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By K. J. Anusavice, R. T. DeHoff, A. G. Guy, T. B. Lindemer

As one oi the approacizes to understanding multicorn-ponent dimsion, an expevinzental sturly is being jnade of tracer diffusion in the copper corner of the CLI-Ni-Zn syste?n, out to 30 at. pct each of nickel and zinc, and in the 150°C range oJ temperature just below tlze solidts te?rlperature. The reslts obtained using the Znm isotope are reported heve, while studies with nickel and copper isotopes are planned for a future paper. The fifteen alloys investigated were melted in sealed wear lubes, sroaged, homogenized, and then analyzed, using the conventional isotope-plating plus lathe- sectiorzing teclzniqlte. The data obtaiued show that the difJusion coeflcient of the zinc isotope increases titlz increase in zinc content, and decreases t'itlz incease in nickel content. The correlation xith solidus temperature is particularly strong. Diffirsiui-ties ranged fro u sq cm per sec nt tlze Iiigh-zinc, low-nickel compositions. The activation energy /or tracer diffusion ravied j.or 31.000 to 54,000 calper mole. It is now generally recognized that diffusion data and theories are needed for multicomponent systems, where extensive practical developments and even some theoretical studies have already been made. For example, much recent work on precipitation from solid solution has been concerned with ternary solid solutions such as A-M-Z' while Zener relaxation has been studied on Au-Ag-Zn alloys,' although adequate diffusion data are available for neither of these systems. Actually, the only ternary systems for which systematic diffusion studies have been begun, in addi- tion to the one reported here, are CO-i-cr3 and Cu-A-Au. Since the theory of multicomponent diffusion is still in the stage of active development5 it is important to distinguish the various kinds of diffusion data that can be determined. An oversimplified approach, widely used prior to 1950, was to determine the influence of a third element, such as nickel, on the diffusion behavior of a binary alloy, such as CU-Z. Later it was recognized7 that four diffusion coefficients can be used to describe ordinary interdiffusion in a ternary system, while as many as six coefficients may be required to include the Kirkendall effect. It is likely that the number of independent coefficients will be shown to be less than four and six, respectively, through the application of the thermodynamics of irreversible processes.5 The simplest type of diffusion in a multicomponent system is tracer diffusion, since each component is characterized by its own tracer-diffusion coefficient in an alloy of a given composition. Thus, in a ternary alloy there are three tracer-diffusion coefficients, each a function of composition and temperature. The present research program is a study of tracer diffusion in the copper corner of the Cu-Ni-Zn system out to 30 at. pct each of Ni and Zn in a 150°C range of temperature just below the solidus temperature. The

Jan 1, 1967

By R. D. Carter

Methods are presented for calculating the performance of multiwell gas reservoirs. These methods account for two-dimensional, unsteady-state flow of a non-ideal gas through a heterogeneous formation. The performance can be obtained for gas reservoirs with known physical properties and configuration subjected to specified development and production schedules. These methods may prove helpful in optimizing the exploitation of gas reservoirs. The numerical solrrtion procedures given for this non-linear problem are extensions of known techniques for the linear diffusion equation. Two of these procedures are based on a new difference equation given by Saul'ev. Limitations and advantages of these procedures are discussed. An example solution is presented and is used to compare the calculation methods. INTRODUCTION Li planning the operation of a multiwell gas reservoir, it is desirable to predict its performance for each alternate development and producing schedule under consideration. This paper presents three numerical procedures that can be used to calculate such gas reservoir performance using a digital computer. These methods account for two-dimensional transient flow of a non-ideal gas within the reservoir. Extension of these methods to three-dimensional flow is possible. The paper is divided into three parts. The first describes the problem for which a solution is wanted and three numerical procedures that can be used to obtain solutions. The second discusses the information necessary to set up a problem. This part will be of greatest interest to the field engineer. The third gives data and results for an example problem. PROBLEM AND SOLUTION METHODS In the following development, a gas reservoir is regarded as a sealed, porous, permeable, heterogeneous body in which a single, non-ideal gas phase is flowing. Flow is permitted in the x- and y-horizontal directions, but is considered to be negligible in the vertical or z-direction. The reservoir can be tapped by one or more wells. Methods to be described provide a basis for calculating the complete performance of the reservoir, including rates and cumulative production from the wells, and pressure distribution and decline in the reservoir. If the isothermal flow of a non-ideal gas obeying Darcy's Law occurs in two dimensions in a region R, the governing equation in this region is:

Jan 1, 1967

By K. M. Rolls, J. Wulff, D. A. Colling

Solid-solution alloys of the Ta- Ti system containing up to 70 at. pct Ti were melted and fabricated into wire. Steady magnetic-field measurements of cold-worked wires at 4.2°K indicate that the resistive critical field increases smoothly with increasing titanium, reaching a maximum of 93 kG (J = 1 amp per sq cm) for a composition of about 50 at. pct Ti. The composition dependence of the resistive critical field indicates it is largely paramagnetically limited for alloys containing more than 35 at. pct Ti. For cold-worked wires the value of the critical current density, Jc , was found to be insensitive to composition changes for compositions in excess of 20 at. pct Ti. It was observed that Jc could be increased by final-size heat treatment at 400°C without altering the value of- the resistive critical field. Experimental data are used to calculate the electronic specific-heat coefficient and the "upper critical field" for the alloys studied. THE effect and importance of metallurgical structure on superconducting properties have been summarized by Livingston and Schadler.1 Specific work on solid-solution alloys such as Nb-zr2-7 and Nb-Ti5-7 have shown that critical current density (Jc) and superconducting transition temperature are structure-sensitive. Berlincourt et al.6,8,9 in their studies of transition-metal alloys find that Ta-Ti alloys remain superconducting at fields comparable to Nb-Ti alloys. 6,8 Transverse critical current tests of a Ta-10 at. pct Ti alloy10 and longitudinal critical current tests of a Ta-25 at. pct Ti alloy1' indicate that such alloys are capable of carrying high currents at intermediate fields (-40 kG). The work reported in the present paper was undertaken to explore the superconducting properties of further compositions in the Ta-Ti alloy system as well as the structure sensitivity of the superconducting properties. I) EXPERIMENTAL PROCEDURE Alloys were prepared by melting tantalum (Fansteel Metallurgical Corp., 99.96 pct purity) and iodide, crystal bar titanium (Foote Mineral Co., 99.92 pct purity) mixtures in an arc furnace on a water-cooled copper hearth using a tungsten electrode. Melting was accomplished in a purified, gettered argon atmosphere at pressures from 250 to 400 Torr. Each alloy was turned and remelted fourteen times to assure complete mixing of tantalum and titanium. Ex- cessive coring in the cast samples was, nevertheless, observed. This was somewhat reduced by annealing in vacuo at 1000°C for 13 hr. The ingots were then machined to 0.250 in. diam, jacketed in Type 304 stainless-steel tubing, and swaged to 0.140 in. diam. They were then drawn to 0.010-in.-diam wire. Alloys containing up to 70 at. pct Ti were readily cold-drawn to wire in this manner. Later experiments showed that oxygen additions up to -3000 ppm could also be cold-worked into wire. Test samples for superconductivity measurements in the 2-in, air-core Bitter solenoids of the M.I.T. National Magnet Laboratory were prepared from 10-in. lengths of 0.010-in.-diam wire, cleaned of residual wire-drawing lubricant. Current contacts were made by clamping clean copper tubing over both No. 18 current lead wire and the ultrasonically indium-tinned ends of the specimen wire.12 Potential leads of No. 32 copper wire were connected to the specimen by ultrasonic soldering in an indium bath. The potential lead separation was about 4 cm, corresponding to the circumference of the Bakelite rod to which the wire was affixed with half-mil Teflon tape. The final specimen configuration is shown in Fig. 1. Specimens were lowered into a liquid helium bath (4.2oK) in a double solenoid dewar and positioned so that the maximum magnetic field was oriented transverse to the wire axis of the gage section. Measurements were made by passing a current through the specimen at a preset solenoidal magnetic field. The current was increased until a 1-pv potential difference appeared across the gage section (1/4 µv per cm). At low magnetic fields, however, it was not possible to use this criterion because power-dissipation difficul-

Jan 1, 1967

By C. C. Shale

Current-voltage relationships for air at high temperature in negative corona are compared with relationships predicted by theory. Deviations are discussed. Eased on the latest theoretical concept of electron detachment from negative ions and recent findings in basic research on free electron gases, results of applied research show the existence of free electrons in air at high temperature and high field strength-to-pressure ratios.

Jan 1, 1967

Magnetic anomalies in the Southern Coalfields have been subdivided into two characteristic types. Each type is attributed to a separate cause, one being basement structure, and the other near-surface igneous intrusions.Detailed geological mapping of the area and the ability to sample throughout the coalmines greatly assisted in this subdivision.The Triassic sequence contributes no magnetic effect of its own except to diminish the effect of sources within the underlying formations by raising the level of observation.Detecting the presence of igneous intrusions ahead of colliery working faces by magnetic observations within the coal mines may be of value in preventing accidents caused by gas outbursts and in planning the workings so as to avoid loss of production time.

Jan 1, 1967

By H. C. Chao, W. F. Hosford, L. H. Van Vlack

The negative "plastic Poisson's ratio" suggested in earlier studies of Mus deformation is analyzed, and the results are verified experimentally with NaCl crystals. In the early stages of deformation where the primary {110}(110) slip predominates, compression along. the [001] direction produces contraction along the lateral [011] direction plus a compensating expansion along. the [100] direction. With additional strain, the primary slip is supplemented by secondary {111}(110) slip so that the above contraction diminishes and a more typical deformation appears. THE shape change of bee and fee crystals deformed by compression or tension along [011] has been analyzed in some detail and shown to be responsible for the development of peculiar microstructures in [011] fiber textured polycrystals of these metals.1'3 This paper concerns the unusual shape change accompanying [011] compression of NaCl crystals. It is the direct outgrowth of an earlier investigation of the deformation of manganese sulfide inclusions in steel.3,4 In that investigation, cylindrical specimens of steel containing small oriented crystals of MnS were prepared by powder metallurgy and plastically compressed. The flow of the inclusions was determined relative to that of the steel by sectioning the composite and measuring the length-to-width ratio L/W of the inclusion and diameter-to-height D/H ratio of the steel cylinder on the plane of section. These L/W ratios, normalized by dividing by the initial LO/WO ratio of the inclusion, were compared with the normalized D/H ratio of the steel cylinder. Of particular interest here are the deformation characteristics of an inclusion oriented with [Oil] parallel to the compression axis. When measurements were made on sections parallel to the (100) plane of the inclusion, the L/IV ratios were only slightly in excess of unity, indicating a high apparent hardness of the [011] criented inclusion. However, measurements on a (011) plane of section resulted in L/W ratios which were much larger, Fig. 1. These observations prompted an analysis of the strains resulting from slip in an MnS crystal compressed along [011.]. CRYSTALLOGRAPHIC ANALYSIS Manganese sulfide has the NaCl crystal structure, and the predominant slip system is {110}(110). A secondary system, {111}(110), has also been reported.= {110}(110) Slip. When a crystal is subject to a uni-axial compressive stress 011 along [011], four slip systems, (101)[101.], (101)[101.], (110)[i10], and (110) [ 110], will be equally stressed with a shear stress t = 0.2 011 while the other two {110}( 110) systems will be unstressed. The normal strain En along any reference axis n resulting from slip is given by Schmid's law: en = S COS ?in COS in ?i 111 where ?in and +in are the angles between n and the i slip direction and n and the i slip plane normal, respectively, and where ?i is the shear strain on the i slip system, For the four active slip systems above, the cos ?in cos +in terms are all equal when the reference axes are the [011] compressive axis, [011] and [ 100]. Eq. [I.] therefore reduces to en - cos ?n cos +ny [2] where y =S?i for all slip systems. Substituting the appropriate angles, Eon = 0.25? 110 eon - 0.25y110 [3] €100 = -0.50y 110 The interesting feature of Eqs. [3] is that they predict that the strains in the [011] and [011] directions, resulting from {110}(110) slip, are equal and of the same sign. Thus when a crystal is compressed along [011], it will contract along the lateral [oil] direction

Jan 1, 1967

By J. C. Griffiths, D. W. Bennion

A mathematical model, which does not assume a priori that stratification exists, but was designed to test for the stratification was developed. The model segmented the reservoir horizontally into areas of common variance, then divided it vertically into strata (if strata were present). Next, trend surface techniques were used to determine the lateral extent and variation of each stratum. The model was tested on two reservoirs (sandstone and limestone) using porosity as the reservoir rock property. The sandstone reservoir contained approximately 60,000 samples from 2,000 cored wells, while the limestone reservoir had approximately 24,000 samples from 430 cored wells. Within the areas of common variance tested, the model was able to distinguish four separate lithological units or zones in the sandstone reservoir, four in the Marly section and seven in the Vuggy section of the limestone reservoir. INTRODUCTION To accurately predict the movement and production of fluids from a reservoir rock, it is necessary that the reservoir engineer have a knowledge of the rock properties and their distribution throughout the reservoir. For this study, a reservoir rock is defined as a solid containing interconnecting holes or voids which occur relatively frequently and are dispersed within the rock in a regular or random manner. The fraction of bulk volume that these interconnecting voids occupy is called porosity. The rock must also possess sufficient permeability to allow fluids to move through it and it may be composed of one or more strata or lithological units. A stratum or lithological unit as defined in this study is a body or volume of reservoir rock whose properties are so distributed that its lateral and vertical extent can be traced throughout or through a portion of the reservoir. Operationally, the existence of strata are question- able unless the variance within strata is less than among strata. Within the past few years computers have been widely used as a tool for calculating movement and production of fluids from reservoirs. Most prediction models require some type of a mathematical description of certain reservoir rock properties. In the past, most of these models have been relatively simple. Some have assumed vertical variation but no lateral variation, while others have assumed lateral variation but no vertical variation. In general, most of these models have not used functional relationships to predict reservoir rock properties as functions of position. The object of this study was to develop a model which would predict lateral and vertical variations of reservoir rock properties. Since samples are usually available from only a small portion of the total reservoir rock, it seemed logical that if measurements from these samples were to be used to infer the properties of the actual reservoir, the data should be treated statistically as a sample from the total population (reservoir). Therefore, the model developed in this study to predict reservoir rock properties was a stochastic model. The model was tested using porosity (a macroscopic reservoir rock property) measurements from two reservoirs — the first, a sandstone reservoir from which 60,000 samples were obtained; and the second, a limestone reservoir with 24,000 samples. Several investigators have proposed methods to determine the vertical and areal variation of a reservoir rock property. Stiles: Dykstra and Parsons 2 and Suder and Calhoun3 have all developed waterflooding prediction techniques which assume vertical variation but no lateral variation. Stiles developed a method to segment a reservoir arbitrarily using frequency distribution. Law4 suggested that porosity has a normal frequency distribution and that permeability has a log-normal frequency distribution. Elkins and Skov 5 proposed that when a reservoir is segmented vertically, the

Jan 1, 1967

By Robert Maes, Robert de Strycker

The solidifzcation reactions in the Cu-Sn-As system were determined by microscopic examination, thermal analysis, and X-ray diffraction. The system presents no ternary compound. There is a quasi-binary section, of a simple eutectic type, between the compounds Cu5As2 and SnAs; the system presents, in addition, one ternary eutectic reaction, one ternary peritectic reaction, and seven transitional reactions. The temp-peratures corresponding to each of these reactions were determined, most of them with an accuracy of *lLC. The isothermal lines of the liquidus surface were also established for almost the entire diagram. NO reference was found in the literature relative to the Cu-Sn-As phase diagram and this is believed to be the first study on this subject. The Cu-Sn diagram was taken from Hansen and Anderko;' it is represented by Fig. 1, with the phase designation which will be used in the remainder of this work. For the Cu-As diagram, the solution proposed by Hansen and ~nderko' must be modified to take account of recent data, principally from Heyding and Despault~ and from Hume-Rothery and Burns; this yields the diagram represented by Fig. 2. As for the Sn-As diagram, it is not established with certainty, particularly so far as concerns the solid solubility of tin in arsenic and the solidification reactions near the compound SnsAsz. For this last point, Hansen and Anderko propose two solutions: congruent melting of Sn3Asz with a eutectic SnsAsZ + SnAs or incongruent melting implying a peri-tectic reaction L + SnAs = Sn3As2. Microscopic examination of the few binary alloys prepared in this composition range made us prefer the second of these solutions, which gives the diagram shown by Fig. 3. EXPERIMENTAL METHODS The experimental techniques used in this work were microscopic observation and thermal analysis; a few X-ray diffraction patterns were taken to verify the

Jan 1, 1967

By Claude H. P. Lupis, John F. Elliott

QUITE generally an increase in the temperature tends to bring a system closer to ideality. It is reasonable as a first approximation to consider that the excess free energy will vary linearly with the temperature, or: where t may be defined as the "characteristic temperature" of the solution, or the temperature at which the system would become ideal if the results at T were linearly extrapolated. It must be emphasized that consideration of this hypothetical property is an appeal to intuition rather than an established physical concept. The order of magnitude of 7 for dilute solutions will depend on the nature of the solvent; a value of 3000° + 1000°K may be suggested for ordinary metallic solutions. In terms of free energy, entropy, and enthalpy first-order interaction coefficients, differentiation of the above equations with respect to composition leads to The concept of t offers a simple and plausible interpretation of Chipman and corrigan's3 recent empirical correlation between and a for a number of groups of ternary systems 1-24. The authors found that in each group the ratio was approximately constant. The corresponding calculated from their data by Eq. [4] are listed in Table I. The expected order of magnitude is obtained for 7. As noted by Darken,4 if a regular solution is not assumed, thus if utj) # 0, Chipman and Crrigan's results imply that, as T is increased, ultimately changes in sign, Fig. 1. Clearly Eq. [4] is valid only in a limited range of temperatures since at the temperature 7 at which the system becomes ideal not only should become null but also and . Thus, both and are functions of

Jan 1, 1967

In presenting the paper, Mr. Davey quoted subsequent work which yielded k, at miscibility gap composition, of about 50.We can confirm the authors' findings for k j 300 for nearly pure tin to k 2 about 50 (average 47) from our own experience and from repeat experiments on materials described by the authors, at 1150°C.During laboratory-scale trials we also found confirmation of the authors' view that it is more difficult to reach equilibrium from the high-iron (in slag) side than from the low-iron (high-tin) side. Working from the high-iron side tends to yield results that point to a high k, leading to optimistic values of iron/tin ratio in final slags. In practice the smelting of a tin concentrate, unless it is exceptionally low in tin and high in iron, must yield initially a tin-rich slag and therefore equilibrium can only be reached from the "tinny" side.

Jan 1, 1967

By S. S. Marsden, S. A. Khan

Externally generated foam was injected continuously into short porous media. Both flow rate and pressure drop were measured. Liquid saturation was determined by electrical conductivity. Foam yuality I, expressed as the ratio of gas volume to total volume, was varied from 0.70 to 0.96. As measured with a modified fann VG Meter, apparent viscosity of this foam µa decreases with increasing shear rate but usually falls within the range of 50 to 500 cp. At a given shear rate, µa increases almost linearly with I-. When measured with a Bendix Ultraviscoson, kinematic pa is independent of V but absolute pa increases with T from about 3 to 8 cp. The effective permeability -apparent viscosity ratio ke/µa decreases almost linearly with V for porous media of high permeability, but the rate of decrease becomes less for tighter ones. The relative permeability-apparent viscosity ratio kr/µa us V data does not fall on a single line. The kr/µa ratio increases with liquid saturation in the porous medium and with surfactant concentration. Estimates of pa for foam in porous media vary from 30 to 100 cp. INTRODUCTION Although research on the development of a foam-drive, oil recovery process has been going on for almost a decade, most of the significant publications have appeared within the last several years. This illustrates well the rate at which interest in this process is accelerating. Bond and Holbrook 1 were the first to describe the use of foam to improve oil recovery in their patent of 1958. They proposed that an aqueous foaming agent slug be injected into the formation and that this be followed by gas to produce a foam in situ. Fried 2 studied the injection of foam into porous media which had already been subjected to conventional gas or water drives and found that gas could be used to drive a foam bank which would, in turn, displace additional oil in the form of an oil bank. He attributed the increased oil recovery to the high effective viscosity of foam flowing in porous media. His microscopic observations showed the importance of foam generation and regeneration within the porous medium. By injecting both air and aqueous surfactant solution, Bernard3 generated foams within the porous medium in which oil displacement was being studied. In a separate empirical test, he also measured the dynamic foaming characteristics of the same surfactants in water and/or oil. With some exceptions and for the seyen surfactants studied, there seems to be a qualitative relationship between the efficiency of liquid rlisplacrment and the dynamic foaming testtsed. This relationship was not consistent enough to eliminate the necessity of actual foam flood tests in porous media for surfactant selection. In a study basic to gas storage in aquifers, Bennett4 described the displacement of brine by foam in consolidated porous media. Among other things, he stated that the ability of a surfactant solution to foam is more important than the stability of its foam. The presence of a foam bank between the displacing air and the displaced brine improved both breakthrough and ultimate recovery. In a continuation of this work Kolb5 attributed the great reduction in surfactant solution production rate as displacement by air progressed to a decrease in relative permeability to gas. These several effects reported by both Bennett and Kolb can all be attributed to the high apparent viscosity of foam which was obviously flowing in the porous media. Bernard and Holm6 observed that gas permeability in the presence of foam was much less than in the absence of foam when both were measured at the same gas saturations. This reduction in permeability was proportionately greater for more permeable sands and sandstones than for the less permeable. Viscosities of the surfactant solution and air were used for their calculations rather than apparent foam viscosities. The foam stability increased with decreasing permeability, which was probably due to the natural regenerative properties of porous media, and the permeability reduction increased

Jan 1, 1967

By Hillary W. St. Clair

The reduction zone of the iron blast furnace is represented by a mathematical model of the chemical reactions and heat transfer that occurs between gas and solids during the deoxidation of iron oxide. The model consists of a set of equations and an algorithm whereby the equations may be solved to give the temperature and composition of gas and solids at any position in the reaction zone and at any time after a specified initial state. The model is applied to the special case in which ferric oxide is reduced by graphitic carbon and carbon monoxide produced by burning carbon in dry air. The rate of reduction, carbon consumption and maximum temperature are shown as functions of the temperature and rate of flow of the incoming reducing gas and external heat loss. The model of the reduction zone is the essential part of a general mathematical model for simulation of the iron blast furnace. The simulation model will serve as a research tool to be used in conjunction with an experimental or operating furnace. After the simulation model has been correlated with the real furnace, it is proposed that further experimentation be done mostly with the model. The real furnace will then be operated primarily to test and confirm the model.

Jan 1, 1967

By R. E. Reed-Hill

A simple accurate graphical method for orienting fcc crystals using (111) slip traces on a single surface is described. Solutions placing the pole of the surface in a unit stereographic triangle are obtained using a Wulffnet, a (111) standard projection showing the four (111) planes, and a (111) standard projection ruled into unit stereogmphic triangles. The multiplicity of solutions is described in relation to this method. AN accurate, rapid single-surface technique for orienting fcc crystals, using (111) slip or twin traces, has been a matter of continuing interest, as evidenced by the periodic appearance of papers on this subject.'-4 This note presents a new method possessing some advantages over those previously reported. It is an analog to the technique for hcp metals5 where the solution is based upon a stereographic rotation of the specimen surface on a (0002) standard projection that contains the planes of the possible features that might account for the observed traces. In the hexagonal solution, the axis of rotation is the basal-plane trace in the surface. In the fcc case, the axis of rotation is one of the observed ( 111) slip or twin traces. It has been observed that the solution is greatly facilitated if the indicated movements of the (111) traces during the rotation of the surface are plotted directly on a paper copy of a Wulff net as shown schematically in Fig. 1. The trace selected to represent the axis of rotation is assumed to fall at the north-south poles of the Wulff net. The directions of the other traces are then plotted as points at the proper angles around one-half of the basic circle of the net. The loci of points corresponding to the movements of these traces (directions) during a 90-deg rotation of the surface, about the polar axis of the net, are then easily and accurately drawn by following the appropriate small circles on the Wulff net. The solutions to the problem are obtained with the aid of a (111) standard projection of the (111) planes, see Fig. 2. This is normally a Xerox copy of a carefully drawn master made on high-quality tracing paper. The (111) standard projection is superimposed over the Wulff net and rotated about its center until the points of intersection of the loci of surface traces, drawn on the Wulff net, and the great circles representing the (111) traces, all lie along a common meridian of the Wulff net as demonstrated in Fig. 3. This latter great circle represents a possible position of the surface. The pole of this plane is then plotted on the (111) standard projection. Its location in a unit stereographic triangle may be readily obtained by superimposing (over the standard projection) another tracing paper (111) standard projection subdivided into unit stereographic triangles. The result of this last operation is shown in Fig. 4. MULTIPLICITY OF THE SOLUTIONS The maximum possible number of (111) traces on a single grain surface is four. Any one may be selected as the axis about which the surface is rotated. Corresponding to each such choice are three possible surface-pole orientations, related to each other by a simple 120-deg rotation about the pole of the (111) basic circle. This is a direct result of the threefold symmetry of the (111) standard projection. Since each of the four rotations will normally give a different set of three-pole positions, there are, accordingly, twelve possible solutions. Each of these twelve solutions places the surface pole in the same relative position in a stereographic triangle so that all are crystallo-graphically equivalent. Accordingly, only a single solution is required to obtain a basic orientation of the crystal. It should be noted, however, that the orientations obtained by reflecting* any of these twelve orien- *The reflected orientations may be obtained by a 90-deg rotation of the opposite sense to that shown in Fig. 1. This rotation places the correspond-ing trace loci in the lower hemisphere of the Wulff net rather than in the upper hemisphere. tations through the surface are also possible orientations that could account for the surface traces. Thus, a given set of four traces always corresponds to a pair of basic orientations related by reflection through the specimen surface. This ambiguity can only be re-

Jan 1, 1967

By J. W. Town

Studies were made by the Bureau of Mines to determine the influence of textural features on the beneficiation of phosphate minerals (pellets) from selected bed and composite samples representing different rock types of the Western Phosphoria Formation. The particle size of the samples was reduced by attrition grinding to minus 20-, 28-, or 48-mesh depending on ore grade and gangue matrix. Sizing of the ground material showed that the phosphate pellets would concentrate in the plus 200-, 270-, or 325-mesh size fractions sufficiently so that the phosphate content was above the 31.5 :cent P2O5 required for acidulation. The phosphate content of essentially pure phosphate pellets was shown to range from 33 to 39 percent P2O5. Microscopic identification of the particles in each size fraction showed that the phosphate was either in the pellet form and readily liberated or so intimately associated with the gangue matrix that size reduction necessary Co obtain liberation was impractical.

Jan 1, 1967

By P. C. Tully

The vapor pressure-temperature relationships for saturated pure liquid nitrogen are calculated by the Strobridge equation using a digital computer. This information is presented in two tables: first) in pressure increments of 0.1 psi from 1.8 to 492.9 psia) and second) in temperature increments of 0.1° from 63.15° to 126.26° K. These tables should facilitate the calibration of temperature-measuring devices over this temperature range.

Jan 1, 1967

By J. E. Flinn, E. R. Gilbert

Recently, Green reported some high-temperature, 0.60 to 0.89 T3, creep results on unalloyed tantalum. From his study he determined an activation energy of 114 kcal per mole for steady-state creep using the T, differential-temperature method25 for testing. He accounted for the difference between this value and 110 kcal per mole for self-diffusion by the temperature dependence of the elastic modulus, 4 kcal per mole. This reported activation energy is in apparent disagreement with that which can be determined from Green's isothermal data, which we have plotted as log creep rate vs 1/T in Fig. 15. From this figure, it appears that there are two activation energies of -185 kcal per mole at the higher temperatures and -75 kcal per mole at the lower temperatures. It is not obvious that the data can be fitted to a straight line corresponding to an activation energy of 114 kcal per mole. One is led to two possible conclusions regarding Green's study: there are two discrete processes controlling the creep rate from 0.60 to 0.89 Tm or the apparent activation energy is not discrete but continuously increases with increasing temperature. The former speculation would be in closer agreement with the high-temperature creep behavior of tungsten.28 The apparent disagreement between the activation energies determined by the AT and isothermal methods certainly suggests that further study on the high-temperature creep of tantalum is needed.

Jan 1, 1967

By C. J. McHargue, J. C. Ogle

Lightly deformed columbiun single crystals which contained only parallel hoins or purullel and intersecting trains were annealed at 1000' and 1600"C. No re-crystallizntion occurred in specimens hawing only parallel twins. Only noncoherent twin boundaries nzipated at 1000°C but both coherent and noncoherent ones moved al 1600°C. Recrystallization occurred within a few minutes at twin intersections at 1000°C. The orientation 01 the recrystallized grains differed front that of both the matrix and deformation twins, but could he derired by (110) and/or(112) rotations. ALTHOUGH twinning in metals has been extensively studied, there have been no definitive studies of the annealing behavior of crystals containing deformation twins. Some effects observed after annealing deformation twins have been summarized by Cahn1 and Hall2. Any or all of these phenomena are observed: 1) The twins may contract so that the sharp edges of the lens become blunted, and eventually the twin may disappear entirely. 2) The twins may balloon out at an edge, giving rise to a large grain having the same orientation as the twin. 3) The specimen may recrystallize; i.e., new grains are nucleated and grow at the expense of the twins and the crystal immediately adjoining the twin. Such grains have orientations which are not present before. Contraction has been observed in iron,3 titanium,3, 4 beryllium,5 zinc,8, 7 Fe-A1 alloy,' and uranium.9 Long anneals at high temperatures are required to have any appreciable effect in these metals and only thin twins are absorbed. Lens-shaped twins are absorbed from the edges: the thin, almost parallel-sided twins are usually punctured in several places and each piece contracts independently. Absorption is very gradual and no sudden cooperative jumps have been observed. The expansion of a twin into a larger grain of identical orientation is unusual, but such growth has been observed in iron,"'" zinc,6 and uranium." Crystals which have been deformed simultaneously by slip and twinning recrystallize first in the area adjacent to the twin. New grains appear faster where the twins intersect: but isolated twins, especially if thick, can also give rise to new grains. This type of recrystallization occurs in zinc.6, 7, 12, 13 and beryllium.14 Reed-Hill noted, in a single crystal of magnesium, the nucleation of a recrystallized grain at a twin intersection which had the same orientation as the second-order twin and which grew into the highly strained matrix.15 Short-time annealing has been reported to cause no change in the deformation twins in vanadium,16 columbium, 17, 18 tantalum,19 tungsten,'' and zinc.7 The purpose of this investigation was to note the effects of annealing on the coherent and noncoherent boundaries of deformation twins in columbium and to locate the nucleating sites for recrystallization. The orientation relationships, which the new recrystallized grains have with the parent crystal and the deformation twins, were also determined. EXPERIMENTAL PROCEDURE Single crystals of columbium were obtained by cutting large grains from electron-beam-melted buttons which contained 10 to 50 ppm C, 10 to 100 ppm O,, 1 to 10 ppm H2, and 10 to 15 ppm N2. The crystals were hand-ground and chemically polished until all grain boundaries were removed. The specimens were mounted in an epoxy resin and a face of each crystal was mechanically polished on a Syntron polisher using Linde A and then Linde B polishing compounds. After all faces were mechanically polished, the crystal was electrolytically polished to remove all distortion due to cutting and grinding. Laue photographs were taken of all faces of the crystals to determine the quality and orientation of each crystal. The crystals were compressed about 10 pct at -196 C in a specially constructed compression cage with an Instron tensile machine. Each crystal was separated from the top and bottom anvils by teflon films which acted as a lubricant. With the specimen crystal in position, the entire cage was cooled to -196°C by being submerged in a Dewar containing liquid nitrogen. The crystals were compressed at a rate of 0.02 in. per min and the load was recorded on a strip-chart recorder. After deformation the crystals were mechanically polished on 600-grit paper and Pellon cloth with Linde A and Linde B polishing compounds. The crystal faces were chemically polished and then etched. The twin planes were identified metallographically from an analysis of the twin traces on two surfaces. Annealing was carried out by placing each crystal in a columbium bucket made from the same electron-beam-melted material as the crystal itself and suspending the bucket by a tantalum wire in a quartz tube. After a vacuum of 10-7 Torr was attained, a furnace at 1000" or 1600 C was raised into position and the crystals held for various lengths of time. The crystals were repolished and etched after annealing to remove any surface contamination. Approximately 0.010 in. was removed during this process. The resulting surface was examined metallographically for microstructural changes due to annealing. A microbeam Laue camera mounted on a Hilger Micro-focus X-ray unit was used to determine the Orientstions of the recrystallized grains. This X-ray micro-beam camera had a 0.002-in.-diam collimator and incorporated the ideas of both and and chisWik21 and Cahn.22

Jan 1, 1967

By T. F. Archbold, P. G. McCormick

Silica fiber 11arkevs and hardness irzdentatiozs have been used to study the thermal diffusion of racancies in zinc placed in temperature gradients of 460o and 706oK per Cm All markers mored toward the higher temperatures, and the data show that the heat of trarlsport Q is greater than the eizthalpy of z,acancj3 forrjalion E by an amount equal to 3.5 kcal per mole. These results ore not in agreement with those obtained in either of the two previous studies with zinc. The problem is discussed in terms of experimental differences and racancy source and sink efficiencies. THE general interest in thermal-diffusion phenomena over the past several years has prompted a number of marker movement studies using pure metals. In order to understand better the relationships between thermal and mass flow, a general goal of the experiments has been to obtain values for the net enthalpies carried by the diffusing atoms. For self-diffusion by means of the vacancy mechanism, the determination of relative marker positions before and after an anneal in a temperature gradient permits a calculation of a value for (Q - Ef). Q is the transferred enthalpy, and Ef is the enthalpy of vacancy formation in the metal being investigated. The initial experimental study of thermal diffusion in pure metals was accomplished by Shewmon who found essentially no movement of surface-hardness indentation markers in single and bicrystals of zinc held for 20 days in a temperature gradient of 310°C per

Jan 1, 1967

By Warren E. Morrison

The continuing high-level performance of the domestic mineral and mineral fuels industries during 1966 was sustained by the longest business upturn in the Nation's history. Spurred by consumer demand at home and the defense production requirements of the Viet-Nam war, the rising trend of economic activity during the year was reflected in the upward movements of the major economic indicators. At yearend the gross national product (GNP), representing the value of all goods and services produced, stood at $740 billion, $58 billion greater than in 1965. Corrected for price changes, the real value of GNP in terms of 1958 dollars was $648 billion and represented an annual increase in economic activity of 5.4 percent. Some 74 million persons were employed during the year out of a total population of 196.8 million, while unemployment fell below 4 percent. The Federal Reserve Index of Industrial Production averaged 156 for 1966, up 13 points from the previous year. However a jarring note in the 1966 expansion, and one which affected the mineral industries in particular, was the increasing pressure on prices and the threat of inflation. From 1961-65 economic growth was facilitated by relatively stable wages and prices and only mild inflation. During the period average wholesale prices hardly moved while average consumer prices rose only about I percent per year. But this long run of relative price stability ended during 1966 when consumer prices rose 2.9 percent and wholesale prices were up 3.2 percent from the previous year.

Jan 1, 1967

By V. B. Kurfman

The temperature, strain rate, and orientation deDendence of defbrnzation of single-crystal MgAg has been examined. The crystals exhibit a tendency to single glide and little or no hardening at 25°C for many orientations. A much higher hardening rate is observed when multiple glide occurs, such as can be initiated by surface defects. The tendency for easy glide becomes less dependent on surface preparation and orientation as T — 100°C and bars so tested often fail after one-dimensional necking-. At T > 200°C (transition temperature for single-crystal notch sensitivity and poly crystalline ductility) single glide diminishes and two-dirnensionul necking begins. The crystals do not strictly obey a critical resolved shear stress law, but show the influence of {loo) cracks in determining the slip mode. The results are correlated with the difficulty of sciperdzslocation intersection and semibrittle behavior of this compound in single-crystal and poly crystalline form. Comparisons are made with the slip selection mode observed in tungsten, with the reported observations of easy glide in bee metals. and with the mechanical behavior of poly crystalline MgAg. PREVIOUS work on tensile deformation of polycrys-talline MgAgl and bending deformation of single-crystal MgAg2 has shown that the compound is semi-brittle (i.e., notch and grain boundary brittle). If this semibrittleness is supposed to result from the difficulty of multiple glide (associated with the problems of superdislocation intersection) one might expect single crystals deformed in tension to show pronounced single glide and strong orientation dependence of hardening rate. These experiments were done to examine this supposition and to study the tensile deformation of a highly ordered system which may be considered bcc if the difference between the two kinds of atoms is ignored (actual structure: CsC1). EXPERIMENTAL Single-crystal ingots were grown by directional freezing as previously described.' These ingots were sliced into a by a by 2 in, rectangular bars by electric discharge machining, then round tensile bars were conventionally machined to 1/8-in.-diam by 1-in.-long reduced section. The bars were typically tested without an anneal because of the problem of magnesium vapor loss and they were typically tested as mechanically polished. The analyses are within the same limits as those reported earlier; i.e., the average composition for each specimen is within 0.5 at. pct of stoichiometry, while the total range from end to end in a given specimen varies from 0.7 to 1.4 at, pct. There has been no indication in the results of any variation in slip or fracture mode attributable to the composition fluctuations. The slip systems were determined by two-surface analysis of the bars after testing to failure at room temperature. Single glide was so dominant that there was little difficulty in identification of the dominant slip system even though the tensile elongation to failure often approached 7 to 8 pct in room-tempera- ture tests. Elevated-temperature testing was done in a silicone oil bath and low-temperature testing was done in liquid Np or a dry-ice bath. All stress measurements are reported as engineering stress unless otherwise specified, and crosshead travel is used as the strain measurement. RESULTS The tendency toward single glide is best seen in the pictures, Figs. 1, 2, and 3, which depict deformation at fracture as a function of test temperature. While it is possible to find regions of secondary slip by careful microscopy, such regions are very small. The development of a ribbon-shaped configuration from an initially round section bar pulled at 100°C is typical, occurred by single glide, and illustrates the degree to which such glide continues. At temperatures =100°C the bars typically show elongation of 20 to 50 pct by predominently single glide. Despite the large elongation, fracture even at 150°C occurs in a brittle mode, Fig. 2, in the sense that it is an abrupt failure which shows no discernible necking in the second dimension of the bar's cross section (i.e., there is no appreciable action of any slip modes which would decrease the broad dimension of the cross section). Near 200°C the fracture mode changes slightly. Although most of the sample extension is by single glide, after the bar develops the characteristic ribbon shape it begins to neck in the second (i.e., broad) cross-sectional dimension. The bar becomes very thin in the "necked down" region, Fig. 3, and the reduction in area approaches 100 pct. Often there oc-

Jan 1, 1967