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By H. T. McAdams

Current theories of fracture maintain that brittle materials contain flaws or regions of weakness at which fracture originates. Whether a particular flaw grows depends upon the stress distribution in its vicinity and upon the presence of other stress relieving mechanisms capable of absorbing the applied energy. Under load, therefore, certain of these flaws will be activated, and the resulting fragments will have a size distribution determined by the spatial distribution of active flaws. Gaudin and Meloy,1 assuming a random occurrence of flaws, have derived the size distribution of fragments as

Jan 1, 1965

By R. C. Wilcox, R. V. Lawrence, P. A. Calhoun

The V-Rh-Si, Nb-Rh-Si, and Cr-Rh-Si systems were investigated to evaluate the extent of solid solubility between binary Cr3O structures. All Cr3O components lie within the favorable atomic size range1 for the formation of the Cr3O structure. Previous studies indicated complete solid solubility between V3Si and V3Sn2 and no solubility between Sn and cr3si3 or Si and Nb3Rh.4 The Cr3O structure is not found in the Cr-Sn and Nb-Si binary systems. Powder compacts were are-melted under argon, homogenized in a vacuum at 1000°C, and water-quenched. Alloys containing greater than 15 at. pet Si were annealed 100 hr. X-ray diffractometer methods were used to study all systems utilizing copper radiation for the Cr-Rh-Si system and chromium radiation for the other two systems. V-Rh-Si System. The alloys prepared in the V-Rh-Si system and the measured lattice parameters for the Cr3O structure found in each alloy are listed in Table I. The characteristic Cr3O diffraction pattern was found in all binary alloys. The measured lattice parameter of V3Rh (VRS-1) is in agreement with the reported value5 while the value for V3Si (VRS-5) is only in fair agreement.' In

Jan 1, 1965

By E. R. Gilbert, D. E. Munson

Creep of copper under 75 to 1.50 kg per sq cm stresses at temperatures near the melting point was found to he a complex reaction controlled by three mechanisms acting in parallel. In order of appearance with decreasing temperature, the auerage activation energies, Qc , are 168, 79, and 24 kcal per mole. Stress dependence of the minimum creep rate was found to he an exponential for the two high-Qc processes and a power law for the low-Qc, process. Transition of control occurs from one mechanism to another. The relative transition temperature depends upon the applied stress, and the range oiler which the transition occurs depends upon the difference in the activation energies of the mechanisms. The creep behavior at high temperature is explained by the climb of dislocations through thermally or mechanically formed jogs, CREEP in pure fcc metals at temperatures in excess of one half the absolute melting point is normally controlled by dislocation c1imb.1,2 A climb model which seems applicable, according to an extensive analysis of data,3 was derived by Weert-man.4 This model assumes jog-saturated dislocations and predicts an activation energy, Qc, nearly equal to that for self-diffusion, USd. Although the requirement of jog saturation is restrictive, agreement between theory and experiment seems adequate. Many other theoretical treatments, including an early model by Mott,5 include detailed consideration of jog formation as an initial requirement for climb. These models predict activation energies for creep which differ from those of self-diffusion. Seeger6,7 postulates an observed activation energy related to the stacking-fault energy. Thus, Usd <Qc<5Usd + Uj where Uj is the jog-formation energy. Seeger incorporated qualitatively the influence of the relative numbers of thermal and athermal jogs. Expanding this concept, Shoeck8 explicitly states a function based on formation mode and relative numbers of vacancies: e r ci exp {-uf/k T} exp {-Um/k T} [ 1 ] where Uf and Um are energies of vacancy formation and migration, respectively. The concentration of jogs, Cj, depends upon the manner of jog production. For intersection jogs, Cj is not sensitive E. R. GILBERT, Junior Member AIME, formerly with De- to temperature; for thermal jogs, Cj is proportional to exp {—Uj /k T}. Schoeck regards each mode as a distinct mechanism; therefore, the mechanisms may act together.299 The diversity predicted by theory, surprisingly, has not been substantiated by experimental results. A significant investigation must include the extremes in stacking-fault energy. Extensive creep studies of aluminum10 and nickel,11,12 high stacking-fault energy metals, have been made. Comparable studies on a low stacking-fault energy metal, such as copper, have not. It is the purpose of this paper to report the results of an investigation of the creep of copper under conditions which favor thermal jogs. EXPERIMENTAL Cylindrical compression creep specimens (0.240 in. in diameter by 0.400 in. long) were machined from cold-drawn rods of electrolytic tough-pitch copper containing 0.0007 Mg, 0.002 Fe, 0.001 Ni, 0.0005 Ag, Cd < 0.005, and Pb < 0.005 wt pct impurities. Undetected spectrographically was a nominal 0.04 wt pct 0, which occurs as a Cu2O constituent distributed discontinuously at grain boundaries. Vacuum annealing at 900°C for 15 min produced a stable 0.03-mm average grain diameter. Testing was carried out using apparatus similar to that described by sherby,13 modified by enclosing platens and a push rod in a vacuum cylinder. Normally this arrangement resulted in pressures less than 10 Only a slight surface tarnish, less than 0.0005 in. in thickness, occurred during the test. The applied stress, corrected for atmospheric pressure, was maintained within 2 pct of the desired true stress by the addition of lead shot at fixed strain increments. Creep strain was measured with dial gages as a relative displacement of the upper and lower platens; accuracy of measurement was 0.0001 in. Two creep-test methods were used, the differential or cyclic temperature14 and the isothermal, to obtain creep data at stress levels of 150, 100, and 75 kg per sq cm over the temperature range of 620° to 1032°C. Minimum creep rates were used from both test methods; this was considered proper because comparable temperature tests or cycling to the same temperature gave the same creep rate, within experimental error. The cold vacuum test chamber, with the unstressed specimen in place, was heated to temperature by placing a preheated furnace over the chamber. Temperature equilibrium was attained within 30 min. For the cyclic tests, the stress was removed during the 5 to 10 min necessary to effect the temperature change and re-

Jan 1, 1965

By J. B. Moritz

From the beginning, man has concerned himself with the task of controlling the elements and forces about him so as to provide a better and easier life. In the accomplishment of this task, he is required to utilize in the best way possible the resources which are available to him. In many cases, the available resources must bee refined before they are in a useable form. Many products in the mining industry fall into this category, as some form of refinement is generally needed to produce a saleable product. Over the years man developed more efficient ways of extracting the resources from earth through the use of electrical and mechanical devices. A reduction in manual labor, which is a by-product of increased efficiency through machines, has also been enjoyed. The combination of man&apos;s senses and new devices has also enabled man to reach a high level of control in the refinement process. Control of a process through machinery and man&apos;s senses has been termed an "art." Until recently man&apos;s senses (sight, feel) were the only method available for making measurements simply because suitable measurement devices (instruments) were not available. Even today some items cannot be measured and man&apos;s senses must be used. However, the development in our instrument laboratories tends to indicate that time will eliminate this. In recent years, control of many processes has been reduced to a science and part or all of the art eliminated. This does not imply that process art should be degraded; however, when a process is reduced to a science, uniformity of the product from day to day is attained. Decreased processing time and more efficient use of additives and raw materials are other benefits that result from control of a process when it is reduced to a science.

Jan 1, 1965

Jan 1, 1965

By G. E. Agar

The energy required for dry grinding of phosphate rock in ball and roller mills has been analyzed by the method suggested by Charles and others. The findings are not wholly in agreement with Charles&apos; predictions; but, nevertheless, the method of analysis is shown to be sound. Some of the deviation is probably attributable to the characteristics of a dry grinding system. Many laboratory and pilot plant scale experiments have been made to determine the energy requirements for size reduction. This topic was recently reviewed by Agar and Brown&apos; and it was apparent that very little if any data exists in the literature which permits one to apply the Charles 2-Holmes3 analysis to industrial size systems. More recently, the idea has been put forward that the postulate of comminution by impact used by Charles and others was not sufficient to explain size-reduction throughout the grinding operation. The opportunity exists in the grinding operations of International Minerals and Chemical Corp. (IMC) to analyze the energy-size relationship for dry grinding phosphate rock in both ball and roller mills. This situation arises because the mills are used for custom grinding and make products from 50% to 85% minus 200 mesh. BACKGROUND A correlation of particle size in a comminuted material with the energy expended in size reduction was proposed by charles2 to be of the form

Jan 1, 1965

By P. M. Robinson, M. B. Bever

THE heats of formation at 273°K of the compounds InBi, In2Bi, and TIBi2 have been determined by metal solution calorimetry with bismuth as solvent. The published information on the thermody-namic properties of these compounds is limited. The structure of the compound InBi (mp, 383°K) is tetragonal of the PbO (B10) type.1 The compounds In2Bi (mp, 362°K) and TIBi2 (mp of highest-melting composition, 486°K) are now believed to have structures of the NizIn (B8) type273 and not the A1B2 (C32) structures reported earlier.4, 5 The compounds In2Bi and TIBi2 have limited homogeneity ranges at room temperature, while the compound InBi has no detectable homogeneity range.&apos; Samples of the compounds were prepared from 99.99 pet Bi (Mallinckrodt Chemical Works), 99.999 pet in (American Smelting and Refining Co.), and 99.99 pet Tl (Amend Drug and Chemical Co.) by melting the components in sealed, evacuated Vycor tubes. The compounds InBi and in2Bi were of the stoichiometric compositions. The compound TIBi2 contained 40 pet T1; this composition was chosen because at room temperature the alloy of stoichiometric composition does not lie within the homogeneity range.&apos; The melts were held approximately 50°C above the liquidus for 8 hr and then quenched into iced brine. The samples were homogenized for 48 hr at temperatures 20°C below the temperature of complete solidification. Metallographic examination of sections taken from the center and the ends of the ingots did not reveal second phases or segregation . The heats of formation were determined as the difference in the heat effects on solution of a compound and of a mechanical mixture of its components added from the reference temperature of 273°K to liquid bismuth at 623°K. The details of the calori-metric procedure and method of calculation have been described elsewhere? The calorimeter was calibrated by adding bismuth at 273°K to the bismuth bath at 623°K. The calculated values of the heats of formation of the compounds, listed in Table I, are based on a value of 4.96 keal per g-atom for the difference between the heat contents of bismuth at 273" and 623oK7 No published values are available for the heats of formation of the compounds InBi and In2Bi. Hultgren et a1.7 have calculated a value of -0.50 i 0.10 keal per g-atom for the heat of formation at 423°K of the compound TIBi2 containing 40 at. pet T1 from heat-content measurements in the range from 398" to 700°K and the heats of formation of the liquid alloy. The difference between this value and the value of -0.66 * 0.01 keal per g-atom at 273°K is too large to be attributed to a difference between the heat capacities of the compound and the components over the temperature range 273o to 423oK7 However, the direct determination of the heat of formation by a calorimetric method should give a more accurate value. The heats of formation at 273°K of the compounds InBi and In2Bi lie on a straight line when plotted as a function of composition, Fig. 1. The compound In2Bi, therefore, appears to be barely stable with respect to its neighboring phases. In order for the free energy vs composition curve to be concave towards the composition axis, the entropy change on formation of In2Bi must be more positive than that on formation of InBi. As the compounds are ordered,2, 3, 8 there is no configurational entropy change on formation. The difference between the entropy changes on formation of the two compounds, therefore, is probably associated with the vibrational entropies. In view of the low heats of formation, the changes in vibrational entropy, due to changes in bond strength on formation of the two compounds, are likely to be small. Owing to the volume contractions on formation of the two compounds,5 the vibrational entropies probably decrease slightly but the decrease of the vibrational entropy of InBi is expected to be larger than that of In2Bi.

Jan 1, 1965

By Arnold B. Hubbard

Automatic control instruments were utilized by the Bureau of Mines for routine assays of large numbers of oil shale samples and other bituminous materials. The standard Fischer assay method was automated by automatically controlling the heating cycles of a battery of 12 electric heaters with electronic controllers and programmers. The condensers were cooled with a modified automatically controlled refrigeration bath. The complete assembly consisted of 12 retort units, necessary control instruments, and the refrigeration bath. This equipment was capable of producing more consistent results than those previously obtained with the gas-heated retorts and of increasing the output of assays substantially with no increase in operating personnel.

Jan 1, 1965

By C. H. Schack

Extractive metallurgy techniques currently employed to recover silver from primary ores and secondary scrap were reviewed and evaluated to identify and delineate metallurgical problems whose resolution would increase the supply of silver from domestic materials. The survey revealed that practically all primary silver is recovered by froth flotation concentration of various types of ores, followed by smelting and refining of the separate lead, copper, and zinc concentrates. Silver losses during the complex processing are, with rare exception, inconsequential. Furthermore, any silver production gain from base metal ores, which contribute about two-thirds of the total primary silver, is directly dependent no improvement in the market for the base metals. Statistical data on new and old silver scrap are wholly inadequate to make reliable conclusions about scrap processing problems and the possibility of increasing the recovery of silver from the many forms of secondary silver-bearing materials. The available information indicates (1) that efficient silver reclamation practices are employed by the larger users of silver, and (2) that recovery of additional secondary silver involves solution of problems of collection rather than of processing. Several possibilities exist for limited increases in silver production from primary ores by improvement in metallurgical practices. Specifically, research is needed to (1) solve the problem of recovering silver from the copper ores of the Copper Range district, Michigan; and (2) devise economically feasible methods for recovery of silver from presently marginal or submarginal ores char because of grade, location, and frequently complex nature cannot presently be exploited by conventional techniques.

Jan 1, 1965

By F. R. Brotzen, D. L. Davidson

ALTHOUGH much effort has been devoted to the problem, the nature of plastic flow in bcc metals is still not fully understood. Some of the difficulties encountered stem from the scarcity of information on orientation effects and the uncertainty as to the glide system in these metals. In an attempt to provide some of this information, the present investigation was carried out, using zone-refined molybdenum single crystals deformed in tension and in direct shear. Considerable evidence exists to indicate that the primary slip system for molybdenum is (110) <111>.1,2 Figs. 1 and 2 indicate that this is, indeed, the case for direct shear at room temperature (see Ref. 3 for a description of the shear-testing equipment and procedure). Moreover, from Fig. 2, the shear stress on the (123) is lower than that on the (112). This would be the case if, as has been suggested,4,5 slip on these two planes is in reality com-

Jan 1, 1965

By G. L. Gates

The Bureau of Mines studied the scales formed in producing wells in the Wilmington field, California. The scales were primarily barium sulfate and resulted from the mixing of injected sea water and formation waters; there was excess sulfate in the injection water and the formation waters contained appreciable barium. After breakthrough, the produced brines were supersaturated with barium sulfate. Laboratory tests indicated that barium sulfate precipitated quickly When the supersaturated brines were agitated with crystals of barium sulfate and fairly rapidly when more sulfate solution was added. Precipitation occurred slowly on standing or under nonturbulent conditions. Both the apparent and equilibrium solubilities of barium sulfate in these brines were determined and compared with equilibrium solubilities in distilled water and sodium chloride solutions.

Jan 1, 1965

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.&apos;-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.&apos; Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By P. G. Meikle, C. T. Holland

The effect of the condition of friction upon the ultimate unit compressive strength as determined between the compressed faces of precisely machined coal specimens and specially prepared testing platens has been examined. Reductions of 30 to 40% in the ultimate unit compressive strength of these model coal pillars have been verified when lubricants areused between the faces as compared to non-lubricated faces. Increase in unit compressive strength due to confinement at each of three levels of friction appears to follow generally the widely accepted "1/2 power law", i.e. S - C (L/T)1/2 where S is the unit ultimate strength, C is a constant dependent on the coal being tested and the coefficient of friction acting at the compression surfaces and L and T are the least width and thickness of the specimen, respectively. Results suggest that the surface condition of both the specimen and platens should be mentioned in detail in conjunction with compression testing, for although the term (L/T)1/2 is adequate for all practical purposes, the coefficient C is directly dependent on the condition of interfacial friction, all else remaining constant. One phase of the investigation of the confining effect of friction on the ultimate unit compressive strength of small coal specimens has recently been completed at the School of Mines of West Virginia University. The efficient control of ground is of fundamental importance to successful mining operations and the design of support pillars has always presented the mining engineer with a difficult and intriguing engineering problem. Since about the turn of the century, many investigators have performed extensive laboratory tests on small coal specimens in efforts to solve some of the perplexing problems of strata control and pillar action in coal mines. A detailed review of this work would serve no purpose here, but a brief mention of the more significant contributions is in order. Muller16 was perhaps the first to illustrate the effect of confining pressure on the strength of coal specimens in compression. His work has recently been more carefully expanded by the experiments of Murrell17 in Great Britain. Rice and Enzian l9 observed that as the size of cubical test specimens increased, the unit compressive strength decreased. These observations were later supplemented by Lawall and Holland, 13 by Greenwald4,5 et a1 at the U. S. Bureau of Mines, by Gaddy3 as well as by Steart,22 Millard15 et a1 and Evans2 et al. Gaddy3 seems to have been first to quantify this relationship with his equation: S = K/vd , where S - ultimate unit compressive strength (psi), K = a constant dependent on the coal, and D =edge dimension (in inches). Holland7 concluded that the strength of coal as affected by lateral dimensions and thickness could be expressed as where K = a coefficient dependent upon the coal, L = least width of pillar (in.) and T = thickness of pillar (in.). Data supplied by this formula have been compared to the estimated stresses in pillars that had been standing for long periods in coal mines and in the cases so far studied the results indicate that the formula predictions are sufficiently accurate for engineering purposes (Holland11 ). This equation therefore is believed to be the simplest and most accurate tool available at the present time for approximating the strength of a coal pillar (over a specified range of L/T) in situ. However, Holland7,9 has indicated that friction between the coal pillars and the top and bottom rock

Jan 1, 1965

By H. J. Ramey

Conventional calculation of total system isothermal compressibility for a system containing a free gas phase involves, among other things, evaluation of the change of oil and gas formation volume factors and the gas in solution with pressure. Preferably, this information should be obtained from laboratory measurements made with particular oils and gases. Often, experimental measurements are not available. In this case, it is necessary to obtain pressure-volume-temperature relationships from general correlations such as those of Standing&apos; for California oils. In order to speed estimates of compressibility, generalized plots have been prepared of the change of both oil formation volume factors and gas in solution, with pressure from Standing&apos;s correlations. A generalized plot for estimating the change in the two-phase (oil and gas) formation volume factor with pressure is also presented. Usually, the effect of gas dissolved in reservoir water upon the total system compressibility is neglected for gas saturated systems, due to the low solubility of gas in water. Results of this study indicate that the increase in total system compressibility caused by solution of gas in water is often as large as the compressibility of wafer, and can be magnitudes larger for low pressure systems. Generalized results for estimating the change of gas in solution in water with pressure are presented in tabular and graphical form. INTRODUCTION During the past decade, pressure build-up and drawdown techniques have gained an important place in reservoir engineering. Build-up and drawdown analyses are only two special applications of the broad field of transient fluid-flow theory. All solutions of transient fluid-flow problems contain a parameter called the total system isothermal compressibility. This property of fluids and porous rock is a measure of the change in volume of the fluid content of porous rock with a change in pressure, and it may vary considerably with pressure. Evaluation of total system isothermal compressibility is not difficult, but it is tedious and time-consuming. Often compressibilities are estimated roughly, or transient flow methods are neglected completely. The benefits of using accurate system compressibility in properly-executed build-up or drawdown analyses are: 1. Better planning of pressure build-ups may be achieved to avoid unnecessary loss of revenue due to excessively long shut-in periods, or to shut-in periods too short to yield useable data. 2. Better and more reliable estimates of static formation pressures for reserves estimates and rate performance estimates. 3. Reliable information for evaluation of well completion effectiveness, and planning and interpretation of well stimulation efforts. The purpose of this paper is to clarify the nature of the total system isothermal compressibility, and to present useful methods for estimation of compressibility, particularly for systems containing a gas phase. DEVELOPMENT Numerous publications have presented solutions to transient single-phase flow of slightly compressible fluids, stressing pressure build-up applications. In transient flow, a compressibility* term arises to permit volume content of fluids in porous rock to change as pressure changes. The basic nature of the compressibility term is usually taken for granted. Problems arise in practical applications of transient fluid theory because most published works consider only one flowing fluid—in an ideal porous system containing only one fluid. In 1956, Perrine2 presented an intuitive extension of single-phase flow pressure build-up methods to multiphase flow conditions. Later, Martin- established conditions under which Perrine&apos;s multiphase build-up method had a theoretical foundation. Perrine has shown that improper use of single-phase build-up analysis in certain multiphase flow situations can lead to gross errors in estimated static formation pressure, permeability and well condition. It is likely that, much pressure build-up data for oil wells should be analyzed on the basis of multiphase flow. For both single-phase and multiphase build-up analysis, the isothermal compressibility term in dimensionless time groups often should be interpreted as the total system compressibility. All real reservoirs contain one or more compressible fluid phases. In addition, rock compressibility can contribute in an important way to the total system compressibility. The proper total system compressibility expression may contain terms for compressibility of oil, gas, water, reservoir rock and terms for the change of solubility of gas in liquid phases.

Jan 1, 1965

By R. E. Ogilvie, J. I. Goldstein

The a and y solubility limits in the Fe-Ni phase diagram have been redetermined at temperatures above 500°C. Both a diffusion-couple and a quench and anneal technique were used. The solubility limits were measured with an electron-probe micro-analyzer. The nickel concentration at the phase boundary is increased below 700°C and the a solid-solubility range is much larger than had been previously measured. The solubility limits are also extrapolated to 300°C. It is suggested that the solubility of nickel in a FeNi reaches a maximum in the temperature interval 400o to 500°C. THE equilibrium diagram has been of great use in the field of meteoritics, where the phase relations between kamacite (a) and taenite (?) in metallic meteorites can be described by means of the Fe-Ni diagram. The study of metallic meteorites by electron-probe microanalysis has cast some doubt on the accuracy of the presently available Fe-Ni diagrams.1, 2 Recent thermodynamic studies of the Fe-Ni system also suggest that the diagram may be in error.3 For these reasons the high-temperature (800o to 500°C) part of the diagram was redetermined. INTRODUCTION The currently accepted Fe-Ni diagram is that of Owen and Liu.4 Above 910°C, there is a region of complete solid solubility, ? (fee). Below 910°C, the a (bee) phase is stable in pure iron. The effect of increasing amounts of nickel is to stabilize the y phase. The phases that form when Fe-Ni alloys are heated or cooled bear little relation to the equilibrium diagram. If an alloy is cooled from the y state and held at a temperature within the a + y field, no evidence has been found for the occurrence of the y - a transformation.5 If the alloy is cooled to low enough temperatures the y phase breaks down into a supersaturated bee phase called a2. In fact, in alloys over 27 pet Ni the y phase is retained at room temperature.6 The a, phase has the same composition as the original y. The temperature at which a2 forms, the M, temperature, has been determined experimentally.&apos; A state of equilibrium can be approached by cooling below M, to form a2 and then reheating the alloy into the two-phase region of the diagram. The y phase will then begin to precipitate out of the a2 phase and grow. The growth of the phase, however, is quite slow. Using the interdiffusion coefficients -Da of Goldstein et al.,8 it is estimated that it takes about 1 year to grow a 10-µ-wide region of ? at 700°C in a 5 pet Ni alloy. Owen and Liu4 used the technique just described to form the equilibrium phases. The phases present were determined by means of X-ray analysis. The accuracy of their diagram depends on the number of alloys available near the phase boundary at a given temperature. In this study two different techniques were used to determine the a/a + ? and ?/a + ? solubility limits. The inherent accuracy of both techniques was greatly improved over that used by previous investigators because the phase-boundary compositions were measured with an electron-probe microanalyzer. PROCEDURE The two methods used to determine the Fe-Ni diagram are the diffusion couple (D.C.) and the quench-and-anneal (Q.+A.) techniques. In the first method, diffusion couples whose diffusion path goes through a two-phase region of the phase diagram were used. A description of the technique used for making the diffusion couples has been described in a previous paper.&apos; After the diffusion treatment a discontinuity in the resultant concentration vs distance profile was measured. The nickel concentrations in the a and ? phases at the interface of the discontinuity are the solubility limits of the a and ? phases in the phase diagram at the diffusion temperature. If the interface com-

Jan 1, 1965

By Carl F. Austin

The subject of strata control in mining can be approached from both static or loading concepts or from dynamic or impulsive loading concepts. The fracture process itself appears to be primarily a dynamic process as is the gross creation of fractures through the use of impact, stress wave passage or in more general terms, the use of explosives. This paper presents experimental results which indicate that the understanding of the fracture behavior of rock that has been, established in the open literature is not always appropriate. In particular, the results of this experimental program have shown very interesting differences between the formation of fractures in rock and the formation of fractures in other materials such as metals and plastics which are often used as models for rock behavior studies Fracture patterns and causes of dynamic fracturing in various rock and artificial materials are presented.

Jan 1, 1965

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

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

Jan 1, 1965

By Arnold M. Lansche

DOMESTIC OUTPUT of white arsenic, As2O3, was derived entirely as a byproduct of smelting arsenic-containing copper ores by The Anaconda Company at Anaconda, Mont., and American Smelting and Refining Company at Tacoma, Wash. Arsenic metal was not produced. Consumption, and Uses.-Most of the white arsenic produced in 1964 was consumed in manufacturing lead and calcium arsenate insecticides. In the 12 year period since 1951 the production of lead arsenate insecticide has varied between 7,800 tons and 4,900 tons, indicating that lead arsenate has maintained its position in competition with organic insecticides.

Jan 1, 1965

By J. M. Dumore

If in a vertical, downward miscible displacement, the transition zone between the displacing and displaced fluids is neglected, a criterion for stable displacement can be obtained by considering a small hypothetical protrusion of one of the fluids into the other. This criterion leads to the definition of the well-known critical rate, uc = kg p/p. The consideration is further extended by taking into account the transition zone that develops as a result of diffusion and mixing. A generalization of the previous criterion leads to the definition of another characteristic rate, the stable rate, which in actual miscible drives will be less than the critical rate. In such drives, the entire transition zone is stable at rates less than the stable rate. At rates between the stable and critical rates, the displacement is only partly stable, i.e. part of the transition zone adjacent to the displaced fluid is in an unstable position. From that part of the transition zone viscous lingers will develop. At rates greater than the critical rate the entire displacement is unstable and viscous lingers will develop more strongly. Results of laboratory experiments are in agreement with the expected behavior based on the theoretically deduced stability of the displacement. INTRODUCTION The simplest form of miscible drive in an oil-bearing formation is the injection of a fluid that is completely miscible* with the oil under reservoir conditions. In general, such a fluid, a solvent for example, is less dense and less viscous than the oil present in the formation. If it is injected into a horizontal homogeneous layer, gravitational forces will lead to the formation of a gravity tongue of solvent in the upper part of the layer and the adverse solvent-oil viscosity ratio will cause viscous fingers to develop. If, however, the solvent is injected up-structure into ,a dipping layer, gravity has a favorable effect, because it tends to keep the less dense solvent up-structure. Tongue formation and viscous fingering are consequently reduced and it is even possible that they will be suppressed completely. Viscous fingering and gravity tonguing are the consequences of the instability of the displacement. A stable displacement cannot result in growing viscous fingers and/or growing gravity tongues. Since large amounts of oil can be bypassed if there is viscous fingering and/or gravity tonguing, the stability of a miscible drive is very important with respect to the recovery efficiency of the drive. The stability is of particular importance in miscible-slug drives, as it determines how quickly the miscible slug between the displaced and displacing fluids will be distorted and broken up, after which the drive is no longer completely miscible. Stability is thus a most important factor in determining the success of a miscible drive, and it is considered that the aspects of stability considered in this paper will make a useful contribution to existing theories. Consideration is given only to vertical downward displacements, in which no gravity tongues can develop and which are therefore simpler than downward displacements in sloping layers. THEORY CRITERION FOR STABLE DISPLACEMENT Let us consider a vertical column of a homogeneous permeable medium saturated with oil. A solvent less dense and less viscous than the oil is injected at the top of the column at a constant rate; in the column the velocities of oil and solvent are assumed to be uniform. Diffusion and mixing of oil and solvent will at first be neglected, i.e. we assume that solvent and oil are divided by a sharp interface. An additional assumption is that the interface is horizontal. Continuity of pressures exists at the interface, because no capillary forces are present between the two miscible fluids. Consequently, at the interface (Z = I)):** Ps = Po - P-where Ps is the pressure at the solvent side and

Jan 1, 1965

By Kenneth B. Higbie

PRESIDENT LYNDON B. JOHNSON announced at midyear that the test flight of the A-It plane, the world&apos;s first super-sonic aircraft capable of flying 2,000 miles per hour, was made possible by "the mastery of the metallurgy &apos;and fabrication of titanium." Not all of the contributions made by the mineral industry in 1964 were acknowledged so widely. Yet the contributions were significant as the search continued for new and improved methods for providing metals and mineral products to meet the ever-expanding requirements of the world economy. This chapter reviews only a few of the metallurgical developments that resulted from U.S. and foreign research efforts. MINERAL BENEFICIATION Up-to-date theory &apos;and practice in the mineral ,Processing field in 1963 involved subjects such as autogenous grinding, high-intensity magnetic separation, and mill control by computers. These subjects were fully discussed at the Seventh International Minerals Processing Congress held in New York City during September.

Jan 1, 1965