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By Russell E. Griffin

Dielectric constants and dissipation factors were measured for six rocks over the 20-to 100-megahertz frequency range by means of the susceptance-variation method. Results for both dry and moist specimens are presented and compared with data reported by others. Loss factors calculated from the data presented are important to the Bureau's study of rock fragmentation by means of dielectric heating.

Jan 1, 1967

By J. Gurland

The wmk is concerned with the estimate of the degee of continuity of a particulate phase dispersed in a matrix. The first section is a verieu: of the parameters nzeasurable by quantitative rnetallogvaphy, namely the contact area and, under certain conditions, the number of contacts between particles of one phase. In the second section, the frequency of particle contacts is related to the degee of continuity of a randomly embedded phase orz the basis of the lattice-percolation model of Hamrnersley and others. THE extent of continuity of the constituent phases may greatly influence the structure-sensitive properties of phase mixtures, particularly if the phase properties differ significantly. An example from the literature1 is shown in Fig. 1. The marked decrease of the electrical resistivity of sintered silver-alumina bodies near 25 pct by volume of silver presumably occurs because the more conductive phase changes from a discontinuous to a continuous structure. Other example of electrical- and thermal-conductivity transitions are cited by kingery In view of these observations, a knowledge and understanding of the connectivity of the microstructure may be of considerable practical importance. This study is concerned with one aspect of the genera1 problem, namely the estimate of the degree of continuity of a particulate phase dispersed in an opaque matrix. The first section reviews the parameters measurable on a polished cross section by auantitative metallography, such as the contact area and under certain conditions, the number of contacts between particles of one phase. In the second section, an attempt is made to relate the frequency of particle contacts to the degree of continuity of a randomly embedded phase. For the purpose of this discussion, the aggregate has two constituents: the particulate phase and the matrix. The latter is considered to be homogeneous. The term "particle" is used with the meaning of "grain", i.e., a minute unit of matter which is usually a single crystal of a readily distinguishable substance within the confines of a simply connected boundary. While many of the concepts which are used here to describe the structural variables characterizing the microstructure of phase mixtures are qualitative and ill-defined, they are presented with the intent of stimulating further work of a more general and rigorous nature. I) PARTICLE CONTACT, CONTIGUITY, AND MEAN FREE PATH 1) Measurement of Contiguity. The fraction of the total internal surface of a phase a shared with particles of that same phase in a two-phase mixture of and $ is indicated by the contiguity ratio:3 whereis the area of the interface between o particles, and Sap is the area of the interface between a particles and matrix P, per unit volume of mixture. The contiguity ratio ranges from 0 to 1 as the distribution of the a phase changes from a completely dispersed to a completely agglomerated structure. The interfacial areas may be obtained from simple intercept measurements on a random plane, after Smith and Guttman where and N are the numbers of intercepts between a random line of unit length on a plane of polish and the interparticle and interphase interfaces, respectively. The equations are valid for any distribution of particle sizes and shapes.

Jan 1, 1967

By P. H. Thornton

MaNY intermediate phases are solid solutions which have a solute-solubility range greater than 3 at. pct. These phases, which are generally very strong and often have simple crystal structures, are usually extremely brittle so that specimens of simple shape cannot be produced by the usual mechanical-deformation techniques. Furthermore, single crystals of reasonably uniform composition are difficult to grow by the Bridgman technique because the phases generally form by a peritectic reaction, which causes pronounced segregation. In this note, a technique is described for the preparation of thin-rod specimens of brittle intermediate phases, which may be used for physical-property studies such as resistivity changes' and for the conversion of such rods into single crystals. The method has been used for the preparation of rod single crystals of the phases and Ingots, of about 100 g weight and 11 mm diam, were made by melting together the appropriate amounts of high-purity materials (usually 99.999 pct) in sealed

Jan 1, 1967

By M. S. Burton, B. W. Christ, G. V. Smith

Evidence of the effects which high-angle grain boundaries and veining subgrain boundaries have on the yield phenomenon of zone-refined iron is reported. Room-temperature tensile tests on 50-mil wive at several gram sizes produced upon recrystallization at diffevent temperatures below 910C (a-y phase-transfornzatzon temperature) show that upper and lower yield stress decrease with increasing grain size. The upper yield point effectively disappears at grain sizes of 81 and 102 u in samples of this diameter. However, samples of 129 p grain size. produced during recrys-tallization at 950°C, exhibit a pronounced upper yield point and an increased lower yield stress. Possible causes of the reversal in the grain-size dependence of yielding are discussed. Veining substructure, detected with picval-HC1 etchant, but not with 2 pct nital, is formed during the a-y transformation, and is believed to account for the observed effecls. The strengthening associated with high-angle boundaries in zone-refined tron is discussed in terms of: 1) the stress dependence of slzp multiplicity, and 2) the stress dependence of dislocation emission from grain boundaries. WIDE use of transmission electron microscopy and dislocation etch-pitting techniques has led to a growing awareness of the presence of dislocation substructures in annealed pure metals. Whereas much speculation'-4 has developed about the influence which subgrain structures have on the mechanical behavior of metals, particularly the yield strength, only limited experimental evidence correlating subgrain structures with lower yield strength has been presented. 2,3,5-7 It is the purpose of this note to present experimental evidence of the effects which grain boundaries and subgrain boundaries have on both the upper and lower yield strength of zone-refined iron. Effects due to high-angle boundaries formed upon recrystallization below the a-y phase transformation are compared with effects due to veining subgrain boundaries formed upon "recrystallization" above the a-y phase-transformation temperature. These effects are further compared with the reported influence 2,3,5-7 which low-angle boundaries have on the lower yield strength of bcc transition metals. EXPERIMENTAL PROCEDURE The starting material for these experiments was a 1-in.-diam zone-refined ingot prepared at Battelle Memorial Institute. Initial purification of electrolytic iron by vacuum-induction melting was improved by a floating zone-melting treatment in ultrapure hydrogen.' Chemical analysis of this zone-refined iron appears in Table I. Tensile samples of 50-mil wire were prepared by rolling and drawing portions of the ingot. An intermediate recrystallization anneal at 625°C after rolling to a reduction in area of 85 pct was carried out in an evacuated Vycor capsule (10-=5 mm Hg). Further reduction in area of 91 pct was followed by recrystallization in evacuated Vycor capsules at temperatures between 600" and 950°C, see Table 111. All samples

Jan 1, 1967

By S. E. Szasz, E. J. Moore, B. F. Whitney

An accurate value of formation water resistivity R, is essential in calculating formation porosity and fluid saturation from electrical well logs. In the cases where R, has not been measured directly, it must be obtained from other data, e.g., the SP curve. This paper deals with another approach: how to calculate R, from the chemical analysis of the formation water. INTRODUCTION It is known that the resistivity of aqueous solutions of pure salts depends on their concentration and on the temperature; the concentrations are given in MPL (mg of solute per liter of solution), or sometimes in ppm (mg of solute per kg of solution): MPL = ppm X specific gravity. Values for different pure salts are available in the literature, but not for solutions of mixtures which are of practical interest. The major component of the dissolved material in almost all formation waters being sodium chloride, it is customary to express the resistivity of formation waters in terms of equivalent sodium chloride concentration, i.e., the concentration of a solution of pure NaCl which has the same resistivity at a given temperature as that of the formation water under consideration. Thus, the problem of calculating R, from the chemical anaylsis can also be stated as how to convert the other constituents of the solute into equivalent NaCl concentration. Salts dissolved in water are at least partly dissociated into ions, and do not conserve their identity. If known amounts of several salts are dissolved in water, the solution does not necessarily contain the same salts in the original proportion, but perhaps some other combination of the ions, along with free ions in solution. This is why the chemical analysis of formation waters is often given in terms of ions, as if all dissolved salts were completely dissociated. Our problem then boils down to how to convert the concentrations of the various ions to equivalent concentrations of Na' and C1-. Dunlap and Hawthorne' have proposed to convert the concentration of all other ions to equivalent Na' and C1-concentrations by means of constant multipliers; e.g., 0.95 for Ca"; 2.0 for Mg"; 0.27 for HCO 3-; 0.5 for SO, -, etc. Their factors were based on measurements made at 68F on 26 formation water samples from the Texas Gulf Coast, ranging in concentration from 1,500 to 75,000 ppm. The Dunlap method is widely used in electric log interpretation, and is often extrapolated beyond its original concentration range. A comparison of R, values calculated by this method and values actually measured on formation water samples has shown large discrepancies, especially at higher concentrations. Therefore, two new methods were developed at Sinclair Oil Corp.'s Tulsa Research Center to calculate equivalent sodium chloride concentration from the chemical analysis of formation water samples. FUNDAMENTAL CONSIDERATIONS The resistivity of a solution, or its reciprocal the conductivity, at a given temperature is determined by the charge, concentration and mobility of the ions actually present. Monovalent ions such as Na' or C1- always carry the same charge. Compounds of polyvalent ions, however. may show incomplete dissociation, e.g., NaSO; + Na' instead of SO,-- + 2Na'. This happens especially in more concentrated solutions. Only very dilute solutions are completely dissociated, as assumed in the chemical analysis report. At higher concentration, the degree of dissociation depends not only on the nature and concentration of the particular salt under consideration but also on the nature and concentrations of the other solutes. Mobility of the ions depends on the viscosity of the solution. It also depends on the degree of hydration of the ions, which in turn is a function of the nature and the charge of the ions and also of the amount of free water available per ion, i.e., the total ionic concentration. The net effect is that the conductivity increases slower than proportional to the concentration, even if a solution contains only one salt such as NaC1, and is different for different salts (Fig. 1). Conductivity can even decline with a further increase in concentration, e.g., if additional salt is little dissociated but ties up some of the free water and/or causes an increase in viscosity. In solutions containing more than one salt, the contribution of one salt to the total conductivity depends not only on the fractional concentration of this same salt, but also on the concentration of all other solutes. A perfect method would give the conductivity or resistivity of a solution as a function of the concentrations of all solutes present. This is so complicated as to be impractical, and a simpler method must be found which is of acceptable accuracy. The Dunlap method, on the other hand. is too simple because it askmes that at any concentration the contrih-

Jan 1, 1967

By Wilbur I. Duvall

In this report, the Bureau of Mines presents a theoretical solution for the stresses and displacements in an infinite elastic plate containing a circular hole the boundary of which is loaded by applied radial stresses over four separated arcs. The problem solved is a two-dimensional approximation of the stresses and displacements developed by a large tunnel-boring machine anchored in a circular tunnel. Analysis of the solution shows that the tangential tensile stresses induced on the boundary of the circular opening can be minimized in the roof and maximized in the floor of the opening by proper spacing and loading of the four arcs.

Jan 1, 1967

By B. C. Allen

Grain-boundary gvoocing was studied irz chronziu?n. molybdenum, tungsten, and the solid-solution alloys, Cr-35Re. Mo-33Re, and W-25Re at 0.6 to 0.9 of the absolute liquidus temperature under an inevt atmosphere , foveign nzetal zlapor, and liquid metal. The controlling mechanism of matter transport was deduced frolr groove size and shape. kinetics of growth, and cotnparisoz with theoretical relatiotzships derived by Mullins. Grooves in chowzizon formed prittzarily by volume diffusion tkrongk kelium or argon at 1 atm pressure and by e1)apovation-condensatiotz in a static vacuum. Groozles in the other nzetals and alloys forrned priniarily by sirface diffusion, the coefficients of which were calculated. Carbon was found to decrease the acti7:ation energy for surface diffusion on molybdenun. Sitrface diffusizities weve sinzilav for iWo-0.0ZC and Mo-33Re. The presence of about 1 -?nm pressure of silver or tin vapor did not affect the neckanis)n of grooz;e formation. In liquid titz or silz:er, pain bolindary gvooves formed by zolume diffusion in the liquid. BASED on theories of ullins," the mechanisms of grain-boundary grooving have been determined for low-melting metals such as copper in an inert atmospheres or in liquid lead.4 The purpose of this investigation was to study grain-boundary grooving in the refractory Group VI-A metals, chromium, molybdenum, and tungsten, and the bcc solid-solution alloys, r-35e, 0-33e,= and -25e,' at 0.6 to 0.9 of included to see whether Mullins' theories were applicable to them as well. EXPERIMENTAL WORK The materials chromium, molybdenum, tungsten, Cr-35Re, Mo-33Re, and W-25Re were in the form of 0.050-cm-thick sheet assaying 99.98 pct or better. The nominal carbon level was generally 30 ppm. The oxygen + nitrogen + hydrogen content was -50 ppm. Mo-33Re and W-25Re were prepared by powder-metallurgy methods and supplied by Chase Brass and Copper Co. The remaining materials were arc-cast. Chromium and Cr-35Re were prepared at Battelle by arc melting, extruding, swaging, and rolling. Mo-0.003C was supplied by Climax Molybdenum Co., and Mo-0.02C and tungsten by Universal Cyclops Corp. As a source of liquid metals, tin and silver granules assaying 99.98 pct were used. Spectrographic analyses indicated the presence of -100 ppm each of iron and silicon. Vacuum melting reduced the combined gas content to c5 ppm (2.60,, 0.9N2, 0.4H2 in tin and l.602, 0.7N2, and c0.04H2 in silver). Specimens were prepared for grain-boundary grooving. Coupons 0.5 by 1.5 cm with a small hole in one end, or substrates 1.5 by 1.5 cm, were cut from sheet. The specimens were annealed in containers of the same material to provide a vapor-solid equilibrium as well as to protect them from gaseous impurities. Outgassing was done at 2 x 10"5 mm for 15 to 30 min at 1150°C for chromium and Cr-35Re, 1750°C for molybdenum and Mo-33Re, and 2600°C for tungsten and W-25Re. Then recrystallization to a stable grain size of about 0.5 mm was accomplished by annealing at least 1 hr at 1600°C for chromium, 1800°C for Cr-35Re, 2350°C for molybdenum, and 2300°C for Mo-33Re in a rhenium-element resistance furnace under 1 atm of static argon or helium. The atmosphere was gettered by tantalum radiation shielding. Tungsten and

Jan 1, 1967

By K. Mukherjee

A quasi-thermodynamic calculation is presented for estirt~ating vacancy Parameters in fcc metals. For fcc metals the equilibrium vacancy concentration at the melting point can be approximated by a constant mole fraction. The Gibbs free energy of formation of the vacancies can then be expressed as a simple function of the absolute melting temperature alone. From this description the formation energy Ef, the vibrational entropy Sv, and the formation volume of a vacancy can be calculated in terms of known thermodynamic parameters. The calculated values are in good agree-rnent with available experimental results. IT appears that many of the physical parameters associated with lattice defects can be empirically related to thermodynamic melting parameters.'-7 Besides the implicit correlations between melting phenomenon and point defects, the melting temperature itself at atmospheric pressure can be used as a reference temperature for the purpose of comparison of vacancy concentrations in a given crystal class. The concentration at the melting point then corresponds to the maximum vacancy super saturation in the crystalline state at a fixed pressure. For pure fcc metals such as Au, Cu, Al, Ag, Pb, and Pt the mole fraction of vacancies at the melting point8 is of the order of 10*"3 to 10"1. The equation expressing the equilibrium vacancy concentration at the melting point contains three parameters: the formation energy, the vibrational entropy, and the absolute melting temperature, see Eq. [2]. Since these three parameters cover a wide range of values8 in the above-mentioned metals, it can be assumed that in other fcc metals, for which no reliable data are available, the mole fraction of vacancies at the melting point most likely lies in the range 10~3 to lO"4. This is then the basis of the calculations described in this article. Within this range the mixing entropy can be linearized and the vibrational entropy, the formation energy, and the vacancy formation volume can be calculated in terms of known thermodynamic constants. 1} LINEARIZATION OF MIXING ENTROPY The Helmholtz free energy of a crystal containing n vacancies at the melting point can be writteng as where Ef, T,, k, and S, are the formation energy of a vacancy, the absolute melting temperature, Boltz-mann's constant, and the vacancy formation entropy, respectively. After applying Stirling's approximation in Eq. [l] and minimizing with respect to n where (n/N), is the equilibrium vacancy concentration in mole fraction at the melting temperature at 1 atm pressure. If instead of setting (6~/6n) = 0 immediately after Stirling's approximation in Eq. [I], the configurational partition function is simplified, then some useful and significant results can be obtained by utilizing the experimental inforrnation After applying Stirling's approximation and rearranging is plotted as a function of (n/N) in Fig. 1. The points, not all of which are shown, are fitted by a straight line substituting from Eq. [5] into Eq. [I] and minimizing with respect to n combining Eqs. [6] and [2] It must be emphasized that Eq. [7] is only a crude approximation based on an oversimplified model of

Jan 1, 1967

By R. J. McLeod

"Grinding at Giant Yellowknife is done in two stages. The first stage consists of two ball mills in closed circuit will: mechanical classifiers, the classifier overflow goes to flotation. The tailings from this flotation circuit are separated into slime and sand portions, the slimes go to an additional flotation circuit while the sand portion goes to the secondary grinding mills.Milltronic automatic sound control units were installed on each of the two primary ball mills and put into operation September 3, 1966. After about two months adjustments to the control units the operators were taken off the grinding circuit on November 1, 1966. The operators duties were taken over by the automatic control units while miscellaneous work was taken over by the helpers in the mill. The labour saving by the installation is approximately $2250.00 per month.After a short period of operation it was apparent there was a slight change in grind. The screen analysis of the primary classifier overflows for the period May to August 1966 averaged 62.23% minus 200 mesh while for the period September to December 1966 averaged 62.0% minus 200 mesh. This is a slight coarsening of the grind. The change in the primary grind has manifested itself also in the screen analysis of the final grind. Before automation the final grind was 80% minus 200 mesh, while after automation it was 7 5% minus 200 mesh. A change of grind was also noted in the flotation concentrates. Before automation the screen analysis of the concentrates was 35% plus 200 mesh and 50% minus 3 25 mesh. A ft er automation it was 35% plus 200 mesh and 47 .5% minus 325 mesh. In other words the grind got coarser or perhaps we should say there was less overgrinding. Another significant change took place in the assays of the slime and sand portion of the primary flotation tailings. It was usual under manual control for the slime portion to assay higher in gold than the sand portion. The reverse is now true."

Jan 1, 1967

By P. L. Rittenhouse, M. L. Picklesimer

A rapid and seniquantitative method of determining prefered orientation on large numbers of. Zircaloy-2 specimens was desired. knoop microhardness measurerrzetzls were irvestigated as a solldtion to this pro6lem. The variation of Knoop microhardness measurerlerzts on selected planes as a function of 'irzdenle axis relutilje lo cryslallograplzic or fabrication divectals were used to corzstrrcl a polar coordinate hardness contour map. With use of an empirical relationslip between the single-crystal hardnesses and those of the polycrystalline material conentional pole figures could be constructed which compare favorably also obtained. To determine preferred oriention qualitatively from hardness data requires a minimum of twelve measurements per plane on three, preferattention to grain size, specimen prepartion, and in-rreinetzt, and analjlsis is of the order of- 45 to 60 rrin. THE design of structures from Zr alloys requires consideration of preferred orientation and the resulting anisotropy of mechanical properties. Rapid and semi-quantitative methods of evaluating anisotropy and of determining preferred orientation are needed for quality control and for examining the large number of test specimens required in development programs. The variation of Knoop microhardness with indenter orientation has been studied in single crystals of several hcp metals including titanium.' beryllium,' magneium, and zinc.4 The maximum hardness observed on any crystallographic plane other than the basal plane invariably occurred when the long axis of the Knoop indenter was either parallel or perpendicular to the projection of the [ OOOI.] direction on the plane of examination. When the major slip mode was (0001)(i2i0j the maximum hardness occurred at the parallel positio! but when the operating slip system was {10i0) (i210) the hardness was a maximum perpendicular to the [0001] projection. A minimum hardness was always observed at a rotation of 90 deg from the maximum. It follows that the orientation of the projection of the [0001] can be determined on any non-basal plane by making hardness measurements at a number of indenter orientations. The determination of the orientation of the [0001] projection on two non-parallel, preferably orthogonal, surfaces of the specimen will allow location of the [0001] direction in the specimen. It seems possible that such measurements could be used to examine, at least qualitatively, the preferred orientation existing in polycrystalline hcp materials. An investigation of the microhardness anisotropy in Zircaloy-2 was undertaken to ascertain whether these measurements could be used for this task. EXPERIMENTAL PROCEDURE Single crystals of Zircaloy-2 were grown by an a-8-a annealing sequence using electron-beam heating.= The orientation of the crystals was determined by a conventional back-reflection Laue technique. The crystals were then mounted on a goniometer head and the desired crystallographic faces were milled and chemically polished. Polycrystalline Zircaloy-2 specimens were prepared from fabricated sheets or plates. Inverse pole figures for these materials were obtained using the X-ray diffraction techniaue described by Jetter, McHargue, and illiams.' A Wolpert-Greis Micro-Reflex hardness-testing machine was used to make the Knoop microhardness measurements. The single-crystal and polycrystalline specimens were loaded to 0.5 and 2.0 kg, respectively. Determination of the scatter of hardness numbers as a function of applied load for several indenter orientations on several specimen surfaces showed that the loads selected were the lightest consistent with minimum scatter. Heavier loads did not appreciably decrease the scatter and produced hardness impressions too large to be conveniently measured with the equipment used. Seven crystallographic planes of the single crystals were examined, while six planes of examination were used in studying Zircaloy-2 polycrystals. The specimens were rotated 10 to 15 deg after each measurement and from four to eight impressions were made at each angle of rotation. RESULTS The two angles which were used to relate crystallographic directions and planes in the hcp cell to the planes of examination of the single crystals are shown in Fig. 1. 8 is the angle between the c axis. [0001]. and the normal, N, to the plane of examination. a is the angle between the long diagonal of the Knoop indenter and the projection of the c axis on the plane of examination. For exampIe, if P = 90 deg and a = 0 deg, the plane of examination is of the family

Jan 1, 1967

By A. J. Rergis

During the past ten years a number of papers have appeared describing zeolite occurrences in the western United States in Mesozoic sedimentary rocks, altered bedded Tertiary pyroclastics, playa lakes, hot springs, and amygdaloidal basalts. With the emergence of natural zeolites as economic industrial minerals it appears, useful to develop a system of classification to delineate those zeolite deposits of economic interest which were not discovered until the middle 1950's. The first attempt at a classification of naturally occurring zeolites was made in 1914 by Lindgren l when he classified the zeolites into eleven groups based on their mode of occurrence. The zoned zeolites in the Mesozoic rocks of New Zealand and elsewhere were classified according to the mineral assemblages by Fyfe, et al.2 in 1958 as a zeolite facies corresponding to low grade regional metamorphism. In 1966, Hay suggested as an alternative to the preceding classification one which would "classify as diagenetic all mineral assemblages produced in sedimentary rocks under conditions in which zeolites are formed." In this paper a classification is proposed with the objective of providing an overall perspective of the zeolite occurrences in the western United States.

Jan 1, 1967

By J. H. Brophy, A. I. Prill

The authors have previously investigated the solid-state activated sintering of tungsten powder with various Ni-Cu additions.' Log shrinkage vs log time plots showed changes in slope from 4 to x at intermediate times during the sintering process. This was attributed to a change in the rate-controlling mass-transport process from solution of tungsten into the tungsten-alloy interface to diffusion of tungsten in this interface. It was postulated that the melting of the activating layer should not affect this transport process. However, the superposition of rearrangement due to the presence of a liquid phase complicates the data analysis. It is the purpose of this note to apply the analysis of Prill, Hayden, and rohy' to account for "rearrangement shrinkage'? in liquid-phase sintering of the W-Ni-Cu system. This results in "solution-precipitation stage" shrinkage plots which were comparable to those obtained in solid-phase activated sintering of the same system. If one assumes total shrinkage to be the sum of rearrangement and solution precipitation, the effects can be isolated easily.2 This results in the general equation:

Jan 1, 1967

By O. C. Baptist

The gravitational pressure gradient (GPG) in porous sandstone containing free gas was determined to define the proper GPG to use when calculating the rate of downdip flow of oil in the Sub-Scalez No, 1 sand, Elk Hills field, Naval Petroleum Reserve 1. The GPG was determined at several gas saturations using long, artificially consolidated sandstone models that were mounted vertically in some tests and horizontally, with rotation, in others. Also determined by laboratory and field tests were relative permeabilities, capillary pressure relations; critical gas saturation, water sensitivity, and depletion drive performance. The critical gas saturation in the models having an absolute permeability of 1 to 2 darcys was about 2 percent of pore volume. The GPG with the critcal gas saturation was that due to the weight of the gas-saturated oil. The GPG in the upper part of the models was reduced as gas saturation increased to a value considerably larger than the critical. The exact gas saturation at which the GPG became less than that due to the weight of the oil could not be determined but was estimated to be of the order of 10 percent of pore volume. Tests indicate that the rate of oil production is not permanently reduced by exposure of the sand to fresh water but that the rate of injection of fresh water will be considerably less than that to brine, Methods for determining the factors mentioned above are discussed.

Jan 1, 1967

By W. V. Long, D. H. Reynolds, R. B. Bhappu

Equilibrium distribution coefficients were determined for some monovalent and polyvalent ions for several absorbing and exchanging media as functions of pH and initial ion concentration. Among ions studied were NH4 (I), K(I), Ni(II), Ce(III), Th(IV), and Mo(VI). Absorbents used were: ion exchange resins; a tertiary, and a quaternary amine in an inert solvent; and some activated carbons. The ions studied were in aqueous HCI, HNO3, H2SO4, or HC104 solutions. The classical mass action expression proved of little value in describing the variations observed. The data indicate that the determining factors in absorption and ion exchange may be the ionic species in the aqueous solution, which in turn depend upon pH, dilution, and perhaps other conditions. Three sorption processes have become prominent in recovering values from leach solutions. These are: 1) ion exchange, 2) solvent extraction (liquid ion exchange), and 3) physical adsorption by materials of high specific surface. In the first two of these processes the exchange reaction is considered chemical in nature, and is discussed in terms of the mass action principle. The third is considered a surface phenomenon and is discussed in terms of surface areas and various forms (Gouy, Stern, Grahame, etc.) of the Helmholtz double-layer theory. Generally speaking, we have found in chemical analysis and hydrometallurgical studies that there are close similarities between the three sorption processes, and also differences which are difficult to reconcile with any of the usual theoretical treatments. That others have experienced the same troubles is shown by the fact that usable processes, in chemical analysis as well as in hydrometallurgy, generally are discovered by empirical procedures. EXPERIMENTAL CONSlDERATlONS The gaps between theory and practice have allowed many conflicting statements to appear in the litera- ture. To learn, in particular, the behavior of some metallic ions on a cation exchange resin at a constant pH, equilibration studies were made over a wide range of concentrations.' Results are shown in Fig. 1 for four metals in hydrochloric acid solution on a strongly acidic cation exchange resin, AG 50W-X8 (Bio-Rad). The distribution coefficient, defined as D = amount of metal extracted per g of resin/amount of metal unextracted per ml of solution is seen to vary in a way to support all manner of reports about its behavior with changes in solution concentration. The metals used were chosen from those least likely to form stable chloro-complexes. The changes of slope in the various isotherms may reflect formation of unsuspected chloro-complexes of low stability (ion-pairing for example) whose concen-

Jan 1, 1967

Jan 1, 1967

By Robert W. Ageton

Optimal planning for mining the deep, lead-zinc-silver deposits of the Coeur d'Alene mining district, Shoshone County, Idaho, could be facilitated by a knowledge of the magnitude and direction of the pressure acting in the virgin rock. The distribution of primary stresses should be considered in order to prevent possibly destructive mining-induced stress concentrations. This particular investigation was concerned with determining stress in a zone 4,000 feet below the surface and known to be ender stress concentrations due to mining operations. Disking of the stress-relief cores obtained in a vertical down hole permitted qualitative evaluation from visual observations; the results indicate that a high lateral stress existed at the time the measurements were made. Stress-ellipsoid determinations gave a compressive principal stress of -13,000 psi oriented about N 45° W and nearly horizontal, a compressive principal stress of -11,000 psi oriented about S 45° W and abut 60° off the vertical pointing away from the vein, and a compressive principal stress -5 -7,000 psi oriented N 45° E and about 60° off the vertical, pointing toward the vein. Subsequent to the overcoring stress-relief drilling, a rock burst occurred about 100 feet northwest of the test site.

Jan 1, 1967

By Raynor Linzey, Karl M. Busen

The formation of thin films of silicon oxide by anodic oxidation of silicon and the subsequent removal of these films by an etch is a process often used for the evaluation of concentration distributions Profiles) in silicon layers by the differential sheet conductance method. The accuracy of the resulting profile is very strongly influenced by the uniformity of the thickness of the reacted silicon. Normally, it would be expected that for a constant number of coulombs passed the thickness would be the same from oxidation to oxidation. Investigations show that in certain electrolytes, for a given number of coulombs passed through an n-type silicon sample, the thickness of the reacted silicon increased with increasing resistivity. Even for the same resistivity the thickness varied sometimes by a factor of 1.5. When an electrolyte was used which consisted of 10 pct water by volume in ethylene glycol with 4.0 g KNO per 1000 ml of solution, anodiza-tion at 5 ma per sq cm led to satisfying results. Short-time anodizations gave oxide layers of a higher apparent density than those experienced from thermally gown silicon oxides. THE functioning and the electrical characteristics of semiconductor devices are based upon the incorporation of "impurities" into a single-crystalline body of suitable material and on the concentration distribution (profile) of this impurity. The incorporation can be achieved by well-known processes as, for example, by diffusion, epitaxial growth, alloying, or ion implantation. Often the profile resulting from these processes is not known. A powerful tool to learn about a concentration distribution is given by the method of differential sheet conductance which employs successive four-probe measurements on a layer subjected to stepwise removal of thin sublayers. Differential sheet conductance vs position (or penetration depth) of a sublayer is plotted and a smooth curve is drawn through the data. From this curve the profile is then calculated. When the semiconductor material is silicon, the sublayers are removed suitably by anodic oxidation of the silicon and subsequent dissolving of the formed silicon oxide by an etch. The accuracy of the resulting profile is very strongly influenced by the uniformity of the sublayer thickness. Normally, it would be expected that, for a constant number of coulombs passed, the thickness would be constant from oxidation to oxidation. Investigations showed that for sublayers several hundred angstroms thick the reproducibility can be rather poor. Therefore, efforts were made to obtain a reliable technique for uniform removal. The present paper describes such a technique and certain phenomena which were encountered during the investigations. APPARATUS AND TECHNIQUE The first report on the investigation of concentration distributions, where for differential sheet conductance measurements thin silicon sublayers were removed from a diffused layer by anodic oxidation, was given by Tannenbaum. The author reports the removal of sublayers which for the most part were 400 thick. More advanced device designs now require much narrower layers. When it was tried in these laboratories to determine profiles within such layers, difficulties were encountered with respect to sublayers which by necessity had to be thinner than the ones reported by Tannenbaum. The apparatus used for the investigations is sketched in Fig. 1. Two cylindrical containers connected by a wide tube are filled with an electrolyte. The left container receives the cathode whereas the right container is closed at the bottom end by a sample support consisting of a Teflon base and a copper pedestal. The silicon sample (1 by 1 cm) is mounted to the pedestal embedded flush in the Teflon base using silver paint (Degussa) for electrical contact. Pyseal is applied to the edges of the sample to protect the copper pedestal from the electrolyte. The base is mounted to the container using a water-tight silicon rubber gasket. Fig. 2 gives a view of the sample support. The copper pedestal is connected to the positive side of a power supply operating at a constant current output (Kepco Model ABC 425M). The electrolyte which has been reported by Duffek et al. consisted of either 2 or 10 pct water by volume in ethylene glycol and 4.0 g KNO3 in 1000-ml solution. The electrolyte is best prepared

Jan 1, 1967

By R. N. Upadhyay, M. Maleki, I. Fatt

Conventional laboratory core analysis tests on samples of two limestone reservoir rocks indicate that about 20 per cent of PV is in dead-end pores. These tests (electric logging formation factor, mercury injection capillary pressure and miscible displacement) were carried out on 1/4-in. diameter test plugs. Test results show a clear dilference between these samples and sandstone or homogeneous limestone reservoir rock. Although the amount of dead-end pore space can be only roughly estimated, the presence of such pore space seems clearly indicated. Pressure transient studies also show presence of deadend PV. Although they do not give quantitative results, pressure transient data yield a reasonable estimate of the size of the neck connecting dead-end pores to the main flow channels. INTRODUCTION Equations conventionally used to describe reservoir flow behavior contain the implicit assumption that all connected pore spaces contributed to both porosity and permeability. Several authors3-7 have pointed out the changes in pressure transient behavior and in electric log interpretation that may result if this assumption is incorrect and, instead, dead-end or cul-de-sac pores are present. There is a need for laboratory tests that can detect presence of dead-end pores in core samples. With such information on hand the petroleum engineer can make more rational use of the mathematical tools now available for analysis of reservoir flow behavior. This paper describes laboratory studies designed to detect and, if possible, give a quantitative measure of dead-end PV in laboratory-size core plugs. Three reservoir rocks were used, two of which were limestones suspected of having deadend pore spaces and a well-known sandstone, used as a comparison standard, in which there is believed to be little or no dead-end pore space. All the studies were designed to measure the natural dead-end PV; i.e., the pore space which is dead-ended because of rock structure. During multiphase flow in a rock without dead-end pores, some parts of one of the phases can become surrounded by the other, thereby giving (for certain flow behavior) an effective dead-end pV8,9. Such behavior will not be described here.

Jan 1, 1967

By A. T. English

X-ray dif action techniques were used to investigate ordering and domain coalescence for the B2 (CsC1) superlattice in this alloy. Essentially complete disorder is obtainable by drastic quenching. isothertmal ordering occurs very rapidly at temperatures between 565° and 680°C, only a few seconds being required for development of substantial long-range order. A very fine antiphase dormain structure, found in samples annealed for short times, undergoes coalescence with further annealing. Domain "size" is found proportional to (t)1/2 . This Yate law can be derived by adapting the formalism of Hillert's analysis 01- metallurgical grain growth. For this Purpose the material is descvibed in terms of a "Swiss-cheese " structure, consisting of two multiply connected, mutually intertwined domain volumes. The observed activation enevgy for coalescence, 70 kcal per g-atom, agrees with an estit~lated value ,for volume diffusion in disordered rrzaterial. It is suggesled that the experimental value vejlects the substantially disordered environment of mobile vacancies located in the moving antiphase domain boundary. The alloy Fe-Co-2V is bcc below about 900'C and orders into a B2 (CsC1) superlattice below about 730c It has important applications in magnetic components, including many requiring extensive cold rolling.* example, Marcinkowski and Brown6 observed a re1atively small as-quenched domain size of about 250Å in B2 Fe3A1. Since there appear to be no published data on domain coalescence in B2 alloys, this process was studied in detail. MATERIALS AND EXPERIMENTAL TECHNIQUES A commercial high-purity alloy, nominally 49 Fe-49Co-2V, was obtained from the Arnold Engineering Co. in the form of cold-rolled sheet 0.004 in. thick. Samples were annealed for 1 hr at 800°C in dry H2 to produce disorder and quenched into iced brine. They were then annealed in a nitrate-nitrite salt bath for various times at temperatures between 525° and 625°C. Estimates of the LRO parameter S and the APD size D were made using established X-ray diffraction techniques. Superlattice peaks are best observed using CoKa radiation, for which the value of (fFe-fCo) is maximized. Peak-to-background intensity ratio was improved by filtering CoKß from the incident beam to eliminate sample fluorescence, and by using a pulse-height analyzer. The LRO parameter S was computed from the ratio of integrated intensities I 100/I 200- Owing presumably to systematic errors associated with the presence of crystallographic texture and X-ray extinction, only rough agreement was obtained between experimental and theoretical (absolute) intensity ratios. For this reason certain experimental refinements (e.g., use of balanced filters) were considered superfluous and were omitted. Emphasis was placed on maximizing intensity in order to reduce the time taken to accurately determine the contour of the very small (loo), peak. This was done by point counting 105 counts at appropriate intervals. Background intensity averaged about 1200 cps.

Jan 1, 1967

By M. J. Mullikin, J. B. Conway

for use in describing combined first- and second-stage creep data. In the above ?o represents the instantaneous strain on loading, ?t the limit of transient creep, ?S the steady-state creep rate, t the time, and ? a constant leading to the exhaustion rate of transient creep. It was noted that this equation was similar in form to that proposed originally2 by McVetty. This type of equation was also suggested by Andrade and Aboav3 in studies of the shear strain of cadmium. Calculation of the constants ?o, ?t, ?, and ?s, in Eq. [ l] is somewhat involved due to the slight complexity of this relationship. In the paper by Garofalo a computer approach based on a least-squares analysis was recommended. Such an approach involves a trial and error solution but when a computer facility is available the difficulties in this calculation are of little consequence. It does mean however that the evaluation of this type of equation would become quite tedious if computer facilities were not available. Some recent studies have identified a fairly straightforward method for calculating the constants in the Garofalo equation. While not leading to a least-squares evaluation the approach is accurate and is recom-

Jan 1, 1967