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By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

By R. Schuhmann

D. W. Fuerstenau (Associate Professor of Metallurgy, Dept. of Mineral Technology, University of California, Berkeley, Calif.) In his excellent paper, Dr. Schuhmann has proposed a mechanism for conlrninution which can be utilized to explain a number of phenomena which have been observed in the size reduction of solids. The difference between the product obtained from a ball mill and from a rod mill can readily be explained by Dr. Schuhmann's hypothesis. Consider that the size distribution of the product from each comminution event is given by y; - 100 (x/ki) (1) where Yi is the cumulative percent finer than size x, ki is the size modulus, and is the distribution modulus for the single comminution event. The total product from a cornminution operation will be the summation of the products from all of the individual cornrninution events. If the size moduli from the various comminution events range from kl to kn , the size distribution of the total product will be a straight line on a log-log plot only to a particle size equal to k ,. Considering 100 volurnes of feed, the value of y for x equal to kl is Riven by where y is the cumulative percent finer than size kj, z is the number of comminution events of kind i, and vi is the volume of each particle crushed. y=z1 qv1+z2 qv2 (k1/k2) +.............zn qvn (k1/kn) (3) F or particle sizes greater than k1 7 e. 6. x = k3, the value of y will be given by k3 A y = z1 qv1 + z2bv2 + Z3uV3 + zn zn qvn (k3/kn)(4) Only when x is equal to k, will y equal 100. 'Thus, the total product from a comminution operation will be a straight line on a log-log plot strictly up to a particle size equal to kl and above that size the line will curve so that y will equal 100 for the coarsest particle or k, (see Fig. 1). The actual shape of the size of distribution curve will depend upon the relative number of conmninution events of different kinds. In the case of ball milling, the ratio kn/kl may be pite large and there will be considerable deviation at the coarse sizes in a Schuhmann plot. kIowever, the grinding action in a rod mill is such that fine particles are protected from the rods by the coarse particles. Consequently, kn/kl will be quite small and the product from a rod mill will give a straight line Schuhmann plot almost to y equal 100%. In his paper, Dr. Schuhmann also has presented a very straightforward definition of grindability derived from the basic energy equation E = Ak-a (5) where E is the energy required to comminute a material to a size modulus of k and A is a constant. According to Dr. Schuhmann, the grindability of a material is the volume of material comminuted finer than unit size per unit of energy expended, this being 1/A. For comparison of grindabilities at any size two numbers are required, both = and 1/A, and anyone tabulating grindabilities should give both of these numbers. Concerning the experimental determination of grindabilities, if the material being comminuted possesses distinct cleavage, the energy re quired for comminution is given by E = Ak-(a-y) (6) where y is small number less than = . Because of cleavage, less energy will be required for comminution. To be certain that cleavage does not affect the gindability of the material being tested, it is suggested that the method used by Dr. Charles for determining grindability be used to ascertain if the deviation exponent y is zero or finite. R. Schuhmann, Jr. (Author's Reply) Dr. Fuerstenau's interesting comparison of rod milling and ball milling

Jan 1, 1961

By A. W. Gauger

For perhaps one hundred years scientists have been engaged in attempts at devising a satisfactory method of classification of coal. During this time many charts, tables and graphs have been proposed, some of which have had considerable merit, but no one system has been found to be applicable to all ranks of coal, nor has any one system received general acceptance. In many of the proposals, water eliminated between room temperature and 105" C. has been regarded as extraneous matter and calculations have been made to the air-dry or water-free basis. Such methods of calculation do not lend themselves to satisfactory grouping of the high-moisture coals.1, 2 A consideration not only of the properties of the high-moisture coals and their behavior on drying but of the generally accepted ideas of the coalification process and the role of water in this process indicates that water is an essential constituent of all coals and therefore should not be neglected. For example, in such low-rank coals as the lignites of the Northern Great Plains' deposits the inherent moisture of the lignite as mined plays a very important part in the physical properties thereof. Freshly mined lignite contains upwards of 30 per cent water and is extremely tough and resistant to shock. Upon exposure to the atmosphere, the lump loses part of its moisture and checks and splits, leaving a friable and broken up residue. So far as we have been able to determine, water is the only thing lost in this process and we are forced to the conclusion that moisture plays an extremely important part in the structural properties of the original lignite. With reference to the coalification process, Mack and Hulett3 pointed out in 1917 the important part that water played therein. They observed that water cannot be removed from peat or coal by pressure alone, but only as the result of chemical reaction, and suggested that peat in its early stages may be largely a hydrosol. Slow chemical changes occur over a long period of time until finally the mass becomes more largely a hydrogel. These views are substantiated to some extent by the experi-

Jan 1, 1932

By AIME AIME

AT a joint meeting of the Tulsa Geological Society and the Mid-Continent Section of the A; I. M. E., held at Tulsa on March 21, the history of unit development in the Kettle- man Hills field was discussed. Robert C. Patterson? Super- visor for the U. S. Geological Survey at Taft, Calif., was the speaker. An abstract of some of his remarks follows: On July 1, 1923, curtailment agreement for two years was made between the operators of North Dome Kettleman and the U. S. Department of the Interior. In this it was agreed to consider a plan of unit development, or other cooperate method of developing the structure. As a result, Kettleman North Dome Association was incorporated in December, 1930, as a non-profit cooperative corporation under the laws of California. Approved in January, 1931, by California Oil and Gas Supervisor and by Secretary of Interior. On Feb. 10, 1931, it became an active organization through election of executive officers and eleven- directors. General manager chosen. Association started to function April 1, 1931. Assumed control of 10,800 acres of proved and semi-proved land, as shown in Table 1.

Jan 1, 1932

By Charles Will Wright

FRANCE will be given a large portion of the Marshall Plan funds for relief, reconstruction, and industrial development in France and in her colonial possessions. At present that country is not in position to export any large tonnages of the mineral products needed in the United States. However, if, through Marshall Plan aid and private capital investment, production of these products can be largely increased, agreement should be made by which the United States is to get a substantial portion of such increased output in part payment for the material and technical aid they receive. France issued a decree, published in the "Official Gazette" on Feb. 3, 1948, which permits conversion into dollars of dividends derived from dollar investment in Government-approved projects and will agree to a scale of capital amortization to be determined in each individual case. This decree is to encourage private capital to cooperate with local capital in industrial undertakings. The French Colonial Ministry has prepared an extensive program for aid to the mining industries in overseas possessions to be undertaken by

Jan 1, 1948

By R. J. Allio, C. H. Randall

An automatic system for the quantitative analysis of microstrulcture has been developed. The method is based upon a statistical model of microstructure and employs phase intercept fractions as fundamental random variables. Structure-sensitive properties can be related explicitly to parameters derived from the distribution of phase intercept fractions in a matevial. THE properties of mechanical dispersions and of multiphase alloys art: intimately related to the amount, distribution, and intrinsic properties of the dispersed material. In many instances, the amount and distribution of the dispersed substances have greater influence on the over-all system properties than do the properties of the dispersed substance-Such properties as average particle size, particle size distribution, homogeneity of dispersion, volume per cent of dispersed phase, and mean free path between dispersed particles thus become critical in any evaluation of the properties of a dispersion. Unfortunately, techniques for evaluating quantitatively the microstructural characteristics of dis~ersions rapidly and accurately have not been available. If necessary, qualitative or semiquantitative devices can be utilized. Some such devices are based merely upon comparison of the specimens in question with arbitrary standards. Other techniques involve superposition of grids and tabulation of particles observed in different portions of the grid. Still other methods based upon lineal analysis entail counting lines or points at random upon the specimen to be examined; the number of intersections of the line with a given phase, the proportion of line or number of points which are covered by given phase are variously recorded. The mathematical basis for most of the techniques of quantitative metallography have been amply reviewed in the literature.'l2 without exctption, however, the standard techniques for quantitative metallography are either imprecise or are exceedingly tedious to apply. For example, tranverse integrating stage for rapid manual areal fraction measurement has been designed by Smith.3 Howerer, as in the case of any device based upon visual eslimation, operator bias may cause appreciable error. Various flying spot devices, on the other hand register particle size distributions in 2-dimensions, from which it is difficult to derive other properties of the dispersion. Thus, e.g., the 3-dimensional distribution cannot be inferred unless certain rather broad assumptions are made concerning the randomness of distribution and geometrical configuration of dispersed phase. Many limitations to the application of quantitative structural analysis can be overcome by the use of the microdensitometer, which is essentially an automated areal analysis device. Data obtained in the form of a distribution of phase intercept values are

Jan 1, 1962

By ROY BERENTZ

MANUFACTURE is the transformation of material by the application of energy and power. The energy of a man exerted throughout a day is equivalent to about one horsepower-hour of mechanical work an amount which can be purchased for less than 2c. It is evident that manual labor is uneconomical if mechanical energy can be applied effectively, or without disproportionate expense. Since manual energy is relatively so costly, economy demands that mechanical power be employed so as to reduce the human effort connected with mining operations to a minimum. Power, like other commodities, is most efficiently produced in large quantities. Mechanical transmission, once prevailing, is being rapidly superseded by electric drive. There are many reasons for this change; such as increased production, ease and accuracy of control, convenient application, ease of moving, etc.

Jan 1, 1930

By ALEXANDER L Hay, Alexander L.

THE Sydney coal field, the largest and most valuable in Nova Scotia, is on the northeastern coast of the Island of Cape Breton, extending from Mira Bay on the south to Cape Dauphin on the north, a distance of 30 miles, and has a general dip northeast under the sea. The field embraces the mining villages of Morien, Birch- grove and Reserve and the towns of Dominion, Glace Bay, Waterford and Sydney Mines. The city of Sydney is about midway between the northern and southern extremities of the field and on the western fringe of the productive coal measures. Sydney harbor crosses the coal field, cutting off direct rail connection between Sydney Mines and the greater part of the field to the southeast.

Jan 1, 1928

By Charles O. Thompson

IN 1867 the city of Worcester walled in the Mill Brook for its main sewer. This stream, one of the important affluents of the Blackstone River, flows through the city in a southwesterly course from Salisbury Pond, and along its valley a considerable part of the heavy manufactories of the city are placed. At two points, a mile apart, a sufficient fall occurs to be turned to account for motive power, and at many points it was the right and practice of the riparian proprietors, prior to 1867, to use the water for steam and other manufacturing purposes. But the

Jan 1, 1881

By Zay Jeffries

In this paper, it is proposed to outline a method for the determination of melting points of those metals and alloys having high fusion temperatures. The application of the method as used to determine the melting points of alloys of tungsten and molybdenum will be given. It will be seen from these results that tungsten and molybdenum form a completely isomorphous series. This is also verified by the accompanying photomicrographs. Tungsten and molybdenum have been found to crystallize in the same system namely, isometric, and the crystal units are cubes. These determinations were made by examining etching pits in the pure metals.

Jan 1, 1917

By L. Burris, C. H. Stockman, I. G. Dillion

Zone melting is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Equations are presented which 1—predict the concentration profiles after successive passes of the zone and 2—give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing in the last zone length. These equations were solved numerically using an electronic computer, and the concentration profiles are presented as a function of the solute distribution coefficient and the ratio of molten zone to total bar length. ZONE MELTING is a purification process in which separation of impurities is effected by slowly moving a narrow melted zone through a bar of solid material. Separation occurs if the solid freezing from a solution at any moment has a composition different from that of the liquid from which it is freezing. Solutes which lower the freezing point will tend to remain in solution and will be moved in the direction of zone travel. Solutes which raise the freezing point will preferentially freeze out, and they will be moved in a direction opposite to that of zone travel. After repeated unidirectional passage of a molten zone through a bar of material, impurities will be concentrated in the ends of the bar. A limiting concentration gradient will be reached in the bar after a large number of passes of the molten zone. Both the magnitude of this limiting concentration gradient and the rate of movement of solute in any pass depend on the zone length and on the equilibrium concentrations of solute in the liquid and solid phases. The basic theory of zone melting was thoroughly covered by Pfann.1 The purpose of this paper is to extend the theory of zone melting by presenting 1—equations which relate the concentration profiles in successive passes of the zone and 2—equations which give the limiting distribution of solute along the bar after an infinite number of passes of the molten zone. These equations take into account the effect of normal freezing* in the last zone length concentration of a given solute in the solid to the concentration of the same solute in the liquid. Analytical methods for determining the concentration profiles after any pass have been developed by Lord2 and Reiss. The method developed by Lord does not take into account normal freezing in the last zone and also becomes very complicated when the number of passes becomes large. The method developed by Reiss enables the direct calculation of the complete concentration profiles (including that in the last zone) after any pass for values of k close to unity (0.9 < k < 1.1). Both methods are useful and provide valuable insight into the zone melting process. The equations given in this article are based on the same assumptions used by Pfann. These are: 1—uniform composition in the liquid, 2—negligible diffusion in the solid, 3—constant distribution coefficient, 4—constant length of the liquid zone (except at the ends), and 5—solubility of the solute in the melt is not exceeded at any point. Equations for Concentrations in Successive Passes For a melted zone of length 1 at the left-hand end of a bar of uniform unit cross-section, the amount of solute in the liquid is J0Cn-1(x) dx [1] where the subscript is the number of the pass. Cn-1(x) represents the concentration (expressed as weight per unit volume) obtained in the previous

Jan 1, 1956

By Charles O. Thompson

In 1867 the city of Worcester walled in the Mill Brook for its main sewer. This stream, one of the important affluents of the Blackstone River, flows through the city in a southwestenly course from Salisbury Fond, and along its valley a considerable part of the heavy manufactories of the city are placed. At two points, a mile apart, a sufficient fall occurs to be turned to account for motive power, and at many points it was the right and practice of the riparian proprietors, prior to 1867, to use the water for steam and other manufacturing purposes. But the

Jan 1, 1881

By W. J. Keep

We have shown in former papers the influence which aluminum exerts when added to cast-iron, and we have presented in another paper, accompanying this one, the physical properties of the metal aluminum and of some of its alloys. The present paper continues the investigation. The reader will find, in our paper on "Aluminum and Other Metals Compared,"* explanations not here repeated, which will render the diagrams in this paper intelligible. The scale of stresses is laid off on the ordinate which rises from the zero-point of the diagram. The scale of deflections is laid off on the abscissa which runs horizontally through this zero-point. By applying a given amount of stress, then running back to zero, and again applying the same stress, we describe a spring-line, in which the deflections are proportional to the stresses. Generally the deflections exceed this proportion during the original application of stress; and the excess is the permanent set. By laying off from the zero-point a line parallel to the springline, we shall generally find that this new spring-line and the diagram coincide for some distance; that is, that the test-bar is

Jan 1, 1890

By G. H. Enzian

THE effects of phosphorus and nitrogen on the properties and behavior of low carbon steels are important considerations to both the manufacturer and the user of such material. For one thing, these two elements are the principal points of distinction between the chemical compositions of Bessemer and open-hearth grades. Further, open-hearth steels themselves may vary considerably in nitrogen content depending on the raw materials and ..practice used. In addition, appreciable amounts of rephosphorized open-hearth steels are being used at the present time in some low alloy, high strength grades and in certain other cases. For these and other reasons, it was felt desirable to obtain more complete knowledge of the effects of simultaneous small variations in phosphorus and nitrogen content on such properties of low carbon steel as tensile strength, impact toughness, sensitivity to cold work, and strain aging. A long range investigational program designed to furnish such information, was carried out, and the present paper summarizes some of the data currently obtained. General Discussion The strengthening effect of relatively small amounts of phosphorus in steel has been recognized, and to some extent utilized, for many years. A number of investigators have pointed out, from time to time, that under proper conditions of control, phosphorus can be a useful alloying element in low carbon steels.1-3 Nevertheless, in spite of the volume of data on the subject, the use of phosphorus for this purpose has always been handicapped by widespread feeling that its presence makes the steel brittle, difficult to cold work, and unreliable at low temperatures. This belief on the part of some steel users is not entirely justified in many cases, and often stems from early experience with acid Bessemer steels which have appreciably higher phosphorus (and nitrogen) contents than basic open-hearth grades. Nitrogen in steel, and its effect on properties, has also received considerable attention in the literature.4 In 1906, Braune5 ascribed the brittleness of Bessemer rails to the nitrogen content, and proposed a schedule of nitrogen limits for steels for various uses. This was one of the first papers to recommend directly the use of nitrogen content as a quality control measure, but it did not meet with much favor or support; as a matter of fact, the Jernkon-toret was rather sharply criticized for publishing the paper. In the intervening years a number of papers have been published on the subject of nitrogen in steel. As a result, it is now generally recognized that nitrogen can have an important effect on the properties and behavior of steel and that the presence of this element should be considered in any systematic study of factors affecting steel quality. In 1932, Graham6 introduced the concept that the quality of various steels could conveniently be evaluated and compared in terms of "sensitivity", which was defined as "the characteristic reaction rate of a piece of steel toward brittleness or hardness." This concept formed the basis for a broad research program into factors causing variations in the quality of commercial steels. At an early stage of this work, it became apparent that the observed effect of either phosphorus or nitrogen on the sensitivity of steel depended, in no small measure, on how much of the other of these two elements was also present. Indeed, the combined effect of phosphorus and nitrogen in steel may often be more important than the specific effect of either. With a few exceptions, it is not possible to predict accurately the effect on steel properties of a change in the amount of either phosphorus or nitrogen in the steel without also specifying the approximate amount of the other element. It seems desirable, at this point, to discuss briefly the distinction between strain-sensitivity and strain aging as used in this paper. In the early stages of its development, the work-brittleness test7 (which will be described in more detail later) was used

Jan 1, 1951

By Larry Kaufman

A useful method for estimating the entropy of NaCl type compounds has been developed by combining the Debye theory of specific heat with the Lindemann formula. This method pemnits calculation of the entropy from a knowledge of the atomic weight, atomic volume, and melting point of the compound. Comparison of the calculated and observed entropies of 35 NaCl type compounds over a wide temperature range yields good agreement thus establishing the usefulness of the method. Application of the method to other crystal types is also discussed. KUBASCHEWSKI~ has suggested a useful method of estimating the enthalpy of formation of inter-metallic compounds from a knowledge of the crystal structure, lattice parameter, and heats of sublimation of the component elements. This method is quite valuable in predicting the tendency for compound formation in a given system and is of particular value in considering systems for which no experimental data are available. In order to supplement the enthalpy calculation afforded by Kubschewski&apos;s method, it would be of value to be able to estimate the entropy of compounds so that the entropy and free energy of formation could be evaluated. Although a considerable body of such data determined by calorimetric and equilibration techniques exists at present, the difficulty of making such measurements (particularly at high temperatures) and the ever increasing number of new compounds which are of interest make the desirability of such a computational method clear. This paper deals with a method for calculating the entropy of a compound from a knowledge of the atomic weight, atomic volume, and melting point. Since these data are generally easier to determine and therefore more readily available than thermo-dynamic data, they should provide an additional tool in estimating the stability and reactivity of compounds at high temperatures. I) THE ENTROPY OF PURE METALS As a first approximation, the specific heat of a pure metal can be represented by a sum of terms where C,($/tI is the vibrational specific heat calculated on the basis of the Debye theory, lo4 TC, (0/T) is an approximation to the Cp - C, correction. T is the electronic specific heat, and Cp (p) is the magnetic specific heat. Although the Debye theory does not provide a complete description of the vibrational specific heat, i.e., the Debye temperature 0 is not a constant, it does provide a good approximation when used properly. Blackman6&apos;7 has written several reviews on this subject discussing the different values of 0 determined by various methods (specific heat, X-rays, elastic constants, electrical resistivity, and so forth), as well as the observed temperature dependence of 0 with T. In the present case the 0 in Eq. [I] naturally refers to the specific heat 0. The variation of Debye 0 (as determined from specific heat measurements) with temperature is observed to exhibit its most radical behavior at very low temperatures. At higher temperatures the 8 values are observed to become more nearly constant. Blackman6&apos;7 has presented the variation of 0 with temperature for several metals. His tabulation is reproduced in Table I. Reference to Table I shows that above a certain temperature level, 0 remains fairly constant. The value of 0 which is most useful in computing the specific heat, and hence the entropy, is the value of 0 in the range 0/6 « T « 0. In 1910, Lindemann&apos; suggested a relation for estimating Debye 0 values. According to this formula, where V is the atomic volume, T is the melting point in &apos;K, M is the atomic weight, and CL is a constant. Mott and Jones9 present this formula and state that there is at present no satisfactory theoretical explanation, but that it does have an empirical basis. By using the valuesof 0 in Table I along with known1&apos; values of M, T, and the molar volume VM, where the Lindemann constant can be evaluated. This

Jan 1, 1962

By Edgar G. Hill

MUCH has been written and said recently about the methods used and materials and equipment employed in building the long tubes that criss-cross a great part of the [ ] united States, like the pattern of a spider&apos;s web. This paper will discuss the fundamentals of design of these lines from the economic as well as the engineering view-point, pointing out the effect of the volumes transported, and the load factor at which they are operated, on the unit costs of transportation, as well as the effects on costs of the character of the fluids the lines are called upon to handle. Generally speaking, crude-oil pipe lines carry oil from the producing fields to the [ ] refineries. Sometimes part of the journey is by pipe line to a coastal point and tank ships are employed for the rest of the trip. The main lines of directional flow of crude oil through pipe lines in the United States are shown on Fig. I, but this, of course, does not always show individual pipe lines. BASIC FORMULA FOR FLOW OF CRUDE OIL The laws governing the flow of crude oil through pipes are well known. The basic

Jan 1, 1942

By W. Rostoker

Single isothermal sections were constructed for the titonium-rich corners of the systems Ti-Fe-O, Ti-Cr-O, and Ti-Ni-0 with a view to locating the shape and disposition of the ternary intermediate-phase fields for the compounds isomorphous with Fe3W3C. IN a previous note,&apos; it was reported that a group of ternary intermediate phases existed which occurred in the general composition range Ti,X,O-Ti&O where X was one of the following elements: copper, nickel, cobalt, iron, or manganese. In two instances, binary intermediate phases occurred (Ti²Cu and Ti²Ni) which appeared to be isomorphous. The X-ray diffraction patterns of the phases could be indexed on a cubic lattice whose cell edge was of the order of 11 kX. Karlsson2 stated that the line extinctions and line intensities indicated that these phases were isomorphous with Fe³W³C and therefore belonged to the space group Oh. This author also noted that no unique phase of this type occurred at the composition Ti,Cr,O. This latter statement was accepted as true at the time the previous technical note was written.&apos; However, work continued along these lines and that reported here has shown that a phase isomorphous with Fe³W³C does exist in the vicinity of the composition Ti³Cr³O but not at or near Ti4 Cr²O. The lattice parameter of this phase was found to be 13.01 kX. Metallographic examination of both as-cast and annealed specimens of these supposed ternary oxide phases disclosed structures which were far from single phase in many instances. It was considered a point of some interest to locate more positively the composition coordinates of the single-phase fields. To this end, single isothermal sections for the systems Ti-Fe-O (1000°C), Ti-Cr-0 (1000°C), and Ti-Ni-0 (900"C) were constructed. Phase relationships were studied by both X-ray diffraction and metallotrra~hic methods. Allovs were prepared as 10 g buttons by melting in a noncon-sumable electrode, water-cooled copper crucible arc-melting furnace using a helium atmosphere. Oxygen was introduced quantitatively by the use of weighed amounts of TiO² or TiO. Iodide titanium and the purest available alloying metals were used. All results are discussed in terms of the nominal composition of the melts. Previous experience with making oxygen-rich alloys had shown that oxygen losses were not significant if a homogeneous melt was produced. Weight-loss measurements were used to check loss in metallics during melting. Anneals were conducted in evacuated Vycor bulbs, and annealing times ranged from 24 hr at 1000 °C to 48 hr at 900°C. To achieve equilibrium in certain sluggish alloys, seven-day anneals were used. Debye-Scherrer powder patterns were taken in a 14 cm diam camera using filtered CuK radiation (K² = 1.541232 kX; K., = 1.53739 kX). Specimens were prepared by crushing and screening previously annealed buttons. In general, the X-ray diffraction results were used to identify the major phases, while the metallographic examinations were more useful in indicating the number of phases present. By the use of the combined results and general fundamental rules governing ternary equilibrium, it was possible to construct isothermal sections in good detail. In some instances where auxiliary lattice-parameter data were available, it was possible to lay down tie lines and to locate more positively corners of three-phase fields. Isothermal Section of the System Ti-Fe-O at 1000°C The binary systems Ti-O³ and Ti-Fe4 have been published. Binary phases, TiO, TiFe, and TiFe2, are likely to be encountered in the titanium-rich corner of the system. The structures are NaCl (Bl), CsCl (B2), and MgZn, (C14) types, respectively. Although preliminary X-ray diffraction studies indicated the presence of a ternary phase in the composition range Ti,Fe,O-TiJ?e,O, metallographic examination of two specimens at these compositions revealed the presence of other phases. Thirty-eight alloys were used to delineate the phase boundaries of the isothermal section illustrated in Fig. 1. The five almost single-phase ter-

Jan 1, 1956

By Samuel M. Dunaway

INTRODUCTION ASARCO Incorporated purchased the East Tennessee Zinc Mines of the American Zinc Company and commenced operating on November 29, 1971. Presently, three mines are operating producing 6620 t/d (7300 stpd). The ore mined is sphalerite which occurs In lower Ordovician carbonates of the upper Knox Group and occurs in open space and fracture filling. Orebodies range from 3 to 46 m (10 to 150 ft) thick with dips from flat to 20º. The mining method is random room and pillar modified by shrinkage and bench stoping. Like other mining departments, the mining group at the Tennessee Mines Division is constantly looking for methods to improve productivity and safety and to reduce mining costs. This involves testing new equipment, trying new ore extraction ideas and making mining plant alterations to meet changes in operating conditions. The areas of change that will be described in this paper are longhole raising, jumbos and LHD loading, shaft sinking, conveyor transport of ore and sublevel haulage developments. LONGHOLED RAISES Raise driving has always been a hazardous occupation for miners and today it is becoming more difficult to get competent people for this kind of work. This problem has led us to seek an easier, safer way in which to excavate raises. The first longhole raises were excavated in the early 1970&apos;s using a Gardner-Denver air trac equipped with a PR-123 rock drill. The machine used 38 mm x 244 cm (1 ½ in x 8 ft) round rods with rope

Jan 1, 1977

By L. D. Jaffe, D. C. Buffum

EARLIER the authors and coworkers had pre sented data on isothermal temper embrittlement of an SAE 3140 steel?&apos; In that work, however, attention was concentrated on embrittlement at 575°C and below. Preliminary measurements showed that embrittlement at 675 °C was much mote rapid than would be expected from the data at the lower temperatures: and indicated the need for further work above 575°C. The possibility of an upper nose in the time-temperature embrittlement diagram above 575°C was pointed out. Procedure The same heat of SAE 3140 steel was used as in the previous work, and experimental methods were the same. All blanks were austenitized 1 hr at 900°C and water, quenched. Groups were then tempered 1 hr at 675"C, water quenched, and given embrittling treatments for times of 5 min to 240 hr at 675" to 600 °C, as shown in Table I. Other groups, after the temper and quench, were embrittled 48 to 1440 hr at 550°C. Another series was tempered 240 hr at 675"C, quenched, and held for various times at 650" to 375°C (Table 11). For comparison, a series was tempered for these same times at 700°, 675", and 650°C (Table 111). The Ae, temperature for this heat of steel had been determined as approximately 690°C;1*a the treatments at 700°C were introduced to determine the effects of tempering in a range where a little austenite would fonn. A large number of other treatments, involving holding at two temperatures in succession after the temper, and occasionally slow cooling or heating, were also studied. These treatments are listed in the tables. Austenitizing was done in air; all subsequent treatments were in salt. Blanks were always water quenched after the last treatment. The heat-treated blanks were machined to standard V-notch Charpy specimens. A transition curve for each group was obtained by breaking the specimens at various temperatures on a 217 ft-lb impact machine having a striking velocity of 16.8 fps, and plotting the observed percentage of fibrous fracture vs the test temperature. From this plot, the transition temperature was taken as the lowest temperature at which the fracture appeared 100 pct fibrous; its accuracy is estimated as +5"C. Generally, hardness was measured on every bar. Since a decrease in hardness itself seems to decrease the transition temperature somewhat, a correctiona of —0.28"C per Bhn was applied to permit comparison of the transition temperatures on a uniform basis of 24 Rc. The transition temperature and hardness results are given in Tables I through VI. Where overlap of earlier work1.&apos; occurred, data were combined.

Jan 1, 1958

By A. T. Corey, C. H. Rathjens

INTRODUCTION Although the oil industry has been aware of the directional variability of permeability in porous rock, the directional variability of relative permeability has been largely ignored. Yet it is apparent that such an effect must be present in a system in which the distribution of oil and gas within the porous matrix is controlled by capillary forces. It is easy to visualize a rock composed of layers of fine and coarse material such that gas flow across the bedding planes would take place only after the average oil saturation had been reduced to a very low value. The fine layers, because of their greater capillarity, would remain saturated and act as barriers to the flow of gas after the coarse layers had been desaturated. Flow of gas parallel to the bedding planes would obviously take place at a much greater liquid saturation. Without more complete information concerning the geology of a reservoir than is generally available, it is not possible to predict exactly how such phenomena would affect the over-all performance of an oil field. It is possible, however, to predict qualitatively the effect of stratification on relative permeability measurements made on laboratory cores. In this investigation the effect of stratification was studied analytically by assuming that two porous materials with different capillary pressure-desaturation curves (but identical relative permeability curves) were in contact and in capillary equilibrium. As a qualitative check on the analytical results, cores having various degrees of visible stratification were used for relative permeability measurements made with fluids flowing both parallel and perpendicular to the bedding planes. A quantitative check was considered impractical because of the difficulty of devising models in which two materials of predetermined properties could be joined without the plane of contact becoming a discontinuity. THEORETICAL CONSIDERATIONS AND ASSUMPTIONS The assumption of capillary equilibrium in an oil-gas system implies that the difference in pressure between oil and gas is everywhere the same. This means that the curvature of the interfaces must be everywhere the same in order to satisfy the equation where PC is the pressure difference between phases, y the interfacial tension and r, and r2 are the major and minor radii of curvature. Depending on the pore size distribution of coarse and fine layers, the volumetric percentages of oil and gas in these layers will differ when equilibrium exists. The exact relationship can only be determined by obtaining the complete capillary pressure-desaturation curves for each of the porous materials in contact. It has been pointed out elsewhere&apos; that the capillary pressure-desaturation curves of sedimentary porous materials can often be approximated by the relation where C is a constant and Soe is the effective saturation to oil based on a percentage of the pore volume effective to flow. In the same paper it was indicated that, as a first approximation, the values of oil relative permeability are given by and the values of gas relative permeability by For this analysis Eqs. 2, 3, and 4 were assumed to apply to each of two components of a hypothetical porous rock in capillary equilibrium. It was also assumed that each of the components had a residual wetting phase saturation of 20 per cent so that 80 per cent of the total pore volume was effective to flow. The permeability of the coarse stratum was taken as 100, and its displacement pressure was such that C in Eq. 2 had the numerical value of 1. The corresponding values for the fine stratum were 10 for the permeability and 10 for C. Units are not specified because they do not enter into the final results. The choice of the permeabilities and displacement pressure ratios was made to expedite the calculations. Any reasonable rock properties could have been chosen without changing the results qualitatively. Several arrangements of the two components were studied. Table 1 summarizes the resultant permeabilities obtained for four types of arrangement. RELATIVE PERMEABILITY CALCULATIONS The first step in the computation of relative permeability for the composite cores was the plotting of the capillary pressure-desaturation curves and the relative permeability curves for the individual components according to Eqs. 2, 3, and 4. At arbitrary

Jan 1, 1957