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By E. Martinez, M. L. Hollander

Sulfurization of copper oxides was investigated using differential thermal analysis (DTA) and thermal gravimetric analysis (TGA). When mixtures of cuprous oxide and sulfur were heated, the surface of the cuprous oxide was converted to cupric sulfide at the melting point of sulfur (119°C); additional sulfuriza-tion took place when the sulfur vaporized above 200°C. Cupric oxide also reacted with sulfur to form cupric sulfide but the starting temperature was approximtely 225°C. When the cupric oxide and sulfur were physically separated, sulfurization still occurred indicating a reaction with the vapor phase of sulfur. Sulfurization was obtained in runs with cuprite, chrysocolla and basic copper carbonate. Further decomposition of cupric to cuprous sulfide was noted at somewhat higher temperatures. The DTA-TGA data made it possible to set up postulated reactions in each system. These techniques were found to be well suited for studies of this type. Because of the difficulty encountered in flotation of many metallic oxide minerals, efforts have been made to find suitable reagent combinations to sulfi-dize these minerals in the flotation circuit. Recently Bautista and Sollenberger,1 using a different approach, showed that the surfaces of many oxide minerals can be converted to sulfides by heating them with sulfur to temperatures between 150° and 225°C. This technique was effective even with chrysocolla, a mineral which is very difficult to sulfidize. The primary objective of the present study was to obtain information on the reactions between the oxide minerals and suIfur. A better understanding of the mechanisms involved might prove useful in pointing the way to improvements in the process. A secondary objective was to demonstrate the value of thermo-analysis in investigations of this type. Bollin and Kerr2 have reported the use of a modification of differential thermal analysis to study the thermal reactions which occur on heating elemental constituents in a closed system to synthesize copper sulfides and iron sulfides. Differential thermal analysis (DTA) was used to detect enthalpic changes as mixtures of minerals and sulfur were heated. The DTA indicated the temperatures at which reactions started and whether they were exothermic or endothermic. Weight change data were obtained by thermal gravimetric analysis (TGA). These data could often be used to support postulated reactions and to eliminate consideration of other possible reactions. EQUlPMENT Differential thermal analysis (DTA) involves measuring the temperature difference between the sample being tested and a thermally inert reference, generally aluminum oxide, as both are heated at a uniform rate. Series connected thermocouples in the sample and reference are used to detect the temperature differences that occur as the sample undergoes enthalpic changes.3 Crystalline transitions, fusions, vaporizations, dehydrations, decompositions and many solid state reactions can be detected. A DTA unit manufactured by the Robert L. Stone Co., Austin, Tex., was used in this investigation with a temperature rate increase of 10°C per min. The samples and reference were placed in Inconel cups with wells in the bottom into which the differential thermocouples fit, and run in a nitrogen atmosphere. Thermal gravimetric analysis (TGA) measures the changes in weight that a sample undergoes as it is heated. A Chevenard thermobalance converted electronically for graphic recording was used with a heating rate of 5°C per minute. An X-Y recorder plotted temperature on the X axis and weight changes on the Y axis. A flow of 250 ml per min of nitrogen was streamed through the furnace. Samples were placed in a porcelain crucible open at the top, unless otherwise noted. EXPERIMENTAL RESULTS Sulfur: Two sulfur samples from different sources were tested. The DTA of a high purity sulfur and a reagent grade sublimed sulfur are shown in Fig. 1. Nearly all the tests were run with the sublimed sulfur due to the difficulty in grinding and high electrostatic charge encountered with the high purity sample. Sulfur undergoes three endothermal reactions below 200°C. The first is a solid-solid crystalline transi-

Jan 1, 1964

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 M. Ahlers, Horace Pops

Slip features and formation of stress-induced mm-tensite have been studied in single crystals of fl phase Cu-Zn alloys in the composition range between 43 and 48 at. pct Zn. A phenomenological analysis is presented in which the glide planes and directions that me associated with the inhomogeneous shear in the martensite phase are predicted from the experimentally determined habit planes and macroscopic shear directions. It is shozun that the resolved shew component of the applied stress on the secondary shew system is a very important factor governing the formation of stress-induced martensite. A comparison is made between martensitic phases that form spontaneously upon cooling and those phases that arise from deformation. THE ß phase in Cu-Zn alloys is unstable and may transform spontaneously by a martensitic transformation1-3 during cooling. Thermoelastic and burst-type spontaneous martensitic phases have been observed3 in the composition range between 38 and 42 at. pct Zn. Martensite forms in alloys containing more than 42 at. pct Zn only by cold work below a temperature denoted as Md.4 Thus, alloys near the equiatomic composition can undergo a stress-induced transformation upon cold work at room temperature. Although data have been obtained concerning the effect of temperature5 and composition4 on the deformation of polycrystalline Cu-Zn alloys, it is rather surprising that few detailed studies6-8 on 6 brass have been conducted for single crystals where the stresses acting on crystallographic planes can be determined. A thorough understanding of transformation mechanisms requires knowledge of the role of stress and plastic strain. With this objective in mind we have made an investigation of the stress-induced rnartensite transformation in single crystals of 0 brass in the composition range between 43 and 48 at. pct Zn. Particular emphasis is given to the morphology and crystallographic features and a comparison is made between stress-induced and spontaneous martensite. I) EXPERIMENTAL PROCEDURE Master alloys having nominal zinc contents of 43, 45, and 48 at. pct were prepared from spectroscop-ically pure metals (>99.999 pct) in sealed quartz tubes under a partial pressure of helium. These alloys were cut into several pieces and converted into small rods by melting in quartz tubes. Subsequently, single crystals were grown from the rods by the Bridgman technique and homogenized for 3 hr at 820°C. Lattice parameter measurements were made from stress- relieved filings. Compositions, as determined from the reported variation of lattice parameter with atomic percent zinc,' indicated a zinc loss of less than approximately 0.25 at. pct. The single crystals were electroturned using a phosphoric acid electrolyte into tensile specimens each with a center section of 1 mm diam and 1 cm gage length. Cylindrical specimens approximately 3 mm in diam and 10 mm long and spark-machined rectangular blocks approximately 3 by 3 by 10 mm were prepared for compression studies. These blocks were stress-relieved and electropolished to eliminate any stresses introduced by spark machining. Crystal orientations were determined to an accuracy of ±2 deg primarily from back-reflection Laue photographs, and sometimes by the rotating single-crystal method. Figs. 1 to 3 show the location of the tension and compression axes within unit stereographic triangles. All specimens were deformed plastically at room temperature using an Instron machine, the crosshead speed being 0.02 or 0.05 cm per min. A hard steel hemisphere was placed at the upper end of the compression samples to achieve uniaxial loading. Trace normals of slip markings and habit planes of strain-induced martensite were determined to an accuracy of ±4 deg from the rectangular blocks by a two-surface analysis and from cylindrical specimens by measuring the angle between the tensile (or compression) axis and the tangent to the surface trace for different rotations about the deformation axis. Slip

Jan 1, 1969

By R. F. Steigerwald

The effects of heat transfer on the corrosion behavior of type 304 stainless steel in boiling water have been studied. Heat transfer conditions increase the tendencies of the stainless steel toward stress-corrosion mucking when the water is contaminated with Cl-. Surface preparation is the most important variable in determining the severity of the stress-corrosion problem in water with a given Cl- content. Heat treatment, chemical cleaning, and degree of wet film boiling also affect the corrosion of stainless steels used as heat transfer surfaces in boiling water. An up-paratus for corrosion testing under controlled heat transfer conditions is described. THE principal objective of this investigation was to study the corrosion behavior of AISI Type 304 stainless steel in boiling high-purity water under conditions of heat transfer. The principal variables in the study were: a) boiling conditions: limited boil, agitated boil; b) metallurgical structure: annealed or sensitized; c) surface condition: rolled, pickled, or ground. The results of the study should elucidate the role of heat transfer in the corrosion of stainless steel in boiling high-purity water and provide a base line from which to assess the severity of this type of corrosion. Although there has been an investigation of the effect of heat transfer on the corrosion behavior of stainless steels in alkaline waters,' work on the corrosion of stainless steels under heat transfer has been largely confined to various acid solutions.'-4 Furthermore, the study of the corrosion of stainless steels in high-purity water has been generally restricted to auto-clave and instream testing in superheated (e.g., 300°C) water and steam.5'6 Cooling water problems led to this study of the corrosion behavior of type 304 stainless steel in high-purity water at its atmospheric boiling point. In addition to the effects of heat transfer, this study also considered the influences of the type of boiling,7 metallurgical structure, and surface condition on the corrosion behavior of stainless steel in high-purity water. Two boiling conditions were investigated in this study: a) limiting boiling, i.e., when the heat-transfer surface had just reached the boiling point and boiling nucleated randomly over the specimen surface and b) agitated boiling, i.e., when a mild degree of superheat had been achieved on the specimen surface and boiling occurred generally over the specimen surface. Both boiling conditions are broadly classified as wet-film boiling. Originally, this program included the study of a third type of boiling, dry-film conditions. At dry-film boiling the temperature of the heat transfer surface is high enough so that it is covered with a continuous film of steam. Experimental difficulties made it impossible to study this kind of boiling with the available apparatus. Since surface condition affects heat transfer rates, three typical surfaces were chosen for study: a) as-rolled, the 2B finish received from the supplier, b) as-pickled, 30 min in 8 pct HNO3-1 pct HF, and c) as-ground on 120 grit paper. In order to evaluate the effect of improper heat treatment or welding on hot wall corrosion, both annealed and sensitized mi-crostructure were included in this study. EXPERIMENTAL Test Apparatus. The particular problems of interest in this investigation required a knowledge of the thermal gradient through the test specimen. From this gradient, the heat flux to the surface and the surface temperature could be determined. In order to satisfy this need, an apparatus similar to the boiling-disk apparatus of Fisher and whitney2 was designed. The solution is contained in a thermally-insulated, steel pipe lined with TEFLON resin. A stainless steel _______;________________________________________

Jan 1, 1970

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

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

By G. S. Cole, G. F. Bolling

ThE exact type of fluid flow which occurs in a solidifying ingot is important in determining subsequent grain structure. This has been shown in studies of natural Convection" and of forced stirring or other disturbances of the melt."16 We shall explicitly argue that a complement to the existing natural flow in an ingot should be more effective than other types of flow in promoting the columnar-to-equiaxed transition. The ultimate effects of fluid flow upon structure is one of the topics of solidification that we have investigated in the alloy system Pb-Sb, under conditions simulating casting. In Fig. 1, the essential features of a bidirectional growth apparatus are shown; horizontal freezing from water-cooled faces within a low-thermal-conductivity lavite boat is a reasonable simulation of an ingot section. Details such as the furnace and thermocouples are omitted in order to show the location of four permanent. magnets, each with a pole separation of 21 in. providing a central field of about 1000 Gauss. When coupled with a dc current imposed through appropriate connections made at the cooled faces, a flow of fluid is produced as shown schematically. This technique described by Pfann and ~orsi" is ideal for our purpose since the flow indicated is the same as that we observe to occur naturally in this system. Components of 99.999 pct purity were used for study and all due precautions were taken in alloy preparation to avoid contaminants. Sections of the specimens were taken to ensure results representative of the interior as well as the surface of specimens. All proportions of equiaxed and columnar regions were measured by tracing the etched grain structures onto graph paper and simply counting squares. Four alloys were examined at superheats of 40" * 5°C and 100" * 9°C. Preliminary tests had shown that no appreciable enhancement of structure was obtained with magnetic field alone, so that this condition is not reported; it should nevertheless be noted that other configurations of magnetic field will reduce convection and thus enhance columnar growth.&apos;8 For the tests reported the magnetic field was applied to a specimen by bringing the four preassembled magnets to a position 2 mm from an outer tube immediately after the ingot was poured. The dc current of 30 amps passed through the sample throughout the entire solidification cycle, resulting in a power dissipation of 9 w per sq cm of interface. This may be compared to the evolution of latent heat of approximately 18 w per sq cm. Table I contains the results of this experiment in terms of the total area ratio, equiaxed/columnar grains, as a function of the field interactions, solute concentrations, and superheats employed. The total structure of the ingot is seen to be most influenced when both the field and current are applied simultaneously; when current acts separately, little effect may be noted in spite of the heat supplied. In addition, the change in structure from the no field-no current case to the field-current condition is more pronounced at the higher superheat, and the higher the concentration of antimony. An example of the grain refinement, as well as the increased equiaxed zone, is shown in Fig. 2. It is now important to prove that there is indeed an increase in fluid flow due to the presence of the field-current interaction; this is done by temperature measurements in the liquid metal. Let us consider a bidirectional casting in which heat is applied to and removed from the system, in such a way that rate of solidification is zero.* When a sensitive thermocouple

Jan 1, 1967

By R. M. Goldhoff, J. W. Spretnak

IN connection with establishing the mechanism by which boron enhances the hardenability of heat treatable steels, this research work has been undertaken. Spretnak and Speiser1,2 indicated the need for studying high temperature effects in boron steels and, chief among these, the possible nonhomogeneous distribution of boron in iron grains. The occurrence of this effect may be of significance in explaining the mechanism of enhancement of hardenability by boron as well as in explaining some of the observed characteristics of boron steel behavior. Primarily, then, this work was undertaken a) to establish whether or not boron is adsorbed in ? solid solutions, b) to determine the nature of any such adsorption effects, i.e., whether it is positive or negative as well as its temperature coefficient, and c) to establish the magnitude of any such effect. While past literature on this specific subject is rather sparse, a number of authors have postulated that the observed temporary loss of hardenability as well as the occurrence of the characteristic boron constituent in these steels is due to the nonuniform distribution of boron in austenite.3-0 Experimental Techniques Attempts to obtain direct evidence of grain boundary effects in boron steels have been unsuccessful, both by using the technique of Chalmers&apos; in which small concentrations of solute made radioactive by irradiation are detected by autoradiographic means, and by means of studying cleavage fractures with the electron microscope.8 The present study attempts the design of experiments to measure the effect of boron on properties which might be subject to variation because of grain boundary effects. A study of the theoretical aspects of grain growth indicates that such studies may be pertinent. Another valid type of experiment involves the measurement in polycrystalline materials of properties whose values depend on the bulk of the grain, being negligibly influenced by grain boundaries. One such property is the lattice parameter measured by X-ray diffraction. The value of the lattice parameter reflects the average conditions which obtain over a relatively large number of atoms in a fixed crystalline lattice, and is therefore mainly dependent on bulk grain material. Measurement of lattice parameter variation over the austenite range of temperature in iron with and without boron should give evidence of concentration variations in the bulk grain material if adsorption effects are significant. Finally, use is made of the Grange and Garvey3 metallographic test for boron in which a characteristic boron constituent can be developed in austenite grain boundaries. The very occurrence of this phenomenon suggests grain boundary enrichment of boron and a study of the occurrence of this constituent and its varation with austenitizing temperature should help to detect grain boundary effects. Materials One lb ingots of pure iron, an Fe-B alloy, an Fe-C alloy, and an Fe-C-B alloy were prepared. The melting technique included an initial melting of electrolytic iron under vacuum followed by remelting under hydrogen and, finally, by melting under argon with the addition of alloying elements. Each ingot was surface machined between meltings. A quantitative spectrographic analysis was obtained on the pure ingot and, in addition, oxygen, nitrogen, and carbon were determined by the vacuum fusion method. The results of these analyses are given in Table I. Semiquantitative spectrographic analyses were performed on the alloy ingots, while quantitative determinations of the alloy additions were obtained. These analyses are shown in Table 11. The cast ingots were subjected to the following sequence of fabrication treatments: forging to 5/8 in. bars, swaging to 0.300 in. rounds, drawing to 0.025 and 0.010 in. wire. Portions of each ingot were retained in the swaged condition for experimental use. For certain portions of the work typical commercial steels were used. These materials were supplied by the Republic Steel Corp., Canton, Ohio, and correspond to AISI 8640 and AISI 86B40 compositions.

Jan 1, 1958

By R. D. Pehlke, J. V. Gluck

The limiting activity coefficient of zinc in a "binary " solvent has been described for several dilute ternary solutions by combining literature data from recent interaction studies in the terminal regions with thermodynamic data for the central regions. Results are discussed in terms of the Alcock and Richardson random solution model. The observed behavior agrees semiquantitatively with predictions using the model. RECENT efforts in the thermodynamics of dilute ternary liquid metallic solutions have been mainly concerned with the interactions between two dilute solutes, that is, the terminal region at an apex of the composition diagram.&apos;-&apos; A more general case is that of the behavior of a dilute solute over the full range of a ternary system, or, more specifically, the limiting activity of solute i as projected to the k-j binary side of the i-j-k composition triangle. An implication of this is that the interaction between i and j at the k apex should connect in some way to the interaction between i and k at the j apex. A model to characterize various types of expected behavior has been discussed by Alcock and Richardson.9,10 Such behavior can range from a simple linear relation for In yi over the 1-k binary to more complex curved relations which depend on various assumptions regarding the heat of solution in the j-k binary system and the presence or absence of clustering with solute i. Quantitative data to assess these concepts have been limited primarily to the cases of nonmetallic interstitial solutes in ferrous solutions. Alcock, Richardson, and various coworkers9-13 have discussed the behavior of oxygen, sulfur, silicon, or hydrogen in dilute solution over the range of iron + metal systems; however, the only data considered by them for substitutional nonferrous metallic solutions were the results of Elliott and Chipman concerning the activity of cadmium in the Pb + Sn, Pb + Bi, and Pb + Sb systems.9 These data were limited and did not cover the terminal regions in detail. An opportunity to extend the Alcock and Richardson considerations to the dilute solution of zinc in various "binary" solvents has been afforded by combining results of several of the recent investigations of ter-minal-region interactions with previous data from the literature for the same more concentrated solutions. RESULTS AND DISCUSSION The results of the analysis are shown in Figs. 1 to 5 where the log activity coefficient, (In yZn)xzn--o, is plotted vs the composition of the "binary" solvent. In these plots the end points are the values for In yzn in the appropriate binary solution with Bi, Pb, Sn, Cd, or In at the indicated temperature—usually 550°C (823°K). For the terminal regions the slopes were drawn using the first-order interaction parameters taken from various studies reported in the literature. The data points shown in the central regions were obtained by the short extrapolation to infinite dilution of the logarithm of the activity coefficient calculated from thermodynamic studies reported in the literature for the same systems. The sources of the data are indicated on each figure. Second-order effects were not considered. Reasonably smooth curves can be drawn to connect the central region with the terminal regions for the Zn-Pb + Bi system, Fig. 1, the Zn-Pb + Zn system, Fig. 1, and the Zn-Bi + Cd and Zn-Bi + Sn systems, Fig. 2. As shown in Fig. 2, where central region data are available from two independent investigations, the agreement is quite good. The Zn-Pb + Cd system does not appear to be as well behaved as the previous four, Fig. 3; however, this type of behavior has also been

Jan 1, 1970

By Richard H. Siller, Rex B. McLellan

A model for interstitial solid solutions has been considered in which a repulsive Potential exists between interstitial atoms in the solvent lattice. It has been shown that this model is consistent with the thermodynamic Properties of certain interstitial solid solutions. The model is then applied to the calculation of the variation of the diffusivity of carbon in au-tenite with composition. Although the energy levels at the saddle point, and thus the absolute values of dif-fusivity, cannot be calculated, it is shown that by taking the repulsive interactions between the diffusing atoms into account the functional form of the dependence of diffusivity on solute concentration can be derived. ThE composition dependence of the diffusivity, D, of carbon in austenite at a given temperature is well-known.&apos;-3 smith3 tried to reconcile the observed composition dependence of D at 1000°C with the previously observed4 composition dependence of carbon activity using equations for D derived by arken5 and Fisher, Hollomon, and Turnbull,6 but was unsuccessful. In this paper we shall modify the approach of Fisher et al. by considering the "blocking" model7 for interstitial solid solutions, based on concept due to Speiser and Spretnak,&apos; in which a repulsive potential exists between interstitial solute atoms in the solvent lattice, causing a certain number of interstitial sites to be "blocked" from occupancy by further solute atoms. We shall thus be able to describe the intimate relationship between the composition dependence of carbon diffusivity, a kinetic phenomenon, and the composition dependence of carbon activity in austenite. THEORY Consider for convenience one-dimensional interstitial diffusion in an fcc lattice in the [loo] direction. Fig. 1. Assume that solute atoms occupy octahedral sites only.7,9&apos;10 These octahedral sites are located on {lOO} planes a/2Å apart. A solute atom, A, occupying an octahedral site on a {100 } plane denoted by 2, has twelve nearest-neighbor octahedral sites: four on plane 1, four on plane 2, and four on plane 3. Diffusion occurs when there is a net flux of solute atoms, through an imaginary plane shown with dashed lines, from plane 2 to plane 3. Fisher et al6. use the concept of activated complexes, as given in the theory of absolute reaction rates." They show that the number of solute atoms per cubic centimeter per second which pc — Fig. 1-Diagram showing the arrangement of octahedral sites (x) in the fcc lattice. pass in the direction of diffusion from activated to new interstitial position is: ?where C is the concentration of the solute in atoms per cubic centimeter, l/m + is the fraction of new interstitial positions corresponding to motion in the forward diffusion direction (transmission coefficient), ?F* is the free-energy difference between the activated complex and the reactants when each is in its standard state at the temperature of the reaction (independent of temperature and composition in the case of carbon in austenite), y is the activity coefficient of the solute species, and, finally, ym is the activity coefficient of the activated complex (assumed constant). The flux of atoms moving in the forward direction through an area of 1 sq cm perpendicular to the direction of diffusion is therefore: m+ Ym l &apos; atoms per second where is the distance between planes. The blocking model states that a nearest-neighbor octahedral site of a given solute atom has a probability, f, of being inaccessible to other solute atoms. The number of available sites for diffusion on a given plane will, therefore, depend on f, which is constant, and Nu, the number of solute atoms on that plane. The effect is to have more available sites in the diffusion direction, thereby increasing the net flux of solute atoms. This is reflected in the transmission coefficient, l/m. To calculate the transmission coefficient for solute

Jan 1, 1970

By David E. Nicholas

INTRODUCTION In this paper, a numerical process for selecting a mining method, with the emphasis on underground mass mining techniques, such as caving, induced caving, and stoping, is proposed. In the past, selection of a mining method for a new property was based primarily on operating experience at similar type deposits and on methods already in use in the district of the deposit. Then, the chosen method was modified during the early years of mining as ground conditions and ore character were bet- ter understood. Today, however, the large capital investment required to open a new mine or change an existing mining system make it imperative that the mining methods examined during the feasibility studies and the method actually selected have a high probability of attaining the projected production rates. Although experience and engineering judgment still provide major input into the selection of a mining method, subtle differences in the characteristics of each deposit, which may affect the method chosen or the mine design, can usually be perceived only through analysis of measured characteristics. The parameters that must be examined when choosing a mining method include: 1) geometry and grade distribution of the deposit; 2) rock mass strength for the ore zone, the hanging wall, and the footwall; 3) mining costs and capitalization requirements; 4) mining rate; 5) type and availability of labor; 6) environmental concerns; and 7) other site-specific considerations. This paper encompasses a detailed look at the first two parameters since they, plus mining costs, have the greatest impact on the selection of a mining method. The proposed method selection process is for a project where drilling has defined sufficient geologic reserves, but little or no underground development has been done. Since each deposit has its own characteristic geanetry/grade distribution, and rock mechanics properties, mining method selection should be at least a two-stage process. In Stage 1, the deposit is described in terms of geometry, grade distribution, and rock mechanics properties. Using these parameters, the mining methods can be ranked to determine which are most applicable; they can then be considered in general terms of mining and capitalization cost, mining rate, type and availability of personnel, environmental concerns, and other site-specific considerations. In Stage 2, the most likely mining methods are costed out, based on a general mine plan. Mining and capitalization costs are used to determine a cut-off grade fran which a minable reserve can be calculated; economic comparisons can then be made to determine the optimum mining method and economic feasibility. During the mine planning phase of Stage 2, rock mechanics information would be used to provide realistic estimates of underground opening size, amount of support, orientation of openings, and caving characteristics, and open pit slope angles. If ground control or operational problems should be encountered with the methods being considered, modifications could be made. Although planning on paper extends start-up time, it is cheaper to err on paper than to find the error after mining has begun. METHOD SELECTION - STAGE 1 The main purpose of Stage 1 is to select those mining methods which should be considered in greater detail. The simplest way to do this is by defining those characteristics required for each mining method and then determining whether the characteristics of the deposit are suitable. However, no one mining method is so restrictive that it can be used for only one set of characteristics, as indicated by the classification system proposed by Boshkov and Wright (1973). In the mining method selection proposed, geometry, grade distribution, and rock mechanics characteristics are ranked according to their acceptability for ten general mining methods.

Jan 1, 1981

By G. C. Bernard, L. W. Bernard, L. W. Holm, W. L. Jacobs

The effect of loam on the permeability of porous media to water was studied as a {unction of foaming agent concentration, specific permeability, pressure gradient, length of a porous medium and its oil saturation. At a given fluid saturation in a porous medium, the permeability to water was found to be the same whether loam was present or not. Foam decreases the permeability to water by developing a higher trapped gas saturation than that obtained by water flooding without loam present, increasing the concentration of foaming agent increased the trapped gas saturation and thereby decreased the permeability to water. The presence of oil reduced the capability of most foaming agents to decrease the permeability of a porous medium to water. A few surfactants were found to be effective loaming agents even in the presence of oil. These results are similar to those reported in a previous paper on the effect of loam on the permeability of porous media to gas. The effect of loam was found to persist in long porous media at moderately high reservoir temperatures and during the passage of many pore volumes of surfactant-free water. INTRODUCTION This paper describes part of a study on a novel approach in the use of surfactants for oil recovery; the use of foam rather than water to displace oil. Previously it was found that foam can displace oil which normally is not displaced by water.4 The foam is formed by successively injecting a suitable surfactant solution and gas into a porous medium. Foam appears to have at least two uses in the field: (1) it shows promise as a superior oil recovery agent, and (2) it shows promise as a selective permeability reducing agent. Foam may be very useful in water floods, or in other oil recovery processes, where highly permeable streaks or unfavorable mobility ratios are a problem. A previous paper reported the effect of foam on the permeability of porous media to gas.1 In the present study the effect of foam on the permeability of porous media to water is reported. The specific objectives of the study were to determine: (1) the effect of foam on the permeability to water in porous media of various specific permeabilities, (2) the effect of foam on the permeability to water in the presence of oil, (3) the effect of foam and crude oil on the trapped gas saturation, (4) the effect of foam on permeability to water at trapped gas saturation, (5) the effect of pressure gradient on the permeability to water under foaming conditions, (6) the persistence of foam during the passage of surfactant-free water through the porous medium, and (7) the effect of various foaming agents, length of the porous medium and temperature on the permeability reduction caused by foam. EXPERIMENTAL PROCEDURES EQUIPMENT AND MATERIALS The experimental apparatus consisted of consolidated and unco n soli dated porous media, wet test meters and constant delivery pumps. The porous media consisted of consolidated sandstone cores (6 to 36 in. long), and unconsolidated sand packs (3 to 30 ft long). The consolidated cores had permeabilities of 32 and 1,000 md and porosities of about 20 per cent. The sand packs had permeabilities of 3,500 to 211,000 md and porosities of about 40 per cent. (Throughout this report a term such as 100 md sand" is used. This term means that the porous medium had a dry, nitrogen permeability of 100 md.) Fluids used in the experiments were distilled water, 1 per cent NaCl solution, aqueous solutions of foaming agents, nitrogen gas, air and crude oil.

Jan 1, 1966

By Henry A. Wriedt, John Chipman

Equilibrium in the reaction of hydrogen gas with oxygen in liquid nickel, iron, and their alloys has been studied at temperatures of 1500° to 1700°C. The equilibrium con^stant, 0/p, [% O], is greater in nickel then in iron by a factor of 45 at 1594 C. In the alloy steel range, the activity coefficient of oxygen is slightly increased by the presence of nickel. NICKEL is more resistant to oxidation than is iron, in both the solid and the liquid state. The solubility of oxygen,&apos; however, is greater in nickel than in iron. The two metals and their liquid alloys constitute an interesting series of solvents in which the chemical behavior of oxygen can be studied by methods similar to those used for liquid iron.&apos; Experimental Method The furnace assembly, including the tube for preheating the entrant gas, was the same as that described by Gokcen and Chipman. " controlled mixture of water vapor, hydrogen, and argon preheated to approximately the melt temperature impinged upon the surface of the liquid metal. The charge, weighing about 35 g, was held in an alumina crucible at constant temperature in the gas stream for a prolonged period, then quenched in a stream of cold helium, sampled, and analyzed for oxygen by the vacuum fusion method. The temperature of the liquid metal was measured by a Leeds and Northrup optical pyrometer which had been checked against a similar instrument certified by the National Bureau of Standards. The freezing point of electrolytic iron in hydrogen, taken as 153j°C, was used for frequent checks. This point and the emissivity determined by Dastur and Gokcen" established the transmissivity of the optical system. The emissivities of Fe-Ni alloys at 1535" are known from the experiments of Smith and Chipman,h nd it was assumed that the variation with temperature is parallel with that of iron. Recorded temperatures are probably accurate within k5"C. Preparation of Gas Mixtures—Since the ratio H,O:H, had to be much higher for nickel than for iron, it was found convenient to construct two separate systems for gas preparation. In both cases, the ratio of argon to the sum of the other two gases was at least 4, the proportion of hydrogen and water vapor being varied to produce H,O:H, ratios from 0.2 to 70. The primary purpose of the argon was to diminish the errors caused by thermal separation&apos; in the gas phase. In addition, its presence lowered the saturation temperature required for a given H,O:H, ratio and minimized the difficulty of preventing condensation. Both systems were modifications of the one used by Dastur and Chipman.&apos; For H,O:HI ratios greater than 2, welding-grade argon purified by passage over magnesium chips at 620°C was mixed with hydrogen produced in the electrolytic cell shown in Fig. 1. The design was based on a cell used by Bodenstein and Pohl," the important features of which area nickel wire cathode and sodium hydroxide solution as the electrolyte. The rate of hydrogen evolution was controlled by a calibrated ammeter and a rheostat in the circuit, the current efficiency being taken as 100 pct. Precise control of the argon flow rate at about 300 ml per min was achieved by means of a capillary flowmeter having a controlled pressure drop. The molar flow rate was measured volumetrically before each run, and a constant flowmeter setting was maintained thereafter. The A-H, mixture passed through a water saturator of the type previously described," the saturation temperature being maintained automatically with a fluctuation of k0.04"C. The tube between saturator and furnace was heated by a resistance winding. The system was of all Pyrex construction with the exception of the stainless steel tube containing magnesium chips. This was connected with the glass tubing at the upstream end by

Jan 1, 1957

By J. C. Griffiths, D. W. Bennion

A mathematical model, which does not assume a priori that stratification exists, but was designed to test for the stratification was developed. The model segmented the reservoir horizontally into areas of common variance, then divided it vertically into strata (if strata were present). Next, trend surface techniques were used to determine the lateral extent and variation of each stratum. The model was tested on two reservoirs (sandstone and limestone) using porosity as the reservoir rock property. The sandstone reservoir contained approximately 60,000 samples from 2,000 cored wells, while the limestone reservoir had approximately 24,000 samples from 430 cored wells. Within the areas of common variance tested, the model was able to distinguish four separate lithological units or zones in the sandstone reservoir, four in the Marly section and seven in the Vuggy section of the limestone reservoir. INTRODUCTION To accurately predict the movement and production of fluids from a reservoir rock, it is necessary that the reservoir engineer have a knowledge of the rock properties and their distribution throughout the reservoir. For this study, a reservoir rock is defined as a solid containing interconnecting holes or voids which occur relatively frequently and are dispersed within the rock in a regular or random manner. The fraction of bulk volume that these interconnecting voids occupy is called porosity. The rock must also possess sufficient permeability to allow fluids to move through it and it may be composed of one or more strata or lithological units. A stratum or lithological unit as defined in this study is a body or volume of reservoir rock whose properties are so distributed that its lateral and vertical extent can be traced throughout or through a portion of the reservoir. Operationally, the existence of strata are question- able unless the variance within strata is less than among strata. Within the past few years computers have been widely used as a tool for calculating movement and production of fluids from reservoirs. Most prediction models require some type of a mathematical description of certain reservoir rock properties. In the past, most of these models have been relatively simple. Some have assumed vertical variation but no lateral variation, while others have assumed lateral variation but no vertical variation. In general, most of these models have not used functional relationships to predict reservoir rock properties as functions of position. The object of this study was to develop a model which would predict lateral and vertical variations of reservoir rock properties. Since samples are usually available from only a small portion of the total reservoir rock, it seemed logical that if measurements from these samples were to be used to infer the properties of the actual reservoir, the data should be treated statistically as a sample from the total population (reservoir). Therefore, the model developed in this study to predict reservoir rock properties was a stochastic model. The model was tested using porosity (a macroscopic reservoir rock property) measurements from two reservoirs — the first, a sandstone reservoir from which 60,000 samples were obtained; and the second, a limestone reservoir with 24,000 samples. Several investigators have proposed methods to determine the vertical and areal variation of a reservoir rock property. Stiles: Dykstra and Parsons 2 and Suder and Calhoun3 have all developed waterflooding prediction techniques which assume vertical variation but no lateral variation. Stiles developed a method to segment a reservoir arbitrarily using frequency distribution. Law4 suggested that porosity has a normal frequency distribution and that permeability has a log-normal frequency distribution. Elkins and Skov 5 proposed that when a reservoir is segmented vertically, the

Jan 1, 1967

By R. L. Segall

AN unusual thermal etch figure in copper is described and an explanation in terms of twinning is suggested. A flat polycrystalline specimen of OFHC copper cut from a rolled sheet was electro-polished in orthophosphoric acid and annealed at 950°C in a vacuum of approximately 10-3 mm Hg for 2 hr. The specimen was found to be thermally etched, the markings on the surface being consistent with the assumption that they were the traces of the (111) planes which are developed preferentially because they have the lowest free energy. However, on one grain (the grain shown in Fig. 1) the traces formed an almost regular pentagon and at first sight it seemed unlikely that they could all be (111) traces. These traces were studied further because it was thought that they might be a type of growth spiral. A fringe pattern showed that this was not so, the grain being sensibly flat and the only features having steps were the striations and the faint curved line passing out from the center of the pentagons. To obtain some additional information, the specimen was deformed in tension. The effect of the stress was first to cause the appearance of lines running from the centers to the apexes of the pentagons and then to tilt the five segments so formed. At a much greater stress, appreciable slip appeared on the grain; these effects can be seen in Fig. 2. The micrograph was taken at a fairly late stage in the deformation and the tilting is quite marked. The magnification is the same as in Fig. 1, and although some slip can be seen it could be observed better by varying the illumination and using higher magnifications. In each segment of the grain, slip (which takes place on the (111) planes) was parallel to the side of the pentagon in that segment. The marked changes in direction of slip from segment to segment seemed to be incompatible with the presence of a regular array of subgrains. These results suggest that some of the five segments were twins. If this is so, since the twinning plane in copper is the (111) plane, the radial lines must be traces of the (111) planes on the surface. From the symmetry of the striations about the radial lines, these planes must be almost perpendicular to the surface. The angle between <III>directions in face-centered-cubic copper is 70&apos;32&apos;. If, in Fig. 3, OAB (triangle 1) is taken as matrix and OA, OB are (111) planes viewed edge on, then AB is in the correct direction to be the trace of either of the other two (111) planes on the surface. If triangle 2 is the twin (about the (111) plane perpendicular to the surface and containing OB) of triangle 1, then once again it can be shown that all lines are traces of (111) planes. Similarly, triangle 3 is the twin of triangle 2, 4 of 3, and 5 of both 4 and 1. (The sequence is, of course, quite arbitrary.) However, if this were the case there would be a discrepancy of 7&apos;20&apos; to be accounted for. It is suggested that the faint curved line passing outward from the center of the pentagon represents either a low angle boundary or a sixth small twin. The slight step shown by the fringes at this line might be an indication that the former is the case. This explanation does not account for the coincidence of obtaining a grain whose surface must be so close to (110) and obtaining the curious twinning described previously; it would be of interest to find a specific mechanism for this.

Jan 1, 1958

By Cleland N. Conwell

APPLICATION of seismic methods to the location of buried channels in placer mining is fairly common knowledge, yet some of the facets of seismic refraction surveys have remained obscure in their application to mining. This description by a member of the U. S. Bureau of Reclamation team investigating bedrock at the Oso Dam site, may offer a lead to wider application of the method for bedrock determinations in engineering of mine and mill plants, tailing disposal, and water supply. It may also offer assistance in planning geological exploration in areas covered by overburden. Pertinent, and perhaps more than passingly significant, is that the seismic survey of the Oso dam site started at noon and was completed the afternoon of the next day. Location Oso dam site is on the Navajo River, Archuleta, County, Colo., 30 miles southeast of Pagosa Springs, Colo., 10 miles northwest of Chama, N. M. Bedrock at the proposed dam site is Mesa Verde Formation, Cretaceous age sandstone. The nearest good sandstone exposure is about 5/8 of a mile upstream from the location of the seismic determinations. The material above bedrock is sand and gravel with sandy loam soil covering benches above the river. The site appeared favorable, after a geologic and topographic reconnaissance, but overburden thickness was unknown. Exploratory drilling was not contemplated in the near future so a short seismic investigation was selected as the most suitable method of determining depth to bedrock. Field Procedure Geophysically, a seismic depth investigation is simply the measurement of depth from ground surface to the top of a layer which transmits seismic waves at a higher velocity. In this case the high-velocity seismic layer tentatively correlates with the Mesa Verde sandstone. Field procedure required a seismic explorationline or "spread" with 12 geophones set at measured intervals. Explosive charges were buried at few feet in the ground and detonated at shotpoints near the ends of the spread, and at intermediate points. The time of travel of the seismic waves from the shotpoints through the ground to each of the geophones along the spread was measured and recorded photographically with equipment housed in a field truck. The seismograph on each spread provided a time-travel graph. From it were computed the speed of seismic waves in various layers below the surface and depth to each different seismic layer below the shotpoint. In the case of the Oso dam site it was possible, in addition, to determine the depths below certain geophones, because there were only two seismic layers involved. Interpretation In seismic exploration waves are refracted from the top of layers which often correspond to divisions between subsurface formations. When drill holes are available the geologic logs offer a means of correlating stratigraphic breaks with seismic layers, improving reliability of seismic interpretation in terms of depth to bedrock or other geologic terms. There were no drill holes available in the case of the work at the Oso dam site. Geologic conditions appeared favorable for seismic technique because of excellent contrast in seismic wave velocity between the overburden and the Mesa Verde formation. The upper layer had a velocity of approximately 2500 fps and was interpreted as overburden, the lower layer had a velocity of approximately 9000 fps and was assumed to be the sandstone. These velocities are of the order expected in these materials. The seismographs obtained at the Oso dam site were excellent. The energy from the shot came in strongly at each geophone, giving an easily read record. Time-travel graphs plotted from wave arrival times were uniform and made interpretation comparatively easy. In Spreads 1 and 2 near the river the lower velocity layer was 12 to 15 ft deep. For the spreads on higher ground, or the bench south of the river, it was from 15 to 29 ft deep.

Jan 1, 1952

By M. T. Simnad, C. E. Birchenall, M. H. Davies

THE marker movements observed by Davies, Simnad, and Birchenall during the growth of magnetite on wustite have been misinterpreted. It is the purpose of this note to correct the original interpretation. In that investigation wustite specimens were prepared by oxidizing pure iron disks in water vapor until the iron was consumed. Argon was used as a carrier gas for the water vapor and on the complete conversion of the metal to its oxides (&apos;FeO&apos; plus a small amount (10 pct) of surface Fe3O) the water supply was bypassed and the specimens were annealed in argon alone in order to equilibrate the wustite with the overlying magnetite. After cooling, the magnetite was ground off, a crude magnetic test being employed to determine its complete removal. Radioactive silver streaks were then applied to the surface and the specimen was oxidized completely in water vapor to prevent hematite formation. After complete oxidation the markers were found to enclose about 80 pct of the magnetite with the other 20 pct lying outside the markers. This observation was interpreted to mean that oxygen transport was four times as great as iron transport during the growth of the magnetite. The conclusion would have been correct if, as in the case of wustite growing on iron, all the iron had started from one side of the marker and all the oxygen from the other side initially. Actually a material balance is required. For simplicity, take wustite to be exactly FeO, and magnetite to be Fe3O,. Then at the start of the reaction 3 FeO + O -> Fe,O., All of the iron and three-fourths of the oxygen of the final product will be within the marker inter- faces. The other fourth of the oxygen is in the gas phase outside the marker. From the experimentally determined final position of the markers simple calculation shows that one-fifth of the total iron has crossed the marker interface, while one-twentieth of the total oxygen has crossed in the reverse direction. The simplified result favors iron transport in the ratio four to one. However wiistite is not stoichiometric FeO. At 900°C, the temperature of the measurement, the composition is about FeO When the material balance for the same experimental result is repeated, assuming the product will be 1 mol of Fe3O4, it is found that 0.6 gram atoms of iron and 0.19 gram atoms of oxygen must have passed the marker in the same direction. (This is readily apparent from the reaction to form 1 mol of Fe3O4 SFeO The total oxygen supplied from the atmosphere is 0.61 gram atoms, but the iron which passes the marker interface, i.e., 0.6 gram atoms, requires 0.8 gram atoms of oxygen to convert it to Fe,O,.) If all the transport during magnetite growth is due to iron ion diffusion, then the marker would enclose about 85 pct of the final magnetite and the original measurement is in error by about 5 pct. This error is probably less than the uncertainty in locating the markers by autoradiography. The possibility also exists that the starting wustite was not quite saturated with oxygen and underwent further enrichment with consequent envelopment of the marker before magnetite caught up with the marker interface. In any case it appears that these measurements actually favor iron ion diffusion in magnetite overwhelmingly as the factor controlling its growth, although further experimental measurements are needed to eliminate the error in material balance described. Such studies are planned.

Jan 1, 1954

By C. G. Dunn

The measurement of interfacial teusions or grain boundary energies in metals is an important metallurgical problem, especially since it bears on growth and nucleation processes. Statistical methods of measuring equilibrium grain boundary angles, which relate interfacial tensions, have been used by some investigators1&apos;2 but more direct methods would be preferred. A direct way, based on a simple extension of a successful method of growing single crystals of silicon ferrite to predetermined orientations in flat specimens,3 is to produce three-grain specimens in such a way that the equilibrium common grain boundary will be perpendicular to the surface of the specimen. The angles to be measured then appear as the grain boundary angles in the surface of the specimen. The method of producing a single crystal specimen with a predetermined orientation is basically the same as that employed by Yoshida and Fuji-wara4 in their work on aluminum wires. The specimen, prior to any single crystal transformation, must have a matrix which will support the growth of a crystal of the desired orientation. Growth may occur through exaggerated grain growth or, if the matrix is strained a critical amount. by normal recrystallization. In either case the matrix must have stability at the temperature used to effect the transformation, this stability appearing as a long induction period for exaggerated grain growth or for the formation of recrystallization nuclei. Additional control is gained by using a high temperature gradient through which the specimen is moved at a suitable rate. To obtain the desired orientation, the specimen is fed a short way into the furnace producing one or more crystals in the hot end. After the specimen is removed from the furnace, the orientation of a crystal is determined, so that this crystal may be reoriented by properly deforming a narrow piece of the matrix between the end crystal and the rest of the specimen. This part of the specimen in the case of silicon ferrite is preferably held at red heat during the reorienting process. Fig 1 shows a specimen which is ready to be transformed into a single crystal through growth of a reoriented "seed" crystal. When the method just described is applied to the production of a three-grain specimen two crystals are grown first side by side in one end, the specimen is then reversed and the third grain grown from the opposite end. A suitable group of grains each of different orientation is one where all three grains have the same crystallo-graphic plane in the plane of the specimen. Fig 2 shows a photograph of a three-grain group prepared as described. The notches are introduced in the open ends of the grain boundaries to anchor them during the final annealing operations which ultimately should bring the grain boundaries to the lowest energy configuration. Two-grain groups with different crystallographic planes in the plane of the specimen can be similarly prepared and treated. If the two grains have different surface (gas to metal) energies per unit area, the equilibrium condition leads to a curved grain boundary.* * This feature of the problem was pointed out by J. c. Fisher. References 1. Cyril Stanley Smith: Grains. Phases and Interfaces: An Interpretation of Microstructure. Trans. AIME 175, 15. Met. Tech. TP 2387, June 1948. 2. D. Harker and E. Parker: Grain Shape and Grain Growth. Trans. A.S.M. (194,5) 34, 156-195. 3. C. G. Dunn, A. Seddon, and R. Wylie: Unpublished Work, 1946-1947. 4. Takeo Fujiwara: A Method of Producing A Long Single-Crystal Wire of Aluminum with any Desired Crystallographic Axis. Jnl. of Sci. Horoshima Univ. A, (1939) 9, No. 3, 227.

Jan 1, 1950

By Norman L. Newbern, Robert E. Green

An investigation of the effect of size on the deformation properties of metal single crystals made it desirable to grow from the melt cylindrical aluminum single crystals possessing exactly the same crystallographic orientation but varying in diameter. Methods for the growth of rather large (up to 3 in. diam) aluminum single crystals in molds of the desired shape are well known. However, when one applies the same techniques to the growth of smaller (less than 1/8-in. diam) specimens many additional problems arise. Two of the major problems are the construction of the molds to be used and the removal of the thin specimens from these molds without deformation after growth has been completed. Also the problem of the constraint forces exerted by the mold on the specimen is much more pronounced for the smaller specimens. The technique described herein is a zone-melting method in which no mold is used since the surface tension of the molten metal and its oxide is sufficient to retain the melt. The specimen is suspended vertically in a manner similar to that of Keck and Golay.2 However, while Keck and Golay supported the specimen from both ends, the method used here supports the specimen only at the upper end. The surface tension of the molten aluminum and aluminum oxide contains the melt and suspends a length of newly grown crystal that has already passed through the molten zone until the weight of the newly grown crystal is equal to the component of surface tension holding the specimen together in the molten region. When the weight of the newly grown crystal is equal to the component of surface tension holding the specimen together the specimen pulls in two in the molten zone. The length of crystal which can be grown before this separation occurs varies with the diameter of the specimen and the size of the molten zone. In order to prevent the specimen from pulling in two a tube of glycerine is placed beneath the furnace in such a manner that the newly grown crystal passes into the glycerine which provides sufficient buoyancy to allow aluminum single crystals in wire form to be grown to lengths determined only by the length of the tube containing the glycerine. A schematic diagram of the experimental arrangement is shown in Fig. 1. The furnace used is constructed as follows. High-resistance nichrome wire is coiled on a 3/8-in. diam fused quartz tube. The distance between the windings is much less over a length of about 3/8 in. at the center so as to develop a hot spot. This core is located in the center of a 4-in. diam steel cylinder 5 in. in height and insulated from it by Kayolite. The temperature of the furnace is controlled by means of a thermocouple located near the central hot spot and a Minneapolis-Honeywell temperature controller. Temperature ins,ide the furnace is measured with a thermocouple and a standard potentiometer in the usual manner. By the above method it is possible to grow high-purity (99.99 pct Al) aluminum single-crystal wires over a range of sizes. Crystals varying from 1/8 to 1/64-in. diam were grown by the authors. Since the tube containing the glycerine cannot contain a crystal longer than approximately 3 ft, the growth of crystals longer than this presents another problem. It was found that one could cut the newly grown crystal without deformation in the region between furnace and glycerine tube try means of a cutting torch and then by moving the glycerine tube slightly aside continue

Jan 1, 1962

By N. K. Chen, R. Maddin

Columbium single crystals were deformed in tension and compression. Reorientation by X-rays and stereographic projections of slip traces indicate that plane of slip may be considered as (110). The plastic behavior is shown to be quite similar to the deformation of molybdenum single crystals. STUDIES on the crystallography of the deformation process in body-centered cubic metals have been renewed recently with investigations of iron single crystals1-" and molybdenum single crystals.4 It is now apparent that too many exceptions to the rationalization based upon the ratio of absolute testing temperature to absolute melting point by Andrade5 exist to permit more serious discussion of this type of analysis. The considerations of resolved shear stress utilizing only planes of the type {ll0}, {112), and {123)³,6 permit analysis of the deformation only on the basis of those three types of planes. The suggestions made by Elam7 and by Greninger8 in which the slip process is envisioned as a composite slip on two nonparallel {110) planes can be illustrated schematically in Fig. 1. It may be seen that an unresolved trace on any plane containing a <111> direction may be accomplished by varying the number of atoms participating in the composite process. By further varying the number of atoms in each plane but keeping the ratio of participating atoms constant, jogs could be obtained in the traces and hence wavy slip lines could be produced. Vogel and Brick&apos; studied the behavior of a iron single crystals in which they suggest that the plane of glide is "non-crystallographic" and may be predicted from the intersection between the great circle joining the slip direction and specimen axis with the great circle whose zone axis is the slip direction. In a more recent investigation on iron single crystals, Steijn and Brick" suggest that the slip mechanism may be considered as made up of a type of composite slip occurring on {110} and {112} planes. Evidence for a possible composite nature of the slip process has been presented for the case of molybdenum in the form of analysis of asterism and specimen axis rotation." Definite proof of a composite slip process must, however, await good electron microscopic resolution of the individual traces making up the unresolved optical trace used in determining the acting slip plane. The present investigation was undertaken to study the behavior of columbium single crystals not only in tension but also in compression since the specimen axis migration should indicate the plane or planes of glide in the same manner that the specimen axis migration in tension indicates the direction of glide. The orientations of eleven crystals investigated are shown in Fig. 2. Specific orientations are missing (those in the vicinity of [Ill] and [001] and consequently the effect of orientation on the crystallography of deformation could not be considered. Experimental Procedure The 1/8 in. rods (7 in. long) were subjected to an axial tension in vacuo while at temperatures in the vicinity of 2000°C for 2 to 4 hr. This treatment resulted in large cylindrical grains (about ½ in. long) occupying the entire cross section. A number of these rods were used for the tension studies by observing the behavior of the individual grains. For the compression studies, single crystals approximately % in. long by 1/8 in. in diameter were cut from the rods; the ends were ground parallel. All specimens were polished electrolytically in a solution of 15 cc HF(48 pct) and 85 cc H2SO4 (concentrated) using a platinum cathode, a current density of 0.04 amp per sq cm and a temperature between 25" and 60°C.10 Orientations were obtained using a Laue back-reflection method (3 cm film to specimen distance) with a ½ mm collimator 9 cm long. For the compression specimens, a reference mark was scratched on one of the compression sur-

Jan 1, 1954