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By F. C. Bond

Since the Third Theory of Comminution was presented eight years ago (I) it has found increasing use in crushing and grinding problems. The practical utility of its wok index equation is quite generally acknowledged (2). However, its theoretical basis has been questioned in at least three technical articles (3) (4) ('). The purpose of this paper is to present experimental proof that it is scientifically correct. Particles under compressive stress are strained and deformed. They absorb strain energy, and when this locally exceeds the breaking strength, a crack tip forms. The surrounding strain energy flows to the crack tip, which rapidly extends and splits the rock, releasing the strain energy as heat. The initial energy flow causes additional crack tips in highly strained areas. If the compression is rapidly applied by impact, crack tips may form before the strain energy has reached equilibrium in the particle, thus decreasing the total work input required for breakage. The energy necessary to break is essentially the energy necessary to produce crack tips, since the energy necessary to extend the cracks to breakage is already present as strain energy in the deformed particles. After breakage nearly all of this energy appears as heat. The crack length cannot be measured directly. However, in particles of regular and similar shape the crack tip length is considered as equal to the crack depth, or crack extension necessary to break, so that the crack length equals the square root of one-half of the surface area. The Third Theory states that the useful work done in crushing and grinding is directly proportional to the total length of the new cracks formed. It can be confirmed by showing that a constant work input produces a constant length of new cracks when reducing the same material to different product sizes. This is done in the present paper on a wide variety of material. The constant work input was supplied by one revolution of the 12" x 12" laboratory ball mill used in making grindability tests by the Allis-Chalmers method (12) (13) The new crack lengths produced per mill revolution were measured from all available grindability test results at 28, 35, 48, 65, and 100 mesh on fifteen different ores, and were found to remain substantially constant for each ore at all mesh sizes. A new technique is used for the measurement of crack lengths. Size distribution plots of the mill feed and product are made by the Third Theory method (9) and the crack lengths are obtained from these plots by the procedure described in the present paper. The energy input required to produce a unit length is of fundamental importance in the size reduction of brittle solids. The crack length Cr is expressed in centimeters per cubic centimeter of solid material. It bears a definite relationship to the external surface area of the crushed or ground solid. A uniform particle shape must be assumed before the surface area and crack length can be evaluated. In this paper it is assumed that the relationship between the surface area and the particle volume of a particle d microns in diameter is the same as that of cube d microns on a side. The external surface areas of particles with a cubical breakage probably agree approximately with this rule, and correction factors can be applied when physical measurements of the surface areas are available for comparison. However, the assumption of equivalent cubes has been found satisfactory for most calculation purposes. Assuming equivalent cubes, one cubic centimeter of particles d microns in diameter will have a crack length Cr of v30.000/d centimeters, and a surface area of 60,000/d square centimeters. The specific crack length is thus equal to the square root of one-half the specific surface area. Where Sa is the surface area in square centimeters per gram and Sg is the specific gravity of the ground solid, then Cr = vSg . Sa/2 = 173.2/ vd (1)

Jan 1, 1961

By C. E. Brukl, E. Rudy, St. Windisch

The ternary-alloy system Nb-Mo-C was investigated by means of X-ray, melting point, DTA, and metallo-graphic techniques; a complete phase diagram for temperatures above 1500°C was established. Above 1960°C, niobium monocarbide and the cubic (Bl) high-tenzperature phase in the Mo-C system form an uninterrupted series of solid solutions. The ternary range of the pseudocubic q MoCl-, is very restricted. Dimolyb-denum carbide dissolves up to 44 mol pct Nb2C (2240°C), whereas the maximum solid solubility of MO2C in Nb2C does not exceed 5 mol pct. The order-disorder transformation temperatures in Mo2C and Nb2C are lowered by the mutual metal exchanges. Six invariant (p = const) reactzons occur in the ternary system; three correspond to class 11-type four-phase reactions involving a liquid phase, one to a class I (eutectoid)-type, and two further isotherms are associated with limiting tie lines. The results of the Phase diagram investigation are discussed, and the thermodynamic interpretation identifies the low relative stability of the binary sub-carbides in conjunction with the large stability diflerences between niobium and molybdenum carbides as the cause for the formation of a stable equilibrium between the monocarbide and the metal phase in the ternary reson. Due to their refractoriness, the carbides of the high-melting transition metals have received increased interest in recent years as base materials in composite structures for aerospace applications at high temperatures and for the development of self-bonded cutting tool materials; other novel fields of application include power reactors, where operation at high temperatures becomes essential for attaining high power efficiencies. In these applications, the increased reaction rates at high temperatures require a close consideration of the chemical interactions between the alloy constituents. As a consequence, a detailed knowledge of the phase relationships in the alloy systems is required in order to provide a sound basis for developmental -type work. Partly as a result of the considerable experimental difficulties associated with the investigation of this high-melting alloy class, no complete studies of ternary metal-carbon systems have been performed until recently. Even the high-temperature phase relationships in the binary transition metal-carbon systems have been delineated only during the past few years to a degree of accuracy required for a more detailed study of ternary or higher-order alloys. In recent investigations of binary and ternary systems of refractory transition metals with carbon, boron, and silicon,&apos; alloys from the ternary systems Nb-Mo-C became of interest because of the demonstrated possibility2,3 of obtaining compatible composites based on metal + monocarbide combinations. In the meantime, however, studies in other, but related, ternary metal-carbon systems, such as Ta-W-C, have shown that the solid-state equilibria may change significantly toward higher temperatures (>2000°C), and that extrapolations based on low-temperature equilibrium data are, in general, not very reliable. Although the lower-temperature (<2000°C) phase relationships in the Nb-Mo-C system are similar to those found in Ta-W-C, a cursory thermodynamic analysis of the equilibria indicated4 that complete solid-solution formation between Mo2C and Nb2C should not occur at higher temperatures. The present work was conducted in order to experimentally verify these expectations and, in addition, to provide phase equilibrium data in the melting range of the alloys. In the boundary systems, niobium and molybdenum are known to form a continuous series of solid solutions.576 The continuous solubility was also confirmed by Kornilov and Polyakova,7,8 who also observed a minimum melting point at 22 at. pct Mo and 2345°C. The phase diagram investigations of the Nb-C system by Storms and Krikorian9 and Kimura and Sasaki10 were recently supplemented by Rudy et al.11,12 The system contains a high-melting monocarbide with the B1 structure, Table I, and a subcarbide, Nb2C, which exists in at least two different states of sublattice order at low temperatures47"-&apos;3 and a disordered state above approximately 2500°C.11,12 The melting-point measurements by Rudy et al .11,14 are in close confirmation of the data by Kimura and Sasaki.10 The rather complex phase relationships in the Mo-C system were only recently Clarified.15,18 The system is characterized by three congruently melting, intermediate phases, MozC, ? MoC1-x and a Mol-,, Table I, of which only Mo2C is stable at temperatures below 1650°C. Substoichiometric MozC exists in several states of sublattice order which interconvert in homogeneous phase transitions. Hyperstoichiometric compositions cannot exist in the ordered state. Upon cooling through a critical temperature range, the

Jan 1, 1968

By Y. C. Liu, R. H. Richman

Deformation and recrystallization textures of the a solid solutions of Cu-P, Cu-As, and Cu-Sb alloys are examined as a function of composition. It is found that the deformation texture of copper is unckanged up to a composition of 0.43, 0.41, and 0.24 at. pct of phosphorus, arsenic, and antimony, respectzvely, and then the transition to the 70 : 30 brass type of deformation texture proceeds linearly as the logarithm of the solute content. Recrystallization textures consist of strong, new components that do not all bear the usual<111> rotational relation to the deformation components. The dependence of the deformation texture transitions and the recrystallization orientations upon composition and solute-element type is discussed. A systematic evolution of individual recrystallization components in the annealing texture of copper was portrayed as a function of germanium or tin content in a previous study.&apos; Similar patterns of tex-tural change have been observed with copper-zinc alloys,2 and in less detailed studies of other systems.3,4 In fact, most of the literature dealing with preferred orientations in copper alloys indicates that the influence of solute elements upon textures in copper is of one general type. As the alloy content of copper is increased, the deformation texture changes from the copper type to the 70:30 brass type, and the annealing texture undergoes a comparable change from the (001) [ loo] orientation of unalloyed copper to the {113} <211> type of 70:30 brass, with the notable exception of copper alloyed with Periodic Subgroup V-B elements.4-8 In almost every case it is possible to describe the reorientations after annealing as 30 to 40 deg rotations about <1ll> poles of the deformation components. Since there is apparently not much difference in the final textures of the copper binary systems already investigated, only a limited variety of preferred orientations has served as the basis for current theories of the origin of annealing textures. In order to test the validity of the proposed theories, and the possibility that the <111> rotations are not unique, it would be most desirable to study the reorientation relationships of additional, and heretofore unanalyzed, recrystallization components if such components exist. Examination of the literature reveals a good deal of uncertainty concerning preferred orientations in copper alloyed with elements in Subgroup V-B of the Periodic Table. Phosphorus is known to inhibit the cube texture in copper when present in amounts as low as 0.01 wt pct,8 but the recrystallized matrix that occurs instead of the cube orientation was reported as either random or weakly textured, with orientations not observed in Cu-Zn, Cu-Ge, or Cu-Sn alloys.4-9 A Cu-0.75 at. pct As alloy apparently contained, along with the (001)[100] and (113) <211> type of recrystallization components, {110} <112> and (110) <001> components, whereas an almost random distribution of orientations was found in alloys of higher arsenic content.4 A {110} <001> component also appeared in rolledand annealed Cu-Sb alloys, but otherwise the recrystallization textures of Cu-Sb alloys seem to con-

Jan 1, 1962

By K. A. Jackson, J. D. Hunt

A general theory for the growth of lamellar and rod eutectics is presented. These modes of growth depend on the interplay between the diffusion required for phase separation and the formation of interphase boundaries. The present analysis of these factors provides a justification for earlier approximate theovies. The conditions for stability of rod and Lanlellar structures are consitleved in terms of the mechanisms by which the structure can change. The mechanisms considered include both small adjustments to the lnnzellar spacing due to the motion of lamellar faults, and catastrophic changes due to instabilities. It is concluded that stable growth occurs at or near the minimum interface undevcooling for a gizierz growth rate. The conseqrlences of the existence of a diffusion boundary layer at the interface are discussed. The experimental results for the variation of growth rate, undercooling, and Lanzellar spacing are cornpared with the theory. We believe that the theory presented in this paper provides an adequate basis for understanding the complex phenomena of lanzellar and rod eutectic growth. The growth of lamellar eutectics has been the subject of several theoretical and many experimental studies. The foundations for the theoretical work were laid by zenerl and Brandt2 in their analyses of the growth of pearlite. Zener estimated the effect cf diffusion, and took into account the surface energy of the lamellar structure. He found that the lamellar structure could grow in a range of growth rates at a given undercooling provided the lamellar spacing was appropriate for the growth rate. Since pearlite grows with only one growth rate and one lamellar spacing at a given undercooling, there is clearly an ambiguity in the theory. Zener removed this ambiguity by postulating that the growth rate was the maximum possible at the given undercooling. He predicted then that the product of the growth velocity v and the square of the lamellar spacing A should be constant, i.e., A2v = const. Brandt2 started out by assuming that the interface between the lamellae and austenite was sinusoidal. Because of this, the ambiguity encountered by Zener did not arise. Brandt was able to obtain an approximate solution to the diffusion equation, but, since he did not take into account the surface energy, his considerations are incomplete. Tiller3 applied some of these ideas to the growth of eutectics, and proposed a minimum undercooling condition to replace the maximum velocity condition used by Zener. These conditions are formally identical. Hillert4 extended the work of Zener. He found a solution to the diffusion equation assuming the interface to be plane. Taking surface energy into account, and applying Zener&apos;s maximum condition, he was able to calculate an approximate shape of the interface. Jackson et al.5 used an iterative method employing an electric analog to the diffusion problem to refine the calculation of interface shape. It was found that the interface shape calculated from a plane-interface solution to the diffusion equation was negligibly different from the exact solution. The method provided an analog only for eutectics for which the volumes of the two phases are equal, growing from a melt of exactly eu-tectic composition. There has also been considerable experimental work on eutectics, Several experimenters8-10 found that A2v is constant as predicted by Zener.1 Hunt and chilton10 demonstrated that ?T/v1/2 is also a constant for the Pb-Sn system as predicted. Lemkey et al.11have recently found A2v to be constant for a rod eutectic. In the present paper, we present the steady-state solution for the diffusion equation for a lamellar eutectic growing with a plane interface, for the general case, that is, with no restriction on the relative volumes of the two phases, and with the melt on or off eutectic composition. A similar solution is also found for a rod-type eutectic. Expressions are obtained for the average composition at the interface and the average curvature of the interface. These equations for the average composition and curvature are similar in form to those derived by Zener1 and Tiller,3 and provide a justification for some of the approximations made by these authors. The mechanisms by which the spacing in a lamellar structure can change are considered. The important mechanism for small changes in lamellar spacing involves a lamellar fault. Examination of the stability of lamellar faults leads to the conclusion that the growth occurs at or near the extremum.* The insta- bilities which can develop in a rodlike structure are also discussed, resulting in the conclusion that this structure also grows at or near the extremum. Comparison of the conditions for rod and lamellar growth permits a prediction of the surface-energy anisotropy required to produce rods or lamellae for various volume-fraction ratios. The diffusion equation predicts the existence of a diffusion boundary layer at the eutectic interface unless the eutectic has 0.5 volume fraction of each phase and is growing into a liquid of eutectic composition. This boundary layer is such as to make the composition in the liquid at the interface approximately equal to the eutectic composition. This boundary layer permits changes in composition during the zone refining of eutectics. Photographs of the eutectic interface of a growing transparent organic eutectic system have been made. Both the components of this eutectic are transparent organic compounds that freeze as metals do.12 The in-

Jan 1, 1967

By H. E. Cline

Mechanical properties of the eutectic between CoAl and cobalt were measured over a range of- temnperatures and strain rates for a variety of microstructures produced by directional solidification and by thermo-mechanical processing. Directional solidification led to rodlike, lamellar, and irregular microstructures. The unusually high volume fraction of the cobalt-rich rods and the lurge spacing of the rods were explained by the phase diagram. The hot-worked structure consisted of fibers of COAL in a cobalt-rich matrix. The roonl- tevlperature strength of the uvrought material increased with decreasing grain size but the 1000°C strength decreased with decreasing pain size. At high temperatures the directionally solidified tnaterial was stronger and less strain-rate-sensitice than the hot-rolled material. The fine-grained hot-worked ma-terial became superplastic at high temperatures, with tensile elongations greater than 850 pct, while at root temperature this material was ductile and impact-resistant because of the ductile matrix. Fracture occurred in the directionally solidified material at elevated temperatures by inter phase separation and at roorn temperature by cracks in the intermetallic phase. Growth of these cracks was impeded by the ductile cobalt-rich phase. It was found that the CoAl intermetallic remains ordered at elevated temperatures. DIRECTIONAL solidification of eutectic alloys has been used to produce structures consisting of parallel rods or lamellae. Although the spacing of the phases depends on the growth rate, it has been observed to be of the order of 1 µ in many eutectics. A strong intermetallic phase has been used to reinforce a ductile matrix in the rod eutectic A1-Al3Ni and the lamellar eutectic Al-Al2cu.1 The microstructure of the eutectics A1-A13Ni and A1-A12Cu remained aligned after samples of these alloys were exposed to temperatures just below their melting points for long times. Stability of the microstructure at elevated temperatures makes directionally solidified eutectics a candidate for high-temperature applications. Recently Thompson4 has developed the Ni-NiMo eutectic containing 40 pct NiMo lamellae, giving a tensile strength superior to nickel-base superalloys. Unfortunately, this eutectic oxidizes rapidly at elevated temperatures. By mechanically processing a two-phase structure, one may reach strengths as high as 700,000 psi, as demonstrated by drawn pearlite.5 In this case the strengthening mechanism was thought to be related to the fine substructure formed during deformation.5 However, a heavily worked structure may recrystallize and coarsen at elevated temperatures. Some worked eutectics such as Al-Al2Cu,6 Pb-Sn,7 and Sn-Bi7 have shown unusually large elongations in tension when tested at elevated temperatures. This phenomenon of large extension, called "superplasticity", was related to the fine grain size of wrought two-phase alloys at elevated temperatures. A mode of deformation of "superplastic" material has been shown to be grain boundary sliding,&apos; which has also been observed during creep of polycrystalline materials.9 The Co-A1 system was chosen for this investigation after examining the phase diagrams of binary eutectics." The high melting point of 1400°C, the aluminum content which was expected to give oxidation resistance, and the properties of the intermetallic CoAl were the chief factors influencing this choice. This eutectic consists of a mixture of the intermetallic CoAl and a cobalt-rich solid solution. The intermetallic CoAl has a large range of solubility and a CsCl structure." From the similarity between CoAl and NiAl one would expect CoAl to be ordered at elevated temperatures; however, specific heat measurements" show a transition at 800°C. West-brookL2 has measured the hot hardness of CoAl and found a rapid decrease in hardness above 600°C. The tensile properties and stress rupture properties of as-cast CoAl-Co eutectic were measured by Ashbrook and wallace13 who report a room-temperature tensile elongation of less than 1 pct. I) EXPERIMENTAL A) Sample Preparation. Experimental materials were prepared by directional solidification, by hot working, and by powder processing. The starting materials were electrolytic 99.9 pct pure cobalt and 99.99 pct pure aluminum. 1) Directional Solidification. A vertical Bridgman apparatus heated by induction was used to directionally solidify cylindrical ingots $ in. in diam and 5 in. long. The apparatus was first evacuated and then an argon atmosphere was introduced to retard evaporation. The ingots were contained in an alumina crucible inside a graphite susceptor that rested on a movable water-cooled base. The base was lowered out of the induction coil at a constant rate. Eight of the ingots were solidified using a drive rate of 2.5 cm per hr, two of the ingots at 1.2 cm per hr, and one ingot at 10 cm per hr. The eutectic composition Co 10 wt pct A1 was used in all but one ingot which had the composition of the stoichiometric CoAl intermetallic, Co 32 wt pct Al. 2) Mechanical Processing. At 1000°C the eutectic Co 10 wt pct A1 is a mixture of an intermetallic phase, Co 21 wt pct Al, and a cobalt-rich phase, Co 5 wt pct Al.10 These phases differ from the stoichiometric CO 32 wt pct A1 and pure cobalt because of the large solubility of this eutectic at elevated temperatures." Four rectangular slab ingots, 4 by 1 by 12 in. high, of Co 10 wt pct Al, Co 5 wt pct Al, Co 21 wt pct Al, and Co 32 wt pct A1 were cast for hot rolling. The cobalt was first vacuum-melted, H2-treated for 20 min,

Jan 1, 1968

By M. R. Lorenz

Efficient visible light emission from p-n junctions in semiconductors is currently achieved in the four materials, Sic, GaP, ]Ga1-xAs and GaAs1-x,. Recent advances in materials preparation and p-n junction formation are briefly reviewed. The radiative recombination processes in the different materials depend largely on the band structure and the impurity states of each material. The spectral distribution of the emission ranges from the blue in Sic, to green in Gap, yellow in Sic and red in Gap, Ga1-x AlxAs and GaAs1-x Px. The origin of the various processes are discussed. The conversion of the electrical power into optical power and the measurement of the conversion efficiency are reviewed. The currently maximum quantum efficiencies at 300°K are: 3 pct in GaP(red), 1 pct in SiC(yellow), 0.1 pct in GaP(green), 0.2 pct in Ga1-x AlxAs at 66001, and 0.1 pct in GaAs1-x Px at 6800. The brightness and the interplay of the quantum efficiency and the luminous efficiency are given detailed consideration. VISIBLE light generated by the application of a direct current to a semiconductor crystal was first observed by Lossev1 in 1923. Light emission came from naturally occurring junctions in Sic crystals but little was known then with regard to the mechanism of charge transport and light emission. Some nearly 30 years later and with a vastly increased understanding of semiconductors the phenomenon of electroluminescence was studied in more detail, for example in p-n junctions of germanium.2 In these early studies, the efficiency of converting the electron current into a photon current was very low and therefore aroused little interest toward practical application. More recently it became apparent that in certain materials, for instance GaAs, and under certain conditions, the conversion efficiency was not low at all.3 The subsequent discovery of the p-n junction laser4-6 provided the impetus for increased studies of electroluminescence. Light emitted from GaAs occurs in the infrared region of the electromagnetic spectrum and is not visible to the eye. At nearly the same time the use of GaAs1-xPx led to laser action at low temperatures which was visible to the eye.7 Later a red light emitting diode, made from Gap, was reportedS which emitted incoherent radiation at 300°K with an external quantum efficiency of about 1.5 pct. The fact that such efficient devices were obtainable led to a more concentrated effort in the search for highly efficient room-temperature semiconductor light sources. It is some of this later work on p-n junction luminescence with which we will be concerned here. Since our aim is centered on visible light, with hv =1.8 ev ( ?=7000?), only the wider band gap semiconductors are of interest, i.e., Eg 1 1.8 ev. Although many compounds meet this criterion, only a limited number of those are also good semiconductors, i.e. contain low resistance n and p regions. Some of the more promising candidates are listed in Table I. We will only be concerned with light generation from a p-n junction. This limitation excludes essentially the group II-VI binary compounds, although we will briefly review the case of ZnTe and the solid solution ZnTe1-xSex. As we will show they may contain a p-n junction but only of a special kind. Most of the discussion will deal with the four materials, Sic, Gap, Gal-xAlxAs, and GaAs1-xPx. These appear to be at the present time the best visible light emitting semiconductors. In the following sections we will briefly consider: 1) the electrical properties of p-n junctions; 2) some recent advances in materials preparation; 3) the formation of p-n junctions; and then in somewhat greater detail we will consider: 4) the various radiative recombination processes; 5) the measurement and observation of the external quantum efficiency; 6) the luminous efficiency; 7) the brightness of light emitting diodes (LED&apos;S). THE P-N JUNCTION The p-n junction in a semiconductor crystal is the interface between two differently doped regions. More specifically the p region is doped predominantly with acceptor impurities and the n region contains predominantly donor impurities. The energy band structure of a degenerate p-n junction at thermal equilibrium is shown in Fig. l(a). The excess electrons on the n side of the junction are confined to this region by the barrier potential Eg. Similarly the excess holes on the p-side of the junction are confined to the p-region by a similar potential barrier. If we now apply a dc voltage V such that the p region is made positive and the n region negative, the barrier potential EB is reduced by the applied voltage, V and the junction is said to be forward biased. With the barrier potential lowered, electrons and holes can drift toward the p region and n region, respectively, see Fig. l(b). The current voltage characteristics of p-n junctions in most wide band gap materials can be described by the relation: J = Joexp(eV/BkT) [1] where the functional form of Jo is determined by the recombination mechanism. Jo is generally a complicated parameter which depends on a number of different factors including temperature, junction width, bias voltage, and carrier lifetimes. The parameter B also depends on the recombination mechanism but

Jan 1, 1970

By W. F. Chiao

With the application of dislocation damping theory an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. A ductile steel was compared with a brittle stee1 by simultaneously measuring the ultrasonic attenuation and velocity during tensile test, and the density of free dislocations and their mean loop length were then calculated as a function of strain. The results showed that in the ductile steel there was always a large generation of dislocations and great extension of loop length occurring at some stage within the early plastic region. In contrast, the brittle steel showed very little or no such sudden changes in dislocation dynamic states after the onset of plastic deformation. Furthermore, a strong temperature dependence of dislocation dynamic states was also observed in the ductile steel and a hypothesis was suggested that a thermally activated process of dislocation rearrangement could occur at higher deformation temperatures. The activation energy of dislocation rearrangement at room temperature was estimated as about 2030 cal per mole.C. DUCTILITY is an indispensible property in the application of engineering materials, especially steel. During the past two decades the theoretical and experimental approach to the understanding of flow and fracture of metals has been constantly undergoing changes and progress." while the fracture behavior of metals can be influenced by many factors such as chemical Composition,3 second-phase particle mor-phology,4 and dislocation arrangement,5 it is now a general belief that the fundamental understanding of the ductile-brittle fracture phenomena of solid materials must stem from the study of dislocation dv-namics developed under stress conditions.6,7 Most of the traditional ductility tests, such as Charpy impact test, slow bend test, and tensile fracture test, cannot by themselves reveal directly the mechanisms of ductile to brittle transition of materials. In the experimental investigation of tensile ductility it would be ideal to be able to study directly the dynamics of dis-locations in a bulk specimen during the process of deformation. Since the ultrasonic pulse technique is the only satisfactory method for studying dislocations and the fine details of deformation characteristics in metals in the course of a tensile test, it would appear that a comparative study of ultrasonic attenuation changes during tensile tests of metallic materials exhibiting different ductility might be very informative. So far no work comparable to this study has appeared in the literature. Recent progress in both theory and experiment has indicated the feasibility of studying the dislocation mechanisms of ductility behaviors by ultrasonic measurements during tensile test. Granato and Lucke8 have developed a quantitative theory that enables the calculation of dislocation density and their average loop length from the measurements of ultrasonic attenuation and velocity, and several investigators, including Chiao and Gordon,9&apos;10 have shown that simultaneous ultrasonic measurements can be successfully made during a tensile test. Furthermore, many investigators11-13 have repeatedly proposed in the past several decades that deformation and fracture are mutually self-exclusive, and that the ability or inability of a material to deform plastically, i.e., to generate dislocations, is a major factor in determining whether the material will be ductile or brittle. Thus, in the present work an attempt was made to determine whether the generation and extension of dislocations is inherently more difficult in a brittle steel than in a ductile steel. This article is principally concerned with the study of the relation between the propagation of ultrasonic waves and tensile deformation in a steel series which displays quite different toughness at room tempera-turk. changes in attenuation and velocity of ultrasonic waves have been measured as a function of strain during the deformation process. The results have been interpreted in terms of the vibrating string model for dislocation damping as developed by Granato and Lucke, and it has been found that some of the more subtle predications of the model are in good agreement with the experiments. This would be especially meaningful because most of the previous experiments in testfying the model were carried out with single crystals of high-purity materials and little work has been done with polycrystalline steel alloys. EXPERIMENTAL PROCEDURES AND RESULTS Specimen Materials. The tensile specimens used throughout this experiment were of two compositions selected from a series of Fe-Mo-0.77 pct Mn-0.22 pct C steels prepared for a ductile-brittle fracture transition study. One steel contains 0.21 pct Mo and the other 1.03 pct Mo. These two compositions were chosen for the present study because they possess quite different toughness properties at room temperature. The 0.21 pct Mo steel is quite ductile while the 1.03 pct Mo steel is rather brittle, as measured by the standard Charpy impact test. The alloys had been prepared by vacuum induction melting and chill casting in steel molds. The ingots were hammer-forged into 1/2-in.-sq bars from which tensile specimen blanks were cut. These blanks were first normalized under argon atmosphere at 1700°F and then reaus-tenitized and isothermally transformed at 1050°F to a bainitic microstructure. The chemical compositions, heat treatments, hardness measurements, and Charpy transition temperatures of the two steels are listed in Table I.

Jan 1, 1970

By G. D. Rieck, M. M. P. Janssen

Chemical diffusion coefficients and heats of activation for diffusion in the NizAh fy), NiAl (6), and Ni3A1 (E) intermetallic phases and the solid solution of aluminum in nickel (( phase) were calculated from layer growth experiments. No finite diffusion coefficient for the NiAl3 ((3) inter metallic phase could be calculated. The values of the diffusion coefficients are dependent both on the method of calculation and the type of diffusion couple. The heat of activation for diffusion in the y phase was found to be 47 kcal per mole in the temperature range oj 428" to 610°C. Heats of activation of 41, 12, and 48 kcal per mole were found for diffusion in the 6, E, and ( phases, respectively , in the temperature range of 655" to 1000°C. Experiments with markers in the diffusion zone demonstrate a very pronounced Kirkendall effect. It appears that only aluminum atoms take an active part in the diffusion process during the formation of the 0 and y phases at temperatures of about 600°C. During the formation of the 6, E, and < phases at higher temperatures only nickel atoms are moving. It is suggested that the great stability of the intermetallic compounds in the Ni-A1 system governs the Kirkendall effect. SOME factors controlling layer growth during inter-diffusion in the Ni-A1 system (phase diagram, see Fig. 1) were studied by Castleman and Seig1e.l&apos;~ They found the NiA1, ((3) and NiAl3 (y) intermetallic compounds to appear in the diffusion zone of Ni-A1 couples at annealing temperatures of 400" to 625°C; the NiAl (6) and Ni3A1 (E) intermetallic compounds appeared in y-Ni couples at annealing temperatures of 800" to 1050°C. These authors carefully examined metallographically Ni-A1 couples after 340 hr annealing at 600°C. Besides the (3 and y phases they found very thin layers of the 6 and E phases. ~n~erman~ and Castleman and Froot4 observed a much more rapid growth of the 5 and E phases at 600°C in Ni-A1 couples in case a crack was present at the /3-A1 interface. Numerous layer thickness measurements carried out by Castleman and Seigle on the y phase prove that the layer growth of this phase obeys the parabolic law after a certain transient period. From this they concluded that the layer growth of the y phase is controlled by volume diffusion. The growth of the 13, 6, and E phases appeared to be volume-diffusion-controlled also. The authors estimated that at 600°C and at atmospheric pressure Dp was 1.8 x lo-"ll sq cm per sec, D, 9.1 x 10" ™ sq cm per sec, Qp 27 kcal per mole, and Qy 31 kcal per mole. The present work was carried out to obtain more quantitative data about the kinetics of growth of the phases of the Ni-A1 system and the reactions that occur during the formation of these phases. Because in this system the diffusion process results in the formation of several distinct intermetallic compounds, the current term reaction diffusion is used in the title of this paper. In order to obtain layers of the fl phase compound of uniform thickness, a new technique for preparing diffusion couples was developed. The kinetics of growth of the y phase in 6-Al, E-Al, and Ni-A1 diffusion couples was studied at different temperatures. The kinetics of growth of the 6, c, and ( phases in Ni-y, Ni-6, and Ni-c diffusion couples was also studied at different temperatures. The calculation of the diffusion coefficients Dp and Dy by Castleman and Seigle are critically considered in this paper; by means of a revised method of calculation more reliable val-ues of , and Dg were found. These values are in good agreement with the values of the diffusion coefficients obtained by the method of Boltzmann-Matano. From the temperature dependence of the diffusion coefficients the heats of activation for diffusion were calculated by means of an Arrhenius-type equation. The investigation of the Kirkendall effect has been used to obtain information about the ratio of the intrinsic diffusion coefficients of the separate atoms5 and the mechanism of diffusion. Moreover porosity as a result of a distinct Kirkendall effect would be of practical importance in connection with the bonding of diffusion coatings. The analyses of the diffusion couples were carried out by metallographic methods. The values of the concentrations at the phase boundaries and the concentration profile in each of the phases, which are needed for the calculation of diffusion coefficients, were obtained by electron-pro be X-ray microanalysis. EXPERIMENTAL PROCEDURE A) Materials for Diffusion Couples. The intermetallic compounds 6 (50 at. pct Ni) and E (74 at. pct Ni) were prepared from the pure metals by high-frequency induction melting in argon atmosphere. Use was made of aluminum wire (99.99 wt pct Al) and nickel sheet (99.95 wt pct Ni). The 6 and E phase melts and the nickel shiet (thickness 0.1 and 0.5 mm) used for preparing diffusion couples were annealed for 64 hr at 1200°~ for homogenization and grain coarsening (final crystal size 1 to 3 mm). composition and homogeneity of the intermetallic compounds were checked by mi-crohardness measurements and X-ray diffraction. From the 6 and E phase melts discs of 0.5 mm thickness were prepared by means of a water-cooled rotat-

Jan 1, 1968

By G. N. Goldberg, Robert A. Rapp

The steady-state kinetics and microstructures of simultaneous internal oxidation and external scale formation were investigated for the oxidation of Cb-Zr and Ch-Zr-Re alloys in pure oxygen at 1000°C. For each binary alloy, a constant rate of scale formation was observed at steady state; the internal oxidatton zone reached a steady-state, time-independent thickness. The dependence of the scaling rate on zirconium content exhibited a maximum at a low zirconium colttent; more concentrated alloys oxidized at a slower rate than pure columbium. This composition dependence of the scaling rate may be partially attributed to the effect of the internal oxidation process as an intenla1 sink for oxygen, with the formation of voluminous, and relatively impermeable ZrO2 precipitates. However, the morphologies of the ZrO2 internal oxide precipitates also affected the scaling rate. The internal oxide precipitates were distributed uniformly in the external scale. The steady-state thicknesses of the internal oxidation zones were not in agreement with those predicted theoretically from an idealized simple model. However, in this particular alloy systen1 the ideal model is not satisfied experitmentally. For ternary Cb- Zr - Re alloys with Nr10e = 0.02 or 0.05, the steady-state thicknesses of the internal oxidation zones were less than those for the corresponding binary Cb-Zr alloys. For ternary alloys with NRe(0) - 0.05, a more adherent and much less porous external scale was formed, and a reduction in the kinetics of scale formation was observed. A number of authors&apos;-7 have reported linear oxidation kinetics for the reaction of pure columbium at 1000°C in air or in oxygen of about 1 atm pressure. A thin and tightly adherent oxide layer is found at the metal/oxide interface beneath a porous external layer of scale. Although the suboxides CbO and CbO2 represent thermodynamically stable phases at 100O°C, generally only Cb2O5* is identified as a reaction product in quenched specimens. Studies at 1000°C at lower oxygen pressures8,10 (Po2 - 10-4 Torr) show that both CbO and CbO2 do form and that CbO2 is a protective oxide. The growth of CbO2 results in parabolic kinetics until Cb2O5 is nucleated and grows. Apparently because of the large volume change associated with its formation, Cb2O5 is porous and does not serve as a diffusion barrier; linear kinetics prevail after the surface is covered with Cb2o5. On the basis of these observations, several authors5,9,10 have suggested that the linear oxidation of pure columbium at 1000°C in air or oxygen of 1 atm is limited by a Loriers-type mechanism,11 whereby the total rate or reaction is controlled by ionic diffusion through a thin layer of CbO2 which is maintained at a constant thickness throughout the linear oxidation. However, the concept of a Loriers model for a three-phase CbOlCbO2 Cb2O5 scale, with the only oxygen activity gradient across the NbO2 phase, is not self-consistent. Further, the suboxides CbO and CbO2 were not observed in the high-temperature X-ray diffraction study of columbium oxidation by Goldschmidt.8 From investigations in which the large PO2, dependence of the linear scaling rate was demonstrated, the importance of an oxygen adsorption or dissolution step has been suggested.4,5,7,10,12 Thus the mechanism for the linear oxidation of pure columbium remains quite controversial. Since further insight into the oxidation mechanism of pure columbium is not provided by this investigation, the authors wish to emphasize at the outset that their experimental results are not interpreted in terms of a particular rate controlling step for the oxidation of pure columbium. Previous investigations13-18 of the oxidation of Cb-Zr solid-solution alloys in air or oxygen at 1000°C suggest a remarkable dependence upon zirconium content. For an alloy of bulk zirconium mole fraction, N2r(0) equal to 0.05 or 0.10, the oxygen uptake is reported to be as high as four times greater than that for pure columbium;13,14 for alloys with NZr(0) 0.05 or 0.10 the oxygen uptake is reported to decrease with increasing NZr(0); to a minimum uptake of about one quarter that for pure columbium at NZr(0): = 0.50.13-15Since zirconium forms a more stable oxide (ZrO2) than the lowest columbium oxide (CbO), and since columbium exhibits a high solubility19,20 and diffusivity21,23 for oxygen, the internal oxidation of the zirconium component to ZrO2 is expected at a reaction front ahead of the advancing metal/scale interface. The external scale is then formed at the metal/scale interface by the inward migration of oxygen through the scale, probably through a series combination of molecular and ionic diffusion. Internal oxidation in conjunction with external scale formation has been investigated by Maak24 for the oxidation of dilute Cu-Be alloys in pure oxygen at 850°C. For cu-Be and many other binary alloys,24-27 very small, essentially uniaxial internal oxide particles are formed in the most dilute compositions; for somewhat more concentrated alloys. the internal oxide particles precipitate as platelets or needles. From pertinent solutions to the diffusion equation, Maak28

Jan 1, 1967

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.&apos; Approximate analytical solutions&apos; 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.&apos; 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&apos; 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&apos;" 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 John Richards

MY remarks will be confined to the experience of our company in mining the No. 8 seam of coal in Ohio, although I believe that the relationship existing here between the method of mining and the method of cleaning will hold true in many of the coal seams throughout the country. The increasing demand for a cleaner and better graded product is being felt throughout the entire coal industry, and the methods of mining are playing an important part in the control of various sizes and quality of coal produced. We have found a definite relation between the mechanical loading of coal and its preparation for the market. In the No. 8 coal seam the location of the non-combustible material is regular. The&apos; marketable coal lies in three benches, separated by streaks or bands of impurities. These impurities must be removed from the coal to properly pre pare the product for the market. Where hand-loading methods are employed, the loader removes as much of this non-combustible material as possible at the working face. The impurities that are missed by the loaders are removed as the coal passes through the preparation plant, by means of picking tables. As this method of cleaning cannot improve the quality of the extremely fine sizes, a practice has been established in the company&apos;s hand-loading mines, of undercutting the coal about 2 in. above the bottom of the seam, thereby eliminating any possibility of impurities caused by the cutting machines cutting into the rock bottom below the coal seam.

Jan 1, 1934

By D. Hawington

HEALTH and safety in the mining and allied industries of the United States have unquestionably been progressing, particularly during the past three or four years, even though the progress has been anything but great in some branches of these industries. Statistical data to support this statement are readily available as to safety, but similar health data are unfortunately not available. In coal mining the rate of occurrence of fatal accidents per million tons of coal produced for the ten-year period 1911.20 inclusive was 4.27; this rate was 3.84 in 1930, .3.31 in 1931, 3.36 in 1932, and 2.69 (tentative) in 1933. In metal mining, the-rate of occurrence of fatal and- non-fatal injuries per .thousand 300-day workers (calculated) was 224.36 for- the same ten-year period. This fell slowly until after 1929 when it was 203.14, dropping to 170.78 in 1930, to 142.09 in 1931, to 138.46 in 1932, and to 155.13 in 1933. Here, again,-the real progress began in 1931 though the rate in 1930 was not particularly bad. For the same ten-year period, the rate of those killed and injured: in: quarrying per thousand 300-day workers (calculated)

Jan 1, 1935

By C. M. Smith

PILOTED by Cadwallader, Evans, Jr., as chairman, the Coal Division got under way Monday morning for the first of three consecutive sessions. N. F. Patton started the ball rolling with a paper on the economics of anthracite distribution, which was ably discussed by H. J. Rose, W. S. Blauvelt, and others. Mr. Patton pointed out many incongruities in freight rates, dealers&apos; margins, and other factors which are disturbing the distribution of anthracite, one result being that trucks are hauling at least six million tons of anthracite annually, half of which is stolen. In the discussion of the papers the desirability of greater uniformity in the production and shipment of coal from month to month was urged; with larger summer price concessions as a means toward this end. "Performance Expectancy of Domestic Underfeed Stokers for Anthracite," by Allen J. Johnson, brought this important platter down to date by showing the range in capacities and efficiencies to be expected from well-made stokers, and by detailing other of their operating characteristics. One of his most interesting points is that the efficiency of domestic stokers is practically equal to that of handfiring for good installations and operations of both

Jan 1, 1935

By Zay Jeffries

Rearmament superimposed on buying sprees by the public, caused a general shortage of metals in 1911. and the rare metals were no exception; they also shared with the more common metals the uncertainty of future demand. In general, the apparent undersupply of metals is a favorable condition for the realization of sleeping possibilities of the rare metals, especially if the supply can he made sufficient to take care of the possible new demand. Many changes in metal usage in 1941 were forced because of shortages. When such changes are in the direction of the economic trend there is a speeding up in the tempo of the inevitable change, but when the forced changes are against the economic trend they are likely to be shortlived. In any event, the latter is not a solid foundation on which to build a future business.

Jan 1, 1942

By Hans Lundberq

IINDUSTRY&apos;S attention is now focused on the production of munitions thereby creating a demand for certain minerals which in prewar days were produced only in limited quantities. Now production of these minerals must he increased from the known deposits and new deposits must be found. Can geophysics help? "War minerals" such as tin, vanadium, tungsten, antimony, manganese, chromium, and cinnabar have no physical characteristics sufficiently different front the country rook to permit their direct location by ordinary geophysical methods. As already demonstrated in work on gold and oil, useful information may be obtained indirectly, however, outlining structural features or geological conditions favorable for the deposition of such ores or the accumulation of oil. Recently, more direct and truly qualitative methods have been brought into a useful and practical stage, and by the combined application of old and new methods a technique has been developed which, it is hoped, will be of importance in the search for these vital minerals.

Jan 1, 1941

By Tom Westgarth

As papers are placed before you upon large gas-engines in Belgium and Germany, it was considered that some information should be given upon the same subject in Great Britain. I therefore agreed to compile these notes, which I have made very short in view of the somewhat full nature of the other papers presented to this meeting, and considering the complete nature of the many publications which have been made recently upon the subject of large gas-engines. I give below Tables I. to VI., showing the number and particulars of large gas-engines which have been built or are building by British makers, and in view of the growing size of gas-engines I have concluded that engines less than 500 h.p. cannot now be included in the category of large gas-engines, and therefore I have not considered engines under that power.

Nov 1, 1906

By T. E. SCHTVARZ

THE publication of the report by Mr. F. L. Ransome was welcomed by many engineers who had mined in the heart of the Sail Juan country, braved its long and snowy winters, climbed its lofty peaks, run the gauntlet of its snow-slides, and studied its problems of geology, while making dividends for their English or American clients. This report helps one to understand why the bonanzas occurred, and why the inevitable borrasca presents itself where least expected. The Red Mountain district of Ouray county, a very productive section from 1884 to 1893, occupies considerable space in the report mentioned.. The character of the ore-occurrence, being distinctive and presenting many features not existing elsewhere, has been deserving of special study. It is to be regretted that Mr. Ransome was .unable to observe the conditions underground, as all the principal properties, many of which I opened and developed, were closed at the time of his investigation: It has been my privilege to have contributed a few brief papers recording my observations in developing these properties ; and it is the object of the present paper to present certain sections of the Yankee Girl mine, which throw additional light on the geology of the section and make the available data more complete. The main Yankee Girl chimney or " stock" was the most productive for the first 500 ft. in depth of any chimney in the district.

Mar 1, 1905

By AIME AIME

ADDRESSING the Ohio Section at a recent meeting in Columbus, Ohio, R. C. Allen, executive vice-president for Oglebay, Norton & Co., Cleveland, spoke on "The Iron-Ore Industry of the Lake Superior Region in Prosperity and Depression." The speaker considered this region in connection with the problem of national security. This is the age of minerals; progress depends on them; and next to agriculture, the mineral industry is of prime importance. The United States has no shortage of minerals rather an over-supply; but many mines have been and are being exhausted. The shifting of the sources of supplies of minerals so important as copper, petroleum, and iron to other countries would create internal strains and affect international relations. There will be no early decline of ore mining in the Lake Superior region unless it is forced by unwise public policies. Iron ore is industrial strength and self-sufficiency. A study of economic geography is important for statesmen and mining men, because the minerals essential for peace and war are haphazardly or irregularly distributed throughout the world. Of these minerals, 75 per cent are owned by 10 per cent of the population, mainly peoples of Anglo-Saxon origin.

Jan 1, 1934

By AIME AIME

A COMMITTEE of the American Railroad Association, consisting of Samuel Rea, president of the Pennsylvania System, Chairman; F. D. Underwood, president of the Erie Railroad; A. T. Dice, president of the Philadelphia & Reading Railroad; E. J. Pearson, president of the New York, New Haven & Hartford Railroad; and C. H. Markham, president of the Illinois Railroad (who was represented at the meeting by J. F. Porterfield of his system), met at the headquarters of the American Institute of Mining and Metallurgical Engineers, New York, on April 6 to assist in the Coal and Coke Committee&apos;s attempt to solve the bituminous coal problem. There was a full discussion of the questions of seasonal freight rates and the purchase by the railroads during the slack months of their winter&apos;s supply of coal. As the question of fuel supply for the railroads is in the hands of the Railroad Association, as well as the coal operators, it was vital that it should be represented at this important conference. The situation from the point of view of the mine operators was presented very thoroughly. No seasonal rates were considered necessary for the year 1920, and, as this matter requires considerable thought, it will be given thorough study and worked out in detail at a subsequent meeting.

Jan 1, 1920

By Dwight L. Sawyer

IF it had not been for the testimony of former Secretary of the Interior, Harold L. Ickes, before the Senatorial investigating committee the public would have heard little about the Federal Government&apos;s suit against California for the ownership of the tidelands. The Ickes-Pauley dispute brought to public attention that the California tideland oil deposits are the last remaining large Federal oil reserves. Ickes contends that these tideland oil deposits belong to the nation for the benefit of all the people of all the states and not solely to the State of California. Ickes also accused California oil man Ed Pauley of offering to give $330; 000 to the Democratic party fund if Ickes would drop the Federal Government&apos;s suit against the State of California for the ownership of said tidelands. The tidelands may be considered as the land bordering the coast line between mean high tide and outward under the ocean for a distance of a marine league, or about three statute miles. This strip of land along the coast of southern California contains large oil deposits which have a present and future prospective value of several billion dollars.

Jan 1, 1947