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By P. Niessen, S. J. Bercovici

RECENTLY Aust et al.&apos; proposed a model of non-equilibrium grain boundary segregation based on a vacancy gradient induced uphill diffusion process of solute to grain boundaries. According to their proposal, solute atoms which are attracted to vacancies would, during the cooling of a sample, migrate with vacancies toward grain boundaries (vacancy sinks) and thereby enhance the solute concentration in boundary regions. For solute atoms which are not attracted to vacancies no such boundary solute enrichment would be expected. These concepts were given experimental support by boundary and bulk mi-crohardness measurements of various thermally treated dilute zinc and lead alloys and also doped aluminum oxide. The underlying assumption in their work was that solute enrichment in boundary regions is indicated by higher microhardness values. From thermodynamic considerations1&apos;2 it appears that the solid-liquid solute distribution coefficient (K), defined as the concentration of solute in the solid to the concentration of solute in the liquid at equilibrium, indicates whether attractive or repulsive forces exist between vacancies and solute atoms. K < 1 indicates a solute-vacancy attractions, K > 1 indicates no, or a repulsive, vacancy-solute interaction. This note is to report on observations of different grain boundary etching phenomena in high purity zinc alloys. These phenomena appear to depend on whether a K < 1 or K > 1 solute is present. In experiments designed to measure directly the solute enrichment in grain boundary regions, samples of zone refined zinc with 0.1 at. pct solute additions were cooled from 380°C at a rate of 3°C per min. A surface layer of approximately 50 was then removed from the samples by chemical polishing. The samples&apos; surfaces were then protected by a chromating treatment such that in a subsequent etch only grain boundary regions were dissolved. The dissolved regions were approximately semicircular troughs, 10 µ in width. The grain boundaries were usually in the middle, i.e., at the bottom, of this trough. For zinc containing the K < 1 solutes cadmium and aluminum, the grain boundary was always indicated by a ridge as shown in Fig. 1. For pure zinc, and zinc containing the K > 1 solutes copper and gold, a groove at the bottom of the trough indicated the boundary position, Fig. 2., To test if these different grain boundary etching behaviors were possibly connected with the segregation process discussed above, the Zn-Cd alloy was again heated to 380°C and quenched into brine. After surface protection and etching it was found that this specimen no longer exhibited the grain boundary ridges but rather grain boundary grooves as shown in Fig. 2. It would appear, therefore, that the boundary ridge is a consequence of a process occurring during the slow cooling of the samples. From absorption spectrophotometric analysis it was found that for slowly cooled samples containing K < 1 solutes, the solute/zinc ratios of the material from the boundary trough were consistently considerably higher than the solute/zinc ratios of the bulk alloys. This boundary region solute enrichment was not observed in quenched samples. It is concluded therefore, that the boundary ridge shown in Fig. 1 is directly or indirectly connected with nonequilibrium solute segregation.

Jan 1, 1970

By C. G. Brennecke, R. T. Gallagher

This paper is the result of a research program entered into cooperatively by the General Reinsurance Corporation and Lehigh University in January 1944. The research program was instituted to find a more positive method to determine the presence of hazardous roof conditions in , mining operations. The co-authors, together with Mr. R. D. Currie, Engineer for the General Reinsurance Corporation, started working on the project in January 1944, first undertaking a library search; second, a preliminary study based on some existing equipment; third, the design of new and more suitable equipment; and finally, the field testing of equipment and methods. Purpose Any study of the accident statistics of mining operations will disclose the rather startling fact that approximately 50 to 60 per cent of all fatal underground accidents in the anthracite and bituminous mines are caused by falls of roof and coal, the metal and nonmetal mines showing only a slightly smaller percentage. Advancements in safety engineering have produced definite results in the decrease of accidents due to blasting, haulage, electricity, and explosions but no such decrease is shown in those caused by falls of roof, coal, or ore. Table Il,2 is a compilation of statistics as published by the United States Bureau of Mines, showing the percentages of fatal accidents caused

Jan 1, 1947

By R. T. Gallagher, C. G. Brennecke

This paper is the result of a research program entered into cooperatively by the General Reinsurance Corporation and Lehigh University in January 1944. The research program was instituted to find a more positive method to determine the presence of hazardous roof conditions in , mining operations. The co-authors, together with Mr. R. D. Currie, Engineer for the General Reinsurance Corporation, started working on the project in January 1944, first undertaking a library search; second, a preliminary study based on some existing equipment; third, the design of new and more suitable equipment; and finally, the field testing of equipment and methods. Purpose Any study of the accident statistics of mining operations will disclose the rather startling fact that approximately 50 to 60 per cent of all fatal underground accidents in the anthracite and bituminous mines are caused by falls of roof and coal, the metal and nonmetal mines showing only a slightly smaller percentage. Advancements in safety engineering have produced definite results in the decrease of accidents due to blasting, haulage, electricity, and explosions but no such decrease is shown in those caused by falls of roof, coal, or ore. Table Il,2 is a compilation of statistics as published by the United States Bureau of Mines, showing the percentages of fatal accidents caused

Jan 1, 1947

By M. R. Tek, R. L. Nielsen

The scaling laws as formulated by Rapoport relate dynamically similar flow systems in porous media each involving two immiscible, incompressible fluids. A two-dimensional numerical technique for solving the differential equations describing systems of this type has been employed to assess the practical value of the scaling laws in light of the virtually unscalable nature of relative permeability and capillary pressure curves and boundary conditions. Two hypothetical systems — a gas reservoir subject to water drive and the laboratory scaled model of that reservoir — were investigated with emphasis placed on water coning near a production well. Comparison of the computed behavior of these par ticular systems shows that water coning in the reservoir would be more severe than one would expect from an experimental study of a laboratory model scaled within practical limits to the reservoir system. This paper also presents modifications of the scaling laws which are available for systems that can be described adequately in two-dimensional Cartesian coordinates. INTRODUCTION Present day digital computing equipment and methods of numerical analysis allow realistic and quantitative studies to be carried out for many two-phase flow systems in porous media. Before these tools became available the anticipated behavior of systems of this type could be inferred only from analytical solutions of simplified mathematical models or from experimental studies performed on laboratory models. To reproduce the behavior of a reservoir system on the laboratory scale, certain relationships must be satisfied between physical and geometric properties of the reservoir and laboratory systems. Where the reservoir fluids may be considered as two immiscible and incompressible phases, the necessary relationships have been formulated by Rapoportl and others.2-5 Rapoport&apos;s scaling laws follow from inspectional analysis of the differential equation describing phase saturation distribution in such systems. It will be recalled that these scaling laws presuppose three conditions: (1) the relative permeability curves must be identical for the model and prototype; (2) the capillary pressure curve (function of phase saturation) for the model must be linearly related to that of the prototype; and (3) boundary conditions imposed on the model must duplicate those existing at the boundaries of the prototype. These three requirements seldom if ever can be satisfied in scaling an actual reservoir to the laboratory system because: (1) The laboratory medium normally will be unconsolidated (glass beads or sand) while the reservoir usually is consolidated. Relative permeability and capillary pressure curves are usually quite different for consolidated and unconsolidated porous media. (2) The reservoir usually will be surrounded by a large aquifer which could be simulated in the laboratory only to a limited extent. (3) Wells present in the reservoir would scale to microscopic dimensions in the laboratory if geometric similarity is to be maintained. In view of these considerations, rigorous scaling of even a totally defined reservoir probably would never be possible. The purpose of this paper is to assess the practical value of the scaling laws in the light of the unscalable variables. This has been done by carrying out numerical solutions in two dimensions to the differential equations describing the flow of two immiscible, incompressible fluids in porous media for a field scale reservoir and a laboratory model of that reservoir. While both the reservoir and the laboratory model were purely fictional, each has been made as realistic and representative as possible. The field problem selected as the basis for the investigation was an inhomogeneous, layered gas reservoir initially at capillary gravitational equilibrium and subsequently produced in the presence of water drive. The laboratory model of this reservoir was designed to utilize oil and water in a glass bead pack. The numerical treatment employed was similar to that of Douglas, Peaceman and Rachford6 and it included both capillary and gravitational forces as

By M. J. Saarivirta

A high-purity copper-zirconium alloy system was imesti-gated. The zirconium content of the alloys studied varied from 0.003 to 0.23 pet. The solid solubility of zirconium in copper and some physical and mechanical properties of the alloys have been determined. By proper heat treatment, Cu-Zr alloy can develop a high electrical conductivity and resistance to softening at temperatures up to 500°C (930°F). This combination of desirable properties makes this alloy superior, to other com-merzcrrl copper base alloys for- use in the electrical conductor field. DEMAND for high conductivity copper alloys that retain their mechanical properties at elevated temperatures is growing rapidly. At present, copper-base alloys such as copper-silver and copper-chromium are used where these characteristics are required. As an example, commutators in electric motors are often made of these alloys. However, the life at elevated temperature of commutators made of copper-silver alloys is much shorter than the life of the same part made of copper-chromium and copper-zirconium alloys. Copper-silver alloys are subject to creep and subsequent failure when the service temperature exceeds several hundred degrees centigrade. Use of copper-chromium alloys has been known for the past several years, but little information is available in the literature concerning the properties of alloys in the copper-zirconium alloy system. Some work had been directed toward determining the solubility of zirconium in copper as well as determining properties of the Cu-Zr alloys. These investigations have revealed the superior high-temperature and electrical conductivity properties of copper-zirconium alloys over copper-chromium alloys. The United States Metals Refining Co., Carteret, N. J. has recently produced OFHC R copper-zirconium alloys for experimentation and evaluation. Because OFHC R copper contains no appreciable oxygen, no harmful oxides are formed and the full benefit of Zr as an alloying addition is obtained. This paper describes the results of this work. It contains room-temperature and some high-temperature data which have been obtained after various processing techniaues. Actual elevated temperature properties are being determined and will be reported in a separate paper. Preliminary results obtained at elevated temperatures suggest that the Cu-Zr alloy is superior to other high conductivity copper-base alloys. WORK PROCEDURE The high-purity oxygen free (OFHC R) copper-zirconium alloys with zirconium content ranging from 0.003 to 0.23 pct were cast into 4-by 4-in. wirebars by both continuous casting and conventional casting methods. Zr was added in the form of a master alloy containing 30 pct Zr and 70 pct Cu. Castings were analyzed for zirconium and nine bars containing various amounts of zirconium were selected for this study. The results of analyses and the sample numbers are given in Table I. Typical analyses of OFHC R copper are also shown. The following properties were studied: A) Solid solubility of zirconium in copper. B) Effect of zirconium on properties of copper. C) Effect of combined working and heat treating on properties of Cu-Zr alloys. The solid solubility of zirconium in copper was determined by metallographic techniques. Specimens for this phase of the investigation were hot rolled at 900oC (1650oF) to 0.250-in. rod. The rolled rods were cut into 2/3-in. long specimens and solution annealed at 950 °C (1740°F), 980°C (1795 °F). and 1020 °C (1870 °F) for 6 hr and quenched in water. In order to find the solid solubility limits at lower temperatures, the homogenized specimens were reheated at various temperatures for 1 hr and quenched. The physical and mechanical properties were determined on 0.250 in. rod, 0.132- and 0.081-in. wires. The wires were cold drawn from the 0.250-in. rods after they were solution annealed at 980 °C (1795°F) and quenched in cold water. Mechanical and electrical properties were determined on cold drawn and

Jan 1, 1961

By Thomas J. Crocker, Galen G. Waddell, Eugene H. Skinner

This paper describes a method of measuring initial and long-term deformations which occur in the medium surrounding mine accessways, and discusses the importance of this type of measurement in assessing support-problem areas. Delineated are (1) description of the rock-deformation monitoring equipment, (2) results of two field tests which monitored rock deformation around 4-foot-diameter raise bores, and (3) a numerical-analysis (finite-element) technique to correlate theoretical with experimental results. Instrumentation developed provided the sensitivity and resolution needed to measure rock deformation around a full-scale raise bore during excavation. Results of the tests conducted at the Lucky Friday mine, Mullan, Idaho, show the relationships between (a) de- formation vs. time, and (b) deformation vs. bit progress. Based on theoretical evaluation of the initial deformation, the medium appeared to behave elastically. Using an estimated field stress of 5,500 psi and Poisson&apos;s ratio of 0.20, the gross modulus of elasticity of the rock was calculated to range from 3.15 to 6.0 x 106 psi (with one outlier which was determined to be >12 x l06 psi).

Jan 1, 1971

By J. C. Williams, M. J. Blackburn

Several of the decomposition processes that can occur in supersaturated phases in a Ti:11.6 wt pct Mo and a Ti:20 wt pct V alloy have been studied by transmission electron microscopy. The deformation induced "marternsitic phase" in the Ti:Mo alloy has been found to have a bcc or bct structure rather than the previously reported hexagonal structure. The morphology of&apos; the transformed region is a rather complex asserrlblage of twins, twinning occurring in one or more systems; this internal twinning has been found to occur on (112). The w phase is formed in both alloys on aging and is present in the Ti:Mo alloy after quenching. The structure of this phase has been confirmed as hexagonal in both systems, however, differences in morphology and stability are found between the two alloys. Thus in the Ti-Mo alloy the w phase has an ellipsoidal morphology with the major axis lying parallel to <111>ß or [0001]w while in the Ti-V alloy the phase forms as cubes, the cube faces lying parallel to {100}ß or {2021}w Some observations on the particle sizes, volume fraction, and composition of the w phase in the Ti-Mo alloy are listed. The mode of formation of The a phase from the (ß + w) structures is also different in the two alloys. In the Ti-Mo alloy the a phase is formed by either a cellular reaction or by the growth of isolated needles, whereas in the Ti-V alloy the a phase is nucleated at an w:ß interface and grow to consume the w phase. Some of the difjerences in behavior of the w phase are attributed to the mismatch between it and the solute enriched ß matrix in which it forms. MaNY transition elements tend to stabilize the bcc or ß-phase when added to titanium. In general two types of phase diagrams are produced, either a ß-stabilized (ß-isomorphous) system, e.g., Ti:Mo, -Ti:V, Ti:Nb, or a ß-eutectoid system, e.g., Ti:Cr, Ti:Fe, Ti:Mn. In previous papers&apos;-4 the phase transformations in the a-phase and (a + ß)-phase alloys have been described and this work has been extended to ß-stabilized systems. Specifically, transformations in the alloys Ti:20 wt pct V and Ti:11.6 wt pct Mo have been studied; in both of these alloys the ß phase is retained at room temperature when quenched from the ß-phase field. A number of phase transformations can occur in such metastable ß phases and the two alloys were chosen to include most of the transformations reported for ß-stabilized systems. We list these possible phase transformations below. Ti:11.6 Mo quenched from >780°C to retain the ß phase: a) The w phase can form on quenching.5 b) Martensite can be produced by subzero cooling or deformation. Two martensite habit planes have been reported in Ti:Mo alloys; (334)ß and (344)ß=6 c) On aging at temperatures <-550° C the w phase is formed before the a-phase.5,7 d) On aging at temperatures >550°C the a phase is formed.7 e) The martensite can be tempered. It has been reported that the a phase rather than the ß phase is precipitated during tempering.&apos; Ti:20V quenched from >660°C to retain the ß phase:9 a) At aging temperatures <260°C separation into two bcc phases occurs. b) The w-phase is produced prior to the a phase on aging at temperatures <-400°C. c) At temperatures 2400°C the a phase is formed directly. T-T-T diagrams describing the temperature and time regimes for the formation of these phases have been published7,9 for a Ti:12 pct Mo and a Ti:20 pct V alloy. We have attempted to investigate these transformations using transmission electron microscopy, however thin foils undergo a spontaneous transformation in all conditions except the equilibrium (a + ß) structure. This transformation has been reported previ0usly10,11 and we will comment on its morphology and nature in the various sections of experimental results. EXPERIMENTAL The compositions in wt pct of the two alloys investigated were: Ti:11.6 Mo, 0.100 02, 0.006 N2, 0.0015 H2 Ti:20V, 0.0574 O2, 0.0111 N2, 0.005 H2 These alloys were cold-rolled to 0.020 in. thick sheet. Specimens were heat treated in vacuum or in inert gas at temperatures >500°C and in a circulating air furnace at temperatures <500°C. Thin foils were prepared using standard techniques, described in detail previously." Dark field micrographs were obtained using high resolution technique. RESULTS Martensitic Transformation in Ti:11.6 pct Mo. Detailed study of the deformation induced martensite is not possible due to a spontaneous transformation which occurs near the edge of thin foils as shown in Fig. 1. Similar transformations have been observed in iron-" and copper-base13 alloys as well as other titanium alloys, but some observations specific to the Ti:1l.6 Mo alloy are listed below. a) The boundaries of these transformed regions are glissile and move under the influence of the electron beam during examination. b) Selected area diffraction indicates the transformed regions have the same structure as the matrix, being separated by tilt boundaries. The misori-

Jan 1, 1969

By E. S. Machlin

The possibility that formation of voids under creep-rupture conditions may take place by the condensation of vacancies has been investigated theoretically. It has been concluded that nucleation of voids under creep-rupture conditions by vacancy condensation is highly improbable. However, growth of pre-existant voids by vacancy condensation is probable. A number of predictions made in this theory have been verified by the data. It has been predicted and checked that the product of rupture life and steady-state creep rate for preannealed metals and single phase alloys is an approximately invariant quantity, independent of stress, temperature, and atomic number for a given type structure. The direction of the effect of cold work on this product has been predicted and found in agreement with experiment. A number of experiments to evaluate the vacancy condensation mechanism further are described. SEVERAL papers have appeared recently which speculate on the origin of voids formed at grain boundaries under stress.&apos; &apos; The object of this paper is to examine quantitatively the proposition that the voids produced in a creep test are a result of vacancy condensation. A result of this paper is a theory of creep-rupture. Void Nucleation Application of standard nucleation theory" to the problem of void nucleation leads to the following conclusions: 1—Homogeneous nucleation of voids requires a supersaturation ratio (concentration of vacancies in supersaturated to that in saturated solution) of 400 for a reasonable surface energy of 1000 erg per cm-and 1.4 for the improbably low surface energy of 10 erg per cm. 2—Heterogeneous nucleation of voids at plane interfaces between two phases requires a supersaturation ratio of 2.5 for a typical contact angle of 145 3-—Void nucleation about a solid particle may be accomplished at a supersaturation ratio of 1.17 for a typical value of work of adhesion? of 60 erg per The work of adhesion is the surface work 10 replace two solid-vauor surfaces by a solid-solid interface. enr &apos; between an oxide and a metal in the presence of a surface active element such as sulphur. Estimates of the supersaturation ratio at which voids are produced in diffusion experiments yield a maximum of 1.01. Inasmuch as the foregoing mechanisms of void nucleation probably will not operate at this level—too low a surface energy is required—the investigatol. is led to the conclusion that voids must already exist. That is, nucleation of voids probably does not occur. Rather, existing submicroscopic voids grow out to visible size. Already existing voids might be produced during solidification or working. Supercritical sized parlicles which contain cracks may act as heterogeneous void nuclei. Gas pockets may act as void nuclei. Experiments are desired to determine the nature of the heterogeneous void nuclei which grow out to voids in both diffusion and creep experiments. Void Growth Void growth might occur in at least two possible ways, depending upon whether the already existing void nuclei are at grain boundaries or within the grains. In the case of a spherical void far from a crystal boundary, vacancies are generated during creep as a consequence of the migration of suitable dislocation jogs&apos; and are also annihilated at sinks. Under these conditions, a steady-state concentration of vacancies is built up in the crystal, defined by the condition that for any differential volume the rate of generation of vacancies in that volume equals the rate of annihilation of those vacancies." This equality would lead to the development of a gradient of vacancy concentration radially outward from the void surface up to a radius where the vacancy lifetime becomes equal for all directions of vacancy migration. The distance over which this vacancy concentration gradient extends equals about 2vD,T* where D, is the vacancy diffusivity and T:&apos; the vacancy lifetime in a crystal outside the gradient in a zone of constant vacancy concentration. The vacancies generated in the region over which the gradient exists will annihilate more often at the void than elsewhere. Approximately a little over one-half the vacancies generated in the gradient zone will annihilate at the void. Hence, the growth rate of the void is given by on where R is the radius of void in centimeters, is the atomic volume, and R is the rate of generation of vacancies, number per centimeter" per second. R D and T* may be estimated in terms of other physical parameters." In particular, R = n.j e/b [3] where n is the average number of vacancy produc-

Jan 1, 1957

By Elton A., Youngberg

The Holden mine operated by the Chelan Division of the Howe Sound Co. is on the east slope of the Cascade Range in north central Washington on the south slope of Railroad Creek valley at an elevation of 3500 ft. The mine may be reached by a 40 mile boat trip from the town of Chelan which is at the southern tip of Lake Chelan, to Lucerne at the mouth of Railroad Creek and an 11 mile bus ride up Railroad Creek to Holden. All freight and concentrate is moved over this route to Chelan Falls on the Columbia River which is on the railroad four miles below the town of Chelan. The mine is now producing 2000 tons of gold, copper, and zinc ore per day which is treated in the Holden mill. Gold-copper and zinc concentrates are made, the first of which is shipped to Tacoma, Wash., and the latter to Kellogg, Idaho, for smelting.

Jan 1, 1949

By R. Ebeling, M. F. Ashby

The paper is in two parts. The first develops the formulae and method needed to calculate the size, nu)nber, spacing, and volume fraction of hard or inert particles in the interior of a specimen from measurernents made on an extraction replica; throughout, the spread of- particle sizes in a single specimen is taken into account, and the extraction efficiency of the replica is considered. A method for testing whether the particles are randotnly distributed in space is described, and the spacing of randomly distributed particles is discussed. The second Part describes the application of the method to copper containing spherical particles of silica; the description includes an estimate of the errors involved, and a comparison of this with alternative methods. All parameters except uolume fraction can be determined satisfactorily, and the method offers advantages over other electron-,rzicroscopic techniques when dealing with hard particles in a softer matrix, or inert particles in a chem-ically less inert matrix. 1 HE experimental measurement of sizes and numbers of discrete particles of a second phase embedded in a matrix material from opaque, plane sections has been considered by many authors, notably by Fullman.&apos; It is assumed that, when the specimen is sectioned, the particles are also sectioned, so that the diameters of the circles of intersection of particles with the plane of the cross section ("surface diameters") are measured. It is difficult to derive the distribution of true particle diameters ("volume diameters") from measurements of the distribution of "surface diameters" on a plane section. The measurement of size and numbers of small second-phase particles by transmission electron microscopy through thin foils of matrix containing the particles has been described by Cahn and ~uttin~&apos; and by ~illiard.~ Because of overlap and the fact that particles which intersect the foil surface may be sectioned whereas those in the bulk of the foil are not, it is again difficult to measure the true distribution of particle sizes. The use of replicas for this sort of measurement has not been analyzed in detail. A replica made from an opaque cross section, thus replicating the circles of intersection of particles with the plane of section, is analyzed by Fullman&apos;s method and suffers from the same difficulties. Under certain circumstances, however, extraction replicas can be used, and offer a special advantage in that they make the determination of the true distribution of particle diameters particularly simple. It is the purpose of this paper to describe this extraction replica method. Consider the example of an alloy consisting of SiOz particles, whose mean diameter is about 1000A, dispersed in a copper matrix. When the alloy is sectioned and mechanically polished, the particles are not sectioned, because they are much harder than the matrix, and so will be either left in the surface or pulled out whole, and because the particle size is smaller than the abrasive size of even the finest abrasive. The particles are chemically inert in solutions which chemically etch or electropolish the matrix, so that chemical treatments do not section the particles either. (Experimental measurements of particle shape in this alloy confirm this—truncated particles are never seen.) Small, hard or inert, particles are therefore not sectioned when the specimen is sectioned and polished. An extraction replica taken from this polished surface shows the true "volume" diameter of each extracted particle; the distribution of diameters seen on the replica is the surface distribution of true "volume" diameters, and the volume distribution of true "volume" diameters is easily derived from it. The extraction replica method is not subject to the difficulties associated with sectioning of particles, and avoids the problem of overlap from which the transmission method suffers. The method is well-suited for studying hard particles in a soft matrix. Examples are provided by internally oxidized alloys, oxide-dispersion strengthened metals like T.D. Nickel, and carbides, nitrides, and strong intermetallic compounds in metals. It should be possible to adapt polishing techniques in alloys containing softer but inert particles to avoid sectioning the particles (say by electropolishing or etching). The method is tested and illustrated in Sections 8 and 9 by applying it to a dispersion of spherical SiO2 particles in a copper matrix. I) SYMBOLS Symbols are defined where they first appear in the text. Volume fractions of particles are denoted by the symbol f, particle diameters by x, center-to-center particle spacings by D, and numbers of particles by N. Mean particle diameters and standard deviations about these means are denoted by x and a. Both arithmetic (subscript A) and geometric (subscript G) means are employed. In this paper we measure the distribution of true diameters of particles which touch or pass through a random-plane section of the specimen. We may want to know the distribution of particle diameters in the

Jan 1, 1967

By H. Kazemi, M. S. Seth

The effects of anisotropy and stratification on flow behavior and production performance of oil and gas wells have been studied by numerous authors.1-3 Lefkovits et al.l studied the performance of totally penetrated, stratified bounded reservoirs with no crossflow. Others have studied a similar problem, but with crossflow; Russell and Prats2 have summarized the findings of these papers. Muskat3 studied the steady-state behavior of liquid flow for a partially penetrating well in an anisotropic system and concluded that the productivity weakly depended on the directional permeability ratios (kz/kr>0.1). Nisle4 used the classical method of point source solution to the diffusivity equation to study the effect of partial penetration on pressure buildup of oil wells in an isotropic system. He found that the theoretical pressure buildup curves consisted of two straight lines, the one at early buildup times having a slope proportional to the flow capacity of the open interval (l-d)k, and the other having a slope proportional to the flow capacity of the entire formation hk,. Later Brons and Marting5 supplemented the findings of Nisle and concluded that partial penetration gave rise to a pseudo damage, which reflected itself as a skin factor in pressure buildup calculations. Using the pseudo skin, they calculated the impairment of productivity of the production wells, which agreed well with the results of Muskat.6 Pizzi et al.,? using an electrical analog of a stratified system, concluded that a high pseudo damage resulted if the reservoir was partially penetrated. Harriss studied the optimum spacing and arrangement of perforations in cased holes. Hantush9 derived an expression for pressure distribution in an unbounded reservoir with restricted flow entry. Seth10 extended Hantush&apos;s work to a bounded reservoir. Odehl1 has studied a similar problem for steady-state conditions. The purpose of this work was to investigate: (1) the combined effects of anisotropy, stratification with crossflow, and restricted flow entry on pressure transient analysis of flow and buildup tests, (2) the feasibility of calculating the horizontal permeabilities of intercommunicating stratified systems, and (3) the pressure interference tests in such systems. Theory The partial differential equation governing the isothermal flow of homogeneous fluids of constant compressibility is given by Eq. 1: The initial and the boundary conditions are: 1. The reservoir potential is initially constant, say 4v

Jan 1, 1970

By M. Schwartz, S. K. Nash, R. Zeman

Knoop hardness in the rolling plane and in the longitudinal plane of hot-rolled and cold-rolled sheets of sublimed magnesiu?w was measured as a function of the angle between the long axis of the indenter and the rolling direction. These measurements were correlated with similar data taken on the (0001) and (1010) planes of a single crystal of magnesium where the hardness was measured as a function of the angle between the long axis of the indenter and the [1120] direction. The results were analyzed for compliance with the hypothesis of Daniels and Dunm to account for slip, and with a similar hypothesis to account for twinning. Some hardness anisotropy data are also presented for magnesium-indium and magnesium-lithium solid solution alloys. It is well known that the hardness of a crystalline specimen is different for its different surfaces, and also that the hardness is a function of direction within a single surface. Variations in hardness for single crystals have been found to be much larger than those for polycrystalline materials. Also, materials having low crystal symmetry were found to have a greater anisotropy of hardness than those of high symmetry. 0&apos;Neill1 and Pfeil,2 using a 1-mm Brine11 ball, studied single crystals of aluminum and iron, respectively; and they found a variation of hardness of about 10 pct between readings taken along the principal crystallographic faces. Daniels and Dunn3 found that the Knoop hardness number varied about 25 pct as the long axis of the indenter rotated on the basal plane of a zinc single crystal. The variation on the (1450) plane was about 100 pct, and the average hardness on this plane was about twice that of the basal plane. They also studied the variation of hardness within the (loo), (110), and (111) faces of a single crystal of silicon ferrite and found variations of about 25 pct although the average values for these planes were almost identical. Single crystals of zinc were also studied by Meincke.4 He found that the Vickers hardness numbers varied about 30 pct depending on whether the axis of the indenter was parallel or perpendicular to the (1010) and (1110) planes. Mott and Ford,5 using a Knoop indenter, found a 25 pct variation in hardness on the basal plane of zinc. Crow and Hinsley6 studied heavily cold-rolled bronze, steel, brass, copper, and other metals. They found that the difference in hardness numbers based on the difference in the length of the diagonals of the Vickers indenter was from 5 to 12 pct. Some minerals and synthetic stones show a very large anisotropy of hardness. Robertson and Van Meter7 found the Vickers hardness of arsenopyrite to vary from 633 to 1148 kg per mm2. stern8 using the double-cone method on synthetic corundum found the hardness number to vary from 950 to 2070. And winchell9 reported a variation of hardness number from 184 to 1205 in kyanite. The variation of hardness as a function of direction in a given crystallographic plane in single crystals possesses a periodicity which is related to the symmetry of the lattice. Daniels and Dunn3 found a six-fold periodicity of hardness in the (0001) plane of zinc. They found that the hardness curves of silicon ferrite had a four-fold symmetry in the (100) plane, a two-fold symmetry in the (110) plane, and a six-fold symmetry in the (111) plane. Mott and Ford5 also reported a six-fold symmetry of hardness in the basal plane of zinc. And vacher10 found two-, four-, and six-fold periodicities of hardness in copper on the (110), (100), and (111) planes, respectively. The purpose of this paper is to report the results of an investigation on the anisotropy of hardness as a function of orientation in single crystals of mannes-ium, and samples of rolled magnesium, magnesium-indium, and magnesium-lithium solid solution alloys. The anisotropy of hardness of pure magnesium which had been hot rolled, and then cold rolled various amounts to fracture, was studied by means of Knoop indentation hardness numbers; and the results were correlated with the preferred orientation as determined by quantitative X-ray pole-figure data. A comparison was made of the hardness data obtained from the rolled sheets and those of single crystals of magnesium. In order to obtain a more fundamental understanding of the variation of hardness and of Knoop hardness testing, the data were analyzed by

Jan 1, 1962

By A. Grant Elliot, H. W. Lavendel

qualitative picture has been developed to describe the oxidation behavior of TaSi2-coated tantalum and CbSi2-coated columbium. These systems have a significantly lower inherent oxidation resistance than MoSi2-coated molybdenum does. This stems primarily from the fact that Ta2O5 and Cb2O5 are nearly as stable thermodynamically as SiO2, whereas MoO2 or Moos are not. Further, diffusion of silicon in the Ta- and Cb-Si system is considerably slower than in the Mo-Si system. These ,factors prohibit the mechanism of selective oxidation of- silicon which accounts for the oxidation resistance 01- MoSi2-coated molybdenum. The silicide can be stabilized by adding suitable Modifiers which increase the thermodynamic stability of the silicate formed during oxidation. Modifiers, such as aluminum, can be inroduced into solid solution in the coating. in controlled amounts through proper selection of the source in the pack cementation process of coating fov~rzatiorz. Addition of aluminum to TaSi2, coatings on tantalum was effective in moderately increasing the oxidation resistance. EXTENSIVE experimental work and analysis have established the nature of the oxidation behavior exhibited by MoSi2- and MoSi2 -coated molybdenum-base alloys, and defined the conditions for maximum protection against oxidation of the substrate.&apos;-* The oxidation resistance of MoSi2 in the temperature-pressure range of 1100°C-PO2 > 10-5 atm to 1900°C— PO2 > 10-1 atm is due to the formation at the surface of a continuous film of SiO2 which results from selective oxidation of silicon. Under the prevailing kinetic conditions, this film is stable toward the molybdenum silicide with which it comes in contact. Initially molybdenum oxidizes also, but it forms volatile species. SiO2, however, nucleates and grows as a condensed phase. Once a continuous film of SiO2 has formed, the oxidation rate falls to that observed for the oxidation of pure silicon indicative of diffusion through the oxide film as the rate-controlling mechanism. This oxidation behavior is of course highly dependent upon temperature and oxygen pressure. Bartlett and Gage13 and Bartlett, McCamont, and Gagelb define precisely this dependence in terms of the oxygen partial pressures and silicon diffusivities required to support a stable SiO2 film. At low temperatures (near 500°C—the "pest" region) silicon diffuses too slowly to be selectively oxidized. Hence, molybdenum and silicon oxidize readily in proportion to their stoi- chiometry. At high temperatures and low pressure, SiOz dissociates to form volatile SiO(g), and a protective film cannot be maintained. Application of the MoSiz/Mo system is limited to temperatures below 1900oC, the eutectic between MoSi, and MO5Si3.5 The oxidation behavior of MoSi2-coated molybdenum is essentially the same as that outlined above with the exception that the MoSi2 is not in equilibrium with the molybdenum substrate. At the temperatures under consideration silicon will diffuse rapidly into the molybdenum eventually converting the coating to MosSi3.4 The rate constant for subsequent decomposition of Mo5Si3 into Mo3Si plus silicon, and/or the diffusivity of silicon through Mo3Si then becomes low enough to allow active oxidation of both molybdenum and silicon with subsequent degradation of the specimen. A stable silica film can be formed but at temperatures and/or oxygen partial pressures higher than those required with MoSi2 present as a source of si1icon.l, 4 Because of the similarity between the silicides of molybdenum and those of columbium and tantalum one would expect similar oxidation behavior for coatings in the respective systems. This is not entirely the case, however, as shown by the experimental results reported herein. Regarding tantalum and columbium disilicide coatings on tantalum and columbium substrates, respectively, the oxygen arriving at the surface of the coating partitions itself nearly equally between the metal and the silicon, and a two-phase oxide layer (Me2O5 plus SiO2) is always formed. The diffusion of silicon in the tantalum and columbium silicides is relatively slow, compared to that in the molybdenum silicides, which further enhances this equipartitioning of oxygen. Thickening of the coating during service by inward diffusion of silicon into the substrate is correspondingly slow, and the effective thickness of the coating at the roots of cracks and defects is only slightly changed providing high probability for premature coating failure. Furthermore, the SiO2 glass that is generated is not thermodynamically stable with respect to the coating. The metal silicide tends to reduce the SiO2 liberating either free silicon or SiO. The situation can be improved by suitably modifying the coating such that the stability of the protective glass which is generated during service is increased. Thus, selective oxidation of silicon and the modifying agent will occur, and the silicide coating will not tend to reduce the oxide layer. Modifying agents can be introduced into the coating by the pack cementation process. Using sources containing the modifier at controlled chemical potentials allows control of the coating composition. Partially substituting aluminum for silicon in TaSi2 coatings by forming a Ta(Si,Al)2 solid solution was effective in moderately increasing the oxidation protection.

Jan 1, 1968

By H. Larson, J. Chipman

The ferrous and ferric oxide concentrations of slags, expressed as j = Fe+++/(Fe+++ + Fe++), have been established through gas-slag equilibrium at 1550°C in a range of oxygen pressure of 10-I to 10-9 equilibriumatm. The value of j is increased by basic additions (BaO, CaO, MgO, MnO) and decreased by acidic oxides (SiO2 and TiO2). Oxygen pressure is shown graphically as a function of composition for slags which are analogous to those at the slag-gas interface of the open hearth furnace. THE progress which has been made in recent years in understanding the chemistry of metallurgical slags has been based largely on studies of slag-metal and slag-gas equilibria. There is a considerable body of knowledge which is applicable to reactions occurring at the slag-metal interface in open hearth steelmaking. There is little information concerning reactions of the slag with the furnace atmosphere and hence little basis for an understanding of the transfer of oxygen, sulphur, or hydrogen between gas and slag. The oxygen pressure of the open hearth atmosphere is normally of the order of 10-1 to 10-3 atm which differs by several orders of magnitude from that of about 10" atm at the slag-metal interface. The chemical properties of the slag, for example, the ratio of ferric to ferrous iron and the ability of the slag to hold sulphur in solution, are greatly affected by changes in oxygen pressure. This investigation was undertaken to enlarge our knowledge of the effect of oxygen Pressure on steel-making slags. Using air or controlled mixtures of CO a CO2 a range of oxygen Pressures from 10.&apos; to 10.&apos; was covered. Review of the Literature There are only a few references in the literature which pertain directly to this investigation. The most important is that of Darken and Gurry1,2 on the system iron-oxygen. This work included the determination of the phase diagram of the system and also a study of the field of homogeneous melts and their oxygen pressures. Their apparatus and procedure were very similar to that used in this study. Iron oxide was melted in a platinum crucible under an atmosphere of CO2:CO, CO2:H2, H2O, CO2, air or O2 depending upon the partial pressure of oxygen desired. After equilibrium was reached, the sample was quenched and analyzed for ferrous and ferric oxide. By appropriate calculations these authors were able to determine the oxygen and iron activities in the various slags, heats of formation of the oxides of iron, and heats of solution of iron and oxygen in the liquid slags. In a subsequent paper&apos; the same authors made a less thorough investigation of the effects of additions of lime and manganese oxide on the composition of iron oxide melts. Only a few experiments were made and those in a narrower range of temperature and oxygen pressure. Darken&apos; has investigated the fusion temperature of iron oxide in contact with silica under various atmospheres. He found that the temperature changes from 1120° to 1447°C as the gas composition changes from CO2/CO equal to 20.8 to pure oxygen. A comprehensive paper by White" predates the work of Darken and Gurry. The decomposition of ferric oxide into oxygen and lower oxides of iron was studied from 1000° to 1650°C and under oxygen pressures from 2 to 76 cm of mercury. The effect of

Jan 1, 1954

By H. C. Fiedler

The development of cube-on-edge secondary re crystallization texture in Si-Fe strip depends upon the ability of inclusions, such as manganese sulfide, to restrain nomal grain gvowth. The ability of inclusions to perform this function is shown to depend upon their size and distribution. The desired uniform dispersion of many small inclusions is obtained by controlling the cooling rate from above the solution tempmature of the inclusions or, alternatively, by drastic &apos;quenching from above the solution temperature followed by heat treating at a lower temperature. The development of the cube-on-edge secondary recrystallization texture in Si-Fe strip depends upon both establishing the proper primary recrystallization texture and having inclusions to restrain normal grain growth. It has been suggested that the first requirement is met with a texture which, though weak, is near (110)[001]. A mechanism for secondary recrystallization originally proposed by ielsen&apos; is consistent with the presence of this primary texture. It is visualized that a secondary grain appears where two adjacent grains happen to be sufficiently similar in orientation to be capable of behaving as a single large grain. This pair of grains will grow at the expense of its smaller neighbors as a consequence of its having lower grain boundary free energy. Other explanations of the origin of the secondary recrystallization texture have been offered,&apos; and it can be concluded that the mechanism is not fully understood. Nevertheless, it is apparent that operationally the necessary primary recrystallization texture is obtained simply by interposing an anneal during the cold reduction to final gage. The role of inclusions in the development of the secondary recrystallization texture has been demonstrated by May and Turnbull4 in a comparison of a high-purity heat and a heat containing manganese sulfide. They showed that the driving force for secondary recrystallization is inversely proportional to the diameter of the matrix grains and that the function of the inclusions is to maintain a small matrix grain size. Other inclusions, such as various sul- fides,&apos;)&apos; silicon nitride,8 and vanadium nitride,&apos; titanium carbide,&apos;&apos; and vanadium carbide," have been shown to be effective in promoting secondary recrystallization to the cube-on-edge texture. There is also evidence that silica inclusions in Si-Fe strip made by powder-metallurgy techniques perform this function.&apos; This report is concerned with the second of the two requirements for secondary recrystallization, namely the importance of the metallurgical control of the size and therefore number of inclusions. While the concepts involved are simple, they are fundamental to the making of this material. EXPERIMENTAL PROCEDURE A heat containing 3.27 pct Si, 0.026 pct S, 0.06 pct Mn, and 0.004 pct C was made in an air induction furnace from electrolytic iron, 98 pct ferro-silicon, electrolytic manganese, and iron sulfide. The heat was divided between graphite and baked-sand molds with a cavity 2-5/8 by 5 in. and with walls 2-3/4 in. thick. Slabs, 1 in. thick and 2-5/8 by 5 in., were cut from the ingots and hot-rolled either in the as-cast condition or after one of the heat treatments described later. After pickling, the 80- to 100-mil-thick hot-rolled band was, unless otherwise noted, heat-treated for 5 min at 900°C before being cold-rolled to 25 mils. After a heat treatment of 1 to 3 min at 860°C, the strip was cold-rolled to 12 mils, the final thickness. The percent cube-on-edge texture was determined by dividing the maximum torque as averaged from four samples by the maximum torque of a 3-1/4 pct Si-Fe single crystal having the (110) plane in the plane of the sample. The torque measurements were made in a field of 1000 oe on 1-in.-diam disks. RESULTS AND DISCUSSION The importance of the thermal history of the ingot is evident in Fig. 1 from the appearance of strips heat-treated in a temperature gradient. The sample

Jan 1, 1964

By Robert S. Dewey

AS a result of drilling operations during 1943, West Texas again added sufficient new oil reserves to replace the oil produced during the year, but failed to maintain its position in currently available reserves because the deeper discoveries will require years for development. Drilling failed to provide the additional oil necessary to meet the increase in current and anticipated market demand. Although 13.3 per cent of the total footage drilled was in wildcat exploration, the ratio of oil discoveries to total wildcats was less in 1943 than in 1942, but comparable to that in 1941. Of the 732 field wells completed, 270 were at Slaughter, 55 at Wasson, 45 at Mascho and 31 at North Cowden. As of Dec. 31, 1943, there were 361 drilling wells including 71 wildcat and 290 field wells; 19.7 per cent were wildcats. It is anticipated that the percentage of wildcats of the total wells will be higher during 1944 than in either 1942 or 1943. Tables 3 and 4 present a three-year comparison of drilling activity and illustrate the downward trend of development that has been in effect during that time. Because of development lag in the deeper Ordovician fields, several years elapse before 2 sufficient number of wells is completed to give a substantial producing rate. As these new oil reserves cost more to find, and will cost more to produce on a barrel basis than the oil marketed during the year, their reserve replacement value to the industry is less in money. Costs While complete costs for deeper drilling are not yet available for analysis, it is evi- dent from the data on drilling rates to comparable depths, contract prices, and general increases in costs, that the cost of drilling has risen approximately 20 per cent during the year. One representative drilling contractor estimates that the average drilling time on a 5000-ft. field well has increased nearly one third and that out-of-pocket costs have increased a dollar per foot. Three major factors contribute to this increased cost: (I) less experienced labor, (2) deterioration in mechanical equipment and expendable material, and (3) increased contract prices. In the past, when there were more drilling rigs than wells to be drilled, some contractors would cut their drilling profit to keep their personnel and rigs working. As this practice is no longer necessary, the contract prices are adjusted upward to assure a profit. On deep and difficult drilling, contracts are let on a cost plus basis. A number of mechanical difficulties have become evident. Inferior quality of steel used in drill pipe and rock bits has added appreciably to drilling time and cost. Contractors are experiencing delay in obtaining repair work and repair parts for prime movers. As the length of drilling time required an shallow-field wells has not increased in proportion to that on deeper wells, it seems that the medium-sized drilling rig is better adapted mechanically than the heavy one to the work imposed. One of the main deficiencies in the heavy rig equipment is inadequate pump capacity. Drilling Mud The increasing amount of deep drilling has emphasized the importance and relationship of good mud to efficient and suc-

Jan 1, 1944

By Robert S. Dewey

AS a result of drilling operations during 1943, West Texas again added sufficient new oil reserves to replace the oil produced during the year, but failed to maintain its position in currently available reserves because the deeper discoveries will require years for development. Drilling failed to provide the additional oil necessary to meet the increase in current and anticipated market demand. Although 13.3 per cent of the total footage drilled was in wildcat exploration, the ratio of oil discoveries to total wildcats was less in 1943 than in 1942, but comparable to that in 1941. Of the 732 field wells completed, 270 were at Slaughter, 55 at Wasson, 45 at Mascho and 31 at North Cowden. As of Dec. 31, 1943, there were 361 drilling wells including 71 wildcat and 290 field wells; 19.7 per cent were wildcats. It is anticipated that the percentage of wildcats of the total wells will be higher during 1944 than in either 1942 or 1943. Tables 3 and 4 present a three-year comparison of drilling activity and illustrate the downward trend of development that has been in effect during that time. Because of development lag in the deeper Ordovician fields, several years elapse before 2 sufficient number of wells is completed to give a substantial producing rate. As these new oil reserves cost more to find, and will cost more to produce on a barrel basis than the oil marketed during the year, their reserve replacement value to the industry is less in money. Costs While complete costs for deeper drilling are not yet available for analysis, it is evi- dent from the data on drilling rates to comparable depths, contract prices, and general increases in costs, that the cost of drilling has risen approximately 20 per cent during the year. One representative drilling contractor estimates that the average drilling time on a 5000-ft. field well has increased nearly one third and that out-of-pocket costs have increased a dollar per foot. Three major factors contribute to this increased cost: (I) less experienced labor, (2) deterioration in mechanical equipment and expendable material, and (3) increased contract prices. In the past, when there were more drilling rigs than wells to be drilled, some contractors would cut their drilling profit to keep their personnel and rigs working. As this practice is no longer necessary, the contract prices are adjusted upward to assure a profit. On deep and difficult drilling, contracts are let on a cost plus basis. A number of mechanical difficulties have become evident. Inferior quality of steel used in drill pipe and rock bits has added appreciably to drilling time and cost. Contractors are experiencing delay in obtaining repair work and repair parts for prime movers. As the length of drilling time required an shallow-field wells has not increased in proportion to that on deeper wells, it seems that the medium-sized drilling rig is better adapted mechanically than the heavy one to the work imposed. One of the main deficiencies in the heavy rig equipment is inadequate pump capacity. Drilling Mud The increasing amount of deep drilling has emphasized the importance and relationship of good mud to efficient and suc-

Jan 1, 1944

By L. S. Darken

It has been known for sometime that in an ionic lattice, such as that of Ag,S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulphide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulphide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall&apos; support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffdsion proposed by several authors, most recently by Bir-chenall and Mehl.2 This theory has, however, also been questioned3v4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however. Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz, who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a Similar mechanism, whatever it may be, at a greater Or lesser rate, thus giving rise

Jan 1, 1949

By L. S. Darken

It has been known for sometime that in an ionic lattice, such as that of Ag,S or FeO, the migration velocity of the anion may differ markedly from that of the cation, the cation being usually the more mobile. It has been shown, for example, that during the formation of silver sulphide tarnish on silver, the tarnish layer grows principally by the motion of silver cations through an essentially stationary silver sulphide lattice. Similarly, the growth of wüstite scale on iron proceeds principally by motion of iron ions, this being accomplished with the aid of vacant iron lattice sites into which the iron may readily move. Likewise investigations of solid solutions of various salts show that there is usually considerable difference in the mobility of the different cations. Measurements of the mobility of various metals in liquid mercury indicate that the various metals move at different rates relative to the mercury. In view of the foregoing it seems reasonable to suppose that when any single phase solution is acted upon by a field, the atoms of different elements respond in different ways; in particular, that the force arising from a particular concentration gradient in a binary alloy would cause the atoms of one component to move with a drift velocity which is in general different from that of the atoms of the other component. The recent experiments of Smigelskas and Kirkendall&apos; support this viewpoint, since they found, in essence, that during diffusion in alpha brass zinc moves appreciably faster than copper. This was evidenced by the relative motion of inert molybdenum wires. Such a phenomenon is incompatible with the place interchange theory of diffdsion proposed by several authors, most recently by Bir-chenall and Mehl.2 This theory has, however, also been questioned3v4 for other reasons, principally because of the high energy required for direct atomic interchange. The rather large difference between self-diffusivity, as determined by tracer technique, and mutual diffusivity, as determined with the aid of another element at low concentration, might also be interpreted as favoring the above idea; however. Birchenall and Mehl have pointed out that there is another possible interpretation of this difference; this is discussed later. A rather interesting and pertinent observation was made by Schwartz, who noticed that tungsten lamp filaments, heated by direct current, commonly fail by necking down in the region at the temperature gradient near the positive end, with a concomitant swelling at the corresponding position near the negative end. He introduces considerable auxiliary evidence to show that this phenomenon is occasioned by the motion of tungsten cations which migrate in the high temperature region from the positive end toward the negative end. The mechanism of this migration is not clearly understood. If, however, this experimental evidence be accepted, we are forced to conclude that alloying elements in the tungsten may migrate by the same or a Similar mechanism, whatever it may be, at a greater Or lesser rate, thus giving rise

Jan 1, 1949

By Erwin L. Zodrow

A geological model of the modes of formation of magnetite and its distribution in the Smallwood iron-ore mine, Labrador, Newfoundland, is given, based on observation and geological mapping. This is called the conceptual model. If mathematical expressions plus probabilistic uncertainty are used to represent the conceptual model, then this is termed a mathematical model. The purpose of this paper is to test if there exists a correspondence between the conceptual model and two related mathematical models (called factor analysis). Details of the statistical technique are given. The results of factor analyses in relation to the magnetite formations in the Smallwood mine are discussed. Several practical mine applications are presented. The difficulty of maintaining quality control over ore mined from any deposit naturally depends on geological conditions; these are usually imperfectly known to concerned mining geologists. One geological condition that would greatly facilitate ore predictions is if a relationship between the observed ore particle distribution* and its mode of origin could be demonstrated. Such a casual interrelationship is normally sought through the application of well-defined geochemical principles of primary mineralization in given geological environments. However, the application of conventional tools of geological research, including geochemistry, to areas that have undergone repeated periods of geological deformation and metamorphism subsequent to primary mineralization becomes rather difficult. More important, the interpretation of such research results are nearly impossible on an objective basis. Mineral assemblages may have been reworked and changed due to tectonic influences to the extent that the present-day observable mineralogy and ore-particle distribution can effectively obscure the mode of origin of the ore. Quantitative measurements, based on petrological investigation of mineral assemblages, reflect the sum-total of all geological influences. Which of several influences had the most effect on existing ore particle distribution is difficult to assess, for these influences can neither be measured directly nor quantified by petro-logical logical or geochemical means. The present study is concerned with the magnetite distribution and its modes of origin within the Small- wood mine,&apos; located in the southern extension of the Labrador geosyncline; see Fig. 1. This geosyncline is thought to have undergone at least two periods of geo-tonic tectonic deformation, separated in time, since the fer-rugenous rugenous sediments were deposited." Detailed geological observations and mappings (1 in. to 40 ft) have highlighted subtle, distinctive features of the magnetite distribution in the Smallwood mine: (1) The magnetite is generally concentrated in bands or layers within this ore body; these bands alternate with specularite-rich bands and quartz bands. The banded or layered nature is common in Precambrian iron-ore deposits, and this has been interpreted as a result of changes in depositional environments. (2) The grain size of the magnetite varies; near the contacts between the iron and quartz-carbonate formations, the magnetite occurs as well-crystallized octa-hedra. In areas of intense folding, magnetite is extremely fine grained and concentrated in bands and occurs in association with earthy manganese minerals. (3) Magnetite tends to be more highly concentrated near the geological contacts of the iron and quartz-carbonate formation in the northeast part of this mine, Figs. 2, 3, and 4. (4) Magnetite is also fine grained and tends to higher concentration near and parallel to fold axes; however, in this case, the ore is much softer than given in item 2. (5) Magnetite mineralization decreases along strike and away from the areas of intense folding, i.e., towards the approximate center of the mine, Fig. 3. How can these variations of magnetite be explained on a geological basis? We can postulate a conceptual model that the distribution of magnetite appears to be related to three basic geological influences: (1) geo-tectonics, i.e., concentrations of magnetite near geological contacts of the iron and quartz-carbonate formations, the fine-grained nature of magnetite and its higher concentrations near fold axes, and decrease of magnetite towards the approximate center of the mine; (2) secondary alterations, i.e., variation of grain size of magnetite near the iron and quartz-carbonate contacts, and in areas of intense folding where magnetite occurs together with earthy manganese minerals: (3) original

Jan 1, 1971