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By H. W. Weart, D. J. Mack

SINCE the first recognition of eutectic solidification as the simultaneous formation of 2 solids from one liquid,1 many complex structures thus produced have been observed. Despite many attempts to ascertain it, however, the detailed mechanism by which these structures develop remains obscure. In an attempt to clarify the origin of eutectic structures, the study described in this paper was undertaken. The broad objective of the study was to investigate the effect of different solidification conditions on the structure of single eutectic grains. It was expected that the eutectic structure would thereby be isolated for study, but preliminary experiments revealed another structure within each grain. When a literature surveye revealed only 1 previous mention of the subgrain structure,' it was decided to determine the origin of the structure and to study its response to various growth conditions. Before presenting the details of the investigation, it is apropos to distinguish carefully among the 3 structures produced during eutectic solidification. This is especially desirable in view of the apparent confusion existing in the literature concerning the structures in a eutectic specimen. The confusion is due largely to the existence of the subgrain structure noted above which is easily mistaken for the grain structure. In the following paragraphs, an effort is made to distinguish the 3 structures by briefly describing their origin during solidification, even though the results are thereby anticipated slightly. The 3 structures produced during eutectic solidification are the grain structure, the colony structure, and the eutectic structure, each one contained by the one preceding it. The grain structure is analogous to the polycrystalline structure of a metal or inle-phase alloy in that each grain grows from a single nucleus. A somewhat broader interpretation is needed here, however, because of the presence of 2 phases in each grain. Since in most eutec-tics particles of 1 phase are dispersed in a matrix of the other, a grain may be taken to be the region in which the matrix phase is monocrystalline.*

Jan 1, 1959

By Alan Morris

BRASS rod for use in automatic screw machines is one of the major products of the brass mills. A large tonnage is consumed each year in the manufacture of an endless variety of finished articles and parts for assembly into other products. The machines that do this work have been developed to a high degree of efficiency, and their manufacturers are still striving for higher production speeds. This development has brought with it a demand for brass rod to meet the increasingly difficult machining conditions. This paper is a report of the results of tests undertaken in an effort to obtain a measure of the effects of such variables as lead content, microstructure and cold work on the machinability of brass rod. It is realized that the term "machinability" has never been well defined. Power, finish and tool life all should have a place in such a. definition. In practice it is sometimes found necessary to sacrifice some of these in order to obtain a rod that will not tend to throw up a burr, or will give a burr which is easily tumbled off. Again a specially stiff rod may be necessary because of long overhang from the chuck or a rod of special characteristics is needed to take a given broaching operation without chattering. It is only through an understanding of the effect of basic mill operations on the machinability of the rod that such problems as these may be solved most economically. It is hoped that this paper, together with the discussion it may evoke, will prove to be a basis for such an understanding.

Jan 1, 1932

By M. A. Grossman

The harden ability of most steels can be predicted within 10 to I5 per cent provided the complete chemical composition is known, including "incidental" elements; and provided the as-quenched grain size is known; and provided, finally, that the composition and heating temperatures for hardening are such as to result in austenite free from carbide particles. In the method proposed herein, the steel is considered as having a base hardenability due to its carbon content alone (the hardenability of a "pure steel" of the given carbon content, without any other elements), and this base hardenability is multiplied by a multiplying factor for each chemical element present. After multiplying all these together, the final product is the hardenability. Grain size may be taken into account either in the base hardenability or after the multiplication. Hardenability is stated in terms of "ideal critical diameter", namely, the diameter of bar, in inches, that will just harden all the way through (absence of un-hardened core) in an "ideal" quench, and the calculation may also be related to the Jominy test The data bring out certain features rather clearly. For example: i. It is quite useless to attempt to predict hardenability unless all elements, including "incidentals,,) are known; thus an "incidental,, chromium content of 0.20 per cent increases the hardenability by about 50 per cent. 2. The relative effectiveness of different alloys is sometimes unexpected; thus molybdenum when calculated in this way appears to be of the same order of effectiveness as manganese, rather than much more powerful, as would appear to be common experience; observe that an increase from no manaanese to 0.20 per cent Mn provides a multiplying factor of 1.67, and an increase from no molybdenum to 0.20 per cent Mo provides a factor of 1.63, an increase of over 60 per cent in each case. However, if to a steel containing 0.50 per cent Mn there is added "20 points of manganese," the factor is raised from 2.65 (for 0.50 per cent Mn) to 3.35 (for 0.70 per cent Mn), or an increase of only 26 per cent. Thus the fist small addition of an element has a much more powerful percentage effect than an equal further addition when some is already present, and in most cases the effect of molybdenum is considered in relation to a steel in which molybdenum is absent. 3. If two elements are equally effective, a greater hardenability will be obtained by using, for example, 0.5 per cent of each than by using I.o per cent of either of them alone. 4. A knowledge of the as-quenched grain size is essential for precise work, since a difference of only one grain size number (say No. 7 instead of No. 6) makes a difference of almost 10 per cent in hardenability (in these units); this, however, does not apply to certain It should be emphasized that in chromium steels (over 0.30 per cent Cr) and chrome-molybdenum and chrome-vanadium steels, un-dissolved carbides are likely to be present in the steel as quenched, and that in such cases the charts can indicate only a maximum Passible hardenability, whereas the extent of hardening actually obtained may be much less. Thus tests on a number of chrome-molybdenum steels have indicated a degree of hardening amounting to only 50 to 65 per cent of the maximum possible, and in chromium steels from full hardening (100 per cent) down to as low as 70 per cent. On the other hand, when the amount of such elements is small (Cr under 0.30 per cent, Mo up to 0.25 per cent in the

Jan 1, 1942

By M. A. Grossman

The harden ability of most steels can be predicted within 10 to I5 per cent provided the complete chemical composition is known, including "incidental" elements; and provided the as-quenched grain size is known; and provided, finally, that the composition and heating temperatures for hardening are such as to result in austenite free from carbide particles. In the method proposed herein, the steel is considered as having a base hardenability due to its carbon content alone (the hardenability of a "pure steel" of the given carbon content, without any other elements), and this base hardenability is multiplied by a multiplying factor for each chemical element present. After multiplying all these together, the final product is the hardenability. Grain size may be taken into account either in the base hardenability or after the multiplication. Hardenability is stated in terms of "ideal critical diameter", namely, the diameter of bar, in inches, that will just harden all the way through (absence of un-hardened core) in an "ideal" quench, and the calculation may also be related to the Jominy test The data bring out certain features rather clearly. For example: i. It is quite useless to attempt to predict hardenability unless all elements, including "incidentals,,) are known; thus an "incidental,, chromium content of 0.20 per cent increases the hardenability by about 50 per cent. 2. The relative effectiveness of different alloys is sometimes unexpected; thus molybdenum when calculated in this way appears to be of the same order of effectiveness as manganese, rather than much more powerful, as would appear to be common experience; observe that an increase from no manaanese to 0.20 per cent Mn provides a multiplying factor of 1.67, and an increase from no molybdenum to 0.20 per cent Mo provides a factor of 1.63, an increase of over 60 per cent in each case. However, if to a steel containing 0.50 per cent Mn there is added "20 points of manganese," the factor is raised from 2.65 (for 0.50 per cent Mn) to 3.35 (for 0.70 per cent Mn), or an increase of only 26 per cent. Thus the fist small addition of an element has a much more powerful percentage effect than an equal further addition when some is already present, and in most cases the effect of molybdenum is considered in relation to a steel in which molybdenum is absent. 3. If two elements are equally effective, a greater hardenability will be obtained by using, for example, 0.5 per cent of each than by using I.o per cent of either of them alone. 4. A knowledge of the as-quenched grain size is essential for precise work, since a difference of only one grain size number (say No. 7 instead of No. 6) makes a difference of almost 10 per cent in hardenability (in these units); this, however, does not apply to certain It should be emphasized that in chromium steels (over 0.30 per cent Cr) and chrome-molybdenum and chrome-vanadium steels, un-dissolved carbides are likely to be present in the steel as quenched, and that in such cases the charts can indicate only a maximum Passible hardenability, whereas the extent of hardening actually obtained may be much less. Thus tests on a number of chrome-molybdenum steels have indicated a degree of hardening amounting to only 50 to 65 per cent of the maximum possible, and in chromium steels from full hardening (100 per cent) down to as low as 70 per cent. On the other hand, when the amount of such elements is small (Cr under 0.30 per cent, Mo up to 0.25 per cent in the

Jan 1, 1942

By William Wraith

1. INTRODUCTION. AT the Washoe smelter,. Anaconda, Mont., the blister-copper from the converters is transferred, by means of a crane, to a refining-furnace,, in which it is brought to proper pitch by means of air and poles. From this furnace the refined copper, containing gold and silver, is poured into cast-iron molds placed on a platform-conveyor, giving an anode 36.75 in. long, 28 in. wide, and 21 in. thick. By reason of a disagreement between the smelter and the refinery, in reference to the silver-content of the anodes, it became necessary to investigate the methods of sampling used. II. SMELTER METHOD OF SAMPLING. At the smelter the sampling is done by " spotting " into water a small portion of the molten stream of copper as it flows from the furnace, by batting" the stream with a wooden paddle. The first sample is taken 30, min. after the pouring is started, three. other samples being taken at 1-hr. intervals, each sample weighing from 4 to 6 oz. The samples are dried, examined for particle's of burnt wood, screened on a 10-mesh screen of No. 8 wire to remove the fines, the oversize then screened on a 4-mesh screen of No. 20 wire to remove the coarse, the undersize of this screen being taken as the sample. Teh four portions thus obtained are thoroughly mixed and spli in half by passing over a 16-slot splitting-device, slots being 0.5 in. wide. One-half of the sample is sent to the laboratory for analysis and one-half kept as a duplicate. III. REFINERY METHOD OF SAMPLING. The method used at the refinery and also used in this investigation is the one developed by Dr. Edward Seller, of

Mar 1, 1910

By D. S. Choi, H. von Schonfeldt, H. D. Dahl

The design of pillars around a longwall panel in which the effect of the adjacent and worked-out panel is taken into consideration is discussed. A mathematical model is used to duplicate field observations such as opening closure and pillar rib movement. The model is then used to predict the effect of changes in mining geometry on the opening stability.

Jan 1, 1976

By E. G. Bailey

The bituminous coal industry faces a real problem, if it desires to retain the position in the power-generation field to which it is economically entitled. More power is probably produced today for electrical energy, for steam-driven and steam-heating industries and processes, for transportation by rail, water, highway and air, collectively, than ever before, and yet the total bituminous coal production has decreased about 38 per cent, from 575,000,000 tons in 1926 to 357,500,000 tons in 1934. It is not the intention of the writer to recommend coal as a fuel for automobiles and airplanes, but rather to point to these forms of transportation as being responsible in a very measurable degree for reducing the coal consumed by railroads. Petroleum products may still further reduce consumption of locomotive fuel through the extension of the use of Diesel-driven trains. Oil-burning steam-driven locomotivcs are replacing coal in some places, where railroads operating high-speed passenger trains are willing, temporarily at least, to pay a premium for the fuel that is low in ash and produces less smoke and practically no cinders. In the navy and ocean-going passenger ships, oil is so firmly established, and has such definite advantages over coal as formerly fired, in steaming radius, in ease of bunkering, cleanliness, and reduction in firing labor, that very outstanding developments in the handling and burning of coal will be rcquired in order to replace oil. For freighters on the Great Lakes, coal is the logical fuel, but there is great and immediate need of radical improvements in its use, else that market also may be lessened. It is not within the scope of this paper to discuss in detail bituminous coal for either locomotive or marine use, but, rather, generation of power in stationary plants, consisting of electrical generating stations and that very large group of miscellaneous industrial plants, such as paper, rubber, textile, steel and other industries that use electrical, mechanical, and steam power, derived from either hydro or some form of fuel.

Jan 1, 1936

By E. G. Bailey

The bituminous coal industry faces a real problem, if it desires to retain the position in the power-generation field to which it is economically entitled. More power is probably produced today for electrical energy, for steam-driven and steam-heating industries and processes, for transportation by rail, water, highway and air, collectively, than ever before, and yet the total bituminous coal production has decreased about 38 per cent, from 575,000,000 tons in 1926 to 357,500,000 tons in 1934. It is not the intention of the writer to recommend coal as a fuel for automobiles and airplanes, but rather to point to these forms of transportation as being responsible in a very measurable degree for reducing the coal consumed by railroads. Petroleum products may still further reduce consumption of locomotive fuel through the extension of the use of Diesel-driven trains. Oil-burning steam-driven locomotivcs are replacing coal in some places, where railroads operating high-speed passenger trains are willing, temporarily at least, to pay a premium for the fuel that is low in ash and produces less smoke and practically no cinders. In the navy and ocean-going passenger ships, oil is so firmly established, and has such definite advantages over coal as formerly fired, in steaming radius, in ease of bunkering, cleanliness, and reduction in firing labor, that very outstanding developments in the handling and burning of coal will be rcquired in order to replace oil. For freighters on the Great Lakes, coal is the logical fuel, but there is great and immediate need of radical improvements in its use, else that market also may be lessened. It is not within the scope of this paper to discuss in detail bituminous coal for either locomotive or marine use, but, rather, generation of power in stationary plants, consisting of electrical generating stations and that very large group of miscellaneous industrial plants, such as paper, rubber, textile, steel and other industries that use electrical, mechanical, and steam power, derived from either hydro or some form of fuel.

Jan 1, 1936

By H. W. Smith, A. K. Bjerring

A nonlinear dynamic model for a flotation cell is developed, using a number of simplifying assumptions, the most important of which is that of essentially complete liberation in the feed material. Using this model, a complete dynamic model for a flotation circuit is developed and calibrated against steady- state process data. The dynamic response of the circuit to disturbances in input feed rate and composition is simulated, as is the response of a linearized and simplified model on which control design might be more easily based. Preliminary results indicate the practicability of the modeling technique. However, difficulties in matching steady-state operating conditions in one process stream, and the apparent importance of recycle streams as indicators of process operation, indicate that inclusion of at least one species of middling particle in the model should be considered.

Jan 1, 1969

By O. C. Ralston

The use of copper sulfate for improving the flotation behavior of sphalerite is probably at least 15 years old. The original discovery of its activating influence is somewhat obscure. The story goes that in the mill at Mascot, Tenn., its favorable action was discovered by accident, early in 1914, as follows: The original laboratory test work on a sphalerite ore gave favorable flotation results, but after a mill had been built the flotation concentration of the ore was very unsatisfactory. In diagnosing the probable reasons, one fact pointed out was that the laboratory test machine had been constructed of bronze whereas the commercial machine allowed pulp to come in contact only with wood and iron. A plate of sheet copper was hung in the flotation machine and results immediately improved. At first fanciful explanations of electrolytic and electrostatic behavior were given credence, but when the copper plate was removed and a small amount of copper sulfate substituted in the pulp an even more favorable result was obtained. Toward the end of 1914 copper sulfate was also adopted in the acid flotation circuit of the Butte and Superior Copper Co. Just who is responsible for the original discovery the present writers do not know. It seems strange that in that era of flotation litigation this discovery was not patented. While for pragmatic purposes it [nay be sufficient to know that the mere addition of copper compounds to a flotation pulp is sufficient to activate the flotation of the sphalerite, for scientific purposes it is quite desirable to know more about how the action takes place. It is the purpose of this paper to present certain evidence dealing with the mechanism of the beneficial effect. The description of the effect as activation in contradistinction to depression is now common in both the English and German languages. It makes no assumptions as to whether the zinc sulfide surfaces have been filmed with copper compounds. In fact, the principal differences of opinion expressed in the literature deal with whether there is an actual formation of CuS (or even Cu2S) on the surface of the sphalerite. Activation of sphalerite takes place in alkaline, neutral or weakly acid solutions and whereas the present day flotation of sphalerite is usually in ah alkaline solution, the early use of copper sulfate was in a sulfate solution.

Jan 1, 1930

By Maurice Ewing, L. Don Leet

The most important quantitative method in seismic prospecting by refraction shooting is the method of profiles. A profile is established by firing a series of charges at various points along a straight line which terminates at the seismograph. The same data are obtained by repeatedly firing charges at one place and recording at a series of stations along the line of the profile. The quantities which are measured are the distance x from each firing position to the seismograph and the time t required for the first disturbance from each explosion to travel to the seismograph. These data are used in plotting the familiar time-distance graph. The only time-distance graphs that will be considered here are those obtained in localities where the velocity of propagation depends solely on the depth beneath the surface; that is, where there is no slope in the subsurface. The essential calculation to be made from such a time-distance graph is the determination of P(x), the maximum depth of penetration of a disturbance coming to the seismograph from a firing point at the distance x from the instrument. If the time-distance graph consists of a series of straight lines, as is often the case, the penetration P(x) can be calculated by means of formulas which appear in almost every description of seismic prospecting.' Until the present, however, the only formula that has been available for calculating P(x) for time-distance graphs which are smooth curves is one which requires an arbitrary assumption regarding the law of velocity increase with depth.2 The practice in these cases has been to approximate the curve by means of a number of straight lines and then to apply the ordinary straight-line formulas. This method clearly can yield accurate results only when a sufficiently large number of straight lines is used. The labor of computation increases rapidly when the number of lines is increased, so too few lines often are used. Further than that, there is a strong tendency to overlook the approximate nature

Jan 1, 1932

By Leslie G. McMillion

A field project to develop and demonstrate a method for alleviating problems of highly mineralized ground water where they occur as isolated zones or pockets in fresh-water aquifers is being conducted in the Ogallala aquifer of eastern New Mexico by the Robert S. Kerr Water Research Center. Removal of contaminated water is by a large-capacity well and the pumped poor-quality water is used locally for secondary recovery of oil. Benefits of the operation are threefold in that the aquifer is being reclaimed for future fresh-water production, contaminated water is being used beneficially, and fresh water which otherwise would have been used for waterflooding is available for other purposes. Ground-water quality in the site has improved markedly after two years of operation. Use of water in the arid and semiarid Southwest has grown so rapidly that demands in many localities far exceed available supplies. In the High Plains region of New Mexico, Oklahoma, and Texas, the only large sources of water are underground reservoirs, being depleted at an alarming rate. In some parts of this region, the aquifers contain pockets of highly mineralized waters; and the mineralized waters in some of them have started spreading in response to the drawdown effects of pumping wells. The aquifers of this region are primarily composed of sand and gravel beds; any cleanup by natural processes will require many tens or even hundreds of years. Most of these pockets of highly mineralized water were caused by oil-field brines seeping downward from earthen disposal pits. Thousands of these pits were in use in the region until only a few years ago when they were prohibited by the oil regulatory agencies of the respective states. The resulting areas of poor quality water are serious enough to warrant much corrective attention. Correction will involve one or more of three approaches: 1) Restrict the pumping of fresh water in the zones where the drawdown of the pumping well will significantly influence the movement of the contaminant. 2) Remove the highly mineralized water entirely from the affected area. 3) Develop and pump the poor-quality water in such a manner that its movement is held in check, even though only a part of the contaminant is actually removed. The principal hurdle to overcome in applying methods 2 or 3 is financing of the operations, since there are very

Jan 1, 1972

By D. H. Davis

HAND picking was the earliest form of coal preparation, first practiced to improve the outward appearance of the coal being loaded and to remove any pieces that might appear objection- able to the buyer. It is still extensively practiced on the plus 1-in. sizes and particularly on the plus 4-in. and larger sizes. The percentage of ash reduction that can be obtained by hand picking depends entirely upon the amount of free impurity occurring in the coal. In a particularly dirty seam, where a considerable quantity of rock occurs with the coal as mined, hand picking produces sizable reductions in ash. If the coal is prepared clean at the working face hand picking is a final check; in some cases, on the smaller sizes, it is practiced only to show that an effort is being made to prepare a clean product. Because of the variety and different methods of handling coal, the early plants were not always adapted for efficient hand picking. At most mines an attempt is made to remove the visual impurities at one or more of the following places in the surface plant? (1) in the tipple during screening; (a) on picking band, belt, or shaking conveyors;*(3) during the loading of the coal as it goes into the railroad car. Whatever the physical arrangements of the plant may be, the usual practice is to run the coal over the screen, picking table or boom at such a rate that each piece of impurity is exposed to the view of the picker. Coal should be uniformly sized and spread out on the table so as not to exceed one particle in depth. The flow should be even in tonnage and the speed of travel should be from 30 to 60 ft. per minute and not exceed 80 ft. per minute. The dirtier the coal, the slower the speed required for a fixed number of pickers. Actually, picking capacity depends on the number of particles per minute that can be picked out and rejected. The percentage of impurity removed is determined by this and the average weight of piece rejected. Handling a mixture of sizes from nut to the largest lump over the same picking table or conveyor is not conducive to efficient separation by hand picking because the lump hides the smaller

Jan 1, 1943

By R. T. DeHoff, L. J. Buteau, J. Kronsbein

Network topology is introduced and used to describe sinter bodies at various stages of the sintering process. The matrices of incidence, loop-branch. tree-branch, and cut-branch are constructed and their relationship to the three-dimensional void space and the common two-dimensional bounding surface is established. The sintering body is assunzed to remain connected but this is not so with the void space. The topological invariants known as Betti numbers are related to this observed fact and provide parameters which measure the progress of the sintering process. They are extracted from the matrices by means of known algebraic operations. Experimental procedures are given which permit actual construction of the various matrices and determination of the Betti numbers by serial sectioning of the sinter bodies. A sinter body is produced by exposing a large number of metallic particles (0.00001 to 0.3 in. diam) to a temperature that is near but below their melting point. When these particles are maintained at such a temperature for a sufficient length of time, it is found that the interparticle contacts become welded. As time increases, these welds, often referred to as necks, grow. All of the space between the particles constitutes a single connected void; an ultimate consequence of sintering is the breaking up of the void into separated parts. A mathematical apparatus for describing the geometric characteristics of a sinter body at each stage of the process was first proposed by F. N. Rhinesl when he introduced the application of topology to this problem. He described the sinter body in terms of one of its topological invariants, the genus. The most important advantage of a topological description is invariance with respect to continuous deformations. This means that particle sizes and shapes need not be considered, resulting in considerable simplification and generalization of the geometric description. In the case of a sinter body, wherein the internal geometry is particularly complex, the simplification provided by topological concepts is absolutely essential. The important parameters in the Rhines model are the number of particles and the interparticle contacts. The invariant considered called genus is given by Euler's formula for the connectivity of two-dimensional surface of the sinter body. This surface includes the pore-solid interface. The Euler formula is G = C - P + 1 [1] where C = number of interparticle contacts, P = number of particles, and G = genus of the surface bounding the sinter body. In topology the term genus may be used to mean the number of self re-entrant cuts that can be made on a closed surface without dissecting it into more than one connected surface. Its use is restricted to the surface and does not apply to the three-dimensional volume enclosed or excluded by it. In the case of sintering, the volume enclosed by the surface is defined as the sinter body; the volume excluded will be referred to as the void space. There is an intrinsic reason for using genus as a characteristic number associated with a sinter body. The genus is related to the Gaussian curvature by the integral of the product of the principal curvatures taken over the entire surface of the sinter body, as given by

Jan 1, 1965

By D. E. Coates, G. R. Purdy, S. V. Subramanian

The morphological stability of the planar solid-liquid interface in dilute ternary alloys, undergoing steady-state unidirectional solidification, is analyzed in terms of both the constitutional supercooling principle and the perturbation methods recently developed by Mullins and Sekerka. First, various steady-state solutions for the two solute distributions ahead of a planar interface are examined. The nature of the solutions depends on the size and concentration dependence of the off-diagonal diffusion coefficients. W~thin the framework of the constitutional supercooling principle, a cumulative contribution to instability frorn the two solutes is found to exist in the absence of diffusional interaction. It is shown that the latter can produce a further enhancement of instability or can have a stabilizing influence, depending on the form of the liquidus surface and on the sign of the solute-solute interaction. A perturbation analysis, which ignores diffusional interaction, verifies the cumulative influence of lhe solute fields and demonstrates that the Mullins-Sekerka stability criterion for binary systems (with capillarity accounted for) can be readily extended for application to ternary systems. SOME time ago, Tiller et al.' calculated the solute concentration distribution ahead of the planar solid-liquid interface of binary alloys undergoing steady-state unidirectional solidification. An earlier qualitative proposal that the transition from planar to nonplanar growth morphologies is associated solely with the onset of constitutional supercooling in the liquid layer ahead of the moving interface2 was used in conjunction with this calculation to put the now well-known constitutional supercooling (C-S) stability criterion into quantitative terms. Mullins and Sekerka,3 in a recent and very elegant analysis, established a more complete criterion (hereafter referred to as the M-S criterion). Interfacial stability was investigated by determining the time derivative of the amplitude of a sinusoidal perturbation of infinitesimal amplitude which had been introduced into the originally planar shape of the moving interface. Of particular importance is the fact that capillarity was included in the boundary conditions of their calculation. The purpose of the present paper is to extend all of this earlier work on dilute binary systems for application to dilute ternary alloy solidification. The analysis is divided into three sections. In the first the two solute distributions ahead of a moving planar interface are considered. Mathematical solutions are de- termined for situations in which: a) diffusional interaction is negligible, 6) diffusional interaction must be considered but circumstances permit use of constant diffusion coefficients, and c) the concentration dependence of off-diagonal diffusion coefficients can be described by first-order dilute solution approximations. In the next section, a stability criterion analogous to the C-S criterion is developed and the influence of diffusional interaction on interface stability is analyzed. Finally, the perturbation formalism of Mullins and Sekerka, with capillarity included in the boundary conditions, is extended for analysis of ternary systems in which diffusional interaction is negligible. The study of interface stability in binary systems usually commences with the assumption that the equilibrium distribution coefficient and the slope of the liquidus line are constant at values corresponding to infinite dilution. Similar assumptions have not been introduced into the present treatment; that is, we do not assume planar solidus and liquidus surfaces joined by tie lines which yield constant distribution coefficients. The latter involves the assumption of no ther-modynamic interaction between solute species in both the solid and liquid. We consider a ternary phase diagram for which the solidus and liquidus surfaces are, in general, nonplanar and of course pass through the corresponding binary solidus and liquidus lines. These lines are not assumed to have constant slope. In the dilute regions we are concerned with, the following assumptions are made: i) The solidus and liquidus surfaces are of a form such that both the solidus and liquidus temperatures are monotonically varying functions of each solute concentration. ii) The tie lines are such that the equilibrium distribution coefficient of a given solute is greater than unity for every point on the solidus (or liquidus) surface or it is less than unity for every point. STEADY-STATE SOLUTE DISTRIBUTIONS IN THE LIQUID As will be demonstrated in the next section, a knowledge of the steady-state solute profiles is not a necessary prerequisite for the formulation of a ternary C-S stability criterion. However, in that details, such as the complete description of the equilibrium liquidus temperature profile, require an evaluation of the solute distributions, the overall treatment is enhanced if these distributions are determined. Consider a ternary system (solvent plus solutes 1 and 2) for which a planar solid-liquid interface is in unidirectional motion at constant velocity V. At this stage it is unnecessary to limit ourselves to dilute solutions. For a stationary frame of reference the generalized forms of Fick's equations are:

Jan 1, 1969

By B. H. Kear, S. M. Copley

A dynamic theory of precipitation hardening in alloys containing cohevenl, stvess-.free, ordered particles is developed. The yield stvess is predicted from the stress dependence of the plastic strain vale, which is related to a derived dislocation velocity-stress function. The theory is shown to predict the magnilude and temperature dependence of the yield stress of a commercial nickel-base superalloy as well as many details of its slip structure. GLEITER and Hornbogen have developed a theory of the yield stress in alloys hardened by coherent, stress-free ordered ptrticles based on the observation that dislocations (b = a/2 (110)) glide in pairs.' When a dislocation pair shears through an ordered particle, the glide motion of the leading dislocation is impeded since it must create antiphase boundary (APB), whereas the motion of the trailing dislocation is assisted because it annihilates APB produced by the first one. Taking into account the APB energy, the size, and spacing of the particles, G-H predict the observed yielding behavior in Ni/18.8 Cr/6.2 A1 alloys composed of a matrix phase y '(nickel-solid solution) and particles of y' (basically Ni3A1). The G-H theory, as well as all previous theories of hardening by coherent ordered particles, do not include the details of dislocation motion; the present dynamic theory is an attempt to overcome this limitation. In the dynamic theory, the yield stress is predicted from the stress dependence of the plastic strain rate, which is related to a derived dislocation velocity-stress function. This function can be evaluated if the structure of the alloy, the APB energy of the ordered phase, and the characteristic drag or frictional stresses of the matrix and precipitate phases are known. The theory is shown to account for the observed temperature dependence of the yield stress in a commercial nickel-base superalloy. 1) NICKEL-BASE SUPERALLOYS Although their compositions are complex, the nickel-base superalloys have remarkably simple structures. A detailed examination of the commercial superalloy

Jan 1, 1968

By Robert I. Jaffee, Walter L. Finlay

IN the broad survey of the nonferrous' metallic elements contained in this book, the reader may well be impressed by the wide range of property combinations offered by the many metals and alloys the metallurgist has prepared since before Kubla Khan. The diversity is great and the overlap is considerable. It is particularly surprising, then, to find the latest structural metal new- comer designated by such extravagant terms as "Cinderella Metal," "Wonder Metal," "Miracle Metal," "The Metal of Tomorrow," "Dream Metal or Nightmare?" and "The Middleweight Champion of the Structural Metals." Of these and others, the most appropriate designation for the metal involved, titanium, appears to be that of The Middleweight Champion. Its intermediate density of 4.5 and elastic modulus of 16 million is a unique combination between the lower density and modulus of magnesium and aluminum and the higher density and modulus of copper, nickel, and iron. It is light, strong, ductile, and corrosion resistant. A chemical neighbor in group IV of the Periodic Table, zirconium, is similar to titanium in many respects but is appreciably denser, 6.5 instead of 4.5, less stiff and relatively much less abundant. On the other hand, the resistance of zirconium to acids and alkalies is better than that of titanium. Also, compensating for its higher density, lower stiffness, and somewhat lower strength level compared with titanium, zirconium has much better permeability to slow neutrons and is much more suitable as a material of construction for nuclear reactors.

Jan 1, 1953

By G. G. Priest, B. E. Morgan

The production of oil and gas from wells is often seriously hindered by the compaction of solids in the perforations during the perforating process. To realize the full productive capacity of a well, it is necessary either to remove the plugging material from the perforations or to perforate in a manner which does not cause plugging of the perforations. The latter method can be accomplished by having a non-plugging fluid in the casing at the time the well is perforated. This paper describes the results of laboratory tests, perforating tests, and experimental field tests which demonstrate that certain emulsions serve effectively as non-plugging perforating fluids. The principal components of these emulsions are two liquids: an aqueous phase consisting of a solution of either sodium chloride or calcium chloride, and an oil phase consisting of diesel oil, tetrachloroethylene, or a combination of both. Small amounts of other agents which serve to stubilize the emulsions, to reduce the fluid loss, and to inhibit corrosion are also present. The density of the emulsions is controllable within the range of 7.5 to 12.5 lb/gal; no insoluble solids are present, the filtration rate is low, and the thermal stability is satisfactory at temperatures as high as 200°F. The corrosion of steel by these emulsions is negligible. Tests conducted under conditions which simulate the temperature and the pressure in an actual well demonstrate that these emulsions fulfill the requirements of a non-plugging perforating fluid. In addition, lirnited field experience furnishes evidence that these emulsions remain in position after they are spotted, that they are retained in the casing after the perforations are made, and that they are easily removed from the perforations when the well is opened for production. When the pressure in the borehole is greater than the formation pressure at the time a well is perforated, plugging of the perforations can be avoided by spotting an emulsion adjacent the interval to be perforated. This procedure should eliminate low well productivity caused by plugging the perforations. INTRODUCTION Nature of Problem The most widely used method for the completion of oil and gas wells is to set and cement casing through productive horizons, and then to obtain production by gun-perforating the section of casing opposite the desired interval. This method is gen- erally successful and it was thought at one time that those failures which did occur were due to insufficient penetration by the perforator. Despite recent improvements in perforators which assure ample penetration, unsatisfactory fluid production continues to be a problem. Evidently, the trouble comes from some other source. Recent results obtained by Allen and Worzel1 demonstrated that low fluid productivity may be caused by the perforating process and/or by the fluid in the wellbore at the time of shooting. They found that perforations are often completely plugged by debris from the perforator, pulverized sand from the formation, and compacted solids from the drilling mud when the pressure in the wellbore is greater than the pressure in the formation at the time of perforation. In some cases a differential pressure in excess of 400 psi was required to initiate flow into the well through these plugged perforations. The plugging of perforations by solids not only causes low productivity from wells, but it creates simultaneously other problems in the production of oil and gas. For example, when most of the perforations are plugged, high rates of flow must occur through the few perforations that are open. The resulting high pressure drop may cause production

Jan 1, 1958

By A Allen, J. A. Garcia

The large increase in the wages of mine workers makes it imperative that all factors tending to limit production per miner be eliminated, if possible. The trolley and storage-battery locomotive, mining machine, hoisting engine, mining system, etc., have increased the possible output per man. But this output is still limited by the capacity of the hoisting engine and cable and by the size of the mine car. The superiority of skip hoisting in metal mining is shown by its almost universal adoption. By varying the size of skip and the rope speed, any desired tonnage can be secured and, since frequently only one kind of material is handled and breakage is unimportant, the loading of the skips can be easily and cheaply effected from bins into which the cars are dumped. The cars may then be designed to fit the conditions in the mine instead of being a compromise between hoisting and mining conditions, very likely suiting neither. In coal mines, the usual practice has been to hoist the car to the surface, either on platform or self-dumping cages. Of late years the number of skip-hoisting plants in coal mines has been rapidly increasing, but there is more or less inertia to overcome in establishing so radical a change in practice; also the earlier skip operations were not uniformly successful. As a result, it became evident that metal-mining practice would require radical modification before skip hoisting could be successfully used in coal mining. Objections to Skip Hoisting Breakage Except where coal is used for coking, or for other purposes whcre breakage is unimportant, breakage of the coal is vitally important all the way from the face to the railroad car. The average selling price is seriously reduced when the percentage of screenings is increased. Following metal-mining practice exactly, the coal would be dumped into a deep pocket, cut off into a skip load by a measuring hopper or other means, dumped into a deep, narrow skip, and dropped into a bin at the top, all of which would contribute to excessive breakage.

Jan 1, 1922

By N. Brown

From the theories of flow and fracture it is shown that the difference in reciprocals of the transition temperatures (OK) is a quantitative measure of temper ernbrittlement. Experimental data are given which support this conclusion. STUDIES of temper embrittlement have been made with various viewpoints; some involved a study of the kinetics of the reaction,',2'" others were concerned with changes in the mechanical properties," . and still others investigated the structural differences between the embrittled and unembrittled states by means of the microscope," -ray ,' measurements of electrode potential," and electrical resistivity." In all these studies, the difference in impact properties was the criterion for distinguishing between the embrittled and unembrittled states. By common agreement the difference in transition temperatures is now taken as a measure of the degree of embrittlement, and this measure is used as the quantitative measure upon which studies of the phenomenon are based. Vidal and Jolivet"' suggested that the degree of embrittlement was the same whether measured by impact or by a slow bend test. Their conclusion was based on tests at constant temperature. Jaffe and Buffum" using the impact and slow bend test showed that, for a given degree of embrittlement, the difference in transition temperatures varied with the method of testing. Hultgren and Chang" showed that the difference in transition temperature produced by the V-notched Charpy impact test was not the same as the value produced by the keyhole-notched impact test. This is a very fundamental point because there can be no true measure of temper embrittlement unless it is invariant with respect to the test method. Theory The purpose of this analysis is to show how the transition temperature depends on the stress distribution and the state of the material. The criterion for fracture may be stated as follws: where iF is some function of the principle stresses and F is a critical condition depending on the state of the metal. Similarly yielding occurs when Where is another function of the prin-ciple stresses and Y is a critical value depending on the state of the material. There is some controversy as to the exact form of the function f,.(u,, u,, us) but most experimental data give the following criterion:= where 8, and 6, = 21 or 0. Combinations of 6, and 8, give the various criteria such as the normal stress, the hydrostatic tension, and the maximum shear stress laws. Agreement is general that the octahedral shear stress law adequately describes the yield condition. where the bracketed factor will be called the design factor and depends on the stress distribution. Whether the metal decides to yield or fracture is given by the condition that The effect of temperature and strain rate upon Y has been studied by various investigators, It has been shown by MacGregor and Fisher" that

Jan 1, 1955