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By C. E. Ells, A. Sawatzky

The effect of neutron irradiation on tensile properties of the Zr-2.5 wt pet Nb-0.5 wt pet Cu alloy has been evaluated for integrated neutron fluxes up to 3 x 1020 n per sq cm (E > 1 Mev). Specimen temperature during irradiation was normally 300°C. The material was studied both in annealed and in quenched and aged conditions. When the alloy (fab-ricatedfrom sponge zirconium) is quenched from a temperature =40°C below the a + ß/ß transformation and aged 6 hr at 535oC, neutron irradiation up to the maximum studied has little effect 071 reduction in area, although there is a drop in uniform elongation and the yield strength is increased by = 25 pct. Conversely, irradiation of the alloy in an annealed condition can result in much greater changes in properties, with yield-strength increases of up to 200 pet. The dose dependence of irradiation hardening obeys the saturation equntion proposed by Makin and Minter to explain hardening in copper and nickel: Act = C[1 - exp(-Døt)/1/2 A rnodel is proposed to explain the effect of niobium content and metallurgical condition on irradiatiotz behavior. THE Zr-Nb alloys form a class of material susceptible to marked strengthening by quench and age heat treatment. With niobium concentrations as low as 2.5 wt pet, strengths can be developed which are double those of annealed zircaloy-2.1 Since the neutron-capture cross section of the Zr-2.5 wt pet Nb alloy is nearly identical to that of Zircaloy-2, significant gains in power-reactor neutron economy could be obtained by replacing stressed in-reactor components of Zircaloy-2 with the heat-treated Zr-Nb alloy. When the solution heat-treatment temperature is in the high (a + ß) phase, then the tensile properties of the quenched (and aged at 500°C) material have been shown to be relatively insensitive to neutron irradiation.1-3 Addition of small quantities of copper to the binary Zr-2.5 wt pet Nb alloy gives a useful reduction to the corrosion rate in air and carbon di- oxide,&apos; and a ternary alloy of composition Zr-2.5 wt pet Nb-0.5 wt pet Cu was chosen for one component in the Douglas Point Reactor. This application utilizes both the corrosion resistance to a moist air-carbon dioxide environment and the strength developed by a quench and age heat treatment. By suitable choice of solution heat treatment and aging temperatures, tensile properties of the ternary alloy can be made nearly identical to those considered as optimum for the binary alloy. One effect of the copper addition, however, is to give marked changes in the aging kinetics of the alloy.&apos; For this reason, it appeared that neutron irradiation might promote overaging in the ternary alloy, particularly at the elevated service temperature (=300°C). This paper describes the effect of neutron irradiation on the tensile behavior of the Zr-2.5 wt pet Nb-0.5 wt pet Cu alloy in several metallurgical conditions pertinent to its use as a reactor material. The metallurgical conditions included those for which aging occurs in the unirradiated material, and fully annealed conditions for which a higher degree of thermal stability could be expected. 1) EXPERIMENTAL Two batches of alloy were used, both made from sponge zirconium. The fabricator&apos;s analysis of principle constituents showed no significant difference between the two batches, Table I. The rod material was rolled to 1.5 in. diam, and then swaged to final sizes of 0.5 to 0.375 in. diam at nominal temperatures of 785" and 625°C for the AM and AS batches, respectively. Subsequent hydrogen analyses at CRNL confirmed that the hydrogen concentration of the as-received rod was indeed <20 ppm. However, it was found that the (a + ß)/ß transus for the AM material was approximately 25°C lower than that of the AS material, indicating rather more difference in oxygen concentration than given in Table I. Except for a small difference in yield-point behavior, the tensile prop-

Jan 1, 1965

By A. G. Guy

Thermodynamic activity rather than chemical composition is basic to the analysis of diffusion. This is the essential conclusion reached by Darken1-3 and by Birchenall and Mehl.4 If so, it is reasonable to expect that diffusion calculations should be carried out using activities. This paper will illustrate a method of employing activities in analyzing interstitial diffusion. For interstitial diffusion (of carbon in iron and probably generally) the diffusion of the solvent atoms, volume changes, and other such complexities not explicitly provided for in the usual diffusion equations cause a negligible error of the order of 1 pct. Therefore it is relatively easy to test the validity of an analysis based on activities in the instance of interstitial diffusion. The mathematical treatment of the more complex substitutional diffusion could be simplified once the adequacy of the activity method had been established for substitutional diffusion. Thus the present work has the purpose not only of providing a superior analysis of interstitial diffusion but also of indicating a possible approach to the more important question of an adequate treatment of substitutional diffusion. Development of the Diffusion Equation Although activities are convenient quantities to determine experimentally, they are derived from the more fundamental fugacities.9 Possible confusion in using activities can be avoided by basing equations involving their use on the relationship, dP = -D1d/ax dt [I] where, dP = the number of grams of solute crossing one cm2 in the time dt sec. D, = the diffusion constant for use with fugacities; it is assumed to be constant at a given temperature, and has units of secs. f = the fugacity of the solute in the solid solution; the units are those of pressure, dynes per cm2. x = the distance in cm. Eq 1 can be considered to be the basic form of the first Fick Law for one-dimensional diffusion. In order to convert Eq 1 into an equation involving activities, a choice of a standard or reference fugacity, f°, must be made: then. a = f [2] where a is the activity corresponding to the fugacity f. However, the value of a is also determined by the relation, a = a\c [3] where a is the activity coefficient and c is the concentration. For a given value of a (such as a = 1) it is evident that the units used for expressing concentration will affect the numerical value of a corresponding to a given amount of carbon dissolved in y-iron. Since weight per cent concentration is so widely used, this unit will be adopted as the standard in this paper. When the value off given by Eq 2 is substituted in Eq 1, the first Fick Law becomes, dP= -D,f°dl [4] Since D,f° is constant (at a given temperature), the second form of Fick&apos;s Law can be obtained in the usual manner, -dt D&apos;f° dx [5] where c&apos; is the concentration in g per cm3. In terms of weight per cent concentration, c, Eq 5 becomes, dc _ 100 d2a Tt = T /f w [6] where p is the density of the solid solution and will be assumed to be constant. In order to simplify Eq6, it is necessary to consider the standard state, f°. Standard states are chosen for convenience. There appears to be one especially convenient choice for the analysis of interstitial diffusion. If the activity coefficient, a, is set equal to unity at infinite dilution of the solute, 100 then — 100D1fl° is approximately equal P to the usual diffusion constant in dilute solutions. This is true since the activity, a, in Eq 6 can be replaced by the concentration, c, with little error in an infinitely dilute solution.* Here f1° is the standard fugacity necessary to achieve this standard state. It is proposed that a diffusion constant Da&apos; be defined, Da1=100/pD1f1° [7] where A is the metal whose diffusion is * The second derivative of a is equal to the second derivative of c in dilute solution only if -da/dr- is. zero. Although theory does not require this condition, in the systems C in Fe, and Zn in Cu, dc is in fact found to be essentially zero.

Jan 1, 1950

By H. Pew, J. H. Field

To alleviate pollution more restrictive legislation is being enacted, either limiting emission of pollutants or the type of fuel that can be utilized. The nature and magnitude of air pollution problems affecting the mining, preparation, coking and combustion of coal are described. Methods for combatting particulate emissions by use of mechanical separators and electrostatic pre-cipitors are discussed. Proposed methods to meet the problem of gaseous emissions currently receiving considerable attention are described, with special emphasis on methods to decrease pollution by sulfur oxides. Concern about air pollution goes back several centuries, but until very recently most effort has been aimed at coal smoke and other visible pollutants. The classic example of a &apos;successful&apos; campaign for smoke abatement and control is the fruitful combined effort of the city of Pittsburgh and its surrounding Allegheny County, which eventually led to the reconstruction of downtown Pittsburgh at an estimated cost of one billion dollars. Historically, the city&apos;s downtown Golden Triangle district had been afflicted by pollutants evolving from steel mills, from a variety of other industries, and from railroad locomotives. Efforts to alleviate the situation prior to 1943 were virtually ineffective. In 1945, however, a comprehensive redevelopment plan was prepared and backed by state authority. Within a few years a clean, modern metropolis has evolved where once stood America&apos;s famous &apos;smoky city.&apos; But the victory in Pittsburgh, as in various other American cities, has not solved the national problem. Current estimates indicate that 133 million tons annually of air pollutants from all sources still are emitted annually into the atmosphere above the United States. About 10% of this annual effluent is particulate matter so that most of the remaining pollution problems will be solved only when other effluents are reduced. Essentially, these are sulfur oxides, nitro- gen oxides, hydrocarbons, and carbon monoxide. Over the years, both states and local communities have tended to increase the restrictions on smoke and fly ash — problems mostly of concern in the combustion of coal. Prior to the middle 1950&apos;s, ordinances sometimes permitted emissions of smoke equivalent to as much as No. 3 on the Ringlemann scale. Since 1956, no ordinance has been passed which allows smoke of greater than No. 2. Under today&apos;s conditions of improved fuels, equipment and practice, a few communities have passed laws prohibiting emission of smoke of any density darker than Ringlemann No. 1. The majority of existing laws on fly ash emission in the U.S. limit emissions equivalent to 0.85 lb of fly ash per 1000 Ib of flue gas. In recent years, however, regulations which have been adopted give cognizance to the higher level of performance now obtainable with improved equipment. A comparison of the restrictions of five codes adopted since 1960 is given in Table I. The most stringent of these is the one for New York City which provides for a maximum emission of 0.6 lb fly ash per million Btu heat release (equivalent to roughly 0.51 lb/1000 lb of flue gas). The first comprehensive effort to restrict the emission of SO2 resulted from the passage of a 1937 law in St. Louis. This regulation stipulated that coal containing in excess of 23% volatile matter and 2% sulfur must be washed, thereby presumably producing some effective reduction in the input sulfur content. This was followed in 1949 by a Los Angeles County law which prohibited the emission of SO2 in concentrations greater than 0.2%. Most SO2-restrictive legislation passed since that date has been based on this limiting 0.2% SO2 by volume, although modifications are occasionally permitted under selected conditions, sometimes based on the fact that certain limiting ground concentrations are not exceeded — such as in the rules adopted by the San Francisco Bay area. To date, no legislation has been passed in the U.S. to limit the generation of nitrogen oxides from the combustion of fossil fuels. However, such oxides are considered to be of potential importance in air pollution control because of their possible detrimental effects on health and their reported role in the formation of photochemical smog. Interest in reducing oxides of nitrogen from powerplant and auto exhausts is increasing and regulations limiting their quantity can be expected in the future.

Jan 1, 1968

By C. H. Mathewson

MY first reflection on the subject assigned to me by the officers of this symposium was that a critical description of these lesser characters in the cast of inanimate actors now before us under the title "The Role of Metals in New Transportation" would be about as well received as the description of a horse race in terms of harness buckles and jock-ey&apos;s buttons. The word "new" in the title of this symposium seems to shout strong aluminum and stainless steel, unless we transfer our attention to transpor-tation on another planet where the strength-density ratios may require very different engineering treatment. To load a speaker with the "heavier nonferrous metals" amidst the airy consideration of flying or 20th century gliding along the earth and through water, like Hermes, the messenger of the immortals, and expect an instructive or enlivening flight into the area of current exploitation and popular interest in transportation would, of course, require the performance of a miracle or at least the exhibition of genius to which I can lay no claim. But copper and nickel, headliners in other classifications, are also indis-pensable as components of the important new structural materials of transportation, and together with lead, tin and zinc perform many minor or contributory functions in this field that may indeed be con-sidered well-nigh indispensable. A complete and well planned fabric of classification, explanation and critique of even these secondary functions would take much time, and I cannot hope in the 25 minutes or so alloted for the purpose to offer more than a rambling treatment, in which a thread of continuity will be sought by anchorage to one after another of the following attributes or appurtenances of the moving vehicle: 1. The machinery and accessories. 2. The framework and superstructure, and the line or travelway. 3. Light, heat, power, water, sanitary and housekeeping services. 4. Embellishment, or style.

Jan 1, 1936

By J. B. Clemmer, W. L. Lennemann, J. B. Rosenbaum

Security restrictions on processing uranium raw materials to yellow cake were lifted in August 1955, coincidental with the Geneva Conference on Peaceful Uses of Atomic Energy. Numerous reports and technical papers on uranium extraction and recovery methods have appeared since that time, and it is doubtful that another review of past and current practices would add much to the technical literature. Development of some promising procedures was arrested, perhaps temporarily, by mechanical handling problems or peculiarities in the chemistry of uranium and associated elements. Some methods have been incompletely evaluated and still others that tested well in the laboratory and pilot plant are dormant because of competition from other processes, or because of their restricted applicability to particular ore types that have not reached quantity production. In view of the vast number of new ideas and procedures that have been advanced, considered, and tested, it would be futile to attempt a comprehensive survey in this article. Only a cross section of the field, based on random sampling, can be provided here. The authors have chosen, therefore, to discuss some innovations that may provide a clue to uranium ore processing techniques of the future. An effort has been made to select unpublicized new metallurgical techniques or interesting applications of established principles and procedures. With the two exceptions noted later, all the research to be described has been sponsored by the AEC. Physical Beneficiation: Individuals and firms engaged in mining and processing uranium ores, and in related research activities, have often had considerable experience in ore dressing. As might be expected, therefore, a prodigious amount of work has been done on physical beneficiation testing of uranium ores, particularly in efforts to concentrate subgrade materials. Although some success has been attained on specific ores by gravity concentration and flotation, ratios of concentration have generally been low and there has been difficulty in making a throwaway tailing.

Jan 9, 1957

By Joseph Pogue

THE past year in the petroleum industry was one of overproduction, rising inventories, low prices, and meagre to vanishing profits. This outcome was the result of a long period of intensive and uncompensated effort on the part of both financial and industrial interests, to stimulate supply on the theory that the primary problem facing the petroleum industry was the development of an adequate reserve of raw material to protect a large and ever-growing investment. The stimulus was applied in various forms and through diverse channels: capital had, long flowed into the industry in excessive amounts under the attraction of large expected profits; the price level for crude petroleum had persistently been influenced -by speculative considerations, with the result that prices declined slowly in periods of flush production and were quick to advance in anticipation of statistical improvement, thus maintaining a superfluous degree of stimulus on wildcatting and on drilling; speculation in inventories had led to the unsound, or at least unusual, business practice of accumulating huge stocks of oil; and, above all, the industry had directed the potent force of technology to the expansion of supply and achieved radical results in accelerating oil discovery, speeding up the rate of oil extraction, and enlarging the recovery of gasoline and lubricating oils from the raw material. In short, the economic conditions of 1927 were exactly those to which the objectively driven enterprise of the petroleum industry had long been directed; and the undesirable financial consequences arising. therefrom reflected no lack of success in what had been set out to be achieved, but rather the failure to have established concurrently the necessary means of economic control to prevent the immediate conversion of reserves into current supply, and likewise the oversight in neglecting to apply the technological force to the enlargement and diversification of the market for petroleum products. Perhaps, when viewed in its longer perspective, 1927 will stand out as the turning point in the economic policy of the petroleum industry, when the technique of rationalizing production made its, initial claim for recognition.

Jan 1, 1928

By George Rice

WITH so tremendous a subject, an attempted review of the coal situation of the world in a short talk must necessarily be of a sketchy character. It is hardly necessary to tell a body of engineers that had it not been for nature&apos;s gift of coal the material side of modern civilization would never have reached its present status. On the other side, it is regrettable that it was a byproduct of coal, T. N. T., which made possible Germany&apos;s initial success in this war, because that country had an enor-mous development of manufacturing plants that could be immediately utilized to make this destructive agent. One sometimes hears the casual remark that when the coal of the world is exhausted we shall use electricity; but, of course, electricity is ordinarily only a means of transforming and transmitting energy derived from fuel or water power, and chiefly from coal. It is true, we have much undeveloped water power, but it is more or less remote from the centers of industry; and when all shall have been developed it will not begin to supply the power requirements of the world. It is, however, reasonable to expect that before the world&apos;s supply of coal shall be exhausted, methods will have been discovered of harnessing other forces of nature, such as the tides, or the energy emanating from the sun. Petroleum and natural gas naturally come to mind, but the days of both, as fuel, appear to be numbered, although the products of petroleum, if economically used, doubtless will be available for internal-combustion engines, automobiles, trucks, and boats. for a long time, provided the reckless use of crude petroleum as an ordinary fuel is stopped. The products of petroleum are too valuable to mankind for such waste to be permitted. The civilization of the world, therefore, appears to rest, and, so far as can be seen, will indefinitely continue to rest, upon coal.

Jan 1, 1918

By Joseph E. Pogue

In 1920, 531 million barrels of crude petroleum were coi~sumed in the United States. As imposing as this figure is, the fact that the domestic consumption of crude petroleum has increased at an average rate of 10 per cent. a year for the past decade is more striking. Will this rate of increase in demand continue? If so, the year 1930 will call for 1260 million barrels of petroleum—a staggering volume. On the other hand, may we expect the demand for petroleum to grow as rapidly as it did when the automotive industry was having its most phenomenal expansion? If not, to what extent will the growth of oil requirements decrease? When and to what degree will the petroleum industry become affected by the economic law of diminishing returns? Obviously, this matter requires careful analysis, especially as both national and industrial planning must be predicated upon present estimates of the requirements of the future. The purpose of this paper, accordingly, is to project, as closely as present limitations of knowledge permit, the course of the demand for petroleum in the United States over the next ten years. At first, the problem of estimating the future of a demand as complex as that for petroleum might appear insoluble. Fortunately, hon~ever, therc are several scientific methods of approaching the problem, centering around a study of rates of industrial growth, which lend considerable hope that the requirements of the immediate future in this field may be approximated with sufficient closeness to have practical value as a basis of action. Growth oF Petroleum Demand The demand for crude petroleum is the resultant of the demands for the products made jointly from this substance—gasoline, kerosene, gas and fuel oil, and lubricating oils. The demands for these have grown at

Jan 1, 1923

By Joseph E. Pogue

In 1920, 531 million barrels of crude petroleum were coi~sumed in the United States. As imposing as this figure is, the fact that the domestic consumption of crude petroleum has increased at an average rate of 10 per cent. a year for the past decade is more striking. Will this rate of increase in demand continue? If so, the year 1930 will call for 1260 million barrels of petroleum—a staggering volume. On the other hand, may we expect the demand for petroleum to grow as rapidly as it did when the automotive industry was having its most phenomenal expansion? If not, to what extent will the growth of oil requirements decrease? When and to what degree will the petroleum industry become affected by the economic law of diminishing returns? Obviously, this matter requires careful analysis, especially as both national and industrial planning must be predicated upon present estimates of the requirements of the future. The purpose of this paper, accordingly, is to project, as closely as present limitations of knowledge permit, the course of the demand for petroleum in the United States over the next ten years. At first, the problem of estimating the future of a demand as complex as that for petroleum might appear insoluble. Fortunately, hon~ever, therc are several scientific methods of approaching the problem, centering around a study of rates of industrial growth, which lend considerable hope that the requirements of the immediate future in this field may be approximated with sufficient closeness to have practical value as a basis of action. Growth oF Petroleum Demand The demand for crude petroleum is the resultant of the demands for the products made jointly from this substance—gasoline, kerosene, gas and fuel oil, and lubricating oils. The demands for these have grown at

Jan 1, 1923

By R. E. Reed-Hill

The lattice reorientations in (1011) and (1013) twins of pure magnesium have been investigated using polarized light. Both forms (Ire subject 20 almost complete second-order twinning on the (1012) plane of the first-order twin. The observed deviations of composition planes by 6 and 3 deg, respectively, from coherent twinning planes are caused by second-order twinning. The experimental data indicate that (1011) and (1013) are reciprocal twins with a twinning shear 0.136. In a previous paper1 it was shown that the primary fracture mechanism in single crystals of magnesium strained in tension parallel to the basal plane is parting or fracture inside twins. In the temperature interval 25oto286oC, the observed twinning form, dominant in fracture, was a very small twin which formed in bands. Because these twins were very small and appeared in extensively deformed regions they did not lend themselves to X-ray analysis. Lacking Cou-ling and Pearsall&apos;s2 recently reported polarized light technique for magnesium, the twinning plane indices (K1) were originally determined by two surface composition plane measurements. This plane fell in a major zone (axis < 1120>) at an angle of 55.75 deg to the parent crystal basal plane. Because its habit deviated by 6 deg from{l0ll), 61.9 deg, the experimental data per se were not consistent with simple (1011) twinning and, for expedience, the twin was designated with habit plane indices (30341, 54.5 deg, representing the lowest set of indices corresponding to measured angles. Couling, Pashak, and sturkey3 have also found bands of reoriented lattice with a similar habit in polycrystalline specimens of magnesium and certain dilute magnesium alloys. These bands are significant because their formation in large numbers during plastic flow permit specific magnesium alloys to undergo very extensive deformation by cold rolling. Using polarized light2 they showed that the basal plane in the reoriented material was nearly parallel to the band habit and, as a result, proposed a mechanism for band formation involving a double twinning process in which (1011) twins form and then retwin according to (1012). Because of the obvious similarity between the twin bands observed in single crystals and in polycrystalline specimens, it was decided to investigate if the two phenomena were not identical and, if possible, to verify the retwinning hypothesis. The present paper is a report of this investigation and shows that the twins with the (3034) habit correspond closely to retwinned (l011) twins. Evi- dence is also given for an analogous retwinning process in (1013) twins. EXPERIMENTAL PROCEDURE Rectangular single-crystal specimen deformed in tension (stress axis in the basal plane parallel to [1010], as previously described,4 were polished electrolytically by Jacquet&apos;s method5 and etched in acetic picral.2 All twins studied in this investigation belong to a major zone, whose axis, [1210], was perpendicular to both stress axis and two sides of each specimen [(1210) surfaces]. These latter contain the plane of shear of the twins and measurements of the basal plane trace of twins on these surfaces determines the lattice orientations of the twins. The position of the basal plane in each case was determined with a polarizing microscope using a modification of the technique of Couling and Pearsall.2 For each twin the four positions of maximum extinction were measured, the data averaged, and then the pair of extinctions corresponding to the basal plane was determined by rotating the microscope stage and observing the position at which the color changed from orange to blue with a gypsum red, first-order plate inserted between the crossed Nicol prisms. EXPERIMENTAL RESULTS (1013) Twins—In general, especially in speci-mens deformed at 150°C, (1073) twins appear in greater numbers and larger sizes than (1011) twins, and the lattice reorientation inside these twins is therefore easier to study and measure. Fig. 1 shows an area of an unetched and unpolished (1210) crystal surface containing a number of (1073) twins sloping upward to the right at about 29 deg with the basal plane of the original crystal (horizontal direction). Slip line segments may be seen in both the parent crystal (running horizontally) and in the twins (sloping downward to the right at approximately -22 deg with the horizontal). As may be seen in Fig. 2, the slip lines in the twin are not at the proper angle (64 deg from basal plane of the

Jan 1, 1961

By J. Campbell

Various models are discussed for the evaluation of the negative pressures which may occur in solidifying materials which exhibit various deformation modes: elastic-plastic, Bingham, viscous, or creep flow. The inadequacy of the previously proposed elastic-plastic solution for solidifying metals is revealed by comparison with the more reliable creep results which are given graphically for aluminum, copper, nickel, and iron. The maximum tensions experienced in the liquid phase of solidifying spheres ranging in size from large castings to submicron powders are in the range from —10&apos; to —105 atm for these metals. THERE has been much recent interest in the negative pressures associated with the volume change on solidification and in the possibility of the occurrence of cavitation. Considering the freezing of a highly supercooled liquid, an attempt to evaluate the stresses in the liquid ahead of the rapidly moving solidification front has been made by Horvay1 on a microscale and by Glicksman2 on a macroscale. In a casting of a wide freezing range alloy, the pressure differential due to viscous flow of residual liquid through the pasty zone has been discussed by Piwonka and Flemings,3 In a previous publication4 the author has attempted to estimate the negative pressure occurring in the residual liquid of a spherical casting, employing an elastic-plastic model to describe the collapse of the solidified shell under the internal tension. An earlier model assuming a rigid shell was shown to be inaccurate by many orders of magnitude. The elastic-plastic model is critically reviewed here, and other models are developed which are thought to be more closely related to metals and other materials near their melting points. The spherical geometry (Fig. 1) is chosen because the highest shrinkage pressures would be developed, although the analyses are readily adaptable to cylindrical geometry. A parallel sided casting experiences little internal tension because of the relatively easy dishing inward of the sides. (This commonly observed phenomenon has previously been attributed solely to atmospheric pressure.) Furthermore, small regions of confined liquid in a large solidified volume of a casting approximate reasonably well to spherical geometry. ELASTIC-PLASTIC MODEL The author has shown4 that as solidification proceeds the internal hydrostatic tension builds up until the elastic limit of the shell is exceeded. At this point the internal pressure is closely -2Y/3. Subsequently a plastic zone spreads from the inner surface toward the outer surface of the shell. When the whole casting is deforming plastically a rather more generalized analysis taking account of the externally applied pressure PA + 2y/b gives the internal pressure as: P = Pa + 2y/a + 2ys/b - 2 Y In(b/a) [1] The 2y/a and 2ys/b terms result from the tendency of the liquid-solid and solid-vapor interfaces to shrink, reducing their energy, and thereby helping to collapse the solid phase and compress the liquid phase. The 2y/b term would be important only for powders. The last term arises because of the plastic restraint of the solid, resisting collapse and so effectively expanding the residual liquid. From Eq. [I] it is easily shown that there is a minimum in the pressure at the radius amia= y/Y [2] which is of the order of 103K for the metals aluminum, copper, and iron, and corresponds to the minimum pressure Pmin = 2 Y[l-ln(bY/y [3] The results of a fully worked out elastic-plastic solution are given in a previous reporL4 The main criticism which may be leveled at this analysis when applied to metals at their melting points is the strong dependence of the yield stress on the strain rate. The strain rate varies with both solidification conditions (e.g., whether chill-cast or slowly cooled) and during solidification, as is indicated in the following section. Thus an appropriate choice of Y is very arbitrary. Before proceeding to a discussion of models which are strain-rate-dependent, it is necessary to evaluate the strain rate as a function of the rate of solidification. SOLIDIFICATION RATE Various empirical relations have been deduced5 for the rate of thickening of the solid shell by pour- out tests on partially solidified spheres. These, however, are unsatisfactory for our purposes since they become very inaccurate when the liquid core is very small. A theoretical approach is therefore necessary, and some solutions are set out below. Making the assumptions of constant surface temperature of the casting during freezing, no superheat, and a material freezing at a single temperature, Adams8 deduces the approximate solution: which becomes when b » a: Employing a semiempirical approach vallet6 finds:

Jan 1, 1969

By A. D. K. Laird, John A. Putnam

This paper describes the application of x-ray theory to design procedures in connection with fluid saturation determinations during fluid flow experiments with porous media. A reliable and rapid method for calibrating the x-ray apparatuy is described. Extension of the method to fluid saturation determinations in three-fluid systems is described. INTRODUCTION In rerearch on oil production problems a method is required which will give quickly the quantity of each component of a fluid flow system present at any cross-section of a porous medium. The sample of porous medium under investigation is usually referred to as a core. The ratio of the volume of one component to the total fluid volume is defined as the saturation of the porous medium by that component. This ratio is generally given as per cent saturation. Some means of measuring saturation which have received consideration include: electrical conductivity of the fluids;1,2 emissions from radioactive tracers dissolved in the fluids; the radioactivity of silver caused by reflection of neutrons from hydrogen atoms in the fluids;&apos; the attenuation of a microwave beam. the diminution and phase shift of ultrasonic wave trains.4,5 and the reduction in intensity of x-ray beams in passing through the fluids. X-rays have already been used with some success. Since every material has a different power to absorb x-rays, the reduction in intensity of an x-ray beam as it passes through a core depends on the fluids present. The strength of the emergent beam can be found by converting its energy into a measurable form such as heat or ionic current. or by its effect on a photographic plate or fluorescent screen. The beam strengths could be interpreted as quantities of known fluids in the core if, previously, these beam strengths had been identified with a known combination of the same fluids. With some fluid cornbinations it might be desirable to dissolve powerful x-ray absorbing materials in one or more of the fluids, to increase the differences in the beam strengths for various fluid saturations. Boyer, Morgan and Muskat6 have described a method of measuring two component fluid saturation. One component was air or water; the other. minerat seal oil in which was dissolved 25 per cent by weight of iodobenzene to increase its absorbing power. The x-ray source was a tungsten target tube operated at 43 kv potential. The beam emerging from the core was measured as ionic current flowing across an air-filled ionization chamber by means of an amplifying circuit and galvanometer. Another portion of the beam from the x-ray tube was passed through a metal plate and measured in another ionization chamber. This portion, called the monitor beam, was used as an indication of the performance of the x-ray tube. The galvanometer readings were calibrated against air-oil core saturations, gravimetrically determined. The method was apparently established by experimental means. In the present investigation the available theory of x-radia-tion was surveyed with a view to extending the usefulness of the method and to developing design procedures for its application to measurement of fluid saturation in porous media. Application of the theory permits prediction of relative meter readings to be expected for any combination of porous matrix, various saturating fluids and auxiliary filtering media. It is thus possible to calibrate the equipment in terms of fluid saturation by an indirect but rapid technique. The results of calculations based on x-ray theory indicate. and results of the saturation calibration technique confirm. that a valid measurement of the saturation of the core can be made for any two components and in some cases for three components. THEORY The strength of an x-ray beam, after it has passed through a distance. 1, of matter of density, p, and mass absorption coefficient, µ at a given wavelength, A, may be expressed by the absorption formula I = I0 e ...........(1) where I, represents the intensity of the incident x-ray beam and I is the intensity of the emergent beam. The expression e is called the transmission factor of the material. The variation of I,, with wavelength depends upon the materials through which the x-ray beam has previously passed and upon the spectral distribution of energy at the source of the x-radiation. A group of curves. called spectra. which show the variation of intensity with wavelength and x-ray tube voltage are given in Fig. 1. These curves represent the general radiation from a tungsten target tube. When the tube voltage is greater than 69.3 kv, the characteristic radiation of the tungsten is emitted and is superposed on the general radiation. At a given voltage the minimum wavelength A,,,,, at which energy can be emitted by an x-ray tube is given by the formula 12,340 xml. = ——..........(2) volts where A,.,,.. is in Angstrom units. The wavelength at which the spectra have maximum intensity a1so decreases with increasing x-ray tube voltaue. The area under each curve represents to an arbitrarv scale the total energy emerging from the x-ray tube for that voltage. The variation of µ with wavelength has been determined for many substances and may be found in such references as those by Compton and Allison7 and by Hodgman.8 The phenomenon of absorption is composed chiefly of the capture of photons by the atoms of the absorbing material with associated displacement of electrons, and of the scattering, or the deflection, of the photons by the atoms. Curves of these mass absorption coefficients show jump discontinuities. or absorption edges. at wavelengths which are short enough for the photons,

Jan 1, 1951

By John A. Putnam, A. D. K. Laird

This paper describes the application of x-ray theory to design procedures in connection with fluid saturation determinations during fluid flow experiments with porous media. A reliable and rapid method for calibrating the x-ray apparatuy is described. Extension of the method to fluid saturation determinations in three-fluid systems is described. INTRODUCTION In rerearch on oil production problems a method is required which will give quickly the quantity of each component of a fluid flow system present at any cross-section of a porous medium. The sample of porous medium under investigation is usually referred to as a core. The ratio of the volume of one component to the total fluid volume is defined as the saturation of the porous medium by that component. This ratio is generally given as per cent saturation. Some means of measuring saturation which have received consideration include: electrical conductivity of the fluids;1,2 emissions from radioactive tracers dissolved in the fluids; the radioactivity of silver caused by reflection of neutrons from hydrogen atoms in the fluids;&apos; the attenuation of a microwave beam. the diminution and phase shift of ultrasonic wave trains.4,5 and the reduction in intensity of x-ray beams in passing through the fluids. X-rays have already been used with some success. Since every material has a different power to absorb x-rays, the reduction in intensity of an x-ray beam as it passes through a core depends on the fluids present. The strength of the emergent beam can be found by converting its energy into a measurable form such as heat or ionic current. or by its effect on a photographic plate or fluorescent screen. The beam strengths could be interpreted as quantities of known fluids in the core if, previously, these beam strengths had been identified with a known combination of the same fluids. With some fluid cornbinations it might be desirable to dissolve powerful x-ray absorbing materials in one or more of the fluids, to increase the differences in the beam strengths for various fluid saturations. Boyer, Morgan and Muskat6 have described a method of measuring two component fluid saturation. One component was air or water; the other. minerat seal oil in which was dissolved 25 per cent by weight of iodobenzene to increase its absorbing power. The x-ray source was a tungsten target tube operated at 43 kv potential. The beam emerging from the core was measured as ionic current flowing across an air-filled ionization chamber by means of an amplifying circuit and galvanometer. Another portion of the beam from the x-ray tube was passed through a metal plate and measured in another ionization chamber. This portion, called the monitor beam, was used as an indication of the performance of the x-ray tube. The galvanometer readings were calibrated against air-oil core saturations, gravimetrically determined. The method was apparently established by experimental means. In the present investigation the available theory of x-radia-tion was surveyed with a view to extending the usefulness of the method and to developing design procedures for its application to measurement of fluid saturation in porous media. Application of the theory permits prediction of relative meter readings to be expected for any combination of porous matrix, various saturating fluids and auxiliary filtering media. It is thus possible to calibrate the equipment in terms of fluid saturation by an indirect but rapid technique. The results of calculations based on x-ray theory indicate. and results of the saturation calibration technique confirm. that a valid measurement of the saturation of the core can be made for any two components and in some cases for three components. THEORY The strength of an x-ray beam, after it has passed through a distance. 1, of matter of density, p, and mass absorption coefficient, µ at a given wavelength, A, may be expressed by the absorption formula I = I0 e ...........(1) where I, represents the intensity of the incident x-ray beam and I is the intensity of the emergent beam. The expression e is called the transmission factor of the material. The variation of I,, with wavelength depends upon the materials through which the x-ray beam has previously passed and upon the spectral distribution of energy at the source of the x-radiation. A group of curves. called spectra. which show the variation of intensity with wavelength and x-ray tube voltage are given in Fig. 1. These curves represent the general radiation from a tungsten target tube. When the tube voltage is greater than 69.3 kv, the characteristic radiation of the tungsten is emitted and is superposed on the general radiation. At a given voltage the minimum wavelength A,,,,, at which energy can be emitted by an x-ray tube is given by the formula 12,340 xml. = ——..........(2) volts where A,.,,.. is in Angstrom units. The wavelength at which the spectra have maximum intensity a1so decreases with increasing x-ray tube voltaue. The area under each curve represents to an arbitrarv scale the total energy emerging from the x-ray tube for that voltage. The variation of µ with wavelength has been determined for many substances and may be found in such references as those by Compton and Allison7 and by Hodgman.8 The phenomenon of absorption is composed chiefly of the capture of photons by the atoms of the absorbing material with associated displacement of electrons, and of the scattering, or the deflection, of the photons by the atoms. Curves of these mass absorption coefficients show jump discontinuities. or absorption edges. at wavelengths which are short enough for the photons,

Jan 1, 1951

By Lynn C. Jacobsen

Among the unforeseen consequences of the 1973 Arab oil embargo has been a considerable array of new or increased taxes on the so-called energy minerals. These taxes will be the subject of this report. Both Federal and State taxes have been enacted, but I will be concerned mostly with state severance taxes and particularly those on uranium. Severance taxes are considered to include all taxes having the distinctive feature of being applied on a natural resource at the stage of extraction. The tax may be based on units of production or on value, and if on values it may be on gross value or on gross value less either arbitrary or cost-related deductions. The tax has a number of aliases - resource excise tax, conservation tax, privilege tax, mining excise tax, ad valorem production tax, and more - and this makes comparison of tax burdens among states difficult. The windfall profit tax on oil is an example of a severance tax at the Federal level. Severance taxes are an established feature of state tax systems, but they continue to be a controversial issue, and proposals to raise or modify existing severance taxes are regularly submitted to the legislatures of the Western energy producing states. No concensus exists as to what is a reason- able and proper level of severance taxation or to the form it should take. The taxes which have been adopted by the various states reflect the interaction of a variety of interests and the specific circum- stances in each state. What follows is a summary of theoretical, practical, and emotional viewpoints and arguments that surface in any statehouse in which a severance tax bill has been introduced. The New Mexico experience will be heavily relied upon. THE ECONOMISTS Marginal effects. A severance tax which is based on a gross percentage of revenue or on units of production is a constant addition to variable costs, and to the mine operator has the same effect as any other increase in operating costs. The direction of these effects is straightforward: the tax will cause the property to have a lowered present value, to be mined at a lower rate than without the tax, raise the minimum grade that will be mined, lead to lower total recovery, make marginal properties sub-marginal and discriminate in favor of richer, more profitable operations (Lockner, 1965; Steele, 1967). In the short run, production facilities are fixed and imposition of a severance tax will have little effect on production levels. In the longer term, capital is mobile and investment and exploration expenditures will shift from minerals and jurisdictions with high taxes to those with low taxes. Over a considerable range of taxation the effect will be to change the relative position of the taxing state, but an overly optimistic evaluation of the capacity of mineral producers to absorb a tax can bring an industry to a halt. It is generally acknowledged that imposition of high severance taxes on taconite in Minnesota stopped development completely, and that only the adoption of a constitutional amendment limiting the amount of taxes that could be imposed in the future brought the firms back and encouraged them to make the huge investments required (Weaton, 1969). A tax which is a percentage of the net operating income (gross revenue less cash operating costs) does not influence the cut-off grade for recovery nor change the time preference for extraction, and hence, is free of the negative features of the tax applied to gross revenues or units of production. In theory it is a more efficient tax but relative administrative complexity and inherent difficulty in predicting revenue have discouraged its use. The Wyoming severance tax on uranium, which uses grade of ore as well as price in establishing taxable value, is the most cost related, and hence, the most neutral and efficient of the various state severance taxes on uranium. Economic rent. Despite the discrimination and the anti-conservation aspect inherent in most severance taxes, economists generally endorse their use because they are seen as a vehicle to appropriate rents - that is, returns greater than the long-run competitive supply price. Conspicuous examples of supposed economic rents are the returns to oil producers because of the OPEC cartel, the returns of the uranium producers under AEC buying contracts in the 19501s, and the high prices obtained by the uranium producers for contracts entered into in the 1976-1979 period. Mining of coal in the Western states is believed by some to generate huge economic rents because of the OPEC caused increase in price of a competitive fuel (McLure, 1978, p. 261), and possibly because of clean air regulations favoring the burning of low-sulfur coal. In theory, such surplus returns could be taxed completely away without affecting supply. In practice, the situation is more complex (Steele, 1967, pp. 234-236); economic rent of mineral production is an elusive quantity involving as it does replacement costs, and technical and market risk, and it, like beauty or pornography, probably exists mostly in the eye of the beholder. Rent may also be perceived to be present in the upper portion of a cyclic market which also has a downside. Where rent exists, it is almost certain to be short-lived - cartels self- destruct, government subsidies end, competitive adjustments occur - but the taxes imposed to capture it tend to be immortal. There is little doubt that the perception of un- usual and undeserved (obscene) profits in the mid- and late 1970&apos;s was a major factor in the adoption of energy mineral taxes strikingly higher than had been previously considered. At the New Mexico legislature of 1977 supporters of a moderate tax were repeatedly confronted with some variant of the statement, "You can&apos;t expect me to believe that a

Jan 1, 1982

By T. M. Geffen, J. L. Sanderlin, F. F. Craig, D. W. Moore

Scaled reservoir models have been used to study the effect of gravity on oil recovery performance in frontal-drive operations; namely, water, gas, or solvent flooding. The difference in density between the reservoir oil and the injected fluid causes their segregation, resulting in a non-uniform advance of the fluid front. In the laboratory flow tests, which simulated both five-spot and linear injection operations in flat reservoirs, the viscous, capillary, and gravity forces present in these operations were scaled. Dyed fluids were used so that the gross movement of the injected fluid could be observed. The studies covered a range of injection rates, formation thicknesses, and rock and fluid properties normally encountered in field operations. The results of the model tests indicate that the volume of the reservoir contacted by the injected fluid at its breakthrough into the producing well is less than that expected based on information which neglects gravity effects. This difference can often be as much as 80 per cent by gas or water injection in uniform sand bodies. Preliminary flow tests on a non-uniform sand body indicate that the uniformity of the flood fronts may in some situations be influenced to a much greater degree by permeability variations within the rock body than by gravity effects. The magnitude of fluid segregation due to gravity is controlled by the average injection rate, rather than day to day or week to week variations. INTRODUCTION One of the important factors controlling the oil recovery from a frontal-drive operation, such as water, gas, or solvent injection, is the volumetric sweep efficiency. This factor is a measure of the gross portion of the reservoir that is contacted by the displacing fluid. The volumetric sweep efficiency is influenced by gravity effects, well arrangements, and variations in rock permeability within the reservoir. The gravity effects are due to the displacing fluid being of different density than the reservoir oil. This causes the displacing fluid to move preferentially toward either the top or bottom of the formation. Non-uniform advance of the flood front can be caused by the relative positions of the injection and production wells. Variations in rock permeability also result in an uneven advance of the displacing fluid. Gas zones, representing paths of low resistance, may result in non-uniform movement of the injected fluid. The more uneven the advance of the displacing fluid, the lower is the volumetric sweep efficiency and thus the lower the oil recovery efficiency. The effects of well arrangement and permeability variations, upon the gross movement of the injected fluid have been the subjects of extensive investiga-ti0ns.1,2,3,4,5,6 Gravity effects have been recognized as being present in frontal-drive operations&apos;.&apos; but there has been little quantitative measure of their magnitude. Very likely the reason gravity effects have not been studied is that this problem does not lend itself to simple experimental or mathematical analysis. The development of reservoir modeling techniques has made possible a quantitative determination of the effect of gravity on fluid segregation and thus upon the oil recovery performance of frontal-drive operations. This paper presents a progress report on a laboratory investigation of gravity effects in fully liquid-saturated, horizontal, uniform as well as non-uniform systems. These results were obtained from scaled experiments on both linear and five-spot systems within the range of conditions normally encountered in secondary recovery operations. This study is concerned with the gross movement of the injected fluid to the time it first reaches the production wellbore. Therefore, it should be emphasized that the results of this paper can not be used to determine the effect of gravity segregation on oil recovery efficiency at abandonment conditions. MODEL SCALING The science of scaling models is relatively new as applied as petroleum production problems, Many of the scaling techniques have been adaptions of those used in basic studies of heat and fluid flow. There are

Jan 1, 1958

By Sid T. Killan

The utilization of the reducing power of blast-furnace gas can be estimated by applying two rectifying calculations to the gas analysis. A resulting corrected CO/CO2 ratio varies inversely with furnace production. Directions for calculating the corrected CO/CO2 ratio are given, and a corrected CO/CO2 ratio is compared with actual furnace production. THE inadequacy of the normally accepted CO/CO, ratio as a measure of blast-furnace performance and furnace efficiency was discussed following the presentation of the paper by H. F. Dobscha.&apos; In this outstanding example of careful observation on large scale blast-furnace operation, the changes occurring with beneficiated ores were: 1—A net gain in tonnage of 21.2 pct. 2—A decrease in net coke of 15.3 pct. 3—A decrease of 1.9 pct in the CO/CO, ratio. In this great change in furnace performance, the CO/CO, ratio proved itself worthless. The discussion of the inadequacy of expressing furnace performance and efficiency by the CO/CO, ratio led indirectly to the calculations forming the basis of this paper. At that time Dr. T. L. Joseph said: "We must consider difference in CO, from the stone in the two cases when we talk about the ratios of CO/C02." This statement is used for the second of the two CO/CO, ratio corrections forming the basis of this paper. The research work in attempting to find out why the furnaces could op-erate so differently with practically the same CO/CO, ratio lead not to the answer sought but, after a shift to the gaseous phase in the research work, the proof that the normal CO/ CO, ratio was outmoded and a new corrected ratio should replace it. To be of any value, any new corrected ratio should express approximate furnace efficiency and give an idea of practical furnace performance to be expected. This the normal CO/CO, ratio has failed to do. However, in the absence of anything better, some credence has been attached to the normal CO/CO, ratio. As far as the writer can ascertain, the present paper is the first attempt to change or improve the normally accepted index of

Jan 1, 1952

By Henry B. Smith, S. Paul Lindau

ThREe years ago it was decided by the management to granulate the matte that is produced in the smelter of the St. Joseph Lead Co. at Hereulaneum, Mo., thereby doing away with a large amount of labor in handling the matte and in subsequent crushing. On Mar. 1, 1915, the granulator was put in operation and up to Jan. 1, 1916, 18,735 tons had been granulated. The four blast furnaces have a daily output of about 280 tons of pig lead and 100 tons of matte assaying about 11.0 per cent. Pb. It is expected that projected improvements in roasting methods will eliminate more sulphur from the charge, and cut down the matte-fall to about one-half of the present figure. The blast furnaces are tapped into movable forehearths or settlers, 6 ft. by 4 ft. by 22 in., the slag overflowing into 27-cu. ft. slag cars which are hauled to the dump by electric locomotives. Previous to the adoption of granulation, the matte was tapped from the forehearths into small slag pots which were dumped after cooling. The matte cakes were broken with sledges, and transported to the crushing plant for fine crushing and screening. Here the matte was reduced to 1/4-in. size before being fed to the roaster bins. A Wedge and a Holthoff mechanical furnace are used for preroasting before sintering on the Dwight and Lloyd machines. The matte is returned to the furnaces as an iron flux until the gradually accumulating copper content reaches about 7 per cent., after which it is put aside to be concentrated in a small copper blast furnace, the resultant high-grade matte being sold. When the matte does not settle readily from the slag, two settling devices are often used, the second one being a large catch-pot, which gathers any matte that may overflow from the forehearth, the slag then overflowing from the catch-pot into the slag cars. When full of matte, the catch-pot is removed, allowed to cool, and the contents broken and crushed. a With the present plan of granulating, the matte is tapped into 6-cu. ft. iron ladles. These are transported to the granulating plant by a 5-ton

Jan 1, 1917

By V. A. Phillips

Transmission-electron micrographs of electro-thinned samples of bulk-aged Cu-3.1 pet Co alloy show an aging sequence, supersaturated solid solution — coherent particles — quasi -coherent particles — noncoherent particles. Hardening is due to precipitation of coherent spherical fee coball-rich particles showing coherency strain fields, which are resolved at between 15 and 30A diameter. Loss of- full coherency did not occur until well into the overaged region, even with the assistance of deformation after aging. Different average particle diameters of 123, 92, and 149 ± 10Å were observed in samples aged to peak yield strength at 600°, 650°, and 700°C, respectively, indicating that there is no critical size for peak hardening. Noncoherent particles tended to develop (111) faces and became octahedral in shape. Dislocations tended to nucleate spherical coherent particles which eventually grew together forming large elongated particles. The surface energy of a noncoherent (low-angle) inter-phase boundary is estimated to he about 50 ergs per sq cm. A number of particle lining-up phenomena were observed. Overaging is principally attributed to increase in particle spacing, progressive loss of coherency, and increase in amount of discontinzdous precipitation. COPPER dissolves about 5.6 at. pet (5.2 wt pet) of cobalt at 1110oC1 and the solubility decreases to 0.75 at. petl (0.54 at. pet)2 at 650°C and to 0.1 at. pet or less at lower temperature.&apos; It has been known for many years3-5 that Cu-Co alloys are capable of age hardening. Since cobalt is fee above 417°C and its atom size is only about 2 pet smaller than that of copper, precipitation of coherent particles would be expected. The equilibrium phase precipitated at 700°C and below contains about 10 pet Cu in solution which tends to stabilize the fee structure, lowering the transformation temperature to 340oc.l The alloy is known to undergo discontinuous precipitation in addition to general precipitation; while the former can be seen with an optical microscope, the latter precipitates are not visible except in the grosly overaged condition.5, 6 Extensive use has therefore been made of the ferromagnetic properties of the precipitate in order to follow the course of aging, and it has proved possible to measure the average particle size, spacing, approximate shape, and volume fraction and to determine that the particles are coherent without ever seeing a particle (see for example Refs. 2, 7, and 8). The magnetic measurements of particle size are limited to diameters below about 120Å.7 The present study was undertaken using the techniques of transmission-electron microscopy in order to check the above conclusions, to extend the previous magnetic work to larger particle sizes, and to attempt a more detailed correlation of properties and structure. A portion of this work has already been published.9-11 The present paper is concerned with the metallographic features of precipitation in relation to aging curves. Bonar and Kelly12&apos;13 have published preliminary results of a similar study on single crystals of Cu-2 at. pet Co. EXPERIMENTAL Preparation of Alloy. A Cu-Co alloy, containing 3.12 wt pet (3.36 at. pet) Co by analysis, was prepared from 99.999 pet purity oxygen-free copper and electrolytic-grade cobalt. The alloy was melted and cast in vacuo in a high-frequency furnace using a graphite crucible and mold: Analysis showed chat 0.004 pet C was picked up during melting. The 1-1/2-lb ingot was homogenized in hydrogen for 24 hr at 1000°C. Slices were cold-rolled to 0.005 or 0.003 in. thickness, with an intermediate 650°C anneal in hydrogen at 0.080 in. thickness. Batches of six to ten strips were solution-treated in sealed-off quartz tubes in high vacuum in a vertical furnace and quenched by dropping into iced brine containing a device which snapped off the nose of the tube. Solution treatment consisted of 1 hr at 990°C or 2 hr at 965°C. The latter was employed for all mechanical-property studies, since a tendency was noted for the higher temperature to give porous material. Strips were usually aged individually in a horizontal vacuum furnace, inserting into the hot zone and withdrawing into a cold zone without breaking the vacuum. This method gave a rapid heating rate, permitting the use of short aging times. In some cases, particularly for the longer aging times at the higher temperatures, samples were sealed individually in quartz tubes in high

Jan 1, 1964

By A. W. Adamson

A model for transport processes in liquid mixtures is discussed which supposes that the elementary act involves a position exchange between two species and that the exchange is so confined by the solvent cage as to occur nearly isosterically. The rate-determining step, thus, is likened to a bi-molecular reaction and is so treated, using absolute rate theory. The cage model has been applied to diffusion, thermal diffusion, sedimentation and viscosity, but only the first and last of these phenomena are emphasized in the present paper. The model leads to semi-empirical relationships between the absolute value for a digusion coefficient and the activation energy for diffusion, between mutual and self-diffusion coefficients and for the variation of the viscosity of a binary mixture with composition. These are discussed in relation to experimental data for various systems, including hydrocarbon mixtures. It is shown that the proposed viscosity equation and seven other commonly used ones all may be regarded as special cases of a single general relationship; a brief critical analysis is made of the basis of selection of one or the other for data fitting or interpolation. INTRODUCTION AND GENERAL THEORY The present paper covers a brief discussion of a cage model for transport processes in liquid mixtures and how this model may be useful in treating the diffusional behavior and the viscosity of such systems. Since diffusion requires the more detailed treatment, it will be taken up first, and the model then applied to viscosity. There are two types of diffusion coefficients that may be measured experimentally, apart from thermal diffusion quantities. The first is the mutual or binary diffusion coefficient, D which may be defined in terms of Fick&apos;s first law. This states that the permeation, or flux P, is proportional to the concentration gradient. In the usual experiment, P is measured relative to a frame of reference fixed with respect to the medium (e.g., the diaphragm in a diffusion cell); as a consequence, the same value of D is obtained regardless of whether P and C refer to Component 1 or to Component 2; i.e., there is only one independent mutual diffusion coefficient for a binary system. In addition to D there will be various self-diffusion coefficients. defined in terms of the gradient in labelled species i and its permeation in an otherwise uniform medium. The thermodynamic approach to mutual diffusion supposes that the actual driving force is the gradient of the chemical potential, i.e., that In the case of a dilute solution of solute, Eqs. 1 and 3 lead to the Einstein equation, If the solution is ideal and the friction coefficient is taken to be then the familiar Stokes- Einstein equation results. Mutual and self-diffusion coefficients can not be related on general thermodynamic grounds; it is necessary to invoke some additional assumptions, i.e., a model; several such have been proposed. Hartley and Crank&apos; supposed the existence of separate, intrinsic diffusion coefficients (Dl and D2) for each component, essentially corresponding to the two self-diffusion coefficients. The two flows can not be independent, however, but must be coupled through the usual restriction that there be no net volume flow. For an ideal solution. one then obtains&apos; Glasstone, et al&apos; treated diffusion in terms of absolute rate theory, but their approach otherwise resembled the previously mentioned one in that each species was considered to move with respect to the general medium in a manner determined by its individual jump distance and specific rate constant. For other than dilute solutions, a coupling of flows leading to an equation such as Eq. 6 would again be present. However, as required by Eq. 6, one does expect that the self-diffusion coefficient for the solute and the mutual-diffusion coefficient for the system become identical at infinite dilution. Lamm4 recognized that there should be three distinctive interactions in a two-component system-1-1, 1-2 and 2-2 — and, therefore, proposed three rather than two fundamental friction coefficients. Mutual diffusion resulted from 1-2 interactions only, and self-diffusion resulted from 1-2 plus either 1-1 or 2-2 interactions. Again, a collective coupling between all motions was imposed to meet the condition of no net volume flow. Laity&apos; has shown how to convert the Onsager equations to a form very similar to Lamm&apos;s. Cage Model For Diffusion Work in this laboratory on diffusion in aqueous sucrose solutions made it apparent that three, rather than two, interactions were indeed needed," but considera-

By F. H. Wilson, M. L. Kronberg

The low temperature recrystalliza-tion of very heavily rolled copper produces a fine grained structure with a high degree of preferred orientation. Additional heating to within a few hundred degrees of the melting point may induce an abrupt and pronounced increase in the grain size, with the resulting crystals having new orientations. This behavior at high temperatures is commonly termed "secondary recrystallization." Several investigations have dealt with the phenomenon arid have served to bare many features of the beha~ior.1-4 In general,observations have been made on the sizes and shapes of the grains, and data have been presented showing the existence of an induction period in isothermal experiments. Although it has been well established that the orientation before the change is statistically (100) 10011, the so-called "cubically aligned" texture, there is no such agreement on the orientation after the change. For example, Dahl and Pawlek1 describe it as being equivalent to an approximately 30" rotation about the [l00] axis of the ideal cubic texture which is parallel to the rolling direction, the resulting orientation being near (210)[001]; and Cook and Richards2 find an orientation of approximately (110)[L12]. Since the completion of most of the work to be reported in this paper, Rowles and Boas3 have published their ver] illuminating paper on "secondary recrystallization," in which they present convincing evidence for a third orientation and show that their esperiments give no evidence for either of the other two orientations. The orientation is described as equivalent to an approximately 30° rotation about a [ 111] pole of the ideal cubic orientation. The existence of a variety of reported orientations is not unique for copper, for a similar state of affairs exists for other systems that have been studied— aluminum, nickel, nickel-iron alloys, and others. It seems therefore that the existence of this variety does not necessarily constitute a contradiction, but rather indicates that different experimental conditions yield different results. The fundamental nature of the phenomenon has not been elucidated. However, it has been generally recognized that the large grains could be the end product of growth of a few select grains already existing in the sample in minor amounts—too small to allow detection—or that entirely new ones could be formed by a process of nu-cleation and growth. Existing experimental evidence does not distinguish between these two most apparent possibilities. Nevertheless, the former has been more generally favored largely because our current understanding of the state of an annealed metal has not made it seem reasonable to expect a nucleation event to occur at temperatures above those required for the primary recrystallization. Observations on the Preparation and Heating of Twin-bearing Cubically Aligned Copper The starting material used throughout. the investigation was a bar of OFHC copper, forged and annealed at 950°C. Visual inspection showed the grain size to be around 0.5 mm, and did not disclose any preferred orientation. A chemical analysis showed the following composition: Cu + Ag— 99.99 Pct S — 0.005 pct 0 — <0.005 pct For the preparation of cubically aligned copper, ¾ in. thick slabs were cut from the bar, heavily pickled in concentrated HNO3 and cold rolled to sheets about 0.012 in. thick. The reduction in thickness was approximately 98.5 pct. Standardized annealing techniques were followed. Samples to be heated were lightly dusted with alumina in order to prevent sticking and then sandwiched between 1/16 in. copper plates. The resulting sandwich was heavily wrapped with copper sheet, and then annealed in air. The protection was such that only very thin films of oxide were formed. That the associated light oxidation of the samples had no specific effect on the recrystallization behavior was shown by the similar results that could be obtained on annealing in highly purified and dried hydrogen. Two methods were used in bringing samples to temperature: (1) by placing the package directly in the furnace at temperature and (2) by placing the package in the furnace at room temperature, and then slowly increasing the temperature. The corresponding heating rates are illustrated in Fig 1, and will be referred to as "rapid" and "slow," respectively. Unless specified otherwise, all anneals will be of the former type. Metallographic examination was made on samples prepared by electrolytic polishing and etching as described in the Metals Handhook.* STRUCTURES FOUND BEFORE "SECONDARY RECRYSTALLIZATION" OCCURS Annealing the rolled material for 1 hr at 400°C produced a heavily twinned, cubically aligned structure, the grain size being of the order of 0.03

Jan 1, 1950