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By Pradeep K. Rohatgi, David N. French, Surendar M. Jain, Clyde M. Adams

The effect of solute concentration and diffussivity on dendritic solidification of dilute binary aqueous solutions has been investigated; chlorides of sodium, potassium, lithiurn, and hydrogen were used as solutes. Dendrite spacings were measured in spherical droplets and in unidirectionally solidified specimens. In the droplets, the freezing rate is uniform over the entire specimen and remains constant from the beginning to the end of solidification. In the unidirec-tionally frozen specimens the freezing rate varies within a given volume of liquid during the solidification cycle; in addition, it varies with location uithin the specimen. Mass transport analysis has been used to calculate the supersaturation, AC, supercooling, AT, and transcerse growth velocity, V , of ice dendrites during solidijication from the dendrite spacings measured in the droplels. The ice dendrite spacing in a given solute increases lineary with the solule concentralion at a fixed freezing rate. The ualues of AC, AT, and V increase with an increase in solule concentration. The value of AT in the aqueous solution is of the same order of magnitude as in Al-Cu alloys of the same concentration; the dendrite spacings in Al-Cu alloys also increase with an increase in solute concentralion. For the jamily of aqueozrs solulions incestigaled, the dendrite spacing increases linearly with solute diffusivity at fixed values of concertralion and freezing ,rate. The values of ?C and ?T decrease, whereas the value of V increases with an increase in solule diffusicity. The measured dendrite spacings , L, can be expressed by the relatiun: L = K;(dfa/db) 4 K2C +K3D - K4 where dfs/d? is-change in fraction solid with time (freezing rate), C is solute concentration, D is solute diffusivit K1 = (14 * 4)pmin1'2, K2 = (70 ± 10) pl (moles)- K3 = (24 r 3) . l05 psec (cm)-~. K. = -132 ± 10) 1. FREEZING of solutions is almost always an ehunmix-ing" process because the composition of crystallizing solid generally differs from that of the parent liquid. " Solute concentration and transport are therefore in]portant considerations in solidification of solutions. The influence of these factors on the dendritic solutions produced from metallic solutions is of practical significance since the properties of the solid aggre-gate are often strongly influenced by dendrite spacing.''' Alexander and Fthines3 found that dendrite spac- ings generally increase with solute concentration in several metallic systems. Michael and Bever1 have observed an increase in a aluminum dendrite spacings in dilute A1-Cu alloys. Rohatgi and AdamsJ have reported a linear increase in a aluminum dendrite spacings with increasing copper contents up to 28 pct in A1-Cu alloys. Bolling and Tiller"' have theoretically examined the effects of solute concentration and diffusivity on the growth of cells and dendrites. Their analysis of dendritic growth assumes a steady-state growth and the maximum possible velocity for dendrite propagation. In addition, the quantitative analysis is restricted to dendrites of rotational symmetry and is therefore not directly applicable to the plate-shaped dendrites of ice obtained in the present study. There are practically no experimental observations of the effect of solute diffusivity on dendrite spacings in metallic systems. The reason appears to be the lack of experimental data on solute diffusion coefficients in liquid metallic solutions. The present work is concerned with the effect of solute concentration and diffusivity on dendritic solidification of dilute aqueous solutions: the solutes examined are potassium chloride. sodium chloride, lithium chloride. and hydrogen chloride. There were several reasons for selecting these solutes. The variation of dendrite spacing with freezing rate in these solutiolls is similar to that observed in A1-Cu alloys.8 These aqueous solutions have almost identical phase diagrams at dilute concentrations. Fig. 1. and the diffusion coefficients show very little variation with solute Concentration.9,10 Dendrite spacings were measured as a function of freezing rate. solute concentration. and solute diffusivity. Dendrite spacings were measured in two different types of freezing systems. droplet and unidirectional, respectively. In the droplet freezing system

Jan 1, 1970

By L. A. Weitzenkamp, N. M. Bashara

A study of the electrical conductivity of gold films less than 200 in thickness indicates a negative temperature coefficient of resistance and a thermal actiuatlon energy of less than 0.25 ev. The films consist of discrete metal islands of linear dimensions from a few angstroms to 1000A. Films were able to withstand applied fields up to 60,000 v per cm before breakdown occurred. A model for the conduction mechanism is proposed which involtes a Potential barrier due to work junction, irriage forces , and an electrostatic potential arising from separating an electron from a neutral island leaving behind a positively charged metal island. Activation energies of less than 0.25 ev ave consistent with this model, which includes a tunneling andor Thermal mechanism for conduction between the separate metal islands. An apparent satuvation effect in conductivity at high fields is observed experimentally. The saturation effect may be explained by the influence of the electrostatic contribution to the potential barriers for the transition through several islands adjacent to the original island which was activated to give up an electron. The proposed model gives Poor quantitative agyeement for the intermal electrical field between islands. ThIS paper will relate the structure of discontinuous metal films to the electrical properties and will emphasize the following topics: 1) the relation of the conduction mechanism to particle size and a comparison of particle size from electrical measurements with electron-microscope studies; 2) the saturation of the conductivity at high electric fields; and finally, 3) a comparison between the external field applied and the apparent field between particles. che- latter comparison points to a need for a modification in the model for the conduction mechanism first proposed by orter' and expanded by Neugebauer and webb2 which will be dealt with in the discussion. The paper is based on results on gold films on glass microscope slides. The clms were vacuum-evaporated and were about lOOA thick, thickness being measured by interferometry. It has been observed that metal films of this thickness do not exhibit bulk metallic conduction. Films thinner than some critical thiclmess, depending upon substrate temperature and other factors, have conductivities which increase with increasing temperature with thermal activation energies of less than 0.25 ev. Electron-microscope studies3 have shown that these films consist of discrete metal islands having linear dimnsions from a few angstroms to approximately 1000A. When the metal is being vacuum-deposited on the substrate, islands on the order of a few angstroms appear first. As the deposition continues the islands may tend to agglomerate into larger particles and may eventually grow together into a continuous film,3''' In our tests the conductivity of the gold films was found to be about ten orders of magnitude less than the bulk conductivity of gold. When oxygen was introduced into the test chamber the conductivity decreased by a factor of about one-third. This can be related to an increase in work function for gold caused by adsorption of oxygen, as reported by Oullet and Rideal.s Exposure to an atmosphere of water vapor caused an increase in conductivity by a factor of 2 or 3 when a low field was applied. When the films were exposed to water vapor under a high field the conductivity increased by as much as two orders of magnitude. The activation energies measured were much less than the work function for gold, 0.25 ev or less, with the smaller activation energies observed for thicker films. It will be shown that the activation energy is a function of particle size and spacing. In general the model for the potential between metal islands would include the effective work function, the image force, the applied field, and an electrostatic term. The electrostatic contribution arises from the potential required to separate an electron from a conducting sphere. According to Neugebauer and webb2 the maximum potential due to the field and the electrostatic term only is

Jan 1, 1967

By R. M. Keeney

Before the outbreak of the war in 1914, the only electric-furnace smelting plant operating on a commercial basis west of the Mississippi River was an electric pig-iron plant in California; rare metal ores were not smelted, concentrates of molybdenum, tungsten, uranium, and vanadium ores being shipped East for reduction. Practically no chrome ore was being mined, and only comparatively small amounts of manganese ore. Today there are two electric smelting plants in California, one in Washington, one in lowa, and four in Colorado; two plants are under construction in California, and one in Montana. Ores of manganese, chromium, molybdenum and tungsten are now smelted in the West, and although uranium and vanadium concentrates are still shipped to the East, they will probably be treated in western plants in a short time. The four electric-furnace plants in Colorado are listed in Table 1. Table 1.—Electric Smelting Plants in Colorado Capacity. Company Location KilowattB PRoductS Tungsten Products Co........... Boulder 800 Ferrotungsten, ferromo- lybdenum. Boulder Tungsten Production Co .. Boulder 400 Ferrotungsten. Ferro Alloy Co.................. Utah Junction 1200 Ferrochrome, ferrotung- sten. Iron Mountain Alloy Co......... Utah Junction 3000 Ferromanganese. Power for all of these plants is supplied by the Colorado Power Co. The plant of the Ferro Alloy Co., at Utah Junction, contains one 750-kw., three-phase furnace, to which power is supplied by three 250-lrw. transformers, connected /Y to give 129 volts on the furnace cables, the transformer ratio being 13,200 to 75 volts. The furnace operates with an actual voltage of 120 volts, and produces about 3 tons of ferrochrome per 24 hr. from 40-per cent. Cr2O3 ore. The furnace consists of a steel shell of circular cross-section, 8 ft. (2.43 m.) in diameter by 7 ft. (2.13 m.) deep, lined with magnesite, and having three vertical carbon electrodes 12 in. (30.48 cm.) in diameter. A 450-kw. furnace, of the same size as the 750-kw. furnace, is also operated on chrome ore. This furnace is three-phase in appearance, but operates electrically as a single-phase furnace. There are three vertical

Jan 1, 1920

By C. H. Stewart, R. A. Fagin

A two-dimensional, three-phasereservoir simulator was programmed for a large memory digital computer. It was designed to provide a practical solution to describing the complex physical relation between the natural forces and the physical properties of a heterogeneous reservoir when subjected to a specific set of conditions. A reservoir study is briefly described to illustrate application of the model. A full volumetric account of three phases (oil, gas and water) is performed simultaneously throughout an integration net representing the reservoir. Absence of one or two of the phases is treated as a special case of the more general situation. Expansion (or contraction) of all phases, including rock expansion, is performed so that the pressure calculation is the general unsteady-state case. To account for the large variations of subsurface elevation encountered in some reseruoirs, and to allow for segregation of the various phases, a gravity head term is included in the basic drive potential. Appropriate fluid and rock properties are used in polynominal surface form (functions of pressure and/or depth) or they can be entered as space variables at each position of the integration net. An unsteady-state water influx calculation, based on the method of van Everdingen and Hurst, l was connected to the boundary of the matrix to simulate aquifers of various sizes. In addition to reservoir calculations, three-phase fluid flow from the producing depth to the wellhead, including provisions for gas lift, was incorporated in the simulator. A workover routine was also built which can automatically switch to a different set of production relations when a gas-oil ratio or water fraction reaches a limit; or it can shut-in the well if prescribed. INTRODUCTION This paper describes a reservoir engineering mathematical simulator used to represent the complex interaction of natural forces and physical properties of a reservoir during natural depletion or with various injection schemes. The simulator, which was programmed for a large memory digital computer, is a two-dimensional calculation which handles three mobile fluid phases simultaneously (oil, gas and water). Basic requisites for the method are individual well production and pressure data, hydrocarbon fluid properties, geological data (producing depth and net sand), capillary pressure data, relative permeability data and permeability and porosity information. Matching the past performance of a combination drive reservoir often has yielded information concerning continuity and the validity of basic data. Detailed predictions of future performance can be made for continuation of current depletion methods (natural depletion) as well as for various types of recovery by gas or water injection. Combination injection cases and pattern studies can also be performed. Workover programs, gas lift and different types of artificial lift programs have been investigated using a technique similar to that described by Kern and Nicholson2 except that conditions of pressure and saturation at the block within which the well is located are used rather than average reservoir conditions. Drilling additional wells to optimize profit was explored, both as to number and location, by placing wells at different spots within the reservoir matrix. Special depletion processes can be examined, such as upstructure drainage and lateral (or strike) waterfloods in thin oil columns. In one case the mathematics of the simulator were modified to calculate the displacement in the vertical plane rather than in the horizontal plane. In this manner specific reservoir problems can be studied, such as coning of gas and/or water around production points, fingering along permeable stringers or, more generally, frontal advances in a heterogeneous section.

Jan 1, 1967

By A. H. Daane, J. F. Haefling

The limits of miscibility in some of the uranium rare-earth alloy systems have been determined in the temperature range 1000°to 1250°C. The solubilities of lanthanum and cerium in uranium are greater than those of the remaining rare earths by a factor of more than two. The solubility of uranium is greater in cerium, braseodymium, and neodymium than in the other rare-earth metals studied. The values found in this study are in qualitative agreement with those which might be expected if the solubility rules of Hildebrand and Scott are applicable. AS interest in nuclear reactors intensifies, many new types of fuels are being suggested in attempts to improve the economics of some of the proposed reactor schemes. To remove some of the difficulties inherent in the use of solid-fuel elements and their reprocessing, many types of liquid-metal reactors have been suggested. One of the more attractive features of several of these reactor concepts is that they include a continuous or semicontinuous process for the extraction of fission products and "bred" fissionable materials from the fuel, utilizing immiscible metal extractants. This would enable a much higher burn-up of fissionable material to be achieved and would present a very attractive economic picture. Several studies have been reported on equilibrium systems in which there exists a high degree of immiscibility between uranium and another metal that might be used as an extractant in such a processing scheme.' Two of these systems in which a high degree of immiscibility exists are those of uranium with the two rare-earth metals, lanthanum, and cerium. Since the rare earths constitute a significant fraction of the fission products, their removal is of prime importance. It is reasonable to believe that this might be accomplished by equilibrating a rare-earth phase with the contaminated uranium fuel in the liquid state. In order to make a more complete study of those systems which would be of interest either as extractants in a liquid-liquid extraction process, or as fission products formed in the fuel, the alloy systems of uranium with lanthanum, cerium, praseodymium, neodymium, and samarium were studied in some detail in the temperature range 1000" to 1250°C; less detailed studies were made with the other rare earths. In addition to being of value to the reactor program, the data obtained in this study should be of help in making a study of the role played by the electronic structures of metals in determining the nature of metallic solutions. The unique electronic structures of the rare-earth elements make them particularly interesting in this respect. EXPERIMENTAL The usual procedure for a solubility determination was to seal equal volumes of uranium and the particular rare earth in a tantalum crucible under an atmosphere of helium; this crucible was then sealed in a stainless steel jacket in an atmosphere of helium. These samples were equilibrated by repeated inverting of the crucibles in a furnace for 15 min at the desired temperature, left in an upright position for 15 min to permit separation of the two phases, and then quenched under a stream of water. In some runs the temperature of the furnace was held 50' to 100°C above the desired quenching temperature while inverting in order to insure good mixing. However, it was found that above 1200°C the crucibles were subject to failure and for these runs the furnace temperature was not raised above the desired quenching temperature. A small amount of tantalum was dissolved in the uranium and the rare earths in these runs, a maximum of 3 wt pct in the uranium phase at 1250°C and up to 1 wt pct in the rare-earth phase at this temperature. On cooling, the major portion of this tantalum precipitated as primary tantalum crystals. Any residual tantalum would probably have a negligible effect on the mutual solubility of uranium and the rare earths in each other. Samples for analysis were cut from each phase with an abrasive cutting wheel; the region near the interface between the two metals was carefully avoided. In the case of the rare earths with melting points above 1250°C no solubility data were taken on the rare-earth phase since this phase could not have achieved equilibrium in a reasonable length of time. (For the same reason no data were taken on the uranium phase below its melting point of 1132°C.) Equilibrium appeared to have been reached in the uranium phase in these cases although the rare-earth phase had not melted. To verify this, samples were melted together in an arc furnace similar to that described by Kroll.2 These samples were sub-

Jan 1, 1960

By J. T. Pardee

INTRODUCTION PLACER is a Spanish word, the definitions of which include "an extensive bank of sand or gravel" and "a place where currents of water deposit particles of gold."l The term, probably first used in the western hemisphere by Spanish or Mexican gold miners, is now generally applied to all detrital deposits that yield valuable minerals by washing. In the Western States placer products other than gold, including the silver alloyed with it, are chiefly sapphires, produced in Montana, and platinum alloys recovered in California and Oregon. During the war tungsten ore (scheelite) was obtained from placers in the Atolia district, California, and a number of diamonds have been found in the Sierra Nevada gold belt. Small amounts of stream tin have been produced in the Black Hills of South Dakota and a little monazite sand in the Boise Basin. Idaho. Magnetite, chromite, ilmenite, zircon, and other useful minerals are more or less abundant in the beach placers of the Pacific coast and in the heavy residues of placer mining elsewhere, but the problems of profitably separating and marketing them remain to be solved. Minerals of lead, quicksilver and other metals occur in many of the placers and although not plentiful enough as a rule to be worth recover-ng, their presence has, in several instances, led to the discovery of valuable lodes, notably at Leadville, Colorado. Historical summary.-In New Mesico, Arizona, and Southern California, placer gold was mined by Mexicans and Spanish priests in the first half of the 19th century or earlier. With these exceptions history of placer mining in the Western States begins with Marshall's discovery of gold in northern California in 1848. During the next twenty years placers were found in all of the principal mining districts that are known today. The richer deposits were soon mined out but a relatively large production was maintained from the leaner deposits chiefly by hydraulic

Jan 1, 1933

By R. L. Slobod, B. H. Caudle, R. A. Erickson

In predicting the sweepout pattern efficiency to be expected in a .secondary recovery operation, the reservoir engineer is often confronted with a situation in which part of the producing formation lies between the last row of wells and the reservoir boundary. To date, there has been little or no reference in the literalure to sweepout pattern efficiencies in such areas. This paper presents the results, of a laboratory study in which the area contacted around the edge of a reservoir injected in a five-spot pattern was determined. The X-ray shadowgraph technique was used in this study. It was found that surprisingly large portions of the reservoir area lying outside the well network are conracted by the injected fluid before, abndonment conditions are reached. In fact, it can he said that at least 00 per cent of the circa lying outside the last row of wells and within a distance of one well spacing of these wells will ultimately be contacted by the injected fluid in the case of most water floods. Frorn the results given in this paper, it is possible to estitilate not only the extent to which encroachment into these areas will occur but also the injection volume necessary to produce the wells to abnndonment conditions. INTRODUCTION While considerable work has hern done in recent years1.?.'.''.' evaluating the fraction of the reservoir contacted as a function of the mobility ratio for several different well patterns, there has been practically no mention of what happens to the oil in that portion of the reservoir which lies between the last row of wells and the reservoir boundary. In fact, the assumption is generally made that little or no recovery can he expected From this area. This assumption is incorrect and in many cases will lead to seriouq errors in calculating reservoir performance. The fraction of the area outside the regular well pattern contacted in a five-spot injection system has been studied using the X-ray technique5 to follow the progress of actual floods in porous models of reservoir elemental areas. In this paper, the method for carrying out such a study and the results showing the fraction of the area in question swept as a function of mobility ratio and the produced fluids are presented. THE REPRESENTATION OF A RESERVOIR BY ITS ELEMENTAL AREAS She portion of the reservoir lying between the edge of a reservoir and a line connecting the outermost wells may be roughly designated as the part of the reservoir outside the regular well pattern. An example of such an area is shown as the shaded portion in Fig. 1. The case of a square reservoir utilizing a five-spot injection program and with one full well spacing between the outermost wells and the boundary (Fig. 1) was selected as the single example which would provide the most insight into

Jan 1, 1956

By E. P. Klier, Taylor Lyman

THE structures formed when austenite is quenched to subcritical temperatures and allowed to transform isothermally have been the subject of intensive study since the work of Davenport and Bain.1 Isothermal transformation diagrams summarizing the results of many of these studies have become widely familiar to metallurgists. Of particular interest to metallographers are the dark-etching, acicular products of transformation formed by isothermal reaction below the temperature of maximum velocity of the austenite to pearlite reaction. These products, the bainite structures, can be formed in a wide variety of steels. However, the constitution of bainite is not well understood and divergent views have been expressed as to its mode of formation. In this investigation a combination of dilatometric, microscopic and X-ray methods has been brought to bear upon the problem in the hope of some elucidation of the bainite reaction as it occurs in hypoeutectoid steels. MECHANISM OF BAINITE FORMATION Davenport and Bain1 considered the mechanism of bainite formation to consist of two steps-an allotropic transformation followed by precipitation of carbide. The separation in time of the two processes was considered to be very slight in the upper temperature range and very marked at temperatures just above the martensite range. This concept has been restated by Vilella, Guellich and Bain2 in the form of a definition of the acicular mode of transformation as: The successive, abrupt formation of flat plates of supersaturated ferrite along certain crystallographic planes of the austenite grains; this supersaturated ferrite begins at once to reject carbide particles, (not lamellae), at a rate depending upon temperature. In effect, this is the acicular mode of transformation, even though the temperature be such as to limit the actual life of the quasi-martensite to millionths of a second. The investigation of isothermal decomposition of austenite in certain alloy steels (notably those containing chromium or molybdenum) has revealed that there may be a range of temperatures between the pearlite and bainite reactions in which the austenite decomposes at a relatively low rate.3-6 Further, it is characteristic that in the second region of fast reaction the decomposition of the austenite is incomplete by one reaction but goes to completion by a second reaction. These observations led Wever7 to a description of the bainite reaction as follows: I. The reaction takes place by initial precipitation of a martensitic intermediate structure. 2. In the upper temperature range this structure readily decomposes into ferrite and cementite. In the lower range carbon separates in an unknown form. 3. In the upper temperature range the precipitated carbide nucleates the precipitation

Jan 1, 1944

By Paul A. Taylor

MUCH information concerning pegmatites which was thought to be true a few years ago has been proved false, and what is now actually known about some pegmatites is not true of many others. The erratic and seemingly unpredictable structure and variable composition of this class of mineral deposits has been widely emphasized. Even parts of the same pegmatite body exhibit marked differences in texture, mineral composition, width, and attitude. Constructive geological thinking in respect to pegmatites now aims to establish general laws rather than to stress the confusing diversity of features having no special economic significance. Substantial progress has been made in classifying different types of these deposits according to general features, internal structure, mineralogy, and origin. In some cases it has even been possible to block out tonnage reserves in advance of mining. It is still easy, however, to make highly erroneous predictions after a preliminary examination of a pegmatite prospect. Pegmatites are important to the economic well being of the country and to its military security. They furnish virtually all the feldspar, strategic mica, beryl, columbium, tantalum, and caesium utilized in the United States, as well as sundry other minerals and significant amounts of lithium and rare earth minerals and gems. With the exception of vermiculite, occasional ilmenite-rutile, and perhaps soda-lime feldspar and garnet deposits, basic pegmatites are of little economic importance. Consequently in this paper, as in common parlance, the term pegmatite generally relates to coarsegrained acidic rocks or what is aptly called giant granite. Available data indicating the size and importance of the production and trade in specified pegmatite minerals are summarized in Table I. Geological Features Much of the latest thinking on the economic geology of pegmatites is now available in a 115-page monograph' by a group of experts who participated with geologists of the Federal Geological Survey in the widespread wartime investigations. Doubtless the most significant feature of the monograph is indicated by the title, The Internal Structure of Pegmatites, but it also contains a vast amount of other new information and includes the assimilated concepts of many earlier writers, whose works are given in a comprehensive list of references. The shape, size, attitude, and continuity of many pegmatite bodies is controlled by the structure of the older rocks in which they occur. If the older rocks are easily penetrated, e.g., biotite schist, most of the pegmatites in a given district will be found outside the parent granite mass as exterior pegmatites. Marginal pegmatites are more prevalent if the older rocks are massive, unsheared, and sparingly jointed. Networks of pegmatites are abundant in highly-jointed rocks. In strongly foliated schists the bodies are usually lenticular, whereas in highly-folded areas they assume tear drop, pipe or pod-like, bow-shaped, or sinuous forms. Jahns2 recognizes five major shape classes: l—dikes, sills, pipes, and elongate pods; 2— dikes, sills, pipes, and pods with bends, protuberances, or other irregularities; 3-—trough-or scoop-shaped bodies with or without complicating branches; 4—bodies with the form of an inverted trough or scoop; and 5—other bodies, including combinations of the above and miscellaneous shapes. Many pegmatite deposits are scarcely big enough to be recognizable as such. Most of them, in fact, are small tabular deposits less than 4 in. wide and usually without economic concentrations of minerals. On the other hand, some pegmatites are more than a mile long and over 500 ft wide. The ratios of length to breadth range from 1 : 1 to 1 : 100. Although the vertical dimension bears no invariable relationship to strike length, tabular deposits or large lenses are often symmetrical enough to show nearly as much continuity down dip as in their horizontal extension, and some pipes or pods are amazingly persistent in the vertical plane. Small pegmatites often string along a fairly definite trend line; in a given district major bodies may lie roughly parallel, and where only a few of them do not, the erratically disposed bodies generally differ in composition from those conforming to the regular pattern. This does not apply, however, in all districts. Characteristically, pegmatite veins pinch and swell or split into branches. When they pinch out entirely it is often possible to find a new body by prospecting the extension of the strike or dip, but the chances of finding a hidden deposit are ordinarily too uncertain to justify much subsurface prospecting. Diamond drilling may yield valuable information as to the continuity of known deposits whose upper portions are well-exposed. Some deposits, in fact, can be proved up for hundreds of feet by surface trenching and then intersected by drill holes at various depths like any other vein-like deposit. Others twist and branch, apparently defying all efforts to explore them short of actual mining.

Jan 1, 1954

By E. Lifshin, R. E. Hanneman

QUANTITATIVE applications of the electron micro-beam probe frequently involve the evaluation of complex mathematical expressions and/or the analysis of large amounts of experimental data. The purpose of this communication is to describe briefly a versatile and useful computer program system that is applicable to analyze rapidly a wide variety of practical microprobe problems. This system consists of a group of ten FORTRAN programs that can be stored on tape, cards, or in the memory disc of the computer. These programs, or links, can be run individually or in any prespecified sequence without interrupting the operation of the computer or without destroying information which is being transfered from one link to another. For the program system described here a GE-235 computer with disc storage was used, so that the DCHAIN method of program linking was employed. Included in the library are programs to: 1) initiate analysis of a new set of data and transfer control between all other programs in any predetermined manner; 2) generate theoretical calibration curves of composition vs relative intensity; 3) generate empirical deviation parameters from least-square fits of experimental calibration data from standards of known composition; 4) convert raw X-ray data to corrected composition; 5) determine inter diffusion coefficients by Matano analysis of con centrat ion -distance data on a uniaxial diffusion couple; 6) determine activation energies and frequency factors of temperature-activated processes such as diffusion; and 7) generate calibration curves for determination of the thickness of thin films using microanalysis. A detailed description of these computer programs and their underlying principles is available on request from the authors."' The first program to generate theoretical calibration curves of corrected relative intensities vs composition uses the Poole and Thomas atomic number correction' and the Philibert absorption factor' with a voltage-dependent mass absorption coefficient for electrons in the alloy. A modified Castaing fluores- cence correction is also used which includes the effects of both Ka and KO radiation and over voltage.' Once the theoretical curves have been calculated in 1 wt pct intervals, these results are least-squares fit to obtain Ziebold deviation parameters' which are stored in COMMON in the computer memory. The net discrepancies between the original theoretical calibration curve and the regenerated curve using the Ziebold parameter are computed. Although this link is explicitly written for K-K fluorescent interactions, it can be applied to K-L, L-K, and L-L interactions as previously disc~ssed."~ Similar programs have also been written to utilize the Wittry fluorescence correction, Birks combined corrections, and various other corrections.' These modified programs have proved to be quite useful for quantitative comparisons of the results of the various theories. The program for conversion of raw X-ray data to corrected composition includes corrections for drift, backround, and instrumental dead time. The corrected intensities are converted to composition by use of the Ziebold equation"2 and parameter obtained from the program system. The results can be obtained for either atom or weight fractions. In addition to accurately computing interdiffusion coefficients the Matano analysis program calculates least-square smoothed values of concentration, concentration gradient, and curvature for each point on the raw input concentration profile. In order to obtain high accuracies a unique method of performing a least-square polynomial fit to incrementally advancing profile segments which overlap is used.' This program has been successfully modified for use in ternary diffusion problems3 and can readily be modified to handle analysis of diffusion profiles which include phase boundary discontinuities. This link is generally applicable to analysis of interdiffusion data obtained by other techniques as well as by the microprobe. The primary function of the next program is to least-squares fit experimental diffusion data to the normal Arrhenius function: D = Doexp(-Q/RT), to obtain values of Do and Q. In addition the probable error and one, two, and three u statistical confidence limits of DO, Q, and log D are evaluated. This program is also directly useful for analysis of any other simple temperature-activated processes including conductivity, and certain deformation and chemical processes. The program to generate calibration curves for film-thickness determination using the microprobe is based on a numerical integration of the equation derived by Cockett and ~avis.' Values of film thickness obtained by this program for copper on various substrates are in good agreement with measurements made by other techniques. Versions of the above program system have been prepared for use with or without a remote teletype connection to the computer for processing on either a real-time or time-share basis. The instrumentation coupling a microprobe to a teletype for automatic data collection and analysis by the presently described program system has been reported elsewhere by the authors.' If teletype equipment is not used to communicate with the computer, standard methods of card reading and tape reading can be used. In either

Jan 1, 1967

By W. C. Ellis, E. S. Greiner, M. E. Fine

Discontinuous changes of Young's modulus, internal friction, coefficient of expansion, electrical resistivity, and thermoelectric power are evidence for a transition in chromium near 37OC. Although the X-ray diffraction pattern gives no clue, a difference between the thermal expansivity and the temperature dependence of the lattice parameter suggests a crystal-lographic change. Young's modulus data disclosed another transition near THE thermal dependence of a number of proper- ties of chromium indicates a transition occurring over a temperature range near room temperature. Bridgman' noted this first from a minimum in the electrical resistivity near 12°C. In a sample of greater purity, Sochtig' observed the minimum at 41 °C. Erfling3 reported an inflection in the thermal expansivity curve at 36°C. These temperature-dependence curves are reversible with no hysteresis being detected. No discontinuity or inflection has been observed in the heat capacity' or the paramagnetic susceptibility.' Likewise, no one has noted a change in crystal symmetry. In the present investigation Young's modulus, internal friction, coefficient of expansion, electrical resistivity, illustrated in Fig. 1, lattice constant, Fig. 2, thermal electromotive force, Fig. 3, and paramagnetic susceptibility, Fig. 4, were measured over an extended temperature range. The samples were prepared in two ways: (1) By cold pressing a sintered electrolytic powder compact,' and (2) by electroforming from an aqueous solution. The electroformed samples were prepared by R. A. Ehrhardt and G. Bittrich by plating on copper or nickel tubes from an aqueous solution according to the method of Brenner, Burkhead, and Jennings.' The pressed powder samples (method 1) were finally annealed at 1400°C in purified helium: the electroformed samples, packed in powdered chromium, were vacuum-annealed at 1000°C. From the composition of the original powder' the purity of the pressed powder samples is estimated to be 99.8 pct Cr. Spectrochemical analysis furnished by E. K. Jaycox, revealed only slight traces of impurities in the electroformed sample (less than 0.001 pct), neither iron nor nickel being detected. Chromium deposited by this method is reported to contain approximately 0.05 pct 0.- Methods and Data Young's Modulus: For measurement of Young's modulus, an annealed, pressed powder sample, 0.114 x0.237x1.845 in., and an electroformed sample, 0.10 in. od, 0.01 in. id, and 1.86 in. long, were prepared. The resonant frequencies of the rod samples in forced longitudinal vibration were measured at a series of temperatures from —192" to 200°C by a method previously de~cribed.6,7 Because the samples were nonferromagnetic, iron- silicon or molybdenum permalloy tips (0.013 in. thick) were soldered to the ends. The softening temperature of the solder limited the temperature of measurement. Young's modulus, E,, of chromium at temperature, T, may be calculated from the resonant frequency of the composite rod, f,; the thickness of the tips, t; the length of the chromium sample at 25°C, l,.; the density of chromium at 25°C, pc (7.20 g per cc);5 and the thermal expansivity, Al/l25. Modulus differences for two temperatures, ET and E, are accurate to +0.002x10" dynes per cm2. ET = 4PAlc+2tyf Young's modulus at 25°C, Fig. la, is 28.2~10" dynes per cm' (40.8xlO" si) in wrought chromium (upper curve). The modulus of the electroformed sample is apparently lower due to cracks. From the modulus measurements two transitions were observed: one with a critical temperature at 37°C, the other at —152°C. Internal Friction: The internal friction, 1/Q, was determined from the width, Af, of the strain amplitude-frequency curve at 0.707 times the strain amplitude at resonance;' the internal friction, 1/Q, then equals Af/f. Fig. lb shows a sharp peak in internal friction at 38°C. The internal friction of the electroformed sample had a similar maximum. Thermal Expansion: The expansivity measurements, shown in Fig. 2, covering the temperature range —195" to +400°C were made by D. MacNair in an interferometric dilatometer8 sing a sample consisting of three pyramids 0.25 in. high prepared from wrought electrolytic chromium. Below —120°C the experimental points deviated up to ±2x10 from the drawn expansivity curve in Fig. 2 because of decreased precision of the quartz wedge thermometer at low temperatures. Near 38°C the thermal expansivity curve, Fig. 2, goes through an inflection corresponding to a minimum in the coefficient of expansion, Fig. ld, and a relative volume decrease on heating. Electrical Resistivity: The variation of electrical resistivity with temperature measured by the po-tentiometric method is also shown in Fig. l. The resistivity of the wrought chromium (upper curve) at 20°C is 13.6 microhm-cm; of electroformed chromium (lower curve) 12.8 microhm-cm. The lower value reflects higher purity and agrees closely with a published value." A minimum at 40°C occurs in the resistivity curves of both samples. No conclusive evidence for a transition near — 150°C was observed, but the points, Fig. 1, appear to deviate from a smooth curve between —120" and —160°C.

Jan 1, 1952

By George W. Pawel

OWING largely to its value as a toughener and strengthener of steel for both industrial and military purposes, nickel is playing, an important role in the current war. It is fine of the metals in which the Allies enjoy a definite edge over the Axis nations and this time there is no place to which the Germans may send another submarine "Deutsehland" and expect to pick up a cargo of nickel to replenish their exhausted supplies. Total world nickel production thanks almost entirely to the expanded operation of the International Nickel Co. of Canada at Sudbury must now be at the rate of around 175,000 tons a year scarcely more than 5 per cent of which is accounted for by Germany, Italy and Japan. This represents more than four times the world output at the end of the first World War.

Jan 1, 1943

By Robert Palmer

So MUCH has already been written on this vast subject of ground movement and subsidence, and so many data collected and commented upon, that in this paper the author proposes to confine himself to the submission of some plans showing what has actually occurred in the mining of several of the orebodies which have, come under his direction during the last 20 years or so at Rio Tinto, Spain. Some notes are added for the purpose of describing the plans. The author does not attempt to give his opinion as to the reasons why the subsidences have occurred in the manner in which they are found, but confines himself to giving as true a picture as possible of the movements that have taken place.

Jan 1, 1930

By M. H. Merriss

IN THE last few years, there have been developed at the plant of the Nichols Copper Co., Laurel Hill, Borough of Queens, New York City, improvements in electrolytic copper refining by the series system that have materially increased the flexibility and economy of that system. The purpose of this paper is to discuss, as of interest to refiners and to those who have copper to refine, as well as to the engineering profession in general, the changes that have taken place resulting in wider application and increased efficiency of the series system. Copper is electrolytically refined in two ways, which are spoken of as the "multiple system" and the "series system." In both systems, the electrolytic tanks are in series electrically. In the multiple system the electrodes in a single tank are in multiple or in parallel, thus: In the series system, the electrodes in a single tank are in series, thus: There are two important adaptations of the series process, one represented by the series electrolytic tank room at the Baltimore Copper, Smelting & Rolling Co., Baltimore, Md., and the other by that of the Nichols Copper Co.'s plant. At Baltimore, the anode is rolled to perfect

Jan 6, 1925

By George A. Roberts

The development of an alloy system, high-speed steel, is used as an example of the progress of physical metallurgy. Tracing the history of men and their thoughts as they studied and invented and modified these materials, the story of high-speed steel since the 1890's is seen to be a long, slow, but steady progression of achievements. Today's multiplicity of high-speed steels are the result. Data are presented on quantitative metallography of carbides in high-speed steel with high vanadium content using the QTM instrument. Grindability as well as mechanical properties are related to the content of excess MC and M6C carbides in a series of high-speed steels and the newer matrix steels. These emphasize the present state of knowledge and show the current stages of thought that may affect the development in succeeding years. It is a great thrill for me, an ex-research metallurgist and ex-practicing metallurgical engineer, to speak to an audience currently engaged in both pursuits on the occasion of the 43rd Howe Memorial Lecture before the Iron and Steel Division of the AIME. I shall not review Henry Marion Howe's distinguished career, so adequately reviewed in Maxwell Gensamer's contribution in the 1965 AIME History of Metallurgy, except to point out that, while leading the life of an intellectual, he worked as a practicing research metallurgist and a practicing metallurgical engineer for significant periods of time and contributed greatly in both areas. For those of you who believe, as I do, that in the intellectual activity of metallurgy we are blessed with an intimate mixture of science and engineering (see Mehl's 1960 Howe Lecture), we might recall that Howe, while pursuing a life of writing and teaching in later years, served as the first Chairman of the Division of Engineering of the National Academy of Sciences. That metallurgists were called upon then to lead an engineering recognition movement is perhaps related to the strong part played by the AIME and its members in the recent establishment of a National Academy of Engineering and to the fact that a metallurgist is its head, 47 years after Howe served. I stress these engineering aspects for I wish to talk about a metallurgical engineering subject today. Alloy systems, physical metallurgy, and steel blended with an historical perspective and a report on new techniques to improve the old will, I trust, be of sufficient interest to bring these lectures back to the physical-metallurgy banner from which they have departed for 4 years. Those process metallurgists, open-hearth fiends, and physical chemists among you will just have to be patient. The development of an alloy system is the engineering application of scientific thought and fact. There are many interesting alloy systems, developed to a high degree of technology and sophistication over the past 40 to 70 years. These systems are bound together and related by a similar set of characteristics. For example, stainless steels are a system in which the members are related by a high chromium content which gives a corrosion-resistant characteristic. A subfamily in this system would be austenitic steels

Jan 1, 1967

By C.H. Davis, W.H. Bassett

The ease and value of the application of spectrum analysis to industrial chemistry appears to be appreciated in few of the large works laboratories of this country. For 8 years, this analysis has been of great value to the authors in both analytical and metallurgical work. To the analyst the complete qualitative analysis of an unknown alloy, revealed by a spectrogram, is a sure basis for the planning of the most direct and rapid method of attack. As the determination of each element proceeds, the purity of precipitates may be checked as often as desired. The spectrograph proves invaluable in the recognition of impurities, the separation of which would entail a lengthy and difficult procedure, or when the weight of an unknown is less than is necessary to complete the desired determinations. A few hundredths of a gram will usually suffice for spectrographic analysis. In the separation of the rarer elements, the spectrograph will show, with precision, the point where each step has been successful. In zinc of certain classes, indium, gallium, and germanium have been isolated in this way; the presence of antimony in lake coppers has been proved; and bismuth has been detected in zinc and in alloys where the presence of a few thousandths of a per cent. would be harmful. An antimony precipitate in a delicate determination may contain a considerable proportion of tin or arsenic, both of which will be revealed. The spectrograph is consequently important to the metallurgist as well as to the analyst. Impurities in raw material are often a source of annoyance, especially when their detection involves delay and costly analytical work. Whethcr low conductivity in copper is due to arsenic, nickel, or something else may be cluickly found out. Residual traces of boron, magnesium, manganese, silicon, vanadium, and other deoxidizing agents are easily identified where wet analysis may fail to reveal their presence, even after days of effort. Complex alloys of any kind are dissociated by the spectro-

Jan 1, 1923

By Sam Tour

Some years ago, the writer described heat checks or thermal cracks that occur in die-casting dies.' The life of dies was considered in relation to. the casting temperature, the material used for the die and the heat to be absorbed by the die per unit volume of casting made. The mechanism of the action that results in thermal failure of dies was described. In the present paper the writer proposes to describe some additional observations in regard to heat checking, make one or two suggestions as to the method or methods for further attack of the problem, and give the results obtained on some work carried out along these lines. Importance of Heat Checking Heat checks in steel are the source of trouble in many industries besides that of die casting. Every shop where metals are subjected to hot working is searching for improvement and hoping for a cure. The development of a material of sufficient strength to be used as a die and yet devoid of the property of heat checking would be a godsend to many shops and many industries. The need for thorough study and research on the subject is evidenced by the wide variety of hot-working die steels on the market. It is peculiar, but true, that in practically every case the maker of the steel can give concrete evidence to prove his contention that his type of hot-working die steel is as good as or better than any other. A number of steel companies have several hot-working die steels from which choice can be made to fit a particular set of requirements. Possibly to expect one material to be universally the best hot-working die steel is unreasonable. In some hot-working operations, as in drop forging, the die must have great toughness to withstand the stresses developed; in other operations, as in hot piercing or punching, resistance to erosion at high temperatures, possibly defined as strength and hardness at elevated temperatures, is required. In still others, as in die casting, only sufficient hardness to resist scoring between moving surfaces is required, whereas the resistance to sudden changes in temperature must be at a maximum.

Jan 1, 1935

By Gustaf Ising

For relative gravity measurements, the author in 1918 described an instrument1 of which the essential part consists of a highly astatized, standing pendulum turning about a horizontal elastic axis. This type of instrument has been used recently in practical field work, therefore a description of its principle and technical development is given herein. Part I, describing the principle, is a direct translation of the original Swedish paper.l Part II gives an account of the practical elaboration of the instrument, together with some description of measurements performed. I. Principle of Using Astatized Pendulums1 In order to reduce the trouble and waste of time attending the use of ordinary pendulums in measuring the force of gravity, various instruments of another type have been suggested for relative determinations, as a rule arranged in such a way that the attraction of the earth on a certain body or mass of fluid is balanced by elastic force from a spring or a shut-in mass of gas. A change in the force of gravity is then made manifest as a change in the position of equilibrium of the body, in that the deformation of the spring (or compression of the gas) is changed. With such instruments there are, however, great difficulties in keeping the elastic force constant or its variation known with sufficient exactitude, because of elastic after-working, influence of temperature, and so on. The author suggests for relative determinations of gravity another type of instrument, in which two directional forces (control coefficients) rather than two forces are compared with one another. By "directional force" or "control coefficient" is meant that quantity in a rotatable system that, multiplied by the angle of deflection, indicates the moment counteracting the deflection. In this way it will be possible greatly to reduce the influence of the elastic after-working, which in instruments with spring devices acts so disturbingly. The instrument is made with a rotatable system arranged in such a way that the total control coefficient acting upon it, is composed

Jan 1, 1940

By W. A. Bruce

This paper covers the theory and present state of development of an apparatus for the nonmathematical analysis of complex problems of reservoir and well behavior. At the present stage of development of this apparatus, it is capable of solving the water-drive problem of any reservoir performance for which a mathematical solution has been presented in the literature, either on the basis of steady or unsteady-state flow analysis. The theory is presented for the extension of the scope of this analyzer along the lines of the present development. The resulting apparatus should be able to solve reservoir-performance problems previously thought too difficult for practical solution by mathematical means. As an illustration of its operation and present scope, the analysis of a reservoir problem and synthesis of expected performance is presented. Introduction In this method† of analyzing problems of petroleum-reservoir and well behavior, the porous continuum of the reservoir is assumed to be divided into small blocks, or units. Each block is assumed to be small enough so that for a material balance on the fluids in the block an average pressure for the block can be used. In analyzing reservoir behavior from this point of view by mathematical means, a set of simultaneous difference equations would be obtained (two for each block), which must be solved or combined into a partial differential equation. In the method to be described here, instead of solving these sets of equations analytically, electrical units are constructed, which will behave in respect to the flow of electricity exactly as the reservoir units behave under various conditions of fluid flow. The electrical units are then wired together in the same way that the reservoir units are connected naturally by virtue of their geometrical locations and shapes. Fluid-Flow Equations Consider a block in a reservoir. Assume that reservoir fluid (or fluids) is flowing in at one face and out at the opposite face, and that the block is small enough so that at all points the stream lines are within one degree of perpendicular to the face. Furthermore, assume that the pressure, pi, at the upstream face (Fig, I) is not more than one per cent greater than P2 the pressure at the downstream face. A material balance will show that the mass of fluid flowing out less the mass of fluid flowing in will equal the change in density times the fluid volume. This is expressed in the equation:

Jan 1, 1943