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By J. Lewis, J. Harper, M. F. Ashby

A grain boundary in a metal interacts with second-phase particles, which exert a pinning force (first estimated by Zener) on the boundary opposing its motion. We have computed the shape of boundaries which interact with more or less spherical second-phase particles and have constructed a soap-film model to reproduce the shape of the boundary surface. An important result is that measurement of this shape allows the pressure, or driving force, on the boundary to be measured. We hare applied this technique to grain boundaries in two alloys and hate measured the pinning force exerted by single second-phase jwrticles on the boundaries. It is in good agreement with Zener's estimate. J\. boundary between two grains, or two bulk phases, interacts with small inclusions or particles of a second phase, whether they are gas or solid. This interaction means that the boundary, forced to migrate by a difference in free energy between the material of the two grains or phases which it separates, exerts a force on a particle which it touches, tending to drag it forward. (The movement of inclusions through metals under the influence of this force, has, in fact, been observed. 1-3) Equally, the particle can be thought of as exerting a pinning force on the boundary, tending to hold it back. Zener (in a celebrated private communication4) first realized that this interaction, and the resulting pinning force, existed. His calculation of its magnitude was crude but adequate: a spherical inclusion of radius r blanks off an area nr2 of the boundary on which it sits; since the boundary has an energy of rMM x per unit area, the blanlung-olf decreases the energy of the system by MM: this energy is returned to the system if the boundary is pulled free from the inclusion— a forward movement of the boundary by a distance r will do this—so that the maximum pinning force is Trrym.M- A similar argument can be made for inter-phase boundaries. The nature of the particle itself did not enter this, or two subsequent treatments.5,6 When it is considered, tic leifthe energyoftheb a) The boundary may enter and pass through the particle if the energy of the boundary is lower within the particle than in the matrix. Fig. l(r/). Certain coherent precipitate particles behave like this. h) More usually, the boundary will bend round the particle, enveloping and bypassing it. Fig. l(b). In doing so, it changes the structure and energy of the interface between the particle and its matrix. This means that the boundary does not touch the particle surface at right angles, as early treatments assumed,5'9 but at some angle a which depends on this change in surface energy of the particle, and can be calculated from the equilibrium of surface tensions. Most precipitate particles and inclusions behave like this. Gas bubbles or liquid drops can be regarded as belonging to either group. The progress of bypassing is conveniently measured by the angle shown in Fig. 1. When the nature of the particle is ignored, its maximum pinning force is exerted when - 45 deg. When it is considered, this critical value of is found to depend on a and thus on the nature of the particle. The maximum pinning force lies between nryMM and 2jtjMM (Appendix 1). not very different from Zener's result. In reality, a boundary between crystals has a specific energy and tension which varies with the orientation of the boundary. Furthermore, recent experiments7 indicate that such a boundary is not atom-ically smooth, but has steps on it: migration of the boundary corresponds to the sweeping of these steps across the boundary surface, like the Frank model of crystal growth from the vapor. This means that the interaction of a boundary with particles should really be considered in terms of the way in which particles hinder the movement of these steps. To suppose a grain boundary or interphase boundary to be smooth, and to ignore the variation of its energy with orientation, is to liken it to a soap film. The advantage of this soap film approximation, which we have used throughout this paper, is that interaction energies and boundary shapes can be calculated easily. We have done this by numerical computation and by using a soap film model, and have compared the results with grain boundaries in an aluminum-based and a copper-based alloy. It turns out that the shape of the boundary which bulges between particles allows the pressure an it to be calculated; that is, the local driving force an the boundary can be measured. This has allowed us to check the Zener relationship experimentally.

Jan 1, 1970

By R. W. Balluffi, R. Resnick

NUMEROUS investigations of chemical diffusion in a brass have been made and the results are collected in several places.1-3 This work has been mainly concerned with the determination of the chemical diffusivity as a function of composition and temperature. In 1947 Smigelskas and Kirken-dall&apos; showed that zinc and copper diffuse at different rates in face-centered-cubic brass, and since then, a number of efforts have been made to determine the intrinsic diffusivities of zinc and copper in this alloy.1, 5-9 Horne and Mehl8 in particular have recently determined the intrinsic diffusivities as functions of temperature and composition using sandwich-type couples and inert markers. Inman et al." also have determined the intrinsic diffusivities in homogeneous alloys using tracer techniques. When the present work was started, no information of this type was available. Consequently, measurements of the intrinsic diffusivities were made as a function of temperature at a constant composition of 28 atomic pct Zn with vapor-solid diffusion couples where the zinc was diffused into the diffusion couple from the vapor phase. The application of these couples to the study of diffusion in a: brass has been described previously.0,7 The temperature dependence of the intrinsic diffusivities was found to follow the relation D, = A, exp(-Hi/RT) and the values of Hzn, and Hcu, were found to be closely the same. It is emphasized, however, that the chemical dif-fusivity (D = N1D2 + N2D1) is a composite diffusivity and does not necessarily follow this exponential form. It is usually found to do so within experimental error for substitutional alloys because the heats of activation of the intrinsic diffusivities generally are not greatly different.&apos;" Also, at the onset of this work, there was no information available concerning possible unequal diffusion rates of individual components and the existence of a Kirkendall effect in alloys with other than face-centered-cubic structures. Since then, two reports indicating a Kirkendall effect in body-centered-cubic ß brass have appeared. Landergren and Mehl" have published a note describing Kirkendall diffusion experiments with sandwich-type couples. Inman et a1.9 also find a Kirkendall effect in this alloy using the tracer technique. In the present work, several aspects of the Kirkendall effect in ß brass were further investigated using vapor-solid couples. Two different couples were used, one in which the zinc was diffused into the specimen from the vapor phase and the other in which the zinc was diffused out of the specimen into the vapor phase. Briefly, the existence of a Kirkendall effect is confirmed and it is found that Dzn/Dcu = 3 at about the 46 atomic pct composition in this alloy at 600°, 700°, and 800°C. As a result of the unequal diffusion rates of zinc and copper, volume changes occur and subgrain formation is observed in the diffusion zone. In addition, significant porosity is produced by the precipitation of supersaturated vacancies. Diffusion in this alloy is therefore outwardly similar to diffusion in a brass where these effects are also observed, a Brass Experimental Methods—The use of vapor-solid couples in studying diffusion in a brass has been described in previous articles.6,7 The method briefly consists of sealing a copper specimen with Kirkendall markers initially placed on its surface in an evacuated quartz capsule along with a large zinc source of fine a brass chips and then diffusing the zinc into the specimen through the vapor phase. The zinc concentration at the specimen surface rises rapidly enough to a value near that of the a brass source so that the surface concentration may be regarded as constant during diffusion. Under these boundary conditions, values of the chemical diffu-sivity may be obtained by applying the Boltzmann-Matano analysis to the concentration penetration curve, and the intrinsic diffusivities may be obtained from Darken&apos;s5 equations when the velocity of marker movement is known. The diffusion specimens were made from OFHC copper in the form of disks 3.2 cm diam and 0.5 cm thick with faces surface-ground parallel to within +0.001 cm. Markers in the form of fine alumina particles <0.0002 cm diam were placed on the specimen surface. These specimens were then sealed in quartz capsules along with enough a brass chips of a 30.0 atomic pct Zn composition to keep the source concentration from decreasing by more than 0.3 atomic pct Zn as a result of the loss of zinc to the specimen during diffusion. The quartz capsules which were initially evacuated to a pressure of

Jan 1, 1956

By W. B. Dancy, A. Adams

Laboratory test work on heavy liquid separation of sylvite from halite is reported. Numerous tests were run on sylvite ore sized in the ranges of 4x20 mesh, 10x65 mesh, 8x100 mesh, -8 mesh and -10 mesh with heavy liquids in the range of 2.05 to 2.15 sp gr. From the test results, it was concluded that, with the type of ore under study and a size in the range of -8 mesh, a recovery as high as 90% could be achieved with a product grade of 70% KCl. However, a final product at an acceptable recovery cannot be made with one pass, and the float must either be further processed with heavy liquids or dried and sent to a conventional froth flotation circuit. Potash ores occurring in this country consist essentially of sylvite and halite plus minor amounts of magnesium sulfate salts and montmoril-lonite-type clays. Recovery of potash minerals from evaporite ores in the North American potash fields is accomplished almost exclusively by use of amine flotation. European practice involves froth flotation as well as solution-crystallization processes. Laboratory and pilot plant test work has been reported in Europe and the U. S. on the application of heavy media separation to potash ore beneficiation. Work was probably discontinued because of lack of ore with the required very coarse liberation characteristics (1/8 to 1/2 in. liberation size). Sylvite, with a gravity of 1.99, and halite, with a gravity of 2.17, appear to be ideal for separation by heavy liquids, which are now available in gravities from 1.59 to 2.95. This paper reviews preliminary results obtained from laboratory test work on heavy liquid separation of sylvite from halite. TEST WORK The heavy liquids used in the tests under discussion were chlorobromethane, with a specific gravity of 1.923, and dibromethane, with a gravity of 2.490. These liquids, completely miscible, were combined in the proportions needed to give a mixture having the desired specific gravity. Feed for the laboratory tests was mine-run ore screened to the desired mesh sizes. In conducting the tests, the sample was fed at a constant rate into a stream of heavy liquid and the mixture directed into a small separatory vessel. The float overflowed into a collecting pan while the sink collected in the bottom of the separatory vessel and was removed at the end of the test. Approximately 500 g of feed constituted a charge. Pulp density of the feed was kept low to prevent particle to particle interference in separation. With feed in the range of 8x100 mesh, a pulp density of under 10% solids by weight was found advisable. With coarser feed the pulp density could be carried as high as 15% solids. Time of separation was very rapid. In the case of 4x20-mesh material, separation was effected in 15 to 30 sec; with -10-mesh feed, separation required about 1 to 2 min. SPECIAL EQUIPMENT Since heavy liquids are toxic to varying degrees, all separatory work was carried out in a standard laboratory fume hood. It was noted that complete removal of fumes was not being effected; therefore the hood construction was modified, resulting in a completely satisfactory arrangement for heavy liquid test work. In the interest of safety, details of this fume hood are reported here. Unlike most fumes, heavy liquid fumes tend to settle and flow like water, rather than to rise like a gas. Working on this assumption, a standard water drain was installed in the hood. Across the front of the hood a 1-in. barrier was constructed. In the rear of the hood a false back was installed, with an adjustable sliding door on both the bottom and top of this panel. As shown in Fig. 1, the exhaust fan pulled a vacuum behind the barrier, sucking the heavy fumes from the bottom of the hood. Another addition was the drying box, shown to the right of the hood. This is simply a box covered on top with hardware cloth and connected by a 6-in. inlet to the hood. Sample trays made of fine mesh wire filter screens were found ideal for drying samples. With this arrangement, air flowed completely through the sample and all fumes were drawn into the hood. In use, it was found effective to cover with a

Jan 1, 1963

By D. Kunstelj, M. Stubicar, A. Tonejc, A. Bonefacic

A. Bonefafcic, D. Kunsfeli, M. Stubicar, and A. Tonejc The present communication is concerned with the variation of the texture in aluminum wires with die angle and temperature, at constant speed of extrusion. Experiments were carried out concurrently on refined samples, with a stated purity of 99.997 pct pure A1 and commercial samples of 99.5 pct Al. Ingots of refined aluminum samples were machined to 30-mm-diam by 150-mm-long billets. These billets were transformed to 5-mm-diam wires by drawing. The final form, suitable for examination, was obtained by extrusion through conical-face dies with a 1-mm hole diam and extrusion ratio 5:l in diam. The initial form of the commercial aluminum samples was drawn wire 5 mm in diam. These samples showed a poorly defined texture with (111) as a major and (001) as a minor component. A similar defined texture appeared in the refined aluminum samples after drawing to 5 mm diam. Conical-face dies with different angles (defined by the axis and the generating line of the cone) were used in our experiments. The values of the angles were 27, 35, 45, 57, 63, and 90 deg. The extrusion container was fitted with a heating element and controller permitting temperatures up to 600°C to be maintained within i5"C. Extrusion was performed at 250°, 300°, 350°, 400°, and 500°C at constant speed (approximately 1 mm per sec) and constant die reduction. The extrusion product was a wire 1 mm in diam and approximately 20 cm long. In order to remove the surface layer with the "conical" texture and to reduce the absorption by the X-ray examination of the samples, the extruded wire was etched to 0.22 mm in diam. Experiments were performed in the middle sections of the 20-cm-long wires. In addition to the die of l-mm hole diam, dies with a 1.5-, 0.7-, 0.6-, 0.5-, and 0.4-mm hole diam and 63-deg die angle were constructed. In our experiments we did not find in these ranges any important difference concerning the texture of the extruded wires and we continued our work solely on the 1.0-mm die. The diffracted X-rays (Cu K radiation) were recorded photographically. Diffracted intensities were measured on the (111) reflection with a microphotometer. The relative amounts of texture components were determined from the areas under the diffracted maxima. We found the texture of extruded aluminum wires to be strongly influenced not only by the temperature of extrusion and the purity of the sample but also by the form of the die. It is generally admitted that cold-drawn aluminum wires have mainly a (111) texture with a small amount of (001) component, Table I of Ref. 1. In our experiments with wires extruded in conditions represented by Fig. 1, in some cases a single (001) texture was obtained. If these wires were drawn repeatedly at room temperature, X-ray measurements revealed a duplex (001)-(111) fiber texture. Further drawings increased the (111) and decreased the (001) texture component. In Fig. 1 the percentage of material oriented with (001) parallel to the extrusion direction is represented as a function of the temperature and the die angle (a), for commercial and refined aluminum samples, respectively. From these diagrams we may draw the following conclusions. The slope of the die (a) influenced more strongly the texture at the lower rather than the higher temperatures. Again, a stronger influence was found in the case of the commercial in comparison with refined aluminum samples. In the case of the commercial aluminum samples the amount of material with (001) texture increases with increasing wire temperature in an approximately linear manner. This effect is less pronounced in the pure aluminum samples, with the exception of the die with a = 45 deg. In this case the (001) texture decreases with increasing temperature, as shown in Fig. 1. Component (001) is more pronounced in higher-purity aluminum samples. Our experiments led to the conclusion that both (001) and (111) components are essentially stable in extruded aluminum wires. As we obtained a single (001) texture starting with a sample of drawn wire in which the (001) component was very weak, our experiments revealed that the (001) component is not a remnant of the initial texture; this is in disagreement with the findings of Vandermeer and McHargue.1 We gratefully acknowledge discussions with Professor M. Paic. 1 R. A. Vandermeer and C. J. McHargue: Trans. 7MS-AME, 1964, vol. 230, p. 667.

Jan 1, 1969

By W. C. Hauber

Techniques previously published to predict the production performance of a water flood when the mobility ratio is not unity have been primarily restricted to a five-spot well pattern. When other types of well patterns are considered, the prediction of performance has required either a model study or a complex numerical solution of a multiple-fluid system with a high-speed digital computer. Simple methods are developed in this report for predicting the areal sweep efficiency and injectivity history of a water flood for arbitrary well patterns and mobility ratios. The effect of an initial gas saturation can be incorporated into this method of prediction. With the layer superposition concepts published by Prats, et al.,1 these methods can be used to predict the production performance of a water flood in a reservoir having a wide range in permeability. A reasonably good agreement is shown by comparisons of the results calculated by this method with those obtained either by model studies or by complex numerical solution of multiple-fluid systems. Therefore, it has been concluded that a reasonably accurate method has been developed for predicting the production performance of a water flood employing an arbitrary type of well pattern for any given mobility ratio. A medium-speed digital computer can be used in applying this method. INTRODUCTION Production performance of multi-fluid five-spot water floods can be predicted by the techniques published by Prats, et al.1 This technique takes into account the effects of initial gas saturation, mobility ratio and vertical variations in horizontal permeability. A basic assumption in applying this technique is that unit displacement efficiency does not vary with time after the passage of the flood front. Prats, et al. demonstrated that this assumption is valid for normal waterflood applications with small mobility ratios. To extend Prats&apos; technique to other types of well patterns has required either an experimental model study or a numerical solution of a multiple-fluid system to describe the performance of an individual homogeneous layer. Sheldon and Dougherty2 presented an exact numerical solution employing any arbitrary well pattern. This technique is complex to apply, requiring (1) numerical solution of the single-fluid system, (2) conformal mapping of the streamlines and iso-potential lines to form a new grid network, and (3) a numerical solution of the multi-fluid system on the new grid network. A method was developed in this paper to approximate areal sweep efficiency and injectivity as functions of time for an individual homogeneous layer for arbitrary well patterns and mobility ratios. Analytic expressions were derived to directly apply this method to five-spot and direct line drive well patterns. For other types of well patterns, this method is similar to the approach of Higgids and Leighton,6 in that it utilizes the stream tubes and iso-potential lines obtained by the solution of differential equations when the mobility ratio is unity. However, this method is easier to apply than the Higgins-Leighton method since it does not require knowledge of the variation between oil and water relative permeabilities and saturation. Using the relationship between areal sweep efficiency, injectivity and the volume of water injected into an individual homogeneous layer as obtained by the method presented in this paper, and Prats&apos; technique for the superposition of individual layers, one can predict the production performance of any water flood. ASSUMPTIONS GENERAL Basic assumptions made in this report are that fluids are incompressible and the layers are horizontal, homogeneous and uniformly thick. It is assumed that as water is injected into the layer, three distinct regions are formed —a water bank, an oil bank, and an unflooded region. Each region is assumed to displace other regions in a pis-tonlike manner, with only one fluid flowing in each region, so that there is no change in unit displacement efficiency with time after the flood front has passed in the reservoir. Therefore, the residual oil saturation in the water bank and the oil saturations in the unflooded region are constant throughout the layer. The ratio (F) of the bulk volume of a layer occupied by the oil and water banks at any time before oil breakthrough, to the corresponding bulk volume of a layer occupied by the water bank, is given&apos; by the equation BREAKTHROUGH AREAL SWEEP EFFICIENCY To predict the behavior of any type of waterflood pattern, one must know the breakthrough areal sweep efficiency Eb(Mc,o, F) for the pattern for any water:oil mo-

Jan 1, 1965

By R. H. Kolb

A long term project at Shell Development Co.&apos;s Exploration and Production Research Laboratory has been the improvement of the accuracy and the ease of BHP measurements. As a result of these efforts, two complete and separate systems have now been built for the automatic logging of BHP variations. The first of these is a small-diameter instrument suitable for running through production tubing on a single-conductor well cable. During the development of this instrument, as much emphasis was placed on providing a high degree of usable sensitivity and repeatable accuracy as on obtaining the advantages of surface recording. The second system combines the benefits of automatic, unattended recording with the convenience of a permanently installed Maihak BHP transmitter.&apos; THE CABLE INSTRUMENT For many years the standard instrument for BHP determination has been the wireline-operated Amerada recording pressure gauge or one of several other similar devices. This gauge records on a small clock-driven chart carried within the instrument, and although relatively precise readings from the chart are possible, they are difficult to ob-tain. a Both the maximum recording time and the resolution of the time measurements are limited by chart size, and when a slow clock is required for long tests, the precision of the time measurement is often inadequate. Since it is impossible to determine the data being recorded until the gauge has been returned to the surface, wasted time often results when a test is protracted beyond the necessary time or when it is terminated too soon and must be re-run. Clock stoppage or other malfunctions which would be immediately apparent with surface recording remains undetected with down-hole recording; the test is continued for its full term with a consequent loss in production time. As new uses for subsurface pressure data evolved, the shortcomings of the wireline instrument became increasingly apparent, and the concurrent development of a surface-recording pressure gauge and the associated high-pressure well cable service unit&apos; was undertaken. Description of the Instrument Because of its ready availability and advanced degree of development, the Amerada bourdon-tube element was chosen as the basic pressure-sensing device. This element converts a given pressure into a proportional angular displacement of its output shaft, and a suitable telemetering system was designed to measure accurately the extent of this displacement and to transmit the measurement to the surface and record it. The telemetering system furnishes a digital record printed on paper tape by an adding machine-type printer. The present arrangement provides a resolution of one part in 42,000 over the angular equivalent of full-scale deflection, giving a usable sensitivity of better than 0.0025 per cent of full scale. An additional refinement simultaneously records on the tape the time or the depth of the measurement, also in digital form. When the instrument is placed in operation, an adjustable programer can be set to initiate a read-out cycle automatically at selected time intervals. When subsurface pressures are changing rapidly, readings may be recorded as frequently as once every 10 seconds; when pressures are more nearly stabilized, the period between readings may be extended to as much as 30 minutes. Because the instrument is surface-powered as well as surface-recording, the maximum period of continuous logging is (for all prac. tical purposes) unlimited. The subsurface instrument is a tubular tool, 1 1/4-in. in diameter and 6.5 ft in length, operating on 12,000 ft of conventional 3/16-in. IHO logging cable. The transmitting section, mounted above the bourdon-tube element in place of the regular recording mechanism, contains no fragile vacuum tubes or temperature-sensitive transistors. This unit has been laboratory-tested to 1 0,000 psi and 300°F and has performed dependably during a number of field operations. The down-hole transmitting arrangement can be fitted to any standard Amerada pressure element, regardless of range and with no modification of the element itself. Calibration To obtain a repeatability commensurate with the sensitivity and resolution of the instrument, it was necessary to develop a special calibrating technique. The manufacturers of the Amerada recording pressure gauge claim an accuracy of only 0.25 per cent of full scale, which is a realistic figure for normal calibrating and operating procedures. An exhaustive investigation was made of the errors inherent in the bourdon-tube element, itself, independent

By W. H. Smith

IN connection with some recent work on the effect of impurities on the ductility of chromium, it appeared desirable to know the solid solubility of carbon in chromium. A literature survey indicated that this information was not available. Although considerable work has been done on the Cr-C phase diagram,&apos;.&apos; previous investigators have been more concerned with the structure and phase boundaries of the carbide phases than with the terminal solid solution. The phase diagram shown in Fig. 1 is taken from the work of Bloom and Grant&apos; and represents the most recent determination. As indicated by the dashed line, the a solid-solubility limit was not determined. Experimental Procedure Alloys of chromium were prepared from hydrogen-treated and vacuum-degassed electrolytic chromium plus spectrographic grade carbon. The oxygen and nitrogen content of the alloys was <0.002 pct. After melting, analysis of the alloys showed them to contain 0.02, 0.08, 0.15, and 0.55 pct C. Pieces of the alloys were heated in a protective atmosphere to various temperatures and then quenched after holding for a time sufficient to insure equilibrium. Microscopic examination of the as-quenched alloys for the presence of a second phase was used as a measure of the solubility limit. The heats were made in a multiple hearth arc-furnace using a zirconium-gettered static argon atmosphere. A zirconium melt was made before each Cr-C heat. Triple melting was used to insure ingot homogeneity as shown by microscopic examination. The alloys were prepared by adding portions of a 4.5 pct C-Cr master alloy to high purity chromium. The carbon contents listed previously were those obtained by analysis. The nitrogen and oxygen contents after arc melting were both <0.002 pct. Sections 1/8X1/4X1/2 in. were cut from the 100-g ingots and a hole drilled in one end in order to suspend the sample from a molybdenum wire. After the surface was carefully cleaned, a sample of each melt was hung in a mullite tube heated externally by a platinum resistance furnace connected to a vacuum system. The lower portion of the mullite tube was sealed to Pyrex and closed off several inches below the furnace. This was filled with sili-cone oil kept cold by circulating cold water around the outside of the Pyrex. Quenching into the oil bath was achieved by melting a fuse wire supporting the sample. It required about 4 sec for the sample to cool from 1400" to 600°C. This severity of quench was considered satisfactory to freeze-in the high temperature equilibrium. For tests made at temperatures of 900" to 1200°C, heating was done in vacuum; for tests above 1200°C, an argon atmosphere was used. The holding time employed ranged from 12 hr at 900°C to 6 hr at 1400°C. Experiments were performed at temperatures of 900°, 1000°, 1100°, 1200°, 1300°, and 1400°C. Microscopic examination for evidence of a second phase was done at X1500. Experimental Result The microstructures of a 0.08 pct C-Cr alloy as-cast and after quenching from 1300°C are shown in Figs. 2 and 3. A 0.15 pct C-Cr alloy quenched from 1300°C is shown in Fig. 4. The data obtained from the quenching experiments is shown graphically in Fig. 5. If the Van&apos;t Hoff equation is obeyed, a plot on a logarithmic scale of the mol fraction of solute vs the reciprocal of the absolute temperature should give a straight line. For dilute solutions the weight percentage can be substituted for the mol fraction without introducing any appreciable error. The Van&apos;t Hoff equation can then be written as where H is the heat of solution in calories per mol. The slope of the straight line on the log pct C vs 1/T plot gives the value of AH. Assuming that the Van&apos;t Hoff equation is obeyed, which is probably justified for the dilute solution of carbon in chromium, the heavy straight line shown on Fig. 5 represents the best fit of the data. This line was obtained as follows. On Fig. 5 the results of the microscopic examination of all alloys following quenching were plotted and designated as to whether one or two phases were seen. Below 1100°C all alloys showed a second phase on quenching. The heavy vertical lines shown in Fig. 5 therefore represent the possible range of the ter-

Jan 1, 1958

By V. B. Kurfman

Grain refinement of Mg-Al melts by carbonaceous additions has been attributed to nucleation by aluminum carbide. The effects of process and alloy variables are interpreted and predicted in terms of the dispersion and chemistry of this phase. The grain coarsening action of Be, Zr, Ti, R.E., chlorination, temperature extremes, and prolonged holding times is described. Measures necessary to insure an adequate dispersion of the catalyst are discussed. CARBON inoculation treatments have become fairly well known and used for grain refinement of magnesium alloys containing Al. Although there is general agreement that a nucleation process occurs, the process is not understood and the inoculants are used in a rather empirical fashion. The treatment is applied to the class of alloys containing 3 to 10 pct Al, i.e., AZ31A to AM100A. Typical methods involve melting, alloying, and adjusting the temperature to 1400° to 1450°F. Then 0.01 to 0.5 pct C as CaC2, C6C16, or lampblack is added by any convenient means, and the melt poured within 10 to 30 min. Investigators generally have been impressed by an assumed similarity of this refinement process to superheat grain refinement, which depends on heating approximately the same alloys to a temperature in the range of 1550" to 1650°F, then pouring promptly after the melt is cooled to the pouring temperature. Various predictions have been made that carbon refinement would replace superheating in commercial practice due to reduced process costs, but this replacement has not fully taken place because of production difficulties and conflicting observations. Davis, Eastwood, and DeHaven1 agree with Nelson2 and wood3 in suggesting that an excess of inoculant may be harmful. Wood however says that overtreat-ment is not a problem in production use of hexa-chlorobenzene inoculation, and Hultgren and Mitchell4 claim no evidence of harm from excess additions. Various grain coarsening reactions are known to occur, including the possibility of overtreatment mentioned above. Trace amounts of Be,2 Zr, and Ti may prevent refinement by either a carbon treatment or a superheat. Occasionally treatment with cl25 may cause coarsening, although the Battelle refinement process&apos; uses a CC14-C12 blend. Grain coarsening also tends to occur on holding at temperatures below 1350°to 1400°F, especially after a superheat treatment, and for this reason Nelson2 stresses the desirability of a refinement method useful at lower temperatures for open pot melting practice. Since a carbon treatment can be made to work at temperatures below 1400°F, it seems desirable to investigate the mechanism of the refinement and the mechanisms of the coarsening reactions in order to establish control conditions for use in commercial production. The identity of the nucleating phase must first be established and then the factors affecting its chemistry and physical dispersion must be determined. THE IDENTITY OF THE NUCLEATING PHASE Davis, Eastwood, and DeHaven suggested that the nucleating phase in this system is Al4c3,1 but Mahoney, Tarr, and LeGrand8 disagree, largely because they found no evidence of the compound in alloys after carbon treatment and because there is no indication that aluminum carbide should be unstable over the temperature range used in the superheat treatment. This latter objection is based on the assumption that both the carbon treatment and the superheat treatment introduce the same nuclei. Electron diffraction studies have been made to identify the nucleating phase. Samples of grain refined A292 have been selectively etched SO that clean surfaces are obtained and so that secondary phases are in relief. Electron diffraction patterns from these surfaces have established that the carbon treatment of A292 introduces into the metal a large number of small, plate-like particles with a structure very similar to Al4C3. In most cases, the plate-like nature of the particles prevented positive identification but in the cases where the identification could be made the particles proved to be AIN A14C3. However, enough variation in lattice constants was observed so that all compositions from pure A14C3 to the 50:50 solid solution A1N.Al4C3 were probably present.14 In A14C3 and especially AlN.Al4C3 the A1 atoms occur in layers within which they have the same hexagonal symmetry and spacing as the Mg atoms in a single basal plane of a magnesium crystal. The solid solution spacing lies between the 3.16 of AIN and the 3.3? for Al4C3, in satisfactory agree-

Jan 1, 1962

By R. T. Hukki

This paper presents a series of equations for mechanical ball wear, relating parameters of ball size, mill speed, and mill diameter. The fundamental equation, Eq. 12, presented here is introduced to correlate these basic parameters and thus define and clarify the concept of ball wear. This equation is offered as a general rule, which may be modified to apply to individual problems of grinding. BALL wear as observed in grinding installations is the combined result of mechanical wear and corrosion. Corrosion should be a linear function of the ball surface available. Ball corrosion, however, has been studied so little that its effect, although of great importance, cannot be included in the analyses given here. In a separate paper&apos; it is shown that 1 n = 0.7663 np----=— rpm [1] vD P = c, np D kw [2] T=c²(np)n De tph [3] In these equations n — actual mill speed, rpm np = calculated percentage critical speed D = ID of mill in feet P = power required to operate a mill, kw T = capacity of a mill, tph C¹ and c² - appropriate constants in = exponent of numerical value of 1 5 m 1.5 Exponent m is the slope of a straight line on logarithmic paper relating mill speed (on the abscissa) and mill capacity (on the ordinate). It is generally accepted, although not sharply defined, that ball wear in mills running at low (cascading) speeds is a function of the ball surface available. Accordingly, the wear of a single ball may be considered to be a homogeneous, linear function of its surface and of the distance traveled. Thus dw = f¹(d2) . f2(ds) [4] where dw is the wear of a single ball in time dt, d the diameter of the average ball in ball charge, and ds the distance traveled by the ball in time dt. Indicating that ds - a D n dt, the wear of the average ball in time dt becomes dw = f¹(d2) . f2(Dn dt) 1 --- f¹ (d1) f² (D c3 np-----— dt) \/D = c,d² n, D dt The rate of wear of the average ball is given by dw/dt. dw/dt = c, d² np D lb per hr [5] The weight of the ball charge per unit of mill length is a function of D The number of balls of size d in the ball charge is = f³(D2)/f4(d³). The rate of wear of the total ball charge equals the number of balls times rate of wear of the average ball. Thus rate of total ball wear = — . (dw/dt) w. c, . (l/d) . n,, D lb per hr [6] which is the equation of ball wear in low speed mills. In a mill running at a low speed, grinding is the result of rubbing action within the ball mass and between the ball mass and mill liners. When the speed of the mill is gradually increased toward the critical, the impacting effect of freely falling balls becomes increasingly prominent in comparison with the rubbing action. Reduction of ore takes place partly by rubbing, partly by impact. The share of the freely falling balls in the reduction of ore reaches its practical maximum at a speed somewhat less than the critical; at that speed grinding by rubbing has decreased to a low value. It may be reasonable to think that size reduction by freely falling balls should reach its theoretical maximum at the critical speed, if the fall of the balls were not hindered by the shell of the mill beyond the top point; grinding by rubbing would cease at the critical speed. As a first approximation, wear of freely falling balls may be considered to be a homogeneous, linear function of the force at which they strike pieces of rock and other balls at the toe of the ball charge. The force equals mass times acceleration. The mass of a ball is a function of d3 and its acceleration is a function of the peripheral speed of the mill. The wear of a single ball of size d representing the average ball in a ball charge will therefore be w¹ = f3(F) = f (d3) f7 (v). [7] Indicating that v = D n, and n = c³ np 1/vD, Eq. 7 becomes W1 = cn d3 np Do.5 lb per hr. [8] Total wear of the ball charge equals number of balls times the wear of the average ball. Number of

Jan 1, 1955

By G. L. F. Powell

g samples of Cu-20 wt pct Ag alloy have been mdercooled to a maximum of 197°C by melting under a slag of commercial soda-lime glass in a vitreous silica crucible. No grain refinement of the primary copper was observed in samples undercooled to the maximum of 197°C. When the samples contained a small amount of oxygen, the copper dendrites were partially recrystallized at undercoolings greater than 97°C. In previous papers&apos;-3 reporting the grain structure of undercooled silver and copper, it was observed that grain refinement was dependent on both undercooling and oxygen content. Grain refinement occurred in undercooled silver when the degree of undercooling exceeded the range 153" to 175"C, while in Ag-0 alloys (0.12 wt pct) fine equiaxed grains were exhibited when undercooling was greater than 50°C. Similarly, copper samples undercooled as much as 208°C displayed fan-shaped growth from a single nucleation site, while the grain structure of Cu-O alloys (0.08 wt pct) was fine and equiaxed at undercoolings larger than 150°C. Thus the presence of oxygen greatly reduced the undercooling at which grain refinement occurred. It was also observed that the change in grain size resulted from recrystallization and was not due to an enhanced nucleation rate in the liquid-solid transformation. It is possible that the influence of oxygen on recrystallization is due primarily to its presence as a solute element. walker4,&apos; reported that, although a grain size change did not occur in pure nickel until the undercooling exceeded 150°C, small grains were observed in samples of Ni-Cu alloy solidified at small and large degrees of undercooling. Jackson et al.6 suggested that the fine grained structure of the Ni-Cu alloy resulted from the melting off of dendrite arms during recalescence. This remelting process may occur in alloys as a result of segregation during freezing which causes a variation in liquidus temperature from point to point within a dendrite. It was therefore decided to undercool copper with a metallic alloying element to ascertain whether the presence of a metallic solute would have a similar effect to oxygen in inducing grain refinement. A Cu-Ag alloy was chosen, since both metals had been shown to behave similarly on undercooling. The alloy Cu-20 wt pct Ag was selected since the eutectic constituent outlines the initial growth form of the primary copper, so that the as-frozen grain structure is not obscured if subsequent recrystallization occurs. This paper describes the results of undercooling experiments carried out with Cu-20 pct Ag samples undercooled to a maximum of 197°C and the effect of oxygen content on the grain structure of the undercooled samples. EXPERIMENTAL Melting was carried out in a small cylindrical resistance furnace using "fine" silver granulate and oxygen-free high conductivity copper. The procedure adopted was to melt the required quantity of silver in air in a clean vitreous silica crucible for approximately 15 min, freeze, and add granulated commercial soda-lime glass to form a complete surface slag cover, after which the sample was melted and frozen several times to reduce the oxygen content. The glass slag cover was approximately 3 in. thick. Pieces of copper (=50 g) were added to the crucible until the required quantity to make 350-g samples of alloy had been charged. Each piece was added quickly to the crucible which was held at a temperature slightly above the melting point of silver. The piece was quickly pushed beneath the glass to minimize oxidation and any oxide coating usually decomposed before the piece had settled down into the silver. After the full quantity of copper had been added, the melt was stirred with a silica rod to hasten homogenization and a Pt/Pt 13 pct Rh thermocouple enclosed in a vitreous silica sheath inserted for temperature measurement. Heating and cooling curves were recorded on a potentiometric chart recorder fitted with a zero suppression unit. The milli-voltage range of the recorder was adjusted so that temperatures could be read to 1°C. Heating and cooling curves were taken every hour until three consecutive readings gave the same solidus-liquidus range, consistent with the solidus-liquidus range for this alloy composition by reference to Hansen and Anderko.7 Metallographic examination of samples frozen at this stage, failed to show any variation in composition from bottom to top of the ingot. Consequently, it was considered that the melt was homogeneous at this stage and undercooling experiments were then car-

Jan 1, 1970

By George S. Ansell, Thomas E. Davidson

It has been known for a considerable period of time that the ductility of even quite brittle materials can be enhanced if they are deformed under a superposed hydrostatic pressure of sufficient magnitude. The response of ductility to pressure, however, has been shown to vary considerably between materials. Prior work has shown that the effects of pressure upon the tensile ductility of Fe-C materials depend upon the amount, shape and distribution of the brittle cementite phase. In this current investigation, the effects of pressure upon the fracture mechanisms in a series of annealed and spheroidized Fe-C materials were examined. It was observed that the principal effect of pressure is to suppress void growth and coalescence, retard cleavage fracture and to enhance the ductility of cementite platelets in pearlite. Based upon the observed effects of pressure upon the fracture mechanisms, a proposed explanation for the enhancement in ductility by pressure and for the structure sensitivity of the phenomena is presented and discussed. THE effect of superposed pressure upon the tensile ductility of a variety of metals has been well documented.&apos;-&apos;&apos; Some of the results from several investigators are summarized in Fig. 1 where tensile ductility in terms of true strain to fracture (ef) is plotted as a function of the superposed pressure. As can be seen, a pressure of sufficient magnitude can significantly enhance the ductility of metals. However, Fig. 1 also demonstrates that the response of ductility to pressure and the form of the ductility-pressure relationship varies considerably between materials. Several explanations have been offered for the observed enhancement in ductility by a superposed pressure. Although no experimental evidence was provided, Bridgman13 and Bobrowsky10 proposed that the observed effect was due to the prevention or healing of microcracks or holes. Bulychev et a1.14 observed that cracks and voids in initially prestrained copper were healed in the necked region of a tensile specimen upon further straining while under a superposed pressure. Also, pugh5 observed that large cavities were suppressed in copper fractured in tension while under pressure. A second proposal has been forwarded by Beresnev et at al.6 This proposal is based upon the hypothesis that a material fails in a brittle manner because the normal tensile stress reaches a critical value before the shear stress is of sufficient magnitude to cause plastic flow. Since a superposed hydrostatic pressure will increase the ratio of shear to normal tensile stress, a sufficiently high hydrostatic pressure should favor plastic flow while retarding brittle fracture. Galli15 reported that a superposed pressure shifts the ductile-brittle transition temperature of molybdenum. This was explained based upon the reduction of the normal tensile stress by the superposed pressure. Pugh5 explained the occurrence of the observed pressure induced brittle-to-ductile transition in zinc in the same manner. Davidson et al.12 proposed an explanation for the enhancement of ductility by pressure based upon the effects of pressure upon the stress-state-sensitive stages of various fracture propagation mechanisms. Basically, they proposed that pressure will retard cleavage and intergranular fracture by counteracting the required normal tensile stress or will suppress void growth. They observed suppression of intergranular fracture and void growth in magnesium by pressure. Davidson and .Ansell16 reported ductility as a function of pressure for a series of annealed and spheroidized Fe-C alloys. Fig. 2, from this prior work, demonstrates that the effect of pressure upon ductility is structure sensitive in terms of the amount, shape and distribution of the brittle cementite phase. As shown in Fig. 2, in the absence of cementite or when the cementite is in isolated particle form (spheroidized), the ductility-pressure relationship is linear and the slope decreases with increasing carbon content. In the annealed carbon-bearing alloys wherein the cementite is in the form of closely spaced platelets (pearlite) or in the form of a continuous network along prior aus-tenite boundaries (1.1 pct C material), ductility as a function of pressure is nonlinear (polynomial relationship) in which the slope increases with increasing pressure. At the highest pressures studied (22.8 kbars), the slope of the curves for these materials tends to approach those for the spheroidized material of the same carbon content. In this current investigation the change in fracture mechanisms as a function of pressure for the materials shown in Fig. 2 has been examined. The possible connection between the observed effects of pressure upon the fracture mechanisms and the effect of pressure upon ductility is discussed.

Jan 1, 1970

By H. R. Cooper, T. S. Mika

T. S. Mika (Department of Mineral Technology, University of California, Berkeley, Calif.) - Dr. Cooper&apos;s attempt to establish a correlation between process behavior and operational variables on the basis of a statistical analysis after imposing a reasonable process model is a very commendable improvement on the use of standard regression techniques. However, it must be recognized that the imposition of a model has the potential of yielding a poorer representation if its basic assumptions or mathematical formulation are invalid. It appears that at least two aspects of his treatment require some comment. First, the limitations on the kinetic law where xta represents a hypothetical terminal floatable solids concentration (cf. Bushell1), should be mentioned. Most current investigations2-9 appear to utilize the concept of a distribution of rate constants rather than a single unique value, k, to describe flotation kinetics. A distributed rate constant is certainly a more physically meaningful concept than that of a terminal concentration. The study of Jowett and safvi10 strongly indicates that xta is merely an empirical parameter, whose actual behavior does not correspond to that expected from a true terminal concentration. Rather than being a strictly mineralogical variable, as Dr. Cooper&apos;s treatment implies, it apparently represents the hydromechanical nature of the test cell as well as the flotation chemistry. The extension of batch cell kinetic results to full-scale continuous cell operation is a suspect procedure if the effect of such nonmineralogical influences on x,, remain unevaluated. There is evidence that introduction of a terminal concentration is necessitated by the inherent errors which arise in batch testing and are eliminated by continuous testing methods.&apos; Possible lack of validity of the author&apos;s use of Eq. 1 is indicated by two unexpected results of the statistical analysis of his batch data. The first is the apparent corroboration of the assumption that the rate constant, k, is independent of particle size, i.e., of changes in the size distribution of floatable material. This assumption directly contradicts numerous results 2,4,11-l8 for cases where first order kinetics prevailed and ignores the phenomenological basis for the analysis of flotation in terms of a distribution of k&apos;s. It must be recognized that, if the rate constant is size dependent, the lumped over-all k would be time dependent; Eq. 1 would then no longer be valid. Cooper&apos;s x,, is determined by batch flotation of a distribution of sizes for an arbitrary period of time. If the size dependence of k is artificially suppressed, x,, will become a function of the experimental flotation time used in its determination. Upon reviewing the rather extensive literature concerning batch flotation kinetics, there appear to be few instances where constant k and x,, adequately adsorb variations in floatability due to particle size. The second surprising result is the low values of the distribution modulus, n, determined. Contrary to Cooper&apos;s assertion, most batch grinding (ball or rod mill) products yield values of n > 0.6, which increase as the material becomes harder.&apos;&apos; It is likely that the values of n = 0.25 and n = 0.42 for Trials 1 and 2, respectively, are completely unreasonable, and even the value n = 0.54 obtained for Trial 3 is unexpectedly low. Possibly, this indicates inherent flaws in the three trial models considered, in particular the assumed particle size independence of the rate constant, k. The above does not necessitate that Eq. 1 (and the terminal concentration concept) is invalid; it could constitute a good first approximation. However, the qualitative arguments used by Dr. Cooper in its justification are somewhat frail and require verification, particularly since much of the flotation kinetics literature is in opposition. Apparently, no effort was made to test these hypotheses on the actual data; in fact, since they pertain to a single batch test time, his data cannot be utilized to evaluate the kinetics of flotation. To evolve a control algorithm on the basis of this infirm foundation seems a questionable procedure. Another difficulty in his analysis arises in consideration of the froth concentrating process. As Bushel1 &apos; notes, for Eq. 1 to be valid it is necessary that the rate of recycle from the froth be directly proportional (independent of particle size) to the rate of flotation transport from the pulp to the froth, a restrictive condition." Harris suggests that it is more realistic to assume that depletion occurs in proportion to the amount of floatable material in the pertinent froth phase volume (treating that volume as perfectly mixed).12,21,22 The physical implications of

Jan 1, 1968

By G. R. Belton, R. J. Fruehan

The Knudsen cell-mass spectrometer combimtion has been used to study the Fe-Al and Ag-Al liquid alloys. By application of the recently developed integration technique to the measured ion-current ratios, activities have been derived for the Fe-A1 system at 1600° C and for the Ag-Al system at 1340"C. The results are partially represented by the following equations: Internal consistency between the data on silver-rich and iron-rich alloys is demonstrated by application of the literature measurements on the distribution of aluminum between the nearly immiscible liquids iron and silver. The usual restrictions on the ratio of the mean free path of the escaping atoms to the orifice diameter of the Knudsen cell are shown not to be limiting in this technique. DESPITE the importance of a knowledge of the activity of aluminum in understanding deoxidation equilibria in molten steel, no direct studies have been made of activities in liquid Fe-A1 alloys at steel-making temperatures. Lower-temperature direct studies have, however, been carried out on aluminum-rich liquid alloys by Gross, Levi, Dewing, and Eilson&apos; at 1300°C and by Coskun and Elliott&apos; at 1315°C. Apart from phase diagram calculations by Pehlke, other determinations have been indirect and were made by measurement of the distribution of aluminum between iron and silver475 and combination of these data with extrapolated activities in the Ag-A1 system.~-% ecently, however, Woolley and Elliott have made a significant contribution by directly measuring heats of solution in the Fe-A1 system at 1600°C. The present authorslo have recently employed a Knudsen cell-mass spectrometer technique in a study of activities in iron-based liquid alloys. In this technique activities and heats of solution are determined from a series of measurements of the ratio of ion currents of the components; and since ion-current ratios are used, problems caused by changes in instrument sensitivity or cell geometry are overcome. Results obtained for the Fe-Ni system were found to be in excellent agreement with previous work, thus demonstrating the reliability of the method. The present paper describes a similar study of activities in the liquid Fe-A1 and Ag-A1 systems, this latter system being included in order that a meaningful comparison can be made with the above-mentioned indirect studies. INTEGRATION EQUATIONS A detailed derivation of the equations used to determine the thermodynamic properties from the measured ion current ratios has been given elsewhere;&apos;&apos; however it is useful to summarize them here. By the combination of the Gibbs-Duhem equation with the direct proportionality between ion-current ratios and partial pressure ratios, it was shown that for a binary system at constant temperature and pressure: where al is the activity of component 1 with pure substance as the standard state, N, is the atom fraction of component 2 in the solution, and I; and t&apos;2 are ion currents of given isotopes of the components. The activity coefficient is given by: this latter equation being more suitable for graphical integration. Combination of Eq. [l] with the Gibbs-Helmholtz equation gives an expression for the partial molar heat of mixing: EXPERIMENTAL A Bendix Time-of-Flight mass spectrometer model 12! fitted with a 107 ion source and a M-105-G-6 electron multiplier, was used to analyze the vapor effusing from the Knudsen cell. The arrangement of the Knudsen cell assembly was essentially that of the commercial instrument (Bendix model 1030) but with several modifications. Instead of heating with a single tungsten filament, a cylindrical tantalum-mesh heater was employed. Up to 1400°C simple resistance heating was used but above this temperature electron bombardment between the tantalum mesh and the tantalum cell susceptor was necessary. The temperature was measured by means of a Leeds and Northrup disappear ing-filament type optical pyrometer sighted on an essentially black-body hole in the side of the cell. Details of the temperature control, temperature measurement, and in situ calibration of the optical pyrometer can be found elsewhere.I0 In the investigation of the Fe-A1 system the Knudsen cells were constructed of thoria crucibles with fitted thoria lids (Zircoa). The cells employed in investigating the Ag-A1 alloys were made up of high-purity alumina crucibles (Morganite) with lids of recrystal-lized alumina (Lucalox). The cells were 0.370 in.

Jan 1, 1970

By I. R. Kramer

Studies of the effect of size of the specimen on the change of slopes of Stages I and 11 by surface removal showed that the change of Stage I was independent of size with respect to the polishing rate; however, the change in the slope of Stage 11 with polishing rate increased directly in proportion to the surface area. The removal of the surface during the test affected the plastic deformation characteristics of gold, aluminum, and zinc single crystals and polycrystalline aluminum. The apparent activation energy of aluminum was found to be decreased markedly by removing the surface during the deformation process. In previous papers1-3 it was shown that the surface played an important role in the plastic deformation of metals. By removing the surface layers of a crystal of aluminum by electrolytic polishing during tensile deformation, it was found that the slopes of Stages I, II, and III were decreased and the extents of Stages I and II were increased when the rate of metal removal was increased. By removing a sufficient amount of the surface layer after a specimen had been deformed into the Stage I region, upon reloading, the flow stress was the same as the original critical resolved shear stress and the extent of Stage I was the same as if the specimen had not been deformed previously. The slope of Stage I was decreased 50 pct and that of Stage 11 decreased 25 pct when the rate of metal removal was 50 X 10"5 ipm. These data show that in Stage I the work hardening is controlled almost entirely by the surface conditions, while in Stages 11 and III both surface conditions and internal obstacles to dislocation motion are important. It appears that during the egress of dislocations from the crystal, a fraction of them becomes stuck or trapped in the surface regions and a layer of a high dislocation concentration is formed. This layer would not only impede the motion of dislocations, but would provide a barrier against which dislocations may pile up. In this case, there will be a stress, opposite to that of the applied stress, imposed on the dislocation source and dislocations moving in the region beyond this layer. It has been found convenient to refer to this layer as a "debris" layer. The "debris" layer may be similar to the dislocation tangle observed by thin-film electron microscope techniques.4 Reported in this paper are the results of studies on the effects of removing the surface during plastic deformation on aluminum crystals of various sizes. The effects of the surface on the yield point behavior of gold and high-purity aluminum crystals as well as the creep behavior were also determined. The effects of surface removal on polycrystalline aluminum (1100-0 and 7075-T6) are also reported. EXPERIMENTAL PROCEDURE For those portions of the investigation involving creep and tensile specimens, single crystals, having a 3-in. gage length and a nominal 1/8-in. sq cross section, were prepared by a modified Bridgman technique using a multiple-cavity graphite mold. The single crystals were prepared from materials which had initial purities of 99.997, 99.999, 99.999, and 99.999 pct for Al, Cu, Zn, and Au, respectively. The aluminum specimens for the size effect studies were prepared through the use of a three-tier mold in which crystals having a cross section of 1/8, 1/4, and 1/2 in. were grown from a common seed. The mold design was arranged so that one 1/2-in. crystal, two 1/4-in. crystals, and four 1/8-in, crystals of the same orientation could be cast. With this technique, it was possible to obtain only one set of crystals with the same orientation. Because of this limitation, it was not possible to determine both the changes of extent and slope of the various stages since a large number of crystals of the same orientation would have been required. Instead, only the change of slope as a function of the rate of metal removal was studied by abruptly altering the current density of the electrolytic polishing bath at various strains within the regions of Stages I and 11. The experimental techniques used for the tensile studies were essentially the same as those used previously.1,3 The specimens were deformed in a 200-lb Instron tensile machine, usually at a rate of 10-5 sec-5. A methyl alcohol-nitric acid solution was used as the polishing bath for aluminum. The temperature was maintained constant within ±0.l°C by means of a water bath. The tensile machine was

Jan 1, 1963

By John C. Martin

The discovery of a new gas reservoir demands that the planning of a sottnd well-spacing program be initiated early in the development stage. It is the purpose of this discussion to illustrate by actual field examples the application of basic well-spacing principles, previously developed for oil reservoirs, to the problem of well spacing in natural gas fields. These studies are presented for the field use of geologists and engineers who are concerned with the initial planning of the proper development of the newly discovered gas reservoir. INTRODUCTION The phenomenal growth of a vigorous natural gas industry emphasizes the increasing importance of natural gas as a source of energy, fuel, and raw materials to our nation&apos;s economy. Since 1945 marketed production of natural gas for the U. S. has increased 21/2 times to a record high of 10.6 trillion cu ft during 1957. As major participants in the gas industry, we share an added interest to develop and produce our natural gas reserves with constantly improved efficiency. The subject of well spacing is vitally important to the gas industry, for the well itself plays a significant role in the development of the natural gas reservoir and in control of the recovery process. Maximum utilization of wells is an integral part of sound conservation practices. The discovery of a new gas reservoir demands that careful choice of well location and well spacing be made and that the planning of a sound well spacing program be initiated early an the development stage. With the drilling of the first development well, efforts of the geologist and engineer must be directed toward acquisition of adequate technical evidence upon which a firm recommendation for a spacing program may be based. With this technical appraisal as a foundation, operators and state regulatory agencies jointly can go far in providing a framework for sound development of gas fields to achieve a program of conservation that avoids the unnecessary well. WELL-SPACING CONCEPTS Through laboratory and field investigations of the mechanism of the recovery of oil and gas, of fluid behavior, and of effective control of reservoir and well, a crystallization of ideas regarding reservoir behavior has emerged as a well-developed technology. Associated with a better understanding of the fundamental principles underlying reservoir and well behavior has been the growth of concepts concerning the role of wells and their spacing in the development and operation of an oil or gas reservoir. In addition to serving as outlets for the withdrawal of fluids from the reservoir, wells are recognized as having two other important functions: (1) providing access to the reservoir to obtain information concerning the characteristics of the reservoir and its fluids, and (2) serving as a means by which the natural or induced recovery mechanism may be effectively controlled. Beyond a minimum number of wells required to fulfill these two functions, additional wells will not increase recovery. With particular emphasis upon well spacing in oil reservoirs, many studies of the well spacing-recovery relationship have evolved the concept that the ultimate oil recovery is essentially independent of the well spacing.&apos; These fundamental concepts are no different when regarding the role of wells and their spacing in the natural gas reservoir. They are equally applicable to the consideration of well spacing in gas reservoirs. For the gas reservoir, the problem of well spacing then revolves around the question of drainage and the degree or extent to which a well may drain gas from its surrounding reservoir environment. Theoretical and Experimental Work During the past 30 years, theoretical and experimental work carried on to study the physical principles involved in the flow of fluids through porous media has shed light upon the matter of drainage. Fundamental mathematical equations have been derived to describe the mechanism of flow of oil and gas through porous rocks. With the recent advent of high-speed digital computers, attempts have been made with mounting success to develop solutions, employing numerical techniques, to mathematical expressions that describe more rigorously the physical behavior and mechanism involved in the unsteady-state flow of compressible fluids, such as a gas, through porous rock. In 1953, Bruce, Peace-man, Rachford and Ricez published a stable numerical procedure for solving the equation for production of gas at constant rate. The results of these calculations are significant with respect to this matter of drainage, for they indicated (1) that depletion of the gas reservoir resulted in a drop in pressure at the extremity of the

By Nicholas J. Grant, John S. Benjamin

A series of composite alloys containing a high volume of NiAl, Ni3Ah or CoAl, bonded with 0 to 40 vol pct of a ductile metal phase, were prepared by powder blending and hot extrusion. The binder metals were of four types: pure nickel or cobalt, near saturated solid solutions of aluminum in nickel and cobalt, type 316 stainless steel, and niobium. Sound extrusions were obtained in almost all instances. Studied or measured were the following: interaction between the alunzinides and the binders, room-temperature modulus of rupture values, 1500° and 1800°F stress rupture properties, hardness, structure, and oxidation resistance. Stable structures can be produced for 1800°F exposure, with interesting high-temperature strength and good high-temperature ductility. Oxidation resistance was excellent. A large number of experimental investigations have been made of the role of structure on the properties of cermets and composite materials. Gurland,1 Kreimer et al.,2 and Gurland and Bardzil3 have indicated the preferred particle size in carbide base cermets to be about 1 µ, with a hard phase content of 60 to 80 vol pct. The optimum ductile binder thickness was noted to be 0.3 to 0.6 µ.1 Complete separation of the hard phase particles by the binder is important in reducing the severity of brittle fracture.&apos; The purpose of the present study was to produce structures comparable to the conventional cermets, using a series of relatively close-packed intermetal-lic compounds rather than carbides as the refractory hard phase, and to study the effects of binder content and composition on both high- and low-temperature properties. The selected intermetallic compounds were particularly of interest because of the potential they offered in yielding room-temperature ductility. The highly symmetrical structures are known to possess high-temperature ductility and room-temperature toughness. Based on a ductile binder, the alloys were prepared by the powder-metallurgy route to avoid melting and subsequent alloying of the matrix, and were extruded at relatively low temperatures. It was expected that the composite alloy would retain useful ductility. In contrast, infiltration and high-temperature sintering led to alloying of the matrix and to decreased ductility. The systems Ni-A1 and Co-A1 were selected for this study. In the Ni-A1 system the compounds NiA1, having an ordered bcc B2 structure, and Ni3Al(?1), having an ordered fcc L12 structure, were chosen. In the system Co-A1 the intermetallic compound CoAl with an ordered bcc B2 structure was used. ALLOY PREPARATION The intermetallic compounds, see Table I, were prepared by using master alloys of Ni-A1 and CO-A1, with additions of either cobalt or nickel to achieve the desired compositions. The master alloy in crushed, homogenized form, was melted with pure nickel or cobalt in an inert atmosphere, cold copper crucible, nonconsumable tungsten arc furnace. The resultant intermetallic compounds were homogenized at 2192°C in argon, crushed, and dry ball-milled in a stainless mill to -100 and -325 mesh for the Ni-A1 compounds and to -325 mesh for the CoAl compound. Finer fractions were separated for some of the composite alloys. Several ductile binders were utilized. These included Inco B nickel, 5µ ; pure cobalt, 5 µ, from Sher-ritt Gordon Mines, Ltd.; fine (-325 mesh) niobium hydride powder; fine (15 µ) type 316 stainless-steel powder; and near-saturated Ni-A1 and Co-A1 solid-solution alloys, also in fine powder form. The niobium hydride was decomposed above about 700°C in processing of the compacts in vacuum to produce niobium powder. The Ni-7.1 pct A1 and the Co-5.3 pct A1 solid-solution alloys were prepared from pure nickel or cobalt and pure aluminum by nonconsumable tungsten arc melting under an inert atmosphere. The ingots were homogenized, lathe-turned to fine chips, and dry ball-milled in air to -325 mesh powder. These solid-solution alloys are designated NiSS and CoSS; see Table I. Subsequently the hard and ductile phases were dry ball-milled as a blend. Experiments clearly established the need to coat the hard particles with the ductile binder to optimize subsequent hot compaction by extrusion. Ordinary dry mixing usually resulted in nonhomogeneous alloys which were quite brittle. Conventional cermets are consolidated by liquid phase sinteiing or infiltration, which resulis in undesirable and uncontrolled alloying of the binder phase. For this study, a loose (unsintered) powder-extrusion process was emploved, minimizing reactions between binder and hard particle, thereby permitting much greater control of composition and structure. The constituent powders were first mixed in the desired

Jan 1, 1967

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By H. C. Chao, L. H. Van Vlack

Small MnS inclusions with known crystallographic orientations were placed inside powder compacts of low-carbon steel. After the metal was axially campressed with negligible end friction, the deformstions for the metal and the inclusions were compared. The MnS inclusions deformed more when the [100] direction was aligned with the compression axis than when the [111] direction was parallel to this axis. The deformations of the inclusions in the two principal radial directions were equal for each of the above orientations. Inclusions with [110] compression alignments did not deform with radial symmetry. The relative deformation of the inclusion and metal was closely dependent upon the relatiue hardness of the two phases. The relative deformation of the two phases was not sensitive to the rate of deformation. RECENT studies by the authors1.&apos; suggested that the plastic deformation of MnS in steel would probably be highly sensitive to the orientation of the inclusions and to the temperature of the metal. This paper reports an investigation of these factors upon MnS behavior within steel. Manganese sulfide (MnS) possesses an NaCl-type structure and typically has extensive (l10) {110} slip as a separate (noninclusion) crystal.&apos; A secondary slip system, ( l 10) { l l l}, has also been observed where the major slip system is restricted. In general, MnS inclusions must be rated as a highly deformable second phase.3 The amount of sulfide deformation varies, however, with several composition and processing factors. Some of these have been only partially assigned. For example, it is known that minor amounts (<0.01 pct) of silicon within free-machining steels will increase the amount of MnS deformation,4 but the mechanism of the added deformation can only be surmised at the present. Manganese sulfide and steel have sufficiently comparable deformation characteristics so that slip which is started in steel may be continued through the sulfide inclusions and back into the steel if the crystal orientations are favorable.5 A more detailed discussion of previous work on the plastic deformation of NaC1-type crystals and on the plastic deformation of inclusions within a metal is given in Chao&apos;s work.6 EXPERIMENTAL PROCEDURE The manganese sulfide which was used in this study was prepared by previously described methods.&apos; Single crystals of MnS, both as cleavage cubes and as spheres, were oriented within steel powder compacts so that the desired crystal directions were parallel to the direction of axial compression. A four-stage hydrostatic compaction procedure was used and involved the following steps. In the first stage part of the powder was placed in a metal die 1 in. in diameter with a thick (1 in. OD, 5/8 in. ID) rubber liner which had one end plugged. The steel powder was hand-rammed, making it as dense as possible before placing a carefully sized MnS crystal (either as a sphere or as a cube) near the center. The crystal was oriented with the chosen direction vertical; viz., [001], [011], or [111], with the aid of a X10 microscope. A pair of tungsten wire threads 0.020 in. in diameter was inserted along the side of this (&apos;core compact" to locate the desired plane after the compression tests. After the crystal was positioned in the center of the die, more powder was added and carefully rammed by hand. The die was then capped with a rubber plug of the same hardness and thickness as that of the liner. The whole assembly as shown in Fig. 1 was compacted by a ram load of 54,000 lb (about 70,000 psi). In the second stage a smaller, 3/4-in, rubber-lined die was used to give a stress of approximately 120,000 psi. The above process was repeated with the initial compact serving as a core for a larger compact. The final product after sintering was a cylinder 1 cm long and 1 cm in diameter, having a density of 7.54 g per cu cm. This was close to the theoretical density since the metal contained a non-metallic phase. There was no evidence of MnS deformation during the hydrostatic compaction or subsequent sintering. Elevated-temperature hardness data were obtained by procedures previously described.2 Compression tests for inclusion deformation utilized the cylinders which were described above. The critical problem in these tests was the lubri-

Jan 1, 1965

By J. T. Norton, Joseph Gurland

IN spite of the extended use and high state of practical development of the cemented tungsten carbides, the structure of these alloys is still a matter of considerable controversy. The characteristic high rigidity and rupture strength of sintered compacts have been attributed to a continuous skeleton of tungsten carbide grains, formed during the sintering process. This view is based mainly on the work of Dawihl and Hinnuber,1 who reported that a sintered compact of 6 pct Co maintained its shape and some of its strength after the binder was leached out with boiling hydrochloric acid. After leaching, only 0.04 pct Co was reported to remain in the compact. They also showed that the assumed increasing discontinuity of such a skeleton, as the cobalt content is increased, could be made to account for the observed discontinuous increase of the coefficients of thermal expansion, the loss of rigidity, and the impaired cutting performance of alloys of more than 10 pct Co. Contradictory evidence was cited by Sanford and Trent,&apos; who mentioned that a sintered compact was destroyed by reacting the binder with zinc and leaching out the resulting Zn-Co alloy. The skeleton theory also does not account for the observed change of strength of sintered compacts as a function of cobalt content. If the skeleton is responsible for the strength, the latter would be expected to decrease with increasing binder content. Actually, the strength increases and reaches a maximum around 20 pct Co. In addition, tungsten carbide is brittle and undoubtedly very notch sensitive. The highest value found in the literature for the transverse rupture strength of pure tungsten carbide prepared by sintering is 80,000 psi.3 herefore, such a skeleton does not easily account for a rupture-strength value of 300,000 psi and higher, commonly found in sint.ered tungsten carbide-cobalt compacts. In view of the conflicting data present in the literature, experiments were undertaken to determine whether the sintering of tungsten carbide-cobalt alloys leads to the formation of a carbide skeleton or whether the densification behavior and the properties of cemented compacts are consistent with a structure of isolated carbide grains in a matrix of binder metal. The specimens were prepared from powders of commercial grade. Tungsten carbide powder ranged in particle size from 0 to 5x10-4 cm. Mixtures of tungsten carbide and cobalt were ball milled in hexane for 48 hr in tungsten carbide lined mills. After milling, the specimens were pressed in a rectangular die (1x1/4x1/4 in.) at 16 tons per sq in. NO pressing lubricant was used. Sintering of the tungsten carbide-cobalt compacts was carried out in a vertical tube furnace equipped with a dilatometer (Fig. I), by means of which the change of length of the powder compacts could be followed from room temperature to 1500°C. An atmosphere of 20 pct H, 80 pct N was maintained inside the furnace. Decarburization of the samples was prevented by the presence of small rings of graphite inside the furnace tube. The temperature of the sample was measured by a platinum-platinum-rhodium thermocouple, which also was part of a temperature control system able to maintain a constant temperature within ±100C. Pure tungsten carbide compacts were prepared by sintering the carbide without binder or by evaporating the binder from sintered compacts in vacuum at 2000°C. Since complete densification of these samples was not desired, they were sintered only to 60 or 80 pct of the theoretical density of tungsten carbide. The specimens were prepared for metallographic examination by polishing with diamond powders and etching with a 10 pct solution of alkaline potassium ferricyanide. Cobalt etches light yellow and the carbide gray. The amount of porosity is exaggerated since it is difficult to avoid tearing out carbide particles, especially from incompletely sintered samples. Experimental Observations A number of specific experiments were carried out in order to study some particular aspect of the sintering problem. The details of these experiments, together with their results, are as follows: Electrolytic Leaching: The binder was removed by electrolytic leaching from sintered tungsten carbide-cobalt compacts for the purpose of determining the continuity of the carbide phase. The method used was based on the work of Cohen and coworkers4 on the electrolytic extraction of carbides from annealed steels. If the sample is made the anode, using a 10 pct hydrochloric acid solution as the electrolyte, the binder is dissolved, but the rate of solution of tungsten carbide is negligible. A current density of 0.2 amp per sq in. was applied. As shown in Fig.

Jan 1, 1953

By A. S. Yue

The movphology of the Mg-32 wt pct Al eutectic has been studied as a function of freezing- rate and temperature gradient. At slow freezing rates a lamellar eutectic was formed; whereas, a rod-like eutectic was generated at fast rates. The inter-lamellar spacing increased as the freezing rate decreased in aggreement with theoretical predictions. Lamellar faults, morphologically similar to edge dislocation models in crystals, were responsible for the subgrain structures in the eutectic mixture. A linear increase in fault density with freezing rate was observed. Fault concentl-ations of the order of 10 per sq cm for a range of freezing rates from 0.6 to -3.0 x 10 cm per sec were estimated. The transformation from lamella?, to rod-like morphologies was determined experimentally to be dependent on the freezing rate and independent of the temperature gradient. Moreover, the number of rods formed per- unit cross-sectional area increased exponentiallv with increasing freezing rote. BRADY&apos; and portevin2 classified eutectic structures into lamellar, rod-like, and globular according to the morphology of the solid phases present. Although this classification is quite descriptive, very little has been reported on the details of the mechanism by which the eutectic structures are formed. Recent work by Winegard, Majka, Thall, and chalmers3 and by chalmers4 on lamellar eutectic solidification suggest that the maximum thickness of the lamellae decreases with increasing rate of solidification due to inadequate time for lateral diffusion. scheilS and Tiller&apos; have shown theoretically that the lamellar widths indeed depend on the solidification rate. However, there has been no experimental evidence to support the theory. Chilten and winegard7 have studied the interface morphology of a eutectic alloy of zone-refined lead and tin. They found that the lamellar width decreased as the freezing rate increased in agreement with the theoretical predictions of scheils and Tiller.&apos; More recently, Kraft and Albright&apos; have investigated the microstructures of the A1-CuA12 eutectic as a function of growth variables. They observed lamellar faults present in the lamellar eutectic, similar to edge dislocation models in crystals. Furthermore, Kraft and Albright reported that they could not designate which extra lamellar was responsible for the formation of a lamellar fault even under electron microscopic magnification. In this paper, the morphology of the Mg-A1 eutectic structure is described. The effects of freez- ing rate on the interlamellar spacing and on the lamellar fault density are presented in detail. The transformation from lamellar to rod-like eutectics is discussed in terms of the freezing rate and the temperature gradient. EXPERIMENTAL PROCEDURE The experimental details of alloy preparation, the decanting mechanism and the determinations of the freezing rate and the temperature gradient have been reported elsewhere. Measurements of plate-edge angles were made with a microscope. The true angles used to determine the interlamellar spacings were determined by a two surface analysis technique.&apos;&apos; Since the decanted interface structure does not represent the true eutectic morphology on the solid,g all measurements were made from an area in the solidified bar behind the interface. Measurements of the apparent interlamellar spacings between the two phases of the eutectic were made on a photographic negative by means of a calibrated magnifier. Each value listed in Table I represents the average of thirty measurements on one negative. In general, these measurements are approximately equal with an error of less than pct. The average rod diameter for each specimen was also measured on a magnified photomicrograph. Each value of the diameter represents the average of fifty measurements. RESULTS AND DISCUSSION The experimental observations and their discussion to be presented here are restricted to the morphology of the eutectic structure and to the effects of the freezing rate and the temperature gradient on the solidification of eutectics. INTERLAMELLAR SPACING It has been shown previouslyg that the micro-structure of the decanted interface and the longitudinal section of the Mg-A1 eutectic is characterized by the presence of both lamellar and rod-like morphologies. The lamellae become more regular as the freezing rate is decreased. A three-dimensional photomicrograph representing a perfect lamellar morphology is illustrated in Fig. 1. The lamellae of the top and longitudinal sections of the specimen are regularly spaced while those in the transverse section are not quite straight and parallel. Their parallelism is slightly distorted because fault lines producing a discontinuity are present. A method for calculating the interlamellar spacings A, is described in Appendix 1. The true

Jan 1, 1962