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By J. C. Shyne, T. D. Gulden

The steady-state creep behavior, in compression, of indium containing a dispersion of atomized glass particles was studzed over a range of temperature, stress, and composition. The observed behavior was not consistent with a simple model of dislocation climb over dispersed particles. From room temperature to about 100°C the temperature dependence could be described by an activation energy about one and a half times that of self-dijfusion in indium while at higher temperatures a much higher ternperature dependence was observed. THE value of dispersion-hardened and precipitation-hardened alloys has long been recognized. The mechanism of hardening, however, is not completely understood, especially at elevated temperatures where dispersed particles increase creep resistance. Following the suggestion of Schoeck1 that the rate of creep in dispersion-hardened materials is controlled by dislocation climb over second-phase particles, Ansel and weertman2 derived steady-state creep equations for dispersion-hardened materials. Their derivation was based on dislocation climb over non-deformable spherical particles in a metallic matrix. For low stresses they predicted a linear relation between applied stress and steady-state creep rate. For stresses large enough to cause dislocations to pinch off around the precipitate particles, the theoretical creep rate was shown to be proportional to the fourth power of stress. For very high stresses an exponential stress dependence was predicted. In all cases the theoretical creep rate is linearly proportional to the diffusion coefficient. This provided the primary temperature-dependent factor. Subsequently, Ansel and Lenel3 reported some experimental data on SAP, a composite of aluminum and aluminum oxide, that was in good qualitative agreement with the above theories. Their experimental creep rates, however, were four orders of magnitude less than the theory predicts. This was attributed to a low density of active dislocation sources in the material; somehow the dispersed particles inactivated the dislocation sources instead of merely interferring with dislocation motion. Meyers and sherby4 have recently reported on the creep behavior of SAP. Their results were inconsistent with a simple dispersion-strengthening model and led them to conclude that a continuous network of oxide controls the high-temperature mechanical characteristics of SAP. Because of the rather complex mechanical behavior of SAP and the lack of agreement about the morphology of its oxide phase, it appeared desirable to study the creep of a dispersion-strengthened material of controlled morphology. For the present work a dispersion of spherical glass particles imbedded in a matrix of indium was chosen. The microstructure of this material was similar to the idealized uniform dispersion of hard spheres in a deforming matrix assumed by Ansel and Weertman in their theoretical treatment. SPECIMEN PREPARATION For experimental convenience, it was decided to use a low melting-point metal in this investigation. It was necessary that the metal not be oxidized readily up to its melting temperature and that it wet the second-phase particles. It was desired that the material chosen for the dispersed phase be available as a fine powder with closely controlled size and shape. The material chosen to satisfy these requirements consisted of a matrix of indium metal containing a dispersion of atomized particles of a soft soda-lime-silica glass ranging from 5 to 30 µ in diam. The glass particles had a highly regular spherical shape. The composite was made by stirring the glass powder into liquid indium maintained at a temperature just above the melting point of indium, 156°C. The creep specimens were prepared by a hot pressing operation. Five to ten g of the mixture were placed in a steel die and pressed at 125°C for 5 min under a pressure of 30,000 psi. The resulting specimens were cylinders about 3/8 in. in diam and ranged from 0.4 to 0.7 in. high. By following this procedure a uniform dispersion was obtained in the creep specimens. Typical microstructures of specimens containing twenty and forty volume percent glass powder are shown in Figs. 1 and 2. Unfortunately, grain size could not be determined by the metallo-graphic techniques used. CREEP TESTING PROCEDURE Creep tests were performed in compression under constant stress. The specimens were placed in

Jan 1, 1963

By John E. Hockett

The need for basic information about the relationship between resistance to dejormatim (flow stress), temperature, strain, and strain rate, for the solution of metal-fovming problems, is pointed out. Some early attempts to satisfy the need are mentioned. A brief description of a machine called a Cam Plastome-ter is given, including the processing of results of testing in the machine. Next, a program of testing aluminum in compression over a wide range of constant true-strain rates (0.1 to > 200 sec-1) and a modevately broad range of temperatures (223° to 673°K) is described. The results of this program are presented in the form of true-stress us true-strain cuvves. The data in these curves are presented in the form of relationships between true stress and true-strain rate in sermilogarithmic and log-log form, as functions of temperatures—for several true strains. Finally, true stress, for a given true strain, is displayed as a function of log true-strain rate and absolute temperature, i.e., a surface. SINCE the publication of Hill's book1 on plasticity theory, increasingly rapid advances have been made in analytical solutions to forming problems. Methods in common use are the slab method, the uniform deformation energy method, the limit analysis method, the slipline field method, and the semiexperimental method called "visioplasticity". These approaches, and examples of their use, are covered in detail by Johnson and Melloor2 and by Thornsen, Yang, and Kobayashi.3 unfortunately, practically all of the above work has had to rely upon a number of basic assumptions, e.g., homogeneous deformation and Coulomb (sliding) friction; and virtually no dependence of the mechanical behavior of the deforming metal, upon temperature, strain, and strain rate, has been included. It is with this dependency that this paper is concerned. Loizou and sims4 looked at the above relationship for lead using both a constant compression-speed Cam Plastometer and a constant true-strain-rate Cam Plastometer designed by Orowan.5 Alder and Phillips8 investigated the relationships for aluminum, copper, and steel in the same constant true-strain-rate Plastometer. cook7 tested twelve steels at temperatures ranging from 1170° to 1473°K in the same Plastometer over a range of true-strain rates of 1.5 to 100 sec-'. The writer tested commercially pure aluminum at room temperature and depleted uranium at temperatures from 573" to 873°K at strain rates from 10-3 to 1.0 sec-1 in a Cam Plastometer designed and built at Los Alamos Scientific Laboratory.8 During the past few years the Cam Plastometer at Los Alamos has been used for a number of relatively minor experiments on brass, mild steel, duralumin, Armco iron, and depleted uranium. In this time the machine has been continually modified and improved. It was decided to utilize fully the wide range of strain rates now available with the machine by testing a material about which some information was already in the literature. Prior work on commercially pure aluminum6 appeared to deserve confirmation and expansion. So it was decided to explore the resistance to compression of this material over the currently available range of constant true-strain rates and a convenient range of temperatures. This paper is a report of that exploration. I) EQUIPMENT AND PROCEDURE The principal item of equipment is, of course, the Cam Plastometer, the working part of which is shown in Fig. 1. In this figure, an aluminum specimen may be seen between two tungsten carbide platens, in position for a room-temperature test. Above the upper carbide platen is a load cell. Output from the load cell is amplified and applied to a galvanometer in a recording oscillograph. Auxiliary equipment includes the oscillograph, the control console, a counter, and a time-mark generator. The counter is first used in adjusting the time base. Then it registers the count, of sixty pips per revolution generated by the rotating cam, in each second. These pips and the time base are also applied to galvanometers in the oscillograph. Thus, load, time, and cam position are recorded simultaneously. Heating of a specimen prior to compression is done

Jan 1, 1968

By J. C. Yannopoulos, N. J. Themelis

Ah electronic thermogravirnetric balance was used to measure the veductioiz rule o single cirpric oxide particles suspended in a stream of hydrogen. Very jzne thermocouples embedded in lie center and at the surface of the sphere recorded the variation of terw perature during reduction. In contrast to iron oxide reduction, where in most instances the rate of interface reactiokl is controlling, the heat- and mass-transfer phenotnena play a predolrinant role in the reduction of cupric oxide. The correlation of experitnental data or tnass lransfev lhrough the boundary layer at Reynolds nunlber 0-4 50 was as jollocs: ThE reduction of cupric oxide by hydrogen is represented by the equation: It is a highly exothermic reaction and the amount of heat released varies only slightly with temperature (-21,430 cal per g-mole at 400°C). Most of the published studies on this system have been conducted at temperatures in the range of 34 to 280c.l-&apos; The concensus of opinion has been that at temperatures below 200°C the reaction is preceded by an induction period during which there is very little or no reduction. The length of this period diminishes as the temperature of the reaction is increased1l5 and aseawa found that at 280°C reduction starts practically immediately when the oxide is exposed to hydrogen gas. The existence of an induction, or incubation, period has led experimenters to believe that the reduction of CuO by hydrogen is catalyzed by metallic copper.&apos; Boldurev and rmolaev found that mechanical additions of powdered copper to oxide did not affect its reduction, although metallic copper produced during the reduction seemed to have a catalytic effect. At least three other authors2&apos;5&apos;7 have reported that addition of copper had no effect on the rate of reduction. Pease and alor&apos; observed that water vapor had a strong inhibiting effect on the reduction at 1503C, but its effect was greatly diminished at 200 C. Pavlychenko and Rubinchik5 studied this reaction at 159 to 235 C and found that, once the reaction had been initiated, there was no inhibiting effect due to the introduction of water in the hydrogen stream; at temperatures above 183°C there was no inhibiting effect due to water vapor, either before or during reaction. The same authors noted that the rate of reduction was independent of pressure in the range of 200 to 700 mm Hg. aseawa investigated the kinetics of the CuO-Hz system at 160 to 280°C and estimated the apparent activation energy at 14,000 cal per g-mole. A similar value (13,500 1200 cal per g-mole) was reported by ond&apos; in the temperature range 148 to 216°C. Bond also reported that there was no incubation period and that water vapor had no inhibiting effect on reduction at temperatures above 190 C. The above studies have been conducted at temperatures below 280°C and the physical configuration of the system under investigation has not been defined adequately. However, it is well-known that the mechanism of gas-solid reactions depends on a number of in series physical and chemical rate prcesses.&apos;&apos; It is, therefore, essential to include among the experimental factors the geometry of the solid system and the mass-transport characteristics of the reducing gas. Scott studied the reduction of packed beds of cupric oxide cylinders by Hz-He streams of very low hydrogen concentrations at temperatures 400 to 600 C, pressure of 10 to 30 atm, and gas velocity from 0.18 to 5.8 ft per sec (3 < Rep < 30). The reduction rate was found to be mainly controlled by diffusion through the boundary layer and through the pores of the reduced copper phase. The following correlation was proposed: Scott in an earlier work studied the reduction of fixed beds of cupric oxide wire and found that the rate of flow of the gas stream through the bed had a controlling effect on the rate of reduction. The same mass-transfer phenomenon was observed by Bond and clark13 on a similar reduction system. The analogy between mass and heat transfer through the boundary layer which exists between a solid surface and the bulk stream stems from the similarity of the differential equations representing these phenomena

Jan 1, 1967

By H. E. Swanson

A description of the field apparatus has been published by D. G. Brubaker. Data from laboratory model studies of the in-line and broadside methods of operation are detailed. The conductor models include a single sheet conductor at several strike and dip angles and a schistose-type conductor. In addition, data on the effects of the strike length and of the depth of the conductor are presented for the broadside method of operation. All of the data show that the inclintion reverses direction over the top edge of dipping single sheet conductors. Differences between anomalies over conductors dipping between 90" and 30" are subtle,but flat-lying sheets can be readily distinguished from steeply dipping sheets. Schistose conductors are easily distinguished from single sheet conductors, and a procedure is given for determing the direction of schistosity. The depth of penetration under ideal conditions is 0.7 of the coil separation. In 1950, The New Jersey Zinc Co. (of Pa.) developed a lightweight apparatus for electromagnetic prospecting. A description of this apparatus has been published by D. G. Brubaker.1 It consists of a small, battery-powered vertical source coil and a direction-finding receiving coil. Source and receiver are kept a fixed distance apart and move as a unit along the survey lines. At each receiver station the inclination of the magnetic field created by the source is measured. Two methods of operation are used, in each of which measurements are taken with a constant source-to-receiver distance and with the plane of the source oriented to pass through the receiver station. In one procedure, called the in-line method, source and receiver travel in tandem along the same line. In the other procedure, called the broadside method, source and receiver move along adjacent lines, with the source-to-receiver direction oriented parallel to the assumed strike direction. The data recorded in either case are the inclinations, measured in degrees from the horizontal, of the magnetic field created by the source. These data are plotted at the receiver stations on a map. Scale-model studies of both methods of operation have been conducted in the laboratory and are reported in this paper. APPARATUS Small source and receiving coils wound with many turns of fine copper wire were used to produce and measure an alternating magnetic field in the same manner as the field apparatus. The model source coil was mounted in a vertical position and oriented so that the receiving coil was in the plane of the source. The receiving coil was mounted in a frame so it could be rotated to obtain the inclination measurements. The source coil was excited by a 100-kc signal generator. A tuned amplifier and a voltmeter were used to detect the null position of the receiving coil. The coils used in the field apparatus are usually spaced about 400 ft. The coils used in the model work were spaced from 4 in. to 4 ft apart. Thus the scale of the model work ranges between 1/1200 to 1/100 natural size. The model conductors were aluminum-coated building paper supported on wooden frames. The conductivity-thickness product was measured using a four-electrode system and was found to be about 300 ohms-&apos;. CONDUCTIVITY CONSIDERATIONS The electromagnetic response from a thin sheet conductor is a function of the product of the conductivity of the sheet times the thickness of the sheet times the frequency of the alternating electromagnetic field times some linear dimension of the system such as the coil separation which indicates scale. The secondary electromagnetic field produced by the conductor increases in amplitude from zero at zero conductivity to a maximum value for infinite conductivity, while the phase of the secondary field with respect to the primary field shifts from 90" at zero conductivity to 0" at infinite conductivity. Several authors2-&apos; have shown that most of both the increase in amplitude and the change in phase of the secondary field takes place over a three-decade range of the conductivity-thickness-frequency product. Only small changes in the amplitude and

Jan 1, 1961

By L. D. Lash, J. R. Ross

Discovery of scandium in the Vitro solvent extraction plant for uranium led to commercial recovery of the byproduct. Micro amounts of scandium were extracted with uranium by dodecyl phosphoric acid, but failed to follow ura-niuminto the hydrochloric acid strip solution and were eventually concentrated in the organic extractant. A fluoride strip system was developed to recover scandium from the solvent in concentrated form. High purity scandium oxide was then prepared in multi-pound lots by chemical separation techniques. The plant recovery operation, final product purification, and analytical procedures are described. Scandium is a pseudo-rare earth which is truly rare and expensive. It has special properties which may make it desirable even at the present price of $2750 per lb. Recently the price was lowered from $5000 per Ib which had prevailed since 1952, and it is anticipated that usage will be stimulated because of the lowered price. This metallic element is distributed widely in trace amounts in the rocks of the earth&apos;s crust. In addition to micro-amounts found in most uranium ores, concentrations of 50 to 100 ppm have been found in Colorado ferberite ore, lateritic nickel ore, heavy sandstone from Utah, Wyoming, and New Mexico, and various zircon sands and monazites from the western part of the U. S. Scandium has been found as an essential constituent of very few minerals, the most important being thortveitite, a scandium silicate. At the present time, this mineral commands a price more than twice that of gold. Chemically, scandium is in group 3A of the periodic table. It is closely associated with yttrium and the rare earths which it strongly resembles in its reactions. It has a valence of three and will form an insoluble hydroxide, fluoride, or oxalate under proper conditions, similar to the rare earths. Eight years before its discovery, scandium was predicted by Mendeleef who ascribed his eka-boron with properties nearly identical to the actual properties of scandium. Its position as the element with Atomic No. 21 and Atomic Weight 44.96 places it between calcium and titanium in Period 4 of the chart. The successful commercial application of scandium must depend on unique properties to justify use of this high cost substance. Greater consumption would allow additional price reductions, but scan- dium will remain a relatively high-priced commodity because of its inherent scarcity. Research reportedly has been oriented toward use of scandium as an agent to achieve high-temperature, low-density alloys with magnesium and tantalum.&apos; Also, the U.S. Air Force sponsored a project for production of research amounts of pure scandium metal.&apos; The oxide has been used experimentally in electronics, ceramics, and metallurgy. The various aspects of scandium are well covered in recent publications.s-5 CONCENTRATE RECOVERY Small amounts of scandium exist in uranium ores and are dissolved during an acid leach yielding up to 0.001 gpl Sc2O9. When Vitro converted their uranium plant from phosphate precipitation to solvent extraction: scandium was found to follow the uranium into the dodecyl phosphoric acid solvent (DDPA). However, scandium did not strip with uranium from the DDPA in hydrochloric acid, but remained in the solvent. Therefore, a concentration of scandium built up in the organic phase. Residues from the solvent were spectrographed by the U.S. Bureau of Mines and found to contain scandium. As a result of this discovery, provisions were made in the plant for recovery of scandium-bearing concentrates. Solvent extraction of uranium was added to a conventional acid leach process in a typical installation? The ore was crushed and ground, and then leached with dilute sulfuric acid. Addition of an oxidant such as sodium chlorate insured conversion of uranium minerals to a soluble form. At this point, the slurry was chemically reduced by a sulfide, such as sodium hydrosulfide, to remove substances such as ferric iron and molybdenum which were partially extracted by the solvent. The solids-liquid separation was accomplished by a four-stage counter cur rent decantation (CCD) thickener circuit. The uranium was extracted from pregnant liquor with 0.1M DDPA in kerosene and stripped with ION

Jan 1, 1961

By H. C. H. Darley

The influence of particle size and concentration on the development of chip hold-down pressure (CHDP) was studied in an apparatus designed to measure the change of filtration rate during the first second of the filtration process. CHDP is controlled by the "bridging" particles (i.e., particles in the 50 to 0.2 micron range), whereas filter loss is controlled by the colloid fraction. The results indicated that a fast drilling fluid with a low filter loss could be obtained if the concentration of bridging solids and the viscosity were kept very low. A novel group of drilling fluids, which we have named colloid emulsions, was developed to meet the above requirements. These colloid emulsions are made by dispersing art oleophilic colloid in oil and emulsifying about 5 per cent of this dispersion in water or a dense brine. Good results have been obtained in field trials with emulsions which use asphalt as the oleophilic colloid. INTRODUCTION In recent years it has been found that fast rates of penetration can be maintained in hard formations by using "clear" water as a drilling fluid. In some cases, however, water cannot be used because the very high down-hole filter loss creates various difficulties in drilling, in logging, or in producing the well. It then becomes necessary to "mud up", which results in a decrease in drilling rate. The reason that mud decreases drilling rates is a complex subject which has been well covered by such authors as Garnier and van Lingen, Cunningham and Eenink,&apos; and van Lingen.3 One of the principal factors involved is the tendency of the drilling fluid to develop a filter cake on the bottom of the hole. The pressure differential which develops across this filter cake opposes the action of the bit in dislodging chips from the rock. This pressure differential is referred to by Garnier and van Lingen&apos; as the chip hold-down pressure, which is denoted by the initials CHDP in this paper. The work described in this paper was undertaken to develop a drilling fluid which would minimize CHDP but which would still have a low filter loss—in other words, a fluid which would deposit a filter cake on the sides but would lay little or no filter cake on the bottom of the hole. EVALUATION OF CHDP EXPERIMENTAL Conditions governing the growth of filter cake on the sides of the hole are obviously different from those on the bottom of the hole. On the sides of the hole, cake will form continuously but at a decreasing rate, until eventually the rate of growth will equal the rate of cake erosion by the mud stream.&apos; On the bottom of the hole, each time a bit tooth dislodges a chip the cake is removed, a fresh rock surface is exposed, and the filtration process must start over again. Thus the CHDP is determined by the amount of cake which can form in the interval between successive tooth strikes at a particular spot, normally a fraction of a second. Our first step therefore was to study filtration rates over the first second or so of the filtration process. These tests were conducted in the simple type of dynamic filter cell shown in Figs. 1 and 2. In this cell the mud was filtered through a train of rock cores while rotating blades kept the mud flowing over the surface of the core. The procedure was to evacuate the cores to 0.05 mm of mercury, saturate with brine, and assemble in the holder under brine. The permeability of the core train was then determined. A plastic seal was placed on the face of the core train, and a rip cord was attached from the seal to one of the blades. At the start of the test, 500 psi was applied to the mud, and the meniscus in the capillary measuring tube was adjusted to zero. When the blades were started, t,he seal was ripped from the face of the core, and filtration began. The filtration rate was at first measured by photographing the advance of the meniscus in the capillary tube. Using

Jan 1, 1966

By M. E. Wadsworth, T. L. MacKay

Sintered UO, samples were leached in sulfuric acid solutions of various concentrations. A pressurized system was used so that it was possible to investigate the kinetics of the reaction to 270°C with oxygen overpressures as high as 900 psi. The rate was observed to be a function of the concentration of hydrogen ions and directly proportional to the partial pressure of oxygen. Evidences are presented which indicate that a UO2 surface site reacts with a molecule of water to form a hydroxyl complex which in turn can dissociate with the characteristics of a weak acid. A rate determining step has been proposed which involves the reaction between an oxygen molecule and the hydroxyl complex on the surface of UO,. ThE 2 principal methods for uranium dissolution are carbonate and acid leaching. The sulfuric acid leach is the more popular and is used for the treatment of the majority of the ores of Africa, Canada, and the United States. Low recoveries in basic leach circuits led investigators at the University of British columbia1 to study leaching of uranium ores in pressurized vessels. Early in the study of dissolution of uranium it was found that only uranium in the hexava-lent state could be leached in acid or basic circuits. Therefore, the use of oxygen over-pressure in an autoclave offered an interesting approach to solving the low recovery problems of carbonate leaching. UO, was used in this study because it could be obtained in high purity and also because it is representative of the most refractory of the primary uranium minerals. A pressurized system was used to provide a means whereby important temperature and pressure parameters could be varied for the evaluation of the kinetic processes. The mechanism for the dissolution of UO2 should be similar for any of the uraninite type minerals. At the present all of the kinetic studies that have been conducted have been in carbonate media. Peters and Halpern2 carried out a kinetic study of the leaching of pitchblende. Their specimens were pitchblende ores selected on the basis of high grade and homogeneity. Pearson and wadsworth3 conducted a kinetic study of the dissolution of UO2 in carbonate solutions with results very similar to those obtained by Peters and Halpern. EXPERIMENTAL The UO2 as received* was found by spectroscopic *Mallinckrodt reagent, supplied by the Atomic Energy Commission. analysis to have a purity of 99.94 pct 0.03. It was ground in a mechanical agate mortar and screened through a 400-mesh sieve. Thin flat disks of UO2 were prepared by pressing the sized powder in a specially constructed die at a total pressure of approximately 25 tons per sq in. The pressed disks were approximately 0.25 cm thick, 1.6 cm diam, and 3.5 g in weight. As pressed, the samples were approximately 65 pct of theoretical density. It was essential that a binder such as poly-vinyl alcohol be added before pressing to prevent formation of cracks when fired. It was found by trial and error that pressed disks sintered close to 1870°C in a hydrogen atmosphere, reach densities between 91 and 91.5 pct of the theoretical density. At this density the samples had no measurable porosity based upon a 2-hr emersion in boiling water. An X-ray examination of these sintered UO2 disks showed them to be identical with the original UO2 received. Reaction of UO2 with the alundum furnace core was prevented by placing molybdenum between the samples and the core according to the method of Corwin and Eyerly.4 Leaching studies were carried out in a specially designed autoclave, the details of which have been presented e1sewhere.6 The main features of the equipment as applied to a kinetic study are: 1) solution samples may be removed during the course of a single run; and 2) temperature and agitation are carefully controlled. Two-ml samples removed from the autoclave during the course of a run were analyzed for U3O8 content with a Beckman model DK-2 spectrophotometer by the method of

Jan 1, 1959

By C. S. Matthews, M. J. F. Rosenbaum

The purpose of thir work wax to lcarn it~lzut infori~lation could he obtained from various typs of pilot water floods and to attempt to find the optunum pilot patter11, for a revervoir which had previously been depleted by a solution gas drive. The study was made in the laboratory with mathemetical methods a dynamic analog and a potentiotnetric analog. Results werp tested against the field llistorics of a nrrnlber of pilot water floods. At a reasonable valrre of currzulative injection, the total production rate for the one-injector five-spot should reach about 6.5 per cent of injection rate, and for a four-injector five-spot, about 9 per cent. Accurate estimates of ultimate recovery cannot be made on the basis of such snzall prorluction rates. However, with a pilot composed of nine ir1jector.s and 16 producers the production rate is approximately 50 pcr cent of injection rate at a reasonable value of camulative injection. Sonle inforn~ation for extended performance predictions might he obtained from such a large pilot. These conclusions were drawn on the basis of results obtained for unit mobility ratio, and a sturly using tlre potentiometric analog was made of the effect of other mobility ratios to determine the range of applicability of these predictions. For the four-injector, five-spot pilot with the ratio of production to injection rate (before water breakthrough) is about twice that for with it is about two-thirds; and with M0= 10, it is about one-third For high mobility ratios, it was found that the production rate increased considerably as water-cut increased. These result can be used to modify, qualitatively, the inter.pretntions based on curves for the unit rnobilit\. ratio CaSeS. It was found that the maximum ratio of production rate to injection rate obseriled in field pilot floods was of rhe scime order as that prerdicted by these methods. The time required to reach thisr maximum did not generally agree with the time predicted for a homogeti~orir reservoir. The differcrlce between predicted and observed time of response gives an indication of the permeability profile and of the condition of the producin,g wells. Pilot water floods of the pattern type are generally carried out in reservoirs which have been depleted by solution gas drive and are at low pressure. Under these conditions, oil and water can be considered incompressible. It is assumed that, as the water is injected, an oil bank forms ahead of it and that there is a distinct interface between the water zone (or bank) and the oil zone (or bank) and between the oil zone and the region ahead of the oil zone. It is further assumed that only gas is mobile in the unflooded (gas) region, only oil is mobile in the oil bank and only water is mobile in the water bank. The saturations and the mobilities associated with each zone are assumed uniform. We idealize our reservoir to be homogeneous, horizontal and of constant thickness. Effects of gravity within the producing layer are assumed negligible. If the actual time-dcpendent flow problem is approximated by a acries of steady-state problems. the potential and stream function in the oil bank and water hank satisfy Laplace&apos;s equation in two dimensions. We can therefore use a poteiitiometric analog of this system. Potentiometric models have yielded uscful results in this laboratory&apos; and clsewhere in the study of a variety of secondary recovery problems. For the case where M = I, we generally prefer to use theoretical mcthods as well as a simpler dynamic analog. Except where otherwise noted, the ratio, side of five-spot/wellbore radius. is taken to be 3,600. a figure which corrcsponds to a normal-size wellbore in a 10-acre well spacing. THEORETICAL EVALUATION OF VARIOUS PILOT PATTERNS, Mw0 = 1 <&apos;he theoretical models which we used to examine the performance of various pilots are shown in Fig. 1. Image theory was used to determine the ratio of production rate to injection rate as a function of the volumc of the flood. The ratio of production rate to injection rate was chosen because this is an easily measurable quantity which is characteristic of a pilot

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 C. Zener

HE present paper has its origin in an attempt A by the author, extending over the last several years, to understand the influence of the magnetic properties of the constituent atoms upon the various properties of metals and alloys. During this study the author has been impressed by the important role which magnetism plays in the many facets of metallurgy. In writing this paper he has attempted to convey to his colleagues some concept as to the role magnetism will play in the future development of metallurgy. In some of the subjects herein discussed, such as the influence of magnetism upon phase boundaries and upon mechanical properties, only general thermodynamical properties associated with ferromagnetism are introduced. For these subjects, it is not anticipated that any serious differences of opinion will be encountered. A discussion of the other subjects requires the adoption of a quite specific model of the magnetic structure of the metal. This model is discussed under "Magnetic Shells and Their Interactions." The simple model adopted in this paper has been criticized&apos; as being mathematically inconsistent. This criticism has been ably silenced by Dr. W. J. Carr&apos; of this laboratory. The simple model adopted in this paper has been criticized as being inconsistent with observations on magnetic structure using neutron diffraction. This apparent discrepancy has been resolved by Bader3 who has shown that the finite velocity of neutrons prevents neutron beams from detecting the anti-ferromagnetic structure of the type predicted by the simple model adopted in this paper. Magnetic Shells and Their Interactions An electronic shell of an atom is specified by two symbols.&apos; The first symbol is a number and denotes the total quantum number of the shell. The second symbol is a letter and denotes the orbital angular momentum of each electron within the shell. The letters s, p, d, f are used to denote an orbital angular momentum of 0, 1, 2, 3, respectively, in units of h/2a, where h is Planck&apos;s constant. As we pass from scandium to nickel in the first transition period, we eraduallv fill the 3d shell. This shell is responsible for ferromagnetism and hence may be called the magnetic shell. The component of the orbital angular momentum along some specified direction must be an integral multiple of h/2~. Thus, for a d electron this component can have any one of the values —2, —1, 0, 1, 2 times h/2a. In addition to its orbital angular momentum, each electron has an intrinsic angular momentum, hereafter called spin, due to a rotation about its own axis. This spin can have either of two components + Yz (h/2a) or — Yz (h/2~) along the specified direction. A fundamental principle of atomic structure, known as Pauli&apos;s exclusion principle, is that no two electrons in a given shell may have identical components of orbital angular momentum simultaneous with identical components of spin. The 3d shell thus may have at most ten electrons. Since an intrinsic angular momentum of a charged particle is necessarily associated with a magnetic moment, the spin of an electron may be thought of as referring to either this angular momentum or to the associated magnetic moment. The electron configuration of the ground state of the isolated atoms in the first transition row is reproduced in Table I. The superscript represents the number of electrons in each shell. For the purpose of this paper, the most important principle of atomic structure relates to the manner in which electrons are added to a shell as the atomic number is increased. This principle, commonly known as the principle of highest multiplicity or more simply as Hund&apos;s rule, states that within a given shell the maximum number of electrons have spins pointing in the same direction as is consistent with Pauli&apos;s exclusion principle. An application of this principle to the d shell is illustrated in Fig. 1, where the spin structure is given for shells containing from 1 to 10 electrons. The physical basis of Hund&apos;s rule is the exchange energy discussed first by Heisenberg in 1928. This is a coupling between electrons with parallel spins (spins pointing in the same direction), the coupling

Jan 1, 1956

By M. M. Mebta, G. W. Dean, W. H. Somerton

With the advent of underground heating operations, interest has developed in the alteration of rock properties by high-temperature treatment. In the present work a number of sandstones were heated to temperatures in the range of 400°C to 800°C under both atmospheric and simulated reservoir pressures. Pertneabilities increased by at least 50 per cent and sonic velocities and breaking strerlgths decreased by an equivalent amount. Differential thermal expansion and other reactions of constituent min-era1 grains are the causes of these alterations. INTRODUCTION In the underground combustion of petroleum reservoirs, temperatures of the order of 600C are reported to have been reached in the combustion zone.&apos; At this temperature rocks are subject to extensive thermal alteration. Temperatures of this magnitude and higher may also occur in subsurface formations when subjected to bottom-hole heating, thermal drilling operations, and underground nuclear explosions. Temperatures of this magnitude might also be generated by conventional rock drilling methods at points of bit-tooth contact. In earlier work, the permanent deformation of rocks resulting from heating was reported. Major structural damage of rocks occurs due to differential thermal expansion of mineral constituents. A number of mineral alterations including crystal inversions, loss of water of crystallization and dissociation, may also contribute to changes in physical structure and properties of rock. In the present work, samples of three typical sandstones were heated to several temperatures up to a maximum of 800C and then allowed to cool to room temperature. Heating was done under both atmospheric pressure and simulated reservoir pressure conditions. Physical properties of the samples were measured before and after heating and comparisons made. Measured properties included permeability, sonic velocity, breaking strength and fracture index. Changes in physical properties were compared to changes in mineralogical characteristics as determined by thin-section. X-ray diffraction and chemical tests. EQUIPMENT AND PROCEDURE Two outcrop sandstones (Bandera and Berea) and one sub-surface sandstone (St. Peter) were selected for the tests. These samples have a wide ranee in composition and physical properties as shown in Table 1. The first series of tests was made on 2-in. diameter by 5-in. long test specimens. Test specimens used in all later work were 3/4-in. diameter by 1 1/8-in. long, this being the specimen size required for heating at simulated reservoir pressures. After careful washing, the cores were oven dried at 100 ± 5C for a minimum of 24 hours before the tests were run. Test specimens were heated in an electric furnace at a constant rate of temperature increase of 3C per minute. When maximum temperature of the run was reached, the sample was allowed to soak for one hour. The furnace was then cooled to room temperature at the same rate of 3C per minute. The entire heating operation was designed for reproducibility without subjecting the test specimens to excessive thermal shock. For samples heated under simulated reservoir pressures, a pressure cell designed by Dean was used (Fig. 1).3 The core sample was inserted into a thin-walled (0.006 to 0.01-in.) copper cup which was then mounted in a high-pressure cell. Provisions were made for the application of internal pore pressure as well as confining pressure. Tests showed that the thin-walled copper cup closed tightly around the core and satisfactorily transmitted confining pressure to the core. The core was heated by placing the entire cell into the electric furnace. The heating program was the same as that used in the atmospheric pressure runs: tempera-ture rise of 3C per minute to maximum temperature of the test, soaking at maximum temperature for one hour, and cooling at a rate of approximately 3C per minute. The cell was designed to withstand 5,000 psi at 1,000C. However, since it was considered likely that repeated heating and cooling would in time weaken the steel, 2,000 psi at 850C was set as a working limit. In the present series of tests, the pore pressure was held constant at 750 psi and the confining pressure at 1.500 psi. The pressure source was a high-pressure nitrogen tank. The two pressures were controlled manually but are accurate well within ± 50 psi.

Jan 1, 1966

By R. H. Edsal, G. Horvay

The transient one-dimensional heat-conduction equation is solved for two semi-infinite media, at different initial temperatures, brought into (poor) thermal contact. It is shown that the two interface temperatures gradually approach the well-known, instantaneously assumed, common interface temperature of the case of zero contact resistance. The present analysis, with slight modifications, may be used in fair approximation also for the class of problems involving a change of phase. One particular application of the boundary value problem solved in this paper concerns the determination of the temerature distribution in metal castings and molds.P This problem has been treated extensively by analytical methods (see e.g., the literature listed in Refs. 1 to 4) by electrical analogs (see e.g., Refs. 11 to 14) and also by experimental methods (see the literature listed in Refs. 4, 5), but prior to the work of Pellini and Ruddle the experimental results were rather unreliable. Immediate motivation for the work described in this paper was to better understand the results of Pellini,&apos; which are typified by the curves of Fig. 1. Pellini cast 20-in. high, 7-in. sq steel ingots into cast-iron molds of various thicknesses. He measured the temperatures at mid-height, at a number of stations in the casting and the mold, and obtained the cooling curves shown in Fig. 1. The most conspicuous thing about Fig. 1 is the large temperature discontinuity at the interface between casting and mold, due presumably to the shrinking away of the casting from the wall and the attendant creation of an airgap, as the casting cools. Such a contact resistance slows down the anticipated freezing rate; an analytical prediction of this is of much interest in foundry practice. The determination of the effect of contact resistance in the presence of a change of phase will be dealt with, by an approximate method, in a separate paper.&apos; In the present paper the much simpler problem is considered in which there is contact resistance but no change of phase. This problem frequently arises in the analysis of aircraft structures.+ It can initial temperature, and may be regarded as semi-infinite. We suppose the thermal properties in the two media to be time, temperature, and space independent; there are no sources or sinks within the media. In Fig. 2(a) we illustrate, schematically, the case of no contact resistance. The semi-infinite media "0" and "2:&apos; initially at temperatures 8 (- m) and 8(+ -), respectively, are brought into contact at time t =0. A common interface temperature 8,i = is instantaneously established, and thereafter remains constant. Temperature curves are drawn for three instants of time. When there is contact resistance between the two media, the temperature equalization occurs as sketched in Fig. 2(b). Fig. 2(c) illustrates a temperature curve, using the dimension-less notation Barber-Weiner-Boley6 have stated the equations [23a, b] given below, which govern the heat transfer in the two media, and solved them for a rather complicated special case. In their example both media "O" and "2" are finite, are insulated at their far ends, and there is steady heat input into medium 2. In Eq. [27] we give the general solution of the most important special case, where the two media are semi-infinite and there are no sources or sinks. In this case the results may be stated in simple closed form. In Fig. 3, to be discussed in the next section, we illustrate the variation of the interface temperature when steel at 2760" is brought into contact with iron at 100". This example, if we disregard the effect of the heat of fusion, is comparable to Pellini&apos;s experimental results, Fig. 1. (Unfortunately, however, experimental determination of the interface temperatures was difficult to carry out, and hence Fig. 1 is not very accurate near the interface.) In Figs. 4 and 5 of the following section, we similarly compare Pellini&apos;s sandcasting tests with analytical results for the case where steel at 2760" is brought into contact with sand at 100". It will be pointed out that, insofar as the interface temperatures are concerned, heat of fusion has a minor effect, and so the present approximation, with small modifications, may be

Jan 1, 1961

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

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

Jan 1, 1968

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman&apos; developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,&apos; and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,&apos; as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman&apos;s work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962

By J. J. Gilman, T. A. Read

S URFACE effects in the cleavage of brittle crystals have been known for some oftime,1, 2 but our knowledge of surface effects in the plastic deformation of crystals is of relatively recent origin. In 1936, Roscoe9 eported his observations comparing oxidized and clean cadmium crystals. He found that cadmium crystals 1/2 mm in diam when covered by an oxide film less than 1200 atoms thick had critical shear stresses about twice those for clean crystals. This effect is anomalous in that it cannot be caused by the inherent shear strength of a normal oxide film. Either an interaction between the film and the crystal causes the large increase in strength, or the oxide film has an abnormal mechanical strength. Several authors since Roscoe have studied surface effects in crystal plasticity. A complete review of the literature will not be presented, but most of the results may be summarized as follows: 1—The critical shear stress for slip is increased markedly by very thin oxide films on zinc4 and cadmium crystals;" &apos; also, the entire stress-strain curve is raised by an oxide coating;3,4 both effects increase with decreasing specimen radius. 2—Surface active substances such as oleic acid destroy the hardening effect of oxide films.4, 6-8 The time required for the reduction of the hardening effect to begin increases with the viscosity of the solvent4~ 3—There has been dispute in recent years about the effects of surface active substances themselves on plastic deformation. Rehbinder, Lichtmann, and Maslenikov9 state that surface active substances reduce the strength of metal monocrystals markedly and increase the number of slip lines per unit length at a given strain. The effect varies with orientation for tin crystals being smallest for x, = 0, largest for x, = 45", and intermediate as x, + 90°.10 Several workers claim to have disproved the results of Rehbinder&apos;)"." but Rehbinder and Lichtmann9 have defended themselves and Masing with his collaborators" has confirmed some of Rehbinder&apos;s results. 4—Immersion of metal specimens in electrolytes such as sodium chloride reduces their strength12,13&apos; and subsequent cathodic polarization increases the strength reduction. For noble metals, the strength reduction occurs for both anodic and cathodic polarization," increasing with increasing polarizing voltage. 5—Electroplated copper coatings effect the creep rates of zinc monocrystals. Poly crystals are not affected." 6—Immersion in dilute acid destroys the hardening effect of an hydroxide film. When an acid solution is applied to a steadily creeping crystal, the creep rate jumps to a very high value and then drops gradually to a steady value which is higher than the initial steady rate.*&apos; " If the hydroxide film to be removed is very thin (about 100A thick), the creep rate does not change measurably, but a small rapid strain-increment is observed when dilute acid is applied." 7—Crystal plasticity depends on specimen dimensions. This was observed by Lichtmann and Ven-stroml" for monocrystalline tin and by Andrade and Kennedy" for polycrystalline lead. 8—Immerson of copper crystals in mercury has no effect on their stress-strain curves.&apos;" 9—Bombardment of creeping cadmium crystals with a particles which penetrate the surface to only 0.005 mm may increase their creep rates as much as five times.&apos;&apos;&apos; The experiments which will be described in this paper pertain to: (a) the effect of a crystal&apos;s shape on its plastic deformation, and (b) the effect of metallic surface films on plastic deformation. For the work pertaining to (a), crystals of zinc, tin, and lead were grown which had various shapes. These were tested in simple tension. Macroscopic rotations about the tension axis which are unpredicted by the classical theory of slip were observed, and serrated edges were observed in tin crystals. For the work pertaining to (b), the effects of evaporated and electrodeposited films of copper, nickel, gold, and zinc on the mechanical properties of zinc, tin, and lead crystals were determined. The films influenced both slip and twinning of the crystals in creep and tensile tests. Experimental Details Chemically pure zinc, tin, and lead were used in this investigation. The zinc was 99.999t pct pure;

Jan 1, 1953

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

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

Jan 1, 1965

By Horace Pops

Martensitic transformation has been studied during cooling and heating in ß-phase Cu-Zn alloys to which small additions have been made of Ni, Ag, Au, Cd, Ga, In, Si, Ge, Sn, and Sb. The start and finish of the martensitic reaction and the variation of transformation temperature with third-element content were determined by electrical-resistivity measurements from alloys which had either constant zinc contents or constant values of electron concentration. All of the third elements, except nickel, lowered the transformation temperature if the results were plotted along the lines of constant zinc contents in each ternary system. A significant difference in the rate of lowering of the transformation temperature per atomic percent of the third element was observed for elements which had the same nominal valence. No systematic variation of transformation temperature with the valence of the third element was observed. It is suggested that the observed increase in transformation temperature for nickel-bearing alloys is due to the transfer of electrons from the conduction band of the alloy to virtual bound states. However, electron concentration is not the most important factor controlling the instability of the 0 phase. The transformation temperatures of the ternary alloys can be predicted from the following approxilnate expression: Ms (°K) = +3280 - 80 Zn + 8 Ni - 30 Ag - 12 Au - 140 Cd -90 Ga- 145 In - 80 Ge -175 Sn - 120 Si - 150 Sb MOST binary ß -phase alloys based upon the noble metals copper, silver, and gold are unstable at low temperatures and transform spontaneously by a martensitic reaction. This transformation has been studied recently in the ordered bcc ß&apos;-phase Cu-Zn binary al1oys1,2 where the transformation temperature is below the room temperature and decreases with an increase in zinc content. It has been reported that the transformation temperatures can be raised above room temperature by small additions of a third element such as silicon3,5 or gallium,4,5 but no quantitative study has been made. The transformation temperature of different binary alloys can be altered by third-element additions. For example, it was shown that nickel and copper may have a large effect on the Ms temperature of CU-Al6 and Au-cd7 alloys. The present investigation was made to determine systematically the influence of various third elements on the martensite-transformation temperature of Cu-Zn ß-phase alloys. Since these alloys have an electronic origin,&apos; alloy compositions were chosen so that the transformation temperatures could be determined at constant zinc contents or at constant values of electron concentration. I) EXPERIMENTAL PROCEDURE Ten ternary alloy systems were obtained by adding nickel, the noble metals silver and gold, and some B-subgroup elements to a Cu-Zn matrix. These are arranged according to their rows and columns in the Period Table as follows: Each ternary alloy was prepared by melting and casting weighed quantities of high-purity metals (99.99+ pct) in sealed quartz tubes under a partial pressure of helium to make a 4-g ingot. The molten alloys were shaken vigorously and then quenched in water. Since the weight loss was negligible, the compositions of the ingots after casting and annealing were assumed to be the same as the nominal compositions. The ingots were homogenized after casting in helium-filled Vycor tubes for 24 hr at temperatures between 750" and 810 C and quenched into brine. Metallographic examination revealed that all alloys were homogeneous, poly crystalline ß-phase alloys, and that the grain size was in the range 1 to 5 mm. Electrical-resistivity measurements were made to determine transformation temperatures of the ternary alloys during continuous cooling or heating. Transformation temperatures of the ternary alloys can be determined by electrical-resistivity measurements since the resistance of the martensitic phase is much higher than that of the 0&apos; phase. The technique has been described previously in connection with a study of Au-Zn alloys.9 The reproducibility of transformation temperature was approximately ±6°C. II)RESULTS A hysteresis was always observed in electrical-resistivity curves and was usually less than about 12°C.

Jan 1, 1967

By H. A. Hoffman

Competition from an all-flotation plant, with demonstrated economies and efficiencies, plus a change in smelting contract and introduction of improved cyclones lead to conversion from gravity-flotation. Detailed descriptions are given of equipment installed and procedures used at St. Joseph Lead&apos;s Federal mill. Future plans include further quality control by instrumentation in all aspects of the mill operation. Also planned are improvements in materials handling systems. Competitive conditions will continue to dictate improvements and changes in the mill flowsheet. The advent of all-flotation mills in the Lead Belt was introduced by the Indian Creek mill in late 1953. This modern and efficient plant then became a pattern for the other mills in this area to re-evaluate their circuits in an effort to develop flowsheets that would improve operating conditions and metallurgy. The Indian Creek mill demonstrated that all-flotation would require considerably less operating and maintenance labor than the combination of tabling and flotation that was common in the Lead Belt at that time. Two significant changes occurred in recent years to allow all-flotation to be seriously considered in other Lead Belt mills. One was a change in the smelting contract which did not require gravity concentrate. Another was the development of cyclones which provided classification of the flotation feed in a very small space. Since the Federal mill was the largest concentrating plant in the Lead Belt it was felt that the greatest savings could be made by investigating the all-flotation possibilities at this mill. Interest was stimulated by the milling and ore dressing Depts. to determine if this mill would be converted without undue cost, provided the metallurgy could be improved. Accordingly, laboratory tests were initiated to learn what metallurgical benefit could be derived. Numerous tests were run which indicated that grinding to all-flotation would improve the tailing by as much as 0.02 pct Pb. This was quite significant when multiplied by the tonnage of ore treated. Projecting the added cost of power for extra grinding and flotation, and the additional flotation reagents required, plus additional new equipment that would have to be purchased, it would still add up to a considerable saving. The all-flotation mill would reduce man power by some 30 pct, and make a metallurgical improvement. Operating costs could be reduced bv 2$ per ton. The metallurgical improvement would amount to 4$ per ton, for a total of 6$ per ton of ore milled. An estimate of the cost of the conversion was set at $250,000. With the savings as estimated this could be paid off in about two years. On paper it therefore seemed attractive enough to justify a mill test. MILL TESTING One section of the Federal mill was made available for use as a separate test circuit. Cyclones and density controllers were borrowed from the Viburnum and Indian Creek mills. Denver flotation cells were obtained from the Desloge mill that was then shut down. Two 10-cell groups of Fagergren flotation machines, consisting of eight roughers and two cleaners in each bank, were segregated from the remainder of the plant. The 9x12-ft rod mill was continued as a primary grinding mill. The two 6%x12-ft mills on this section were converted from rods to balls, and the speed increased to 22.0 rpm. Cyclones were installed to close the circuit of these ball mills. The ground pulp from each of the ball mills was fed separately to its own bank of flotation cells so that two completely separated test circuits could be run in parallel. This test circuit operated on a three-shift basis from Dec. 22, 1959 to Mar. 21, 1960. The first few weeks were occupied in developing conditions for proper metallurgy and trouble-free operations. Results were rather erratic but as the ore dressing laboratory and the mill operators became more familiar with conditions they were able to obtain expected results, which could be duplicated day after day. The last five weeks of testing indicated the best results and are tabulated in Table I. During the first two weeks a Denver unit cell was used on No. 1 flotation circuit. Even though it recovered almost one half of

Jan 1, 1962

By H. C. Chang, N. J. Grant, A. R. Chaudhuri

During the creep of coarse-grained polycrystalline magnesium at elevated temperatures, a nonbasal type of slip was found to play an important role in the deformation processes. The nonbasal slip traces were examined metallographically in eight specimens (13 grains) and the observed glide plane located stereographically for each grain. The tests were run at 500&apos; and 700°F at stresses of 148 to 786 psi. Based on these measurements and theoretical calculations, the crystallographic elements for nonbasal slip were determined. WHEN a metal deforms by slip, the conventional appearance of the slip bands on the surface of a specimen is that of straight lines. Such is the behavior of the face-centered-cubic metals, as for example, aluminum. The particular slip system on which slip occurs in these metals is governed by the criterion of resolved shear stress. Work on the body-centered-cubic metals a-iron,&apos;. &apos; molybdenum, and columbium4 has shown that the process of slip is somewhat more complicated than the simple gliding of one close-packed plane of atoms over another in a close-packed direction and that it results in the formation of wavy and irregular slip traces on the surface. The recent reviews and experiments of Vogel and Brick and Chen and Mad-din3 show that, for the body-centered-cubic metals, the resolved shear stresses along the planes and the degree of close-packing do not necessarily determine the slip system. Theirs and other investigations indicate that a complete understanding of the slip process in the body-centered-cubic metals is not yet possible. However, one behavior displayed by all these metals is that the slip direction is invariably one of the close-packed directions <11l>. The wavy nature of the slip-band traces has been explained on the basis of cooperative slip by planes sharing this same slip direction.1&apos;3l&apos; It is generally acknowledged that, when the hexagonal-close-packed metal magnesium (axial ratio c/a = 1.624) deforms by slip at room temperature, it does so by basal slip in the close-packed direction <1I%>. This type of slip has the conventional appearance of straight lines and is governed by the critical shear-stress law. Schmid and coworkers" showed that basal slip was operative in the temperature range of —185" to 300°C (—300" to 572°F). Work by Servi, Norton, and Grant6 has shown that, during the creep of coarse-grained aluminum at high temperatures, new slip systems come into operation. The existence of a new high temperature slip system at temperatures greater than 225 °C (437°F) for magnesium was suggested also by Schmid. This was later indicated by Bakarian and Mathewson&apos; to be slip along the pyramidal planes (10i1) in the close-packed direction <11%>.* They * Mention will be made in the text of pyramidal planes and prismatic planes. The pyramidal planes referred to are the type I. order 1 of the form {10il); and the prismatic planes of the type 1 of the form (10i0). For the sake of brevity, they are termed in the teat as pyramidal (10il: and prismatic (10i0) planes, respectively. Where reference is made to the pyramidal plane type 1, order 2 of the form {10i2), they are referred to as the pyramidal planes of the type (10i2:. observed that this kind of slip resulted in irregular markings on the specimen surface. According to them, a possible cause for the appearance of the markings was due to "limited accessory slip on the pyramidal {10i2) planes." Burke and Hibbard," on deforming a single crystal of magnesium at room temperature, found evidence of slip on a pyramidal plane {1011). They explained it as being due to the effect of grip restraints. It is pertinent to note at this point that, although basal slip has received a fair amount of attention, only two specimens have been investigated, that of Bakarian and Mathewson and of Burke and Hibbard, to establish the elements of nonbasal slip in magnesium. During the study of the deformation mechanisms

Jan 1, 1956

By J. E. Burke, A. M. Turkalo

IN 1923 Desch¹ pointed out that the grains in a metal which is anisotropic with respect to its thermal coefficient of expansion would contract differently upon cooling, and that the stresses developed might approximate the plastic strength of the metal. More recently Boas and Honeycombe2-5 studied the behavior of several metals upon thermal cycling and observed that the stresses developed in arlisotropic metals are great enough to produce slip lines in individual grains and a roughening of the specimen surface. This phenomenon they have named "thermal fatigue." The mechanism they propose involves essentially a kneading of the grains, the deformation being alternately in compression and tension in a given grain as the temperature is changed in one direction and then the other. The present work was undertaken to investigate the possibility that an additional mechanism might operate to produce plastic deformation during thermal cycling—a "thermal ratchet" that depends upon a combination of grain boundary flow to relax the stress that develops between differently oriented grains upon raising the temperature and transcrys-talline slip to relax the oppositely directed stress which develops on lowering the temperature. Thus, thermal cycling should produce a nonreversible distortion such that certain grains will change shape differently from their neighbors with a simultaneous displacement being produced at the grain boundary. Temperature Dependence of Grain Boundary and Grain Strength The critical resolved stress for the initiation of slip in metal grains is only mildly affected by temperature." For example, in cadmium it decreases from 0.15 to about 0.05 kg per sq mm when the temperature is increased from 20° to 458°K and further temperature increase causes little further decrease. On the other hand, the work of KG1 indicates that the grain boundaries behave in a viscous fashion that can be described8 by the expression: t = BVexp(Q/RT) [1] t is the shearing stress on the boundary; B, a constant; V, the flow rate at the boundary; Q, the activation energy for grain boundary flow; R, the gas law&apos;s constant; and T, the absolute temperature. Eq 1 indicates that the stress necessary to cause a given grain boundary flow rate, V, decreases rapidly with increasing temperature. The value of the constant B is such that at sufficiently low temperature and ordinary strain rates deformation will occur preferentially by slip rather than by grain boundary flow. There is considerable evidence to indicate Consider the bicrystal shown in Fig. 1. In grain 1 the slip plane lies 45 " to the boundary while in grain 2 the slip plane is 90" to the boundary. The coefficients of expansion of the grains in a direction parallel to the length of the crystal are a1 and a, with a, > a2 for the orientations shown. The sequence of events that can occur upon heating and cooling this specimen is illustrated schematically in Fig. 2. Initially there is assumed to be no stress in the specimen (A). Upon heating, grain 1 attempts to become longer than grain 2, but is constrained by grain 2. Thus grain 1 is loaded in compression and grain 2 is loaded in tension, and a shearing stress is present across the boundary (B). As the temperature is increased, the stress will build up, and finally grain 1 will be plastically deformed by slip, since the greater stress is resolved on its slip planes. Any further heating will result in more slip and the stress will remain constant until some temperature T* is reached where the stress can be relaxed by grain boundary flow.† At this relaxation temperature (C) a step will appear between grain 1 and grain 2. Further heating above T* will cause grain 1 to become relatively longer, but no stress will appear because the grain boundary is too weak to support the stress (D). Upon cooling again, at T* (E), the grain boundary will again be able to support a shearing stress, and upon cooling further, grain 1 will be loaded in tension and grain 2 in compression (F). When the decrease in temperature below T* is sufficient to impose the critical shear stress upon the slip plane of grain 1, it will be stretched by slip.

Jan 1, 1953