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By T. H. Alden

Using alternating tension-compression straining, the hardening of magnesium oxide single crystals was studied up to large stresses and strains. At 0.25 pct plastic strain amplitude, the hardening curve is approximately linear with slope 25,000 psi from the shear yield stress, 7 to 8000 psi, to 35,000psi. Above this stress, the slope decreases. The strain hardening behavior of MgO is considered qualitatively similar to that of metal single crystals. The relatively high stress attainable by strain hardening is associated apparently with the high yield stress on the cross-slip system, (001) <110>. Cleavage fracture during testing is uncommon. It is argued that the centers of high internal stress at glide band intersections, at which cracks tend to nucleate, are dispersed by cyclic strain. Special features of the glide band structure produced by cyclic strain and revealed by dislocation etch pits, support this view. Strain hardened MgO has mechanical properties greatly superior to the as-received material: yield stress, greater than 100,000 psi; elongation to fracture about 1 pct. A material is said to strain harden if the yield stress increases with an increment of plastic strain. This definition is usually applied for straining done in one direction, but is also applicable when the strain direction is periodically reversed, Fig. 1. For certain metal single crystals, data are available which permit a comparison of the hardening behavior for cyclic straining and for tension straining.&apos;-4 With certain qualifications, these data show that the same processes of hardening are operative in each type of test.5 Despite this fact, the importance of the technique is not immediately evident, although tension-compression studies of the common metals appear to suggest some deficiencies in theories of strain hardening developed exclusively on the basis of tensile tests. However, a recent observation suggests that the cyclic straining method may be very useful for studying semibrittle crystals in which large plastic strains are not accessible in unidirectional testing. The observation is that zinc crystals, when strained in tension-compression at -52°C, do not fail by cleavage at low stress (-500 psi)6 as they do in tension, but harden to a limiting stress of more than 5000 psi over a total plastic strain of about 600 pct.2 An important characteristic of the behavior of zinc crystals is the high stress, relative to the yield stress, attainable by strain hardening. By comparison, the hardening of aluminum single crystals tested by an identical technique saturates at 1100 psi. This difference is best explained by the cross-slip hypothesis of dynamic recovery.7,8 In zinc, cross slip is difficult because of the high yield stress for glide on planes other than the basal plane in the < 1120 > zone. The present work was undertaken in order to test whether these methods and ideas are applicable to other materials. Magnesium oxide single crystals, in common with most crystals of the rock-salt structure, deform plastically but fail by cleavage after a small strain when tested in tension. It was hoped that larger strains would be attained using tension-compression. There is, in addition, evidence 8a which shows that slip on the probable cross system, (001) < 110>, is difficult in magnesium oxide; it may therefore be possible to attain high stresses by strain hardening. 1) EXPERIMENTAL PROCEDURE Experimental methods used in this study were based in part on techniques reported in papers of Stokes, Johnston, and Li.&apos; MgO blocks, purchased from Norton Co., were used without further annealing. Specimens were cleaved to dimensions approximately 0.125 in. sq and 1 in. in length. The gage section, formed by chemical polishing, was sprinkled with 280 mesh silicon carbide particles in order to introduce fresh dislocations. The crystals were then cemented into cylindrical aluminum adapters and clamped in an Instron testing machine. One of two alternating straining programs was used. In the first, total cross-head travel was established and increased in steps after various numbers of cycles. In the second, a capacitance gage was used to directly measure the elongation of the specimen and the crosshead was controlled so as to keep the plastic strain amplitude constant. The straining was always symmetrical with respect to the initial, zero strain condition. While both procedures produce strain hardening, only the latter permits a measure of the total plastic strain so that hardening curves may be drawn. Constant plastic strain amplitude tests were done

Jan 1, 1963

By R. D. Nelson, J. C. Shyne

The ß and a ß transformations in plutonium were studied with particular emphasis on the transformation kinetics and microstructure. Significant observations are: 1) The kinetic data show conclusively that the ß — a transformation in high-purity plutonium can proceed isothermally with no athermal component. 2) Plastic deformation of the stable (3 phase retards the subsequent (3 — a transformation. 3) Plastic deformation of the stable a phase accelerates the a — ß transformation; the acceleration is attributed only to residual stresses. 4) The a and a?a volume changes occur anisotroPically in textured plutonium. 5) An apparent crystallogvaphic relationship exists between the parent and the product phases of the and (3 — a transformations. 6) Both applied uniaxial compressive stresses and uniaxial tensile stresses raise the starting temperature for the ß — a transformation. 7) A given uniaxial tensile stress favors the a — ß transformation more than an equivalent applied uniaxial compressive stress opposes the transformation. These observations of the (ß —a and a — ß phase changes in plutonium are consistent with known mar-tensitic transformations. ThIS paper elucidates some of the characteristics of the a— ß and ß —a transformations in plutonium. Because considerable conjecture exists about the mechanisms by which the phase transformations occur in plutonium, experiments have been performed to provide indirect information concerning the mechanisms responsible for the a —ß and ß -a transformations. Indirect information is of particular value in the study of plutonium because of the experimental difficulties presented by the metal. Single crystals have not been produced in any of the allotropes. The large density results in high X-ray and electron-absorption factors and consequently complicating X-ray and electron diffraction. The kinetics of ß — a and a — ß transformations of plutonium and the behavior of the transformations under a variety of conditions have been investigated in detail. Information about the mechanisms of the allo-tropic transformations of plutonium was obtained indirectly from three sources: 1) the effect of plastic deformation of the stable parent phase upon the transformation kinetics; 2) the behavior of the metal transforming under applied stresses; and 3) the microstruc-tural and crystallographic features between parent and product phases. PHASE-TRANSFORMATION CHARACTERISTICS In characterizing solid-state phase transformations in metals and alloys, it is useful to define several types of transformations. An aim of the present work was to identify the low-temperature transformations in plutonium by type, i.e., as martensitic or nonmar-tensitic. Practical definitions for these terms follow. The terms commonly used to categorize phase transformations lack universally accepted definitions. This confusion arises doubtlessly because some terms specify crystallographic or morphological character while other words have a kinetic or a thermodynamic connotation. For example, martensitic specifies certain definite crystallographic restrictions. Unfortunately, martensitic is sometimes used in an ill-defined way to imply kinetic characteristics. Further confusion attends the use of such expressions as nucleation and growth, diffusional, and massive. From time to time new systems of phase-transformation nomenclature are suggested; unfortunately none of these has gained general acceptance.1,2 The authors of the present paper have no intention of entering the controversy. We recognize that some readers may object to the nomencliture used here. For exampie, the terms military and civilian have recently been used in much the same way as martensitic and non-martensitic are used in this paper. This paper is intended to describe several specific details of the low-temperature phase transformations in plutonium. The authors have found it useful to identify these transformations as martensitic; the term was chosen as the best available to describe the experimentally observed features of the transformations studied. A martensitic transformation is one that occurs by the cooperative movement of many atoms; the rearrangement of atoms from parent to product crystal structure occurs by the passage of a mobile semico-herent growth interface. The geometric features characteristic of a martensitic transformation are a specific orientation relationship between the product and parent phase lattices, a specific habit-plane orientation for the growth interface, and a shape change with a specifically oriented shear component. There is no alloy partition between the parent and product phases in a martensitic transformation. Martensitic transformations may display either athermal kinetic behavior or thermally activated isothermal kinetic behavior. Some martensitic transformations occur isothermally, although more commonly martensitic transformations are athermal. Isothermal martensitic transformations are suppressible by rapid cooling. In athermal martensitic transformations, nucleation and growth are not thermally activated and the transformations are essentially time-independent. Nucleation, growth, or both can be thermally activated in isothermal martensitic reactions. Transformation of the parent phase into a marten-

Jan 1, 1967

THE following letter from the Rector of Louvain University, addressed to Mr. Adams and the other delegates of the Founder Societies, will be of interest to members of the Institute. It is my duty, in the name of the University of Louvain and in my own personal name, to thank you and the representatives of the Founder Societies of the "United Engineering Society" for the very kind letter of congratulations which you sent to me from Brussels on the 5th of July.

Jan 1, 1928

By F. W. Jessen, G. F. Sears

Cavities in massive salt for the purpose of storage of liquid hydrocarbons have assumed a prominent position in recent years. This paper describes a program to facilitate leaching operations for the formation of specifically shaped storage cavities. Various forms and sizes of cavities may be possible through use of the techniques developed. INTRODUCTION The creation of large under ground storage facilities for natural gas and liquified petroleum gases has been practiced for many years. Use of cavities obtained through solution of salt for this purpose is a fairly new and novel approach, but has gained increasing importance due mainly to the economics of this type of mining operation opposed to hard rock mining or surface and pit storage.1 The idea of controlling the shape of any cavity dissolved from massive salt has not been a prime consideration of companies engaged in the formation of storage space. This has been due mainly to an insufficient knowledge of the mechanics of the leaching process and a dearth of published information dealing with both the desirability and ease of control possible for this type of operation. Two distinct advantages are readily ascertainable. From a stability standpoint (i.e., the ability of the completed cavity to withstand stress imposed by overburden pressure and lateral tectonic stresses) a controlled cavity may be generated which will yield the most favorable attitude to these external forces and remain in operable use for longer periods of time.2 A second advantage is that for a given volume, a sphere (which is one controlIed shape possible) represents the minimum surface area exposed. This may become more important in the future when dealing with refrigeration and product losses in underground cavities. The basic solution mining process, without regard for controlling the final shape, is quite simple in that the equipment and materials required to dissolve a cavity in a salt dome or layered salt section are a source of fresh water, a circulating pump, several strings of tubing and a means of disposal of the return brine. To add control measures involves the use of an inert blanket material above the position at which solution proceeds. Initially the annulus of the largest wash pipe is filled with this blanket down to the top of the proposed cavity. The bottom of the proposed cavity is determined by the depth of the original drilled hole or a blanking plug. The blanket material is added incrementally in stages and displaces the water in the enlarging cavity downward. Where the blanket material has displaced the water, no further solution takes place. The rate at which to add this controlling blanket material so as to be able to form specifically shaped cavities of any particular size is of considerable importance. THE PROBLEM It is desirable to have as much information as possible as to the behavior of the mining operation since visual observation obviously is impossible. It would be advantageous, for example, to have a step-by-step program showing how much salt is to be removed, at what rate and the time required. This type of program would facilitate procurement of surface equipment and provide for proper management of manpower requirements, as well as yield a host of intangible benefits. As mentioned earlier, only rule-of-thumb estimates were available until recently and made this type of pre-planned operation haphazardous at best. Recent work3-&apos; has done much to clear up the ambiguities and inaccuracies attendant to solution mining of salt and has helped to place the operation on a more scientific basis. This study attempts to correlate much of the information thus far developed into a complete mining program; to extend the idea of controlled solution mining to include not only spheres, but solid conic sections of the ellipsoidal variety; and to refine the computation of the rate of removal of salt during the various stages of mining. Dommers3 and IIemson4 made extensive laboratory

Jan 1, 1967

By R. L. Schmidt, J. D. Verhoeven

The diffusion coefficients and electrotralzsport mobilities of aluminum, gallium, and arsenic have been determined in molten germanium with the capillary reservoir technique. The diffusion coefficients are slightly higher than those determined by the solidification technique of Brirton et a1.1 It was found that aluminium and gallium migrate to the cathode in molten germanium) whereas arsenic migrates to the anode under an electric field. A possible technique for producing p-n junctions by means of electric field freezing is discussed in view of the experimental data. In the past decade or so the literature has abounded with articles concerning the solid-state properties of the semiconducting elements germanium and silicon. It is surprising by comparison how little has been published concerning the liquid-state properties of these materials. In the production of doped germanium or silicon the diffusion coefficient of the dopant in liquid germanium or silicon is an important quantity. Yet, to the best of our knowledge, no one has ever made a direct measurement of the diffusion coefficient of solutes in either molten germanium or silicon. A number of authors&apos;-4 have determined some diffusion coefficients by the indirect technique developed by Burton et al.1 This technique appears to give numbers of the correct order of magnitude but it does depend upon a number of assumptions in the analysis and also requires prior knowledge of the viscosity of the melt. In the present work a more direct measure of the diffusion coefficients of arsenic, gallium: and aluminum in molten germanium has been made. It has been shown independently by two groups of authors5, 6 that, when an electric current is passed through the interface of a solidifying metal containing an impurity, the resulting electrotransport in the liquid boundary layer at the interface offers a mechanism for control over the redistribution of the impurity accompanying the solidification. These authors show that the degree of control is proportional to the mobility, U of the impurity atoms in the liquid boundary layer, where the mobility is defined as the drift velocity relative to the solvent per unit electric field. In principle the results apply to the solidification of a doped semiconductor and offer an interesting technique for control of the doping of a semiconductor. In the present work the mobilities of aluminum, gallium, and arsenic were determined in molten germanium in order to evaluate the potential usefulness of electro-transport as a technique for solute control when applied to the solidification of doped germanium. EXPERIMENTAL PROCEDURE Both the diffusion coefficients and the mobilities were measured using high-purity alumina capillaries and a resistivity technique for analysis. A schematic diagram of the electrotransport apparatus is shown in Fig. 1 and the details of the cell design are shown in Fig. 2. For the mobility experiments electrical contact with the bottom of the capillary was made with graphite, as shown in Fig. 2. In order to prevent electrical contact with the melt the graphite was coated with a thin layer of alumina using a plasma spray torch. The cell assembly, a graphite electrode, and another assembly containing two blank capillaries were fastened to the lavite disk shown in Fig. 1. To make a run the system was evacuated and the doped germanium was outgassed at the operating temperature of 1030°C. The cell and blank capillaries were then submerged beneath the melt and a slightly positive pressure of helium was introduced to fill them. After passing current through the cell for a given time the cell and blank capillaries were raised from the melt and the furnace was shut off. The temperature of the cells dropped below the freezing point of germanium within 1 to 2 min after the furnace was shut off.

Jan 1, 1968

By D. T. Goettge, E. L. Robinson

The phase changes occurring in low carbon steel during hot strip mill rolling are shown to be metallurgically significant when related to commonly used temperature control points, particularly finishing and coiling temperatures. In combination, these temperatures are shown to have an important influence on the level and uniformity of hardness, grain size, and carbide characteristics of the finished hot and cold rolled sheets. PRODUCTION of wide flat-rolled products ordinarily requires a number of operations in sequence to prepare the material for shipment to the customer. Most products are tailor-made for specific end uses, with each operation contributing certain properties to the finished material. Since the characteristics imparted to the semifinished product by a given step in processing carry through to the finished product in varying degrees, it is important that the intermediate stages of production of flat-rolled strip be carried out with the same care which characterizes the last or finishing operations. The step of hot strip mill rolling is common to the production of all of the various types of flat-rolled product; therefore, the hot strip rolling is an especially important point at which to recognize and control those variables which have an effect on the surface characteristics and metallurgical properties of the finished product and which influence the ease of conducting subsequent operations. Orders entered at a producing mill usually show an end use or describe an article or part into which the ordered product is to be fabricated. Applying his experience as to the properties necessary in a finished sheet to suit the end use and to perform successfully in the fabrication involved, the metallurgist selects a steel of suitable composition and deoxidation practice, and slabs of appropriate dimensions are produced for rolling on the hot strip mill. At this stage of processing, the metallurgist faces the problem of controlling hot strip mill practice in the light of his diagnosis of the properties necessary to meet the end use, paying due attention to the accompanying problem of producing a strip which can meet processing requirements on subsequent units in the mill. It is the purpose of this paper to describe some of the factors which he must consider in solving these problems and to indicate some of the principles which guide him. Equipment, Physical Requirements of the Strip, and Temperature Measurement The metallurgist must, of course, be familiar with the physical layout of the mill, the temperature-measuring equipment available, and the physical requirements of the hot strip product before he can apply his metallurgical knowledge to the problem; hence, the first section will consist of a brief discussion of these matters. The usual hot strip mill consists of reheating furnaces, five or six roughing stands including a scale-breaker, holding table, and second scalebreaker, six-stand finishing mill, runout table with spray cooling facilities, and coilers. A schematic diagram of a typical layout is shown in Fig. 1. Slab temperatures are primarily a function of heating time and furnace temperatures, while mill speeds, spray practice, drafting practice, available water pressure, temperature of the cooling water, cross sectional dimensions of the strip, coil size, and equipment limitations, either singly or in combination, determine what rolling temperatures are practical on a given hot strip mill unit. Thus, it is possible that a set of temperatures which can be utilized successfully on one mill cannot be used on another. However, adjustments in temperatures and rolling practice can usually be made to develop the desired metallurgical properties. In addition to the metallurgical properties developed through proper temperature control, the hot strip mill must also provide strip with certain physical attributes which may be summarized as follows: Strip Cross Section—The strip contour should conform to a section which will give the best results in the cold reduction operation. This is generally recognized as a strip with 0.001 to 0.003 in. crown or shoulder-to-shoulder convexity depending on width, and freedom from concave, flat, or wedge-shaped cross sections which cause metal buildup in cold reduction. Excessive drop off in thickness at the edges can also be very detrimental in cold reducing to light gages. Gage, Width, and Camber—All of these must be controlled. For example, rundown or increasing thickness from the front to the back of the coil results in nonuniformity in the thickness of hot-rolled sheet product and in added difficulty with gage and welds in cold reduction. Similarly, excessive width variation is the cause of guide trouble and excessive edge scrap at later stages of processing, while excessive camber is the source of a variety of processing troubles. Type of Oxide—Product intended for pickling should have a predominance of the type of oxide most easily removable in sulfuric acid. It is generally recognized that this type is obtained by use of maximum table cooling water and cold coiling

Jan 1, 1957

By AIME AIME

THIS year&apos;s Chairman of the Institute of Metals Division is a relatively rare phenomenon in the metallurgical profession; he is an expert historian of metallurgy, he is a confirmed collector and student of old works on alchemy, chemistry, and metallurgy-vide: the famous Biringuccio and he is a profound student (with a somewhat idealistic slant) of recent trends in world affairs and in what some incurable optimists call civilization; and at the same time he is still possessed of a sense of humor. Incidentally he is also one of the bestknown nonferrous metallurgists in this country and abroad, and for fifteen years has been a willing worker in A.I.M.E and the Institute of Metals Division.

Jan 1, 1943

By S. G. Cupschalk, F. A. Dahlman, J. J. Wert

Studies have been undertaken to determine the indicidual effects of particle size, degree of long-range ovder, antiphase domain size, and root mean square stran on the microhardness and yield strength of ordered alloys. Dnta have been analyzed for Cu3Pt initzally ordered to a value of 0.82 and after deformations of 1 and 6 pct. It was observed that deformation fleatly reduced the degree of long-range order. Furtherrnore, wztkin this range of relatively small deforntntlons, the average particle size changed very little while the antiphase domain size was greatly reduced. Smultaneosly, the mcrohardness changed by a factor of two durzng the deforrtation process. PREVIOUS studies have reported some of the effects of cold work on the broadening of X-ray diffraction peaks. These investigations were performed on powder and wire samples representing both ordered and disordered states; i.e., the specimens were initially studied in a severly cold-worked condition. By comparing the difference in line shape between the annealed and cold-worked peaks, fundamental information was obtained concerning particle size, strain distribution in different crystallographic directions, degree of long-range order, and change in antiphase domain size. Considerable theoretical work has been done concerning the analysis of diffraction data obtained from cold-worked metals. Stokes&apos; expressed the change in diffraction profiles in terms of Fourier coefficients. Much of the work in this area has been summarized by warren2 in an extensive review article concerning the analysis of plastic deformation by X-ray diffraction. Cohen and Bever3 applied these techniques in studying the effects of cold work on alloy systems exhibiting long-range order. They utilized the Fourier coefficients of fundamental peaks in conjunction with those of the superlattice peaks to determine the change in antiphase domain size. Little work of this nature has been reported for ordered systems that have undergone small degrees of plastic deformation. The purpose of this investiga-tion was to determine the effects of small deformations in such a material with respect to particle size, strain distribution in various crystallographic directions, antiphase domain size, degree of long-range order, and hardness. EXPERIMENTAL PROCEDURE CusPt was used for the initial investigation since the order-disorder transformation takes place with- out a change in crystal structure. The transformation is readily detectable via X-ray diffraction techniques due to the large difference in the scattering factors of copper and platinum. Additionally, the alloy is relatively low melting (approximately 1300°C) and is easily deformable in both the ordered and disordered states. 1) Specimen Preparation and Cold Working. A 100-g, 12-in. diam., cylindrical specimen of Cu3Pt was prepared by melting and casting 99.99 pct pure Cu and Pt i.n vacuo. Prior to any mechanical working, the material was homogenized in a vacuum for 60 hr at 100O0C, and surface defects were removed by machining to a depth of approximately 116 of an in. The material was then cold-rolled, with an intermediate anneal, into a strip approximately 12 in. wide by 14 in. thick. Straightening and flattening removed another 0.025 in. from the thickness. After a recrystallization treatment at 750°C for 30 min, the specimen was slow-cooled from 55OoC, at the rate of 6°C per hr, down to 150°C to induce superlattice formation. This treatment yielded an ASTM grain size of 7 and a degree of long-range order equal to 0.83 0.06. After obtaining X-ray and Knoop hardness data, the sample was cold-rolled approximately 0.75 pct in one pass through a hand-operated jewelers&apos; mill. X-ray and hardness data were again obtained and the specimen was reduced an additional 5.41 pct in a single pass through the mill. 2) X-Ray Measurements. The specimen was examined in the ordered condition and after the two degrees of cold working previously mentioned using a General Electric XRD-5 unit equipped with a spectrometer and scintillation counter. Using Mo-Ka radiation with a zirconium filter, six orders of the 100 reflection were obtained. It was anticipated that point counting would be necessary for an accurate determination of the low-intensity peaks and tails: however, it was demonstrated that, by using a scanning speed of 0.2 deg per min and the appropriate time constant, the recorded data were sufficiently accurate. Thus, for ease of experimental procedure, all peaks were recorded on chart paper. Specimen position in the holder was considered to be insignificant after making a series of measurements of the same peak area in different positions with respect to the beam. Since peak overlapping did occur at high values of 20, it was necessary to separate the peaks graphically prior to analyzing the data in order to minimize this source of error. The peak tails were also carefully drawn to obtain the best possible data. Fourier coefficients of the line profiles were calculated on an IBM 7072 computer, and graphical meth-ods2j3 were employed in analyzing the results. For this type of calculation, in which the line profile is represented by intensities taken at set intervals, the intervals selected must be sufficiently small to give an accurate representation of the line profile. It was decided that for 20 = 0.02 deg the line profiles were

Jan 1, 1967

By W. Shockley

THIS lecture can best begin with a statement of the chief conclusion: The metallurgical industry will find profit in supporting fundamental research on dislocations. This support should be done both in their own laboratories and in universities. My lecture consists of an exposition of the basis for this conclusion. The experience on which I base it is drawn largely from two fields in solid state physics—one field is transistor electronics and the other is dislocation theory. At present the relationship of solid state physics to technology is different in these two fields. In electronics without question, the physics has led the technology. In metallurgy, on the other hand, the technology in the form of metallurgical art is far ahead of the fundamental science. In transistor electronics, physics has suggested and can still suggest previously unachieved combinations of matter that will have new and useful properties; that is, the physicist can make specific predictions. The physicist can also have some confidence that the predicted devices will actually come into existence in a matter of months or years and that they will live up to the predictions. In metallurgy, the physicist cannot to a comparable degree make predictions and have the same hope that they will lead to something new and valuable. There are a number of reasons for this difference. The first is simply historical. Transistor physics is young. It may be regarded as dating from the announcement of the transistor, in which case it is about four years old, or from the first real control of semiconductors as materials (this was accomplished largely by metallurgists, by the way) in which case it is about ten years old. Metallurgical art, on the other hand, is thousands of years old. There is no doubt that the advance of this art has been and will be hastened by a good fundamental understanding of the quantum theory of atomic phenomena. It, is too much to expect, however, that theory will soon catch up with the lead that practice has gained in a thousand years, and that theory will then point out specific pathways to better materials. It seems more probable that modern atomic theory will serve to interpret and organize information much as thermodynamics has done through phase diagrams. In this lecture, I shall emphasize an important feature common to both solid state electronics and to metallurgy. This common feature is the harmonizing principle that justifies discussing electronics and metallurgy as related topics in solid state physics. In both cases the important properties of the materials arise from imperfections. By imper- fections I mean deviations of the materials from perfect single crystals. The imperfections may be of many forms. From the point of view of utility they may be either good or bad, and a given type may be good or bad depending on circumstances. The technical material of my lecture will be divided into two parts. The first will be chiefly concerned with four types of imperfections in germanium crystals. The control of these imperfections makes possible the fabrication of useful electronic devices. A good example of such control is the junction transistor, which I shall discuss from this viewpoint later. The junction transistor, as some of you may have heard, can be used as an amplifier of electrical signals and in a number of respects surpasses what has hitherto been achieved with vacuum tubes. The second part of my technical material will be concerned with dislocations. For about fifteen years the theoretical physicist has had dislocations in mind as the most important kind of imperfection in metals. He has, however, until recently had experimental material of a highly speculative nature to back up his assertions. I am fortunate in the timing of this lecture to be able to describe some recent results that put dislocations on a far more definite basis than has been the case in the past. In fact there are now some experiments which reveal the characteristic properties of dislocations almost as clearly as experiments in transistor physics reveal the properties of holes and electrons, properties that I shall soon describe. It is this advance in the status of dislocations that emboldened me to make my initial assertion that the metallurgical industry will profit from supporting fundamental research on dislocations. Transistor Electronics In order to discuss imperfections in semiconductors, it is necessary to visualize a reference condition that may be regarded as perfect. In the cases of silicon and germanium, which find application in transistor electronics,&apos; the perfect structure is the diamond structure shown in Fig. I. In this structure, each atom is surrounded by four neighbors with which it forms four covalent or electron-pair bonds. These bonds use all of the four valence electrons possessed by each of the silicon or germanium atoms. The electronic structure of the crystal is thus complete and perfect. A crystal of silicon or germanium with a perfect electron-pair bond structure would be an insulator, In order for electrical conduction to occur, it is necessary for imperfections to arise in the electronic structure. In this lecture, I shall discuss four possible imperfections whose symbols and relationships are indicated in Table I. We shall consider first, as an example, a crystal of silicon containing an arsenic atom as an impurity.

Jan 1, 1953

By C. A. Stickels, C. M. Yen

Secondary recrystallization was investigated in vacuum-melted electrolytic iron to which 70 pm N was vacuum-meltedadded. The secondary texture is "near {554}<225>" for material cold-rolled 75 to 90 pct, the sharpness of the texture increasing with increased rolling reduction and with decreased annealing temperature. At reductions of 95 and 97.5 pct the secondary texture is &apos;"near {322)(296)". Both secondary orientations also exist as major components of the primary re-crystallization texture. Development of a strong "near {554) (225)" secondary texture appears to depend on the evolution of the Primary texture to a transition texture depleted in orientations near the secondary orientation before the onset of secondary growth. A variety of qualitative experinzents have been used to show that nitrogen is important in limiling primary grain growth. The presence of nitrogen does not seem essential for the establishment of a transition texture, but a loss of nitrogen during annealing may facilitate growth of grains in the secondary orientation. Secondary grains we shown to form initially at the specimen surface. This is not thought to indicate that surface energies are important in the growth process. It is proposed that the quasi-two-dimensional character of surface grains permits discontinuous growth parallel to the surface before secondary growth of interior grains is possible. An earlier study of recrystallization textures in 90 pct cold-rolled electrolytic iron showed that secondary recrystallization occurred after annealing for several days at 700C1 This type of secondary recrystallization, which had not been reported previously, results in the formation of a strong texture, best described by the indices "near {554}(225)". The purpose of the present work was to investigate the effect of various processing variables on secondary recrystallization in this material and determine the mechanism of secondary grain growth. LITERATURE REVIEW An understanding of the mechanism of a secondary recrystallization process depends on knowing: 1) how grains in the secondary orientation come to be in the primary recrystallization texture; 2) why normal grain growth does not occur; and 3) what factors determine the strength of the secondary texture. For secondary growth of grains of a particular orientation, a certain minimum fraction of the grains must be in that orientation after primary recrystallization. This requirement is apparently satisfied "naturally" in certain systems, i.e., when the primary texture obtained by rolling and recrystallizing material initially randomly oriented contains a sufficient fraction of primaries in the secondary orientation. However, in other cases, e.g., {110}<001> and {100}<001> secondary growth in silicon iron,2 it is necessary to enhance the fraction of primary grains in the secondary orientation by rolling and recrystallizing textured material. In the present case, the "near {554}<225>" orientation is contained within the spread of orientations found in the primary recrystallization texture of iron or bbc iron-base alloys. In systems where the main driving force for secondary growth is the reduction in total grain boundary energy, secondary growth is observed only when normal grain growth is minimized. Four ways in which normal grain growth can be limited are: 1) Limitation by a strong primary texture. When a very strong primary texture consisting of a single component or twin-related components develop, most primary grains are separated from one another by relatively immobile small-angle grain boundaries. The classic instance of this is secondary growth into the primary cube texture in some fcc metals. 2) Limitation by precipitates. Precipitates present in the proper volume fraction with a suitable dispersion will limit primary grain growth. The role of MnS inclusions in impeding normal grain growth in Si-Fe is well-documented.5 3) Limitation by sheet thickness. Normal grain growth slows drastically when the mean grain diameter is of the same order as the sheet thickness. This effect has been used to obtain secondary recrystallization in thin sheets of high-purity silicon iron.&apos; 4) Limitation by solute impurities. It is well-established that certain impurity elements in solution can have a large effect on grain boundary mobility.&apos; However, there does not seem to be any secondary recrystallization process in which primary grain size stabilization has been shown to be due to the drag exerted on grain boundaries by dissolved impurities. In certain systems, e.g., secondary recrystallization in silver,&apos; the means by which normal grain growth is limited has not been identified, and solute-impurity limitation might be suspected. In order to understand the factors which determine secondary texture strength in three-dimensional growth, it is necessary to examine in more detail the current picture of general secondary recrystallization processes. Following Cahn,9 it is assumed that the primary grains have a range of sizes and that secondary growth of one of the large grains in this distribution is possible when it exceeds a critical size with respect to its neighboring grains. The critical size depends on the ratio ?S/?p, where ?s is some sort of average grain boundary energy between the potential secondary and the primary grains and ?p is some sort of average grain boundary energy between primary grains. For a constant primary grain size, the critical size for secondary growth increases as ?$/?p increases. May and Turnbull5 have incorporated the

Jan 1, 1969

By J. D. Verhoeven

The effectiue distriblltion coefficient has been Measured in a series of vertical, normal freezing experirtzents with large current densities passing through the solid-liquid interface. The results indicate that the effect of the current on solute redistribution is due to electvotransport in the liquid. The high currents produced extensive mixing in the liquid which was considerably reduced by solidifying in small lubing. Analysis of the convection indicates that it probably vesulls from a horizontal temperature gradient produced by the Joule heating- of the electvic crirver~t. Due to the strong dependence of this convection upon the specimen radius, it is conclnded that only for specit~ens with radii of less than somewhere between 1 and 2 mm wilt electric field freezing be getlerally effec-tire at enhancing the purification of zone-melting experittierats in loe-melting alloys. Experiments on 0.8-mm lubes illustrate some interesting potential applications of this techniqne as a means of solute control on smcrll specimens. In a number of papers published within the last few years&apos;-4 it has been found that passage of large dc currents through the solid-liquid interface of a freezing alloy produces a change in the solute redistribution accompanying the solidification. It had been predicted theoretically by Hucke et al.s and by Pfann and Wagner that such an effect would occur as the result of electrotransport within the liquid boundary layer at the solid-liquid interface. These authors independently derived the following relation between the effective distribution coefficient and the variables of the process: Where k0 is the equilibrium distribution coefficient, V is the mobility of the solute relative to the solvent, E is the electric field intensity, D is the solute diffusion coefficient, R is the rate of interface motion, and 6 is the boundary layer thickness. Both groups of authors show that this equation predicts the possibility of extending the purification ability of zone-melting experiments by the addition of an electric current. However, there are other effects in addition to electro-transport which could be produced by the high dc current and might, perhaps, invalidate the applicability of Eq. [I]. For example, high electric current might affect the interface reaction or perhaps the equilibrium distribution which was assumed to exist at the interface. It was the purpose of this work to determine the applicability of Eq. [I] by systematically investigating a simple system for which all of the necessary parameters were known. It was of particular interest for speculating on the potential usefulness of this technique to determine the maximum practical field intensities obtainable, and the effect of these high fields upon convective mixing in the liquid. The initial work in this study was published in a previous paper3 which will be referred to as I. In that work, a current density of 2000 amps per sq cm was used with specimen diameters of 5 mm. The results gave a qualitative confirmation of Eq. [I.], and also showed that a large amount of convective mixing was produced in the liquid by the current. The present study is an extension of that work to smaller specimen diameters and higher current densities. Two points were overlooked in I and will be emphasized here: a) the value of ko has not been well-established in the Sn-Bi system and b) the observed convection could be due to thermal convection produced from the Joule heating. EVALUATION OF k0 To evaluate Eq. [ I.] it is necessary to know the value of the equilibrium distribution coefficient, k,. Tn I the value of k, was taken as 0.3 from a published phase diagram.7 According to ansen&apos; the best data on the phase boundaries of the Sn-Bi system are those of Davidson.5 The data of Davidson give a k, value ranging from 0.21 to 0.25 for the compositions studied in this work, or an average value of around 0.23. In a recent publication, Rigaud and Tougas&apos;10 determined ko by means of a solidification technique. For an alloy of approximately the same composition as that used in this work they obtained a ko value of 0.39. Hence, there is considerable uncertainty in the value of ko and, consequently, a series of experiments were made to determine k, more accurately.

Jan 1, 1968

By R. J. Fruehan

The oxygen activity and concentration were measured in Fe-Cr-0 melts in equilibrium with an oxide phase at 1600°C (2912°F). The activity was determined by ,use of the following solid oxide -electrolyte galvanic cell CY-Cr8,(s) I ZrOz(CaO) I Fe-CY-G(saturated)(l) The oxygen concentration decreases with increasing Cr concentration to about 270 ppm 0 at about 7pct CY and then increases gradually. The activity coefficient of oxygen (fo) decreases with increasing Cr. In melts containing up to about 20 pct Cr, log f is approximately a linear function of wt pct Cr with a slope (e q 2) of —0.037. The activity of chromium was calculated and found to exhibit a small negative deviation from Raoult&apos;s law. From the activity and solubility data for low chromium melts, the free energy of formation of chromite, FeCr204, was found to be -79.8kcal per mole where pure liquid chromium and oxygen at I wt pct in Fe are the standard states. ThE effect of chromium on the chemical behavior of dissolved oxygen in liquid iron is of great importance in controlling the deoxidation of steels containing a significant amount of chromium. Chen and chipman&apos; equilibrated Fe-Cr melts in the presence and absence of slag with hydrogen-water vapor mixtures. They concluded that at 1595°C chromite was the oxide phase in equilibrium with Fe-Cr alloys containing less than 5.5 pct Cr while at higher chromium concentration Cr,O, was the stable phase. In the composition range 0 to 10 pct Cr they found that the interaction coefficient, was equal to -0.041. Turk-dogan,&apos; Schenck and Steinmetz,, and pargeter4 measured egr) in a similar manner and found the value to be -0.064,-0.04, and -0.052, respectively. McLean and Be11 evaluated egr) from their data on the equilibrium of Fe-Cr-Al-0 alloys with H2/H20 mixtures and found it to be -0.058. However, McLean and Bell&apos;s value should only be considered an estimate because the effect of aluminum on the activity coefficient of oxygen is about a hundred times greater than that of chromium. Consequently, an error in the value of egl) used, which at the present time is not well-known, or an error in aluminum analysis, which is present in very small quantities, will result in a significant error in egr). Fischer et a1.6 determined the interaction coefficient (eEr) in Fe-Cr-0 melts not in equilibrium with an oxide phase and containing less than 18 wt pct Cr at 1600°C electrochemically. They determined a value of -0.031 for egr). Hilty et aL7 measured the oxygen content of Fe-Cr melts in equilibrium with an oxide phase containing up to 50 pct Cr. They found that the solubility of oxygen decreased as the chromium content increased to about 6 pct Cr and then increased gradually. They concluded that the equilibrium oxide phase was chromite below 3 pct Cr, distorted spinel from 3 to 9 pct Cr, and Cr,04 above 9 pct Cr. Adachi and lwamotoa also investigated this system, but did not find Cr30,. They X-rayed the equilibrium oxide phases and did not find the presence of Cr,O,. They also X-rayed the oxide phase extracted from a 65 pct Cr melt which was heat treated and did not find metallic chromium as would be expected if Cr3O4 were the equilibrium oxide phase as indicated by the reaction : 3Cr3O4 — 4Cr2O:, + Cr [lj It was the purpose of the present investigation to determine the effect of chromium on the activity coefficient of oxygen in Fe-Cr melts by measuring the activity and solubility of oxygen equilibrated with an oxide phase in the composition range 0.18 to 50.5 wt pct Cr at 1600°C (2912°F). The activity of oxygen in the melts was determined by use of the following galvanic cell: The relationship between the partial pressure of oxygen in equilibrium with the melt and the reversible electromotive force of the cell (E) is where 11 = 4, F is the Faraday constant, pb, is the oxygen pressure in equilibrium with the meit and is the oxygen pressure in equilibrium with Cr203 as determined from the free energy data compiled by Elliott et al? The oxide phase in equilibrium with pure chromium was assumed to be Cr If Cr30, were the equilibrium phase the activities derived would be approximately the same, since the best estimated free energy of formation of Cr,O,, if it does exist, is approximately % the free energy of formation of The activity of chromium in Fe-Cr alloys at 1600° C was also determined from the measured electromotive force. The activity of chromium (aCr) is related to the electromotive force as follows: , The oxide phase in equilibrium with pure chromium and Fe-Cr melts from 10 to 52 pct is assumed to be Cr203 so that n equals three. If future work proves the existence of Crs04 in equilibrium with Fe-Cr melts and pure chromium, the experimental results can be reevaluated using a value of $ for n in Eq. 141. A value of ^ for n will make the activities about 10 pct higher. In order for Eqs. 131 and [4J to be valid the electrolyte, ZrOa(CaO), must exhibit predominantly ionic conduction at the temperature and oxygen partial pressure of its use. Previous work1&apos; has demonstrated that ZrOz(Ca0) is predonlinantly an ionic conductor

Jan 1, 1970

By E. Heaton Hemingway

DURING the past year, the Watertown Arsenal has been interested in the occluded gas and oxide content of certain ordnance steels in order to determine, if possible, whether some of the peculiar failures in their physical properties might not be traced to these causes. For the purpose of best accomplishing a study of this nature, it was decided to heat the various samples of steel in a vacuum for definite periods of time at high temperatures and carefully examine the quantity and composition of the gases evolved. By the use of a fused quartz tube fitted with a water-cooled, ground-glass stopper, it was possible to maintain a vacuum at a temperature of 1000° C. for 10 hr. without perceptible leakage being evidenced as measured by a McLeod gage. The silica tube was connected with an evacuating system so constructed that the volatilized gases could be removed from time to time and a low vacuum of 0.002 to 0.0010 mm. of mercury continuously maintained. At no time during the period of heating or in the removal of the gases did the evacuated system come in contact with rubber stoppers or any rubber connections, making contamination from such a source impossible. In other words, the only volatile products that could be obtained must necessarily have come from the steel itself or from the glass and fused quartz system or from the mercury used as a sealing agent. In the earlier experiments, the steel treated was in the form of turnings, but this practice was discarded because the weights of the turnings before and after being heated were widely inconsistent, even when taken from the same piece of steel. This discrepancy developed largely through variation in the amount of metal volatilized with the gases; this metal could always be seen in the form of a ring where it condensed in the cooler portion of the tube either in the amorphous or crystalline condition. Because of the frequency in occurrence and the variation in the manner of deposition, this material was roughly analyzed and found to consist for the most part of iron. At the same time two samples of steel that had been

Jan 8, 1920

By R. L. Ash, R. R. Rollins, C. J. Konya

An investigation was performed to determine conditions for optimizing the spacing of simultaneously initiated multiple explosive columns. This was done by using models of mortar, dolomite, and Plexiglas with 10-grain mild detonating fuse as the explosive charge. It was desired to simulate blastholes with multiple primers initiated by detonating fuse or when high-velocity explosives are used in low-velocity materials. It was found that optimum spacing between multiple charges was strongly influenced by charge length. At less than optimum charge length, the spacing at which complete shearing was possible between adjacent charges decreased exponentially with a subsequent loss of broken material volume. For charges fired simultaneously, larger burdens and spacings were possible as compared to those necessary for single-crater charges. For each material studied, there was a characteristic optimum charge length and a maximum attainable spacing at any given burden. Proper selection of the spacing distance between charges is fundamental to successful blasting. Its value directly affects the cost of drilling and explosives used per unit of broken material. In addition, the choice of a spacing that is Compatible with a given set of blasting conditions aids in the control of fragmentation sizing, ground vibrations, overbreak, and throw which in turn, influence other production costs. For example, normally loaded blastholes that are spaced too closely invariably promote overbreak and usually give coarse fragmentation. Unless care is taken, airblast and violent flyrock will occur and under certain conditions cutoffs and misfires may result. Too large a spacing, on the other hand, frequently leads to conditions that form bootlegs or toes. The choice of a particular spacicg to use, however, is largely a matter of individual experience and judgment, usually based on trial and error. Very little is known or can be found in the literature with regard to how the spacing between charges is related to field conditions and charge geometry. As a general rule, the firing time sequence of adjacent charges and properties of a material are thought to have the most significant influence on the spacing distance best suited for any given field condition. For example, delayed initiation of adjacent charges usually always requires a closer spacing than when charges are fired at the same time. This should be expected if one considers that the energy normally dissipated and lost in the surrounding ground from charges fired independently would be captured and utilized for breaking material between charges when they are initiated together. Spacing can be extended also when charges are aligned with structural planes of a material, such as jointing, along which shearing is relatively easy. It is customary to relate the spacing (S) between charges to their common burden (B) in the form of a spacing ratio, or SIB. The burden normally is considered as the optimum depth or distance from any single charge perpendicular to the nearest free or open face at which the desired fragmentation and maximum crater yield are obtained. For production blasting, value of the ratio is generally considered to vary from 1 to 2, depending on conditions.1-6 When adjacent charges are fired independent of one another, the value varies from 1 to about 1.4, the closer amount being employed to square corners or produce craters having the ideal 90" apex angle. The larger ratio is the geometric balance value for craters having an apex angle of 135". The basic ideal crater forms in the plane of the charge diameter for charges fired independently are shown in Fig. 1. In the event charges are fired simultaneously, geometric balance in the plane of their charge diameters suggests that a spacing ratio near 2 would be appropriate, as illustrated by Fig. 2. In practice, however, some compromise ratio value must be selected to conform with the specific ground conditions. An example would be where the jointing planes tend to produce 60° or 120° crater angles, the appropriate geometrically balanced charge arrangement being given by Fig. 3. In this condition, the spacing ratio is 1.15, not 1 or 1.4 as suggested for the 90° cratering of independently fired adjacent charges. In view of the foregoing, it would seem logical to assume that whenever charges all having the same burden are fired at the same time, spacing distances always can be greater than those permitted by charges fired independently. In practice this is not the case, however.

Jan 1, 1970

By William Y. Holland, Roger H. Cook

Dexter H. Reynolds (Chapman and Wood, Mining Engineers and Consulting Geologists, Albuquerque, N. M.)—A number of questions are raised by conclusions and inferences made in the above-mentioned paper. The more troublesome of these concern use of the various pozzolans to combat the deleterious effects of the alkali-aggregate reaction. The most alkali-reactive materials listed are opal and rocks containing opaline silica. The pozzolans mentioned specifically for use as amelioratives are opaline shales and cherts. These are stated to retard the expansion caused by the alkali-aggregate reaction. Another well-recognized pozzolan is diatomaceous earth, which consists principally of opaline silica. A pozzolan presumably owes its effectiveness to its high reactivity with the alkaline liquid phase of the concrete mix. It appears reasonable to expect that finely divided opaline silica added as a pozzolan would be more susceptible to reaction with the alkalies present than would larger particles of the same material. The authors report that work with high and low alkali cements indicates that in the presence of alkali-reactive materials, deleterious expansion depends upon the alkali content of the cement. The total effect, therefore, should be more or less independent of the amount of reactive aggregate present, and still more independent of its state of subdivision. The deleterious effects should, if anything, be aggravated by the addition of a finely divided, highly reactive pozzolan. Further, if the alkali-aggregate reaction is of great importance in the long-term soundness of concrete structures, the addition of a pozzolan to a concrete made with aggregate free from known deleterious materials would be a questionable procedure. The benefits reportedly accruing from such use of pozzolans are greater ultimate strength for a given cement content, increased resistance to deterioration by exposure to sulphate solutions and other mineral waters, and greater resistance to damage by wetting and drying and freezing and thawing. In view of the deleterious effects of highly reactive materials are these benefits ephemeral? The same considerations apply to another alkali-reactive material, chalcedony, which appears to consist of ultrafine-grained quartz, with opal absent in detectable amounts. Quartz flour is notably reactive chemically and physiologically (cf. Ref. 11 of Holland and Cook&apos;s paper), a fact borne out by its effectiveness as a pozzolan, which presumably might be expected to offset the deleterious effects of the presence of chalcedony in the aggregate. A second question of some importance concerns the reportedly highly deleterious reactivity of acidic and intermediate volcanic glasses, such as rhyolite, perlite, and pumice. Air entrainment is listed as one of the ameliorative measures to combat the deleterious effects of the alkali-aggregate reaction. The alkalic-silica gel formed by the reaction may expand into air bubbles and thus not cause appreciable expansion of the concrete mass. It would appear then that pumice and perlite, particularly perlites of the pumiceous types and other types after expansion, would also tend to counteract the expansion, since these materials consist largely of voids and air bubbles. Certainly this would be expected of structural concrete in which pumice or perlite is used as total aggregate. Finely ground pumice, perlite, and volcanic ash have been demonstrated to be active pozzolans (cf. Pumice as Aggregate for Lightweight Structural Concrete by Wagner, Gay, and Reynolds, Univ. of New Mexico Publications in Engineering No. 5, Albuquerque, 1950). In fact, the term pozzolan was first associated with finely divided pumice or volcanic ash. Such materials were used with hydrated lime as the sole cementitious agent in constructing public buildings, roads, and aqueducts by the ancient Romans. The deleterious alkali reactivity of the volcanic glass, itself containing several percent of the alkalies, apparently did not contribute to the remarkable state of preservation of those ancient structures, as exemplified by the Appian Way and the Pantheon Dome. Still a third question involves .the reactivity of constituents of concrete when exposed to various salt solutions. Resistance to. deleterious expansion and cracking as a result of contact with mineral waters and its relationship to the mineral content of the aggregate are not mentioned by the authors. Yet the phenomena pictured in Fig. 1, and especially in Fig. 2, appear very much like those caused by exposure to mineral waters. The deterioration of concretes exposed to sulphate waters is generally considered related to the chemical constituency of the cement itself, particularly to the relative amount of tricalcium alum-inate contained. Could not many of the ill effects presently blamed on alkali-aggregate reaction really have been caused by contact with sulphate or other salt-containing mineral waters? Or perhaps their use as mixing waters? May not the deleterious expansion be as much a function of the chemical makeup of the cement as it is of the mineral constituency of the aggregate? Would it not be just as important to use alkali-free mixing water as it is to use a low-alkali cement? It appears obvious that resistance of cements and concretes to sulphate and other salt solutions cannot be left out of account in discussion of deterioration of concrete structures with time. This factor may be of equal or even greater importance than the alkali-aggregate reaction, particularly for concrete subjected to wetting and drying cycles, such as airstrip paving, water-retaining dams, and highway structures. Another very important factor is called to attention on page 1022 of the article in Mining Engineering, October 1953, in that failure of concrete structures may result from poor construction practices and use of too high water-cement ratios. Both of these can contribute remarkably to decreased resistance to attack by sulphate waters, and presumably could have an equally remarkable effect upon extent of damage resulting from the alkali-aggregate reaction. From the above remarks it appears that while alkali-aggregate reaction may be an important factor in decreasing the useful. life of a concrete structure, it is not the only factor involved, and it may not be even a controlling factor. Likewise, many of the phenomena apparently associated with the alkali-aggregate reaction may have resulted from cond&apos;itions which had little relationship to the alkali-reactivity of a constituent of the aggregate. Certainly if alkali-aggregate reactivity is a major factor in bringing about early failure, one cannot help feeling anxiety concerning the future of the many concrete structures in this country and abroad in which pumice and perlite were used as total or partial aggregates. This anxiety can only be dispelled by calling to mind that among the best-preserved relics coming down to us from ancient times are structures made with mortars containing highly alkali-reactive aggregates.

Jan 1, 1955

By T. K. Perkins, R. N. Hoffman, O. C. Johnston

A simplified theory of viscous fingering in miscible systems has been developed. It predicts the correct functional relationship between pertinent variables and permits the calculation of the order of magnitude of fingering behavior for simple systems, such as linear or radial. The theory is based on the following four observations: (1) cross-flow takes place only near the ends of fingers; (2) the relative finger width is about 0.5; (3) fingers can be suppressed by transverse dispersion, the suppression being quantitatively described by a critical ratio of dispersion times; and (4) the widths of extending fingers are close to the minimum size finger that can grow at any stage of displacement. Fingering is studied in two-dimensional linear and diverging radial systems, both theoretically and experimentally. For linear systems, the length of the fingered region is proportional to mean displacement; the finger width is proportional to square root of mean displacement; and there is a small initial region void of fingers because of suppression by longitudinal dispersion. For the radial system, two limiting conditions are recognized. If the mean displacement is small compared with the wellbore radius, the length of the fingered region is proportional to the mean displacement. The width is proportional to the square root of mean displacement. If the mean displacement is large compared with wellbore radius, length of the fingered region is proportional to mean displacement, but the number of fingers approaches a constant value. Also, in the radial case there is a small initial region void of fingers because of longitudinal dispersion. INTRODUCTION The behavior of viscous fingers in miscible systems has been of interest to the oil industry for many years. Previous studies have clearly shown the existence and nature of fingers in small models.1,2,3,4 Engineering techniques for extrapolating to reservoir situations have been proposed. 5,6 Still, because of the lack of a real understanding of the mechanics of fingering, there remains uncertainty and disagreement as to the best way to scale or calculate fingering behavior in the reservoir. In this paper we discuss a study of the mechanics of fingering in miscible systems (i.e., why do fingers behave as they do?). A simplified theory is developed which we believe will (1) predict the correct functional relationship between pertinent variables, (2) permit us to calculate the order of magnitude of fingering behavior for simple systems such as linear and radial, and (3) give further insight into the problem of scaling or otherwise extending the results to more complicated reservoir conditions. The paper includes the following sections: (1) brief summary of the mixing behavior of miscible fluids in linear and radial systems; (2) four fundamental observations of fluid flow (under fingering conditions); (3) based on these four observations, a simplified theory of fingering in linear and radial systems is developed; and (4) the theoretical equations are compared with experimental fingering data measured in laboratory models. A REVIEW OF DIFFUSION AND DISPERSION As will be shown later, the behavior of viscous fingers in miscible systems is controlled in large degree by the mixing between the two fluids. A quantitative description of fingers will first require a quantitative description of mixing. Fortunately, much work has been done to clarify this subject; a fairly comprehensive review has been presented in a previous paper. 7 For present purposes let us (1) briefly summarize the quantitative description of diffusion and dispersion (both longitudinal and transverse) within a differential element; (2) present a simplification of the "width of mixed zone"; and (3) describe the effect of geometry on width of mixed zone. If one fluid is displaced from a porous medium by another miscible fluid (in the absence of fingers)

Jan 1, 1966

By R. H. Richman, F. Borik

A 0.3 pct C-12 pct Cr-6 pct Ni steel was rolled to 93 pct reduclion in area as austenite at 510°C, and then partially transformed as desired to ~rlartensite by qnenching to - 196°C. Pole figures for the austenitic matrix and for the martensitic product were separately determined by an X-ray transmission method. The deforitration texture of&apos; the warm-worked austenite is characlerized by (110)(225) components, and is thus closely similar to those produced in a brasses. The pole jigure of the martensite in partially transformed material agrees well with that which can be constructed by transfortnation of the {110)(225) orientations according to either the Kuvdjuniov- Sacks or the Nishi-yatuu relatiotship. Howeuer, an important result of this construction is that me-third of the predicted orientations are missing. A graphical analysis can then be used to show that in deformed austenite certain crystallographic variants of martensite (related to the most probable austenite slip systems) are suppressed, resulting in this preferred transformation. The evidence for preferred transformation is corroborated by the measured elastic anisotropy of warm-rolled and fully transformed H-11 steel. EXTENSIVE plastic deformation of a polycrystal-line aggregate in a manner that causes flow predominantly in one direction results in a preferred orientation of the constituent crystallites. The particular orientations that are produced depend upon the crystal structure and composition of the material, as well as upon the temperature, mode, and degree of deformation; in any case, the preferred crystallo-graphic orientations, or textures, are reflected in directionality of mechanical properties. Although such anisotropy may be exploited in certain specialized applications, it is more commonly diminished or eliminated by heat treatment lest it interfere undesirably in subsequent forming operations or in structural design. In the recently developed thermomechanical treatments that significantly enhance the strength of some steels,1,2 considerable deformation of the metastable austenite prior to the martensite transformation is essential to the strengthening process. If the austenite is textured by the deformation, and if the transformation to martensite proceeds according to one of the relationships established for transformation in annealed austenite, then it must be expected that the martensite will also possess a preferred orientation even though the multiplicity of martensite orientations possible in a given austen- ite crystal will tend to restore some degree of randomness. The existence of a residual anisotropy, both mechanical 3-6 and crystallographic,&apos; has been substantiated. In the latter crystallographic investigation, preferred orientations were determined for the martensitic structure of an SAE 4340 steel rolled 72 pct as austenite at 833°C and then quenched. However, the choice of a composition that transformed almost completely to martensite during the quench to room temperature did not permit direct measurement of the prior austenitic texture. In fact, when the "ideal orientations&apos;&apos; associated with well-known fcc rolling textures were converted, alone or in combination, to martensite according to the Kur-djumov-Sachs (K-s)&apos; or Nishiyama8 relations, the agreement obtained with the observed martensite texture was only fair at best. Recently a pertinent aspect of the austenite to martensite transformation was reported by Bokros and parker,10 who found that certain habit-plane variants of martensite were suppressed by tensile deformation of Fe-31.7 Ni single crystals prior to the necessary subzero cooling. It might be anticipated that the consequences of such preferred transformation are sustained during the formation of martensite in warm-worked austenite that has a well-developed deformation texture. The present investigation was undertaken first to establish more firmly the relation between preferred orientations in plastically deformed austenite and in the resulting martensite, and second to examine the textures for evidence of deformation-induced preferred transformation. EXPERIMENTAL PROCEDURES An alloy containing 0.3 pct C, 12 pct Cr, 6 pct Ni, and the balance iron, was selected because the mar-tensite-start temperature (M,) of about -100°C allowed convenient experimental manipulation of either austenite or martensite at room temperature. Furthermore, this composition can be readily deformed as metastable austenite at moderately elevated temperatures without intervention of appreciable isothermal or athermal decomposition products. The alloy was austenitized at 1150°C, aircooled to 510°C, rolled unidirectionally at this temperature to 93 pct reduction of cross-sectional area, and finally oil-quenched to room temperature. Partial transformation to martensite was accomplished by quenching to -196°C as needed. The rolled stock was reduced in thickness from 0.067 to 0.010 in. by etching in a solution of 5 pct HC1, 45 pct HNO3, and 50 pct water, and further thinned by careful mechanical polishing to maintain the two sides of the sheet parallel within 0.0003 in. After mechanical polishing to 0.005 in., electropolishing in 1:9 perchloric-acetic acid solution produced a final thickness of 0.002 in. The preferred orientations were determined from

Jan 1, 1968

By G. W. P. Rengstorff

In an effort to find an oxidation-resistant alloy of molybdenum, binary and ternary alloys containing aluminum, chromium, cobalt, iron, nickel, silicon, titanium, tungsten, vanadium, and zirconium were screened. Fourteen other alloying additions were also tested. Many of the alloys were more oxidation-resistant than molybdenum, but none were entirely satisfactory. MOLYBDENUM oxidizes extremely rapidly above 1450°F in air. At 1800°F, a loss of metal at the rate of 0.1 in. in 4 hr is typical. The high speed of this oxidation may be judged by comparison with the oxidation rate of 0.1 in. per year (0.00005 in. in 4 hr), sometimes taken as the maximum permissible oxidation rate at 1800°F for a satisfactory Fe-Cr-Ni alloy. Great strides have been made in the development of coatings and cladding to protect molybdenum from oxidizing atmospheres. These developments in surface protection will undoubtedly make it possible to take advantage of the excellent hot strength of molybdellum and its alloys in many new applications. Still, even the best coating can protect molybdenum only as long as the surface layer is unbroken. Research was undertaken to determine whether an alloy of molybdenum could be found which would resist oxidation. Such an alloy would not deteriorate suddenly when the protective surface layer was destroyed in a small area. In seeking an alloy of molybdenum to resist oxidation, the physical properties of molybdenum could not be sacrificed entirely. The development of an alloy with the desired resistance to oxidation was not achieved. The information obtained on the effect of a large number of elements on the oxidation of molybdenum is, however, of value in the development of coatings. Indeed, many of the alloys tested for oxidation resistance were already known to have poor mechanical properties but were tested to aid in the development of coatings. Oxidation of Molybdenum The rapid oxidation of molybdenum is usually attributed to the volatility of Moo,,. Gulbransen and Wysong have shown that molybdenum oxidizes very slowly up to 850°F, the temperature at which the oxide film begins to evaporate. Melting as well as evaporation of molybdenum oxides promotes the oxidation of molybdenum. MoO melts at 1465°F. MOO, the oxide which is believed to form at the metal-oxide interface, combines with MoO, to form a eutectic having a melting point of 1432°F.&apos; The liquid oxide, even if nonvolatile, could cause poor resistance to oxidation by allowing easy transport of molybdenum and oxygen ions through the oxide. Actually, a sudden increase in the rate of oxidation of molybdenum at 1460°F has been observed to coincide with the appearance of a liquid phase. The formation of a volatile oxide is not unique with molybdenum. The problem is also encountered with vanadium, tungsten, and some of the Pt-Pd group of metals. Vanadium not only forms the volatile V2O3 but, like molybdenum, forms a liquid oxide coating. Few attempts have been made, however, to prevent the rapid oxidation of these metals by alloying. Oxidation of Molybdenum Alloys At the beginning of this work, very little was known of the oxidation resistance of molybdenum alloys. It was known that molybdenum disilicide (with 37 pct Si) has extremely good oxidation resistance,&apos; but this compound is so brittle that it has few uses. It is an effective protective coating for molybdenum when allowance can be made for its brittleness. Chromium was known to retard the oxidation of molybdenum,&apos; but at least 50 pct Cr was necessary to have an appreciable effect. Other, unpublished, reports show that a few other alloys have been given preliminary tests, but the results have not been promising." Choice of Alloys to be Investigated An alloying element might be expected to protect molybdenum in either of two ways: Its oxide might combine with molybdenum oxide to form a stable, nonvolatile complex oxide (a molybdate); or the oxide of the alloying element might form in preference to molybdenum oxide, developing an impervious layer which would prevent the formation of a volatile molybdenum oxide. The knowledge available about the formation of molybdates was meager. Therefore, the initial study was made on alloys of molybdenum with elements having especially stable oxides. On this basis, binary and ternary alloys containing the following six elements were investigated: aluminum, chromium, titanium, zirconium, silicon, and vanadium. Nickel was also added as an alloying element. Although it does not form a more stable oxide than molybdenum, it does impart some oxidation resistance to copper and iron. Its inclusion in the study was fortunate because its alloys proved to be the most promising of those first tested. Apparently nickel formed a stable molybdate. Because nickel was effective in reducing the oxidation rate of molybdenum, the elements iron, cobalt, and tungsten were added to the list. The ten alloying elements mentioned form ten binary and 45 ternary alloying systems with molybdenum. A series of alloys was tested in each of these systems. In addition, at least one test was made on the effect of each of the following alloying elements:

Jan 1, 1957

By J. D. Livingston, H. E. Cline

Cu-Pb alloys in the vicinity of the monotectic composition have been directionally solidified under a high temperature gradient at rates up to 2 X l0-&apos; cm per sec. Over a wide range of compositions, high growth rates yield a composite structure consisting of continuous rods of lead in a copper matrix. This range of compositions increases with increasing growth rate, in agreement with arguments based on the relative velocities of composite growth and the growth of copper dendrites or lead drops. The breakdown of the composite structure at slow growth rates is explained in terms of the relative interphase surface energies. The observed interrod spacings of the composite structure are large compared with the predictions of the Jackson-Hunt equations of eutectic growth. ThE directional solidification of many eutectic alloys produces fine composite structures of parallel lamellae or rods. There has been considerable interest not only in the fundamentals of this two-phase solidification process,&apos;-3 but also in the interesting physical properties produced by such regular and aniso-tropic microstructures. Composite structures can be grown only over a limited range of composition, beyond which coarse primary dendrites of one phase appear. In organic eutec-tics, this composition range of composite structures has been shown to increase with increasing growth rate.7"10 These results were explained in terms of the relative velocities of composite (coupled) growth and dendritic growth. Although similar arguments should apply to metallic eutectics,11-13 suitable experimental results are lacking. In contrast to the work on eutectics, the directional solidification of monotectic alloys has received little attention. (The monotectic reaction is similar to the eutectic reaction, except that one of the resulting phases is a liquid, which subsequently solidifies in a separate reaction at a lower temperature.) Directional solidification of some monotectic alloys&apos;4715 yields regular rodlike microstructures, whereas in other cases macroscopic separation of solid and liquid phases occurs.16 chadwick17 rationalized these results in terms of the probable relative magnitudes of the various interphase surface energies. A recent study of chill-cast Cu-Pb alloys18 revealed a fine rodlike microstructure in alloys near the monotectic composition. It was decided to investigate the directional solidification of such alloys, and to determine the range of composition and growth conditions yielding composite structures. The Cu-Pb system is convenient for such a study, both because it is simple metallurgically, with no compound formation and negligible solid solubilities, and because its basic properties are well-documented. Recent literature on the Cu-Pb system includes studies of bulk thermo-dynamic properties,&apos;g surface energies,20"21 densi-ties,25 and diffusion constants.a6 A similar study of the directional solidification of Cu-Pb alloys was recently undertaken, independently, by Kamio and Oya." EXPERIMENTAL Alloys were prepared by melting 99.999 pct Cu and 99.999 pct Pb in a graphite crucible, stirring well, and pouring into a cold graphite mold. Rods 0.175 in. in diam were machined from the ingots. Alloy compositions studied ranged from 25 to 55 wt pct Pb. Samples were placed in graphite crucibles 5 in. long with 4 in. OD and 0.035-in. walls. They were melted under flowing argon in a vertical, two-zone. platinum -wound furnace. A voltage stabilizer was used to minimize fluctuations in input power. The narrow specimen diameter minimized convection. Directional solidification was achieved by driving the crucible downward into a +-in. hole in a water-cooled copper toroid. The toroid was located immediately below the narrow end zone of the furnace. The end zone was separately powered to maintain high local temperature. Therefore a high temperature gradient (approximately 300 deg per cm) was maintained in the specimen throughout the run. The crucible motion was screw-driven. and a wide range of drive speeds were available. The limited rate of heat removal caused a thermal lag in the specimens at high drive rates. However. temperature-time curves from thermocouples imbedded in a representative sample indicated that the average growth rate still approximately equaled the drive rate. Although the specimens were initially homogeneous, melting and re solidification redistributed the lead. producing composition variations of several percent along the specimen length. (During melting. lead melted first and ran down the sample surface. Rapid freezing tended to reproduce the resulting composition gr~dient, but slow freezing did not because a slow-moving interface tended to reject lead. as discussed later.) To determine local composition. ;-g samples were cut from regions exhibiting various microstructures and were chemically analyzed for lead content. Micrographs were taken on as-polished or lightly etched surfaces. Three-dimensional structure of the lead network was viewed with a scanning electron microscope after removal of some of the copper matrix with nitric acid. RESULTS Several different microstructures are observed, depending on composition and drive rate. Because melting and resolidification produced composition gradients, results are best presented in t&ms of final local composition, rather than initial or average composition. The ranges of local compositions and drive

Jan 1, 1970

By John E. Conley, John A. Ruppert

W. B. Mather—A minor recommendation that may be offered to improve the paper is the inclusion of a map of Oregon showing the general location of the various deposits. This is of especial importance to persons like myself who are not familiar with the various areas and counties mentioned. N. S. Wagner and R. S. Mason (authors&apos; reply)—We agree that an index map of Oregon showing the location of the various nonmetallic deposits would add to the paper (fig. 1).

Jan 1, 1951