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By R. E. Ogilvie, N. L. Peterson

Intevdiffusion and intrinsic diffusiorz coefficients were determined in the uranium-niobium system from diffusion couples analyzed with an electron microbeam probe. A Previously unveported intermediate phase, designated in this report as the delta phase, was found to exist along the mobium-rich side of the miscibility gap. Its composition width was determined from the concentration gradients in the diffusion couples. The presence of this phase was also confirmed by microhardness analysis and metallographic observations. THE excellent corrosion resistant properties, high-temperature strength and reasonable nuclear properties of niobium have prompted its use as an alloying element with uranium and as a possible cladding material for reactor fuel elements. Hence the formation and growth of intermetallic phases as well as diffusion data for the uranium-niobium system are of considerable practical importance to metallurgists and nuclear engineers. Diffusion zones may exhibit varying degrees of complexity dependi.ng upon the mutual solubility of the metals involved, and the intermediate phases which may form. In the simplest case where the metals exhibit a calmplete range of solid solubility, a single phase region is produced. Generally, however, the metals may react to produce a multiphase diffusion zone containing several layers of intermetallic phases. A number of investigatorsl-6 have analyzed the concentration gradients present in diffusion couples in order to investigate phase equilibria and solu- bility limits. If diffusion is the rate-controlling process in establishing a concentration gradient, the compositions at the interfaces of the intermediate phases will represent the equilibrium values expected from the phase diagram at the temperature at which diffusion has taken place. No published information is available at this time on diffusion in the uranium-niobium system. A number of investigators7-" have contributed information to the construction of the uranium-niobium phase diagram from other than diffusion techniques. There is good agreement on the high uranium side of the phase diagram, but the high niobium side of the miscibility gap still remains somewhat in doubt. The phase diagram as determined by B. A. Rogers, et al.7 is shown in Fig. 1. The present work was aimed at obtaining fundamental information about the solubility limits of the miscibility gap and diffusion in the uranium-niobium system. A Kirkendall effect, which might be expected on the basis of the rather large difference in melting points between uranium (1132°C) and niobium (2415" C), was also investigated. The concentration gradients were measured by an electron microbeam probe technique, similar to that used by Castaing,l2 Adda and philibert,13, l4 and Macres.4

Jan 1, 1961

By T. A. Read, M. W. Burkart

The crystal geometry of the cubic-tetragonal interface after partial transformation of an indium-thallium alloy single crystal is described and a general theory is presented. The effects of applied stresses on this transformation are interpreted and the latent heat of transformation is obtained from observations of transformation under stress. A DIFFUSIONLESS phase transformation between face-centered cubic and face-centered tetragonal structures has been reported for the indium-thallium system by Bowles, Barrett, and Guttman1, 2 The transformation takes place at approximately 105 "C at 18 atomic pct Tl and 25°C at 23 pct Tl. In their study, Bowles, Barrett, and Guttman used poly-crystalline samples whereas in the present study single crystals were used to eliminate the transformation constraints imposed by adjoining grains. The use of single crystals made possible a comprehensive study of the effect of stress on the transformation. In the course of the work, it was possible to formulate a new method of analyzing dif-fusionless transformations (presented in this paper) which permits calculation of the geometry of the interphase interface from a knowledge of the crystal structures of the initial and final phases. The specimens were prepared from chemically pure thallium and 99.97 pct In which were weighed out to produce 3 to 4 grams of alloy of the desired concentration. The metal was placed in clean fused silica tubing, then melted, degassed and sealed under vacuum. (To obtain single crystals, it was found that both degassing and extreme cleanliness were essential.) Single-crystal specimens were grown by a modified Bridgman technique.8 pecimens were removed from the tube by dissolving the quartz in concentrated hydrofluoric acid which attacks the specimen very slowly. The specimen then was polished mechanically to produce four flat surfaces, electropolished, and annealed at 140°C for 48 hr. The electropolishing solution used was that described by Bowles, Barrett, and Guttman and the polishing was carried out on both the high and low temperature phases of the alloy. The high temperature polishing was done at 110°C with a stainless steel cathode. Visual Observation of the Transformation in Single Crystals A visual study of the transformation was made on specimens which had been electropolished in the high temperature phase. The specimens were supported on the stage of a metallograph by an electrically heated holder which contained an opening for observing the specimen. Visual evidence of transformation was found in the presence of an interface which separated the two phases. The interface plane defines the boundary of the phase undergoing transformation and manifests itself by the sharp change in angle between the surface of the specimen and the incident light at the juncture of the two phases. On slow cooling, well-annealed specimens transformed from the face-centered cubic structure to the face-centered tetragonal structure by the motion of a single plane interface which traversed the specimen from one end to the other. Upon heating, the interface moved back in the reverse direction. The interface could be started, stopped, or reversed at will. A temperature hysteresis of about 31/2oC was observed in the reversal of the interface. Holding an interface stationary caused it to disappear completely in most cases, whereas in other instances the interface became less distinct depending upon its orientation. The interface could be made to reappear by changing the temperature of the specimen. The low temperature tetragonal structure exhibits only the fine markings or subbands reported by Bowles, Barrett, and Guttman and is illustrated in Fig. 1. These subbands are twin-related. Back-reflection Laue patterns show the breakup of the cubic spots into pairs of spots corresponding to the twin orientations of the tetragonal phase.

Jan 1, 1954

By O. K. Riegger, L. H. Van Vlack

The median angle of relatively few two-dimensional observations provides a satisfactory value for dihedral angle determinations. Those data that contain bimodal or non-equilibriated dihedral angle distributions are readily detected. THIS paper is concerned with a statistical simplification for determining dihedral angles in solids. Microstructures are partially controlled by relative energies of interphase boundaries and grain boundaries. smith1 has shown rather conclusively that such boundaries may be equilibrated to give a vectorial balance at grain and phase edges. Thus if an accurate measurement is made of the dihedral angle associated with grain and phase edges, an accurate calculation of the relative energies may also be made. The accurate measurement is difficult because the dihedral angle involves two planes in three dimensions, and only a two-dimensional cut through the dihedral angle is usually observed. Such a two-dimensional cut is statistically random provided there is no preselection or orientation. Harker and parker2 have shown that the mode of the frequency distribution of observed angles is within 5 deg of the true angle if the true dihedral angle is 120 deg. smith1 had calculations made to show that the same generalization could apply to dihedral angles of 30, 60, 90, and 150 deg. This procedure of requiring the determination of the statistical mode is time consuming because experience has shown that more than 200 angle observations are necessary before the mode is clearly indicated. It is possible to determine the dihedral angle with equal accuracy with only 25 angle observations if the median angle is used in place of the mode angle. Use is made of Harker and parker's2 basic equation tan =2 sin x cos

Jan 1, 1961

By Josef Intrater

A dilatometric determination of the a + ß region temperature limits was performed on vacuum melted Zircaloy-2. The temperature of transformation for a-a+ß and a+ß — ß on heating and cooling as a function of rate of heating and heat treating history was studied. The limits were found to be 815° to 830°C to 975° to 995°C on heating and from 960° to 930°C to 785° to 770°C on cooling. A 5° to 15°C increase was observed for a- a + ß with increased rate of heating and a 20° to 30°C decrease for ß - a + ß with increased rate of cooling. 1 HE transformation temperature for pure zirconium has been determined by many investigators1-5 using metallography, electrical resistivity measurements, and dilatometry. The effect of the rate of cooling on the transformation temperature of zirconium has been studied by Hayes and Kaufmann6 and Duwez,7 and the effect of alloying elements by pfei18 and McGeary.13 Since the development of Zircaloy-2, the limits of the a + ß region for that alloy have been also determined. The first reported temperature for the a — a + a transformation in Zircaloy-2 was 900°C and for a + ß - ß 1000C Subsequent studies by Picklesimer and damson" indicated the beginning of the transformation at 810°C, and the metallographic study by the Technology Group of the Special Materials Section at the Westinghouse Bettis plant1' suggested that 820°to 830°C is the temperature of transformation. The dilatometric investigation by the latter group yielded 830°C for the beginning of the transformation. Thomas and Forscher12 set the beginning of the transformation at 900 °C on heating and the end of the transformation at 870°C on cooling. The above investigators stated in their paper that the dilatometric curve exhibits features caused by a eutectoid reac-

Jan 1, 1962

By M. T. Hepworth, W. B. Sample

HYDROGEN solubility and linear contraction measurements were made at constant temperature on an alloy of titanium of constant oxygen-to-titanium molal ratio but variable hydrogen content. A cylindrical specimen of titanium (0.25 by 1.6 in.) containing 0.75 at. pct 0 and less than 0.03 at. pct N was cast from a master button of iodide process titanium which had been alloyed with titanium dioxide. Four vacuum fusion analyses, which were made along the length of the cylinder after the hydrogen solubility studies were made, revealed a variation of oxygen content of less than 0.02 at. pct. The specimen was introduced into a quartz furnace tube, annealed and outgassedat 1050"~ for about 1 hr, and then held at 800" * 0.5" for about 30 hr, during which latter time experimental data were taken. The leak rate to the furnace chamber was not sufficient to contaminate the specimen during the run as determined by leak-rate studies and vacuum fusion analyses for oxygen and nitrogen before and after the runs. The furnace chamber was attached to a modified Sieverts apparatus used to introduce measured quantities of purified hydrogen to the specimen. A quartz pushrod transmitted changes in length of the specimen to a Chevenard dilatometer. The push-rod passed through a vacuum grease seal to the dilatometer which amplified motion of the rod by a factor of 319. During hydrogen addition, the pushrod did not contact the specimen. Measured quantities of hydrogen were added to the specimen and equilibrium hydrogen pressures recorded as a function of hydrogen content. The solubility data, which appear in Fig. 1, agree well with a separate investigation made with a different apparatus. The solubility limit of the hcp a phase appears as an abrupt discontinuity in slope at 3.4 at. pct H. The solubility plot has been extended as a dashed line at this discontinuity in order to emphasize the discontinuity. The hydrogen content at which bcc P appears is not clearly defined. An arrow indicates solubility data were taken upon hydrogen addition. Upon reaching the arbitrary maximum hydrogen content of the run, the quartz pushrod was pressed against the specimen in order to record the change in length with hydrogen removal. A pressure of about 100 g per sq cm was required to overcome the friction of the vacuum seal in order to obtain reproducible linear contraction data. The contraction ratio ~2/1", change in length divided by original length, was set equal to zero for the maximum hydrogen content. The relative contraction of the specimen was observed upon removal of hydrogen in the following manner. The system was opened to the pumps for a few seconds and an unknown quantity of hydrogen was removed. The system was then isolated from the pumps by closing a stopcock and allowed to return to equilibrium. When the temperature returned to 800°C, the pressure stabilized, and contraction ceased, measurements of contraction and pressure were made. The hydrogen content of the specimen was then deduced by measuring the equilibrium PIydrogen pressure and referring to the solubility plot. Linear contraction was then plotted against interpolated values of atomic percent hydrogen. The justification for this procedure is the established reversibility of the hydrogen equilibrium.' Uniaxial compression was assumed to have no effect on hydrogen pressure. The isothermal linear contraction data are plotted on Fig. 1. An arrow indicates data were taken upon removal of hydrogen. The solubility limits of the two phase a i /3 region can be identified by discontinuities ill slope of the dilatometric plot at 9.1 and 3.4 at. pct H, agreeing well with other studies.' Dashed extensions of the plots emphasize the discontinuities. Isothermal studies of expansion made upon hydrogen addition gave curves of much smaller slope and less pronounced discontinuities. A uniaxial compressive stress tends to accentuate volume changes in going from the more open bcc phase to the hcp phase.2 Incomplete data on ex-

Jan 1, 1962

By E. P. Abrahamson

The effect of transition element binary solid solution additions upon the re crystallization temperature of nickel has been investigated. All additions raised the re crystallization temperature. Both the rate of change of re crystallization temperature with at. pet solute and the limit of initial linearity are found to correlate with the free atom ground state outer electron configuration of the solute element. A comparison of all of the correlations for the transition elements studied has yielded a set of empirical relations, which allows the prediction of the effect of dilute binary transition elements on the recrystallization temperature of other transition elements. The work of Abrahamson, et al.1-7 on dilute binary solution alloys indicated a correlation between the free atom ground state electron configuration of the solute and both the brittle-ductile transition and re-crystallization temperature. Further, it has been shown3,4 that the limit of initial linearity may also be correlated with the solute electron configuration. Since previous studies have dealt with bee and hexagonal base elements, this study is made to note what effect, if any, the fee base structure might have. Nickel also serves to give a solvent configuration which will allow the comparison of all of the transition element solvents. Olsen8 has studied the effect of some trace elements upon the recrystallization of nickel. He included only Ti, Zr, W, Mn, and Co of the transition elements. The differences in change of recrystallization temperature were attributed to the solute atom size and to the solubility of the solute in nickel. PROCEDURE All alloys were made using 99.9 + pet Ni with 0.003 C, 0.015 Fe, 0.007 0, and 0.0007 H. The solute elements were 99.9 + pet pure. According to the published binary phase diagrams9 and metallo-graphic examinations at X750, all solute elements were in solid solution. The alloys were arc melted and remelted four times in the form of cubic 200-g buttons under an argon atmosphere. They were then hot forged at 800oC to 0.750 in. diam, machined to 0.60 in., vacuum annealed for 1 hr at 700°c, swaged to 0.40 in. and annealed at 700oC for 1 hr in vacuum. The grain size was checked and found to be 77 * 20 grains per sq mm. The specimens were then swaged to 0.187 in., yielding 76 ± 1 pet cold work. All alloys were then chemically analyzed for the solute addition. The interstitial contents remained at the values of the starting material when checked on random alloy specimens. The swaged rod was cut into 8.25 in. lengths and heat treated in a gradient furnace for 1 hr. The gradient was maintained at 250" to 850°C over an eight inch length, recorded by twelve thermocouples. Control was ± 3oC, accomplished at the hot end. The recrystallization was determined metallo-graphically over the entire specimen. The criterion chosen was that point on the specimen showing the first recrystallized grain at a constant magnification, X200. Specimens were repeated, and the agreement was found to be generally ± 3oC.

Jan 1, 1962

By J. A. Hren, G. Thomas

A high-temperature stage has been used to study precipitation and dissolution in thin foils of Al-20pct Ag alloy directly in the electron microscope. The results show that the aging characteristics are similar to those observed for bulk materials, and in addition, direct evidence is presented for clustering at the solid solution temperature. The limit of solubility of G. P. zones is-350°C. The heterogeneous precipitation, the growth and dissolution of ?&apos;have been studied in detail. Growth of ?&apos; parallel to the basal planes, occurs by continuous motion of inter -facial partial dislocations. Growth stops at intersecting particles due to formation of sessile a/6 <110> interfacial dislocations. Growth normal to the habit plane occurs by the spontaneous nucleation of partial dislocations on alternate (111) planes and the thickening rate is --10-3= times the lengthening rate. The precipitates dissolve in layers and the final product is a whole a/2 <110> dislocation . The nucleation -growth -dissolution processes are thus completely reversible. Kinetic data obtained from the dissolution rates of ?&apos;particles enable the diffusion coefficient to be determined and the activation energy is found to be 37.5(±4) kcal mol-1, which is that expected for dzffusion of silver in aluminum. The velocity of the interfacial dislocations is thus dependent solely on the rate of diffusion of silver atoms. RECENTLY it was demonstrated that a high-temperature stage could be effectively used in the electron microscope to follow directly the processes of precipitation and dissolution in thin foils of A1-4 pct Cu alloy.&apos; These experiments also provided kinetic data which enabled the diffusion coefficient to be estimated. This new development of electron metallography opens up many fruitful areas of research and it was decided to investigate the aging behavior in thin foils of A1-20 pct Ag alloy, particularly the mechanism of heterogeneous precipitation (i.e., precipitation on lattice defects). This system was chosen because the aging characteristics of bulk specimens are now well known,2"7 and because we wished to obtain more details of the role played by partial dislocations and stacking faults in the nucleation growth and dissolution of the hcp ?&apos; phase. This is of interest for the general case of fcc-- hcp transformations. Part of the A1-Ag phase diagram is shown in Fig. 1. The use of a high-temperature stage also enables a study to be made of the clustering process (formation of G. P. zones) and to determine the structure of the solid solution prior to the usual quenching and aging procedures. It is also possible to obtain kinetic data from measurements of the rates of dissolution of precipitate particles. Unlike the results of previous experiments on A1-4 pct CU 1 where much of the initial precipitation occurred on the foil surfaces, the results on the A1-20 pct A1 alloy were identical to those reported for bulk specimens6,7 and no surface precipitation was ever observed. Thus, it was possible to follow the aging sequence: G.P. zones — ?&apos; — ? directly in the thin foils. This paper is concerned with the formation and dissolution of zones and the ?&apos; phase, and no attempt has been made so far to follow the mode of discontinuous precipitation of ?. I) EXPERIMENTAL DETAILS The high-purity A1-20 pct Ag alloy was prepared by the Aluminum Co. of America in the form of 0.001-in.-thick sheets. These were cold rolled with intermediate anneals to a thickness of 0.0004 in.,

Jan 1, 1963

By Hsun Hu

Direct observations were made on the recrystalli-zntion of a cold-rolled (110) [001] crystal of 3 pct Si-Fe by annealing thin sections of the specimen inside the electron microscope during examination. Subgrain formation, presumably by polygonization, occurs rapidly, followed by a slow increase in the subgrain size before recrystallization can be detected. No migration of the subgrain boundaries was observed, and the formation of recrystallization nuclei by coalescence of subgrains is suggested. Re-c~ystallization characteristics of various texture components were individually examined. AS reported in a previous paper: orientations of the various deformation texture components in a 70 pct cold-rolled (110) [0011 crystal of 3 pct Si-Fe were completely confirmed by transmission electron diffraction patterns taken at various areas of the specimen. These orientations can be summarized as follows: Over most areas of the deformed crystal (111) planes are parallel to the surface. These areas correspond to either $- the two main defor: mation textures, the (111) [112] or the (111) [112].2-5 Within a few areas, (100) planes parallel to the surface are frequently found. These areas represent the minor deformation texture component, the (100) [Oll] type, which is derived from rotated Neumann bands.2&apos;4&apos;5 Only in very rare instances are (110) planes found parallel to the surface. This orientation corresponds to the very weak texture component of the (110) [001] type. In a pole figure, this (110) [0011 orientation is located within the orientation spread between the two main (111) [1121 type textures. Usually the electron diffraction patterns taken at various areas of the specimen are very simple ones, i.e., for any one area the pattern consists only of sharply defined spots of a single orientation. In some areas, however, more or less continuous rings of weaker intensities are superimposed on a simple pattern, indicating the presence of a wide range of additional orientations. In order to understand in detail the recrystallization of this cold-worked crystal, the recrywtallization characteristics of each of the various deformation texture components must be examined. This can best be done by using a high-temperature stage and transmission electron microscopy techniques, whereby small areas corresponding to the various texture components can be selected individually for examination. The present paper presents results obtained by this method. MATERIAL AND METHOD Specimens were prepared from a previously studied1 single crystal of a commercial grade 3 pct Si-Fe alloy with an initial orientation (110) [00l], cold-rolled 70 pct from 0.014 in. to 0.004 in. in thickness. Thin foils were prepared by electrolytic polishing as described in the earlier paper.&apos; Specimens of this thin foil were then mounted in a high temperature stage similar to the one designed by Whelan.6 A direct current was used as the heating source. The temperature of the heating grid was calibrated by means of a Pt vs Pt-10 pct Rh thermocouple in a vacuum chamber (0.01 to 0.02µHg). Maximum variation within the temperature range of 250o to 000°C was about ± 25°C. After the desired areas were selected for examination, the specimen was heated to a low temperature for some time while the selected area was constantly watched. When no further change in structure and orientation could be observed, a higher temperature was applied. Photomicrographs and diffraction patterns were taken from time to time during examination, with the heater temporarily turned off* while the photographs were

Jan 1, 1962

By J. B. Clark, A. S. Yue

PfANN1 has shown that when a cylinder of molten binary alloy freezes directionally, the solute distribution can be described analytically by cg=k(l-g)k-1 [1] in which Cg is the solute concentration in the solid at the point where a fraction g of the original liquid has frozen and Co is the initial solute concentration. The term k is the effective distribution coefficient of the solute and is defined as the ratio Cx/CL where Cl is the solute concentration in the main body of the liquid. Both the slope and the intercept at -log (1 - g) = 0 of a logarithmic plot of Eq. [I.] provide a measure of k. Under conditions of freezing where diffusion in the solid is negligible and the solute concentration in the liquid is uniform, the effective distribution coefficient k, derived as above, is equal to the equilibrium distribution coefficient taken from the phase diagram. However, under ordinary freezing conditions, even though solid-state diffusion is negligible, the solute rejected from the freezing solid does not have sufficient time to diffuse uniformly throughout the main body of the liquid. A concentration gradient is formed in a boundary layer in front of the advancing solid-liquid interface as pointed out by Rutter and Chalmers.&apos; Thus, under these conditions, the concentration of the freezing liquid in the boundary layer is higher than that predicted from the equilibrium phase diagram and consequently the effective distribution coefficient k, obtained from directional freezing experiments, is larger than the equilibrium distribution coefficient. The symbol k will designate the effective distribution coefficient in the discussion which follows. In this paper, the determination of the effective distribution coefficient is demonstrated for several dilute binary alloys and a polynary magnesium alloy. The effect of freezing rate on the value of the derived k is presented in detail. An example for the calculation of the solidus in a dilute binary solution using the experimentally determined effective distribution coefficient is given. MATERIALS STUDIED Binary magnesium alloys of copper, nickel, and zinc containing approximately 0.10 wt pct solute and a polynary alloy containing approximately 0.10 wt pct each of several elements were selected for study. The spectrographic analyses of these alloys are given in Table I. The analyses are believed accurate to within +5 pct of the stated value. EXPERIMENTAL PROCEDURE Extruded rods of the alloys, 3/8 in. in diam and 11 in. long were used for directional freezing studies. The alloy rods were melted horizontally in a high-purity graphite boat by a Nichrome-wound tube furnace which moved parallel to the length of the rod. The boat was supported inside a Vycor tube suitably connected to provide a protective atmosphere of dry SO2. For an experimental run, the following procedure was used. The alloy rod was cleaned in dilute HNO, and dried. The graphite boat containing the alloy rod was placed within the Vycor tube and the tube connected to the gas train&apos; The &apos;ystem was purged for 20 min with dry argon and then a flow of dried SO, was maintained for the duration of the run. The movable furnace was positioned and either all or a desired portion of the alloy rod was melted. After attainment of steady-state temperature gradients the molten bar was solidified from one end to the other at a controlled rate by pulling the furnace along the length of the bar at the desired speed. At the conclusion of the run, the directionally frozen alloy rod was analyzed spectrographically at 1 1/4-in. intervals.

Jan 1, 1961

By F. R. Morral, K. T. Aust

The preferred orientation and earing characteristics of ZS aluminum were studied. An empirical correlation was obtained relating earing behavior and variation of mechanical properties for face-centered cubic metals. Strain-ratio mecsurements for ZS were found to be in good agreement with Hill&apos;s theory of plastic anisotropy. DIRECTIONALITY in sheet metals may be revealed by earing in a cupping test, or by the variation of mechanical properties of tensile specimens taken at different angles to the rolling direction. However, no simple correlation appears to exist between earing and variation in mechanical properties in metals and alloys studied.1-5 Aluminum of commercial purity (known as 2S, with a specified minimum of 99.0 pct Al) cast by the direct casting process was chosen in the present investigation since ears at 45° or 0°, 90° can readily be obtained. Preferred orientation is often the principal cause of uneven metal flow, such as earing, and variation in mechanical properties. Consequently, the preferred orientation characteristics of 2s aluminum were initially studied using both X-ray diffraction and micrographic techniques. The variation of mechanical properties with angle to the rolling direction was next determined in an effort to clarify the apparent lack of correlation of earing behavior with mechanical properties for face-centered cubic metals. Strain-ratio*5,8 measurements were finally conducted to determine first, if the maximum values of the strain ratio occurred at the earing positions, and second, if Hill&apos;s theory of plastic anisotropy7 is applicable to other face-centered cubic metals such as aluminum. Detailed treatments, working, and heat treating are not given in this paper since this study is not concerned with the methods to produce earing, but to correlate earing with other properties and characteristics of the material. The percentage of earing was measured using the formula specified by the x—Y Aluminum Association, -------- X 100 = pct earing, where x is the height of the ear and y is the height of the valley from the bottom of the cup. Preferred Orientation Characteristics of 2S X-ray Studies: Beck and coworkers8 have determined that the rolling texture of 2s after 95 pct cold reduction may be approximately described by four equivalent ideal orientations near (123) [121]. Also, the recrystallization or annealing texture of 2s aluminum consists of four components of the (123) [l21] type, retained from the rolling texture, and of a (100) [001] or cube texture component." Fig. 1 illustrates the typical appearance of deep drawn earing cups with the corresponding X-ray diffraction patterns. The X-ray patterns were taken with copper radiation using the structure-integrating method&apos;" in which the specimen is scanned during the X-ray exposure. The rolling direction was vertical and the rolling plane was perpendicular to the horizontal X-ray beam. It was found that an increase in the retained rolling texture component resulted in a greater 45" ear height, while an increase in the recrystallization texture component (i.e., cube texture) caused greater 0°, 90° earing. X-ray diffraction studies of 2s cold rolled to final thickness followed by a final anneal have shown that the rolling texture, and also the retained component of the rolling texture after annealing, are increased with greater cold-rolling reduction. The preferred orientation characteristics of 2s sheets given an intermediate anneal between cold rolling followed by a final anneal were found to depend on the position of the intermediate anneal during cold rolling. For instance, three identical samples of 2s homogenized ingot, each 1 in. thick, were given the following cold-rolling and annealing treatments: 1—50 pct reduction, intermediate anneal, 96 pct reduction to 0.020 in. and a final anneal; 2—75 pct reduction, intermediate anneal, 92 pct reduction to 0.020 in. and a final anneal; and 3—90 pct reduction, intermediate anneal, 80 pct reduction to 0.020 in. and a final anneal. The intermediate and final annealing treatments consisted of a 70°F per hr heating rate, held 6 hr at 800°F and air cooled. Typical X-ray patterns after each of these treatments are shown in Fig. 2. It was evident that after treatment 1, the retained rolling texture component predominated; after treatment 2, the retained roll-

Jan 1, 1954

By Harmon D. Nine

DISCONTINUITIES in the strain vs cycles to failure (S-N) fatigue curves have been reported for polycrystalline materials by Porter and Levy for copper,&apos; by Benham and Ford for mild steel,&apos; and by Williams and Stevens for 18/5 stainless steel.3 However, the considerable scatter of the points for polycrystalline materials have made a statistical analysis of the data necessary to confirm the discontinuities. By using oriented single crystals of high-purity material and low grown-in dislocation content, the reproducibility has been improved to a degree which makes statistical analysis unnecessary and clearly shows discontinuities in the S-N curves. A recent publication4 reports an abrupt change of slope in the S-N curve for ( 100) axially oriented copper single crystals fatigued in torsion. The reported discontinuities in the S-N curve, along with a different mode of failure in the two branches of the curve, have been interpreted as being due to two different amplitude-dependent mechanisms. Further work on copper single crystals of (111) axial orientation has now been completed which supports the existence of an amplitude-dependent change in the mechanism of fatigue. In the present study torsional-fatigue experiments were performed at room temperature in air on (111) axially oriented single crystals. The crystals were grown and prepared as reported in Ref. 4. Two different methods of growing the crystals also discussed in Ref. 4 produced crystals of two different perfections: Type I with dislocation density of >l06 per sq cm and Type I1 with dislocation density of <l05 per sq cm. In accordance with the accepted hypothesis that crystal flaws are primarily responsible for the scatter of fatigue lifetimes, particularly at low amplitudes, the values for the three lowest amplitudes for Type I crystal are believed to be uncertain. They are marked in braces in Fig. 1. On the other hand, at amplitudes above a surface shear strain (SSS) of *0.003, the data for both types of crystals are in agreement. Most remarkably the S-N curve for torsional fatigue of (111)-oriented single crystals is composed of three segments separated by rather large discontinuities, Fig. 1. Metallographic and X-ray measurements indicate that the lower branch corresponds to the low-amplitude (F) region of the (100) copper single-crystal results as discussed in Ref. 4, and the two upper branches correspond to the high-amplitude (H) region. The lower discontinuity in the (111) S-N curve and metallographic evidence give further support to the hypothesis that different mechanisms of failure operate for high and low strain amplitudes. Reference to the resolved shear stress diagram, Fig. 2, shows that the highest stressed systems in

Jan 1, 1965

By A. R. Troiano, E. A. Steigerwald, F. W. Schaller

The kinetics of crack propagation in a hydrogenated high-strength steel at subzero temperatures indicated that cracking progressed in a discontinuous fashion. The delayed failure process thus involves a series of crack initiations rather than the continuous growth of a single crack. The incubation time required for the initiation of delayed failure was controlled by the diffusion of hydrogen. The activation energy for the process was 9120 cal per g-alom. As the test temperature was lowered the incubation time constituted a greater percentage of the total tinze to fracture, and al -50°F the incubation and fracture times were essentially coincident resulting in instantaneous, catastroplzic fracture. A unique feature of hydrogen embrittlement is the delayed failure process in which the material fails under the action of a sustained load even though it is capable of supporting a higher load for a finite period of time.&apos;)&apos; Delayed failure of steel and titanium is characterized by an incubation time, preceding the initiation of a crack in a highly localized region, and the subsequent growth of the crack to ultimate failure.3-5 The kinetics of crack growth in hydro-genated high-strength steels have been studied through the use of resistance measurements and have an important bearing on the mechanism of delayed failure. Delayed failure is believed to be merely a facet of hydrogen embrittlement in which sufficient time is allowed during a test for hydrogen diffusion. The current theories employed to explain hydrogen em-brittlement can be grouped into two types. one6-8 explains the embrittlement on the basis of the pressure exerted by molecular hdrogen in lattice voids or defects while the other9-10 attributes the embrittlement to the influence of hydrogen in the lattice. The mechanism used to explain the nature of the crack kinetics in delayed failure is based on the stress-induced diffusion of hydrogen to the area of maximum triaxiality.3 When the hydrogen concentration in this region reaches a critical value, a crack is nucleated. This initial crack propagates instantaneously until stopped by the higher fracture stress of the adjacent material of lower hydrogen content. The continuation of cracking must then await the further diffusion of hydrogen to the new region of triaxiality near the base of the crack where another initiation will occur. From this mechanism it follows that crack propagation is nothing more or less than a series of initiations with limited fracture. The purpose of this investigation was to examine the kinetics of crack growth in an effort to determine whether or not the process was discontinuous. Studies of crack propagation were conducted at low temperatures to retard the diffusion of hydrogen which is presumed to be the rate controlling process in delayed failure. MATERIALS AND PROCEDURE Specimen Preparation—A commercial heat of air-craft quality SAE-AISI 4340 steel, designated as Heat G, was furnished by the Republic Steel Co. in the form of %-in. hot-rolled bars. The material had the following chemical analysis: Composition of 4340 Steel—G Heat C Mn Si Ni Cr Mo 0,395pct 0.82pct 0.29pct 1.76pct 0.85pct 0.25pct Notched tensile specimens with less than a 0.001 in. radius, Fig. 1, were used throughout the investigation. The specimens were heat treated to a 230,000 psi strength level according to the following sequence: a) Normalize bar stock at 1650°F for 1 hr, b) Stress relieve at 1200°F for 4 hr and furnace cool,

Jan 1, 1960

By I. R. Kramer

In his technical note entitled "Specimen Temperature During Electropolishing of Aluminum Crystals" Dr. Nakada 1 reported that the temperature of his aluminum specimen increased 65°C when it was polished electrolytically; he therefore concluded that the temperature of the specimens used in our work (Nakada&apos;s Refs. 4 and 5) similarly increased by this amount. From this he further concluded that the change in plastic-flow characteristics associated with the removal of the surface by electropolishing during deformation were due solely to a temperature effect. We believe that these conclusions are not justified. It is, of course, realized that the amount of the temperature increase is associated with the total heat transfer of the entire system, including the efficiency of the stirring action, heat flow through the grip on the specimen, and so forth. Of great importance is the type of electrolyte used for polishing. For example, in Dr. Nakada&apos;s experiment a methanol-perchloric acid solution was used. This solution has a relatively low conductivity and for the current densities of 0.3 amp per sq cm the electrical input appears to be 30 to 40 w. In our research a methanol-nitric acid solution was employed and for the size of specimen employed by Dr. Nakada the power never exceeded 7 w. There are major differences in his test apparatus which also appear to affect the temperature rise. In our case a steel specimen holder was used in order to provide a good heat sink and conduction path. The cathode was a coiled aluminum tube through which a coolant was passed to provide additional cooling capacity near the specimen. The stirrer was placed in a position to obtain maximum cooling efficiency. On the other hand Dr. Nakada used a teflon grip to support the specimen at one end only and a flat copper cathode, thus providing a much less efficient heat sink as compared with the metal grips used in our studies. The relationship between current density and the temperature increase for two sizes of aluminum crystals tested in our tensile apparatus is shown in Fig. 1. The temperature measurements were determined from a thermocouple spot-welded to the surface of the specimen. The thermocouple was protected from the acid by means of a thin film of stop-off lacquer which covered just the outer surface of the thermocouple junction. Whereas Dr. Nakada reported a time delay of 8 min to obtain thermal equilibrium, our temperature change occurred in less than 15 sec. This emphasizes the importance of the heat transfer in the entire system. However, readings were taken over a period in excess of 5 min to assure thermal equilibrium. The data given in Fig. 1 were also confirmed by determining the thermal expansion of the specimen in a sensitive creep apparatus. As may be seen, for the smaller specimen the increase in temperature is 8°C for a current density of 1.5 amp per sq in. The majority of our data on the effects of surface removal on the plastic behavior of aluminum were obtained at current-density values at or below this value. Above 1.5 amp per sq in. the temperature rise is uncertain; for under certain conditions, especially in the vicinity of 2 amp per sq in., the anode can become polarized and the current flow is erratic. This condition is easily recognized because wide fluctuations in the creep and stress-strain data make it virtually impossible to obtain reliable results, a condition which was always avoided in our work. The temperature increase for the larger specimen is less than that of the smaller specimens below a current density of 1.5 amp per sq in. At a current density of 2 amp per sq in. the temperature increased 13°C. The above temperature data are in accord with observations made during creep experiments. Using a transducer capable of detecting strain in the order of 10 -6, temperature changes in excess of 8°C were not detected when the current density was increased to as high a value as 1.5 amp per sq in. Finally we wish to point out that our experimental data cannot be explained solely in terms of a heat effect. For example in Fig. 1 of Ref. 2, the change in slope of Stage II as a function of the rate of re-

Jan 1, 1965

By James C. M. Li, J. Weertman

James C. M. Li (United States Steel Covp.)—The author has discovered a single analytical relation between the minimum, or the steady-state, creep rate and the applied stress confirming a statement made earlier by orn" that such relation should exist and should reduce to the power law at low-stress levels and to the exponential law at high-stress levels. However, as pointed out by the author, all the available theories of creep are not adequate to explain such a single relation. Inspired by such a statement, I have made a suggestion concerning a possible explanation13 of the new relation. This is based on the concept that the rate-controlling step is the cooperative motion of a short dislocation segment. The nature of and the reason for the cooperation have been discussed13 as well as the reason why the motion of the dislocation could be controlled by the mobility of the short segments. A natural short segment has been proposed13 to be the node formed at the intersection of two dislocations. The reason why the node may contain only a few atoms has not been discussed and the application of the proposed model to all the metals and alloys reported in this paper has not been attempted. It seems appropriate to include these in this discussion. The model was partly inspired by the substructure recently observed in the electron microscope on creep specimens. One such example is shown in Fig. 48 in Darken&apos;s Campbell Memorial Lecture. The substructure is a collection of dislocation intersections and irregular networks. No pileups have ever been observed in such specimens. A closer look at the network indicates that one set of dislocations is more straight than the other set sug- gesting that the other set may be mobile in the plane of the net. Since, for the network to survive the creep deformation, some dislocation reaction has to take place at the intersection of the two sets of dislocations, the mobile dislocation, even if it can slip in the plane of the net, will have difficulty in moving at these intersections. To illustrate, an idealized network is shown in Fig. 9. The thin lines represent the set of dislocations which are mobile and can slip in the plane of the net except at the nodes which are formed at the intersection of the two sets of dislocations. The other set of dislocations, represented by the thick lines, may have a Burgers vector which is not parallel to the plane of the net, and therefore may be immobile. Because of this nonparallel Burgers vector, the Burgers vector of the node, which is avectorial sum of the Burgers vectors of the two sets of dislocations, will also be nonparallel to the plane of the net. Therefore, the node cannot slip in the plane of the net and the set of mobile dislocations will have to drag the node along as indicated in Fig. 9. Now the problem is how many atoms could be involved in the nodes. Exact calculation of the length of the node is a difficult task especially since the length should be a steady-state length and not an equilibrium length. An estimate of the equilibrium length can be made by balancing the line tension of all the dislocations. The results would be a small fraction of the length 1 between nodes as shown in Fig. 10. In some instances such a calculation shows that the node will not be formed. But, since the calculation is only approximate, it does not rule out the possibility of the formation of a short node. In other instances the equilibrium length of the node is an appreciable fraction of I. Such a node would

Jan 1, 1963

By T. H. Alden

T. H. Alden (General Electric Research Laboratory)—This paper as well as earlier ones of Dr. Wood represent an important contribution to the experimental description of fatigue fracture. The mechanism of fracture proposed by the authors, however, is not established by this data nor supported by other data existing in the literature. Although taper section metallography provides a rather detailed picture of fatigue crack geometry, photographs so obtained must be interpreted with care. The narrow bands revealed by etching, frequently associated with surface notches, are labeled by the authors "fissures". Measurement shows, taking into account the 20 to 1 taper magnification, that the depth of these structures is at most 2 to 3 times the width. This distinction is important in the conception of a mechanism of crack formation. It is difficult, for example, to imagine a deep, narrow fissure arising from a "ratchet slip" model. A surface notch, on the other hand, may form easily by this mechanism. The notches observed in the present work are the subsurface evidence of the surface slip bands or striations in which fatigue cracks are known to originate.4-6 It is clear that an understanding of the structure of these slip bands is of key importance in understanding the mechanism of fracture. The evidence presented shows that these regions etch preferentially, possibly because they contain a high density of lattice defects, or as the authors state equivalently, because they are "abnormally distorted." However, it is not possible to conclude that the distortion consists of a high density of vacant lattice sites. The fact of a high total shear strain in itself does not assure a predominance of point defects as opposed to other defects, for example, dislocations. Other evidence in the literature which suggests unusual densities of point defects formed by fatigue7-&apos; refers not to the striations or fissures, but to the material between fissures (the "matrix"). If a choice must be made, the preferential etching would seem to be evidence for a high dislocation density, since dislocations are known to encourage chemical attack in copper;g no such effect is known for the case of point defects. A third alternative is that the slip bands are actually cracked, but that near its tip the crack is too narrow to be detected by the authors&apos; metal-lographic technique. In this case the rapid etching can be readily understood in terms of the increased chemical activity of surface atoms. Unless a vacancy mechanism is operative, the motion of dislocations to-and-fro on single slip planes will not lead to crack growth. Point defect or dislocation loop generation are the principal non-reversible effects predicted by this model. In any case, the nonuniform roughening of the surface in a slip band6 requires a flexibility of dislocation motion which is not a part of the to-and-fro fine slip idea. The same is probably true of crack growth by a shear mechanism. Either some dislocations must change their slip planes near the end of the band and return on different planes,&apos;0 or dislocations of opposite sign annihilate." The mechanism by which these processes occur in copper at room temperature or below is that of cross slip. Thus cross slip appears to be essential to fatigue crack growth.6&apos;10"12 The fact that a tensile stress opens the slip bands into broad cracks does not indicate the structure of the bands or the mechanism by which cracks form. The charactersitic concentration of slip into bands during fatigue shows a low resistance to shear strain in these regions. (This fact in itself may be inconsistent with a high concentration of vacancies.) The authors contend also that continuing shear produces an additional mechanical weakening so that the bands fracture easily (are pulled apart) under the influence of the superimposed tensile stress. It is equally possible that the only weakness is a weakness in shear, that the crack propagates by a shear mechanism, and that subsequently the tensile stress pulls the crack apart. Even the direct observation of bands opened by a tensile stress would not be conclusive since, as argued above, they may be fine cracks. The same argument applies to internal cracks, their existence in the presence of a tensile stress not indicating the mechanism of formation. Internal cracks originating in regions of heavy shear have also been seen following tensile deformation of OFHC copper,13 so that this mode of fracture is not unique to combined tensile and fatigue straining. The authors point out in their companion report14 that 90 pct of the cracks formed during pure tor-sional strain were within 8 deg of the normal to the specimen axis. If the tensile stress were an important factor in crack propagation, it is surprising that the cracks cluster about the plane in which the normal stress vanishes. Similarly, a study of zinc single crystals showed that for various orientations the life correlated well with the resolved shear stress on the basal plane,&apos;= and was not dependent on the normal stress across this plane. W. A. Wood and H. M. Bendler (Authors&apos; reply) -Dr. Alden&apos;s discussion emphasizes the essential point in the relation of slip band structure to

Jan 1, 1963

By R. C. Gifkins, A. Gittins

A. Gittins and R. C. Gifkins (University of Mel-houvne)— Evidence from somewhat similar experiments to those described in this paper has led us to the conclusion that possibility 2) of the four listed on p. 319 is a description of what happens in grain boundary sliding. That is, sliding is limited by accommodation deformation, it being necessary to the Continuance of sliding that this accommodation should take place. An example of such accommodation, though probably not the most important, is fold formation at triple points. The evidence and arguments for this point of view are set out in Refs. 14 to 16. In particular, an experiment with a lead bicrys-tall5 seems to support point 2) rather than 3). In creep of this specimen it was found that at least 90 pct of the extension of a zone 0.3 mm wide at the boundary was supplied by sliding at the boundary. The sliding was localized in a region at the boundary very much smaller than 0.3 mm, in fact, in a region too narrow to resolve optically. In poly crystalline Specimens&apos; there appears to be a surface effect, as found by Rachinger," but it appears that this may not manifest itself at low strains. "Low strains" means <10 pct for a Pb-TI alloy, <2.5 pct for magnesium or "Magnox" A12 alloy, or <40 pct for a 0 brass. Up to this extension the sliding, measured by the mean vertical step at boundaries, is proportional to extension. We are able to say this with some confidence, since the error bars on our points are statistically derived. Our results would lead us to think that the error bars on other work, including that of Mullendore and Grant, are much too large at low strains to show this

Jan 1, 1963

By M. Bevis, A. G. Crocker

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and "{2,3,10)" or "(127)". (It is now thought1&apos; that the "{0,1,13)" habit reported for the Fe-Ni-C alloys&apos;&apos; is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove.&apos; The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and tj2 = vi (i = 1, 2, 3), the Kz qd 771 elements are given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics cij Iand cij reduce to the unit tensors 6ij and 6ij so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and 77~ are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc

Jan 1, 1963

By G. N. Maniar

G. W. Healy (union Carbide Metals Co.)-The author&apos;s paper is a useful contribution to the store of maps of chemical activities of oxides in multi-component slag systems. It is also a good example of the utility of the Gibbs-Schuhmann technique for calculating activities in a system where that of one of the components has been measured. This paper Koh and Caugherty. This plot is reproduced by alor in X-ray Metallography. Because of this nonlinearity, preparation cf suitable standards and/or correction for absorption and enhancement are essential in microanalysis. However, our objection is not the conclusion that Dr. Aaronson has arrived at nor the technique he has used; but only to the foot-note credited to V. Macres. The level of chromium that he was concerned with (less than 3 pet) is so low that the deviation of uncorrected Cr-curve will be negligible. Besides Dr. Aaronson has used chromium intensity from martensite and set it equal the bulk chromium content of the alloy. Using this chromium-intensity as a reference, he has calculated the amount of chromium in the ferrite. This amounts to the same as using an internal standard. Since the chromium content in austenite and ferrite are almost the same, enhancement due to iron in both will be the same and therefore does not need to be corrected. together with the author&apos;s recently published one1 on the CaO-FeO-Fezo3 system will be most helpful to others learning to apply Schuhmann&apos;s method, which merits a far wider application than it has received to date and should greatly aid our understanding of equilibria between metal and oxide phases. As shown by okcen" its use may even be extended to sections of systems with any number of oxides. I have some questions as to the selection of equilibrium constants made by Dr. Turkdogan. He has chosen one for the formation of Fe2O3 from FeO and oxygen which gives Fea3 activities 50 pct higher

Jan 1, 1963

By M. Bevis, A. G. Crocker

A. G. Crocker and M. Bevis (Battersea College of Technology)— Richman and Richman and conard17 have recently published the very interesting results of their studies on the plastic deformation of Fe-Ni-C martensites and of an Fe-5 wt pct Be alloy. Other work on the range of Fe-Be alloys containing between 16 and 27 at. pct Be has also been reported by Richman." One of the fascinating features of this work is that the materials investigated deform primarily by means of twinning and that several twinning modes are operative in addition to the well-established (112 ) mode of bcc materials The composition planes of these unusual twins were determined using a single-surface analysis and reported as (0131, "{045)" or "{089)", and It is now thought1&apos; that the "{0,1,13)" habit reported for the Fe-Ni-C alloys&apos;&apos; is more likely to be near "{127)". Although the full twinning elements of these unusual twinning modes could not be determined directly from the experimental results, the authors attempt to deduce the elements by considering twin intersectionslQ and by using the projection technique of Jaswon and Dove. The basic assumption of their approach is that the (013) habits are truly rational planes but that the other habits are irrational and merely approximated to by the indices quoted above. They thus deduce that the twinning mode describing the (013) habit is either Type I or compound and that the modes describing the other habits are Type 11. This deduction must however be false as all twinning modes in cubic structures obeying the classical orientation relationships of deformation twinning must be compound. Type-I and Type-I1 modes can occur in all of the other crystal systems (indeed in the triclinic system compound modes are not allowed), but in the cubic system only compound modes can arise. This fact, which does not appear to be well-known, fol- lows immediately from the relations between the four twinning elements defining a twinning mode. Thus for a Type-I mode which is uniquely defined by the rational twinning elements K1 = hi and given by: where the summation convention of the tensor calculus has been adopted. For cubic materials the metrics and reduce to the unit tensors and j so that we have It is clear from these equations that both ki and ui must take on integral values; i.e., Kz, and ql must be rational, if hi and vi are integers, i.e., if K1 and are rational. Thus for cubic materials a Type-I mode must degenerate into a compound mode and the same result also arises for Type-II modes. The apparently irrational habits observed by the authors can thus not be explained in terms of Type-I1 twinning if the classical laws of deformation twinning are to be obeyed. An alternative explanation of the irrational habits is that they may arise from twinning modes with four irrational twinning elements. These modes, which do not obey the classical orientation relationships associated with deformation twinning, have been shown to arise as the result of double twinning processes in magnesium,22 but may also describe a simple shear on an irrational plane in an irrational direction. Indeed double twinning processes in bcc

Jan 1, 1963

By S. J. Rothman, L. T. Lloyd

S. J. Rothman and L. T. Lloyd (Argonne National Laboratory)— Hagel&apos;s paperz0 discusses the question of the mechanism for self-diffusion in bcc transition metals. Recent work21"23 has led us to agree with him in reabandoning the ring mechanism in favor of a defect mechanism, most likely vacancies. On the other hand, we think that Hagel&apos;s attempt to group together all self-diffusion in bcc transition metals is wrong. We prefer the scheme of Peart, Graham, and omlin," who separate them into two groups. One group contains the anomalously behaved metals P titanium,&apos;, y uranium, and perhaps zirconim.&apos; The other group contains a iron," this alloy was held at 1800°C for 2 hr before quenching, its structure was all a. B. C. Giessen, I. Rump, and N. J. Grant (Authors&apos; reply)—We very much appreciate the discussion by Deardorff and Kato regarding the a to /3 transformation temperature of hafnium. In the W-Hf program, as well as in a current study of the system Cr-Hf, standard precautions were exercised against contamination, including vacua of less than 10"5 mm Hg and a weight control check of all specimens to insure an impurity rise of less than 100 ppm. Following receipt of the above discussion, a revision was made in the annealing process. Arc-cast specimens were etched with a 10 pct HF-90 pct HNO solution until 1 mm of surface, including a possible oxide film, was removed. Annealing was done in a hafnium container which provided a long diffusion path for gaseous contaminants. Finally, the heat treating time was shortened. Structural changes were noted to occur quite slowly. A 99.5 at. pct Hf alloy showed 70 pct /3 after 30 min at 1700°C and was 100 pct /3 after 10 min at 1715°C. After 24 hr at 1740C, the alloy was found to be 10 pct/3. This change is due to contamination; it was estimated that it corresponds to an increase of 60°C in the transformation temperature over a 24 hr period. The corresponding change in 30 rnin would be slight. Using the same hafnium as in the above publication, and three new alloys at 98, 99, and 99.5 at. pct Hf, the transformation temperature was indicated to be 1715" 15°C. Since this hafnium contained 4.4 at. pct Zr, a correction of 40 5C, based on an assumed approximately linear transformation temperature curve, must be made for pure hafnium. This yields a value of 1755 20°C in good agreement with Deardorff and Kato&apos;s value. Because the slope of the boundary is small, this permits a good extrapolation, and we regard the W-Hf alloys as well suited to check the Hf transformation temperature. niobirn,&apos;&apos; and molybdenum,22 whose activation energies correlate with the melting temperature and whose Do values follow Zener&apos;s predictions.28 We have no quarrel with Hagel&apos;s placing chromium into the second group; we disagree with his interpreting our data to make uranium fit into that group. Hagel considers that the measurements of self-diffusion in uranium below about 950°C represent combined volume and grain boundary diffusion. This contention is based on the curvature of the penetration plot for our 891°C run,4 which also has a nearly straight line plot of log c vs x. Hagel has extrapolated these characteristics to our 803.5C run and fitted his Arrhenius plot for self-diffusion in y uranium to our four highest temperature points only. We think this is wrong for the following reasons.

Jan 1, 1963