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By K. C. Hong, R. B. Jensen

The problem of determining the optimum set of steam volumes and cycle lengths for a single well undergoing multicycle steam stimulation in order to maximize the cumulative discounted net income has been formulated mathematically and programmed for a digital computer. The mathematical fonnulation of the problem and the method for its solution are discussed in this paper. The oil production performance during each stimulation cycle was simulated by either a constant percentage or a harmonic decline. Using simple analytical expressions for production performance, the cumulative discounted net income and cumulative time of operation were related to the pertinent process and cost parameters and two principal process control variables (cycle length and steam injection volume). The discrete maximum principles was used to transform the equations for cumulative time of operation and cumulative discounted net income into a set of simultaneous equations. The simultaneous equations then were solved by trial and error on a digital computer to determine the set of cycle lengths and stem injection volumes that gives maximum cumulative discounted net income over the project life. INTRODUCTION Steam stimulation is a process for improving the oil recovery rate from wells producing high-viscosity crudes. The process is applied on an individual well basis and is executed in a series of cycles, each consisting of three phases: steam injection, soaking (steam condensation), and production. Significant increases in production rate following the stimulation operation result from heating the reservoir around the wellbore. As heat is removed with produced fluids and dissipated into nonproductive formations, the production rate declines, usually to near the prestimulation value. Typical production responses are given in case histories reported by Owens and Suter,l and are depicted in Fig. 1. Duration of the production phase is equal to the time for the oil production rate to decline to some specified value and is called the cycle length. (Cycle length is defined as the producing portion of the cycle and does not include the downtime required for steam injection and soaking operations.) Termination of the production phase coincides with the start of steaming for the next cycle. The process is continued, cycle by cycle, until it becomes unprofitable. Models 2-4 have been developed to simulate behavior of a single well during one cycle of steam stimulation and have been used to investigate the effects of system and operating conditions on the production responses. However, these investigations have not shown how the models can be used to determine a most profitable set of operating conditions for a multicycle stimulation project. Perhaps these models are too complicated mathematically to be adapted readily to an optimization study. This paper presents a method for optimizing a multicycle steam stimulation project based on simple production performance models. First, the performance of a steam-stimulated well during each cycle was simulated by either a constant percentage or a harmonic decline model. Using these simple analytical expressions for production performance, the cumulative discounted net income (before tax) and cumulative time of operation for each cycle were related to the pertinent process and cost parameters and two process control variables—the cycle length and the steam injection volume. Finally, the profit function to be maximized was formed. The analogy between the above problem and problems of optimizing multistage decision processes that have been reported extensively in the chemical engineering literatures5-10 in recent years has led this investigation to the use of the discrete maximum principle.5-7 This principle was used to transform the equations for cumulative discounted net income and cumulative time of operation into a set of simultaneous equations characterizing the optimum operating conditions in terms of the two control variables. These equations

Jan 1, 1970

Jan 1, 1918

By Arthur F. Taggart

The major portion of the work described in this paper was performed by R. W. Young, † a graduate student in the department of Mining and Metallurgy, Sheffield Scientific School, Yale University, working under a cooperative agreement between the Hardinge Conical Mill Co., the Sheffield Scientific School, and himself. Since this cooperative scheme is at present in effect in the case of a considerable number of other students in the department and since it is the hope of the school that the privilege thus extended may be utilized even more freely in the future by mining and manufacturing companies, it may not be amiss at this point to give a summary of the general plan. Briefly it is as follows: A graduate student, whose undergraduate work in this or other universities shows promise of ability to handle research work, is chosen by conference between the company and instructor involved. The aim of the company in the agreement then entered into is to obtain the solution of one or more of the technical problems with which it may be confronted, or, at the end of 1 or 2 years, to obtain as an employee a man especially trained in its work. As a means to accomplish one or both of these ends, the company furnishes the machine, apparatus, or material to be tested and pays the student during his graduate work a small salary, usually just sufficient to cover his living expenses, tuition and fees. The aim of the student is special training along a line in which he is particularly interested, the attainment of his advanced degree, and the chance to show to his future employer ability to handle such problems as may be presented to him. In return for the financial aid which he receives he agrees to devote at least half of his working time to the special problem submitted by his company. The other half is devoted to study of the collateral subjects required by the department for the granting of the degree which the student seeks. The student further agrees to enter the employ of the company in question at a wage not greater than that paid in like positions to recent graduates not specially trained and to remain with his employer at such wage for at east 1 year. If the student is to obtain a degree, the special work forming the basis of his investigation must be such as will involve real research and not mere routine manipulation. The subject is chosen by conference between the three parties to the agreement. The work is carried on under the direct supervision of the instructor involved. The school furnishes the general laboratory and library equipment essential to the pursuit of any extended investigation. In

Jan 1, 1918

By C. W. Wahsburne

Former studies of sedimentatry strata have been based upon the mineralogical and mechanical characters of the solid components, rather than upon the open spaces between them.

Jan 1, 1915

By Kenneth K. Humphreys

INTRODUCTION What is automation? Why automate? Webster's New Collegiate Dictionary defines automation as "the automatically controlled operation of an apparatus, process or system by mechanical or electronic devices that take the place of human organs of observation, effort, and decision." This definition gives an implied answer to the second question, )"Why automate?" Automation, automatic control devices and process control equipment receive their justification in supplementing or replacing manpower, which results in decreased operating costs. In the past, processes were operated with a minimum of instruments for the purpose of merely guiding the operators. Processes were manually controlled by the operator on the basis of simple temperature, pressure, flow and level indications on a panel. Today the tendency is to design a new plant to operate in a fully automatic manner according to a preset pro- gram utilizing a minimum of manpower. In addition to this direct cost reduction savings in manual labor, increased equipment capacity results from uniformity of flow and uniform control of process variables. This control eliminates or minimizes surges and permits equipment to be operated at or near its ultimate capacity and, for a given material through- put, permits the use of smaller process equipment. Automatic control, therefore, be it in the field of coal processing or in any industrial field, is simply a problem of economics. Control equipment is justified in terms of its contribution toward increasing productivity, increasing profit margins or producing a new and saleable product at a profit. Instruments and control devices can be divided into two general groups: (1) units which measure, and (2) units which both measure and control a process variable. In coal processing, the first class of instruments, those which measure only, include analytical devices such as automatic ash, moisture and sulfur measuring units and the simple pressure, temperature, flow and level indicating devices mentioned previously. The second group of instruments, those which both measure and control, include a wide variety of units such as continuous weighing devices on conveyor belts and photoelectric cells which gauge the position of railroad cars on the track and insure that the cars are in the proper location for loading (see Chapter 15). The latter types of units as used in the coal industry differ from those used in other industries in one significant point. In coal processing these instruments need not be as highly sophisticated and accurate as in other industries; hence their cost is proportionately lower than in other industries. Because of the economic fact that coal sells for only a fraction of a cent per pound compared to dollars per pound for many chemical products, and

Jan 1, 1968

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

For four years your Committee has been engaged in the study of problems connected with the educational preparation of professional geophysicists. The Present report represents the conclusions drawn from the investigations and deliberations undertaken since it was first organized. These studies have shown that the evolution of geophysics has proceeded along lines that differed from those marking the advance of classical geology. The latter science developed as a descriptive one, dealing with directly observable terrestrial phenomena, and the elementary, rational explanations that could be offered therefor. The fact that these phenomena were also chemical and physical in nature was seldom given more than passing acknowledgment. During the last half century, however, a new approach to problems of terrestrial phenomena has become of greater significance. This new attack has come through the sciences of physics and chemistry, as the people trained therein have investigated the facts of the earth as problems in their respective sciences. This development has been chiefly at the hands of European investigators, and European universities have long recognized it by establishing departments or institutions of geophysics. In the universities of North America, their arbitrary departmentalization into fields of physics, chemistry, astronomy, geology, etc., has prevented the academic recognition of such domains of science as geophysics and geochemistry. In consequence, the development of these subjects in the United States has been largely at the hands of nonacademic institutions, while the universities themselves are evidently in a state of confusion as to how the subject should be handled. In some places an attempt to teach geophysics is made in the physics department, in others in the geology department, in some in the engineering school, and occasionally as a cooperative effort; a Department of Geophysics is seldom found in North America. In some instances, proper academic plan. ning has been precluded by interdepart. mental jealousies, or by lack of appreciation of the significance of the subject. For the background upon which these conclusions are based, the reader is referred to reports previously issued or SPonsored by Your Committee. The "First Report of the A.I.M.E. Mineral Industry Education Division's Committee of Geophysics Education, 1939," summarizes the replies received to question-

Jan 1, 1946

By W. H. Emmons

Although gold is one of the rarer metals, it is widely distributed; it is found on all of the continents and in each of the grand metallogenic provinces of the earth. It is prominent particularly in the shield areas of the earth; these areas have produced a large part of the world's lode gold and in most of them gold lodes are more important than the lodes of other metals. The Scandinavian shield is the only one that has not produced much gold. Nearly all of the world's gold has been derived from lodes and from sands and gravels where gold placers formed by the destruction of lodes. The gold derived from magmatic segregations, from pegmatites and from contact metamorphic deposits is quite subordinate to that derived from auriferous lodes. The lodes include all veins and related deposits that are formed by hot waters that move along fissures or other openings and that deposit vein 'matter :in the fissures and by replacement of the country rocks along the fissures. All of the shield areas of the earth are characterized by large areas of granitic rocks including granitic gneisses, granodiorites and other acid intrusives which here are included in the general term "granite." The granites are intruded into schists, ancient lavas and other rocks which here are designated as the "invaded" rocks. The granites are parts of what once were great batholiths: that is, they are the remaining portions of great deep-seated bodies that slope outward, have very irregular roofs and so far as known have no floors but extend downward to great though unknown depths. Some of them are scores or hundreds of miles across and contain islands or "roof pendants" of the invaded rocks at places where the roofs of the batholiths were low—that is, where erosion has not yet completely unroofed the batholiths. It is in these islands of older rocks and in the narrow marginal belts and cupolas of the batholiths that practically all of the gold lode deposits of the shields are found. Valuable lodes are lacking generally in the granites themselves except in grahite within a mile or less from .the contacts with rocks of the islands (Fig. 1). It is probable that the great areas of granites and gneisses that surround the islands are not all of the same age, and that at places unmapped granite intrudes gneiss or older

Jan 1, 1932

By Howard Scott

Manganese being perhaps the least expensive of the metallic alloying elements that can be advantageously added to iron in considerable quantities, the basic characteristics of its alloys with iron are properly receiving much attention at present. In the course of a dilatometric investigation of this system several years ago, the writer observed certain transformation phenomena not found in other iron-base alloys. The interpretation of those effects was not evident from the information then available, but recent X-ray studies clear up at least one anomaly and permit a more satisfactory description of the results than would have been possible otherwise. Aside from the new phenomena observed, the effect of manganese on the Arg transformation is of timely interest because of its bearing on the critical compositions of austenitic alloys, the applications of which are now being greatly extended. It is known that the properties of these alloys are unstable unless the As transformation occurs at a tem-pcrature considerably below atmospheric and that manganese is very effective in depressing the temperature of this transformation. The writer aims to establish a simple general relation which expresses the location of Ar3, quantitatively in terms of the content of the common alloying elements used in steel. A step in that direction is taken here. Early dilatometric investigations1 indicated that only one transformation other than the eutectoid A1 occurs in the high-iron alloys of the iron-manganese system. Dejean represents the Arg point as falling to 0" C. with a manganese content of 11 per cent and carbon content of between 0.30 and 0.40 per cent. Esser and Oberhoffer," sing alloys low in carbon (under 0.03 per cent), arrived by extrapolation at 14 per cent for the manganese content at which As is depressed to 0" C. Not until both low carbon contents and alloys having a manganese content

Jan 1, 1931

By P. J. Dean

This Paper contains a comprehensive survey of the known electron-hole radiative recombination mechanisms in the family of III-V compounds. Because of space limitations, the luminescence properties of each III- V compound are not reviewed separately and exhaustively. Instead, the different known types of recombination processes are discussed in turn and exemplified with reference to the III- V compound in which they were first recognized, or are best understood. Electron-hole recombinations usually occur predominantly at impurities or lattice defects either introduced de1iberately or inadvertently present, but radiative intrinsic interband electron-hole recombinations, which occur in perfect crystals, have been observed. Recombination processes which involve the participation of impurities or lattice defects ("extrinsic" recombinations) considered include transitions in which a) free carriers recombine with carriers trapped at impurities ("free to bound" transitions) , b) electrons bound at donor impurities recombine with holes trapped at acceptor impurities ("donor-acceptor pair" recombinations), C) excitons bound to charged or neutral donor or acceptor impurities recombine radiatively (both "resonance" and "two-electron" "bound exci-ton" transitions have been observed), d) excitons bound to neutral donor or acceptor impurities recombine non-radiatively (an example of an "Auger" recombination), and e) excitons bound to impurities with the same number of valence electrons as the host atom which they replace ("isoelectronic " traps) recombine radiatively. In addition, Auger recombination processes involving one or more free carriers have been observed. These extrinsic processes all involve impurities which are present as point defects. Some apparently well-authenticated examples of the recombination of excitons bound to complex impurity-lattice defect centers including nearest-neighbor donor-acceptor pairs are also discussed. Identificalions of the transitions involved in stimulated emission from the direct gap III-V compounds are briefly reviewed. Although the examples of these recombination mechanisms are selected from the III-IV compounds ia this review, these processes have quite general relevance in semiconducting crystalline solids; irrdeed most of them have also been identified in the 11- VI compounds and elernental semzconductors. THE development of crystal growth and purification techniques in recent years and concurrent advances in the understanding of physical processes in solids has accelerated the development of a wide variety of solid-state electronic devices of proven utility. These de- vices are generally used for switching or amplifying operations in electrical circuits. Most solid-state circuit elements are very photosensitive. This photo-sensitivity is generally undesirable and the single-crystal chip forming the active portion of the solid-state device is mounted in an opaque container. The photosensitivity is made use of in phototransis-tors and photodiodes, which are among the most sensitive detectors of electromagnetic radiation particularly in the near infrared.' In these devices, light is converted into electrical power. The solid-state lamp utilizes the inverse effect, namely the conversion of electrical power into light. There is an increasing tendency to use single-crystal diodes rather than the earlier electroluminescent cells in which the active material is present as a powder embedded in a suitable dielectric.' The radiation is emitted at a rate far in excess of the thermal equilibrium rate for the frequencies and temperatures involved; i.e., luminescence occurs. The development of practically efficient solid-state lamps is at an early stage compared with solid- state circuit elements or even photodetectors. Considerable progress has been made in recent years, however.3 The present review is devoted to a survey of the radiative recombination processes in the semiconducting compound crystalline solids formed from elements in groups I11 and V in the periodic table. These materials exhibit the full range of known recombination processes in solids. In fact many of these processes were discovered in 111-V semiconductors. Nonradiative recombination processes, which control the lutninescence efficiency, are also discussed. Luminescence is efficiently excited in semiconductors through processes which produce large excess concentrations of free electrons and holes in the energy bands of the crystal. Transitions induced by lattice defects or impurities usually predominate in the recombination process. By contrast, luminescence in the conventional fluorescent lamp is excited by optical absorption at the luminescent impurity center itself (the activator) and/or at a second type of impurity center (the sensitizer). This latter type of photoluminescence process, occurring in doped ionic crystals with wide band gaps, is outside the scope of this review.4 I) ENERGY BAND DESCRIPTION OF ELECTRON STATES IN CRYSTALS The energy band description of the energy states available to an electron in a crystal forms the basis of our understanding of the empirical division of crystalline solids into metals, semiconductors, and insulators in accordance with their electrical and optical properties.' Nonmetallic crystals have a finite energy gap between the highest energy band which is

Jan 1, 1969

By W. A. Jr. Slippy, E. P. Dahlberg, R. B. Reed-Hill

A large room-temperature mechanical-hysteresis effect under cyclic tensile loading was observed in zivconium specimens prestrained at 77°K so as to form large numbers of (1121) twins. The observed hysteresis loss was a maximum when the prestrain was just under 1 pct It also depended strongly on the maximum applied cyclic stress, but only moderately on loading rate and temperature (-72°to 100°C). The phenotnena have also been studied in terms of the elastic aftereffect where the data has been found to cotlforln closely to the functional relationship between strain and time, c = -RT/a In tank ft. t to)/Zr, for strains cts large as about 10-4 This eyication can be derived directly from the strain-rate equation There may be important commercial implications to the present discovery since it appears that within rather wide limits it may be possible to obtain any desired magnitude of damping capacity in zirconium melal. The damping propevties may also be given directional characteristics. It is shown that the observed anelaslic phenomena can he explained on the assumiplion that they are the resuilt of stress-induced twin-boundary movements in which the average twin increases its thickness by only a few percent. In polycrystalline zirconium, a grain is least favorably oriented for slip when its basal plane, containing the (1130) slip directions, lies nearly perpendicular to the principle normal stress. Mechanical twinning is favored by this orientation and under simple tensile deformation at room temperature the primary twinning mode is {1012).' The (1012) twinning shear is small (0.17) so that, during deformation, twin growth does not greatly enhance ductility. At 77°K, on the other hand, the predominant twinning mode shifts to {1121), and many thin (1121) twins can form at small strains.' Twins thus nucleated can grow readily during subsequent room-temperature deformation and permit easy deformation in unfavorably oriented grains. In addition, the (1131) twinning shear is large: 0.63. These facts have lead to a process' for greatly improving the room-temperature ductility of zirconium when it contains a sizable fraction of grains with basal planes nearly normal to the stress axis. Optimum results are obtained by slightly less than 1 pct prestrain. The effect is large so that a 50 pct elongation increase is readily attained. A large room-temperature mechanical-hysteresis effect has also been observed in zirconium specimens prestrained at 77°K. The present paper is concerned with some aspects of this effect which the experimental observations strongly indicate is primarily the result of strain-induced {1121) twin-boundary movements. This clearly suggests that mechanical twins formed by plastic deformation can cause anelastic effects similar to those previously observed2 for annealing twins and twins associated with phase transformations. EXPERIMENTAL PROCEDURES All specimens were prepared from arc-melted sponge zirconium plate stock as previously described,3 which has a preferred orientation with basal planes aligned parallel to and uniformly distributed around the rolling direction. Both lonti-tudinal and transverse tensile specimens, with axes parallel and transverse, respectively, to the plate rolling direction, were cut from this plate. In a longitudinal specimen most grains are favorably oriented for slip, while in a transverse specimen a large fraction are unfavorably oriented. Prestraining at 77°K was performed in two ways. In one, annealed zirconium plate stock was cooled in liquid nitrogen and then rolled in the transverse plate direction to strains varying from 0.5 to 12 pct. Cylindrical 1/8-in.-diameter by 1-1/4-in.-gage-length tensile specimens were machined from this material. In the other, previously machined tensile specimens were prestrained in tension at 77°K between 0.2 and 3.8 pct. Type FA 25-12 SR4 strain gages were cemented to all specimen gage sections. All tests were performed on an Instron testing machine of 10,000-lb capacity. EXPERIMENTAL RESULTS Fig. 1 shows a typical two-cycle room-temperature stress-strain diagram for a specimen prestrained 0.65 pct by rolling at 77°K. The maximum stress in both cycles was 14,500 psi. Note that in the first cycle the loading and unloading curves are unsymmetrical so that a residual strain, er, remains after unloading. In the second cycle the stress-strain curves form a nearly symmetrical hystere-

Jan 1, 1965

By L. D. Jaffe, J. H. Hollomon

The effect of tempering temperature and time upon the properties of quenched steel is clearly a subject of great practical importance, as well as of considerable theoretical interest. It would be very desirable to be able to predict the properties of a quenched steel when given any selected tempering cycle, with a minimum of experimental work upon that heat or even type of steel. Two problems are involved: one consists of relating the structure obtained to the physical properties, and will not be discussed here; the other, with which this paper deals, involves the relations of time, temperature and composition with the structure obtained 011 tempering. Indentation hardness is perhaps the most convenient quantitative measure of the tempered structure, or of what might be called the "degree of tempering." Undoubtedly, it is not an exact measure, and in some cases (as when temper-brittleness occurs) pieces of the same quenched and tempered steel may have widely differing properties at the same hardness. However, hardness has the advantage of being simple to determine and is certainly the most widely used indication of the degree of tempering. Moreover, for fully quenched steels that are not temper-brittle and do not contain retained austenite when quenched, it appears that, in general, if the hardness of the steel is the same, the tensile and impact properties will also be identical, whether a high or a low tempering temperature is used. The tempering charts available in the metallurgical literature usually give the hardness as a function of tempering temperature for only one tempering time. However, in practice, tempering times frequently vary, and a method of converting tempering curves for one time to tempering curves for some other time would be very valuable. It is also advantageous, in determining the tempering treatment necessary for a given part, not to have to temper samples at several temperatures for the time used for the commercial tempering operation. A more satisfactory procedure would be to employ times of the order of 10 to 30 min., rather than 5 or 10 hr., and if possible to use only one temperature. Furthermore, it is frequently desirable, for reasons such as temper-brittleness,* to obtain a given hardness with short times at relatively high temperatures, and it would be convenient to be able to compute without tests the time required to produce this hardness. Remarkably few quantitative studies of the hardness of quenched steel tempered over wide ranges of temperature and time

Jan 1, 1945

By D. Dever, E. S. Fisher

Measurements of the temperature dependence of the elastic moduli in single crystals of hep ruthenium, rhenium, cobalt, dysprosium, and erbium were carried out for various temperature ranges so as to investigate the correlation, suggested by prior work, between the shear anisotropy ratio, A = C44/C66, and the occurrence of the hcp — bee phase transformation. These measurements confirm the suggestion that A has a positive temperature dependence in that group of hcp metals that undergo thermally induced transfornzations to the bee structure and a negative or zero temperature dependence in the other hcp metals. It appears, from indirect evidence, that the hcp -fee transformation in cobalt is preceded by a highly negative temperature dependence of A. These results indicate that elastic anisotropy is an important factor in determining the temperatures at which martensitic phase transformations occur. Two possible roles for elastic anisotropy are proposed: 1) the shear-modulus ratio within the habit planes must be nearly similar for the two phases and 2) a large anisotropy decreases the stress necessary for the movement of the transfornzation dislocations. FUCHS' calculations of the elastic moduli in the alkali metals have shown that the high shear-anisotropy ratios, c/c', in certain bee metals and alloys are the result of large negative contributions to c' = (c11 - c12)/2 arising from the nearest-neighbor repulsive forces.' On this basis, and following Zener,2 the association between high c/c' ratios and the martensitic phase transformations that occur upon cooling certain bee metals is explained as a unique characteristic of the bee structure. Recent measurements of the elastic moduli in hcp titanium and zirconium show, however, that a high elastic anisotropy also exists in these hcp structures at the temperatures at which they transform to bee upon heating3. If there exists a direct and consistent correlation between the elastic anisotropy in close-packed structures and the occurrence of transformations to the bee phases then there is evidently a need to re-examine the conclusions of Zener theory. Elastic anisotropy may also be the result of the effects of temperature on the stability of the low-temperature close-packed structures or it may play an important role in the mech- anism of the martensitic transformations. The present measurements were aimed at establishing the phenomenological correlation between elastic shear anisotropy in hcp structures and the thermally induced hcp —bee transformations that occur in the majority of the twenty-three hcp metals, as shown in Table I. Prior to the present work the temperature dependence of the anisotropy ratio, A = c44/c66, was known at various temperatures for nine of the metals listed. The data showed a negative temperature dependence of A for cadmium, zinc, magnesium, and cobalt, which do not transform to bee, and a positive temperature dependence of A for thallium, zirconium, titanium, hafnium, and yttrium. The correlation was, however, ambiguous in that these two groups of metals are also separated with respect to the c/a ratios as noted in Table I. There remained the possibility that the temperature dependence of A is a function of c/a and not consistently associated with the transformation. The measurements of the elastic moduli in rhenium and ruthenium, in which hcp —bee transformations do not occur, were needed to help decide this question. The studies of dysprosium and erbium were undertaken to determine whether the correlation holds for the heavy rare earth metals.

Jan 1, 1968

MINING, to be precise, ends when the ore is delivered to a bin outside the mine. Usually the next step is concentrating; or, as it is more often called, milling. A few elementary definitions will help make clear the discussion that is to follow. A rock is an aggregate of minerals; copper ore is rock that contains copper-bearing minerals in quantity sufficient to make it profitable to mine and recover the copper in the form of marketable metal. Manifestly, under a literal interpretation, a mass of material might be copper ore one day and merely copper-bearing waste rock a week later, if the price of copper happened to drop in the interim. Emphasis already has been placed on the expansion that took place in the ore reserves of the Porphyry companies as a consequence of the great strides made in the technique of mining and ore treatment. So, even if one inserted a qualifying phrase, "at an average price for the metal," after the word "profitable," the definition would still be open to criticism. Place is another factor. It is evident that a body of excellent ore in Arizona might cease to be ore in the economic sense if it were moved intact to the interior of China. However, it is with ore in its technical and scientific aspect that this chapter is concerned. Speaking in general terms, the ton of Porphyry ore as it arrives at the surface contains 25 to 70 lb. of copper minerals in the form of disseminated particles or thin coats along fracture planes. When subjected to appropriate treatment this ton yields 12 to 40 lb. of metallic copper. These ranges take into account conditions of today and of 25 years ago. Two procedures are available: (1) concentration, followed by smelting of the concentrate, or (2) leaching and precipitation, usually by electrolytic deposition. Smelting and leaching are metallurgic processes in that they involve chemical change; concentration

Jan 1, 1933

By H. l. Burghoff, A. I. Blank

The state of knowledge bearing on the stability of copper under stress at elevated temperatures is generally known to be in need of revision and extension. The present investigation, dealing with the creep characteristics of a deoxidized copper of low residual phosphorus content, is intended to contribute in some small measure toward this end. The experimental data presented herein have been correlated by methods of evaluation and interpretation familiar to those who are concerned with crecp of metals. In practice it is common, if not requisite, to use structurally stable materials at elevated temperatures. It is frequently desirable, however, to test materials under conditions that produce structural change, in order to determine the extent of such change and its effect on physical properties, thus making it possible to establish accurately the limiting conditions to which such materials may be safely exposed. The creep characteristics of the drawn copper wire of this investigation arc directly associated with its structural instability at elevated temperatures. Complete realization of this fact is essential to the evaluation of its creep resistance under various conditions. Creep results should apply to steady deformation under equilibrium conditions, but these are seldom attained in only one or two thousand hours. It will be shown that steady creep rate for copper at useful stresses does not usually begin until considerably more time has elapsed. A wholly satisfactory substitute or shortcut for extensive creep testing does not appear to be evident in the application of mathematical analyses to limited experimental data. Material A single lot of phosphorized copper wire was drawn down to 0.125-i11. diameter with a final reduction of 84 per cent. After mechanical straightening, a portion of this wire was annealed to an average grain size of 0.013 mm. in a controlled-atmosphere furnace. The composition and initial properties of the copper in these two conditions are listed in Table I. Photomicrographs of the original structure are shown in Fig. I.

Jan 1, 1945

By J. T. Michalak, H. W. Paxton

The recovery of the initial flow stress of poly-crystalline iron is characterized by a) a logarithmic time dependence; b) an increasing activation energy with increasing recovery; c) an increased ?,ate and fraction of recovery with decreased temperature of deformation; and d) an increased rate with increased deformation. Isochro)ml studies of the recovery of single crystals revealed more sluggish recovery. The original flou3 stress of single crystals could be regained by recovery anneals at 800"or 900°C. ThE great majority of the theoretical treatments and experimental studies of strain-hardening have been concerned with the close-packed lattices.' Very little effort has been expended on the bcc structure so that the theory of work-hardening of this lattice is essentially nonexistent. The limited amount of experimental data resulting from the direct studies on silicon-iron,2 low-carbon steel,3 and purified irons4"7 does not as yet permit a detailed analysis of the strain-hardening. Studies concerned with the effects of annealing following deformation have been few in number," have been somewhat limited in extent, and have had the disadvantage of using irons containing a substantial impurity content. The present research was undertaken to augment the limited knowledge we have of the characteristics of a bcc metal as regards strain-hardening and recovery from the strain-hardened state. The recovery of the flow stress has been employed since it was felt that the stress associated with the hardened state gives at least a fair qualitative description of the state of the imperfections causing the hardening. The study was concerned primarily with the recovery of flow stress following strain-hardening of polycrys-talline, zone-melted iron as a function of the amount of deformation, the temperature of deformation, and the time and temperature of the recovery anneal. A limited investigation of the recovery of the initial flow stress of single crystals of this same material as a function of the recovery temperature was also conducted in conjunction with the Lambot X-ray technique." MATERIAL The zone-melted iron used in this investigation was obtained through the courtesy of the American Iron and Steel Institute and Battelle Memorial Institute. The analysis, as given by the supplier indicated a maximum impurity content of 0.02 wt pct excluding those impurities listed in Table I. (The actual impurity content is very probably less than this since detection limits were considered as the amount of a particular impurity level.) Also listed in Table I are the interstitial impurity contents of the iron at various stages of experimental work indicating that these im-

Jan 1, 1962

By Raymond L. Orr

Calorimetric measurements have been made of the heats of solution of gold axd indium in a number of liquid tin-rich alloys at a temperature of 705°K. Relative partial molar enthalpies of gold were determined as a function of dilute solute concentrations in the binary Au-Sn system and in the ternary Ag-Au-Sn and Au-In-Sn systems. Relative partial molar enthalpies of indium were determined for dilute solute concentrations in the In-Sn, Ag-In-Sn, and Au-In-Sn systems. Through application of the interaction coefficient concept introduced by Wagner and more recently extended by Lupis and Elliott, ualues have been obtained for the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. The results are inte@reted in terms of solute atom distributions through comparisons with the predictions of dilute solution models. INTEREST in the thermodynamic behavior of dilute liquid alloys stems from two primary sources. From a practical viewpoint, it is often of importance to know or to be able to predict the effect that one solute will have on the thermodynamic properties of the other solutes in a multicomponent system. Studies of dilute solutions may also be rewarding from the theoretical point of view. Some of the difficulties arising from the more complex interactions possible in concentrated solutions are avoided, leading to easier interpretations in terms of solutibn models and bonding energies. For example, in a binary alloy the limiting values of the partial molar properties of the solute represent the case for which each solute atom is completely surrounded by atoms of the solvent, and no other interactions are possible. Solute - solute interactions in dilute solutions are conveniently treated by the interaction coefficient concept of ~agner.' Using a Taylor series expansion for the logarithm of the activity coefficient, In yi, of a component, i, in a solution consisting of dilute solutes with atomic fractions xi, xj, xk, and so forth, in a solvent, s, and neglecting the second- and higher-order terms, Wagner obtained the expression: Where Wheyz is the limiting value of yi in the pure solvent, s. The interaction coefficients, e:, e:, and so forth, are defined by: Since yi is related to the excess partial molar Gibbs energy of component i by GfS = RT In yi, E: is re- ferred to as the "Gibbs energy interaction coefficient". Lupis and Elliott~ extended Wagner's treatment to the relative partial molar enthalpy, aHi, and the excess partial molar entropy, qS. They defined the enthalpy interaction coefficient as: and the excess entropy interaction coefficient as: leading to expressions similar to Eq. [I]: The three interaction coefficients are related by? The self-interaction coefficients, E:,qf,and at, represent the effects of interactions between atoms of component i in solvent s; €3, q{, and 03 represent the effects of interactions between i and j atoms in solvent s; and so forth. From the Maxwell-type relationships between partial molar quantities, it may be shown1'2 that e{ = ej, r}\ =tj), and ai - crj. Experimental determination of the interaction coefficients requires extremely precise measurements of the appropriate properties as functions of solute concentrations in very dilute regions. Few such data exist for intermetallic alloys, even for binary systems, because of experimental difficulties. This is especially true with respect to enthalpy data for dilute alloys. Examination of the compilation of data for binary alloys by Hultgren, Orr, Anderson, and ~elle~~ reveals that determination of limiting values of &fii(Xi =0) often requires extrapolations to infinite dilution from xi = 0.05 to 0.10. Direct measurements of the enthalpy interaction coefficient, qi, for multicomponent systems are virtually nonexistent. This quantity is of course subject to direct calorimetric measurement, but its determination must be limited to cases where high experimental precision is possible. The heats of solution of gold and indium in liquid tin can be measured with relatively high precision, which makes determinations of 73 involving these metals as the measured solutes experimentally attractive. This paper presents the results of such determinations of the Au-Au, Ag-Au, Au-In, and Ag-In enthalpy interaction coefficients in liquid tin. MODELS FOR DILUTE-SOLUTION BEHAVIOR Random-Solution Behavior. In the quasi-chemical treatment of solutions, only nearest-neighbor bonds are considered, and a composition independent value

Jan 1, 1967

By T. V. Philip, R. E. Lenhart

When commercial silicon iron sheets of varying magnetic quality are isothermally annealed at high temperatures, extremely large grains develop in the material having good magnetic properties. These grains are of the (110) [001] orientation and are formed by secondary recrystallization. The primary driving force for this secondary recrystallization is grain boundary free energy. For the secondary grains, activation energies of 103 kcal per mole for nucleation, and of 75.5 kcal per mole for growth, were obtained. The activation energy for nucleation of the secondary grains is consistent with a model involving redistribution of a precipitate acting as the primary grain growth inhibitor. SINGLY oriented silicon iron sheet was first produced in 1935.1 The material as commercially produced today has a very highly developed preferred orientation or texture; up to 95 pct of the grains are crystallographically oriented with their (110) planes in the plane of the sheet and their [loo] directions parallel to the rolling direction. This texture, usually written as (110) [00l], is referred to as the "GOSS" or the "cube-on-edge" texture. Because the magnetic properties of this material are superior to those of the nonoriented sheets in the direction of rolling, the oriented silicon iron has acquired tremendous industrial importance especially in the manufacture of transformer cores and other electrical equipment. The commercially produced material is essentially an iron-silicon alloy containing about 3 1/4 pct Si with minor impurities totaling less than 0.15 pct. The silicon steel heat is melted in the open hearth or electric furnace. The ingots are hot rolled, with or without being slabbed, to strips of 0.100 to 0.080 in. thickness. They are then cold reduced to an intermediate thickness, recrystallized, cold reduced to final thickness, decarburized, and finally annealed at a high temperature. During this high-temperature anneal, extremely large grains with the cube-on-edge texture are produced in the sheet. Several papers have appeared in the literature2-10 relating to the production of the Goss-textured material. Most of these describe the textures produced on cold rolling and on subsequent annealing of single crystal or polycrystalline silicon iron. May and Turnbull11,12 have recently shown the necessity of a second-phase dispersed impurity in the material for the production of the Goss texture. However, none of these papers describes in detail the nucleation and growth kinetics of the (110) [001] grains during the final high-temperature anneal.* The present work, therefore, is an attempt to understand the nucleation and growth kinetics of the cube-on-edge grains in the silicon iron sheet during the final high-temperature anneal.

Jan 1, 1962

By Lennart Wellenius

LAISVALL - ONE OF THE BOLIDEN MINES Until the Aitik Mine (2,000,000 mtpy) started in 1968 the Laisvall Mine (1,200,000 mtpy) was the biggest unit of about 20 producing mines, belonging to the Boliden Company Ltd. As shown in Fig. 1 the mines are spread over a wide area. Most of them are small complex ore mines (50,000 - 300,000 mtpy), for which reason the total mine production does not exceed 5,500,000 mtpy. When our company was invited to present a paper, Laisvall was chosen because it is the biggest European galena-mine in production today. The Laisvall Mine is situated in the county of Norrbotten, Sweden, at the eastern border of the Caledonian mountain-chain. The road distance to Slagnäs, the nearest railway station, is 60 miles. The railway between Slagnäs and BOLIDEN's smelting plant, the Rönnskär Works, is 140 miles long. PRODUCTION STARTED IN 1943 In the Autumn of 1938 a boulder was discovered, consisting of sandstone with galena, on the shore of the Lake Stor-Laisan. The boulder came from an Eocambrian sandstone formation, which is overlain by Cambrian-Silurian rock.

Jan 1, 1970

By Robert Keeney

THE electric smelting of manganese ore and the production of ferro- manganese did not exist as an industry, in the United States or elsewhere, previous to the outbreak of war in 1914. Ferromanganese had been produced, electrically, during times of high prices by two companies at Niagara Falls and by several European companies, but the production. was spasmodic, and none was electrically produced when ferromanganese sold at from $35 to $40 per ton. Thus the electric smelting of manganese ore must be considered as a development caused by the high prices prevailing during the years 1916, 1917 and 1918, and the necessity of smelting domestic ore in order to fill the ferromanganese requirements of the steel industry of the United States, which increased from 189,088 tons in 1914 to 356,356 tons in 1918. The electric furnace is well adapted to smelting domestic-ore because it can be located in small units near the source of ore supply. In 1918, the ferromanganese production of the United States was 333,027 tons, of which about 7 per cent., or 23,000 tons, was produced in the electric furnace. The electric furnace not only assisted materially in the development of a domestic-ore supply but made a considerable saving of coke, as it requires about 1,4 tons of bituminous or lignite coal per ton of ferromanganese compared with a blast-furnace consumption of 2.9 tons of coke per ton of ferromanganese. Some of the plants in the United States that smelted manganese ore in the electric furnace during the war and in 1920 are listed in Tabled. From early in 1919 to about February, 1920, little ferromanganese was produced in the electric furnace. During this period the price of ferro-manganese (78 to 82 per cent. manganese) was about $100 per ton. During the first half of 1920, several plants resumed operation when the, price of. ferromanganese (76 to 80 per cent. grade) gradually increased to $200 per ton, delivered.

Jan 2, 1921