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By Karl A. Bauer, Cornelis Bezemer

The deposition of calcium carbonate scale on surface and subsurface production equipment creates an operation problem in many oil fields. The formation water in which the carbonate-scale-forming components are initially dissolved becomes supersaturated with calcium carbonate as a result of the drop in pressure during production. The continuous flow of a supersaturated solution through the production equipment results in the growth of a dense layer of calcium-carbonate crystals. For a scale layer to be built up, the supersaturated formation water should contact the walls of the production equipment. The tendency for scale to be deposited, therefore, will be low, if the crude has a low water cut and if the water is finely dispersed in the oil. A scale problem will occur, if at a high water cut part of the water is present as free water. The rate of scale deposition will then be approximately proportional to the rate of free water production. Depending upon where the formation water becomes supersaturated, scale may be deposited in the flow line only, in both flow line and tubing, and in some cases even in the perforations and in the formation near the wellbore. In the South Sumatran fields (Indonesia) the main difficulties encountered due to the deposition of calcium-carbonate scale have been restriction of flow through tubings and flow lines, wear and abrasion of plungers and liners, and stuck plungers or wellhead valves. So far, the only methods of combating the *Presently associated with Brunei Shell Petroleum Co., Ltd.. Seria. scale problem have been routine acidizing and additional well pulling. As for the pumping wells, it was estimated that some 50 percent of the total well-pulling effort was directly attributable to scale deposition. The most promising alternative was to prevent the deposition of calcium carbonate scale by means of chemicals. Inorganic polyphosphates such as sodium hexametaphosphate and trisodium polyphosphate are known to retard the formation of scale by the "threshold action". They are adsorbed on specific faces of the crystal nuclei and thus prevent crystal growth, thereby stabilizing supersaturation. Polyphosphates are effective at very low concentrations ( a few ppm), and far less than stoichiometric quantities are required to keep the scaling ions in solution. Recent investigations on barium sulfate scale1 have confirmed this mechanism. The types of polyphosphate mentioned can be applied as concentrated aqueous solutions either squeezed into the formation, lubricated down the annulus or injected via macaroni string. Several squeeze jobs with polyphosphate solutions have been carried out in the South Sumatran fields, however, with disappointing results. Lubrication down the annulus and injection through a macaroni string were not considered attractive in this area because of the kind of equipment and the degree of supervision these techniques require. Polyphosphates are also available in a granular, glassy form, which, in contrast with the readily soluble types already mentioned, show an extremely low

Jan 1, 1970

Large deposits of manganiferous iron ores, representing several million tons of metallic manganese, occur in the United States. The Minnesota deposits of such ore are of outstanding importance because of their size, state of development, ease of mining and proximity to the Great Lakes, which permits water transportation to steel centers. In view of the fact that our steel industry requires large quantities of manganese, for which no satisfactory substitute has been found, and because our reserves of ferro-grade ore are comparatively small, the development of methods that will make our large deposits of manganiferous iron ores available as a source of ferromanganese is an important problem. Realizing the importance of this problem, some years ago the North Central Station of the U. S. Bureau of Mines and the Minnesota School of Mines Experiment Station undertook jointly the development of methods for recovering the .manganese content of manganiferous iron ores in a form suitable for the production of ferromanganese, the 80 per cent. alloy indispensable in producing steel. Two types of manganiferous iron ores have been described in previous reports.' The brown ores are higher in iron and lower in manganese than the black ores; the black ores are more siliceous but contain less phosphorus. The utilization of the iron content of the brown ores in the production of steel appears to furnish the best basis for their treatment. The method of attack has been to work out modifications in iron and steel practice so as to recover manganese in the form of slag comparable to ferro-grade ores. The greater part of the experimental work has been conducted with a 6-ton blast furnace and a 1/2-ton basic open hearth. This paper is devoted mainly to open-hearth tests in which high-phosphorus spiegel

Jan 1, 1930

By George S. Rice

STUDIES of ground movement and subsidence caused by mining necessarily chiefly deal with causes and effects of making extensive excavations underground with spans beyond the strength of the un- supported or temporarily timbered roof or hanging wall. Perhaps no other phase of engineering is so de- pendent for results upon the assemblage of what may be called "experience data." That this is the case is cot surprising when one considers the number of variables involved in any at- tempted mathematical formula to determine the angle of draw or the angle of permanent slope of the rocks in any particular case. It is not like dealing with construction materials in which, through testing of. small specimens, in conjunction with the tests of large built- up specimens, relative stresses and strains may be deter- mined and formulas closely approximated for still larger constructions.

Jan 1, 1931

By K. P. Fournier

This report describes work on the problem of predicting oil recovery from a reservoir into which water is injected at a temperature higher than the reservoir temperature, taking into account effects of vis cosity-ratio reduction, heat loss and thermal expansion. It includes the derivation of the equations involved, the finite difference equations used to solve the partial differential equation which models the system, and the results obtained using the IBM 1620 and 7090-1401 computers. Figures and tables show present results of this study of recovery as a function of reservoir thickness and injection rate. For a possible reservoir hot water flood in which 1,000 BWPD at 250F are injected, an additional 5 per cent recovery of oil in place in a swept 1,000-ft-radius reservoir is predicted after injection of one pore volume of water. INTRODUCTION The problem of predicting oil recovery from the injection of hot water has been discussed by several researchers. l-6,19 In no case has the problem of predicting heat losses been rigorously incorporated into the recovery and displacement calculation problem. Willman et al. describe an approximate method of such treatment. 1 The calculation of heat losses in a reservoir and the corresponding temperature distribution while injecting a hot fluid has been attempted by several authors.7'8 In this report a method is presented to numerically predict the oil displacement by hot water in a radial system, taking into account the heat losses to adjacent strata, changes in viscosity ratio with temperature and the thermal-expansion effect for both oil and water. DERIVATION OF BASIC EQUATIONS We start with the familiar Buckley-Leverettg equation for a radial system:* This is sometimes referred to as the Lagrangian form of the displacement equation. If the injection water is at some temperature Ti which is above reservoir temperature TR, then lw, the flowing fraction which is water, is a function of both water saturation and fluid temperature at any given time and position in the reservoir. The temperature dependence of lw results from the temperature dependence of the viscosity ratio µo/µm of which lw is a function. Thus:

Jan 1, 1966

By C. L. Dake

AN insistent and steadily growing demand is evident for the broadening of undergraduate curricula in engineering. Among suggested additions are training in public speaking, report writing, business law and contracts, accounting, finance, money and banking, scientific management, economics, social and labor problems, psychology, and ethics. The demand for these subjects comes from the older engineers and from the industries that employ our graduates. Of course, many of the men who suggest such changes are influenced largely by their personal needs and contacts, but the demand is sufficiently widespread to merit serious study by educators. In fact, many educators themselves concur in the proposals for broader training. These matters were examined intensively a few years ago in an exhaustive study of engineering education. Opinion at that time was rather strongly against any profound change. Since then, however, the whole economic system has undergone violent disruption. Even if recommendations made a few years ago were appropriate to the conditions then- obtaining, the enormously changed conditions of the present make advisable a further careful study of this problem. In recent years, mergers, to reduce costs, have sharply limited the number of engineers employed and have thereby intensified the struggle to secure positions. In this stiffer competition, engineers with the most adequate training undoubtedly fare the best.

Jan 1, 1934

By Arthur L. Hall

The purpose of this symposium is to challenge industry to better air classification, and as a first step toward fulfillment, to spotlight three fairly recent, aerodynamically designed, highly efficient air classifiers. This discussion does not intend to imply that present practice is bad. Actually, when present air separators are used for the jobs for which they were originally designed, they give high production and uniform operation, with a minimum of maintenance. The customers of nonmetallic mineral pigment producers, however, are making increasing demands for finer products, such as 99.9 pct -20µ, which appears to be beyond the economic capabilities of standard air separators industrially used over the last 10 to 30 years. Here is an actual example. A 10-ft diam pebble mill is in closed circuit with a conventional 12-ft diam centrifugal air separator, grinding 20-mesh wollastonite to a series of fine grades up to 99.97 pct - U.S. No. 325 mesh (44µ). Fig. 1 shows variations in fineness of mill discharge (or air separator feed), recycle for regrinding (or air separator tails), and product as measured by a wet rotating sieve test. For example, when the mill is turning out a product 80 pct -325, the mill discharge or separator feed is 30 pct -325, and the coarse tailings or recycle is only 5 pct -325. Hence 25 pct of the 30 pct available is accepted as product. This is efficient separation, and the ratio of recycle to feed is only about 2: 1. How- ever, to make a product testing 99.97 pct -325 the separator feed is 62 pct -325 and the coarse tailing 60 pct -325. In this case the recycle ratio is about 13: 1 and the economic limit to produce fineness has been substantially reached with this given equipment and process arrangement.

Jan 10, 1957

[JOSEPHSON, W. G.: The Argonaut Mine of Today, M88, 475 JOUET, C. H., biography, M29, 258 Joule-Thompson effect, 98, 381 JOWETT, J. H., biography, M83, 276 JUDSON, S. A.: Operations in the Gulf Coast of Texas and Louisiana for 1926, G26, 659 JUDSON, S. A., EASTON, H. D. JR. AND SCHAEFFER. W. A. JR.: Estimation of Petroleum Reserves in Prorated Fields 114, 11. Abs., YB35, 50 JULIHN, C. E.: Copper---An Example of Advancing Technology and the Utilization of Low-grade Ores. Brookings Lecture, in Mineral Economics (1931 volume, B. W. Mudd Fund)]

Jan 1, 1936

By E. H. Jr. Dix

THE use of magnesium as an alloying element in aluminum alloys has been limited, in general, to comparatively small quantities. In duralumin-type, strong-aluminum alloys, magnesium is present to the extent of ½ to ¾ per cent. and various grades of Magnalite and the "Y" alloy of the National Physical Laboratory of England contain up to 1 1/2 per cent. In this country small quantities of aluminum alloy sheet containing 4 per cent. magnesium are produced commercially. All commercial aluminum contains sufficient silicon to convert a portion of the magnesium added to the compound Mg2Si. It is well known that the solubility of both magnesium and magnesium-silicide decrease with decrease in temperature. It is, therefore, impossible to separate the age-hardening effect of the magnesium-silicide from that of magnesium, except by the use of aluminum of such high purity that the silicon content is negligible. The present paper is the fifth1, 2,3,4 of a series from the laboratories of the Aluminum Co. of America reporting the results of investigations of the equilibrium relations in aluminum-rich alloys made from the high purity aluminum manufactured by this company .5

Jan 1, 1929

By CLARENCE WM. POY

THE most common difficulty faced by an engineer or mine operator when opening a new property in a new field is the lack of roads and of cheap transportation. This one item often swings the balance of success or failure in starting a project. In Alaska, as elsewhere, such problems are more or less serious. In the boom days around the Valdez district, as well as in other parts of this territory, freighting was accom¬plished by dog teams or horses, or even by men that were willing to put their shoulders into harness, because there were virtually no roads. More important, there was only one time when supplies could be transported, and that was when there was suffi¬cient snow on the ground following a heavy wind. Then, and only then, could one depend on the snow to support horses and sleighs, and be sure that the gulleys, streams, and crevices in the glaciers were filled with snow to avoid pitfalls. These methods were used when one had no roads, no streams in the summer to float a barge, or even a trail for a pack train. If the snow was deep and soft, trans

Jan 1, 1935

THE twelfth annual meeting of the American Asso-ciation of Petroleum Geologists will be held in Tulsa, Okla., on March 24 to 26, at the Mayo Hotel. The per-sonnel of the committee on arrangements for this meet-ing is as follows : Chairman, M. M. Valerius ; finance, J. H. Gardner; program, Sidney Powers,; publicity, Luther H. White; reception, L. G. Welsh; registration, Frank A. Herald; exhibits, Frank C. Greene; entertain¬ment, Harry H. Nowlan ; ladies' entertainment, T. E. Weirich; golf tournament, A. L. Beekly; hotels, G. C. Potter; transportation, A. W. Duston; banquet, R. Hughes; decoration, V. H. Hughes.

Jan 2, 1927

By P. K. Leung, S. R. Allada, P. M. Dranchuk, D. Quon

The alternating direction explicit procedure (ADEP) makes use of the boundary conditions to reduce multi-dimensional problems to a series of one-dimensional problems. The method, previously applied to reservoirs containing only an under-saturated oil, has now been extended to cover the case of natural gas reservoirs. l his involves solving a non-linear partial differential equation, application of the procedure is straightforward and no calcuIational problems were encountered. INTRODUCTION There has been a growing interest in formulating mathematical models of petroleum and natural gas reservoirs — models which permit the engineer to examine and evaluate the physical and economic consequences of various alternative production policies. The tremendous reduction in the cost of solving such models in recent years has made possible their use as an almost routine management tool. This reduction is the result not only of improved computer hardware but also of the development of more efficient mathematical techniques. The present paper is concerned with the application of a recently proposed numerical method (ADEP) to two-dimensional gas reservoirs. STATEMENT OF THE PROBLEM Given a two-dimensional Region R, bounded by a closed Curve C (Fig. 1) such that the behavior on Curve C is known, the differential mass balance for each fluid phase in R, neglecting gravitational effects and assuming Darcy's law for fluid transport, can be written as:

Jan 1, 1967

By Ivan B. Cutler, Milton E. Wadsworth

Coprecipitation of anionic and cationic polyelectrolytes has been applied to floccula-tion of several mineral systems. Results obtained in a study of the flocculation of kaolinite and hematite suspensions of polycationic and polyanionic electrolytes are presented. Greatly increased settling rates were observed following precipitation of positive and negative polyelectrolytes on the surface of finely divided minerals in aqueous suspension. The ratios of polycationic to polyanionic electrolytes required to produce maximum sedimentation have been shown to correspond closely with the equivalence points obtained by light scattering studies of systems containing the positive and negative polyelectrolytes by themselves. DISPERSION of colloids has been of interest to surface chemists for many years. Flocculation studies have been employed to evaluate the limits of colloid stability. In water suspensions, colloids become unstable and flocculate when the 5 potential, the potential of the kinetic solvation sheath, falls to a value at which van der Waals forces may act to draw the particles together. This may happen through an adjustment of the pH of the suspension or by addition of a salt. Optimum conditions for rapid formation of large flocs are found in the region of minimum < potential. In addition to these well known considerations, colloids in water suspensions are known to be flocculated by certain large organic macromolecules. These polyelectrolytes in some cases minimize the 5 potential and in other instances increase the attractive forces by supplying sites for hydrogen bonding.&apos; Use of organic polyelectrolytes in flocculation of mineral colloids has increased rapidly in recent years. These materials are now recognized as indispensable aids to fluid-solid separations in many extractive metallurgical operations. They have been found to increase both the settling rate in thickeners and the filtration rate of filters. In the elucidation of the characteristics of these organic reagents as floc-culants in this laboratory, it was discovered that interaction of certain polyelectrolytes had a surprisingly good effect on flocculation of mineral colloids. Experimental Procedure: The anionic flocculants used in this study were Lytron 886 and 887, produced by Monsanto Chemical Co. Both reagents are copolymers of vinyl acetate and maleic anhydride. Lime is added to Lytron 886, whereas Lytron 887 is all organic. These reagents possess two carboxyl groups for each acetate group and are therefore anionic in character. The cationic reagents used were the Peter Cooper Co. 1-X and 2-X glues. The structures are not definitely known, but the re- agents are amines and are cationic in character. The glues were prepared in the chrome-alum form. Both types of reagents may be classified as polyelectrolytes in that they are high molecular weight polymers and ionize in water. All data presented are in terms of sedimentation rate, measured in 250-ml glass-stoppered graduated cylinders. With suitable precautions such measurements are fairly reproducible and provide a sensitive means for selecting important parameters such as PH, reagent concentration, and floc size and density. Agitation was standardized with five complete end over end cycles of the suspensions in the stoppered graduated cylinders.

Jan 1, 1957

By W. L. Connell, O&apos

The properties of some heavy liquids which can be used in sink-float separations are discussed with major emphasis being given to the halogenated hydrocarbons. Data are presented on density, viscosity, thermal characteristics and the effects of moisture and temperature on the corrosiveness of the liquids towards various materials of construction. The toxicity of these materials, the hazards involved in handling them, and the procedures for handling them safely are also discussed. True liquids have certain advantages over colloidal suspensions for sink-float separation of minerals which makes their use especially advantageous when close separations, fine particle sizes or water-soluble minerals are to be treated. For best separating results, the medium should have an easily controlled, uniform, stable density. Here, true liquids have the advantages of allowing closer control of density and of not requiring agitation to maintain a uniform den- sity in the equipment. Low viscosities are desired in a separating liquid so that rapid separations of fine material can be made. Many liquids have lower viscosities than the colloidal suspensions at operating gravities of 1.4 to 5.0. For economic reasons and to prevent contamination of the product, the separating medium must be easily and completely removed from the ore. Normally, true liquids must be more completely removed than the cheaper suspensions and thus cause more problems in this area. The fact that the medium should not react with the minerals, air, water or the common materials of construction limits the choice of liquids which can be used, but many are available which are sufficiently stable. A more serious objection to the use of true liquids is that many of them present a toxic hazard to operating personnel and users of the product. Most true liquids are toxic to some extent, but modem knowledge of toxicity allows us to recognize the hazards inherent in handling them and enables us to design around them. Three types of true liquids are available for this use: 1) Halogenated hydrocarbons cover the gravity range from 1.2 to 3.3. They are generally more volatile and less viscous than the other liquids.

Jan 1, 1963

By Hubert E. Risser

Although, for about a half-century the percentage of coal production provided through strip mining has steadily increased, recent trends indicate that a peak in percentage (not tonnage) is being approached, principally because of the decline in economic adrantage enjoyed by strip mining compared to underground mining. Factors contributing to the decline are the decrease in the margin of advantage in manpower requirements held by strip mining; an increase in depth and volume of overhurden, requiring larger equipment and capital investment; increasing lack of reserve land blocks large enough to support extensive strip mining operations; more stringent legislation for reclamation of stripped land, with increasingly higher costs of such reclamation; and the increasing costs of land surface rights for strip mining. Already there has been a peak and suhsequent decline in relative importance of strip mining insome major Eastern coal-producing states; trends indicate that a peaking for the whole Eastern region is on the way. Although, in the West the pressures are less severe, they will, nevertheless, reduce to an increasing degree the advantage that strip mining has possessed. For about half a century, strip mining has been providing an ever-increasing share of total coal output in the United States, and in the past 30 years this share has grown from less than 8% to 33.7%, as shown in Fig. 1. Fig. 1 also shows that strip mining is gaining faster in the West than in the East. From 1961 to 1967, output from strip mines grew 63.6 million toqs, or 52.2%. Certainly there is nothing in such performance to indicate any peaking in the level of strip coal-mine production. But the fact is that, if not in actual tonnage, strip mining appears to be reaching its peak in relative importance, at least east of the Mississippi River. And the area east of the Mississippi provides 90.0% of the strip and 94.9% of the total coal production of the nation. The relative economic advantage which spurred strip mining&apos;s growth for a third of a century has been diminishing markedly in recent years. Fig. 2 shows evidence of this decline. From 1947 until 1961, strip tonnage output remained fairly stable, at the end of the period showing only a 12.5% decline. Meanwhile, underground coal production fell 44.5%. As the result of the greater decline in underground coal, strip coal in 1961 furnished 30.3% of the total coal produced, compared to only 22.1% in 1947. In the succeeding six years, however, underground coal output increased by 76.5 million tons, while strip output increased only 63.6 million. Further evidence of the strengthening of underground coal&apos;s relative position — or if you will, the weakening of strip coal&apos;s position — can be found in the major coal stripping states: Illinois, West Kentucky, Ohio, Pennsylvania, Indiana, and West Virginia, which in 1966 provided 80% of the nation&apos;s strip coal. Fig. 3 shows what has been happening in three states lying in the Appalachian field and in the total output of these three states. In the figure, the column height represents the output of coal mined by all methods. The number at the base of each column is the percentage mined by stripping. In Pennsylvania and Ohio, the percentage of strip mining increased between 1956 and 1961, but by 1966 had declined from the 1961 level. In West Virginia, a decline occurred during the first five years but was followed by a rise. In January 1968, Coal Age published an article listing the locations and capacities of new large mines in the planning and construction stages that would be operating by 1968-1971. The plans for West Virginia and Pennsylvania indicated all the new mines would be underground. Except to the extent they might replace existing under-

Jan 1, 1970

By J. Douglas, W. T. Ford, G. E. Henderson, I. F. Roebuck

An implicit numerical method is presented for simulating the differential and algebraic relations governing one-dimensional three-phase flow in porous media. The method is based upon compositional representation of the hydrocarbon system. Variable physical properties and water-oil capillary forces are included in the formulation; however, the effect of gravity is ignored. The effects of changing composition and mass transfer are considered through the use of known phase behavior concepts and correlations. The differential and algebraic equations and the numeric approximations to these equations are presented, and the computing algorithm is discussed in detail. This method is used to simulate a single-phase, two hydrocarbon-component gas displacement laboratory experiment. The method is also applied in simulating a solution gas drive and a gas injection problem using a reservoir oil represented as a nine-component mixture. For comparative purposes, the latter two problems also are examined with a one-dimensional volumetric model. The results of the simulation of the laboratory experiment demonstrate the relevance of this method to problems wherein the effects of mass transfer significantly enter the displacement process. The comparison of the results of the volumetric and compositional methods applied to a reservoir system illustrates not only the advantages and benefits derived from examining the hydrocarbon system composition, but also the necessity of this approach in application to a general reservoir problem. INTRODUCTION The advent of large memory, high-speed digital computers enabled reservoir engineers and mathematicians to pool their knowledge in the development of sophisticated techniques for the prediction of oil and gas reservoir performance. These techniques have progressed from volumetric and trend analysis calculations to the development of "mathematical models", or reservoir simulators. These latter models, in general, utilize finite difference approximations to the rather complex partial differential equations that mathematically describe the physics and thermodynamics of fluid flow in porous media. Many forms of this "model" type are available today, and much of the recent literature has been devoted to either improving known methods or developing new techniques for use in these prediction methods. The more advanced techniques in use at this time consist of the solution of differential and algebraic relations that describe a reservoir geometry in one, two or three dimensions and that incorporate reservoir hydrocarbon and water fluid systems that obey specified physical laws, having properties that might easily be measured in the laboratory. This type of model utilizes formation volume factors and other volumetric data, expressed directly as functions of pressure, to represent the reservoir fluid system. Experience gained with this type of simulator, commonly known as a "beta-factor model", has indicated that the approach has many outstanding defects, most of them due to the assumption that those properties measured in the laboratory completely describe the behavior of the fluid system throughout the life of the project under study. The effects of varying hydrocarbon composition and mass transfer between the phases of this hydrocarbon system must, by definition, be ignored. These defects, which may often be ignored in

Jan 1, 1970

By H. A. Domian, H. Biloni, G. F. Bolling

Jan 1, 1965

By R. M. Asimow, J. J. Svitak

Tile crilical resoll,r,d shear stress, CRSS, for slip of slow1y cooled Ag-All single crystals was measured at 201K. Tlze importance of short-range order and Suzuki sogregalion was inrestigated by deter~rlining llze ciic.cl of quenching on the CRSS. Thr obserz.ed rfrtenching effects were generally small and indicate that short-range ordcr and Slczuki srgregation do no1 account for n significant portion of the solid-solution strengthening in this system. However, all alloys slzozcwi yield drops ulhich rilere heat- lreat nrenl-sensiline THERE have been a number of mechanisms proposed to explain alloy strengthening in the Ag-Au system. The effectiveness of some of the proposed mechanisms, especially those that depend on Suzuki segregation1" or on short-range order,2-6 SRO? should be strongly dependent on heat treatment. Since internal friction investigations in this system indicate that there is stress-induced order,&apos; we must also consider the possibility of local atomic rearrangement or short-range ordering in the stress field of a dislocation. There is not complete agreement whether these mechanisms should be most effective in raising the flow stress, in causing yield drops. or some combination of these two effects. This work was undertaken to determine the effects in the Ag-Au system of mechanisms that depend on segregation or order by using known but drastically different cooling rates following a high-temperature treatment. By comparing the critical resolved shear stress, CRSS, for slip measured after a very slow cool and again after a fast cool (quench) of the same crystal, it is possible to determine the effect of cooling rate on CRSS* and on yield drops. The single-crystal CRSS was determined at several compositions because there has been no data published across the phase field since the publication of room-temperature flow stress by Sachs and Weerts.&apos; EXPERIMENTAL PROCEDURE Starting with materials of 99.999 pct purity, single-crystal specimens of random orientation 1.25 mm square by 4 cm long were prepared with 0, 10, 14, 25, 30. 50, 70. 75. 80, 90. and 100 at. pct Au. Crystals were grown in an inert atmosphere using a modified Bridgman technique with a growth rate of 1.5 cm per hr in a gradient of 3°C per cm. To obtain a maximum practical degree of SRO, the crystals were cooled at a rate of 275&apos;C per hr to about 310°C and then cooled at 6°C per hr to approximately 200°C. Specimens were tested in tension immersed in an alcohol bath at -72°C (201°K) at a strain rate > = 0.003 mm"1 to determine the CRSS (7). The activation volume of several crystals was determined from the flow stress increment (72 - T1) for a tenfold increase in strain rate. The total shear strain varied from 0.05 to 2.3 pct but was generally less than 0.4 pct. After testing, each crystal was then held at 500°C for 10 min, quenched into brine at -35°C and. after storage at -71°C for 1 day, retested in tension using a procedure identical to that of the first test. The quenching apparatus, see Fig. 1, was designed to enable accurate temperature control and rapid quenching while preventing specimen contamination and accidental deformation. Test data from a specimen with a fine thermocouple spot-welded to it indicated a cooling rate of 104C per sec. The relatively low heat-treatment temperature was chosen to minimize quenching defects caused by a large vacancy

Jan 1, 1970

By W. R. Hibbard

Evidence is presented which confirms previous findings that models of solution strengthening depending solely on lattice parameter changes are incomplete. Direct evidence for the Suzuki interaction of chemical effects was obtained from alloys with constant lattice parameter, for which solution strengthening was nearly independent of temperature from 300° to 20°K. SOLUTION hardening principles have been reviewed recently by Parker and Hazlett.&apos; In addition, the interactions of dislocations and solute atoms were reviewed by Cottrell.&apos; It is not proposed to review this information again here, but to refer only to those details which are pertinent to the developments which have occurred since these papers were published. Literature Survey To set the stage, it has been known for some time that solid solutions are stronger than the pure parent metals, and that the strength increases with increasing amounts of alloying element. One of the most extensive earlier investigations was that of Lacy and Gensamer,3 who reported that the solid solution strengthening of iron is a power function of the composition, that the relative strengthening is a function of the solubility limit, and that the rate of strain hardening is a function of the amount of solution hardening. Thus, the slope of the plastic portion of the stress-strain curve increases with increasing yield strength. An approach to the development of principles resulted from work by Gulyeav,4 who reported that the strengthening effect of solid solution alloys is periodic in character when plotted as a function of the atomic number of the solute. A more quantitative approach was to relate the amount of solution hardening to the lattice parameter of a solid solution. This was done quite early by Norbury,5 and later by Brick, Martin, and Angier,6 Frye and Hume-Rothery,7 and French and Hibbard. This relationship is only approximate in character. The next development was to relate the amount of solution hardening to lattice stress, as proposed by Frye and co-workers.9 They calculated what they called ionic overlap from the lattice parameter changes represented as a change in volume, using Bridgman&apos;s hydrostatic compression equation. The resulting correlation was somewhat improved as compared to the simple correlation with lattice parameter. The next step was carried out by Dorn, Pietrow-sky, and Tietz,10 who suggested an effect of valence differences in addition to the effect of lattice parameter. Their proposed parameter shows flow stress as a single valued function of the concentration and a relationship involving these two atomic variables. In addition, they contributed new data on the temperature dependence of solution hardening which indicated that it was a strong function of temperature for aluminum alloys. Allen, Schofield, and Tate11 carried the valency effect even further by reporting data indicating that with a given solvent element the stress-strain curve is a function of electron density, entirely neglecting the size factor, which varied by a factor of two. This evidence led to a quantum mechanical calculation by Cottrell, Hunter, and Nabarro,12 based on the formation of a dipole around an edge disloca-

Jan 1, 1959

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall&apos;s statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949

By Lester Guttman

The connection between short-range order and thermodynamic activities in binary solid solutions has been pointed out by Birchenall1 who calculated approximate values of the energy of interaction of Zn and Cu and of the degree of short-range order in alpha-brass at one composition and two temperatures. The purpose of this note is to call attention to a somewhat more accurate theory than that used by Birchenall and to extend the calculations to a wider range of temperatures and compositions as a means of testing its applicability. This is an example of the well-known general method of comparing measured thermodynamic functions of a system with those calculated from a microscopic model by means of statistical mechanics. In this case, mathematical approximations must be used which make difficult any decision about the validity of the model. Birchenall&apos;s statistical method resembles closely that calletl by Fowler and Guggenheim2 the "quasi-chemical" method which has been shown to lead in certain cases to results identical with those obtained by the method of Bethe.3 The quasi-chemical method has been extended by Takagi4 to give general formulas for the free energy of binary solid solutions based on several lattices at all compositions and temperatures. Specifically, he treats the four systems typified by: I. ß—brass; 2. a— brass; 3. AuCus; 4. AuCu. When the temperature is so high that no long-range order exists, these formulas reduce to the same form for all lattice types, namely: F - FO = (E - EO) - T(S - S°) = ½N(c — x)(2vAB — vAa - Vbb) + M1/2KTzN[x log x + 2(c - x) log (c - X) + (I - 26 + X) log (1 - 2c + x)] -kT(z - I)N[c log c+(I-c) log (I -c)] Eq 1 Here the symbols have the following meanings: F—Helmholtz free energy E—nergy 5—ntropy k—the gas constant per molecule z—coordination number, (e.g. I2 in a-brass). N—total number of atoms c—atomic fraction of A Vaa, vbb, vab—nergy per bond of the corresponding bonds log means log, throughout The superscript ° denotes the thermodynamic fuliction in the standard state, which has been chosen to be pure A or B with the same crystal structure as the solid solution. The quantity x is the ratio of the number of A-A bonds to the total number and for minimum F satisfies the equilibrium condition Vaa + Vbb — 2Vab _ (c — x)2 kT l0g x(i - 2C + x The free energy may also be written in terms of /La and B, the chemical potentials or partial free energies per alom:

Jan 1, 1949