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By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman's arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman's paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman's work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"'. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963

By R. L. Slobod, B. H. Caudle

In the past, the main emphasis in attacking the problem of the recovery of oil has been on the determination of fluid flow characteristics and residual oil saturation in the part of the reservoir which is contacted by a displacing phase. It is recognized that the determination of the fraction of the reservoir contacted in secondary recovery operations is also of great importance in predicting the ultimate recovery to be expected. A method is described in which radiographic techniques are used to determine these areal sweepout factors for any type of well spacing. Data showing the relationship of viscosity ratio and relative permeability to areal sweepout efficiency are presented for the five spot and the direct line drive well spacing patterns. Further applications of the method to studies of the displacement efficiency in the area contacted are mentioned. INTRODUCTION The problem of increasing oil recovery from typical reservoirs is generally attacked by trying to devise some means for reducing the residual oil in that part of the reservoir which is contacted. The fraction of the reservoir contacted in the displacement process. however, is also of major importance but has been given less consideration in the past. one reason for this neglect is the meager information available on the portion of the reservoir contacted and the magnitude of changes in this factor as operating conditions are varied. Until recently, the only means available for determining this quantity has involved the use of the electrolytic or poten-tiometric modelsl in which one is limited to working with a mobility ratio of unity. while means for calculating the volume of a reservoir contacted do exist. the calculations are very tedious for systems with mobility ratio different from unity. Recently several such determinations have been reported,213 and an experimental method involving a step-wise use of potentiometric models has been described.' A new method which has been developed for studying the areal distribution of phases in a porous medium is discussed below. This tool can be' used to determine the effect of operating variables such as viscosity, relative permeability, presence of gas, mobility ratio, rate and stratification on the fraction of the reservoir contacted by the displacing medium. This development based on the use of X-rays gives a pictorial representation of the location of the phases. Further, the amount of each phase at each point of interest can be determined quantitatively. X-RAY METHOD FOR AREAL STUDIES In this method the location of various phases distributed Over a test area are observed simultaneously by obtaining a photographic record of the transmission of X-rays through the test plate. This procedure is an adaptation of the radiographic techniques which have 10% been used in the medical and industrial fields. Just as the medical profession uses a chest plate to show spatial interrelationships, the location of an X-ray absorbing fluid and a nonabsorbing fluid in a porous medium can be determined by obtaining a photographic record of transmitted X-rays. Moreover, as changes occur in such a System, these changes can be observed by taking successive photographs. Previously, X-ray methods have been used in fluid flow studies to determine quantitatively the saturation at a given point in the system. The intensity of the transmitted X-rays was measured by an ionization chamber, so that a point by point survey of saturation could be made. In comparison with this earlier quantitative procedure, the photographic procedure which simultaneously observes the saturation at many

Jan 1, 1952

By D. J. DeLazaro, W. Rostoker, R. E. Riley, M. Hansen

KNOWLEDGE of the isothermal transformation behavior and the TTT chart method of graphically summarizing such information has been of invaluable aid to the ferrous metallurgist in understanding and developing heat treatments intended to provide specific mechanical properties. It is to be expected that similar lines of study directed to titanium-base alloys will be as profitable. This paper summarizes, on conventional TTT charts, the isothermal transformation products and pertinent reaction rate data for binary alloys of titanium containing 1, 3, 5, 7, 9, and 11 pct Mo, respectively. The results so presented were derived from metal-lographic examination. Some X-ray diffraction work was done to clarify certain points of question. Ti-Mo System To the authors' k.nowledge, TTT charts have only been used to describe the reaction rates of eutectoidal decompositions. It would seem that the kinetics of decomposition of any unstable solid solution might be conveniently described in this manner. The equilibrium diagram of the Ti-Mo system' is shown in Fig. 1. The similarity with the Fe-Ni system will be recognized. Additions of molybdenum serve to stabilize the /3 phase to increasingly lower temperatures. The solubility of molybdenum in the a phase is restricted to less than 1 pct at 600°C. Under normal conditions. a homogeneous ,8 structure quenched to a, temperature in the a f & field will reject a of invariant composition. The rate at which this occurs depends on the degree of undercooling and the degree of supersaturation of /3. The structural character of the rejected phase may also be expected to be related to the undercooling. Materials and Experimental Methods A sponge titanium was used which has a nominal impurity content as reported in Table I. The nominal composition of the molybdenum used is also included. The alloys were prepared in 150 g melts by arc melting in an evacuated water-cooled copper crucible of the type reported in an earlier paper.' The pancake-type ingots were forged to 1/4x1/4 in. bars and homogenized for 24 hr at 1000°C in evacuated Vycor bulbs. Specimens Vi in. thick were cut from these bars for heat treatment. The heat treatment cycles followed an invariant procedure. The specimens were soaked at 1000°C for 20 min under a helium protective atmosphere prior to quenching into a lead bath held at a temperature corresponding to a chosen degree of undercooling. After a prescribed period of time at this temperature, the specimen was removed and water quenched. A series of specimens so treated for progressively longer periods served to establish the times for initiation and completion of the decomposition of the /3 phase at a particular temperature. Although heat treatment of unprotected specimens in a lead bath does permit surface contamination by lead diffusion, this method is necessary to insure sufficiently rapid quenching rates. As long as the bath treatments were of less than 1 hr duration. the contaminated surface was not unduly deep and could be removed without excessive grinding. Metal-lographically, the contaminated zone could be readily distinguished from the pure binary alloy. Transformation Characteristics of Ti-Mo Alloys Metallographic examination showed that a supersaturated p phase may decompose by one of two processes. Alloys containing 1 to 9 pct Mo, when quenched in water from the homogeneous /3 field,

Jan 1, 1953

By J. F. Evers, S. Sadiq, F. W. Preston, G. W. Swift

Proper scaling of unsteady-state flow in laboratory gas reservoir models can be achieved if the permeability/fractional porosity ratio is less than 0.5 md. Porous media meeting this specification can be obtained from mixtures of sand and Portland cement provided (1) the water/cement ratio is in the range of 0.35 to 0.40, (2) the sand/cement ratio is in the range of 1/1 to 2/1, (3) the sand grain size is in the range of 48-100 to 18-28 mesh, (4) the mortar curing time is 7 days or more and (5) the cured mortar is dried under vacuum to reduce the temperature level employed during the drying process. The areal homogeneity of the mortars tested is reasonably good, although significant trends in vertical permeability were noted. The Klinkenberg and non-Darcy coefficients of mortar are such that proper scaling of these effects in the laboratory model could be expected. INTRODUCTION A long term deliverability prediction for a gas well is generally based on data determined from flow tests that are of short duration relative to the producing life of the well. These data, together with an estimate of gas reserves in place, form the basis for establishing the parameters of the mathematical model used to predict performance at future times. Results obtained from a mathematical model represent only an interpretation of the physical process being modeled. Experimental verification of the production process from discovery to abandonment is needed where production occurs under carefully controlled conditions. Ideally, one might consider such an experiment to be conducted in the field. Even if the cost of such an experiment could be justified, the time required would make it impractical to consider. However, if the time scaling problem could be handled properly, an experimental model of the gas reservoir production process could provide the necessary data to study the mechanisms of the production process in a reasonable time period. An experimental model has been designed and constructed using the data of this study as a basis. The model reservoir system consists of one producing well located at the center of a right-circular cylinder of porous material. Ten to 15 observation wells are located at strategic offset positions from the producing well. These wells, and the producing well, are fitted with pressure transducers so that the pressure-time history can be recorded at various radial and azimuthal positions in the drainage area during the entire production life of the system. Time is scaled in the model so that the time required to produce gas from discovery pressure to abandonment pressure is about 2 hours. This compares with a 20-year producing life in the model's field counterpart and gives a time scale factor of approximately 1:100,000. DESIGN CRITERIA To establish design criteria for the experimental model, the reservoir is considered to be a finite right-circular cylinder of radius rr, and height h with a producing well of radius rw located at the center and completed through the producing formation. This reservoir consists of a porous medium which has a uniform permeability k and gas porosity and the gas contained in the reservoir has density p, viscosity µ and molecular weight M. Initially, the pressure at all points within the reservoir is uniform at po. and the reservoir temperature is T. Since the reservoir production process has been demonstrated to occur in two distinct transient modes for either Darcy or non-Darcy flow,l it is

By Thomas W. Healy

Particles present in mineral processing systems that are termed ultrafine are those that are small enough to be unaffected by gravity or the flow conditions imposed on the pulp. As such, their interaction with one another and with other larger particles are controlled by specific attractive and repulsive colloidal or surface interactions. Electrostatic repulsion between ultrafines is dominated by surface potential, double layer thickness and specific adsorption potential effects - controlled by pH, salt and complexing ion concentrations. Attraction due to van der Waals interactions must be assessed in terms of bulk and surface coating effects and of particle size and shape. The net effect of attraction and repulsion must finally be related to the average kinetic energy of particles in the real system.

Jan 1, 1979

By Gopalan Ramadorai

Tailings water from primary flotation concentrators usually contains minor amounts of pollutants such as heavy metals, cyanide and solubilized molybdenum, which are solubilized in the flotation process. A review of various techniques to reduce pollutants to acceptable levels is presented. Generally, molybdenite ores are processed by conventional size-reduction techniques, followed by flotation to produce a metallurgical-grade concentrate of 88% to 92% MoS2. Reagents commonly used in the milling process include: vapor oil (collector); pine oil, MIBC (frother); Dowfroth 250 (water-soluble frother); lime (rougher pH control); and sodium cyanide (Fe and Cu depressor). For lead depression, Nokes reagent is stage-added to the regrind mills and cleaners. Flocculant is added to obtain clear overflows in the intermediate thickeners.

Jan 9, 1978

By R. B. Gordon, D. A. Koss

Ultrasonic-atlenuation changes due to the formation of free dislocations have been observed during tensile tests of magnesium and LiF single crystals and samples of polycrystalline Results on the LiF and samples are similar: A preyield attenzration increase is observed which, however, be-corlzes smaller as the magnitude of the drop in load al yielding increases. This indicates that the yield point observed in these materials is due to dislovation rather than dislocation unpinning and that the initial density ' free dislocations must be low if the yield point is to be sharp,. Tests on the magnesium ere conducted at both 27" and 200C. Magnesium has the unusual property that the yield drop is larger at the higher test temperature and is accomplished by a decrease in attenuation. The latter is due principally to the temprovary pinning of detained dislocations by highly solute atoms. After strain aging., a stress as low as 0.3 bur suffices to unpin dislocations; microstrain measuements of sufficient sensitivity should. reveal plastic flow at stress levels this low IN another paper,' we describe the technique of simultaneously observing ultrasonic-attenuation changes and plastic microstrain during deformation of spher-oidized carbon steels. Changes of ultrasonic attenuation indicate damping effects caused by the oscillation of long, freely moving dislocation segments. Simultaneous microstrain measurements are used to indicate total dislocation motion. The dislocation-damping observations are most useful in the study of the early stages of deformation where the dislocation density is low and the plastic strain is small and relatively difficult to measure. Particularly interesting results are found in materials which display sharp yield points. Observations of these phenomena are reported here for three materials: single-crystal LiF and magnesium, and poly crystalline molybdenum. EXPERIMENTS Dislocation-damping effects were observed by measuring changes in acoustic attenuation with the ultrasonic-pulse method. The end faces of each of the specimens were ground flat and parallel and a quartz 10 Mc per sec, x-cut transducer was attached to one face. The bonding agents used were: a) "Nonaq" stopcock grease with magnesium, b) beeswax with LiF, and c) salol with molybdenum. With the LiF, the best acoustic signals were obtained at 45 and 50 Mc per sec; all other measurements reported are at 10 MC per sec. The Sperry Ultrasonic Attenuation Comparator2 was used to measure attenuation changes. In the

Jan 1, 1967

By E. K. Landis

The question of magnetic concentration is assuming considerable importance, and the efficiency of the different concentrating-machines is widely discussed. As the amount of iron left in the tails must vary with commercial requirements, and with the nature of the minerals in the tails, the writer feels justified in calling attention to some points often overlooked. In almost every such commercial operation a point is reached beyond which it does not pay to go, the material saved by further operations being obtained at a cost too great. The amount of iron left in the tails from concentration must depend, therefore, upon the cost of crushing, the size to which the ore is crushed, the nature of the minerals in the gangue, and the nature of the ore itself. Some ores are so intimately mixed with their gangue that a large loss of iron in the tails is unavoidable. In many cases the gangue contains hornblende, pyroxene, serpentine, etc., which carry considerable iron as silicate, or otherwise combined, and this iron a magnetic machine cannot extract, since the minerals themselves are not magnetic. It is evidently unfair to charge the machine with this loss of iron; and hence a satisfactory test of any such apparatus would require that the iron present in the ore as magnetite should be determined, and the proportion in the tailings of such iron only should be the measure of the loss, as compared with theoretical efficiency.

Jan 1, 1892

By A. S. Callen

These iron mines of Spain are located on the mountain ridge forming the boundary between the Teruel and Guadalajara provinces, called Sierra Menera. They form a property of 25 mines extending over an area of 1,677 hectares (4,140 acres) situated at a height varying from 1,200 m. (3,940 ft.) to 1,500 m. (4,920 ft.) above sea level. The deposit follows the direction north to south; huge masses of ore are being found both on the slopes and at the summit of the Sierra. The ore occurs among quartzites and magnesite limestone, in some places overlaid by quartzite 15 m. (50 ft.) thick; in some others (and this is more general) the ore is overlaid by earth and boulders of quartzite origin; this layer is about 8 m. (26 ft.) thick. The ore beds occupy the geological horizon of the Superior Trias or Muschelkask, which are here in direct contact with the Silurian quartzites. The lime-stones have been more or less transformed. There is ample evidence to show that these mines were worked in very ancient times—objects and tools employed in mining by the ancient Romans and Arabs are to be found plentifully in old workinigs which extend down into the deposits. It has been estimated that more than 10,000,000 tons of ore were mined in the old days in this district and carried to the primitive forges in the vicinity where iron of much renown in Spain was extracted. Remains of more than 20 of these forges are found in the neighborhood of Sierra Menera and are usually situated near waterfalls and forests. Much investigation has been carried on for the purpose of determining the quantity of ore to be found in these mines, but no exact calculations can be made at present. When the investigation is completed it will surely be found that the deposit contains a much larger quantity than the 100,000,000 tons indicated by the present workings. The mines are now worked as open quarries and this method can and will be followed for a long time, probably until the deposit is worked out. Figs. 1 and 2 give some idea of the quarries in operation and the reserves, the iron-ore stocks, screening installation and general arrangement. From these quarries 1,000,000 tons can be mined annually (987,000

Jan 1, 1916

Discussion of the paper of W. H. Gunniss, presented at the Butte meeting, August, 1913, and printed in Bulletin No. 81, September, 1913, pp. 2309 to 2310. PROF. J. W. RICHARDS, South Bethlehem, Pa. :-In regard to the physical nature of quartz for making silica brick, is the coarse-grained preferable ? E. P. MATHEWSON, Anaconda, Mont. :-A dense quartz is preferable. The quartzite is the actual material used by the Anaconda Company. The sandstone referred to, the foreign quartz, was a very pure sandstone and bad hardly any impurities in it, and the brick made from that particular material, while apparently beautiful while coming out of the kiln, and true, immediately on heating in the furnace buffed up half an inch and were cracked open.

Jan 11, 1913

By F. D. Weeks

The Salida smelting plant, owned by the Ohio & Colorado Smelting & Refining Co., is situated at an altitude of 7,000 ft., about 2 miles west of Salida, Colo., and 215 miles southwest of Denver. Salida is a division point on the Denver & Rio Grande R. R. where the narrow-gage line serving the San Juan region joins the through standard gage. This narrow-gage road also serves the coal and coke companies at Crested Butte and the lime quarries and mines at Monarch and Garfield, which are only 20 miles distant. These facts, together with the possibility of an appropriate site, doubtless influenced the builders to locate at this point. The smelting plant and yard occupy 80 acres of land on the northeast side of the Arkansas River. The slope of the ground is such as to permit of the ore being delivered by cars at a point 25 ft. above the feed floor; and in front of the furnaces there is a fall of 50 ft. for the slag dump. A recent purchase of river bottom has provided slag room for 20 years. As originally constructed, the plant consisted of four blast furnaces, 40 by 144 in. at tuyéres, two copper-matting furnaces, dust chamber, stack, power plant, blowers, sampling works, and one railroad trestle about 16 ft. from bed floor to rails. Later 12 hand roasters of excellent design were added and the practice of smelting leady matte in a copper-matting furnace was abandoned. Since the plant passed under the present management the equipment has been increased so that the following is a brief description of the same at this date: Two lead blast furnaces, 48 by 180 in. at tuyéres, 17 ft. 6 in. tuyéres to feed floor; four lead blast furnaces, 40 by 144 in. at tuyéres, 17 ft. 6 in. tuyéree to feed floor; two copper-matting furnaces, not used; blast-furnace flue, 900 ft.; area 245 sq. ft.; blast-furnace stack, 150 ft.; above furnace floor, 190 ft. When smelting a 500-ton charge per day, the gases approximate 63,700 cu. ft. per minute and travel at a speed of 260 ft. per minute. The slag is hauled by a 10-ton electric locomotive; the slag shells and settler refuse are elevated to a bin on the feed floor by an electric hoist. The matte is tapped in 1,600-lb. cakes and loaded into cars

Jan 1, 1916

By J. R. Martson

The arrangement of the larger furnace at the United Verde smelter, together with the boiler layout and connecting flues, is shown in Fig. 1. The important dimensions are given in the figure, and cross-sectional areas of combustion space, flues, etc., are recorded. The location and extent of the baffling in the boilers also are shown because of their importance in the interpretation of the data. Two boilers serve each reverberatory furnace. They are of the class M-26 Stirling type (rated at 713 boiler hp. each). Steam is generated at 178-lb. gage pressure at a total temperature of 528" F., from feed water at a temperature of 113" F. The feed water is condensate from turbogenerators plus make-up softened by the lime-soda process. The make-up is rather large in amount as it must match the amount of steam consumed in reciprocating blowing engines and the like, which are not served by surface condensers. As a result the boiler feed water has a hardness of 1.5 to 3.0 grains per gallon, but this results in the formation, during six months to one year of boiler operation, of scale only of "eggshell " thickness or less. The boilers are set at the same elevation as the tapping floor of the furnace, which results in the introduction of the waste-heat gases at the top of the front bank of tubes and necessitates the inversion of the usual baffling arrangements. The boilers are equipped with valve-in-the-head soot blowers, which keep most of the dust blown off the surface of the tubes, but it is necessary to supplement the soot blowers by high-pressure air lances, inserted by an attendant through side doors in the boiler setting. Deposits of coal ash and of dust from the furnace charge accumulate in the flues between the reverberatory furnaces and the boilers and this necessitates cleaning of these connecting flues by hand during the greater part of one of the three 8-hr. shifts during each 24 hr. This cleaning operation requires the opening of clean-out doors, which, of course, has some effect on the yield of steam. Revebberatory Furnace Practice The United Verde furnaces are fired with pulverized coal of sub-bituminous type of which the screen and chemical analyses are given in Table 1.

Jan 1, 1934

By H. W. Highriter

THE method developed and used in this laboratory for the production of metallic uranium of such purity that it is ductile and can be cold-worked to fine wire or thin sheet by rolling has already been described1. It consists, briefly, in the electrolysis of potassium uranous fluoride (KUF5) in a molten bath composed of equal parts of sodium and calcium chlorides. The bath is contained in a graphite crucible, electrically heated to about 775° C., the crucible serving as the anode for electrolysis. The uranium deposits in finely divided form mixed with salts upon a molybdenum cathode suspended axially in the crucible. Upon com-pletion of the electrolysis the cathode is removed and cooled, the deposit broken and leached to remove salts. The metal powder is washed with water and dilute acetic acid and dried in vacuo to reduce oxidation. Suitable amounts are then pressed into pellets and heated in vacuo by high-frequency induction, using a thoria crucible. The uranium melts and flows away from the pellet, leaving a shell, which is largely oxide. In general, this method produced a satisfactory metal, although at times the uranium was not ductile. The investigations recorded here were made to find the cause of this embrittlement. It was known that the metal generally contained carbon, derived from disintegration of the graphite crucible in which electrolysis is conducted, in amounts dependent upon the thoroughness of washing the metal powder. Accordingly, analyses of several samples, both ductile and brittle, were made by combustion and absorption of C02 in Ascarite, using air instead of oxygen to reduce the temperature and rate of oxida-tion. Several of these metals were made with special precautions to reduce carbon content. The results show no relationship between ductility and carbon content in the range investigated (Table 1).

Jan 1, 1935

By Frederic H. Wright

The secondary metals industry might well be defined as the group of remelters, smelters, refiners, and manufacturers that convert scrap metals or residues to commercial forms. In this industry, scrap metals and residues are processed to pro- duce refined metals, ingot alloys, fabricated shapes, and chemical products. Secondary metal is defined as metal recovered from commercial scrap, that is, scrap that has entered the processor's plant in scrap form. Metal recovered by a manufacturer from "home scrap" generated in his own plant is not considered to be secondary, because it represents part of the original stock that simply requires additional treatment before emerging as a finished product. In any economic study, a basic point of measurement must be chosen, and in the case of secondary metals, the melting pot or its counterpart represents the stage in which metal is converted from scrap to some more usable form. Beyond this point there is often no means to distinguish between secondary metal recovered from scrap and virgin metal produced directly from ore. In the last fifteen or twenty years the secondary metals industry has grown to major importance. Some consumers distrust secondary metals, but frequently this distrust serves only to prove an inability to keep up with the times. A rapidly decreasing number of manufacturers like to boast that they use only virgin metals, but a little investigation would show them that more than one third of all

Jan 1, 1943

By Gareth Thomas

The analysis of Kikuchi pattersns of exct ovientalions from single cryslals and paired Kikuchi lines from single and overlapping crystals is shown to be useful and quanlitalve and is applied to Phase transfovnzcitions including ordering, spinodals, mavten-silic, and nuclealion and growth pyocesses. 112 pinciple, the analysis of exacl orientations enables the crystal system and the Bravais lattice of a crystal to he determined. The advantages of the davk-field imaging technigure for detecting vevy small precipitates are also described. ALTHOUGH Kikuchi electron-diffraction patterns were first observed nearly 40 years ago,' little systematic application seems to have been made of them, until fairly recently during electron microscopy, when their usefulness in contrast experimen and for determining exact orientations8'9 has been pointed out. With the availability of gonio-metric specimen tilting stages it has now become possible to make much wider use of diffraction patterns, particularly the Kikuchi pattern, which is the main subject of this paper. The treatment presented here is not exhaustive but it is hoped that it will stimulate more use of Kikuchi patterns during electron-microscopy investigations. The Kikuchi pattern is formed as a result of Bragg diffraction of the inelastically scattered electrons produced during the interaction of the beam and thick specimens, The important feature of these patterns is that they give an accurate representation of the symmetry of the crystal being investigated, so that it is possible to identify crystal systems and even the Bravais lattice. This means that new structures, e.g., formed in phase transformations, may be identified during normal electron microscopy, so that Kikuchi-pattern analyses considerably extend the uses of the electron microscope. Recent work has also shown that dark-field images are more informative than bright-field images, particularly, for observing small precipitates. The second part of this paper discusses some applications and advantages of dark-field imaging in studies of two-phase systems. 1) DIFFRACTION PATTERNS 1.1) Spot Patterns. Electron-diffraction spot patterns have their limitations because of the importance of the form factor on the intensities and shape of the reciprocal lattice points. Because of the extension of these points into relrods, reflections are possible over a large angular range (+5 deg) and the patterns from thin regions can be complicated because second-layer relrods intersect the reflecting sphere. Spot patterns can thus give only an approximate idea of the crystallography unless the foil is tilted into exact orientation. In this case the spot pattern is symmetrical, with equal numbers of spots on the positive and negative zone directions about the origin. Such cases are necessary for structural analyses and have been used recently to determine the crystal structure of the ordered Ta64C phase." Exact orientation means that the plane of the reciprocal lattice lies exactly normal to the incident beam as shown in Fig. 1(b). It should be noted that in exact orientations the angle of reflection is less than the exact Bragg angle 9 so that the reciprocal lattice points lie to the outside of the sphere, Fig. 1(b). This deviation is denoted by the parameter s and in the usual convention4 s is negative for exact orientations and, of course, zero at the exact reflecting position shown in Fig. l(a). In order to avoid secondary reflections from thickness relrods it is advantageous to work in thicker regions of foils. Diffraction from thick regions may also produce Kikuchi patterns and as dis-

Jan 1, 1965

By K. D. Hester, A. W. Fletcher

A nickel-copper sulphide concentrate was treated in a pilot plant at Warren Spring Laboratory during 1961, by a hydrometallurgical roast-leach-solvent extraction process devised to cleanly separate the metal values and produce acid sulphate liquors containing the metals. It is shown that 86 pct of the nickel and 95 pct of the copper could be leached from the calcine, after a sulphatizing roast on finely ground flotation concentrate. Iron was removed from the leach liquor by limestone neutralization with a small loss of values. Copper and nickel were separated by solvent extraction with naphthenic acid in kerosene after partial neutralization of the iron-free liquors with ammonium hydroxide. Hydrogen sulphide and chlorine were used to remove zinc (and residual copper) and cobalt impurities respectively. The recovery of pure copper and pure nickel, by electrowinning, from the acidic solvent extract strip liquors finally produced, appears technically feasible. An economic analysis of production costs shows that small, geographically isolated, nickel-copper sulphide deposits cannot usually be worked profitably by established processes. The requirements for profitable operation on a comparatively small scale could possibly be met by a flotation-roast-leach process. Two difficulties, obtaining satisfactory extraction of nickel from a sulphide concentrate and separating the copper and nickel in solution, have prevented the previous use of this method. A solution to the first problem, dissolution of the nickel, was described in a recent paper by Thornhill.1 It was shown in this paper that copper and nickel in a flotation concentrate could be oxidized to water soluble sulphates by roasting in a fluidized bed with added salt cake. Workers at the Warren Spring Laboratory have shown that the separation of copper and nickel can be accomplished by solvent extraction using a relatively inexpensive carboxylic acid, naphthenic acid. Moreover, the mineral acid required to strip values from the loaded solvent could be produced, and the metals recovered, by electrowinning; thus the latter section of the process was regenerative. The removal of iron from the leach liquor and the elimination of impurities such as zinc and cobalt before nickel electrowinning would be necessary to complete the flowsheet. The process under investigation could therefore be summarized (Fig. 1) as follows: 1) Flotation to produce a bulk sulphide concentrate. 2) Fluidized bed roasting to sulphate the nickel and copper minerals. 3) Leaching of roaster calcine to extract soluble nickel and copper. 4) Precipitation of iron from the separated leach liquor by air oxidation after the adjustment of pH and temperature. 5) Recovery of copper from the iron-free Liquor by pH adjustment and liquid-liquid extraction. 6) Purification of the copper raffinate by removing zinc and residual copper as insoluble sulphides and cobalt as cobaltic hydroxide. 7) Recovery of nickel from the purified liquor by pH adjustment and liquid-liquid extraction. Laboratory and pilot plant studies detailed below, were carried out at the Warren Spring Laboratory, to test the feasibility of each one of the unit processes and to obtain preliminary plant design data. FLOTATION The ore was an altered basic rock containing concentrations of magmatic sulphides.

Jan 1, 1964

By N. J. Grant, H. Brunner

This paber is concerned with the determination of equations relating elongation to the amount of shear taking place both along grain boundaries and in slip planes of poly crystalline aggregates during creep. Certain discrepancies with previously used equations are pointed out. Grain boundaries were observed to become serrated during creep, but it is shown that this does not necessarily prevent further grain boundary sliding. Direct obser-vations of subgrain boundary ingration lead to the conclusion that this migration facilitates sliding along serrated grain boundaries. It is bointed out that the state of stress at triple boints is still unknown. MOST of the mechanisms of deformation contributing to elongation are shear processes, such as slip, kinking, grain boundary sliding, and twinning. For quantitative investigations of individual deformation mechanism it is necessary to know the equation which permits the calculation of speci-tnen elongation from measured amounts of shear. This calculated elongation must then be compared with the observed total elongation. The authors' special interest concerned grain boundary sliding during creep. Although this subject has already been investigated quantitatively by McLean,' Rachinger,' and Fazan, Sherby, and Dorn, calculations indicated that none of the equations used thus far to relate shear with elongation were sufficiently well founded. A basic study of this relationship was thus made and the results of this study (which do not entirely agree with those previously used) are presented. Most of the ideas set forth apply not only to grain boundary sliding but to other mechanisms of shear as well. THE SPEAR-ELONGATION RELATIONSHIP Basic Models—The relationship between shear and elongation is trivial in the simplest case of shear, which is shown in Fig. l(a). The vector A; designates the displacement across the shear interface, and Au, and Aut are its components parallel and normal to the tensile direction, respectively. It is evident that the specimen elongation due to shear is equal to the longitudinal component of the shear vector, and it should be noted that the normal component does not contribute to the elongation of the specimen (there are, of course, two normal components in a three-dimensional model). The model shown in Fig. l(b) may be applied to mechanical twinning and to subgrain boundary tnigration. In this case the width (h) of an already existing shear band increases by the migration of an interface, but the shear angle y (angle of mis-orientation in the case of a subgrain boundary) remains constant. The geometrical relationships indicated in Fig. l(b) permit this case to be reduced to the one shown in Fig. l(a). For the resulting elongation A6 we find: where AV/V = fraction of the volume of the specimen swept by migrating interfaces , and 1 = length of specimen. Thus, assuming for example that the angle of mis-orientation is 1 deg, and that P = 45 deg, we find that the specimen elongates 0.87 pct of its length if the entire volume of the specimen is swept once by such a subgrain boundary. An example of deformation by migration of subgrain boundaries is shown in Fig. 2. The specimen shown was repolished after 9.8 pct creep strain and the test then continued for another \ pct. Since the shear vector has, in general, a component normal to the surface, subgrain boundary migration results in the formation of an inclined band delineating the region swept by the subgrain boundary. These inclined bands become clearly visible when observed with oblique illumina-

Jan 1, 1960

By G. M. Gay, R. L. Perrine

This paper describes a method of numerical computation for three-dimensional, unstable, miscible displacement behavior useful for heterogeneous systems, as well as for more ideal conditions. In the method, flow equations are first linearized by a perturbation approach. The basic flow process is separated and a solution for its behavior readily obtained. The remaining problem of deviations from the basic flow caused by non-ideal conditions is then subjected to numerical analysis. Results obtained from use of the method are also presented. Although conditions assumed in the test cal-culations were severe, results show the type of dispersing flow expected and appear quite satisfactory. The method has eliminated or reduced in importance problems of oscillating values near steep fronts, excessive computer smoothing, etc. A unique advantage of the method is that the source of variations from ideal behavior can be observed. ,The one serious drawback results from the algebraic complexity of the perturbation approach, and the need for second-order terms to be retained in calculations of interest. Fewer array points are available and more computer time is required than would be desired. However, these difficulties are also experienced with other approaches to the solution of three-dimensional dispIacement problems. INTRODUCTION Prediction of behavior of the miscible displacement process within a porous medium for any system of engineering importance is plagued by a number of difficulties. With typical fluid properties the displacing fluid has the lower viscosity, and there is a natural tendency toward flow instability. The problem of predicting instability is compounded by the fact that every real system is heterogeneous. Permeability will vary from point to point — not entirely systematically, and yet not in a random fashion leading to a readily defined average. Furthermore, permeability is unlikely to be isotropic. These permeability properties, which are characteristic of any real porous medium, accentuate the effects of flow instability. Another factor to be considered is that flow dispersion accompanies the displacement process in a porous medium. Mechanistically, dispersion is due to the fact that flow between any two points in the medium follows multiple tortuous paths, each characterized by slightly different flow properties. The fact that the coefficient characterizing dispersive properties of the real medium JS a tensor with variable elements complicates matters. Further difficulties arise because the parabolic influence, while not negligible, is small. Thus, there is a tendency toward steep and uneven displacement fronts along which dispersion smoothing must be represented accurately. Yet frequently used numerical analysis schemes may tend toward either instability, oscillation or excessive smoothing, none of which gives the desired accurate picture of flow behavior. Thus, while many experimental and analytical studies of the process have been made, predictions of actual performance are still subject to considerable uncertainty and possible improvement. This paper reports on part of a study which attempts to develop improved methods for solution of the flow equations describing the miscible displacement process. Of necessity, the calculations were performed on a large digital computer. A three-dimensional system is represented, and the coefficients defining dispersion and permeability can be varied in a manner representative of a real system. Because the differential equations are nonlinear, a first step is to linearize them using a perturbation approach. Objective of this approach has been to separate the basic flow which would occur in an ideal system and for which predictions are readily made. Then the numerical analysis, which is necessarily complex, is directed toward solution of the perturbation equations. These equations state how the basic flow is modified

Jan 1, 1967

By R. Buehl

ALTHOUGH the main features of the transformations occurring in 18-8 have been published already,1-4 certain conclusions merit questioning and discussion. The questions may be summarized as follows: PERCENT REDUCTION BY COLD ROLLING FIG. 1.-VARIATION OF FERRITIC INDUCTION AND PERCENTAGE OF FERRITE WITH COLD REDUCTION. Composition of Alloy: C, 0.08; Mn, 0.40; Si, 0.24; P, 0.014; Cr, 18.13; Ni, 8.94. 1. If ferrite is formed by cold-working austenite, what happens to the carbon with which the ferrite and austenite are both pre-sumably supersaturated? 2. What is the nature of the alpha-ferrite formed at grain boundaries by chromium-carbide precipitation at these boundaries?

Jan 1, 1939

By Donald L. Katz

Charts for predicting the pressure to which natural gases may be expanded without hydrate formation have been prepared for gases of even gravity. Pressure-temperature curves for hydrate formation were established for gases having gravities from 0.6 to 1.0. These curves and the thermal behavior of the gases during free and adiabatic expansion were used to prepare the charts for estimating the permissible expansion of natural gases without hydrate formation. The problem was solved by L. F, Albright, W. T. Boyd, J. J. McKetta, G. Martin, P. Poettman. and A. P. Snyder.-, who are first-year graduate students in the department of Chemical and Metallurgical Engineering at the University of Michigan. This paper is essentially a summary of their results. Prediction of Conditions for Hydrate Formation in Natural Gases Each natural gas under a given pressure will form solid hydrates at a corresponding temperature provided sufficient water is present.1-5 The temperature of natural gases below about 5000 lb. per sq. in. decreases when the gases are expanded freely.6,7 This decrease in temperature may cause the expanding gas to enter the region of temperature and pressure at which hydrates will form' The final pressure to which a natural gas may 'be expanded without hydrate formation depends upon the initial temperature and pressure and the gas composition. This paper presents charts that give the final pressures to which gases of gravity 0.6 to 1.0 at given initial temperatures and pressures may be expanded without formation of hydrate. Hydrate-forming Temperatures and Pressures as a Function OF Gas -Gravity Experimental data of pressure versus temperature at which solid hydrate will form, provided sufficient water is present, are available for a series of gases.2,3 A method of predicting the pressure-temperature curve for a given gas composition has been reported.' The solution to this problem requires that these curves relating pressure to temperature be established for gases of given gravities.

Jan 1, 1945