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By L. J. Kashar

By means of a continuum-mechanics approach, the following equation for calculuting the pressure for axisymmetric cold forging has been derived: where P is the extrusion pressure; K and n are the strength coefficient and the strain-hardening exponent of the steel, respectively; a and b are strain factors, primarily dependent on the die design; and R is the extrusion ratio. Data from compression and backward-extrusion tests performed at a crosshead speed of 0.5 in. per min on a nonwork-hardening material pure lead) and on a work-hardening material (1018 steel) indicate that the predicted extrusion pressures obtained from the derived equation agree very closely with the actual extrusion pressures. Therefore, the equation can be used to predict backward-extrusion pressures from standard mechanical-test data. The decision to cold-forge a part is based on several considerations, most of them related to economics. However, the production feasibility is usually determined by the pressure needed to extrude the part and the availability of tooling that can repeatedly sustain this pressure for over several hundred thousand cycles. A major contribution to the cold forging of steel would result from the development of steels that could be forged at reduced pressures and from the development of techniques that permit the accurate prediction of the pressure necessary to cold-forge the part. The ability to predict extrusion pressures is necessary to properly design the tooling required for the cold-forging process. Attempts to theoretically predict the cold-forging pressure, especially for work-hardening materials, have been unsuccessful in previous investigations of the cold-forging process.1-3 Many empirical relations have, therefore, been proposed relating the extrusion pressure to the chemical composition,' the extrusion ratio,2 the tensile strength,273 and hard- ness, 2 and the yield strength3 of the material being extruded. However, these empirical relations are valid only for the specific conditions used in their development, and, in some cases, the empirical relations had a scatter band greater than * 10 pct. A study of the extrusion process was undertaken with the objective of developing predictor equations for extrusion pressure by using a continuum-mechanics approach to the problem of metal flow. The derivation of such an equation is summarized in this paper, and data are presented that confirm the validity of the derived equation. DERIVATION OF THE EXTRUSION EQUATION If the extrusion of a material through a die is considered in terms of a work balance, it has been shown that it is possible to derive an equation relating the work necessary to move the material through the die to the deformation work undergone by the material. The work done, W, in moving the material is given by where F is the extrusion force, I, is the distance the material was moved, A, is the original cross-sectional area of the material, P is the extrusion pressure acting on A,, Ap is the cross-sectional area of the extrusion punch, and Pp is the punch pressure acting on Ap. The deformation work, WD, is given by where V is the volume of metal deformed, ay is the flow stress of the metal, and E is the total strain undergone in the extrusion. If there are no frictional losses, the work done, W, is equal to the deformation work, WD; therefore, Since the volume of a metal does not change during deformation,

Jan 1, 1968

By W. A. Tiller, W. C. Johnston

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By J. E. Harris

By elimination of other possible nucleation processes, it has been demonstrated, for commercially pure magnesium and a Mg-Al alloy, that at stresses less than that necessary for triple-point cracking creep cavities are most probably nucleated heterogeneously at second-phase particles. Evidence for the existence of such particles is presented and the role of grain boundary sliding in the nucleation process is examined quantitatively. DURING creep deformation of polycrystalline magnesium and its dilute alloys in the temperature range 0.45 to 0.7 Tm (Tm = absolute melting temperature) cavities form mainly along grain boundaries oriented normal to the stress axis and failure eventually occurs by their growth and impingement.' The possibility of low-ductility creep failure of magnesium-alloy reactor cans during service has prompted a number of studies of cavity formation in these materials.2-5 In this paper divergent theories of cavity nucleation6-10 are examined critically and conclusions drawn regarding the most probable mechanism of formation of cavities in magnesium. The paper is divided into two parts. The first section consists of the review and quantitative assessment of the possible role of grain boundary sliding in the nucleation process. In the second part an experimental program is described where an electron-microscope technique has been used to determine if second-phase particles exist in as-received commercially pure magnesium and in a magnesium alloy 1) THEORETICAL REVIEW Possible nucleation sites for creep cavities are: a) high-angle grain boundary triple points,11-14 b) subboundary/grain boundary intersections,15-18 c) ledges in the grain boundary, 19-25 d) second-phase particles. 9,26-30 Each of these possibilities is now considered with special reference to deformation of magnesium. 1.1) Triple-Point Cracking. The stroh31 condition to nucleate fracture is: " > vr [1] where ss = applied shear stress, ? = surface energy, C = shear modulus, L = length of sliding interface. This relationship is independent of the nature of the interface and it is possible to calculate the stress concentration at the end of a sliding high-angle grain boundary and thus deduce, approximately,* the minimum applied stress necessary to nucleate triple-point cracking. Such theoretical predictions for Nimonic alloys have been made by McLean13 and found to agree quite closely with the minimum stress determined by experiment. Stresses capable of nucleating triple-point cracking should also be sufficient to nucleate fracture at a grain boundary due to intragranular slip, for the lengths of sliding interface in the two cases are approximately equal. Thus the minimum stress for triple-point cracking should represent a demarcation between failure due to general "cracking" and that due to cavitation. Hauser, Landon, and Dorn32 have demonstrated that for polycrystalline magnesium in the temperature range 78° to 298°K the fracture stress is inversely proportional to the square root of the mean grain diameter. As pointed out by stroh31 this result indicates that Eq. [I] describes the fracture characteristics of magnesium at low temperatures. Heal3 has reported that for rapid deformation (112 pct hr-1) of polycrystalline magnesium the transition from cracking to cavitation occurs in the temperature range 175" to 275°C. He also presented the fracture-stress values for the same material tested under similar conditions. From Eq. [I] taking G = 1.3 x 10" dynes , ? = 600 ergs . cm-2,33 and L = 0.017 cm, a Stroh-McLean13,31 tensile stress of -266 kg. cm-2 is calculated, corresponding to a transition temperature of -190°C; this is in

Jan 1, 1965

By W. A. Backofen, M. L. Ebner

SINCE the early work of Gough with Hanson and Wright,l-3 the study of fatigue has been characterized by experiments on single crystals only in recent times.9-10 Now, increasing attention is given to this aspect of fatigue research for the insight that it may provide into details of mechanism. The investigations have concentrated to a large extent on the development of deformation markings on fatigued crystals, and have shown the cracks to originate in slip bands possibly preceded or accompanied by slip-band extrusions. Experiments of special interest to the present work were conducted by paterson5 on copper crystals and involved both metallographic examination and measurement of change in flow stress. Crystals were cycled in alternating tens ion-compress ion with a constant plastic shear-strain amplitude of approximately 0.8 pct, and were particularly revealing for their demonstration of hardening with accumulated strain similar to that in unidirectional straining, through an easy-glide stage I followed by a stage II of rapid hardening; deformation was not continued beyond 40 cycles, however, so that the eventual course of the hardening curve could not be decided. For the conditions used by Paterson, surface slip markings were similar to those observed in unidirectional straining, but there were no X-ray asterisms and no deformation bands on the surface. In current thinking about the nature of fracture in fatigue, two views relative to mechanism are generally acknowledged, with the reservation that both could apply simultaneously in some measure. As one possibility, fracturing across a slip plane is regarded as a result of loss of cohesion from the creation of many point defects by dislocation movement under the cyclic loading.'' On the other hand, fracture has also been taken to follow as a consequence only of the geometry of slip at a free surface, consisting of offsets and crevices which eventually become fatigue cracks.12, l3 The work of McCammon and Rosenbergl4 showing fatigue in polycrystals at 4.2oK makes clear that any long-range diffusion of point defects is unnecessary, yet studies such as those of Forsyth and stubington15 show that accelerated diffusion may be a characteristic of deformation under fatigue loading. Interest in obtaining data of possible use for resolving such questions led to the experiments described below. Copper crystals were conveniently loaded in alternating four-point bending at constant deflection, a test condition shown to approximate a constant plastic strain amplitude for a wide range of axial orientations. The method of testing was not readily adapted to extensive study of temperature effects, but an investigation of the geometry of crack formation could simply be made by orienting,the slip direction at different angles to the surface. EXPERIMENTAL PROCEDURES Single crystals were grown by a modified Bridgman method in a stationary gradient furnace under an atmosphere of purified dry nitrogen. Purity of as-grown crystals was 99.999 pct as determined by spectrographic analysis plus vacuum fusion and gravimetric analyses for oxygen and sulfur, respectively. Crystals were of reasonable perfection as evidenced by a critical resolved shear stress at 10 deg from (110) of 60 g per sq mm and half-width of a (400) X-ray diffraction line from one crystal of

Jan 1, 1960

By Clark L. Corey, Bogdan Lisowsky

Electrical resistivity, X-ray line positions, degree of order, and microstructures have been investigated for Ni-A1 alloys near the Ni3Al composition. The results indicate that Ni3Al undergoes disordering between 1250oC and the mp; also supersaturated y, produced in y + y' alloys by gas quenching, is extensively ordered prior to y' (Ni3Al) phase separation. The latter reaction, if not both, must follow the cooperative phenomena model. Shifts in line position as a function of quench-indulced super satulration are shown. Lattice pavarneters of equilibriunz and nonequilibrium phases are given. THE objective of this investigation was to determine the mechanism and kinetics of the reactions which occur in Ni3A1 and hypostoichiometric Ni3A1 alloys. The results are of particular significance relative to pre-precipitation phenomena. Early work on Ni-A1 binary compositions near the Ni3A1 composition (13.6 wt pct Al) has been adequately reviewed by Hanssen,1 whose phase diagram is presented in Fig. 1. williams2 verified the suggestion made by Taylor and Floyd3 and others4 that y', Ni3A1, may precipitate coherently on (100) planes of the y phase (see Fig. 1 for phase nomenclature); he further suggested a two-step precipitation mechanism consisting initially of probably short-range ordering followed by actual precipitation of y'. The precipitation stage in low-aluminum hypo-eutectic compositions has been studied by a number of investigators;*"7 short-range order or "zone" formation have been suggested as explanations for various diffuse X-ray scattering effects. The ordering reaction in Ni3A1 alloys is characterized by a) a very rapid rate of ordering in nonstoi-chiometric compositions, b) absence of a disordered phase region for the stoichiometric compound, y', or Ni3A1, c) precipitation phenomena as a dominant aspect in hypoeutectic alloys, and d) an increase in elec-trical resistivity on ordering.' The latter two factors were found by Newkirk to characterize ordering in Co-Pt, for which an extensive and detailed analysis was made.' An electrical-resistivity increase on ordering has also been reported for cuAu3.10 PROCEDURE Ni-A1 alloys in the form of 1300-g chill-cast ingots were prepared by vacuum melting electrolytic nickel and high-purity (99.99 pct) aluminum. Very small heats prepared from high-purity carbonyl nickel, supplied through the courtesy of Dr. Goff of the Naval Research Laboratory, were used for comparison with the larger ingots and no differences were noted. The cast material was homogenized in purified argon for a minimum of 72 hr at 1200°C and water-quenched from 1350°C. Compositions studied are given in Table I. The 10 pct A1 alloy was both hot- and cold-rolled. X-ray superlattice line intensities and peak positions were obtained from -270 mesh filings, using CuK, radiation with a LiF crystal monochromat adjusted to receive both 01 and a2. One-degree slits and a 1/8 deg per min scan rate were used to record line traces. A standard tungsten powder, obtained through the courtesy of G.E. Research Laboratory, was used to calibrate line positions.

Jan 1, 1968

By Jim D. Mote, Eugenia M. Howard, Willis L. Barmore, John E. Dorn

The effect of stress and temperature on the creep rate of Ag-33 at. pct A1 and Ag-33 at. pct Al-1 at. pct Zn for prismatic slip was determined over a range of temperatures from 440º to 700°K. The alloys exhibited a brief initial inverted transient creep over which the creep rate increased slightly to a steady-state value which depended only on the stress and temperature, regardless of the previous strain history. The steady-state creep rates were found to be given by: where the activation energy is independent of the stress and strain and agrees fairly well with that estimated for diffusion. The observed creep behavior was shown to be in qualitative agreement with a model based on the stress-induced local disordering in the vicinity of a dislocation. OVER the past fifteen years, considerable progress has been made in correlating the experimen-entally observed plastic behavior of pure metals over each temperature range with one or more of a series of theoretical strain-rate controlling dislocation mechanisms. Despite the current interest in the plastic behavior of intermediate phases and inter metallic compounds, however, very little has been done in identifying the operative dislocation mechanisms in these materials. It is anticipated that the plastic behavior of intermediate phases can be rationalized in terms of the same dislocation mechanisms that are appropriate to pure metals and a solid solutions, provided the additional complexities arising from crystal structure, bonding, long-range order, short-range order, and defect lattices are taken into account. As part of a more extensive investigation on the plastic behavior of intermediate phases, Mote, Tanaka, and Dorn1 recently reported on the effect of temperature on the yield strength for prismatic slip in the hexagonal Ag-33 at. pct A1 intermediate phase as recorded in Fig. 1: Over Region I the deformation was observed to take place as a result of the thermally-activated Peierls mechanism, and over Region II the athermal disordering mechanism applied. The experimental data at that time, however, were not sufficiently extensive to identify the thermally activated mechanisms operative over Region III. It is the purpose of this investigation to attempt to identify the mechanisms that are operative over this high-temperature region. It will be shown that the same mechanism operates all over Region Ill, although the activation energy for this mechanism is in good agreement with that for diffusion, the process cannot be attributed either to the motion of jogged screw dislocations or the climb of edge dislocations. The results, however, are in good qualitative agreement with stress-induced disordering localized at dislocations. EXPERIMENTAL PROCEDURE The alloys studied in this investigation were prepared from silver, aluminum, and zinc (each of purity greater than 99.995 pet) by induction melting under an argon atmosphere and chill casting in a copper mold. Rectangular bar single crystal specimens (1/4 by 1/8 in. in cross-sect ion) of Ag-33 at. pct Al were grown in vacuum by a modified Bridgman technique. Similar Ag-33 at. pct Zn specimens were produced by an identical technique employing an argon atmosphere. The specimens were so oriented that the angle 90-Xo between the tensile axis and the normal to the prismatic plane and the angle A, between the tensile axis and the slip direction were 45 ± 1 deg. The effect of a change in temperature on the creep rate and a change in stress on the creep rate were determined over the temperature range

Jan 1, 1963

By Mark J. Klein

An internal-friction profile induced by nitrogen in Cr-35 at. pet Re was studied as a function of nitrogen concentration and heat treatment. From these studies, the solubility of nitrogen in this alloy was deduced. The equilibrium solubility of nitrogen in chromium does not appear to be substantially changed by the addition of 35 at. pet Re to chromium. However the precipitation kinetics of nitrogen from solution are significantly decreased. IT has been found that rhenium has a beneficial effect on the low-temperature ductility of Group VI-A metals. As part of a study to investigate the mechanism of this increased ductility, it was of interest to compare the concentration of interstitials retained in solution in one of these ductile bee alloys with the concentration retained in solution in its base metal. In this regard, a study of the solubility of nitrogen in ductile Cr-35 at. pet Re was selected for this phase of the investigation because the solubility of nitrogen in the base metal, chromium, has been determined over a fairly large temperature span.1-3 In addition, nitrogen is known to have an embrittling effect on chromium,4 but does not appear to have a comparable embrittling effect on Cr-35 at. pet Re.5 The experimental method selected for this study was the measurement of internal friction. This technique allows interstitial-concentration measurements to be made in bee metals that are sensitive to small changes in the concentration of a particular interstitial, even when other interstitials are present. When subjected to a cyclic stress, interstitial atoms in solid solution give rise to an internal-friction peak whose origin is the stress-induced ordering of interstitials into preferred lat- tice sites. These internal-friction peaks signify a dissipation of elastic energy which is greatest when the period of oscillation is comparable with the relaxation time for the attainment of an equilibrium interstitial distribution. For dilute interstitial binary alloys, the height of the internal-friction peak is proportional to the concentration of interstitial atoms in solid solutions. snoek8 has shown that the internal friction, Q-1, may be expressed by the equation where A is the relaxation strength, ? is the angular frequency, and 7 is the relaxation time. The relaxation strength, A, is proportional to the concentration of interstitials taking part in the relaxation if no interaction occurs between solute atoms. Thus values of peak height, which can be determined as a function of temperature, give a measure of the relative concentration of interstitial atoms in solution at various temperatures. If equilibrium has been attained, the peak heights will be proportional to the interstitial solubilities. The constant that relates A to the interstitial concentration can be determined experimentally from peak-height measurements as a function of concentration for specimens of constant crystallographic orientation. When this has been done, Q-1 measurements can be used to determine solubilities according to the equation C - KQ-1 where C is the soluble interstitial concentration and K is a constant that can be experimentally determined. It is possible, however, that lattice imperfections may bind interstitials to certain lattice sites. Internal friction does not measure these interstitial~, but does measure interstitials which are free to move in the normal lattice sites when subjected to an applied oscillating stress. On alloying the pure metal with a substitutional

Jan 1, 1965

By I. R. Kramer

The delay time for single crystals of iron, zinc, and pre-strained aluminum was measured under conditions of high-speed deformation. The delay time of aluminum was found to be affected by the orientation of the crystal. Under the dynamic conditions employed, tile calculated "activated volume" term appears to be very small for the three metals studied. IN a previous paper,1 it was shown that under dynamic testing conditions at 78° K, there was a delayed yield in single crystals of aluminum and copper which had been cold-worked prior to testing. The experimental results also indicated that the delay-time effect was not due to the interaction of dislocations with impurity atoms or vacancies, but rather to a dislocation-dislocation interaction since aluminum which has not been prestrained shows no delay-time phenomenon. In this paper, some data are reported on the effects of orientation on the delay time of aluminum single crystals; the delay time of zinc single crystals saturated with nitrogen and the delay time of iron single crystals also were measured. EXPERIMENTAL PROCEDURE Aluminum (99.997 pct) and zinc (99.999 pct) crystals, 1/2 in. in diam and 8 in. long were grown by the Bridgman technique. The iron single crystal was supplied by Dr. R. Maddin. The zinc crystals containing nitrogen were prepared by melting high-purity zinc in a graphite crucible and the nitrogen was introduced by additions of ammonium chloride. The liquid zinc was then drawn up into glass tubes of 1/2 in. diam and allowed to solidify. The rods were cooled to room temperature before the transfer to the mold for conversion into single crystals. The orientation of all specimens was determined by the Laue' back-reflection technique, Fig. 2 and Table I. To prepare for the delay-time measurements, the crystals were cut with a fine jewelers saw and the ends carefully machined. The specimens then were electrolytic ally polished to remove the cold-worked metal, mounted in a special fixture and hand-lapped. As a final step, the crystals were annealed in evacuated tubes. Specimens of aluminum crystals, Nos. 24 and 26, were compressed 0.5 and 2 pct, respectively, in the direction of the later impact. The zinc specimens were aged at 50°C for 15 min, In the case of iron, only two specimens could be obtained. To obtain sufficient data, it was necessary to resort to a reaging treatment. After each delay-time test, the specimens were aged at 65° C for 100 min. This treatment, according to Clark,2 is sufficient to restore the original delay time. It is believed that although the specimens were plastically deformed approximately 10-4 pct, after each test the delay-time values are reliable. The delay-time measurements were made in an apparatus similar to that described previously.' Single crystals approximately 1 in. long and having a diameter of 1/2 in. were placed in a pendulum which consisted of a bar 1/2 in. in diam and 8 ft long, designed with a crystal holder to accommodate the specimen at low temperatures. The crystal was held at a position 2 ft from the front part of the pendulum. This portion of the apparatus was supported on a fine molybdenum wire. A projectile bar of the same diameter and length comprised the other portion of the apparatus. This bar was supported on

Jan 1, 1962

By C. S. Samis, J. C. Mitchell

Sodion activity data have been obtained for the Na-A1 system for sodium concentrations in aluminum between NN, = 25 . 10-and 300 x 10'. This concentration intert-a2 encompasses those sodium concentrations nor1)zally encountered in aluminum reduction cell operation. The sodium activity data were measured by a two-phase equilibration of sodium between a lead and an aluminam rich phase. The Na-Pb system was emplojed as a reference for the determination of the actiz7itj 0.f sodium. The activity of sodiin in aluminuwz exhibits large positi2.e deviations frorn ideality and a strong dependence, on concentration below NN, = 100 x 1K6. The inteated data indicate that the activity of aluminium is equal to its mole fraction over the range of miscibility of the Na-A1 sgstem. The data on the Na-A1 binary have been combined with experimental data on the cryolite-A1 system at 1025°C to obtain the activities of Na F and AlF, in liquid cryolite oz2er the cornposition 1-ange encountered in aluminum cell operation. The results are in agreement with activities calculated from the NaF-AlF, phase diagram. ALUMINUM is produced commercially by the electrolytic reduction of aluminum oxide dissolved in molten cryolite. There is considerable controversy over the actual mechanism of the discharge processes, but sodium potentials in the systems appear to play an important role in the reduction mechanism. The metal-salt reaction involving NaF and aluminum to produce A1F3 and sodium is responsible for the presence of sodium in the aluminum metal phase. Additional sodium may be produced from the simultaneous deposition of sodium and aluminum at the cathode as a result of a cathodic overvoltage. runert' has suggested that sodium gas at atmospheric pressure would be the result of reaction between cryolite and aluminum at 1000°C. Subsequent investigations have shown that production of sodium at atmospheric pressure does not occur. These later investigations can be conveniently separated into two categories. The first involves sodium, aluminum, and cryolite, in which the sodium activity was measured. The second includes a lead phase for sodium activity measurement. Jander and errmann,' studied the reaction: at 1090°C in alumina crucibles under an atmosphere of dry, oxygen-free nitrogen. The equilibrium constant for the reaction was expressed in terms of concentration. Their results in Fig. 1 show an increase in sodium content of the aluminum with increasing NaF/A1F3 weight ratio. Pearson and waddington3 performed similar experiments at 1000°C. Their results are included in Fig. 1. Dewing and ollinshead have measured the sodium content of aluminum as a function of the NF/AF, ratio at 1025"C, Fig. 1, and ewin' measured the sodium content of the aluminum in a system involving the solid reactants NaF, cryolite, and liquid aluminum. This reaction is different from those discussed above. Two solid phases, NaF and Na3A1F6, and a liquid aluminum phase were present. The sodium concentration in the aluminum was determined by the temperature. Dewing's measurements covered the temperature range 679" to 896°C. Omo, Matsushima, and 1t02" investigated the equilibrium 6NaF ential thermal analysis. Stokes and Frank6 determined sodium activities by

Jan 1, 1970

By R. D. Young, E. A. Harre

Nitrogen exists in two broad categories commonly designated as elemental nitrogen and fixed nitrogen. Elemental nitrogen is found in nature as a diatomic molecule and constitutes about 78%, by volume, of the earth's atmosphere. Fixed nitrogen is a common term used for nitrogen that is chemically bound to other elements. Although elemental nitrogen is very abundant, nonleguminous plants cannot utilize nitrogen unless it is in the chemically combined form. The content of this chapter is confined to fixed nitrogen since the uses and properties of elemental nitrogen and the fixed nitrogen compounds are different. Certain bacteria associated with legumes are able to fix atmospheric nitrogen, but not to the extent required by succeeding nonleguminous crops. The need to use fertilizers containing fixed nitrogen compounds to grow food crops has been recognized for hundreds of years, and from antiquity farmers have used organic wastes such as animal manures, vegetable wastes, sewage sludge, fish scraps, etc., containing these compounds for fertilizers. These organic materials have a low nitrogen content, however, and cannot support large-scale food production. Known commercial-size deposits of natural nitrates containing much higher nitrogen content exist only in Chile, and the possibility of the discovery of other significant deposits is remote. The Chilean deposits were the major source of nitrogenous fertilizers until the Haber-Bosch process for the production of synthetic ammonia was developed. In the Haber-Bosch process, nitrogen reacts with hydrogen at high temperatures and pressures and in the presence of a catalyst to form ammonia. Modern plants use air, water, and natural gas or other hydrogen sources to produce the ammonia that is now the key building block of the fixed nitrogen industry. Several major problems that developed in the 1970s continue with the nitrogen industry into the 1980s. These are (1) the continuing sharp escalation in the cost of feedstocks for ammonia production as well as all energy sources, and (2) the very steep increase in the investment cost of production facilities. More than 75% of the fixed nitrogen produced domestically is consumed as fertilizers. The types of materials used as fertilizers have changed significantly during the past years. There has been a trend from the use of low-analysis fertilizers to types which contain high percentages of plant nutrients. The average plant nutrient content (N + P2O5 + K2O) of fertilizers used in the United States has increased from 18% in 1930 to 32% in 1960 and today approaches an average of 44%. In the case of nitrogen fertilizers, the low analysis natural nitrates (16% N) gave way to ammonium sulfate (20% N) after about 1920. After World War II, ammonium nitrate (33.5% N) previously used in munitions, became established as the leading nitrogen fertilizer. Urea use as a fertilizer (46% N) began in the 1960s, and in the past 10 years has become the world's leading solid nitrogen fertilizer. Nitrogen Materials Anhydrous Ammonia-Anhydrous ammonia is a colorless gas at ambient temperatures and pressures and has a sharp pungent odor. Anhydrous ammonia is stored and transported as a liquid in high-pressure cylinders and tanks at ambient temperature, and in low-pressure tanks, barges, and ships at -28°F. Anhydrous ammonia is applied directly at 4 to 7-in. depths in the soil as a high-pressure liquid by special applicators, after which it expands to a gas that dissolves in the soil moisture or is absorbed on soil colloids. In other systems ammonia is metered into irrigation water and is thereby introduced into the soil.

Jan 1, 1983

By C. R. Johnson, R. A. Greenkorn, L. K. Shallenbarger

This paper describes a study, based on core data, of the directional permeability of a sandstone reservoir. Directional air permeabilities are explained and correlated with lithology by the tensor theory of permeability, which is extended to the more general case of heterogeneous anisotzopic porous media. In this case, the permeability tensor is made up of two components: (I) anisotropy (variation around a point) which correlates with bedding, and (21 heterogeneity (variation from point-to-point) which correlates with grain size. INTRODUCTION Previous studies of directional permeabilityl.5-8 have concerned themselves only with anisotropy at a point, rather than with both point-to-point differences and local anisotropies. In this paper, we present the existing tensor theory of permeability for anisotropic porous media and then extend it to the more general case of heterogeneous anisotropic porous media. The laboratory measurements of directional permeability are explained in view of this extended theory and the data are discussed in terms of the lithologic factors that correlate with it. The results show what the heterogeneity and anisotropy of the reservoir element are, and that the directional permeability correlates with lithology. Data used in this paper are measurements of air permeability in eight directions, spaced at 45° intervals, on 142 2-in. vertical plugs from 30 cores. The core data are meaningful in terms of directional permeability because the cores were oriented to within 45O during drilling and coring.3 Although we initially thought that only 60 per cent of the core material was reliable, subsequent study showed that almost all of it was reliably oriented. After determining the air permeabilities, the data were reduced to three independent variables for each plug: the major and minor permeability axes, and the direction of the major axis. These were obtained by converting the permeability data to the reciprocal square root of permeability and fitting the transformed data with ellipses according to the tensor theory of permeability.8 The point-to-point areal variation of the minimum permeability axis is related to grain size. The direction of the permeability axes, where the major axis exceeds the minor axis by at least 5 per cent (measured variation is about 4 per cent), correlates with the bedding. The permeability tensor used in this study must be considered as the sum of a scalar and a tensor, with the scalar being the minor axis permeability as a function of position, and the tensor the directional effect, which is additive permeability over the minor axis. In this case, the point-to-point variation or heterogeneity (minor axis) is substantially larger than the variation at a point or anisotropy. It may be important that this separation of "directional permeabilities" be recognized when considering migration of fluids due to permeability variation. Local migration may be due to anisotropy and point-to-point migration may be due to heterogeneity, but the direction and magnitude of these may not be the same. Furthermore, in truly heterogeneous systems, one would expect that anisotropy would be the smaller of the two effects. THEORY TENSOR THEORY OF PERMEABILITY FOR ANISOTROPIC POROUS MEDIA8 Darcy's law for flow in porous media in its usual form is where qis the flow rate vector, k is the permeability, is the viscosity, is the vector differential operator, and P is the Pressure. Consider flow, q, through a unit area in the direction of the unit vector n from elementary flow tubes parallel

Jan 1, 1965

By K. P. Gupta

The Cb-rich boundary of the (Cb,Al) a phase field at 1250OC is near 41 pct Al. The Al atoms tend to occupy the C. N. 12 sites in this structure. A homologous (Ta,Al)a phase was identified. No a phase was found in the Mo-Al system at 1200°C. The first binary o-phase with a non-transition element as a major component was found1,2 in the Cb-Al system. The composition of this phase was reported2 as approximately 34 at. pct Al, based on X-ray diffraction patterns taken of alloys in the as-cast condition. Further study of the composition of this o-phase, therefore, appeared desirable. Since Si was previously found3,4 to occupy preferentially the lowest C.N. sites (I and IV) in the a phase, and preliminary resultsa indicated that Al may show similar ordering, one of the aims of the present work was to obtain more complete information on ordering in (Cb, Al) o. Among the binary systems of Al with Ti-, V-, and Cr-group elements, the Ti-Al, Zr-Al, V-Al, and Cr-Al systems are known to comprise no o-phase. In the present work a Ta-Al and a Mo-Al alloy were studied in an effort to find additional o phases with Al as a major component. EXPERIMENTAL PROCEDURES AND RESULTS An alloy with the intended composition of Ta + 40 at. pct Al was prepared by arc melting in He atmosphere. In both the as-cast condition and after annealing for 10 days at 1250°C and quenching in cold water this alloy consisted of two phases, as seen in the X-ray pattern and the microstructure. One of these phases was identified as the o-phase; the observed and calculated d-spacings are shown in Table I. The lattice parameters of this o-phase are a = 9.972 A, c = 5.214 A and c/a =0.5228, as determined from a Debye-Scherrer pattern using Fe K a radiation. The d-spacings for the unknown second phase are given in Table 11. The alloy contained approximately 25 pct of the unknown phase after annealing, as estimated on the basis of microscopic examination. A Mo-Al alloy was prepared by arc melting, with an intended Al-content of 35 at. pct. The alloy button was annealed for 7 days at 1200°C and water quenched. The X-ray pattern of the alloy in both the as-cast and the annealed state showed the reflections of Mo3Al (Cr30 type structure) and an unknown phase different from a. Six Cb-Al alloys were prepared in the composition range 30 to 50 pct Al. All alloys were arc melted in He atmosphere. After annealing for three days at 1175oC in evacuated silica capsules and quenching in water, the alloys with 30 to 40 pct Al contained three phases, namely the o-phase, Cb3Al (Cr3O-type structure) and an unknown phase. The alloys with more than 40 pct Al contained two phases, namely, what appeared metallographically, the o-phase and the same unknown phase. In the alloys containing less that 38 pct Al, the unknown phase was not present after annealing for 4 days at 1250°c,

Jan 1, 1962

By J. Lemish

Considerable research has been conducted in Iowa in recent years on carbonate aggregate reactions in concrete. Groups outside the state have become active in the past few years after recognizing that certain carbonate aggregates are reactive in concrete. The paper reviews the nature and extent of the problem and a summary is given of research by the author and his associates. In recent years considerable research has been conducted in Iowa on carbonate aggregate reactions in concrete. The research is part of a general study on the behavior of carbonate rocks as concrete aggregates sponsored by the Iowa State Highway Commission. Research on carbonate aggregates has not been extensive in the past. Laughlin1 published one of the first papers on carbonate aggregates in 1928 and was followed by others, notably H. S. sweet,' B. Mather et al.,3 and K. Mather4 who emphasized the petrographic and physical aspects of carbonate aggregates. The recognition that certain carbonate aggregates are reactive in concrete has led to increased participation in research in the past few years by groups outside of Iowa. Significant contributions have been made by Swenson and Gillot,5 Hadley,6 and Chaiken and Halstead7 in work which emphasizes the expansion of carbonate rocks in alkaline environments and the reaction of carbonate minerals or dedolomitization with alkalies. It is the purpose of this paper to review briefly the nature and extent of the problem and present a summary of the research by the author and his associates. EXTENT AND NATURE OF THE PROBLEM The problem is the deleterious behavior of certain carbonate aggregates in concrete. It was first recognized in Iowa over 20 years ago when poor service records of certain highways were correlated with aggregates produced from the Glory and LeGrand quarries. Deleterious behavior of carbonate aggregates have been reported in Canada and, more recently, in New York and Virginia. As more knowledge is gained concerning the problem, distress in concrete related to carbonate aggregates may be recognized over a widespread area. The problem may potentially exist in the Midwest, the Northeast, and other parts of the country underlain by thick sections of carbonate rocks readily available for utilization as aggregates. The nature of distress in Iowa highways is a general weakening and deterioration of concrete characterized by progressive cracking and spalling away from joints and edges (Fig. 1). The distress generally occurs after 15 years of service and becomes progressively worse. Specimens of such concrete lack the toughness of sound concrete and break easily under the hammer in the manner of a soft brick. The matrix is generally highly carbonated and dark borders, or reaction shells or rims outline the argillaceous carbonate aggregate fragments (Fig. 2). Cracks observed in cores cut across the aggregates and concrete matrix. Although localized volume change (expansion) is associated with spalling, there is no definite field evidence in Iowa that excessive growth of concrete slabs has occurred. The experience with carbonate aggregates in Iowa indicates that the concrete deterioration is not the same as that induced by the alkali-aggregate reaction associated with siliceous aggregates. The principal difference is that in Iowa the distressed concrete is weakened throughout the slab. In concrete affected by the alkali aggregate reaction, the

Jan 1, 1961

By V. Koump, T. F. Perzak, R. G. Olsson

The vate of dissolutioz of carbon in molten Fe-C alloys urns studied by votating- cylindrical g-vaphite sairlples in a stationary crucible containing the melt. The rate of dissolltion was determdined from the change in the bnth co)npositiorz. Alccss-tvansfev coeffi'cients, calcilated with the assurlption that the inte)yacial liquid ulas saturated with carbon, were found to be in agreement with an existing Correlation fov mass transfer jroni votating cylinders. It is corzcllrded tlat, itz the wnge of- Reynolds' numbers itzvestigated (790 to 18,000), the vate of dissolutio of carborz in Fe-C alloys is controlled by tile rate of carbon difirsion from the interface. The dissolution of carbon in molten Fe-C alloys has been the subject of a number of investigations. Most of these investigations have been inconclusive because of poorly defined experimental variables. Two of the more sophisticated studies are summarized below. Dahlke and Knacke' studied the phenomenon by, in part, immersing graphite rods into 0.5 pct carbon-steel for different lengths of time. Since the experiments were conducted in air or in CO atmospheres, the melt was strongly agitated by gas evolution. It was concluded that the change in bath composition as a function of immersion time was in agreement with the assumption that the dissolution process was transport-controlled. The hydrodynamic conditions in these experiments, however, were not well-defined and gave no indication of the nature of the dissolution process at higher fluid velocities. In a recent study Shurygin and ruk investigated the dissolution of carbon in molten Fe-C, Fe-Si, Fe-P, and Fe-Ni alloys. Small graphite disks were rotated in a crucible containing molten alloys under such conditions that only the lower face of the disk was exposed to the melt. The results of this investigation indicate that, over the range of velocities (100 to 1000 rpm) and bulk liquid concentrations (0.7 to 4.5 wt pct C) considered, the dissolution of carbon in the iron alloys is limited by the diffusion of carbon from the interface to the bulk liquid (a transport mechanism). For the particular geometry used by these authors, exact analytical solutions of hydrodynamic and diffusion problems are aailable. Hence the experimental results obtained by Shurygin and Kryuk permit the evaluation of diffusion coefficients of carbon in the four systems investigated. In the present investigation a series of experiments were conducted in which the rate of dissolution of carbon in Fe-C alloys was measured under conditions which permitted wide variation of the fluid velocity and the carbon concentration of the bulk liquid. Graphite cylinders were rotated at different speeds in a stationary concentric crucible containing various molten Fe-C alloys. THEORETICAL DEVELOPMENT In general, the resistance to mass transfer from a solid interface to a turbulent liquid is assumed to reside in a laminar boundary layer adjacent to the interface. If it is also assumed that the diffusion coefficient is independent of concentration, the steady-state rate of dissolution for the case of arbitrary liquid and solid densities can be obtained from the integration of the equations of continuity. The derivation is similar to that used by Lommel and chalmers4 for the case of pl = ps. The solution, expressed in terms where N = rate of diffusion of the solute from the interface. Exact analytical solutions of the hydrodynamic equation for the boundary layer thickness are available for only a limited number of geometries. Consequently, a mass-transfer coefficient, k, is usually

Jan 1, 1967

By George P. Chapman

Mica is a platy mineral occurring in a variety of complex hydrous aluminosilicate forms with differing chemical composition and physical properties. Principal minerals in the mica group include: Muscovite-potassium mica (colorless or pale green/ ruby) Phlogopite-magnesium mica (dark brown or amber) Biotite-magnesium-iron mica (black or dark green) Lepidolite-lithium mica (lilac) Selected properties are given in Table 1. Muscovite is most important commercially with phlogopite of lesser use. The laminated structure of mica enables it to be split into very thin films which are transparent and tough as well as having outstanding dielectric and insulating properties. Commercially, mica is used in a number of forms (Chowdbury, 1941; Rajgarhia, 1951; Skow, 1962). Sheet mica consists of flat sheets mined from naturally occurring books of mica, free from defects and capable of being punched or stamped into required shapes. Sheet mica is separately classified into blocks, films, or splittings according to thickness. Built-up mica, or micanite, is made by arranging overlapping splittings in layers , cemented with a binder and pressed together at high temperature. Reconstituted mica, or mica paper, is made by depositing fine flakes of high-quality scrap mica in a continuous film impregnated with binder. Scrap and flake mica are normally unsuitable in quality or size for making sheet mica. Originally the term scrap mica referred to the waste byproduct of mining and fabricating sheet mica, and distinct uses were developed for this material. Subsequently it became economically feasible to mine lower quality mica for these uses, and the term flake mica was introduced. Although the two terms are still used somewhat synonymously, it is considered better, at least in the United States, to use the term flake mica in referring to mica mined for uses other than as sheet mica; and to restrict the term scrap mica to mica mined for or with sheet mica, but which will not meet the specifications. Synthetic mica, such as fluorophlogopite, is produced by slow crystallization of a melted blend of pure raw materials. Mineralogy In the true sense the term mica does not relate to, a particular mineral, but to a group or family of minerals of similar chemical composition and to some extent similar physical properties. These minerals are predominantly potassium aluminum silicates with varying amounts of magnesium, iron, and lithium. The precise formulas and isomorphic relationships of the various group members have been studied, but general agreement has not been reached (Grimshaw, 1971; Hurlbut, 1952; Skow, 1962). The general formula describing the chemical composition of micas is [X2Y4-6Z8020(OH, F)4, where X is mainly K, Na, or Ca; Y is mainly Al, Mg, or Fe; Z is mainly Si or Al (Deer, et al., 1962).] These minerals have an internal structure of the layered lattice type where the silicon atoms are in the center of a tetrahedral grouping of oxygen atoms. The groups are linked together in a single plane by three oxygen atoms that lie within the common plane. Each of these oxygen atoms is shared by two tetrahedra. These linked tetrahedral groups, when continually extended, produce a hexagonal network within the plane. This internal structure of the mica has been used to explain the ex-

Jan 1, 1983

By F. V. Lenel, G. S. Ansell

The creep behavior of an aluminum -aluminum oxide alloy, A T 400, fabricated by compacting an atomized aluminum powder, extruding the compact, cold working, and recrystallizing the extrusion, was investigated. This alloy has a dispersion spacing of 1 . Previously Ansell and Weertman determined the steady-state creep rate of a recrystallized aluminum-aluminum oxide SAP-type alloy, MD 2100, with a 0.48-p dispersion. This alloy was found to have a steady-state creep rate of less than 10-6 min-1, too small to be measured accurately. By employing a more sensitive method of measuring creep rate, it was possible to determine the steady-state creep rate of AT 400 alloy, which is somewhat faster than that of MD 2100, at a series of temperature and applied stresses. Above a stress of Burger's vector, A = dispersion spacing, u = is a shear modulus) the rate follms an equation of the type: Steady-state creep rate K = A exp. where A is a constant, Q is the activation energy for sey-diffusion, and is the applied stress. At stresses lower than the steady-state creep rate drops off sharply and is no longer in agreement with this equation. This behavior is in good agreement with that predicted by the model for dispersion strengthened alloys in the stress and temperature range investigated. The absolute value of the creep rate is, however, four orders of magnitude lower than that predicted if the normal number of active dislocation sources are assumed to be present. It is concluded that in this SAP-type alloy the usual three-dimensional dislocation network is not present. Instead, short dislocation segments extending from one dispersed particle and terminating at a neighboring particle may act as dislocation sources. With this provision the creep model proposed by Ansell and Weertman reasonably accounts for the creep behavior which was observed. RECENTLY, Ansell and Weertman1 proposed a dislocation model from which they derived creep equations to describe the steady-state creep behavior of dispersion - strengthened alloys. Following Schoeck,2 they assumed that the rate controlling process for steady-state creep is the climb of dislocations over the dispersed particles. In order to verify their creep model, Ansell and Weertman determined the steady-state creep behavior of an aluminum-aluminum oxide SAP-type alloy, MD-2100, in both the fine-grained as-extruded, and coarse-grained recrystallized conditions. Since the grain size was the order of the dispersion-spacing, their model was not applicable for the as-ex- truded alloy. It should, however, be applicable to the coarse-grained recrystallized alloy. The results they obtained were rather unexpected. No meas-ureable steady-state creep was observed for the recrystallized MD-2100 alloy. If their model is correct, and if the second-phase particles act solely to hinder dislocation motion, then some measureable steady-state creep would have been expected. On this basis, they postulated that, in this SAP-type alloy, the main effect of the fine dispersion was to inactivate dislocation sources rather than to hinder the movement of dislocations. In order to understand more fully this unusual creep behavior, and to determine the validity of the model proposed,' the steady-state creep behavior of an aluminum-aluminum oxide recrystallized SAP-type alloy, with a somewhat coarser dispersion spacing, was investigated. The results of this study are presented in this paper.

Jan 1, 1962

By R. D. Carnahan, G. A. Stone, R. J. Arsenault

An experimental technique has been developed for carrying out a dynamic tensile stress-strain test in which plastic strain is measured continuously throughout the microstrain region extending through the macroflow region to total deformations of 5 pet. The tests were carried out on niobium, samples having interstitial impurity levels of 160 and -800 ppm at temperatures ranging from room temperature down to 100°K. A band spectrum of activation energies was obtained from calculations based on the measured activation volumes and temperature dependence of flow stress. The inability of a single rate-controlling process to predict such a phenomenon has led to the proposal that several sequential rate-controlling dislocation mechanisms are operative in the preyield micro-strain region. These are thought to be: the motion of geometrical kinks, the formation of double kinks in edges, and finally in the macrostrain region the formation of double kinks in screws. In less pure niobium the effect of interstitial impurities is shown to be dominant in the microstrain region, suggesting that a fourth probable mechanism is overcoming interstitial barriers instead of geometrical kink motion and the formation of double kinks in edge dislocations. THE principal fundamental aim of most mechanical properties studies of crystalline solids is to determine the dislocation mechanisms responsible for the plastic behavior. The extension of such studies to the region of preyield microstrain behavior has received renewed attention in the past few years as the details of macroscopic flow behavior have become better understood. For the most part, microstrain studies have been carried out using one of two variations of a single experimental technique.1 The first method involves loading the sample at a constant extension rate to a predetermined stress level (less than the macroscopic yield stress), instantaneously unloading, and then determining the extent of plastic deformation to a sensitivity of 10"6. The microscopic stress-strain curve is then constructed from the results of a repeated series of such individual measurements, each of which involves loading to an incrementally higher stress level, by relating the accumulated plastic microstrain for each step to the maximum applied stress in that step. The second variation, also carried out by step-wise increases in stress, measures the total strain to a sensitivity of ~10"6 and relates the maximum stress to the area of closed hysteresis loops that are generated under certain conditions (namely, prestrained samples). The foregoing methods have yielded interesting information about the nature of preyield deformation and plastic response to stresses below the yield stress, but they offer certain disadvantages for studying the dynamic behavior of dislocations. In the first method it is physically impossible to specify a plastic strain rate inasmuch as the test sample is reexposed, as it is loaded to its maximum stress in a particular step, to lower stresses at which flow will take place. The strain corresponding to a given stress level on the stress-microstrain curve thus generated will then always be greater than that at the corresponding stress level of a truly dynamic test carried out at the same extension rate. The second method has been used to obtain correlations with dynamic macroscopic flow parameters by applying dislocation damping theory to the hysteresis loop areas.2 The approach has had some success but suffers in that only samples that have been prestrained a few percent can be studied. Although the stresses

Jan 1, 1968

By Eugene N. Cameron

Pegmatites of these areas have become important sources of beryl and lepidolite and have yielded cassiterite, columbite-tantalite, and other minerals. Examination of about 60 of these pegmatites leads the author to question the opinion of earlier investigators that the concentrations of beryl, lepidolite, and columbite-tantalite found have mostly formed by hydrothermal or pneumatolytic replacement of previously formed quartz-feldspar pegmatites. The author concludes, on the contrary, that present knowledge of the occurrence of minerals in zoned pegmatites can be applied to prospecting and mining of pegmatite deposits in these two areas of South West Africa. PEGMATITES occur in abundance in certain areas of South West Africa and in adjacent parts of northern Cape Province in the Union of South Africa. Some of the pegmatite deposits were prospected before World War I, and intermittent mining was done during the period between the two World Wars. The deposits of the Jooste lithium mines became an important source of lepidolite, and beryl, columbite-tantalite, wolframite, and other minerals were produced. Since World War II prospecting and mining have been carried on vigorously, with the result that South West Africa produced nearly 3000 tons of beryl during 1949 through 1953, together with more than 40,000 tons of lithium minerals, chiefly lepidolite and petalite. Small amounts of tantalite, columbite, and other minerals have also been produced during the postwar period. Most of this mineral production has come from two pegmatite areas roughly outlined in Fig. 1. One is the Karibib-Omaruru area of north central South West Africa. The second is the northeastern part of the Orange River pegmatite area, which extends into adjacent parts of Namaqualand, in northern Cape Province of the Union of South Africa. The writer visited the two pegmatite areas in July 1951. The visit was brief. but it gave an opportunity to compare some of the' pegmatites of these areas with those studied and described in detail by many investigators in the U. S., Brazil, and Canada during and since World War 11.'-l' The writer has attempted to determine, in a preliminary way, whether the concepts of internal structure and distribution of minerals in pegmatite bodies developed out of these studies are applicable to prospecting and exploration of pegmatites in South West Africa. Previous Work In an important series of papers (1929 to 1942) T. W. Gevers, H. I?. Frommurze, S. H. Haughton, G. K. Joubert, and other geologists of the Geological Survey of South Africa described and discussed the pegmatites of the two areas.*-" These works are the principal sources of information on the pegmatite mineral deposits of South West Africa. The investigations showed that in the two areas pegmatites are profusely distributed in pre-Cambrian rocks. These rocks are meta-igneous and metasedimentary units that have been folded and subsequently invaded by younger pre-Cambrian granites and by other igneous rocks. The pegmatites are considered to be genetically related to the pre-Cambrian granites. Pegmatites occur in the granite bodies themselves but are most abundant in the surrounding metamor-phic rocks, a pattern repeated in many pegmatite districts of the world. The origin of the pegmatites and the factors controlling the occurrence of mineral deposits in them were discussed at length by Gevers and Frommurze (1929)" and later by Gevers 14, 15 pp. 41-51, Ref.

Jan 1, 1956

By M. B. Bever, A. K. Jena

Equations for the heat effects of additions of mixtures of multicomponent phases to a solution have been derived in terms of the enthalpy interaction coefficients. By these equations and the measured composition dependence of the heat effects on addition of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions, values of the enthalpy in-teraction coefficients in tin-rich solutions at 541°K have been obtained. Analysis of these results in terms of the regular solution theory and the quasichemical theory suggests that near the melting point of the solvent association in the solution becomes important. SEVERAL recent papers have discussed the nature of dilute solutions on the basis of measured enthalpy interaction coefficients. l-3 These coefficients contribute to the understanding of the constitution of solutions and can be used for the evaluation of thermo-dynamic data of multicomponent systems. Their experimental determination, however, is laborious. This communication reports values of the enthalpy interaction coefficients of silver, cadmium, and gold in liquid tin-rich solutions obtained from the measured heat effects of additions of mixtures of Ag-Cd solid solutions and elemental gold to liquid tin-rich solutions. These measurements were made in the course of the determination of the heats of formation of Ag-Cd solid solutions reported in a concurrent publication.4 THE HEAT EFFECT OF AN ADDITION TO A SOLVENT This analysis is concerned with the addition of a mixture of multicomponent phases from the temperature To to a solvent of known composition at temperature T. If Nmixture << Nsolvent, where N designates the gram-atoms involved, the heat effect per g-atom of mixture added can be expressed as (HT - HT )i = difference in heat contents of component element i in the mixture at T and To Q = heat effect on solution of the mixture at temperature T Also1 Q = S Xi [2] where ?Hi ,T,x = relative partial enthalpy per g-atom of i in solution at temperature T and composition of the solution x x = average of the atom fractions of the added material in solution before and after the addition The relative partial enthalpy ?Hi per g-atom of an element i in a dilute solution composed of a solvent 1 and the solutes j = 2, ... m is related to the interaction coefficients by the following equation5 ?Hi - ?Hi-?Hi,x1-1 + S n1ixj+ . . . +S...S...S nrixn2... Xnji...Xnmm+... [3] vhere Xj = atom fraction of solute j in the solution nri = the rth order enthalpy interaction coefficients, which can also be represented by the more general designation5 L(i)n2,n3...nm and nj may have any positive integral value or zero. For identification of various rth order interaction coefficients, nri is written as nn2i2,...nij,...nmm. Eqs. [1], [2], and [3] combine to give the following general equation for the heat effect on addition of a small quantity of a mixture to a large quantity of a dilute solution n = _?ga ?Ha,To + ? Xi(HT - HT o)i a. i + ?xi?Hi,X,i?1 + ??xnjixj + . . . + ???. . .?. . .?xinrix2n2. . . xnji. . . xnmm+ . . . [4] The first term on the right-hand side of this equation is the heat of decomposition at the addition temperature of the phases present in the mixture, the second term is the heat required to raise the temperature of

Jan 1, 1970

By A. Heim, M. Gondouin

Invasion experiments were run on Berea sandstone cores to get laboratory measurements of resistivity and saturation profiles characteristic of water and oil sands invaded by mud filtrate. Injection rates were as low as 1.13 cm/D, and the cores were 30 to 36 in. long, cut parallel to the bedding planes. In the water-sand case, the resistivity profiles revealed the existence of an extensive transition zone between flushed and uncontaminated zones. In the linear geometry of the experiment, the width of the transition zone increased as the square root of the injected fluid volume. For the oil-sand case the core was prepared by displacing the formation water with kerosene to minimum water saturation. During the subsequent invasion experiment. oil saturation was measured directly by means of an oil-soluble radioactive tracer, and resistivity profiles along the core were taken at the same time. These data were interpreted in terms of an oil-water front, followed by a formation water bank, a zone of mixed waters, and finally, invaded mud filtrate near the borehole. Micro-fingering and capillarity seemed to affect considerably the resistivity profiles observed in the invaded oil-sand experiment. Beyond the regular conductive annulus or "low zone", it was found that a resistive "anti-annulus" could also be formed. As a result of these experiments, some simplified invasion profiles have been accepted and are being used in Grand Slam* interpretations. INTRODUCTION The importance of the mud filtrate-invaded zone in interpreting electrical logs has long been recognized.&apos;,* In trying to account for its effect, only very simple models of the resistivity profiles in the radial direction from the borehole have been used. In fact, most log interpretation charts have been based on resistivity models consisiting of two media of uniform resistivity (R, and R,) abruptly separated at the diameter of invasion. Such a clean separation of the media of different resistivities seems unrealistic, since flushing may not be perfect and may vary with radial distance into the formation.3** The nature of the transition zone, when it is within the radius of investigation of the surveying devices, may affect the log readings. Campbell and Martin&apos; verified that a conductive annulus containing a high percentage of formation water may be formed when mud filtrate invades an oil-bearing sand. Interpretations which are to include the effect of such an annulus require the addition to the model of a conductive zone located at the outer rim of the invaded zone.&apos; Using the Buckley-Leverett relations,6 aturation profiles may be derived, from which resistivity profiles can be calculated. Results of such computations by K. S. Kunz and J. H. Moran were given in a paper by Dumanoir. Tixier and Martin,7 and led to the construction of log interpretation charts which were based on a representation with three media of resistivities R, R0 and R1. Fig. 1 shows a schematic representation of a resistivity profile which includes an annulus. Campbell and Martin realized that, during the invasion of an oil sand, both capillarity and mixing would contribute to rounding of the profile shown in Fig. 1. Capillarity tends to draw some of the formation water from the annulus into the uncontaminated (Rt) zone, whereas mixing of the mud filtrate with formation water of the

Jan 1, 1965