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By L. R. Duncan, O. M. Wicken

Magnesium, the eighth most abundant element in the earth's crust, is found widely distributed in a variety of minerals. Among the more commercially important ones are magnesite (MgCO3), brucite (Mg[OH]2), dolomite (CaMg[C03]2), and the salts magnesium sulfate and chloride often found in natural brines. Among other commercially important magnesium-containing minerals are olivine ([MgFe]2Si04), talc (H2Mg3[Si03]4), and serpentine (H4Mg3Si2O9). These are valuable because of desirable characteristics given them by the magnesium content and its placement in the particular crystal structure. These minerals are the raw materials for a host of products including magnesium metal and several grades of magnesia or magnesia-containing materials for refractories, fluxes, fillers, insulation, cements, decolorants, fertilizers, and chemicals. Considering only those minerals valued for their magnesia or magnesium content, over 85% of the material tonnages are processed to be used as refractories. Dolomite, which is used in enormous tonnages for its physical properties in construction, has an important use as a refractory raw material in its own right and, after calcination, as a precipitant for magnesium hydroxide, which is an intermediate for the production of magnesia or magnesium metal. Magnesia from the reaction of calcined dolomite (or limestone) with seawater or magnesium-containing brines has supplanted much of the production of magnesia from mined magnesite, particularly in the United States. The best known of the minerals directly and widely exploited for magnesia content is magnesite, one of the calcite group of rhombohedral carbonates which includes calcite (CaC03), siderite (FeCO3), and rhodochrosite (MnCO3) among others. The members of this group enter into a wide range of substitutional solid solutions when the positive ions have similar radii. The radii of magnesium and iron ions are within 6% of each other; hence, magnesite and siderite form a complete series of which breunnerite (ferroan magnesite) is a well-known end member. However, the radius of calcium ion is 36% larger than that of magnesium ion, and only limited substitution exists at each end of the MgCO3-CaCO3 series. Dolomite is not a member of the calcite group, but results when calcium and magnesium ions alternate in equal number in an ordered structure among carbonate ions. The result of these relationships is that calcite and dolomite, often found intermixed with magnesite, occur commonly as identifiable crystal entities which can often be separated to a varying degree from the magnesite by various beneficiation techniques. Magnesite, when pure, contains 47.8% MgO and 52.2% CO.. The pure mineral is sometimes, but rarely, found as transparent crystals resembling calcite, but, preponderantly, magnesite contains variable amounts of the carbonates, oxides, and silicates of iron, calcium, manganese, and aluminum. Magnesite may be either crystalline or amorphous (cryptocrystalline). The crystalline form has a hardness of 3.5 to 4.0. The color may range from white to black with shades of yellow, blue, red, or gray. The color is not a fundamentally significant indicator of purity, but in a given deposit, an experienced person can often roughly grade magnesite by assessing color and crystallinity. The crystalline form of magnesite occurs in

Jan 1, 1983

By C. H. Lee, R. Maddin

The diffusion rates of Ag110 in cylindrical single crystals of 99.99 pct pure silver, which were twisted to a total surface strain of 0.91 during the diffusion anneal at temperatures of 700°, 750°, and 800°C, were measured by sectioning and counting as a function of the strain rates. The ratio of the diffusivities while strain ing occurred (Ds) to those of the unstrained specimens varies linearly with the rate of twisting and attains values of near 100 for some of the rates used. The enhancement of diffusion by straining is inversely proportional to the temperature at which diffusion occurs. The activation energy for diffusion determined from the data plotted as a function of the rate of twisting decreases from 44,090 cal per mole for zero strain, to an asymptotic value of 21,000 cal per mole for the strain rates of 22 x it)"5 see-l. Qualitative explanation for the observations based on the generation of nonequilibrium number of defects by plastic deformation will be discussed. The initial research of Buffington and cohen1 on self-diffusion in a iron under compressive stresses contributed the first quantitative information concerning the effect of applied stresses on diffusion. These results were obtained from radioactive Fe55 plated on one of the horizontal surfaces and compressing the large-grained specimens while the diffusion-anneal was occurring. Enhancement of diffusion of a maximum of seventeen times was observed provided the strain was in the tertiary stage of creep and the rates of straining were at least as fast as rates used in the normal creep test. On the other hand, Darby, Tomizuka, and Balluffi,2 extending silver single crystals up to 30 pct elongation at rates of straining about equal to those used by Buffington and Cohen observed no effect. For the past two and a half years at the University of Pennsylvania, we have been investigating the effect or torsional strains on self-diffusion in silver single crystals. If enhancement is observed as has been reported1 a possible explanation may be based upon the generation of fairly large numbers of point defects and their role in the diffusion process. Hence, since torsion should produce an abundance3 of point defects, an increase in the diffusivity while the crystal is being twisted should easily be measured. EXPERIMENTAL PROCEDURE Our research uses single crystals of silver prepared from 99.99 Ag by the Bridgman method in a dynamic vacuum of less than 25 µ. As grown, they are about 25 cm long by 1.3 cm in diam. The crystals are cut into 7.5 cm lengths with a jeweler's saw and machined to the shape shown in Fig. 1. The test length of the crystal is machined to a 0.6 cm diam after which the ends are masked and the test section etched heavily in HNO3, and KCN:(NH4),S2Os , solution to remove the effects of machining. The specimen is then annealed in vacuum for 8 to 12 hr at 800°C to remove any residual stresses and also to recrystallize the end sections. The recrystallized ends are necessary since experiments showed that single-crystalline end sections are too soft to transmit the desired torque. Occasionally, recrystalliza-

Jan 1, 1960

By H. P. Stuwe

It is investigated whether a model of sphere packing permits the computation of the lattice parameters and their variation with concentration in various a phases; it does, except in phases containing silicon. Several observations indicate that a particular role is played by the "E-atoms" in the lattice. THE phase is formed by many alloys of the transition elements.'-' Its structure has been described by Bergman and Shoemaker,5,8 Dickins, Douglas, and Taylor,7 and Kasper, Decker, and elanger.' There are five kinds of crystallographically equivalent positions for the 30 atoms in the unit cell which have been designated by these authors I, 11, 111, IV, and V or, in the same sequence, A, B, C,D, and E, as shown in Fig, 1. For the purposes of the present paper two elements of the lattice will be discussed separately: The lattice planes perpendicular to the c-axis which are made up by the atoms A, B, C, and D and which determine the a-parameter; and the close-packed "vertical rows" of E-atoms which determine the c-parameter. asper,9 and Frank and kasper10 described the a phase and other complex structures as sphere packings. In these papers particular attention is paid to the coordination polyhedra. Lattice positions with an equal number of nearest neighbors are considered equivalent regardless of their crystallo-graphic description. This seems to work very well for the explanation of ordering phenomena in the a phase as far as information on this is available." If the description of the phase as a sphere packing is valid it should be possible to draw two further conclusions: 1) It should be possible to calculate the lattice parameters from the atomic radii of the components, and 2) It should be possible to predict the variation of the lattice parameters with concentration within one phase field. Both points are discussed in this paper. PROCEDURE Measurements of lattice constants were done with a symmetrical back-reflection X-ray camera. With Cr-radiation, about a dozen a1 lines could be observed with most samples. From the (550/710)- and 720-lines the a-value was computed. With this value the c-parameter was calculated from the (333)- and (413)-lines. Finally, the position of all the other lines was computed from the lattice parameters thus obtained. In this way the validity of the indexing could be checked and, at the same time, this proce- dure gave an estimate of the accuracy of the lattice parameters. A correction was made for film shrinkage. The atomic radii used in the computations are the Goldschmidt radii for coordination number 12. Actually, some of the atoms have a coordination number of 14 or 15, but the error thereby introduced is small. * For the computation of lattice constants from the atomic radii an "average atomic radius" of all components was used, i.e., complete disorder was assumed. Although this seems to be true for some systems like OS-Cr,4 it is not true in others.11,13,14 The ordering model, however, which has been suggested by Kasper on the basis of extensive research lets both kinds of atoms contribute to both the ''vertical rows" and the lattice planes perpendicular to them, so that even with ordering of this kind the assumption of complete disorder cannot introduce a very serious error in calculating lattice parameters. RESULTS Bergman and shoemaker6 gave a table of the interatomic distances in the Fe-Cr phase. If we disre-

Jan 1, 1960

By Henry A. Stiff, J. P. Hammond, A. B. Westerman, H. C. 195-000-000-014 Cross, and Lawrence E. Davis

The phases in Cr-Fe-Mo alloys have been investigated with homo-genization, aging temperature, composition range, and alloy addition as variables. Metallography, three X-ray methods, and hardness were used as methods of study. The behavior of s, M23,C8, and Z phase are reported for cornpasition range 60 pct Cr-15 to 25 pct Fe-15 to 25 pct Mo-<0.005 to 0.36 pct C with aging at 1400º to 2000°F. With 2 pct Ti, Tic and TiC-TiC are formed; with nitrogen Cr2N. THE recently developed class of chromium-base heat-resistant alloys shows appreciably higher strength than commercially used high temperature alloys. However, further developmental work is required to impart needed shock resistance and some degree of room-temperature ductility to these alloys. Extensive exploratory work on chromium-base alloys was begun in a program initiated by the War Metallurgy Committee of the National Defense Research Council at the Climax Molybdenum Co. in the early part of 1942.&apos; Alloys were sought for gas-turbine blades for use at 1600°F. A minimum of 5 pct elongation in the stress-rupture test was a requirement. From the Climax work, ternary alloys of chromium, iron, and molybdenum appeared to show the greatest promise as materials for gas-turbine blades. The composition line in the ternary diagram joining the 60 pct Cr-15 pct Fe-25 pct Mo and 60 pct Cr-25 pct Fe-15 pct Mo alloys was indicated as representing the most useful combination of strength and ductility.&apos; Strength increased while ductility decreased as molybdenum was raised in this composition range.&apos; The 60 pct Cr-15 pct Fe-25 pct Mo type alloy was thought to have the most suitable properties for gas-turbine blades.&apos; Concurrent with the study reported here, other investigations were being made on Cr-Fe-Mo alloys. The liquidus temperatures on a series of low carbon, ternary alloys were being determined, and isothermal sections drawn at 2370°, 2010°, and 1650°F (1300°, 1100°, and 900°C).2 Also, various methods of preparation and some mechanical and physical properties of chromium-base alloys, particularly the 60 pct Cr-15 pct Fe-25 pct Mo type, were being investigated., At the inception of the present program, only a limited study had been made of etchants for developing the microstructures of chromium-base alloys; X-ray analysis of the microconstituents had not been made. A review of the literature revealed that no phase-diagram work had been reported on the Cr-Fe-Mo system. Scope of Work The work on chromium-base alloys includes the following: 1—The development of etching methods for differentiating between the microconstituents; 2—The identification of microconstituents by X-ray diffraction methods; and 3—A comprehensive metallographic and hardness study after various heat treatments. The phases were studied by three standard X-ray techniques: 1—The block-sample focusing-camera method; 2—The powder-diffraction method on elec-trolytically separated residues; and 3—The powder-diffraction method on cold-worked aggregate samples. The results by the first two methods were correlated with the metallographic data. The third method was used largely to study conditions approaching equilibrium, since cold working prior to heat treating accelerated precipitation. Seven types of alloys were investigated: 50 pct Cr-50 pct Fe, 40 pct Cr-40 pct Fe-20 pct Mo, 55 pct

Jan 1, 1953

By N. F. Schulz, H. A. Lex, J. D. Zetterstrom

A green ball of iron ore faces many perils from the time it is formed until it finally emerges from the pelletizing furnace as a hardened pellet. For instance, if the rate of heat transfer into a ball is sufficient to produce vapor from either the free or combined water more rapidly than it can escape at a tolerable pressure, the ball may split, spall, or even explode, a failure commonly known as decrepitation. To avoid such failures, one must either limit the rate of heat transfer during the drying and preheating stages, at the expense of production rates, or improve the decrepitation resistance of the green balls. The latter remedy may often be accomplished through changes in ore preparation, balling procedures, or the judicious use of binders or other additives. INTRODUCTION Pelletization has become established as an especially desirable method for the agglomeration of fine taconite concentrates and it promises to be equally satisfactory for improving the physical structures of certain natural ores. A high-quality pelletized iron ore consists of uniformly sized spheres, usually about 1/2-in. diam, which are strong enough to resist abrasion and breakage during handling and which reduce well without disintegration in the blast furnace. The unfired agglomerates, "green balls", are subject to several destructive effects that must be avoided or minimized if a high-quality product is to be obtained by pelletization. Among these are abrasion and impact deformation or breakage during handling of the wet green balls, deformation and breakage by compressive forces in the bed of ore in the pel-letizing furnace, decrepitation during drying and preheating, wind erosion, and radial cracking at firing temperatures. Moisture condensation from the warm saturated gases downstream from the drying zone on wet, cool balls may cause bed collapse if it becomes excessive. Decrepitation is defined as the sudden disintegration of green balls, usually with an audible pop, that occurs when they are heated too rapidly during the drying or preheating stages of the pelletization process. The extent of ball disintegration may vary from merely splitting off a small fragment to almost total disintegration into the original ore particles making up the ball. Such ball destruction results in a decreased yield of pellets, and the fragments, which also tend to interfere by obstructing the gas flow through the bed, must eventually be screened from the fired product and recycled. The closely related type of ball failure that sometimes occurs during the high temperature firing stage, resulting in radial cracks without fragmentation, was not considered to be decrepitation for the purpose of this investigation. Failure by decrepitation is not usually a serious problem in the pelletization of taconite concentrates. The problem is significant, however, in the pelletization of some natural ores, especially those containing hydrous iron oxides. In some instances, economicd production rates cannot be maintained if the drying and preheating rates are slowed down enough to avoid decrepitation. OBJECTIVES This investigation was undertaken to: (1) Develop a practical laboratory means for quantitatively measuring the tendency for green balls to decrepitate in iron ore pelletizing furnaces, and (2) Investigate the causes and cures of ball decrepitation. MATERIALS Two iron ores were used in the work reported here: a taconite concentrate at 90% minus 325 mesh, containing 65.0% Fe, 8.4% SiO2, and no loss-on-ignition; and a crude oxidized ore at 54% minus 325 mesh, containing 59.1% Fe, 3.6% SiO2, 1.1% A12O3, and 9.5% loss-on-ignition. For a special test of effect of particle size distribution on decrepitation, two other

Jan 1, 1967

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper&apos; a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By Arnulf Muan, Carlos Landolt

Equilibria involving Cu-Pt alloys, copper oxides, and atmospheres of known ox2gen pressures have been determined at 1000&apos; and 1200 C. The data obtained have been used to calculate activity-composition relations in the alloys. A moderate negative deviation from ideality is found. At high copper concentrations, the results of the present study are in good agreement with those of previous investigators, whereas at low copper concentrations the activities obtained in this investigation are slightly higher than those reported previously. The present study is part of a research program dealing with the determination of phase relations and thermodynamic properties of copper-containing systems at high temperatures. The information available for such systems is very scanty, particularly for copper oxides and their combinations with other oxide components. Platinum is commonly used as a container in studies of oxide equilibria. To evaluate quantitatively the extent of reaction between the oxide and the container, a knowledge of activity-composition relations in Cu-Pt alloys is necessary. Such data are not available for Cu-Pt alloys in the temperature range of particular interest in the present research program, and particularly for alloys low in copper. Studies of various aspects of the systems Cu-Pt and Cu-0 have been reported in previous literature. The system Cu-Pt is known1 to form a continuous solid-solution series above 812.C, whereas ordered phases are present in certain composition ranges at lower temperatures. Thermodynamic data for the system have been reviewed by Hultgren et al.,&apos; who presented free energies of mixing at 65Oo C, mainly derived from electromotive force cell measurements by Weibke and Matthes.3 Enthalpies of mixing at 640°C have been obtained by Oriani and Murphy4 with liquid tin calorime-try. Their results differ considerably from those derived from the temperature dependence of the data of Weibke and Matthes. Thermodynamic data for the disordered alloys have been obtained by Assayag,5 and more recently by Schmahl and Minzl,6 by Myles and Darby,7 and by McCormack, Myers, and Saxer.8 The two latter sets of data7&apos;&apos; became available after the present study was completed. In the system Cu-0+ two oxides are stable at high temperatures, CuO and CuzO+ each having only minor deviations from stoichiometry. Equilibria in the liquidus temperature region of the system Cu2O-CuO have been studied by Roberts and systemsmyth,9&apos;10CuzO-CuO by Vogel and ocher,I1 by Osterwald,12 and recently the the present authors.13 The system is of the eutectic type with a eutectic temperature of 1083.C The composition of the eutectic liquid corresponds to Xcu0 = °.44, and the oxygen pressure of the coexisting gas phase is Po2 = 0.55 atm.13 Equilibrium oxygen pressures for coexistence of solid CuO and solid Cu2O have been determined by Schmahl and Muller,l4 by Gadalla, Ford, and white,l5 by Bidwell,16 and recently by the present authors.13 There is reasonably good agreement among the various sets of data. Free energies of formation of Cu2O(s) from the elements have been derived by Tretyakov,17 by Bidwell,16 by Kiukkola and wagner,18 by Pal&apos;guev and Neuimin," and by Steele and Alcock,20 There is particularly good agreement among the latter three1&apos;-20 sets of data. THEORETICAL BASIS Consider a subsolidus isothermal section of the system Cu-Pt-0, as shown in Fig. 1. Two phase as-

Jan 1, 1970

G. D. Kneip, Jr., and J. 0. Betterton, Jr. (Union Carbide & Carbon Corp., Oak Ridge, Tenn.)—The authors have contributed to the theory of zone melting by considering the effects of the solidification of the final zone on the distribution curves for the finite length bar. However, they do not consider in sufficient detail the restrictions imposed by the particular metals involved. Eq. 4 has the analytical solution which is equivalent to Pfann&apos;s&apos; equation for normal solidification of the final zone. For distribution coefficients less than one, it is apparent from this form of the equation that, as the solidification approaches completion, the concentration attains extremely large values which are inconsistent with the density of physical materials. The necessary restrictions then are that the solute concentration cannot exceed the density of the alloy, or more frequently, the solubility limit in the solid phase. Secondly, the distribution coefficient cannot be constant from 0 to 100 pet solute unless the liquidus and solidus coincide over this whole region. It would thus be more correct to impose limits on the solubility such as would be indicated by a typical eutectic diagram. Furthermore, in this case the assumption that the distribution coefficient remains constant is more likely to be realized. Eq. 4 should then be replaced by the following C,,(x) =k/L-x [ ?11 3 C11 (x)Ddx - ?11 4 Cn(x)dx= k[Cn (L-l)/k] [ L-x/l]x-1 L-l = x = L-l [kCenterlie/Cn (L-l)]1/k-1 The typical shape for the distribution curve in the final zone is indicated schematically in Fig. 12 for the simple eutectic case. The solidification proceeds according to Pfann&apos;s&apos; expression until the concentration reaches the maximum solubility in the solid phasc. At this point, the concentration changes abruptly to the eutectic composition and remains at this value for the duration of the solidification. The width of the flat region, and the back reflection of this effect into the concentration curve on subsequent passes, depends upon the ratio of the eutectic concentration to the original concentration, upon the distribution coefficient, and upon the number of passes. Similar effects on the concentration curves in the first zone length would be expected in many systems for which the distribution coefficient is greater than one, and where the maximum solubility is not too much larger than the original concentration. The discussers agree with the authors that the assumption that the liquid is uniform in concentration should be considered with caution. Kneip and Better-ton&apos; have shown, however, that in floating zone refining of zirconium, using induction heating, the distribution of iron agrees with theory which assumes a uniform liquid composition. Hence, in this case, the experimentally realized distribution coefficient agrees with the present phase diagram within the experimental uncertainty. L. Burris, Jr., C. H. Stockman, and I. G. Dillon (authors&apos; reply)—The authors are happy to have received the comments of G. D. Kneip, Jr., and J. 0. Betterton, Jr., which provide additional insight into the zone refining process. It is true that the equations developed are inapplicable if the solute solubility in the solid phase is exceeded. However, this restriction on the use of the equations was clearly stated in the paper. A closer approach to

Jan 1, 1957

By W. A. Tiller, W. C. Johnston

The solute distribution ahead of an advancing solid-liquid interface is controlled by varying the momentum boundary layer thickness in the liquid adjacent to the interface. Single pass zone-melting experiments on Pb-Sn alloys are described in which the liquid is caused to rotate in the plane of the solid-liquid interface due to the influence of a magnetic .field rotating in this plane. The variation of the diffusion boundary layer thickness with field strength is determined. DURING the freezing of an alloy a partitioning of solute occurs at the solid-liquid interface, the magnitude depending upon the difference in the solid and liquid solubilities at the interface temperature. Because the diffusion coefficient is so small in the liquid relative to normal freezing rates, either a pileup or a depletion of solute occurs at the interface when the partition coefficient, kO, is either less than or greater than unity, respectively. This solute distribution is completely characterized by i) the solute concentration in the liquid far from the interface, C) the ratio of freezing velocityf, to diffusion coefficient, D, iii) the partition coefficient, ko, and iv) the thickness of the diffusion boundary layer, 6,, at the interface (this assumes that an electric field is not applied across the interface). For a particular system, C ko and D are fixed so that the character of the solute distribution can be changed only by a variation of either f or 6c. As is well known, the freezing velocity can be changed by varying the thermal environment of the alloy. Whereas, the thickness of the solute rich layer can be changed by varying the fluid flow conditions in the liquid. It is the purpose of this paper to describe a technique for controlling the fluid flow conditions in the liquid. During most solidification experiments the driving force for fluid flow arises from either mechanical mixing, thermal convection or electromagnetic mixing. The momentum boundary layer thickness, 6m at the solid-liquid interface, within which negligible movement of the liquid occurs, has been calculated for the special case of mechanical mixing where crystals are solidified by the Czochralski technique.l,2 The calculation of 6m for the case of thermal convection has also been made.3 In some calculations it has been assumed that the momentum boundary layer thickness, 6,, may be equated to the thickness of the diffusion boundary layer 6c, at the interface. However, as may be seen from Appendix I this is only true in very special cases and in general where a is a constant of magnitude determined by the particular liquid alloy. Neither calculations nor experimental data exist for the dependence of upon electromagnetic mixing. In this paper experiments are described in which the liquid is caused to rotate in the plane of the interface due to the torque developed on it by a magnetic field, H, rotating in this plane. The variation of is controlled by the variation of H. A magnetic field rotating in a plane perpendicular to the interface has been used for the purification of aluminum. Experimentally, we determined the variation of 5C with H by using the zone-melting technique of pfann5and a theoretical relationship of Burton et a1.2 pfann5 has shown that, after the passage of one molten zone through a long cylindrical charge of uniform concentration, CO, the solute distribution, C,, in the solid is as shown in Fig. 1. The equation describing this distribution is

Jan 1, 1962

By M. R. J. Wyllie

Eight laboratory-prepared aqueous base drilling muds representing common mud types, and 15 aqueous base drilling muds sampled in the field, have been used in an experimental investigation of the relationship between the streaming potential developed across a mud filter cake and the differential pressure causing filtrate flow. It has been established that the relationship is of the form, ES = kPy, where Es is the streaming potential, P the differential pressure and k and y are constants for any particular mud system at constant temperature. Beyond a certain minimum thickness this relationship is independent of filter cake thickness. Experiment has shown that both k and y are temperature dependent parameters and that in certain mud systems there is a critical value of P above which the simple relationship Es = kPY ceases to hold. The constant k tends to be a function of the mud resistivity at 77ºF, but the exponent y has not been found to be related to any commonly measured mud property. Certain field experiments are described which serve to demonstrate that the total SP (self potential) developed opposite a formation may be quantitatively accounted for as the algebraic sum of an electrochemical potential and an electrokinetic potential. A chart to permit the simple use of mean solution activities in the interpretation of electrochemical SP data is given and its use described. Various field methods for computing the electrokinetic SP component of the total SP are considered and rejected as being unduly complicated and inaccurate. It is shown that the employment of low resistivity drilling muds is essential if optimum accuracy is desired in the use of the S.P. curve for the purpose of computing connate water salinities by the electrochemical SP method. The use of such low resistivity drilling muds is accordingly recommended. INTRODUCTION In a previous paper&apos; a quantitative analysis of the electrochemical compovent of the SP (self potential) curve was made and it was shown that the electrochemical* emf, E, could be expressed as E = ZtRT/F In a,/a,, where t is the transference number of the chloride ion, R is the gas constant, T the absolute temperature of the formation water and mud, a, the mean activity of the connate water (assumed to be sodium chloride) and a, the mean activity of the mud (as sodium chloride). The essential accuracy of this expression was confirmed by an investigation 2 of the SP kicks opposite sands of known water salinity. The logs examined had been routine runs in oil wells in a number of Mid-Continent states. Further confirmation of the original analysis of the electrochemical SP is implicit in the paper by Tixier3 wherein a relationship between the SP and the ratio of connate water and mud resistivities, based only on field data, is given. Allowing for the fact that mud and connate water resistivities were used instead of activities, and that electrokinetic effects were ignored, the constant reported by Tixier is essentially 2tRT/F. The error involved in the universal substitution of resistivities for activities will receive further reference below. Possible reasons for the fact that the electrochemical properties of shales do not appear to be significantly dependent upon either the nature or the quantity of cation exchange materials, such as clays, they contain has been considered at some length by Wyllie and Patnode.4 In the same paper, the probable effects of shale thickness and compaction on electrochemical efficiency, and hence the inherent difficulty of obtaining reliable laboratory-scale data, were also pointed out. However, it is

Jan 1, 1951

By R. G. Gifkins

Mean boundary migration depended linearly upon creep extension under various conditions. Prolonged annealing or air-casting increased the proportion of immobile boundaries at a given stage of tests. Grain growth during annealing followed a power law. The linking of migration and sliding in creep and models for migration are examined; activation energies are calculated from these models. Segregation of oxygen to boundaries appears to be a controlling factor. THE idea that boundary migration and boundary sliding during creep are linked has often been suggested,&apos;-5 especially when evidence has been obtained for an alternation between the two processes. In simple bicrystals sliding can occur without any migration6 but in more complex bicrystals7 it is observed. McLean&apos; and Couling and Roberts 5 made measurements of both sliding and migration; McLean concluded that there was no linking of the two processes whereas Couling and Roberts supported the idea. McLean&apos; also developed a model for migration during creep and annealing. The present work was initiated as part of a study of the recrystallization of lead during creep9 but has been extended to examine some aspects of the mechanism of migration. MATERIALS AND METHODS Specially refined high-purity lead* was used; the total of impurities, excluding oxygen, was 0.0008 wt pct. Oxygen was removed as far as possible by melting in vacuo, treating at 550" to 600°C with hydrogen and then casting at 450°C under a vacuum of 10-2 mm Hg; the oxygen was then believed to be 0.00005 wt pct. Specimens were made from extruded strip and then annealed at the required temperature in an air oven, controlled to 5 lac. They were then polished in a mixture of acetic acid and hydrogen peroxide. At this stage some specimens were etched to give grain contrast and their grain sizes determined by the intercept method. Migration of boundaries during creep was measured on the surface of polished (not etched) specimens, directly loaded at room temperature (22°C) or 50°C (52"C) to initial stresses of 300 to 700 1b per sq in. Twenty six vacuum-cast hydrogen-reduced specimens were used and, in addition, two specimens were from material air cast after hydrogen reduction ("partial" air cast) and two from air-cast material not treated with hydrogen ("full" air cast). Duplicates were made in the majority of tests. At intervals through the creep tests, specimens were unloaded and the migration measured, normal to the direction of migration at the point of measurement, for each boundary along standard traverses. Usually between 110 to 180 boundaries were measured at each of some twelve stages of the tests. Migration was measured on the projected image (X100) using prism illumination. Fig. 1 illustrates the method of measurement and shows the kind of variation of migration found from boundary to boundary and along particular boundaries. Fig. 2 gives an example of more extensive migration. The mean value of distance migrated was generally reproducible to *10 pct but occasional points gave a scatter of *20 pct. The correctibn applied by McLean8 to allow for the contribution sliding makes to the apparent distance of migration could not be used, for the sliding at most boundaries was too small to measure with the equipment available. There were two reasons for supposing the correction unnecessary in the present work;

Jan 1, 1960

By G. V. Jere, V. Krishnan, C. C. Patel

Standard free energy and standard enthalpy changes as a function of temperature have been calculated for the chlorination reactions of different oxides constituting columbite and tantalite. The tallies of standard lee-energy change (F) indicate the possibility of pvefeential chlorination of different oxides but the ease 0.f chlorination of columbium pentoxide at about 250°C and the chlorinating tendency of columbium pentachloride in promoting the chlorination of tantalum and other metal oxides, p7-evetzt the separation of columbiu?n and tantalum from other oxides and pom each othel.. It is likely that low temperatuves of chlorination and continuous 1err2oval of columbium pentachloride from the ..eaction zone may help partial separation of columbium from tantalum as well as from titanium. The standavd enthaply change (AH?) values shotr that 1ou.-temperature chlorination around 300" to 500°C is likely to sustain the chlorination , without external heating. COLUMBIUM (niobium) and tantalum metals, their alloys and interstitial compounds are finding extensive uses in nuclear reactors and high-temperature equipment.la-3 These metals also find uses in chemical process plants, electrical rectifiers and capacitors and as "getters" in electronic tubes.la With the development of Kroll process of reduction of volatilized titanium tetrachloride by magnesium for the production of titanium metal, chlorine metallurgy is receiving greater attention. Chlorine metallurgy has several advantages, the foremost amongst them are: the ease of chloride formation, separation of the different constituents of minerals by selective chlorination, and the reduction of the chlorides in vapor phase to the respective metals. Recently, Si-bert, Kolk, and Steinberg4 have considered a number of methods for the preparation of columbium metal and the most promising is found to be the halide reduction. Since the minerals columbite and tantalite are comparatively abundant in nature, the future of the metallurgical processes depends on the utilization of these minerals for the production of columbium and tantalum chlorides by chlorination. In this paper, an attempt has been made to interpret thermodynamically the chlorination of individual oxides constituting columbite and tantalite, with the help of the recent thermodynamic data.5-8 For this purpose, standard free energy and standard enthalpy changes of the chlorination reactions of the oxides with chlorine, both in absence and presence of carbon as the reductant, have been calculated as a function of temperature and represented graphically. Similar calculations for the reactions employing carbon tetrachloride and carbonyl chloride as chlorinating agents have also been incorporated in this paper. REPORTED WORK ON CHLORINATION Cuvelliezg has patented a process for the separation of columbium and tantalum from their concentrate, wherein 75 pct Cb05 is claimed to be chlorinated at 1050°C in the course of 7 hr using chlorine or chlorine containing nonreducing gases, the products of reaction being CbC1, or CbOC1,. At this temperature, Ta,05 is claimed to remain unaffected. It is further claimed1° that at higher temperatures, the proportion of Ta205 chlorinated increases while that of Cb205 diminishes. During the studies on the action of chlorine on individual metal oxides, Kangro and Jahn" have observed that Ta,05 is not chlorinated even at 1200" in the stream of chlorine, while 75 pct of Cb,05 is converted into CbOC1, around 900 to 1100°C. The chlorination of Cb205 by chlorine in the presence of carbon, investigated by Lind and Ingle,&apos; and

Jan 1, 1962

By V. O. Struebing, K. A. Johnson, F. H. Ellinger, C. C. Land

The system Pu-Ce-(Pu,Ce)Co2 has been investigated by thermal, micrographic, and X-ray diffraction methods. The principal characteristics of this system were found to be: 1) a "eutectic" valley extending across the phase diagram from the 6 Pu/Pu3 Co eutectic at 408°C to the 7 Ce/Ce24Co11 eutectic at 42Z°C, the maximum temperature in the valley being 443°C; 2) three ternary inter mediate phases, each having an appreciable mutual solid solubility for plutonium and cerium; 3) eleven four-phase equilibria comprising one eutectic, four peritectics, and six Class II reactions; 4) a pseudobinary section between the ternary phase A and the y Ce solid solution, and another such section between the 6 Pu solid solution and the 77 phase (Pu3 CO) containing cerium in solid solution. ALLOYS of plutonium that are completely molten at temperatures in the vicinity of 500°C are of interest for use in the liquid state as fast reactor fuels. Since exploratory work1,2 on Pu-Ce-Co alloys had indicated that a "eutectic" valley extended across the ternary system between the Pu-co[6 Pu/n (Pu3co)] and the Ce-CO[? Ce/? (ce24co11)] binary eutectics, thus allowing alloys of any plutonium concentration to be selected within the temperature limitation, the present investigation was begun for the purpose of accurately defining the "eutectic" valley. However, when the existence of three ternary intermediate phases and the consequent complexity of the liquid-solid equilibria were discovered, the investigation was expanded to cover the complete system, except for the corner between the isomorphous series PuCo2-CeCo2 and pure cobalt. 1) EXPERIMENTAL The purities of the alloy components are given in Table I. Alloy buttons, each weighing about 5 g, were prepared by arc melting the accurately weighed components (±0.1 mg) under a purified He-Ar atmosphere. Weight loss as a result of melting was usually less than 1 part in 1000; therefore, the buttons were not chemically analyzed. One half of each button was re-melted by induction heating in vacuo in a magnesia crucible and furnace-cooled, so as to produce a somewhat coarser microstructure than that of the rapidly cooled arc-melted button. About 20 g of each alloy to be examined by thermal analysis were remelted in vacuo in a tantalum crucible of the inverted thermocouple well type. The thermal, X-ray diffraction, heat treating, and micrographic methods used in this investigation were essentially the same as have been described in earlier reports.3,4 Two etchants for these alloys were found to be satisfactory: A) 8 (parts by volume) orthophosphoric acid, 5 ethanol, and 5 glycol; B) 7 tetraphosphoric acid, 36 water, and 57 2-ethoxyethanol. Etchant A was used at 5 to 6 v for 15 to 20 sec, and etchant B was used at 10 v for 10 sec. 2) THE LIMITING BINARY SYSTEMS 2.1) Plutonium-Cerium. The phase relationships of this system have been investigated by Ellinger, Land, and Cramer,5 and by Selle and Etter.6 The over-all agreement of their phase diagrams is good, but there are some discrepancies in the positions of some phase

Jan 1, 1967

By Roland de Wit

Conclusions reached in a paper by weertmanl are amplified in a mathematical and graphical way. It is shown that in a stressed crystal a straight dis-location may be in a position of unstable equilibrium with respect to helix development, and how a small perturbation may start the dislocation off on its helical path. Helix development occurs by diffision; bulk diffusion is necessary for development from a screw, but core diffision is sufficient for development from an edge dislocation. For a mixed dislocation helix development can take place by core diffusion if the helix also climbs; a diffusion reversal takes place when the slope of the helix equals the slope of the Burgers vector. The work done on a crystal by the external forces is graphically shown to be consistent with the direction of motion of the dislocation in helix development. Finally a detailed mechanism for tangle formation from helices is presented. In the course of helix development a glide situation may be reached where a segment of each helix loop lies in a slip plane in which it can expand by glide. Thus is it visualized how a helix can deteriorate into a tangle. A paper by weertmanl proposes dislocation-tangle formation by a helical dislocation mechanism. The present paper amplifies Weertman&apos;s arguments in a mathematical and graphical way and presents some further ramifications of the proposed model. The importance of dislocation tangles is discussed in Weertman&apos;s paper and the references cited therein. The mechanism of their formation is not yet understood. Weertman proposes that in cold-worked crystals conditions exist suitable for the conversion of straight dislocations into helices and subsequently into tangles. Helix formation occurs by a diffusion process and Weertman proposes that at low temperatures only core diffusion is important. The present paper necessarily repeats some of Weertman&apos;s work. Since the mathematical development and notation used are slightly different from his, this was thought necessary for clarity. GEOMETRY OF THE HELIX weertman2 has shown that the equilibrium form of any dislocation line is a helix if it is assumed that the energy per unit length (line tension) of the dis- location is constant. For the special case that no external forces act on the dislocation, the helix reduces to a straight line. We shall assume in this paper that the dislocation has a helical form even when it is not in equilibrium. The parametric equation of a helix is, see Fig. l: where a is the radius of the cylinder tangent to the helix, and 270 the pitch of the helix. The pitch is related to v, the number of turns per unit length (along the axis) by the relation: When a = 0 Eq. [I] gives a straight line in the z direction. The growth of a straight dislocation into a helix is now described mathematically by letting a vary from zero to its final value. The tangent to the helix is given by where is the path length along the helix. This gives the direction of t and since its magnitude is unity we must have So that dcp/ds = (a2 +p2)-"&apos;. The curvature of the helix is given by where n = -(cos + sin) is a unit vector normal to the helix. Note that the vectors k and n always point toward the axis of the helix, Fig. 1. FORCE ON THE HELIX The external force which makes the straight dis-

Jan 1, 1963

By C. E. Turner, J. R. Elenbaas, R. D. Grimm, J. A. Vary, D. L. Katz

A technique is presented by which well samples and core plugs of dolomite formations are classified by microscopic examination into seven different porosity grades. Quantitative values of porosity and permeability are determined for each grade by a statistical correlation of the core plug test data with the porosity grading system. These quantitative values are applied directly to the grades exhibited in the well samples for the purpose of estimating the reservoir void space for wells that were not cored. The procedure is described for estimating the gas reserves per unit area lor the South Hugoton gas field. but a reserve estimate for the field is not given. INTRODUCTION The miscroscopic examination of well sample; and the graphic recording of their lithologic qualities and other distinguishing characteristics of various geologic formations drilled is both a science and an art of long standing and wide application. Usually the primary objective of a geologist who "sits on the well" and examines the samples are: to identify the formation being drilled, determine the total depth, casing point. and completion interval. In most cases the porosity is described. if done at all, in general terms. such as: trace, scattered, fine, poor, fair, medium. good, excellent, or in some other relative terms. In fields where various geologists have examined samples and recorded observations on many wells considerable variations in lithologic terms and porosity descriptions occur unless there is primary effort to establish uniformity of logging observations and standards of recording observable porosity. When an estimate of the pore volume of a reservoir is made a geologic concept of the processes that control the magnitudes of porosity and permeability is developed by microscopic examination of well samples. The characeristics and appearances are then mentally related to rather general quantitative units of porosity based on physical core data from the same reservoir or on such data or experience in other reservoirs that have similar qualities. The reliability of such estimates depends largely on the variations of the lithology of the formations, the geometric properties of its void system. the extent of comparisons of sample appearances with porosity data, as well as the uniform recording of all relevant characteristics. This statement is particularly significant for dolo-mitized limestone formations of substantial thicknesses and heterogeneity such as the Permian Dolomites of the Hugoton gas field. Jn this field, as well as in most of the Permian Dolomite fields, the producing formations are of relatively great thicknesses in which the porosity and permeability of the reservoir varies substantially in all directions, depending on the crystalline structure. degree and kind of impurities, kind of fossils anti cementation thereof, degree of dissolution. and fracturing. The variations of the lithologic texture of the dolomites and post deposition alterations have resulted in porosities and permeabilities of such magnitudes that only a part of the gross thickness can be counted as "pay." At the time of this study insufficient gas production had been experienced to apply the pressure decline production method in the South Hugoton Field and the electric logs are not definitive enough. The problem of estimating gas reserves in the south part of the Hugoton Field is primarily one of determining the pay thickness and porosity from well samples and core data. The area studied embraced all that part of the field lying south of an east-west line through Guvmon, Okla., anti containing approximately 1.000,000 acres. This paper describes a technique of correlation of physical core data with well samples so that quantitative values of pay thickness, porosity. Permeability, and connate water may be assigned to well samples that are representative of a given interval, and thereby permitting the estimation of gas reserves lor a given unit area. The procedure was developed by a uniform microscopic qualitative porosity grading of the dolo. mite core plugs.. and relating these grades to the respective physical core data on a statistical basis The well sample-were also graded in a Similar manner in order that the quantitative values established lor the core plugs could be applied to the well Sample for wells that were not cored. GRADING OF DOLOMITE A group of experienced geologists was given the assignment of examining the samples on all wells in South Hugoton in order that they could log their observations in a uniform and standardized manner and grade the observed porosity so that it could be related quantitatively to the core data. The group initiated the study 011 chips from cores which bad been tested for porosity and permeability. This study continued until all of the geologists developed a common knowledge of lithologic terms and of the characteristic appearances of the samples and their relations to measured porosity. The characteristic appearances of the dolomite samples under twelve-power magnification as related to their qualitative porosities afforded a classification of the dolomite into :even grades of porosity, ranging from dolomite of no-visible porosity under twelve-power magnification to dolomite of excellent porosity. The assigned grade for a specific 10-ft interval is a weighted average of all visible grades of porosity exhibited by the cuttings representing that interval. The porosity characteristics were recorded by a color graph adjacent to the lithology column in conjunction with a numerical system for further definition of relative porosity as shown in Fig. 1. The three vertical lines to the right of the lithology column each represent 33 1/3 per cent. which lines were used to record the percentage of the samples, for any particular interval. that showed porosity under the microscope. The colors were used to denote actual pore size. i.e., orange. blue and I-ed for pore diameter of one-fourth or less. one-fourth to one-Ilalf. and greater than one-half millimeter, respectively. The area colored 1)). one or more colors represents the percentages of the samples exhibiting pores of the respective size or sizes. The numerals from one to six inclusive shown on the log in

Jan 1, 1952

By J. V. Gluck, Ping-Wang Chiang

The tellurium-rich region of the Sb-TI-Te ternary system was investigated by means of DTA, metallo-graphic, X-ray, and electron beam microprobe techniques on the sections Sb2Te3-T12Te3, SbTlTe2-Te, SbT1Te2-Sb2Te3, and SbTlTe2-T12Te3. The phase behavior of this region is summarized in terms of four ternary invariant reactions and a schematic reaction diagram is suggested. Isopleths for the sections SbT1Te2-Sb2Te3, Sb2Te,-T12Te3, and SbTlTe2-Te were constructed, and a schematic diagram of the projections of the liquidus lines and invariant planes is presented. No evidence was found to support the existence of the ternary compound "SbTlTe3", or pseudo-binary behavior of the section T12Te3-Sb2Te3, as reported by Borisova and Efremova. Electrical conductivity, Seebeck coefficient, and thermal conductivity measurements were made at room temperature on fully annealed samples. 1 HE phase relationships in chalcogenides are often complex and difficult to resolve, particularly since the approach to equilibrium is a rather slow process. For example, the phase diagram of the T1-Te binary system was in doubt until clarified by Rabenau et al.,1 the phase fields at compositions near Bi2Te3 in the Bi-Te binary system have only recently been satisfactorily elucidated by Glatz,2 and there may still be some question as to the extent of the Sb2Te3 field in the Sb-Te system.3-5 In ternary systems, the existence of the compound "AgFeTe2" was the subject of a number of conflicting reports6-8 and the stoichiometry of the composition "AgSbTe2" was in doubt for a period of time.9 Recently, questions have arisen regarding the existence of certain compounds in the ternary systems Bi-Tl-Te10-14 and Sb-Tl-Te.15 The impetus for studies of these latter systems stemmed from the report of Borisova et a1.10 of a congruently melting ternary compound, "BiTlTe3", which apparently had extremely favorable thermoelectric properties for room-temperature cooling applications. Attempts by other investigators to produce the compound or confirm the transport properties proved to be unsuccessful.12-14 Recently, Chiang and Gluck14 reported studies of the phase relations in the tellurium-rich region of the Bi-T1-Te system which indicated that the section T12Te3-Bi2Te3 was not pseudobinary as suggested by Borisova et a1.10 The contention of Spitzer and sykes12 was supported that the composition "BiT1Te3" was multiphase, with the primary constituent actually being BiTlTe2, a compound whose existence has been well demonstrated.16,17 The investigation reported in the present paper was prompted by a later report of Borisova and Efremova15 on a similar study of the section T12Te3-Sb2Te3 from the Sb-T1-Te system. They also claimed this section to be pseudobinary, and that a ternary compound "SbTlTe," was formed peritectically. Some "preliminary" crystallographic data were given for the compound and thermoelectric transport properties were presented. In view of the questions concerning the behavior of the Bi-T1-Te system and the existence of the compound "BiT1Te3" it was suspected that the Sb-T1-Te system might behave in a similar fashion, particularly in light of the known existence of a compound SbT1Te2, iso-structural with BiT1Te2.17 Consequently, an investigation was undertaken to clarify the phase relationships in the tellurium-rich region of the Sb-T1-Te system. It is the purpose of this paper to present the results of this study, including a representation of the phase relations, isopleths for various composition sections, and the determination of some phase compositions and transport properties. EXPERIMENTAL PROCEDURES Commercially available high-purity (99.999+ pct) elements, purchased from the American Smelting and Refining Co., were used for the sample preparation. All samples were made from thoroughly mixed powders of previously prepared master alloys: SbTlTe2, Te, Sb2Te3, and T12Te3. Stoichiometric quantities of the constituents for each 10-g sample were weighed into a specially cleaned fused silica tube and sealed under a vacuum of better than 5 x 10-5 torr. The sealed constituents were fused and reacted at 650° to 750°C for at least 4 hr under continuous agitation in a "rocking" furnace, and the resulting product was air-cooled. The tube was opened and the sample was ground to a powder. A portion of the powder was rebottled in a DTA tube under vacuum, and the rest of the material was similarly resealed in a separate tube, re-fused in the rocking furnace, and again cooled to make the ingots for electrical and microstructural studies. All samples were subjected to further heat treatments as discussed in the section on experimental results. Each DTA tube was made of 7-mm-OD fused silica tubing with a concentric 2-mm-ID depression about 4 mm long formed in the bottom to accommodate a thermocouple. The size of a DTA sample was 0.5 to 1.0 g. An Aminco Thermoanalyzer whose accuracy was within 2°C18 was used for the DTA measurements. The metallographic samples were prepared by conventional techniques. A solution of FeCL dissolved in a methanol-HC1 mixture was found to be the most satisfactory etchant. Electron beam microprobe scanning and point-count examinations were made on polished and unetched samples using an ARL Electron Microprobe at an electron beam voltage of 20 kv. The detectors were set to receive characteristic La1 radiation. Calibration standards of the pure elements were incorporated in each sample mount; quantitative point counts were calibrated by a method similar to Ziebold

Jan 1, 1969

By Luc Delaey, Horace Pops

The structure and morphology of thermoelastic and burst type martensitic phases that form upon cooling in Cu-Zn-Si p phase alloys have been studied by transmission electron microscopy. The martensitic phases are composed of a lamellar mixture of two close-packed structures with different stacking sequence, namely ABCBCACAB (orthorhombic) and ABC (fcc). Striations within thermoelastic martensite are most likely produced during interaction with impinging burst-type martensite and not as a consequence of secondary shears. In a study of the martensitic transformation in ternary Cu-Zn based 0 phase alloys1 the dependence of the martensitic transformation temperature, M,, with composition shows variations for elements within a constant valence subgroup and between different subgroups. Such variations are not reflected in a change in habit plane, which is approximately the same for each ternary alloy, namely in the vicinity of (2, 11, 12 Ip. The fact that the habit plane remained constant, despite large differences in M, temperature and electron concentration, suggested2 that the crystal structures of the martensitic phases could be nearly the same. Crystal structures of ternary Cu-Zn based martensites have been determined recently for alloys containing the three-valent elements gallium3, 4 and aluminm. The present studies have been made to examine the structures and morphology of the martensitic phase in ternary Cu-Zn based alloys containing a four-valent element, silicon. I) PROCEDURE Two alloys were prepared by melting and casting weighed quantities of the component high-purity metals in sealed quartz tubes under half an atmosphere of argon. They were subsequently remelted by levitation under a protective atmosphere of argon. After allowing for losses of zinc as determined by the difference in weight before and after casting, the compositions in atomic percent of both alloys were established to be Cu-33.5 Zn-1.8 Si and Cu-27 Zn-5.0 Si. These alloys were homogenized in the P-phase field for 2 days at 800" C. Bulk samples consisted of a martensite phase at room temperature, the M, temperature being approximately 30&apos; and 200" for the 1.8 and the 5 pct Si alloys, respectively. Thin disks were cut from the ingots using a spark machine, and they were heated for 5 min at 800&apos; and quenched into water in order to obtain martensite. These slices were thinned chemically at room temperature in a solution consisting of 40 parts HN03, 50 part H3PO4, and 10 parts HC1 and thinned further electrolytically by the Window technique, using a voltage of 15 to 25 v and a mixture of 1 part HN03 and 2 parts methanol, which was kept at a temperature near -30° c. Foils were examined by transmission electron microscopy using a Philips EM 200 electron microscope. 11) RESULTS AND DISCUSSION 1) Structure and Morphology. Fig. 1 shows the martensitic phase in the alloy containing 1.8 at. pct Si. This phase is composed of contiguous platelets, each containing striations. The direction of the striations changes at the boundary between individual platelets. These internal markings resemble the striations that are usually identified as stacking faults, as for example in Cu-A1 martensites6-a or the lamellar mixture of two close-packed phases in Cu-Zn-Ga marten-sites.3p &apos;9 lo In the present alloys, selected-area diffraction experiments have been obtained in order to determine the nature of the striations. Figs. 2(a), (61, and (c) are electron diffraction patterns of an area inside a single martensite plate. Fig. 2(a) contains diffraction spots which correspond to two close-packed structures with different stacking sequences, namely ABCBCACAB (orthorhombic) and ABC (fcc). Spots belonging only to the fcc structure are indicated by arrows. By tilting the foil either the orthorhombic structure, Fig. 2(b), or the cubic structure shown in Fig. 2(c) may be obtained. When the foil is oriented so that only the diffraction spots of the orthorhornbic structure are present, bright-field illumination shows small lamellae, as seen in Fig. 3. In this figure the lamellae that belong to the fcc structure are bright bands inside the dark extinction contours of the orthorhombic structure. The boundaries of the lamellae are parallel to the basal planes of the orthorhombic structure and to the {Ill} planes of the cubic structure, the close-packed directions of both structures being parallel. The 5 pct Si alloy shows similar features as those described for the 1.8 at. pct Si alloy.

Jan 1, 1969

By Robin O. Williams

Robin 0. Williams (Oak Ridge National Laboratory)— The authors have questioned the degree to which the coherency strains between the iron-rich and chromium-rich phases are isotropic as proposed in Ref. 5 on the basis of the difference between the elastic properties of the two phases. The relative magnitude of the stresses is determined by the moduli as shown by Eqs. [2], [3], and [4] of Ref. 34. However, the moduli of the two phases have no direct bearing on the uniformity of either the stress or strain within either phase. The idea that the strains are isotropic within each phase (but normally of different magnitude and always of different sign) is based entirely upon the experimental observation that X-ray line broadening has not been detected even when the particles become rather large. It has not proven possible to grow the particles sufficiently large that they lose coherency. Based upon this lack of line broadening one can estimate an upper limit for the nonuniformity of the strains within each phase as follows. It is considered possible to detect line broadening if it is as great as 10 pct of the separation of the K, doublet for the (211) line using chromium radiation. The doublet separation would correspond to a total strain of 0.0017 such that the total variation of lattice parameter relative to the average lattice is now k0.05x0.0017 or something less than ± * For the present case the strain in each phase is roughly 0.002 such that the variation of strain within a phase will not exceed 5 pct. It is stated that the expression derived for strengthening for the hydrostatic straining as observed in this system would substantially overestimate the magnitude due to dislocation flexure. This is contrary to the conclusion reached in the original paper34 for the present range of particle sizes. What is the lowest temperature at which a has been observed to form in this alloy? M. J. Marcinkowski, R. M. Fisher, and A. Szirmae (nutlzors&apos; reply)— -Williams&apos; arguments based on X-ray findings for a chromium-rich precipitate and an iron-rich matrix strained to a common lattice parameter are certainly convincing. This being the case, there are no shear components of strain associated with the precipitate-matrix aggregate to interact with the shear components of the dislocation stress fields, contrary to the opinion expressed by the present authors. On the other hand, the present authors, in spite of this error, did not expect the shear interactions to be significant. The chief objection to Williams&apos; model in the present case is that the various segments of the dislocation line are assumed to pass from one potential valley to the next independently of neighboring segments. This is only true for a highly flexible dislocation line, i.e., one whose radius of curvature is something less than the center to center distance between precipitate particles which amounts to about 90A in the present alloy. In order to maintain this curvature, an externally applied shear stress of at least 230,000 lb per sq in. would be required or about four times the observed stress. It is therefore concluded that the dislocation lines move rather rigidly through the lattice. This being the case, the forces on the dislocation resulting from the hydrostatic interaction between the stress fields of the edge-dislocation components and the precipitate particles should average out to zero; that is particles above the below the slip plane produce forces on the dislocation of opposite sign and therefore will cancel when averaged over the entire length of the dislocation. On the other hand, since the dislocation is not perfectly rigid, Williams&apos; model may lead to some strengthening, but far less than that predicted. A second and equally serious objective to using Williams&apos; strengthening model for the present alloys is that profuse wavy slip due to the motion of screw dislocations played a predominant role not only in the unaged alloys but in the fully aged ones as well. Since the screw dislocation has associated with it only shear components of stress the hydrostatic strengthening model no longer applies. In view of these arguments the present authors must reject Williams&apos; model of strengthening as being pertinent to the present alloy system. The present authors have made no detailed study of the lowest temperature at which a forms in the quenched ferritic alloys. None was ever observed n the alloys aged at 500°C so that forma-tion must occur at temperatures higher than this and was therefore not a factor in the present study.

Jan 1, 1965

By Y. Nakada, U. F. Kocks, B. Chalrners

THE orientation dependence of work hardening has previously been studied over the entire range, i.e., including special orientations of high symmetry, in aluminum1-3 and silver.* The differences between various orientations are substantial, and the trend is the same in all fcc crystals. However, there are quantitative differences in behavior between aluminum and silver at room temperature, particularly in the (100) orientation. While many experiments on gold have been reported,5&apos;9 none included the special orientations. We therefore undertook tension tests on gold crystals of the axial orientations (100),(110), (Ill), (211), and, as a representative of single slip, one whose Schmid factor was 0.5 (hereafter referred to as m = 0.5). Single crystals of dimensions 1/4 by .1/4 by 6 in. were grown from the melt1&apos; at a rate of 4 in. per hr, using gold of 99.99 pct purity obtained from Handy and Harman. A growth rate of 1/8 in. per hr, or a purity of 99.999 pct,ll produced no difference in results. The crystals were annealed at 1000°C in air for 24 hr and furnace-cooled down to room temperature, after which they were electro-polished in a solution of potassium cyanide (40 g), potassium ferrocyanide (10 g), soda (20 g), and enough distilled water to make 1 liter of solution, at a current density of 0.02 amp per sq mm. After 2 or 3 hr, a very smooth surface was obtained by this method. Nine m = 0.5, two (loo), one (110), three (Ill), and one (211; crystals were tested at room temperature in a floor-model Instron machine at a tensile strain rate of 0.5 pct per min. The accuracy of the stress measurement was k10 g per sq mm up to 500 g per sq mm, k2 pct for higher stresses. The strain measurement was accurate to t2 pct. The scatter of stress at a given strain among the crystals of the same orientation was small, *5 pct being the largest. The representative stress-strain curves for various orientations are shown in Fig. 1. Table I summarizes the work-hardening parameters as used by seeger.12 Results of other investigators are also included in this table for comparison. There are no previous data for the corner orientations. Values for m = 0.5 crystals agree fairly well with those of Berner. Tm is defined as the stress at which the stress-strain curve begins to deviate from linearity of Stage 11. However, in practice this is a very difficult value to estimate because each investigator has a different idea of linearity. Therefore, the comparison with the values of other investigators may not be valid. In the present experiment, (100) crystals had the highest 111, followed by (111) crystals. The work-hardening rate in Stage I1 was highest for the (111) crystal followed by the (100) crystals. Our value for 0x1 of m = 0.5 orientation agrees very well with those of other investigators. 1) Single-Slip orientation (m = 0.5). These crystals were oriented so that the primary-slip vector was contained in one side face. The dimension perpendicular to this side should then not change if single slip indeed takes place. Within the accuracy of measurement, this dimension did not change during the deformation. Since the accuracy is k0.2 pct, the amount of secondary slip is less than 0.7 pct of the slip on the primary-slip system at 30 pct tensile strain. This is in conformity with the results obtained by Kocks" for aluminum crystals. The tensile axis moved toward (211) during the deformation. Slip bands, Fig. 2(a), were very fine and closely spaced. Some deformation bands were observed. There were no clear-cut cross-slip traces such as the ones observed on aluminum m = 0.5 crystals. 2) (111) Crystals. The orientation of the tensile axis was stable during the deformation. From this observation, one can deduce that at least three slip systems must have operated, and probably all six because the remaining three all have cross-slip relation to one of the first three.&apos; It was very difficult to observe the slip markings. Consequently, we could not confirm by this method that six systems were operative during the deformation. At high strains (above 50 pct shear strain), this orientation had the highest stress-strain curve. At 80

Jan 1, 1964

By W. H. Smith

IN connection with some recent work on the effect of impurities on the ductility of chromium, it appeared desirable to know the solid solubility of carbon in chromium. A literature survey indicated that this information was not available. Although considerable work has been done on the Cr-C phase diagram,&apos;.&apos; previous investigators have been more concerned with the structure and phase boundaries of the carbide phases than with the terminal solid solution. The phase diagram shown in Fig. 1 is taken from the work of Bloom and Grant&apos; and represents the most recent determination. As indicated by the dashed line, the a solid-solubility limit was not determined. Experimental Procedure Alloys of chromium were prepared from hydrogen-treated and vacuum-degassed electrolytic chromium plus spectrographic grade carbon. The oxygen and nitrogen content of the alloys was <0.002 pct. After melting, analysis of the alloys showed them to contain 0.02, 0.08, 0.15, and 0.55 pct C. Pieces of the alloys were heated in a protective atmosphere to various temperatures and then quenched after holding for a time sufficient to insure equilibrium. Microscopic examination of the as-quenched alloys for the presence of a second phase was used as a measure of the solubility limit. The heats were made in a multiple hearth arc-furnace using a zirconium-gettered static argon atmosphere. A zirconium melt was made before each Cr-C heat. Triple melting was used to insure ingot homogeneity as shown by microscopic examination. The alloys were prepared by adding portions of a 4.5 pct C-Cr master alloy to high purity chromium. The carbon contents listed previously were those obtained by analysis. The nitrogen and oxygen contents after arc melting were both <0.002 pct. Sections 1/8X1/4X1/2 in. were cut from the 100-g ingots and a hole drilled in one end in order to suspend the sample from a molybdenum wire. After the surface was carefully cleaned, a sample of each melt was hung in a mullite tube heated externally by a platinum resistance furnace connected to a vacuum system. The lower portion of the mullite tube was sealed to Pyrex and closed off several inches below the furnace. This was filled with sili-cone oil kept cold by circulating cold water around the outside of the Pyrex. Quenching into the oil bath was achieved by melting a fuse wire supporting the sample. It required about 4 sec for the sample to cool from 1400" to 600°C. This severity of quench was considered satisfactory to freeze-in the high temperature equilibrium. For tests made at temperatures of 900" to 1200°C, heating was done in vacuum; for tests above 1200°C, an argon atmosphere was used. The holding time employed ranged from 12 hr at 900°C to 6 hr at 1400°C. Experiments were performed at temperatures of 900°, 1000°, 1100°, 1200°, 1300°, and 1400°C. Microscopic examination for evidence of a second phase was done at X1500. Experimental Result The microstructures of a 0.08 pct C-Cr alloy as-cast and after quenching from 1300°C are shown in Figs. 2 and 3. A 0.15 pct C-Cr alloy quenched from 1300°C is shown in Fig. 4. The data obtained from the quenching experiments is shown graphically in Fig. 5. If the Van&apos;t Hoff equation is obeyed, a plot on a logarithmic scale of the mol fraction of solute vs the reciprocal of the absolute temperature should give a straight line. For dilute solutions the weight percentage can be substituted for the mol fraction without introducing any appreciable error. The Van&apos;t Hoff equation can then be written as where H is the heat of solution in calories per mol. The slope of the straight line on the log pct C vs 1/T plot gives the value of AH. Assuming that the Van&apos;t Hoff equation is obeyed, which is probably justified for the dilute solution of carbon in chromium, the heavy straight line shown on Fig. 5 represents the best fit of the data. This line was obtained as follows. On Fig. 5 the results of the microscopic examination of all alloys following quenching were plotted and designated as to whether one or two phases were seen. Below 1100°C all alloys showed a second phase on quenching. The heavy vertical lines shown in Fig. 5 therefore represent the possible range of the ter-

Jan 1, 1958