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By D. C. Hilty, W. Crafts

A qualitative pseudoternary solidification diagram for the Fe-S-O system modified by manganese is proposed and supported by experimental derivation of an isothermal section at 1475°C and substantially 1 pct Mn in the solid-metal phase. The solubility of oxygen in liquid iron containing 1 pct Mn and sulphur contents up to 0.9 pct has been measured at 1600°C and found to increase as the sulphur content exceeds 0.15 pct. AS has been pointed out previously,' all oxide and sulphide inclusions in steel, excluding mechanically entrained matter, result from modifications of the basic Fe-S-O system. Therefore, one method of attack on the problem of the mechanism of deoxida-tion and inclusion formation is to examine the influence of deoxidizers on the Fe-S-O liquidus diagram. This approach has been adopted in work on the subject being carried out at the Metals Research Laboratories of the Electro Metallurgical Co. and has resulted in the postulation of types of solidification diagrams for the Fe-S-O system modified with common deoxidizers. This method has been of considerable assistance in interpretation of the factors affecting the formation of inclusions.' For the most part, however, these diagrams have been highly speculative. They were constructed primarily by inference from the pertinent binary and ternary systems and from the appearance of inclusions produced by specific deoxidizers. Moreover, since the systems contain four or more components, simplifying assumptions and qualifications were necessary in order to permit their representation as modifications of the Fe-S-O diagram. Consequently, experimental confirmation of the type of construction employed for these diagrams is desirable, and the present paper is concerned with such evidence. The addition of manganese to the Fe-S-O system was selected for initial investigation. Manganese is an important component of practically all steel and is, therefore, of fundamental interest. Because of its great affinity for sulphur, manganese has a more profound effect on the sulphide side of the Fe-S-O diagram than any of the other common deoxidizing eletments. In addition, more quantitative information pertaining to the contiguous binary and ternary systems involving iron, manganese, sulphur, and oxygen is available than for the other deoxidizers. Fe(Mn)-S-O Solidification Diagram Many of the side diagrams of interest in connection with this system are known. The Fe-Mn binary has been well established by several investigators;% the Fe-O system has been clarified by Darken and Gurry;' and FeO-MnO diagrams have been published by Herty,5 Andrew, Maddocks, and Howat,6 and by Hay, Howat, and White.7 The Mn-O diagram does not appear to have been derived experimentally, but the portion of 'it that is of interest can be visualized easily from a consideration of the melting points of Mn and MnO and the fact that a broad miscibility gap must exist between them. The ternary Fe-Mn-O diagram has been discussed by Benedicks and Löfquist,8 Wentrup,9 and by Körber and Oelsen.10 Experimental study of the Fe-Mn-O system has been carried out by Körber and Oelsen and to a lesser degree by Chipman, Gero, and Winkler,11 Hilty and Crafts," and others. On the basis of published information, then, an outline of the Fe-Mn-O liquidus diagram can be constructed as illustrated by Fig. 1. In this, as in all succeeding diagrams, transformations such as the ?-? reaction in iron have been ignored for purposes of simplification. The arrows denote falling temperature. The distinguishing feature of this diagram is the broad region of liquid immiscibility extending

Jan 1, 1955

By G. R. Speich, D. J. Mack

The transformation of was studied by isothermal methods. At all temperatures, the ß transforms quickly to fine grained ß" which develops silver-rich striations. At higher temperatures the striations disappear, the final structure being Widmanstatten a in ß'. At lower temperatures, the striated ß" is consumed by pearlite nodules of a + ß' which in turn form the Widmanstatten a in ß'. The transformation is unlike any previously reported for a eutectoid. AS part of a general program of study on the eutectoid reaction, the Ag-Cd eutectoid seemed particularly attractive because the ß phase which undergoes the reaction is another of the typical "electron compounds," AgCd, having the disordered body-centered cubic structure. This work deals with the eutectoid which occurs at 50.5 wt pct Ag, and not with the eutectoid which has been reported at 42.9 pct Ag.' There has been no work reported specifically on the Ag-Cd eutectoid which was studied. The only information available on this eutectoid is that work done in the determination of the phase diagram. For the most part, the terminal portions of the diagram, Fig. 1, are well established; however, the region from 40 to 60 pct Cd is still somewhat in doubt. The X-ray evidence'..' in this region is in conflict with the results of thermal analysis. X-ray analysis3 does not show a polymorphic transformation at about 240°C as indicated by thermal analysis.1,5 Even the X-ray evidence, within itself, is confusing in this region of the diagram. One investigator2 reports the ß phase as hexagonal close-packed and has found three phases in the one-phase ß field. Other X-ray investigators"' ' report the ß phase as body-centered cubic. The authors believe that much of the confusion resulted from incomplete homogenization of the alloys. It was found that it takes almost a week to produce a completely homogeneous two-phase structure at 370°C. Another possible source of error is the volatilization of cadmium from the surface and cracks of the specimen during annealing with the possible formation of a cadmium-poor phase. The only metallographic data available on this eutectoid alloy are those of Durrant1 and Fraenkel and Wolff.5 his information is very limited. The phase diagram chosen as most nearly correct is that in the Metals Handbook," which is almost identical with the phase diagram suggested by Durrant.1 Materials and Procedure The alloy was prepared from high purity silver (999.5 plus fine) and high purity cadmium (0.02 Pb, 0.005 Cu, trace Fe). The metals were melted in carbon under a nitrogen atmosphere. Some cadmium was lost by volatilization but by remelting several times and adding cadmium a 200 g ingot of approximately eutectoid composition was obtained. Because the CdO fumes are quite toxic, the exit gas from the furnace was led through a water trap to condense the CdO. The ingot was homogenized at 650°C for 24 hr, no attempt was made to prevent decadmiumization. This resulted in a narrow decadmiumized rim on the ingot which was removed. Filings for analysis were obtained from cross sections of the ingot. Silver was determined by the Volhard thiocyanate method,? cadmium by difference. The ingot analyzed 50.8 pct Ag at the top of the ingot and 50.7 pct at the middle and at the bottom of the ingot. This alloy was only slightly hypo-eutectoid compared to the accepted value of 50.5 pct Ag and was used for the isothermal studies. It was felt that further attempts to adjust the composition might be futile because of the volatility of the cadmium. The ingot was sectioned to specimens approximately 3/4 x 3/4 x 1/8 in. These specimens were "austeni-tized" for 3 hr in air at 650°C to yield homogeneous ß and then quenched into a salt bath held at constant subeutectoid temperatures where the transformation

Jan 1, 1954

By C. H. Li, R. J. Stokes, T. L. Johnston

The phenomenon of solid-solution strengthening has previously been studied in a number of binary alloy systems.1-8 There has been, however, very little information published concerning the strengthening effects of specific solutes in magnesium alloys. Schmid and his coworkers9,10 investigated the behavior of aluminum and zinc in binary and ternary magnesium-alloy single crystals, but this work was done before high-purity materials were readily available. Workers at the Dow Chemical companyH reported increases in the critical resolved shear stress upon alloying magnesium single crystals with zinc and indium. Recently, Hardie and parkins* investigated the extent of hardening produced by the addition of various solutes to poly crystalline magnesium. The present work was undertaken to provide data on the strengthening effects of a number of solutes in high-purity magnesium, for the purpose of supplying further experimental information which might be useful in describing a general mechanism for solid-solution strengthening. To simplify interpretation of the results, the mode of deformation was limited to basal slip, through the use of single crystals. EXPERIMENTAL PROCEDURE Magnesium and magnesium binary-alloy single crystals containing indium, cadmium, thallium, aluminum, and zinc were prepared in the form of l/2-in.-diam rods, approximately 8 in. long, using a modified Bridgman technique in which the crystals were slowly cooled from the melt in a steep temperature gradient, in an atmosphere of helium. It was found that a solid-liquid interface travel speed of about 0.7 in. per hr consistently produced single crystals. The poly crystalline starting materials for the preparation of single crystals consisted of 1/2-in.-diam extruded rods, prealloyed to the desired composition. The unalloyed magnesium and magnesium-indium extrusions were furnished by the Dow Chemical Co. The other alloys were prepared at the Rensselaer Polytechnic Institute Metallurgical Laboratories. Some preliminary studies of the strengthening effect of indium were conducted at room temperature using a constant rate of tensile loading of 1040 g per min. Stress was applied to the crystals by means of a simple 5:l lever arm. The lever was loaded by a constant rate of flow of shot into a receptacle suspended from the long arm of the lever. Plastic flow was detected by an electrical resistance strain gage cemented to the surface of the crystal normal to the minor axis of the predicted glide ellipse. The crystals were acid machined to produce tensile specimens with a reduced section between the grip ends, with an additional step in the center of the reduced section to compensate approximately for the slip-retarding effect of the strain gage. The balance of the single crystals were extended in an Instron tensile tester. This machine employs a synchronously driven screw and automatically records applied load as a function of cross-head separation. It became unnecessary therefore, to employ a strain gage to detect deformation or to acid machine a reduced section. Preparation for testing reduced merely to chemical cleaning of the surface, thus minimizing the amount of handling and probability of accidental damage to the crystals. The rate of elongation employed in all the tests was 0.002 in. per min, corresponding to a strain rate of approximately 0.0004 per min. EXPERIMENTAL RESULTS The investigation confirmed the finding of many workers that the yield strength of hexagonal metal crystals is strongly orientation-dependent. This is illustrated in Fig. 1, in which o, the tensile stress required to produce gross plastic flow in eleven unalloyed magnesium crystals stressed at a constant rate of loading is plotted as a function of sin X, cos Ao where X, is the angle between the

Jan 1, 1960

By A. R. Gregory

A shear wave velocity laboratory apparatus and techniques for testing rock samples under simulated subsurface conditions have been developed. In the apparatus, two electromechanical transducers operating in the frequency range 0.5 to 5.0 megahertz (MHz: megacycles per second) are mounted in contact with each end of the sample. Liquid-solid interfaces of Drakeol-aluminum are used as mode converters. In the generator transducer, there is total mode conversion from P-wave energy to plain S-wave energy. S-wave energy is converted back to P-wave energy in the motor transducer. Similar transducers without mode converters are used to measure P-wave velocities. The apparatus is designed for testing rock samples under axial or uniform loading in the pressure range 0 to 12,000 psi. The transducers have certain advantages over those used by King, 1 and the measurement techniques are influenced less by subjective elements than other methods previously reported. An electronic counter-timer having a resolution of 10 nanoseconds measures the transit time of ultrasonic pulses through the sample; elastic wave velocities of most homogeneous materials can be measured with errors of less than 1 percent. 5- and P-wave velocity measurements on Bandera sandstone and Solenholen limestone are reported for the axial pressure range 0 to 6,000 psi and for the uniform pressure range 0 to 10,000 psi. The influence of liquid pore saturants on P- and S-wave velocity is investigated and found to be in broad agreement with Biot's theory. In specific areas, the measurements do not conform to theory. Velocities of samples measured under axial and uniform loading are compared and, in general, velocities measured under uniform stress are higher than those measured under axial stress. Liquid pore fluids cause increases in Poisson's ratio and the bulk modulus but reduce the rigidity modulus, Young's modulus and the bulk compressibility. INTRODUCTION Ultrasonic pulse methods for measuring the shear wave velocity of rock samples in the laboratory have been gradually improved during the last few years. Early experimental pulse techniques reported by Hughes et al.2 and by Gregory 3 were beset by uncertainties in determining the first arrival of the shear wave (S-wave) energy. Much of this ambiguity was caused by the multiple modes propagated by piezoelectric crystals and by boundary conversions in the rock specimens. Shear wave velocity data obtained from the critical angle method, described by Schneider and Burton4 and used later by King and Fate sand by Gregory, 3,6 are of limited accuracy, and interpreting results is too complicated for routine laboratory work. The mode conversion method described by Jamieson and Hoskins7 was recently used by King 1 for measuring the S-wave velocities of dry and liquid-saturated rock samples. Glass-air interfaces acted as mode converters in the apparatus, and much of the compressional (P-wave) energy apparently was eliminated from the desired pure shear mode. A more detailed discussion of the current status of laboratory pulse methods applied to geological specimens is given in a review by Simmons.8 A new shear wave velocity laboratory apparatus has been developed for testing rock samples under elevated pressures. This apparatus employs liquid-solid interfaces as mode converters. The technique for generating pure shear waves at liquid-solid interfaces was developed from studies of critical angle methods.6 Two identical transducers are placed in contact with opposite ends of the rock sample, one transducer acting as an ultrasonic energy emitter or generator and the other acting as an ultrasonic energy receiver or motor. The P-wave energy emitted from the piezoelectric crystal in the generator transducer is converted into pure S-wave energy at the Drakeol-aluminum

By R. V. Smith

The theory for unsteady radial flow of gas, as simplified by Aronofsky and Jenkins, has been reviewed and compared with actual well performance. This study indicated that the theory should be modified by the introduction of an empirical "rate of flow" function "Y(q)". The expansion of the theory on the flow of gas to include a Y(q) term bridges the gap between the theory of unsteady-state flow of gas and actual gas-well behavior. Apparently, the Y(q) term is a function only of the rate of flow for a given well. The completion factor or skin effect is associated with the Y(q) function in such a manner that at least two or more sets of drawdown or pressure build-up tests are needed to separate the Y(q) function and the completion factor. Since the Y(q) function used in this report represents an energy loss dependent on rate of flow near the well-bore of a gas well which is in addition to the loss required by Darcy's law, the Y(q) function is related to the exponent of the back-pressure curve for a gas well. Techniques and equations are presented which permit the estimation of stabilized and "short-time" deliver-abilities. INTRODUCTION The published theory of radial unsteady-state flow of gas through porous media may be divided into papers1-" which use Darcy's law as a premise and other papers4-7,16-10 which recognize that Darcy's law may not hold for flow into gas wells. Miller8 compared theory based on Darcy's law with actual gas-well behavior and concluded that flow into gas wells deviates from Darcy's law. Houpeurt4,5 in a thorough investigation of flow into gas wells concluded that the flow rate into a gas well is proportional to the difference between the squares of upstream and downstream pressures elevated to a power between 1.0 and 0.5. Houpeurt also concluded that the deviation from Darcy's law is caused by irreversible, kinetic energy exchange between the flowing gas and the porous media. Tek9 presented a complete evaluation of the flow problem in gas wells. Several investigators state that the inclusion of gas compressibility into flow equations based on Darcy's law does not begin to explain the flow problems suggested by gas-well behavior. For many years, natural-gas engineers have realized that gas wells by actual test exhibit behavior which cannot be explained entirely by Darcy's law. Many tests on gas wells have indicated that a value of 0.85 for the exponent in the back-pressure equation is a fair average for many wells. However, Darcy's law either for steady or unsteady-state conditions indicates that the exponent should be 1.0. The purpose of this paper has been to examine this deviation from Darcy's law and to present a reasonable mathematical means of evaluating the deviation. The method presented in this paper combines previous theory with an empirical function to provide a description of gas-well behavior. All equations in this report are for constant terminal-rate-of-flow conditions. While present methods of testing wells usually are not based on this concept, they are believed to approach the constant terminal-rate conditions closely in many tests. However, several gas wells were tested by holding the rates of flow constant in order to approach more closely the constant terminal rate of flow; the results confirm the concepts presented in this paper. REVIEW OF THEORY FOR UNSTEADY-STATE FLOW OF GAS The basic partial differential equation for the flow of natural gas has been given in technical literature; the equation for a cylindrical reservoir with the well in the center is

By K. E. Brown, G. H. Fancher

An 8,000-ft experimental field well was utilized to conduct flowing pressure gradient tests under conditions of continuous, multiphase flow through 2 3/8-in. OD tubing. The well was equipped with 10 gas-lift valves and 10 Maihak electronic pressure recorders, as well as instruments to accurately measure the surface pressure, temperature, volume of injected gas and fluid production. These tests were conducted for flow rates ranging from 75 to 936 B/D at various gas-liquid ratios from 105 to 9,433 scf/bbl. An expanding-orifice gas-lift valve allowed each flow rate to be produced with a range of controlled gas-liquid ratios. From these data an accurate pressure traverse has been constructed for various flow rates and for various gas-liquid ratios. A comparison of these tests to Poettmann and Carpenter's correlation indicates that deviations occur for certain ranges of flow rates and gas-liquid ratios. Numerous curves are presented illustrating the comparison of this correlation with the field data. Poettmann and Carpenter's correlation deviates some for low flow rates and, in particular, for gas-liquid ratios in excess of 3,000 scf/bbl. These deviations me believed to be mainly due to the friction-factor correlation. However, Poettmann and Carpenter's correlation gives excellent agreement in those ranges of higher density. This was as expected and predicted by Poettmann. He pointed out that their method was not intended to be extended to those ranges of low densities whereby an extreme reversal in curvature occurs.l As a result of these experimental tests, correlations using Poettmann and Carpenter's method were established between the friction factors and mass flow rates which are applicable for all gas-liquid ratios and flow rates. Definite changing flow patterns do not allow any one correlation to be accurate for all ranges of flow. INTRODUCTION The ability to analytically predict the pressure at any point in a flow string is essential in determining optimum production string dimensions and in the design of gas-lift installations. This information is also invaluable in predicting bottom-hole pressures in flowing wells. Although this problem is not new to industry, it has by no means been solved completely for all types of flow conditions. Versluys,2 Uren, et al, 3 Gosline,4 May,5 and Moore, et al,6,7 were all early investigators of multiphase flow through vertical conduits. However, all of these investigations and proposed methods were very limited as to their range of application. Likewise, many are extremely complicated and therefore not very useful in the field. Only in the last decade have any significant methods been proposed which are generally applicable. The most widely accepted procedure in industry at the present time is a semi-empirical method developed from an energy balance, proposed by Poettmann and Carpenter8 in 1952. Their correlation is based on actual pressure measurements from field wells. Accurate predictions from this correlation are limited to high flow rates and low gas-liquid ratios. Although this method will be discussed in detail later, it should be pointed out that two important parameters, namely the gas-liquid ratio and the viscosity, were omitted in their correlation. The viscosity was justifiably omitted since their data was in the highly turbulent flow region for both phases, and most wells fall in this category. The gas-liquid ratio was incorporated to some extent in the gas-density term. In 1954, Gilbert9 presented numerous pressure gradient curves obtained from field data for various flow rates and gas-liquid ratios for the determination of optimum flow strings. However, no method is presented for predicting pressure gradients except by comparison to these curves. Baxendell, et al,10 proposed a method based on Poettmann and Carpenter's procedure

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij'usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith's determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej'ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of' damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.'2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968

By M. A. Dayananda, R. E. Grace

Vapor-solid diffusion couples were employed in a study of ternary diffusion in the single-phase copper-rich corner of the Cu-Zn-Mn system Interdiffusion coefficients were measured at three different compositions corresponding to the intersections of diffusion paths determined at 850°C. Intrinsic diffusion coefficients were determined at two compositions by the Philibert-Guy method. New relations between the various intrinsic diffusion coefficients are also presented. MOST of the investigations of ternary diffusion have been made with "sandwich" couples formed by welding together two homogeneous solid solutions with or without markers placed at the interface. With such couples Kirkaldy and his coworkers1,2 have determined interdiffusion coefficients which describe ternary diffusion in the substitutional alloy systems, Cu-Mn-A1 and Zn-Cu-Al. Guy and Leroy3 have reported intrinsic diffusion coefficients for Co-Ni-Cr alloys as a function of composition using the analysis of Philibert and Guy.4 The use of semi-infinite diffusion couples, for example, vapor-solid couples, where the diffusing species are supplied from a vapor source in contact with a diffusion disk, has so far been confined to studies of binary diffusion. Balluffi et a1.5,6 have successfully determined the interdiffusion as well as the intrinsic diffusion coefficients in several binary metallic systems employing vapor-solid couples with markers initially placed at the vapor-solid interface. They have also discussed the general advantages and limitations of such couples. Vapor-solid diffusion couples can successfully be employed in ternary diffusion studies. The importance of such couples in ternary diffusion lies in the fact that inert markers lie close to the vapor-solid interface, and the composition of the marker plane is virtually known before experimentation begins. Another minor advantage is that the method of Philibert and Guy4 may be used with three alloys instead of four. Lastly, the diffusion paths need not be S-shaped, as pointed out by Meijering7 for "sandwich" couples. The Cu-Zn-Mn system is convenient for ternary diffusion studies because of the large single-phase field in the copper-rich corner. The vapor pressure of zinc above such alloys is known, and X-ray measurements indicate that the molar volume is nearly constant over a wide range of compositions.8,9 It is the purpose of this paper a) to extend the analysis of Balluffi and seigle5 to permit an evaluation of interdiffusion coefficients in ternary vapor-solid couples, b) to use the method of Philibert and Guy to determine intrinsic diffusion coefficients with such couples, and c) to present experimental data on both interdiffusion and intrinsic diffusion coefficients for the Cu-Zn-Mn system at 850°C. INTERDIFFUSION IN TERNARY VAPOR-SOLID COUPLES The analysis of Balluffi and seigle5 is extended in this section to a vapor-solid couple where two solutes diffuse from a vapor source into a ternary solid solution. To take into account the expansion of the diffusion disk caused by the absorption of mass from the vapor phase, the total fluxes are expressed on the basis of a coordinate system that moves with the velocity of the vapor-solid interface; thus. where D3ij are the intrinsic diffusion coefficients,4 v(x, t) is the local Kirkendall velocity of mass flow, and F(t) is the negative velocity of the vapor-solid interface (x = 0). Both these velocities are based on a fixed coordinate system far removed from the diffusion zone. Using the continuity relations and Darken's method1' for a ternary system in which components 1 and 2 diffuse from the vapor phase into a solid of negligible vapor pressure, one obtains

Jan 1, 1965

By L. C. Brown, A. J. Stewart

Phase transformations have been studied in Ag-Zn alloys quenched from the high-temperature bcc 0 phase and lying in the composition range 37.4 to 50.0 at. pct Zn. On quenching, the alloy with the lowest zinc content transformed to massive a (fcc); all other alloys formed the ordered (3' phase. On deformation, a martensitic reaction took place forming a close-packed structure. At Lou' zinc contents transformation to this structure was complete. However, above 43 at. pct Zn a p.rogressively increasing amount of ß' was retained following deformation. The close-packed structure was fcc at lower zinc contents (under 47 at. pct Zn) and either hcp or a mixture of fcc and hcp at high zinc concentrations. The structures produced by cold working were unstable and on aging transformed to the ß' phase or the complex hexagonal to phase. For low zinc contents (under 43 at. pct) the fcc st-ructure transformed directly to the equilibrium To phase. With higher zinc contents, some 13' was retained following defownation, and on aging the amount of this phase relative to the close-packed structure increased. On further aging both structures transformed cornpletely to PO. Metallographic examination indicated that the nature of the deformation product depended very markedly on the mode of deformation. Tensile deformation gave a microstructure characteristic of thermal martensite. KING and Massalski1 have shown that an alloy of Ag-50 at. pct Zn quenched from the high-temperature bcc ß phase undergoes a low-temperature ordering reaction forming ß' which can be retained to room temperature. On deformation an hcp phase is produced, although this is unstable and the structure reverts completely to ß' on aging. In the present paper, the work of King and Massalski is extended to cover a wide composition range in the p phase, observations being made of the structure of the quenched 13 and of the effects of deformation and aging. The relevant portion of the Ag-Zn phase diagram is shown in Fig. 1. King and Massalski have shown that close to stoichiometry the ß' phase is the equilibrium structure at low temperatures. The approximate composition range of this phase, taken from a recent paper by Pops and Massalski,3 is shown on the phase diagram. The locations of atom sites are very similar in the ß' and to structures, and the 4, structure can be derived from the 0' structure by a small movement of atoms mainly in the direction of the cube diagonal.4'5 However, the probability of filling any particular atom site by a silver or a zinc atom is markedly different in the two structures. The structure can be considered partly ordered but the arrangement of the ordered atoms is completely different from that in the p' structure and transformation from ß' to requires a large fraction of the atoms to change position. It has been shown that the ß' transformation is thermally activated involving normal nucleation and growth processes.5,8 Massalski and Barrett7 have shown that in the Cu-Zn binary the (3 phase can be retained in the ordered state to room temperature over a wide composition range. On deformation a new close-packed phase is produced, the structure varying from fcc to a mixture of fcc + hcp to hcp alone with increasing zinc concentration. It appears that an ordering reaction is necessary to retain the bcc phase to room temperature. In CU-Ga,8 the bcc phase cannot be retained to low temperatures as it transforms by a massive reaction above the ordering temperature of the ß phase. The structure of the massive phase is very similar to that in Cu-Zn, varying from fcc to fcc + hcp to hcp with increasing zinc concentration. Similar structures have also been observed in CU-A1,9 Ag-Cd,10,11 and Ag-Al.12 EXPERIMENTAL The alloys were prepared by melting fine silver (99.99 pct purity) and electrolytic zinc (99.999 pct

Jan 1, 1969

By T. J. Whalen, M. Humenik

The liquid surface tension of copper-nickel ad copper-nickel-titanium-carbon alloys and the wettability of titanium caybyde by these alloys have been measuhed. It was found that the surface tensions of the binary copper-nickel alloys Lie on a smooth curve between the end members, copper and nickel. The addition of small amounts of titanium and carbon has nO effect on the surface tensions of copper-nickel alloys. Small additions of nickel to copper significantly reduce the contact angle of Ike alloy with titanium carbide. From a Gibbs treatment, nickel is shown to be adsorbed at the titanium carbide-alloy interface. X HE microstructure of two-phase materials has been shown to be influenced largely by the interfacial energies between the phases present.' , In systems prepared by powder metallurgy techniques and densi-fied in the presence of liquid phase, a precise analysis of microstructure and interfacial energy relationships requires a knowledge of the solid-solid interface energies and liquid-solid interface energies. However, marly metal-nonmetal systems are characterized by the "sweating" of the liquid during sintering, and in these systems wettability is a principal consideration. The wetting in turn is dictated by the various interface energies of the system, as shown in Fig. 1 for a liquid drop formed on a solid substrate. The equation which expresses the vectorial balance of surface forces in the horizontal plane, at the point of contact, A, is given by: where ssv = solid-vapor interface energy sSL = solid-liquid interface energy sLV= liquid-vapor interface energy 6 = contact angle measured through the liquid phase. The angle and the surface tension, slv, can be measured accurately by the sessile drop method.3, The absolute value of the surface energy of the solid cannot be determined by this method, but with reasonable changes in the composition of the liquid only, the value of ssv can be considered constant. The changes in contact angle, then, can be attributed to changes in sSL and sLV and since sLV can be measured, the changes in sSL can be determined. Several studies have indicated that the surface and bulk properties of solid alloys can be correlated with electronic structure. The catalytic activity of copper-nickel alloys was reported to follow the dband vacancies in these alloys.5 Nickel has been considered to have 0.6 holes per atom in the d-band. The addition of copper to nickel is thought to bring about a filling of the d-band of nickel, since each copper atom contributes one electron. Thus, at an atomic concentration of 60 Cu-40 Ni (62 wt pct Cu-38 wt pct Ni) the d-band is believed to be full, and magnetic measurements support this view.6 If the electronic structure is influencing a property of the alloy, this property should show some sort of discontinuity as the composition changes from one side of the 60 Cu-40 Ni composition to the other. Since the catalytic activity can be considered as a surface property of the alloy, it is logical to assume that other surface properties, such as surface tension, may also be influenced by electronic structure. The suggestion has been made that there is a correlation between the solid titanium carbide-liquid Cu-Ni alloy interfacial energy and d-band filling.7 One purpose of this investigation was to determine if the changes taking place in the electronic structure with compositional changes in the solid copper-nickel alloys were reflected in the surface tension values of the liquid alloys. Such a change, if present, would lend support to the suggestion that one can refer to discrete energy bands in the liquid state. Other purposes of the present study were to investigate in detail the wettability in the system copper-nickel-titanium carbide, and to discuss the possible processes which take place during wetting in this system.

Jan 1, 1961

By Bernhard Blumenthal

A melting process was developed by which high purity electrolytic uranium crystals can be converted into sound ingots without serious contamination. Careful preparation of the crystals, melting in a high vacuum, and directional solidification led to a metal of better than 99.993 wt pct purity. The metallographic examination showed a substantially clean metal with only residual amounts of a second phase which responded to heat treatment. The density of high purity uranium is 19.05 g per cu cm. FOR the study of the fundamental properties of uranium and its alloys, a base metal of high purity is needed, and an investigation was started at Argonne several years ago to examine various methods of preparing high purity uranium. Early success was achieved by the fused salt electrolysis process in preparing high purity metal in crystal form,' and the problem became that of melting the crystals into ingots without contamination. The electrolytic crystals contained a few ppm of heavy metals, less than 15 ppm C, and large quantities of potassium and lithium in the form of trapped fused salt electrolyte. On melting in vacuo in magnesia or urania crucibles, the metal picked up considerable quantities of carbon and some iron, copper, and silicon but lost most of the potassium and lithium. It was not metallographically clean, and much research work was necessary to determine the optimum melting conditions for minimum contamination. This work has resulted in the development of a melting procedure by which sound ingots can be prepared with only a limited contamination by carbon. In the section entitled "Melting of the Electrolytic Metal," the equipment and processes that have been developed for melting the electrolytic crystals are described in detail. The "Metallography" section is devoted to the metallography of high purity uranium, and the section "Density of High Purity Uranium" contains the first property measurement on high purity uranium—a density determination. Melting of the Electrolytic Metal Apparatus—Melting and Vacuum Equipment: Uranium may be melted in either resistance or induction-type electric furnaces. Resistance heating was found to be preferable to induction heating for melting down the electrolytic crystals, for several reasons: Although induction heating permits fast heating, this advantage cannot be utilized when crucibles with limited thermal shock resistance are used. Temperature control of induction-heated melts is poor, and the stirring effect increases the rate of contamination of the melt from the crucible, slag, or the furnace atmosphere; liquation and controlled solidification are difficult to carry out. Because of these objections, resistance heating was chosen. A 10 kw Globar resistance furnace of low heat capacity permitted uniform heating of a uranium charge to its melting point in 45 min. The furnace was insulated with a removable aluminum shield so that, after melting and removal of the shield, the furnace could be quickly cooled to room temperature. The furnace was equipped with an apparatus for directional solidification; see Fig. la. The crucible was suspended in the center of the furnace; and when the melting was complete, the crucible was slowly lowered into the cold end of the furnace tube. Solidification took place upward from the bottom; and when the rate of lowering was small, a sound ingot free from sink holes and shrinkage cavities was produced. To remove the large quantities of gas contained in the electrolytic crystals, melting in a high vacuum is mandatory. While, from the standpoint of contamination, melting in a highly purified argon atmosphere appeared feasible, lithium and potassium removal proved less efficient under such conditions. Also, a vacuum-melted ingot has a cleaner surface than one melted in an inert atmosphere. The vacuum system must be of very high pumping speed and leak tight so that a vacuum of less than 2x10-7 mm Hg is attainable when the system is pumped down cold. The system must have a high pumping speed, so that the pressure maximum which may rise to 1x10-4 mm during heating can be quickly reduced

Jan 1, 1956

By M. H. Caron

THE most outstanding property of ammonia liquors, used in the ammonia leaching process is their very limited ability to dissolve all compounds present in reduced ore except nickel and cobalt. Although they do have such a high degree of purity, even the smallest amounts of impurities contaminate the precipitate of basic nickel carbonate that may be obtained from pregnant liquors by straight distillation. Figures have been given in a separate paper regarding the extent of such contamination. The product of straight distillation is likely to contain small amounts of Fe, Mn, MgO and SiO2 as well as some sulphate and sulphide. The sulphur can be readily eliminated by calcination of the product at the proper temperature and MgO and SiO2 by reduction and melting of the metal with a suitable flux. After such treatment the metal is relatively pure, and the iron and manganese content will be very small. The cobalt content, however, may vary considerably, depending upon the ore treated. The metal obtained from pure true garni-erite ores usually has only a small cobalt content of less than 1 pct. Metal obtained from medium grade iron-rich nickel ores may show cobalt values from 2 to 3 pct, and the alloy obtained from laterite is likely to contain as much as 10 pct cobalt. By proper treatment a good deal of cobalt may be recovered from lateritic nickeliferous iron ores, and cobalt will become the major constituent of the pregnant liquor if asbolan ores or similar products are treated. The pregnant liquor of "run of mine" nickel ores may have a pinkish shade, indicating the presence of cobalt. It is evident that from such liquors the metals should be recovered separately. Even if cobalt is present in only very small amounts, it would probably be economically justifiable to recover both metals as pure as possible if a suitable process could be devised. The author has made investigations along this line and has patented some processes adapted to the treatment of this type of solutions. Selective Dissolution of Nickel from Basic Nickel Carbonate Containing Some Cobalt: Basic nickel carbonate obtained from true garnierite ores by straight distillation of the pregnant liquors, always contains some cobalt as well as the normal impurities. In. order to improve the quality of the nickel product and to recover most of the cobalt, the following process has been devised. By using liquors with a low CO2 to NH3 ratio, nickel can be redis-solved preferentially to cobalt. It is not a sharp and clean separation but a selective one, for the bulk of the nickel may be redissolved with a small amount of cobalt, and a small residue may hold the bulk of the cobalt. The greatly increased cobalt content of the residue is indicated by a pronounced olive green color, in contrast with the light green color of pure basic nickel carbonate. The following example is given from Dutch patent No. 52788, Klasse 40a. 43 granted June 17, 1942: The original precipitate contained about 0.55 pct cobalt calculated on total nickel + cobalt. Eight hundred and fifty grams of the basic nickel carbonate were redissolved in leach liquor containing 7.12 pct NH3 and 2.12 pct CO2. The weight of the dry residue was about 3.5 pct of the original weight. By analysis it was found that the residue contained: Fe 1.93 pct, Co 6.01 pct, Ni 34.87 pct and also a certain amount of silica. The clear filtered blue liquor was distilled and the precipitate of basic nickel carbonate from this analyzed: Fe 0.008 pct, Co 0.0146 pct, Ni 42.37 pct. It is obvious that this product is considerably more pure, since calculation shows that about 94 pct of the original cobalt remained in the residue. Cobalt and nickel can be recovered by further

Jan 1, 1951

By Nicholas J. Grant, H. C. Chang

Microscopic observations during creep tests were made on AI-20 pet Zn, 80 pet Ni-20 pet Cr, and 25 and 3S aluminum specimens. All these materials failed in an inter-crystalline manner under certain stress and temperature conditions. Particular atten-tion was given to the initiation and propagation of intercrystalline cracks in coarsegrained AI-20 pct Zn specimens. The geometry of the grains and grain boundaries in these specimens was known before the tests. On the basis of the observations and a knowledge of the interaction between grains and grain boundaries, a mechanism of intercrystalline fracture and propagation of the fracture has been proposed. METAL, and alloy fracture occurs essentially in two ways: transcrystalline and intemrystalline. In the past most of the work done in this field was centered on the determination of stress criteria for fracture. The specimens used for these studies were tested under varying conditions of stress state, temperature, and strain rate. Unfortunately, very little attention was given to the initiation and propagation of the fracture, whereas the nature of fracture was examined closely only after failure. Several extensive reviews of these studies have been published by Orowan, Smith, Barrett, and Petch.1, 4 It is well known that a material which exhibits a ductile and transcrystalline fracture can be made to exhibit a brittle and intercrystalline fracture by modifying its composition and by heat treatment. This modification may or may not result in microscopically observable precipitation in the grain boundaries." In the creep of any one alloy the transition of transcrystalline to intercrystalline fracture is a function of stress, strain rate, and temperature." The tendency for intercrystalline fracture to occur increases as the strain rate decreases and the testing temperature increases. Extensive work on high purity aluminum (99.995 pet) under creep conditions showed the importance of the interaction between grains and grain boundaries, and the different responses of grain and grain boundaries to the variables: stress, strain rate, and temperature.7, 8 It was also shown that grain boundary deformation necessarily has to be accommodated in the grains by various deformation means as. for example, fold formation. The type of fracture resulting from the creep of high purity aluminum was invariably found to be transcrystalline. On the other hand, 2S and 3s aluminum were, under certain conditions, found to fracture in an intercrystalline manner." One reason given for this was that the grains could accommodate to a lesser extent the deformation of the grain boundaries.19 It was decided to examine this line of reasoning in greater detail and to investigate the particular interactions between grains and grain boundaries that result in the incidence and progression of inter-ct,ystalline fracture. It is also the purpose of this paper to show where and how intercrystalline cracks start and how they propagate to result in fracture. Several alloys—Al-20 pct Zn, 80 pet Ni-20 pet Cr, 2S and 3s aluminum-— were used for this study, but attention was paid mainly to the behavior of an A1-20 pet Zn alloy, since its general creep behavior has been established." From the results of this study a mechanism of intercrystalline fracture is proposed. Experimental Procedure The experimental procedure was similar to that used in previous work and has been detailed elsewhere.' Two parallel flat surfaces were milled from an originally round specimen, giving a gage portion which was 1x0.09X0.17 in. Some round specimens, 1/4 in. round by 1 in., were also tested. The A1-20 pet Zn specimens. which were annealed at 1030°F for 24 hr, showed two to four grains across the width of the test bar, and most of the grains occupied the whole thickness of the specimenu. Before some of the specimens were subjected to creep, the grain arrangement was mapped out in a development drawing, Fig. 1. The initiation and

Jan 1, 1957

By R. A. Graham, R. W. Rohde, J. R. Holland

In a shock wave compression study of a martensitic Fe-30 pct Ni alloy, Graham, Anderson, and Holland' found a region of unusual compressibility extending from a few kilobars up to about 20 kbars. This region was characterized by a continuously decreasing shock wave velocity with increasing stress. In this note, we report the results of a study initiated to determine the source of this unusual compressibility. In earlier shock-loading experiments on martensitic Fe-30 pct Ni, Loree et a1.' determined that a phase change occurred at about 80 kbars. Subsequently, Bowden and elly found that samples of a similar material shock-loaded at about 100 kbars experienced a martensite-to-austenite transition. Their crystal-lographic analysis showed the transition was a direct reversal of the established martensite system to the austenite phase. The shock loading in the present experiments was accomplished by precisely controlled plane impact between two discs of the sample material. This configuration created a state of uniaxial strain in the two the front of a projectile which was accelerated to various velocities. Planarity between the impacting discs was controlled to 5 x 10-4 rad, and impact velocities were measured to 0.5 pct. From a knowledge of the Hugoniot relationships of the material and the impact velocity, the shock-wave stress can be calculated. Samples were shocked at 18, 50, 70, and 100 kbars. The specimen discs shocked at 18 and 50 kbars were instrumented with quartz gages to observe the stress time profile. A more detailed description of the experiment has been given previously.4 The shock-loaded specimens were recovered intact by decelerating them in a catcher filled with soft wood. Discs of Fe-30 pct Ni nominally 12.7 mm thick and 64 mm in diam were cut from bar stock. Chemical analysis of the material provided the following composition in weight percents: 29.5 Ni, 0.50 Mn, 0.21 Si, and 0.10 C, with traces of Cr, Cu, Mo, Al, and Co. The discs were austenitized at 650° C for 2 hr at a pressure of less than l0-' torr, and furnace-cooled. Martensite was then produced by quenching the discs at -196" and holding 168 hr. The initial martensitic structure formed is shown in Fig. l(a). Typical microstructures of samples shock-loaded at 18 and 100 kbars are shown in Figs. l(b) and l(c). The banded structure with the austenite regions running parallel to the shock propagation direction was characteristic of samples shock-loaded at all stresses. No such banding was found in samples that were not shock-loaded. Comparison of Figs. l(b) and l(c) shows that, although under the optical microscope the two microstructures are quite similar, the martensite plates of the specimen shocked at 100 kbars etched in a distinctly different manner. This unique etching behavior of martensite in samples shock-loaded above the 80 kbar transition point has also been observed by Leslie el al.' These investigators determined from X-ray and electron microscope studies that fcc martensite, similar in appearance to normal bcc martensite, had been formed under shock loading. A quantitative determination of the amount of austenite present after shock loading was made by X-ray techniques. Both the methods of Lindren' and Miller' were utilized. The results are shown in Table I. The error limits are those experimentally observed from two independent analyses of each sample and represent the precision of the experiment. The absolute error, which should be similar for each sample, is believed to be about 10 pct. It is seen that as the shock stress increases the amount of austenite present also increases. On the basis of the X-ray and microscopic observations, we conclude that shock loading below the 80 kbar ersal will initiate a martensitic reversal: the amount of reversal that occurs increases with in-

Jan 1, 1969

By H. Schwartzbart, J. R. Low

Annealed, .Poly crystalline, low carbon steel exhibits a phenomenon known as the "yield point." If such a steel is loaded in tension, the load increases steadily with elastic strain, drops suddenly, fluctuates about some constant load value for a time and then rises with further strain. The load at which the sudden drop occurs is called the "upper yield point"; the load at which deformation proceeds at constant load is known as the "lower yield point"; the amount of elongation at constant load is termed the "yield point elongation." Deformation which occurs during the yield point elongation is heterogeneous in nature, deformed metal existing next to undeformed metal. The drop in load from the upper yield point is concurrent with the formation of a band of deformed metal which usually appears at a stress concentration such as a fillet and at an angle of approximately 45" with the direction of pull. As deformation proceeds during the yield point elongation, the deformed region grows until the entire specimen has been strained an amount equal to the strain in the first band. A phenomenon very often associated with the yield point is that of strain aging. Aging in steels may be of two types: quench aging, or precipitation hardening, and strain-aging. Strain aging differs from precipitation hardening in that if the metal is merely strained instead of given a solution anneal and quenched, it then undergoes changes in properties similar to those observed in quench aging. The yield point effect and strain aging are most markedly exhibited by low carbon steel, but have been observed in other alloys. Numerous explanations for the mechanisms of both phenomena have been advanced, but the evidence for the acceptance of any of the hypotheses is incomplete. One of the explanations of the yield point phenomenon frequently proposed is that there exists a honeycomb of grain boundary material that supports the load above the yield strength of the ferrite and that when this network ruptures, the ferrite flows with no increase in load. This notion was first advanced by Dalbyl in 1913 and has been since put forward in more concrete form by many investigators. The testing of this hypothesis was, in part, the object of the present investigation. Similarly, the mechanism by which strain aging occurs remains to be explained. Presumably, it is a precipitation hardening phenomenon similar to quench aging, the precipitation being initiated by strain. However, it is not known whether the process is a solution and precipitation effect or a change in solubility due to strain. One obvious method of determining whether or not the yield point is a grain boundary phenomenon is to determine if single crystals exhibit a yield point. Low and Gensamer2 have shown that carbon and nitrogen are responsible for the yield point and aging in steel and that these effects can be eliminated by the removal of these elements through wet hydrogen purification. Single crystals that have been grown in wet hydrogen treated material must then be recarburized or re-nitrided in order to evaluate the effect of grain boundaries. In the present investigation, single crystals of iron which had been annealed in wet hydrogen to remove the carbon and nitrogen were cut into two specimens having the same orientation with respect to the tension axis. Of these, one specimen was pulled in tension in the wet hydrogen treated state and the other was carburized or nitrided and tested similarly. All the crystals were examined for a yield-point and strain aging. The grain boundary hypothesis for the explanation of the yield point in steel has been tested only indirectly previously. Arrowsmith,3 Andrew and Lee,4 Edwards and Pfeil,5 Fell,6 Ludwik and Scheu,7 Winlock and Leiter8 and others found a decrease in proportional limit and yield point effect with an in-

Jan 1, 1950

By A. L. Lee, M. H. Gonzalez, R. F. Bukacek

Experimental viscosity data for methane are presented for temperatures from 100 to 340F and pressures from 200 to 8,000 psia. A summary is given of the available data for methane, and a comparison is presented for that data common to the experimental range reported in this paper. Correlation of the data is presented, and predicted values are given for temperatures up to 460F and pressures up to 10,000 psia. INTRODUCTION The increasing ranges of temperature and pressure at which fluids are produced, transferred and processed in the petroleum and chemical industries stress the need for accurate information on physical properties, both for engineering calculation and for improving the methods used to estimate physical properties. A survey of the literature reveals that disagreements between published data on the viscosity of methane are common and that most investigations have been conducted over restricted temperature and pressure ranges. This situation made it desirable to undertake an investigation with a scope common to most of the literature data available. APPARATUS AND MATERIALS The apparatus used in this investigation was the capillary tube viscometer'described by Dolan,10 with modifications introduced in the general design and operation of the instrument. It has an effective pressure range from 14.7 to 10,000 psia and a temperature range from room temperature to 400F. The design of the viscometer is based on the establishment of a manometric head between two vessels containing the test fluid and a volume of mercury. The reservoirs are connected by a capillary tube through which the test fluid flows and a tube through which mercury flows. A pressure gradient is established by elevating one of the vessels above the other, the resulting flow of mercury displacing the test fluid through the capillary. The schematic diagram of the system (Fig. 1) shows the arrangement of the equipment auxiliary to the viscometer. The density cells assembly (E, Fig. 1) was not used in this investigation since reliable data are available on methane. 23 The assembly consists of a bank of eight 316 stainless steel pycnometers. Experimental values of the density of a natural gas19 and i-butane14 samples have been obtained for pressures up to 8,000 psia and temperatures up to 340F. The methane used was obtained from the Southern California Gas Co. Mass spectrometric analysis showed a composition of 99.8 percent CH4, 0.1 percent C2H6 and 0.1 percent C3H8. EXPERIMENTAL VALUES AND ACCURACY OF DATA Determinations were carried out at several temperatures. With the temperature in the cabinet controlled at a given level, a series of runs were made at various pressures. To establish pressures lower than that obtained from the methane cylinder, it was necessary to vent the gas slowly to the atmosphere until the desired pressure was reached. The consistency of the test run time for a particular condition can be used as a criterion for the accuracy of the data. A further check is obtained by comparison of the viscosity values obtained using different driving heads. To establish the instrument's reproducibility, a large number of runs were made at three completely different conditions of temperature and pressure. Data obtained were analyzed statistically to determine the most reliable value for the variance of the experimental data. It was found that the variances of the data taken at different experimental conditions were not statistically equivalent, but they were small. The largest variance was found at 8,000 psia and 100F, where the standard deviation was 0.385 micropoise. Therefore, 99.9 percent of the data can be expected to fall within 1.15 micropoises of the population mean, except for the intervention of systematic errors in operation.

By W. R. Strickler, P. Hazebroek, M. Prats

The pressure and production behavior of a homogeneous cylindrical reservoir producing a single fluid through a centrally located vertical fracture of limited lateral extent was determined by using mathematical methods to solve the appropriate differential equation. It is assumed that there is no pressure drop within the fracture — that is, that the fracture capacity is infinite. It was found that the production-rate decline of such a reservoir is constant (except for very early times) when the flowing bottom-hole pressure remains constant. The production-rate decline increases as the fracture length increases. Thus, the lateral extent of fractures can be determined from the production-rate declines before and after fracturing or from the decline rate after fracturing when the properties of the formation and fluids are known. The production behavior over most of the productive life of such a fractured reservoir can be represented by an equivalent radial-flow reservoir of equal volume. The effective well radius of this equivalent reservoir is equal to one-fourth the total fracture length (within 7 per cent); the outer radius of this equivalent reservoir is very nearly equal (within 3.5 per cent) to that of the drainage radius of the fractured well. The effective well radius of a reservoir producing at semisteady state is also very nearly equal to one-fourth the total fracture length. It thus appears that the behavior of vertically fractured reservoirs can be interpreted in terms of simple radial-flow reservoirs of large wellbore. INTRODUCTION An earlier report1 has considered the effect of a vertical fracture on a reservoir producing an incompressible fluid. That investigation of the fractured reservoir producing an incompressible fluid was started because of its simplicity. Thus, pertinent behavior of fractured reservoirs was obtained at an early date, while experience was being gained of value in the solution of more complicated fracture problems. One of these more complicated problems, and the one discussed in this report, considers the effect of a compressible fluid (instead of incompressible fluids) on the production behavior of a fractured reservoir. In the incompressible-fluid work mentioned, it was shown that the production rate after fracturing could be described exactly by an effective well radius equal to one-fourth the fracture length whenever the pressure drop in the fracture was negligible. Because of the simplification in interpretation, it is a matter of much interest to determine whether the production behavior of reservoirs producing a compressible liquid could be described in terms of an effective well radius which remains essentially constant over the producing life of the field. The details of the mathematical investigation are given in the Appendixes. IDEALIZATION AND DESCRIPTION OF THE FRACTURED SYSTEM It is assumed that a horizontal oil-producing layer of constant thickness and of uniform porosity and permeability is bounded above and below by impermeable strata. The reservoir has an impermeable circular cylindrical outer boundary of radius re. The fracture system is represented by a single, plane, vertical fracture of limited radial extent, bounded by the impermeable matrix above and below the producing layer (reservoir). It is assumed that there is no pressure drop in the fracture due to fluid flow. Fig. 1 indicates the general three-dimensional geometry of the fractured reservoir just described. When gravity effects are neglected, the flow behavior in the reservoir is independent of the vertical position in the oil sand. Thus, the flow behavior in the fractured reservoir is described by the two-dimensional flow behavior in a horizontal cross-section of the reservoir, such as the one shown in Fig. 2. Production is due to the expan-

By Arthur Hockman, Howard W. Jaffe, Howard F. Carl

THE problem of establishing practical techniques for evaluating natural corundum ores arose from the desire to improve the existing purchase specifications for crystal corundum procured by the Federal Government for stockpiling. Such purchase specifications had been developed for a large number of products, including minerals and ores considered to be critical and strategic because of the country's dependence on foreign sources of supply. It will be apparent to anyone considering the subject of purchase specifications that the determination of whether or not a submittal meets the specifications is a prime consideration. Consequently satisfactory specifications for minerals should not only incorporate physical, chemical, and mineralogical requirements that are practical but should also establish the means by which both buyer and seller can be assured that materials meet stated requirements. The Munition Board's Material Purchase Specification for corundum, dated February 1954, covered two grades of crystal corundum intended primarily for abrasive use. It established limits of size and of composition: Grade A, at least 95 pct +3 mesh and 92 pct alumina (Al2O3); Grade B, at least 95 pct +7 mesh and 90 pct alumina. It also specified that "of each lot of material, not less than 95 percent shall have a hardness equal to or exceeding nine (9) on Moh's Scale." These specifications were unsatisfactory for several reasons. They did not allow the purchase of lower grades of corundum being used by industry. Neither did they specify exactly what a corundum ore actually was, except that it should contain so much alumina and have a certain scratch hardness. Nothing was said about the abrasive qualities of the material that was to be purchased primarily for abrasive use. During the period 1946 to 1948 supplies of the two grades defined in the then current specifications continued to decrease. Early in 1949 industry recommended that the finer sizes of corundum known as "crystal corundum concentrates," ¼-in. to 16-mesh material, be added to the stockpile specifications and that lower grades of crystal corundum also be included. In the spring of 1949 the National Bureau of Standards and the Bureau of Mines were asked by the Munitions Board to cooperate in developing more practical specifications for grading natural corundum ores. The National Bureau of Standards indicated that it would investigate physical test methods for determining abrasive characteristics of corundum, and the Eastern Experiment Station of the Bureau of Mines at College Park, Md., stated that it would consider the mineralogical aspects of the problem. Members of these two agencies, in consultation with representatives of the Office of Materials Resources of the Munitions Board and of the Federal Supply Service of the General Services Administration, and with the cooperation of industrial suppliers and consumers of abrasive corundum, developed, in a fairly short time, more practical specifications for six grades of corundum ores. The new specifications, issued January 1951, were for corundum, natural crystals, as by this time high-purity synthetic corundum was available and widely used. Nevertheless, for certain specific applications the natural product was preferred over the synthetic material. It has been extensively used in forming snagging wheels. It breaks into more or less cubical particles, whereas artificial corundum fractures into splintery shapes. These produce irregular cuts in glass, while the more symmetrical shape produces a more uniform ground surface. For this reason natural corundum has been preferred for certain types of lens grinding. Pure corundum is clear, colorless alpha alumina (A12O3), but it is rarely found in nature in this form. The most important gem varieties include the blue and yellow sapphires and the ruby. Minute impurities of titanic oxide impart a blue color,

Jan 1, 1955

By B. A. Wilcox, A. H. Clauer

The tensile and creep deformation characteristics of fiber reinforced composites have been studied, primarily at room temperature. The matrix was an alloy of Mg-14 wt pct Li-1 wt pct Al (LA141A alloy) and the reinforcing fiber consisted of continuous wires of a high strength precipitation hardening stainless steel (AFC-77 alloy). The ultimate tensile strength and strength-to-density ratio of composites were much improved over that of the mmix, both at room ternperatwe and up to 200°C. Creep studies at room temperature revealed logarithmic weep behavior for wires and composites and steady state creep for the nonreinforced matrix. It was concluded that creep of the fibers controlled composite creep. The instantaneous logarithmic weep rate of the composite, 6, was related to the average tensile stress on the fibers, where n = 3.4. Mg-Li alloys are the lightest structural metals commercially available, e.g., the alloy LA141A (Mg-14 wt pct Li-1 wt pct Al) is 27 pct less dense than beryllium Although Mg-Li alloys have moderate tensile strengths at normal strain rates and ambient temperature, their creep strength is relatively poor, even at room temperature. Reinforcement by fibers offers a means of increasing the tensile strength as well as overcoming the limitations of low creep strength. With a proper choice of reinforcing filament, composites could be designed with higher strength-to-density and modulus-to-density ratios than the matrix alloy. This communication reports a study on the tensile and creep characteristics of alloy LA141A reinforced with continuous wires of a high-strength precipitation hardening stainless steel (AFC-77 alloy). The matrix has a bcc structure, with possible precipitates of AlLi and MgLi2A1,3 and is ductile at room temperature Stainless steel wire was chosen as the -reinforcing filament since previous work at Battelle4 showed that a good bond between wire and matrix could be produced in this system. For all volume fractions of reinforcing wire, the theoretical composite strength-to-density ratio is greater than that of the matrix and the modulus-to-density ratio is somewhat lower than that of the matrix. EXPERIMENTAL PROCEDURES The 0.004-in. diam AFC-77 wire was obtained from two suppliers: National-Standard Co.* and Crucible 0.13 Si, 0.18 V, 0.011 P, 0.012 S, balance Fe. In the as-received condition, wires from both sources had room-temperature ultimate tensile strengths of 585,000 to 590,000 psi with approximately 2 pct total elongation and 40 pct reduction in area. Composite preparation was accomplished by the vacuum infiltration technique. This involved placing the continuous wires in a mild steel tube (1/8-in. ID), capping one end of the tube with a sheet of the matrix alloy, and evacuating the other end of the tube. When the capped end was placed in a crucible of the molten matrix alloy and held for 31/2 min at 70O°C, the liquid metal was drawn up the tube approximately 7 to 8 in. A cross-sectional view of a typical composite is shown in Fig. 1. This preparation technique promoted excellent bonding between the matrix and wires, and porosity was rarely observed. Test specimens for both creep and tension studies were prepared by machining off the steel tube. Tensile tests on the wires and composite specimens were made in an Instron using a cross-head speed of 0.01 in. per min. The composite specimens had no reduced section and were held in self-tightening grooved serrated grips. Most of the specimens broke in the effective 1-in. gage section. Even though several tests fractured in the grip section, their ultimate strengths were essentially the same as those of specimens which fractured in the gage section. Creep specimens of the composite were gripped in a similar manner, and

Jan 1, 1970

By H. M. Manasevit, R. L. Nolder, L. A. Moudy

The observation that silicon-on-sapphire crystallo-graphic relationships exist which are unrelated to one another implies that there are regions of sapphire orientations containing these relationships which are separated by boundaries. The presence of these boundaries is demonstrated, initially on rounded cylindrical surfaces md more definitively on flat sapphire substrates with orientations along primary crystallograPhic zones. By means of reflection electron and X-ray diffraction techniques the crystallographic relationships have been studied. Two new relationships have been found, viz., (111) Si (1014) sapphire and (001)Si (1012) sapphire. Also found were multicrystalline relationships. The approximated boundaries between the crystallographic regions for each relationship are shown by means of a stereo-graphic projection. These studies also clarify discrepancies in the literature concerning the silicon-sapphire relationships on the (1120) sapphire substrate. SINCE the first report of the deposition of single-crystal silicon on sapphire in 1963' this epitaxial system has been the object of study by many semiconductor laboratories. In particular, there has been strong interest in the crystallographic relationships between the two materials. In 19652,3 we demonstrated that at least four distinct modes of orientation relationships can occur, namely, (100)Si (0112) sapphire, (111)Si 11 (1124) sapphire, (111)Si (1120) sapphire, and (111)Si (0001) sapphire. Each relationship could be obtained when the substrate plane was at the particular orientation indicated. Other workers as well as our laboratory concurred in general with the initial results. However, two discrepancies were observed. First it was observed by Joyce et a1.4 that on a (1120) substrate a (110) silicon deposit could be obtained. This was actually consistent with the (111)Si (1124) sapphire mode. Second, two other laboratories,5,6 as well as our own,7 have found a deposition on the basal plane which is different than our initial findings. Even though a (111)Si deposit was obtained, the crystallographic relationships were not identical to those previously found. Subsequent work in our laboratories has confirmed that the form found in these later investigations of the basal plane is by far the more predominant, and the original finding was an anomaly. The relationships which have been previously estab1.ished are summarized in Table I. It is seen that at present a rather small number of possible substrate orientations has been investigated. Therefore, it seemed appropriate that a systematic investigation of silicon epitaxy on various sapphire substrate orientations would be of value. It was expected that the answers to three questions could be obtained from such an investigation. These are as follows: 1) Since we know of at least four distinct modes of orientation relationships, over what range of substrate orientation do these modes occur and what is the form of the boundary expected between the different regions in which each mode occurs? 2) Are there other modes which occur on substrate orientations not previously investigated? 3) What is the explanation for the discrepancy between our laboratory's findings and those results reported by Joyce et al.4 concerning the relationships occurring on (1120) substrates? APPROACHES AND EXPERIMENTAL METHODS Two different approaches were used. Initially, depositions were carried out on rounded cylindrical surfaces which lay perpendicular to the (0112) plane.* By this means the presence of boundaries and their approximate positions could be determined. Finally and more definitively, depositions on flat sapphire substrates with a variety of orientations, mostly along primary crystallographic zones and about the (1120) plane, were studied by means of reflection electron diffraction and X-ray diffraction (using back-reflection Laue patterns and full circle goniometer techniques) in order to determine crystallographic relationships. The sapphire orientations investigated by these means

Jan 1, 1969