pool to a depth of 6 in. In about 30 sec no indication of the can or its contents remained. The surface of the open-top ingots solidified in 20 to 30 sec. A study of liquid metal movement and the precipitation of oxides was facilitated materially by use of the tracer technique as titanium has a low distribution coefficient between solid and liquid steel while vanadium has a high distribution coefficient.

Jan 1, 1965

By J. R. Elenbaas, J. A. Vary, D. L. Katz

The development of gas fields, oil fields and aquifers for storing natural gas is treated from two main vieu.-points: (I) the volumetric storage capacity for gas in a given situation and (2) the prediction of the number of wells required for the delivery of gas. Other experiences in the design and operation of storagc fields are incluclerl INTRODUC TION Storage of natural gas in underground reservoirs near the terminus of long distance pipelines has been the prime factor in opening the space heating market to the natural gas industry. Storagc has permitted a major. increase in both the load and the load factor of pipe-lines; some are now operating at steady load throughout the year. Thus, underground storage has been responsible for the rapid increase in demand for natural gas in recent years. Three types of reservoirs have been used for gas storage: natural gas reservoirs, oil reservoirs, and waterbearing sands or aquifers. This paper presents the factors to be considered when developing gas storage reservoirs of these three categories. There are two prime considerations tor any storage reservoir: (1) the volume of gas which a given reservoir will store advantageously and (2) the number 01 wells needed to provide the required peak deliverability. These two problems will be considered for the three types of reservoirs just noted STORAGE IN PARTIALLY DEPLETED GAS FIELDS Early storage operations consisted of replenishing the natural gas in a depleted gas field situated adjacent to the market. Today, newly discovered fields near the market may be considered for storage, and this discussion applies equally to both types of reservoirs. For reservoirs originally containing gas or oil, the question of the impermeability of the cap rock nor-mally does not arise. However, such fields are likely to have many wells drilled either to or through the reservoir under consideration. Positive assurance must be obtained that such wells are or can be made mechanically tight. Corroded casings may need to be lined or permanently plugged. Abandoned wells should bc reopened and properly cemented. The volumetric capacity for gas storage depends upon space available in the porous rock as well as pressure and temperature of the gas in the reservoir. The production-pressure decline data on partially depleted gas reservoirs without water drive permit calculation of the reservoir space for gas. Isopachous maps of sand volume and porosity data for the reservoir rock provide an alternate method of calculating the pore volume for water-drive reservoirs. The pressure range selected for the storage cycle depends upon ()) the safe upper limit of pressure. 2) the flow capacity of wells and (3) compression requirements when injecting gas into the reservoir or delivering to market. Normally, gas and oil fields have pressures at discovery in the range of 0.43 to 0.52 psi/ft of depth. Pressures of around 1.0 to 1.2 psi/ft of depth appear to lift the overburden1-3 and invite uncontrolled movement of fluids in the porous rock. Some top pressure is normally selected for a storage reservoir ranging from below discovery pressure for deeper reservoirs to 0.65 psi/ft of depth for shallower reservoirs. Pressures to 0.66 psi/ft have been experienced without difficulty. The lower pressure limit is set by water intrusion accompanying low pressures, reduced flow capacity for wells at lower pressures and compression requirements. Depletion-type gas reservoirs often encounter water problems in the later stages of gas production. Such water intrusion may be due to movement from the surrounding aquifer. Accordingly, displacement of this water back into the aquifer by gas pressure and subsequent surges of water corresponding to the gas storage pressure cycle must be considered. Storage fields often produce in four months a volume of gas equal to its initial content. Rapid decreases in reservoir pressure occur, such as 20 psi/day. Accordingly, closed-in pressure observation wells which reflect the pressure in the bulk of the reservoir are required for following the operation of the reservoir. It has been found that a plot of observation wellhead pressures against gas content, Fig. 1, is very useful in observing operation of the field, checking the inventory and predicting future behavior. The plot is based on a given quantity of base or cushion gas in place. The injection and withdrawal curves may spread depending upon the homogeneity of the reservoir rock. permeability of the rock, well spacing and flow rates.

By R. Bakish, M. A. Badiali, N. W. Kirshenbaum

One pound of ultra pul-e molybdenum has been produced containing both metallic and nonmetallic impuvities close to or less than the limits of detection. various purification methods were investigated; althouglz the use of move than one purification step was consideved, it was found that a single, caefully-controlled sublimation of MoCl5 yielded a highly puvified product without prior treatment or recourse to repeated sublimation. Hydrogen reduction of MoC1, to metal was attempted at atmospheric pressure; however, reduced pressure was necessary to obtain substantial yields. The tubular deposits of metal were consolidated into bulk fovm by electron beam melting undev high vacuum yielding a very low gas content. Boblems involved in monitoring the puvity of these materials and analytical results obtained are also presented. THE pronounced effect of even trace amounts of impurities upon fundamental properties of materials is well known to metallurgists and solid-state physicists. Consequently, groups interested in basic studies of metals have in recent years immensely stimulated the preparation and production of numerous ultra-pure metals. Increased demand by scientists for these high purity materials has necessitated development of facilities to prepare them in significant quantities; the procedures reported here were devised to produce significant quantities of ultra-pure molybdenum. Previous work performed in the field of vapor phase purification and hydrogen reduction of several other refractory metal chlorides had demonstrated valuable techniques applicable to molybdenum.' Various purification and reduction steps were individually investigated. Those procedures which showed the most favorable results with respect both to attainment of high purity and to ease of operation were then incorporated in the process utilized to produce the metal.' STARTING MATERIALS It is well known that because of differences in volatility, chlorides may be separated by fractional distillation. It was presumed that distillation of molybdenum pentachloride offered a simple and straightforward method of purification due to its relatively low boiling point. Alternatively, sublimation of the solid chloride also appeared feasible since MoC15 has both a reasonably narrow temperature range in which it exists as a liquid (a property typical of refractory metal chlorides) and a low enthalpy of sublimation. Pertinent thermochemical data of MoC15 are given in Table I. It should be noted that this compound must be handled with care as it is extremely hygroscopic. Anhydrous MoC15 was obtained from the A Metal Climax Co. METHODS OF PURIFYING MOLYBDENUM PENTACHLORIDE Distillation. It was expected that distillation methods, while affording an efficient purification, would prove simple to control and would have a higher production rate than sublimation processes. Also considered was the possibility of effecting a high degree of purification by using both these volatilization methods in conjunction—possibly a distillation followed by sublimation of the solidified condensate. Distillation of MoC15 was investigated using a single stage distillation column packed with chemically resistant glass beads. Heating coils were wound around the column and collection tube (condenser). As-received MoCl5 was charged into a flask connected with the column using a side loading arm under an argon flow. After the column and condenser were brought to about 270" and 210°C, respectively, the apparatus was lowered until the flask was fully immersed in a constant temperature fused salt bath maintained at about 285 °C. Distillation was continued for about 10 or 15 min until 50 to 70 g of distillate had been collected. Analyses of these distillations indicated that several elements, e.g., Cu, Fe, Ni, Cr, and Mg, were lowered in quantity although not all were removed to the same extent. The occurrence of Na, B, Si, and A1 in the distillates appeared to be due to contamination, possibly from corrosion of the pyrex glass. An improved distillation system of larger capacity and longer distilling column was built. Improvements were effected in lowering the amounts of such impurities as B, Mn, Ni, Na, Mg, Cr, Cu, and Fe. These studies were pursued concomitantly with efforts to purify by sublimation; it was subsequently found that although improvements in purity were obtained by distillation, sublimation processes were simpler to control and effected a high degree of purity.

Jan 1, 1963

By J. W. Rutter, K. T. Aust

The migration of individual, large-angle grain boundaries has been studied as a function of tempereature and solute concentration in specimens of zone i.e filled lead containig very small additions of silver and of gold. Tile results are compared with various the-ories of grain boundary migration and with observations made prev.iorlsly of grain boundary migration in similar specimens of zone-refined lead containing tin additions. A previous investigation by the authors dealt with [he temperature dependence of grain boundary migration in bicrystals of zone-refined lead containing small additions of tin.' It was shown that tin additions as low as a few parts per million cause a large decrease in the grain boundary migration rate at any given temperature, as well as a marked increase in the temperature dependence of the migration rate. It was found that existing theories of grain boundary migration. based on the motion of dislocations. or upon the concept of atom transfer in groups across the boundary (group process theory). or upon the control of grain boundary motion by volume diffusion of impurity atonls along with the boundary. are incapable of accounting for the observations. The single process theory of grain boundary migration. which is an absolute reaction rate calculation based on the transfer ui atoms singly across the moving boundary, was found to predict the migration rate reasonably well for a number of boundaries whose motion was shown to be very little influenced by impurities, but not for boundaries whose illation was influenced markedly by impurities. It was concluded that the elementary process of grain boundary migration involves the activation of single atoms during transfer across the boundary. and that inadequate knowledge is available to permit the influence of impurities to be properly taken into account. The present study was initiated to check the validity of the above conclusions with other alloy systems, namely high-purity lead with small additions of silver and of gold. Both silver and gold diffuse faster. and with a lower activation energy of volume diffusion. than does tin in lead;' consequently, a study of the effects of silver and gold on grain boundary migration in high-purity lead offered a means of testing theories of boundary migration based on bulk diffusion of the solute (eg. ref. 3). In addition. it was hoped that the present work, in comparison with the results for tin in lead, would provide information concerning which factors are important in determin- ing the interaction between solute atoms and a grain boundary. EXPERIMENTAL PROCEDURE The preparation of bicrystals of zone-refined lead, with various silver or gold additions, was identical to that previously described for the lead-tin alloys.''4 Each bicrystal consisted of a striated crystal which was grown from the melt. and an adjacent striation-free crystal which was introduced by artificial nucleation and growth.''4 The striation or lineage substructure in the melt-grown crystal provided the driving force for grain boundary migration. During the preparation of striated single crystals by growth from the melt, it was found that silver or gold concentrations as low as 2 or 3 ppm by atoms were sufficient to cause formation of the hexagonal cell structure. which is due to the presence of impurity, during freezing. This structure is revealed on the solid-liquid interface by decanting the liquid during freezing. The hexagonal cell structure was observed previously4 in zone-refined lead crystals with tin contents above approximately 200 ppm by atoms. These concentrations of silver, gold, or tin are in agreement with the predicted amounts required for cell formation in lead,5'6 under the present conditions of freezing.4 The absence of cell structure at decanted interfaces, therefore, served as a useful indication that the silver or gold contents were less than 2 or 3 ppm by atoms in the specimens as grown. It was found that grain boundary migration occurred only very slowly when the solute content approached that necessary for cell formation. As a result, the present experiments were conducted with silver or gold additions less than 1 ppm by atoms. This impurity level is well within the solid solubility limits for silver and gold in lead.7 The annealing treatments, measurements of grain boundary velocities, and orientation determinations were carried out as described previously.' However. each bicrystal was also chemically polished in a solution consisting of 8 parts glacial acetic acid and 2

Jan 1, 1961

E. A. Loria (Product Metallurgical Engineer, Crucible Steel Co. of America, Pittsburgh)—In this interesting paper, our introductory work was quoted. We would like to call attention to our sequel paper on the experimental determination of oxygen in cupola-melted cast iron,20 which was not mentioned. Vacuum-fusion oxygen values (as well as hydrogen and nitrogen) were reported for nine heats of cast iron melted in the Battelle 10-in. cupola under normal operating practice and under oxidizing conditions. The oxygen analyses ranged from 12 to 68 pprn compared to the author's computed range of 10 to 80 ppm. The average amount of oxygen found in our irons was about 20 pprn and changes in the silicon content of the iron from 1.32 to 2.35 pct had no consistent effect on the oxygen content of the iron. The gas determination specimens were poured in split steel molds that produced a clean pin, 3/8 in. diam and 2 in. long. Because freezing was almost instantaneous, the pins were entirely white iron (nongraphitic). In the early stages of the investigation, the pins were transferred to a mercury-filled trap system immediately after pouring. This was done to collect gas evolved between pouring and analysis. However, it was found that during storage for 4 weeks gas evolution was negligible. Because the vacuum-fusion analysis was usually completed within 4 days of pouring, pins from later heats were not stored in the mercury-trap system. We found some evidence that cast iron picks up oxygen during long storage, because of rusting. Earlier work by the British Cast Iron Research Association has shown that cast irons may be stored for a long time without significant change in their oxygen content. The practical significance of this study (and our own) would be in the improvement of cast-iron quality. Has the author investigated this aspect and reached any conclusions on the effect of oxygen on the mechanical properties of cast iron? The second phase of our study was to determine the properties of the test bars poured simultaneously with the gas analysis specimens. We realize that there may be complicating factors attendant in this procedure.21 Results from many test specimens measuring chill depth, transverse flexure and deflection strength, spiral fluidity, and sensitivity to hardness of gray irons ranging from 12 to 68 pprn oxygen showed that the lowering of transverse strength was the only significant undesirable effect of high oxygen content. A statistical study of the chill test results21 showed that the iron containing 22 to 46 pprn oxygen had forced chill depths that were 2/32 in. below the expected value from their composition, and irons containing less than 16 ppm oxygen had forced chill depths averaging 1/32 in. greater than the expected chill depth. Higher oxygen contents, within the range of 12 to 68 pprn did not increase forced chill depth. With the wedge tests, there was a good linear relationship between carbon equivalent of the irons and their chill depth. The results indicated that oxygen contents below 50 ppm in the iron did not affect chill depth. With 50 to 70 ppm oxygen in the iron, oxygen appeared to have a slight graphitizing tendency. These results are in disagreement with the common belief in gray iron foundries that "oxidized irons" produce high chill depths. It would be appreciated if the author would comment on this subject. Gustaf Ostberg (author's reply)—In Fig. 1 the legend of line I should read 2 pct C, 1 pct Si. The author wishes to thank Mr. Loria for calling attention to his later work, which was published after the present paper was concluded. The range of oxygen contents quoted seems to agree well with the author's values. The lack of response to variations in silicon content is probably due to the fact that the oxygen content in most cases was below the saturation level. The absence of temperature dependence, even in the case of saturation, is understandable if the difficulty in formation and escape of the deoxidation products is taken into account.

Jan 1, 1960

By K. G. Davis, P. Fryzuk

The diffusivity of silver in liquid tin has been determined, using the capillavy-reservoir technique, over the temperature range 250° to 500°C. The new value, D = 2.5 x 10'* exp(-2480/ RT) sq cm per sec, differs from that obtained by other workers in an earlier investigation. The analysis of data from the capillary-reservoir technique is discussed. In a recent investigation of the solidification of dilute alloys, values for the diffusion constant of silver in liquid tin were required in the analysis of the formation of impurity substructures. AS a result, measurements were made of the diffusion constants in the temperature range 250° to 500°C (melting point of tin 232°C), for the alloy concentrations used in the solidification experiments and at higher concentrations, to verify previous determinations.I)2 The capillary-reservoir method was adopted, using experimental procedures similar to those followed by Ma and Swalin,1 with the main exception that radioactive silver was used in the present investigation to facilitate solute-concentration measurements. EXPERIMENTAL PROCEDURE a) 100 ppm Samples. Glass capillary tubes of 2 mm inside diameter and approximately 5 cm- long were sealed at one end, evacuated, and filled with tin of 99.999 pct purity. The region of shrinkage near the mouth was cut off, and the tubes were then placed in a graphite holder and immersed, with the open end up, in an unstirred bath of alloy containing 100 ppm Ag 110, where they remained for periods of up to 30 hr. On removal from the bath they were cooled by an air blower. The bath was kept under a small positive pressure of argon, and the temperature controlled to within +1°C. A 10-hr diffusion period was used in the majority of the tests, scatter on runs of less than 5 hr being rather large. The procedure outlined above was chosen in preference to putting alloy in the capillary and pure tin in the bath, in order to avoid segregation when the tubes filled with alloy were first solidified. To minimize segregation when the diffusion period was complete and the capillaries again solidified, the earlier samples were held in thin-walled silica tubes which could be cooled very rapidly. Later tests were made in precision-bore Pyrex tubes, to eliminate effects caused by variations in the capillary diameter. No consistent differences in diffusivity as measured in the two types of tube were detected. After removal from the glass tubing, the samples were sectioned into 2.5 mm lengths and counted for y activity, using a scintillation counter with fixed geometry. Samples were also drawn directly from the bath and counted, so that values for C/C,, the ratio of the weight of Ag 110 in the sample to that in the bath, could be obtained. b) 5000 ppm Alloy. To check for possible effects of concentration, the silver content of the bath was increased to 5000 ppm. Complete mixing was found to have taken place in the capillary after a 10-hr period at 300°C. It appears that the greater density of the alloy was sufficient for buoyancy forces to cause instability in the alloy-tin interface, leading to rapid convective mixing. For the 5000 ppm alloy, therefore, the bath was of pure tin and the capillary tube was filled with alloy. With this arrangement, values of D consistent with those for the 100 ppm alloy were obtained, Fig. 1. CALCULATIONS OF DIFFUSIVITY The terminology used applies to a capillary of pure tin immersed in a bath of alloy. 1) Error-Function Method. under the present experimental conditions, the rod of liquid tin into which silver is penetrating may be considered semi-infinite. Assuming the concentration at the mouth of the tube to remain constant at Co, the concentration C at distance x from the mouth of the tube at time / is given by3 Plots of the inverse error function of (1 -C/Co) vs .v gave straight lines passing through the origin with slope 1/2-, x being corrected for shrinkage both on solidification and while cooling to the melting point (total correction about 6 pct at 500°C). Values for log D obtained in this manner are shown in Fig. 1. A least-squares fit to the relation D = Do exp(-Q/RT)

Jan 1, 1965

By J. Washburn, R. Drouard, E. R. Parker

Temperature dependence of the rate of recovery in zinc single crystals after a simple shear deformation at low temperature was investigated. Some tentative suggestions regarding the annealed and strain-hardened states of a crystal are discussed. RECOVERY may be defined as the gradual return of the mechanical and physical properties of strain-hardened metal to those characteristic of the annealed material; an increase in temperature increases the rate of recovery. The annealing process in strain-hardened polycrystalline metals is complicated by the inhomogeneity of strain which always exists in aggregates. Polygonization in bent regions of the crystals and growth of new almost strain-free grains starting at points of severe local distortion1-:' make it almost impossible to isolate and study the recovery process. Homogeneously strained single crystals, however, do not polygonize or re-crystallize and hence they can be used advantageously to study recovery. In such crystals strain hardening is completely removed by recovery alone. Since recovery is a process whereby certain lattice disturbances introduced by plastic flow are gradually reduced, a knowledge of the rate and temperature dependence of this process for various conditions of prestrain might be helpful in formulating a model of the strain-hardened state. For simplicity it seemed desirable to limit the type of prestrain to the simplest obtainable, i.e., simple shear strain. In the experiments to be described, recovery was studied by observing changes in the stress-strain curve of prestrained zinc single crystals held for various times at temperatures above that employed for straining. Single crystals were grown from the melt by a modified Bridgeman technique from Horse Head Special zinc 99.99 pct pure, and from spectrographically pure zinc 99.999 pct pure. They were grown as 1 in. diameter spheres and acid-machined' to the final specimen contour. The test section was a cylinder about 1/8 in. high and 3/4 in. in diameter. The conical sections adjacent to the test section were cemented into the grips so the load could be transmitted to the crystal as uniformly as possible. The specimens were oriented so that in testing the maximum shear stress was applied along one of the slip directions, [2110], in the (0001) plane. Details of the production and testing of such specimens have been presented.' Each test was carried out according to the following schedule: 1—The crystal was strained at — 50°C until it reached a maximum shear stress, ,,,. The strain rate was approximately 5 pct per min in all cases. 2—After straining, the crystal was unloaded before the temperature was changed. Unloading required about 3 min. 3—The temperature of the specimen was then increased from — 50°C to the temperature, T, of recovery. This change in temperature was completed in a time of less than 2 min. The specimen remained at temperature, T, for a time, t, which differed for the various specimens. 4—Thereafter the temperature was again reduced to — 50 °C in approximately 3 min. 5—While at —50°C, the stress-strain curve after recovery was obtained. 6—The specimen was then unloaded and annealed for 1 hr at 375 °C in a helium atmosphere to bring about complete recovery. Cooling to room temperature after anneal required 90 min. 7—The same crystal could be re-used for another test because the plastic properties after annealing closely duplicated those of the original crystal. The specimen was immersed during the test in a bath of methyl alcohol which, through a system of tubes, could be pumped through either of two heat exchangers to regulate the temperature; this was accomplished by circulating the liquid through coils immersed in a bath of acetone and dry ice for cooling or in a bath of warm water for heating. Test temperatures were thus maintained constant within ±1°C. The — 50°C temperature was low enough so that no measurable recovery occurred during unloading and reloading. The stress-strain curve continued after recovery along a path below, but approximately parallel to, the path of a curve obtained in an uninterrupted test. Fig. 1 shows some of the results from a specimen of 99.999 pct Zn. The amount of downward displacement of the curve due to recovery was a

Jan 1, 1954

By H. J. Ramey

The wellbore acts as a storage tank during drawdown and build-up testing and causes the sand-face flow rate to approach the constant surface flow rate as a function of time. This effect is compounded if non-Darcy flow (turbulent flow) exists near a gas wellbore. Non-Darcy flow can be interpreted as a flow-rate dependent skin effect. A method for determining the non-Darcy flow constant using this concept and the usual skin effect equation is described. Field tests of this method have identified several cases where non-Darcy flow was severe enough that gas wells in a fractured region appeared to be moderately damaged. The combination of wellbore storage and non-Darcy flow can result in erroneous estimates of formation flow capacity for short-time gas well tests. Fortunately, the presence of the wellbore storage eflect permits a new analysis which can provide a reasonable estimate of formation flow capacity and the non-Darcy flow constant from a single short-time test. The basis of the Gladfelter, Tracy and Wilsey correction for wellbore storage in pressure build-up was investigated. Results led to extension of the method to drawdown testing. If non-Darcy flow is not important, the method can be used to correct short-time gas well drawdown or build-up data. A method for estimation of the duration of wellbore storage effects was developed. INTRODUCTION In 1953, van Everdingen and Hurst generalized results published in their previous paper3 concerning wellbore storage effects to include a "skin effect", or a region of altered permeability adjacent to the wellbore. Later, Gladfelter. Tracy and Wilsey4 presented a method for correcting observed oilwell pressure build-up data for wellbore storage in the presence of a skin effect. The method depended upon measuring the change in the fluid storage in the wellbore by measuring the rise in liquid level. To the author's knowledge, application of the Gladfelter, Tracy and Wilsey storage correction to gas-well build-up has not been discussed in the literature. It is, however, a rather obvious application. Gas storage in the wellbore is a conlpressibility effect and can be estimated easily from the measured wellbore pressure as a function of time. Several approaches to the wellbore storage problem have been suggested. As summarized by Matthews, it is possible to minimize annulus storage volume by using a packer, and to obtain a near sand-face shut-in by use of down-hole tubing plug devices. Matthews and Perrine have suggested criteiia for determining the time when storage effects become negligible. In 1962, Swift and Kiel' presented a method for determination of the effect of non-Darcy flow (often called turbulent flow) upon gas-well behavior. This paper provided a theoretical basis for peculiar gas-well behavior described previously by Smith. Recently, Carter, Miller and Riley observed disagreement among flow capacity k,,h data determined from gas-well drawdown tests conducted at different flow rates for short periods of time (less than six hours flowing time). In the original preprint of their paper, Carter et al. proposed that the discrepancy in flow capacity was possibly a result of wellbore storage effects. Results of an analytical study of unloading of the wellbore and non-Darcy flow were recorded by carter.14 In the final text of their paper, Carter et al.!' stated that they no longer believed wellbore storage was the reason for discrepancy in their kgh estimates. In view of the preceding, this study was performed to establish the importance of non-Darcy flow and well-bore storage for gas-well testing. In the course of the study. a reinspection of the previous work by van Everdingen' and Hurst' was made, and the basis for the Gladfelter, Tracy and Wilsey' wellbore storage correction was investigated and extended to flow testing. WELLBORE STORAGE THEORY As has been shown by Aronofsky and Jenkins,11-12 Matthews," and others, flow of gas can often be approximated by an equivalent liquid flow system. The following developnlent will use liquid flow nomenclature to simplify the presentation. Application to gas-well cases will be illustrated later. First, we will use the van Everdingen-HursP treatment of wellbore storage in transient flow to establish (1) the duration of wellbore storage effects, and (2) a method to correct flow data for wellbore storage. DURATION OF WELLHORE STORAGE EFFECTS When an oil well is opened to flow. the bottom-hole pressure drops and causes a resulting drop in the liquid level in the annulus. If V. represents the annular volume in cu ft/ft of depth, and p represents the average density of the fluid in the wellbore, the volume of fluid at reservoir conditions produced from the annulus per unit bottom-hole pressure drop is approximately: res bbl-- (V, cu ft/ft) (144 sqin./sq ft) psi -(5.615 cu ft/bbl)(pIb/cuft) ........(I)

Jan 1, 1966

By Joachim J. Hauser

Experiments on latent hardening were peyformed by compressing single crystals along a direction perpendicular to the tension axis. The slope and length of easy glide in the tension test were found to depend only on prior deformation in the same slip plane. Prior deformation on a different slip plane changes the stress level of the resulting stress-strain curve. The yield points appearing upon reloading after prior extension and unloading were related to the end of easy glide. SEVERAL researchers have studied the latent hardening due to deformation of a crystal by slip on a slip System after prior deformation. These experiments can be divided into those in which the prior deformation was on the same plane as the subsequent and those in which the two deformation processes were in different planes. In the former category are the experiments of Buckley and Entwistle,1 Parker and washburn,2 and Haasen and Kelly.3 The latter case has not been studied systematically; it was the main purpose of this investigation to produce this type of latent hardening and explain the results in terms of the existing theories of work hardening. In general, tension producing slip on a certain slip system can be preceded by tension, transverse compression or longitudinal compression, each with predictable dislocation movement and intersection. The intersection of dislocations can lead to glissile or sessile jogs, Cottrell-Lomer locks and other sessile dislocations. The effect on the stress-strain curve could depend on which combination of the former mechanisms is operating. Haasen and Kelly3 have studied the yield points which occur in aluminum and nickel single crystals upon reloading after prior unloading in a tension experiment. They attributed this effect to the anchoring of dislocations occurring during unloading. As Cottrell and stokes4 have shown that dislocations cutting through the "forest" could only lead to reversible changes, they attributed the anchoring to the formation of sessile dislocations during unloading. However, different kinds of sessile dislocations could be formed during unloading, and it was the purpose of this experiment to determine whether Cottrell-Lomer locks are responsible for the yield effect and for the end of easy glide. The case where a longitudinal compression is followed by tension along the same axis is commonly referred to as a Bauschinger test. This type of effect was studied by Buckley and Entwistle1 on aluminum single crystals and by Parker and washburn2 on zinc single crystals. In such a test, the tension and the compression activate the same slip plane with opposite slip directions. The use of sideways compression in the present experiments permits the activation of different types of slip systems and the study of their effect on the easy glide region and on the transition between the elastic and easy glide region. The theory of seeger5 for the flow stress in fee materials is applied to explain the latent hardening. EXPERTMENTAL PROCEDURE All the single crystals used in this investigation had an axial orientation close to <210>, called the "0.5" orientation. This is the orientation for which the tensile axis is 45 deg from both the slip plane and the slip direction. The single crystals were grown from the melt under a helium atmosphere using milled graphite boats,=at a rate of 8.6 mm per min. The silver used in the experiment was 99.98 pct pure. The single crystals had a square cross section about 0.9 by 0.9 cm and a length of 14 cm. The orientation of the specimen was determined within ±2 deg by the Laue back-reflection method. The specimens were annealed at 940&apos; ± 2°C in a helium atmosphere for 24 hr and then furnace cooled over a period of 7 hr. The specimens were electropolished in a solution of 9 pct KCN in water. The specimens were tested in a soft-type tensile machine (the load is prescribed) up to 3 pct strain. The stress was increased continuously at approximately 30 g per mm2 per min. The strain was measured over a 5 cm gage length with a mechanical extensometer employing an optical lever. The strain and stress were measured with accuracies of i 2 X 10-5 and ± 2 g per mm2, respectively. The remainder of the stress-strain curve up to 20 pct strain was obtained in a hard-type tensile machine (the strain rate is prescribed). The strain and the stress were measured in that machine with an accuracy of ±2 pct. The compression tests were performed in the hard-type machine using accurately machined steel blocks without lubrication. The blocks were used so as to apply a uniform compression over a length of 13 cm. The strains were measured on the hard-type machine and with a micrometer.

Jan 1, 1962

By Carl J. McHargue

Mechanical twins were produced in electron-beam melted columbium by high-speed impact at room temperature and by slow or fast compression at -196°C. The composition plane of the twins was { 112} and the shear direction was <111>. Notches in the twin bands often corresponded to traces of {110) of the matrix and appeared to be untwinned regions. Markings within the twin bands were interpreted as resulting from {110} slip in the twins. THERE has been much work in recent years concerning plastic deformation by glide, and the dislocation theory relating to glide has reached a relatively high degree of development. On the other hand, there have been fewer studies of deformation by mechanical twinning, and understanding of this process is far from satisfactory. This method of deformation is of interest for at least two reasons. First, it provides a mechanism in addition to glide for the relief of stresses, and, in the bcc and hexagonal close-packed metals may result in significant amounts of plastic flow. Secondly, there is the possibility that twins may act as barriers for dislocation movement, resulting in pile-ups which could nucleate cracks. As might be expected, the bulk of the literature on mechanical twinning in the bcc metals is concerned with iron. A good summary of the work done prior to 1954 is contained in the book by all.&apos; Recently the refractory bcc metals have become increasingly important. Limited studies have shown that tantalum,2,3 molybdenum,4,5 vanadium,6,7 tungsten,&apos; and columbium9-11 deform by mechanical twinning under some conditions. Alloys of molybdenum with rhenium and tungsten with rhenium show extensive deformation by twinning at room temperature.I2-l4 Most of these studies have dealt primarily with mechanical properties at low temperatures or have shown the existence of twins, and there is only a small amount of information concerning the conditions under which they form. The subject of the present paper is the formation of twins under stress in columbium with a consideration of their morphology. EXPERIMENTAL PROCEDURE The material used for these studies was taken from an ingot of columbium which had been melted twice by the electron-be am-method. The analysis of the ingot was (in ppm): B < 1, C = 10, Fe < 100, The cast ingot contained very large grains, and it was possible to obtain single-crystal prisms which measured from ¼ to 3/4 in. on a side. A few experiments were conducted on polycrystalline plate which was prepared by rolling material from the same ingot at room temperature and annealing at 1000 in a dynamic vacuum of 10-6 mm Hg. This gave a plate in which the grains had an average diameter of 3 mm. After the specimens were cut from the ingot, the six faces were metallographically polished and elec-tropolished to remove all traces of cold work. Most of the observations were made on the surfaces of the deformed specirllens without further treatment. Occasionally, etching after deformation was desirable. In these cases, an etchant of the composition 50 parts H2O, 5 parts HNO3 25 parts HF, and 10 parts H2SO4 was found to delineate the twins very well. Unless considerable care was taken to ensure the removal of all disturbed metal left by the mechanical polishing, etching failed to reveal many of the features discussed in this; paper. The specimen&apos;s were deformed either by impact or slow compression at 77°K (liquid-nitrogen coolant), 198°K (dry ice and acetone coolant), and 298°K. The impact load was delivered by a hammer except in one case where the load was delivered by a bullet. Slow compression was carried out on a hydraulic testing machine equipped with a chamber to hold the coolant. EXPERIMENTAL RESULTS It has been generally believed that the conditions favoring the formation of deformation twins are large grains, low temperature, and impact loading. In fact, Barrett and Bakish2 found twins in tantalum only after impact deformation at 77°K, and Adams, Roberts, and Smallman10 observed twins in columbium only at 20 For these reasons, the initial experiments of this study used impact loading. Hammer blows caused many bands resembling twins in single crystals a.t 77" but not at 198°K. Only a few slip lines were observed on any of the single-crystal specimens of this study—essentially all the deformation occurred by twinning. The appearance of the twins on the as-deformed surface is shown in Fig. 1. Although both Figs. 1(a) and l(b) are photomicrographs of twins taken at the same magnification and from the same crystal, they are startlingly different in appearance. Fig. 1(a) was taken from the crystal face approximately perpendicular to the shear direction, whereas Fig. 1(b) was taken from

Jan 1, 1962

By T. L. MacKay

Oxidation rates of single-crystal and poly crystalline zirconium in oxygen at temperatures from 307° to 815°C obey the parabolic rate law for short ex-posure time, 4 to 6 hr. The activation energy for the oxidation of single-crystal zirconium between 420° and 790°C is 42.6 ± 0.7 kcal per mole, and in the temperature range 307" to 600°C the activation energy for oxidation of poly crystalline zirconium is approximately the same. The high-activation energy is indicative that diffusion through the bulk oxide film is the primary mode of mass transport for both types of metal. The higher oxidation rates for poly -crystalline zirconium in this temperature range were attributed to differences in the orientation of the grains in the metal with respect to the oxidizing surfaces. Above 600°C, vain growth was observed in polycrystalline zirconium, and the oxidation rates approached those of single-crystal zirconium. ThE kinetic data of previous oxidation studies1-&apos; of zirconium in oxygen have been interpreted by both parabolic and cubic rate laws. There is some evidence that there is a transition from the parabolic to the cubic rate law at prolonged exposures, but the question is still controversial. For the parabolic rate law activation energies are reported in the range 18.6 to 35 kcal per mole, and for the cubic rate law in the range 38 to 47 kcal per mole. So far as the mechanism of zirconium oxidation is concerned, inert marker studies10,11 have indicated that the oxidation proceeds by oxygen (anion) diffusion through the oxide film toward the metal-metal oxide interface. Pemslerl2 observed that the orientation of the grains in the zirconium metal substrate affected the rate of formation of the oxide film on the surfaces of the grains and that the orientation dependence of the corrosion rate persisted beyond the initial stages of reaction. The rate of oxidation was a minimum when the c axis of the grain was parallel to the surface of the sample, and rose to a maximum when the c axis was inclined at about 20 deg to the plane of sample surface, and decreased again at higher inclinations. cox13 observed that in 300°C steam a thin oxide film was formed initially on zirconium and that this oxide film, which exhibited interference colors, became dark first along the grain boundaries and then over the whole surface in an inhomogeneous manner as the film thickened. Cox proposed a mechanism in which oxygen diffused along preferred paths created by grain boundaries in the metal and formed a much thicker film at or near the grain boundary than on the central zone of the grain. In the present study, the oxidation rates of single crystals of zirconium were measured in oxygen and compared with the oxidation rates of polycrystalline zirconium of the same bar stock. It was felt that such a comparison would elucidate the role of grain boundaries in the metal substrate. SAMPLE PREPARATION Single crystals of zirconium were prepared by following the procedure of I3apperport,14 starting with 1/4-in. rod purchased as crystal-bar zirconium. Zirconium rods 2 in. long were wrapped in tungsten foil and sealed in quartz tubes at pressures of less than 10-6 mm of mercury. Large single crystals were grown by thermal cycling above and below the a-/3 transformation temperature, 862°C. Several specimens were simultaneously subjected to the same cycling procedure, heating to 1200°C, holding for 4 hr, then cooling in the furnace and holding at a temperature of 840°C for 5 to 10 days. This cycle was repeated five or six times for each set of specimens. The grain size of the crystal-bar zirconium before thermal cycling was between 10 and 30 p. Fig. 1 shows the microstructure of an end section of as-received crystal-bar zirconium. A longitudinal section of each zirconium rod after thermal cycling was polished and examined under polarized light, see Fig. 2, and the largest single crystals were selected for this study. Zirconium rods 1/8 in. in diameter and 1/2 in. long with spherical ends were machined from the single crystals and from the as-received bar stock. An X-ray examination showed that the c axis of the single crystals made either a 34-deg or an 89-deg angle with the rod axis. The specimens were chemically etched for 2 min in solution consisting of 15 parts hydrofluoric acid (48 pct), 80 parts nitric acid, and 80 parts water. The chemical polish removed 1 to 2 mils from the surface. EXPERIMENTAL The Sartorius vacuum microbalance used in this study has a sensitivity of 0.5 pg and a capacity of

Jan 1, 1963

By M. O. Abo-el Fotoh, J. B. Mitchell, J. E. Dorn

The effect of strain rate and temperature on the tensile flow stress of a polycrystalline bcc alloy of magnesium containing 14 wt pct Li and 1.5 wt pct Al was investigated for strain rates of 3.13 x lom5 to 3.13 x 10-3 per sec over the range from 20° to 300°K. From about 180° to 300°K the alloy exhibited an ather-ma1 deformation behavior where the flow stress was independent of strain rate and increased only slightly with decreasing temperature. At lower temperatures the flow stress was strongly strain-rate- and temperature-dependent, characteristic of deformations controlled by thermally activated mechmzisms. The activation volume for thermally activated plastic defornzation was between 5 and 30 cu Burgers vectors, independent of plastic strain. This low-temperature thermally activated deformation behavior was found lo be in satisfactory agreement with the theoretical dictates of the Dorn-Rajnak1 formulation of the Peierls mechanism where deformation is controlled by the rate of nucleation of pairs of dislocation kinks over the Peierls energy barriers. SEVERAL studies of the low-temperature thermally activated deformation of bcc metals and alloys (molybdenum,1 tantalum,1 Fe-2 pct Mn,2 Fe-11 pct MO,3 and AgMg4) have revealed that the strain rate is controlled by the activation of dislocations over the Peierls-Nabarro energy hills. Although there is some uncertainty as to the nature and effect of solute atom-dislocation interactions during low-temperature deformation of bcc metals, it has been concluded by Dorn and Rajnak,1 Conrad,1 and Christian and Masters6 among others that overcoming the Peierls-Nabarro stress which arises from the variations in bond energies of atoms in the dislocation core as it is displaced is the probable mechanism controlling low-temperature deformation. The purpose of this research was to investigate the low-temperature plastic deformation of the bcc alloy Mg-14 wt pct Li-1.5 wt pct A1 to determine if the behavior of this alkali metal alloy might be analogous to that for other bcc metals. This alloy was selected because of its availability and its current industrial importance as a lightweight material for aircraft and aerospace applications. I) EXPERIMENTAL PROCEDURE Polycrystalline tensile specimens having cylindrical gage sections 2 in. long by 0.2 in. in diam were machined from as-received alloy sheet stock of Mg-14 wt pct Li-1.5 wt pct Al. Specimens were annealed in an argon atmosphere at 423°K for 4 hr and maintained in a kerosene bath together with the sheet stock to prevent corrosion. The resulting specimen microstructure consisted of a coarse uniform dispersion of incoherent precipitate MgLi2Al particles7 in a bcc 0 phase matrix having an average grain size of 150 p. Prior to testing the specimens were chemically polished in dilute hydrochloric acid. Comparison of tensile properties and microstructures of specimens cut from center and edge sections of the sheet stock revealed no effects of inhomogeneities in the sheet material. Tensile tests were performed on an Instron machine at crosshead speeds corresponding to tensile strain rates of 1.56 x 10-5 and 1.56 x 10"3 per sec. Stresses were determined to ±2 x 106 dynes per sq cm and strains to within ±0.0001. Average values of shear stress t and shear strain y reported were taken as one half the tensile stress and three halves the tensile strain, respectively. Flow stresses were taken at 0.05 pct strain offset. Test temperatures down to 77°K were obtained by immersing the specimens in constant-temperature baths. Lower-temperature tests were performed in a liquid helium cryostat to within ±2°K of the reported values. Prior to testing at the various temperatures and strain rates all specimens were prestrained at 2 35°K at a shear strain rate of 3.13 x 10-5 per sec to a stress level of 0.606 x 10&apos; dynes per sq cm to obtain a uniform initial state. Additional tests were made to determine the effect of changes in strain rate and strain on the flow stress by rapidly changing the crosshead motion during testing. Shear moduli of elasticity, needed for analyses of the data, were obtained at several temperatures by a common technique of determining the resonant frequencies of vibrations of rectangular test specimens. 11) EXPERIMENTAL RESULTS Fig. 1 shows the experimentally determined flow stress vs temperature for two strain rates. Two distinct regions of behavior are evident. Below about 180°K the strong increase in flow stress with increased strain rate and decreasing temperature indicates that deformation is controlled by a thermally activated dislocation mechanism. At higher temperatures an athermal region is evident where the flow stress is independent of strain rate and only slightly dependent on temperature. The applied stress t to cause plastic flow was separated into two components:

Jan 1, 1969

By Paul A. Taylor

MUCH information concerning pegmatites which was thought to be true a few years ago has been proved false, and what is now actually known about some pegmatites is not true of many others. The erratic and seemingly unpredictable structure and variable composition of this class of mineral deposits has been widely emphasized. Even parts of the same pegmatite body exhibit marked differences in texture, mineral composition, width, and attitude. Constructive geological thinking in respect to pegmatites now aims to establish general laws rather than to stress the confusing diversity of features having no special economic significance. Substantial progress has been made in classifying different types of these deposits according to general features, internal structure, mineralogy, and origin. In some cases it has even been possible to block out tonnage reserves in advance of mining. It is still easy, however, to make highly erroneous predictions after a preliminary examination of a pegmatite prospect. Pegmatites are important to the economic well being of the country and to its military security. They furnish virtually all the feldspar, strategic mica, beryl, columbium, tantalum, and caesium utilized in the United States, as well as sundry other minerals and significant amounts of lithium and rare earth minerals and gems. With the exception of vermiculite, occasional ilmenite-rutile, and perhaps soda-lime feldspar and garnet deposits, basic pegmatites are of little economic importance. Consequently in this paper, as in common parlance, the term pegmatite generally relates to coarsegrained acidic rocks or what is aptly called giant granite. Available data indicating the size and importance of the production and trade in specified pegmatite minerals are summarized in Table I. Geological Features Much of the latest thinking on the economic geology of pegmatites is now available in a 115-page monograph&apos; by a group of experts who participated with geologists of the Federal Geological Survey in the widespread wartime investigations. Doubtless the most significant feature of the monograph is indicated by the title, The Internal Structure of Pegmatites, but it also contains a vast amount of other new information and includes the assimilated concepts of many earlier writers, whose works are given in a comprehensive list of references. The shape, size, attitude, and continuity of many pegmatite bodies is controlled by the structure of the older rocks in which they occur. If the older rocks are easily penetrated, e.g., biotite schist, most of the pegmatites in a given district will be found outside the parent granite mass as exterior pegmatites. Marginal pegmatites are more prevalent if the older rocks are massive, unsheared, and sparingly jointed. Networks of pegmatites are abundant in highly-jointed rocks. In strongly foliated schists the bodies are usually lenticular, whereas in highly-folded areas they assume tear drop, pipe or pod-like, bow-shaped, or sinuous forms. Jahns2 recognizes five major shape classes: l—dikes, sills, pipes, and elongate pods; 2— dikes, sills, pipes, and pods with bends, protuberances, or other irregularities; 3-—trough-or scoop-shaped bodies with or without complicating branches; 4—bodies with the form of an inverted trough or scoop; and 5—other bodies, including combinations of the above and miscellaneous shapes. Many pegmatite deposits are scarcely big enough to be recognizable as such. Most of them, in fact, are small tabular deposits less than 4 in. wide and usually without economic concentrations of minerals. On the other hand, some pegmatites are more than a mile long and over 500 ft wide. The ratios of length to breadth range from 1 : 1 to 1 : 100. Although the vertical dimension bears no invariable relationship to strike length, tabular deposits or large lenses are often symmetrical enough to show nearly as much continuity down dip as in their horizontal extension, and some pipes or pods are amazingly persistent in the vertical plane. Small pegmatites often string along a fairly definite trend line; in a given district major bodies may lie roughly parallel, and where only a few of them do not, the erratically disposed bodies generally differ in composition from those conforming to the regular pattern. This does not apply, however, in all districts. Characteristically, pegmatite veins pinch and swell or split into branches. When they pinch out entirely it is often possible to find a new body by prospecting the extension of the strike or dip, but the chances of finding a hidden deposit are ordinarily too uncertain to justify much subsurface prospecting. Diamond drilling may yield valuable information as to the continuity of known deposits whose upper portions are well-exposed. Some deposits, in fact, can be proved up for hundreds of feet by surface trenching and then intersected by drill holes at various depths like any other vein-like deposit. Others twist and branch, apparently defying all efforts to explore them short of actual mining.

Jan 1, 1954