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By J. B. Wagner, B. Swaroop

The atomic ratios of oxygen to iron in zlarious corn-posilions of wustite in the vicinity oj the reported p to n transformation were determined in the temperalure range between 950" and 1250°C. For these conditions, equilibrium vacancy concenrations have also been determined at vatious mixtures of C0,-CO. The data show a continuos introduction of iron vacancies as oxygen is introduced into wuistite. No phase change is observed with in the wuustite field. However, the value of n in the isothermal oxygen pressure dependence, the weight change shifts to 1ower values as the concentration of oxygen increases. WUSTITE is a metal deficit semiconductor with the majority lattice disorder being cation vacancies. Using the notation similar to that of Kroger and ink,' the dissolution of oxygen into wiistite using C02-CO mixtures is represented by, WHere v+! denotes a cation vacancy with k effective negative charges and kh • denotes k electron holes, h -. Applying the law of mass action and assuming a dilute solution of defects in the wiistite yields Where the square brackets denote concentrations. Furthermore, when k = 2 the cation vacancies are completely ionized, and both the concentration of cation vacancies and the concentration of electron holes are proportional to the third root of the ratio, PC /PCo. This analysis is valid for one particular mael based on an ideal solution at elevated temperatures (in this case t > 1000°C). At lower temperatures, it has been shown2 that the pressure dependence of the electronic conductivity changes in a manner which suggests that vacancies interact with or "trap" electron holes. At the very high concentrations of defects, 10'' to 10" per cu cm, these simple models no longer hold. Recently Tannhauser,3 Geiger et a1.' Bransky and Tannhauser; and Hillegas' have found an apparent p to n transformation in wiistite in the temperature range of 950" to 1300°C. This junction was found by thermoelectric and electronic conductivity measurements. Geiger eta1.' found that the electronic conductivity became almost independent of the oxygen pressure at high temperatures and oxygen concentrations within the experimental error. In addition, Vallet, Raccah, and coworkers6'7 have reported the existence of several "varieties" of wiistite which were reported to exist within what was heretofor presumed to be a

Jan 1, 1968

By C. R. McEwen

The displacement equations of Buckley and Lever-ett' have been successfully applied to the prediction of oil recovery in frontal drives for a number of years. Commonly, the capillary pressure term is omitted from Leverett's fractional flow formula. The resulting satura-tion-vs-distance curves become multi-valued, however. Buckley and Leverett, recognizing that the neglect of capillarity was most likely the cause, proposed that this part of the solution he ignored. An ingenious method of propagating a discontinuity in place of the multi-valued portlon of the curve was devised by Cardwell using "non-capillary displacement theory". However, it would seem that a completc description of the displacement pracess would require the inclusion of capillary forces. Three publications on displacement theory have appeared in which capillary pressure was included. Ter-williger. et al', calculated saturation profiles which matched those which they observed when gas displaced water vertically downward. Based on their study, Jones-Parra and Calhoun5 roposed a method of computing saturation distributions sufficiently removed in time from the initial conditions so that all saturations in the flood front region were assumed to move with the same velocity. This latter assumption corresponds to the tangent construction on the flowing fraction-vs-satura-tion curve proposed by Welge." A numerical solution to the problem of water displacing oil from a water-wet porous medium was recently presented by Blair, ef at'. The initial conditions included a uniform saturation slightly above interstitial water saturation. that is, the permeability to water ahead of the front was not zero. This appeared to result in a region of slowly rising water saturation ahead of the front, at least for the particular set of relative permeability and capillary pressure data used to illustrate the computation. The authors also postulated an "end-effect" at the outflow face of the system, whereby no water could pass out of the system until the water saturation had built up to a high value. The saturation profiles computed under these assumptions show water accumulating at the downstream end of the system while the flood front proper is still traveling toward the outlet. The purpose of this paper is to present the results of a numerical solution to the one-dimensional water-flooding equation in which no outlet end-effect is considered and where there is no flow of water ahead of the flood front. It should be noted that the contemporary paper of Fayers and Sheldon8 deals with the problem under discussion. For a thorough treatment including both capillarity and gravity the reader is referred to their paper.

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (-=,6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By C. S. Smith, L. H. Beck

KNOWLEDGE of the Cu-Zn constitution diagram was critically examined in 1944 by G. V. Ray-nor,1 who suggested the diagram reproduced in Fig. 1 as the best evaluation of available data. No pertinent work on the constitution has been published since that time, although a number of authors have discussed transformation kinetics and theory. Despite the large amount of work that has been done on the constitution of these industrially important and scientifically interesting alloys, minor uncertainties still exist. For example, it is still not possible to say definitely whether a two-phase region exists between the ordered and disordered forms of the 8 phase. A careful re-examination of the phase boundaries in this part of the diagram was therefore undertaken. Two methods were selected for the new investigation—quantitative metallography for the higher temperatures and precision lattice parameter measurement for lower temperatures. Because of the relatively narrow two-phase regions flanking the ß phase in these alloys, quantitative metallography is particularly suited for their examination, since the relative amounts of the two phases are very sensitive to their compositions. The method, however, is useless below about 350°C because of the inadequate resolution of the two constituents. Below 400°, however, the X-ray diffraction method is applicable, although it is of somewhat lower sensitivity in this system. The changes of composition that occur during quenching from above about 500°C entirely vitiate X-ray measurements at room temperature though they do not affect metallographic area measurements. The two methods overlap and supplement each other admirably. Both methods depend on the attainment of equilibrium composition of the two phases in a more or less intimate mixture and thus avoid the difficult problems of nucleation and long range diffusion involved in the conventional metallographic bracketing method. The alloys were melted from a master alloy made from re-electrolyzed cathode copper and Horsehead 99.99 pct Zn. Melting was done under a cover of either borax or charcoal and the alloys cast into a 7/8 in. sq graphite mold for the a-ß alloys or a 3/8 in. diam cylindrical graphite mold for the ß-? alloys. The a-ß alloys were rolled at 750°C to 5/8 in. sq; annealed for 24 hr at 800°C and quenched; then rolled and swaged at 200°C to 3/8 in. diam rods, annealed 24 hr at 200°C, quenched and cold rolled 2 pct reduction. This treatment was intended to obtain a small grain size and to produce many nuclei of the minor phase for growth on subsequent heat treatment. The unworkable ß-? alloys were given preliminary treatment by sealing in Vycor tubes in vacuum and annealing for 4 hr at 800°C followed by cooling in air. Samples of homogenized alloys were checked spectrographically for impurities, but the principal components were determined on samples subsequent to heat treatment. The impurities analyzed averaged approximately as follows: Ag, 0.0002 pct; Fe, 0.004; Si, 0.0008; Cd, 0.005; Mg, 0.0002; and Pb, 0.002. For metallography, samples of appropriate composition were cut into rods 5/8 in. long, sealed in pyrex tubes in vacuum and annealed for eight weeks at temperatures of 470°C and below, two weeks at 480°, 500°, and 600°C, and 4 hr at 700°C, followed by quenching in cold water. Temperatures were accurate to ±2°C. The cylinders were then machined to 8.7 mm diam and a slice weighing 1.5 g cut with a thin saw transversely from the center of each. This

Jan 1, 1953

By L. W. Davies

A problem often encountered is the provision of materials which have impurity contents below a certain specified level. This problem is in some cases solved by making use of the segregation of the impurity with respect to the liquid and solid states of the material: an ingot of the material is subjected to directional solidification and the ends of the ingot. which are richer in solutes which respectively raise and lower the melting point of the solvent, are removed. An important extension of this process is the zone-refining process invented by Pfann,' in which molten zones are passed successively along the length of an ingot and displace solutes towards the ends. Pfann's process is particularly appropriate in cases for which the segregation coefficient k does not differ greatly from unity, or when the impurity content must be kept extremely low (=10-6 atom fraction); it is widely used, particularly in the purification of materials for use in semiconductor electronic devices. It is the purpose of this paper to investigate theoretically the efficiency of the above refining processes; that is! we determine the most economic method of attaining a given yield of solvent of specified purity, taking into account the variables of the process. One variable of interest is the effective value of the segregation coefficient. which depends on the rate of movement of the liquid-solid interface and on the degree of stirring in the liquid; in addition to this, in the zone-refining process we are also interested in the choice of zone length for most efficient operation. A mathematical determination is made here of the lengths of successive molten zones which give, for an initially uniform distribution, the most efficient removal of a solute of arbitrary distribution coefficient. In order to be able to give a quantitative treatment of efficiency, we first define figures of merit applicable to a given distribution of solute. FIGURE OF MERIT Let an ingot of length L contain a distribution y(x) of solute: we confine our discussion to mono-tonic distributions, in order to avoid inconsistencies in the subsequent analysis. The first moments of the distribution about the origin and x = L are respectively L F = hy{x)dx [I] G = f(L -x)y(x)dx = YoL2-F, [21 where yoL is the total amount of solute present. We shall see that the quantities F and G are useful figures of merit for a discussion of the efficiency of zone-refining processes. In the first place, it is

Jan 1, 1960

By J. Szekely, G. P. Martins

A formulation is given and a general analytical solution is presented for the problem of spherical phase growth in multicomponent systems. The results are valid for describing the rate of bubble growth in the absence of translational motion and, therefore, should be relevant to heterogeneous nucleation processes. Typical worked examples are given, which include bubble growth due to the simultaneous diffusion of hydrogen and nitrogen in molten steel, and the growth of CO bubbles in steel, due to the reaction: C + 0 = CO. The calculations predict that the presence of additional components would enhance the growth rate and also increase the absolute rate at which the individual components are transferred into the bubble. These findings should be relevant to degassing processes. THE problem of spherical bubble growth in the absence of translational motion is appropriate to the description of the heterogeneous nucleation and subsequent growth of gas bubbles while attached to a solid surface. Such problems are of considerable practical relevance to various vacuum degassing and steelmaking processes where bubble nucleation and subsequent growth play an important part in the overall reaction mechanism. A definitive formulation of spherical phase growth has been given in the now classical paper by Scriven1 and the analogous problem for solid phase growth has been discussed by Horvay,2 furthermore a thorough review of the relevant literature has also become available.3 All this previous work was concerned with one component or binary systems. The purpose of this paper is to show that the technique developed by Scriven may be generalized to alow the consideration of multicomponent systems. The results of this generalization would be particularly relevant, as gas bubble nucleation in the metallurgical systems previously mentioned frequently involves the simultaneous diffusion of several components. In the following a general formulation is given and typical worked examples are presented. FORMULATION Consider the growth of a spherical gas bubble due to diffusion in a quiescent liquid of infinite extent, as sketched in Fig. 1. The formulation of such problems requires the statement of the following conservation equations relating to the liquid phase: Equation of continuity Equation of motion Conservation of the diffusing species—Diffusion Equation. The following assumptions are made: a) The fluid is incompressible, quiescent, and of infinite extent b) The bubble is stationary, i.e., it undergoes no translational motion c) Spherical symmetry is observed throughout d) The mass diffusivity is constant e) Chemical equilibrium exists at the surface of the bubble, and any reactions occurring there are fast compared to the diffusion process f) Inertia and surface tension effects are neglected. Equations derived on the basis of these assumptions by previous investigators were found to provide a reasonable representation of bubble growth while attached to a surface in organic and aqueous systems4,5 For gas bubble growth in molten metal systems assumptions a) to d) chould hold reasonably well. The exclusion of chemical kinetics as a possible rate limiting step may not be universally valid, but should hold for many systems operating at high temperatures. The effect of hydrodynamic inertia may be neglected for moderate growth rates; finally, the assumption neglecting the effect of interfacial tension on the bubble growth was made for the sake of mathematical convenience; its inclusion would have required the use of quite cumbersome numerical techniques. While surface tension effects could be appreciable on the initial values of the overall growth rate, especially at low absolute pressures and in case of small bubbles, they are not thought to modify the relative effects present in multicomponent systems, the study of which is the objective of this paper. Within the framework of the above assumptions

Jan 1, 1970

By H. E. Cline

A criterion for stability of a lamellar structure in two-phase alloys ulas derived froflr perturbation analysis of the steady-state solutions for eutectic growth. Both the mass and thermal diffusion were considered with boundary conditions for coupled lamellar growth. The concept of an effective liquidus slope was introduced. Excellent agreement was found with the experiments of Mollard and Flemings and the theory predicted a range of compositions on one side of the eulectic composition in which stable growth may occur with zero temperature gradient. The lamellar structure was found to be more stable than predicted by simple constitutional supercooling. The effect of impurity additions was also considered. DIRECTIONALLY solidified eutectic alloys may have a structure consisting of parallel plates or rods. It is important to know the range of composition and growth conditions that produce this ideal composite structure. Breakdown of the planar solid-liquid interface during growth may lead to a dendritic or cellular structure as in single-phase alloys. In the case of single-phase alloys, the concept of constitutional supercooling1 may explain breakdown, but in two-phase alloys the concept is no longer valid because the melting point is not given by the liquidus of one phase. Both phases must be considered in the mass and thermal diffusion problem. In the following theory a boundary condition at the solid-liquid interface was determined by using the steady-state equations of Jackson and ~unt' to relate the average temperature and composition of the liquid at the interface. Then a sinusoidal perturbation in the shape of the interface was introduced to test for stability as in the analysis of Mullins and ~ekerka.~ The wavelength of the important perturbation was assumed to be much larger than the lamellar spacing, h, and the perturbation was assumed not to change the lamellar spacing, A. Both the mass and thermal diffusion equation were used with averaged quantities at the boundary to determine whether the perturbation grows or shrinks in time. A stability criterion was determined by considering the case in which the perturbation remains stationary. An example of Pb-Sn alloys was used to illustrate the validity of this theory. I) THEORY A) Temperature at the Interface. The temperature of the interface in coupled two-phase growth is close to the eutectic temperature TE even for alloys off eutectic composition. It is assumed that the interface is in local equilibrium and one expects the temperature at the intersection of the liquid phase and the solid phases a and 0 to be near the eutectic temperature. The interface is undercooled because of curvature and the deviation of the composition in the liquid from the eutectic composition. The average interface temperature Ti for steady-state growth of a lamellar eutectic with a plane interface was determined by Jackson and Hunt' as given in their Eq. [17c]. Instead of using the ratio of the lamellar widths hp/h, as a parameter, the volume fraction of the 0 phase, +, will be used as it simplifies the algebra. The average interface temperature using this notation becomes: The average temperature of the interface depends on the volume fraction of the 0 phase, +, which may be related to the composition of the solid or the bulk composition of the liquid Co by: where C, and Cp are the average compositions of the solid phases. In steady-state growth, the composition of the solid is equal to the composition in the liquid far from the interface. The variation of the average interface temperature with composition is illustrated in Fig. 1 for the case of Pb-Sn alloys with a 10"4 cm lamellar spacing as calculated from Eqs. [I] and [2]. The interface temperature goes through a maximum at a composition near but not exactly at the eutectic composition. There is no reason why the composition corresponding to the maximum temperature should be equal to the eutectic

Jan 1, 1969

By H. D. Outmans

In steady vertical flow, the interface of an immiscible liquid-liquid displacement is horizontal for any flow rate below the critical. In nonvertical flow, however, the shape of the interface in the steady state does depend on the flow rate, and the purpose of this paper is to calculate the unsteady interfaces during the transition of one steady state of flow to another. A knowledge of these transient interfaces is of considerable importance in reservoir engineering where the calculation of breakthrough recovery depends on the instant the interface reaches the producing wells and on the shape of the interface at that time. Although the emphasis is put on transient interlaces, which eventually approach stable equilibrium, it is shown that if the displacement exceeds a critical rate no equilibrium is possible. The interface is then unstable and viscous fingers are formed during the displacement. The critical rate and the shape of the transient and equilibrium interfaces are affected by the effective interfacial tension; but since this effective interfacial tension appears in the calculations only in combination with the inverse square of the thickness of the medium, its effect in the reservoir would appear to be negligible compared to its significance in model experiments. INTRODUCTION Stability criteria and the early growth of interfacial disturbances in a plane parallel to the boundaries of a dipping formation in which oil is displaced by an incompressible fluid were described in a previous paper.l This type of instability is significant in thin reservoirs. However, if the reservoir has appreciable thickness, then interfacial stability in vertical planes, normal to the upper and lower boundaries, also becomes important (the displacement is supposed to be parallel to these vertical planes). The difference between the two stability problems is that, in the first case, the intersections of the interface with planes parallel to the boundaries are normal to the direction of the displacement; in the second case, the intersections, this time with vertical planes, are not normal to the displacement. Instead, they are tilted at an angle which depends on the displacement rate. The tilt of steady interfaces was calculated by Dietz2 who also determined the critical rate of displacement for stability in the vertical plane by assuming that this rate would coincide with an interfacial tilt equal to the dip of the formation. The critical rate thus calculated is the same as has been found for thin reservoirs (see Eq. 1.1 of Ref. 1 and of the present paper). Dietz's calculation of the stable tilt was verified by laboratory experiments and the agreement was found to be fairly good.3 It is doubtful, however, that stable tilts actually exist in the reservoir because a change in production rate is not followed by an instantaneous adjustment of the interface to the new rate but, rather, by a transition period during which the interface changes from one equilibrium tilt to the other. The principal objective of this paper has been to describe these transient interfaces without putting any restrictions on the flow conditions or the shape of the interface, as had been done previously. The second objective was to compute the critical velocity, taking into account capillary effects, and the third was to evaluate, at least qualitatively, the shape of the front at rates above the critical, again without making the simplifying assumptions introduced by previous investigators.2,3 In the following sections two examples are given of the calculation of interfacial motion. The first describes this motion for an initially horizontal interface in a dipping layer, and the second for a vertical interface in a horizontal layer. The mathematical formulation of the problem is nonlinear in the boundary conditions, and this prohibits its solution in closed form. Instead, the solution is obtained in the form of higher-order approximations. 1 Before proceeding to a description of the mathematical model, however, we define two quantities

By L. D. Jaffe

From the limited experimental data in the literature, preliminary values were derived for the thermal diffusivity of titanium alloys and for the quenching severity of various mediums used in heat treating them. The thermal diffusivity, under quenching conditions, was found to be approximately 0.006 sq in. per sec. The quenching severity H for brine is approximately 8, for water 4, for oil 0.9, for air 0.08, and for argon 0.02 in. -' The quenching severity of the Jominy-Boegehold end quench water jet against titanium alloys appeared effectively infinite. Using these results, graphs were prepared showing ideal round sizes and Jominy positions having cooled conditions equivalent to those at the center and surface of titanium alloy rounds, plates, and sheets quenched in various media. THE importance of proper quenching of steel parts has long been recognized, and much quantitative work has been done on the subject. Recently, it has become evident that for titanium alloys, too, the rate of cooling from high temperature is important in obtaining high strength and hardness. Maximum hardness and strength may not be attained in the as-quenched condition but rather after a subsequent tempering or aging treatment. Nevertheless, if cooling from temperatures near the ß transus is too slow, for the hardenability of the alloy used, a soft a-ß structure will be produced which will not harden on subsequent aging.'-" The quenching of parts of practical interest can usually be approximated by simple shapes, such as cylinders (rounds) and plates (or sheets) of various thickness and combinations of these. A standard that has been used extensively for comparison purposes is the center of an ideal round: a cylinder quenched in a medium that instantly cools its surface to room temperature." For steel, considerable practical use has been made of the Jominy-Boegehold end quench hardenability specimen,".' and its value for titanium alloys is becoming evident. It therefore appeared worthwhile to attempt comparison of cooling conditions in titanium alloy rounds and plates of various sizes quenched in various media with cooling conditions in ideal round and Jominy quenches. These comparisons are based upon measurements reported in the literature. Quenching Severity of Jominy Water Jet and of Brine As one starting point, there were available the data of Phillips and Tobin8 for positions on a Jominy specimen having the same hardness as the centers of round bars of various size quenched in 5 pct NaOH brine, shown in Table I. The Jominy speci- men is a round bar, normally 1 in. diam and 4 in. long, quenched by a water jet at one end and air cooled on the other surfaces.' After quenching, hardness is measured vs distance from the quenched end on longitudinal flats ground 0.015 to 0.10 in. deep. The data of Table I were based on a subsized specimen of 3/4 in. diam. Since the positions tested are close to the jet quenched end, cooling there may be taken as due solely to the jet, and air cooling can be neglected. These positions are then equivalent to various locations near one surface of an 8 in. plate jet quenched on both sides. Assuming that the thermal diffusivity is constant and that Newton's law of cooling holds, temperature vs time curves at corresponding positions in Jominy specimen and round bar then may be calculated for various assumed quenching severities of the water jet and of the brine. Cooling curves are generally taken to be metallurgically equivalent when they show the same time to reach a temperature halfway between the initial (heat treating) temperature and the final (quenching medium) temperature.5 On this basis, using Russell's tables,9 upplemented by heat flow tables derived in similar fashion by the author for positions near the surface of severely quenched plates, it was found that the experimentally observed equivalence, Table I, was best matched if the quenching severity H of the Jominy water jet was taken as infinite (H = co). This means that the jet quenched surface should be considered as instantly cooled to the temperature of the water

Jan 1, 1956

By R. S. Rickard, M. C. Fuerstenau

Anodic polarization curves for iron dissolution and cathodic polarization curves for copper deposition and ferric and hydrogen ion reduction were studied. These results were used to predict the relative rates of the reactions: The rates of the first two reactions were found to be first order with respect to the reacting ion, and the rale-controlling step was diffusion of the ions to the callzode surface. The rate of hydrogen ion reduction in an oxygen-free solution is dependent on the reciprocal of the square root of the hydrogen ion activity. In solutions containing oxygen, the rate of hydrogen reduction becomes dependent on the square root of the partial pressure of oxygen. At equal concentrations copper precipitation occurs about twice as fast as ferric ion reduction. In an air-saturated solution containing 0.01 M cupric ion at pH 2, the rate of hydrogen ion reduction zs about 10 times slower than that of copper precipitation. At pH values below 3, the rate of hydrogen reduction in oxygen-free solutions is very slozu. COPPER cementation has been utilized industrially for many years as a means of recovering copper from aqueous solutions. There are many different types of cementation plants, but all simply provide a means of contacting iron with relatively dilute copper solutions. In the past little or no attention has been paid to rates or mechanisms of the reactions involved. As a result, this and other studies'-3 have been undertaken recently to establish the important parameters in this system. The reactions involved in copper cementation by iron are: Since transfer of charge is involved in every case, these reactions should be considered from an electrochemical point of view. In any electrochemical system involving electrolytic conduction, passage of electrons necessitates ion transfer to the respective electrodes according to Faraday's law. The current in the system will be proportional to the rate of ion transfer, and, therefore, when the current in the galvanic cell is known, the rates of the reactions involved can be determined. Galvanostatic electrode measurements5" are applicable for these electrochemical studies, in that with this technique polarization curves (current density vs electrode potential) are established by impressing a constant current through an electrode and measuring the electrode potential. Once the current density, electrode potential, and reacting area are known for each reaction in this cementation system, the rates of the iron-consuming reactions can be determined. EXPERIMENTAL MATERIALS Several metal electrodes were used in this investigation; they are shown in Table I. Solutions were made with reagent-grade salts and conductivity water. Air, nitrogen, and oxygen were employed. All of these gases were saturated with water and degreased prior to use. EXPERIMENTAL PROCEDURE The experimental work was divided into two general areas. The first area involved galvanostatic measurements, which were used to determine the rates of reactions as a function of various parameters. The second area comprised actual cementation experiments to check the rates predicted from the electrode measurements. Galvanostatic Electrode Experiments. Polarization curves were obtained using a standard galvanostatic technique5'= with the apparatus shown in Fig. 1. The various electrode polarization experiments were run the same way except for changes in solution composition, polarity, and type of measured electrode. The general procedure involved the following steps: 1) a solution was made 0.5 M in sulfate ion and to the desired cation concentrations; this solution was placed in a constant-temperature bath and saturated with the desired gas; 2) the electrodes were cleaned and placed in the electrode holder; 3) the previously cleaned apparatus was assembled and immersed in a constant-temperature water bath (temperature controlled to ± 0.05"C); 4) the electrode was then positioned; the solutions were introduced, and the polarization meas-

Jan 1, 1969

By Leonard R. Weisberg

HE procedure of directional freezing by the Bridgman technique1 is frequently used in crystal preparation. On those occasions where the crystal is regrown, it can be advantageous to Crop part of the ingot before regrowth to achieve purification. This note describes some simple, yet interesting, observations concerning the effects of cropping an ingot between successive freezes. First, it is not effective to Crop the front end of an ingot, whether or not the distribution coefficient, k , of the impurities is greater or less than unity. This can be shown as follows. The concentration C, of an impurity in a directionally frozen ingot of length d with a uniform cross section is given by where x is the distance along the ingot, and C0 is the initial concentration per unit length. It is assumed in deriving this equation that diffusion is negligible in the solid, is complete in the melt, and that k is constant. Consider that a section of the ingot Ad is removed from the front end. Then the average impurity concentration in the remaining (d- Ad) section of the ingot can be shown by integration to be given by When the ingot is remelted and refrozen, the new impurity distribution is given by where xl is the distance along the refrozen ingot. Substituting the value of c into Eq. [3], one finds This is identical to Eq. [11 when x = (x, Ad), which represents the original impurity distribution in the (d - Ad) section of the ingot after the first directional freeze. Therefore, the cropping and re-freezing accomplished nothing. This can also be seen physically by realizing that the average impurity content in the melt after the first Ad section is frozen, is identical to that after the resulting ingot has been cropped and remelted. Hence, it is assumed in the following sections that only the tail end of the ingot is cropped. However, it must be realized that for impurities with k greater than one, the pieces cropped from the tail end are purer, and are therefore saved. After cropping an amount Ad from the tail end of an ingot, the average impurity concentration of impurities in the remaining portion of the ingot is given by wheref= d/d. For the case of k < 1, the purification is defined as c,/c. It is obvious from Eq. [5] that the purification increases asf increases, but the increase in purification is not large. For example, iff is doubled from 0.1 to 0.2, the purification increases by only 10 pct for k = 0.5, by only 24 pct for k = 0.1, and by 32 pct for k =0.01. Much smaller values off than 0.1 are not desirable since insufficient purification is achieved. These figures indicate that much larger values off do not lead to substantial improvement, especially considering that much of the original ingot is lost. Therefore, it is generally useful to Crop about 1/10 of the ingot to achieve purification. As compared to doubling the value off, it is much more helpful to remelt, refreeze, and crop the ingot twice. Using Eq. [51 reiteratively, and assuming f= 0.1, it is found that the purification after this process is found to be increased over the purification after a single freeze and cropping by 33 pct for k= 0.5, 450 pct for k = 0.1, and 4100 pct for k = 0.01. This indicates that considerable purification can be obtained by this procedure. However, if purification is the main goal, one should resort to zone refining,3

Jan 1, 1962

By H. L. Overton, J. B. Lipson

The concept of sodium single-ion equivalent activity as developed by Gondouin, Tixier and Simard,&apos; was used to determine the filtrate resistivity-activity relationships for 150 laboratory and 49 field drilling muds. With the exception of the native and phosphate high-resistivity muds and the calcium-treated muds, the filtrate resistivity-activity relationships were found to be within 20 per cent of that for pure sodium-chloride solutions. Gondouin, et al,* previously suggested a method of treating the high-resistivity muds in quantitative electrical log analysis. A new treatment is presented which uses the P-alkalinity of the filtrate as a correlating parameter in handling the calcium-treated muds in quantitative electrical log analysis. INTRODUCTION Gondouin, Tixier, and Simard in 1957 introduced new interpretive procedures for analyzing the self-potential curve of electric logging. They re-emphasized the previous work of the Schlumberger brothers, Wyllie and others, and re-defined the activity concept in terms of a number which they termed the effective resistivity. Their procedures are particuarly effective when the connate-water resistivities are less than 0.08 ohm-m or greater than 0.3 ohm-m. For gyp muds where the calcium content is known, a procedure was presented which allows calculation of the connate-water resistivity with improved accuracy. These procedures assume that one of the fluids in the system is a pure sodium-chloride solution, but they are not limited by the assumptions. For the fresh and saline connate waters, for instance, it is assumed that the drilling mud filtrate is a pure sodium-chloride solution. For the gyp mud interpretive procedure, it is assumed that the connate water is a pure sodium-chloride solution. Brown,&apos; on the other hand, has suggested that it would be extremely fortuitous if drilling mud filtrates could all be treated electrochemically as sodium-chloride solutions, and he cites some examples where discrepancies exist. A study has been made of the deviations of sodium single-ion equivalent activities, an of drilling mud filtrates from that of pure sodium-chloride solutions. Drilling fluids in common use on the Texas and Louisiana Gulf Coast and laboratory-controlled muds were investigated. Using a cell patterned after Gondouin, et al, (Fig. I), the equivalent activities were measured. It should be remembered here that the activity measured is merely an index which uses numbers that represent the sodium single-ion equivalent activity a,., of the mud filtrate. The membrane potential developed across the cell was determined with a null-type potentiometer. The resistivities of the solutions were measured by the four-electrode method. The resistivity system was calibrated by using saturated KC1 solution as a standard. Chemical properties of the drilling fluids studied were measured with standard API-approved equipment for the particular property in question. For the activity measurements, two shale discs were chosen to serve as cationic membranes. These two discs were both 1 1/4 in. in diameter and, respectively, 1/4 and 1/8 in. in thickness. The membrane potential, Em, was determined using the shale discs as cationic selective membranes separating two standard sodium-chloride solutions of known mean activity. Then by comparing the constant Km in the following equation, with the theoretical value of — 59 mv at 75OF, the perfection of the membrane was determined. The variation of Km for the two membranes used in this experimental work, as well as one of the many unsuitable membranes, is shown in Fig. 2. The measurement of the activity of mud filtrate involves the balancing of its combined individual activities against a standard solution of known mean activity. At the point where there exists zero potential across the membrane cell, the activity effects may be assumed equal for all practical purposes. The mechanics of making a null reading of this sort requires having a large number of different mean activity solutions. A more practical method involves

By O. N. Carlson, H. A. Wilhelm, J. M. Dickinson

On the basis of microscopic studies, melting-point observations, and X-ray analyses, a phase diagram is proposed for the Cb-V system. A complete series of solid solutions is formed with a minimum in the solidus at 1810°C near 35 wt pct Cb. No compounds or intermediate phases were found in the system above 650°C. THERE is an ever increasing need for better structural metals and alloys for use in nuclear reactors. In addition to the normal properties of engineering structural materials, such as high temperature strength, resistance to corrosion, and fabric-abil~ty, the nuclear properties of the material must be considered. In a nuclear reactor it is important to conserve neutrons, so a material which removes these neutrons from the reaction excessively is considered to have unfavorable nuclear properties. In nuclear-reactor design the engineer must have nuclear as well as other data available on alloys in order to make a wise selection of materials. Due to the fact that many of the common structural materials have undesirable nuclear properties, it is vital that new alloys of metals having more favorable nuclear properties be investigated. Columbium and vanadium are both high melting metals, both exhibit resistance to chemical attack, and no great difficulty is encountered in fabricating them into desired shapes. With proper treatment both metals can be cold rolled extensively without failure. In addition they have desirable nuclear properties for certain types of reactors. Therefore, the alloys of columbium and vanadium should be of interest in the atomic energy program. Since an alloy-development program is enhanced by a knowledge of the phase equilibria of the components, this investigation was undertaken to establish the phase diagram for the Cb-V system. According to the Hume-Rothery rules for alloying,&apos; the chemical similarity, crystal structure, and atomic-size factor are favorable for a complete series of solid solutions for this system. Both elements are in the same family of group V of the periodic table and thus are quite similar chemically. The crystal structures of columbium and vanadium are compatible for extensive solid solubility, since both have body-centered-cubic structures. The atomic diameters of columbium and vanadium are 2.85 and 2.62Å, respectively. This difference of slightly more than 8 pct is well within the 15 pct maximum difference allowed for extensive solid solubility. Experimental Procedures Source of Materials: Columbium powder and sheet trimmings were obtained from the Fansteel Metallurgical Corp. According to the manufacturer the metal contains less than 1 pct impurity. An analysis of the metal showed approximately 1800 ppm C in the powder while the sheet trimmings contained less than 500 ppm C. Spectrographic analysis showed minor amounts of Ca, Cr, Fe, Mn, Si, Ti, V, and Zr in both forms of the columbium. No commercial source of vanadium having the ductility and purity desired was available to the authors at the beginning of this investigation. As a result, all of the vanadium used in this study was prepared by the bomb reduction of vanadium pen-toxide with calcium employing the method reported by Long.&apos; Yields of massive vanadium normally were about 80 pct. Chemical analysis of the vanadium prepared in this manner showed the presence of 200 to 500 ppm N and 800 to 1000 ppm C. Minor amounts of Ca, Fe, Mn, Si, Zr, Cr, and Cb were detected by spectrographic analysis. This vanadium metal was ductile and was cold rolled into 5 mil sheet. Annealing was not necessary during this rolling and the metal retained its cold-rolling characteristic after are-melting. Preparation of Alloys: The Cb-V alloys were prepared by melting pieces of vanadium sheet togethel-with columbium in the form of sheet or pellets of powder. The melting was carried out under argon in conventional arc-melting equipment employing a tungsten electrode and a water-cooled copper crucible. Each alloy was remelted three or four times, inverting the alloy after each melting in order to assure complete mixing. Alloys normally were obtained as round flat disks, weighed approximately 70 grams, and had roughly the shape of a disk 1 1/2 in. in diameter and 1/4 in. thick. Half of each alloy

Jan 1, 1955

By W. V. Green

The creep-rupture behavior of commercial powder-metallurgy tungsten rod is reported for temperatures of 2250°, 2500°, 2700°, and 2800°C, stresses up to 7000 psi, and times up to 4 hr. The temperature dependence and the stress dependence of creep rates are evaluated. Rupture time is fitted to the Larson-Miller parameter and compared to lower-temperature and higher stress results reported by pugh.4 THE tensile strength of single-crystal wire1 and of polycrystalline wire2 have been measured by Goucher. More recently Bechtold3 and pugh4 have studied the mechanical properties of tungsten rod between room temperature and 1200°C. Since tungsten has the highest melting point of all metals, it should retain useful strength to very high temperatures, and should find many applications in missiles, rockets, and so forth. Therefore, the mechanical usefulness of polycrystalline tungsten rod was investigated in the 2250" to 2800°C temperature range by short-time creep-rupture tests. MATERIALS TESTED Creep specimens were machined from 1/2-in. round commercial tungsten rod which was manufactured from powder by cold pressing, sintering, and hot swaging. Purity reported by the vendor was 99.95 pct W. Spectrochemical analyses showed "traces" (less than 0.01 pct) of silicon, iron, and titanium, and "faint traces" (less than 0.001 pct) of calcium and manganese. Carbon content was 30 ppm and nitrogen content was 70 to 110 ppm. No oxygen analysis was obtained. Room-temperature stress-strain tests on the as-received tungsten gave badly scattered results. Threaded end specimens broke at the threads. When these specimens were retested using shoulder grips, the specimens broke at the shoulders. No fractures occurred in the gage lengths. The fracture stresses were: 127,000; 137,000; and 154,000 psi for three specimens which fractured at the shoulders. The microstructure of the as-received tungsten rod is shown in Fig. 1. SPECIMENS USED Fig. 2 shows the two types of creep specimens tested. The threaded-end type specimen, which was used in most tests, had a 3/4-in. gage length and 1/4-in. gage diam. The cone-end specimen, which was used primarily to investigate the effects of a smaller gage diameter and the practicability of the modified grips and specimen, had a 3/4-in. gage length and a 1/8-in. gage diam. In both cases, the gage length terminated at 0.005-in. high shoulders which served as fiducial marks for optical strain measurements. Surface finish on the gage length was 16 µ-in. rms. Creep rates and rupture times were not significantly different for the two types of specimens and were not affected by electropolishing the specimens before testing. TESTING PROCEDURE The constant-load creep-testing machine used has been described by Smith, Olson, and Brown.5 In it the specimen is held vertically by grips of similar material and on the axis of a cylindrical tungsten or tantalum heater-tube. The specimen is loaded by means of the specimen grips, a pull rod (which is sealed to the chamber lid by a vacuum-tight bellows), a mechanical lever system, and hanging dead weights. Both specimen and grips are heated by radiation from the heater-tube, which is heated by its own electrical resistance. An optical system views the incandescent specimen through slits in the radiation shielding and heater-tube. The optical system projects an enlarged image of the specimen gage length on a ground-glass screen. Periodic gage-length measurements are made on this image with two cathetometers. Thorium oxide coatings on the specimen threads or conical end surfaces completely prevented diffusion-welding of specimens to grips, and were used

Jan 1, 1960

By E. Miller, J. M. Eldridge, K. L. Komarek

The thermodynamic properties of- liquid Mg-Pb allojs have been determined by an isopiestic method from 18 to 42 at. pct Pb and by a thevmodynumic analysis of the phase diagram frofiz 0 to 100 at. pct Pb. In the overlapping composition range the magneszupn activity values derived by the two methods are in excellent agreement, thus mutually supporting the correctness of the Mg-Pb phase diagram previously determined by the authors and of the acticitzes deriz~ed isopiestically. SEVERAL studies have been made of the thermody-namic properties of liquid Mg-Pb alloys. Wagner and Engelhardt,1 Lantratov,2 Knappwost,3 Sryvalin et al.* and Wilson5 used the electromotive-force method, Scheil and Wolf8 and Schmahl and Sieben" applied the transpiration technique, and the present authors8 utilized the phase diagram to determine the activity of magnesium in the Mg-Pb system. The results of these studies are not in very good agreement and could not be incorporated into a general systematic analysis of the thermodynamic properties of the homologous series of the Mg-Group IV B systems Mg-Pb,8 Mg-Sn,° Mg-Ge,10and Mg-Si.11 The thermodynamic properties of the Mg-Pb system were therefore re investigated by an isopiestic technique which has been developed for similar studies in the Mg-SnB and Mg-Ge10 systems- Lead specimens, contained in iron or graphite crucibles, were heated in a temperature gradient in an evacuated and sealed titanium reaction tube and equilibrated with magnesium vapor of known vapor pressure to form alloys of compositions which depended on their temperatures, the temperature of the magnesium vapor source, and the thermodynamic properties of the system. EXPERIMENTAL PROCEDURE Magnesium (Dominion Magnesium Ltd., Toronto, Canada) of 99.99+ pct purity and lead (American Smelting and Refining Co.) of 99.999 pct purity were used. In the early experiments, Runs 2 and 3, the alloys were contained in uncovered high-purity iron crucibles. Alloys formed in the uncovered iron crucibles had to be chemically analyzed owing to the slight volatility of lead under the imposed experimental equilibration conditions. The compositions of these alloys were determined by a gravimetric analysis of lead as lead chromate. To avoid this problem, the remaining runs were made in covered graphite crucibles machined from high-density (1.92 g per cu cm) graphite rods (Basic Carbon Corp., Sanborn, N.Y.) which had a maximum ash content of less than 0.04 pct. The non- i reactivity of graphite with lead and magnesium has been previously established,&apos; and the experimental procedure has been described in full detail.&apos; In the runs using covered graphite crucibles it was found that the weight increases of the crucibles and their contents after equilibration equaled the magnesium contents of the alloys within the accuracy of the chemical analysis (i0.3 at. pct Pb). Clearly, the small lid openings of the graphite crucibles prevented significant lead losses during a run, and the weight increase was therefore taken as the magnesium content of the alloys. EXPERIMENTAL RESULTS At thermodynamic equilibrium the magnesium partial pressure of the specimens equaled that of the reservoir. Since the magnesium reservoir was always maintained at the temperature minimum of the system, the activity of magnesium of any specimen was given by the ratio of the magnesium reservoir pressure to the vapor pressure of pure magnesium at the specimen temperature. The standard state was chosen as liquid magnesium and the vapor pressure of liquid magnesium

Jan 1, 1968

By J. C. Holm

ALTHOUGH the main constituents of Portland cement are the oxides of calcium, silicon, aluminum, and iron, characteristics of the cement are seriously affected by such contaminants in the raw materials as magnesium, phosphorus, sodium, potassium, sulfur, and others of lesser importance. Sources of cement raw materials comprise a long list of minerals occurring in nature in various degrees of purity. The calcareous raw materials are generally limestone of purity varying from calcite to cement rock (a low-grade limestone of natural, almost correct chemical composition), chalk, marl, seashells, coral, and coral sand. The argillaceous raw materials supplying silicon, aluminum, and iron are mainly various forms of clay and shale, to which may be added silicious sand, iron ore, bauxite, or kaolin for minor adjustment of the chemical composition. The quality of Portland cement in this country, as in most parts of the world, is controlled by rigid specifications limiting both its chemical and physical characteristics, and cement manufacturers must comply with these specifications to market their products. Brandon Raw Materials: An unusual deposit of marl, limestone, and clay occurs 12 miles east of Jackson, Miss., near the village of Brandon. The deposit is of sedimentary origin and of relatively young geological age. Layers of marl vary from putty-like consistency to such hardness that it can be cut with a knife. Interspersed between the layers of marl are bands of limestone varying from very soft to hard. the compressive strength of the hardest layers exceeding 15,000 lb per sq in. The layers of marl range in thickness from a few inches to about 25 ft. The limestone bands seldom exceed 2 to 3 ft but often occur in thinner veins in the quarry face. Above the top layer of the deposit, which may be marl or limestone, a layer of clay ranges in thickness from a few inches to more than 20 ft. Part of this clay is harvested with the raw material to supply part of the argillaceous components, but most of it is stripped as overburden and wasted. A highly silicious clay of extreme fineness, harvested from the bottom of the quarry below the marl and limestone bands, is to correct the silica content. Fig. 1 shows typical examples of the interrelation of the various materials, based on drill logs obtained during exploration of the deposit. The marls vary in moisture content in the bank from 15 to 30 pct and contain up to 70 pct -200 mesh particles and up to 40 pct —10 p particles. A large percentage of the fine fraction is within the colloidal range, making the marl extremely sticky. The limestone beds range in hardness from that of the hardest marl to a medium hard limestone and in moisture content from 2 pct to approximately 14 pct. The line of demarcation is often difficult to draw and the moisture content is possibly the best means of classification. The ratio of soft to hard material is not constant throughout the deposit, but the average is approximately 70 pct soft to 30 pct hard material. Through the years this deposit had been repeatedly explored by cement companies and rejected as unsuitable for cement manufacture, mainly because of physical characteristics. In 1950, after careful exploration of the deposit and comprehensive laboratory and pilot plant tests of the raw materials, officials of Marquette Cement Mfg. Co. of Chicago were convinced that a practical and economical method of processing the raw materials had been devised and authorized construction of a new plant that began production in December 1951. Marl and limestone, common raw materials for Portland cement, usually occur in such a manner that they can be worked separately. Their harvesting and processing normally have presented no difficult problems, as standard equipment and methods are available for handling either sticky or hard materials. No other cement plant utilizes a deposit of the nature of that at Brandon, however, and for this reason no prior art was available for design. When properly blended, the raw materials produced an excellent cement without additives. Basic problems to be solved in designing the cement plant were:

Jan 1, 1957

By R. T. Hukki, P. Voutilainen

This paper describes a new apparatus for continuous wet fine-screening. Its preferred size range seems to be from 0.1 to 1 mm. The supercritical trommel screen is a short cylindrical trommel of wedge-bar type construction operated at a speed greater than the calculated theoretical critical speed and at a speed lower than the speed at which particles introduced into it will centrifuge. The paper describes results obtained with the prototype supercritical trommel screen in pilot plant scale. The results point to a high capacity and simultaneously to a high sharpness of screening. Finally, an analysis is presented of the forces acting in screening on a supercritical trommel screen. In the era of high speed, high capacity processing of raw materials the conventional slowly rotating trommel screen is often considered a relic from the times passed. A typical trommel screen is the cylindrical trommel rotated about a horizontal or slanting axis at a relatively low speed. Its screening characteristics are well known. Trommel screens of various types of construction, methods of operation, performances and other characteristics have been described in detail by Taggart.1 The theoretical critical speed of a trommel screen is defined by the same well known equation as that applied for grinding mills: where ncritical = the numerical value of the theoretical critical speed in rpm, D 1 = the inside diameter of the trommel in feet, and D2 = the inside diameter of the trommel in meters. ncritical corresponds also to the centrifuging speed provided that the coefficient of friction f between the trommel surface and the outer layer of the charge is = 1.0. In a general case: From Eq. 2 it is seen that in all cases where f < 1.0 the centrifuging speed of the trommel is greater than the theoretical critical speed. The supercritical trommel screen concerns screening operations within that speed range which is between the theoretical critical speed defined by Eq. 1 and the centrifuging speed defined by Eq. 2, under conditions such that the coefficient of friction f<1.0. It is reported by Taggartl that the optimum speed of a conventional cylindrical trommel screen 36 in. in diam was experimentally found to be about 16 rpm. From Eq. 1, the critical speed of this trommel is 44.2 tpm. The indicated optimum speed corresponds to (16/44.2) x 100% = 36.2% of the theoretical critical speed. The optimum speed range based on information available seems to vary from 33% up to 45% of the theoretical critical value. The trommel screen operated at a supercritical speed: operates at a speed greater than the calculated theoretical critical speed; operates at a speed lower than the speed at which the charge introduced into it will centrifuge; operates within the supercritical speed range in such a way that the coarse fraction of the charge must slide in respect to the inside surface of the trommel; the outer layer of the said fraction next to the screen tends to proceed in the same direction as any selected point on the trommel surface, but now at a lower speed, and indeed at a subcritical speed; allows to a certain degree adjustment of the maximum determining particle size x of the fine product simply by a variation of the speed of the trommel within the supercritical speed range. With increasing trommel speed, finer and finer material only will get the opportunity to find its way into the fine product while the screen opening remains constant. In conventional practice, the low speed trommel is generally used for sizing of coarse and medium coarse material, but seldom for fine screening. The characteristic feature of the product passed through the conventional trommel is that the determining size x of the biggest particle is barely smaller than the nominal size of screen opening. The supercritical trommel screen, on the other hand, is best suited for sizing of relatively fine material. Furthermore, the characteristic determining size x of the biggest particle in the fine product can be substantially smaller than the nominal width of the screen opening or slot. In the trommel screen best suited for the applications

Jan 1, 1965

By G. R. Speich, Morris Cohen

The growth rate of bainite has been determined by hot-stage metallography in five hypereutectoid high-purity iron-carbon, iron-carbon-chromium, and iron-carbon-nickel alloys. The studies have been confined essentially to lower bainite. The growth rate is independent of time at constant temperature, but both the edgewise and sidewise growth rates increase with increasing temperature. Increasing the carbon content, or adding chromium or nickel, decreases the growth rate without greatly affecting the temperature dependence. The results lead to separate diffusion-controlled models for the edgewise and sidewise growth rates. ALTHOUGH bainite has been subject of many detailed investigations,1,2 the growth mechanism of this intermediate transformation product of steel remains unclear. One difficulty has been that practically all the kinetic measurements have been restricted to studies of the overall reaction rate. Only a limited amount of information3, 4-6 is available on the growth process itself. The purpose of the present work was to investigate the effect of time, temperature and composition on the growth rate of bainite using hot-stage metallography. This method makes it possible to observe continuously the isothermal growth of individual bainitic units because of the surface upheavals accompanying their formation.3 This information is needed to test the existing growth models and to obtain a better understanding of the factors controlling the bainitic transformation. EXPERIMENTAL PROCEDURE Alloys—The compositions of the alloys used in the present work are shown in Table I. The five alloys were vacuum-melted and cast, and were prepared from high-purity materials. The three iron-carbon alloys were available from the work of Roberts et al.7 in the form of 3/8-in. diam rods.* To facilitate machining, the rods were ing. The rods were then tempered for 3 hr at 650°C to allow machining. The iron-carbon alloys in Table I were selected for investigating the effect of carbon on the bainitic growth rate. Due to the rapidity of the transformations involved, it was not feasible to measure the growth rates in iron-carbon alloys having carbon contents much less than 0.9 pct C. The iron-carbon-chromium and iron-carbon-nickel alloys were selected to study the influence of chromium and nickel on the growth rate at a carbon level of about 1.1 pct C, since this carbon content was intermediate among the iron-carbon alloys. The concentrations of chromium and nickel were chosen to match isothermal trans formation diagrams in the literature.8&apos;9 Hot-Stage—Since the iron-carbon alloys had such low hardenabilities, it was necessary to quench the hot-stage specimens drastically from the austentiz-ing temperature to the isothermal transformation temperature to prevent the formation of pearlite or proeutectoid constituents. A rapid-quenching metal-lographic hot-stage was built for this purpose. A maximum temperature of about 1100°C and quenching rates up to 500°C per sec could be attained with this equipment. The details of the apparatus are described in a recent publication. After being polished and mounted on the hot-stage, the specimen (0.020 in. thick) was protected from oxidation and decarburization during austenitizing by a vacuum of 10-4 to 10-5 mm. The quench to the reaction temperature was accomplished with a helium blast, and the isothermal run at this temperature was conducted in a helium atmosphere. A fine-wire thermocouple spot-welded to the sample and a high-speed

Jan 1, 1961

By F. Wald, A. J. Rosenberg

The general features of the constitution of the B-Pt system were determined using standard rnetal-lograph~c, thermoanalytic, and X-ray diffraction techniques. Three compound were found. Two of these, Pt3B and Pt,B, are formed by peritectic reactions at 523° and 890°C, respectively. The third, Pt3B,, is congruently melting with a flat maximum at 940°C but decomposes eutectoidally in to Pt,B ant1 boron nt - 600° to 650°C. THE low-temperature allomorph of boron (red, simple rhombohedra1 a boron) is of scientific and technological interest as an elemental semiconductor.&apos; However, the studies of this material have been hampered by its reported instability above 1200"~ which precludes crystal growth from the melt (mp - 2200°C). Crystallization from platinum solutions has been suggested as an alternative crystal-growth technique, but has met with only limited success.&apos; The technique depends upon the existence of a significant difference between the eutectic temperature and the transformation temperature of boron. In order to clarify the conditions for further crystal-growth experiments, we found it desirable to redetermine the main features of the B-Pt phase diagram since previous reports on the system1&apos;5&apos;6&apos;7 are in marked disagreement. EXPERIMENTAL The experimental methods used were thermal analysis, metallography, X-ray analysis, and, to a lesser extent, measurements of microhardness. Most of the alloys were prepared from spectrograph-ically standardized boron obtained from Johnson-Matthey &Co., Ltd. (212 ppm impurities, exclusive of carbon and oxygen) and platinum powder obtained from F. Bishop & Co. (200 ppm impurities, mainly of other platinum group metals). Some alloys were also prepared with very high-purity, float-zone refined boron (99.9999 pct obtained from "Wacker Chemie" and extrahigh-purity platinum (99.999 pct) obtained from Johnson-Matthey & Co., Ltd. The reported results did not depend on the choices of these starting materials. Five-gram alloy specimens containing 10, 20, 25, 27.5, 30, 33.3, 34, 35, 37, 37.5, 38, 39, 40, 41, 42, 43, 45, 50, 55, 60, 70, and 80 at. pct B were made by melting the elements together in boron nitride crucibles using rf heating of a graphite susceptor, either in vacuum or under high-purity argon. All alloys were heated to at least 1800°C for -5 to 15 min. Most of the alloys did not wet the crucibles when the latter were outgassed by preheating under vacuum. In any event, no weight loss was detected after melting, and the nominal composition was assumed for all specimens. Thermal analysis on 2.5-g samples were carried out in boron-nitride crucibles under a vacuum of 5 x X torr. The apparatus was heated in a "Kan-thal A 1" wound furnace, which limited the maximum temperature to about 1100°C. The output of the indicator thermocouple was fed to a dc recorder with a 1-mv full-scale span and an adjustable zero. The apparatus was calibrated repeatedly, using the freezing points of high-purity aluminum, silver, and gold. The results justified the use of the NBS voltage vs temperature tables for Pt/Pt 10 pct Rh thermocouples. All thermal analyses were run at least twice and both the heating and cooling effects were recorded. Most of the alloys had a very strong tendency to supercool. However, the use of mechanical vibration permitted reproducibility within *5°C for all alloys, except in the region around 40 at. pct B. Only the cooling effects are plotted in Fig. 2, since they appear to be more reliable. For metallography, the alloys were cut with a diamond cutting wheel, cast in a polymethacrylate resin, ground and polished with diamond paste, and etched with dilute aqua regia, a common etch for platinum alloys. Both copper and molybdenum radiation were employed to obtain X-ray diffraction data using Debye-Scherrer cameras and a "Norelco" diffractometer Diffractometry with high scanning speeds (1 deg per min) using nickel filtered CuK, radiation was used to identify the main regions of the diagram. However, molybdenum radiation was used for the detection of boron, since the latter showed very strong absorption and fluorescence effects with CuK, radiation. RESULTS AND DISCUSSION Three intermediate compounds, corresponding to the compositions Pt3B, Pt2B, and Pt3B2, were found in the system. Fig. 1 reproduces their X-ray diffraction spectra, together with those of pure boron and pure platinum. As can be seen from the thermal-analysis data in Fig. 2, Pt3B and Pt2B are formed by

Jan 1, 1965

By W. Rostoker, A. S. Yamamoto, K. Anderko

ALTHOUGH the corrosion resistance of magnesium and its alloys is closely related to iron content, there has been no direct measurement of the solid solubility of iron in magnesium. Bulian and Fahrenhors;1 and Mitchel]2 agree that pure iron or a limited terminal solid solution crystallizes from the Mg-rich liquid. For this reason a magnetic-moment method was selected to estimate that portion of the total iron content which is not in solid solution. Since iron in solid solution in magnesium cannot contribute to ferromagnetism, the difference between chemical and magnetic-iron analyses should yield the solid solubility. By experimentation it was found that the melting of pure sublimed magnesium (99.995 wt pet purity) in Armco-iron crucibles at about 800°C is a convenient way to introduce small amounts of iron. Melts retained 5, 10 and 20 min at 800°C analyzed 0.003,, 0.005,, and 0.018 & 0.001 weight pet Fe, respectively, after being stirred, heated to 850°C, and cast into graphite molds. The as-cast alloys were pickled in acid (dilute HC1 + HNO3), annealed at 600°C for 3 days, scalped on a lathe to remove the pitted surface, pickled again, extruded at about 100°C to 3-mm wire, reannealed 41/2 days at 500°C, and water-quenched. The specimens were again scalped, pickled, and used both for chemical and for magnetic analysis. Most of the precautions described were intended to prevent iron pickup by contact with tools or superficial iron enrichment by volatilization of magnesium during heat-treatment. It is believed that the specimens ultimately used for test were homogeneous and characteristic of phase equilibria at 500°C. Magnetic Analyses A susceptibility apparatus of the Curie type was used for magnetic analyses. Field strengths of up to 10,400 oersteds could be generated. By this method, an analytical balance measures the force of attraction which a calibrated magnetic field exerts on a suspended specimen. The force equation is as follows f/m = M dh/dy where f/m = force per unit mass of sample M = magnetic moment per unit mass dH/dy = magnetic field gradient The dH/dy characteristic of the instrument is determined by the use of a standard palladium sample, and the calibration is made independently for all values of H. Since a large finite field is required to saturate an assembly of ferromagnets, it is necessary to measure the apparent magnetic moment for increasing steps of H until a saturation value is obtained. The percentage of iron in the sample as free ferromagnetic iron may then be computed simply C= 100 (M1/M1) where C = percent content of undissolved iron in sample M1 = saturation magnetic moment of sample per unit mass M1 = saturation magnetic moment of iron per unit mass taken as 217 emu-cm per gm There is no serious difficulty in applying this method except for the unusual magnetic behavior of very fine particles of ferromagnetic substances. It has been found and is the basis for a widely accepted theory that with sufficient subdivision, the magnetic fields required to saturate and the coercive force after saturation rise to exceedingly high values. Recent work on precipitates of Fe and Co from copper solid solutions8 showed that about 5000 oersteds were necessary to approach saturation. The magnetic moments as a function of field strength measured in the present investigation are listed in Table I. Only the 0.018 wt pet Fe alloy yielded a magnetization curve with a fairly well-defined saturation plateau at 3.76x10 -2 emu-cm/ gm. This corresponds to 0.017 & 0.001 wt pet Fe in the alloy. This indicates that the solid solubility must be of the order of 0.001 wt pet Fe. The magnetic-moment data of the other two alloys are badly scattered, indicating that the amount of ferromagnetic iron in these samples is so low that the magnetic forces acting on them cannot be measured accurately by the analytical balance used. Nevertheless, the fact that even the 0.003, wt pet Fe alloy shows ferromagnetism indicates that the solid solubility must be below that value. Acknowledgment This work was sponsored by the Pitman-Dunn Laboratory of Frankford Arsenal, Philadelphia, Pa. The support and permission to publish are gratefully acknowledged. References W. Bulian and E. Fahrenhorst: Zeic. Metallkunde, 1942, vol. 34, pp. 116-170. 2 D. W. Mitchell: AIME Transactions, 1948, vol. 175, pp. 570-578. 3 G. Bate, D. Schofield, and W. Sucksmith: Philosophical Magnsine, 1955, vol. 46, pp. 621-631.

Jan 1, 1959