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By W. A. Backofen, F. de Kazinczy

FRACTURING under conditions of particular interest is identified with the junction of curves relating tensile yield and fracture stresses to test temperature; the intersection point gives the lowest stress, for brittle fracture (at the ductility transition temperature). An expression for is found in Cottrell's brittle-fracture analysis, Eq. [15],1 while measurements of this stress and temperature have been reported for a low-carbon steel heat treated to differ-

Jan 1, 1962

By Roy J. Greenfield, Charles H. Stoyer

A geophysical survey was made in Kylertown, Pa., in an area where the ground water is polluted with acid mine drainage. Since acid mine water is a good electrical conductor, both direct-current electrical and electromagnetic loop methods were examined for their ability to determine the subsurface electrical conductivity structure and from this to imply the location of the acid water. Consistent results were obtained with the two methods and the interpreted subsurface resistivities were consistent with the electrical resistivity measured for water samples. It was demonstrated that fracture traces which act as conduits for ground water flow can be located with electromagnetic surveying methods. Thus geophysical methods for measuring subsurface electtrical resistivity can be used to advantage for monitoring the environmental impact on the ground-water system of acid mine water.

Jan 1, 1977

By H. C. Fowler

No exact demarcation can be made between producfion engineering and engineering research projects which interest production engineers because the results of today's engineering research make possible many of the applied production engineering methods of tomorrow. A corollary of the development of fundamental research is that so-called practical research becomes necessary. Assuming engineering research to include all subjects related to oil and gas production on which knowledge is being increased through experimentation and through analyses of data obtained from both the laboratory and the field, a review of the work of 1932 shows that the fundamental concepts of at least three major problems have become better understood—bottom-hole pressures, solubility of gas in oil, and fluid movement—and that the established data on the relationships of oil and gas have been applied to obtain more efficient and more economic production of both. Engineers no longer are concerned primarily with the initial development of devices for obtaining the pressures at the bottom of wells. Advancement in the technique of obtaining reliable pressure readings in wells has been rapid. One of the first public suggestions regarding apparatus for obtaining precise information at the bottom of oil wells was made before the Petroleum Division of the A.I.M.E. in 1928. Even during the early development stages in East Texas, reservoir pressures were estimated from well-head observations. Soon, however, a number of proved devices and methods were available, and today bottom-hole pressures in many fields are being recorded and studied as an essential part of the production programs. The research now turns to interpretations of data, obtained with these devices, in terms of reservoir energy and to the development of methods whereby the oil and gas will be withdrawn in accordance with rational and equitable programs based on oil-gas-energy relationships. The term ((bottom-hole pressures" should not be interpreted as indicating the full scope of all research on this problem. By using pressure (and temperature) data obtained in related vertical-flow studies,

Jan 1, 1933

By Ben B. Sweet

The ongoing controversy over mining and agricultural use of ground water in Arizona underscores the importance of this commodity to both industries. Although the principles presented in this article are fundamental, a method of systematic data collection and interpretation is provided for evaluating a water well by a set of uniform standards common to all areas where ground water is a primary source of supply.

Jan 8, 1978

By Bernard Kopelman

The particle size of tungsten metal powder used to make tungsten wire for use in radio tubes and incandescent lamps must be closely controlled if the highly desirable feature of nonsagging is to be achieved. Our knowledge of factors affecting the particle size of tungsten powder has been limited by lack of any extensive literature on the subject. There are no publications in the English language discussing this problem in any but the most general terms. In this paper the published experimental information on this subject is reviewed. Based on the published data and some experimental data obtained by the author, a general theory of factors affecting the particle size of tungsten metal powder obtained by reduction of the oxides in hydrogen is offered. The various forms of the tungsten oxides and tungsten metal used in the experiments described were those prepared by commercial processes, so that the experimental results obtained on a laboratory scale would be more directly applicable to actual commercial reduction conditions. The effects of time of reduction, temperature. and concentration of water vapor in the hydrogen were observed by counting microscopically the particle distribution obtained. Such a method is very time-consuming, but the data obtained by this method are more reliable and more fundamental than those obtained by any of the several instruments available for measurement of particle size. Review of the Literature Until the year 1912, tungsten powder was prepared commercially by reducing tungstic oxide in the presence of carbon or one of its compounds (such as glycerin or ethylene glycol), usually by firing the mixture in a closed fire-clay crucible. The resultant powder contained about 95 per cent tungsten.' When reduction of tungsten oxides by H² was introduced Commercially,²,³ several investigators became concerned with the equilibria between tungsten metal and its several oxides in an atmosphere of hydrogen and water vapor.4-l3 While these many investigations were in fair agreement on the equilibria WO³ + H2 = WO2 + H2O and WO2 + 2H2 = W + 2H2O there arose considerable controversy as to the chemical composition of the oxide between WO³ and WO², because of very poor agreement on the equilibrium constant of this intermediate oxide reduction reaction. The controversy on this intermediate oxide has been in progress for more than 100 years. Thus Malguti,14 in 1835, decided it was WO2.56 In 1857, Riche15 proposed the formula W³O8. Usler,16 in 1865, confirmed the existence of WsO8 and further proposed W1O1l. In 1897, Desil7 agreed upon W²O8 but also found W5O14.

Jan 1, 1947

By Bernard Kopelman

The particle size of tungsten metal powder used to make tungsten wire for use in radio tubes and incandescent lamps must be closely controlled if the highly desirable feature of nonsagging is to be achieved. Our knowledge of factors affecting the particle size of tungsten powder has been limited by lack of any extensive literature on the subject. There are no publications in the English language discussing this problem in any but the most general terms. In this paper the published experimental information on this subject is reviewed. Based on the published data and some experimental data obtained by the author, a general theory of factors affecting the particle size of tungsten metal powder obtained by reduction of the oxides in hydrogen is offered. The various forms of the tungsten oxides and tungsten metal used in the experiments described were those prepared by commercial processes, so that the experimental results obtained on a laboratory scale would be more directly applicable to actual commercial reduction conditions. The effects of time of reduction, temperature. and concentration of water vapor in the hydrogen were observed by counting microscopically the particle distribution obtained. Such a method is very time-consuming, but the data obtained by this method are more reliable and more fundamental than those obtained by any of the several instruments available for measurement of particle size. Review of the Literature Until the year 1912, tungsten powder was prepared commercially by reducing tungstic oxide in the presence of carbon or one of its compounds (such as glycerin or ethylene glycol), usually by firing the mixture in a closed fire-clay crucible. The resultant powder contained about 95 per cent tungsten.' When reduction of tungsten oxides by H² was introduced Commercially,²,³ several investigators became concerned with the equilibria between tungsten metal and its several oxides in an atmosphere of hydrogen and water vapor.4-l3 While these many investigations were in fair agreement on the equilibria WO³ + H2 = WO2 + H2O and WO2 + 2H2 = W + 2H2O there arose considerable controversy as to the chemical composition of the oxide between WO³ and WO², because of very poor agreement on the equilibrium constant of this intermediate oxide reduction reaction. The controversy on this intermediate oxide has been in progress for more than 100 years. Thus Malguti,14 in 1835, decided it was WO2.56 In 1857, Riche15 proposed the formula W³O8. Usler,16 in 1865, confirmed the existence of WsO8 and further proposed W1O1l. In 1897, Desil7 agreed upon W²O8 but also found W5O14.

Jan 1, 1947

By M. S. Klima, P. T. Luckie

An evaluation of the operating performance of a recently designed pneumatic centrifugal classifier is presented. This classifier has been modified from a separate air and feed input design to an entrained solids in air feed input. The evaluation first required determining the size distributions for the three streams (feed, fine, and coarse). Using size distribution data and mass flow rates, a size selectivity curve was calculated for each operating condition tested. This curve, in turn, was characterized by appropriate selectivity parameters (i.e., the equiprobable or cut size, the sharpness index, and the apparent bypass values). The variation of these parameters with classifier operating conditions was examined. From these evaluations, the "best" operating conditions for the classifier were then determined.

Jan 1, 1985

By Christopher Haycocks, J. Richard Lucas

The growth of computer and ground control technology in recent years, combined with an urgent demand for low-cost fossil fuels and mineral resources, has set the stage for full-scale utilization of computers in mine planning. Steeply rising production costs and the need to preserve the environment are placing great demands on engineers to improve their mining efficiencies, which can best be accomplished by applying the full capabilities of the computer. Pressure to develop and perfect programs with an immediate potential for improving mine design, reducing mining costs and extending the viable coal reserves of the country has already come to bear in the form of exploding energy requirements, environmental considerations and the visible limitations of other energy sources.

Jan 4, 1973

By William Brewster

DATING back some five years ago, various foundries made inquiries as to the probable total carbon content in a given specification and grade of pig iron. Up to that time we had no data, and except for a few occasional determinations of total carbon, no attempt had ever been made to set up routine determinations of total carbon. In fact, at that time, a cast analysis was considered sufficient, without examining at further length into possible variations of analysis between ladles of the same cast. In view of the various inquiries as to total carbon, we sampled all piles of all grades of pig iron, making complete analyses. Finding some variation in carbon content, we secured more samples and plotted the carbon content with respect to silicon in each grade of iron except for the higher phosphorus foundry iron, where it was necessary to divide the group into twenty-point phosphorus ranges. This is easily understood, owing to the falling off of carbon content with the increase in phosphorus con-tent, silicon in each case being the same. In addition, these curves clearly demonstrate the lowering of the carbon content as the silicon is increased. In order to insure accuracy and reliable determinations the following method of sampling and analysis was employed: Two pigs selected from each end of the car, each car containing iron from one 50-ton ladle, are drilled with a 5/16-in. drill all the way through from top to bottom in the center of one section of the pig. The drillings are collected and transferred to an 80-mesh sieve; the portion passing through and the portion retained are placed in separate envelopes and labeled accordingly. The amount of sample in each envelope is weighed to obtain the proportionate amount of coarse and fine drillings, then a factor weight of sample (1.3636 grams) made up of proportionate

Jan 1, 1936

By Milton Williams

IT is generally recognized that fluid is lost from rotary drilling mud s to permeable strata during normal drilling operations;1,2,3 but that this fluid is the filtrate from the mud, rather than the mud itself, has been shown by various workers.1,4,5 . The presence of this filtrate in oil-bearing or gas-bearing strata is undesirable and harmful. The decreased permeability of the stratum to oil effected by the presence of water has been pointed out by several investigators,6,7 and since, in the production of the reservoir fluid, the greatest pressure drop occurs immediately adjacent to the borehole, it follows that infiltered water is particularly objectionable in this region. Again, this filtrate tends to make electrical logs less reliable, since oil in the proximity of the borehole is probably flushed out to an appreciable ent by the water.8 Observation of side wall cores may be misleading for the same reason. Drill-stem tests in low-pressure areas may be of doubtful value where no oil is recovered, unless sufficient time is allowed for production of water lost from the mud. The infiltered water may hinder drilling operations by softening shales and causing sloughing; the "tight hole" occasioned by excessive deposition of filter cake in the hole is a common occurrence. The filter cake remaining on the face of the producing formation may itself sometimes be detrimental to production.9 In view of these implications of the importance of filtration of mud, an investigation was undertaken to determine the factors involved in the infiltration process, and to correlate these in such a manner that the values obtained in routine filter tests employing a conventional filter of the "wall-building tester" type,10 together with data on size of hole, drill pipe, and rate of mud circulation, could be used to estimate water loss and distance of penetration of the filtrate into strata.

Jan 1, 1939

By J. E. Lawrence

Copper-decorated lattice disorders in silicon have been analyzed by electron transmission microscopy, chemical etching, and P-N junction reverse current measurements before and following different gettering treatments. Lattice disorders acted as the nucleating sites for copper precipitation. Copper precipitates in silicon resist chemical etching, absorb electron beams more than silicon, and cause excess reverse currents. Totally gettered disorders will chemically etch rapidly, be transparent to electron beams at extinction contrast, and not contribute to excess reverse currents. Three different gettering procedures were performed to determine the effectiveness of different EXTRANEOUS metal contamination can alter the minority carrier lifetime and resistivity of bulk silicon as well as cause excessive reverse currents in semiconductor devices. Previous workers have reported such activity for gold,1,2 copper,'-* iron,' and rnanganese.2,5 Gettering is a method employed to render these impurities electrically inactive. However, some property of the junction-degrading metals prevents gettering procedures from being wholly reliable. The comparative effectiveness of gettering with different agents has been the topic of earlier publications.2,3,6-11 Two mechanisms for gettering metallic impurities have been proposed: the distribution coefficient mechanism by Thurmond and Logan7 and the compound formation mechanism by Goetzberger and Shockley.2 Both of these models evolved from data gettering mechanisms. First, phosphorus was allowed to enter a protective SiO2 film but remain away from the Si-SiO2 interface to test the effectiveness of the compound formation gettering mechanism. Second, phosphorus was allowed to enter the backside of silicon wafers to test the effectiveness of the lattice strain gettering mechanism. Finally, nickel was diffused into the backside of silicon wafers to test the effectiveness of the distribution coefficient gettering mechanism. In each case, copper precipitates dissolved as a result of the gettering treatment. Tightly packed precipitates will resist gettering more than loosely packed copper precipitates. acquired by the electrical analyses of gettered semiconductor materials. An electrical analysis, however, cannot identify the fate of the gettered metals. The radiotracer technique has recently been applied to determine the redistribution of metals following different gettering treatments.3,9,10 The spatial resolu tion of the radiotracer technique prevented the analysis of metal precipitates which contribute to the excessive reverse currents of P-N junctions. The gettering processes employed by the earlier workers, almost without exception, allowed the gettering agent to enter the silicon lattice. This procedure makes it quite difficult to differentiate between the distribution coefficient and the compound formation mechanisms. The metallographic analysis of gettered copper precipitates discussed in this work supplements the earlier work by obtaining direct evidence of silicon lattice defects decorated with copper before and following different gettering treatments. The effectiveness of a process which restricts the gettering agent, phosphorus, to a dielectric film and thus away from the silicon lattice is discussed in addition to the ef-

Jan 1, 1969

By P. M. Blair, D. W. Peaceman

The shape and position of the gas-oil transition zone during downdip displacement of oil by gas has been calculated using flow equations which include the effects of gravity, relative permeability, capillary pressure and compressibility of the fluids. The calculations treat the problem in two space dimensions, and results are compared with data from a laboratory model tilted at 30° and 60° from the horizontal on displacements near and above the maximum rate at which gravity segregation prevents channeling of the gas along the top of the stratum. The good agreement between calculated and experimental results demonstrates the validity of the tecbnique as well as that of the flow equations. INTRODUCTION Knowledge of the fluid distribution and movement in an oil reservoir is important in producing operations and estimation of reserves. The history of the oil industry has included steady progress in improving the accuracy of calculations which provide the required knowledge. The earliest method of calculating reservoir performance consisted of material-balance equations based on the assumption that all properties were uniform throughout a reservoir.l For many reservoirs such a simple formulation is still the most useful. However, when large pressure and saturation gradients exist in a reservoir, the assumption of uniform values throughout may lead to significant error. To reduce these errors, Buckley and Leverett2 introduced a displacement eqation which considers pressure and saturation gradients. Methods available at that time permitted solutions to the Buckley-Leverett equation in one space dimension; these solutions have been very useful in solving many problems related to the production of oil. However, the one-dimensional methods are not adequate for systems in which saturations vary in directions other than the direction of flow. An example of such a system is the case of gas displacing oil down a dipping stratum in which the gas-oil contact becomes significantly tilted. Of course, the Buckley-Leverett displacement method cannot predict the tilt of the gas-oil contact. Recent improvements3,4 of the one-dimensional Buckley-Leverett method achieve some success in predicting the tilt of the gas-oil contact at sufficiently low flow rates. However, at rates high enough that the viscous pressye gradient nearly equals or exceeds the gravity gradient, even these improved one-dimen,sional methods incorrectly predict the shape and velocity of the contact. Further progress in estimating such fluid movements in a reservoir appears to require consideration of the problem in more than one space dimension. The recent two-dimensional method of Douglas, Peaceman and Rachford5 appears adaptable to calculate changes with time of the saturation distribution in a vertical cross-section of a reservoir. The movement of saturation contours should represent the moving fluid contacts and include the effects of crossflow due to gravity, as well as variations in the rock and fluid properties. The nonlinear nature of the equations used in the method has prevented proof of the validity of the solutions. Douglas, Peaceman and Rachford made some comparisons with experiment but did not include cases in which gravity was important nor cases involving displacement by the nonwetting phase.For these reasons, a test of the two-dimensional method for a case in which these factors are included would be very desirable. The test selected was a comparison of calculated results with those from a carefully controlled laboratory experiment on a model with measured physical properties. The model selected was one in which gas displaced oil down a tilted, rectangular sand pack. The model can be thought of as representing a vertical cross-section taken parallel to the dip of a reservoir. The displacement thus simulates gas displacing oil downdip that might result from gas-cap expansion or gas injection. This report outlines the calculation method used

By D. L. Katz

In the management of oil properties, it is always desirable to know the future behavior of oil wells and oil reservoirs. Some estimation of the quantity of oil and gas that will be produced must be made as a basis for decisions on possible returns on investments in lifting equipment, drilling of additional wells, and other operating expenditures. In new or wildcat areas, operating expenditures are considered highly speculative, but in the completion of partly drilled and the operation of producing fields it is good business to remove as much speculation as possible. An accurate knowledge of oil and gas reserves in such cases would solve many management problems. The term "oil reserves" usually signifies the future ultimate recovery without specifying the method of production. Thus with changing methods and innovations in the production industry, reserves of any definite reservoir may be increased by increasing the portion of oil recovered. The usual reserve estimates are made by comparisons of well and formation characteristics, by using a percentage recovery on the oil content of the formation volume using porosity data, by extending production curves on non-prorated wells, or by extending bottom-hole pressure-production curves. The most reliable method would appear to be one that would estimate the initial quantity of oil and gas present and then obtain percentage recovery values for various productive methods and formations from experience. It is the purpose of this paper to describe a method of estimating the initial quantity of oil and gas present in a reservoir. The method is based on field operating data and the properties of crude oil-gas mixtures. The principles involved, the data required, the assumptions necessary, and an example of the method will be given. The method is entirely independent of sand volumes and formation porosities. Principles of Method The method of estimating the initial quantity of oil and gas present is based upon the premise that the volume occupied by oil and gas in the reservoir is constant and that a mixture of crude oil and gas will behave in

Jan 1, 1936

By D. L. Katz

In the management of oil properties, it is always desirable to know the future behavior of oil wells and oil reservoirs. Some estimation of the quantity of oil and gas that will be produced must be made as a basis for decisions on possible returns on investments in lifting equipment, drilling of additional wells, and other operating expenditures. In new or wildcat areas, operating expenditures are considered highly speculative, but in the completion of partly drilled and the operation of producing fields it is good business to remove as much speculation as possible. An accurate knowledge of oil and gas reserves in such cases would solve many management problems. The term "oil reserves" usually signifies the future ultimate recovery without specifying the method of production. Thus with changing methods and innovations in the production industry, reserves of any definite reservoir may be increased by increasing the portion of oil recovered. The usual reserve estimates are made by comparisons of well and formation characteristics, by using a percentage recovery on the oil content of the formation volume using porosity data, by extending production curves on non-prorated wells, or by extending bottom-hole pressure-production curves. The most reliable method would appear to be one that would estimate the initial quantity of oil and gas present and then obtain percentage recovery values for various productive methods and formations from experience. It is the purpose of this paper to describe a method of estimating the initial quantity of oil and gas present in a reservoir. The method is based on field operating data and the properties of crude oil-gas mixtures. The principles involved, the data required, the assumptions necessary, and an example of the method will be given. The method is entirely independent of sand volumes and formation porosities. Principles of Method The method of estimating the initial quantity of oil and gas present is based upon the premise that the volume occupied by oil and gas in the reservoir is constant and that a mixture of crude oil and gas will behave in

Jan 1, 1936

By William E. Brewster

Dating back some five years ago, various foundries made inquiries as to the probable total carbon content in a given specification and grade of pig iron. Up to that time we had no data, and except for a few occasional determinations of total carbon, no attempt had ever been made to set up routine determinations of total carbon. In fact, at that time, a cast analysis was considered sufficient, without examining at further length into possible variations of analysis between ladles of the same cast. In view of the various inquiries as to total carbon, we sampled all piles of all grades of pig iron, making complete analyses. Finding some variation in carbon content, we secured more samples and plotted the carbon content with respect to silicon in each grade of iron except for the higher phosphorus foundry iron, where it was necessary to divide the group into twenty-point phosphorus ranges. This is easily understood, owing to the falling off of carbon content with the increase in phosphorus content, silicon in each case being the same. In addition, these curves clearly demonstrate the lowering of the carbon content as the silicon is increased. In order to insure accuracy and reliable determinations the following method of sampling and analysis was employed: Two pigs selected from each end of the car, each car containing iron from one 50-ton ladle, are drilled with a 5/6-in. drill all the way through from top to bottom in the center of one section of the pig. The drillings are collected and transferred to an 80-mesh sieve; the portion passing through and the portion retained are placed in separate envelopes and labeled accordingly. The amount of sample in each envelope is weighed to obtain the proportionate amount of coarse and fine drillings, then a 1/2 factor weight of sample (1.3636 grams) made up of proportionate

Jan 1, 1936

By William E. Brewster

Dating back some five years ago, various foundries made inquiries as to the probable total carbon content in a given specification and grade of pig iron. Up to that time we had no data, and except for a few occasional determinations of total carbon, no attempt had ever been made to set up routine determinations of total carbon. In fact, at that time, a cast analysis was considered sufficient, without examining at further length into possible variations of analysis between ladles of the same cast. In view of the various inquiries as to total carbon, we sampled all piles of all grades of pig iron, making complete analyses. Finding some variation in carbon content, we secured more samples and plotted the carbon content with respect to silicon in each grade of iron except for the higher phosphorus foundry iron, where it was necessary to divide the group into twenty-point phosphorus ranges. This is easily understood, owing to the falling off of carbon content with the increase in phosphorus content, silicon in each case being the same. In addition, these curves clearly demonstrate the lowering of the carbon content as the silicon is increased. In order to insure accuracy and reliable determinations the following method of sampling and analysis was employed: Two pigs selected from each end of the car, each car containing iron from one 50-ton ladle, are drilled with a 5/6-in. drill all the way through from top to bottom in the center of one section of the pig. The drillings are collected and transferred to an 80-mesh sieve; the portion passing through and the portion retained are placed in separate envelopes and labeled accordingly. The amount of sample in each envelope is weighed to obtain the proportionate amount of coarse and fine drillings, then a 1/2 factor weight of sample (1.3636 grams) made up of proportionate

Jan 1, 1936

By J. J. Becker

BEAN1 has discussed the magnetic behavior of mixtures of small ferromagnetic particles on the order of 20 to l000A in diam. As he points out, there are three size categories with characteristic properties: 1) Particles large enough to contain many ferromagnetic domains magnetize initially by the motion of domain walls. The initial susceptibility of such particles, if domain-wall motion is assumed to be perfectly easy, depends only on their shape. It is equal to the reciprocal of the demagnetizing factor (and is thus 3/4 tt for a sphere) and is independent of temperature. 2) Smaller particles find it energetically undesirable to contain domain boundaries. They are always spontaneously saturated, and reverse their magnetization only by rotation of their entire magnetic moment. As assemblage of such particles has a remanence which is a large fraction of the saturation of the assemblage; its coercive force is on the order of 2K/1,, where K indicates magnetic aniso-tropy from any source, and I, is the saturation magnetization of the substance of which the particles are made. 3) Particles which are still smaller continue to be single-domain, but the direction of their magnetization fluctuates thermally, as first pointed out by Neel.' They have no remanence and no coercive force and possess the temperature-dependent magnetization curve of a paramagnetic substance with a very large moment. Bean calls this superpara-magnetism. All of these kinds of behavior are observable in alloys consisting of a precipitate of ferromagnetic phase in a nonferromagnetic matrix. Fig. 1 shows a typical aging curve for the room temperature coercive force of a sample of 98 pct Cu-2 pct Co alloy

Jan 1, 1958

By J. D. Meakin

J. D. Meakin (The Franklin Institute Laboratories)— In a recent paper Garofalo12 has shown that a number of experimental creep results can be represented by the empirical relation In this expression ? is the steady creep rate, s is the applied stress, and A is a constant at a given temperature; a and n are adjustable parameters. Garofalo has shown that Expression [6] approximates to a power function at low stresses and a simple exponential function at high stresses. Among the data used by Garofalo are the results we published for creep of copper." For these results we found that the best correlation was an exponential law with different parameters in the low-and high-stress region, respectively. That is, i = A exp qs where A and q have different values above and below a critical stress a,. In Ref. 13 are listed a variety of observations which support the proposal that different mechanisms are operative at stresses above and below a,, and it is not felt appropriate to repeat those observations here. The purpose of this note is to demonstrate that, although the representation used by Garofalo does fit the experimental data very well, this fit cannot be used to conclude that only one mechanism is rate-controlling. The argument is best made graphically and is illustrated in Fig. 9. The continuous curves 2 and 3 represent pairs of simple exponential functions which intersect at i = 10-5. The curve 2 closely resembles the copper results in that a change of slope of 2:1 occurs at i = 10-5; the two functions shown are in fact: e = 10-7 exp (1.150) and ? = 10-6&apos; exp (0.576s) For purposes of comparison, curve 3 represents two exponential functions with a change of exponent of 3:1 and curve 1 has the exponent 1.150 throughout. It is quite clear that a satisfactory straight-line fit is obtained on a Garofalo plot for all three curves. The curves represent processes which have either a single stress exponent or two ex- ponents in a ratio as high as 3:l. It must, therefore, be concluded that the ability to obtain a linear dependence between log i and log (sinh cyo) cannot be taken as evidence for a single activated process. In fact, to some extent the way the experimental points quoted by Garofalo lie about a best fit straight line on the log (sinh as) plot indicates that two processes are indeed occurring. This is seen in Figs. 7(c) and 8(c) of Ref. 12 where it is particularly evident that the experimental points deviate from the straight line in a manner similar to curves 2 and 3 of Fig. 9. It is, of course, recognized that the generally used exponential form is an approximation to the hyperbolic sine function which is not valid for exponents of less than 1.2, e.g., qs < 1.2. The only curve in Ref. 12 which is affected by this restriction is Fig. 6(b) where the deviation from a In ? vs s

Jan 1, 1964

By A. C. Heath, E. H. Dix

THE importance of aluminum-silicon alloys in the light alloy field is now generally recognized. Where silicon was once considered detrimental to the properties of aluminum, useful alloys now contain as much as 13 per cent. Furthermore, silicon is present as an impurity in aluminum of even the purest grades. Iron is another important impurity in aluminum and like silicon is found in small quantities in the purest aluminum available today. The manner of occurrence of iron and silicon in commercially pure aluminum and many of its alloys exerts a very pronounced influence upon their properties. The effect of large quantities of iron in aluminum-silicon alloys is so detrimental that it has been found necessary to limit the allowable maximum percentage to as low a figure as is consistent with quantity production and satisfactory physical properties. The intimate relation existing between iron and silicon in aluminum and aluminum alloys makes necessary a more complete knowledge of this ternary system. This paper is divided into two principal parts, dealing respectively with aluminum-silicon solubility equilibria and the constitution of aluminum-iron-silicon alloys. PART I.-ALUMINUM-SILICON ALLOYS The early work on this system was largely confined to determining the general form of the diagram and in this respect the results are in good agreement. Briefly, aluminum and silicon form a simple eutectiferous series without compounds. Until recently the solid solubility of silicon in aluminum had not been accurately determined. Fraenkel1 (1908) stated that aluminum will retain 0.5 per cent. silicon in solid solution. Rosenhain, Archbutt and Hanson2 gave the maximum solubility as about 1.50 per cent. and added that "this solubility does not appear

Jan 1, 1928

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967