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By R. E. Ogilvie, J. I. Goldstein

The a and y solubility limits in the Fe-Ni phase diagram have been redetermined at temperatures above 500°C. Both a diffusion-couple and a quench and anneal technique were used. The solubility limits were measured with an electron-probe micro-analyzer. The nickel concentration at the phase boundary is increased below 700°C and the a solid-solubility range is much larger than had been previously measured. The solubility limits are also extrapolated to 300°C. It is suggested that the solubility of nickel in a FeNi reaches a maximum in the temperature interval 400o to 500°C. THE equilibrium diagram has been of great use in the field of meteoritics, where the phase relations between kamacite (a) and taenite (?) in metallic meteorites can be described by means of the Fe-Ni diagram. The study of metallic meteorites by electron-probe microanalysis has cast some doubt on the accuracy of the presently available Fe-Ni diagrams.1, 2 Recent thermodynamic studies of the Fe-Ni system also suggest that the diagram may be in error.3 For these reasons the high-temperature (800o to 500°C) part of the diagram was redetermined. INTRODUCTION The currently accepted Fe-Ni diagram is that of Owen and Liu.4 Above 910°C, there is a region of complete solid solubility, ? (fee). Below 910°C, the a (bee) phase is stable in pure iron. The effect of increasing amounts of nickel is to stabilize the y phase. The phases that form when Fe-Ni alloys are heated or cooled bear little relation to the equilibrium diagram. If an alloy is cooled from the y state and held at a temperature within the a + y field, no evidence has been found for the occurrence of the y - a transformation.5 If the alloy is cooled to low enough temperatures the y phase breaks down into a supersaturated bee phase called a2. In fact, in alloys over 27 pet Ni the y phase is retained at room temperature.6 The a, phase has the same composition as the original y. The temperature at which a2 forms, the M, temperature, has been determined experimentally.' A state of equilibrium can be approached by cooling below M, to form a2 and then reheating the alloy into the two-phase region of the diagram. The y phase will then begin to precipitate out of the a2 phase and grow. The growth of the phase, however, is quite slow. Using the interdiffusion coefficients -Da of Goldstein et al.,8 it is estimated that it takes about 1 year to grow a 10-µ-wide region of ? at 700°C in a 5 pet Ni alloy. Owen and Liu4 used the technique just described to form the equilibrium phases. The phases present were determined by means of X-ray analysis. The accuracy of their diagram depends on the number of alloys available near the phase boundary at a given temperature. In this study two different techniques were used to determine the a/a + ? and ?/a + ? solubility limits. The inherent accuracy of both techniques was greatly improved over that used by previous investigators because the phase-boundary compositions were measured with an electron-probe microanalyzer. PROCEDURE The two methods used to determine the Fe-Ni diagram are the diffusion couple (D.C.) and the quench-and-anneal (Q.+A.) techniques. In the first method, diffusion couples whose diffusion path goes through a two-phase region of the phase diagram were used. A description of the technique used for making the diffusion couples has been described in a previous paper.' After the diffusion treatment a discontinuity in the resultant concentration vs distance profile was measured. The nickel concentrations in the a and ? phases at the interface of the discontinuity are the solubility limits of the a and ? phases in the phase diagram at the diffusion temperature. If the interface com-

Jan 1, 1965

By R. W. Heckel, R. L. DeGregorio

The DeHoff method of determining the size distribution of ellipsoid-shaped, second-phase particles has been applied to the spheroidization of cementite in a eutectoid steel. The surface area of Precipitates determined from the various size fractions in the distribution was correlated with surface-area measurements based on the number of intersected interfaces on a random lest line. The precipitate particles were found to be oblate ellipsoids with an axial ratio of about 0.90. The size distributions were found to be log-normal. A method is proposed whereby the shrinkage of small particles and growth of large ones can be determined from the experimental data. The experimental data are compared to previously proposed mathematical models describing diffusion-controlled kinetics and various types of interface-controlled kinetics. The experimental growth and shrinkage rates are considerably slower than those predicted by diffusion-controlled kinetics. The best fit is obtained for a model describing interface-controlled kinetics limited by the rate of formation of cementite at the growing interfaces where the interfacial reaction rate is proportional to the solute thermodynamic activity gradient across the surface. THE subject of spheroidization of second-phase particles has been considered previously by other investigators. Livingston1 has studied the precipitation of the cobalt-rich phase from copper alloys containing 0.7 to 3.2 wt pet Co. His results indicate that the average particle size increases as the cube root of the heat treatment time in accord with diffusion-controlled kinetics.'-' Komatsu and rant' in their studies of the growth of SiO2 in a dispersion-strengthened copper-silica alloy found that the initial growth of SiO2 proceeded by diffusion-controlled growth and later stages were limited by interface-controlled growth. The values of the activation energy obtained for the interface- controlled process led them to the conclusion that the process was limited by the dissociation of SiO2 at the shrinking interface. The transition from diffusion-controlled growth to interface-controlled growth was characterized by a particle size which varied with the heat-treatment temperature. It is also interesting to note that the particle-size distribution as found by Komatsu and Grant exhibits log-normal behavior when replotted on log-probability coordinates. Dromsky, Lenel, and Ansell9 have observed the growth of Al2O3 particles having a mean free path of about 1.5 to 13 µ. Their photomicrographs indicate that the Al2O3 particle sizes were larger than those observed by Komatsu and Grant. Dromsky, Lenel, and Ansell concluded that the Al2O3 coarsened by an interface-controlled growth mechanism limited by the solution of A12O3 at the shrinking interfaces. Bannyh, Modin, and Modin10 have studied the spheroidization of a eutectoid steel (0.83 wt pet C). Their spheroidization (tempering) treatments were carried out in the range from 210o to 700°C for times between 1.5 sec and 20 hr. Measurements of mean particle size as a function of time indicated a cube root of time dependence of size at 700°C, in agreement with previous analyses of diffusion-controlled kinetics.2°7 At lower temperatures, the time dependence was less than the one-third power. It is important to note that, although mathematical models of growth* considering particle-size distribution have been available, measurements of only mean particle size have been carried out. DeHoff11 has presented a quantitative metallography technique which is applicable to the determination of the size distribution of ellipsoids of constant shape. This method is applicable to both oblate and prolate ellipsoids of all ratios of minor to major axis and is based upon an extension of Saltykov's analysis12 of the distribution of spheres of varying size. DeHoff's analysis is based upon measurements of the minor axis of the particles on a random plane of polish in a unit area. This method provides a measure of the number of ellipsoids in various size ranges per unit area. As pointed out by DeHoff, such measurements may be used to obtain surface area and total precipitate volume data. Thus, the accuracy of the distribution analysis may be checked by comparison of the surface and volume

Jan 1, 1965

By J. M. Dumore

If in a vertical, downward miscible displacement, the transition zone between the displacing and displaced fluids is neglected, a criterion for stable displacement can be obtained by considering a small hypothetical protrusion of one of the fluids into the other. This criterion leads to the definition of the well-known critical rate, uc = kg p/p. The consideration is further extended by taking into account the transition zone that develops as a result of diffusion and mixing. A generalization of the previous criterion leads to the definition of another characteristic rate, the stable rate, which in actual miscible drives will be less than the critical rate. In such drives, the entire transition zone is stable at rates less than the stable rate. At rates between the stable and critical rates, the displacement is only partly stable, i.e. part of the transition zone adjacent to the displaced fluid is in an unstable position. From that part of the transition zone viscous lingers will develop. At rates greater than the critical rate the entire displacement is unstable and viscous lingers will develop more strongly. Results of laboratory experiments are in agreement with the expected behavior based on the theoretically deduced stability of the displacement. INTRODUCTION The simplest form of miscible drive in an oil-bearing formation is the injection of a fluid that is completely miscible* with the oil under reservoir conditions. In general, such a fluid, a solvent for example, is less dense and less viscous than the oil present in the formation. If it is injected into a horizontal homogeneous layer, gravitational forces will lead to the formation of a gravity tongue of solvent in the upper part of the layer and the adverse solvent-oil viscosity ratio will cause viscous fingers to develop. If, however, the solvent is injected up-structure into ,a dipping layer, gravity has a favorable effect, because it tends to keep the less dense solvent up-structure. Tongue formation and viscous fingering are consequently reduced and it is even possible that they will be suppressed completely. Viscous fingering and gravity tonguing are the consequences of the instability of the displacement. A stable displacement cannot result in growing viscous fingers and/or growing gravity tongues. Since large amounts of oil can be bypassed if there is viscous fingering and/or gravity tonguing, the stability of a miscible drive is very important with respect to the recovery efficiency of the drive. The stability is of particular importance in miscible-slug drives, as it determines how quickly the miscible slug between the displaced and displacing fluids will be distorted and broken up, after which the drive is no longer completely miscible. Stability is thus a most important factor in determining the success of a miscible drive, and it is considered that the aspects of stability considered in this paper will make a useful contribution to existing theories. Consideration is given only to vertical downward displacements, in which no gravity tongues can develop and which are therefore simpler than downward displacements in sloping layers. THEORY CRITERION FOR STABLE DISPLACEMENT Let us consider a vertical column of a homogeneous permeable medium saturated with oil. A solvent less dense and less viscous than the oil is injected at the top of the column at a constant rate; in the column the velocities of oil and solvent are assumed to be uniform. Diffusion and mixing of oil and solvent will at first be neglected, i.e. we assume that solvent and oil are divided by a sharp interface. An additional assumption is that the interface is horizontal. Continuity of pressures exists at the interface, because no capillary forces are present between the two miscible fluids. Consequently, at the interface (Z = I)):** Ps = Po - P-where Ps is the pressure at the solvent side and

Jan 1, 1965

By Luke L. Y. Chang, Bert Phillips

A number of molybdenum oxides have been synthesized and their crystal structures have been described.' No data have been published on the stabilities of these oxides nor on the phase relations in the system Mo-0. It is probable that the tendency toward oxidation of both the metal and the oxides with low oxygen content in addition to the high volatilization rate of the oxides with high oxygen content have precluded accumulation of reliable data for establishing phase relations. These problems make experimentation difficult, but a modifi-

Jan 1, 1965

By J. E. Harris, J. A. Whiteman, A. G. Quarrell

The graphitizing reaction has been studied in a number of Fe-C-Si alloys in the temperature range 550° to 725°C. The TTT relationships exhibit "C" curve behavior except where nuclei, either foreign or graphite itself, are present before the start of the reaction. It is suggested that the rate -controlling process is diffusion of carbon through ferrite. For the reaction to proceed at the observed rate it is calculated that the matrix surrounding the particles must deform plastically; experimental evidence for this deformation is presented. It is well-established that the decomposition of austenite to pear lite occurs at a maximum rate at an intermediate temperature.l-5 This "C curve" be- havior, which has been reported in a number of other systems,5-10 is a consequence of the relatively low rate of nucleation of the pearlite at small degrees of undercooling of the austenite. The cemen-tite phase in the pearlite is, in turn, metastable with respect to graphite and if steels are held for prolonged periods at elevated temperatures decomposition of the pearlite occurs. It is difficult to predict the shape of the subcriti-cal graphitization TTT (time, temperature, transformation) diagram for, in this case, undercooling does not occur. However, the free-energy change for the reaction does decrease with increasing temperature" (Fig. 1) and it is thus anticipated that the rate of nucleation will fall as the temperature approaches that of the eutectoid. In addition, a decreasing growth rate with increasing temperature is predicted in some circumstances with pure Fe-C alloys. However, apparently similar conditions exist for first-stage graphitization in the austenite range (malleabilization) but no evidence for C curve behavior has been presented in the extensive liter-

Jan 1, 1965

By W. A. Rachinger, C. Graeme-Barber, R. L. Bell, R. C. Gifkins, T. G. Langdon

R. L. Bell. C. Graeme-Barber, and T. G. Langdon (Imperial College. London)— The internal-marker technique developed by Ishida, Mullendore, and Grant has enabled them to make some interesting observations on the role of grain boundary sliding in creep. Certain of their conclusions are supported by our own similar experiments on Magnox AL80 (Mg-0.8 pct Al) specimens containing several markers, full details of which will be published shortly. In particular, we would agree that: 1) Using the internal-marker method, there is little difference between Egb, the contribution made by grain boundary sliding to the total strain, measured at the surface and in the interior of a specimen. 2) The measurement of the change in grain shape during creep leads to an underestimation of the grain strain, and hence an overestimate of Egb.. However, the discrepancies between the values obtained by this method and those obtained using markers are not as great as Tables IV and V of Ishida, Mullendore, and Grant would suggest; see below. The authors' Eq. [I] which is used to compute Egb from the transverse displacement ITt of longitudinal marker lines is not given in the reference quoted,'' where in fact only relations for Egb in terms of the longitudinal displacements of markers were developed. As first pointed out by Gifkins and Gittins,12 a problem arises in the use of longitudinal markers. and we will show that Eq. [1] underestimates Egb in the interior by a factor of 2. In Fig. 12, two grains X and Y have become displaced by the vector AC which lies in the plane of the grain boundary ABCD separating them. A longitudinal marker has been split by this displacement into the two parts LA and CAW. If these were surface grains the transverse displacement, Ut. could be obtained by viewing normal to the "top" surface. If interior, a section through CD parallel to the top surface would show the same result, provided the longitudinal internal markers delineated planes normal to the top surface. (This is an essential feature of the markers not pointed out in the paper.) The important point is that the quantity Ut tan B (=BE=DF) only gives the elongation due to the one component AB of the sliding. The elongation V/tan 8 (=GD) due to the component AD must be added to produce the total elongation resulting from the boundary displacement AC. If the grain boundaries in a poly crystalline specimen are randomly oriented with respect to the stress axis it follows that In the interior of a specimen the two sums depend for any difference simply on the definitions "top'' and "side". On the surface it is possible that the two sums could differ somewhat. In either event it is clear that the authors' Eq. [I] underestimates Egb, and in the interior, and perhaps at the surface also, the appropriate formula is given by The suggested modification probably makes little difference to the comparison between surface and interior values of Egb where both were obtained from marker measurements. For the estimation of the correction becomes extremely important where the boundary contribution is large. In our own work on magnox, for example, we have obtained values of as large as 70 to 80 pct, under conditions of high temperature and low strain rate. The use of planar markers transverse to the stress axis would simplify the comparison between surface and interior behavior, because measurement of the longitudinal offsets Us of these markers could be summed to give the total elongation di-

Jan 1, 1965

By K. G. Davis, P. Fryzuk

A study has been made of the effect of undercooling on the grain structure and solute distribution in small ingots of pure bismuth and of a 100 ppm Ag in bismuth alloy. Autoradiographic evidence shows that in undercooled melts a network of dendrites is formed throughout the melt immediately after nu-cleation. At large undercoolings the dendrites are very thin and closely spaced. The origin of the observed grain morphology can be explained on the basis of information about the mode of solidification revealed by the impurity substructure. WHILE a great number of studies of nucleation in undercooled molten metals have been made, comparatively little attention has been given to the mode of solidification from melts with large undercool- ings. Colligan and Bayles1 and Walker2 have measured the rate of advance of the solid-liquid interface in undercooled nickel melts, but the morphology of the solidifying material remained a matter of speculation. Fehling and Scheil3 have described the grain structure in ingots formed from undercooled melts of nickel, palladium, and copper, and a series of Ni-Cu and Ni-Pd alloys. At small undercoolings, equiaxed structures are observed, the grain diameter tending to increase as the temperature of nucleation is lowered. At greater undercoolings, a columnar structure is developed, while with still further undercooling there is a smaller grain size incorporating rather coarse subgrains. All-bright and Colligan4 examined the grain structure shown by ingots solidified from melts of nickel and of Ni-Ag alloy at an undercooling of 105°C, and concluded that considerable grain growth had taken place after solidification. The object of the present work is to correlate the mode of solidification from undercooled melts with both the grain structure and impurity segregation, using tracers to examine the latter.

Jan 1, 1965

By W. F. Chiao, R. B. Gordon

Tile sharp-yield point found in magnesium crystals in the solulion-treated and aged condition is studied by dislocation internal-friction experiments. The results show that the sharp yield is not file to the sudden release of pinned dislocations hut is movc likely due to the rapid multiplication of an initially small number of dislocations. Recovery or the dislocation internal friction after deformation is also studied. This yecovery results from the re-pinning of dislocations by a solute, presumably nitrogen, which moves with a relatively small activation energy. SHARP-yield points, when they occur, are a striking feature of the stress-strain curve generated during a tensile test. Although commonly associated with steel, sharp yielding has been found in a variety of metallic and nonmetallic crystalline materials. In particular, sharp-yield points have been found in zinc"' and cadmium3 containing nitrogen. With this background, Geiselman and Guy4 investigated the tensile properties of magnesium single crystals containing nitrogen to see if sharp yielding also occurs in this system. They found that sharp yields did indeed occur in solution-treated and aged specimens tested at elevated temperature but were not able to give conclusive proof that the sharp yield was caused by nitrogen, a yield drop being observed even in their purest crystals. Sharp-yield points have also been found in various polycrystalline magnesium alloys.7'8 In the study of the sharp-yield phenomenon it is desired to observe the behavior of dislocations in the earliest stages of the deformation process. Internal-friction experiments are useful for this purpose because dislocation damping is sensitive to the mobility of free-dislocation segments. At low strain amplitudes the damping, A, due to the the forced vibration of dislocation segments of average length L is ? =KAL4 [1] where A is the dislocation density and K, if the applied frequency is well below the resonant frequency of the dislocation segments? is a constant for the sample under observation.5 Dislocation damping, because of the fourth-power dependence on L, is particularly sensitive to the creation of free-dislocation segments during deformation. Since sharp yielding is associated with the sudden release of pinned-dislocation segments, marked changes in the dislocation damping are expected at the yield point.6 The use of the dislocation-damping observations to help elucidate the incompletely understood mechanism of yielding in magnesium is the primary objective of the experiments reported here. PROCEDURE Many investigations have shown that very marked and rapid changes occur in the dislocation damping of of a deformed material as soon as the straining is stopped.5 It was quite essential, then, for the purpose of this investigation, to make the damping measurements during the deformation of the samples. This can only be accomplished through the use of the ultrasonic-pulse method. In this method traveling sound-wave pulses are used and, in contrast to resonating-bar methods, only the sample ends are set in vibration. Thus, the sample can be gripped along its sides in the tensile-test machine without disturbing the damping measurements. In the pulse method, the decrease in the amplitude of a sound pulse is measured as it travels back and forth through the sample. If A is the amplitude after traversing a distance x and A. is the initial amplitude, A=Aoe-ax [2] and a is called the attenuation. It is commonly measured either in units of cm-I or as db per µ sec. The observed attenuation in a metal sample is due to a number of causes. These include scattering by grain boundaries and impurity particles, thermo-elastic damping, diffraction effects, stress-induced ordering of solute atoms, and dislocation damping. The total observed attenuation in a given sample usually cannot be resolved into these various components, but changes in a due solely to changes in dislocation damping can be accurately determined, provided the experiment is arranged so that all other sources of damping are held constant. It is desired to reduce the extraneous sources of attenuation to a minimum and for this reason the experiments are done on single crystals of high purity. Magnesium crystals offer the further advantage that, when properly oriented, only a single set of slip planes is active during deformation. Crystal Preparation. The method of sample preparation is similar to that of Geiselman and Guy.4 The starting material was high-purity, sublimed magnesium rod supplied by the Dow Chemical Co. Melting under Dow 310 flux was used to reduce the nitrogen content of the starting material: the fluxing was done under an argon atmosphere and the

Jan 1, 1965

By J. L. Brimhall

Slip-line formation during bending has been studied on neutron-irradiated molybdenum single crystals. For equivalent strains, the slip lines are coarse and distinct in the irradiated molybdenum and not resolvable in the unirradiated molybdenum. The slip lines have been directly correlated with dislocation channels present in the irradiated and deformed thin foils. The heterogeneous distribution of the dislocations during deformation in the irradiated material results from dislocation interaction with the dejects produced during irradiation. Impurities , in the form of' carbides, affected the dislocation channeling Principally by acting as dislocation sources. ALTHOUGH the mechanical behavior of irradiated materials has been studied extensively, the precise mechanism of irradiation hardening has not been established. Some information on the microstructural species responsible for hardening of irradiated materials has been derived from direct and indirect observations. The direct observation of the structure of deformed irradiated metals, particularly by transmission electron microscopy, is a relatively new and unexplored area. Slip-line studies in fcc metals have been restricted primarily to copper.1-3 Very coarse slip lines, representing slip on many closely spaced planes, have been observed in deformed, irradiated copper. Coarse slip lines have also been observed in irradiated aluminum.4 Clear channels in irradiated copper caused by dislocation motion through the defect structure have been seen by transmission electron microscopy and correlated with slip lines.5-6 To date, little work has been reported on the irradiated bcc metals. Eyre described the slip lines around hardness indentations on irradiated iron and found them to be more distinct than lines in unirradiated material.' Mastel et al.' have observed channels in deformed irradiated molybdenum similar to those reported in copper. As part of a program concerned with the effect of neutron irradiation on metals, the slip-line

Jan 1, 1965

By Charles L. Bauer

WHEN a single crystal is annealed following plastic deformation recrystallization usually occurs rather than polygonization. Consequently, re-crystallization has received the overwhelming amount of attention albeit the intrinsic mechanisms by which dislocations rearrange and annihilate one another are just as well revealed by crystal polygonization. It is the purpose of this note to demonstrate the usefulness of studying the polygonization process by means of an etch-pit technique in sodium chloride. Sodium chloride deforms easily (the slip system is of the [110], (110) type), readily cleaves on (100) planes, and can be chemically etched so as to reveal the intersection of dislocations with a free surface. Thus it is possible to observe the distribution of dislocations after a crystal has undergone a specific deformation and annealing cycle. Various phases of the polygonization process

Jan 1, 1965

By H. H. Podgurski, Hsun Hu

Large cryslals of high-purily iron (99.996+ pcl) cannot be obtained by the usual strain-ameal technique. Repealed phase transformation by thermal cycling prior to crilical deformation improves the capabilily of cryslal growith but fails to yield satisfactory crystals. Imperfect columnar crystals can be produced by the phase-transition method. The addition of a small amounl (0.005 wl pet) of nilrogen IT was reported'-4 that for metals of very high purity the usual procedures of the strain-anneal technique fail to produce large crystals. This was eliminates practically all the difficulties in crystal growth by the normal strain-anneal procedures. An actual example is presented, showing that most parts of a strip have been converted into a large crystal by this method. The addition of nitrogen, which can be removed from iron with less difficulty, is believed to be more desirable than carbon additions for the same purpose. thought to be due to the strong tendency for recovery in the high-purity metals: hence the critically strained matrix undergoes polygonization instead of recrystallization upon annealing for crystal growth. Talbot1,2 succeeded in overcoming this difficulty by adding 0.03 to 0.04 pct C to high-purity iron before critical deformation. followed by annealing in hydro-

Jan 1, 1965

By L. F. Rooney

In June 1964 the Indiana Geological Survey discovered gypsum beds more than 10 ft thick in rocks of Devonian age in La Porte County, Ind. Although the extension of the Michigan Basin evaporites into northern Indiana has been recognized for some time, the gypsum beds have been regarded as either too thin or too deep for exploitation. Current Survey research, however, indicates that exploration by industry might find commercial deposits of gypsum less than 50 miles from Chicago. In four cores taken by the Survey within 1 sq mile in La Porte County, the maximum thickness of inter-bedded gypsum and anhydrite is 35.8 ft. Both gypsum and anhydrite beds contain irregular masses of limestone and dolomite that average a few inches in cross section and total about 20% of the rock by weight. The maximum thickness of gypsum in one minable unit verified by core is 12.5 ft, and its purity is 81.3%. Chloride content of the gypsum beds is less than 0.005%. Depth to the gypsum in La Porte County is 330 to 500 ft, about the same depth as the gypsum being mined in Martin County, Ind. In June 1964 the Indiana Geological Survey discovered gypsum deposits of probable commercial thickness near La Porte, Ind. (Fig. 1). This article presents preliminary data on the distribution, thickness, depth and chemical composition of the gypsum, the possible causes of gypsification, and economic considerations of immediate interest to industry. Because of the preliminary nature of the work, only a few geologic relationships concerning the genesis of the deposits will be mentioned. DEFINITIONS The following terms used throughout this article have been restricted to the following definitions: evaporites: anyydrite (CaSO4) or gypsum (CaSO4 . 2H2O). minable evaporites: any evaporite unit which may contain more than 80% evaporites, which is more than 10 ft thick, and which in places may be completely gypsified. PREVIOUS WORK The presence of gypsum and anhydrite in the Devonian rocks of northern Indiana has been recognized for at least 70 years1-4 and can be inferred from a number of reports on the geology of Michigan. For example, in a cross section from southwestern to central Michigan, Ells5 indicated the presence of

Jan 1, 1965

By N. De Nevers

A calculation method has been developed for carbonated water flooding. This method takes into account the effects of oil viscosity reduction and oil swelling, due to carbon dioxide transferred to the reservoir oil from the carbonated flood water. It shows the effect of changes in carbonation pressure and carbonated water slug size. The method is based on a Buckley-Leverett-type linear flow model. The mathematical approach is similar to that developed by Welge, et al, for enriched gas drives. However, it contains a very important advance over the previous papers in its solution to the problem of injection of a "slug" of carbonated water rather than continuous injection of fluid of constant composition. The method also shows the chromatographic nature of the transport of Co 2 in a carbonated water flood. Sample calculations indicate that viscosity reduction is the most important source of incremental oil recovery. Swelling contributes to a lesser extent. Raising the carbonation pressure increases recovery, but this effect diminishes as pressure is increased. increasing the slug size also increases recovery, but again this effect diminishes as slug size is increased. INTRODUCTION In recent years there has been considerable interest in carbonated water flooding as a secondary recovery method. Several carbonated waterflood field tests are now in progress.1'3 Yet there is no published method for predicting the results of a carbonated water flood. This paper presents a method for predicting the oil recovery for ; carbonated water flood. In a carbonated water flood. a carbonated water slug is injected into the reservoir. Then this slug is driven forward by injecting plain water behind it. The field operator must choose the carbonated water slug size and the CO2:water ratio in the slug. The calculation method presented here shows the effects of both slug size and CO2:water ratio on oil recovery. The calculation assumes that the addition of carbon dioxide to flood water increases the oil recovery by two mechanisms: 1. Carbon dioxide transfers from the flood water to the oil, thereby reducing the viscosity of the oil. At the lower viscosity, the oil flows more readily and is more easily swept out by flood water. 2. The carbon dioxide which transfers to the oil phase causes the oil phase to swell. Assume that the residual oil saturation (volume per cent of pore space) is the same whether the oil is carbonated or not. Then the same volume will contain less stock tank oil if it is carbonated, due to oil swelling. The plain water driving the carbonated water slug forward will strip the CO2 out of this residual oil., causing this oil to shrink. This swelling-followed-by-shrinking leaves behind a lower residual oil saturation than would have been left behind by a plain water flood. Since some oils swell to almost twice their original volume at reasonable CO2 pressures, this effect may be large. Two additional benefits sometimes claimed for carbonated water flooding are: 1. Adding CO2 to flood water greatly increases the water injectivity in some cases.1 (Injectivity = BPD of water injected/ft of sand x differential bottom-hole pressure, psi.) CO2 forms a weak acid in water; injecting carbonated water is, therefore, somewhat like acid treating. If a formation responds to acid treating, it will probably have a higher injectivity for carbonated water than for plain water. Although the increased injectivity increases the profitability of a carbonated water flood over a plain water flood, it does not change the production curve based on total fluid injected. Therefore, the method presented here does not show any effect of increased injectivity. 2. It is claimed in one patent4 that carbon dioxide will react with some constituents of the oil to form detergents. These detergents are expected to increase the oil recovery. There is little data available to support this idea. The calculation method presented here takes no credit for extra oil recovery due to the formation of any such detergents.

Jan 1, 1965

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen's method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen's method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen's5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen's method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen's method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen's method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By R. W. Hertzberg, F. D. Lemkey, J. A. Ford

The effect oj unidirectional solidification upon the microstructural, crystallographic and mechanical characteristics of high -purity A1-A13Ni eutectic a1loy specimens has been investigated. varying the growth rate caused the morphology of the Al3Ni phase to gradually change from platelets to rods. In addition, the effect of increasing the rate of planar liquid-solid interlace movement is to decrease the Al3Ni rod diameter and inter-rod spacing. The platelets and rods grow approxinlately parallel to each other and are aligned in a faulted substructure. A single unique crystallographic relationship hetween the A1 and ASNi phases was found and may he descrihed as : interface {001} Al3Ni {331} Al and growth direction <010>Al3Ni || <110> Al The platelet interlace and the aligned rows of rods are both uniquely defined by the above statements. Alignment of the Al3Ni phase by unidirectional solidification has given rise to a threefold increase in strength over that exhibited by specimens with an as-cast microstructure. These results illustrate the possible use of this eutectic alloy as a zohisker -reinforced structure. It has been demonstrated by Winegard et al.,1 Kraft and Albrighht,2 Chilton and winegard,3 Chad-wick,4 Yue,5 Tiller,6 and others that a planar liquid-solid interface may be established in binary eutectic alloys by proper control of heat flow during the solidification process. The unidirectional movement of such an interface results in a eutectic mi-crostructure consisting of an essentially parallel array of the two phases over an entire ingot. Two dominant phase micromorphologies have been produced using this technique: that of substantially parallel alternating lamellae of each phase or long thin parallel rods of one phase imbedded in a continuous matrix of the other phase. While not all eutectics can be controlled in this manner, it has been shown that a "normal" eutectic may, under properly controlled conditions of purity, liquid and solid thermal gradients, and solidification rate, be forced to solidify with essentially parallel phase particles. Kraft and Albright2 have demonstrated that, when the growth rate is too rapid or when the thermal gradient in the liquid at the growing interface is too low, a layer of constitutionally supercooled liquid, formed by impurity build-up, will stabilize a cellular rather than a planar interface. The unidirectional movement of the cellular interface forms the macrostructure of eutectic colonies.7 Chilton,3 Chadwick,4 and Tiller,&apos; studying eutectics of zone-refined Pb-Sn, A1-CuAl2, Zn-Sn, and Cd-Zn systems, noted that in the absence of impurities a planar interface is stabilized even when rapidly solidified. Although it is generally agreed that impurities break down a planar interface to form the eutectic-colony macrostructure, at present the origin of the varying micromorphologies (i.c., plates or rods) in a given normal eutectic alloy is not completely understood. Tiller8 has predicted that the micromor-phology produced may be dependent on solidification rate (i.e., at fast rates a rodlike structure is preferred whereas at slow rates a lamellar structure should form), and also suggested that rod formation may be favored at large phase-volume ratios. yue5 has experimentally verified Tiller&apos;s prediction in the eutectic Mg-Mg17Al12 by observing a lamellae-to-rod transition with increasing growth rate where the phase-volume ratio was approximately 2.3:1. However, Hunt and chilton9 more recently unidirec-tionally solidified over a wide range of growth velocities six different eutectic systems with phase-volume ratios between 12:l and 2.7:1 and observed no lamellae-to-rod transition. chadwickl0 has proposed that the change in micromorphology in some eutectic alloys is due entirely to the presence of impurities and further states that the lamellar structure is the characteristic structure of pure eutectic alloys even when the phase-volume ratio is as great as 12:l. Kraft11,12 has shown that the parallel lamellae in certain eutectic alloys assume a unique crystallographic relationship during unidirectional growth. This preferred crystallography may be developed

Jan 1, 1965

Jan 1, 1965

By W. C. Hagel, H. J. Beattie

Phases present at 2200° and 1500°F (1204° and 816°C) were identified in sixty wrought developmental austenitic alloys possessing wide compositional variations. The bases were iron-, cobalt-, and nickel-rich as well as a base with equal parts of each. There are only two structure types previously not found in similar alloys, viz .-the Co3 W and the Fe3Al types. A molybdenum-rich monocarbide decorates dislocations with unusual clarity. Other results provide correlations between alloy composition and phas e precipitation. Grouping intermetal -lic phases into three general classes : I) geometrically close-packed, 2) topologically close-packed, and 3) bcc derivatives, the nickel base prefers the first, the iron base the second, and the cobalt base the third—each base tending to shun the other two classes. Thus, a crystal-chemistry effect previously noted by Laves and Wallbaum can he expanded for these Group VIII elemental bases. There appear to he no quaternary or higher -order structure types requiring more than three atomic species. AFTER studying aging reactions in many diverse commercial austenitic alloys1-4 as a function of detailed time-temperature variations in heat treatment, it became apparent that matrix composition influenced structure types and morphologies to a large extent. These tendencies were related4 to a crystal-chemistry effect uncovered by Laves and Wallbaum.5,6 We have now directed our efforts to exploration of the whole ternary field, covering the standard base elements—iron, cobalt. and nickel— with 10 to 20 pct Cr and moderate amounts, up to 10 pct, of the usual alloy additions. Solutioning and aging treatments were held constant with major emphasis on X-ray identification of microconstituents. The possible existence of exceptions to the Laves-Wallbaum effect, or any new phases, was sought. Phases appearing in austenitic alloys can be classified as geometrically close-packed (gcp), octahedral or nonoctahedral interstitial compounds, topologically close-packed (tcp), semicarbides, and bcc derivatives. Crystal structures of the first four classifications can be visualized as a dense packing of semirigid spheres of different sizes, while the bcc derivatives represent a less efficient packing of spheres. The Laves-Wallbaum effect involves the gcp and tcp phases. Gcp phases possess both tetrahedral and large octahedral interstices; examples are Ni3Ti(n), NiSAl(y&apos;), Co3W(E), and other ordered AB3 compounds where B atoms are smaller than A. Their precipitation is primarily intragranular, presumably coherent with an austenitic matrix, and a chief source of strengthening. Most octahedral interstitial compounds (e.g., CbC, Tic, TiN, Mo2C) have a gcp lattice of large metal atoms which accommodate small carbon or nitrogen atoms in the octahedral interstices. The compound Ti2SC, previously designated Y phase or T phase, can, with some reservation due to its partial co-valency, be placed in this category.7 The nonoctahedral interstitials (e.g., M7C3, Fe3C) represent close-packings of spheres in structures that provide larger triangular-prism interstices for carbon, since the octahedral interstices formed by chromium and iron atoms are too small. Tcp phases possess only tetrahedral interstices; examples are Laves (Fe2Ti, Fe2Cb, Fe2W...AB2), p(Fe7MO6, Co7W8.... A8B7), and (FeCr, Co2Cr3)

Jan 1, 1965

By R. L. Grunes, F. K. Kies, C. D&apos, Antonio

THE several studies concerned with the annealing of thin nickel films have largely been restricted to films of a single thickness.1-4 It is well-known, however, that both physical and mechanical properties depend upon film thickness.5, 6 The strength-thickness relations found in vapor-deposited nickel films in the annealed and as-deposited states, as an example, are at least partially due to the density and arrangement of imperfections within the films.7, 8 For these reasons, the annealing characteristics of thin nickel films as a function of thickness were investigated. Electrical resistance was chosen to monitor annealing behavior since resistance changes are partially dependent upon defect structure. In addition, the equations predicting film resistivity as a function of thickness are already available.9, 10 Further advantages afforded by electrical-resistance measurements are its adaption to continuous readings during annealing and its relative simplicity. Nickel films were vapor-deposited, at average rates of 60Å per sec, on Vycor substrates held at room temperature in vacuums of about 10-5 torr. Afterwards, deposition-thickness measurements were made using a multiple-beam interferometric technique. A more detailed description of deposition procedures and the interferometer appear elsewhere.7, 8 The four-probe method was employed in measuring electrical resistance since this technique measures film resistance without contributions from lead wires and contacts. Resistance measurements were made before, during, and after annealing to temperatures of 700°C under vacuums of approximately 10-4 torr. Measurements were made every 25°C or more often when necessitated by unusual resistance changes. Cooling and heating rates were maintained at approximately 5°C per min. Typical resistivity vs temperature curves are shown in Figs. 1 through 4. It is apparent from these

Jan 1, 1965

By R. H. Barham, G. W. Nabor

Linear aquifers, either limited or essentially infinite, may be encountered in reservoir engineering practice. In areas where faulting fixes reservoir boundaries, the fault block reservoir may have an aquifer of limited extent whose geometry is best approximated as linear. An infinite linear aquifer can occur as a regional feature whenever water movement through the aquifer member is constrained to one direction. Such constraints can arise from major faults, facies changes or pinchout of the member. Miller* pointed out that linear aquifers have received only meager attention in the past. He analyzed the performance of finite and infinite aquifers, developed working equations and curves, and presented examples. While Miller&apos;s curves may be used fairly easily, a separate one is required for each size of aquifer. In this paper, Miller&apos;s equations have been used as a starting point. By modifying them slightly, they can be reduced to a form which yields a single working curve, applicable to any size of aquifer. Thus. interpolation between curves is eliminated and accuracy is improved. Miller&apos;s results for finite aquifers covered only the boundary condition of no flow across the outer aquifer boundary. This paper also includes the case of constant pressure at the outer aquifer boundary.

Jan 1, 1965

By M. C. Lavine, H. C. Gatos, R. S. Mroczkowski

The structure of GaAs-Ge heterojunctions prepared by a back-melting process was studied by X-rav diffraction, melallographic, and electron-micro-analyzer techniques. The boundary region between the GaAs and the germanium was found to consist of a four-layered band. A discontinuity between the two inner bands was brought about by solidification occurring simultaneously from the GaAs and the germanium side. The junction material OH either side of the central discotinuity was found to have grown as a single Crystal with the orientation of the parent substrate. It was found essential to determine the GaAs-Ge phase diagram. This was accomplished by a series of alloys containing 0 to 40 wt pet GaAs. Over this range the diagram is a simple eutectic with the eutectic point at 74 wt pet Ge and 845 C. The limiting- solubility of Coils in germanium was found to bc less than 5 wt pet. The Kossel divergent-beam X-ray technique was used to study orientation relationships across the boundary lager. A great deal of effort has been recently expended on the electrical properties of heterojunctions. Little attention, however, has been given to the metallurgical variables which may be of importance in the formation of the junctions. The present work was undertaken to investigate some of the more pertinent metallurgical aspects of interface-alloyed GaAs-Ge heterojunctions. Such parameters as solidification processes, composition gradients, orientation effects, and the accommodation of crystal structures have been the objects of study in this program. EXPERIMENTAL PROCEDURES Phase Diagram. The phase diagram of the GaAs-Ge pseudobinary system was determined by means of cooling curves. A Bridgeman furnace was employed with the center section maintained at 1200°C and the upper section at 800°C. Melts varying from 0 to 40 at. pct in GaAs content were used. Each charge was incapsulated under a two-thirds atmosphere of argon in a carbon-coated quartz tube. Five min in the furnace hot zone provided rapid melting and homogenization. The capsule was then removed to the cooler portion of the furnace. Cooling times were of the order of 3 min. The resulting homogeneous microstructure indicated that equilibrium conditions were obtained by this procedure. Formation of Heterojunctions. Rectangular parallelepiped single-crystal samples were cut with the large faces of either the (l00), (110), or (111) orientation. The remaining four surfaces were also cut to specific orientations to permit accurate relative orientation of the GaAs-Ge pairs. The

Jan 1, 1965