Search Documents

By E. S. Bumps, M. Baeyert, W. F. Craig

SOME time ago during a study of impact properties of tempered martensite,1 it was postulated that the consistently good ductility of tempered martensite might be caused by its relatively small and peculiarly shaped ferrite grains. The fer-rite grains of tempered martensite have approximately the same size and shape as the martensite "needles." Thus they form an interlocking mass of needle-shaped grains quite different from equiaxed or lamellar ferrite grain structures. When the common mechanical test methods are applied to steel, variations are often observed in the ductility of specimens that have closely similar hardness and tensile strength values. The ductility so measured appears to be structure dependent. When steel from the same heat has been heat treated to produce different structures with the same hardness, the elongation and reduction of area values from the tensile test and the transition temperature determined by the notched-bar impact test vary according to whether pearlite, tempered martensite, or other structural constituents were produced by the heat treatment. It has been widely recognized that tempered martensite gives a consistently good performance, when tempered to the same hardness as many other structures with which it has been compared. In recent years the isothermal transformation of austenite to specific structural products and the quantitative evaluation of the character of these products with respect to their nature and response to deformation has received considerable attention. The objective of the present study was to pursue somewhat further the dependence of ductility upon structure; specifically, it was desired to ascertain whether ferrite grain structure, including both shape and size of the grains, can account for the consistently good performance of tempered martensite in the notched-bar impact test. It was thought that a simple experiment would indicate whether the ferrite grain structure plays any part in the good ductility exhibited by tempered martensite in contrast to other steel structures with different types of ferrite grains. By determining the impact transition temperature, it was proposed to compare spheroidites having similar carbide particle size and spacing but obtained in such a manner that their ferrite grain structures would be very different. Spheroidite obtained by tempering martensite, with its small, needle-shaped grains, was to be compared with spheroidite from pearlite. If the latter is produced by sub-critical annealing, the ferrite grains correspond to the pearlite colonies. Thus, if the pearlite was not too coarse, the ferrite grains of spheroidite from pearlite are equiaxed in contrast to the needle-shaped grains of spheroidite from martensite. It was thought that the ferrite grain structure of spheroidite from martensite might depend to some extent upon the grain size of the prior austenite. The austenite grain boundaries limit the maximum attainable size of the martensite needles and thus of the ferrite grains in the derived spheroidite. In order to evaluate any possible influence of prior austehite grain size, spheroidites were to be prepared from martensites that had been formed from fine-grain austenite and also from coarsened austenite. As the carbide particle size and distribution were to be essentially alike in the various spheroidites, the difference would be in the ferrite grain size and shape. Thus any marked difference in transition temperature could be attributable to the character of the ferrite grain structure. There are certain considerations in assuming that these spheroidites would be equivalent in all respects except ferrite grain structure, and an attempt was made to take them into account. One of the considerations was the choice of the carbon content of the steel. An approximately eutectoid steel was selected for two reasons. First, the pearlitic structure would contain no proeutectoid ferrite which might complicate the picture by producing a non-uniform ferrite grain structure in the resulting spheroidite. Then, too, the high-carbon content would inhibit ferrite grain growth during the sub-critical treatment. Another factor to be taken into account was the choice of an alloying element to assure a martensitic structure throughout on quenching the impact specimens. Nickel was chosen, because it is a common alloying element and resides in the ferrite both upon its formation from austenite and throughout tempering. The formation of alloy carbides, or even a large solubility of the alloying element in cementite, would have complicated the interpretation by changing the composition of the ferrite .during spheroid-ization. The possibility of temper brittleness was minimized insofar as possible by using a tempering temperature as high as consistent with the 1 pct of nickel in the steel, namely, 1150°F. While it certainly is not claimed that no difference other than ferrite grain structure could exist between the spheroidites, nevertheless, reasonable precaution has been exercised within the limits of steel metallurgy. It is believed that any large difference in transition temperatures would reflect the difference in ferrite grain structure and that relatively good ductility in the spheroidites from mar-

Jan 1, 1951

By Jei Y. Choi, P. G. Shewmon

The surfrrce-diffusion coefficients (DJ for Aulg8 on (100) and (111) surfaces of copper have been determined between 1050" and 780°C using a new avuzlysis imd experimental procedure. The results are: D, has also been determined fm cua4 at 870°C, and the values found are 4.5 times larger than those measured by the grain boundary grooving technique for the same surface orientations. This difference is felt to result from the approximate nature of the mathematical solution used in the present work. Attempts to measure D, for silver on copper and silver surfaces indicated a means of matter transport different from surface diffision was dominant in moving tracer from the source out over the surface. Cnlculations and experiment both indicate that this is the flow of silver through the vapor phase which completely masks the much smaller flow due to surface diffusion. The previous self-difhsion studies of D, for silver and copper are discussed in terms of our own analysis and found to yield values of D, factors of lo5 or more greater than those found by the grain boundary grooving tech -nique. UNTIL about 5 years ago it was widely believed that the activation energy for surface diffusion, AH, , was less than that for grain boundary diffusion, AHb,, which in turn was less than that for diffusion through the lattice, AHz.' This was concluded from various evidence that D,> Db>Dl, and one tracer study of D, for silver on silver from which AH, was inferred.2 In 1959 Mullins and Shewmon demonstrated that D, could be determined from the kinetics of the growth of grain-boundary grooves.3 Using this procedure, Gjostein measured D, on copper between 800" and 1050°C and found that the activation energy was roughly equal to AHl .4 Subsequent work on copper,5" silver,',' and goldg between the melting temperature T, and 0.87 T, confirmed that AH, as determined using the grain boundary grooving or scratch-relaxation technique was equal to or greater than AHz. During the same period, Drew and Pye again determined AH, for silver on silver using a tracer techniquelo and a mathematical solution similar to that of Nicker son and arker.' Though the values of D, Drew and Pye measured at any given temperature were about 200 times smaller than those reported by Nickerson and Parker, they again found a low activation energy of about 10 kcal, or about one fifth that found at the higher temperatures with the mass transport technique. A distinguishing characteristic of these two previous tracer studies is that they have worked at low temperatures (-1/2 T,) where they felt volume diffusion was negligible and then analyzed these data as if all tracer atoms leaving the source flowed out into and remained in a homogeneous high-diffusivity surface layer of undefined thickness. This is totally different from the model used in the mass-transport studies or the studies of grain boundary diffusion, which assume the high-diffusivity surface layer to be only a few angstroms thick. If this latter model is applied to the earlier tracer studies, it is shown that the tracer has really pe!etrated into the lattice a mean distance of 1000A. Thus the tracer distribution observed after an anneal is thought to be due to the combined effects of surface and volume diffusion. Independent of the relative validity of the two models, it seems evident to us that any comparison of the values of D, as determined in these two ways is meaningless and misleading, since the values of D, and AH, obtained in these two ways would be totally different for the same physical distributions of tracer. Once the fundamental difference in the approaches of the two techniques is established, we are faced with the question of which model better approximates physical reality. Here all the evidence seems to be on the side of the ''thin surface layer" analysis. In fact, the authors of Refs. 2 and 9 do not argue for the "thick-layer model" we have described; they simply invoke it through the equation they use to calculate D, . The primary evidence for the thin-film approach is: a) grain boundary grooves and scratches widen in proportion to tU4 and Mullins' rigorous analysis shows that this is only valid for a surface layer which is quite thin relative to the width of the groove;11 b) all accepted or seriously discussed models of solid-vapor interfaces and high-angle grain boundaries assume that the disturbed region of the interface is at most a few a0 thick. With the above in mind, it was desirable to determine D, using a radioactive tracer and a "thin-

Jan 1, 1964

By A. Bauer, P. Calder, N. H. Carr, G. R. Harris

Since both rotary and jet piercing drills are used by the Iron Ore Co. at Smallwood, it is often desirable in planning to know in which regions of the orebody or new orebodies a particular drill will be the most economic. This makes it necessary to establish a correlation between drillability and pierceability and some physical rock properties. For rotary drills a good correlation was found with penetration rate and grinding factor index. The jet piercers were found to have a reciprocal relationship in the sense that the best rotary ground was the worst jet ground and vice versa. It is also indicated how an economic comparison could be made using these penetration rate versus grinding factor index curves, the hole size distribution curves for single pass and chambered holes and the mine distribution curve for grinding factor index. A discussion is presented on the fuel oxygen ratios to be used in jet piercing and on the site gas sampling and analysis which has been used to set up the drills. The fuel has been cut back so that stoichio-metric conditions exist, carbon monoxide is drastically reduced and pop-up or exploding holes eliminated. No decrease in penetration rate has been observed contrary to the published results of previous workers. The blasting procedure and results at Smallwood are discussed and the operation of Iron Ore Co.'s slurry pump-mix truck is also described briefly. Smallwood mine is part of the Iron Ore Co.'s Carol Lake operation and is situated in Labrador, 240 miles north of Sept-Iles, Quebec. Last year 15 million tons of crude ore were crushed to yield 6.3 million tons of concentrate and pellets. This year the figures will be 17 million tons of crude and 7% million tons of concentrate and pellets which is the full plant capacity. Carol Lake ores consist primarily of specularite and magnetite mixed with quartz. For convenience the ore has been split-into the following classifications depending on the percentage of magnetics in the sample, shown in brackets: specularite (0 to 10%), specularite-magnetite (10 to 20%), magnetite- specularite (20 to 30%), magnetite (>30%). The order of classification also represents the order of increasing grinding difficulty - the specularite generally being the easiest and the magnetite the hardest. The orebody also contains a small percentage of waste materials consisting of limonite carbonate, quartz carbonate and quartz magnetite. The first two materials are among the softest in the mine, generally softer than the specularite, and the quartz magnetite is amongst the hardest. The bulk of the material in the mine is of the specularite-magnetite and magnetite-specularite classifications. As a result of test drilling at Smallwood in 1960 with rotary, jet and percussion drills, the Iron Ore Co. purchased four JPM-4 jet piercers for the bulk of production drilling and set up an oxygen plant to supply 20 tons of oxygen per day. This oxygen is sufficient for two machines operating full time and one part time. In addition, there are two 50-R, one 60-R and one 40-R machines in use. The benches are 45 ft high and 50 ft holes are generally drilled. JET DRILLING At the onset of jet drilling in the late fall of 1962, two major problems were encountered: 1) freezing due to winter operations; experience and the use of heat at more places, such as the rotary head, has eliminated this,'" and 2) exploding or "popping" drilled holes; this happened frequently (several holes "popping" each day) and was the cause of two lost time accidents. In one instance a hole was being measured with a tape which fell down the hole causing it to "pop." Safety glasses though pulverized saved the wearer's eyesight. Various methods were then employed to detonate the holes before measuring or loading (dropping lighted rags of fusees down, or sparking across a spark gap). These methods were time consuming and far from completely successful. Consideration was given to the fuel oxygen ratio on the machines and what this would produce in the way of product gases. A fuel oxygen weight ratio of 0.35 which was quite oxygen negative was being used. Theoretically appreciable carbon monoxide would be produced at this fuel oxygen ratio. On the close down procedure of the jet which calls for low oxygen after flame out, oxygen would be left in the hole along with this carbon monoxide. This is an explosive mixture. The fuel oxygen ratio was cut back to stoichiometric

Jan 1, 1967

By Jun Hino, P. G. Shewmon, P. A. Beck

THE investigations of Crussard,' of Guinier and Tennevin,' and of Dunn and Daniels," indicate that the subgrains formed in a cold worked and annealed metal are capable of growing at each other's expense during annealing, if the temperature of annealing is sufficiently high and the time is long enough. The results of Dunn and Daniels are particularly convincing in showing that subgrain growth is essentially the result of the free surface energy associated with the subboundaries. In subgrain growth, as in ordinary grain growth, energy is gained as a result of the decrease in total subboundary surface area per unit volume. Recently, Wood and Scrutton4 found that the rate of subgrain growth upon annealing increased very considerably, if simultaneously a creep strain was applied to the specimen at a low strain rate. Working with 99.98 pct pure fine-grained aluminum, these investigators found that the continuous X-ray diffraction back-reflection rings of material strained at room temperature remained continuous after heating for ten days at 250 °C. However, when heated at the same temperature under a stress of 1000 psi even for only three days, the formerly continuous X-ray diffraction rings broke up into numerous dots, which were fairly clearly separated from each other. The continuous X-ray diffraction rings were interpreted as indications of a very small subgrain size, not resolved by the X-ray diffraction method used. The breaking up of the continuous X-ray diffraction ring during annealing under stress was taken as an indication of a great increase in subgrain size, so that the individual subgrains could then be resolved. The effect of simultaneous strain at a low strain rate in accelerating subgrain growth, discovered by Wood and Scrutton and designated by them as "cell growth," is of fundamental importance. The experiments described in this note were carried out in order to confirm Wood and Scrutton's results by direct metallographic observation. Also, information was sought as to the minimum creep strain necessary to produce this effect. A fine grained high purity aluminum strip was prepared by alternate 33 pct rolling and annealing treatments for 1 hr at 350°C. Specimens cut from this strip were subjected to a relatively fast creep strain of 7.2 pct in 3.5 min at 300°C under a constant load initially corresponding to 1185 psi. The subgrains set up were large enough (about 0.015 to 0.03 mm) to be clearly observed (Fig. 1) at X200 magnification with polarized light, after electrolytic polishing and anodic etching, producing a fine oxide film." The corresponding X-ray diffraction pattern is shown in Fig. la. After the fast creep strain treatment a portion of the specimen was subjected to a creep strain of 8.3 pct in 44 hr at 350°C under a constant load initially corresponding to 320 psi. Another portion, annealed under the same conditions, but not strained, served as control specimen. The subgrain size of a typical area of the specimen annealed under strain and of the one annealed without strain is shown in Figs. 2 and 3 (X-ray diffraction patterns, Figs. 2a and 3a). Annealing without strain produced clearly observable subgrain growth (subgrain size: about 0.03 to 0.05 mm). The effect of simultaneous strain was to increase greatly the rate of subgrain growth (resulting in a subgrain size of approximately 0.05 to 0.13 mm), in accordance with Wood and Scrutton. In another experiment, the effect of the amount of simultaneous strain was studied. The initial subgrain structure was set up by fast creep, as described previously. The specimen was then heated at 350 °C under a constant load initially corresponding to 320 psi, as above, for 2.2 hr (0.24 pct strain), and 8.8 hr (0.58 pct strain). Comparison with the corresponding unstrained control specimens by means of X-ray diffraction showed that 0.58 pct strain definitely had an effect, but the effect of 0.24 pct strain was doubtful.

Jan 1, 1953

By J. T. Norton, J. G. McMullin

The ternary system of gold-silver-copper is characterized by a solid solubility gap and a two phase region in which copper-poor and silver-poor phases coexist. At about 30 pct gold, the two phases become mutually soluble at temperatures below the melting temperature. As the gold content is increased, the solubility temperature of the alloys decreases until at about 80 pct gold, the two phases are soluble down to the lowest temperature at which the alloys will recrystallize. Although the general form of the two phase region is known, its boundaries do not seem to have been investigated extensively. In an X ray diffraction study, Masing and Kloiberl have outlined the boundaries of this two phase field at 400 and 750°C. Using only microscopic techniques, Pickus and Pickus2 determined a vertical section of the ternary diagram showing the 14 kt alloys (58.3 pct gold). These two reports are riot in complete agreement. It has been shown3 that some of the ternary alloys are susceptible to age hardening and that the hardening is caused by the separation of a homogeneous alloy into two phases at the aging temperature. While the gold-copper binary system is an outstanding example of super lattice formation, Hultgren4 has shown that a few per cent of silver added to gold-copper destroys the tendency for ordering. Because of the age hardening possibilities of these alloys, it seemed advisable to investigate the boundaries of the two phase field more in detail using an X ray diffraction method, so as to permit a better understanding of the aging phenomena and enable predictions as to the behavior of other alloys to be made. This is especially true for the 18 kt alloys (75.0 pct Au) at the lower temperatures since they are known to exhibit age hardening. Twelve ternary alloys were prepared having the compositions shown in Table 1 and graphically in Fig 1. The gold used was fine gold bars supplied by Handy and Harmon. The silver was a bar of high purity silver from the U. S. Bureau of Standards. The copper was a bar of vacuum-treated, high conductivity copper from the National Research Corporation. The pure metals in the form of powder were weighed out in proper proportions and melted in graphite in a high frequency induction vacuum furnace. They were heated to 1100°C and slowly cooled. The ingots were then removed from the crucible, inverted, returned to the crucible and remelted. This remelting procedure was intended to reduce segregation in the ingots. After remelting, the ingots were checked for weight loss. The weight loss in each ten gram ingot was held to less than 25 mg. The remelted ingots were cold rolled and then given a homogenizing heat treatment of 16 hr at 760°C to remove any remaining segregation. Powder specimens were prepared by cutting the ingots with a fine file, one half the required amount of powder being taken from each end of the ingots. When the X ray diffraction pattern showed any difference in lattice constant between the ends of the ingot, the ingot was remelted and given an additional homogenization treatment. All powder samples were sealed in evacuated pyrex tubes for heat treatment. Ordinary pyrex proved satisfactory for temperatures up to 650°C but above that temperature it was necessary to use a special high temperature pyrex glass. Annealing at temperatures below 500°C was done in a salt bath whereas for temperatures of 500°C and above an electric muffle furnace was used. In both furnaces the temperature control was ± 5°C. In all annealing treatments samples of cold worked powder were placed in a furnace which was already at temperature. In this manner the specimens recrystallized directly to the equilibrium structure for that temperature. Time at temperature was selected so as to allow complete recrystallization, but very little grain growth. Specimens were quenched from the annealing temperatures by breaking the pyrex tubes in cold water. X ray diffraction photograms were made of all the heat treated powders using copper radiation and a Phragmen

Jan 1, 1950

By W. W. Mullins, F. A. Nichols

Solutions are developed, assuming surface diffusion and both internal and external volume diffusion, for the relaxation of bodies slightly perturbed from spherical and cylindrical geometries. Combined with those previously published for the nearly planar case, these results provide a means of gaging the relative contributions of the two diffusional proc-cesses in any given case. It is shown that in all sintering experiments to date, and probably in any attainable in practice, surface diffusion has played the dominant role, although most previous authors have assumed otherwise. It is also shown that surface diffusion predominates in normal field-emission tip blunting and also for the coalescence of gas bubbles introduced into metals by a bombardment. The surface-diffusion solutions for a perturbed sphere are combined with previous results for volume diffusion to show that the inclusion of interface diffusion permits considerably larger spheres to develop in diffusion-controlled precipitate growth before the onset of instability. A mechanism is also proposed for the spheroidization of precipitate platelets as well as rods. In a previous paper1 the relaxation of a nearly plane surface to flatness by the combined action of the transport processes of viscous flow, evaporation-condensation (in a closed system), volume diffusion, and surface diffusion has been analyzed under the assumption that all surface properties are independent of orientation. In this treatment, criteria were developed for deciding which process predominates, and solutions valid in the latter stages of the sintering of small wires and particles to a plane were obtained. A numerical solution, valid throughout the entire particle-sintering process for the case of surface diffusion, was subsequently obtained by the present authors.' It was found that the analytic solution (which assumed small slopes everywhere) is accurate to within -10 pct when the maximum slope of the profile is less than 0.3; the wire-sintering problem has also been solved nu- merically for the case of surface diffusion and here again the results converge to the analytic small-slope solution at late stages of the process, the two solutions agreeing in this case to within 10 pct when the maximum slope of the profile is less than -0.6. The purpose of this paper is to extend the perturbation solutions to nearly spherical and nearly cylindrical geometries. We treat only the two principal diffusional processes, i.e., surface and volume, but for these geometries we discuss volume diffusion both inside and outside of the solid. Our results, when coupled with Mullins' solutions1 for nearly planar surfaces, provide criteria for gaging the relative contributions of surface and volume diffusion to the over-all transport process in three basic geometries. A very interesting feature in the cylindrical case is the occurrence of instability for longitudinal perturbations with wavelengths greater than the cylindrical circumference, a classical result. This instability of the cylindrical surface is applied to give a quantitative explanation for the often-observed "erratic" pore closure in the late stages of the sintering of wire compacts; also, the theory previously presented for the spheroidization of rod-shaped precipitates by surface (interface) diffusion' is expanded now to include volume diffusion inside and outside of the particle. The results for circumferential perturbations on a long cylinder allow quantitative estimates for gaging the relative importance of surface or volume diffusion in the early stages of the sintering of spheres or wires. The results here demonstrate clearly that surface diffusion has played a very important, if not dominant, role in all sintering experiments discussed in the literature, although the surface-diffusion contribution to the kinetics has usually been ignored. The results for the sphere (surface-diffusion case) are added to the results obtained previously by Mullins and sekerka3 concerning instabilities of a growing spherical precipitate particle (with interface diffusion disallowed) to obtain a general solution to this problem including interface diffusion. The inclusion of interface diffusion is found to increase significantly the range of stability of a growing spherical precipitate for typical metallurgical cases. The following assumptions are made: (i) the initial surface lies everywhere near and has a slope differing only slightly from that of the reference

Jan 1, 1965

By G. Osuch, G. Derge, G. M. Pound

Using a new dternating-current potentiometer circuit and a specially designed four-terminal cell, the specific conductance of molten Cu2S-FeS mattes was measured as a function of temperature, from the liquidus to 1500°C, over the complete range of composition. The high conductivities, about 1500 ohm-I cm-l for FeS and 100 ohm-l cm-l for Cu,S, indicate that the conduction is electronic rather than ionic. Molten FeS has a negative temperature coefficient of specific conductance, resembling metallic conduction. Molten Cu,S has a positive temperature coefficient, resembling semiconduction. The binary roughly follows an additive rule of mixtures with respect to both magnitude and temperature coefficient of specific conductance. Metallic bonding in the liquid is postulated to explain these phenomena. MUCH has been learned in the past about the nature of liquids and the ionic or molecular species in solution by means of electrical measurements. Thus, dielectric constants','2 have given information about molecular liquids such as water and benzene. Measurements of dielectric constant usually are impossible in electrically conducting liquids, such as aqueous solutions of ionic salts and molten ionic salts. However, measurements of electrical conductance and ionic transference have provided much knowledge about the latter systems.a-" In recent years, the ionic nature of certain molten metallurgical slags has been established by Derge and Martin7 through electrical conductance and electrolysis measurements. Chipman, Inouye, and Tom-linsonq ave studied the electrical conductance of molten FeO and report a high specific conductance of about 200 ohm-' cm-' (compared with 4 ohm" cm-' for an ordinary ionic liquid such as molten NaCl) and a positive temperature coefficient of conductance. They interpret these results in terms of p-type semiconduction by analogy to the situation in solid FeO.Y imnad and Derge" have studied cell efficiency in the electrolysis of molten FeO-SiO, systems and conclude that ordinary ionic conductance increases with SiO, content. Very recently, interest has been revived in the electrical conductance of liquid metals and liquid metallic solutions. Scala and Robertson1' report a close resemblance between the liquid and solid states with respect to thermal, structural, and compositional relationships. Molten sulphides have not received a great deal of attention. Bornemann and von Rauschenplat" measured the specific conductance of molten Cu2S as a function of temperature with a four-terminal cell using direct current. A high specific conductance and a positive temperature coefficient were found in that investigation." Using a two-electrode apparatus, Savelsberg" electrolyzed various molten sulphide mixtures. He concluded that pure molten Cu,S and FeS were electronic conductors but that the mixtures exhibited some ionic conduction. In the present investigation, the specific conductance of the industrially important Cu-Fe sulphide mattes was measured as a function of temperature and composition in order to investigate the mode of electrical conduction and the structure of these molten mattes. An alternating-current circuit was used to eliminate the effect of any possible electrode reactions. Apparatus The Conductance Cell: Due to the high specific conductance of the systems studied (10' to 10" ohm-' cm-'), the classical two-terminal cell and Wheat-stone bridge apparatus could not be used. A four-terminal cell was developed in order to eliminate lead resistance, and an ac potentiometer circuit was designed to give rapid and sufficiently accurate measurements of the cell resistance. A diagram of the conductivity cell is given in Fig. 1. The molten matte is contained in a dense alundum crucible, and spectrographic graphite rods that dip into the molten matte serve as the four conductance terminals. Two of the graphite rods on opposite sides of the cell serve as current-carrying leads, and the other two graphite rods are null-current probes that detect the potential drop across the cell. These graphite rods are contained in silica tubes, and the lower constricted portions of the two silica tubes define the column of liquid whose electrical resistance is being measured. The electrical resistance of the broad ex-

Jan 1, 1956

By R. C. Earlougher, F. G. Miller, T. D. Mueller, H. J. Ramey

There are many studies of flow in radial systems that can be used to interpret unsteady rerervoir flow problems. Although solutions for systems of infinite extent can be used to generate solutions fur finite ow systems by superposition, application is tedious. In this paper a step is made toward simplifying calcu1ations of such solutions for finite flow systems. Superposition is used to produce a tabulu-lion of the dimension1e.s.s pressure drop function at several locations within a bounded square that has a well at its center. The square system provides a useful building block that may be used to generate flow behavior for any rectangular shape whose sides are in integral ratios. Values of the tabulated dimensionless pressure drop function are simply added to obtain the dimensionless pressure drop function for the desired rectangulm system. The rectangular system may contain any number of wells producing at any rates. Furthermore, the outer boundaries of the rectangular system may be closed (no-flow) or they may he at constant pressure. Mixed conditions also may be conyidered. Tables of the dimensionless pressure drop function for the square system are presented and various applications of the technique are illustrated. Introduction In 1945, van Everdingen and Hurst' published solutions for the problem of water influx into a cylindrical reservoir. Since this problem is mathematically identical with the depletion of a cylindrical reservoir with a well at the origin, the van Everdingen-Hurst solution may be used to study the depletion problem. In their analysis, they assumed that the fluid had a small, constant compressibility such that flow was governed by the diffusivity equation For a constant production rate q starting at time zero, van Everdingen and Hurst showed that the unsteady pressurc distribution for both finite and infinite systems could be expressed in terms of a dimensionless pressure 'Sabulations of the dimensionless pressure drop for a unit value of r, were provided by van Everdingen and Hurst,' and later by Chatas.' Others also presented values in graphical or tabular form." If the radius of the well becomes vanishingly small, r,+ O, the line source solution may be used for Eq. 2 when infinite systems are considered. Eqs. 5 and 6 are excellent approximations for Eq. 2 under certain conditions: In 1954, Matthews, Brons and HazebroekV emonstrated that solutions such as Eq. 5 can be superposed to generate the behavior of bounded geometric shapes; i.e., the behavior of a bounded single-well system can be calculated by adding together the pressure disturbances caused by the appropriate array of an infinite number of wells producing from an infinite system. These wells are referred to as image wells. Matthews, Brons and Hazebroek considered systems containing a single well producing at a constant rate. This superposition can be represented analytically as

Jan 1, 1969

By J. F. Wolff, Anson A. Betts

The following correspondence relating to a paper bearing the above title, presented by J. F. Wolff, at the New York meeting in February, 1917, and published in the Transactions, Volume LVI, page 142, has passed between the author of the paper, and Mr. Anson G. Betts, and is interesting, although it was received much too late for incorporation in its proper place in Volume LVI. Anson G. Betts, Asheville, N. C.—1. I should like to ask Mr. Wolff if he finds from analysis of the iron formation and of the iron ore, and from the relative amounts of each in each unit area of the formation, unleached and after leaching, that the iron remains entirely insoluble and the total quantity still remains present; or whether he finds that some of the iron is removed, or possibly even added by deposition from the water passing through the formation. 2. The water that passed into the iron formation had to go somewhere; was it absorbed by underlying formations through hydration, or, after passing through the ore formation, did it come to the surface in springs at a lower elevation, or how did it escape from the ground? 3. I should like to ask Mr. Wolff whether he finds that the iron formation in the sedimentary series does not come next to the quartzites and generally between the quartzites and slates. J. I?. Wolff, Duluth, Minn.—1. In common with others, you appear to have some hesitancy in accepting the fact of the removal, by solution, of the enormous quantity of silica which has been leached out of portions of the Biwabik iron formation, thus forming orebodies of merchantable iron ore. I believe that even Dr. Waldemar Lindgren once hesitated to accept this fact. However, the evidence is so simple and absolutely conclusive that the fact is established beyond all question. At the contact of orebodies with their rock walls, the bands of iron ore in the orebody can be seen in contact with the corresponding bands of original iron oxide in the rock wall, and the chert layers in the rock wall can be seen to give place to fine granular material (fine silica and iron oxide) and pore space. This is especially noticeable where slumping at the rock walls has not been so great as to displace the layers in the orebody from their contact with their corresponding layers in the rock wall. Although complete analyses of the entire original rocks in the iron series have not been made in any place, to my knowledge, from the best data at hand as to the average analysis of the Biwabik series and the

Jan 1, 1920

By C. C. Templeton, J. C. Rodgers

A key step in feed water treatment for generating wet steam for thermal oil recovery is the removal of calcium and magnesiunt hardness by cation-exchange series softening. Knowing the solubility of any scale forming salts in brines at elevated temperatures is necessary for fixing the level to which the feed water must be softened. Such calcium sulfate solubility data, previously not available above 392F, were determined by the authors in a flow equilibrium apparatus mud will be reported elsewhere. These data were used to develop a method for predicting the solubility of anhydrite in hot water or steam droplets for saturated steam pressures as high as 2,000 psig (637F). (The calcium sulfate solubility product is represented by a combination of two factors, one reflecting the effects of ionic strength and the other accounting for the effects of complex ion formation in either calcium-magnesium-rich or sulfate-rich brines.) The method is applied to a calcium-magnesium-rich brine If moderately high salinity from a pilot hot-water flood, I nd to several sulfate-rich, low-salinity feed waters and l lowdown (cooled steam droplets) samples from steam s ak operations. The predicted calcium hardness levels corresponding to the calcium sulfate solubilities agreed reasonably well with the results of laboratory solubility determinations run on the field samples. Further testing of the method is needed for brines of other composition classes. Existing field cation exchange softeners in the cases tested are performing adequately since all the samples were found to be undersaturated with respect to calcium sulfate at their operating temperatures. Introduction Prevention of scaling caused by precipitation of calcium sulfate (anhydrite) is of considerable concern in connection with thermal recovery processes using wet steam or hot water. To avoid anhydrite precipitation in a heated system, an engineer must keep the product of the calcium and sulfate concentrations in the water or steam droplets below the value of the solubility product of anhydrite for the temperature and brine composition in question. Usually it is most practical to keep the concentration product lower than the solubility product by keeping calcium low in the presence of high sulfate, or by keeping sulfate low in the presence of high calcium. This can be done by a choice of combinations of natural waters and water treatment processes (such as series cation exchange softening to remove calcium). Until recently, few anhydrite solubility data, particularly for solutions containing other salts, were available for temperatures above 392F (211 psig steam); Marshall, Slusher and Jones' studied the CaS0,-NaCI-H,O system up to 392F and surveyed the work of previous investigators. To model natural brines, one needs to study the solubility of anhydrite in aqueous solutions of sodium chloride, sodium sulfate, calcium chloride, magnesium chloride and their mixtures. Since steam pressures as high as 2,000 psig (637F) may be involved in thermal oil recovery projects, a solubility study was conducted between 482 and 617F.' Discussed in this paper is the application of these data to the prediction of anhydrite precipitation in some practical steam soak and hot-water injection projects. Any simple method for predicting the solubility of an inorganic compound over a wide range of temperatures and solution compositions must be based on some assumptions, and therefore must yield approximate results. On the one hand, natural brines contain too many ionic species for all to be included in a simple scheme; on the other hand, there is no adequate theoretical basis for the exact prediction of solubility in even simple solutions of mixed electrolytes. However, it is possible at a given temperature to base a reasonable prediction scheme on two phenomena:'-' the increase in solubility with increasing total concentrations of all ions (as measured by the ionic strength; see the Appendix), and an increase due to formation of cornplexes between calcium ions and sulfate ions and between sulfate and magnesium ions. Stiff and Davis' developed such a scheme for predicting the solubility of gypsum (CaSO, ¦ 2H,O) in brines at temperatures u~ to 212F. However, for the higher temperaturei of present interest, the stable solid phase is anhydrite (CaSO,). This study involves a two-part method for predicting anhydrite solubility products. First, one predicts a value K, for a given ionic strength I and a given temperature T corresponding to mo./msr, = 1 from data of the CaS0,-NaCI-H,O system. Second, one determines a group of factors F .= F(Ca) • F(Mg) • F(SO,), where the individual factors account for increases in the solubility product due to complex formation by high concentrations, respectively, of calcium, magnesium and sulfate. Combining the two parts, one obtains the solubility product in molalities as

Jan 1, 1969

By R. T. Hukki

John F. Myers (Consulting Engineer, Greenwich, Corm.)—Since the art of comminution has lain practically dormant for many years, it is very interesting that R. T. Hukki approaches the subject with a new concept. One is reminded of the research carried on by A. W. Fahrenwald of Moscow, Idaho, a few years ago. Fahrenwald mounted a steel bowl on a vertical shaft. The balls and ore placed in the bowl were rotated at fast speeds, thus simulating the supercritical speeds used by Hukki. The rolling action of the balls against the smooth shell liner has pretty much the same effect. The action is horizontal in one case and vertical in the other. Both researchers report good grinding activity. It is also constructive that such able investigators give to the students of comminution their interpretation of their laboratory results in terms of large-scale operation. History shows that it takes a lot of time for such radically new ideas to be absorbed by the industry. Typical of this is the present-day activity of cyclone classification in primary grinding circuits. The idea of cyclone classification has been kicking around for 30 or 40 years. Certainly we all suspect that the ponderous grinding mills of today, and their accessory apparatus, large buildings, etc., will ultimately give way to small fast units, just as this has occurred in other industries over the past 50 years. At the moment there is no evidence that ball and liner wear is prohibitively high. In fact, at the time Fahrenwald was demonstrating his high-speed horizontal machine at the meeting of the American Mining Congress, several years ago, he assured this writer that the balls retained their shape much longer than they do in conventional tumbling mills. Rods and balls that slide (as some operators in uranium plants are experiencing) get flat. Apparently the balls have a rolling action. Mr. Hukki's references to the processing capacity of the Tennessee Copper Co. mills is adequate. Those studying this subject will be greatly interested in the paper presented by Richard Smith of the Cleveland-Cliffs Iron Co. at the annual meeting of the Canadian Institute of Mining and Metallurgy in Vancouver April 24, 1958. This paper will be published during the latter part of 1958 in the Canadian Institute of Mining and Metallurgy Bulletin. Hukki's pioneering spirit is to be commended. R. T. Hukki (author's reply)—It has been heartening to read the objective discussion by J. F. Myers. The sincerity of his opinions is further strengthened by the fact that the article he has discussed contradicts in a major way the parallel achievements of his life work. Myers is right in his opinion that in general it takes a long time before new ideas are accepted by the industry. On the other hand, revolutions usually take place at supercritical speeds. There are many indications at present that both the unit operation of grinding and the related subject of size control are now just about ripe for a revolution. In grinding, brute force must ultimately give way to science. Rapid progress can be anticipated in the following fields: 1) Autogenous fine grinding at supercritical speeds will be the first advance and the one that will gain recognition most easily on industrial scale. At this moment, little Finland appears to be leading the world. Crocker recently made a statement that in nine cases out of ten, your own ore can be used as grinding medium more effectively and far more economically than steel balls. This is true. The present author would like to introduce a supplementary idea: In eight cases out of the nine cited above, it can be done at the highest overall efficiency in the supercritical speed range. Fine grinding must be based on attrition, not impact. The path of attrition may be vertical, horizontal, even inclined. 2) In coarse grinding, the conventional use of rods is sound practice. However, even the rods can be replaced by autogenous chunks large enough to offer the same impact momentum as the rods. To obtain the momentum, the chunks must be provided with a free fall through a sufficient height in horizontal mills operated at supercritical speeds. Coarse grinding must be based on impact. Detailed analysis of the subject may be found in a paper entitled "All-autogenous Grinding at Supercritical Speeds" in Mine and Quarry Engineering, July 1958. 3) All conventional methods of classification, including wet and dry cyclones, are inefficient in sharpness of separation. Continuous return of huge tonnages of finished material to the grinding unit with the circulating load is senseless practice. In the near future the present methods will be either replaced or supplemented by precision sizing. These three fields are also the ones to which J. F. Myers has so admirably contributed in the past. Fine Grinding at Supercritical Speeds. By R. T. Hukki (Mining EnGineERInG, May 1958). Eq. 9, page 588, should be as follows: T , c, (a — 6') n D Ltph On page 584 of the article the captions for Figs. 4 and 5 have been placed under the wrong illustrations and should be interchanged.

Jan 1, 1959

By Fred C. Bond, Walter Maxson

Since the last publication of tabulated results of grindability tests by the authors1 the total number of ball-mill tests made has more than doubled, and rod-mill tests have become increasingly important. Nearly all of the standard closed-circuit ball-mill and rod-mill tests made to date are included in the present tabulation, together with additional information not previously published. Standard Ball-mill Grindability Tests The method of conducting these closed-circuit tests has not been altered. A sample of the ore or other material is stage-crushed in rolls set at 1/16-in. opening with a 6-mesh screen until all of it has passed the screen. The combined minus 6-mesh screen undersize is mixed, sampled and screen-analyzed, and its apparent specific gravity is determined by packing and shaking in a standard container, and weighing. The apparent specific gravity ordinarily is about 60 per cent of the true specific gravity. The unit volume present in the mill .in all tests is 700 C.C. of the packed minus 6-mesh roll product, and the number of grams occupying 700 C.C. is the unit test weight. This weight is placed in the mill dry, ground for the number of revolutions estimated to be necessary, discharged, and screened mechanically in three testing sieves of the mesh size at which the test is to be conducted. The oversize, or circulating load, is weighed, sufficient fresh minus 6-mesh feed is added to bring the total weight up to that of 700 c.c., and the charge is returned to the mill for a second grinding period. All standard ball-mill tests are conducted at 250 per cent circulating load, and the number of revolutions in the mill necessary to obtain this circulating load at any grinding period is estimated from the results of the previous period. The number of net grams of screen undersize produced per revolution of the mill approaches its final equilibrium value after several grinding periods, and this is recorded as the grindability, or relative ease of grinding, of the sample. A cylindrical ball mill, 12 by 12 in. inside, with a smooth lining and rounded corners, is used with a revolution counter Under standard grinding conditions it runs at 70 r.p.m., and contains a charge of 285 iron balls weighing 20,125 grams, ranging from I½ to ¾ in. in diameter. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the capacity- to be expected from a given mill is calculated by comparing the grindability with that of a similar standard ore whose performance characteristics arc known. No satisfactory general formula for convertillg standard grindabilities into corn; rnercial power-consumption values has been

Jan 1, 1943

By Walter Maxson, Fred C. Bond

Since the last publication of tabulated results of grindability tests by the authors1 the total number of ball-mill tests made has more than doubled, and rod-mill tests have become increasingly important. Nearly all of the standard closed-circuit ball-mill and rod-mill tests made to date are included in the present tabulation, together with additional information not previously published. Standard Ball-mill Grindability Tests The method of conducting these closed-circuit tests has not been altered. A sample of the ore or other material is stage-crushed in rolls set at 1/16-in. opening with a 6-mesh screen until all of it has passed the screen. The combined minus 6-mesh screen undersize is mixed, sampled and screen-analyzed, and its apparent specific gravity is determined by packing and shaking in a standard container, and weighing. The apparent specific gravity ordinarily is about 60 per cent of the true specific gravity. The unit volume present in the mill .in all tests is 700 C.C. of the packed minus 6-mesh roll product, and the number of grams occupying 700 C.C. is the unit test weight. This weight is placed in the mill dry, ground for the number of revolutions estimated to be necessary, discharged, and screened mechanically in three testing sieves of the mesh size at which the test is to be conducted. The oversize, or circulating load, is weighed, sufficient fresh minus 6-mesh feed is added to bring the total weight up to that of 700 c.c., and the charge is returned to the mill for a second grinding period. All standard ball-mill tests are conducted at 250 per cent circulating load, and the number of revolutions in the mill necessary to obtain this circulating load at any grinding period is estimated from the results of the previous period. The number of net grams of screen undersize produced per revolution of the mill approaches its final equilibrium value after several grinding periods, and this is recorded as the grindability, or relative ease of grinding, of the sample. A cylindrical ball mill, 12 by 12 in. inside, with a smooth lining and rounded corners, is used with a revolution counter Under standard grinding conditions it runs at 70 r.p.m., and contains a charge of 285 iron balls weighing 20,125 grams, ranging from I½ to ¾ in. in diameter. Tests are conducted at the mesh size to which the ore is to be ground in practice, and the capacity- to be expected from a given mill is calculated by comparing the grindability with that of a similar standard ore whose performance characteristics arc known. No satisfactory general formula for convertillg standard grindabilities into corn; rnercial power-consumption values has been

Jan 1, 1943

By R. Schuhmann

The expression "unit process " comes up with increasing frequency in discussions among metallurgists and mineral engineers, especially among those concerned with training the next generation. The unit process approach characterizes a significant advance along the road from metallurgy as an empirical art to metallurgy as a branch of engineering. The purposes of this paper are to define and list the unit processes in specific terms, to indicate the scientific and engineering principles basic to all the unit processes, and finally to show how these ideas have been applied to a reorganization of instruction in chemical metallurgy. Unit Operations and Unit Processes Metals are extracted from ores and other raw materials by stepwise procedures. In general, each metallic element is extracted by a different procedure. For many of the metals there is a choice of several flowsheets. However, the procedures all have steps in common. In fact, the many different flowsheets are all made up of a relatively small number of steps which are combined in different groups and sequences. For example, crushing, screening, roasting, sintering, melting, and gaseous reduction are steps which each appear in the Bowsheets for extracting the majority of the metals. The individual steps or flowsheet units can be designated as unit operations or unit processes. These terms are well established in the field of chemical engineering, as the American Institute of Chemical Engineers' definition of chemical engineering shows: " Chemical engineering is that branch of engineering concerned with the development and application of manufacturing processes in which chemical or certain physical changes of materials are involved. These processes may usually be resolved into a coordinated series of unit physical operations and unit chemical processes. The work of the chemical engineer is concerned primarily with the design, construction, and operation of equipment and plants in which these unit operations and processes are applied. Chemistry, physics, and mathematics are the underlying sciences of chemical engineering, and economics its guide in practice."'1a In this definition, the distinction between unit operations and unit processes is that the unit operations are physical while the unit processes are chemical. Table I gives a list of the principal unit operations and unit processes of chemical engineering, taken from Shreve.1b Table 2 lists the principal unit operations and unit processes used for metal extraction. The division between unit operations and unit processes is similar to the chemical engineers' distinction and also correspollds approximately to the division of labor bctween mineral dressing and chemical metallurgy which has been customary in the past. Furthermore, it will be noted that in the proposed classification the unit processes primarily involve chemical reactions and/or changes in state of aggregation; the unit operations primarily do not involve either bulk

Jan 1, 1949

By A. W. Schlechten, A. H. Larson

Equilibrium H2S/H2 ratios were determined as functions of temperature (500o to 900°C) and composition in a hydrogen-circulation apparatus. Within the composition range studied there exists a two-phase region of "Zr3S4" and "ZrS2". The upper composition limit of this two-phase region is hounded by a disulfide phase and is practically constant over the temperature range investigated. The lower composition limit of this two-phase region is bounded a "Zr3S4 " phase and varies appreciably with tem- perature. The upper composition limit of the homogeneous region of the disulfide phase is not definitely determined, but it appears to he bounded by the stoichiometric composition of ZrS2. The lower composition limit of the homogeneous region of the Zr3S4 phase could not he determined due to the extremely low values of the equilibrium H2S/H2 ratios. Various thermodynamic quantities are evaluated from the data. PUBLISHED free-energy data for the Zr-S system are practically nonexistent. Strotzer, Biltz, and Meisel1 measured the sulfur pressures for the reaction 2ZrS2(s) + S2(g) = ZrS3(s) in the temperature range 783" to 874°C. The average heat of reaction calculated from the temperature dependence of the sulfur pressure is -47 keal. It should be noted, however, that according to these investigators, the two-phase region as determined by sulfur pressure constancy under isothermal conditions extended from approximately ZrS2, 3 to ZrS2.7. From consideration of X-ray data they concluded that the homogeneous regions of the disulfide and trisulfide phases are ZrS1.8-2.0 and ZrS2.8-3.2, respectively. Hahn and coworkers2 have made a structure study of the zirconium sulfide phases. They summarized the zirconium sulfide phases as follows: the compounds ZrS3 and ZrS2 with narrow homogeneous regions, a "Zr3S4" phase with a homogeneous region roughly within the limits of ZrSl.5 and ZrSo.9, the compounds ZrS and Zr4S3, and a "Zr3S2" phase with a homogeneous region within the limits ZrSo.8 and ZrSo.5. It is noted that the compounds ZrS and Zr4S3 are only formed in the gaseous state through sublimation of a phase which has the approximate composition of the compound. This paper describes the determination of the stability of the zirconium sulfide phases by a hydrogen-reduction method in which hydrogen is circulated over the heated sulfide until equilibrium is attained. The resulting H2S-H2 mixture is then analyzed. Partial molar free energies, enthalpies,

Jan 1, 1964

By D. M. Davidson

THE drill sampling and evaluation of the Piney River ilmenite property was carried out during the early part of 1944 by E. J. Longyear Co., using the company's standard core-drill outfits to complete 44 holes to an average depth of 110 ft., from which were collected 1100 samples. The Piney River ilmenite-apatite lode is 25 miles north of Lynchburg, in Nelson and Amherst Counties, Virginia (Fig. I). Its elevation is about 900 ft. above sea level and it lies in the old pre-Cambrian complex of crystalline rocks that make up the Piedmont physiographic province lying east of the Blue Ridge Mountains. The terrain is gently rolling and well watered, and is drained by the Piney and Tye Rivers, which are tributary to the James. GEOLOGY The Piney River ore body comprises the upper, weathered part of a tabular basic rock, which occurs in a large area of granite-gneiss. The section containing profitable ore is about 3000 ft. long. It is separated naturally by thinning, into northeastern and southwestern segments with widths of 300 and 100 ft. respectively. The dip averages 45° southeast but steepens locally (Figs. 2 and 3). The unaltered rock is an even, granular mixture of feldspar, ilmenite, and apatite, to which Watson1 gave the name Nelsonite. The decomposed ore body, which is now being exploited by open cut, is a yellowish clay material in which black ilmenite and glassy apatite are the only conspicuous minerals. An economically important structural feature of the deposit is a banding of minerals coinciding with the dip and strike of the dike. This is more promounced in the footwall of the northeastern part of the intrusive, where there is also a higher than average concentration of ilmenite. According to Watson,1 the Ti02 content of the Nelsonites of this region ranges from 10 to 42 per cent, while P205 varies from 4 to 15 per cent. It is inexpedient at present to disclose exact metal content of the Piney River ore body; suffice it to say that the average tenor lies well within the extremes noted by Watson. SAMPLING METHODS AND PROCEDURE During a preliminary inspection of the ore body, Longyear engineers surmised that because of its soft, clayey character, drill sampling would yield little core, therefore they made all possible preparations to procure accurate samples of the drill cuttings, or sludge. The first requisite in obtaining representative drill cuttings is to secure their full recovery. Only under certain conditions, and by employing a most careful and rigid sampling technique, is this possible. There must be no loss of the water circulating in the hole, and the velocity

Jan 1, 1946

By F. E. Jaumot, R. L. Smith

Self-diffusion in zinc at temperatures below 200°C has been studied using both single crystal and polycrystal samples. Anomalous results were obtained for single crystal samples, the data indicating that in some cases grain boundary diffusion predominated. These anomalous results are presumed to be due to low angle lineage boundaries in the single crystals. When volume diffusion occurred in either single or polycrystal samples, the values for the diffusion coefficient were as much as several orders of magnitude larger than would be expected from high temperature data. ONSIDERABLE work has been done on self-^-*diffusion at temperatures in the neighborhood of two thirds of the melting temperature (in OK) and higher, but very little has been done at lower temperatures. This is particularly true of self-diffusion in single crystals. This paper reports work on self-diffusion in zinc at temperatures below 200 °C where both polycrystalline and single crystal samples have been used. The measurements were made using both the sectioning and absorption techniques. The experiments on diffusion at low temperatures were initiated primarily for three reasons: to obtain data from single crystal diffusion covering a wide range of temperatures, to obtain values of the activation energy for grain boundary diffusion, and to obtain, if possible, a lower limit to the temperatures at which the absorption technique may be used. It is possible to determine whether volume or grain boundary diffusion predominates at low temperatures by analyzing the manner in which the concentration of the diffusing atoms varies with the depth of penetration. The analysis is possible only for the sectioning technique. For volume diffusion and for the boundary conditions of the present experiment, the curve of the logarithm of the concentration, C, vs the square of the penetration depth, x, is a straight line with the slope proportional to — 1/D. If grain boundary diffusion predominates, Fisher' has shown that a curve of In C vs the first power of the penetration depth should be a straight line. This linear dependence of concentration on depth has been observed experimentally by several investigators. (See, for example, refs. 3 and 4.) Following Fisher's analysis, the grain boundary diffusion coefficient can be written as where 8 is the grain boundary width, D, is the volume diffusion coefficient at the temperature involved, t is the time of diffusion, C is the concentration of diffusing material, and x is the depth of penetration. A more general analysis employing the same model as Fisher's but with fewer assumptions has been given by Whipple.' In contrast to Fisher's analysis the more general analysis of Whipple does not always yield a straight line relation between In C and x. Recently Turnbull and Hoffman have discussed both analyses and have applied the Fisher-Whipple model to a more refined dislocation model of the grain boundary. They have also discussed the possibility of a large effect of grain boundary direction on diffusion. In the case of the absorption technique, for which results are also given, one simply gets a value for the diffusion coefficient with no indication of the predominating mechanism. Experimental Techniques Single crystals of 99.99+ pct Zn were grown using a modified Bridgman method. Polycrystal samples were prepared in three grain sizes (small, about 4 mm2; medium, about 9 mm'; and large, about 25 mmz) by quenching, air cooling, and furnace cooling. The grains of the polycrystalline samples tended to be columnar, with some preferred texture such that the c-axis was inclined at about 20" to 25" from the normal to the diffusion face, particularly in the medium and large grain size samples. The samples were cut from the rod, polished, and heavily etched, and faces cut accurately parallel using a jeweler's lathe. They were again etched to remove the lathe smear and annealed for 3 hr at 250" to 300°C. After annealing, they were etched, examined, and the orientation determined by Laue back reflection photographs. They were then electroplated with Zn. The plated surfaces were examined for uniformity; nonuniform coatings were removed by etching and the samples replated without additional preparation. For the diffusion anneals, the samples were placed in pairs, with active faces together, in evacuated Pyrex tubes. Constant temperature baths were used, and the variation in temperature did not exceed ±l°C, Diffusion runs were made at l00°,

Jan 1, 1957

By P. Somasundaran, D. W. Fuerstenau

The length of the collector is found to influence the flotation of the mineral even at incipient conditions, which are below the concentration at which interaction at the solid-liquid interface begins to take place to form hemi-micelles. To study this dependence, concentration for incipient flotation of quartz was determined as a function of pH with collectors of various chain lengths. The observed effect of chain length on flotation is ascribed to that of collector adsorbed on the bubble surface. In previous studies, it was shown that at low concentrations the alkyl collector ions adsorb at the solid-liquid interface as individuals.''2 At higher concentrations, the collector ions adsorbed at the solid-liquid interface associate with each other to form two-dimensional aggregates called hemi-micelles. Above the hemi-micelle concentration, the length of the hydrocarbon chain is extremely important since the hydrocarbons are in effect removed from water during the association, making the energetic conditions more favorable for adsorption at the interface. Because of this enhanced adsorption, one observes a very rapid increase in flotation associated with the hemi-micelle formation at the solid-liquid interface. However, a dependence of flotation on the chain length at concentrations below that required for hemi-micelle association was also observed,' and this cannot be explained by the above mechanism which postulated hydrocarbon chain interactions only at the solid-liquid interface. This prompted an investigation into other possible reactions of the hydrocarbon chains and an examination of the conditions at the bubble surface involved in the flotation system and how these observations might explain the reactions at the solid-gas interface which cause the particle-bubble attachment required for flotation. To obtain more information on chain length effects, flotation, under incipient conditions, was tested by vacuum flotation techniques. The collector-concen-tration-pH relationships for flotation of quartz with alkyl ammonium acetate collectors was delineated by observing the pH at which quartz particles begin to float to the liquid surface. By investigating flotation as a function of pH, it was also possible to study the effect of neutral molecules on incipient flotation conditions, since the aminium ions hydrolyze to amine molecules at higher pH values. EXPERIMENTAL WORK Brazilian quartz specimens were crushed and sized, and the 270 x 400 mesh fraction was used for flotation studies. The samples were leached with concentrated hydrochloric acid until no coloration of the acid occurred. The leached material was washed free of chloride ions and stored in distilled water. The vacuum flotation technique developed by Schuhmann and prakash3 was used to determine the critical pH-concentration curves. This method, which can be used to delineate conditions for incipient flotation, is fairly simple and rapid. About 0.5 gm of 270 x 400 mesh quartz was placed in a 100 ml graduated cylinder which was then filled to the 100 ml mark with the collector solution made from high-purity alkyl ammonium acetate salts. The water used for the test was conductivity water saturated with air that had been passed through a cleansing train consisting of Drierite, Ascarite, a water wash bottle, and a trap. After the pH was adjusted, the cylinder was then conditioned for thirty minutes. In the tests where an acid pH was desired, sufficient acid was added before the collector solution to avoid any effect due to slow desorption of collector from the quartz surface. After conditioning, vacuum was applied to the system and the flotation or nonflotation of the quartz was noted. The pH at which the quartz particles began to float to the liquid-gas interface was taken as the critical PH. Critical pH curves were thus determined for different concentrations of the various collectors. Hallimond tube flotation data were taken from the authors' previous publication1 for correlation with that from the vacuum flotation. RESULTS AND DISCUSSION The results of vacuum flotation studies for determining critical pH-concentration curves, i.e., curves which delineate conditions for incipient flotation, are shown in Fig. I. In generaI, all the curves exhibit an upper and lower pH limit between which flotation will

Jan 1, 1969

By Kenneth A. Moon

An exact statistical treatment of a one-dimensional model is used as a basis for evoluating the reliability of certain simplified expressions for the activity of the solute in interstitial solutions, including one obtained from the exact expression by setting the repulsive interaction equal to infinity. The latter approximation is found to be satisfactory at low and moderate concentration if the repulsive interaction is large, even though not infinite. A similar expression (identical if the co-odination number is two) is derived from the quasichemical expression of Lacher, and is recommended as the best available expression for the excess configurational entropy of interstitial solutions with excluded sites. Some reasonable models are discussed, and the nature of the saturated solutions is determined by inspection. Some of the models reduce to the one -dimensional case. An analysis is given of the excess partial entropy of hydrogen in V-H; Nb-H; and To-H solutions. MOST treatments of the statistical thermodynamics of interstitial solid solutions have followed the classic paper1 of Lacher in making the simplifying assumption that the configurational entropy of the solution is ideal. However, it is becoming increasingly apparent that there are many interstitial solutions with very large so lute-solute repulsions, and for these the assumption of ideal entropy is not valid or useful. It is important to realize that with substitutional solutions large repulsions between the component atoms must lead to phase separation, whereas in interstitial solutions the free energy of the solution is not drastically increased by large solute-solute repulsions until intrinsic saturation is reached at the concentration where further solute would be forced to enter a site in which it would experience the repulsive effect of one or more solute atoms already present. In the limiting case of an infinitely large repulsive interaction, the excess free energy would be attributable entirely to excess entropy, the enthalpy of mixing being zero. AS will be shown below, even if the repulsions are less than infinite, a treatment based on an assumption of infinite repulsions may be very satisfactory up to moderately high concentrations of the interstitial component. Often in solutions where large repulsive interactions exist, there are also small interactions — often attractive—between solute atoms in configurations other than that corresponding to the large repulsion. In such cases the excess free energy will consist of an excess entropy term attributable to the large repulsive interactions, and an enthalpy term corresponding to the other small interactions. Nomenclature to differentiate succinctly between important cases would be a convenience. In this paper the nomenclature shown in Table I will be used. In Table I, and in the preceeding discussion, excess quantities are defined in terms of standard states which are pure solid solvent and pure (possibly hypothetical) solid saturated phase of the structure in question. In practice, it is more convenient to choose the interstitial element as a component, and its conventional standard state. This will add a composition-independent term to the excess entropy and the enthalpy. The earliest paper known to the present author which treats the thermodynamics of athermal interstitial solutions was given by schei12 in 1951, but the statistical derivations in that paper are open to criticism. Speiser and Spretnak were the first to give a correct statistical treatment,3 limited, however, to concentrations sufficiently low that the number of empty sites excluded from occupancy by more than one filled site is negligible. The purpose of the present paper is to extend the statistical treatment to more concentrated solutions, and to examine the magnitude of the errors introduced by assuming that the repulsive interactions are infinite when in fact they must be finite. THE QUASICHEMICAL APPROXIMATION Fortunately, a standard method already exists for taking into account the effect of large interactions upon the entropy of mixing. This is the quasi-chemical method, in which the probability of existence of a given pair of solute atoms in a certain proximate configuration is assumed to be proportional to exp(-w/kT), where w is the energy increase of the solution when the two atoms are moved from isolated locations in the solution to the configuration in question. A quasichemical treatment of interstitial solutions was given in 1937 in a widely neglected paper by Lacher.4 The result comes out

Jan 1, 1963

By R. A. Breitrick, J. N. Swinderman, J. J. Cooper, H. L. Bauer Jr.

The Robinson Mining District, near Ely, Nev., is one of the major porphyry copper districts in the world. Within the district is an eight mile long east-trending zone of altered porphyry, metamorphosed sedimentary rocks, and sulphide mineralization surrounded by Paleozoic limestone, dolomite, shale and sandstone, Tertiary volcanics, and Quaternary alluvium. Six major disseminated ore deposits have been exploited in this zone. About 20% of the district production has come from disseminated ore in metamorphosed sedimentary rocks found adjacent to altered quartz-monzonite porphyry. The following brief statements summarize some of the relations between porphyry alteration, metamor-phism, and mineralization: 1) Disseminated copper ore does not occur in unaltered porphyry or in m-metamorphosed sedimentary rocks. 2) Sedimentary rocks have been only weakly metamorphosed where intruded by unaltered porphyry. 3) Intensely metamorphosed sedimentary rocks are found only adjacent to altered porphyry. 4) Many hydrothermal minerals are common to both altered porphyry and adjacent metamorphosed sediments. 5) Disseminated ore is found in altered porphyry and adjacent metamorphosed sedimentary rocks. 6) In general, there is a direct correlation between grade of ore in porphyry and copper content in the adjacent rocks. 7) Chemical changes in the altered porphyry and metamorphosed rocks appear to be related. The foregoing relations support a hypothesis that the porphyry alteration, the metamorphism of the sedimentary rocks, and the ore deposition were all part of a continuous hydrothermal process which probably closely attended the porphyry intrusion. The Robinson Mining District, most often referred to as the Ruth or Ely District, is located in eastern Nev. and is one of the major porphyry copper districts of the world. Production from 1908 through 1962 was nearly 250 million tons of ore averaging a little over one percent copper with a total metal value of nearly one billion dollars. The ore has been produced from six major disseminated-type deposits with the Liberty Pit deposit accounting for 70% of the total district production. Less than one million tons of base metal and gold ores have been produced from the replacement-type deposits of the district. Approximately 20% of the district production has come from underground mining operations; the pit ore has been mined with shovels and removed by train haulage, truck-train haulage combinations, truck haulage, and presently by a combination truck-skip system. Many of the ore deposits formerly worked by underground methods have been and are being exploited by open pit methods. (See Fig. I.) Two co.'s have accounted for virtually the entire production from the district. In 1958 Kennecott Copper Corp. acquired the district assets of Consolidated Coppermines Corp. and is now the sole ore producer in the district. Present operations are confined to the Liberty Pit where 22,500 tons of ore averaging a little less than 0.8% copper is mined per day. Cutoff grade is 0.4% copper, and the stripping ratio is three to one. The ore is hauled by rail 23 miles to the McGill Reduction Plant where it is concentrated to about 20% copper. Molybdenite is recovered as a by-product in the mill. The copper concentrates are smelted in McGill, and the blister copper is shipped for refining to Balt. where gold, silver, platinum and palladium are recovered. The Robinson Mining District has been well known as a porphyry copper district for the past fifty years, but many geologists are unaware of the fact that a large portion of the production has come from disseminated ore found in metamorphosed sedimentary rocks. The scope of this paper describes the occurrences of disseminated ore in the various metamorphosed sedimentary rocks, and presents evidence for the hypothesis that these ores are genetically, spacially, and coevally related to the disseminated ore in the porphyry rocks. Publication of this paper was granted by the management of Kennecott Copper Corp. A. H. James suggested and encouraged the writing of the manuscript. Special mineralogical and spectrographic analyses were performed by the Kennecott Research Center. The deposits of the district have been studied by many geologists since the turn of the century, and

Jan 1, 1964