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By Marcel Daly

THE writer has devoted a number of years to practical operations and to the study of geology in the oil fields. In consequence, he has been brought to investigate the theories advanced to account for the accumulation of oil and gas in commercial deposits. It is the result of these investigations and his personal conclusions that he wishes to sum up in this paper. The writer is an advocate of the organic origin of petroleum found in pools. He has been led to believe that the present theories of oil and gas accumulations are incomplete and, in certain respects, incorrect, although they may embody certain elements of truth; that the forces that are called upon to explain the movement are only secondary forces in the process, and insufficient, by themselves, to cause this movement; and that the phenomenon of accumulation is of much larger order than heretofore admitted and bears an intimate relation with the general as well as with the local deformations of the crust and is a direct consequence and a mechanical effect of these deformations to which the term "diastrophic" has been applied. As a complement to this theory, the writer offers a new interpretation of the "rock pressure" and of the mechanism of the "sealing up" of this pressure in oil and gas pools.

Jan 7, 1916

By E. Lancaster-Jones

THE gravity magnitudes obtained by means of observations with the Eötvös balance in the field are necessarily resultant or total effects due to all abnormalities of mass distribution, including even the effects due to the ellipticity and rotational motion of the whole earth. Since the object of the survey is to isolate the effects which arise solely from some particular subterranean feature, and to deduce therefrom the configuration and extent of this feature, the first step is to eliminate from the observed effects all those due to "disturbing" (i. e., unwanted) features, whether above or below the surface of the ground. The disturbing features have different characteristics, according to their situation relative to the center of the balance and to the horizontal plane through the foot of the balance, or station point; this diversity was recognized by Eötvös, who divided the total effects into so-called Normal, Terrain, Topographical, Cartographical and Subterranean effects. This classification has been adhered to by most subsequent investigators, but the writer prefers to employ the term "three-dimensional," which really indicates the essential character of the class of effect known as "Subterranean," at any rate from the standpoint of the computer of effects. Before disturbing effects can be eliminated, the features must be measured up or surveyed, whether by topographical, mining, or boring methods, and then the effects of each feature calculated and subtracted from-the total observed effects. After this the problem of interpreting the residual effects will itself necessitate the computation of the assumed feature, or even a series of trial features.

Jan 1, 1928

By S. J. Green, R. D. Perkins

Little data exists on the high strain rate behavior of geologic materials. Uniaxial stress tests by Kumar1 and by Serdengecti and Boozer2 present some results to strain rates in the range 10 to 103 per sec. The two references cited are the only ones the authors found for high strain rates. Techniques for experiments at high strain rates are not well developed and, in general, leave questions with respect to interpretation of data when the material behaves in a brittle manner. The most reliable data at very high strain rates (104 to 106 per sec) are found in some recent flat-plate work3-5 where experimenters have impacted one plate into another, thereby creating a uniaxial strain loading. The standard uniaxial stress-strain curves cannot be obtained directly from these tests; however, yield (or fracture) may be studied by measuring the "elastic" wave magnitude. These data then may be compared to uniaxial stress data by resorting to some preassumed yield/fracture criteria. Even with the most liberal interpretation of existing data, little can be said of the effects of high strain rate on stiffness, yield/fracture, and post-fracture behavior of geologic materials. It is the purpose of this work to begin to add to the understanding. The data presented here are intended to provide material information for use in calculating the response of geologic materials to high rate deformations. These data can be applied directly to determine parameters such as the elastic modulus and Poisson ratio as a function of stress. Furthermore, these data can be used to derive an understanding of yield/fracture and the effect of rate on the yield/fracture surface. The work presented is a first step, and is

Jan 1, 1972

By Mark Malamphy

DURING colonial times, Brazil was famous for the richness of her alluvial gold deposits. Paul Ferrand has estimated that the gold produced during the period from 1700 to 1820 was the equivalent of some 64 million pounds sterling. Since that time, most of the more prolific alluvial deposits have been exhausted. A few gold mines are still func-tioning, notably the Morro Velho mine, which is one of the deepest mines in the world. Today, the gold production of Brazil is insignificant when compared with world figures, but there are still many gold-bearing regions and it is probable that in at least some of them profitable returns would result from an exploitation program taking advantage of all the most modern innovations in gold mining and ore treatment on a large scale. In order to demonstrate the value of some of these abandoned pros-pects and stir up interest in increasing the national gold production, the government has stimulated research. Experimental plants have been and are being established in various places, and tests on large quantities of ores are being carried out on a semicommercial basis. The Geological Survey of the State of Minas Geraes is very active in this line and the Federal Institution is also showing an increased interest in the matter. One of the lesser known gold-bearing regions of Brazil is in the vicinity of Lavras, in the State of Rio Grande do Sul. Gold was first reported from this region in the early part of the nineteenth century. In 1811, D. João VI sent an experienced prospector from Minas Geraes to investi-gate the validity of the reports. According to the reports of Baron

Jan 1, 1934

By Irving Fatt, R. M. Weinbrandt

Efforts have been made for many years to observe pore structure of sedimentary rocks on a microscopic scale. A better description of the pore structure in reservoir rock would aid in the development of relations between flow through tube network models and flow in consolidated reservoir rock. The unique qualities of the scanning electron miscroscope (SEM) make it the ideal tool to use in a study of pore structure. Previous methods of studying pore structure included plastic casts of pore space and optical microscopy.l-7 There is now available a new method to observe three-dimensional flow channels in reservoir rock: a scanning electron microscope having variable magnification from X20 to X20,000 and approximately 1000 times the depth of focus of the conventional light microscopes. This microscope also can obtain stereoscopic images and can measure and diagram flow channels so that it is possible to construct a network of tubes that will model consolidated reservoir rock. THEORY OF THE SCANNING ELECTRON MICROSCOPE The scanning electron microscope (SEM) functions by projecting a beam of electrons through magnetic focusing lenses at a specimen and recording secondary electrons excited by the primary beam. The amount of secondary electron emission portrays the topography of the specimen because more secondary electrons are emitted from high points than from low points. A schematic of the SEM is shown in Fig. 1. The property of the SEM that is of most importance in this study is its great depth of focus. The depth of focus results from using electrons

Jan 1, 1970

By L. D. Godshall

A great deal has been written of late regarding the loss of silver in assaying; very discordant results have been published by different writers, and much uncertainty exists concerning even approximate losses in a careful determination of silver, as represented by a fire-assay. In the present paper it has been the aim of the writer to determine as accurately as possible the losses sustained by silver, under certain specified conditions, during the process of cupellation. Such losses are well known to be due to absorption by the cupel and volatilization. The conditions, however, which govern these losses are not believed by the writer to be so well understood. The most important of these are : 1. The effect of variable quantities of silver used. 2. The temperature of cupellation. 3. The character and quantity of impurities in the lead button. 4. The weight of the lead button. 5. The nature of the cupel. The following experiments were made for the purpose of demonstrating, as nearly as possible, the total loss of silver in cupellation under the most favorable conditions to be obtained in commercial assaying. Chemically pure silver and pure lead were taken. The latter was obtained from test-lead, first melted into a bar, from which pieces of the desired weight were cut and accurately weighed. The experiments recorded in this paper were planned by the writer, but executed throughout by Mr. J. N. Walker, whose ability as an accurate, careful and painstaking assayer is too well known and recognized throughout the West to require any further endorsement from me.

Jan 1, 1897

By Albert Sauveur

(New York Meeting, February, 1913.) IT is delightful to read a technical paper like that of J. E. Johnson, The Effect of High Carbon on the Quality of Charcoal-Iron, presented in October, 1912, at the Cleveland meeting of the American Institute of Mining Engineers.1 The clear, simple, and straightforward manner in which he describes his experiments and results makes you feel as if you had been, so to speak, at his elbow during the course of his investigations, while his method of procedure is so rational that you can fairly anticipate each step in the logical sequence of the tests performed. The following notes suggested by Mr. Johnson's paper are presented here in the hope that they may help, if only a mite, towards the final solution of a problem of considerable scientific and industrial importance.

Jan 3, 1913

By Warren Smith

IT has been 5 years since the writer left the Philippine Islands and while in that country his chief work did not lie in this field, though he has visited all but one of the localities mentioned in this article. The principal field studies relating to oil were made by his colleague, Mr. Wallace E. Pratt. The writer's investigations dealt with the general stratigraphy and paleontology of the Philippines. With the exception of the investigations made by Mr. Pratt and the writer very little information on this subject is available. A number of geologists in the employ of large oil companies have visited the Islands from time to time but, following the general rule, the public has scarcely ever been permitted to learn anything of the results. The writer is indebted to the Bureau of Insular Affairs, Washington, for late information regarding recent legislation in the Islands relating to petroleum. All the known oil seeps, petroleum residues, such as ozocerite, and natural-gas emanations are associated with Tertiary sediments. The chief seeps and most promising prospects are located as follows: 1. Bondoc Peninsula (lower end), Tayabas Province, Southeast Luzon. 2. The west coast of the island of Cebú from Alegria north to, and perhaps beyond, Toledo. 3. Central Mindanao not far from Lake Lanao. 4. The ozocerite veins on the Island of Leyte in the northwestern part in the vicinity of the town of Villaba. 5. Natural gas from some deep wells in Tertiary shale formations on the eastern flank of the Cordillera and extending out under the plain on the island of Panay.

Jan 2, 1920

By H. L. Bridgman

The correct sampling of ores is a subject of far greater importance than is usually conceded to it. Of the little which has been published on this subject, the recent paper by Mr. Glenn, with the accompanying discussion by Dr. Raymond (Trans., xx., 155), is the latest and best, and well worthy the careful perusal of all interested in accurate sampling, whether by hand or by machine. It is doubtless true that thorough hand-sampling gives as good average results as can be obtained; but all hand-sampling is subject to the possible incompetency, carelessness, or dishonesty of the workmen employed. It is, moreover, tedious and expensive, requires large space, and usually entails considerable delay, both in unloading and in sampling. For these and other reasons, machine-sampling is now regarded with more favor than ever before. So-called machine-sampling may be accomplished in two radically different ways: 1. Part of the stream of material is taken for the whole time. 2. The whole stream of material is taken for part of the time. Under the first case the stream, as it issrles from the deliveryspout of the crusher, is cut continuously in any given proportion, such as one-tenth, one-fourth, or one-half, by some fixed apparatus, which, as it contains no moving parts, is strictly speaking not a machine at all, but may be termed an appliance. The principle under which these appliances operate is now pretty generally conceded to be wrong, becanse of the practical impossibility of' cutting such a

Jan 1, 1892

By Petri Bryk, John Ryselin, Rolf Malmstrom, Jorma Honkasalo

THE theoretical possibilities for the realization of flash smelting have been known for a long time. Calculations concerning the same can be found in previously published literature,1 and suggestions for its accomplishment in practice are described in patents on the subject. Likewise a smaller number of practical test results are known. Autogenous smelting is closely connected with flash smelting, since in flash smelting techniques it is possible to use the heat evolved by oxidation of the sulfides for the smelting process to such an extent that under certain conditions smelting can proceed without additional fuel. However, in the event that insufficient heat is available from the oxidation of the sulfide concentrates, then additional heat may be supplied by preheating the air, using oxygen enriched air, on burning additional fuel with the concentrate.

Jan 6, 1958

By R. U. Jackson

Belt conveying is a method of transportation that requires proper servicing and maintenance if completely economical results are to be obtained from the system. With a trucking system, it is common practice to deliver the trucks to a servicing station each day or at the end of each shift. With railroad transportation there is a similar procedure. Sufficient credit is seldom given to this periodic inspection and maintenance procedure, yet it is the key to the successful operation of trucking and rail haulage systems. How about the belt conveyor transportation system? Here is a system that requires no operator for each individual unit. It requires only a main switch and an adequate sequence interlocking system, and the system is so simple to operate that maintenance is considered as only a casual requirement-nothing is done about it until after trouble has developed.

Jan 1, 1956

By Michael A. Devane, Neil Duncan

Inclines and tunnels can extend from ground surface to considerable depths traversing a wide range of lithologies. The strata encountered may be affected by loosening and induced stresses at different locations along the route. It is suggested that Phase I of the pre- driving assessment process should include study of the geology, hydrogeology, rock material and rock mass characteristics. A rock mass disruption factor is used to express the ratio of the unconfined strength of intact rock material to the unconfined strength of in situ rock mass. It is suggested that there is a relationship between in situ (secondary) permeability values and the disruption factor, since the permeability of the rock mass is governed by parameters which influence strength. In Phase I1 of the pre-driving assessment, consideration should be given to the prediction of primary loosening which results largely from disturbances to the rock mass arising from the driving process. Also in Phase 11, preliminary assessments are made of the effects of induced stresses and of the geodurability characteristics of the rocks. In Phase 111, the mechanics of various secondary loosening pro- cesses are considered along with their relevance to estimates of stand up time and support requirements. Yield-line analysis is introduced for the study of plastic and brittle type bending deformations. Stand up time and support characteristics are also assessed. In Phase IV, the effects of induced stresses are analysed. It is suggested that even for broken rock in the Yield Zone, the rock mass disruption factor may not often increase above lo which is equivalent to an in situ permeability of 10-1 m/s.

Jan 1, 1983

By R. W. Diamond

THREE mills are now operated by the Consolidated Mining & Smelting Co. of Canada, Ltd.: (1) The Sullivan Concentrator, Chapman Camp, B. C. (near Kimberley, B. C.), (2) the, St. Eugene Concentrator, Moyie, B. C., and (3) the. Tadanac (Customs) Concentrator,Trail, B. C. Differential flotation is the only concentration method employed in all three plants. Tables are used for pilot work only. Values in all ores treated are as minerals of some or all of the metals -lead, zinc, gold or silver. Occasional customs ores contain small amounts of copper. Sulfide iron content of ores treated varies from a FIG. 1.-THE SULLIVAN CONCENTRATOR, CHAPMAN CAMP, B. C. (NEAR KIMBERLEY, B. C.). low figure in some ores to 38 per cent. iron in Sullivan ore. Gangue minerals vary considerably. A few customs ores are somewhat oxidized and as a result present difficulties. Flotation equipment and control are similar in the three mills, and the flow sheets at the St. Eugene and Tadanac mills, while much simpler, are modeled after that of the Sullivan Concentrator. In this paper I will not detail treatment nor equipment in any of our plants but will describe special features in, or in connection with, all of them. I will then deal with flotation reagents, describing our use of each of them, particularly where differing from general practice. I will conclude with comments on special subjects related to differential-flotation.

Jan 1, 1927

INTRODUCTION TO PROBABILITY THEORY The mathematical theory of probability provides the foundation for the interpretations and inferences that can be made from statistical techniques. Probability theory is a broad field of study in itself, and can only be touched on here in order to provide the necessary back- ground for a more complete understanding of statistical analysis. Probability is concerned with the outcome of random events. It had its beginnings in the theory of games of chance which were of great interest to European mathematicians during the last half of the 17th century. The outcome of a random process or experiment is defined as an event. The collection of all mathematical points associated with each event is called the sample space for an experiment. Consider a random experiment having a finite number, n, of possible outcomes, some of which have a characteristic A. What is the probability that A will result from a single

Jan 1, 1980

By Sidney Cornell

THE technical- advantages of adding oxygen to air and producer gas, or using it as a reactive agent, producing 400 B.t.u. gas instead of. the present 150 B.t.u., with higher flame temperatures and a reducing flame possible, with a smaller volume of gases passing through a furnace, will result in quicker melting, sharp working, and the production of a higher quality steel. Probably electric-furnace quality steel can be produced in an open-hearth furnace using oxygen. A modern, standard, 100-ton open-hearth furnace, with all equipment, costs from $350,000 to $500,000; there are about 1000 open-hearth furnaces in this country. When considering the use of oxygen in the open-hearth furnace, it is necessary to study: (1) The use of oxygen in the present furnaces, such that modification of existing furnaces and equipment cost the minimum, although the full advantages of oxygen are not thus obtainable. (2) The use of oxygen in a furnace designed for its use, producing quality and quantity steel at the lowest possible cost. This entails the junking of approximately one-half the value in existing equipment-writing off $250,000,000. The basis of such an estimate is the present cost of manufacturing open-hearth steel. Objection may be taken to some of the unit prices here given, but while some companies obtain their ores for much less, the prices quoted are -market price. They are used to show the maximum economy obtained by oxygen at that point.

Jan 11, 1924

By R. C. Ku, A. J. McEvily, T. L. Johnston

The microplastic response of a series ofas-quenched Fe-Ni-C martensites has been measured at 77°K. At strains less than JO'3 the flow stress is governed primarily by the transformation-induced dislocation structure of the martensite. Only at strains in excess of 10-3 is the influence of carbon manifested in the flow stress. At these macroscopic strains, typically 10-2, the solid-solution hardening is proportional to (wt pct C)1/3, and, in an alloy containing 0.39 wt pct C, amounts to 50 pct of the flow stress. THE technological significance of high-strength ferrous martensite has stimulated many investigations of its structure and properties. Although our knowledge of the characteristics of martensite has increased immensely, especially with the advent of high-resolution techniques, an understanding of the basic strengthening mechanism still remains elusive. The purpose of the present paper is to consider certain aspects of micro-plastic behavior of Fe-Ni-C martensite which we feel can help to resolve this important problem. Such alloys are particularly suitable for experimental investigation because their compositions can be adjusted to reduce the M, to a temperature low enough essentially to eliminate the diffusion of carbon in the freshly formed martensite.1 The mechanical properties in this condition are of interest inasmuch as they reflect a state that is free of the important but complicating influence of precipitation processes. In this virgin martensite the carbon is distributed as it was inherited from the parent austenite; i.e., it is present interstitially, and gives rise to tetragonality through strain-induced ordering.' In order to determine the source of strength of such alloys, Winchell and Cohen1 investigated the low-temperature macroscopic stress-strain behavior of a series of virgin martensites of increasing carbon content but of common M, temperature (-35°C). They found that the flow stress increased rapidly with carbon content up to 0.4 wt pct; beyond this point the flow stress increased at a much slower rate. It was concluded that martensite is inherently strong. To account quantitatively for the strength of virgin or as- quenched martensite in terms of the role of carbon, Winchell and cohen3 suggested that the carbon atoms, trapped in their original positions by the diffusionless martensite transformation, interfere with dislocation motion according to a model akin to that of Mott and Nabarro. 4 In this treatment, individual carbon atoms are considered to constitute centers of elastic strain and thereby generate an average stress resisting the motion of dislocations throughout the lattice. The additional stress necessary to move dislocations, over and above that necessary for motion in a carbon-free martensite, is given by where L is an effective length of dislocation capable of motion. L was assumed to be limited to the spacing between the twins that are an essential structural element of Fe-Ni-C martensites. They assumtd the spacing to be invariant and of the order of 100A. However, recent work5 has shown that L is variable and can be in excess of 1000Å, so that the assignment of an appropriate value of L is not straightforward. In contrast to the above conclusion that there is an intrinsically high resistance to plastic flow, it has been suggested by Polakowski6 that freshly quenched martensite is in fact "soft" in the sense that dislocations are initially free to move upon application of stress. The high indentation hardness and macroscopic yield stress of ferrous martensites are then a consequence of rapid strain hardening that depends upon carbon in solution. Consistent with this point of view are the results of Beau lieu and Dubé who measured the rate of recovery of internal friction as a function of aging (tempering) temperature in a freshly quenched steel containing 0.90 wt pct C, 0.37 wt pct Mn, 0.1 wt pct Cr, and 0.07 wt pct Ni. The kinetics were clearly consistent with the idea that many dislocations are unpinned in the as-quenched state and that during aging they become progressively pinned by carbon at a rate controlled by carbon diffusion in the body-centered martensite lattice. In order to provide a basis upon which to distinguish between the "hard" and "soft" interpretations indicated above, we have made studies of the initial stages of plastic deformation in Fe-Ni-C martensites similar to those'used by Winchell and Cohen. It will be shown that the results support the contention that dislocation segments in as-quenched material are indeed

Jan 1, 1967

By B. C. Wonsiewicz, W. W. Wilkening

Following a procedure proposed by Wheeler and Ireland, Plane stress yield loci were constructed from Knoob hardness numbers. Basically, six differently oriented hardness measurements were made on three orthogml surfaces through pure poly crystalline magnesium sheet, a magnesium single crystal, and sheet of the magnesium alloys: Mg + 0.5 pct Th, Mg + 4 pct Li, AZ31B, and EKOO. Hardness loci were found to be in poor agreement at small strains (E < 0.05) with loci established by a more rigorous technique. At larger strains (E - 0.10) the agreement is fair, but at this stage in deformation the conventional locus has lost much of the asymmetry that characterizes these anisotropic materials. Two effects which will lead to distortions in the Khn locus are discussed with reference to the geometry of plastic flow during a hardness test. DETERMINING a material&apos;s resistance to multiaxial loading is of interest not only from a structural design viewpoint but also from that of deformation processing. Unfortunately, the determination of the yield locus, although simple in principle, involves tedious procedures if the results are to be at all rigorous.&apos; The idea, first proposed by Wheeler and 1reland2 of determining the yield locus by means of six Knoop hardness impressions along the principal directions in a material has obvious appeal. It is simple, quick, and should be applicable to very thin sheets. If such a technique could be demonstrated to produce consistently reliable results, it would be of interest to both researcher and designer. Lee, Jabara, and ackofen have compared the yield locus determined by Knoop hardness measurements (the Khn locus) to a locus determined by more rigorous techniques. They found good agreement for two titanium alloys at a plastic strain of about 1 pct. The purpose of this paper is to investigate if the Khn locus construction is a reasonable approximation to the locus of a highly anisotropic material. Examples of such materials are magnesium and magnesium alloys which have severely distorted yield loci which in turn reflect markedly dfferent yield strength in different directions.&apos; In pure magnesium, for example, the yield stress in tension along the transverse direction may be four times the yield stress in compression in the same direction and twice the tensile yield stress in the rolling direction. Predicting such large differences ought to serve as a severe test of the Khn locus construction. EXPERIMENTAL PROCEDURES Samples of rolled sheet, 0.250 in. (6.35 mm) thick, of pure magnesium and four magnesium alloys (Mg experimental materials. The pure magnesium together with the lithium and thorium alloys were those used in the study of Kelley and Hosford. The grain size was ASTM number 4 for the pure magnesium and number 6 for the alloys. HARDNESS TESTING The materials were sectioned along the rolling and transverse planes, mounted in a quick setting resin, and mechanically polished. Most of the hardness tests were performed on a surface prepared by electro-polishing (30 pct nitric acid in methanol at 0°C and 20 v) with the exception of the AZ31B and EK00 alloys which were made directly on a metallographically polished surface. However, subsequent hardness tests on the same sample after heavily electropolishing, revealed essentially the same hardness as before. At least twenty Knoop hardness impressions under a 100-g load were made in each of the six orientations shown in Fig. 1. The average hardness number and standard deviation were then calculated for each orientation. CONVENTIONAL LOCUS CONSTRUCTION Yield loci were constructed using a technique described in detail by Lee and ackofen,&apos; in which the flow stress (stress at a given plastic strain) fixes the coordinates of a point on the locus and measurements of the strain ratio serve to establish the slope of the locus at that point. The loading paths which correspond to uniaxial tension or compression tests establish the four intercepts of the locus with the coordinate axes plus one point on the balanced biaxial tension line Tensile testing was performed along the rolling and transverse (r, t) directions. Samples had a uniform rectangular gage length 1 by 4 by 4 in. (25.4 by 6.35 by 6.35 mm) and were deformed at a strain rate of 3.33 x 104 sec-&apos;. The tests were interrupted periodically to unload the sample and measure the plastic strains by means of X-Y post yield strain gages. Compression tests in the rolling, transverse, and through-thickness (r, f, z) directions were performed on 1/4 in. (6.35 mm) cubes at an initial strain rate of 8.33 x sec-&apos;. Lubrication was provided by 0.002 in. (51 pm) Teflon sheet which was renewed after unloading for micrometer measurements used to calculate the strains.

Jan 1, 1970

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By P. E. Rider, K. A. Gschneidner, O. D. McMasters

The solid solubilities for thirteen rare-earth metals in gold were determined by using the X-ray parametric method. Solubilities ranged from 0.1 at. pct for lanthanum in gold up to 8.8 at. pct for scandium in gold. The solubilities from lanthanum to gadolinium were very small and essentially constant, but a sharp increase occurred from gadolinium to scandium. The large solubilities for the heavy rare-earth metals were not expected because of the large size and electrochemical differences between rare-earth atoms and the gold atom. Contributions from first- and second-order elasticity theory plus an electronic contribution were found to reasonably account for a more favorable size factor. Electron transfer from the rare-earth metal to the gold Is thought to occur such that the resultant rare-earth and gold electronegativities are favorable for solid-solution formation. It was also found that this mutual adjustment of size and electronegutivity does not occur if the pure-metal size factors are greater than a critical value of 25 pet. The eutectic temperatures for ten systems were determined and these remained fairly constant at approximately 809 "C for the lighter lanthanide metal-gold systems until the Er-Au system was reached, at which Point the eutectic temperature successively increased reaching a maximum of 1040°C in the Sc-Au system. This rise was correlated to the size factor becoming more favorable for solid-solution formation at erbium. The valence state of ytterbium was found to change from two in the pure metal to three when ytterbium is dissolved in the gold matrix. RECENT results1 reported concerning the solubility of holmium in copper, silver, and gold, showed that the solubility of holmium in gold was quite large, 4.0 at. pct, compared with 1.6 in silver and 0.02 in copper. The small solubilities of holmium in silver and copper are quite reasonable in view of the large size difference (22.2 and 38.2 pct, respectively), large electronegativity difference (0.59 for both systems), and possible unfavorable valency factor (assuming one for silver and copper and three for holmium). The large solubility in gold, however, is unexpected because these same factors are also unfavorable for holmium and gold (22.5 pct size difference and 0.69 electronegativity difference), and because the light rare-earth metals, lanthanum, cerium, and praseodymium, have negligible solid solubilities in gold.2 In view of this unexpected behavior, it was felt that a study of the solid solubilities of most of the rare-earth metals in gold would be desirable to better understand the factors involved in the formation of solid solutions. Of the rare-earth metals added to gold in this study, only ytterbium is divalent in the pure metallic state (the other rare-earth metals are all trivalent) and many of its physical properties (such as the metallic radius, electronegativity, and so forth) are much different from those of the normal trivalent rare-earth metals.&apos; The properties of ytterbium are such that one would expect solid-solution formation to be less favorable for ytterbium in gold than for any of the normal trivalent rare-earth metals. But chemically ytterbium is known to possess a stable trivalent state, and it is quite possible that ytterbium may alloy as a trivalent metal under certain conditions rather than as a divalent metal. Because of the dual valency nature and because so little is known about the alloying behavior of ytterbium, the gold-rich ytterbium-gold alloys are of special interest. EXPERIMENTAL PROCEDURE Materials. The gold used in this investigation had a purity of 99.99 pct with respect to nongaseous impurities. In general the rare-earth metals were prepared by reduction of the corresponding fluoride by calcium metal.3 The impurity contents of the metals used in this study are given in Table I. Preparation of Alloys. Two- or 3-g alloy samples were prepared by arc melting. The samples, with the exception of some of the Er-Au alloys, had weight losses of 0.5 pct or less. All alloy concentrations noted in this paper are nominal compositions. After arc melting, the alloys were wrapped in tantalum foil, sealed off in quartz tubing under a partial atmosphere of argon, homogenized for approximately 200 hr at 780°C, and then quenched in cold water. X-Ray Methods. The X-ray parametric method was used in determining the solubility of the rare-earth metals in gold. filings were sealed in small tantalum tubes by welding under a helium atmosphere. The tantalum tubes were then sealed in quartz tubing under a partial argon atmosphere, and annealed for times ranging from 1/2 to 3 hr (the length of time was inversely proportional to the an-

Jan 1, 1965

By R. A. Oriani

The partial molal volume of hydrogen is one of the parameters that describe the elastic interaction between the solute and the stress fields about inclusions, dislocations, and cracks. As such the partial molal volume is probably of importance in the elucidation of phenomena such as hydrogen embrittlement and hydrogen yield point. A knowledge of this quantity would also be helpful in thinking about the state of dissolved hydrogen in iron. However, because of the very low lattice solubility of hydrogen in iron the usual ways of determining the lattice expansion are not practicable. It is therefore of interest to apply the thermodynamics of stressed bodies to two sets of measurements of the effect of elastic stress upon the permeability of hydrogen in order to deduce a value of the partial molal volume, VH, of hydrogen dissolved in a iron. Beck ..&apos; and previously de Kazinczy, observed that a uniaxial tensile stress increases the permeability of hydrogen in iron and in various steels. Beck et 01. employed Armco iron and A.I.S.I. 4340 steel, whereas de Kazinczy used a steel the composition of which was 0.13 C, 0.23 Si, 0.46 Mn, 0.006 P, and 0.038 S. Upon releasing the stress the permeability increment disappeared if the stress was below the elastic limit. Both investigators employed cathodic charging to introduce the hydrogen. de Kazinczy measured the permeation through a thin-walled tube by collecting the gas, whereas Beck et al. measured the permeation through sheets of various thicknesses by a very sensitive electrochemical technique. Both investigators measured the steady-state permeation at constant rate of hydrogen ion discharge, and Beck measured in addition the hydrogen diffusivity by a time-lag technique which is independent of the boundary conditions. Beck et al. and de Kazinczy found a linear relationship between log (J,/Jo) and the stress, where Ju/Jo is the ratio of the flux of hydrogen when the metal is under uniaxial tensile stress, a, to the flux under zero stress, for the same temperature and charging current. Beck et al. found in addition that the diffusivity of hydrogen is not changed by stress. Both investigators concluded that the observed change in permeability is due to an increase in hydrogen concentration, and furthermore that the increase in concentration is due directly to the thermodynamic effect of stress upon concentration. Accepting this assessment of the situation for reasons given below, one may use the equation3j4 in order to evaluate I/H, the partial molal volume of hydrogen. This equation is valid for the domain of a/E «¦ 1 (where E is the Young&apos;s modulus) and under the assumption that hydrogen expands the lattice isotrop-ically. From the data of Beck el al, one calculates V7H - 2.0 cu cm per g-atom, and from those of de Kazinczy one obtains 1.8 cu cm per g-atom. That the increase of concentration with stress is indeed of thermodynamic origin is attested to by the facts that the experimental results conform to the thermodynamic relation, Eq. [I], and that the results are the same whether a pure iron1 or each of two different steels172 is used. Neither of these facts wou1.d necessarily be expected if the effect of stress were, rather, to increase the ratio kn/k, of the kinetic factors of the following competing reactions: H(ads) — H (dissolved) Such a change of kinetics at the surface could be an alternative explanation of the effect of stress on the permeability. Although this writer does not deem this explanation to be the correct one for the reasons given above, it must be admitted that unambiguous proof that the phenomenon has a thermodynamic origin does not yet exist. Two kinds of experiments may be suggested. One is to plate a variety of metals on the input surface of the steel and repeat the stress experiment at a variety of hydrogen charging currents. The other is to employ somewhat thicker specimens in order to be able to apply uniaxial compressive stress. Eq. [I] shows that ln(c,/c,) depends on the sign of the stress, but it is difficult to see a physical basis for which k2/kl would depend on the sign of a. The present value of V^ in a iron agrees with phragmen&apos;s5 estimate, which he based on comparisons with the lattice expansion by hydrogen of titanium, zir-

Jan 1, 1967