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By S. P. Chong, N. C. Shih, G. A. Turner

Fine powders, with the bulk of the particle diameters Jess than 10 microns, were aerated so that each particle was, on the average, separated from its neighbours by 1.3 to 2 mean diameters. In this state, measurements were made of the viscosity and settling rate of the powder, and the interfacial tension between it and a moist pellet. From the viscosity measurements, qualitative analogies are drawn between the behaviour of the aerated powder and that of a dense gas near its critical point.

Jan 1, 1970

By L. Donovan Clark

The term "powder factor" is almost universally accepted as the measure of the efficiency of a blasting program. It represents the economics of blasting since it designates quantity of explosive (thereby providing quality control in rock fragmentation) in terms of the associated volume broken. It is the wide use of this concept that explains the interest shown in an approach to rock blasting preferred by A. W. and Z. W. Daw* in a treatise on 3 blasting (1) substantiating its use in the form, Q = CVW3 for single shot hole, where Q = quantity of explosive lb Cv = blasting coefficient W3 = unit volume of rock It is obvious that the term Cv could also be called the apparent powder factor should the equation be written in the form, Cv = Q/W3 (lb per cubic unit). However, while the approach was ingenious** and the practical applications straightforward, their original, rather limited experimental work, along with certain assumptions, was questioned.

Jan 1, 1970

By R. Ehrlich, F. E. Crane

A consolidated porous medium is mathematically modeled by networks of irregularly shaped, interconnected pore channels. Mechanisms are described that form residual saturations during immiscible displacement both by entire pore channels being bypassed and by fluids being isolated by the movement of an interface within individual pore channels. This latter mechanism is shown to depend strongly on pore channel irregularity. Together, these mechanisms provide an explanation for the drainage-imbibition-hysteresis effect. The calculation of steady-state relative permeabilities, based on a pore-size distribution obtained from a Berea sandstone, is described. These relative permeability curves agree qualitatively with curves that are generally accepted to be typical for highly consolidated materials. In situations where interfacial effects predominate over viscous and gravitational effects, the following conclusions are reached. 1. Relative permeability at a given saturation is everywhere independent of flow rate. 2. Relative permeability is independent of viscosity ratio everywhere except at very low values of wetting-phase relative permeability. 3. Irreducible wetting-phase saturation following steady-state drainage decreases with increasing ratio of nonwetting- to wetting-phase viscosity. 4. lrreducible wetting-phase saturation following unsteady-state drainage is lower than fir steady-state drainage. 5. Irreducible nonwetting-phase saturation 101lowing imbibition is independent of viscosity ratio, whether or not the imbibition is carried out under steady- or unsteady-state conditions. Experiments qualithtiveIy verify the conclusions regarding unsteady-state residual wetting-phase saturation. Implications of these conclusions are discussed. INTRODUCTION Natural and artificial porous materials are generally composed of matrix substance brought together in a more or less random manner. This leads to the creation of a network of interconnected pore spaces of highly irregular shape. Since the geometry of such a network is impossible to describe, we can never obtain a complete description of its flow behavior. We can, however, abstract those properties of the porous medium pertinent to the type of flow under consideration, and thus obtain an adequate description of that flow. Thus, the Kozeny-Carmen equation, by considering a porous medium as a bundle of noninterconnecting capillary tubes, provides an adequate description of single-phase flow. With the addition of a saturation-dependent tortuosity parameter in two-phase flow to account for flow path elongation, the Kozeny-Carmen equation has been used to predict relative permeabilities for the displacement of a wetting liquid by a gas. 1-5 It has long been recognized that relative permeability depends not only on saturation but also on saturation history as we11.6,7 Naar and Henderson8 described a mathematical model in which differences between drainage and imbibition behavior are explained in terms of a bypassing mechanism by which oil is trapped during imbibition. Fatt9 proposed a model for a porous medium that consisted of regular networks of cylindrical tubes of randomly distributed radii. From this he calculated the drainage relative permeability curves. Moore and slobod,10 Rose and Witherspoon,11 and Rose and Cleary12 each considered flow in a pore doublet (a parallel arrangement of a small and large diameter cylindrical capillary tube). They concluded that, because of the different rates of flow in each tube, trapping would occur in one of the tubes; the extent of which would depend upon viscosity ratio and capillary pressure. They limited

Jan 1, 1970

By Neil C. Hario

The purpose of this paper is to explore the various designs and design alternates available for large fine crushing plants, and to discuss objectives and criteria upon which these designs are founded. Common practice for size reduction of run-of-mine or run-of-pit ore in preparation for subsequent treatment utilizes a three-stage system. First stage, or primary breaking is generally carried out with jaw or gyratory crushers. The usual output from this stage provides a feed for fine crushing in the size range of 6 to 10 inches. This discussion is limited to the process of fine crushing, and we will further limit it to what is commonly called secondary and tertiary crushing. We define a large crushing plant as one with a minimum capacity of 2,000 tons per hour. Generally, these plants utilize cone type crushers to reduce ore for rod, ball, or pebble mill feed.

Jan 1, 1970

By John Parker

During 1965, a new stoping method was developed at the Bunker Hill Mine at Kellogg, Idaho to enable the profitable mining of a large low-grade zinc orebody. This method, called the Bunker Hill pillar system, incorporates the use of the air-powered Atlas Copco T2GH or CAVO 310 as the prime production component. The method and equipment proved highly successful and was the first step in mechanizing what had been a classic example of a square-set and horizontal cut-and-fill operation. Since that time there has been a realization that the small rubber-tired type of loader could be effectively used to advantage in increasing productivity and decreasing costs in many different stoping and development applications throughout the mine. The net result since 1967 has been that a large and increasing portion of the mine production and an increasing share of the development is being done with small rubber-tired loaders. Presently, ten Atlas Copco T2GH and six CAVO 310 air-operated loaders are in use, having replaced the time-honored slusher which was first introduced into the Bunker Hill Mine in about 1898 in the form of a slip scraper. The recent advent of diesel powered loaders in the one yard size range has in 1970 further accelerated the trend toward rubber-tired mobile equipment at the Bunker Hill Mine. Although The Bunker Hill Company is using small diesel loaders of several different types and manufactures for inclines, declines and level development and will undoubtedly find stoping applications for this equipment, .the bulk of this paper will be confined to the use of the air-operated loader, leaving the diesel equipment to a future presentation. It is sufficient to say that we feel at this time that the Autoloader type air-powered equipment and the small diesel front end-loader

Jan 1, 1970

By Meguru Nagamori

DURING the smelting of the sulfide ores of copper, nickel, and certain other metals, a matte phase is formed. For a better understanding of the physico-chemical properties of mattes, binary systems such as Cu-S, Ni-S, Fe-S, and so forth, should be studied, especially in the vicinity of liquid compounds such as Cu2S, Ni3S2, FeS, and so forth. These compounds are relatively stable in the solid state although they can exhibit appreciable deviations from stoichiometry. With small deviations from stoichiometry there are large changes in the activity of both sulfur and metal this is a characteristic of both solid and liquid sul-fides near the stoichiometric compositions. In the vicinityof molten Cu2S,1 for instance, the activity of sulfur increases about 100 times for a 0.012 increase in the mole fraction of sulfur and, correspondingly, the activity of copper decreases greatly. In this sens the minor deviations from stoichiometry should be carefully taken into account in studies of such metal-sulfur melts. Metal-sulfur melts may be considered to have properties intermediate between metallic solutions and molten salts, i.e., neither entirely metallic nor entirely ionic. The radius of the ion sZ- is 1.84 as compared with 1.04? for a single bond covalent s.2 It is therefore inferred that when the sulfur is more ionic its partial molar volume is larger, although metal-metal, metal-sulfur, and sulfur-sulfur interactions may bring about further complexities. Thus, it is to be expected that the molar volumes, which are derived from density-composition relations, will help in resolving the structure of the melts. In this study the maximum bubble pressure method with bubbling gases of H2, H2S, and Ar, .was employed to measure the density. EXPERIMENTAL Materials. Silver of 99.95 pct purity was melted in an alumina crucible and hydrogen gas was then bubbled through the liquid for the deoxidation. In preparation of Cu2S, electrolytic copper powder (>99.9 pct Cu) was mixed with precipitated sulfur and heated to 1200°C in an alumina crucible under a hydrogen atmosphere. Mixtures having the approximate compositions FeS and Ni3S2 were prepared by heating reagent grade electrolytic iron or reduced nickel powder with precipitated sulfur under a hydrogen atmosphere. The H2S gas was of 98.5 pct purity, the impurities being mostly CO2 and CS2 which hardly contaminate the melts. Apparatus. The crucible system is shown schematically in Fig. 1. To minimize the variation of melt composition during a density measurement, the apparatus was designed in such a way that either Ar, H2, H2S, or mixtures of these gases could be used as the bubbling gas. When the melt had a high partial pressure of sulfur, H2S gas was used. When the partial pressure of sulfur was so low that oxygen might dissolve in the melt, the use of H2 was preferred. In intermediate cases, argon or mixtures of H2-H2S were used. Density of Dibutylphtalate. Dibutylphtalate was used as the manometer fluid. Relative to distilled water, the density of the dibutylphtalate, pdib g per cc, was measured and found to be: pdib (25°C) = 1.046 i 0.002. With the use of the temperature coefficient reported by Kemppinen and Gokcen,3 the following value was

Jan 1, 1970

By Keros Cartwright

Sanitary landfilling has become one of the most widely used methods of disposing of solid refuse. A principal concern of regulatory agencies and the public itself is that landfill operations do not degrade the physical environment, including water resources, and the ground-water reservoir in particular. Ground-water and engineering geology can guide landfill operations into suitable terranes or develop measures to compensate for any natural limitations at a particular site Experience and research in Illinois suggest four activities relating to landfill disposal that warrant attention by geologists and engineers: (1) Regional delineation of favorable and unfavorable hydrogeologic conditions to facilitate planning and preliminary screening of potential landfill sites. (2) Site evaluations, with considerations of geologic materials, topography, water levels, flow systems, and local occurrence and use of water resources. (3) Re- search on aspects of the hydrogeologic environment that control effects of, or are modified by, landfills. (4) Formulation of practices in the siting, construction, and operation of landfills that prevent, mitigate, or isolate deleterious effects. The first two activities are basically in the domain of earth science, requiring the application of fundamental concepts of geology and hydrology and conventional site-exploration methods. The third activity, research, requires contributions from geology as well as other disciplines, including soil physics, sanitary engineering, and chemistry. The fourth calls for policy decisions by regulatory agencies and elected officials, using the contributions of scientists and engineers.

Jan 1, 1970

By R. K. Govila, E. H. Parkison

THE interplanar angles for hcp metals vary with c/a ratio, and therefore must be computed separately for each particular metal or alloy. Manual computation of these angles is laborious and time consuming, and for this reason computer programs have been developed to accomplish this task.1"3 However, these programs have certain disadvantages. For example, they require prior knowledge and understanding of ALGOL or FORTRAN languages. Further, they will not print out specific angles but instead give all angles between given limits—thus program2 prints out a total of 26,649 angles between planes with indices and in the range from (4 4 4) to (4 4 4) for any given c/a ratio. The purpose of this note is to present a simple and inexpensive computer program for accomplishing this task. This program is written in BASIC language4 which does not require any prior knowledge of computer programming, and is ideally suited for nonprofessional programmers. It also provides flexibility for the user by allowing him to select any indices for as many or few planes as desired for any given c/a ratio. The computer program proposed below is based on the relationship in which + is the angle between any two planes and . TO illustrate use of the program, consider the problem of calculating the interplanar an-

Jan 1, 1970

By P. W. Jeran

The Stereonet Analysis Program (SNAP) is a mathematics tool which, by means of a computer, reproduces mathematically the manual techniques of pre- paring stereograms. This computer program was developed to provide a fast, accurate, and economical means of analyzing fracture orientation data. It is mitten in FORTRAN IV for use on a UNIVAC 1108 operating under an Exec II system, but can be adapted to other systems. SNAP is currently being used to aid in the analysis of cleats and other geologically induced fractures associated with coalbeds that are being mined underground, Methane flows through the coalbed and into these mine workings predominantly through the fracture system. Therefore, knowledge of fracture orientation is an invaluable aid in the development of methane control technology.

Jan 1, 1970

By H. P. Dibbs

An account is given of the application of neutron activation analysis to the rapid, non-destructive determination of copper in minerals, using a 14-MeV neutron source. Elements that interfere in the determination of copper by this method are given, together with the errors in the estimation of copper that result from the presence of varying amounts of these elements. The possible use of a compact "sealed-tube" 14-MeV neutron generator for the field assay of copper in minerals is discussed.

Jan 1, 1970

By E. H. Herron, J. H. Perry

Mathematical simulation of reservoir behavior may be used to help understand reservoir processes and to predict reservoir behavior, thereby leading to the most economically desirable form of exploitation. In addition, simulation can be used as a tool for reservoir description to learn more about the physical nature of the reservoir and the mode of primary recovery. This use is essential in most reservoir studies and represents one of the more significant applications of simulation. Prediction of reservoir behavior provides information concerning displacement efficiency, optimum well locations, and the comparison of alternative producing processes. Since oil, water and gas all commonly occur in many reservoirs, a simulation that takes into account the simultaneous flow of three immiscible phases is a prerequisite for obtaining such information. Furthermore, a simulation that describes this flow in two dimensions provides the capability of evaluating combination gas- and water-drive reservoirs with either an areal or a cross-sectional description. Many reservoir problems require such a simulation. The objective of the research described here was to develop a mathematical model and associated computer program for accurate, efficient, and economical prediction of the reservoir flow of three phases in two-dimensional geometry. Several authors have discussed multidimensional reservoir simulation of two phases.l-3 Gottfried et al.' presented an analy- sis of three-phase simulation in one dimension. Fagin and Stewart" and Garrett6 have discussed the simulation of three-phase flow in two dimensions, but their solution techniques were different from the method discussed in this paper. In particular, previous models and computer programs have usually involved either fewer capabilities or inefficient and less rigorous descriptions resulting in limited applicability. In the following sections, we present a description of the model, an evaluation of the method, and the application to reservoir problems. Additional and supporting material is presented in the Appendix. The Three-Phase Model General Description The three-phase model consists of the mathematical description of the flow of oil, water and gas in a reservoir. Conceptually this description considers flow in all three space dimensions, but in the subject simulator it is assumed that no flow occurs in the third dimension. The model includes the effects on reservoir behavior of fluid and rock compressibility, viscosity, gravity, capillary pressure, relative permeability and gas solubility. Within the two-dimensional restriction, the reservoir considered may be completely heterogeneous and anisotropic. The differential equations governing multiphase, multidimensional flow in a reservoir are too complex to be solved analytically, so they are approximated by a system of finite difference equations and solved

Jan 1, 1970

By Lester J. Crow

This study advances the use of elemental sulfur in structural materials by demonstrating its value in bonding high-strength, well-graded basalt aggregates to form sulfur-basalt concretes. Sulfur is an excellent bonding agent, and the strength of a thermoplastic sulfur-aggregate mixture depends, to a large degree, on the strength and grain-size distribution of the aggregate used. A 3-cubic-foot, electrically powered mixer with heat applied to the barrel was used to mix the sulfur and aggregate. Sulfur content of several mixtures was varied to obtain the best workability with a minimum of sulfur in excess of that necessary to fill the voids. The average grain sizes and grain-size distributions were also varied to determine their effects on strength. Unconfined compression tests of forty-five 6-by l2-inch cylinders yielded average strendths of 3,348 psi to 10,398 psi. The highest strength single cylinder was 10,717 psi. The cylinders were tested from 24 hours to 6 days after pouring; after 24 hours the rise in strength was very slight. From the results obtained it appears that sulfur can be a useful construction material. An evaluation was made of a high-vacuum application for sulfur concrete. Sulfur has a high vapor pressure at elevated temperatures, 50° to 100° C; consequently, significant losses by sublimation can be expected. At lower temperatures the losses are not significant; however, this factor will limit its use at a higher temperature.

Jan 1, 1970

By Frank M. Randall

The Buick mill is located at the site of the old Buick general store, approximately 4 miles south of Bixby, Missouri on route KK. It is a part of the operations in the area now called the "New Lead Belt". The ore body lies at an elevation of 270 feet above sea level, and is fairly flat lying, becoming slightly deeper toward the south. The mineralization is due to the secondary deposition of galena, sphalerite, chalcopyrite, pyrite, calcite, dolomite and some localized drusy quartz in a country rock of dolomitic limestone. The galena is fairly coarse grained with some large crystaline structure, and some oxidized surfaces. The sphalerite is fine grained- small crystals containing Cd (about 0.7%) and Ag (about 10 oz per ton) in solid solution. The chalcopyrite is fine grained, fine crystals that are sometimes massive in nature. The mine plan is a modified room and pillar system. Broken ore at the mine face will be transported to several different ore passes by rubber tired load-haul-dump units. Ore passes will drop the ore to a rail haulage level some 90 feet below the mining level where bottom dump cars will deliver it to a 42 in. Nordberg gyratory crusher. Two 12 ton capacity skips in balance carry the ore some 1,200 feet to the surface. The hoist is equipped with automatic controls for loading, hoisting and unloading.

Jan 1, 1970

By C. W. Kovach, A. Moskowitz

Studies were undertaken to investigate the effects of manganese content on the machinability and other Properties of a free machining martensitic stainless steel (AISI Type 416). Machinability was found to be significantly improved in steels of high manganese content, and a direct relationship was obtained between machinability and steel Mn:S ratio. As the manganese content of the steel increases, the sulfide Phase present changes from CrS to (FeMn)Cr2S4 to (MnFeCr)S, and finally to MnS. The average sulfide inclusion hardness decreases through the same range of increasing manganese content. The mechanism for machinability improvement is discussed in terms of a soft ductile sulfide affecting deformation in the secondary shear zone. Type 416 containing relatively high manganese for improved machinability shows good general properties. The effects of increasing manganese content on mechanical properties, cold formability, and corrosion resistance are described. THE addition of sulfur is commonly used to improve the machinability of stainless steels. However, little attention has been paid in the past to the composition and characteristics of the sulfur-containing phase or phases present in these resulfurized steels. Recent information on the properties of sulfide phases, and their role in metal cutting, suggests that variations in these phases could have critical effects on machin-ability, as well as important effects on formability and other properties such as corrosion resistance. Manganese, chromium, and iron are strong sulfide forming elements present in stainless steels! of these, manganese has the greatest sulfide forming tendency and iron the least.1"1 The manganese content of resul-furized 13 pct Cr steels, often about 0.5 pct, can be insufficient or only barely sufficient to combine with the sulfur that is present; thus, the precise level of manganese can strongly influence the nature of the sulfide phase. Sulfide phases which may be present in stainless steels have been reported to include CrS, a spinel-type sulfide, chromium-rich manganese sul-fide, and manganese Sulfide.5,6 Detailed phase relationships for the Fel3Cr-Mn-S system have been reported by the present investigators,7 and a portion of this work will be referred to subsequently in this paper. Recent work by Kiessling6 and Chao et a1.8 has shown that sulfide phases can display wide variations in hardness, and may undergo considerable plastic deformation under isostatic loading.9-12 Early theories of metal cutting attributed the influence of sulfur to a lubricating effect. It is now apparent that the influence of the nonmetallic inclusions and their properties on crack initiation, deformation in the shear zones, and boundary films must also be considered in relation to the machining process. This paper presents the results of studies conducted to relate machinability to the various sulfide phases which occur in stainless steels. This work has led to the development of alloys with improved machinability, and has generated information on the effects of inclusions on metal cutting processes. Effects of sulfide inclusions and steel composition on other important metallurgical properties are also discussed. MATERIALS For drill machinability and inclusion studies, 10 lb laboratory heats were melted in an air induction furnace. These heats were made with sulfur contents be tween 0.10 and 0.50 pct and manganese contents be tween 0.05 and 3.0 pct. Residual elements were added to the heats in amounts typical for commercial steels. The typical compositional range covered by the heats is shown below: C Mn P S Si Ni Cr Mo Cu N 0.10 0.05 0.007 (M0 0.40 0.40 13.0 0.20 0.10 0.03 3.0 0750 The laboratory ingots were forged in the temperature range of 1800" to 2100°F to 3/4-in. sq bars, and all bars tempered to a hardness aim of 200 Bhn prior to testing. Because of differences in composition and tempering response, the tempered bars showed some variation in hardness (175 to 275 Bhn) as well as variations in delta ferrite content (0 to 50 pct). Composition, hardness, and delta ferrite content were considered in the analysis of the machinability data. Additional tests involving tool-life evaluation and determination of other properties were conducted on materials from commercially melted and processed 15-ton electric furnace heats. TESTS AND PROCEDURES Machinability of the laboratory heats was evaluated in a drill test. In this test, 1/4-in. diam holes, 0.4 in. deep, were drilled alternately in a test bar and in a standard bar for a total of four holes in each. This sequence was repeated three times using a freshly sharpened drill each time. The average time required to drill a hole in the test bar was compared to that for the standard bar. A drill machinability rating was assigned to the test bar relative to a rating of 100

Jan 1, 1970

By T. H. Patching

This paper provides a review of the available information on the origin and mechanisms of the release of gas from coal seams. With the opening up of new mines in Western Canada and the increased mechanization of underground coal mines, the study of gas emissions is of increasing importance in providing safe working places underground.

Jan 1, 1970

By John J. Stetler

The Companhia Vale do Rio Doce in Brazil operates one of the most extensive systems in the world for the mining, transportation, processing, pelletizing and shipping of high grade hematite iron ore and pellets. Current shipping of unbeneficiated, sized, high grade ore from its ports at Tubarão and Vitória is now at the rate of 17,500,000 metric tons annually. An increase in this annual rate is now under study. Using the technology and facilities of Lurgi (1) and Arthur G. McKee company CVRD undertook a program to process and pelletize two types of fines - "Blue Dust" and ?Itabira Fines?. Blue Dust is a high grade fine ore which was bypassed while mining the direct shipping ores and which, also, exists as a very large ore body called the Conceição Mine. Itabira Fines is a lower grade of fine ore which is comprised of in-situ fines and, also fines which are generated in sizing the direct shipping ores for a rigid specification market.

Jan 1, 1970

A portable electronic instrument was developed which will measure change of longitudinal wave velocity with change of uniaxial stress in rock columns. The instrument is a solid-state device powered by nickel-cadmium batteries. It uses a probe of two piezo-electric crystals spaced inches apart to send and receive a pulse through a stressed rock. A one-inch cathode ray oscilloscope visually displays the longitudinal wave. A reference chart is used to find the stress. Laboratory results have indicated that the average stress on a sandstone column can be found to within 35 psi. The feasibility of using this instrument to determine stresses in mine pillars is to be studied. The instrument may be used to investigate physical properties of rock.

Jan 1, 1970

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Jan 1, 1970

By C. H. P. Lupis, Henri Gaye

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

Jan 1, 1970

By R. Kossowsky, W. C. Johnston

CONSIDERABLE experimental data has been published in recent years on a few directionally solidified aluminum base eutectic alloys. The mechanical properties of A1-Al3Ni eutectic have been studied by Lemkey, Hertzberg, and Ford1',2 and Salkind et a1.3 where the alloy has been demonstrated to behave as a whisker reinforced composite with superior properties over many aluminum alloys. It has also been shown4 that aluminum reinforced with Al3Ni whiskers R. KOSSOWSKY, Member AIME, is Senior Metallurgist, Westing-house Research Laboratories, Pittsburgh, Pa. W. C. JOHNSTON, formerly with Westinghouse Research Laboratories, is Head, Department of Physics, George Mason College, University of Virginia, Fairfax, Va. Manuscript submitted March 28. 1969. IMD__________________ possesses excellent microstructural stability to 508°C. The effect of lamellar structure in A1-CuA12 eutectic was compared3 to the rod-like structure in the A1-Al3Ni eutectic, and was found to be better in low cycle fatigue. This was rationalized3 by postulating that a lamellar reinforcement was more efficient at blocking lateral plastic flow than a rod-like rein-forcement. The purpose of this study is to explore eutectic strengthening in other aluminum base alloys. The Al-Pd system5 forms a eutectic with aluminum and the intermetallic compound A13Pd at 25 wt pct Pd, and has a melting point of 615°C. A13Pd has an orthorhom-bic structure and transforms to hexagonal Pd2A13 at 785°C. Growth characteristics, compression yield strength, creep rupture, and microstructural stability of directionally solidified and as-cast alloys are investigated. Eutectic ingots having a nominal composition of 25 wt pct Pd were prepared by first compacting 1/2 in. diam by a in. high pellets from 99.99+ pct A1 and 99.99 pct Pd powders. The pellets were then levitation cast into 1/4 in. diam by 2 in. long copper molds. Directionally solidified bars were prepared by grinding the cast ingots to 0.195 in. diam, inserting them into alumina

Jan 1, 1970