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By M. T. Simnad, G. Derge, Ling Yang

STUDY of diffusion in molten substances is important in at least two respects. Diffusion data, combined with thermodynamic and kinetic information, throw light on the structure of the liquid state. Moreover, a knowledge of diffusion coefficients and their temperature dependence is useful in ascertaining the controlling step in many metallurgical reactions. Although diffusion measurements have been made on a number of molten salts, slags, metals, and alloys,'-'" the results available are still limited and widely scattered, especially for the high temperature melts. It is the purpose of this investigation to establish reliable procedures for the measurement of self-diffusion coefficients in high temperature melts and to use these procedures to determine the self-diffusion coefficients of iron in molten Fe-C alloys of different carbon contents. Experimental Measurement of self-diffusion coefficients in high temperature melts is usually carried out by using one of two methods. In the first, diffusion takes place between two cylindrical samples of the same material, one of which is made radioactive. The diffusion coefficient is calculated from the radioactivity penetration curve in the solidified sample after the diffusion. In the second method, samples contained in capillaries of an inert substance are immersed in an infinite reservoir of the same material. Either the material in the capillary or that in the reservoir is made radioactive and the diffusion coefficient is calculated from the change of the radioactivity of the sample in the capillary after the diffusion. The second method is simpler because a radioactivity penetration curve is not needed for the calculation of the diffusion coefficient; however,.it is valid only when no convection has occurred in the capillary during the diffusion. A radioactivity penetration curve is therefore always useful in indicating that the required conditions for the diffusion are ful- filled. Towers and Chipman" recently studied the self-diffusion of calcium and silicon in CaO-Al,O,-SiO, melts by using the capillary method. Instead of measuring the change of the radioactivity of the sample in the capillary, they autoradiographed the sample after the diffusion and calculated the diffusion coefficient from the intensity distribution of the autoradiograph. Their method is useful when the radioactive isotopes are weak ß-emitters, but is very difficult, if not impossible, to apply to cases involving strong ß or y-emitters. For such cases, sectioning of the sample according to the method of Morgan and Kitchener' may be used for the construction of the radioactivity penetration curve. The self-diffusion of iron in molten Fe-C alloys has been studied in this manner and the experimental procedures are described as follows: The diffusion apparatus is shown schematically in Fig. 1. The bath consisted of about 200 g of an Fe-C

Jan 1, 1957

By J. L. McK. Yardley

There are two general classes of problems in connection with electric furnaces. First, those relating to the best utilization of the electrical power inside the furnace; second, those connected with the bringing of the electrical power to the point where it is to be utilized. Referring particularly to the latter class of problems, many calculations have been made, covering a wide variety of furnaces, to check the electrical capacity and power factor found from test. The following analysis, made for the purpose of determining the maximum capacity and approximate performance of a new furnace, to operate at 160 volts on a 60-cycle circuit, may be of interest. The first characteristic necessary to determine is the inductance, since this is the factor that limits the amount of power which can be put into the furnace. Inductance is calculated from the dimensions of the furnace, according to formulas of the U. S. Bureau of Standardsll as follows. Formula 99, for mutual inductance, is: M = 2l [log 2l/d-1 +d/l] Formula 103, for self-inductance, is: Both of these formulas are approximations which are nearly correct when 1 is great compared to d or R. 1 = length of circuit, in centimeters, d = separation between the conductors, in centimeters, R = geometric mean radius of conductors. For a circular tube, R = the radius of the circle. For a solid circular conductor, R = 0.7788 X the radius of the conductor. For a rectangular conductor, R = 0.2235 X (a + b), a being the length, and b being the width of the rectangle. To calculate the inductance of a three-phase circuit, it is customary to figure the inductance of one leg. In circuits where the three conductors

Jan 1, 1920

By C. Q. Payne

The art of crushing ores and other materials by means of rolls is a comparatively recent one. While the first record of rolls using iron crushing-surfaces dates hack to the year 1806, when they were employed in Cornwall, their principal developmcnt has taken place during the past 30 years. To Stephen R. Erom belongs the credit of the pioneer in introducing the belted high-speed roll, which has had its origin and a marked development in this country. His notable contrib'ution to the art was in the use of a single bed-plate or frame supporting the roll-shafts, and to which levers holding the mova, ble roll-bearings were pivoted. He also made use of steel tension-rods to support the crushing-strains, and of hammered-steel tires for the crushing-surfaces. These changes brought the design of crushing-rolls to a high level. Following closely thereon, about 1885, W. R. Eckart conceived the idea of the swivel or ball-and-socket support for the roll-shaft bearings. This is an excellent mechanical conception, especially for bearings held against a spring pressure, and while it may not be necessary for all types of rolls, yet it has been quite generally adopted by other roll-designers, and illustrates the refinement which roll-construction has now reached. Other engineers, as, for example, Argall, Vezin, Roger, and Sturtevant, to mention only a few among many, have also given the closest attention to the various details of rolls, such as the frame, springe, bearings, and shafts, and have developed many novel and original designs. It has remained, however, for the boldness and originality of Mr. Edison to extend the field of crushing-rolls in two new directions, and to cause them to ex-

Jan 1, 1913

By H. A. Saller, F. A. Rough

Studies of the V-U system have been made to determine the constitutional diagram. The diagram is fairly simple, since no intermediate phases are formed. Additions of vanadium lower the uranium melting point and allotropic transformation temperatures. The maximum solid solubility of vanadium in uranium is 12 atomic pct and the maximum solid solubility of uranium in vanadium is about 4 atomic pct. WITH the advent of high purity iodide vanadium,' it became of interest to study the alloying characteristics of vanadium and uranium. Alloys were prepared covering the entire system and were studied using a combination of metallographic examination and thermal and X-ray analyses. As a consequence of this work, the V-U constitutional diagram was evolved. In order to prepare suitable alloys for equilibrium-phase studies, it is desirable to have the purest possible starting materials. For this investigation, calcium-reduced vanadium, de Boer process crystal-bar vanadium, and good Mallinkrodt Chemical Co. uranium were used. The first work was done using the best vanadium then available, that being calcium-reduced vanadium produced at Knolls Atomic Power Laboratory. Subsequently, the important features of the diagram were checked using alloys made with crystal-bar vanadium produced at Battelle. These checks are in agreement with the earlier work. Analyses of the starting materials are contained in Table I. Only minor amounts of any impurities were present in either the vanadium crystal bar or uranium. Nevertheless, care was exercised in selecting the uranium for the alloys. The procedure followed was to section the stock into suitable pieces for melting, and macroetch each piece. Only those pieces which appeared to be clean by macroetch examination were used for alloying. Experimental Procedure Melting: Alloys with 0 to 50 atomic pct V were induction melted in beryllia (BeO) crucibles under vacuum of 10 microns pressure or better. A number of remelts was frequently required to insure uniformity of the individual ingots. Although no visible reaction between the alloy and crucible was found in any of these operations, the alloys were checked by spectroscopic analysis. Only trace amounts of beryllium were detected in the alloys. Alloys containing 50 to 100 atomic pct V were arc melted in a water-cooled copper crucible under an atmosphere of helium. A tungsten electrode was used. Ingots of 10 to 15 g were produced readily by turning and remelting a few times. Such small ingots were necessary because high purity vanadium was not available in appreciable quantities at this time. After melting, the ingots were examined metal-lographically for segregation and were consolidated by remelting before fabrication was attempted. Spectroscopic analyses showed that only small amounts of tungsten were picked up during the arc-melting process. Fabrication of Alloys: Alloys containing up to 20 atomic pct V could be fabricated by rolling in air at 600°C with 5 min between passes. After each pass through the rolling mill the alloys were returned to

Jan 1, 1954

By Henry A. Stiff, J. P. Hammond, A. B. Westerman, H. C. 195-000-000-014 Cross, and Lawrence E. Davis

The phases in Cr-Fe-Mo alloys have been investigated with homo-genization, aging temperature, composition range, and alloy addition as variables. Metallography, three X-ray methods, and hardness were used as methods of study. The behavior of s, M23,C8, and Z phase are reported for cornpasition range 60 pct Cr-15 to 25 pct Fe-15 to 25 pct Mo-<0.005 to 0.36 pct C with aging at 1400º to 2000°F. With 2 pct Ti, Tic and TiC-TiC are formed; with nitrogen Cr2N. THE recently developed class of chromium-base heat-resistant alloys shows appreciably higher strength than commercially used high temperature alloys. However, further developmental work is required to impart needed shock resistance and some degree of room-temperature ductility to these alloys. Extensive exploratory work on chromium-base alloys was begun in a program initiated by the War Metallurgy Committee of the National Defense Research Council at the Climax Molybdenum Co. in the early part of 1942.&apos; Alloys were sought for gas-turbine blades for use at 1600°F. A minimum of 5 pct elongation in the stress-rupture test was a requirement. From the Climax work, ternary alloys of chromium, iron, and molybdenum appeared to show the greatest promise as materials for gas-turbine blades. The composition line in the ternary diagram joining the 60 pct Cr-15 pct Fe-25 pct Mo and 60 pct Cr-25 pct Fe-15 pct Mo alloys was indicated as representing the most useful combination of strength and ductility.&apos; Strength increased while ductility decreased as molybdenum was raised in this composition range.&apos; The 60 pct Cr-15 pct Fe-25 pct Mo type alloy was thought to have the most suitable properties for gas-turbine blades.&apos; Concurrent with the study reported here, other investigations were being made on Cr-Fe-Mo alloys. The liquidus temperatures on a series of low carbon, ternary alloys were being determined, and isothermal sections drawn at 2370°, 2010°, and 1650°F (1300°, 1100°, and 900°C).2 Also, various methods of preparation and some mechanical and physical properties of chromium-base alloys, particularly the 60 pct Cr-15 pct Fe-25 pct Mo type, were being investigated., At the inception of the present program, only a limited study had been made of etchants for developing the microstructures of chromium-base alloys; X-ray analysis of the microconstituents had not been made. A review of the literature revealed that no phase-diagram work had been reported on the Cr-Fe-Mo system. Scope of Work The work on chromium-base alloys includes the following: 1—The development of etching methods for differentiating between the microconstituents; 2—The identification of microconstituents by X-ray diffraction methods; and 3—A comprehensive metallographic and hardness study after various heat treatments. The phases were studied by three standard X-ray techniques: 1—The block-sample focusing-camera method; 2—The powder-diffraction method on elec-trolytically separated residues; and 3—The powder-diffraction method on cold-worked aggregate samples. The results by the first two methods were correlated with the metallographic data. The third method was used largely to study conditions approaching equilibrium, since cold working prior to heat treating accelerated precipitation. Seven types of alloys were investigated: 50 pct Cr-50 pct Fe, 40 pct Cr-40 pct Fe-20 pct Mo, 55 pct

Jan 1, 1953

By Thomas O. Ziebold, Robert E. Ogilvie

Experimental analysis of diffusion samples covering the entire Cu-Ag-Au system at 725°C has been carried out. Experimental coefficients are computed at twenty-eight points in the lermary system. It is found that the direct coefficienl for copper is nearly independent of the silver, content for 1ow-silver alloys and that the cross coefficient for silver correlates with the ther-nzodynatnic properlies. This lalter observalion leads to the conclusion that the mobililies of copper and gold are nearly equal. Thermodynarmic actiuilies for Cu-Ag-Au were computed from binary data and adjusted to be consistent with neasured tie lines across the two-phase region which extends into the ternary diagram at 725°C. Application of these therknodynarnic calculaliorls to the dijftcsion data terifies the Onsager reciprocal relations to the extent that experimental uncertainlies will allow. It is jound that diffusion neav the critical point of the 1200-phase field in the isothermal section at 725°C causes the composition gradients for copper and silver to approach infinity while the direct and cross coeficients become equal. From the standpoint of experimental Procedures, it has been shown that microanalysis of ternary samples may be carried out using a simple expression for the conversion of X-ray zntensily to composilion. The accuracy of&apos; this method has been demonstrated by the analysis of standard alloys and by the reproducibility of composition determinations using differed X-ray lines. DIFFUSION in a ternary alloy system is basically and significantly different from diffusion in binary alloys. When only two elements are present there is just one independent composition variable, and the diffusion profile of composition vs distance across a sample must change monotonically through all solid solutions bracketed by the terminal alloys. If two-phase regions are stable for compositions between the terminal values, these must appear as planar interfaces in the diffused sample, with the composition profile exhibiting sharp discontinuities. Adding a third element may alter this picture completely. Because of the additional degree of freedom in the composition, we may see composition profiles which do not change monotonically through solid-solution ranges, and stable, nonplanar phase interfaces. Even though two-phase regions may lie between the terminal compositions of a diffusion sample on the constitution diagram, they will not necessarily appear in the diffusion profiles. In binary diffusion only one coefficient is needed to describe the interdiffusion process. From Fick&apos;s law this coefficient relates the diffusive flux of one component to its own composition gradient. In ternary diffusion we must allow for cross interaction between the two independent species. By a linear extension of Fick&apos;s law we introduce "cross" or "off-diagonal" diffusion coefficients which relate the flux of one component to the composition gradient of the other independent constituent. Thus, we require four interdiffusion coefficients to describe the transport process in a ternary system. In its most general form,1,2 the rate equation for mass transport by isothermal diffusion in a system of s components states that the diffusive flux of component i, Ji, is a linear summation of all driving forces, Xk, each force being multiplied by an appropriate compliance coefficient:

Jan 1, 1968

By C. B. Manula, H. Gezik

In planning modem-day mining operations, management needs to pass from the area of subjective decision-making to an area of objective decision-makirlg. Planning procedures currently being practiced by many mine managers depend primarily on common sense and trial-and-error methods which oftentimes never reach optimum solutions. For this reason, an attempt is made to provide an understanding of linear programming to solve production planning problems. More specifically, a linear programming model is proposed to solve the production scheduling problem as it was found to exist in the crushed stone industry. Optimal production scheduling is of prime concern here, since the industry has to cope with seasonal demands for its products. The solution, as determined through the application of the model, provides management not only with an optimal production schedule but also with the following information regarding the improvement of existing facilities: (I) the location of bottlenecks which limit production and profit; (2) the directions in which the company i fixed equipment should be expanded or modified; and (3) the evaluation of unused resources. Future trends in stone production will quite likely parallel those in the construction industry. Continued record expenditures for structures such as dams, highways, and buildings are the reasons for this accelerated growth. Production forecasts for the next decade are predicted to be around one billion tons with an approximate 7% annual increase. The problem of increasing production from 570 million tons in 1966 to 1 billion tons by 1976 offers no small challenge. This situation is further compounded by other problems and economic factors. Population expansion, government regulation, labor agreement, and changes in technology wd cause managers and operators to be confronted by many more complexities than characterize present-day operations. Some of these. problems and economic factors are: (1) In some metropolitan and other urban areas, easily accessible sources of stone are almost depleted. Transportation costs will be a prime concern of the industry. (2) Population growth has forced residential expansion to a point where many quarry operators must conform to urban and suburban regulations. (3) Government regulation in regard to air and water pollution, noise, and reclamation as well as zoning developments necessitate that crushed stone producers keep abreast of changing conditions and requirements. (4) The crushed stone industry operates under pressure of a highly competitive situation. Every company&apos;s objective is to retain a favorable marketing position by exercising great attention to production and marketing costs. This is rather difficult, since the crushed stone industry is one segment of modern mining which has to cope with a seasonal demand for its products. Among the problems posed here, the one of exercising great attention to production and marketing costs is of current interest to management. Under seasonal demand conditions, this problem creates further difficulties for managers who need to plan and forecast. STATEMENT OF THE PROBLEM Various methods of Operations Research have been developed to handle a problem whose genesis is explained above. It is very seldom, however, that these quantitative means are used in practice by the mining industry. This paper describes the use of Operations Research methods to solve a production planning problem when demand is seasonal. The seasonal production planning problem is an important one because of the substantial costs associated with changing production, employment, and inventory levels to adjust to seasonal sales patterns. Most companies try to operate within reasonable levels of employment changes and hold inventories within storage capacities. In general, little or no attempts were made to develop minimum cosl schedules or to provide objective means to compare various production policies. When demand varies within a fixed time period, 11:-oduction requirements may be met by following one

Jan 1, 1970

By T. A. Rickard

Do not write until you have something to say. Think first; then write. In order to be understood, you must know what you wish to say. Clear writing is the consequence of clear thinking. Therefore consider your subject well before you begin to write; ruminate on it; marshal the salient facts in your mind; saturate yourself with the ideas you wish to express and with cognate ideas; then express yourself deliberately. If you are bubbling over with your subject the words will come, but you might as well expect to sail without a breeze as hope to give life to words without the living thought. Here I may advert to the fact that among the uneducated it is a common expectation to acquire the knack of writing without taking the trouble to study the art of literature. I overheard a woman in a suburban train remark to her neighbor: "I&apos;d like to be able to write well without stopping to think about it". She was one of many that would like to do a thing well without the trouble of thinking; but it cannot be done in respect of anything to which thought is essential. The possession of a good voice does not justify a person in expecting to sing successfully to a large audience; before singing in public one has to master the technique of singing; one has to learn first how to breathe properly, how to enunciate, and many other things. The successful singer is an artist, not a megaphone. Most of us would regard a man or a woman without any training in the art of singing as a fool or an impostor if he or she were to give a public concert, yet we do not recognize the equal foolishness and imposture of persons that write books before they have studied the technique of writing. That is why so many books are unreadable, and why many books by clever men are difficult to read. They start to write books before

Jan 1, 1931

By Harold R. Larson, John F. Elliott

The standard free energies of formation of several nzetallic sulfides have been measured by a reversible electromotive-force cell employing stabilized zir-conia as the electrolyte. The oxygen potential at the cathode was fixed by the use of pure oxygen gas at 1 atm. It was established at the anode by bringing to equilibrium the reaction between the sulfide and oxide species present. Thus, Gf: for the sulfide could be obtained from the cell potential and the standard free energies of formation of the oxides participating in the reaction. The results in calories per cam rnole for the temperature range 850" to 1100°C are: Use of the reversible electromotive-force cell having an oxide-ion electrolyte to obtain the standard free energies of formation of some of the more stable metallic sulfides offers a convenient experimental method that is very productive. It also avoids some of the problems inherent in the experimental methods&apos; for such studies which rely on precise determination of gas compositions, particularly if these compositions lie near the limits of our capabilities for accurate chemical analyses. The reaction equilibrium between the lowest sulfide of a metal, SO2 at a fixed pressure, and an oxide of the metal has a characteristic oxygen potential. For example: and for metals whose lowest sulfide is much more stable than the oxides of the metal, the equivalent reaction might be:

Jan 1, 1968

By A. V. Deforest, A. R. Anderson, C. W. MacGregor

ONE of the important problems in the design of structures and machine parts subjected to rapidly applied loads is the determination of the strength and ductility of the material itself under such conditions. Realizing the need for such information, many investigations have been carried out in the past. Most of these experiments have been made using notched bars in bending either with the Charpy or Izod impact machine. While yielding valuable data on the effect of notches in the energy absorption of the material and on the condition of heat-treatment, this form of test does not lend itself readily to a determination of fundamental stress-strain relations. For this and other reasons, more attention has been paid recently to the tension impact test. An extensive literature already exists on the subject and only those investigations somewhat closely related to the present paper will be mentioned. For a more comprehensive list, the reader is referred to the Symposium on Impact Testing of the A.S.T.M., 1938. The work of Mann,1 Clark and Dätwyler,2 Nádai and Manjoine,3 Winlock and Leiter,4 Deutler,5 and Brinkmann,6 however, deserve especial mention. In most of the previous investigations on the subject, when stress-strain relations were obtained under high rates of loading, it was the common procedure to determine stresses based on the original area and strains based on the original length. Stress-strain curves were then constructed by plotting [So = ooT as a function of eo =o] where A o and Lo refer to the original area and gauge length, respectively. At present there exists a paucity of true stress-strain data in the impact problem. The advantages of constructing so-called true stress-strain curves in order to reveal the fundamental physical properties of the material for the tension test were discussed recently by one of the authors? It was shown that the true physical behavior of the material in the tension test could best be represented by plotting the average true stress, [S = P] as a function of [e = q&apos; = log A-le = log Lo] where P, A, L, S, [e], and q&apos; refer to the load, the cross-sectioned area while the load P is applied, the actual gauge length, the average true stress, the true strain and true reduction in area, respectively. Besides giving a better physical representation, the method has certain additional advantages in that the stress-strain curve so plotted becomes a straight line from the maximum load point to fracture. The construction of such curves, however, while comparatively simple for the slow rates of loading customarily used in the tension test, presents certain difficulties for tensile impact in that both loads and diameters are required throughout the test. The continuous measurement of test-piece

Jan 1, 1941

By R. W. Raymond

(Pittsburg Meeting, March,1910.) THE Giroux Consolidated Mines Co. is equipping a five-compartment shaft at Kimberly, Nev., which will serve the Alpha mice. The depth of this shaft, January, 1910, is 963 ft., and of this depth 948 ft. was opened by raising, 15 ft. of sinking was done so that the bearers, collar-set, and three shaft-sets might be installed and concreted, and with this done it was possible to erect the necessary surface-equipment for resuming shaft-timbering on the completion of the raise. The arrangement of the shaft-timbering is shown in Fig. 1. At the 1,000-ft. level of the Alpha, and 750 ft. SW. from the Alpha shaft, a 14- by 18-ft. station was cut, and a 25-h-p. air-hoist *as installed. From here the raising commenced on July 5, 1909. The raise was cut approximately 13 by 21. ft. in area, and supported by timbering with square sets, illustrated in Fig. 2, which shows the division into four compartments. The end compartments, which were used as chutes, had the center girts heavier than in the others on account of the wear from falling rock. The chute-lining was braced by inserting 8- by 8-in. stiffeners parallel to and half way between successive caps. Similarly, the lagging on the wall sides of the cage-way and the compartment for pipes and ladder was stiffened with 4- by 6-in. timbers. In the pipe-and-ladder compartment the chute-stiffeners were reinforced with 8- by 8-in, struts, and as the cage-way was partitioned off by braced lining, there was practically no chance of rock entering the ladder-way in case a chute burst into the cage-way. Over the two center compartments the last two, sets were always bulkheaded with 8- by 12-in. timbers, shown in Fig. 3, and from the lower bulkhead the cage sheave-wheel was suspended. After a round of holes had been blasted and the loose

Jun 1, 1910

By B. A. Wilcox, A. H. Clauer

The steady-state creep of TD Nickel NL + 2 001 pct TltOz) has been studied orer the telirperatve range 325&apos; to 1100O and the stress range 15,000 to 36,000 psi. At high temperatures (aboue 0.5 T& gran-boundary slzding is the )nost znportant )node of creep deformation, and the steady-state creep rate, is, can be related to stress and temperature by: where Q = 190 kcal pev mole and n has an unusually high value of 40. A creep mechanism based on cross slip of dislocations around The O2 particles can satisfactovily explain the low-temperature (T < 0.5 T,) cveep behavior, and the follo wing relation is applicable: Q, (a) is found to decrease from 57 to 46 kcal per mole as the stress is increased from 32,000 to 36,000 psi. THERE have been a variety of theories proposed to explain the influence of dispersed second-phase particles on the yield strength and flow stress of metals, and these have been reviewed recently by Kelly and icholson.&apos; However, only several attempts2"4 have been made to develop mechanistic treatments which characterize the creep behavior of dispersion-strengthened metals, and to date these have not been fully evaluated experimentally. weertman2 and Ansell and weertman3 proposed a quantitative creep theory for coarse-grairzed dispersion-strengthened metals, based on the concept that the rate-controlling process for steady-state creep was the climb of dislocations over second-phase particles, as suggested by choeck. The theory predicted that the steady-state creep rate, <,, was proportional to the applied stress, a, for low stresses and that is a4 o for high stresses. The activation energy for creep, Q,, was equivalent to that for self-diffusion, Qs.d., in the matrix. Some limited experimental evidence in support of this theory was obtained on a recrystallized Al-Alz03 S.A.P.-type alloy by Ansell and Lenel.6 Ansell and weertman3 also developed a semiquanti-tative theory for high-temperature creep of lineg-rained dispersion-strengthened metals in order to explain their results on an extruded S:A.P.-type alloy, which had a fine-grained fibrous structure. They suggested that the rate of dislocation generation from grain boundaries was the rate-controlling process, and fitted their results to the equation: where Q, was found to be 150 kcal per mole, i.e., QC- 4Q,.d. in aluminum. Similar high activation energies for creep7-&apos;&apos; and tensile deformation" of dispersion-strengthened alloys have been observed by other investigators for S.A.P.,&apos;" indium-glass bead omosites, and Ni + A1203 alls.&apos; There is no general agreement regarding the mechanisms involved in the creep of dispersion-strengthened metals, and this is due in part to the lack of detailed studies relating the structures of crept specimens to the mechanical behavior. The present investigation on thoriated nickel was undertaken with the aim of studying the structural changes which occur during creep of a dispersion-strengthened alloy and rationalizing the observed mechanical behavior in terms of the creep structures. EXPERIMENTAL METHODS The material used in this investigation was 1/2-in.-diam TD Nickel bar, which contained 2.3 vol pct Tho,. Obtained from E. I. duPont de Nemours & Co., Inc. The final fabrication treatment by DuPont consisted of -95 pct reduction by swaging followed by a 1-hr anneal at 1000°C. Transmission and replica electron microscopy revealed that the material had a fine-grained fibered structure with an average transverse grain size of -1 p and a longitudinal grain size of 10 to 15 p. Selected-area diffraction indicated that the fiber axis was parallel to (OOl), in agreement with the results of Inman eta1." All creep specimens were vacuum-annealed at 1300°C for 3 hr prior to testing. Transmission electron microscopy showed that the only structural change due to annealing was a slight decrease in dislocation density, confirming the reported high degree of structural stability.13 Furthermore, recrys-tallization or grain growth during creep was never observed. The structure typical of uncrept material (after the 1300 C, 3-hr anneal) is shown in Fig. 1. The grain boundaries are predominantly high angle and. although some areas show a tangled cell structure, the grain interiors are relatively dislocation-free. Individual dislocations are strongly pinned by the Tho2 particles; i.e., very rarely did dislocations move within a thin foil. The grey "halos" around some of the larger particles which protrude out of the foil surface arise from contamination in the electron microscoge. The Tho, particle size ranged from -100 to IOOOA, and the distribution is shown in Fig. 2. The technique used to obtain the data in Fig. 2 consisted of dissolving the nickel matrix in acid, collecting the Tho2 particles on cellulose acetate, and measuring about 1000 particle diameters in the electron microscope. Similar results were obtained by measuring about 600 particles in thin foils, an; the average particle size was found to be 2r, = 370A. Using the data in Fig. 2 (annealed structure), the mean planar center-to-center particle

Jan 1, 1967

By A. J. Conelius, D. P. Sobocinski

This paper presents a correlation for predicting the behavior of a water cone as it builds from the static water-oil contact to breakthrough conditions. The correlation is partly empirical and involves dimensionless groups of reservoir and fluid properties and of production and well characteristics. The groups were deduced from the scaling criteria for the immiscible displacement of oil by water. The correlation is based on a limited amount of experimenfal data from a laboratory sand-packed model and on results from a computer program for a two-dimensional, incompressible system. Because the correlating groups are dimensionless, they can be used to estimate the performance of water coning cases not specifically considered in the correlation. However, despite its dimensionless nature, the correlation is not completely general and will not provide meaningful estimates of cone behavior in many situations. INTRODUCTION AND BACKGROUND The production of water from oil wells is a common occurrence which increases the cost of producing operations and may reduce the efficiency of the depletion mechanism and the recovery of reserves. We will deal with one cause of this water production, namely, coning. The coning of water into a producing well is caused by pressure gradients established around the wellbore by the production of fluids from the well. These pressure gradients can raise the water-oil contact near the well where gradients are most severe. Gravity forces that arise from fluid density differences counterbalance the flowing pressure gradients and tend to keep the water out of the oil zone. Therefore, at any given time, there is a balance between gravitational and viscous forces at points on and away from the completion interval. When the dynamic forces at the wellbore exceed gravitational forces, a cone of water will ultimately break into the well to produce water along with the oil. We can expand on this basic visualization of coning by introducing the concepts of stable cone, unstable cone and critical production rate. For instance, if a well is produced at a constant rate and the pressure gradients in the drainage system have become constant, a steady-state condition is reached. If, at this condition, the dynamic forces at the well are less than the gravity forces, then the water or gas cone that has formed will not extend to the well. Moreover, the cone will neither advance nor recede, thus establishing what is known as a stable cone. Conversely, if the pressure in the system is in an unsteady-state condition, then an unstable cone will continue to advance until steady-state conditions prevail. If the flowing pressure drop at the well is suffcient to overcome the gravity forces, the unstable cone will grow and ultimately break into the well. It is important to note that in a realistic sense, stable cones may only be "pseudostable" because the drainage system and pressure distribution generally change. For example, with reservoir depletion, the water-oil contact may advance toward the completion interval, thereby increasing chances for coning. As another example, reduced productivity due to well damage requires a corresponding increase in the flowing pressure drop LO maintain a given production rate. This increase in pressure drop may force an otherwise stable cone into a well. The critical production rate, well known in the literature, is the rate above which the flowing pressure gradient at the well causes water (or gas) to cone into the well. It is, therefore, the maximum rate of oil production without concurrent production of the displacing phase by coning. At the critical rate, a built-up cone is stable but is at a position of incipient breakthrough. Numerous papers have been published on critical rates. Some of the better known of these include the work of (1) Muskat and Wyckoff,&apos; who first dealt with the coning problem; (2) Chaney, et al,&apos; who developed expressions similar to those of Muskat but who presented results in a conven ient-to-use graphical form (the "Sun" method); and (3) Meyer and Garder,b hose analysis is based on radial-flow formulas. One assumption in critical production rate analyses is that the cone has built-up to just before its breakthrough into the well. But, these analyses reveal nothing directly about the time it takes for the cone to build up to this incipient breakthrough position. Thus, water-free oil can be produced from a well for prolonged periods at rates above the critical rate before the well reaches the condition to which the critical rate applies. The published literature contains little on the rate of growth of a cone. Experimentally, Meyer and Searcy studied the rate of rise of a cone in a Hele-Shaw model.&apos; Additional related work on water breakthrough and produced water-oil ratios in water driven reservoirs was reported by Muskat," Hutchinson and Kemp," Henley, et al,&apos; and Stevens, et a1.B Theoretically, the basic coning equations for a water-oil system can be developed by applying the conservation of mass to each of the phases, relating flow velocities with pressure by Darcy&apos;s law, and relating pressures across water-oil interfaces by capillary pressure. With the usual boundaries at the well and reservoir limits, the solution of the resulting equations for the time behavior of a water-oil interface constitutes a free-surface, boundary-value problem. The shape of the boundary depends on the internal potential distribution, while this

Jan 1, 1966

By Charles C. Fatino, Joel S. Hirschhorn

Loose compacts of strained and annealed stainless-steel powders were sintered at various temperatures and times to determine the effect of residual strains on the sintering behavior. The atomized powders were prepared by annealing, ball milling, and rean-nealing. The residual strains and domain size were determined by a Fourier analysis of X-ray diffvaction dala. The specimens were prepared by siwzultaneously sintering cylinders of both strained and unstrained powder. The evaluation of the sintered compacts included density measurements, metallographic examinations, and analyses of X- ray diffraction data. The results of these studies reveal a definite increase in sintered density and sintering rate for the strained powders. THE pressure compacting of metal powders causes deformation of the particles, mechanical interlocking, and increased contact area. After the deformation, severe residual strains remain in these particles. The subsequent contributions of these strains to the sintering process have been considered to be negligible, since the recovery and recrystallization temperatures usually occur prior to the temperature required for the sintering process. Sintering is con-sidered to be the process by which the powders are transformed into solid compacts at temperatures below their melting points. The sintering operation for stainless steel usually takes place in the range of 2050" to 2400°F (0.84 to 0.95 T,, where T, is the absolute melting point or liquidus temperature) while the temperature required for recovery is approximately 1800°F (0.75 T,). However, it has been shown for several metal powders that densification becomes significant in the range of 0.35 to 0.45 T,.&apos; It is the purpose of this study to determine what effect residual strains have upon the sintering behavior of stainless-steel compacts. Loose compacts were selected for study in order to isolate the strain contributions and eliminate the variables inherent in sintering of pressure-formed compacts. Additional variables were minimized by using only one mesh size, one composition, one particle shape, and also by simultaneously sintering both types of powder. Very little work has been carried out previous to the present study to delineate the effect of strains on sintering behavior. Lenel et 01.2 observed that residual stresses in copper compacts caused shrinkage at comparatively low temperatures. Delisle3 loose-sintered ball-milled electrolytic iron and observed that bonding among particles began at a lower temperature as compared to the behavior of annealed powder. Increased densification of ball-milled oxide powders has also been noted.4&apos;5 EXPERIMENTAL PROCEDURES Powder Preparation. The powder used for this study was a commercial-type 316L stainless steel made by the atomization process. A typical chemical analysis is: C- 0.025 pct Mo- 2.2 pct Cr-18.6 pct Ni-12.5 pct Fe—Balance The atomizing process is essentially the rapid freezing of liquid droplets. This nonequilibrium cooling causes coring to occur and two distinct phases are present within the solid particle, the austenitic phase and the ferritic phase. Due to the presence of this ferritic phase, the particles tended to fracture as well as become cold-worked during the subsequent ball-milling operation. (It was also found that this type of cooling produced a broadened and shifted

Jan 1, 1968

By Jesse O. Betterton

IN the last analysis, two basic factors influence the use of metals and alloys; namely, cost and adaptability to the use under consideration. These are so interrelated that to study the properties of metals or alloys without considering the prices and price trends is quite illogical. Lead has been a cheap metal, selling in 1932 for the extremely low price of 2.56 cents per pound. The cheapness of lead in the past was not due to a particularly abundant supply of the element in the earth&apos;s crust but rather to the ease with which it was won from its ores and to the chemical stability of the metal, preventing its dissipation. Today, however, our modern economy has caught up with the distribution of lead in the earth&apos;s crust and the price is largely dictated by the supply of concentrates readily available for smelting, and which can be placed quickly upon the market. The demand for lead, particularly in times of stress, has brought the price up to the level of 19 cents in the United States, where the price is controlled by Government decree, and the price has been even higher in the world markets. The higher price for lead has changed the uses for this metal to a marked degree, driving it out of the fields where it is not essential. Lead articles of great antiquity have been found in Egyptian ruins, proving the stability of the element and indicating the basic simplicity of its metallurgy. It is probable that lead was the first

Jan 1, 1953

By L. G. Schulz, P. Spiegler

The electrical resistivity and the temperature coefficient of resistivity were measured with a potentiometric method using pure mercury as a reference material. Measurements were made nea,v roorn temperature. A detailed study was made of Hg,TI, near its melting temperature. THE work to be described was originally undertaken to provide the necessary data for interpreting the results of some optical experiments,&apos; but because of the growing importance of liquid metals,273 it appeared that the results of the resistivity measurements should be published separately. For convenience the alloys selected were those which are liquid at room temperature. Special consideration was given to the Hg-T1 alloy closely corresponding to Hg,Tl, because recent X-ray diffraction results of Smallman and Frost seemed to show that the solid structure may persist to some extent into the 1iquid. EXPERIMENTAL PROCEDURE A potentiometric method was employed in which the resistivity of mercury was used as a reference. The essential features of the samples are shown in Fig. 1. A capillary tube CT with a bore of approximately 1.5 mm was fitted into two end cups, T, which were made of Teflon. A pair of current electrodes CE were immersed into the excess liquid metal which partly filled the end cups. The potential electrodes PE were inserted into CT through short pieces N of a no. 18 hypodermic needle held in place with Saureisen cement SC. As shown, the lower ends of the PE7s were reduced in diameter to 0.25 mm to minimize the distortion of the liquid metal cross section. Several methods were used to insert an alloy into the sample, but the usual one with mercury alloys was to fill the sample container with a weighed quantity of pure mercury* and then add weighed the sample tube in a vacuum. Because of rapid corrosion, samples containing gallium were of necessity prepared in a vacuum. To obtain the specific resistivity of an alloy the resistance of the sample containing the alloy was measured and compared with the resistance when the container was filled with mercury. Resistances were measured in the temperature range of 20" to 60°C to obtain the temperature coefficient of resistance. The electrical measurements were made by connecting the sample in series with the standard one-ohm resistance, and the potential drop measured alternately over the sample and the standard resistance. To correct for stray thermoelectric effects provision was made for reversing the direction of the current, and the true potential drop was taken to be the average of that obtained for the two directions of current flow. Various materials were used for the electrodes, the most uniform results being obtained with nickel. EXPERIMENTAL RESULTS The numerical results are presented graphically in Figs. 2 and 3 and in tabular form in Tables I and 11. Following are remarks on results of individual alloys. 1) Hg-In—This was the first alloy studied, and

Jan 1, 1960

G. D. Kneip, Jr., and J. 0. Betterton, Jr. (Union Carbide & Carbon Corp., Oak Ridge, Tenn.)—The authors have contributed to the theory of zone melting by considering the effects of the solidification of the final zone on the distribution curves for the finite length bar. However, they do not consider in sufficient detail the restrictions imposed by the particular metals involved. Eq. 4 has the analytical solution which is equivalent to Pfann&apos;s&apos; equation for normal solidification of the final zone. For distribution coefficients less than one, it is apparent from this form of the equation that, as the solidification approaches completion, the concentration attains extremely large values which are inconsistent with the density of physical materials. The necessary restrictions then are that the solute concentration cannot exceed the density of the alloy, or more frequently, the solubility limit in the solid phase. Secondly, the distribution coefficient cannot be constant from 0 to 100 pet solute unless the liquidus and solidus coincide over this whole region. It would thus be more correct to impose limits on the solubility such as would be indicated by a typical eutectic diagram. Furthermore, in this case the assumption that the distribution coefficient remains constant is more likely to be realized. Eq. 4 should then be replaced by the following C,,(x) =k/L-x [ ?11 3 C11 (x)Ddx - ?11 4 Cn(x)dx= k[Cn (L-l)/k] [ L-x/l]x-1 L-l = x = L-l [kCenterlie/Cn (L-l)]1/k-1 The typical shape for the distribution curve in the final zone is indicated schematically in Fig. 12 for the simple eutectic case. The solidification proceeds according to Pfann&apos;s&apos; expression until the concentration reaches the maximum solubility in the solid phasc. At this point, the concentration changes abruptly to the eutectic composition and remains at this value for the duration of the solidification. The width of the flat region, and the back reflection of this effect into the concentration curve on subsequent passes, depends upon the ratio of the eutectic concentration to the original concentration, upon the distribution coefficient, and upon the number of passes. Similar effects on the concentration curves in the first zone length would be expected in many systems for which the distribution coefficient is greater than one, and where the maximum solubility is not too much larger than the original concentration. The discussers agree with the authors that the assumption that the liquid is uniform in concentration should be considered with caution. Kneip and Better-ton&apos; have shown, however, that in floating zone refining of zirconium, using induction heating, the distribution of iron agrees with theory which assumes a uniform liquid composition. Hence, in this case, the experimentally realized distribution coefficient agrees with the present phase diagram within the experimental uncertainty. L. Burris, Jr., C. H. Stockman, and I. G. Dillon (authors&apos; reply)—The authors are happy to have received the comments of G. D. Kneip, Jr., and J. 0. Betterton, Jr., which provide additional insight into the zone refining process. It is true that the equations developed are inapplicable if the solute solubility in the solid phase is exceeded. However, this restriction on the use of the equations was clearly stated in the paper. A closer approach to

Jan 1, 1957

By Samuel Dolbear

PUBLIC discussions of mine finance in the tech-nical press have been confined mainly to methods of providing funds for the development of pros-pects or other mining operations which have not reached the stage of productivity. The application of modern financing methods to mines which have behind them a successful record of net earnings has, for some reason, been given scant consideration by mine owners and managers. In a few conspicuous cases, such for example as the Anaconda Copper Mining Co., Chile Copper Co., and one or two others, industrial finance has been applied to mining operations on the scale and after the fashion of other operations. When extensions are needed re-course is usually had, however, to the sale of common stock, with the obvious disadvantage of diluting the holdings of every stockholder of record prior to such financing. In some cases, it has been sought to over-come this disadvantage by issuing stock purchase rights to shareholders of record. If the stockholder is in a position to acquire additional stock, he may then pre-serve his interest intact, otherwise he must suffer a dilution of his holding. If he purchases additional stock he is, from one point of view, paying more for his in-terest than he bargained for when he made his original purchase. In many cases development and equipment are paid for out of surplus or current earnings. It is sometimes most difficult to explain to a manager why he can afford to borrow money when funds are available from a sur-plus account. Nevertheless, industrial enterprises with adequate surplus accounts often finance new construc-tion by the issuance of bonds. Such a procedure enables the company to maintain its surplus intact, and to con-tinue the payment of dividends during a temporary period of unusual expenditures.

Jan 2, 1927

By J. A. Bartnik, Gerald D. Rose, William H. Benson

New techniques in the magnetite and heavy media beneficiation industries demand more efficient magnetic dispersion and flocculation of the finely ground particles. Demagnetizing coils must produce several major effects, such as improving classification and screening efficiency, decreasing moisture content in filter cake and improving separation selectivity and green pellet properties. Likewise, magnetic flocculators must increase filtering rates and the settling rates of solids, improve magnetite recovery and produce cleaner water. To improve the design of equipment and to conduct tests leading to the optimization of such dispersion and flocculation, a program was initiated at Eriez Magnetics. The major conclusions reached are: 1. Laboratory and plant scale tests conducted on magnetite products show that a demagnetizing force of 450 rms oersteds at 60 cycles for 1/20- second duration will depolarize natural magnetite particles coarser than approximately 10 microns. This has been found satisfactory for most applications. 2. Effective flocculation of magnetite was obtained when a slurry with more than one percent magnetite was exposed for a period of approximately 1/15 second to a 600-gauss field. 3. The cost of demagnetizers (or flocculators) increases rapidly for larger diameter pipes. In order to reduce the cost, narrow rectangular sections are recommended for magnetic flocculators. 4. For minimum operating cost, permanent magnetic flocculators are ideal, chiefly because they do not require any maintenance and have no operating cost. 5. A newly designed electro-demagnetizing coil with high heat dissipation and a nonmetallic core provides high efficiency and long life. 6. To select the correct magnetic flocculator (or demagnetizing coil) the following information is necessary: a. Magnetic product susceptibility b. Magnetic product coercive force c. Percent of magnetic product d. Flow rate e. Viscosity f. Structure of magnetic product

Jan 8, 1968

By Ralph H. Sweetser

In these days of the almost exclusive use of byproduct coke as the blast-furnace fuel in this country, it may seem out of place, and smacking too much of reminiscing, to say anything about the use of anthracite coal for blast-furnace fuel. Viewed in the light of present day research and of developments in alloy steel, some observations seem appropriate regarding this raw material that played such an important part in the development of the iron and steel industry during 50 years of the past century. The research work of that period, in which the whole iron and steel industry was revolutionized, passing from wrought iron to steel and from charcoal to three new mineral fuels for blast furnaces, was done chiefly in the full-sized plants of that day; and it was done largely by the ironmasters themselves. The laboratory had not become a part of the ironworks, and scientific instruments were lacking around the blast furnaces; "rule o&apos; thumb" and erroneous theories prevailed—and have not yet all been eliminated. The recent interest in meteoric iron in connection with nickel steels and other alloys proves that it is worth while to search for the reasons for excellence and the causes for failures in the metallurgy of bygone days. Turner1 gives the reasons why the blast furnace of Dr. F. W. Geissen-hainer on Silver Creek, Schuylkill County, Pennsylvania, about 10 miles northeast of Pottsville, was operated successfully with anthracite2 in August and September, 1836, and why several other attempts failed. It has taken a long time for us to find out that there are great differences in the behavior of anthracites from the several parts of the anthracite region, as well as differences in coking coals from the bituminous fields.

Jan 1, 1935