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By Tibor Stefansky, John E. Dorn

MOTT and Nabarro1-5 were first to illustrate the importance of the flexibility of dislocations in accounting for the strengthening that metals undergo due to the presence of internal-strain centers. Such strain-centers might arise from a number of causes such as radiation damage, the presence of semicoherent and coherent precipitates and clusters, as well as individually dispersed interstitial and misfit substitutional solute atoms. Each strain-center induces positive and negative shear stress fields on the slip planes of the surrounding alloy matrix. In order to effect plastic deformation, therefore, the alloy must be subjected to sufficiently high applied shear stresses to push dislocations past all such internal stress fields. If dislocations were inflexible and moved as rigid lines, they would be equally pushed and pulled by internal stress fields. At this extreme the strengthening would be vanishingly small. Dislocations, however, are not rigid; they are flexible and extensible. They wiggle between positive and negative strain-centers, thus increasing their line energy at the expense of their interaction energy with strain-centers. cottrel16 and Friedel7,8 have independently presented lucid reviews of the significance of the Mott-Nabarro dislocation-flexibility concept to the strain-center strengthening of alloys. Their analyses however were only semi-quantitative. There is evidence in the recent literature of renewed interest in a more rigorous analysis of flexibility. Thus, Gleiter9 and Gerald" have shown that the calculated strain-energy interaction between a dislocation and the stress fields of coherent precipitates can be seriously in error if the flexibility of the dislocation is not taken into account. This report will be concerned with a more detailed analysis of the problem based on the following approximations: 1) Although many types of strain-centers exist, the following analysis will be limited to the case of solute-atom strain-centers in fcc substitutional alloys. 2) To facilitate the analysis by avoiding statistical considerations, the strain-Centers are assumed to be in regular arrays on the slip plane. Although the quantitative results are somewhat dependent on the type of array that is assumed, the qualitative trends are similar for various arrays that were studied. 3) An adjustment of the results from those for square arrays to those for the more realistic case of a random distribution of strain-centers is accomplished by adopting the interesting statistical theory first introduced by Kochs,11,12 elaborated on by Dorn, Guyot, and stefansky,13 and analyzed by Foreman and Makin14 in their computerized experiments. 4) For simplicity the dislocation lines are taken to wiggle about their edge orientation and no correction is applied to their line energy for deviations from edge configurations or for the elastic interaction between segments of the now curved dislocation. It will be shown that for extremely low concentrations of atomic strain-centers the strengthening increases with the square root of their concentration. For slightly higher concentrations the strengthening rate becomes less rapid. At a critical concentration a maximum strength is obtained and a decrease in the strengthening takes place as the concentration of solute atoms is further increased. These trends are a direct consequence of dislocation flexibility. They arise from changes in the amplitude of the waviness of the dislocation line at the yield stress with solute atom concentration. Despite the simplifying assumptions that were made, the results agree qualitatively with appropriate experimental data. I) STRESS FIELDS ON SLIP PLANES Internal stresses are introduced in a lattice whenever a host atom of radius ro is replaced by another that has a different atomic radius. According to the classical theory of linear elasticity,15 the stress field about a solute atom at the origin of a spherical coordinate system is given by arr=-4G€(?_0)3 ffflfl ="W =2G€{t) f°rr^ro(l+e) UJ where G is the shear modulus of elasticity and Y, = ro(l + E) is the radius in situ, of the substituted atom. As shown by ~shelb~,'~ this approximation assumes that the bulk modulus of elasticity of the substituted atom is identical with that of the host species. ~abarro'~ suggested that the strain E can be deduced

Jan 1, 1970

By F. H. Froes, D. H. Warrington

Electron microscope evidence which indicates that TaC may precipitate at random sites in the matrix is presented. Initially the particles are almost spherical and coherent with the matrix. However, as they grow in conditions in which there are insufficient vacancies to relieve lattice strain, the particles rapidly lose coherency in two directions and continue to grow as plates with approximately the full lattice mismatch strain present perpendicular to the plane of the plate. The necessary relief of strain comes from dislocations loops which do not become visible until the later stages of aging. The rapid decrease of apparent strain to low values of appoximately 1 pct at small particle sizes arises not from a complete incoherency but from applying a model wrong for the particle shape and strain distribution. PREVIOUS work has shown that MC-type carbides may precipitate intragranularly in austenitic stainless steel on dislocations,1&apos;2 in association with stacking faults,3&apos;4 and randomly through the matrix,5-7 In investigations of the matrix precipitate by thin-foil electron microscopy, considerable lattice strain has been found to occur around the precipitating phase.7&apos;8 Attempts have been made to evaluate the amount of lattice strain by using the methods developed by Ashby and brown.9,10 Values of the linear strain, much less than the 17 pct theoretical mismatch (for TaC), have been reported; it has been suggested that this is due to either a loss of coherency1&apos; or vacancy absorption which occurs during either the initial nucleation or growth of the precipitate." This report is an extension of earlier work7 that dealt with the precipitation of TaC from an 18Cr/12Ni/ 2Ta/O.lC alloy after it had been quenched from 1300°C and aged between 600" and 840°C. In particular, the shape of the precipitate particles and the amount of strain in the matrix, due to the precipitate, have been studied. The work described here is part of a wider investigation of factors that affect carbide precipitation in austenitic stainless steel," details of which are to appear elsewhere. RESULTS The present investigation can be conveniently split into two aspects of the strain-fields surrounding the matrix particles: 1) information derived from the strain-field which indicates the shape and habit plane of the precipitate particles and 2) the magnitude and sign of the strain-field. The Shape and Habit Plane of the TaC Precipitate. In the early stages of aging twin lobes (normally black F. H. FROES, formerly at the University of Sheffield, Sheffield, England, is Staff Scientist, Colt Industries, Crucible Materials Research Center, Pittsburgh, Pa. D. H. WARRINGTON is Lecturer, Department of Metallurgy, University of Sheffield. Manuscript submitted November 1, 1968. IMD on white background, i.e., for the deviation parameter, S > 0) that indicate the strained region of the matrix define the position of the particles by bright field transmission electron microscopy. The actual particles were not detected until they were approximately 120Å diam; below this size they were too small to be imaged in the electron microscope. This meant that particle growth that had occurred before this stage had to be inferred from the matrix strain-field contrast. In all cases when diffraction effects were observed from the precipitate particles, a cube-cube orientation relationship (i.e., (llO)ppt Il<llO>matrix and {1ll }ppt {III} matrix) existed between the precipitate and the matrix. From the matrix precipitate particles lying along edge-on {111} planes (e.g., at A, Fig. I), the precipitates are seen to be plate-like with their diameter being roughly 18 times their thickness after 5000 hr at 650°C. However, the exact shape of the particles cannot be determined because of the masking effect of the strain-field contrast. If a dark-field micrograph, using a precipitate reflection, is studied, Fig. 2, a number of the projected images of the TaC particles [on the (110) foil surface] apear to have straight edges parallel to projected f111) planes. Thus, it appears that in the later stages of aging the TaC particles are plate-like with some tendency for the edges of the plate to be bounded by the matrix close-packed {ill} planes (though the general shape of the particles in the plane of the plate is circular and thus the "diameter" of the particles has a real physical significance). It should be noted that the bands of fine discrete particles observed in Figs. 1 and 2 are not the matrix precipitate discussed in this paper but are precipitates associated with extrinsic stacking faults3j4 occurring on (111) matrix planes. **£** ****** \ *x 23 Fig. 1—18/12/2~a/0.1~ alloy. Solution treated at 1300°C for 1 hr, water quenched, and aged 5000 hr at 650°C. The (112) directions shown are the traces of the e&e-on (111) planes. Foil normal [110]; operating reflection (331); bright field micrograph.

Jan 1, 1970

By E. R. Buchanan, R. E. Reed-Hill

Cylindrical magnesium single crystals were deformed in torsion. The axis of torsion was the basal pole. Five crystals were deformed to different strains between 0.08 and 1.03 and then sectioned in order to determine their dislocation densities using the transmission electron microscope. The work hardening rate of all specimens was at least an order of magnitude higher than that normally associated with easy glide in a tension test and comparable to that obserzed in stage B of a tension test. The correspondence between stage B in a tension test and the initial stages of a torsion test is believed to result from the fact that in both cases deformation occurs in a structure containing roughly equivalent densities of the dislocations associated with the three basal slip vectors. THERE are three basic ways of changing the shape of a crystal using slip dislocations. The crystal can be sheared along a slip direction in a slip plane; it can be bent about an axis in the slip plane normal to the slip direction; and, if the slip plane contains multiple slip directions, it can be twisted or rotated about the slip plane normal. Of the three processes, generally known as translational, flexural, and rotational slip, only rotational slip has not been extensively investigated. The object of the present research was to obtain basic information about this phase of crystalline plasticity. This paper is concerned with some aspects of the stress-strain curves obtained by twisting magnesium crystals about their basal poles. Magnesium was selected for four reasons. One, its recovery rate at room temperature is relatively low. Two, single crystals may be easily grown. Three, at room temperature the critical resolved shear stress for basal slip is about two orders of magnitude lower than that for nonbasal slip, so that rotational slip might be expected to occur primarily by basal slip. Finally, relationships between flow stress, shear strain, and dislocation density have been determined for tensile deformation of magnesium crystals,&apos; thereby providing a basis of comparison for the torsional results. EXPERIMENTAL PROCEDURES Crystals were grown from 0.5 in. diam extruded sublimed magnesium rod furnished by the Dow Chemical Co. who reported that it contained in weight percent less than 0.0003 Al, 0.01 Ca, 0.01 Cu, 0.0012 Fe, 0.001 Mn, 0.0005 Ni, 0.003 Pb, 0.001 Si, 0.01 Sn, and 0.02 Zn, with the balance magnesium. All crystals were grown in a dried argon atmosphere using Jill-son&apos;s2 modified Bridgman technique. Two different methods were used to obtain crystals with the basal plane normal to the specimen axis. These included direct growth from seeds of the proper orientation, and spark machining (trepanning) of 0.5 in. diam cylinders from larger (1.5 in. diam) randomly grown crystals. The crystals thus produced were polished in a 20 pct HC1 water solution and then etched in a 1 pct HC1 water solution to develop etch pits lying in rows parallel to the basal plane trace. The crystals were then revolved about their axes on the stage of a low-powered microscope. Torsion specimens were prepared only from those crystals whose axes were normal to the rows of etch pits. It is estimated that this simple orientation method was accurate to about 51 deg. 1.625 in. long cylinders were next cut from these selected crystals and then acid machined in a 20 pct HC1 water solution into torsion specimens with a 1 in. long by 0.30 in. diam reduced gage section. Following this, they were annealed in air at 400°C and furnace cooled to room temperature. The specimens were given a final polish in a 10 pct HC1 water solution, rinsed in ethanol, dried, and cemented into brass grips with an epoxy resin. In addition to the torsion specimens, several tensile specimens with their basal planes at 45 deg to the stress axis were also prepared with similar dimensions except that the gage sections were increased to 4 in. in length. The torsion specimens were tested in the apparatus

Jan 1, 1970

By M. Deighton, R. N. Parkins

The metals Cd, ,Wg-, Sn, TI, Zn, and Zr reach a peak hardness after a criticfir1 deformation by rolling- and then soften with fwther rolling-, thereby exhibiting wovk softening. Optical metallography on Cd, Mg, and Zn shows that work softening is accompanied by a change in grain size occurring during deformation. The creep of zinc from -1l° to +60°C at stresses in the range of 7.9 to 17.3 kg per sq mm is given by € = e0 -t- Bt + Kt +at6. The third and second rate constcints are related by the equation a = K~ K6 and their stress and temperature dependence can be represented by the equations K = A, . exp - (u, - Bu)/kT. A model based upon the stress activated glide of sub-boundaries is proposed which qualitatively accounts for the metallog-raphic observations. Expressions, which are in reasonable quantitative agreement with the ex-pe~inzental observations, are derived for the creep of zinc. THE term "work softening" has been used previously by Polakowski1 and by Cottrell and stokes2 to describe phenomena where further strain of a deformed material leads to a decrease in flow stress. In both cases, however, the conditions were changed for the second straining. Here, the term "work softening" is intended to refer to a decrease in flow stress after continued straining in the same direction at the same temperature: work softening is the antithesis of "work hardening". Work softening of zinc was reported by chadwick3 and in discussion of that paper Jenkins4 indicated that cadmium also work softens. More recently work softening has been reported5 in two magnesium alloys, -99.5 pct Mg. Chadwick found that the hardness, 0.2 pct Proof Stress and the UTS of electrolytic zinc all increased with progressive cold reductions up to 30 pct and then progressively decreased with further rolling. Gay and Kelly6 used a back-reflection X-ray technique to study the effect of cold rolling zinc and found that although deformations greater than 2 to 5 pct reduction in thickness produced some recrystallized grains, deformations greater than 40 pct caused com-plete spontaneous recrystallization. At deformations greater than 60 pct the material was found to consist solely of recrystallized grains, -20 pm diam, the size of which decreased with increasing reduction and was much less than the initial grain size of the annealed material (-300 pm diam). Similar results were also reported for cadmium, tin, and lead.6 Gay, Hirsch, and Kelly&apos; suggest that these experiments indicate recrys-tallization takes place when the dislocation density exceeds a certain value. However, no measurements of MATERIALS AND EXPERIMENTAL PROCEDURE The purity of the metals used in this work is indicated by the following figures: Zn (99.99); Cd (99.94); Mg (99.95); T1 (99.99). The zirconium was iodide crys tal bar with a probable purity of about 98 pct. The metals were obtained in the form of 0.25 in. thick strip or 0.425 in. diam rod by various fabrication methods and then annealed to ensure complete re-crystallization. Hardness-deformation curves were obtained at room temperature by rolling 4 in. thick strip under conditions which left a surface adequate for diamond pyramid hardness tests immediately after rolling. The hardness was taken as the niean of five impressions made using a 5 kg load and the time elapsing between rolling and making the last impression never exceeded 5 min. The zinc specimens for creep testing were from 3 by 3 by 4 in. cast slabs which were rolled to 0.10 in. thickness starting at 350°C and finishing cold. The resulting strip was cut into pieces 1 in. wide and annealed in batches. With suitable choices of annealing temperature between 100" arid 400°C five different grain sizes varying from 4.54 x 10&apos; to 3.03 x l05 grains per sq cm (530 to 20 um diam) were obtained. Creep tests were done in compression using a sub-press, based on a design after Ford,8 in which the strip is compressed between dies 0.100 in. wide under conditions of plane strain. Since there is no lateral spread of the material, the area of contact between the dies and strip remains constant throughout the test and the application of a constant load, using the load maintaining device of a hydraulic testing machine, resulted in a constant stress. Covering the dies with strips of P.T.F.E. reduced frictional effects to a minimum. The creep strain was obtained by measuring the travel of the crosshead of the testing machine to a sensitivity of 0.1 pct reduction in thickness. The complete subpress assembly was contained in a steel box and for tests above the ambient this was filled with liquid paraffin and heated electrically. Temperatures below the ambient were obtained with a cooling mixture of acetone and solid carbon dioxide in the box. The liquids were stirred and the temperature of the specimen, which was controlled to ±0.5"C dur-ing a test, was measured by a thermocouple placed near the dies. Compression testing of cylindrical specimens was also carried out in the subpress using hardened flat discs separated from the test material by P.T.F.E. sheets which obviated barrelling of the specimens. Various initial strain rates were supplied by the hydraulic testing machine, and the deformation was measured by a clock dial gage resting on the cross-

Jan 1, 1970

By J. Gurland

The wmk is concerned with the estimate of the degee of continuity of a particulate phase dispersed in a matrix. The first section is a verieu: of the parameters nzeasurable by quantitative rnetallogvaphy, namely the contact area and, under certain conditions, the number of contacts between particles of one phase. In the second section, the frequency of particle contacts is related to the degee of continuity of a randomly embedded phase orz the basis of the lattice-percolation model of Hamrnersley and others. THE extent of continuity of the constituent phases may greatly influence the structure-sensitive properties of phase mixtures, particularly if the phase properties differ significantly. An example from the literature1 is shown in Fig. 1. The marked decrease of the electrical resistivity of sintered silver-alumina bodies near 25 pct by volume of silver presumably occurs because the more conductive phase changes from a discontinuous to a continuous structure. Other example of electrical- and thermal-conductivity transitions are cited by kingery In view of these observations, a knowledge and understanding of the connectivity of the microstructure may be of considerable practical importance. This study is concerned with one aspect of the genera1 problem, namely the estimate of the degree of continuity of a particulate phase dispersed in an opaque matrix. The first section reviews the parameters measurable on a polished cross section by auantitative metallography, such as the contact area and under certain conditions, the number of contacts between particles of one phase. In the second section, an attempt is made to relate the frequency of particle contacts to the degree of continuity of a randomly embedded phase. For the purpose of this discussion, the aggregate has two constituents: the particulate phase and the matrix. The latter is considered to be homogeneous. The term "particle" is used with the meaning of "grain", i.e., a minute unit of matter which is usually a single crystal of a readily distinguishable substance within the confines of a simply connected boundary. While many of the concepts which are used here to describe the structural variables characterizing the microstructure of phase mixtures are qualitative and ill-defined, they are presented with the intent of stimulating further work of a more general and rigorous nature. I) PARTICLE CONTACT, CONTIGUITY, AND MEAN FREE PATH 1) Measurement of Contiguity. The fraction of the total internal surface of a phase a shared with particles of that same phase in a two-phase mixture of and $ is indicated by the contiguity ratio:3 whereis the area of the interface between o particles, and Sap is the area of the interface between a particles and matrix P, per unit volume of mixture. The contiguity ratio ranges from 0 to 1 as the distribution of the a phase changes from a completely dispersed to a completely agglomerated structure. The interfacial areas may be obtained from simple intercept measurements on a random plane, after Smith and Guttman where and N are the numbers of intercepts between a random line of unit length on a plane of polish and the interparticle and interphase interfaces, respectively. The equations are valid for any distribution of particle sizes and shapes.

Jan 1, 1967

By R. B. Gordon, D. A. Koss

Ultrasonic-atlenuation changes due to the formation of free dislocations have been observed during tensile tests of magnesium and LiF single crystals and samples of polycrystalline Results on the LiF and samples are similar: A preyield attenzration increase is observed which, however, be-corlzes smaller as the magnitude of the drop in load al yielding increases. This indicates that the yield point observed in these materials is due to dislovation rather than dislocation unpinning and that the initial density &apos; free dislocations must be low if the yield point is to be sharp,. Tests on the magnesium ere conducted at both 27" and 200C. Magnesium has the unusual property that the yield drop is larger at the higher test temperature and is accomplished by a decrease in attenuation. The latter is due principally to the temprovary pinning of detained dislocations by highly solute atoms. After strain aging., a stress as low as 0.3 bur suffices to unpin dislocations; microstrain measuements of sufficient sensitivity should. reveal plastic flow at stress levels this low IN another paper,&apos; we describe the technique of simultaneously observing ultrasonic-attenuation changes and plastic microstrain during deformation of spher-oidized carbon steels. Changes of ultrasonic attenuation indicate damping effects caused by the oscillation of long, freely moving dislocation segments. Simultaneous microstrain measurements are used to indicate total dislocation motion. The dislocation-damping observations are most useful in the study of the early stages of deformation where the dislocation density is low and the plastic strain is small and relatively difficult to measure. Particularly interesting results are found in materials which display sharp yield points. Observations of these phenomena are reported here for three materials: single-crystal LiF and magnesium, and poly crystalline molybdenum. EXPERIMENTS Dislocation-damping effects were observed by measuring changes in acoustic attenuation with the ultrasonic-pulse method. The end faces of each of the specimens were ground flat and parallel and a quartz 10 Mc per sec, x-cut transducer was attached to one face. The bonding agents used were: a) "Nonaq" stopcock grease with magnesium, b) beeswax with LiF, and c) salol with molybdenum. With the LiF, the best acoustic signals were obtained at 45 and 50 Mc per sec; all other measurements reported are at 10 MC per sec. The Sperry Ultrasonic Attenuation Comparator2 was used to measure attenuation changes. In the

Jan 1, 1967

By C. C. Koch, M. L. Picklesimer

PHYSICAL metallurgists interested in the alloying behavior and phase transformations in rare-earth metals and alloys require a strain-free polished and etched surface for both metallographic and X-ray examination. However, the rare earths have presented a problem in this respect since they are difficult to polish free from strain and are very reactive to the atmosphere. Their tendency to oxidize readily even at room temperature necessitates careful preparation and rather elaborate protection if their surface is to be examined for any length of time. The "light" lan-thanides (i .e., atomic numbers less than 63), especially lanthanum and cerium, are particularly bad in this regard; they oxidize very rapidly at room temperature. To eliminate the problem of plastic deformation remaining on the surface after mechanical polishing, electropolishingl and chemical polishing techniques2 have been developed. The electropolishing technique requires the specimen to be immersed in an electrolyte at -77°C and thus obviates a metallographic study of, for example, the fcc —double-hexagonal close-packed (dhcp) transformation in cerium which begins at -10°C. The chemical polishing solution has been used only on several of the "heavy" rare-earth metals. However, a convenient method for protecting the polished and etched surfaces from atmospheric corrosion has not been available. Our interest in the superconducting properties of lanthanum, and in the phase transformations in lanthanum and cerium, has led us to develop a technique for the metallographic preparation of lanthanum and cerium which clearly reveals the microstructure and preserves the etched surface for days. The specimens are chemically polished and anodized. The chemical polishing is performed at room temperature, the anodic oxide film provides the required protection from the atmosphere, and colors produced in the film provide a simple positive technique for phase identification. Lanthanum and cerium metal ingots obtained from Johnson Matthey and Co., Ltd., were remelted to suitable shapes and heat-treated to produce various microstructures. The samples were placed in epoxy mounts and, after a small hole was drilled in the back of the mount for electrical contact, were ground on silicon carbide

Jan 1, 1968

By R. G. Fenish

THE B-Ni system was chosen for this study because of the great interest being shown in boron-fiber-strengthened composite materials. Boron fibers were obtained from Texaco Experiment, Inc. They average 4.2 mils in diam with a 0.5-mil tungsten wire in the center. In order to make the diffusion couple, the fibers were included in the nickel matrix by electroforming. The samples were placed in a preheated furnace for the desired temperature and length of time. Sectioning and polishing the samples revealed concentric rings as shown in Fig. 1. The average penetration distance, X, was calculated by measuring the radius of the second phase (the white shell in Fig. 1) and subtracting the original radius. The second phase was identified as NiB by X-ray diffraction. This allows the kinetics of the formation of the phase NiB to be calculated by Eq. [I], which is taken from Hoffman:"

Jan 1, 1967

By R. N. Orava

TO the author&apos;s knowledge, only one satisfactory high-resolution technique for etch-pitting dislocations in Cu-Zn alloys has been published.&apos; In that account, pits in 70/30 brass single crystals were produced by etching electrolytic ally in a 30 pct orthophosphoric acid bath. Thereafter, observations were made from surface replicas by electron microscopy. The method of pitting and observation permitted the high resolution necessary for the distinction of individual dislocations in arrays of pile-ups. However, no comment was offered concerning the possibility of obtaining pits which are amenable to optical resolution. Moreover, for adequate results, the electrolytic pitting process is invariably preceded by a polishing stage which could obscure the surface features of interest. Consequently, it would be desirable to be able to delineate, by solely chemical means, dislocations which could be detected by both optical and electron metallo-graphic techniques. This was achieved by the simple expedient of modifying two etchants reported by young2 to reveal dislocations on the (100) planes of pure copper. Single crystals of 70/30 a brass, described previously,3 were sectioned to provide a surface parallel to a set of {100) planes, mechanically polished, and subsequently electropolished at 2.4 v in a solution comprised of 2 parts H3PO4, 4 parts ethanol, and 3 parts water. The inclusion of ethanol tended to inhibit nonuniform surface attack. Etch-pitting was effected by a 2 to 3 sec immersion in a 70 pct aqueous solution of HNO3. The samples were then washed in a fast-flowing stream of water, and rinsed further in distilled water, and ethanol, before drying. It is important to note that this reagent should be either used immediately after mixing, or, if allowed to cool, reheated to about 35°C prior to use. No pitting was obtained at room temperature. Typical results are shown in Fig. 1 where (a) is an optical view of the pitted surface and (b) is an electron micrograph of a silicon monoxide replica shadowed with tungsten oxide. The former is characteristic of a somewhat longer etching time (-6 to 8 sec) which varied with bath temperature. Similar pits accrued from a 1/10 aqueous dilution of another of Young&apos;s solutions2—2 M FeC1,6H20 and 7.8 M HBr.

Jan 1, 1968

By J. Stringer, I. W. Edington, C. R. Rarey

THE geometrical interpretation of transmission electron micrographs of hcp metals is more complicated than the equivalent interpretation of cubic metal for two reasons: firstly, prominent zone axes are not in general normal to prominent planes, so that a simple diffraction pattern often corresponds to a nonra-tional foil plane; and secondly, the Miller-Bravais sys-tem of indexing directions is not easy to visualize. In this, the indexing is referred to the Bravais four-axis system, and the direction is labeled [hkil], chosen so that and I are shown in Fig. 1. Some geometrical relationships useful for the interpretation of transmission micrographs have been calculated and are tabulated below: 6) Direction of the intersection of two planes; this is easily calculated by applying Condition 4 to both planes: a direction that lies in both planes is clearly their direction of intersection. Some of the above expressions have also recently been given by Otte and Crocker;&apos; Expression 5 is of course in most standard crystallographic texts. It is generally considered easier and quicker to use graphical methods for the interpretation of electron micrographs than analytical methods. For this purpose, it is most convenient to use a "double stereo-gram" in which both the poles alzd the rational directions are plotted. It is, of course, necessary to orient

Jan 1, 1967

By J. D. Verhoeven

In a recent study1 this author has investigated the effect of an electric field upon the solute redistribution accompanying solidification of Sn-Bi alloys. It was concluded that the primary effect of the electric current upon the solute redistribution resulted from electrotransport within the liquid boundary layer at the solid-liquid interface. In order to maximize the electrotransport effect all of the experiments were conducted at the highest current densities experimentally attainable. It was found that these high current densities produced considerable convective mixing within the liquid metal. This mixing reduces the boundary layer thickness and consequently reduces the effectiveness of the electric field in producing solute redistribution. Consequently, it is quite possible that the condition of maximum achievable current density would not correspond to maximum solute redistribution. It may be that, as the field intensity is increased, a point is reached where the additional solute redistribution from the increased electrotransport is more than offset by the decrease in solute redistribution resulting from the increased mixing in the liquid. In order to check this possibility the effective distribution coefficient has been determined as a function of current density in a series of experiments. The experiments were conducted on 6.6 at. pct Bi

Jan 1, 1968

By Don H. Baker

THE need for new or improved refractory materials has caused metal phosphides to be given renewed scrutiny. Some metal phosphides show high-temperature inertness, are exceptionally hard, and exhibit a marked resistance to chemical attack. Various metal phosphides have been prepared for study by direct combination of the elements,&apos;-&apos; by reaction of metal or metal compounds with phosphine or phosphorus trichloride,&apos;"&apos; by thermal decomposition of a metallic phosphate or phosphite,"-&apos;8 and by molten salt electrolysis.19 Electrolytic preparation of phosphides of titanium, manganese, and chromium from their oxides is reported in this paper. An externally heated 3-in.-ID by 6-in.-deep graphite cell, that served as the anode as well as a container for the electrolyte, was used in these investigations, and a suspended, centrally positioned graphite rod served as the cathode. A closely fitting silicon carbide furnace liner minimized atmospheric oxidation of the crucible. Electrolyses were performed for predetermined periods and current settings. Preliminary research had indicated the more efficient current and potential settings that could be used. Upon completion of the deposition period, the deposit was hot-stripped from the cathode. The mass of crystalline deposit, plus occluded and adhering salt, was crushed to minus 10 mesh and hot-leached in dilute hydrochloric acid. The leached crystalline material was water-washed, dried, and sampled for analysis. Products were identified by X-ray diffraction and standard analytical procedures. Electrochemical studies were initiated to establish the optimum conditions necessary to produce manganese phosphide (MnP), titanium phosphide (Tip), and chromium phosphide (CrP). Among the factors studied were the operating temperature, the imposed current, and the electrolyte system. If the temperature, or imposed current, was too high, deposition of phosphorus resulted, and if either were too low, partially reduced lower oxides were deposited. The operating conditions established for repetitive high-quality production of metal phosphides of the MP structure are presented in Table I. The metal phosphide crystals varied in size, but all had a definite metallic appearance. Typical are the crystals of CrP shown in Fig. 1. Evaluation data and analysis of the crystals are presented in Table 11. Efforts to measure resistivity of these three compounds over the temperature ranges of 250o to 400°K were hampered by the small physical size of the crys-

Jan 1, 1968

By N. R. Adsit

THE B-Ni system was chosen for this study because of the great interest being shown in boron-fiber-strengthened composite materials. Boron fibers were obtained from Texaco Experiment, Inc. They average 4.2 mils in diam with a 0.5-mil tungsten wire in the center. In order to make the diffusion couple, the fibers were included in the nickel matrix by electroforming. The samples were placed in a preheated furnace for the desired temperature and length of time. Sectioning and polishing the samples revealed concentric rings as shown in Fig. 1. The average penetration distance, X, was calculated by measuring the radius of the second phase (the white shell in Fig. 1) and subtracting the original radius. The second phase was identified as NiB by X-ray diffraction. This allows the kinetics of the formation of the phase NiB to be calculated by Eq. [I], which is taken from offman:"

Jan 1, 1967

By C. M. Wayman, M. Miyagi

COMPARED to many of the binary alloys of iron, Fe-Ir alloys have received very little tud.&apos;&apos; Virtually nothing is known about the Fe-Ir equilibrium diagram&apos; except for a few details concerning the liquidus-solidus positions for dilute iron-based alloys. It is reported1 that the y to a transformation temperature in Fe-Ir alloys (up to 40 wt pct Ir) is composition-dependent, varying from -900°C for pure iron to 0" to 100°C for Fe-40 pct Ir in an almost linear manner. The y to a transformation appears to be reversible,&apos; the transformation hysteresis width increasing with increasing iridium content. In a qualitative way, the composition dependence of the y to a (and vice versa) transformations appears similar to those in the widely studied Fe-Ni system. In that the y phase (in Fe-40 pct Ir) can transform at -1000C, it

Jan 1, 1967

By Horace Pops

THE martensitic transformation occurring at cryogenic temperatures in the bcc ß-phase Cu-Zn binary alloys has been discussed in a number of publication~.1-3 Addition of a second solute element to the binary Cu-Zn alloys enables the ternary martensitic phase to be stable at temperatures above room temperature, and the variation of the MS temperature with third element content has been determined recently4 for a series of Cu-Zn based alloys in which either the zinc content or the electron concentration was maintained at a constant value. The present paper describes some characteristic growth features of martensite observed in ternary alloys. Alloys were prepared by adding small amounts of Ni, Ag, Au, Cd, Ga, In, Si, Ge, Sn, or Sb to a a -brass Cu-Zn master alloy. Details of the melting and casting technique, homogenization, examination by cold-stage microscopy, and the determination of the

Jan 1, 1968

By J. B. Berkowitz-Mattuck, R. Hopper, L. Kaufman, E. V. Clougherty

MARNOCH has reported on the attractive high-temperature oxidation resistance of Hf-Ta alloys.&apos; In view of current interest in these alloys, three Hf-Ta alloys were tested in the present study. These included a Hf-27Ta alloy and a Hf-20Ta-2Mo alloy which were supplied by Marquardt Corp. and a Hf-20Ta-Zr alloy provided by Illinois Institute of Technology Research Institute.&apos; The microstructure of these alloys was heated inductively in a glass vacuum system; the oxidizing gas, helium carrier plus a known partial pressure of oxygen (35-102 Torr), was continually passed over the sample at temperature for a given time period. The concentration of oxygen in the gas stream was continuously measured by a differential thermal conductivity technique2 so that the rate of oxygen picked up by the sample could be obtained. The flow rates were 0.1 to 0.2 ft per sec in the vicinity of the specimen. The concentration of oxygen did not fall below 50 pct of the input level in any of the experiments. In several cases a single sample was exposed consecutively at a series of increasing temperature levels. In a second system at ManLabs, cylindrical specimens were exposed to flowing air in a z irconia tube which was heated by radiation from a carbon tube resistance furnace. The specimen was heated from room temperature to the test temperature in flowing argon, then oxidized in air flowing at 0.1 to 0.2 ft per sec. Following exposure, the air was displaced by argon and the specimen was cooled. Postoxidation metallography was performed on every sample. The depth of conversion of the metal matrix to oxide was measured as shown in Fig. 1. The conversion depth was obtained by measuring the oxygen-contaminated metallic zone (which is bounded by a dense outer oxide and a subscale oxide region), subtracting its dimensions from the original dimensions, and dividing by two. Preferential oxidation of

Jan 1, 1968

By W. W. Gerberich

SINCE the original formulation of fracture mechanics concepts,&apos;y2 relatively little work has related the fracture mechanics description of metal behavior on a gross, structural component scale to the behavior of its microstructural constituents. The purpose of this note is to suggest the utilization of fracture mechanics to describe material behavior on a microscopic scale. A Fracture Concept for Two-Phase Structures. A critical displacement concept considering the tough unidirectional phase in a relatively brittle matrix is first examined. It is assumed that a flaw exists at position 1 as depicted in Fig. 1. As the crack moves from position 1 to 2 the plastic zone could be of the shape described with the size approximated by the Dugdale3 model: where c is the half-crack length, OO is the applied stress, and oyS is the yield strength. Hahn and Rosen-field4 have presented a simple fracture criterion for homogeneous materials based upon the displacement at the crack tip. They also have shown the equivalence of the critical displacement, v*, to fracture toughness by Kc = (2v*oysE)1/2 [2] The displacement at the crack tip is given by and the displacement at any distance in front of the crack tip may be determined knowing the plastic zone size and utilizing the development of Goodier and Field.5 Recalling Fig. 1, the value of v* for fracture in material M1 may be calculated from Eq. [2] providing the critical stress intensity factor is known. As the material is loaded, when vc > vM1 the crack moves from position 1 to position 2 where it encounters the tough second phase. If vc2 < vm2, then the crack will be arrested providing the width of the M2 phase is sufficiently large. This condition is necessary since the displacement at position 2 has increased due to the longer crack length. Thus, the displacement at the distance X (representing the dimension of the second phase) in front of the crack may be larger than the critical displacement for failure in the brittle material. If v, > vm, then failure will proceed in the brittle material. The value of v, may be calculated as indicated above. This latter consideration is the same as predicting fracture of a brittle second phase at some distance in front of a crack located in a ductile matrix. Experimental Evidence. On a macrostructural scale, tungsten wires in a ductile Be-Cu matrix are seen to fracture well ahead of the main crack front in Fig. 2. Utilizing a Kc value of 14.2 ksi-in.1/2 obtained by Schroder et al.6 for as-received tungsten, the critical displacement 2v*, for fracture is calculated from Eq. [2] to be about 6.5 X 10-5 in. The crack tip displacement, 2vc, is calculated from Eq. [3] to be 0.0028 in. indicating that fracture would occur at a considerable distance in front of the crack tip. From the ratio of v*/vc and the plastic zone estimate of Eq. [I], the distance in front of the crack tip at which a tungsten wire should fracture is calculated to be about 0.195 in. As shown in Fig. 2, a fractured wire occurs at a distance of 0.140 in. (fractured in three places), not at 0.250

Jan 1, 1968

By N. A. D. Parlee, I. D. Shah

ThIS reports on some work done on the solubility and diffusivity of oxygen in liquid silver. Solubility. Improvements in the measurement of the solubility of oxygen in silver and silver alloys were made because precise data were needed for calculating diffusion coefficients of oxygen in these alloys. The apparatus and the procedure used were similar to those of Parlee and Sacris.&apos; The main improvement was in the temperature-measuring technique. A MV30 mullite protection tube containing a calibrated Pt-Pt, 10 pct Rh thermocouple was inserted in the reaction tube from the top through a vacuum-tight swage-lok fitting. The protection tube was well-immersed in the liquid silver, which was heated by induction. A Leeds and Northrup potentiometer was used in connection with the thermocouple. All runs reported were made at 1 atm. The temperature range investigated varied from 940" to 1200°C. The ternary point in Ag-0 phase diagram2 is at 939°C and 0.32 wt pct O. This point was reinvestigated using the above-described apparatus and was found to be at 939°C and 0.315 wt pct 0. It was determined by observing the sudden evolution of oxygen at this point while the solubility measurements were made. The point was easily reproducible if precautions were taken to keep the liquid silver essentially in equilibrium with oxygen and to lower the temperature very slowly. All of the results of this new solubility investigation are plotted in Fig. 1. They are represented by the "least-squares" line shown in the figure and the following equation for solubility at po2 = 1 atm: log% O =695.4/T - 1.086 This equation differs only slightly from that proposed by Parlee and sacrisl and that of Diaz, Masson, and Richardson.3 The points of Parlee and Sacris, using an optical pyrometer, are shown for comparison.

Jan 1, 1968

By J. H. Brophy, A. I. Prill

The authors have previously investigated the solid-state activated sintering of tungsten powder with various Ni-Cu additions.&apos; Log shrinkage vs log time plots showed changes in slope from 4 to x at intermediate times during the sintering process. This was attributed to a change in the rate-controlling mass-transport process from solution of tungsten into the tungsten-alloy interface to diffusion of tungsten in this interface. It was postulated that the melting of the activating layer should not affect this transport process. However, the superposition of rearrangement due to the presence of a liquid phase complicates the data analysis. It is the purpose of this note to apply the analysis of Prill, Hayden, and rohy&apos; to account for "rearrangement shrinkage&apos;? in liquid-phase sintering of the W-Ni-Cu system. This results in "solution-precipitation stage" shrinkage plots which were comparable to those obtained in solid-phase activated sintering of the same system. If one assumes total shrinkage to be the sum of rearrangement and solution precipitation, the effects can be isolated easily.2 This results in the general equation:

Jan 1, 1967

By J. M. Seeman, R. A. Dodd

If some solution-quenched supersaturated aluminum solid solutions, e.g.., Al(Cu), are plastically deformed at room temperature and then aged at 200oC, the hardness may first decrease before increasing in the usual manner &apos; A similar transient softening is observed, even in the absence of plastic deformation, when a thin foil or small-diameter wire Al(Cu) specimen is rapidly quenched from the solution-treatment temperature and then aged.&apos; Also, some solution-quenched and neutron-irradiated alloys undergo an initial hardness decrease during subsequent aging.3 The usual explanation of the transient softening in the above examples involves the effect of vacancies introduced by plastic deformation, rapid quenching, and neutron irradiation, respectively However, the mechanism of softening is not unequivo-cably established. In the first-noted case, Gane and parkins&apos; observed that the softening was approximately proportional to the difference in the atomic diameters of solute and solvent, and it was argued that, if a large relative difference in atomic diameter promoted vacancy-assisted room-temperature solute diffusion to dislocations, dislocation climb occurring during subsequent aging at 200°C could cause transient softening. Some substantiation of this theory was offered by the additional observation that discontinuous yielding of solution-quenched polycrystalline Al(Cu) tensile specimens was suppressed by interrupting the test for a short aging treatment at 200°C. Of course, reversion (resolution of GPI) at 200°C would also cause softening, and Sil-cock4 expressed the opinion that the softening in the case of Al(Cu) must be partly associated with reversion. Also, Hirsch5 commented on the possibility that, if jogs cause hardening, an anneal at 200°C should straighten the jogged dislocations and result in softening. However, parkins&apos; has re-expressed his belief that these mechanisms are not entirely consistent with the observed serrated stress-strain curves. Experimental. New data has now been obtained for Al(Cu), Al(Ge), Al(Mg), and Al(Zn) primary solid-solution alloys. These alloys were prepared from metals exceeding 99.99 pct purity, and specimens 4 by 4 in. diam were solution-treated, quenched, deformed 10 pct in compression at room temperature, and aged at 200&apos;C in a cottonseed oil bath for various times. Generally, these operations could not be carried out in rapid succession, so the alloys were stored in a freezer between treatments to minimize aging. The variation in hardness with aging time, Figs. 1 to 4, was determined by microhardness testing with a 3.0-kg load. At least five readings were averaged to obtain each data point, and all measurements were taken about the center circumference of each cylinder (region of maximum deformation). Each specimen was used to obtain only one data point, i.e., specimens were not replaced in the aging bath after measurements were made. In

Jan 1, 1968