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By A. Mitchell, M. Etienne

VARIOUS'-3 reports on the electroslag remelting process refer to the "thin skin of slag" existing around the slag pool and the solidifying ingot, but none considers the various mechanisms by which this layer forms and thus influences the surface quality of the ingot. A vertical section4,5 of the Cao-CaF2-Al2O3 diagram is shown in Fig. 1 between CaF2 and 6Al2.CaO3 From this, it is seen that a typical "70:30" CaF2:A1a3 slag will solidify to produce 6Al2O3.CaO primary phase in a eutectic matrix. The commercial slags contain sufficient CaO to produce* this composition by both the

Jan 1, 1969

By R. W. Smith, G. W. Delamore, J. A. Spittle

RECENT work by the authors1 has demonstrated that the crystals constituting the equiaxed zone in small ingots originate, on quenching, in the chilled liquid. Whether any partial remelting2 takes place of the den-drites nucleated in the chilled region was not examined. However, the claim3 that this normally occurs, leading to crystal multiplication, has been disputed.4 Thus, for an equiaxed zone to form in the central region of an otherwise columnar ingot, it is necessary to transport crystallites from the chill zone to this region. In view of the work of Uhlmann et al.,5 it was considered desirable to examine the transport process further. Experimental Technique and Results. In the earlier experiments by the authors.1 a stainless-steel crucible 17/8 in. diam, 41/2 in. high, ad containing an alloy of A1-4 wt pct Cu, was quenched from 660°C into a bath of Wood's metal maintained at 100°C. Under these conditions a central zone of equiaxed crystals was obtained. However, if a 2250-G unidirectional magnetic field was applied for 2 sec immediately following the instant of quenching, or subsequently, the equiaxed zone did not appear. Careful thermal analysis showed that the short application of the field had virtually no effect on the thermal conditions of the melt. It thus appeared that the crystallites which were ultimately to grow large enough to form the equiaxed zone existed in the liquid immediately ahead of the interface, occlusion being prevented by the convective fluid flow induced by freezing from the walls of the cylinder. When this relative movement was prevented by the Lorenz forces induced by the application of the magnetic field, the crystallites were caught up in the rapidly advancing dendrite solid-liquid interface. To test this assumption, a small ingot of super-purity aluminum was partially melted and poured into a heated stainless-steel mold which was then immediately quenched into molten Wood's alloy. The resulting structure is shown in Fig. 1, and consists of columnar grains with a central fine-grained zone. Thus the unmelted solid present at the beginning of solidification had been transported ahead of the columnar interface. Discussion. There appears to be little or no information available on the interaction of suspended particles with a metallic solid/liquid interface. However, some information is available for transparent organic sys-

Jan 1, 1969

By J. C. M. Li

A dislocation model is constructed for a cylindrical tilt boundary of which the axis of tilt is parallel to the axis of the cylinder. The strain energy per unit area calculated from this model agrees with thut of an infinite vertical wall of edge dislocations. Based on this model, a dislocation mechanism for the shrinking of such a cylindrical boundary is proposed. The power relation between the grain boundary velocity and the driving force is accounted fm by the stress dependence of dislocation velocity. The activation area for grain boundary motion is found to correlate with that .for Creep in aluminum. In the preceding paper' the velocity of a curved grain boundary is found to be a power function of the driving force, [1] where M is the velocity at unit driving force, y is the grain boundary energy, and p is the radius of curvature. This finding adds another nonlinear rate equation to metallurgical phenomena. While a macroscopic theory for the steady state as just presented2 can be used to understand the shape of the moving boundary, such theory usually does not provide any information about the atomistics of the process. It is attempted in this paper to discuss the nonlinear rate equation in terms of a dislocation mechanism. A DISLOCATION MODEL FOR A CYLINDRICAL TILT BOUNDARY Before a dislocation mechanism can be proposed for the motion of a cylindrical tilt boundary, it is necessary to construct a dislocation model for the boundary. For simplicity, a tilt boundary in a simple cubic lattice will be examined. Although this does not represent the situation in aluminum, it is expected that the general features will be similar. The details of the model in the fcc lattice can be constructed when a refinement of the simple model is called for. A cylindrical low angle tilt boundary in a simple cubic lattice is shown in Fig. 1. Two sets of edge dislocations are needed as shown. A schematic representation is shown in Fig. 2(a). In terms of a continuous distribution of dislocations, the density of dislocations n, of Burgers vector b, in the small segment ds of the grain boundary is Similarly the density of dislocations n, of Burgers vector bz in the same segment ds is where is the tilt angle of the grain boundary. Based on this continuous distribution of dislocations in the grain boundary, it can be shown that the interaction between a small segment of the boundary and the rest of it is zero. Furthermore, the stress produced at any point inside or outside the cylinder is also zero. This shows that the model is acceptable in the sense that the boundary has no long-range stresses. Since the model of continuous distribution of dislocations in the grain boundary does not reveal the interactions among individual dislocations, a discrete dislocation model has to be used for such purpose. For simplicity, an equivalent model is shown in Fig. 3. This arises because the total Burgers vector is, from

Jan 1, 1970

By A. W. D. Hills

This paper describes the development of a generalized integral-Wofile method for the analysis of heat transfer dwing solidification. The method is extremely flexible, and can be applied to a wide range of situations. This flexibility has been achieved by characterizing the solid metal layer in terms of two parameters, and by developing two simultaneous nonlinear differential equations for these parameters in terms of the heat fluxes crossing the boundaries of the solid layer. The use of these equations is illustrated in a series of examples which involve the solidification of pure metals at zero superheat cooling under different conditions. The simplicity with which the method can be extended to treat more complicated jwoblems is illustrated in a further example which involves natwal convection effects in the liquid metal. ThE rate at which molten metal solidifies in an industrial casting process, and the structure of the cast product, are both controlled by the rate at which heat can be removed from the casting. A knowledge of heat transfer rates is thus essential to the control of the process and to the control of the structure and soundness of the final casting. Heat transfer rates during real solidification processes cannot be predicted by formal mathematical techniques, however, because nonlinear boundary conditions are involved. Approximate methods are normally used, and these have included electrical and hydraulic analogue techniques, finite difference methods, and the integral-profile method. Considerable effort has been devoted to the development of the first two techniques, but the integral-profile method has been used very little so far. This is unfortunate because the method is capable of providing relatively accurate solutions for the heat transfer equation during solidification without involving large amounts of computer time. A further advantage of the method is its flexibility, although this is not apparent from the integral-profile solutions that have been developed to date. These solutions have been derived for the solidification of molten metal at zero super-heat under cooling conditions involving either a constant heat flux from the cooled surface;' a constant heat transfer coefficient at the surface,'-3 or a specified variation in the surface temperature.4,5 A generalized integral-profile method is presented in this paper which can be used to predict unidirectional solidification rates under a very wide range of more realistic cooling conditions. The use of the method is illustrated in a series of problems involving pure metals, or skin forming alloys, solidifying at zero super-heat. However, the principal advantage that this method has over the previous integral-profile methods is the ease with which it can be extended to treat more complicated solidification problems. This is illustrated by considering a problem in which super-heat is liberated from the liquid metal by natural convection during the solidification process. In the final section of the paper the generalized method is compared with previous methods used to predict solidification rates and its extension to more complicated solidification problems is briefly discussed.

Jan 1, 1970

By A. K. Mukherjee, J. E. Dorn

A modified Peierls model is Presented for the rationalization of the asymmetric plastic behavior of single crystals of bcc metals. The model assumes that the asymmetry of slip arises from a tendency toward asymnetric splitting of the a/2[111] screw dislocation. The approach differs from former theories however insofar as it assumes that the splitting is so minor ttut only the core energy is modified and that no real partial dislocations exist. As a consequence, the concepts of a line energy of a partial dislocation, interaction between partial dislocations, constriction energies, and stacking fault energies are not invoked. Instead the present analysis is based on a specialization of the Peierls mechanism which assumes an asymmetric dislocation core which is modified by the effective stress and permits cross slip. The theoretical predictions on the stress-temperature -strain rate and orientation relationship agree qualitatively with the limited experimental data that are currently available. Additional experimental work over wider ranges of conditions is suggested to provide more complete evaluation of the possible validity of this theory. RECENT experimental investigations on the low-temperature thermally activated deformation of bcc metals have confirmed the existence of several unique orientation effects. These will be described with the aid of the standard stereographic projection shown in Fig. 1. If slip were determined exclusively by crystal symmetry, the deformation characteristics would be symmetrical about X; = 0 and independent of whether the specimen were subjected to a tension or a compression stress, regardless of what combinations of slip planes might be operative. Experiments, however, reveal that neither of these symmetry based predictions are valid. A schematic representation of the commonly observed asymmetry of both the yield stress and the plane of slip is shown in Fig. 2. A reversal of the direction of stressing results in an inversion of the asvmmetric behavior. 1) Asymmetry bf Yielding. A detailed investigation on the asymmetric yielding in an Fe-2.7 pct Si alloy was repoEted by Tabka, Tikeuchi, and Furubayashi,1 Similar trends have been observed by Keh and Nakada on iron,' Stein on molybdenum,3 Bowen, Christian, and Taylor4 on columbium, Sherwood, Guiu, Kim, and pratt5 on Ta, Cb, and Mo. The degree of asymmetry not only depends on the atomic number and alloying but, in all cases that have been examined, it also increases with a decrease in the test temperature. 2) Asymmetry of the Slip Plane. Asymmetric $I-~: curves of the type shown in Fig. 2 have been found for several Fe-Si alloys6-8,1 and columbium.4 There is general agre_ement that near X: = 30 deg slip occurs by the [111](211) mode so that ?1 = 30 deg. As X; decreases it appears that [111](211) to [111](101) cross slip takes place leading to slip band traces on intermediate planes. And as xi approaches 0 deg, sharp

Jan 1, 1970

By W. R. Wilcox

The camphor-anthracene system was chosen as a transparent low-melting analog of the zirconium carbide -graphite system. Camphor and zirconium car -bide both grow nonfaceted, while casting of mixtures yields platelets of both anthracene and graphite. Zone melting of thin layers of organic was observed under the microscope. Irregular lamellar structures were produced at high values of the ratio of the temperature gradient G to the zoning rate V. The anthracene invariably led the camphor, indicating lower kinetic undercooling for the anthracene. The lamellar spacing was an order of magnitude greater than typical spacings for metal eutectic systems. Exact behavior depended on orientation of the anthracene. Oriented dendritic structures were produced at low values of G/V. Transient and oscillatory behavior were also observed—much of it unexpected. A.RC-CAST refractory carbide-graphite mixtures are promising thermal-shock resistant materials. Oriented structures of these materials would be superior to arc-cast materials for many applications. Mollard and Flemings1 and Cline2 have shown that aligned structures can be obtained for a wide range of Pb-Sn alloys. However, these metals both solidify in a nonfaceted manner while graphite yields platelets or flakes. In addition only small diameter samples of Pb-Sn alloys were produced because it was necessary to avoid free convection and to have high temperature gradients. The purpose of the present work was twofold: 1) To observe the solidification of a transparent low-melting analog of carbide-graphite systems and 2) to see if larger diameter samples can be produced. EXPERIMENTAL PROCEDURE When zirconium carbide-graphite mixtures are cast, the resulting structure naturally depends on composition. Carbide-rich mixtures yield metal-like nonfaceted carbide dendrites in a eutectic matrix. Graphite-rich alloys have graphite platelets in a eutectic matrix. Empirically it was found that camphor-anthracene mixtures produce similar structures with camphor being nonfaceted and anthracene forming plates. The organic eutectic melted at 116°C and was composed of 78 wt pet camphor.3 The camphor used was U.S.P. grade from Fisher Scientific Company; the anthracene was 98+ pet fro Aldrich Chemical Co. The impurity content is judged to be on the order of 1 pet. Mixtures ranging from 50 to 88 wt pet camphor were employed for the experiments. All but one of the experiments were performed on the microscope-stage zone melting apparatus described in detail elsewhere.4 The organic mixtures were contained in horizontal cells made of microscope slides or cover glasses. In most of the cells the organic was present as a very thin layer, thus giving almost two-dimensional growth behavior. The cells were moved slowly under a heated wire, which caused a molten zone to move through the solid at rates ranging from 0.01 to 5.4 cm per hr. The temperature gradient was estimated before moving the zone by measuring the distance between the line where all solid was melted (freezing point) and that where solid first began to melt (eutectic temperature). The temperature gradient was found to be 465°C per cm in the thinnest cells used, which were made by pressing together two microscope cover slips in the organic melt and then rapidly withdrawing them. RESULTS The experimental results are described in four parts: simultaneous growth, dendritic growth, irregular growth, and transients and erratic phenomena. Steady state data are summarized in Fig. 1. Except where noted all comments are for the cells containing a thin layer of organic. A) Simultaneous Growth. Simultaneous and roughly parallel growth of anthracene and camphor was obtained over the full range of compositions investi-

Jan 1, 1970

By E. T. Turkdogan, L. J. Martonik, R. J. Fruehan

Electrochemical measuretnents of the solid oxide electrolyte galvanic cells CY-Cr2O3 I ZrO2 (CaO) 1 O (in Fe alloy) CY-Cr2O3 I Tho2 (Y2O3)I O en Fe alloy) have been made at 1600°C (2912°F) in order to test the Performance of such cells at liquid steel temperatures. The oxygen pvobe (cell) consists of a disk of ZrO2 (CaO) or Tho2 (Y2O3) electrolyte fused at one end of a silica tube filled with a mixture of Cr-Cr2O3 which is the reference electrode. Upon immersion in liquid steel, the electromotive force readings achieve a steady value within a few seconds, and remain steady for 30 win or more. The perforwzance of the probes has been tested using Fe-O, Fe-Si-O, Fe-Cr-O, Fe-V-O, and Fe-Al-O alloys; the oxygen contents of liquid steel derived from the measured electromotive forces are in satisfactory agreement with those determined by arulysis. Use of the probe in the deoxi-datiorz of steel, in laboratory experiments, is discussed. The results indicate that there is insignificant electronic conductivity in ZrO2(CuO) at oxygen activities down to those corresponding to 10 ppm in steel. At lower oxygen activities, probes tipped with ThOn (Y2O3) disks perform satisfactorily at oxygen activities down to 1 ppm O or less. THE key to the control of deoxidation of steel is a sensing device to measure rapidly the concentration of oxygen in liquid steel in the furnace, ladle or tun-dish at any desired stage of deoxidation. The analysis of the cast steel by the neutron-activation or vacuum-fusion method gives total oxygen as oxide and silicate inclusions. This analysis is important for guidance to steel cleanliness; however, such a postmortem is of little value in the control of deoxidation of liquid steel. At the General Meeting of the American Iron and Steel Institute in New York, 1968, Turkdogan and Fruehan' presented a paper on the preliminary results of the work done in this laboratory on rapid determination of oxygen in steel by an oxygen probe. Details of the work done in this laboratory leading to the development of a galvanic cell for the determination of oxygen in liquid steel, and the results of the tests made are given in this paper. It was through Wagner's contributions, since the early Thirties, to the physical chemistry of semiconductors in general that it ultimately became possible to construct galvanic cells for application at high temperatures. In 1957, Kiukkola and wagner2 successfully demonstrated the use of several solid electrolytes in measuring the free energies of several chemical reactions, in particular, the use of lime-stabilized zir-conia in high-temperature oxidation reactions. Starting 7 years later, a number of papers appeared in the technical literature3-' demonstrating possible applicability of galvanic cells for the determination of oxygen in liquid steel. In the earliest work, Japanese investigators3j4 experimented with various types of reference electrodes, e.g., graphite-saturated liquid iron at 1 atm CO or Ni-NiO mixtures; the results obtained, though promising, were not of sufficient accuracy. Except for the work of Baker and West,6 all other investigators5,7,8 showed that ZrO2(CaO) electrolyte could be used for this purpose. The main part of the galvanic cell used by Fischer and ~ckermann' and by schwerdtfeger7 (the latter work was done in this laboratory), consisted of a ZrO2(CaO) tube, -1 cm ID, closed at one end, with a platinum contact wire fixed mechanically inside the closed end. The tube was flushed with a gas of known oxygen partial pressure, e.g., air, CO-CO2 or H2-CO2 mixtures; gas along with the platinum lead wire served as the reference electrode. The oxygen contents derived from measured electromotive forces agreed reasonably well with the oxygen contents determined by vacuum-fusion analysis. It is evident from recent investigations that the electromotive force technique using a solid oxide electrolyte is fundamentally well suited for the determination of oxygen in liquid steel. However, it is equally clear that the cell arrangement of the type as commonly used is in need of considerable improvement, as it exhibits several shortcomings for industrial and even laboratory use. 1) Because of its size, the zirconia tube, though stabilized, has a poor resistance to thermal shock. 2) Fine pores and microcracks, which are invariably present in zirconia tubes, are detrimental to the satisfactory operation of the cell, particularly when gas reference electrodes are used. 3) Air or carbon dioxide reference electrodes give rise to high electromotive force readings; as a result, the determination of oxygen in steel becomes less accurate. For higher accuracy, the oxygen partial pressure of the reference electrode should be in the range similar to that of oxygen in steel. 4) Even in laboratory experiments, difficulties are experienced when flushing the tube with gases and maintaining the proper gas flow rate. Fischer and Ackermann,' who used air as the reference electrode, reported that when the flow rate was too low, furnace gases would leak into the electrolyte tube, therefore lowering the oxygen potential and measured electromotive force. The required flow rate in order to avoid leakage depended on the tightness of the electrolyte tube which varied with different tubes, thus making it difficult to predict in advance the required flow rate. However, if the flow rate is too high the inside wall of the electrolyte tube would be cooler than the wall

Jan 1, 1970

By B. B. Rath, Hsun Hu

In wedge-shaped bicrystals of zone-refined aluminum it is observed that (111) pure tilt boundaries migrate under the driving force of their own inter-facial free energy. The boundary velocity is a power function of the driving force. The driving force exponent decreases with decreasing angle of misorien-tation. For example, at 64O°C, the exponent decreased from 4.0 for a 40 deg to 3.2 for a 16 deg tilt boundary. An evaluation of the driving force acting on the boundaries during their motion indicates that for low driv-forces, up to about 2 x l03 ergs per cu cm, the velocity is relatively independent of misorientation, whereas at higher driving forces a 40 deg tilt boundary exhibits the highest velocity. The measured activation energy for boundary migration approaches that for bulk self-diffusion at low driving forces, decreasing from 33 to 27 kcal per mole as the driving force is increased from 1 x l0 to 5 x l03 ergs per cu cm. These results are compared with current theories of grain-boundary migration. In previous experimental studies of grain boundary migration the driving force has been limited to a difference in stored energy across the boundary. This stored energy has been introduced into the crystal either by prior deformation1-3 or by grown-in lineage structure. A part of the energy stored in the deformed crystal is released by recovery either prior to or concurrently with grain boundary migration, thus introducing an uncertainty as to the magnitude of the driving force responsible for grain boundary migration. The grown-in lineage structure, though thermally stable during annealing, neither provides conditions under which different levels of energy may be stored in the imperfect crystal nor provides a control of orientation difference across the migrating boundary of a growing grain. Furthermore, because of variation in the lineage structure, it is difficult to determine accurately the energy stored in the imperfect crystal. Several investigations of grain boundary migration during normal grain growth have also suffered from difficulties in estimating the driving force because of uncertainties in the principal radii of curvature.~ In the present investigation the velocity of pure tilt boundaries in zone-refined aluminum bicrystals of selected orientation (40, 30, and 16 deg around the [Ill] tilt axis) has been measured in the absence of a dislocation density difference across the moving boundary, thus eliminating the previous experimental difficulties. The driving force for boundary migration is derived from a gradient of the total interfacial free energy of the migrating boundary in wedge-shaped bicrystals. A similar method was attempted by Bron and Machlin in a study of grain boundary migration in silver. However, they found that one of the crystals was deformed and consequently the motion of the boundary was partly due to a difference of stored energy across the boundary. The observed behavior of boundary velocities as affected by the driving force is examined in the light of the predictions of the current theories of grain boundary migration.7"10 The effect of boundary misorientation on velocity is compared with the theory of " which is based on a dislocation core model for high-angle boundaries. EXPERIMENTAL METHOD Seed-oriented bicrystals of zone-refined aluminum, 2.5 cm wide, 0.5 cm thick, and 12 cm long, containing tilt boundaries with a common (111) axis, were grown from the melt in the direction of this axis. Spectro-graphic analysis, reported earlier,'' indicated the purity of the crystals to be 99.999+pct. Three such bicrystals containing 16, 30, and 40 deg tilt boundaries were used. Wedge-shaped specimens were prepared from these bicrystals by spark cutting followed by electrolytic polishing. The angle of the wedge was usually 40 deg and the specimens were usually 0.25 cm thick. The intercrystalline boundary was located within 0.2 to 0.5 cm from the tip of the wedge. Fig. 1 shows a section of an oriented bicrystal containing an outline of a wedge-shaped specimen. The crystallographic directions shown in Fig. 1 represent the orientation of one of the crystals (the larger section of the bicrys-tal); the orientation of the other crystal differs only by rotation around the common [lil] axis. The parallel faces of the wedge always corresponded to the common (171) planes in both crystals, whereas the orientation of the side faces varied, depending on the misorientation angle. The bicrystal orientations were determined

Jan 1, 1970

By J. W. Spretnak, V. Kandarpa

Stress -induced ordering of carbon atoms is studied in a series of Fe-Mn-C alloys. A prominent peak is found in the vicinity of 280°C at frequencies of the order of 1.0 cps, with an associated activation energy of 37 kcal per mole. The height of the peak is linearly rekzted to the concentration of carbon in solution. The distortion of octahedral holes by manganese atoms appears to be predominant over carbon-carbon pair interactions. RELAXATION by stress-induced ordering of point defects is expected whenever the introduction of these point defects produces distortions which have a lower symmetry than that of the lattice. Under zero stress, the isolated point defects occupy the crystallographic-ally equivalent positions in the lattice, as these represent states of equal energy. However, if the defect sites are asymmetric, application of an uniaxial stress will split the energy states, and a redistribution of the defects among various states will take place. This is the case of the internal friction peak called the Snoek peak,1 resulting from isolated interstitials in bcc metals. The interstitial sites in this case have tetragonal symmetry. In the case of fcc and hcp lattices, such an effect is not expected from isolated point defects because of the symmetrical nature of the interstitial sites. However, internal friction peaks arising from interstitial diffusion have been reported both in hcp2,3 and fcc4-8 lattices. These peaks are often explained on the basis of stress-induced ordering of interstitial solutes, caused by the deviation of interstitial sites from their cubic symmetry through the presence of nearby defects. In the case of fcc lattices, evidence for interactions of both the substitutional-interstitial4,6,13 and interstitial-interstitial types5'798'14 have been presented by various investigators. The purpose of the present investigation was to study the internal friction peak attributed to the diffusion of interstitial carbon atoms in high purity austenitic manganese steels and to account for the peak in the light of the existing models. MATERIALS The Fe-Mn-C alloys used in the present investigation were made in two different ways, designated as Type I and Type 11. Type I alloys were made from high purity Fe-Mn alloys obtained in the form of 0.04- in.-diam wires from Materials Research Corporation, Orangeburg, N.Y. These alloys were carburized to different levels using gas mixtures of H2 and CH4 at 1000°C. Type I1 alloys were made in this laboratory starting with zone refined iron, spectrographically pure manganese, and spectrographically pure carbon. They were melted in an argon arc melting furnace and drawn into 0.04-in.-diam wires. All the wires were annealed at about 900°C for 3 hr prior to the internal friction experiments. After the measurements of internal friction, the phases in the samples were identified by X-ray diffraction and the carbon determined by the combustion method. EXPERIMENTAL PROCEDURE In the present work, a classical Ke-type pendulum was used. The details of the equipment were described previously by D. T. Peters.9 Dry helium at 40 torr was used in all the experiments. The internal friction, measured as the logarithmic decrement of the torsion amplitude of vibration was determined as a function of temperature, from ambient to about 500°C. The background internal friction was assumed to have the form of the exponential of the inverse temperature and was subtracted from the raw data. The height of the peak was measured at the position of the maximum in the plot of the internal friction versus temperature. The activation energies of the peaks were measured by the peak shift method. The internal friction values for an alloy were obtained as a function of temperature at different frequencies of vibration. The position of the peak changes with frequency, the higher the frequency the higher the peak temperature. The activation energy of the process associated with the peak is obtained using the formula

Jan 1, 1970

By J. C. M. Li

The steady state shape of a shrinking cylindrical grain boundary of miform boundary energy is shown to be circular. This is based on the principle of either the minimum rate of entropy production or the minimum thermokinetic potential. The circular shape corresponds also to a state of minimum (not maximum) velocity. The steady state shape of a grain boundary moving between two inclined surfaces is a circular cylindrical arc whose position and curvature will be afjected by the nature of the surfaces. The minimum thermokinetic potential is the only valid criterion in this case. THE preceding paper1 reports an interesting experiment in which it is shown that a grain boundary moving between two inclined surfaces assumes a circular cylindrical arc whose axis nearly coincides with the line of intersection of the two surfaces. The driving force is well defined since it is the energy of the grain boundary itself. The velocity of the grain boundary is found not to vary linearly with the driving force. Several interesting questions arise: 1) What principle determines the shape of a moving grain boundary? 2) What is the effect of the inclined surfaces? 3) How do we understand the nonlinear velocity-driving force relationship? It is attempted in this paper to discuss the first two questions based on irreversible thermodynamics and in a following paper to discuss the third question based on dislocation theory. STEADY STATE SHAPE OF A SHRINKING LOOP (A CYLINDRICAL GRAIN BOUNDARY) In irreversible thermodynamics, there are two criteria for the steady state. One is the minimum rate of entropy production2 which is based on the symmetry of phenomenological coefficients and is applicable to linear force-flux relations with constant coefficients. The other is the minimum thermokinetic potential3 which is based on the integrability of a certain Pfaffian differential equation and is applicable to nonlinear systems with variable coefficients. In the case of a shrinking grain boundary loop (a two dimensional version of a cylindrical grain), the flux of atoms across the grain boundary can be taken as the local boundary velocity v measured perpendicular to the boundary (the number of atoms transferred per unit area per second is equal to the product of atom density and the velocity of the boundary). The local thermodynamic driving force can be taken as y/p with y being the grain boundary energy (invariant with respect to the orientation and curvature of the grain boundary) and p being the radius of curvature. Such driving force can be understood by considering the loop as an elastic string with tension y. As shown in Fig. 1, across a length ds along the loop, the direction of y changes by an angle d@ which is ds/p. Because of this change of direction, the tension exerts a force perpendicular to the curve equal to yd@. The force per unit length is then y/p. According to the experimental observation, the velocity v is a power function of y/p, where M is the velocity at unit driving force and 'n is a constant. The rate of entropy production per ds along the loop is vyds/pT, where T is the temperature. For a given length L of the loop, the total rate of entropy production is The thermokinetic ptentia13 has only a differential definition and its existence depends on the integrability of this definition. In this case, Eq. [3] happens to be a total differential and the thermokinetic potential can be defined as which turns out to be the same as the rate of entropy production, Eq. [2], except for a constant factor n + 1. Strictly speaking, since the flux-force relation is not linear, the rate of entropy production may not be a minimum at the steady state. However, because of the proportionality between Eqs. [2] and 141, the state of minimum thermokinetic potential happens to be the same as that of minimum rate of entropy production. The steady state shape thus can be obtained by minimizing either integral [2] or [4] for a given L.

Jan 1, 1970

By R. E. Zinkham

An investigation has been conducted to compare short transverse and longitudinal fatigue and fracture properties in 4.25-in.-thick, high strength aluminum alloy plates. One plate was produced using standard rolling techniques while the other was pre.forged before rolling. Little difference was shown in fatigue strength of longitudinal specimens taken from mid-thickness of the plate. Howeuer, in the short transverse orientation fatigue strengths at 107 cycles were about 25 and 50 pct less, respectively, for the preforged and standard rolled plate. Differences in fatigue strengths were attributed to grain size and shape as well US orientation of constituents. Fatigue crack propagation rates and fracture toughness were compared at three different stress intensity (K) levels, using a constant compliance, double cantilever, wedge-shaped specimen. In a given plate, comparable fatigue crack Propagation rates were observed in the longitudinal (i9W) and short transverse (TW) orientations. Somezuhat gveater rates were observed in the short transzerse (TR) orientation. The preforged plute gave a lower rate for all three directions. Considerable secondary cracking developed, at times, over portions of the fatigue crack in both plates, particularly at the lower stress intensity levels in the short transverse specimens. Micro structure revealed constituent stringers as possible causes of the crack branching. Fracture toughness was considerably less in both plates in the short transuerse orientation. It is concluded that preforging not only improved directional tensile properties but also the fatigue and fracture properties in general. On occasion, aluminum plates have been milled away for hinges or bolted connections and stressed through the thickness or short transverse direction. Little or no information is available concerning fatigue characteristics or fracture toughness in this loading orientation in aluminum plate, or of the effect of fabrication on these properties. It was the intent of this project to examine, develop, and apply a unique specimen that has been advocated by others to study the fatigue characteristics and fracture toughness of two differently fabricated high strength aluminum plates. Linear elastic fracture mechanics criteria may be applied to the specimen so that the fatigue crack propagation rate and fracture toughness data may be of use for design or inspection applications. Fatigue characteristics are generally measured in the longtudinal or long transverse direction, where fairly large specimens such as center notched panels,' are usually employed. Limitations are evident due to plate thickness, however, in the type and size of specimen that may be tested in the short transverse direction without extensions. Therefore, a specimen that is to be loaded in this direction should, for convenience, be compact. The general type of fatigue crack propagation specimens discussed and employed herein meet this requirement. These specimens are commonly called double cantilever beam specimens and lately "crackline-loaded edge-crack specimens".2 They may vary from a slope of zero (parallel-sides) to a wedge shape, the type employed herein. In general for most specimens the stress intensity KI at the tip of a crack is a function of the load, P and crack length, a. Some varieties of the wedge shaped specimen, however, give essentially a constant stress intensity KI over a considerable range of crack length.' This feature can be a valuable asset in fatigue crack propagation experiments because the stress-intensity can be controlled simply by controlling the load without regard to crack length. MATERIAL AND METHODS Material. A standard rolled (light pass reduction) and a ~reforged and rolled (heavy pass reduction) plate of 7179-T651 material were used for the evaluation. The chemistry, processing history and average tensile properties are shown in Table I. Specimen Selection and Preparation. The specimen selected for the generation of fatigue initiation or S-N data was an axial tension type and is shown in Fig. 1. Specimens were taken from mid-thickness in the longitudinal and short transverse directions from both plates. Specimens were polished with 500 grit paper in a direction parallel to the loading axis. For the fatigue crack propagation tests, the specimen shown in Fig. 2 was used. This is similar to a specimen that has been employed by Mostovoy3 for fracture toughness studies on 7075-T6 aluminum alloy. It also fortuitiously agrees quite well with the dimensions of a specimen for which Srawley and Gross2

Jan 1, 1970

By W. O. Philbrook, K. Natesan

A mathematical model was derived for the temperature change in a particle undergoing heterogeneous chemical reaction and heal exchange with a stream of fluid. The model has been applied specifically to the exothermic oxidation of spherical particles of zinc sulfide. Very good agreement was obtained between the theoretical prediclion and experimental observation. It was found that at no stage of the reaction was the particle subjected to a state of thermal instability. In studies of gas-solid reactions, it is generally assumed that the gaseous and the solid phases are at the same temperature throughout the reaction period. This is not strictly true since most of the reactions are either exothermic or endothermic in nature. This paper deals only with heterogeneous gas-solid reactions of noncatalytic type. In the case of exothermic reactions (e.g., roasting of sulfides), there may result an increase in temperature of the particle due to the release of the heat of reaction, and this increase in temperature may enhance the reaction rate and thus cause further release of heat. Such a "spiralling" effect may lead to a thermally unstable situation within the particle. On the other hand, in the case of endothermic reactions (e.g., calcination of limestone), there may occur a decrease in temperature of the particle as the reaction proceeds, leading to a virtual "quenching" of the reaction front. A general discussion of autothermic processes with emphasis on properties and reactor design is given by Van Heerden. 1 Levesque and cubicciotti 2 observed self heating of the sample in the oxidation of thorium. Anous et al. 3 observed self cooling of the sample in their dehydration studies on chrome alum. Cannon and Denbigh, 4 and Ong et al.5 reported self heating of the sample in their studies of the kinetics of oxidation of zinc sulfide. A typical plot of heat generation and heat loss rates with reaction temperature is shown in Fig. 1.'14 The Sigmoid curve represents the heat generation rate while the straight lines represent the heat loss rate. The main objectives of this analysis are to estimate the temperature increase of a single particle undergoing an exothermic reaction and to study the possibility of a thermally unstable situation within the particle. Also, a study of the dependence of the tempera- ture increase on different process variables has been attempted. A "she ll-by-shell" method has been proposed to analyze the problem. The shells may be made as small as necessary, and equations may be set up for heat transfer by various mechanisms. Such equations will have to be solved for each shell, with the boundary conditions for ith shell being obtained from the (i - 1)th shell, using a high speed digital computer. The oxidation of spherical particles of zinc sulfide is considered for this analysis, but the treatment is general enough to be applicable to other reactions and particle shapes. The oxidation reaction can be written as AH =« -115 kcal/mole ZnS [1] Such a reaction has been found to proceed in a topo-chemical manner; i.e., as the reaction proceeds, a progressively thicker outer shell of zinc oxide is formed, while the inner core of unreacted sulfide decreases. It has been found experimentally, both in the present work and in the previous investigations,4-6 that the particle retains its original dimensions. Therefore, at any given time, the particle may be

Jan 1, 1970

By H. Doi, Y. Fujiwara, K. Miyake

In order to throw light on the mechanism of plastic deformation of WC-Co alloys, compressive tests of WC-(7 to 43) vol pct Co alloys have been carried out at room temperature, and stress-micro strain relation has been investigated in detail. The analysis of the factors affecting the yield stresses reveals that the yield stresses can be predicted by modified Oro-wan's theory if one properly estimates the planar in-terfiarticle spacings. Conzpressive straining of some of the alloys by 0.066 to 0.17pct increases the decrements by a factor of as much as 3.4 to 14, whereas the corresponding increase in the electrical resistivities is less than 10 pct. The analysis of the decrement data in terms of -Gramto and Lücke theory shows that the marked increase is attributed to increased dislocation darnping itt the binder (cobalt) phase. By cornbilling the decrement data and the conzjwession duta, one obtains the relation between flow stress in shear (?t) and increase in dislocation density (p): At = const . v6 . This is interHeted to mean that the mechanism of strain hardening of CirC-Co alloys is essentially sarne as the one for dispersion strengthened alloys. The possible effect of bridge formations between the carbide particles has also been examined. OWING to the combination of hardness, strength, and other physical and chemical properties, WC-Co alloys have opened the way for unique fields of applications, the recent ones being, for instance, anvils for super-high-pressure generation apparatuses. In such applications, the alloys are frequently subjected to very high compressive stresses: these stresses may cause the alloys to deform plastically and eventually to fail. However, much remains obscure regarding the nature of the plasticity of the alloys. Evidently, the alloys owe their high strength to the hard carbide particles which frequently occupy as much as 80 to 90 pct in volume fraction, whereas the ductility required for practical applications is provided by the small amount of the binder phase between the carbide particles. When the volume fraction of the carbide phase is not very large, deformation behavior of the alloys may be described by some of the current dispersion strengthening theories. However, greatly increasing the carbide phase is thought to lead to some carbide skeleton structure or bridge formations owing to the increased chances for direct contacts between the carbide particles;1,2 this may appreciably affect the plasticity of the alloys. Regarding the effect of formation of the carbide skeleton structure, it is interesting to note the work by Ivensen et al.3 on compression tests of the alloys containing somewhat large carbide particles; they observe extensive generation of slip bands in the carbide particles after application of some preliminary compressive stresses. They interpret the results in terms of plastic deformatiot: of the carbide particles which are supposed to have formed a skeleton structure; the binder phase plays only a passive role, at least in the early stages of the deformation. That carbide crystals exhibit microplasticity at room temperature is apparent from the work of Takahashi and Freise4 and French and Thomas5 on indentation of WC single crystals. On the other hand, Dawihl and coworkers6-10 maintain that even when volume fraction of the carbide phase is very large (for instance, more than 90 pet), a very thin binder layer generally exists between the carbide particles. They interpret the results of the extensive mechanical tests in terms of the plasticity of such a layer. Gurland and Bardzil11 point out that decrease in ductility of the alloys with increase in the carbide phase is caused by the effect of plastic constraint exerted by the dispersed carbide particles. Drucker12 further develops this concept from a continuum-mechanics approach on an assumption that a continuous thin binder layer separates the carbide particles. A common feature of the studies reported so far on the plasticity of the alloys is that the information deduced is invariably qualitative in nature. Thus, very few systematic experiments for obtaining reliable and sufficiently detailed stress-strain curves of the alloys varying widely in the microstructural features have been carried out. In particular, it may be of special interest to investigate in detail the early stages of the plastic deformation of the alloys in order to shed light on the strengthening mechanism. However, such work appears to be extremely rare. Doi et al.13 recently reported a first brief account of the results of some quantitative analysis of the plasticity of the alloys in terms of dislocation theory. Their experiment was rather limited in the composition range covered (volume fraction occupied by the carbide phase: 79 to 83 pct), and thus they could not necessarily elucidate the controlling mechanism of plastic deformation of the alloys of a more general composition range. Consequently, in the present investigation, deformation behavior and some other physical properties of the alloys were investigated and discussed in more detail over a much wider composition range. SPECIMEN PREPARATION WC-Co alloys used in this experiment were prepared in cylindrical or rectangular form by sintering in vacuo compressed mixtures of tungsten carbide and cobalt

Jan 1, 1970

By M. J. Marcinkowski, K. S. Raghavan, A. S. Sastri

A detailed transmission electron microscopy investigation was carried out in connection with a manganese Hadfield Steel. At small plastic strains, numerous individual intrinsic stacking faults are observed. With increased plastic deformation, the stacking faults thicken into twin lamellae which in turn subdivide the original austenite matrix into smaller domains. The twin boundaries act as strong barriers to subsequent dislocation motion and is in a sense equivalent to grain refinement. It is this "grain refinement" which is believed to be the cause of the very high work hardening rates in the Hadfield Steels. In many cases, especially where an hcp phase is the stable one at low temperatures, the stacking fault energy in fcc metals and alloys decreases with decreasing temperature.' Since stacking faults of the intrinsic type are precursors of both twins as well as the hexagonal close packed structure, both of these entities should become more frequent as the temperature of a fcc crystal is lowered. In the case of the twin, there is no chemical driving force for its formation and it is generally necessary to provide the required driving force by an applied stress, i.e., strain energy. In the case of the hcp structure the transformation from the fcc modification can occur spontaneously (marten-sitically) since a decrease in chemical energy does in fact occur; however, an applied stress will provide an even greater driving force toward complete transformation. Since the transformation products mentioned above occur in an inhomogeneous manner throughout the crystal and since these can act as potential barriers to further plastic deformation2 marked strengthening effects can be anticipated. Also because metal and alloy strenghening is in general proportional to the shear modulus, these effects should be greatest in steels of the austenitic type (y), i.e., the fcc types. Perhaps the two most important steels in this category are the austenitic stainless steels and the Hadfield manganese steels. Both may be quenched from elevated temperatures so as to retain the austenitic states characteristic of those temperatures. The effect of subsequent deformation at lower tem- peratures has a profound effect on the stress-strain curves of these alloys. In particular Fig. 1 shows the compressive stress-strain curves obtained with an 18-8 stainless steel which was quenched from 1850°C after annealing for 1 hr so as to produce all y. As the temperature is lowered, the work hardening rate increases markedly. Although some hcp or c mar-tensite can be generated by plastic deformation as the temperature is lowered,~ it is believed to be a transition phase4 and most of the martensite produced is of the bcc or a variety.3 It is this stress induced martensite which gives rise to the very low initial work hardening at 77°K as can be seen in the stress-strain curve in Fig. 1. Similar low initial work hardening rates have been observed in the stress induced Ni-Ti martensites.5 Fig. 2 shows that an even more rapid rate of work hardening occurs in the Hadfield steels treated in the same way as that described for the 18-8 stainless steels a; the temperature is lowered. It is this ability to work harden to such high stress levels that makes the Hadfield steels particularly suitable for armor plate and heavy construction equipment. However, unlike the case of Fig. 1, no initial low rate of work hardening is observed in any of the curves in Fig. 2. Thus the stress induced formation of any low energy martensite phase in any significant quantity must be ruled out. This observation is in accord with the X-ray findings of Otte.~ On the other hand, small quantities of the E phase have been observed by other investigators using transmission electron microscopy (TEM) above Even more significant was the fact that large numbers of deformation twins were observed in the deformed Hadfield steels,678 which were postulated to be one of the reasons for the high work hardening ability of this class of steels.8 It is the purpose in what follows to discuss a series of experimental observations pertaining to the stress induced transformation in a Hadfield steel and to formulate a dislocation mechanism which adequately accounts for the observed results. EXPERIMENTAL PROCEDURE The stainless steel used to obtain the curves shown in Fig. 1 was of the AISI Type 303 containing approximately 18.0 pct Cr and 8 pct Ni. On the other hand, the Hadfield manganese steel used to obtain the curves shown in Fig. 2 contained between 1.00 to 1.25 pct and 11.5 to 13.5 pct Mn. In all cases the samples were in the form of compression cylinders 0.220 in. in diam and 0.370 in. long. Prior to testing the samples were annealed for a hr at 1050°C and rapidly quenched into a brine solution. This treatment was sufficient to preserve the y phase for subsequent testing at lower temperatures. All samples were compressed in an Instron testing machine using a cross head speed of 0.02 in.

Jan 1, 1970

By H. H. Podgurski, H. E. Knechtel

Annealed Fe-Al alloys do not react readily to form AlN when held at 500ºC in NH3-H2 gas mixtures, but do so upon the introduction of dislocatims. Nuclea-tion of the nitride phase occurs on dislocation sites. In turn, the growth of the aluminum nitride particles causes the ferrite phase to yield plastically, generating more dislocations for the nucleation process. The nitride phase extracted from an Fe-2 pct A1 alloy nitrogenated at 500°C was identified as stoichio-metric aluminum nitride with a hexagonal crystal lattice. THIS investigation reveals the role that dislocations play in initiating and sustaining the nitriding reaction in Fe-A1 alloys. As early as 1931 the work of Meyer and Hobrock1 suggested that the initiation of the nitriding reaction could involve a nucleation controlled process. Recently Bohnenka2 depicted the gas-phase nitriding process below 600°C as one of mixed control limited by nitrogen penetration through the surface, by nitrogen diffusion, by aluminum diffusion, and by nucleation of the nitride phase, Fig. l(a). In our research in a comparable alloy (0.57 pct Al) at 575ºC, we have observed a nitrogenation which we feel is better described by Fig. l(b). In the case of a 2 pct-A1 alloy partially nitrided at 500°C we propose the profiles shown in Fig. l(c). For a complete and accurate description of the process, a concentration profile of the dislocation density in the test specimen would be needed. EXPERIMENTAL Nitrogenization was conducted between 500" and 575°C in a variety of NH3-H2 gas mixtures on three Fe-A1 alloys: 1) zone-refined iron + 0.16 i 0.2 pct Al—levita-tion melt, 2) zone-refined iron + 0.57 0.02 pct Al— levitation melt, 3) plastiron + 2 pct Al—melted by induction heating. To demonstrate the effect of dislocations on reactivity, both cold-worked and annealed samples were investigated. All nitrogenation rate studies were conducted gravimetrically with a gold-plated invar balance4 contained in a gas-flow system. To avoid contamination of the specimens in the reaction zone of the system, the reaction chamber was constructed of high-purity dense alumina. The activity of nitrogen was fixed by specific NH3-H2 gas mixtures whose compositions were continually monitored by calibrated thermal conductivity gages and checked by chemical analysis. Variations of ± 0.1 pct NH3 could easily be detected by both methods. Throughout this paper the activity of nitrogen is defined as PN3 /PH23/2 , where PNH3, and Ph2 are partial pressures in atmospheres. Electron transmission, density measurements, and chemical analyses were made on specimens before and after nitrogenating in order to reveal structural and chemical changes. Similar studies as well as X-ray diffraction studies were conducted on nitride extractions from the nitrogenated 2 pct-A1 alloy. These extractions were obtained by the use of an anhydrous bromine-methyl acetate solution which dissolves the iron and leaves the insoluble nitrides as a residue. Hardness profiles were obtained on cross-sections of partially nitrided specimens to demonstrate the extent of nitriding through the thickness of the specimens. RESULTS AND DISCUSSION The nitrogen activity in the NH3-H2, atmospheres was never allowed to reach a level capable of producing iron nitride (Fe4N). Hence, the term nitriding as used in this paper refers only to the formation of aluminum nitride whereas nitrogenation refers to the total uptake of nitrogen regardless of how it is distributed throughout the alloy. The weight increases observed during the initial stage of a nitrogenating treatment are due primarily to the solution of nitrogen in the ferrite phase, particularly when starting with annealed specimens. Because this initial nitrogenation rate in the case of the 0.57 pct A1 alloy, see Figs. 2 and 3(a), was most rapid the weight change that occurred thereafter might be attributed to the nitriding reaction with the exception of a small weight increment due to the irreversible pickup of oxygen by aluminum. The oxygen (<70 ppm) came from traces of H2O and 0, in the hydrogen and ammonia gases. On the basis of discrepancies between total weight increase and the increase in the nitrogen content of the sample as determined by chemical analysis, it was estimated and later established by activation analysis, that as much as 200 ppm of oxygen were taken up by a fully nitrided Fe-0.57 pct A1 specimen at 575°C. Most of the oxygen could have been picked up from the nitriding atmosphere on the surface of the samples during cooling to room temperature. Even 50 ppm of water in the gas phase will become oxidizing to iron before the sample has cooled to room temperature. The lack of reactivity* of these alloys in the annealed

Jan 1, 1970

By R. G. Davies, P. Beardmore, T. L. Johnston

The flow stress of a series of Ni-Cr-A1 alloys consisting of a dispersion of y&apos; (based on Ni3Al) in a rnatrix of nickel-base solid solution y has been measured at temperatures up to 950°C as a fwzction of the volume fraction of y&apos;. At high temperatures the flow stress is controlled by the amount of Y&apos; in the alloy, i.e., the higher the volume fraction of y&apos;, the greater is the flow stress. This simple relationship is not obeyed at low temperatures in so far as a peak in the flow stress-volume fraction relation occurs at about 25 pct y&apos;. The variation in the mechanical properlies of these alloys as a function of both temperature and volume fraction of y&apos; has been correlated with changes in distribution of both the dislocations and y&apos;. The results are interpreted on the basis that at low temperatures the y matrix is strengthened significantly bv the presence of a hyperfine y&apos; precipitate due to decomposition on cooling; at high temperatures the y matrix is a single phase of low strength. It is clearly recognized that the high temperature strength of most nickel-base superalloys depends upon a dispersion of the ordered fcc phase y&apos;, based on Ni3A1, in a fcc solid solution matrix y based on nickel. Although the volume fraction of y&apos; varies widely from about 0.2 in Nimonic 80A to about 0.6 in Mar-M200, all such nickel-base alloys manifest an unusual insensi-tivity of the flow stress with respect to temperature. In Mar-M200 for example, the 0.2 pct flow stress remains essentially constant from room temperature to 750°C. The conclusion has been drawn1 that the characteristically low temperature dependence of the flow stress of y-y&apos; nickel-base alloys is obtained when the state of dispersion of y&apos; is such that dislocations are forced to cut through the y&apos; particles at the onset of yielding. When the spacing between the y&apos; particles is so large that the flow stress is controlled by dislocation bowing between particles, then the initial flow stress decreases progressively with an increase in temperature at a rate determined by changes in elastic properties. The same conclusion is inherent in the detailed, mechanistic model of the deformation process in commercial superalloys which has been developed by Copley and ear&apos; in which the temperature independent flow stress is attributed primarily to the contribution of the antiphase boundary energy created in the y&apos; particles during deformation. In this theory the temperature insensitivity of the flow stress is a reflection of the constant antiphase boundary energy as a function of temperature. An important microstructural parameter that is relevant to the explanations that have been suggested&apos; to account for the temperature insensitivity of the flow stress is the volume fraction of y&apos;. To vary the latter to any significant extent in a given commercial alloy is clearly difficult. However, it is possible in a relatively simple Ni-Al-Cr ternary system which manifests analogous microstructures in terms of the distribution of y&apos; in y and contains specific alloys which have flow properties that depend on temperature in a manner quite similar to their more complex commercial counterparts. Hornbogen et . have studied precipitation phenomena and deformation mechanisms in such alloys but only where the y&apos; volume fraction was small (less than 0.2) and the y&apos; particle size varied from less than 100A up to a maximum of -1000A. In the present study, a series of alloys was prepared in which the volume percent of y&apos; at 900°C was varied from 0 to 100 pct with the y&apos; particle size (of the order 0.5 p) comparable to the sizes obtained in commercial superalloys. Particular attention has been given to the relationship between variations in the volume fraction and distribution of y&apos; and the temperature dependence of the flow stress EXPERIMENTAL TECHNIQUES The Ni-Cr-Al system was selected because it is well characterized, bears a close relationship to commercial alloys, and offers the advantage of an extra degree of freedom over a binary system. In the present investigation, a series of alloys across the tie line between NisA1 and Ni3Cr (Ni3Cr is not an in-termetallic compound, the nomenclature is only used to designate the composition) were vacuum cast. The pseudobinary6 and the composition of the alloys used are shown in Fig. 1. It is important to note that the compositions of the y phase and the y&apos; phase in the two-phase alloys was always the same. Alloy compositions were selected from the binary diagram, Fig. 1, in order that aging at 900°C would produce from 0 (100 pct y) to 100 pct y&apos; by volume percent. (The size of the y&apos; particles produced during the equilibrium aging treatment increased as the volume fraction of y&apos; increased, ranging from about 0.2 p at low volume fractions up to about 0.8 p at the highest volume fraction.) The y&apos; phase is based on the inter-metallic compound Ni,A1 which has the fcc LIZ type superlattice structure, and chromium substitutes for aluminum in the structure. The y phase is a disordered fcc solid solution. The alloys were heat treated at 1150°C for 2 hr, air cooled to room temperature, and finally annealed for 16 hr at 900°C. The rods were then centerless ground to 0.25 in. diam and cut into compression samples 0.5 in. long. The compression tests were made on an In-stron machine at a strain rate of 7 x 10"4 sec-&apos;. A rapid heating radiant heat furnace was used which minimized the heating and temperature stabilization time to 10 min for the highest testing temperature. All the tests were stopped after 5 pct plastic strain.

Jan 1, 1970

By N. S. Stoloff, J. N. Mushovic

Age hardening response of a Mg-Th-Zr alloy has been studied at temperatures in the range 60° to 450°C. Transmission microscopy revealed clustering of thorium atoms at low aging temperatures, supporting a previous report of GP zone formation. Peak strengthening, which is observed at 325°C, is due to the formation of a coherent, ordered, DO19 type superlattice structure, of Hobable composition Mg3Th, as plates parallel to the matrix prism planes. These plates later reveal a Laves phase structure of composition Mg2Th. The equilibrium Mg4Th phase begins to precipitate in two different forms at an early stage, competitively with the Mg2Th plates. RECENT work on the Mg-Th system indicated that, unlike most magnesium-base alloys, complex precipitation phenomena may be occurring. The partial phase diagram of the Mg-Th system indicates that an equilibrium phase, Mg5Th, is the sole intermediate phase.&apos; sturkey,&apos; however, has reported, using X-ray and electron diffraction techniques, that a metastable fcc Laves phase, Mg2Th, precedes the formation of the equilibrium compound, which he identified as closer in composition to Mg4Th. Murakami et al.3 reported that the equilibrium phase precipitates preferentially on grain boundaries and dislocations in a Mg-1.7 wt pct Th alloy; Kent and Kelly4 aged a more dilute alloy, Mg-0.5 wt pct Th, for 4 days at 220°C and found similar results. In addition, they reported that a platelike phase with a structure close to that of the magnesium matrix forms perpendicular to the basal plane and is probably ordered. Research on a Mg-4 wt pct Th alloy by electrical resistance measurements and transmission electron microscopy has suggested that GP zones may form at low aging temperatures.3 However, the electron micrographs purporting to show this phenomenon were not conclusive. In view of the fragmentary evidence concerning the nature of the precipitation processes in the various Mg-Th alloys, an aging study was undertaken to clarify the characteristics of the various precipitates which form and to correlate the mechanical properties of the system with the direct precipitate-dislocation interactions. The latter results are presented elsewhere.&apos; The purpose of this paper is, therefore, to discuss the precipitation sequence in this system. EXPERIMENTAL PROCEDURE Sheet stock (0.060 and 0.010 in. thick) of a commercial Mg-3.93 wt pct Th-0.42 wt pct Zr alloy (designated HK3lA) similar to that studied by sturkey2 was supplied through the courtesy of Dr. S. L. Couling of Dow Metal Products Co. Zirconium does not enter into any precipitation reactions,&apos; but is present primarily as a grain refiner. The alloy was chill cast, warm rolled to 0.090 in. thick stock, and then finally reduced by a combination of hot and cold rolling. The alloy chemistry is given in Table I. This material was solution treated at 580°C for 4 hr in a dry CO2 atmosphere, and then water quenched. Material in this condition was fairly clear of precipitate particles and was fully recrystallized. Aging at temperatures less than 200°C was accomplished by immersing the alloy in a silicone oil bath; for higher temperatures, aging was done in a salt pot. Age hardening treatments were conducted at 60°, 80°, 105°, 135°, 160°, 250°, 325°, 350°, and 450°C for times ranging from 5 min to 400 hr. Hardness tests were performed on chemically polished 0.060-in.-thick blanks of solution treated material which were aged at the various temperatures for increasing lengths of time. For aging temperatures above 150°C the Rockwell Superficial 30T scale was employed, while samples hardened at temperatures below 150°C were monitored with the 45T scale. Each data point consists of at least three separate readings. Yield stresses also were measured at room temperature on both 0.060 and 0.010 in. sheet specimens aged at 325°C. The aged foils were thinned by the window method in a solution of 80 pct absolute alcohol and 20 pct concentrated perchloric acid (70 pct) maintained at 0°C. A stainless steel cathode was used and the applied voltage was 10 to 15 v. Thinned samples were rinsed in distilled water and pure methanol. After the me-thanol rinse the thin foils were quickly dried between filter paper. Foils prepared by the above method were examined in a Hitachi HU11B electron microscope operating at 100 kv. RESULTS A) Hardness. The hardness data are depicted in Figs. 1 and 2. Peak strengthening occurs at 325°C after aging about 6 min, see Fig. 1. Significant strengthening is achieved also at 350°C, but aging at 450°C produces only softening. The stepped curve at 250°C indicates that a complicated precipitation process may be occurring at that temperature. Fig. 2 suggests that at least two hardening mechanisms exist since the lowest temperature hardness peaks are displaced to the left of the peaks obtained at 135° and 105°C. A great deal of scatter is observed at long times in all cases due to magnesium surface degradation caused by the silicone oil bath. B) Identification of the Strengthening Precipitates. The structure formed atlowagingtemperatures (c10O°C) was not clearly resolvable by transmission microscopy. The only bright-field evidence for a change in structure was a mottled appearance which could be observed at extinction contours, as shown in Fig. 3(a), and the disappearance of this effect when dislocations produced under the influence of the electron beam passed through the matrix, as noted in

Jan 1, 1970

By E. Miller, N. Chou, K. Komarek

The solid solubilities of the compounds PbS, PbSe, and PbTe have been determined by equilibrating single crystals with two phase alloys. The solubilities were determined by measuring the Hall coefficient of the equilibrated samples. The observed maximum deviations from stoichiometry on the lead rich and the chalcogen-rich side of the phase fields were: at. pct excess Pb at pct excess S at 850°C; PbSe--4 x 10&apos;" at. pct excess Pb at at. pct excess at 800°C; and PbTe-2.8 x 10 4 at. pct excess Pb at 780°C, 10"1 at. pct excess Te at 720°C. The previously developed theory of retrograde solubility has been expanded to include intrinsic disorder in the compounds, and the experimental results are in agreement with the theory. THE solid solubility limits of intermetallic semiconducting compounds are of considerable interest, since many of these compounds have potential use as thermoelements in thermoelectric devices, as infrared detectors, or in semiconductor devices. The solidus curves of a significant number of these compounds have been reported to be retrograde with the maximum solid solubility occurring between the eu-tectic and the maximum melting temperatures. In a previous paper,&apos; equations were derived which permit calculation of the maximum solid solubility of an AB compound exhibiting retrograde solubility. Derivation of these equations was based on the assumption that the compound is a nondegenerate semiconductor at the temperature under consideration, that the defects were unassociated, and that the vibrational contribution to the entropy of the compound could be evaluated by the Einstein approximation. It was shown that at the temperature of the maximum solid solubility The entropy term ASS is composed of the entropy of formation of the solid stoichiometric compound (AS$)*, and the entropy due to deviations from stoichiometric composition which is the sum of a con-figurational term (aS*), a vibrational term (AS,), and an electronic term (AS,). In the previous paper the positional entropy was evaluated considering the con- N. CHOU, Member AIME, formerly Graduate Student, New York University, N. Y., is with IBM, Yorktown Heights, N. Y. K. L. KOMAREK, Member AIME, formerly with New York University, is Professor, Department of Inorganic Chemistry, University of Vienna, Vienna, Austria. E. MI LLER, Member AIME, formerly with New York University, is Associate Professor of Mechanical Engineering, California State College at Long Beach, Calif. The paper is based on a thesis submitted by N. CHOU to the Graduate Division, School of Engineering and Science, New York University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Materials Science. tributions from defects arising from deviations from stoichiometric composition. The derivation is generalized in the appendix to include intrinsic disorder. The electronic entropy term is also recalculated in the appendix. Of the various semiconducting compounds, the solidus curves of Pbs,&apos; and ~b~e,~ have been most extensively studied. The solidus of PbSe has also been determined, but the temperature of maximum solubility has not been accurately established.5129 The present investigation was undertaken to compare the experimental solid solubility data for these systems with the values predicted theoretically. Since the temperature and composition of the maximum solubility of PbSe has not been accurately determined, experimental emphasis was placed on determining the solidus curves for PbSe in the region of maximum solubility, although experiments were also performed on PbS and PbTe at several temperatures. X-ray diffraction studies were also made on carefully prepared powder samples of PbSe to determine the variation of lattice parameter with composition. EXPERIMENTAL PROCEDURE The procedure of Brebrick and Allgaier was employed for determining the solidus data. Monocrystal-

Jan 1, 1970

By K. P. Gupta, P. C. Panigrahy

The stabilization of the R, a-Mn, and 0-Mn phases have been studied in the Mn-Ti-Fe and Mn-Ti-Co systems. Iron and cobalt both appear to stabilize the (Mn-Ti) R phase to almost the sarne extent. The R-phase region was found to extend from the lowest e/a to slightly beyond the maximunz e/a limit known for this phase. But, while iron appears to stabilize the a-Mn phase, cobalt tends to stabilize the p-Mn phase. In the two systems manganese appears to get replaced by iron and cobalt in each of the mentioned phases. The instability of the a-Mn phase in the Mn-Ti-Co system and the /3 -Mn phase in the Mn-Ti-Fe system cannot be explained on the basis of adverse size effects because atomic diameters for both iron and cobalt (C.N. 12 at. diam) are ziery similnr and not much different from manganese which they replace. Qualitatively, the reason for the stability of the a-Mn and the p-Mn phases can be traced to the more favorable e/a ratio prevailing in the respective systems and to a competing tendency between the two phases. In transition metal alloy systems the o, p,P, R, a- Mn,&apos; and p-Mn2 phases have been claimed as electron compounds. A large volume of work has been done to establish the criterion for the formation of the o phase but until very recently practically no systematic work was done on the a-Mn and the /3-Mn phases. A recent investigation on the P-Mn phase3 indicates the e/a criterion for p-Mn phase stabilization. Since the R phase was first known to appear only in certain ternary systems1 no detailed work was then possible for this phase. The R phase has been recently discovered as a binary intermetallic compound in the Mn-Ti~ and Mn-si~-&apos; binary systems. The existence of binary R phases opens up the possibilities of studying the effect of alloying elements on the stabilization of the R phase. Of the two binary systems possessing an R phase, the Mn-Ti system appears to be more interesting because at a suitable high temperature it is possible to find the three electron compounds, the a-Mn, p-Mn, and R phases, side by side and it is possible to study the effect of a third transition element on these three electron compounds. For the present investigation iron and cobalt, so called B elements for the formation of electron compounds, have been used as the third element to study the stabilization of the a-Mn, P-Mn, and R phases. EXPERIMENTAL PROCEDURE The alloys were prepared by using 99.9 pct pure electrolytic Fe and Mn, 99.5 pct Co, and crystal bar titanium, supplied by Semi Elements Inc., New York and Gallard Schelsinger Mfg. Co., New York. Weighed amounts of the components were melted in recrystal-lized alumina crucibles in an inert atmosphere (argon) high-frequency induction melting unit. Titanium was made into fine chips for easy dissolution and a special charging procedure was adopted to avoid contacts of titanium chips with the alumina crucibles. Up to 20 at. pct Ti, the maximum titanium content in the investigated alloys, there was no visible sign of reaction of titanium with the alumina crucibles. With a careful control of melting time and temperature the losses were minimized and were always found to be below 0.1 pct. Because of such small and almost constant weight losses, the alloys were not finally analyzed. The alloys were wrapped in molybdenum foil and annealed in evacuated and sealed silica capsules at 1000" * 2°C for 72 hr and subsequently quenched in cold tap water. Annealed samples were examined metallographically and by X-ray diffraction. For all high manganese alloys oxalic acid solutions of various concentrations and 1.0 pct HN03 solution were found suitable as etching reagents. Best contrast between the a-Mn and the R phases could be obtained by using freshly prepared 60 pct glycerine + 20 pct HN03 + 20 pct HF solution. For high iron and cobalt containing alloys, especially for alloys containing the a-Fe, y-Fe, and P-Co phases, 15 cc HNOJ + 60 cc HC1 + 15 cc acetic acid + 15 cc water solution was found to be the best etching reagent. All X-ray diffraction work was carried out (using specimens prepared from annealed powders) with a 114.6 mm diam Debye-Scherrer camera using unfiltered FeK radiation at 25 kv and 10 ma. All calculations for X-ray diffraction work were carried out using an IBM 7044 digital computer RESULTS AND DISCUSSION The two ternary systems, MnTiFe and MnTiCo, were investigated near the manganese rich end, Figs. 1 and 2, and show some common features. In both alloy systems large extensions of narrow R phase regions occur at almost constant titanium contents. At titanium contents higher than that of the single phase R-phase alloys, the same unidentified X phase was found in both ternary systems. The extensions of the X phase close to the Mn-Ti binary indicate that this phase could be the TiMns phase. Too few X phase diffraction lines were present in the diffraction patterns to make positive identification of the X phase. In contrast to this similarity the two systems show opposite behavior in the extensions of the a-Mn and 8-Mn phase regions; while iron tends to stabilize the a-Mn phase, cobalt

Jan 1, 1970

By R. A. Vandermeer, J. C. Ogle

Two distinct types of depth-dependent variations in texture have been observed in niobium cold-rolled various amounts up to 99.5 pct reduction in thickness. These nonuniformities are thought to be the results of nonhomogeneous plastic dewmation during rolling. The first type is characterized by a zone at intermediate depths that tends to lack certain strong orientations which are present in the surface and center layers of the rolled stock. This type of texture modification seemed to be associuted with "high" body rolling and may be related to the shape of the zone of deformation in rolling. The second type of texture inhomogeneity found involved the formation of a unique texture in the surface layers of heavily rolled strip. High fiiction forces between work piece and rolls appear to be needed to generate and maintain this texture. We believe that this unique surface texture results from a shear mode of deformation in the surface layers. THE evolution of texture in both the surface and center regions of cold-rolled niobium as a function of increasing deformation from 43 to 99.5 pct reduction in thickness was reported in a previous paper.&apos; It was noted that for strips rolled between 95 and 98 pct reduction a distinctly different texture appeared in the surface layers which was unlike the center texture. Certain other layer to layer textural variations were also detected during the experimental phase of that work but were not described in the paper. Surface textures have been reported previously for the bcc materials iron and Steel2-4 and are well known in the fcc metals.5 It is usually stated that these are shear textures which arise under conditions of high friction between specimen and rolls. Work by Mayer-Rosa and Haessner5 n niobium rolled under conditions presumed to be high roll friction gave no indication, however, of a surface texture in that material. This is indeed puzzling in view of our results.&apos; Thus we undertook additional experiments designed to study the stability of the surface texture for certain rolling variables. The variables investigated were the presence or absence of lubrication, amount of reduction per pass, and reverse vs unidirectional rolling. It is the purpose of the present paper to describe the kinds of depth-dependent textural inhomogeneities that we have observed in rolled niobium as well as to present the results of our recent experiments on the stability of the surface texture. Possible explanations for the depth-dependent texture variations will be discussed in terms of nonhomogeneous plastic deformation during rolling. EXPERIMENTAL Specimens cut from the niobium rolled to different reductions in the previous study1 were examined at various layer levels throughout the strip thickness for textural inhomogeneity. The specimen surfaces were either etched or machine ground and etched to remove material to a specific depth. Textures were determined by means of the Schulz X-ray reflection pole figure method with a Siemens texture goniometer and Cum X radiation. Since the important intensity peaks of the textures in niobium are usually located on the normal direction (N.D.) to rolling direction (R.D.) radius of the (110) pole figures, it was sufficient in many cases to scan only along this radius. At selected depths or where additional information was required the entire (110) pole figure was also obtained. In studying the stability and formation of the surface texture, experiments were conducted on 0.400-in.-thick, fine-grained, randomly oriented niobium specimens extracted from the same starting stock as that used in the earlier study.&apos; Two of these specimens were rolled at room temperature to a total reduction of 96.4 pct. One was rolled between cleaned and degreased rolls with no lubrication. The other was lubricated between passes with Welch Duo Seal vacuum pump oil. The rolling schedules of each were kept as nearly identical as possible. Drafts were of the order of 0.006 to 0.012 in. per pass. Other experiments consisted of rolling specimens at constant fractional reduction per pass, i.e., (ta- tb)/ta equals a constant where ta and tb are the entrance and exit thickness of the rolled stock, rather than at a constant draft, i.e., ta- tb equals a constant. Ten specimens were rolled at room temperature on a two-high, motor-driven rolling mill with 8-in.-diam rolls. These specimens were rolled to thicknesses of between 0.041 and 0.073 in. (82 to 90 pct total reduction) at approximately constant reductions per pass ranging from 9 to 45 pct. Kerosene was used as a lubricant. Half of the specimens were always rolled in the same direction while the other half were reversed end to end at each pass. The texture in the surface regions was determined with the X-ray technique described above. RESULTS The textural inhomogeneities noted in niobium rolled from fine-grained, randomly oriented stock 1.5 in. long by 0.75 in. wide by 0.40 in. thick can be classified into two types. The first may be discussed with the aid of Figs. 1 to 3. Fig. 1 is a three-dimensional plot of the X-ray intensity in units of times random vs f , the angle from the N.D. to any point along the N.D. to R.D. radius of the (110) pole figure, and depth, given as percent of the thickness (?t/to X 100, where at is the thickness of material removed and to is the as-rolled

Jan 1, 1970