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By T. N. Dixon, J. E. Briggs

A study was made of numerical techniques for solving the large sets of simultaneous equations that arise in the mathematical mode ling of oil reservoir behavior. It was found that noniterative techniques, such as the Alternating Direction Implicit (ADI) method, as well as some other finite difference approximations, produce oscillatory or unsmooth results for large time steps. Estimates of time step sizes sufficient to avoid such behavior are given. A comparison was made of the Point Successive Over-Relaxation (PSOR), Two-Line Cyclic Chebyshev Semi-Iterative SOR (2LCC), and iterative ADI methods, with respect to speed of solution of a test problem. It was found that, when applicable, iterative ADI is fastest for problems involving many points, while 2LCC is preferable for smaller problems. INTRODUCTION With the advent of high speed, large memory, digital computers, there has been an increasing emphasis on the development of improved methods for simulating and predicting reservoir performance. Two-dimensional, three-phase reservoir models with various combinations of PVT effects, as well as gravity and capillary forces, are common throughout the industry. Such models are also available through consulting firms, to anyone desiring to use them. Three-dimensional models will probably be practical in only a few years. We conducted a study of some of the numerical methods used for solving the large sets of simultaneous equations that arise in such models. A typical set of equations for a reservoir model is shown below:

Jan 1, 1969

By F. F. Aplan, E. C. Dowling, R. R. Klimpel

Numerous flotation models have been proposed in the literature. Thirteen of these have been applied to batch flotation data and evaluated with respect to one another using statistical techniques. Flotation tests were carried out on samples of a US porphyry copper ore (Pinto Valley, AZ). The ore was tested using various collector and frother systems to produce different time-recovery profiles. These were used to calculate flotation rate and ultimate recovery parameters for each model. The models were then evaluated statistically to determine the overall fit of the calculated to the observed data and to test the range of significance of the parameters in each model.

Jan 1, 1986

EUGENE COSTE, ? Calgary, Alta.-Evidently in Argentine they have a petroliferous province just east of the Andes where very much the same conditions exist as are found on the east side of the Rocky Mountains and in the plains adjacent. It strikes me, though, that the same mistake is being made in Argentine in the exploration for oil as was made in Alberta, Canada; viz., drilling the wells too .near the seepages in the belt in the eastern part of the petroliferous province, too near the mountains. This same mistake was made in Alberta, with disastrous results; viz., only fissure production was found. The strata so near the mountains are tilted at a very strong angle, such as is described in this paper, and the dislocations are intense. On the other hand, we have found that when we get 100 or 200 mi. away from the mountains we get into oil and gas belts which are very prolific. So far our fields in Alberta have been gas, but in Wyoming, as you know, they get many thousands of barrels a day. I have no doubt that conditions in Argentine are exactly similar but that they have so far kept too near the mountains and that they want to explore the belts farther east to obtain better results.

Jan 4, 1919

By J. W. Mitchell

Season cracking of 70-30 cartridge brass cases of small arms and artillery ammunition has been under investigation at the Frankford Arsenal for many years. The nature of this stress-corrosion failure has been found to be intergranular. Much of this work, however, has been directed toward improvements in method of manufacturing the cases so as to reduce the tendency to season crack and little progress had been made toward finding the source of the chemical agent producing the inter- granular corrosion. Ammonia has been shown to produce season cracking in brass and is known to be present in certain atmospheres, particularly industrial, in sufficient concentration to cause cracking. However, in the case of small arms ammunition, the hypothesis that atmospheric ammonia is the cause will not hold, since small arms ammunition is hermetically sealed during storage and yet occasional lots are found to have cracked after 3 to 5 yr. storage. Much of the early study of season cracking in small arms ammunition was done by Nicholas H. Murdza of the Frank- ford Arsenal. In 1936, he suggested that the corrosive agent might be one of the decomposition products of smokeless powder and mentioned nitrogen oxides specifically. Then in 1937, Murdza suggested that the breakdown of smokeless powder in storage resulted in the formation not only of nitrogen oxides but also ammonia

Jan 1, 1945

By James L. Kelly

Stripping of the Twin Buttes copper deposit started in 1965. Total material removed for the first 10 yr of operation is approximately 879 million tons. The sulfide concentrator has treated about 45 million tons. The Twin Buttes mineral zone was concealed under several hundred feet of recent alluvium. Beneath this post-minera1 cover, Paleozoic limestone, siltstone and quartzite, and Mesozoic metaarqillite, arkose, conglomerate, and volcanic rocks are intruded by an igneous complex of quartz monzonite and diorite. All rock units are erratically mineralized, principally with copper and molybdenum. Strongest copper mineral favors the Paleozoic calc-silicated limestone and siltstone, often preferential to individual beds.

Jan 1, 1978

By W. C. Leslie

W. C. Leslie (Edgar C. Bain Laboratory for Funda mental Research)—This investigation, with its com bination of high-purity metal, calorimetry, and metallography, will serve as a model for annealing studies for a long time to come. The evidence for a competition between recovery and recrystalliza-tion is particularly convincing. The demonstration of edge-nucleated recrystallization was so clear that it may obscure the necessity for other types of "nucleation" sites; otherwise, single crystals of aluminum could not be recrystallized after cold work. At least three types of sites have been found to operate in iron: 1) high-angle boundaries, probably in the same manner as in aluminum, 2) matrix sites, 3) inclusions or second-phase particles. In each instance, the cells developed during cold work and perfected during recovery are the "nucle for recrystallization. Observations by ourselves and others of the dislocation structure of cold-worked metals and of the structural changes that occur during annealing have led us to doubt the validity of the basic assumption of the Lucke-Detert theory, and of the modification developed by Gordon and Vandermeer, that during recrystallization of a metal containing foreign elements in solid solution a high-angle boundary is ad vancing into a cold-worked matrix having a random distribution of solute atoms. We contend that an es sential part of the cold-working and annealing of solid solution alloys is the trapping of solute atoms by the low-energy "wells" afforded by individual dislocations and by dislocation arrays. If cells are formed during cold work, the cell walls are stabilized by this concentration of solute atoms. Thus, solutes inhibit recrystallization not only by decreas-ing the rate of high-angle boundary migration, but also by preventing the formation of high-angle boundaries by subgrain growth or coalescence, i.e., solutes can inhibit both "nucleation" and growth. In addition to stabilizing the dislocation Structure, the solute-dislocation interactions may produce clusters of solute atoms which are not as readily assimilated into the recrystallized grains as are individual solute atoms. There is an additional complication. The dislocation structure formed upon cold working a dilute solid solution may not be the same as that formed during cold working of the pure solvent metal. The solute can either enhance or minimize the formation of cells during cold working. Both effects have been observed in binary alloys of iron. The annealing process is inextricably connected with the mechanisms of strain hardening and solid solution hardening. Although the correlation between experimental boundary migration rates and the predictions made from the theoretical equations are impressive, it should be mentioned that in at least four other instances (Pb-Ag and pb-Au,15, Fe-Mn,16, Fe-Mo)17 the agreement was rather poor. In brief, while it is probable that the migration of high-angle boundaries is held back by solutes in the manner described, this is only a partial explanation of the total effect of solutes upon recrystallization of cold-worked alloys. Paul Gordon and R. A. Vandermeer (author's reply)— The authors first wish to thank Dr. Leslie for his compliments of this work. It is perhaps worth pointing out that some of Dr. Leslie's remarks are directed toward subject matter covered in two earlier papers in our work.18,19 We agree with Dr. Leslie's main contention that the exact nature of the metal structure in the vicinity of a boundary should have an effect on the boundary migration. The theory of Lucke and Detert does not take such detail into account, nor does it account for orientation effects on the migration rates. We assume that since our data checks the theory so well, the effects of detailed structure are statistically averaged out by the polycrystalline techniques used just as are the effects of orientation factors.

Jan 1, 1963

By J. O. Betterton, W. M. Spicer

The solubilities of antimony in the a and ß-forms of zirconium were determined between 750" and 1300°C. The a-phase forms by a peritectoid reaction, and the a/(a + ß) and ß/(a + ß) phase boundaries rise in temperature with in- ' creasing antimony. Impurities in the 99.95 pct zirconium were sufficient to influence the phase boundaries and the variation reported is approximate. The restricted solid solubility of the terminal zirconium phases, which is especially characteristic of this system, is thought to result from the low free energy of the Zr2Sb phase. ZIRCONIUM-antimony alloys are important in zirconium alloying studies since antimony is one of the highest valent elements which can be used to make zirconium alloys. The dilute alloys are of further interest as they have somewhat better corrosion resistance' than pure zirconium. The first investigation of the phase diagram was made by Russi and wilhelm2 who found a eutectic reaction, liquid (- 17.5 at. pct Sb) = ß zirconium (- 11 at. pct Sb) + Zr2Sb, at 1430°C'. The Zr2Sb phase was of complicated hexagonal structure, and by thermal analyses of the relatively impure alloys then available, Russi and Wilhelm found evidence for the peritectoid formation of the a-phase. EXPERIMENTAL In the present work, the phase diagram was re-investigated in the region 0 to 5 at. pct Sb and 750" to 1300°C using iodide-zirconium alloys. Details of the procedure have been described earlier. Essentially the alloys were prepared by arc casting and were then examined by the annealing and quenching method. The times of annealing varied from 1 hr at 1300°C to 30 days at 760°C. As in other zirconium phase-diagram studies1"5 the impurities in the zirconium were still sufficient to affect the results, and the experiments will therefore be described in 3 parts. The results from the first 2 parts of the work are shown in Fig. 1. Here the ß/(ß + Zr2Sb) and a/(a + ZrzSb) phase boundaries were determined with alloys made from 99.9 pct zirconium,* and cast under such conditions that the Vickers hardness of a alloys extrapolated to 95 to 110 VPN at 0 at. pct Sb. Such alloys were not suitable for investigations of the (a + ß) region, and the results shown in Fig. 1 near the (a+ ß) and (a +ß + Zr2Sb) regions were determined with purer alloys. These alloys had an extrapolated hardness range of 75 to 85 VPN and were made from 99.95 pct zirconium. A deviation from binary equilibrium occurs in Fig. 1 as indicated by the (a + ß) region of pure

Jan 1, 1959

Jan 1, 1933

By William P. Blake

In the recent litigation for the possession of franklinite by one party and of zinc-ore by the other party, it was shown by the evidence of experts familiar with the original condition of the outcrops that at Mine Hill a more or less disticctly defined layer of red zincore underlay the heavier and larger body of the franklinite, so-called ; this layer or bed of zinc-ore dipping under the franklinite upon the western cropping, while at Stirling Hill, two miles south, the conditions were apparently reversed, the zinc-ore overlying the franklinite. An explanation being required, it was shown, first, that at both places, at Mine Hill on the north and at Stirling Hill on the south, the ore-bed lies in a synclinal or trough-like fold with the red zincore under the franklinite; and secondly, that at Mine Hill, we see chiefly the outcrop of the western part of the folded bed and at Stirling Hill the eastern part; the Mine Hill cropping being on the western slope, and the Stirling Hill cropping on the eastern slope of the hill. Thus the ''back vein" at Stirling (the western outcrop) corresponds with the front-vein at Mine Hill, and, like it, has the red zinc-ore on the foot-wall, while the front-vein or eastern cropping at Stirling corresponds to the back-vein or eastern cropping at Mine Hill in the part of the bed generally known as the " buckwheat-field vein." If the ore-bed were continuous in one synclinal trough between the two localities, no further explanation would be required. But it is not so ; and the synclinal folds at both places pitch steeply to the north, bringing the beds to the surface in horseshoe-like curves at their southern ends or croppings, and carrying the beds far below the surface northwards. This justifies a doubt

Jan 1, 1895

By N. E. Holden, R. R. Goodrich

TheRe is a small area about Murray where bedded gold quartz veins occur in Prichard slate. The ore taken from the upper levels, during the early days, was free milling and was treated by stamp milling and amalgamation. There was likewise a considerable placer working. The report is current that tungsten (scheelite) was encountered, which interfered with the amalgamation in the stamp mills and which, in placering, collected in the riffles in the sluice boxes and clogged them. Consequently, in the quartz mines, the scheelite, when encountered, was rejected, being thrown into the waste, sometimes inside the mine and at other times outside on the dump. The free surface ores became worked out and as the ore in depth became pyritic and rebellious to amalgamation the mines closed down. Last spring tungsten ore brought a high price, near $80 per unit, 60 per cent. W03 and up. This so stimulated the output of tungsten ore that old dumps were explored and waste stored in the mines was gone over. Tungsten was likewise mined from virgin ground. So the district produced quite heavily for a time. The condition now is different. The price is not so high, about $20 per unit WO3, which makes profits questionable when mining in new ground. The accumulations from early day mining have been exhausted and the output has greatly declined. The Golden Chest mine was the heaviest producer of tungsten. The months of June and July were spent at this mine studying the problem. Since the mine had produced both gold and tungsten, we looked forward to the problem of recovering both from what might be called a gold-tungsten ore. A study of the Golden Chest vein showed this was not to be the case. While gold ore and tungsten ore come from the same vein, the tungsten ore is confined to a more or less disturbed or distorted portion

Jan 1, 1918

By I. R. Kramer

Single crystals of aluminum were pulled in tension in a solution of paraffin oil and stearic acid. The critical resolved shear stress did not change with the concentration of the stearic acid solution; however, the extents and slopes of Stages I and II were affected greatly. The observations lend evidence that the weakening effect of surface-active agents is controlled by the rate of desorption of the metal soap formed by the reaction of the surface-active agent and the metal surface. IT has been shown by various investigators1-" that surface-active agents markedly affect the mechanical properties of single crystals. (A surface-active agent, for the purpose of this report, is defined as a long-chain organic molecule which contains one or more polar groups. Usually, however, investigations have considered only molecules having one polar group.) In general, when single crystals are deformed in some solutions containing surface-active agents, the creep rate, Fig. 1, is increased and the yield strength is decreased. The fatigue strength has been reported to be affected also.ll Rehbinder and his asociatesl' explained the "weakening" effect of surface-active agents in terms of physical adsorption. They assumed that a large pressure was created in microcracks which existed on the surface of the crystal." Harper and Cottrell,' from their study of the effects of surface conditions, found that the deformation characteristics of zinc single crystals were not altered by a solution containing a surface-active agent unless the surface of the specimen had an oxidized surface. They concluded that the role of the polar molecule was to remove the strengthening effect of the oxide coating. Later, And-radeetBpresented additional evidence which appeared to agree with this conclusion. In contrast, Klinken-berg et al.7 reported data which confirmed the results of Rehbinder. Using zinc and cadmium crystals which had been cleaned by electrolytic polishing, a large increase in the creep rate was observed when Lle specimens were tested in a 1 pct oleic acid-paraffin oil solution. They also reported that the creep rate

Jan 1, 1962

By L. Obert, D. E. Stephenson

The objectives of this investigation were to develop a laboratory procedure in which core discing could be produced under known (and variable) stress conditions, and to study the discing characteristics of several fypes of rock. Discing of rock cores refers to the formation of discs or wafers of relatively uniform thickness which fracture or rupture on surfaces approximately *Fracture is a type of failure in which there is a complete loss of cohesion and fresh surfaces are created. Rupture is a type of failure in which there Is only a partial loss of cohesion. normal to the axis to the core (see Fig. 1). Usually the surfaces of the discs are concave-convex with the concave side toward the collar of the hole. The surface of the fractured discs are like those created by a tension failure (or possibly a shear failure with virtually no normal compressive stress). This phenomenon has been observed by a number of investigators1-5 in the course of diamond drilling in underground mines, especially in areas suspected of being under high stress. The state of stress in the core required to produce discing is not exactly known. Tranter and craggs6 theoretically investigated the stress distribution in an infinite cylinder, subjected to hydrostatic pressure, minus p, from z = 0 to z = 8 and unloaded from z = 0 to z = 8, Fig. 2. The exact solution to this problem shows that a tensile stress develops in the loaded region near z = 0 with the greatest tensile stress on the axis of the cylinder. A tensile stress also developed on the surface of the cylinder at a point just outside of the loaded zone. Jaeger and Cook3 experimentally investigated the discing mechanism by biaxially loading cores in a pressure jacket sealed at the ends by O-rings. According to the Tranter and Craggs theory it would be expected that failure should occur at the pressure discontinuity at the O-rings. The experimental results showed that if the specimen was unjacketed it broke at random points within the pressurized zone and at a pressure somewhat greater than the tensile strength of the specimen, presumably due to the development of a

Jan 1, 1965

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

The initiation of localized cracking in hydrogenated high strength steel was dependent on the developmeni of a critical hydrogen conceniration and relatively insensitive to the magnitude of the applied stress. The stress was believed to influence the deluyed failure process by providing the means for grouping the hydrogen. On the basis of an assumed distribution law the observed changes in the lower critical stress as a function of notch acuity, yield strength, and temperature were predictable over a significant range of these variables. THE phenomenological characteristics of delayed failure in high-strength steel have been comprehensively investigated and the behavior has been attributed to the strong embrittling action of hydrogen.1-3 Delayed failure or, as it is also termed, static fatigue, is the most sensitive means of detecting hydrogen embrittlement since it allows the maximum time for hydrogen diffusion during a test.3 The nature of delayed failure cail be aptly described by four parameters which are schematically depicted in Fig. 1. The upper critical stress corresponds to the rupture stress in a conventional notch tensile test. The lower critical stress or static fatigue limit is the stress below which no delayed failure will occur. The incubation period is the time required for the formation of the first crack and the fourth parameter is the failure time. An increase in hydrogen content, notch acuity, or strength level of the material increases the susceptibility for delayed failure by decreasing the lower critical stress, the incubation period, and the time to failure.lY3 A decrease in test temperature prolongs the incubation period in accordance with the lower diffusion rate of hydrogen, and also de-

Jan 1, 1961

By John K. Kennedy

ThE basic equations describing continuous zone-melting via the zone-void method were reported by Pfann. Using these equations, a theoretical study was undertaken in this laboratory on the effect of the variation of the significant parameters of the zone-void system. These parameters are the zone length, 1, the heater length, h, and the effective distribution coefficient, k. The object of this study was to determine the effect of these parameters on and (where a = Cp/Cf and ß = Cw/Cf, Cp, C,, and Cf being, respectively, the solute concentration in product, waste, and feed) so that, in future application of this technique to the ultrapurification of materials, the effect of 1 and h would be predictable regardless of the value of k. The basic assumptions made by pfannl were, for the purposes of this study, assumed to hold. For k < 1, the steady-state solute distribution in the stripping section and the shift in this distribution brought about by passage of a void is shown in Fig. 7 of Ref. 1. In this section the definition of k and ß precludes the possibility of ß assuming values less than unity when k < 1. In the course of this investigation it was found that computations based on Pfann&apos;s equations gave values of ß less than unity in the region 1 > k > l/h for almost all values of Ls, where Further computations showed that 6 assumes negative values when k > 1 for many values of L,, 1, and h. A check of the derivation of the stripping-section equations showed that an error had been

Jan 1, 1964

By A. U. Seybolt, R. L. Fullman

THE Hume-Rothery rule relating the relative sizes of the solvent and solute atoms in a substitutional solid solution for moderate to extensive solubility is, of course, well known and much used in the design of alloys. No such rule has been obtained for interstitial solid solutions, although a qualitatively similar relationship would be expected. Among the most common interstitial elements, oxygen, carbon, and nitrogen which can dissolve in important amounts in the transition metals, only in the case of oxygen is there enough solubility data available for an examination of the possibilities of a simple relationship between the extent of solubility and the properties of the metal solvents. Three properties were examined: 1—size of the octahedral space V into which oxygen atoms fit, 2— the elastic modulus E, and 3—the free energy ?F of formation of a low oxide, such as is known to be, or would be expected to be, in equilibrium with the terminal solid solution. The size factor or octahedral volume is so closely associated with the well known Hume-Rothery con- cept of size factor that additional development of this subject is hardly necessary. The octahedral volume used was not corrected to an elevated temperature, as this correction would have made no significant difference. The second factor, Young&apos;s modulus E, must be considered, since it is a measure of the strain energy required to force neighboring atoms apart so that an oxygen atom may enter the octahedral volume. The temperature dependence of the elastic modulus of many metals has been reported by Köster,1 but for a rather limited temperature range. Since the

Jan 1, 1955

By Fred D. DeVaney and

The coercimeter, as its name implies, is an instrument for measuring the coercive forcet of magnetic substances. It was developed by Davis and Hartenheim in the Special Studies Section, Metallurgical Division. A detailed description of this apparatus may be found elsewhere.2 The coercive force determinations of magnetic materials are interesting because of the relationship established by Gottschalk,4 who showed a linear relationship between the magnetization coercive force and the specific surface of comminuted particles. The value of this relationship in determining grinding efficiency has been shown by Dean.3 The determination of the surface contained in the subsieve sizes has always been a difficult problem for investigators. They made approximate measurements of the surface of coarse materials by sizing on screens, but for the determination of the surface of the sub-sieve sizes it was necessary to make detailed grain counts or elutriation tests, or to study dissolution rates. The technical literature contains many references to other methods for determining these surfaces, either by some special apparatus or by mathematical calculations based on distribution lines. Many of the methods are long and tedious, and the results of some, at least, are questionable. he turbidimeter gives quick results on ground cement. By using magnetite as the material to be ground, a simple determination of its coercive force by the coercimeter, requiring 10 minutes or less, can be transposed directly and accurately into units of relative surface. This subject has been pursued further by the U. S. Bureau of Mines in cooperation with the Missouri School of Mines and Metallurgy, Rolla, Mo., and the following is a description of the results.

Jan 1, 1939

By Fred D. DeVaney and

The coercimeter, as its name implies, is an instrument for measuring the coercive forcet of magnetic substances. It was developed by Davis and Hartenheim in the Special Studies Section, Metallurgical Division. A detailed description of this apparatus may be found elsewhere.2 The coercive force determinations of magnetic materials are interesting because of the relationship established by Gottschalk,4 who showed a linear relationship between the magnetization coercive force and the specific surface of comminuted particles. The value of this relationship in determining grinding efficiency has been shown by Dean.3 The determination of the surface contained in the subsieve sizes has always been a difficult problem for investigators. They made approximate measurements of the surface of coarse materials by sizing on screens, but for the determination of the surface of the sub-sieve sizes it was necessary to make detailed grain counts or elutriation tests, or to study dissolution rates. The technical literature contains many references to other methods for determining these surfaces, either by some special apparatus or by mathematical calculations based on distribution lines. Many of the methods are long and tedious, and the results of some, at least, are questionable. he turbidimeter gives quick results on ground cement. By using magnetite as the material to be ground, a simple determination of its coercive force by the coercimeter, requiring 10 minutes or less, can be transposed directly and accurately into units of relative surface. This subject has been pursued further by the U. S. Bureau of Mines in cooperation with the Missouri School of Mines and Metallurgy, Rolla, Mo., and the following is a description of the results.

Jan 1, 1939

By Carl Henrich

The Ducktown copper-mines are located in the southeast corner of Tennessee. The name Ducktown was originally given to a district occupying the southeast corner of Polk county, which in turn occupies the southeast corner of the State. Fig. 1 is a map of the vicinity of Ducktown, taken from the topographical surveys of the United States Geological Survey. The Ducktown district is bounded on the east by Cherokee county, North Carolina (the boundary-line between the two States running here a little east of north along the western slope of Pack mountain), and on the west by the eastern foot-hills of Little Frog mountain. On the north, Stansbury mountain, really a chain of low mountains or hills, forms the dividing-line between Ducktown and Turtletown districts. On the south, the Ducktown district extends beyond the Ocoee river to the Georgia State line.. This line, in going west, gradually recedes southwards from that river into the foot-hills of Big Frog mountain, the highest mountain of the neighborhood, which rises about 4300 feet above sea-level, while the surface of the Ocoee river, where it leaves the Ducktown district, is less than 1500 feet above sea-level. It will be seen from this description, and from a study of the map, that the Ducktown district occupies the northern part of a kind of basin, bounded on the east by Pack mountain and on the west by Little and Big Frog mountains. Between these mountains the Ocoee river, draining the basin, cuts its way to the Hiwassee and the Tennessee rivers in a narrow gorge, through the crystalline slates and schists, which from their excellent exposure in this Ocoee gorge have received the local

Jan 1, 1896

By William P. Blake

THE occurrence of enormous masses of pure copper has given the mining district of Lake Superior worldwide reputation. The first masses brought from there excited great attention, and directed the notice of the mining world to the few particular mines from which they were taken. It may not now be generally known that nearly all the veins which are worked, and which cut across the trap ridge, contain mass copper, and that large masses are continually being raised from them. The largest continuous mass which has been taken out was probably that from the Minnesota, in 1857, which is variously stated as weighing 420 tons and 470 tons. Its length was about 45 feet, its breadth or height 22 feet, and its greatest thickness 8 feet. All such masses are very irregular and ragged in their form and thickness, thinning out generally from a foot to a few inches, and straggling through the vein until they connect with other large masses. This was the character of a mass found in the Phoenix Mine, one of the oldest on the lake, which mass altogether weighed some 600 tons. But this was really a series of masses more or less connected by strings of metal, yet no one large part of it weighed, singly, over 200 tons. A similar series of masses, weighing about 600 tons, was extracted from the Minnesota. Some of the Phoenix masses were four to five feet thick of solid copper. The Cliff Mine has yielded masses weighing from 100 to 150 tons in one piece. One of 40 tons was taken out this year, besides numerous blocks weighing from 1 to 8 tons. This mine and the Central are now yielding mass copper in abundance. It is, of course, impossible to pick, or drill, or to break out such huge masses of solid metal when they are found, by drifting upon the course of the vein. The method of extraction is as follows The miner picks out or excavates a narrow passage or chamber upon one side of the mass, laying it bare as far as possible over its whole surface. It is usually firmly held by its close union with the vein-stuff, or by its irregular projections above, below, and at the end. If it cannot then be dislodged by levers, the excavation of a chamber is commenced behind the mass, and this excavation is made large enough to receive from 5 to 20 or more kegs of powder. In one

Jan 1, 1876

By E. S. Machlin, Morris Cohen

The martensite reaction in single crystals and polycrystals of 70 pct Fe-30 pct Ni alloys is shown to be autocatalytic in nature, producing bursts of transformation during cooling. The temperature of the first burst of transformation, called Mb, occurs below M, in these alloys. Experiments were devised to test the athermal embryo and strain embryo theories of martensite nucleation. The results indicate that internal strains, either within the virgin austenite or around existing martensitic plates, control the nucleation process in these alloys. Furthermore, the growth of martensitic plates is not limited by the attainment of an elastic balance with the austenitic matrix, but by the occurrence of plastic deformation at the martensite boundaries which interferes with the propagation mechanism. IN an investigation of the martensitic habit in single crystals of a 69 pct Fe-31 pct Ni alloy,&apos; it was observed that about 25 pct of the austenite transformed during subatmospheric cooling within the time-interval of an audible click. This event proved quite spectacular: The shock wave sent out from the specimen freely suspended on a thread in the refrigerating liquid was occasionally sufficiently intense to shatter the Dewar container and to separate the toluene column in the immersed thermometer. The Present investigation was undertaken to determine- the kinetics and mechanism of this "burst" type of martensitic reaction. The analyses of the alloys studied are given in Table I. The composition of the single crystal specimens is designated by alloy A, while the polycrystal-line specimens were made of alloys B and C as noted in the text. The single crystals were prepared in a vacuum furnace, using a modified Bridgman technique. Most of these crystals were homogenized by holding for 24 hr at about 1300°C just after solidification. However, it may be emphasized here that the degree of homogenization was not a controlling factor in the subsequent experiments, inasmuch as specimens having different degrees of homogenization yielded the same results. All of the single crystals were fully austenitic as slowly cooled to room temperature. An illustration of the burst phenomenon is given in Fig. 1, which shows oscillograms of electrical resistivity and temperature vs. time during the continuous quenching of 1/16 in. wire specimens (alloy B) in a dry ice and acetone bath at —77°C. There are at least two observable bursts in this case, as indicated by the sharp decreases of resistance accompanying the sudden formation of substantial quantities of martensite. The thermal arrest during the quench probably corresponds to the larger burst. Usually the bursts are followed by more or less progressive transformation during continuous cooling. It will also be noted that the resistance continues to decrease after the specimen has reached the bath temperature. This isothermal change denotes the formation of martensite at constant temperature, and will be the subject of another paper. Examination of fiducial scratches on the surface of a transformed single crystal has shown2 that the scratches in adjoining nonparallel martensitic plates are usually bent in opposite directions, as though one plate forms in such a way as to relieve the matrix stresses set up by the adjacent plate. This, together with some of the results described in ref. 1, Table I. Compositions of Alloys Studied, in Percent Alloy Ni C N Mn Si P S Cr A 31±0.3 0.048 0.027 0.003 0.56 0.007 0.002 B 29.5±0.2 0.036 0.02 0.19 0.09 0.008 0.006 C 19.99 0.52 0.37 0.47 0.010 0.015 0.04 led to the tentative concept that a cooperative action exists which provides the impetus for much of the transformation that appears during the burst. The following series of experiments were performed in order to test this idea. Cooperative Nature of the Burst Two adjacent disks, Va in. thick x % in. diam, were cut from a single austenite crystal of alloy A using a jeweler&apos;s saw. One of the disks was then cut into 15 parts. Then 12 of the latter pieces and the second disk were austenitized (stress relieved) at 600°C for 30 min and water quenched to room temperature. The temperatures at which the first burst of transformation appeared were determined for

Jan 1, 1952