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By D. Atkinson, C. Bodsworth, I. M. Davidson

A geometric model of interstitial solid solutions, which has been used previously as a basis for the prediction of carbon activities in Fe-C austenite, is shown to serve also for the calculation of nitrogen activities in Fe-N austenite. The model has been developed to enable predictions to be made of the activities of an interstitial element in the presence of two host atom species. The activities calculated via the model are shown to be in satisfactory agreement with the measured values in the austenite phase for carbon in Fe-C-Co, Fe-C-Cr, Fe-C-Ni, Fe-C-~n, Fe-C-Si, and Fe-C-V alloys and for nitrogen in Fe-N-Ni alloys. The effect of the second substitu-tional solute on the logarithm of the activity of the interstitial element is expressed as the product of a constant mad the atomic concentration of that solute. The constants so derived we related to the thermo-dynamic interaction coefficients which describe the effect on the activity coefficient of carbon of an added solute element. In recent years the thermodynamic activities of carbon and nitrogen in the single-phase austenite field have been determined for iron binary alloys and for several iron-base ternary alloys. In order to extend the use of these measurements, it is desirable to be able to predict with reasonable accuracy the activities of the interstitials at compositions and temperatures other than those which have been measured experimentally. In all the systems studied to date, the interstitial elements do not conform to ideal behavior. Hence, the available data cannot be extrapolated or interpolated using the simple thermodynamic concepts of solutions. Several models have, therefore, been formulated for the purpose of predicting the activity of an interstitial element in the presence of one species of host atom. These models can be divided into the geometric1"5 and energetic6-' types. The former group is based on the assumption that at low concentrations the activity of the interstitial species is determined by a composition-dependent configurational entropy term and an excess free-energy term which is temperature-dependent but independent of composition. The purpose of this paper is to show that the treatment, based on a geometric model, can be extended to enable predictions to be made of interstitial activities in the presence of two substitutional host atom species. THE CONFIGURATIONAL ENTROPY OF MIXING ICaufman5 has shown that the configurational entropy, S,, for a binary solution comprising of a host atom species, A, and an interstitial species, I, can be expressed as: where NI is the atom fraction of the interstitial species, R is the gas constant, and (2 - 1) is the number of interstitial sites excluded from occupancy by the strain field around each added interstitial atom. The number of interstitial sites per host atom, p, is unityg for the fcc austenite solutions considered here. The configurational entropy of mixing for a ternary solution comprising two substitutional atom species, A and B, and one interstitial species, I, can be derived similarly. Let the number of atoms per mole of each of these species in the solution be represented by «a, ng, and nI. From geometric considerations, it is improbable that the addition of a few atom percent of a second host atom species will change the type of sites (i.e., octahedral) in which the interstitial atom can be accommodated in the austenite lattice. At higher concentrations (determined largely by the relative atomic radii of the atomic species present and any tendency to nonrandom occupancy of the host lattice sites) other types of interstitial sites may become energetically favorable. Restricting consideration to compositions below this limit, for 1 = 1 the number of suitable interstitial sites is given by (n + nB). However, if each interstitial atom excludes from occupancy (Z - 1) additional sites, the total number of sites available for occupation is reduced to (n + ng)/Z. The number of vacant interstitial sites is given by: The total number of recognizable permutations of the atoms must include the recognizable, different configurations of the A and B atoms on the host lattice. Assuming that these arrangements are purely random, and are not affected by the presence of the interstitial species, the total number of recognizable permutations in the ternary alloy is given by: The configurational entropy is obtained by expanding, using Stirling's approximation, and collecting like items, as:

Jan 1, 1969

By Charles E. Lundin

The character of the Er-D system was established by determining pressure-temperature-composition relationships. A Sieuerts&apos; apparatus was employed to make measurements in the temperature range, 473" to 1223"K, the composition range of erbium to ErD3, and the pressure range of 10~s to 760 Torr. The system is characterized by three homogeneous phase regions: the nzetal-rich, the dideuteride, and the trideuteride phases. These phases and their solubility boundaries were deduced from the family of isotherms of the system zchich relate the pressure-temperature-composition variables. The equilibrium plateau decomposition relationships in the two-phase regions were determined from can&apos;t Hoff plots to be: The differential heats of reaction in these two regions are AH = - 53.0 * 0.2 and -20.0 *0.1 kcal per mole of D2, respecticely. The differential entropies of reaction are AS = - 36.3 * 0.2 and - 31.0 * 0.2 cal per mole D2. deg, respectively. Relative partial molal and intepal thermodynamic quantities were calculated from the pure metal to the dideuteride phase. The study of the Er-D system was undertaken as a logical complement to an earlier study of the Er-H system.&apos; The primary interest was to compare the characteristics of the two systems and relate the difference to the isotopic effect. Studies of rare earth-deuterium systems by other investigators have been very limited in number and scope. Furthermore, there is even less information available wherein an investigator has systematically compared a binary rare earth-hydrogen system with the corresponding rare earth-deuterium system. The available information consists primarily of dissociation pressure measurements in the plateau pressure region of a few rare earths. Warf and Korst&apos; determined dissociation pressure relationships for the La- and Ce-D systems in the plateau region and several isotherms for each system in the dideuteride region. They compared these data with those of the corresponding hydrided systems. The study of these systems as a whole was very cursory and did not give sufficient data for a thorough comparison of the effect of the hydrogen vs the deuterium in the respective rare earths. The heat capacities and related thermodynamic functions of the intermediate phases, YH, and YD2, were determined by Flotow, Osborne, and Otto,~ and the investigation was again repeated for YH3 and YD3 by Flotow, Osborne, Otto, and Abraham.4 This investigation studied only these specific phases. Jones, Southall, and Goodhead5 surveyed the hydrides and deu-terides of a series of rare earths for thermal stability including erbium. They experimentally determined isotherms of selected hydrides and plateau dissociation pressures for deuterides. These data allowed comparison of the enthalpy and entropies of formation of the dihydrides and dideuterides. To date, no one rare earth has been selected to thoroughly establish the complete pressure-temperature-composition (PTC) relationships of binary solute additions of hydrogen and deuterium, respectively. The objective in this investigation was to provide the first comparison of a complete family of isotherms of a rare earth-deuterium system with those of a rare earth-hydrogen system. This would allow one to determine what differences exist, if any, in the various phase boundaries and the thermodynamic relationships in various regions of the systems. I) EXPERIMENTAL PROCEDURE A Sieverts&apos; apparatus was employed to conduct the experimental measurements. Briefly, it consisted of a source of pure deuterium, a precision gas-measuring buret, a heated reaction chamber, a mercury manometer, and two McLeod gages (a CVC, GMl00A and a CVC, GM110). Pure deuterium was obtained by passing deuterium through a heated Pd-Ag thimble. A 100-ml precision gas buret graduated to 0.1-ml divisions was used to measure and admit deuterium to the reaction chamber. The reaction unit consisted of a quartz tube surrounded by a nichrome-wound furnace. The furnace temperature was controlled by a recorder-controller to . An independent measurement of the sample temperature in the quartz tube was made by means of a chromel-alumel thermocouple situated outside, but adjacent to, the quartz tube near the specimen. Pressure in the manometer range was measured to k0.5 Torr and in the McLeod range (10~4 to 10 Torr) to *3 pct. The deuterium compositions in erbium were calculated in terms of deuterium-to-erbium atomic ratio. These compositions were estimated to be *0.01 D/Er ratio. The erbium metal was obtained from the Lunex Co. in the form of sponge. The metal was nuclear grade with a purity of 99.9+ pct. The oxygen content was reported to be 340 ppm and the nitrogen not detectable. Metallographically the structure was almost free of second phase (<i vol pct). A quantity of sponge was arc-melted for use as charge material. The solid material was compared with the sponge in the PTC relationships. They were found to be identical. Therefore, sponge material was used henceforth, so that equilibrium could be attained more rapidly. The specimen size was about 0.2 gr for each loading of the reaction chamber. The procedure employed to obtain the PTC data was to develop experimentally a family of isothermal curves of composition vs pressure. First, a specimen

Jan 1, 1969

By S. Luszcz, R. W. Vook, Fred Witt

In situ X-ray investigations were made on polycrys-talline silver films deposited by vacuum evaporation on (111) CaF2 and (100) NaCl single-crystal substrates at 80°K. The films were evaporated and annealed in an X-ray diffractometer attachment having a residual gas pressure of 2 x lo-&apos; Torr. All measurements were made without exposing the films to the atmosphere. Measurements were made on the films in the as-deposited state and after various annealing treatments. The intrinsic stacking and twin fault densities, the magnitudes of the uniform and nonuniform strains, and the crystallite sizes were determined. In addition the textures in the films were measured qualitatively. The results obtained for the as-deposited films on single-crystal substrates are in substantial agreement with previously reported results for silver films deposited on glass. Intrinsic stacking and twin faults, as well as uniform and nonuniform strains, were present in these films. During the various annealing treatments (up to 350°C) the faults and nonuniform strains annealed out. Considerable grain growth and texture changes occurred also. The effects were much greater for the NaCl substrate than for the CaFz substrate. The relative magnitudes of the grain growth in the variously oriented grains could be explained qualitatively in terms of the thermal strains and strain energies introduced into the differently oriented grains during the initial, irreversible anneal. These strains were due to the different thermal expansion coefficients of the film and substrate. X-RAY diffraction measurements on evaporated films deposited on substrates at low temperature have the advantage that many of the imperfections introduced into the film during deposition are "frozen in". Thus, the influence of a very important experimental variable, substrate temperature, on the imperfection structure of evaporated metal films may be studied. Moreover, the effects of annealing such films makes possible the study of thermally activated recovery processes in these films. The present study was designed to determine the influence of single-crystal substrates on the resultant film structure relative to the previous results obtained using glass substrates.&apos; To this end great care was taken to keep the experimental variables the same in the two cases. Different experimental conditions would, of course, result in films having different physical properties. Again the initial substrate temperature was in the neighborhood of 80°K and the films were subsequently annealed to 350°C. The pure metal silver was chosen for evaporation, primarily because of its relatively low stacking fault energy and consequent high fault density in the as-deposited state. The silver films were formed by evaporation onto air-cleaved {ill} CaF, and (100) NaCl surfaces cooled to 80°K in an X-ray diffractometer attachment2 having a base residual gas pressure of 2 X l0-&apos; Torr. The films were not exposed to the atmosphere until all of the X-ray data had been recorded. In this way one of the most important experimental variables, environment, could be well-controlled and reproduced. X-ray measurements were made at the temperature of deposition and included determinations of the diffraction line peak positions, line shapes, and integrated intensities. The peak position measurements were used to determine the intrinsic stacking fault densities and the average uniform strain in the film. The shapes of the diffraction lines provided information on the twin fault density, true crystallite size, and average nonuniform strain. The preferred orientation in the film was determined qualitatively from the integrated intensities. I) EXPERIMENTAL PROCEDURE The evaporator attachmentZ was charged with 99.999 pct Ag pellets positioned in a tantalum filament which had been outgassed previously at l0-8 Torr. The CaFz and NaCl single crystals were cleaved in air and then placed in position in the chamber so that their cleavage surfaces were on the diffractometer axis. The chamber was prepumped using a sorption pump, sealed off, and then baked at 150°C for 24 hr. The ion pump operated during the bakeout cycle. The substrate was then heated to 500° C by means of an auxiliary heater and kept hot until the rest of the chamber was cooled slowly to room temperature. This bakeout procedure consistently resulted in an ultimate pressure in the low lo-&apos; Torr range. The substrate was then cooled down on 80°K. Its temperature was monitored by a thermocouple wedged into the rear of the copper substrate holder. The diffracted intensity and peak position of the 111, 222, and 333 CaF, lines were measured prior to evaporation. Nickel-filtered, pulse-height-discriminated copper radiation was used. Similar measurements were made for the 200 and 400 lines from NaC1. These measurements were used as a lattice parameter check and to determine the thickness of the evaporated silver films from the attenuation of the substrate lines. The evaporation rates were approximately 3A per sec for both films while the maximum pressures during evaporation were 3 x lo- &apos; and 7 x 10"8 Torr for the CaF, and NaCl cases, respectively. The film thickness was measured by the attenuation of the CaF, and NaCl substrate lines and by at optical interference method. Values of 1700 and 1500A, respectively, were obtained for the silver

Jan 1, 1969

By M. H. Richman, W. D. Sproul

THE indexing of a field-ion micrograph is in many cases similar to the indexing of the poles of a stereo-graphic projection.* If one has a standard projection as a guide, the task of indexing is relatively simple. In this way, field-ion micrographs of bcc and fcc wires have been oriented from projections available in most any text on X-ray diffraction. These books always illustrate the projections for the bcc and fcc structures and even for a particular hcp structure. There is no "standard" hcp projection because the angles between planes depend on the c/o ratio of the unit cell. In order to index field-ion micrographs of hcp metals, one must compute the angles between various planes—a rather laborious task. In recent work,, we have had to identify the structure and index the orientation of field-ion micrographs of the compounds WC and W,C. To overcome the problem of computing angles by hand or calculator, a program was written in Fortran lV for use on the IBM 360, Model 50 which will compute all angles between planeswith indices (hlklll) and (17,k,l2) in the range from (447) to (444) for any given c/o ratio. The program, which is more specific than that of Camp and clum, was so written as to take advantage of the multiplicity of the hexagonal system, and, for the limits defined above, only 26,649 values out of a possible 265,721 values had to be computed. This is a 90 pct saving in time (and cost) and was accomplished in the following way. Because the lattice parameters of the hexagonal crystal system are defined such that: a = b * c [1] the I index does not enter into the multiplicity (i.e., it cannot be transposed with the h or k indices), and all possible values of h and I, from 4 to 4 must be used—a total of eighty-one combinations. The index h2 varies the most—it must assume values from - Ill,: to 3Ihl. The indices kl and k2 are always equal and vary

Jan 1, 1969

By M. E. Straumanis, R. P. Shodhan

LATTICE parameters of molybdenum of various purities are summarized in Table I. The latter shows that the parameter fluctuates between 3.1467 and 3.1475A. The room-temperature expansion coefficient a is also not well-known as values from 4.90 to 5.20 x 10-6 can be found in the literature.=-&apos; It, therefore, seemed appropriate to repeat the measurements under exactly controlled conditions, using high-purity Hilger molybdenum powder (containing 0.0015 wt pct of Fe, 0.005 of Si and traces of other elements) and a 99.95 pct pure Sylvania Electric preparation (containing Cr, Fe, Ni, Si, Sn, and C in amounts of 50 ppm of each and in still smaller amounts Cu, Pb, Mg, and Mn). Of course, both samples could have contained at least 0.01 pct of oxygen in form of a surface oxide. However, oxygen, because of its small solubility in molybdenum, does not influence its lattice constant.g The determinations were made in a cylindrical precision X-ray camera, 64 mm in diam, the temperature of which was controlled within *0.05"C, by inserting it into a special thermostat." To exclude the film shrinkage effect (after the development of the film), the asymmetric film placement method was used." Absorption corrections (e.g., by extrapolation)" were unnecessary because of the use of a thin Li-B-glass fiber (about 0.08 mm in diam) which was fastened to the sample holder of the camera and dusted with the fine molybdenum powder. Cum radiation of the wavelength 1.389350 kX was applied because it produced in 30 min the line (420) having a high Bragg angle of about 81.6 deg. The conversion factor of 1.00202 gave the results in angstroms. To obtain the expansion coefficient a, exposures were made at various temperatures t, see Fig. 1, on at least two films at each temperature. The films were measured with a componator and the lattice constants a were calculated. The expansion coefficient was found from: where a2s is the constant at 25°C and A is the change in a and t. The same equation (knowing a) was used to reduce all the constants obtained at various temperatures to that of 25"C, Table 11. The probable error S507p (at a 50 pct confidence limit) was calculated from the reduced constants:

Jan 1, 1969

By L. C. Brown, E. B. Hawbolt

If a single-phase alloy is rapidly cooled such that insufficient time is available for an equilibrium transformation to occur, the high-temperature phase may be retained to room temperature or may undergo a massive or martensitic reaction. The massive or martensitic product develops without a composition change and usually has a crystal structure approximating an adjacent equilibrium phase. The characteristics of a massive transformation are intermediate between the equilibrium reaction in which long-

Jan 1, 1969

By Colin M. Sargent

ALTHOUGH annealing twins are frequently observed in many fcc metals, their occurrence in aluminum is relatively rare. ~ahn&apos; in his review of twinning has listed only a few references to observations of twins in aluminum, e.g., Refs. 2 and 3. They have also been shown to occur in evaporated aluminum layers.4 During the present work, several annealing twins were studied in aluminum. The specimens of 1099-grade aluminum had the following thermomechanical treatment: deformed 90 pct by rolling, partially re-crystallized, further deformed 60 pct to a final thickness of 100 p, then annealed for 24 hr at 120°C. This treatment produced several annealing twins—-about ten per electron microscope specimen. The specimens were produced by the window technique and examined in a Phillips E.M. 200 operating at 100 kv. A typical twin boundary is shown in Fig. 1. For several of the twins studied the twin plane could be tilted so that it was parallel to the electron beam, e.g., Fig. 2. The associated diffraction pattern, Fig. 3, shows the twinned relationship between the grains. The twinning plane in each case was (111). Use of a reflection common to both the twin and the matrix,* i.e., using reflecting planes parallel in the twin and the matrix, the coherent twin boundary becomes invisible and only the noncoherent segments of the stepped boundary are seen, e.g., Fig. 4. Trace analysis of the boundaries showed that the long straight portions were invariably the twin plane; i.e., these portions are coherent. The planes of the shorter segments are shown by Fig. 5 to be (551 1, (7111, and {211).

Jan 1, 1969

By Raymond D. Daniels, Frank E. Rizzo, James D. Gerber

ThIS discussion describes a method for the addition of small amounts of oxygen to columbium (niobium) in an accurate and reproducible manner. The method is based on the complete reduction by columbium of a carefully weighed amount of another metal oxide. The equilibrium Pq associated with Cb-CbO mixtures is extremely low, e.g., 10"25 atm at 100O°C, and the pressures over Cb-0 solutions are even lower. The equilibrium Pq associated with a given metal-metal oxide mixture can be easily obtained, with the aid of a Richardson-Jeffes chart.&apos; Although columbium should effectively reduce almost any metal-metal oxide combination, the proper choice of a metal-metal oxide system is complicated by the low rate of oxygen transport in the gas phase at low oxygen pressures and the difficulty in reducing any columbium suboxide formed during the reduction of the oxygen source material. Thermodynamically, oxide formation on columbium will be avoided so long as the oxygen partial pressure over the columbium is below the equilibrium pressure associated with the mixture Cb-CbO. The logical choice of a source for oxygen would appear to be a mixture of Cb-CbO, since oxide formation would be precluded by nucleation difficulty. But calculations using the kinetic theory of gasses indicate that, for a temperature of 900°C, the reaction would proceed too JAMES D. GERBER, formerly Research Assistant, University of Oklahoma, Norman, Okla., is Research Metallurgist, Air Force Weapons Test Laboratory, Kirtland Air Force Base, N. Mex. FRANK E. RIZZO, Junior Member AIME, formerly Assistant Professor of Metallurgy, University of Oklahoma, is Associate Professor of Metallurgy, University of Texas at El Paso, El Paso, Tex. RAYMOND D. DANIELS, Member AIME, Professor of Metallurgical Engineering, University of Oklahoma, is an NSF Fellow, Institute de MBtallurgie Structurale, Universite de euch:tel, Neuchitel, Switzerland. Manuscript submitted October 28, 1968. IMD

Jan 1, 1970

By R. W. Heckel, R. A. Tanzilli

ANALYTICAL results have previously been presented for the diffusion-controlled solution of a second phase in a finite medium for planar, cylindrical, and spherical geometries.&apos; These results were obtained by numerical methods using digital computer techniques and are applicable not only to the stage of the problem where the unstable phase shrinks to zero size, but also the subsequent stage where the concentration gradients in the matrix phase become negligible (essentially complete homogenization). It is anticipated that the results of such an analysis may be of use to those workers who are interested in the processes

Jan 1, 1970

By R. M. Waterstrat

The phase VPt has been reported to have a crystal structure of the B19 (AuCd) type at low temperatures.&apos;&apos;&apos; A recent investigation3 has indicated that this phase forms by an ordering reaction from the disordered fcc Pt(V) solid solution which is stable at high temperatures. olander4 has shown that there exists a close structural relationship between the orthorhombic B19 structure and a fcc structure possessing the L1 , (CuAu) type of atomic ordering. One may derive the B19 structure by a shear-like displacement of the atoms in the (002) plane of the ordered fcc lattice along the (010) direction through a distance equal to one eighth of the unit cell dimension, see Fig. 1, followed by an orthorhombic distor; tion of the cube axes such that a = 2.693A. h = 4.413A. and c =4.767A (estimated uncertainty 0.005A). Filings of this phase were produced by grinding a VPt alloy having the B19 structure with a diamond dental grinding disc. When these filings were subjected to X-ray diffraction examination, a pattern of a severely cold-worked fcc structure was obtained. higher solution temperature used (1200 C) or to a much lower oxygen pressure than he reported, due to transfer through many bends and tubes in his complicated apparatus. An interesting observation was made when an oxygen addition was attempted in a cylindrical sample of columbium in the cold worked condition rather than in the annealed condition. The interior of the sample re-crystallized during the oxygen addition at 900°C. The periphery, however. (1 mm) did not recrystallize. A similar sample without oxygen recrystallized throughout the entire cross section. It appears that the re-crystallization is hindered by interstitial oxygen. Presumably, the interior recrystallized before appreciable oxygen could diffuse into the core. This work was supported by the United States Atomic Energy Commission. When the filings were annealed in a high vacuum furnace for 15 min at 110O0C, however. they returned to the B19 structure perhaps as a result of reordering. Subsequent less-severe cold-working of these filings by grinding in a hardened steel mortar and pestle at room temperature produced a transformation into a cold-worked L1, structure which was slightly tetragonal. Thus it appears that the degree of deformation may influence the final structure. Considerable line-broadening was observed in X-ray diffraction patterns obtained from the cold-worked filings and therefore no attempt was made to obtain accurate lattice parameters. Vacuum annealing treatments at 1100&apos;C intended

Jan 1, 1970

By Edward A. Loria

Vanadium is one of the materials being considered for use in fast-breeder nuclear reactors. It is a good heat conductor and nearly transparent to radiation, properties regarded as ideal for nuclear fuel containers. The problem has been the metal lacks ductility needed for forming. In our program at Reno Laboratory the effects of the U.S. Bureau of Mines (previous affiliation) the effects of oxygen, nitrogen, and carbon have been reported21,22 nd most recently the effects of boron and boron with carbon.23 The continuing study by the Ames Laboratory of the effects of hydrogen, the most subtle and fugitive element in its relationship to structure and properties, is commendable. The solubility of oxygen, nitrogen, and hydrogen in vanadium (and other bcc metals as well) is related to material purity. With the available limit on metal purity and the interaction (clustering) of hydrogen with the other interstitial and substitutional elements present in their base metal, would the authors comment on the tolerance of hydrogen in relation to oxy- gen that will avoid intergranular fracture and above what content or how seriously harmful in oxygen at various carbon levels? Understanding the true effects of hydrogen (and other interstitial impurities) in vanadium depends on knowledge of the amount present under various conditions and its distribution between various possible positions. Significant amounts of hydrogen may be in "thermo-dynamic" solution, but not as individual atoms in interstitial positions. It may be in grain boundaries, in subgrain boundaries, in vacancies, or in dislocations. Some of the hydrogen may be paired or in complexes with impurities in substitutional solid solution in vanadium. This makes the analysis of the effect of hydrogen vastly more difficult. It should not be expected that hydrogen in grain boundaries will affect slip in the same manner as hydrogen in interstitial positions, nor will the complexes react to heat treatment the same way as hydrogen in dislocations. It is gratifying that the authors have quoted results from two of our inestiations,&apos; but neglected one2&apos; which applied the Petch theory to electrorefined vanadium of high purity and analyzed the effects of oxygen, nitrogen, and carbon on the ai and ky values obtained by the extrapolation and grain size methods. Details can be found in the paper. Briefly, we obtained a ui value of 10,300 psi (t = 5150 psi) at 273°K. The metal also exhibited profuse twinning with high ductility at 123" and 77°K. Nitrogen was more effective than oxygen in increasing ui, the increase being about twice as much for the same impurity level. Carbon additions resulted in only minimal changes in Ui. The corresponding ky increased as oxygen and nitrogen increased, with nitrogen being more effective. Carbon additions resulted in little change. Although the difference in yield strength of vanadium was explained on the basis of the Cottrell-Bilby model of the tearing away of dislocations from the impurity atoms,

Jan 1, 1970

By W. A. Backofen, N. E. Paton

DEFORMATION twinning contributes to the plasticity of titanium and has been reported on {10i2}, {1121},{11221}, {1123}, and {1124} planes.&apos; Twinning on {1011} has also been reported in commercially pure titanium as a result of quenching from 1000&apos;, but no reports of such twins occurring as a result of deformation alone are known to the authors. In this study single crystals grown from iodide titanium were compressed parallel to the c axis over the temperature range 25 to 800°C. From it has come evidence that (10il) deformation twins are the most common type between 400" and 800°C. Crystals about 6 mm high with a rectangular cross section measuring about 3 by 4 mm were used in the tests. Chemical analyses showed them to contain 220 to 250 ppm 0 arid 10 to 15 ppm N. The long axes of the crystals were made parallel to the c axis while the sides were parallel to (i100) and (1120), as shown in Fig. 1. The crystals were compressed between polished alumina platens with no lubrication, in a vacuum of 2 x lom5 torr. Between 25&apos; and 300°C the predominant twinning mode was (11221, which is to be expected for this stress state. There was an abrupt change at 400°C, however, and from that temperature up to 800°C twinning took place almost entirely on (10i1 ). Twin planes were determined by the two-surface rnethd. Measurement of the crystal orientation within several (10i1) twins by means of polarized-light4 and transmission electron microscopy showed that the lattice reorientations were the same as those previously reported for the (10i l ) twinning in magnesium.&apos; This reorientation is consistent with The calculated (10il ) twinning shear for titanium is 0.10, while that measured from surface offsets on a (1150) face, which is parallel to the shear direction, was about 0.15. Slip within the twins, or in the matrix adjacent to the twins, probably accounts for the larger measurement. Slip in both locations was judged to have occurred from observations on foils in the electron microscope.

Jan 1, 1970

By H. Biloni, H. R. Bertorello

GruZLESKI and winegard1 have recently reported on the origin and development of the cellular substructure in Sn-Cd eutectic unidirectionally grown with different amounts of constitutional supercooling (CS). This communication deals with the results obtained in a parallel study on the instability of a plane interface in Al-Cu eutectic unidirectionally grown. Similarities as well as differences with the results of these authors1 will be presented. A1-Cu eutectic alloy ingots of 99.999 pct purity were grown unidirectionally under different G/R ratios where G = thermal gradient in the liquid, R = solidification rate. The ingots were cut in slices perpendicular to the solidification axes and the substructure studied on parallel sections following the sense of growth. It was generally found that the last part of the ingot to solidify presented a well developed colony substructure as a result of impurity build up and constitutional supercooling. The results obtained were: 1) When the structure was observed with low niagnification (of the order of 150 to 300 times) the first instabilities were observed at the grain boundaries and node-like structures formed at the junctions of the growth-induced boundaries, as reported by Gruz-leski and Winegard.1 Inside the grains the first signs of instability appear later and correspond to the type shown in Fig. 1; this is a two dimensional cell substructure. &apos; 2) Figs. 2 and 3 correspond to the evolution from a two dimensional substructure to a cellular type. In the A1-Cu eutectic the boundaries of the two dimensional cell are always perpendicular to the laniellaes instead of parallel as in the Sn-Cd eutectic. 1

Jan 1, 1970

By P. O. Metz, E. L. Wiehe, J. S. Foster

BASED on their analyses of growth kinetics, ibbs&apos; and Harris et al.&apos; have recently proposed that the rate of subcritical graphitization of steel is controlled by the rate of diffusion of carbon in ferrite. illert has concluded that this is the rate controlling growth mechanism when the growing graphite particles are relatively large. Harris et al.&apos; also propose that the matrix surrounding a growing graphite particle is plastically deformed to make room for the growing particle. If this plastic deformation does occur, then preferred recrystallization may be observed around the larger particles. If diffusion of carbon in ferrite is rate controlling, then a graphite particle growing in a matrix of, say, tempered martensite or pearlite, should be surrounded by a carbide depleted zone. Thus, the simple metallographic experiments reported here are sufficient to determine whether or not diffusion of carbon in ferrite is the dominant mechanism for the growth of graphite in steel. The present investigation considers graphitization in five alloys. The compositions are given in Table I. Graphitization was carried out at three temperatures: 900°K (627"C), 950°K (677"C), and 990°K (&apos;717°C). Samples were reacted in both the martensitic and the pearlitic initial conditions. In the hypoeutectoid steels, Sets 7 and 8, .and in the hypereutectoid Fe-C binary, Set 6, graphitization was very limited after 1000 hr at temperature. In these samples graphite particles observed were less than 10 p in diam. In the hypereutectoid commercial steels, Sets 1 and 3, large graphite particles (100 p) did not appear until after 250 hr at temperature. The limited number of graphite particles observed and the range of sizes obtained prohibited measurement of growth rates in this investigation. However, in all samples showing graphitization, neithe a carbide depleted zone nor recrystallization was observed. illert&apos;s model predicts that diffusion of carbon in ferrite should become dominant for graphite particles larger than about 300 p in diam. The largest graphite particle observed in this investigation was approximately 450 p in diam. No evidence of carbide depletion was noted. Fig. 1 shows a typical graphite particle. This nodule is from an initially pearlitic sample from Set 3 after

Jan 1, 1970

By R. E. Miner, J. K. Jackson, T. L. Wilson

THE nature of the decomposition reactions producing hardening in aluminum-rich A1-Ag alloys is now fairly well understood. The silver is not uniformly dispersed even at temperatures above the solvus line: rather, it is clustered into zones and associated with dislocations.&apos; During quenching, nearly all of the silver segregates into zones&apos; and some is attracted to dislocations, producing stacking faults. Growth of these faults produces the semicoherent y precipitate.1 During aging, the larger zones and the y precipitates grow at the expense of the smaller zones. The large zones persist up to about 350°C; where they redissolve in favor of the y&apos; and y precipitates.&apos; The equilibrium hcp y precipitate occurs both by a cellular reaction at the grain boundaries1 and by growth of the Y&apos; plates to a critical size where incoherency results. Damask and Nowick 4 observed an internal friction peak in an A1-6 at. pct Ag alloy at about 140°C (0.25 cps). The peak was found to exhibit a systematic instability. After aging at successively higher temperatures between 155&apos; and 23Z°C, the peak first migrated to higher temperatures while increasing in height, then returned to lower temperatures and decreased in height. After aging at temperatures above about 200°C, the peak position remained constant while the height decreased very slowly. In quenched specimens, elastic after-effect measurements inhcated a rapid initial transient in peak position from low temperatures up to 155°C. The authors concluded that a stress induced growth and resolution of the clusters and the 7&apos; was the most reasonable mechanism to account for the behavior. It would seem, however, very unlikely that both the clusters and the y&apos; precipitate would provide damping contributions whose relaxation time and activation energies were identical, which is required for them to produce the same internal friction peak. The present investigation was motivated by this apparent anomaly and the development of a very low thermal inertia torsion pendulum5 capable of monitoring transient behavior. Low frequency internal friction measurements were made on four binary A1-Ag alloys nominally containing 5, 10: 15, and 20 at. pct Ag. The results of measurements made on a 10 at. pct Ag alloy in the quenched condition are shown in Fig. 1. There are two peaks apparent in the spectrum, one centered at about 160°C, the second at about 210°C. The two peak spectrum was observed in each alloy, but it was best resolved in the 10 pct Ag specimens. Because of the instability in the internal friction, 4 it seemed possible that the second peak was not a peak at all, but simply a manifestation of a single, sharply transient, peak. This effect has been observed in Au-Ni alloys.6 The existence of the higher tempera-

Jan 1, 1970

By Thomas C. Wilder

ALTHOUGH there is an abundance of thermodynamic information available in the literature today, no experimental data on the standard molar properties of formation of zinc oxide have ever been reported for the temperature range 419.5" to 908°C. This is the temperature range for which zinc metal is a liquid. so that the formation reaction is: Data have been reported for Reaction [I] where zinc is a solid or a gas. Maier. Parks, and nderson&apos; measured the electromotive force of the cell: in order to obtain the free energy of the reaction: over a limited temperature range. With the known properties of H2O, those of ZnO were calculated. These workers found that t;j of ZnO is -75,930 ± 150 cal per gfw and Mtf is-83,000 300 cal per gfw at 25°C. akolkin made similar measurements to obtain ilF7 and AH; of -75,870 and -82,540 cal per dw respectively at the same temperature. Truesdale and arirlg and Kitchener and 1gnatowicz4 measured the equilibrium of the reactions: respectively, in order to determine Ff of ZnO from the known values of CO, CO2, and H/X The thermodynamic properties of ZnO, presumably taken from the above investigations, are tabulated by Kubaschewski and vans&apos; and Wicks and Block" The latter reference also gives values for the range where zinc is a liquid. These numbers are probably acquired from the known extremities of the range plus Cp data of the components. In the present work the electromotive force of the cell: was measured in order to calculate the properties of ZnO from the well known values of NiO for the temperature range where zinc is a liquid. In Cell [B] the cathode reaction is: and at the anode: The overall reaction is: for which the free energy change is: where is the electromotive force in volts of cell [B] after correction for the Pt-Ta thermocouple. The standard molar free energy of formation of NiO is very well known as a function of temperature. Kiukkola and agner&apos;s data are used in most tabulations. The error is probably less than I00 cal per gfw, The latter authors were the first to use solid mixed oxide electrolytes in galvanic cells. Their work with NiO and other oxides was performed with cells similar to Cell [B] using a variety of reference electrodes of fixed oxygen potential. There may be a small composition range for which either NiO, ZnO or both exist. If nonstoichiometry does exist for these oxides, then the properties described herein are those for the metal saturated compositions. The simple cell design was the same as described elsewheres except that the molten metal electrode was about 125 g of pure zinc including a small (0.25 to 0.50 g) amount of ZnO. The mixture of pure nickel and NiO powders making up the reference electrode was contained in a tube of the ZrOl + CaO electrolyte which was immersed in the molten zinc. A platinum contact was made to the reference electrode; tantalum to the zinc. A refractory cement plug was necessary at the open end of the electrolyte tube in order to prevent zinc vapor from contaminating the reference electrode. Experimental details such as the vessel containing the cell, furnace, temperature control and measurement, and electromotive force determinations of the cell have all been outlined previously. The temperature was varied randomly in the range between the freezing and boiling points of zinc. After each temperature change, time was allowed for the drift at the new temperature to be less than +;"c whereupon a series of three cell readings was taken at least 10

Jan 1, 1970

By C. Laird, C. E. Feltner

IN previous workif2 we have shown that the steady state cyclic stress response of pure copper tested in the low cycle fatigue range was determined only by the plastic strain amplitude and the test temperature. hus, copper, at any given temperature, has a unique cyclic stress-strain curve independent of prior history. Cu-7.5 wt pct Al, however, showed a stress response for a given plastic strain amplitude and temperature which depended sensitively on prior history. From this work we predicted that all wavy slip mode materials, typified by copper, would have a unique cyclic stress-strain curve; whereas all planar slip mode materials, typified by Cu-7.5 pct Al, would not. This prediction has now been tested for a number of materials of widely varying crystal structure and slip character. Wavy slip mode materials studied include: Fe. Al, Cd, disordered FeCo-V, and Cu-3 pct Co (quenched and aged). Planar slip mode materials investigated include: Fe-3 pct Si, ordered FeCo-V, disordered Ni3Mn, ordered Ni3Mn, and Zn. The treatment and properties of these materials are listed in Table I. Cyclic stress-strain curves were determined by controlled plastic strain tests (see Ref. 1 for details) at room temperature for all materials in both the initially annealed and cold worked conditions. The results obtained for iron and Fe-3 pct Si are typical of wavy and planar slip mode materials, respectively. The cyclic stress-strain curves for these materials are shown in Fig. 1 and it can be seen that iron has a unique cyclic stress strain curve while Fe-3 pct Si does not. Aluminum, Cu-3 pct Co, and disordered FeCo-V showed a behavior like that for iron, while Ni3Mn in both the disordered and ordered condition behaved in the same manner as Fe-3 pct Si. These results therefore support the general conclusion drawn in Refs. 1 and 2 that. for wavy slip mode materials, a cyclic mechanical equation of slate it =t.(hcp, i. T) is approximated in which the satura-

Jan 1, 1970

By L. W. Sink, B. H. Kear, S. M. Copley, M. F. Hornbecker

IT is well known that under appropriate conditions of chill casting, many metals and alloys develop a columnar grain structure having a high degree of preferred orientation.&apos; In cubic materials, this principle has been employed to produce shaped castings with a unidirectional cube oriented columnar grain structure as well as shaped single crystals with a cube axis parallel to the growth ais.&apos; "he purpose of this note is to describe how this same principle can be enlployed to produce wires, rods, or more complex crystal Shapes with a variety of conlpositions in cube or random orientations by a single casting operation. The procedure for directional solidification of in Fig. 2. Examination under crossed polarizers indicated that the striations were a second phase (presumably the B19 phase) which frequently forms initially at primary grain boundaries and then grows toward the interior as thin ribbons. X-ray studies on filings of this alloy reannealed at 1300°C for 15 min indicated a strong pattern of the fcc phase together with a substantial pattern of the B19 phase. The un-annealed filings, however, showed only the pattern of a cold-worked, fcc structure. In these two-phase alloys it appears, therefore, that the B19 phase is transformed into a disordered fcc structure by cold-working. The mechanical properties of these alloys would be of some interest since a fcc structure might be expected to possess greater ductility than the or-thorhombic B19 structure from which it forms. The author wishes to thank Mr. Harvey Yakowitz and Mr. Richard Manuszewski for obtaining the photomicrograph in Fig. 2. This research was partially supported by Research Grant DE-02455 from the National Institute of Dental Research. columnar grained ingots involves pouring a melt into a preheated mold having a water-cooled copper chill at its base? and controlling the temperature gradient in the mold so as to maintain columnar grain growth from end to end of the ingot.4 This is illustrated schematically in Fig. l(a). It should be noted that the longitudinal temperature gradient promoting unidirectional columnar grain growth is maintained by heat loss primarily through the solidifying ingot to the chill, so that both the temperature gradient and the growth rate diminish with increasing distance from the chill. As the distance from the chill increases? the columnar structure coarsens, and the perfection in preferred orientation tends to increase progressively. Using this same procedure of gradient solidification, Fig. l(b) shows a simple scheme for producing a batch of crystals having the same cube orientation rather than an assemblage of columnar grains. Wires and rods are produced by cementing ceramic tubes to the wall of the mold. The steep temperature gradient produced in the central chamber is controlled by the mold heater to produce favorable conditions for crystal growth. Clearly the success of the operation lies in the selection of individual growing columnar grains by some kind of orifice at the base of each channel in the mold. Using simple constrictions, experience with nickel-base alloys has shown that 4 -in.-diam holes at a distance of -1 in. from the chill yield crystals within 7 deg of (100); closer control of orientation is possible by placing the crystal selector farther away from the chill.

Jan 1, 1970

By Michael A. Arkoosh, E. A. Peretti

ANALYTICAL results have previously been presented for the diffusion-controlled solution of a second phase in a finite medium for planar, cylindrical, and spherical geometries.&apos; These results were obtained by numerical methods using digital computer techniques and are applicable not only to the stage of the problem where the unstable phase shrinks to zero size, but also the subsequent stage where the concentration gradients in the matrix phase become negligible (essentially complete homogenization). It is anticipated that the results of such an analysis may be of use to those workers who are interested in the processes

Jan 1, 1970

By B. C. Wonsiewicz, W. W. Wilkening

Following a procedure proposed by Wheeler and Ireland, Plane stress yield loci were constructed from Knoob hardness numbers. Basically, six differently oriented hardness measurements were made on three orthogml surfaces through pure poly crystalline magnesium sheet, a magnesium single crystal, and sheet of the magnesium alloys: Mg + 0.5 pct Th, Mg + 4 pct Li, AZ31B, and EKOO. Hardness loci were found to be in poor agreement at small strains (E < 0.05) with loci established by a more rigorous technique. At larger strains (E - 0.10) the agreement is fair, but at this stage in deformation the conventional locus has lost much of the asymmetry that characterizes these anisotropic materials. Two effects which will lead to distortions in the Khn locus are discussed with reference to the geometry of plastic flow during a hardness test. DETERMINING a material&apos;s resistance to multiaxial loading is of interest not only from a structural design viewpoint but also from that of deformation processing. Unfortunately, the determination of the yield locus, although simple in principle, involves tedious procedures if the results are to be at all rigorous.&apos; The idea, first proposed by Wheeler and 1reland2 of determining the yield locus by means of six Knoop hardness impressions along the principal directions in a material has obvious appeal. It is simple, quick, and should be applicable to very thin sheets. If such a technique could be demonstrated to produce consistently reliable results, it would be of interest to both researcher and designer. Lee, Jabara, and ackofen have compared the yield locus determined by Knoop hardness measurements (the Khn locus) to a locus determined by more rigorous techniques. They found good agreement for two titanium alloys at a plastic strain of about 1 pct. The purpose of this paper is to investigate if the Khn locus construction is a reasonable approximation to the locus of a highly anisotropic material. Examples of such materials are magnesium and magnesium alloys which have severely distorted yield loci which in turn reflect markedly dfferent yield strength in different directions.&apos; In pure magnesium, for example, the yield stress in tension along the transverse direction may be four times the yield stress in compression in the same direction and twice the tensile yield stress in the rolling direction. Predicting such large differences ought to serve as a severe test of the Khn locus construction. EXPERIMENTAL PROCEDURES Samples of rolled sheet, 0.250 in. (6.35 mm) thick, of pure magnesium and four magnesium alloys (Mg experimental materials. The pure magnesium together with the lithium and thorium alloys were those used in the study of Kelley and Hosford. The grain size was ASTM number 4 for the pure magnesium and number 6 for the alloys. HARDNESS TESTING The materials were sectioned along the rolling and transverse planes, mounted in a quick setting resin, and mechanically polished. Most of the hardness tests were performed on a surface prepared by electro-polishing (30 pct nitric acid in methanol at 0°C and 20 v) with the exception of the AZ31B and EK00 alloys which were made directly on a metallographically polished surface. However, subsequent hardness tests on the same sample after heavily electropolishing, revealed essentially the same hardness as before. At least twenty Knoop hardness impressions under a 100-g load were made in each of the six orientations shown in Fig. 1. The average hardness number and standard deviation were then calculated for each orientation. CONVENTIONAL LOCUS CONSTRUCTION Yield loci were constructed using a technique described in detail by Lee and ackofen,&apos; in which the flow stress (stress at a given plastic strain) fixes the coordinates of a point on the locus and measurements of the strain ratio serve to establish the slope of the locus at that point. The loading paths which correspond to uniaxial tension or compression tests establish the four intercepts of the locus with the coordinate axes plus one point on the balanced biaxial tension line Tensile testing was performed along the rolling and transverse (r, t) directions. Samples had a uniform rectangular gage length 1 by 4 by 4 in. (25.4 by 6.35 by 6.35 mm) and were deformed at a strain rate of 3.33 x 104 sec-&apos;. The tests were interrupted periodically to unload the sample and measure the plastic strains by means of X-Y post yield strain gages. Compression tests in the rolling, transverse, and through-thickness (r, f, z) directions were performed on 1/4 in. (6.35 mm) cubes at an initial strain rate of 8.33 x sec-&apos;. Lubrication was provided by 0.002 in. (51 pm) Teflon sheet which was renewed after unloading for micrometer measurements used to calculate the strains.

Jan 1, 1970