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By W. A. Backofen, D. L. Holt

Push-pull fatigue tests have been carried out at 4.2°K, 77oK, and room temperature on two poly crystalline materials of widely different stacking-fault energy (?): pure copper (? - 70 ergs per sq cm) and the Cu-8 wt pct A1 alloy (? - 2.8 ergs per sq cm). Constant stress-amplilude was imposed and measurement was made of the plastic-strain amplitude (ep) at saturation. Lives extended from 104 to 106 cycles. Designating lives at the various temperatures by NRT, N77, and N4.2. the ratios N77/NNT and N4.2/N77 ranged from 3.5 to 18 under the condition of common Ep . Metallo-graphic examination revealed different crack morphology in Cu-8 Al fatigued at room temperature, and at 77" and 4.2oK. At room temperature, cracks lay in or near grain and lain boundavies; at 77o and 4.2oK. cvacks were transcrystalline. Tests on single crystals of Cu-8 A1 showed that such a change in the cracking mode in polycrystallitle material accounted for a factor of- about 3.25 in N77/NRT . The longer life at lower tewperatztre (conslant cp) has heels attributed to two deuelopinents: a reduced production of the dislocation tangles and subgrain boundaries which serve as paths of rapid cracking, and suppression of oxygen chetni-sorption at the crack tip It was concluded that in both materials the luller accounted for an extension of the life at 4.2oK beyond that at room temperature by a factor of 15. XV ECENT experiments on the fatigue of Cu-A1 alloys in the so-called high-cycle range (greater than lo4 cycles) have emphasized the importance of stacking-fault energy (y) as a quantity affecting crack propagation rate and fatigue life.1,2 It was found in comparisons at essentially fixed plastic-strain amplitude that crack growth rate decreased by a factor of about 5 over the composition range from copper (? - 70 ergs per sq cm) to Cu-8 wt pct Al (? - 2.8 ergs per sq cm). The argument was made that, when stacking-fault energy is high, cross slip and climb are favored, so that dislocation tangles and/or subgrain boundaries form more readily under cyclic loading. Since the boundaries and tangles act as paths of rapid crack propagation ,3, 4 life is shortened as a result. However, when stacking-fault energy is reduced (as by alloying), cross slip and climb become more difficult, with the result that substructure formation is retarded and growth rate is also reduced. A purpose of the present work was to investigate the substructure effect in relation to temperature. As temperature is lowered, ? is varied only slightly (if at all), but decreased thermal activation can interfere with cross slip and climb. Thus substructure formation could be curtailed and life increased. Fatigue life in the high-cycle range is also known to be strongly influenced by environment. Working with copper, Wadsworth and Hutchings observed that life in a vacuum of 10-8 mm Hg exceeded life in air by a factor of 20.5 They isolated oxygen as the agent that furthered cracking. While the details are still unclear, a requirement in any mechanism of oxygen-accelerated cracking is that there be chemisorption at the crack tip. That could prevent welding on the compression half cycle,= interfere with reversal of slip,1, 6 or aid in breaking metal-metal bonds at the crack tip.5'7 In the work being reported here, temperature was lowered by immersion in liquid nitrogen and helium, which also served to reduce both the oxygen concentration and chemisorption rate. A possible effect upon life, i.e., a lengthening, had to be recognized. Several researchers have determined fatigue lives at low temperatures presenting their results in the form of stress amplitude (S) vs cycles in life (N) curves.8-11 Such curves reflect, primarily, the fact that metal is strengthened by lowering temperature; effects of substructure and changing environment tend to be masked. The difficulty can be overcome by comparisons based on identical plastic-strain amplitudes, and in the present work the dependence of life on both plastic strain and stress amplitude was established. EXPERIMENTAL Materials. The principal materials were polycrystal-line copper (? - 70 ergs per sq cm)" and the Cu-8 wt pct Al alloy (? - 2.8 ergs per sq cm),I3 the latter being near the limit of solubility of aluminum in copper and having, therefore, the lowest stacking-fault energy in the CU-Al system. Specimens were machined from 0.118-in.-diam cold-swaged rods of high-purity (99.999 pct) copper and the Cu-8 Al alloy, the latter produced initially in a graphite boat by induction vacuum melting a mixture of 99.999 pct Cu and 99.99 pct Al. The machined specimens were annealed to produce mean grain diameters of about 0.070 mm in copper and 0.190 mm in the alloy. Specimen dimensions are given in Fig. 1. Values of the tensile yield stress, ultimate strength, uniform strain (determined by the Considgre construction), and reduction of area, for both materials at 4.2oK, 77oK, and room temperature, are listed in Table I. The tensile apparatus in which these results were obtained has already been described.14 Apparatus. Specimens were fatigued in push-pull with a machine that is illustrated schematically in Fig. 2. The specimen is first soldered into the top grip (1) with Woods metal, and the grip is then screwed into the inner tube (2) which is connected to the drive rod of the Goodmans vibration genera-

Jan 1, 1968

By H. H. Stout

THE high copper price during the war stimulated the capacity to produce far beyond a possible normal consumption. The curves in Fig. 1 show this. The line YZ indicates, what the world production and consumption of primary copper nor-mally would have been, had not the 3 war upset the rhythm of industry. Granting that the maximum world production of 3,150,000,000 lb. in 1917 was obtained by crowding both the equipment and the grade of ore mined, yet in many instances addi-tional capital was invested, upon which the producer will be driven to earn at least a reasonable interest. During the period of deflation, or C liquidation, which we have entered, the consumption of copper will nat-urally be below the normal. Fig. 1 shows the actual consumption ex-pressed-in per cent. of normal : 1919, 96 per cent.; 1920, 94 per cent.; 1921, 70 per cent. The copper industry, consequently, faces: (1) Potential over-production capacity; I (2) Diminished consumption. To deny the existence of these factors would be illogical. To minimize the menace of this potential producing capacity might lead to regret. All past attempts at artificial control have not proved very successful. Obviously the remedy is to increase, if possible, the consumption of copper to a point where these factors cease to be dangerous. In ultimate analysis, this means: Produce an article so cheap and so good that no one can afford to use substitutes. The problem can be solved by: (1) Re-ducing price; (2) Improving product offered.

Jan 11, 1922

R. F. McELVENNY.- The next item is: "Center and other methods, vs. side charging." That was all discussed in the Carson case, and I do not know but what many of the plants are still using center charging. Some are using side charging. Did I understand that where you use the wet charge it is all side charging on the wet ore? B.-G. C. HONEYMAN.- We were on center charging for about a year with wet ore. R. F. McELVENNY.- Then you went to side charging. Has anyone any remarks to make on side versus center charging? E. A. BARNARD.- We have one side and one center, both on deep bath. It is an experimental proposition so far, but the side charge looks very favorable.. R. F. McELVENNY.- This is with calcine? E. A. BARNARD.- This is with calcine on a floating charge proposition.. They are both water jacket. The charge acts very similar on both center and side charging. The calcine spreads much the same as it does on the center charge. It will run down 75 ft. on the furnace side as well as the center. The advantage is in taking care of secondaries and things of that nature. C. BARDWELL.- Do you get any side wall protection from it? E. A. BARNARD.- No. R. F. McKENZIE.- Do you not project the side wall up to protect the skewback? E. A. BARNARD.- There is a slot projection down around the top of the bath; but the repairs on the side wall have been practically the same; that is, they, have been practically the same as they have on the center charge. A. H. RICHARDS.- A point I would like to make is that if you have any doubt about the center charging, we feel that we get better tonnages and lower fuel ratios and better slags with center charging than we ever got with side. Different kinds of charges would, of course, vary, and I could readily see that if you had the same advantage with deep bath smelting that you mention you would probably get just as good a slag and as good fuel ratios. E. A. BARNARD.- In fact, I think the calcine charge spreads more on the side than on the center charge. A. H. RICHARDS.- If you maintain a deep bath. E. A. BARNARD.- That is one thing we have to be careful about, to hold the charge back.

Jan 1, 1930

By T. W. Atkins

ATHOUGH the magnesium industry in this country is about thirty years old, not until American industry began to amaze the rest of the world and confound our enemies with the extent and variety of our war production did the industry begin to come into its own. At the outset of the war, only three companies were producing and fabricating magnesium in this country. Today, about sixty companies are producing, casting, forging, extruding, rolling, and stamping this lightweight champion of metals. Experience in alloying, processing. and fabricating the metal gained during the war years is now being translated into hundreds of civilian peacetime applications. In no sense should magnesium be considered as a substitute for other metals. It has come into popular favor because If many unique properties in addition to is being the lightest known structural metal. These attributes are toughness, igidity, corrosion-resistance, and the ease with which it can be machined and worked. Magnesium is the third most abundant element in nature. Sea water, magnesite,

Jan 1, 1946

By Olav Idelgeland

FROM indirect evidence point defects have been believed to influence the fatigue behavior of metals and alloys.1,2 Measurements of changes in resistivity made after cyclicstressing at low temperatures indicate that a very high density of defects is present, part of which may be removed by room-temperature annealing.3'4 These results are consistent with the generation of a high number of point defects at low temperatures. Corresponding measurements made after room-temperature stressing did not show any recovery effects.3 This was attributed to a stabilization of the dislocation network after a few thousand cycles without generation of vacancies. In this laboratory resistance measurements of copper single crystals, shaped as normal fatigue specimens ,5 have been made with a Kelvin double bridge at room temperature during and after cyclic stressing at 80 cps by comparing with a dummy at a close and constant temperature. Temperature differences were measured to ±0.025°C with fine thermocouples taped onto the gage lengths. Potential leads were tin-soldered into small holes in the gage length to give stable values. Corrections for differences in temperature and changes in mean length of the specimen were made according to the formula:

Jan 1, 1968

By W. Rogers Wade, Alfred Wandtke

The Pilares mine of the Moctezuma Copper Co. is situated at Los Pilares de Nacozari, Sonora, Mexico, about 75 mi. (120.7 km.) south of the international boundary and about 7 mi. (11.26 km.) east of the town of Nacozari de Garcia. It is situated at an elevation of 5000 ft. (1524 m.) in one of the northward trending ridges that form part of the mountain mass that culminates in the Sierra Madre de Mexico. To the east, south, and west, the topography is rugged and diversified; to the north less diversity exists, ranges of mountains rise sharply out of almost level ground and give the basin range structure characteristic of the Southwest. The climate is dry, the average rainfall of 15 in. (38 cm.) being confined almost entirely to the months of June, July, and August. The winter consists of a few days of disagreeable weather when a little snow may fall; the remainder of the year is thoroughly delightful. Vegetation is typical of a semi-arid region. In the canons near the mine, where water flows intermittently, willows thrive; on the northern slopes of some of the mountains and in some of the broader canons pines may even become abundant. The dominant rocks are flows and pyroclastics which are cut by dykes, stocks, and batholiths. The mountain just west of Nacozari is, in part, composed of limestone of an unknown age which occurs as a syncline and is undoubtedly a part of a prevolcanic land surface. Overlying the limestone and faulted against it, are the volcanics; cutting the limestone is a coarse biotite granite. Whether the granite is older or younger than the volcanics has not been definitely established. No attempt has been made to differentiate the rock types of the volcanic~, of which there are exposed 3000 ft. (914 m.) in thickness of basic and acid flows (andesites, latites, and rhyolites) and andesite and latite tuffs and breccias. The latite breccias, the youngest of these volcanic~, cover the highest mountains in the immediate vicinity. The

Jan 1, 1920

By D. E. Swets, R. C. Frank

It is well known that hydrogen is introduced into iron or steel as a result of many chemical processes (acid pickling, electrolytic cleaning, plating, etc.). One of the reactions that has been of recent interest1 is the reaction between an iron surface and water vapor. It was shown a few years ago2-4 that hydrogen can be introduced into steel at an accelerated rate during abrasion as a result of this reaction. Grun-berg and Scott have also observed that water in mineral oil lubricants increases pitting failure in ball bearings5 and they have suggested that hydrogen from the water is the primary cause of this effect.' In this laboratory, the question was raised as to whether or not hydrogen is also introduced into the metal surface of a bearing as a result of the decomposition of the hydrocarbon lubricant itself, and an experiment was performed to try to find a satisfactory answer. All steel parts contain some residual hydrogen. Therefore, it appeared that the best way to carry out this experiment without the need for highly accurate quantitative analyses was to use deuterium as a tracer. The natural abundance of deuterium in H2 is only 0.015 pct. The tracer was obtained in the form of deuteroparaffin (CD,(CDJ, CD,) and 0.25 g were dissolved in 20 cc of mineral oil to form the lubricant to be used in the tests. The bearings used were New Departure Type QOLOO ball bearings with a ball diam of 0.187 in. Prior to adding the mineral oil-deuteroparaffin lubricant, the bearings were cleaned in warm trichloroethylene to remove the packing grease. After packing with the new deuterated lubricant, the bearings were operated in a bearing fatigue test machine under a radial load of 190 lb and a thrust load of 190 lb at a speed of 3800 rpm. The expected life under these conditions is about 500 hr. Two tests were made; one for a period of 27 hr and the other for a period of 102 hr. The bearings achieved a temperature of 120o F during the tests. When the tests were stopped the balls were mechanically removed from the bearings and were immediately placed in liquid nitrogen to reduce degassing until the analysis for deuterium could be made. Before analyzing, the balls were warmed to room temperature and scrubbed with several degreasing agents to remove all traces of the deuteroparaffin mixture. This cleaning procedure was shown to be satisfactory by running a control test in which one ball bearing was subjected to all parts of the test except running in the fatigue machine. The hydrogen and deuterium were removed from the balls using a hot extraction apparatus attached to a mass spectrometer. Four balls from each bearing were analyzed. Each one was analyzed separately by removing it from a cold storage volume of the hot extraction apparatus and transferring it to the oven tube with a magnet. As the gases were evolved they were analyzed with the mass spectrometer. Since the hydrogen and deuterium pass through steel in the atomic form and since there are many more hydrogen atoms than deuterium atoms in the sample, the probability of forming an HD molecule is greater than forming a D2 molecule. For this reason the evolution of HD and H was followed as each ball was placed in the oven. The results showed that as each ball from the test bearing was dropped into the oven, the mass spectrometer recording of the HD evolution increased by about ten divisions. When balls from the control test bearing were dropped into the oven, the increase was about one division or less. The hydrocarbon background in the mass spectrometer was also monitored to see if hydrocarbons or deuterocarbons were given off when the balls were dropped into the oven, but no change in the hydrocarbon peaks was observed. Since the balls contained a fair amount of residual hydrogen, isotope ratio measurements were made on the gas obtained from each ball. The D/H value found for those balls which had been operated in the fatigue testing machine was consistently about 0.3

Jan 1, 1962

The fundamentals of blasting involve both the properties of explosives and of the rock being blasted. Four of the most important explosive properties appear to be energy density, bulk density, rate of energy release and the pressure- time history of the gases produced. Important rock properties are density and porosity, strength, and energy absorption including the effective moduli of elasticity. Rock structure also has a marked effect on its properties: for example, joints, bedding, and fracture alteration. Several mechanisms enter into rock fragmentation by blasting. These include slabbing, radial fracturing, crushing and bursting by the gas bubble. All of these factors are closely related to properties of both explosives and rock. Slabbing depends upon the first generated stress wave, whose shape and magnitude are a result of the pressure generated by the explosive, its time history and the resultant response of the rock, including its ability to sustain the stress wave. Actual slabbing, in turn, is a function of the magnitude and shape of the pressure pulse and the tensile strength of rock. Further fragmentation depends to a great extent upon the amount of gas in the bubble and its energy and pressure.

Jan 10, 1967

By H. l. Burghoff

DURING the course of preparation of crystals of alpha brass for an investigation of their creep characteristics, a number of critically oriented crystals were produced. In each of these specimens, P0, the specimen axis, lay near some important crystallographic direction or on or near the border of two possible slip systems. Because of the unusual nature of their orientations, it was considered of interest to deform these speci-mens in simple tension and to study orientation changes and any unusual occurrences, different from what would be expected for specimens in which only one slip system had distinctly the highest maximum resolved shear stress. Choice of actual operating slip system in a crystal offering an immedi-ate possibility of two slip systems would be expected to be due to chance, defect, or some inhomogeneity. Even in an ideally perfect crystal so oriented, the natural oscillations of the atoms about their lattice positions would give rise to a condition wherein one slip system would be favored over the other at the critical shear stress. In the large, nonperfect crystals of the present investigation, slip on both systems, but in different portions of the specimen, might occasionally be expected.

Jan 1, 1940

By Kenneth E. Mathews, Ross D. Hammett, S. Byron Stewart

Theoretical models have been important throughout the history of engineering as a means of understanding past experiences and predicting future performance. Most modelling involves assumptions and a degree of idealization, and it is shown that it is important that the effects of these be recognized when making use of models. One of the principal concerns in underground mining is the effect of the excavations on the states of stress in the rock adjacent to these excavations. As mining proceeds to depth, stress concentrations may be sufficiently high to cause inelastic behaviour of the rock and yielding along joint surfaces. At this stage, attention must be given to the sequencing of the mining process to ensure that the ground control techniques applied are optimized. Increasing use is being made of computer modelling techniques to assist with design. Three case studies are presented to illustrate the application of computer models in mine planning and ground control. In all cases, the data available for design was limited, but the mines were fully developed and openings could be inspected. The mining methods studied are cut and fill stoping, room and pillar stoping, and longhole stoping.

Jan 1, 1983

By R. E. Hook, R. L. McGaughey, A. M. Adair

The initial yielding characteristics of a vacuum-melted iron have been measured as a function of thertnal history after slow cooling or quenching from a 700°C recrystallizntion anneal. A thermal history favoring the segregation of interstitials to grairz boundaries results in a material having high values of upper and lower yield stress and long, irregutar Luders' plateaus, wheueas specimens treated to minimize grain boundary segregation have significantly lower values of these yielding characteristics. The struc- ture of typical grain boundary areas as revealed by electron transmission microscopy is consistent with these findings. The grain boundaries in iron are considered to be principally responsible for the release of dislocations during macroscopic yielding and it is suggested that strong locking results when a substantial amount of grain boundary segregution is present; it follows that weak locking results from a more random distribution of interstitials to grown in dislocations. RECENT years have seen an increased emphasis placed on a more quantitative study of the influence of grain boundaries on the yield behavior of bcc metals. The earlier picturk of dislocation pileups at grain boundaries building up a sufficient stress concentration to unlock dislocations in neighboring grains1

Jan 1, 1967

By T. L. Johnston

MUCH has been said and written about deep mine shafts and deep drill holes as man in his search for mineral wealth digs deeper into the earth's crust. Each year some new extra depth is heralded as a record, but with unlimited possibilities of going still deeper. In contrast to "digging deep," "mining high" is limited by the height of the mountains (Mt. Everest being the maximum with its 29,000-ft. elevation) and also by the extent of human endurance. An ex- ample of what might be called near- stratosphere mining in what is probably the highest mine worked by compressed air in the world is seen in a recent project in the Andes mountains of southwestern Bolivia.

Jan 1, 1939

By M. F. COOLBAUGH

WHEN I was asked to speak on the subject of leaching, I did not realize that a complete summary of recent progress in leaching had been given by Stuart Croasdale. I shall try to give some other phases of the subject that were not touched by Mr. Croasdale. Not all metallurgists are in harmony as to their methods of treating metals. If they were it would probably mean lack of progress. They can be divided into two classes-the pyrometallurgists, using fire means, and the hydrometallurgists, or those using leaching methods. Conflict is always good for progress; we have it in politics, and in religion there are fundamentalists, and those who are not fundamentalists. As representing pyrometallurgy, may I hope not to be classed among the fundamentalists. The leaching of ores is not new. The leaching of ores for the recovery of metals, however, is quite new. The older leaching was simply to recover the salts. Agricola, back in 1555, I think it was, outlined a great many methods of leaching for the recovery of salts. They called them solid juices at that time. There was no real competition, however, between leaching meth-

Jan 1, 1926

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

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

Jan 1, 1970

By Richard J. Robbins

Mechanical moles have developed through a tedious process of evolution. At times it has seemed that tunnel borers have been subject to the same Darwinian rules of evolution as their zoological namesakes who, despite their efficiency, are highly specialized and still restricted to soft soil conditions near the surface of the ground. HISTORICAL HIGHLIGHTS The Robbins Co. began its work in this field in 1947 with the development of a twin-bore continuous coal miner. Although these machines were used primarily in coal, two of the early prototypes were used to bore tunnels through shale. Disk cutters were first used on these machines and showed promising results as core breakers between drag-bit kerfs. In 1953, James S. Robbins and Assocs. undertook the development of a 25-ft 9-in.-diam circular tunnel borer for Mittry Construction Co. to be used at Oahe Dam in South Dakota (Fig. 1). This is believed to be the first rock tunnel-boring machine built since the end of the 19th century when short sections of the Channel tunnel were successfully bored in chalk from both the English and French shores. Another Oahe Dam machine was built in 1955, and then a series of three small-diameter machines for the company's first real experience with medium-hard and hard rock (Fig. 2) None of these three could be considered a success, although they laid the groundwork for the success that followed. Interbedded shale and limestone in Pittsburgh and hard limestone in Chicago quickly pointed up the weaknesses in these machines which were used by Perini, Dravo, and Healey. Among the problems were the high breakage rate of tungsten-carbide drag bits, too much flexibility in the drive shafts, failure of high-pressure hydraulic systems, chain-conveyor failure, and general lack of rigidity and strength. In 1956 another attempt at medium-hard and hard rock-boring proved this time to be a success and a significant turning point in the development

Jan 1, 1970

By C. H. P. Lupis, Henri Gaye

There are m -I conditions for the stability of a solution of m components with respect to infinitesinzal flucturations. However, in most cases, only one of these conditions has to be considered to determine the domain of instability and the existence of this more restrictive condition greatly simplifies the calculations. It may be used advantageously for the prediction of miscibility gaps and the method is illustrated in details for the case of the Ag-Pb-Zn system. THE thermodynamic conditions for the formation of a miscibility gap may be viewed as a necessary consequence of the conditions for spinodal decomposition. A previous article1 has examined in detail the form of these conditions for multicomponent systems. There is only one condition for the stability of a binary system (with respect to infinitesimal fluctuations), but there are two conditions for a ternary system, and m — 1 conditions for an m-component system. The probability of violating a stability condition, and thus forming a miscibility gap, obviously increases with the number of components, a result which is rather intuitive since the atoms of the solution have now many more ways of redistributing themselves and introducing complexities in the form of the free energy hy-persurface. It is of interest to take advantage of this possibility of precipitating new phases and to examine which stability condition is the likeliest to be violated, that is, which stability condition is thermodynamically the most restrictive. The finding of such a condition would greatly simplify the application of the stability criteria since only one condition could then be considered, instead of m - 1. In Ref. 1, coherency strain energy terms were neglected, thus restricting the applications of the treatment to solutions where they are negligible, such as liquid alloys. In the following study the same assumption will be made. To generalize the treatment to systems where the strain energy terms are sizable, the reader is referred to Cahn's classical article on spinodal decomposition.2 Let us designate by Gij the second derivative of the Gibbs free energy with respect to the number of moles ni and n j. There are several equivalent sets of m — 1 stability conditions.' The one considered here expresses that the successive diagonal determinants of order 1, 2, ... m — 1, associated with the symmetric Gij matrix (for 2 5 i, j 5 m) are positive.' For a binary solution 1-2, the condition for stability is: O(u=G22^0 [1] For a ternary system 1-2-3, the condition [I.] is re- tained (the value of G22 will differ, of course, according to the concentration of 3) and another condition is introduced: £>(21 = G22G33 - Gl3 ^ 0 [2] In a composition diagram, these two conditions define two domains of instability. Starting at a point where the solution is stable (for instance at a point where the solution is very dilute) we gradually change the composition until the condition [I] or [2] is violated. As already noted in the literature, e.g., in the work of Prigogine and Defay,3 it is the boundary of the domain (2) which is first crossed. For if we assume that the boundary of the domain (1) is reached first, at this point G22 = 0 and the second condition is necessarily violated (D(2) = -& 5 0), in contradiction with our original assumption. An exhaustive study of the ternary regular solution case may be found in the work of Meijering.4 Moreover if the boundaries of the two domains have a common point, they also have a common tangent. For if the two lines were to cross each other as is illustrated in Fig. 1(a) any point M in the line QP would be such that £> = 0 and 0"' > 0 which, as shown above, are incompatible results. Thus, the two lines must be tangent at their common point Q as illustrated in the example of Fig. l(b). The reasoning of Fig. l(a) implies that the point Q is not a "singular" point for either boundary line. This singularity may be of two types. First, the lines meet without crossing each other and without being tangent. Second, the tangent at Q for D"' or 0"' is not single-valued. Other types of singularity are unlikely because of the usual analytical forms of D"' and 0"'. The exception to the common tangent requirement due to the first type of singularity was pointed out by John Morral;5 it occurs when the common point, Q' or (3" in Fig. l(b), is located at a boundary of the composition diagram, e.g., at the line X3 = 0. It may also be noted that at the common nonsingular point Q of D(1) and D(2), Fig. 1(b), G23 is necessarily equal to zero, whereas at a point such as Q' or Q", this conclusion is no longer valid because the product G22G33 is now indefinite (of the form 0. a). The exception to the common tangent requirement due to the second type of singularity occurs when two branches of the same boundary line intersect, for example when D(1)or D(2) decomposes into a product of functions, at a point which belongs to the boundary of the other condition. It is possible to show by a simple analytical calculation that, in this case, if Q is a singular point of D(1), then it is necessarily a singular point of D(2), and that the reciprocal is true except if G33 = 0 at Q. For the present article, however, more elaboration on these singularities appears to be unwarranted. To generalize the previous results to an m -component system, we use the mathematical theorem stating that if the diagonal determinant D(r) = 0, then

Jan 1, 1970

By Philip D. Wilson

SPEED is essentiaI in this war program and it is hard to keep up with developments. When the title of this paper was chosen, the contemplated magnesium production for which plants were then under construction was some 200,000 tons of metal per year or sixty times the 3350-ton production in prewar 1939. A few- days later an analysis of the President's 185,000-plane pro-gram, incendiary bomb schedules, and the additional requirements of the Army. Navy and Maritime Commission made it apparent that a much greater amount of magnesium must be provided in 1943. The new figures are huge but the censor will not per-mit their disclosure.

Jan 1, 1942

By Karl W. Mote

CALIFORNIA'S iron and steel industry had its beginning in San Francisco in 1849 when the first iron casting was poured at the old Union Iron Works. Soon after, in 1856 at Grass Valley, enough iron ore was smelted to supply pig iron for the castings of a quartz mill there. From 1880 to 1886, iron ore was produced from the Hotaling mine in Placer County and converted to pig iron in a local blast furnace using charcoal. From 1907 to 1914, the Noble Electric Steel Co. produced pig iron from iron ore mined at the Shasta Iron Co. mine, and followed this for three years in the production of ferro-alloys. Between 1917 and 1941, the State's industry in- creased its capacity for open hearth and electric furnace scrap treatment, but the real impetus was supplied by the need for more steel at the beginning of World War II. The result was the State's first integrated steel plant-the Kaiser Steel Corp. facilities at Fontana.

Jan 7, 1958

By Ralph Arnold

Since 1915, when Elk Basin field was brought in, eight oil fields have been developed in Montana and the production has arisen from 50,000 bbl. in 1916 to 8,000,000 bbl. in 1926. The production for 1927 was 5,121,600 bbl. and the total up to the end of 1927 was 27,138,239 barrels. The eight fields, with their year of discovery are: Elk Basin, Carbon County (1915); Devil's Basin, Petroleum County (1919); Cat Creek, Petroleum County (1920); Soap Creek, Big Horn County (1921); Kevin-Sunburst, Toole County (1922); Lake Basin, Stillwater County (1924); Pondera, Pondera and Teton counties (1927); and Bannatyne, Pondera and Teton counties (1927). About 170 wildcat wells have been drilled in the state of which 8 were successful and 162 gas wells or dry. Hence, only one out of 21, or 5 per cent. of the wildcats have been successful. The average depth of the wells has been 1600 ft. and the average cost $32,000 apiece. • Up to Jan. 1, 1927, a total of 1376 wells have been drilled in the producing oil and gas fields of the state, of which 904, or 66 per cent., were successful oil wells; 82, or 6 per cent. were gas; and 390, or 28 per cent, were dry. The percentage of dry wells is excessive as compared to the wells in other states, due to the uncertainties of limestone reservoir rocks. The total production of oil to Jan. 1, 1927, has been 22,016,639 bbl. and of gas 7,265,330,000 cu. ft. The average price at the well for the oil has been $1.47 per bbl. and for gas about 4 c. per 1000 cu. ft. The value at the point of consumption has been about 23 c. per 1000 cu. ft. The total revenue derived from crude oil has been $32,277,119, and from gas 8350,613, or a total income to the producer of $32,727,832. Each well drilled in the state has already (to Jan. 1, 1927) averaged a return of over $21,000. The total number of domestic (Montana) oil and gas companies organized, since the first in 1885, has been 844, of which 702 are still alive and 142 dead. Oil and gas companies registered for operation within the state to Jan. 1, 1927, but with outside charters, are 143, of which 66 are alive and 77 are dead. Outside the few distributing companies, which are included in these figures, the grand total of 997 companies which have

Jan 1, 1928

By Will H. Coghill

WITH gold at $35 for the last four years, almost double the old figure, and 'an unlimited market, there is perhaps more activity in the mining and milling of that metal than in that of any other of the widely distributed ores. Despite threats from Russia, the Rand district is still dominant. In South Africa in 1936, 48,200,000 tons of gold ore was crushed after sorting out about 10 per cent of that mined. The pounding of 5914 trusty stamps on the 60 mi. of Rand reefs is noteworthy. At the end of 1935, 466 tube mills were operating on the Rand, the popular size being 6 1/2 by 20 ft. The grinding medium normally consists of ore pebbles picked from the ore but recently a composite load of 3-in. steel balls and pebbles has found favor for added capacity, a ratio of 2.5 tons of pebbles to one ton of halls being maintained. The total ore fed to the mills is only about 0.14 ton per hp.-hr. Such a slow rate 'of feed cannot help but result in overgrinding. Ball mills, 9 by 8 ft., some of which have come from Canada, are now being tried. Stamps have been ousted from all new flow sheets, but the old stamp mills are continually renovated and kept on duty as they are at the Homestake in the United States. Half of the world's gold and silver ores is still crushed by stamps, a few of which are single, dropping in individual mortars.'

Jan 1, 1938