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By R. W. Armstrong, D. H. Feisel

Self-diffusion in pure crystalline solids has been described through extension of the Cohen and Tum-hull volume -fluctuation model originally proposed for diffusion in simple liquids. It is shown, for a number of crystalline solids, that the self-diffusion coefficient, D, obeys the relationship where a is the lattice spacing, v the Debye frequency, Z' the lattice-volume fluctuation per atom required for a diffusion jump, and (?V/Vo) the relative increase in the lattice volume resulting from thermal expansion between O°K and the temperature under consideration. The calculated value of Z' is dependent upon the difiusion mechanism and the lattice geometry. ThE need for an increased understanding of mass-transport processes in crystalline solids has resulted in much research to determine rates of self-diffusion.' For several metals (e.g., copper, silver, and iron), the experimental values of the self-diffusion coefficient, D, have been determined over a large interval of temperature and the accuracy of D has been investigated through repeated experiments. Also, a number of empirical and theoretical diffusion studies have established a rational basis for understanding the D values for the different elements.2"6 The empirical diffusion analysis by Sherby and simnad6 supplied the main stimulus for the present study. Sherby and Simnad, reviewing the self-diffusion data for a substantial number of pure crystalline solids, suggested that sufficient data were available to establish with some certainty the apparent intrinsic material properties which influence D. Without explicit regard for any mechanism of diffusion, these investigators obtained an empirical relationship for D which correlated the self- diffusion coefficient for each element with the melting temperature, crystal structure, and valence of the particular element. Their analysis is only unsatisfactory in that the effect on D of crystal structure is not very clear and the valence to be assigned to an element is not always straightforward. The present study is an attempt, from a very different viewpoint from that of Sherby and Simnad, to establish a basis for understanding the self-diffusion coefficients for crystalline solids. This analysis was undertaken for the purpose of developing a general expression for D which would explicitly depend on the mechanism of diffusion. The main result of the study is that diffusion in crystalline solids may be described in terms of a volume-fluctuation model which was originally proposed by Cohen and Turnbull7 to describe diffusion in simple liquids. The model appears to be useful for predicting self-diffusion coefficients in crystals. The following sections describe the volume-fluctuation model for diffusion, the application of this model to crystals, and the resultant agreement with experimental data. 1) THE VOLUME-FLUCTUATION MODEL FOR DIFFUSION Cohen and Turnbull7'8 developed their model for liquid self-diffusivity for the purpose of describing certain properties of liquids, glasses, and the liquid-glass transition. A hard-sphere model for the liquid structure is used. In this model, the size of a spherical molecule or atom is fixed for all temperatures by the interatomic spacing at the absolute zero of temperature. At any temperature above O°K, the atom is viewed as being contained within a larger spherical cage defined by the interatomic spacing of the atoms at that temperature. A random distribution of varying cage sizes is assumed to exist in the liquid. An individual diffusion jump occurs when the free volume of an atom (the volume of the cage containing the atom minus the volume of the atom) is large enough for the atom to jump out of its cage. With this physical picture of diffusion in liquids, Cohen and Turnbull derive the following equation for self-diffusivity: D=Doe-yv*/vf [1] where Do is the product of three factors which are the diffusion-path geometry, the diffusion-jump distance, and the velocity of the diffusing atom, v*

Jan 1, 1964

By A. J. Shaler

The subject of the mechanism of sintering has received much attention in the past few years, particularly since the beginning of the series of AIME seminars in powder metallurgy of which this paper introduces the fourth. In the first of these, F. N. Rhines1 brought together and discussed the available experimental data on the sintering of pure metallic powder, and succeeded in bringing to a sharp focus the attention of workers in this field on the established observations which a satisfactory theory must explain. Several other authors3,5,6 have, in the last few years, studied the phenomena that occur when cold metallic powders, loose or in the form of compacts, are first brought to elevated temperatures. Some workers' in the field of friction have recently studied the adhesion of solid metal surfaces when they are brought into close contact. These researches have indicated that several separate mechanisms operate simultaneously, at least during the first part of the sintering process. Some of them have been called transient mechanisms4 because they are in general not absolutely necessary to sintering. Powders may be so prepared and so treated that these transient phenomena do not take place during subsequent sintering. This does not mean, of course, that their industrial and scientific importance is any less than that of the steady-state phenomena. The latter are changes that go on during sintering no matter how the powders are made or treated; they cannot be divorced from sintering. One way to analyze the process of sintering into its component parts is perhaps to distinguish between these transient and steady-state phenomena. Some of the transient phenomena have been studied in the past few years. Huttig3 has shown that, when the temperature of metallic powder is slowly raised, the following events generally occur in order: (1) physically adsorbed gases are desorbed; (2) there is an atomic rearrangement of the surface, a sort of two-dimensional "surface-reciystallization"; (3) there is a breakdown of chemically adsorbed surface compounds; (4) there is a recrystalliza-tion in the volume of the metal. All these changes are shown by Huttig and his coworkers to be completed fairly rapidly at lower temperatures than those generally used in sintering and are therefore not a part of the mechanism whereby the density of a mass of powder continues to change after long heating at an elevated temperature. But the first and third of these changes release gases in quantities which may or may not help to control the steady-state mechanisms, depending on when the voids become isolated from the outside of the compact. Among the phenomena studied by Steinberg and Wulff,8 there is the effect on sintering of residual stresses arising from the pressing operation. They found that the lateral surfaces of a green compact of iron are under a longitudinal residual tension-stress of the order of magnitude of half the yield-point for solid iron. If the outside surface is in tension, the core must be under longitudinal compression. When the compact is heated, the surface residual stress is thermally relieved first, and the compact therefore initially expands in the direction of its axis. This is a transient phenomenon, if for no other reason than the possibility of sintering unpressed powders, as demonstrated by Delisle,9 Libsch, Volterra and Wulff10 and others.1 The subject of recrystallization is dealt with further in a separate section, in view of its prominent place in sintering literature. It, too. is one of these transient phenomena. Among the steady-state parts there may be distinguished the attraction between particles and its consequences, the spheroidization of voids in the compacts, and the densification or swelling of the compact. There is considerable evidence4,7 showing that cold metallic surfaces, when brought to within a few interatomic distances of one another, are attracted to each other by forces of the order of many thousands of pounds per square inch. A calculation, discussed in greater detail in another section, shows that this force changes but slightly when the temperature of the surfaces approaches the melting point. Actual measurements of forces of adhesion of this magnitude have been made by Bradley12 on some nonmetals, but none has yet been made on cold or hot metals. This force is of sufficient magnitude to cause some plastic deformation in powder compacts, as will be shown below. A second force of steady-state nature is due to the surface tension, which probably has the same origin as the force of attraction between surfaces.164 A paper by Udin, Shaler, and Wulff1,3 gives the results of precise direct measurements of its value for solid copper. The demonstration of the tendency for the surface tension to shrink a pore was long ago given by Gibbs.17 He showed that its effect on a curved surface between two phases is equivalent to a pressure perpendicular to that

Jan 1, 1950

By J. B. Cheatham, C. E. Murphey

Presently, computer control of Borobolic direction cannot be obtained during drilling, and most straight-holc drilling methods attempt to resist hole deviation rather than control direction. Many of the theories advanced as possible explanations of the cause of hole deviation are Summarized berein. A new correlation of physical partables is introduced to indicate bow factors such iis drill collar stiffness clearance and hit weight influence borehole deviation, .A methord is proposed for predicting the rate of change of hole angle when drilling conditions are changed. INTRODUCTION Control of borehole direction during drilling can be difficult and costly. Unintentional crooked holes are often lrilleti in dipping formations and many times directional drilling is required when the surface location is not directly above the target area —- for example, at offshore and mountainous locations. Prilllng progress can be greatly hindered in either air or liquid drilling when it be comes necessary to use low bit weight to prevent excessive hole angle build-up. If hole inclination becomes too great, drill pipe drag becomes excessive and fishing risks are increased, logging is more difficult and problems of differential sticking, key seating and fatigue failures may be encountered. Dog-legs and key seats are more serious problems than steep inclination angles: therefore, reducing rate of direction change is preferred to attempting to maintain absolutely vertical holes. Consequently, a straight inclineti hole is preferable to a nearly vertical crooked hole containing numerous dog-legs. In this paper, theories of the cause of hole deviation and analyses of drill string behavior under down-hole conclitions are summarized. Methods for computing hole deviation are presented und systems for resisting deviation as well as neans for provic!ing control of holt- direction are iliscusseI. A new correlation of physical variables is introduced tu indicate how factors such as drill collar stiffness, clearance and bit weight influence borehole deviation. A method is oroposeti for predicting the rate of change of hole anFrle when drilling conditions are clianged. IIEVIEU' OF PREVIOUS WORK ON HOIaE DEVIATION Significant progress in the theoretical analysis of hole deviation problems has been made in the past 1 5 years. The pioneering work has been primarily a result of the efforts of Lubinski and Woods.l-5 In 1950, Lubinski 1 considered the buckling of a drill string in a straig:rt vertical hole, a problem also considered by Willers6 in 1941. It wns concluded that very low bit weights must be used to prevent hole deviation resulting from drill collar buckling. The use of conventional stabilizers was proposed2 in 1951 by Mac Donald and Lubinski as a method for permitting greater Sit weights to he carried without drill collar buckling. These authors pointed out that a 2° nearly vertical spiral hole can cause severe key seatinp, and drill pine near, wilereas n 3 straight inclined hole with deviation all in one direction, while not vertical, will not result in serious drillirig or producing problems. Studies were continued with an investigation of straight inclined holes by Lubinski and Woods3 in 1953. In this paper they concluded that perfectlv vertical holes cannot be drilled even in isotropic forriations unless extremely low bit P-eights are used. .l'l~ey postulated that constant drilling conditions produce holes of constant inclination angle and varying conditions cause the hole to drill at a neiv equilibrium angle. This analysis was not concerned with drill string buckling since it was based on an equilibrium solution in which the ~irill string Was presumed to lie along the lower side of the hole abcrve the point of tangency. Weight of the drill collars below the point of tangency tends to force the hole toyard the vertical, whereas the weight on hit tends to force the hole aurav from the vertica l. The concept of an anisotropic formation Lvas introduced as an empirical method for explaining actual drilling data and as a means for extrapolating known deviation data to otiier conditions of hit

Jan 1, 1967

By W. M. Rust, W. D, D. W. Mounce

The almost universal acceptance of electrical logging by the petroleum industry calls for a critical examination of the physical bases of the common methods. This is particularly needed for the natural potential log. The conventional explanations are based on the phenomena of electrofiltration and electro-osmosis. However, experimental data show that they fail to give a basis that is quantitatively sound. Moreover, they lead to interpretations of details of electrical logs that are erroneous. It was found experimentally that when a plug of shale is placed in a chain of dissimilar electrolytes, a current flow results. Experiments on oil-well cores and fluids similar to those existing in wells show that potentials are set up which are in reasonable agreement with those encountered in electrical logging. Doubtless other sources of potential are important but this explanation not only accounts for much of the potential but also clarifies some fairly familiar examples of misinterpretations. Introduction The extraordinary value of electrical well logging as a tool for petroleum engineers and geologists is now so uni- versally recognized that it is not necessary to point out the ways in which it can be useful. It is sufficient to mention only the saving that has resulted from the elimination of much coring that would have been necessary under former practices and the considerable additions to reserves resulting from the discovery of sands missed in coring. Paradoxically, the very remarkable success that has resulted from the application of electrical logging to correlation and completion problems has cost some of its most consistent users dearly.' The fact that some operators have placed unwarranted faith in erroneous interpretations of electrical logs does not reduce the value of the logs. It should, however, make one pause long enough to ask why experienced users should be misled. The answer to this question is not hard to find. In nearly every case, the fault has been oversimplification. This is illustrated very aptly by the familiar interpretation and theory of the natural potential log. Recording and Interpreting Logs The natural potential log is extremely simple to record precisely enough for all present-day uses. One needs only an electrode, a cable to lower the electrode through the drilling mud, a recording meter and a surface ground connection. The electrode can be elaborate but need not be. A simple brass rod 2 in, in diameter and 2 or 3 in. long is quite satisfactory. The cable need not be particularly well insulated, nor need it have a very low resistance. The recorder can be a vacuum-tube 1 References are at the end of the paper.

Jan 1, 1944

By W. D, D. W. Mounce, W. M. Rust

The almost universal acceptance of electrical logging by the petroleum industry calls for a critical examination of the physical bases of the common methods. This is particularly needed for the natural potential log. The conventional explanations are based on the phenomena of electrofiltration and electro-osmosis. However, experimental data show that they fail to give a basis that is quantitatively sound. Moreover, they lead to interpretations of details of electrical logs that are erroneous. It was found experimentally that when a plug of shale is placed in a chain of dissimilar electrolytes, a current flow results. Experiments on oil-well cores and fluids similar to those existing in wells show that potentials are set up which are in reasonable agreement with those encountered in electrical logging. Doubtless other sources of potential are important but this explanation not only accounts for much of the potential but also clarifies some fairly familiar examples of misinterpretations. Introduction The extraordinary value of electrical well logging as a tool for petroleum engineers and geologists is now so uni- versally recognized that it is not necessary to point out the ways in which it can be useful. It is sufficient to mention only the saving that has resulted from the elimination of much coring that would have been necessary under former practices and the considerable additions to reserves resulting from the discovery of sands missed in coring. Paradoxically, the very remarkable success that has resulted from the application of electrical logging to correlation and completion problems has cost some of its most consistent users dearly.' The fact that some operators have placed unwarranted faith in erroneous interpretations of electrical logs does not reduce the value of the logs. It should, however, make one pause long enough to ask why experienced users should be misled. The answer to this question is not hard to find. In nearly every case, the fault has been oversimplification. This is illustrated very aptly by the familiar interpretation and theory of the natural potential log. Recording and Interpreting Logs The natural potential log is extremely simple to record precisely enough for all present-day uses. One needs only an electrode, a cable to lower the electrode through the drilling mud, a recording meter and a surface ground connection. The electrode can be elaborate but need not be. A simple brass rod 2 in, in diameter and 2 or 3 in. long is quite satisfactory. The cable need not be particularly well insulated, nor need it have a very low resistance. The recorder can be a vacuum-tube 1 References are at the end of the paper.

Jan 1, 1944

By S. A. TAYLOR

AN EDITORIAL on the Strike Situation in the Coal mining industry in the New York Evening Post of Nov. 4, 1919, gave what purported to be statistics of the Department of Labor, for a period of two weeks, which showed an average for the year, based on these two weeks, of 32% hours per week. This mode of arriving at the number of hours per week, while not accurate, is not so far off from the facts as to call for any special comment. The report of the U. S. Geological Survey, Department of Coal Statistics, give so the number of days worked in 1917 as 243; reducing the same to hours per week, assuming 8 hours per day, shows a weekly operation of mines at an average of 36J4 hours. But this assumption is not exactly correct, for the reason that it is not very often that the miners work the full 8 hours per day. There are many explanations for this, but it is not pertinent to this statement to discuss them now, as the important thing to consider is whether a 30-hour week would be for the best interest of not only the men themselves, but the public or country in general.

Jan 1, 1920

By H. Bartholomew, L. Bernstein

Experirmental bonds of Ag-In SLID to gold, copper, nickel, Kovar, Dumet, nickel-plated molybdenum, ALL-Pt vrzetallizing on ceramic, and nickel-plated Mo-Ti metallizing on Al2O3 ceramic have been made and exalnined. Metallographic taper sections were made of all bonds for Phase identification. In addition, failuve temperatltres were determined for bonds heated undev shear load. Sowe bonds were subjected to electvon-probe microanalysis. The ternary SLID system Ag-In-Sn was similarly evaluated. Plwtonticrogaphs and electron-probe data are discussed and related to over-all phase diagrams , diffusion effects, and wetting properties of the liquid. The rates of diffusion andor compound formation of gold, silver, and copper in indium and In-Sn liquids are found to descend in that order, as measured by the relatzve thickness of phase layers in the interfaces of bonds made at 200to 400°C. It is concluded that the SLID process enables one to produce bonds which are stable at high temperatures, after having been fabricated at low temperatures, and meet most requirements for application in interconnection, silicon bonding, or hermetic sealing of electronic devices. In a previous publication by one of the authors, the theory and principle of SLID bonding in simple binary systems was discussed. SLID bonding can be defined as a joining process using a preform with a laminated structure: a low-melting material clad on a high-melting core. During the bonding cycle a metallurgical transformation occurs such that the resultant structure can withstand, without reliquefying, temperatures higher than those at which the bond was made. The phases present in the joint interface region are high-melting compounds or, if equilibrium is reached, solid solution. Properties will depend on the phases present, ultimately approaching those of the solid substrate core of the SLID preform. The high-temperature strength of bonds made in these systems was correlated to phase identification in the interfacial bond regions from metallographic cross sections and electron-probe X-ray microanalysis data. When complex electronic components are assembled, multiphase systems result at the interfaces of bond regions. In these ternary and higher-order systems very little diffusion and phase-diagram data is available with which to predict the nature of the interfacia1 region that will result from conventional fabrication processes and subsequent field use of the component. Clarke and Rhines did early work in the field using the Al-Mg-Zn system as a vehicle. Guy and co-workers studied a portion of the Cu-Zn-Ni system and some mathematical4 and general5 aspects of multiphase diffusion. irkald' and coworkerse recently studied diffusion in the Cu-Zn-Sn system. No diffusion studies have been made on ternary systems directly applicable to this investigation but some phase diagrams are available: g-u-n, u-i-n, and CU-i-n. I) DESCRIPTION AND EXPERIMENTAL PROCEDURE The elements Au, Ag, Cu, Ni, In, and Sn are found in alloy systems commonly used in fabricating and assembling electronic components. Reference to the appropriate phase diagrams9 and the previous publication will indicate that the binary systems of any of the two low-melting elements, indium and tin, with any one of the other four higher-melting elements are capable of producing SLID bonds. It is not unreasonable to assume that any ternary or higher-order alloy system containing at least one of the elements gold, silver, copper, or nickel and one or both of the elements indium and tin could be used to produce bonds which are stable at high temperatures, after having been fabricated at low temperatures. Indeed, the liquidus contours and isothermal sections of those phase diagrams available7 do so indicate. The parameters affecting the bond and the equipment used in evaluating the bond were described in an earlier paper.' The current investigation used the

Jan 1, 1967

By Ming-Kao Yen

S. E. MADDIGAN*—I think Mr. Yen should be complimented on doing a very excellent and a very comprehensive piece of work. I was particularly pleased to note the use of X rays in a somewhat less tedious technique than pole figures. In the past I think many workers have been diverted away from the use of X rays in such investigations because of the large amount of work involved in pole figures if one is dealing with a great number of specimens. The same thing, I think, applies to the determination of orientations by counting of twins which is also a very tedious procedure; as a result several papers which have otherwise been of excellent quality have depended upon etching techniques for determination of orientation. The present paper indicates that the results reported in those previous papers were correct, but I think the use of etching techniques alone is a rather shaky basis for setting up theories in the literature. W. M. BALDWIN, JR.*—This discussion will be a short note of correction and apology. In my discussion of Brick, Martin and Angier's paper I incorrectly reported the orientation of phosphorus deoxidized copper annealed at temperatures. When I learned that Mr. Yen was preparing the present paper I asked that he correct this previous error, which he most graciously consented to do. However, through my ambiguity the correction noted on p. 59 of Mr. Yen's paper is still not the proper one. For this I take full responsibility. The orientation which I observed in phosphorus deoxidized copper at high temperatures is the (112) [111] which agrees with the pole figure given in Fig 8a, on p. 65 of Mr. Yen's paper. Our observations were made on the basis of twin counts rather than X ray determinations and therefore serve as an independent confirmation of Mr. Yen's data. M. K. YEN (author's reply)—The author wishes to thank Dr. Maddigan for his comments in regard to the application of glancing technique to textures. As a matter of fact, considerable work has been done recently in connection with

Jan 1, 1950

By N. J. Grant, Masao Adachi

A number of Cu-SiO, and Cu-A1203 alloys of low oxide content, produced by internal oxidation of copper-silicon and copper-aluminum dilute solid solutions, were exposed at temperatures up to 1050°C for fairly long times to bring about partial or total re crystallization. The creep-rupture properties of these re crystallized alloys were compared to those in the as-extruded condition at 450° C. Some of the alloys were cold worked after re crystallization to note changes in creep-rupture properties, also at 450OC. SINCE the introduction of the SAP alloy in 1949,~ many studies have been carried out on similar oxide and intermetallic dispersion hardened alloys to determine properties and to establish the mechanisms involved in the strengthening process which led to stable, high-temperature behavior.'-' To date, it has been indicated that, however achieved, the structure should be composed of a continuous ductile metal matrix in which is dispersed a fine, submicron size, hard, insoluble second phase (or at least, essentially insoluble at temperatures very near the melting point), with a submicron or near submicron interparticle spacing. Stored energy, obtained by a high strain rate deformation process appears desirable, as an additional strengthening means beyond pure dispersion.=

Jan 1, 1961

By R. T. DeHoff

In any structural transfortnation which is driven by surface tension, the geometric variable of fimdamental importance is the local value of the mean surface curvatuve. Acting through the suvface free energy, this quantity determines the magtnitude of both the pressure and the chemical potential that develops in the neighborhood of an arbitrarily curved surface. A metallographic method which would permit the quaniitatiue estinzation of this propevty is of fundarnerztal irztevest to studies of such processes. In the present paper, it is shoun that the average value of the mean surface curvature in a structuve can be estimated from two simple counting measuretnents made upon a vepresentative metallograpIzic section. No simplifyirlg geonzetric assurmptions are necessary to this deviuation. It is further shoum that the result may be applied to parts of interfaces, e.g., interparticle welds in sintering, or the edge of growing platelets in a phase transformation, without loss of validity. In virtually every metallurgical process in which an interface is important, the local value of the mean surface curvature is the key structural property. This is true because the mean curvature determines the chemical potential of material adjacent to the surface, as well as the state of stress of that material. The theoretical description of such broadly different processes as sintering,1,2 grain growth,3 particle redistrib~tion4,5 and growth of Widmanstatten platelets8 all have as a central geometric variable the "local value of the mean surface curvature". The tools of quantitative metallography currently available permit the statistically precise estimation of the total or extensive geometric properties of a structure: the volume fraction of any distinguishable part:-' the total extent of any observable interface,10,11 and the total length of some three-dimensional lineal feature:' and, if some simplifying assumptions about particle shape are allowed, the total number of particles.'2"3 The size of particles in a structure, specified by a distribution or a mean value, can only be estimated if the particles are all the same shape, and if this shape is relatively simple.14-16 The relationships involved in converting measurements made upon a metallographic section to properties of the three dimensional structure of which the section is a sample are now well-established, and their utility amply demonstrated. In the present paper, another fundamental relationship is added to the tools of quantitative metallography. This relationship is fundamental in the sense that its validity depends only upon the observation of an appropriately representative sample of the structure, and not upon the geometric nature of the structure itself. It involves a new sampling procedure, devised by Rhines, called the "area tangent count". It will first be shown that the "area tangent count" is simply related to the average value of the curvature of particle outline in the two-dimensional section upon which the count is performed. The average curvature of such a section will then be shown to be proportional to the average value of the Mean surface curVature of the structure of which the section is a sample. The final result of the development is thus a relationship which permits the evaluation of the average value of the mean surface curvature from relatively simple counting measurements made upon a representative metallographic section. The result is quite independent of the geometric or even topological nature of the interface being studied. QUANTITATNE EVALUATION OF AVERAGE CURVATURE IN TWO DIMENSIONS The Area Tangent Count. Consider a two-dimen-sional structure composed of two different kinds of distinguishable areas (phases), Fig. l(a). If the system is composed of more than two "phases", it is possible to focus attention upon one phase, and consider the remaining structure as the other phase. The reference phase is separated from the rest of the structure by a set of linear boundaries, of arbitrary shapes and sizes. These boundaries may be totally smooth and continuous, or piecewise smooth and continuous. An element of such a boundary, dA, is shown in Fig. l(b). One may define the "angle subtended" by this arbitrarily curved element of arc, dO, as the angle between the normals erected at its ends, Fig. l(c). Now consider the following experiment. Let a line be swept across this two-dimensional structure, and let the number of tangents that this line forms with elements of arc in the structure be counted. This procedure constitutes the Rhines Area Tangent Count. Suppose that this experiment were repeated a large number of times, with the direction of traverse of the sweeping lines distributed uniformly over the semicircle of orientation.' Those test lines which ap- proach from orientations which lie in the range O to O + dO form a tangent with dA; those outside this range do not, see Fig. l(c). Since the lines are presumed to be uniformly distributed in direction of traverse, the fraction of test lines which form a tangent with dA is the fraction of the circumference of a semicircle which is contained in the orientation range, dO; i.e., vdO/nr or dB/n. If the number of test lines is N, the number forming tangents with dA is N(d0/n). Since each test line sweeps the entire area of the sample, the total area traversed by all N test lines is NL2. The number of tangents formed with dA, per unit area of structure sampled, is therefore

Jan 1, 1968

By Franc R. Joubin, D. H. James

Uranium exploration in the North Shore area of Lake Huron goes back to 1847 when J. L. LeConte, a distinguished American geologist, identified a pitchblende-like mineral which he called coracite from specimens sent from a locality north of Sault Ste. Marie. In 1948 a search for the LeConte occurrence resulted in discovery of the Camray field, some 70 miles north of Sault Ste. Marie. Prospecting the Camray field yielded about 30 pitchblende occurrences spread over approximately 200 sq miles. Almost without exception these discoveries consisted of narrow, short, pitchblende-filled fractures, within or along the contacts of diabase dykes cutting pre-Cambrian Archean granite and gneiss. Eight discoveries were diamond drilled and three were explored underground, but none proved to be of economic value. Uranium prospecting at this time spread far afield, and it was in 1949 that radioactive conglomerate was discovered in Long Township of the Algoma district midway between and 90 miles from Sault Ste. Marie and Sudbury. F. Joubin examined this discovery at that time but could not interest capital in its development.

Jun 1, 1956

A recent study estimates that a 10% improvement in the performance of wire rope used on draglines could save the US coal industry $2 million annually in rope costs. In addition, such an improvement could boost annual coal production by allowing the industry's draglines to remove an extra 1.5 million m3 (2 million cu yd) of solid overburden each year. These findings, although admittedly preliminary, suggest the magnitude of benefits that can be derived from a well-planned wire rope maintenance program.

Jan 3, 1978

By George H. K. Schenck

Diminishing returns in management's fight to lower manufacturing expenses have added luster to savings that can be achieved in delivered costs through creative management of the distribution function. This is especially true for companies engaged in the production of bulk commodities, for which transport costs may represent 25 to 50% or more of total delivered price, A. E. Cascino, vice president of International Minerals and Chemical Corporation, recently gave an example of why top management in his firm is concerned with distribution: "The price of a ton of phosphate rock, f.o.b. mine, is about $7. The cost of warehousing, freight, and handling frequently totals an additional $11 . . . . If one of our competitors . . . discovers a way in which he can cut his distribution costs by $3, we're dead! Even if we wanted to offset our competitor's more efficient means of shipping with reduced f.o.b. price for our product-we don't have that much profit margin . . . ." In a special report on the revolution now occurring in transportation of goods, Business Week stated in its September 24 issue: "Moving and storing goods on their way from mine and mill through various sub-assemblies to their final markets costs anywhere from $50 billion to $75 billion a year- $100 billion if paperwork costs are included.

Jan 1, 1967

By Mason K. Banks

A process has been developed which produces spodumene concentrates assaying 6.0 pct Li20 and 0.45 pct Fe203, with 70 to 75 pct recovery of spodumene. Two flotation separations are required: the simultaneous removal of mica, feldspar, and quartz as a froth product using a cationic collector, and the subsequent removal of iron-bearing minerals as a froth product while spodumene is depressed as a tailing.

Jan 2, 1953

By R. W. Kraft

A comprehensive analysis of the crystallographic and metallographic structure of several Al-CuAl, lamellar eutectic grains solidified under equilibrium conditions has been performed. A consistent pattern was discovered which was interpreted in terms of a detailed atomistic model of an interface describable as: Interface II {111} AL 11 {211} <101>Al <120> ? Several arguments are presented to substantiate the theory. It is compared in detail with another interface model characteristic of the Wid-manstatten precipitate of CuAl2 in A1 at low Cu levels. In addition, a concept is proposed to help explain the structure of the compound CuAl2. It has been shown that the eutectic alloy between A1 and CuA1, can be forced to solidify as substantially parallel lamellae throughout a relatively large volume&apos; by appropriately controlling the solidification parameters of growth rate, thermal gradients, and impurity level and by causing solidification to proceed in a unidirectional fashion from one end of an ingot to the other. A typical ingot solidified in this manner shows three distinct zones along the length of the ingot, Fig. 1. At the head end is a region consisting of many different grains, some of which are elongated slightly in the direction of solidification. After a few centimeters of growth, this polygrained region gradually merges into the second zone which consists of a very few elongated coarse grains. The third zone at the tail end is a region of eutectic colonies caused by segregation of impurities. Microscopic examination of transverse and longitudinal sections of the ingots reveals that during the initial stages of growth (zone I) the lamellar structure is frequently highly distorted and twisted but that it straightens out in zone 11. This characteristic pattern suggests that nucleation of a eutectic grain begins randomly at the head end of the ingot, and that some particular orientation relationship between the phases is more favorable from an energy consideration than others for one reason or another, so that some grains grow and others which are less favorably oriented do not. The favorably oriented or "low energy" grains continue to grow until excess solute rejected at the advancing liquid-solid interface destroys the parallel lamellar structure by forming a cellular rather than a substantially planar interface. When this occurs, the parallel lamellae fan out and eutectic colonies are formed because the lamellae grow perpendicular to the local interface. Questions naturally arise as to the crystallographic nature of the "low energy" grains. What do the grains which persist into zone II have in common? Can this explain the stability of such grains during growth? To answer the first question it is necessary to determine the crystallographic orientation of the lamellae of each phase relative to one another. This has been done for Al-CuAl2 eutectic alloys by two different techniques on specimens prepared in different ways.2&apos;3 The results were different from each other and from a third orientation relationship between A1 and CuA1, reported for overaged A1-Cu alloys.4 The three orientation relationships are summarized below to illustrate their similarities and their differences. (001) ? 11 (001) A1; [l00] ? 11 [l00] Al Eutectic, Ref. 2 (001) 8 1) (001) A1; [1001 ?11 [1101 A1 Eutectic, Ref. 3 (001) ? 11 (001) A1; [l00] ? 11 [310] Al; Widmanstfitten, Ref. 4 It is not surprising that different orientation relationships were found by Ellwood and Bagley,&apos; and Takahashi3 since the solidification conditions were quite different. Nor is it surprising that Mehl, Barrett, and Rhines 4 found still another value since they were studying another type of alloy. Nevertheless, it would be expected that some logical and systematic pattern could be found if all the alloys were at equilibrium since the same two phases are

Jan 1, 1962

By Norman A. Jull, A. L. Mular

Fundamentals of cyclones are reviewed briefly, where a typical cyclone is considered. Graphical cyclone data available in the literature have been converted to mathematical equations for convenience. Preliminary selection and design procedures for both cyclones and pumps are provided, and a sample calculation for a hypothetical grinding circuit is covered in some detail. In general, cyclone and pump suppliers should be consulted for definitive design purposes. Some cyclone suppliers currently employ digital computers for definitive design to ensure greater accuracy.

Jan 1, 1978

By R. W. Heckel, R. L. DeGregorio

The DeHoff method of determining the size distribution of ellipsoid-shaped, second-phase particles has been applied to the spheroidization of cementite in a eutectoid steel. The surface area of Precipitates determined from the various size fractions in the distribution was correlated with surface-area measurements based on the number of intersected interfaces on a random lest line. The precipitate particles were found to be oblate ellipsoids with an axial ratio of about 0.90. The size distributions were found to be log-normal. A method is proposed whereby the shrinkage of small particles and growth of large ones can be determined from the experimental data. The experimental data are compared to previously proposed mathematical models describing diffusion-controlled kinetics and various types of interface-controlled kinetics. The experimental growth and shrinkage rates are considerably slower than those predicted by diffusion-controlled kinetics. The best fit is obtained for a model describing interface-controlled kinetics limited by the rate of formation of cementite at the growing interfaces where the interfacial reaction rate is proportional to the solute thermodynamic activity gradient across the surface. THE subject of spheroidization of second-phase particles has been considered previously by other investigators. Livingston1 has studied the precipitation of the cobalt-rich phase from copper alloys containing 0.7 to 3.2 wt pet Co. His results indicate that the average particle size increases as the cube root of the heat treatment time in accord with diffusion-controlled kinetics.&apos;-&apos; Komatsu and rant&apos; in their studies of the growth of SiO2 in a dispersion-strengthened copper-silica alloy found that the initial growth of SiO2 proceeded by diffusion-controlled growth and later stages were limited by interface-controlled growth. The values of the activation energy obtained for the interface- controlled process led them to the conclusion that the process was limited by the dissociation of SiO2 at the shrinking interface. The transition from diffusion-controlled growth to interface-controlled growth was characterized by a particle size which varied with the heat-treatment temperature. It is also interesting to note that the particle-size distribution as found by Komatsu and Grant exhibits log-normal behavior when replotted on log-probability coordinates. Dromsky, Lenel, and Ansell9 have observed the growth of Al2O3 particles having a mean free path of about 1.5 to 13 µ. Their photomicrographs indicate that the Al2O3 particle sizes were larger than those observed by Komatsu and Grant. Dromsky, Lenel, and Ansell concluded that the Al2O3 coarsened by an interface-controlled growth mechanism limited by the solution of A12O3 at the shrinking interfaces. Bannyh, Modin, and Modin10 have studied the spheroidization of a eutectoid steel (0.83 wt pet C). Their spheroidization (tempering) treatments were carried out in the range from 210o to 700°C for times between 1.5 sec and 20 hr. Measurements of mean particle size as a function of time indicated a cube root of time dependence of size at 700°C, in agreement with previous analyses of diffusion-controlled kinetics.2°7 At lower temperatures, the time dependence was less than the one-third power. It is important to note that, although mathematical models of growth* considering particle-size distribution have been available, measurements of only mean particle size have been carried out. DeHoff11 has presented a quantitative metallography technique which is applicable to the determination of the size distribution of ellipsoids of constant shape. This method is applicable to both oblate and prolate ellipsoids of all ratios of minor to major axis and is based upon an extension of Saltykov&apos;s analysis12 of the distribution of spheres of varying size. DeHoff&apos;s analysis is based upon measurements of the minor axis of the particles on a random plane of polish in a unit area. This method provides a measure of the number of ellipsoids in various size ranges per unit area. As pointed out by DeHoff, such measurements may be used to obtain surface area and total precipitate volume data. Thus, the accuracy of the distribution analysis may be checked by comparison of the surface and volume

Jan 1, 1965

By J. D. Forrester, Erich Sarapuu, T. C. Cheasley

John G. Tripp-—The concept of converting fuel deposits in-situ to useful forms of energy and chemical raw materials has important possibilities as a means of stretching out our fuel resources. The authors have worked in this field for years and in fact are among the pioneers in developing in-situ techniques based on underground electrocarbonization. Their efforts have aroused great interest in this subject and their contributions will undoubtedly gain even more significance as time goes on. The 4 to 5 billion tons of petroleum are proved reserves, that is, they are completely defined and could be produced economically with present methods of recovery. Reserves of coal, tar sands, and oil shale shown in Table I are not equivalent to proved reserves as the term is used in the oil industry. Incidentally, the 4.3 billion tons of oil shown in the tabulation is equal to about 28 billion barrels of oil and, therefore, presumably does not include reserves of natural gas liquids estimated at about 5 billion barrels. The relative comparisons would be more complete if these liquids together with the reserves of natural gas were included in the tabulation. It is stated in the report that production costs of the order of 10c per million Btu&apos;s could be expected from a large industrial electrocarbonization installation. The authors state that the operation probably could be operated successfully and at a profit. I would like to express my view that for the operation to be profitable extremely favorable conditions would have to prevail. For example, the coal seam would have to be thick and close to the surface in order to minimize drilling costs; the deposit should be dry and so situated that there would be little, if any, inflow of ground water; and the seam would have to be relatively gas tight to avoid excessive gas leakage. Notwithstanding the tremendous strides that have already been made, it is my hope that the authors plan to continue their development work. Experiments on underground electrolinking and initial carbonization at Gorgas, Ala., indicate a need for improved control over the operation. Subsequent examination of the underground system at Gorgas has shown that the gasification zone did not always follow a direct path between the electrodes. Undoubtedly the control of the in-situ thermal processes can be improved by further development work. With respect to the electrocarbonization of oil shale it may be well to point out that the cost of mining oil shale is estimated to be 50c to 60c per ton. These are low mining costs as compared to coal. Thus it would appear that there is less economic incentive for applying in-situ thermal methods to oil shale than there is for applying these methods to coal. As is the case with in-situ methods for petroleum, the product from the shale having the most economic interest would be liquid oil rather than gas. The authors point out that for distances up to several hundred miles it is cheaper to transmit energy as electricity than it is to ship energy as coal. This is a very important point, and with coal shipping rates rising periodically, it could prove increasingly important in the future. I believe that the authors deserve great credit for their outstanding work on underground electrocarbonization. The knowledge resulting from their efforts is of great value to our fuels technology. James L. Elder—The experimental work conducted by the authors on the electrolinking-carbonization of carbonaceous materials in situ is of great interest. The method is of great importance in the development

Jan 1, 1955

By J. B. Cheatham

The influence of friction on the force required for an idealized bit tooth to penetrate a "plastic" rock is analyzed. The rock is assumed to obey the Coulomb-Mobr yield criterion and the tooth is represented by a two-dimensional sharp wedge. At the tooth-rock interface the stress field not only satisfies the yield condition but also is such that the ratio of the shearing stress to the normal stress is equal to the coefficient of friction. The solution relates the force on the tooth to the depth of penetration, the tooth angle, the coefficient of friction between the rock and bit tooth and the angle of internal friction and compressive strength of the rock. INTRODUCTION Most rocks are brittle at atmospheric pressure but exhibit ductility and increased strength as the confining pressure is increased. In a previous analysisl the force required for a bit tooth to penetrate a rigid-plastic rock was computed for two limiting conditions: (1) a perfectly lubricated tooth-rock interface which should correspond to a lower limit for the penetrating force, and (2) a perfectly rough interface which should provide an upper limit. Experimental results2 for rock indentation under confining pressure have confirmed that the analysis generally predicts upper and lower limits for the penetrating force as a function of rock properties and tooth angle. The present analysis extends the previous work to account for the friction between the rock and the tooth. ANALYSIS The force required for incipient plastic flow of an idealized model of a rock under a bit tooth is computed subjected to the following assumptions. BIT TOOTH 1. sharp two-dimensional wedge (end effects neglected) 2. rigid tooth (elastic deformation of tooth neglected) 3. displacement of tooth is normal to rock surface 4. friction exists between tooth and rock ROCK 1. semi-infinite, isotropic and homogeneous 2. rigid-plastic (elastic deformation of rock neglected) 3. non-work hardening (horizontal stress-strain curve) 4. Coulomb yield condition* (linear Mohr envelope) 5. smooth, flat surface According to the Mohr theory of failure it is assumed that failure occurs when the state of stress is such that the Mohr stress circle becomes tangent to an experimentally determined envelope. The Mohr failure curve is frequent1y approximated by a straight line and referred to as the Coulomb-Mohr failure criterion. If the rock is under sufficient pressure to be ductile we can use the linear envelope as a yield condition. The Coulomb-Mohr yield criterion is illustrated by Fig. 1 and is expressed by the following equation:l

By AIME AIME

MEMBERS of the Engineering Education Committee held two meetings at Joplin preliminary to the opening of the main meeting there. The first was held on Sunday afternoon. It was attended by all who had arrived early enough and as among the dozen or&apos; fifteen who were present the heads of a half dozen schools of mines were included it was a representative gathering. C: H. Fulton, chairman of the Committee presided and T. T. Read acted as secretary of the meeting. The chair., man reminded those present that last year there had been some discussion as to the advisability of the proposal, made by Edward Steidle, that a, separate society, devoted to education in the mineral industry, he organized. Many .people had felt that there are already so many societies in existence to demand one&apos;s time and attention, that it would be a mistake to add to their number and the counter suggestion had been made that the work of this committee could be so reorganized as to meet all the needs that a separate society could fill. He therefore presented for discussion these four&apos; questions: (1) Shall a subcommittee .be appointed to study, and report in February, 1932, the possibility of the reorganization of the work of the Engineering Education Committee into the equivalent of an&apos; Institute division; (2) if the work is so reorganized what shall be the relation of the work of the Committee (division) to the work of the-Society for the Promotion of Engineering Education; (3.): what are the, cardinal objectives of education for the mineral industry; and (4) what should be done as regards the movement in some institutions to plan their work-in the light of that being done in other institutions, for example, in geophysics?

Jan 1, 1931