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Jan 1, 1958

By J. D. Meakin

The self-diffusion coefficients of ß tin have been deterttlltled using a plating and sectioning technique. The principal diffusivities pavallel and perpendicu1ar to the "c" axis are given by the Arrhenius relations Dc = 8.2 exp (-25,600/RT) sq cnl per sec and Da = 1.4 exp (-23,300/RT) sq cm) per sec. The results are discussed in terms of a vacancy mecharism of diffusion. In conjunction with an investigation of diffusion in dilute indium-tin alloys we have reexamined self-diffusion in tin single crystals. The published self-diffusion coefficients of tin, eensham') have always appeared anomalous in comparison to diffusion data for other metals and do not correlate with parameters derived from creep tests.' In addition to the necessity of confirming the self-diffusion values for use in analyzing the alloy work, self-diffusion in an anisotropic lattice is of considerable fundamental interest and confirmation of the published data seemed worthwhile. For a crystal with an axis of symmetry three-fold or higher the diffusivity at an angle 6 to the axis is given by D? = (Da - Do) sin2?+ Do [1] where Da and Do are the principal diffusivities perpendicular and parallel to the axis. For a particular diffusion mechanism, again in a crystal of axial symmetry, these principal diffusivities are [2] Do - ? ?i2 COS?i In these expressions ?i is the displacement undergone by the ith atom and 8, is the angle this displacement makes with the symmetry axis. In this, as

Jan 1, 1961

By Harry R. Hall

The proposition to make pig-iron from magnetic concentrates and cobbed ore with charcoal-fuel weighing from 12 to 20 lb. per bushel is, on the face of it, not inviting; but the work that has been done under these adverse conditions may be worthy of record as furnishing a comparison with coke blast-furnace practice under similar conditions.' The record of the furnace-practice is briefly summarized as follows :—the charcoal was made of hemlock, pine, spruce, balsam, maple, beech and birch woods. All the concentrates, containing from 62 to 65 per cent. of iron, would pass 1/8in. screen, of which about 34 per cent. would pass an 80-mesh screen. The cobbed ore, varying in composition from 32 to 47 per cent. of metallic iron and from 23 to 32 per cent. of silica, would pass through a 1-in. ring, and of this ore about 25 per cent. would pass a 1/8-in. screen. The furnace was blown-in October 20, 1903, with charcoal which was supposed to weigh, when dry, 18 lb. to the bushel. Some charcoal similar to this was stored in the stock-house for about a year, and was then found to weigh 12 lb. per bushel.

Jan 1, 1906

By H. Eklund, R. T. Hukki

This article presents a simple arithmetic derivation for the relationship between sharpness of classification and circulating load, as well as world-wide industrial data which are compatible with the derived equation. It is shown that the sharpness of classification decreases with increasing circulating load. Based on the evidence available a comparison is presented between the performance of the present-day hydraulic classifiers. In a continuously operated closed circuit grinding system the tonnage and the fineness of the components may be indicated as follows: Eq. 8 expresses the relationship between sharpness of classification and circulating load in closed grinding circuits. If CL = 0, E = 100% according to the definition used. This, however, is a purely theoretical case because any apparatus to be called a classifier must produce the conventional two products. Furthermore, if CL = m, E =0%. In order to visualize the meaning of Eq. 8, the effect of factors d (fineness or percentage of under-size of classifier overflow at size x) and b (fineness or percentage of undersize of classifier sands at size x) should be studied. By the most rigid standard, factor d should be given the value of 100%. By so doing the size of classification is defined as that screen size x through which 100% of the classifier

Jan 1, 1965

ONE HUNDRED AND FOURTEENTH MEETING OF THE INSTITUTE, MONDAY, FEBRUARY 19, TO THURSDAY, FEBRUARY 22, INCLUSIVE, 1917 Committee on Arrangements DAVID H. BROWNE, Chairman LAWRENCE ADDICKS Louts D. HUNTOON E. MALTBY SHIPP PERCY E. BARBOUR H.A. MEGRAW BRADLEY STOUGHTON GEORGE D. BARROW _ THOMAS T. READ EDWARD B. STURGIS KARL EILERS BURR A. ROBINSON ARTHUR L. WALKER F. T. RUBIDGE Summarized Program MONDAY, FEBRUARY 19 9:00 a.m. to 5.00 p.m. Registration at Institute Headquarters. , 10.00 a.m. Simultaneous Sessions on Geology and on Metallography.

Jan 2, 1917

By H. H. Stoek, G. W. Harries

The term " Anthracite Coal-Field " is generally used to refer to a comparatively small territory lying in the eastern-central part of Pennsylvania. This territory includes about 3,300 sq. miles of area, located chiefly in five counties in which anthracite-mining is the dominant industry. Although an area of 3,300 sq. miles is embraced in the region, less than one-fifth of this area, or only 484 sq. miles, is underlain by workable coal-seams. Moreover, this prorluctive portion is not a continuous area, but consists of a number of detached basins. These are known as the Northern, containing 176 sq. miles; Eastern-Middle, containing 133 sq. miles; Southern, containing 181 sq. miles; and western-Middle,containing 194 sq. miles. From the standpoint of business and trade, the region is divided into three districts, known as (1) the Wyoming, which includes the Northern field and the small Bernice basin; (2) the Lehigh region, which includes all of the Eastern Middle field and that part of the Southern field east of Tamaqua; and (3) the Schuylkill region, which includes the WesL ern-Middle field and that part of the Southern field west of Tamaqua. The relative commercial importance of these districts at the present time is shown by the coal-shipments as given in the following table :

Jan 1, 1904

By Henry M. Rowe

Professor Ruff's most illuminating paper' describing his extremely valuable investigation of the carbon-iron equilibrium diagram assigns definite temperatures to certain very important lines in the diagram, viz.: the eutectic temperature EB (Fig. 1) and the " near-eutectic " temperature E'B', but without indicating clearly enough the reasoning which warrants these assignments. These temperatures are of such primary importance that it is well to indicate the apparent gaps in the reasoning, in the hope that they may be filled in. In his diagram, Fig. 1, the point X and the liues B'D'lII represent the experimental results reached by Ruff and Goecke;a AB, AEB, and SE represent the liquidus, the solidus, and the solubility of the carbon in solid austenite in the absence of graphite according to Gutowsky,3 AB being also in accordance with Spiecker's data; S'E' the solubility of carbon in solid austenite in the presence of graphite according to Ruer and Iljin;5 GS the line A3 after Ooerens and Meyer; 6 and EBC the true eutectic line as inferred by Prof. Ruff from Gutowsky's data. B'D' is the carbon content found in cast-iron which had apparently saturated itself with carbon in the presence of the graphite of the enclosing graphite crucibles in which the determinations were made. From its straightiiess and its sharp inflection near 6.67 per cent. of carbon, the carbon content of

Jan 1, 1913

By Howard Evans

Moderate but substantive gains were recorded in 1972 in the minerals processing industry. In the area of mill design, a number of large plants under construction during the past two to three years were tuned up and went into production. The application of operating controls has also made some significant strides. Progress here has been made in the areas of on-stream particle size analysis, on-stream x-ray analysis, slurry transportation, tripper control, flotation reagent control and digital control of grinding circuits. The major contributions to improved equipment are coming from smaller specialized equipment makers.

Jan 2, 1973

By Walter Harvey Weed

Introductory.............449 Summary oF Types............452 I. The Virgilina Type...........452 The Virgilina mines...........452 Location.............452 History.............453 The rocks of the district..........453 The veins.............454 Notes on the mines.... 458 The Holloway. 458; Yancey and Durgy. 465 ; Copper World. 467 ; Frazier. 467 ; Thomas. 467 ; Anaconda. 468; Blue Wing. 468; High Hill. 472; Dorothy.......474 II. The Gold Hill Type...........474 The Gold Hill mine...........475 Location.............475 History............• 475 Surface improvements.......... 476 The rocks............478 Vein.phenomena...........478 Character of the ore..........481 Origin of the ore...........481 Notes on the mine.workings.........482 Other occurrences of ore-deposits of the Gold Hill type.. .. 483 III. The Ducktown Type..........484 The Ducktown mines...........485 Other examples of the Ducktown type....... 494 Alabama mines...........494 North Carolina examples : Ore Knob.......496 Virginia examples..........497 IV. The Catoctin Type.. ......... 498 General characteristics,......... 498 The Linden district...........499 General distribution of the Catoctin type.......503 Introductory. In the early history of this country the existence of copper in the Appalachian region was well known. but no mining mas attempted until the discovery of the Ducktown deposits in

Jan 1, 1901

By A. Raman, P. P. Singh

The constitution of the La-Rh system was studied by powder X-ray diffraction, metallopaphic, and differential thermal analysis techniques and an equilibrium diagram is presented. Eleven intermediate phases occur in the system and the crystal structural data for nine of them were determined. La3Rh crystallizes in an orthorhombic structure of undetermined type, whose unit cell is obtained by doubling the 'a; and 'c,,' edges of an FesC type unit cell. The other intermediate phases of the system are LarRh-3( undetermined structures also occur in the system. LaRh, undergoes a polymorphic phase transformation at 1240°C. LaRh3 and La2Rh7 also exhibit polymorphisnz. The phases Laah and LazRh7 melt congruently. The latter undergoes a eutectoid transformation into LaRh, and Rh at 1205°C. Laah3 is formed by a peritectoid reaction between Laah and La,Rh,,. The other Phases result from peritectic reactions between the liquid and the adjacent rhodium-rich phases. The intermediate Phases of the La-Rh system are compared with those of the La-Co and La-Ni systems. DURING the course of a detailed investigation to study the occurrence of CrB, FeB, A1B2, and related structures in the rare earth alloys it was found that much information is lacking for the rare earth noble metal systems. Although the structures of several rare earth alloys containing the noble metals at the AB and AB2 stoichiometries have been reported, the occurrence of related structures at other stoichiometries has not been studied. We have initiated a project to study the crystal structural features of selected rare earth-rhodium alloys and to map the equilibrium diagrams of representative systems with conventional methods. The results of our investigation in the La-Rh system are presented in this paper. Two phases were known in the La-Rh system. LaRh has the CrB-type structure.' LaRhz is a MgCu2-type Laves phase.z EXPERIMENTAL PROCEDURE Alloys weighing less than 1 g were prepared from commercially pure lanthanum (99.9 pct +), supplied by Lunex Company, Pleasant Valley, Iowa, and rhodium (99.92 pct +), supplied by Engelhardt Industries, Newark, N.J., in a conventional arc melting furnace under argon atmosphere. The buttons were turned upside down and remelted three times to insure homogeneity in the samples. Since negligible loss of material was encountered during melting, a chemical analysis of the alloy buttons was not undertaken. Powder specimens for X-ray diffraction studies in the as cast state were then prepared. The buttons were wrapped in thin molybdenum foils and homogenized by heating in vacuum at suitable high temperatures for more than 1 week. They were then broken into three or four pieces for annealing experiments. The pieces were wrapped in molybdenum foils and annealed at various temperatures in evacuated quartz capsules. The annealing was carried out for 2 hr at or above 1200°C, 1 day at temperatures close to llOO°C, 2 days at 1000°C, and for 1 week at temperatures below 1000°C. After annealing the alloy pieces were again broken and powder specimens for X-ray diffraction were prepared. The powders of the lanthanum rich alloys with more than 80 at. pct La were prepared by filing. The filings were sealed in molybdenum tubings and stress-relieved at 600°C in vacuum. It was not deemed necessary to stress-relieve the powders of the other alloys, since the alloys were very brittle and were ground easily. POWDER X-RAY DIFFRACTION X-ray diffraction photographs of powders (-325 mesh size) of the alloys in the as cast and annealed states were prepared in a Guinier-de Wolff focussing camera with copper K, X radiations. These patterns were studied to identify the stoichiometries and the crystal structures of the intermediate phases. The lattice parameters of the phases were calculated after minimizing the differences between the observed sin2 6 values, calculated from the diffraction angles 8, and the sin2 8 values, calculated using approximate lattice constants obtained from a few lines. These differences were minimized manually to less than 0.0005. The latLice constants are judged to be accurate to *0.005A for values less thp about 10A and to k0.01~ for values greater than 10A. The relative intensities of the lines were calculated using a computer program written by Jeitschko and Parthk.~ No attempt was made to refine the atomic positional parameters in the phases. METALLOGRAPHY The phase equilibria in the investigated alloys in the as cast and annealed states were also studied by metallographic examination. The polished specimen surfaces were etched with 10 pct picric acid in alcohol (alloys up to 25 pct Rh), concentrated picric acid (from 25 to 37.5 pct Rh), 2 pct nital (40 to 50 pct Rh), 10 pct nital (from 50 to 66.7 pct Rh) and with concentrated 48 pct HF for the other rhodium-rich alloys. Selected microstruture~ were then photographed using a Po-laroid Land camera. THERMAL ANALYSIS Differential thermal analysis of the alloys was carried out in DTA-668 Stone differential thermal ana-

Jan 1, 1970

By H. I. Aaronson, C. Laird

The kinetics of thickening and of lengthening of ?' plates in an Al-3.93 pct Cu alloy in the temperature range 203" to 300" C were determined by means of transmission electron microscopy. The rate of thickening was found to be less than that allowed by volume diffusion control at all temperatures, by amounts which increased with decreasing temperature, in agreement with the predictions of a general theory of precipitate morphology.1 Thickening was treated on the basis of the ledge mechanism. Ledges were deduced to spread across the broad faces of ?' plates at volume dzjrfusion-controlled rates, as anticipated from the disordered structure of their edges. Lengthening of 8' plates, on the other hand, took Place more rapidly than allowed by volume dzjrfusion. This occurred despite clear morPhological evidence of a bmrier to growth at the edges of these plates. It was concluded that the misfit dislocation structure comprising the barrier requires that lengthening take place by a jog mechanism. The tnisfit dislocations, however, also serve as diffusion short circuits, and allow high overall lengthening rates to be achieved. In Part I' it was shown that, within the range of aging temperatures and times studied, the broad faces of 8' plates formed in Al-4 pct Cu are fully coherent with the a, matrix. Virtually .all of the dislocations present in these faces were found to have developed as a result of plastic deformation in the a phase. Such dislocations are thus "intruders", rather than the more usual misfit-compensating variety. The edges of 8' plates were confirmed, by extension of the earlier studies of Mat-suura and Koda,3 to be made up of edge-type misfit dislocations, in sessile orientation with respect to lengthening of the plates. These interfacial structures should cause 8' plates to thicken and to lengthen at rates less than those allowed under the condition of volume diffusion control, such as would be expected if the interphase boundaries had disordered structures.' The narrow width of 8' plates, the reproducible crystallography of their broad faces, and the appearance of these plates in cross section as octagons rather than as circular discs2 provide qualitative support for these deductions. The present study of the rate of thickening and the rate of lengthening of 8' plates was undertaken in order to examine them on a quantitative basis. I) THICKENING KINETICS OF THE BROAD FACES OF?' PLATES A) Literature Review. The measurements now available on the thickening kinetics of single-phase precipitate plates consist of one plot of the thickening of a proeutectoid ferrite plate in an Fe-C alloy,' showing (as predicted) thickening rates less than those allowed by volume diffusion control. B) Experimental Procedure. Details of the preparation of the 4-3.93 pct Cu alloy used in this study have been previously reported.4 As in Part 1,' transmission electron microscopy was the observational tool employed. A general description of the apparatus and procedures of the electron microscopy studies is given in Section I of Part I. In thin foils, 0' plates tend to form at and parallel to the foil surface.' A direct investigation of the thickening process by means of hot-stage transmission electron microscopy was therefore not feasible. It was thus necessary to use the conventional method of aging individual bulk specimens for a wide range of different times at the various temperatures studied. In each specimen, the thicknesses of a number of plates were measured. Since thin foils prepared from "bulk-aged" material contain a large proportion of grains with orientations near (001) , it was relatively easy to find, near the edges of the foils, the characteristic multifold patterns of intersecting extinction contours which indicate regions where the foil is exactly at an (001) orientation. The thicknesses of large numbers of plates were measured along the (200) branches of the "stars" so that the 8' plates were precisely parallel to the optical axis of the microscope. Wherever possible, intersecting extinction contours were adjusted with the parameter s > 0 to improve the visibility of the plates in bright-field illumination. These precautions, in combination with taking the measurements at the thinnest parts of the foils, minimized the errors in the measurement of the thickness of the plates resulting from inexact parallelism to the electron beam. Since the plates were very thin, it was not easy to measure their thickness on the photographs. The techniques of enlargement and of microdensitometry were employed to minimize errors from this part of the measurement. A further source of possible error, that the plates can appear thicker because of contrast associated with mismatch normal to the plane of the plate, was also considered. The images of the plates were usually thinner than those of dislocations, however, and no anomalous changes in apparent plate thickness were observed when regions of foil containing plates were tilted through various diffracting conditions. Any error from this cause must therefore be small. Other sources contributing errors were: a) the microdensitometer traces per se and the subjective estimates of their peak limits, and b) slight fluctuations in magnification associated with small changes in the current of the objective lens of the electron microscope. The overall error probably amounted to no more than 5 to 10 pct. In order to obtain readily interpretable data on thickening kinetics, it is essential that the diffusion fields of adjacent ?' plates not be allowed to overlap. Calculations'-' showed that this condition is definitely not ful-

Jan 1, 1969

By Charles E. Barker

Jan 1, 1985

Jan 1, 1933

ALABAMA Anniston.-Bretz, J. A. Carrington, F. G. Gerber, A. B. Klugh, B. G. Semple, R. A. Ashland.-Barton, .J. Bessemer.-Abbott, C. E'. Ball, T. L. Beaver, J. J. Ferguson, V. Salmon, H. S. Sehaber, C. F. Whatley, W. J.

Jan 1, 1923

By V. A. Phillips, M. Safdar Ali

The tensile properties of Cu-0.20 pct Al, Cu-0.45 pct Mg, Cu-0.27 pct Cr, and Cu-0.22 pct Be solid-solution alloys were studied at -196°, 18°, 2509 and 500°C on wires internally oxidized at 900°and 1000°C. Internal oxidation produced marked increases in yield strength relative to pure copper, particularly at low temperature. The yield strength decreased with increase in temperature to a much greater extent than predicted by current theories of dispersion hardening. The strengthening effect of internal oxidation persisted throughout the entire stress-strain curve, but since a marked loss of ductility occurred at all test temperatures, only modest increases in tensile strength were realized. INTERNAL oxidation involves the preferential oxidation of a baser solute in a relatively noble solvent by diffusion of oxygen into the solid. Since the process is diffusion controlled, it is expedient to carry it out at a high temperature often approaching the melting point. The amount of solute is limited and the oxidation conditions adjusted so that oxygen diffuses inwards to meet the solute causing reaction to progress inwards and form subscale instead of only sur face scale. The reaction can be made to occur throughout the thickness of thin material producing a fine dispersion of oxide inside the metal. C. S. Smith1"3 appears to have been the first to recognize the true nature of the process of internal oxidation. Although extensive kinetic and metal-lographic studies followed by Rhines and coworkers,4-5 Chaston7 andMeijering and Druyvesteyn8 working independently were the first to report hardening effects due to internal oxidation. These results prompted detailed studies of the effects of internal oxidation on the hardness, tensile, creep, and fatigue properties of a number of alloys by G. C. Smith and coworkers9-12 in England, on hardness by Gottardi13 in Italy, and on hardness and tensile properties by wood14 in the U.S.A. Publications dealing with other aspects of internal oxidation will not be reviewed here. Internal oxidation of solutes having a high affinity for oxygen provides a means of obtaining very fine dispersions stable in a suitable atmosphere at temperatures well above those at which most age harden ing precipitates coalesce. The process therefore offers a method of producing thin sheet and wire of possibly outstanding creep resistance. The size limitation might be overcome by internally oxidizing porous powder compacts made from alloy powder before final sintering. PREPARATION OF ALLOYS The alloy ingots, which were approximately 5 1/2 in. long by 1 in. diam, were made up in a high-frequency furnace, using as raw materials OFHC copper, 99.99 + pct Al, high-purity magnesium, and master alloys of Cu-4.19 pct Be and Cu-10 pct Cr. The alloys containing aluminum and magnesium were melted ii closed high-purity graphite crucibles and solidified in the crucible which was lowered partly Out of the coil to give a hot-top effect. The alloys containing beryllium and chromium were made by melting in vacuo in alumina-lined sillimanite crucibles. The magnesium, chromium, and beryllium

Jan 1, 1960

By A. L. Mular

Two equations express the integral rate at which fines are produced from a homogeneous material: It has been demonstrated that the Gaudin-Meloy distribution for single fracture is equally applicable to multiple fracture and is related to the Gaudin-Schuhmann distribution at least when the distribution modulus a is close to unity. A, xoY was found to be independent of starting mass over the range studied when particle size was held constant. The equations are related to the input energy to the mill. In an earlier paper,' it was shown that when Mo g of uniformly sized homogeneous material is ground dry in a batch rod mill, the energy-size reduction equation is expressed at any time by the mass of unbroken starting material left at time t, ku is the size modulus of the portion Mo - Mt, and P is a constant that is generally equal to the distribution modulus a. If the power to the mill is constant, Et is proportional to time and Eq. 1 is rewritten where (Mo -Mt)/t is actually the integral rate at which fines are produced from a parent material, and A, is another constant. The size modulus, k,, is determined from the Gaudin-Schuhmann equation:2 where y is the cumulative fraction finer than any size x. Recently, Gaudin and Meloy derived a distribution equation for single fracture on the assumption that the random fracture of a homogeneous material produces daughter particles of similar shape. Their equation is given by where y is the cumulative fraction finer than size X, x, is the size of the unfractured parent, and r is designated the size ratio. Although Eq. 4 is derived for a single event, it should also approximately hold for a series of com-

Jan 1, 1962

By Philip D. Wilson

AS thin most important and vital component of an airplane aluminum hay rapidly become the heart and tome- of the war program. Its production ham increased amt will continue to increase, in comparison with its pre-war position further than that of any of lie other important critical metals except magnesium. Compared with the 1939 production of tons of primary ingot coming from four plants, all owned by the Aluminum Company of America the 1942 figures are more than three timer as large. Including, recoverable scrap and contracted ingot from Canada the 191,, supply of aluminum for the United States will be over siren times dial of 1939- A substantial part of this increase has been achieved during the past year as total production in 1941 was only some 307,500 tons. During 1942 six great new ingot plants sponsored and owned by the Government have come into production and three others are nearing completion.

Jan 1, 1943

By E. L. Dougherty

A phenomenological theory for a one-dimensional unstable miscible displacement similar in type to the Buckley-Leverett model but including the effects of mixing is proposed An equation giving the fractional flow of pure solvent through an oil phase containing dissolved solvent is derived including the effects of gravity and nonbomogeneities. Numer ical integration of the resulting pair of nonlinear hyperbolic partial differential equations gives volumes of dissolved and undissolved solvent as functions of space and time. Parameters in the model which characterize mixing due to dispersion were determined from experimental data; the parmeters correlated with viscosity ratio. The results indicate that the rate of dispersive mixing is proportional to volumetric flow rate Incorporated into our equations were Koval's heterogeneity factor H. which characterizes mixing due to channeling. This allowed satisfactory predictions of displacement behavior observed in horizontal floods in nonhomo-geneous cores; but in most cases the values of H which we used were considerably larger than those used by Koval. INTRODUCTION It has been shownl,2,3 that for favorable viscosity ratios, the diffusion equation with convection satisfactorily describes the behavior of a miscible displacement in a porous media. Numerous attempts to develop a satisfactory mathematical description for the case of unfavorable viscosity ratio have been reported, but they have met with only partial success. These attempts, which are reviewed by oval! have taken two approaches: (1) development of a flow model akin to the Buckley-Leverett approach for immiscible displacement neglecting the effects of mixing5,6 and (2) simultaneous application of Darcy's Law for flow and the diffusion equation with a convection term for mass transfer.7,8,9 We set out to construct a mathematical model of Type 1 including, though, the effects of mixing. Based upon a set of hypotheses, we derived a pair of nonlinear hyperbolic partial differential equations which describe in a one-dimensional system the combined effects of flow and mixing. To work with these equations it was necessary to develop a fractional flow formula. The combined system was integrated numerically using the method of characteristics. In our equations the mixing process is characterized by four parameters. Three of these, labeled ß, P1 and P2, account for dispersive type mixing. The fourth is the heterogeneity factor H, proposed by Koval to account for channeling due to nonhomogeneities in the porous media. Values of the parameters which would cause agreement between theory and experiment were determined by trial-and-error for miscible floods conducted in horizontal cores of both homogeneous and heterogeneous materials. Calculations were also performed for vertical floods in homogeneous cores. The purpose of this paper is (1) to present the details of the mathematical analysis, (2) to present the results of the calculations, (3) to consider what light the results shed on the mixing process in an unstable miscible displacement, and (4) to provide a firmer foundation for the correlation technique developed by Koval for predicting the behavior of unstable miscible floods. STATEMENT OF PROBLEM The problem is to construct a mathematical model which describes in one dimension the observed behavior in an unstable miscible displacement. The approach is phenomenological in that the equations are based on assumptions which violate certain physical precepts known to apply to the displacement phenomenon. However, the assumptions do allow us to account mathematically for the more essential phenomena. The work is of value if we can quantitatively predict experimental results which heretofore could not be predicted, even though the synthetic nature of the model belies complete explanation of the observations. We assume that the system is comprised of two contiguous flowing phases. One phase, which we call free solvent, has the properties of pure solvent. We call the fraction of the pore volume occupied by this phase the solvent saturation, designated s. The oil phase consists of oil containing dissolved

By William J. Coulter

WITHIN the past thirty years the United States has been involved in two tragic, vicious, and costly world wars. To make the world safe for democracy was the reason given for our participation, but the confusion and misunderstanding that prevails all over the world today suggests that war is not the proper approach to the attainment of that utopia. These conflicts were conceived and prosecuted by nations far advanced in civilization and culture. Their best manhood was sacrificed, a staggering tax burden was saddled on their peoples, huge financial losses were incurred, destruction of property was appalling, and cultural and peaceful scientific advancement received a setback that may require centuries to retrieve. Therefore, some basis is established for the conclusion that progress in the past fifty years has been most outstanding in the development of instruments used for death and destruction, and that progress in this direction between the two World Wars would indicate that the next war will go far toward total destruction of world civilization.

Jan 1, 1946

By Eugene F. Broome, Hugh A. Walls

Self-diffusion coefficients were measured using the modified shear cell technique over a temperature range from 31" to 401°C. These data agree within experimental error with those of Petit and Nachtrieb, which were determined from 30°to 99°C. LIQUID self-diffusion behavior in gallium has been studied previously by Petit and Nachtrieb&apos; using their shear cell technique.&apos; Data were obtained in that investigation over temperatures ranging from 30.6 to 98.7"C, and these comprise the only published data for liquid gallium. In the work reported here, diffusion data were obtained from 30.8 to 400-9.Cusing a shear cell technique different from that of Petit and Nachtrieb. This modified shear cell method and the mathematical analysis for diffusion in a finite capillary geometry have been previously described.3 PROCEDURES AND ANALYSIS The segments of the modified shear cell were fabricated from types 304 and 316 stainless steel. No corrosion problems with gallium were encountered until attempts were made to obtain data at 500°C. The diffusion capillary diameter was 1.59 mm and capillary lengths for the four sets of cell segments used are given in Table I. Gallium with a purity of 99.999 wt pct was obtained from Var-Lac-Oid Chemical Co. The gallium-72 isotope used to measure the self-diffusion coefficients was produced from this inert gallium by irradiation in The University of Texas Reactor Facility, and was checked for radiochemical purity. Following a period of isothermal diffusion controlled to within 0.0l°C, the contents of each capillary section were emptied into a counting planchet, weighed to assure that gallium had not been lost during handling, and the radioactivity determined by windowless gas-flow proportional counting. Great care was taken to obtain a reproducible counting geometry for the samples. Diffusion coefficients were obtained from the solu-tion3 to the diffusion equation for the modified shear cell problem, viz.: in which B2= C2(t)Li + L2)- CSL1-COL2 P* (C0-Cs)(L1+ L2) and L, and L2 are the capillary segment lengths. The step-function initial concentration distribution was expressed as C(x,O) = C, for -L1 = x < 0 and C(x,O) = Co for 0 < x 5 L?. Also, C2(0 = ^- fcix,t)dx Computation of the diffusion coefficients was done numerically as described in our earlier paper.3 Because of the short half-life of gallium-72 (14.1 hr) and the relatively long counting times taken to give a precise value of the diffusion coefficient, it was necessary to account for the radioactive decay both during the actual count and between counts for different samples (before and after diffusion). Thus, the average count rate Cz(t) for a second sample counted from times t3 to t4 can be made consistent with the average rate Co determined for a first sample counted from times t1 to t2 by the relationship: N(e-»i-e-M») , , C2(f) " &-«,)(*-«.-«-»«) [21 in which N is the total number of counts taken and is the decay constant. RESULTS AND DISCUSSION The self-diffusion coefficients determined in this investigation are listed in Table 11. Values of the parameters used to calculate the coefficients are given in the table, as are values of the random counting error &apos; for the concentration ratio pz and the corresponding expected random variation AD in the diffusion coefficient. The quantity is calculable from: &apos;Cg — C2(t)} , „ ,2 .-„¦, M co-csl(ACs)J W in which AC is the error in the individual count rate. The mean values of the diffusion coefficients within each temperature group are also given in Table 11. Such temperature groupings of data are reasonable because of the small variations between the temperature~.~

Jan 1, 1970