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By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,'~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro'~ suggested that the strain E can be deduced

Jan 1, 1970

By Appendix by A. S. Goldoni, R. E. Tate, E. M. Cramer

The diffision coefficient for self-diffision of plutonium in the temperature range 350" to 440°C has been measured by using puZ3 as the tracer isotope. Autoradiopaphic techniques were used to inzlestigate the possibility of grain boundary diffusion, hut only evidence for volume diffusion was found. The least-squares fit of the data gives the .following equation for the diffision coefficient: The computer least-squares technique for fitting the nonlinear equations is outlined. DETERMINATION of the self-diffusion coefficient of the fcc 6 phase of plutonium is in principle a straightforward experimental task. However, the chemical reactivity, the intense @ activity, and the toxicity of plutonium put limitations on the experimental techniques. The technique selected included roll bonding for preparation of the diffusion couples and pulse-height analysis of the @-particle activity to determine the distribution of the PU tracer in the diffusion couples. EXPERIMENTAL PROCEDURE Couple Preparation. Cylinders about 0.5 in. in diam were cast from two special stocks of plutonium, one of which had been enriched in puZ3', as shown in the isotopic analyses listed in Table I. For each roll-bonded composite sheet, a cylinder 0.437 in. in diam and 0.190 in. thick was turned from each kind of plutonium on a lathe in a 98 pct He atmosphere. The two freshly machined cylinders were positioned face to face in a tube of commercially pure aluminum which had been sealed at one end by welding and the assembly was evacuated on a vacuum manifold overnight. The elapsed time between machining the faces of the plutonium cylinders and evacuating the loaded tube was about 15 min. After overnight evacuation of the assembly the indicated vacuum was 1 X 10"5 torr or better. The aluminum tube was then warmed and pinched off with a cold-welding tool. The pinched-off weld was also fusion-welded as an additional precaution against leakage of air into the evacuated assembly. The assembly was immediately heated for 30 min in a 250°C furnace and reduced in thickness by being passed through a rolling mill with rolls heated to 200°C. The rolling schedule (four passes of 100 mils each with a 10-min reheat after two passes) reduced the thickness of the assembly to 100 mils. The rolled assembly was allowed to cool normally in air. The rolled assembly was sheared at the edges and the aluminum peeled from the composite plutonium sheet. The elliptical sheet was about 0.060 in. thick and usually three 0.383-in.-diam disks could be punched from its central portion. The sheet was heated on a hot plate to the ductile low 0 range (140°C as measured by temperature-indicating pellets) before each disk was quickly punched. The quality of the bond in the disks was evaluated by metallographic examination of the scrap sheet adjoining the hole left by the punch. Only well-bonded specimens without oxide in the interface (as indicated by metallography) were considered satisfactory for further use. More than half of the specimens so examined contained sufficient oxide in the interface to be rejected. Diffusion Anneal. Each disk to be diffusion-annealed was wrapped in 1-mil-thick tantalum foil and sealed within a Pyrex capsule evacuated to 1 x 10~5 torr or better. This capsule was then sealed within another Pyrex capsule at a similar pressure. The diffusion anneals were carried out at temperatures between 350" and 440°C in Marshall furnaces adjusted to have a temperature gradient of not more than *1/2"C over a 5-in. length. This gradient was then further smoothed by using a nickel tube as a liner in the furnace. The liner was divided into three longitudinal cavities by a septum of nickel sheet to which two calibrated Chromel-Alumel thermocouples were attached. One thermocouple was used for controlling the furnace temperature by means of a Brown Pyrovane controller equipped with a Capaciline anticipation circuit; the second thermocouple was monitored twice daily with a Leeds and Northrup K-2 precision potentiometer.

Jan 1, 1964

By W. O. Philbrook, H. E. Burner, F. S. Manning

The equation of continuity for the hydrogen reduction of hematite in a fixed bed of closely-sized particles is solved assuming a flat velocity profile, negligible temperature gradients, md negligible axial diffusion. A kinetic expression from the literature is used which assumes the reduction process is controlled at the oxide-metal interface. The integral fractional conversion is computed, and the importance of particle diameter, flow mte, temperature, bulk axial diffusion, and inter- and intra-particle mass trarnsfer is predicted. Comparison with experimental data suggests one or more additional undefined variable(s) is significant. Equipment modifications are suggested for fidture experimentcll work. WITH the increasing desire to "design" the ore feed of a blast furnace, it has become necessary to define more quantitatively the process variables and to evaluate the extent of their control upon the reduction process. The bulk of the work reported in the literature has centered about the reduction of single particles; however, the blast furnace process more closely resembles reduction of a fixed bed than that of single particles. To simplify this analysis, the isothermal reduction by hydrogen of a natural hematite in a fixed bed of closely-sized particles is examined. With appropriate modifications in the kinetic and flow rate expressions, the approach employed should be extensible to mixtures of carbon monoxide, hydrogen, and inert nitrogen, and to adi-abatic conditions, thus approaching the blast furnace process more closely. The fixed bed variables which are investigated in this study are particle diameter, flow rate, temperature, and bulk axial diffusion, as well as inter-and intra-particle mass transfer. Of particular interest is the effect of particle size upon fractional conversion for a bed operating under constant pressure drop. The constant pressure drop concept bears a close resemblance to the blast furnace process, where regions of larger particles may provide a greater permeability to divert most of the reducing gas flow from the regions of smaller ore particles. Under such conditions one would expect qualitatively that, for sufficiently small particle sizes where the flow rate is small and the total surface area is large, the reduction rate would be limited by the gas flow rate. Initially the gas entering the bed reacts very rapidly and the composition approaches the equilibrium conversion value a short distance from the reactor inlet. This concentration "wave-front" then moves up the bed as the flow of reducing gas is continued, leaving in its wake an ever increasing layer of reduced particles. Providing that the reducing gas leaves the bed at equilibrium concentrations, conversion is expected to increase with an increase in flow rate, and hence with an increase in particle diemater. Conversely, for sufficiently large particles the flow rate will be high but the surface area available for reaction will limit the reduction rate. Since the total surface area decreases with an increase in particle size, conversion, in this case, is expected to decrease as the particle diameter is increased. It is clear then that between these two extremes an optimum particle diameter must exist. THEORETICAL DEVELOPMENT Above the temperature where wiistite is stable (about 560°C) the reduction of hematite proceeds through the series Fe2O3/Fe3O4/FeO/Fe. On the basis of microstructural studies and earlier work, Edström1 has postulated a mechanism for the reduction of an ideal hematite lattice: 1) Iron phase formation at the boundary between wiistite, iron, and gas (for sufficiently porous iron). 2) Diffusion of iron across a wustite layer. 3) Phase boundary reaction of Fe3O4 to FeO. 4) Diffusion across a dense magnetite layer. 5) Phase-boundary reaction of Fe2O3 to Fe3O4. According to the mechanism postulated, gaseous reaction product has to be removed only at the boundaries between wüstite and iron or gas, the only possible exception being enveloped Fe3O4 specks. On this basis McKewan2,3 has proposed that one may consider the hematite reduction process as a simple two-phase system of oxide/metal. If, for FeO and Fe3O4 layers of negligible thickness, the hypothesis is made that the rate of formation of a

Jan 1, 1963

By H. C. Casey, M. B. Panish

The roles of the phase diagram and the diffusion and solubility analyses in the selection of sources for the diffusion of zinc into GaAs are discussed. Isothermal sections of- the phase diagram are described at 1000°, 775°, 744°, and 700°. Below 744° the three solid phases, Zn3As2, GaAs, and ZnAsz, may be in equilibrium. In the composition regions where the three solid phases are in equilibrium, the partial pressures of the components do not vary with composition and there is no liquid phase. A diffusion source composition within that region containing 5, 50, and 45 at. pct Ga, As, and Zn was selected to yield reproducible diffusion profiles without surface damage. The 5/50/45 ternary source Provides a significant improvement in the reproducibility and planarity of- the zinc diffusion as compared with other zinc diffusion sources that result from starting with elemental zinc, dilute solutions of zinc in gallium, or various combinations of zinc and arsenic. Several experimental diffision profiles for the 5/50/45 diffusion source have been determined. The profiles are very steep in the region of the junction and produce devices that exhibit step junction behavior. The junction depth varies as the square root of time. Diffusion at 700°C for 4 hr gives a 5-µ junction depth and a surface concentration of 2.4 x1020 cm-3. The surface concentration is enhanced by a factor of three and the junction depth decreased by a factor of ten as compared with diffusion with a starting source 01- elemental zinc. The differences in dijyusion behavior with these two sources are due primarily to the approximately 10' greater equilibrium As4 partial pressure for the 5/50/45 source. ThE most common technique for the preparation of GaAs p-n junctions for diverse applications ranging from switching diodes to injection lasers has been to diffuse zinc into the solid from the vapor phase. The zinc impurity has generally been provided by introducing into a diffusion ampoule elemental zinc, dilute solutions of zinc in gallium, or various combinations of zinc and arsenic. For the purpose of eliminating surface deterioration, zinc has been diffused into GaAs through SiO2 films1 and from zinc-doped SiO2 films.2 During a study of the injection and recombination mechanisms in GaAs junctions, we found that these diffusion techniques either resulted in nonreproducible diffusion profiles and nonplanar junction interfaces or were extremely inconvenient to use. An unpublished report by Allen and pearson3 emphasized that an understanding of diffusion requires relating the diffusion conditions and system compositions to the ternary phase diagram. Recent studies have made it possible to relate the effect of starting source composition on the GaAs sample surface and diffusion profile reproducibility and, in addition, to estimate the expected surface concentration and zinc diffusivity. These studies include the Ga-As-Zn phase diagram,415 the determination of the incorporation reaction for zinc as a substitutional impurity,6 and the analysis of the concentration dependence of the diffusion coefficient.' In this paper the role of the phase diagram in the selection of the starting diffusion source composition is illustrated, and an application of the diffusion and solubility analyses is used to demonstrate their utility in the estimation of surface concentration and diffusivity for various starting source compositions. Consideration of the isothermal sections of the ternary phase diagram shows that below about 744° C a composition region exists where the three solid phases Zn3As2, GaAs, and ZnAs2 are in equilibrium without a liquid phase. In this region the partial pressures of the components do not vary with composition, and thus the surface concentration and diffusivity depend only on temperature. A diffusion source composition within that region containing 5, 50, and 45 at. pct Ga, As, and Zn was selected. As will be described in detail, this diffusion source yields reproducible diffusion profiles without surface damage, planar junction interfaces, and steep profiles that result in devices with step junction behavior. Only closed diffusion systems are considered. Open or flowing vapor systems require the maintaining of constant vapor pressures in the flowing gas and represent control problems outside the scope of this discussion.

Jan 1, 1969

By Morris Muskat, James M. McDowell

A report is given of electrical analog experiments on the effect of casing perforation completions on well productivity for ideal uniform reservoirs under steady state homogeneous fluid flow conditions. Graphical results are presented for the effect of perforations of different densities and various degrees of penetration into the formation surrounding the casing or cement sheath. The latter range from perforations which terminate flush with the casing to those which extend into the formation a distance equal to the casing diameter. For the special case where the perforations terminate immediately beyond the casing with semi-spherical protrusions the electrical analog results correct and supersede previously reported theoretical calculations. It is found that the penetration of the perforations into the surrounding productive section may so increase the resultant productivity as to approach or even exceed that for open hole completions. INTRODUCTION A theoretical analysis of the effect of casing perforation on well completion, without additional penetration of the formation, was reported several years ago.' In this treatment the perforations were represented by mathematical sinks and no explicit account was taken of the imperviousness to flow of the casing in which the perforations were made. This procedure was justified by consideration of the mutual interference between the sinks, which seemed to indicate that the analytical method automatically eliminated flow across the casing radius between the perforations. However, both further theoretical investigation and the electrical analog measurements described below showed that this assumption in the previously developed theory was not valid and that the calculated well capacities would considerably exceed the correct values. § Even if this simplifying assumption were retained the generalization of the theory to situations where the perforations extend into the producing formation would be extremely difficult. On the other hand, the electrolytic model analog of this type of steady-state homogenous fluid system is, in principle, so simple that it has not been worthwhile to attempt to develop the exact analysis even for the more limited case of strict casing perforation. The whole problem has therefore been studied anew by electrical models to cover the range from holes in the casing which terminate flush with the casing surface to such as extend into the surrounding rock to a depth equal to the casing diameter. It is to be expected that the productivity of a well completed with casing radius* rw, perforated with holes of radius Tp, and extending to depths d into the surrounding rock, would depend primarily on the dimensionless geometrical parameters Te Tw TP d of the system, such as —, —, — , and —, where re is the Tw, a a rw external boundary radius and a is the mean vertical separation between the perforations. It will also depend, of course, on the number of perforation lines or total perforation density. While such parameters automatically control analytical treatments, it would require a very extensive series of model experiments to fully disclose their functional effect on the well productivity. For practical purposes, however, a rather limited range of the variables suffices to give the effects of interest. Accordingly, in the experimental study reported here the casing diameter has been kept fixed? at six in., the perforation diameter has been taken as either one-fourth in. or one-half in., their density has been varied from one to eight per ft, and their penetration into the formation has ranged from zero to six in., with a primary scaling factor of one to six. EXPERIMENTAL METHOD AND RESEARCH Although electrolytic model experiments have been made for years, there still seems to be some question as to what set of conditions will give the best results. For this reason a number of electrode materials and electrolytes were tried. Those chosen for the final experiments were copper electrodes and a weak copper sulphate solution as the electrolyte. This 'Assuming that the casing has been cemented with a uniform and impermeable cement sheath, the effective casing radius is to be interpreted as the external radius of the cement annulus. It is also assumed here that the casing is set through the complete producing section that it is perforated throughout with a uniform density and that tie formation has a a and isotropic permeability. As noted later, however, a uniform scale change permits reinterpreting the primary measurements to correspond to a casing diameter of 12 in.

Jan 1, 1950

By J. Downie, H. A. Kendall, G. H. F. Gardner

Some cases of the motion of two miscible fluids in uniform linear models are discussed. There is no bulk flow through the models, and the convection currents are caused solely by density gradients. Horizontal, vertical and inclined positions of the models are treated separately. Analytical formulas for the motion of a narrow transition zone between the fluids are obtained and compared with measurements, and the limitations are discussed. Observations of the ultimate stabilizing effect of diffusion on the motion me compared with the theory. It is shown that fluid motion in an inclined model with a constant rate of bulk flow can be directly deduced from the cases discussed, provided the viscosity ratio is small. INTRODUCTION In some reservoirs, convection currents caused by variations in the fluid densities may be significant. For practical purposes it may be desirable either to minimize the effect, particularly in miscible displacement, or to maximize the effect as in some schemes for the production of heavy crude oils by combustion. Experiments by Craig, et al,l have shown the effectiveness of gravity in reducing the efficiency of a miscible displacement when the mixed zone between the displacing and displaced fluids is narrow compared with the height of the system. The presence of a board transition zone from one fluid to the other has been shown by Perkins, et al,2 to nullify considerably the influence of a difference in density. Indeed, the theoretical discussion given by Perrine3 has shown that when the transition zone exceeds a certain critical length the efficiency approaches 100 per cent. Many additional results 495 have been published on miscible and immiscible displacements which show the importance of density difference and also mobility ratio. The aim of the present paper is to discuss some cases of gravity segregation of miscible fluids in linear models such as are often used in the laboratory to evaluate recovery processes, and to supply additional experimental evidence in support of the conclusions. An attempt is made to calculate simply the magnitude of the fluid motion caused by density pdients and mobility ratios, and to quantify the modifications in the fluid motion produced by the combined effect of molecular and convective dispersion. However, it should be pointed out that the uniform permeability of the models and the use of only a single pair of fluids (whereas several pairs of fluids may be employed in a recovery scheme) severely restricts direct conclusions about natural reservoirs. For conciseness, the motion generated by density gradients is emphasized for the case of no bulk flow through the models. This is not a drastic limitation because, as shown in Appendix A, a fluid motion with a constant bulk flow through any linear model is equivalent to a fluid motion with no bulk flow in the same model inclined at a different angle to the horizontal, provided only that the density is a linear function of the viscosity of the fluid mixture. HORIZONTAL MODEL In this case the model is assumed to have a rectangular cross-section with a horizontal breadth b, vertical height and a great length L. Throughout.the paper it will be assumed that x-axis points along the length, the y-axis along the width and the z-axis along the height. Thus, in the present case the x, y plane is horizontal. Initially, the transition zone between the fluids is assumed to be thin and parallel to the y, z plane. An example of this situation in a practical problem arises in a scheme for using air for cushion gas in the storage of fuel gas in aquifers. 6 With the passage of time the denser fluid sinks and spreads along the bottom of the model while the lighter fluid rises. The interface extends from the top plane of the model to the bottom. Experiments have shown that for practical purposes this interface may be treated as a plane surface at all times. The surface is significantly curved, however, for viscosity ratios greater than about 10. Other complications arise with large viscosity ratios because of the nonlinear dependence of the viscosity on the composition of the mixture, so that the simple results given here are restricted to fairly low viscosity ratios.

By E. M. Kalar, I. Iwasaki, J. D. Zetterstrom

Several methods of removing fatty acid coatings from iron ore flotation concentrates were tested both on a Mesabi oxidized iron ore and on a magnetic taconite concentrate, and their effects on the duplex flotation process and on pelletizing were compared. Either acid or alkali alone could not remove the coatings, but a combination of such reagents as lime and quebracho, calcium chloride and pyrophosphate, or sulfuric acid and an organic acid (oxalic, malonic, or citric acid) was quite effective. The use of activated carbon was found to be particularly promising. The removal of fatty acid coatings from iron ores is of much practical interest when a pelletizing process is being considered for a concentrate floated with a fatty acid collector or when a duplex flotation process is being considered for upgrading an oxidized iron ore. A duplex flotation process is a fatty acid flotation of iron minerals followed by an amine flotation of the siliceous gangue from the rougher iron concentrate. Such a process is being used in the Florida phosphate fields.' Although in northern Michigan mills fatty acid flotation concentrates have been pelletized successfully, at other locations fatty acid coatings on iron flotation concentrates have proved so undesirable in the agglomeration operation that other methods of concentration had to be sought.' Since fatty acid coatings cannot be removed as readily with a simple acid or alkali treatment from iron oxide surfaces as from Florida phosphates, a combination of reagents, such as lime and quebracho,3 lime and alkali phosphate,4 or sulfuric acid and oxalic acid,' has been proposed. It was also thought that activated carbon might be effective in removing fatty acid coatings due to its high adsorptive capacity. Activated carbon, with its enormous surface per unit of volume, is well known for its exceptional efficiency in removing organic pollutants from industrial effluents. This article presents the practical aspects of the above methods when they are applied to the duplex flotation process and to the pelletizing of iron flotation concentrates. The article also includes a preliminary investigation of the common parameters involved in the depressant activity of the reagents. EXPERIMENTAL WORK Initially, the experimental work was directed towards the optimization of each method for the removal of hydrophobic coatings from iron oxide surfaces floated with fatty acids. Subsequently, the methods thus optimized were tested in the duplex flotation process with an oxidized iron ore and in the pelletizing process with a magnetic taconite concentrate. Preliminary Flotation Tests: Although the three types of chemical treatment reported in the literature were briefly investigated for the purpose of comparison, major emphasis was placed during the preliminary flotation tests on the use of activated carbon because it was thought to have certain advantages over the chemical methods. LIME AND QUEBRACHO - To obtain a flotation concentrate for optimizing the lime and quebracho method of fatty acid removal, the magnetic taconite concentrate was used. The concentrate had a size consist of 90% passing 325 mesh and analyzed 64.5% iron. After a few preliminary tests the fatty acid flotation procedure with the magnetic taconite concentrate was standardized as follows. A 1200-g sample of the magnetic concentrate was pulped in a Fagergren laboratoy flotation cell to 40% solids, conditioned with 0.5 lb of soda ash per ton for 2 min, and then further conditioned with 1.0 lb of Acintol FA-2 per ton for 2 min. After 5 min of flotation, recovery was nearly complete, averaging 98.6% of the weight and 98.7% of the iron. The cell product, which amounted to 1.4% by weight and analyzed 63.2% iron, consisted mainly of relatively coarse middling particles. Since the repro-ducibility of the flotation concentrates produced by this procedure was vey high, the same procedure was used to prepare fatty acid concentrates for each of the six tests of the lime and quebracho method. To test the removal of the fatty acid from the magnetite surfaces by the lime and quebracho method, a fatty acid froth product was returned to the flotation cell, repulped by 30 sec of agitation, and then con-

Jan 1, 1968

By J. L. Huitt, J. L. Pekarek, D. K. Lowe

In a theoretical study of hydraulic jetting, the velocity of the abrasive material relative to the velocity of the fluid in the jet stream is analyzed as the jet stream moves through the convergent and straight sections of the nozzle and the region between the nozzle exit and target. The results revealed that the abrasive material exits from the jet nozzle at a lower velocity than the fluid. The exit pmticle velocity can be increased by increasing either the density of the fluid or the length of the nozzle, and/ or decreasing either the particle density or particle diameter. In the divergent jet stream, there exists a point after which the particle velocity exceeds that of the fluid. The relative velocities were considered in the derivation of an equation to predict cutting rate of a circumferential notch and maximum notch depth. Data of a general nature and data which substantiate the theoretical results were obtained experimentally. INTRODUCTION The use of a fluid containing an abrasive material has been an established technique for cleaning and cutting for many years. In the petroleum industry, the early effort to use this technique1 to perforate and/or to overcome wellbore damage met with only limited acceptance because of the short life of the jet nozzle. With the introduction of improved perforating techniques, and later, hydraulic fracturing, the use of hydraulic jetting as a well completion technique became even less appreciated. It was only in recent years that interest in hydraulic jetting was revived. Once this interest was revived, the results of surface tests stimulated the interest of the industry even more than the state of the technology probably warranted because many of the tests were not appropriate for down-hole conditions. However, because of the stimulated interest, the development of the jet nozzle progressed very rapidly to the point where the nozzle life was no longer a prob- lem. With this accomplished, the use of hydraulic jetting in well completion became an accepted practice in a short time. The purpose of this paper is to present a theoretical analysis of the hydraulic jet stream as it passes through the nozzle and travels to its target. With a better understanding of the jet stream and the effects of various parameters, the performance of the process can be predicted more accurately. Equations are presented for cutting rate as applied to circumferential wellbore notching that relate the jet stream make-up, notch configuration and formation material. Also, experimental data are presented on some factors pertinent to hydraulic notching that are not theoretically analyzed. RELATED STUDIES Most of the studiesl-5 reported in the recent literature have pertained to the more practical aspects of hydraulic jetting; i.e., the effects of certain parameters as interpreted from experimental results, and the application of hydraulic jetting in well completion. In reviewing the effects of various parameters, it is interesting to note the reported depths of penetration obtained under various imposed conditions. In general, the depths vary from a few inches to several feet; however, a depth of penetration of less than 6 in., as reported by Thompson,4 seems more realistic for the usual field practice of hydraulic jetting with sand in water for a period of 20 to 30 minutes. In addition to the practical aspects, the study of Brown and Loper5 included a theoretical approach to hydraulic jetting. Their study resulted in the development of a theoretical expression for the maximum depth of penetration if jetting were continued for an infinite time. An analysis of the equations presented reveals that the initial cutting rate is infinite. The equation expressing centerline velocity is that of Forstall and Gaylord,6 which is applicable for a jet stream exiting in a large stationary medium. Since practically all of the fluid pumped into a perforation (or cut) must flow back through the perforation prior to re-entering the wellbore, a description of the medium as finite and non-stationary seems more reasonable. Thus, in this

By J. J. Pfeiffer, A. A. Oming, J. W. Myers

The method used to process washery refuse for use as a building material aggregate is described. Results of studies made in investigating this process are summarized. The Bureau of Mines, in cooperation with two commercial coal producers, studied the feasibility of using coal washery refuse in manufacturing lightweight aggregate for building materials. Lightweight aggregate is used in making masonry products of lower bulk density than can be produced from conventional aggregate such as sand, gravel, and crushed rock. Among the advantages of lightweight masonry are reduced deadweight loads which reduce materials cost, lower cost of construction labor, and improved thermal and sound insulation. A process for making lightweight concrete aggregate from coal-washery refuse appeared attractive because of the availability of raw material which contained sufficient fuel to carry out the processing. Vast quantities of such refuse have accumulated throughout the coal-producing areas of the U.S. Generally it is stored in unsightly piles, creating a problem of air pollution and using space that could be devoted to other purposes. Conversion of the refuse to lightweight aggregate could remedy these conditions and effectively utilize a material normally considered waste. The first part of the program was conducted in cooperation with the Truax-Traer Coal Co. to determine the feasibility of utilizing refuse from the company's coal preparation plant at Ceredo, W. Va., in manufacturing lightweight aggregate. The aggregate was to be used in making cement blocks comparable to those known in the building trades as cinder blocks. This project was completed in 1954. Based on the results of this work, the cooperator began commercial development and formed the Trulite Corp. for this purpose. A plant capable of handling 120 tpd of refuse was constructed for approximately $120,000. It began operating on June 1, 1955.' In 1959 a similar study was made, under a cooperative agreement with the Carbon Fuel Co. of Charleston, W. Va., to rrscertain the suitability of refuse from its plant for conversion to lightweight aggregate. Under this program various modifications of equipment were made, and the investigation of process variables begun in the previous project was extended. PROCESSING METHOD The formation of lightweight aggregate from coal-washery refuse js governed, in part, by the fusion characteristics of the mineral constituents of the refuse when heated above their softening temperatures. The heat required for this purpose is supplied by the combustihle matter in the refuse. Some of this combustible matter is coal with high ash content, but most of it is carbonaceous shale. Whereas the density of aggregate prepared from clay or shale depends largely on expansion, the density of aggregate made from refuse is reduced by burning out the combustible matter and, to a lesser extent, by expansion of the residue in the fuel bed. A chain-grate stoker with an updraft air system was chosen for the conversion process in preference to a downdraft sintering machine or a rotary kiln. In down-draft sintering, which operates on the overfeed burning principle, the volatile matter from the refuse would distill off without burning, resulting in inefficient combustion and interfering with proper operation of the equipment. The rotary kiln is designed primarily for processing material that lacks, or is low in, combustihle matter with the heat of reaction supplied from external sources. Washery refuse, which is relatively high in carbonaceous material, could burn at the wall of the kiln causing clinker formation with resultant decrease in throughput and increase in production cost. With an up-draft air stream on a chain or traveling-grate stoker, the volatile matter would be carried into the ignition and burning zones where the heat could be utilized more efficiently. The combustion procedure in this type of unit may be considered as consisting of four periods: 1) initial ignition of the top of the bed by furnace radiation, 2) ignition travel through the bed until the whole bed is ignited, 3) burnout of the combustible material with high air rates to fuse and expand the residue, 4) a cooling period. Investigation of the process required a study of the variables that affect both

Jan 1, 1962

By G. Gutierrez, D. A. Elgillani, M. C. Fuerstenau

The zero-points-of-charge of apatite, calcite, and fluorite are pH 6.4, 10.8, and 10.0, respectively. Scheelite is negatively charged above at least pH 3. In this article, the flotation responses of these minerals in the presence of potassium oleate and sodium silicate are described and compared with electrokinetic data. Colloidal silica appears to be the species principally responsible for calcite depression, while silicate anion is the species responsible for fluorite depression. Additions as high as 1 x 10-3 mole/liter silicate have no effect on the flotation responses of apatite and scheelite. Selective flotation of nonmetallic minerals is difficult to achieve with fatty acids or soaps by themselves. As a result, specific reagents are added to aid these separations, and one of the reagents commonly employed for this purpose is sodium silicate. Flotation separations of various calcium-bearing minerals such as fluorite from calcite1-3 and scheelite from calcite2,4 and apatite,2,5 for example, almost always involve the use of sodium silicate. The mechanisms by which sodium silicate functions as a depressant are still not understood, probably for a number of reasons. For one thing, the dissolution process of sodium silicate is complex, giving rise to a number of ionic and colloidal species.' Moreover, the type and concentration of these species depend on the ratio of Na2O to SiO2, the concentration of sodium silicate, and the pH of the system.' At the present time, it is not known which species, colloidal silica or silicate anion, is responsible for depression. If colloidal silica is the species that is adsorbing, then adsorption must occur by electrostatic attraction between the colloid and the mineral surface. Silicate anion, on the other hand, may adsorb either physically or chemically. The objective of this paper is to determine first the active species of sodium silicate and then the conditions under which this species will adsorb and function as a depressant. EXPERIMENTAL MATERIALS AND METHODS Pure samples of apatite (Durango), calcite (Iceland-spar), fluorite, and scheelite were used in this investigation. Pure potassium oleate was used as collector, while reagent-grade HC1 and KOH were employed for pH adjustment. The sodium silicates used were samples obtained from the Philadelphia Quartz Co. In one series of experiments, various sodium silicates containing different ratios of SiO2 to Na2O were added to calcite systems. These sodium silicates contained SiO2-to-Na2O ratios of 3.75 to 1, 3.22 to 1, 2.40 to 1, and 1.60 to 1. All other experiments were conducted with the sodium silicate containing the ratio of 3.22 to 1, which is the one that is normally used in industry. Flotation experiments were conducted with 21/2-g charges of 48 x 150-mesh material in conductivity water with an apparatus and technique described previously. Electrokinetic experiments were conducted with both a Zeta Meter and streaming potential apparatus. Particle size was 48 x 65 mesh for the streaming potential experiments. EXPERIMENTAL RESULTS The first series of experiments involved flotation of scheelite in the absence and presence of sodium silicate. As shown in Fig. 1, flotation response was not affected with even the relatively high addition of 1 x 10-3 mole per liter sodium silicate. Interestingly though, no flotation was effected below pH 6 with this collector addition. The responses of apatite to flotation under these same conditions are given in Fig. 2. Similarly, no depression was obtained in basic media under these conditions. Similar experiments were conducted with fluorite, and in this case, depression was noted above about pH 11 with 1 x 10-3 mole per liter sodium silicate (Fig. 3). When calcite was floated with these same levels of addition of sodium silicate, essentially no flotation was possible above pH 7 (Fig. 4). The effect of collector addition with a constant addition of sodium

Jan 1, 1969

By E. T. Turkdogan, J. H. Swisher

The solubility of oxygen in zone-refined iron was determined in the temperature range.from 881" to 1350°C. The solubility in a iron at 881°C ms found to be about 2 to 3 ppm; in y iron, the solubility was found to increase from about 2 to 3 ppm at 950°C to about 25 ppm at 1350°C. The permeability of oxygen in an iron -0.1 pct Al alloy was determined in the y iron range, using an internal oxidation technique. By combining the permeability and solubility data, the diffzisivity of oxygen in y and a iron was calculated. The oxygen diffusivity in solid iron may be s~immarized as follows: 8820 For 6 iron and IN a recent paper, Hepworth, Smith, and Turkdogan1 reported on the solubility, permeability, and diffusivity of oxygen in 6 iron, together with permeability data for oxygen in a iron. In the present investigation, similar measurements were made in the ? phase region. In addition, a solubility measurement was performed in the a phase region to permit calculation of the diffusivity of oxygen in a, iron. References to early work on this subject are given in the previous publication.' EXPERIMENTAL Solubility Measurements. The oxygen solubility was determined by equilibrating cylindrical samples 0.3 in. diam by 14 in. long of zone-refined iron in water vapor-hydrogen gas mixtures. The zone-refined iron was prepared by B. F. Oliver of this laboratory, using an apparatus and technique described elsewhere.2'3 Six zone-melting passes were used to achieve a total impurity level of about 30 ppm. Of this 30 ppm, the combined nickel and cobalt content was about 20 ppm, oxygen was 4 ppm, and all oxidizable impurities less than 1 pprn each. A vertical resistance furnace wound with molybdenum wire was used for the experiments. The temperature was measured before and after each experiment with a Pt/Pt-10 pct Rh thermocouple. In the gas train, flow rates of hydrogen and argon were measured with capillary flow meters, and the resulting mixtures were passed through a column containing 90 pct oxalic acid dihydrate and 10 pct anhydrous oxalic acid to obtain predetermined ratios of H2O to H2. The vapor pressure of H2O above this mixture as a function of temperature is well-known.4 The exit gas was ana- lyzed periodically for H2O, and good agreement (+3 pct) with the calculated composition was obtained. The zone-refined iron specimens were held in the furnace for a sufficient length of time for equilibration, e.g., 18 hr at 1350°C and 1 week at 881°C, then quenched in a brine solution. After removing the surface oxide from the samples by machining, duplicate analyses were obtained by a combined vacuum fusion-infrared method; oxygen analysis was reproducible within 2 ppm. Permeability Measurements. The permeability of oxygen in alloys containing about 0.1 pct A1 was determined by internal oxidation and measurement of the subscale thickness as a function of time. The experimental alloys were prepared by adding aluminum to electrolytic iron (grade 104A plastiron) that had previously been vacuum-carbon deoxidized. The resulting ingots contained about 20 ppm O, 100 pprn C, 40 pprn Si, 50 ppm Mo, 20 ppm P, 20 ppm S, and 20 pprn Zr as the principal impurities. After hot rolling the ingots to 1-in.-thick slabs, specimens were machined from the stock in the form of rectangular plates, 4 by 5 by 2 in. The general procedure for the permeability experiments was the same as those for the solubility measurements. The specimens were cooled in a reducing atmosphere rather than quenched, however, in order to maintain a clean surface for measurement of the sub-scale thickness. This measurement was made on a polished cross section of each specimen, using a microscope with a micrometer stage. The inclusions formed at the lowest temperature 1033°C were too small to be seen with an optical microscope. An electron micrograph showing the size and shape of individual particles is shown in Fig. 1. The dark band in the picture is a boundary between two subgrains. The subscale thickness in these samples was measured with an optical microscope after heavily etching in 2 pct nital, which gave contrast between the subscale and the unoxidized zone.

Jan 1, 1968

By C. S. Smith

The solubility of tantalum at 1100°C is 0.025 pct in pure copper, 1.2 pct with 20 pct Ni, and 2.7 pct with -30 pct Ni. The solubility decreases with temperature, and the alloys are precipitation hardenable. A 79/20/1 Cu-Ni-Ta alloy reaches maximum hardness after aging at about 750°C and, if cold worked, does not recrystal-lize below that temperature. The alloys have good tensile properties at moderately elevated temperatures and, since they can be hot and cold worked nearly as easily as cupronickel, they are suggested for service at temperatures above the usual limits for copper alloys. MASSIVE tantalum dissolves extremely slowly in copper-rich alloys, and tantalum powder forms refractory surface layers which prevent its solution unless special precautions are taken. After many trials, an 80 pit recovery was consistently obtained by using a mixture of a finely divided tantalum powder with two or three times its volume of potassium tantalum fluoride (K2TaF1,-melting point about 750°C) poured in a slow stream directly on to the surface of the molten copper alloy, so that each particle would remain coated with flux and be immediately and individually wetted by the molten metal. A 50-50 nickel-tantalum alloy has a melting point of about 1400°C and small lumps of it slowly but satisfactorily dissolve in molten copper-nickel alloys as does commerical "ferro-tantalum." The high affinity of tantalum for carbon makes it necessary to avoid carbonaceous crucibles. COPPER-TANTALUM ALLOYS Castings with good shrinkage resulted when 0.1 pct Ta or more was added to copper melted under charcoal and cast in air. Copper in two-pound melts to which 0.1, 0.15, and 0.2 pct Ta had been added retained residual amounts, by analysis, of 0.025, 0.023 and 0.026 pct, respectively. The solubility of tantalum in molten copper at about 1200 °C is therefore about 0.025 pct. The electrical conductivity of these three samples was 100.48, 100.00 and 100.20 pct IACS in the annealed condition, and 98.24, 97.98 and 98.08 in the cold-drawn condition. Wires 0.080 in. in diam withstood from thirteen to nineteen reversed bends after annealing for 30 min in hydrogen at 850°C and the metal was therefore completely deoxidized. The annealing temperature corresponding to 50 pct loss of work hardness in 1 hr in a strip cold rolled 77 pct reduction was 175C, compared to 230°C for equivalent undeoxidized material. It is unusual for a decrease of recrystallization temperature to result from an alloying addition, and the tantalum probably combines with and removes some minor impurity in the original copper that restrained its recrystalliza- tion. No difficulty whatever was encountered in hot or cold rolling or drawing these ingots, and were tantalum not so expensive it would make an excellent deoxidizer for copper. COPPER-NIcKEL-TANTALUM ALLOYS Studies were made of the solubility of tantalum in a large number of copper-rich alloys, but of these significant solubilities were found only in the case of an iron alloy (which, however, separated into two immiscible liquid layers) and alloys of copper and nickel, in which tantalum is freely soluble and which were found to have interesting properties. The latter alloys are the subject of U. S. Patent No. 2,430,306 (1947). They are not at present available commercially. The Ternary Constitution Diagram—The copper-rich corner of the constitution diagram was constructed on the basis of microscopic examination of samples of various composition and treatments. The alloys were hot rolled to 0.25 in. from castings 0.625 in. thick, then annealed for 1 hr at 1000°C, quenched, cold rolled to 0.10 in. and finally annealed for various periods of time at temperatures between 800" and 1100°C in a nonoxidizing atmosphere and quenched. When the solid-solubility limit had been transgressed, particles of a compound believed to be Ni2Ta*were

Jan 1, 1960

By C. W. Mueller, P. H. Robinson

A technique was developed for depositing single -crystal films of silicon on single-crystal sapphire substrates via the pyrolytic decomposition of SiH4/H2 mixtures. Electron diffraction and X-ray Laue reflection examinations of these films revealed single-crystal patterns. These films were characterized by measuring conductivity type, thickness, resistivity, and Hall mobility. Chemical etching, dislocation staining, and electron-microscopy examination have indicated the presence of low-angle grain boundaries and microtwinning in the silicon films. The role of the sapphire substrate with respect to its quality, orientation, surface finish, and thermal and chemical treatment was investigated. Hall mobility as a function of sapphire orientation was measured. A mobility equal to 88 pct of bulk silicon mobility was attained. Insulated-gate field-effect transistors which have a transconductance of 4000 pmho at 6 ma were fabricated using these films. THE technology of the fabrication of microelectronic circuits with active and passive components directly on a single wafer of semiconductor material has attained a high degree of perfection during the last few years. One inherent difficulty with the single-wafer approach has been undesirable coupling between components arising from the common base material. Several techniques have been developed for minimizing this coupling and obtaining good electrical isolation between components; however, these result in extra capacitance being added to the circuit. The extraneous capacitance of the connecting leads, resistors, and capacitors degrade circuit performance and limit the high-frequency operation of these circuits. Recently there has been considerable interestl-3 in the deposition of silicon films upon insulating substrates. The use of silicon as the semiconductor allows the subsequent utilization of the large amount of technology which has been developed for silicon for the fabrication of good active components. A sapphire substrate supplies an excellent insulating material which at the same time gives a thermal-conductivity improvement of an order of magnitude over glass-type substrates. This paper will describe the results obtained for the deposition of single-crystal silicon layers upon single-crystal sapphire substrates as well as the characterization of these films. I) APPARATUS The 'system used for the growth of silicon films on sapphire substrates by means of the pyrolysis of SiH4/H2 mixtures is shown in Fig. 1. The all-quartz reaction chamber is water-cooled and includes a quartz optical-flat window for use in conjunction with a 5 kw, 2.5 Mc per sec constant-temperature controlled rf generator. The temperature sensor for the rf generator is a thermopile which is focused through the quartz optical flat onto the susceptor surface. With this system the rf generator will hold the temperature of the susceptor to about +0.3°C at 1200°C. The susceptor is supported on a quartz sled inclined to the gas flow to increase the uniformity of the deposition. The water jacket surrounding the reaction chamber is used to keep the quartz wall temperature low enough to limit the decomposition of the silane to the rf-heated susceptor which contains the sapphire substrates. This eliminates the reaction of silicon with the hot quartz to form SiO which deposits out on the apparatus walls, thus obscuring vision, and interferes with the optical measurements of the temperature as well as with the growth process itself. Provision is also made for "n"- and 'p"-type doping by using mixtures of either phosphine or diborane in hydrogen which are added to the silane during the growth process. The hydrogen used is the purest commercially available tank hydrogen further purified by use of a palladium diffuser. The susceptors which were used include 1) spectro-scopically pure graphite, 2) high-purity molybdenum, 3) high-resistivity silicon using a low-resistivity insert to facilitate coupling to the rf generator, 4) silicon carbide-coated graphite. The latter two susceptor materials produced silicon films on sapphire substrates with more reproducible resistivities. Prior to silicon deposition all connecting lines as well as the reaction chamber are thoroughly flushed with argon and then hydrogen. After the hydrogen flow is set, the growth temperature is adjusted to 11009 to 1150°C, and when thermal equilibrium is reached the silane flow is started. The flow rate of the hydrogen must be fast enough so that turbulent flow occurs in the size of reaction tube used, otherwise a streaked nonuniform silicon deposit occurs. After the deposition

Jan 1, 1967

By J. Hudy

An investigation has been made to determine the applicability of the Cendrex X-ray instrument for the measurement of the ash contents of washed bituminous coal products. The results obtained for selected products from five preparation plants in the northern Appalachian region are described. Emphasis of the study was placed on low-ash bituminous coals suit-able for utility or metallurgical markets. There was good agreement between the results obtained by conventional ash determination methods and by the Cendrex for all the products tested. A principal disadvantage of coal in competition with other fuels has been its inconsistent quality, especially with respect to ash content. Mine rnechanization and production from coalbeds of inferior quality have accentuated this failing. Present quality control methods in coal preparation plants are inadequate because (1) control samples taken over a production shift only serve to give the average quality of the product, (2) conventional sampling and analysis data are usually not available at the time a shipment is scheduled, and (3) the plant operator does not have the use of such data when the coal is being processed so that operating conditions may be adjusted for correcting variations in quality. Thus, the development and use of continuous-control monitoring instruments is of prime importance. The Federal Bureau of Mines arranged to investigate an instrument using x-rays for rapid continuous ash determinations. Developed by the Dutch State Mines and first described in 1958,' this instrument, which has found widespread acceptance in Europe, is designed to provide ash analysis of any desired coal feed or product stream with only a five-minute time lag between sample collection and analytical results. With limit controls, this unit could be used to feed back signals to preset the separating gravity of coal washers, control the ratio of various coals needed to produce an acceptable blend, and permit the sorting of a washed product into two qualities, one which is below and the other which is above a prescribed ash content. This unit can also be used discontinuously for rapid determination of coal samples taken in the usual manner. THEORY Di jkstra and Sieswerda of the Dutch State Mines studied the effect of chemical composition and ash content on the absorption coefficient of coal with the transmitted radiation method.' They found that with an X-ray wavelength of 1.79 A and values calculated for the absorption coefficients of ash and combustibles, the absorption coefficient of coal gave a linear relationship when plotted against the ash content. Thus, a method of measuring the absorption coefficient of coal could also be used to measure the ash content. However, practical attempts to measure the ash content of coal by comparing the intensities of the transmitted X-rays failed. The absorption coefficient of coal can also be obtained by irradiating a layer of coal with x-rays and measuring the intensity of the diffused reflection (backscatter method). The relationship between the diffused reflection and the ash content is actually hyperbolic but approximates a straight line over a narrow range. A measuring circuit that balanced the difference in intensity of the reflected radiation from a standard surface against that from a coal sample was used. By plotting this difference of reflected radiation against the ash content, a curve which approximated a straight line over a range of 8 percentage points of ash was obtained. DESCRIPTION OF EQUIPMENT The apparatus performs two distinct functions: (1) the preparation of the sample to a suitable size consist and moisture content for delivery to the x-ray element, and (2) the measurement of the ash content by the x-ray element. In a continuous operation the coal sample is delivered to a conditioner where it is dried to a maximum of 1% surface moisture and pulverized in a high speed mill to -48-mesh. This material is fed, at a rate of 250-300 gpm onto a rotating disk, shown in Fig. 1, where it is mixed with material already present. The mixture is rotated on the disk and

Jan 1, 1969

By C. J. Frosch, J. A. May, H. G. White, C. D. Thurmond

Gallium phosphide epitaxial layers were grown from the vapor phase on undoped single-crystal galliurn arsenide substrates in silica tubes by an open-tube wet-hydrogen process. The epitaxial layers were grown over a range of water pressures at three substrate temperatures. Excess donor concentrations were determined by surface barvier capacitance measurelrzents without removing the layers from the substrates. The excess dmlor concentration, ND-NA, is fo~ind to vary approxilnately inversely with the pressure of water added to the hydrogen carrier gas. This is the relationship that would be expected for singly ionized silicon donors on gallium sites in extrinsic galliunz phosphide, with the silicon coming from the SiO generated by the reaction of hydrogen with the silica tube. An increase in the partial pressure of water in the hydrogen stream decreases the SiO pressure. The results indicate that ni, the intrinsic hole and electrmt concentration for gallium phosphide at the three substrate temperatures, is smaller than the concentration estimated from available data for the density of states effective masses and the energy gap. Mass-spectrographic measurements confirm that the dono?, introduced into gallium phosphide is silicon. The equilibrium concentrations of silicon in vapor-flown gallium Phosphide have been estimated from available thernzodynamic information that includes the solubility measurements of silicon in gallium phosphide in equilibrium with a gallium-rich liquid phase. Satisfactory agreement with the measured silicon concentrations is obtained. FROSCH1 has described an open-tube process for growing single-crystal Gap from the vapor phase by a GazO transport mechanism. The method depends upon the reaction of H20 in an H2 carrier gas with a heated source of polycrystalline Gap which provides the necessary vapor species. When the temperature of these vapor species is lowered, super saturation occurs and single-crystal Gap will deposit on a suitable substrate. Unintentionally doped single crystals of Gap grown by the wet H2 process in silica tubes are n type. Evidence is presented to show that the donor introduced is silicon, and that a qua si-equilibrium model accounts for the inverse dependence of the donor concentration on the water partial pressure and predicts the magnitude of the donor concentrations. Ainslie et al. experimentally showed a similar inverse relationship between the carrier density and oxygen pressure for GaAs. Emission-spectrographic analyses showed a decrease in the silicon concentration with increasing oxygen overpressure for GaAs. Cochran and Foster suggested the theoretical possibility of suppressing silicon contamination by using Ga20 generated by the reaction of gallium with water vapor. 1) EXPERIMENTAL The apparatus and procedures are essentially the same as those described by Frosch.' The apparatus consists of a 25-mm-ID SiO2 tube extending through a controlled high-temperature flat zone for the location of the polycrystalline Gap source and a downstream temperature gradient falling at a rate of about 14°C per cm. The latter provides the region of super saturation for the location of the single-crystal substrate. The partial pressure of water in the inflowing hydrogen stream, pA2, O was controlled by mixing me-tered proportions of dry H2 with H2 saturated with H2O vapor at 0°C. The total gas flows were about 200 cu cm per min in all experiments. The Gap sources were prepared by pulverizing boat-grown polycrystalline ingots to pass a 20-mesh sieve. The substrates were cut from an undoped single-crystal boat-grown GaAs ingot purchased from Monsanto. This ingot had a carrier concentration of about 1015 atoms per cu cm, a resistivity of about 5 ohm-cm, and a mobility of about 5000 sq cm per v sec at 25°C. Substrates with dimensions of 1 by 1 by 5 x lo-' cm were employed. The growth faces were chemically polished (111) arsenic faces. Epitaxial layers, at least 7.5 x 10-3 cm thick, were grown,. This required from 1 to 24 hr depending upon the Pii2Q values and the temperatures. In all of the runs, the source temperatures were 50°C higher than the substrate temperatures. Samples were prepared

Jan 1, 1968

By E. R. Helderman, C. Y. Ang, C. C. Nealey

Beryllium-base alloys have been successfully p7.-epared by the liquid-phase sintering technique. Depending orz the composition and amount of the intended liquid please, microstructures either single -phase or duplex in feature with randomly oriented grains have been obtained. Qualitative and semi-qualitative determination of distribution of alloying elements md microsegregations in some experi)uzental alloys haue been made by electron-micro-probe analysis in conjunction with microliardness testing and standard metallography. Tensile tests reoealed that some conzpositions possess attractive elastic properties with Young's mot1uli greater than 40 X 10' psi. In powder metallurgy, liquid-phase sintering is a process or phenomenon that has proven to be of practical value. For example, the heavy metals such as tungsten-copper-nickel, high-strength heavy gyro alloys,' heavy-duty electrical contacts,' and tungsten carbide tool materials are all products of liquid-phase sintering. Mechanisms involved in liquid-phase sintering, however, are not completely understood. Questions regarding the exact roles played by rearrangement of particles, liquid/vapor surface energy, solution and precipitation, and so forth, have not been completely answered. Evidence has been cited3 that at least volume shrinkage in the densification process is diffusion-controlled. It is possible that the predominant mechanisms for the complete densification and grain growth in a liquid-phase sintered system depend primarily on the alloy systems involved, in addition to processing conditions. Despite the lack of sound understanding of the mechanisms of the process, liquid-phase sintering has been and is being used to advantage either to synthesize microstructures for their special properties or to prepare alloys which are difficult to form by fusion process. Liquid-phase sintering of beryllium alloys was first attempted by Jones and Williams.4 They first tried infiltrating beryllium with magnesium, and then succeeded in preparing the alloy by sintering Be-Mg powder compact in molten magnesium bath. This investigation resulted in the identification of some Mg-Be intermediate phases. Crossley et a1.5 also used liquid-phase sintering technique in an attempt to produce ductile beryllium alloys for structural applications. The major liquid-phase components investigated by Crossley et al. were aluminum and silver with minor additives of germanium, calcium, lanthanum, cerium, and yttrium. The lack of wetting and the bleeding out of liquid phase were the difficulties encountered during experimentation. According to Hodge,6 the two compositions investigated by Crossley, which showed some promise based on compression tests, involved large amounts (over 35 wt pct) of silver, thus making them too heavy to be of practical interest to the aerospace industry and military users. The present investigation was prompted by the search for light-weight (density less than aluminum) beryllium alloys exhibiting small anisotropy in physical properties for precision inertial navigation instrument applications. In addition to isotropy, good structural properties such as high elastic modulus or desirable combination of mechanical and physical properties are also objectives of this investigation. The technique of liquid-phase sintering was chosen for its versatility in producing either duplex or homogeneous microstructures. This report is concerned with the use of copper and aluminum, with or without silicon addition, as the intended liquid phase, and the resultant micro-structures and some physical properties of the beryllium alloys. Qualitative and semiquantitative electron-microprobe analyses of some of the alloys are presented to illustrate the usefulness of this microanalytical technique for the identification of microconstituents and their distribution. EXPERIMENTAL PROCEDURES The beryllium powder used was -200 mesh Brush Beryllium Co. QMV NP-50 grade. Typical chemical analysis of the powder is shown in Table I. Commercial high-purity copper, aluminum, and silicon powders all screened to —100 mesh were used as additions. Mixed powder compositions were ball-milled in ceramic jars for 1/2 hr to ensure thorough blending. Milled powder was loaded either in 3/4-in.-diam button die or in Metal Powder Association flat tensile specimen die and compacted under top and bottom pressure. No lubricant or organic binder was used. Sintering was carried out in a quartz tube under a vacuum of 50 to 100 µ pressure. Surface hardness and some microhardness readings were taken on sintered specimens. Sintered density was

Jan 1, 1965

By Ralph Hultgren, Prodyot Roy

Manganese vapor pressures from 1250° to 1500°K were measured by conventional Knudsen and torsion-effusion methods in twelve Fe-Mn alloys with compositions from 9 to 80 at. pct Mn. The Knudsen re-sults agveed approximately with previous measurements found in the literature which indicated the solutions were nearly ideal. However, except for the higher manganese compositions, the initial torsion readings indicated much (up to 50 pct) higher vapor presszcres than the Knudsen method. These high readings decreased steadily with time. The results are interpreted as due to depletion of surface concentration of manganese during evaporation. Thus the initial torsion readings are the most nearly correct and Knudsen methods on alloys are to be regarded with suspicion unless it can be demonstrated that diffusion rates are rapid enough to replenish surface concentrations depleted by evaporation. For the lowest manganese contents and highest temperatures, depletion causes initial torsion readings to be too low. FEW thermodynamic data are available for alloys of the high-melting transition metals due primarily to experimental difficulties at the high temperatures involved. Measurement of vapor pressure is one of the most promising techniques to be applied to this problem. From the vapor pressure of a component of an alloy phase, its activity or its partial molar Gibbs energy can be directly calculated. From measurements over a sufficient range of temperatures and compositions the partial and integral Gibbs energies, enthalpies, and entropies may be determined through Gibbs-Duhem integration. For solid phases of variable composition, which commonly are found in alloys, measured vapor pressures are low because of depletion of the surface concentration of the more volatile component as it is selectively vaporized. Diffusion from the interior tends to restore the depleted concentration. The seriousness of the effect depends on the relative rates of diffusion and vaporization. Although depletion has been recognized as a factor,' direct measurements of its rate are lacking and quantitative estimates of its effect on measurements are uncertain. In the present work the vapor pressures above a series of Fe-Mn alloys have been measured by the torsion-effusion method. This method permits a measurement of the vapor pressure of manganese as soon as the sample comes to temperature and continuously throughout the run. The rate of decline of the apparent vapor pressure measures the rate of depletion and the torsion reading at zero time should be correct. At high manganese concentrations (70 and 80 at. pct Mn), the torsion reading remained nearly constant; surface depletion was negligible. There was a slow drop in measured pressure due to bulk loss of manganese from the sample. However, for lower manganese contents, especially at high temperatures, the depletion effect was considerable and the apparent vapor pressure decreased steadily with time. For these alloys the Knudsen method should give pressures which are too low. The measurement of pressure in the Knudsen method cannot be made until enough manganese has been vaporized to be weighable. The Knudsen result is therefore an integrated average between the initial and final vapor pressures. To verify this, conventional Knudsen measurements were also made with results in approximate agreement with previously published Knudsen measurements for these alloys. As expected, for the lower manganese contents the initial torsion readings of pressure were as much as 50 pct higher than the Knudsen. THE APPARATUS The apparatus, shown in Fig. 1, is capable of operating to temperatures up to 2000°K. A vacuum of 5 x 10"6 mm Hg can be maintained. Temperatures were measured to +3° by a W-Re thermocouple placed in the dummy cell, N. The torsion cell consisted of two alumina crucibles with holes in their covers. They were placed in the molybdenum holder shown suspended from the torsion wire. Rectangular torsion wires (1 by 4 mm) were found to have superior sensitivity and less residual distortion than circular (2-mm-diameter) wires. The precision of angular measurement was found to be *0.025 deg; the variation is no doubt due to temperature fluctuation and vibration. For the Knudsen experiments the alumina cell was set on the support, N. SAMPLE PREPARATION 800-g samples were prepared by melting together electrolytic iron and electrolytic manganese and pouring the melt into a water-cooled copper mold. Melting and pouring were done under a helium at-

Jan 1, 1965

By Robert E. Green, P. W. Kingman

Application of a constant geometry compression test to single crystals of aluminum of selected diameters from 1/4 to 1/64 in. showed the presence of a diameter-dependmt size effect. The most pronounced effects were found in those crystals oriented for single slip, while for specimens possessing orientations in the comers of the standard stereographic triangle virtually no size effect was exhibited. The yield stress of the crystals oriented for single slip was found to increase with decrease in specimen diameter, while the strain-hardening rate was found to be lower for the smaller specimens. The experimental results are in general agreement with those of other investigators obtained from lensile tests on copper and aluminum crystals. THE earliest systematic investigation of a possible size effect on the plasticity of metals was that of no,' who in 1926 performed tensile tests on cylindrical aluminum single crystals with diameters of 3 to 8 mm. Ono concluded that the gross stress-strain curve did not show a diameter dependence, but that the resistance to slip for strains of 0.1 pet and less appeared higher for 3-mm-diam crystals than for larger sizes. Later studies of aluminum by Maddin et al2 tentatively concluded that a size effect exists, but the conclusions were again open to question because of inconsistencies in the experimental data. Wu and Smoluchowski3 had previously shown that the slip system activated in a single-crystal sheet specimen of aluminum is a function of the specimen cross section in the slip direction, but no stress-strain data were obtained. Subsequently Fleischer and Chalmers4 studied the effect of the length of the slip direction of the primary-slip system on the stress-strain curve by testing aluminum crystals with geometrically dissimilar cross sections. In the course of this investigation a size effect was indicated in rather large crystals; however, the number of these tests was small. Other investigators have indicated that a size effect in aluminum is appreciable only for diameters of 0.5 mm or less.5, 6 Size-effect studies have also been carried out on copper crystals, the most detailed being that of Suzuki et a1.7 who performed tensile tests on specimens of many diameters ranging from 2 to 0.12 mm. Suzuki found a strong size dependence in the easy-glide region, both the extent of the easy glide and the hardening rate in easy glide were size-dependent, and the size effect was found to be orientation-dependent. Suzuki's results are in agreement with the less extensive observations of Pater-sonB and those of Garstone et al.9 A size effect was found by Rebstock using tubular copper crystals.'0 Size effects have also been noted in a brass,6, 11 in cadmium,12'19 and in hexagonal crystals.14 All the previously cited works have been entirely concerned with the variation of specimen cross section. The effects of specimen length and the change of specimen geometry which results from using progressively thinner specimens while maintaining the same specimen length have been largely ignored. A theoretical discussion of the effects of specimen length and geometry has been given by Hauser and Jackson,15 who predict a grip effect on easy glide as a function of specimen geometry provided that the specimen dimensions are large compared with the spacing between the slip bands, and by Fleischer and Chalmers,18 whose analysis of grip effects resulting from lattice rotation predicts an increase in easy glide with an increase in specimen length. A study of size and geometry effects in aluminum crystals by Kitajima and shimba17 indicated increasing amounts of easy glide in specimens of increasing length and identical cross section, and nearly identical stress-strain curves for specimens of different sizes having constant length-to-diameter ratios. Since the present study is primarily concerned with diameter dependence, the following factors were taken into account: specimen material, specimen geometry, testing method, range of sizes to be tested, and possible influence of surface and volume effects. Aluminum was chosen because of the present lack of conclusive results and the seeming possibility of size effects at relatively large diameters, the

Jan 1, 1964

By H. R. Gardner

The heat treatmmt of plutonium was studied using the Jominy end-quenching technique commonly used for determining the hardenability of steel. Plutonium specimens were end-guenched from temperatures in each of the ß, y, d, d') and E phases. One series of specimens with a low-iron content, 165 pprn Fe, and another gvoup with a high-iron content, 678 pprn Fe, were used in order to study the effect of a Pu-Pu,Fe eutectic network on the hardness and micro-structure. Hardness traverses indicated no significant variations in hardness with either cooling rate or quench temperature. Metallographic studies indicated major effects on microstructure. Grain size was found to vary markedly with quenching temperature and cooling rate. It was determined that the Pu-PueFe eutectic network could be modified extensively by heat treatment, including spheroi -dization in the y phase and 6 phase below 413°C. An unidentified spheroidal inclusion was observed to go into solution in the delta and higher temperature phases. 1 HE element plutonium is unique among metals in that it has six allotropic forms in the solid state.' These have been designated' as the a, ß, y, d, d', and phases. The respective phase transformations occur at approximate temperatures of 122", 210°, 319°, 450°, and 480°C with a melting point at 640°C. With this number of phase transformations it becomes pertinent to consider the effect of heat treatment and cooling rate in the various phases on the microstructure and hardness of plutonium. To determine; the effect of a wide range of cooling rates, the Jominy end-quenching technique was applied to cylindrical plutonium specimens. In addition, since the presence of iron in amounts greater than 500 pprn is common in plutonium and results in a network of the Pu-Pu6Fe eutectic, it was decided to study heat treatment effects on two bomb reduced plutonium buttons with different iron contents. A low iron button containing 165 ppm Fe and a high iron button containing 678 ppm Fe were selected for this comparison. EXPERIMENTAL PROCEDURE Experimental Material. The cylindrical bars for Jominy quenching were cast from button stock in vacuo in MgO coated graphite molds. Metal pouring temperature was approximately 950°C and the molds were preheated to 300°C. The castings were machined to 0.5 in. diam. by 2.5 in. long cylinders. Chemical analysis and density data for the two groups of Jominy specimens containing different iron contents are presented in Table I. Except for iron, heats 19-12-1 and 20-2-1 are comparable within the limits of analytical accuracy. Representative specimens from the low-iron and high-iron bars were taken for metallographic examination. The low iron specimen was found to have extensive microcracking, Fig. 1. In addition, numerous unidentified spheroidal inclusions were present, Fig. 17. The average grain size of the low-iron plutonium is 0.068 mm, Fig. 4. In the high-iron plutonium, a Pu-Pu6Fe eutectic network is prominent, Fig. 7. The average size of the network is 0.100 mm. Unidentified spheroidal inclusions were also common in the high-iron plutonium. The average grain size of the high-iron plutonium is 0.036 mm. Experimental Technique. A Jominy end-quenching fixture was fabricated for glove box use. A 2.5 in. water height was used with an orifice of 0.250 in. ID. The orifice to specimen distance was maintained at 0.5 in. Annealing temperatures of 160°, 265°, 400°, 465°, and 535°c were chosen for the study of the effect of quenching from ß, y, d, d', and e phases on microstructure and hardness. During quenching, cooling curves were obtained from the Jominy specimens at distances from the quenched end of 1/16, 1/8, 3/8, 3/4, 1-1/4, and 2 in. Cooling rate calculations were made from the cooling curves for temperature intervals of 100° to 110° 160" to 170°, 330" to 340°, 420° to 430°, and 490° to 500°c. These temperature intervals were chosen

Jan 1, 1962

By Charles R. Stewart, William W. Owens

Reservoir performance predictions based on laboratory core test data assume that fluid flow is laminar for the laboratory test. A study has been made to determine the validity of this assumption for laboratory tests on various types of porosity found in producing limestone formation. Data are presented which show that turbulence and slippage can occur during laboratory tests on hetero-geneous-type porosity limestones, thus causing serious errors in measured single-phase permeabilities and two-phase relative permeability characteristics. In single-phase flow tests it is possible to eliminate turbulence and correct for slippage or to eliminate both factors by controlling test conditions. It is not always possible to control test conditions and thereby eliminate turbulence and slippage in two-phase .flow tests. A correction method is presented which can be used to calculate the true two-phase laminar flow relative permeability characteristic even though furbulence and slippage exist. .INTRODUCTION It is customary to make use of Darcy's law and modifications of this law, together with laboratory data on formation core samples to predict the performance of producing reservoirs. Such predictions are based on an assumption that fluid flow is in the laminar or streamline region for the laboratory test. It was the purpose of this inves- tigation to determine the extent to which turbulent flow may occur in laboratory fluid flow tests on hetero-geneous porosity limestones. Considering that turbulent flow conditions might exist in some laboratory fluid flow tests, additional emphasis was placed on the development of a method to correct for turbulence when laminar flow conditions could not be attained. FLUID FLOW CONCEPTS FOR POROUS MEDIA The Influence of Pore Geometry on Fluid Flow One of the more important factors influencing fluid flow in porous media is the geometry of the pore space which includes such characteristics of the pores as size, shape, distribution, roughness, uniformity, etc. In general, oil- and gas-producing formations can be divided into two broad types on the basis of pore geometry. One has been called sandstone-type porosity media, which is characterized by a small range in pore size, uniformity in shape of the pores, smooth pore surfaces and a regular and uniform distribution of pores. The other type has been called heterogeneous porosity media and is usually limited to the dolomites and limestones. This type is characterized by a wide variation in the size, shape, and distribution of the pores and rough, irregular pore surfaces. It is therefore apparent that conditions are much more favorable for turbulent flow* in heterogeneous-type porosity media than in sandstone-type porosity media. Interrelationship Between Turbulence and Gas Slippage In studying the problem of turbulent flow in laboratory tests on porous media, it is necessary to be aware of the interrelationship between slippage and turbulence for gas flow. As a result of slippage or the Klinken-berg effecta, apparent perrneabilities to gas are greater than the true value because there is no stationary layer of gas in contact with the walls of the flow channels. Gas slippage decreases as the mean free path of the gas molecules decreases. Since the mean free path of any gas decreases with increasing density, increases in static pressure result in lower apparent gas permeabilities. However, a reduction in gas permeability can also be due to turbulence. Therefore, in studying only turbulent flow in porous media, it is necessary to hold gas density, and slippage, constant or to reduce slippage to a negligible value by operating at high static pressures. Presentation of Laminar and Turbulent Flow Data A graphical relationship between permeability and a pseudo-Reynolds number, N,, will be used to show the two types of fluid flow, i.e., laminar and turbulent. The usual graphical method for such a description has been the use of friction factor-Reynolds number charts4. On such a logarithmic diagram, the laminar region appears as a straight line having a slope of 45 degrees. As the friction factor decreases and the Reynolds number increases, the turbulent region is reached and appears as a deviation from the 45-degree slope line. However, in petroleum engineering literature resistance of por-