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By R. E. Ogilvie, J. I. Goldstein, R. E. Hanneman

The interdiffusion coefficients for the Fe-Ni system were determined as a function of composition in both the a and y phases at 1 atm pressure. The inter diffusion coefficients were also determined in the y phase at 40 kbar pressure. The concentration gradients were measured with an electron probe, and the diffusion coefficients were calculated by the Matano analysis. At 1 atm, Ey increases with nickel content up to 65 at. pct Ni. The relationship of Dy with temperature and nickel concentration, up to 50 at. pct Ni, is given by the equation DY-l atm = exp(.0519 CN~ +1.15) MANY of the transformations that occur in the solid state are diffusion-controlled, especially those involving precipitate growth in most metallurgical systems. Multicomponent diffusion is usually expressed in terms of a chemical or an inter diffusion The activation energy Q at 1 atm decreases from pure iron to 60 to 70 at. pct Ni and decreases from pztre nickel to 60 to 70 at. pct Ni. The Kirkendall marker movement indicates that DFe is greater than DNi zcp to about 60 at. pct Ni. Above 60 at. pct Ni, however, DNi becomes peater than DFe The inter diffusion coefficients were also compared with those calculated from self-diffusion data. A comparison between calculated and measured coefficients shows only rough agreement. The effect of 40 kbar pressure is to decrease DyPl atm by an order of magnitude. The activation volumes for high-pressure diffusion are in favorable agreement with theoretical models developed for self-diffusion. coefficient which determines the rate at which material is transferred from the matrix phase to the precipitate and hence determines the growth rate of the precipitate. Since the numerical values of the diffusion coefficients differ widely as a function of the metallic system, temperature, and pressure, the diffusion coefficients must be determined for each particular environmental condition. Of long-standing interest is the growth of the classic Widmanstatten pattern in metallic (Fe-Ni) meteorites. The growth rate of the pattern is controlled by the diffusion coefficients in the Fe-Ni system. Since these coefficients are essential to calculating the growth rate of the pattern, we found it necessary to determine the diffusion coefficients

Jan 1, 1965

By T. Kunitake, H. W. Paxton

The self-diffusion coefficient of chromium in various alloys in the iron-chromium system has been measured. A variation in Dofrom 10-4 for pure chromium to a maximum of 102 near 60 pct Cr appears with a range of activation energy from about 50 to 80 kcal per mol. The general pattern of behavior observed is not consistent with present theories of diffusion by a vacancy mechanism. Suggestions are made for further clarifying experiments. RECENT work on the self-diffusion of chromium,' ?-uranium2-4 and ß-zirconium,23, 26 has indicated that these elements have very low Do (10-3 to 10-4) compared to that conventionally expected for vacancy diffusion. Pound et al.5 have suggested that this may be due to ring diffusion being operative, and have proposed a model which gives Do of the correct order of magnitude. The essential difference between this model and Zener's earlier model6 is that whereas Zener assumes tight coupling between atoms in a ring to establish a vibrational frequency, Pound's model allows the atoms to vibrate essen- tially each in their own normal modes. The probability of each atom moving in the correct direction to cause a ring of n atoms to rotate by 2p/n must then be calculated as a "synchronal entropy" which may be -20 e.u. for a 4 atom ring. In iron, the latest determinations of self-diffusion yield Do in the range 18 to 522.7-9 The most accurate is probably that of Borg and Birchenall8 which is 118 ± 3. This value is not inconsistent with that expected for a vacancy mechanism. Since iron and chromium are very closely similar in size, are both transition metals, and their solution is thermodynamically ideal at temperatures of interest in diffusion, it appeared that a determination of self-diffusion coefficients, Do and Q as a function of composition would be of substantial interest to diffusion theory. The following measurements were made with this purpose in mind.

Jan 1, 1961

By Cyril Wells, Paul E. Busby, Donald P. Hart

EARLY workers in the field have established that the diffusion of nitrogen follows normal diffusion laws. Concentration-penetration data from layer analyses of reasonably pure iron specimens nitrided in an atmosphere of CO-NH, are given in the literature,' and were utilized to calculate diffusion constants for nitrogen. The diffusion of nitrogen in y-iron may be represented approximately by the equation D - 1.07x10-' e-:".'m'"'r The diflusion coefficients, D, given by this relation represent mean values, since carburization occurred simultaneously with nitriding. The rate of diffusion in a-iron has been determined from calculations based on data obtained by measuring the internal friction of samples at each of several frequencies and temperatures.' The expression for the diffusion of nitrogen in a-iron derived from these experiments is D= 1.4x10-1 e-it tudent Increasing carbon content decreases the diffusion of nitrogen in a-iron.3 Oxygen, either dissolved or combined, has been shown' to exert a marked influence on the diffusion of nitrogen from a nitriding atmosphere. D values increase rapidly with increasing amount of dissolved oxide in the metal, but diffusion is completely inhibited if preliminary oxidation has produced the slightest trace of iron oxide on the surface. Diffusion coefficients have also been calculated from permeability and solubility data,' but these values are of questionable accuracy since the boundary conditions assumed may not actually exist. Experimental Method The method selected for determining the diffusion coefficient of nitrogen in a-iron in the present investigation was the so-called fractional saturation method. This method consists of heating the specimen in an atmosphere of H2-NH8 mixtures of known composition for a predetermined time. Following this treatment, the specimen is analyzed for nitrogen; and the diffusion coefficient is calculated from a known relationship of the fractional saturation, time of diffusion, and dimensions of the specimen. This relation is based on a solution of Fick's second law and assumes that the surface of the specimen immediately reaches a given concentration which remains constant during the diffusion anneal. Tabular solutions are available4-5 and provide the relationship between fractional saturation and the quantity \/Dt /a, where D is the diffusion coefficient in cm2 per sec, t is the time of the diffusion anneal in seconds, and a, in the present experiments, is the half-thickness of the slab specimen in cm. The method is adequately discussed elsewhere.9-10 Material The material for this study consisted of 3/32 in. thick (0.24 cm) carbonyl iron plate. The major impurities in this iron are oxygen and carbon, which are readily removed by long time high temperature treatment in an atmosphere of purified hydrogen. In order to reduce the diffusion anneal time for saturation runs, some of this material was rolled to a thickness of 0.015 in. (0.038 cm) prior to the hydrogen treatment. Hydrogen treatments were carried out in a hydrogen-purified Armco iron tube heated in a global

Jan 1, 1957

By George Mah, Charles Wert

Internal-friction peaks caused by diffusion of oxygen and nitrogen have been observed in ytterbium. They are thought to be caused by the redistribution, under stress, of strain dipoles around an interstitial oxygen or nitrogen and a neighboring substitutional impurity. With the use of a simple geometrical model, diffusion coefficients for oxygen and nitrogen between special interstitial sites have been calculated. a) APPLICATION OF INTERNAL FRICTION TO MEASUREMENT OF DIFFUSION RATES IN DISSOLVED INTERSTITIAL ATOMS In bcc metals, the interstitial atoms occupy the centers of cube faces (0, 1/2, 1/2), or their equivalents, the center of the cube edges (0, 0, 1/2). An interstitial atom in this position causes an aniso-tropic distortion in the lattice. When stress is applied, mechanical relaxation can take place by the movements of the interstitial atoms. This relaxation has been used to obtain information concerning the movements of the interstitial atoms in the bcc metals. Data for these alloys have been compiled by Stanley and Wert. Other researchers have extended the investigation of interstitial diffusion to the close-packed metals. Gupta and weinig2 found an oxygen peak in a titanium, the height of which is linearly dependent on the oxygen concentration. They assumed, therefore, that they were dealing with movement of atomic ally dispersed oxygen in titanium. KG and wang3 determined that the diffusion coefficients of carbon in fcc steels and in nickel obtained by internal-friction methods were consistent with those obtained by macrodiffusion methods at much higher temperatures. Bisogni found oxygen and nitrogen peaks in hafnium by use of which he deduced the diffusion coefficient of these gases in hafnium. He observed further that the half-widths of these peaks corresponded almost exactly with those of a single-relaxation process; he assumed it to be caused by movement of atomically dispersed oxygen and nitrogen. From these studies, the deduction can be drawn that, in general, diffusion data can also be obtained for the interstitial diffusion in close-packed metals (or more precisely, in slightly impure close-packed metals). One group of such metals for which little data exist for the diffusion of dissolved oxygen and nitrogen is the rare earths. They have great affinity for gases, which enter solution interstitially. In this investigation results were obtained for the Yb-O and Yb-N interstitial solid solutions with traces of substitutional impurities; these solid solutions are of fcc structure. b) MECHANISM OF THE RELAXATION IN FCC CRYSTALS In the fcc structure, an interstitial gas atom is usually situated in the octahedral position (1/2, 1/2,

Jan 1, 1964

By T. S. Lundy, J. I. Federer

Chemically purified Zr95and Cb95 have been used in determining self-diffusion coefficients in the bcc phase of iodide zirconium over the temperature range of 900o to 1750°C. The temperature dependence of the diffusion coefficients could not be described by the usual Arrhenius-type equation over the entire temperature range. Values of the apparent frequency factors (D0)a and activation energies (Q)A for ZR95 varied from 4.8 x 10-6 to 2.5 x 10-2 sq cm per sec and 20,700 to 46,900 cal per mole, respectively, between 900°and 1750°C. Similarly, for Cb95, values of (Do) a and (Q)A varied from about 2.4 x 10'5 to 0.25 sq cm per sec and 26,500 to 56,800 cal per mole, respectively. The data may be described in terms of the a to ß transition temperature of 1136 °K and the absolute temperature of the diffusion anneals by the following eauations: SEVERAL studies on the diffusion of Zr95 in zirconium have been reported.1"5 The values of the constants contained in the usual Arrhenius-type equation for describing the temperature dependence of the diffusion coefficient, D = Do exp [- Q/(RT)], are summarized in Table I. The reported values of Do, the frequency factor, and Q, the activation energy, are seen to vary by factors of about 60 and 1.6, respectively. Examination of the data from any one study indicated reasonable consistency of measurements. The large discrepancies of over-all results, therefore, cannot be explained on the basis of experimental scatter. One possible explanation for the differences in results could be a varying impurity content of the zirconium. Another possibility is that the radioactive daughter, Cb95, influenced the values of some of the determined diffusion coefficients. Therefore, the first of the three purposes of this study was to reconcile the large differences in diffusion results that have been obtained. Several empirical relations have been proposed to relate the diffusion coefficients in solids with physical properties, such as the absolute melting point, the heat of fusion, and the heat of sublimation.

Jan 1, 1963

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 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 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 R. E. Smallman, J. C. Terry

J. C. Terry and R. E. Smallman (Llniuersity of Birmingham, England)—In a recent publication53 Wood and Westbrook have reported the results of an investigation of the tensile behavior of fl-phase AgMg alloys. These results agree in broad outline, but differ in the details, with those obtained in the above laboratory and, consequently, some discussion of their paper would seem appropriate. In our experiments, tests were carried out on extruded wires, 2 mm diam, in a hard-beam tensile machine, and while an oil bath was used for the tests up to 150°C, above this temperature the oil bath gave rise to serious contamination of the specimens and hence tests above 150°C were made in vacuo. This procedure is different to that adopted by Wood and Westbrook. The ß-phase alloys exhibit differences in mechanical behavior when they are tested in different temperature ranges. In agreement with Wood and Westbrook, three characteristic ranges are observed which may be classified as low, intermediate, and high temperatures, respectively. Our experiments show that in the low-temperature region, the shape of the stress-strain curves is similar to that reported. However, in addition, it is observed that the temperature at which the low-temperature region ends is markedly dependent on strain rate, and increase with increasing strain rate as shown in Fig. 18. The temperature at which a transition from the low to the intermediate temperature takes place is about 0.4 to 0.45 of the absolute melting point, Tm. This transition temperature coincides with that at

Jan 1, 1963

By D. K. Deardorff, Haruo Kato

D. K. Deardorff and Haruo Kato (U. S. Bureau of Mines)—We wish to refute the 1875" 20°C value that Giessen, et al., report as the transformation temperature of hafnium. Although these authors state that their work along this line will be reported later, we can&apos;t leave their value undiscussed, for we believe it to be 125°C too high. Our value of 1750° 20°C, which the authors mention, has been substantiated in our laboratories by the use of three other methods. The first method of substantiation was by heating and cooling curves using a hafnium/tungsten thermocouple, the couple having first been calibrated against a t/Pt-10 pct Rh couple. The second method was by quenching and metallography of dilute Hf-Ta alloys. The third cussion, it may be pointed out that the observations of Rogers referred to large unidirectional strains where the internal cracks or voids appeared only after a strain of 32 pct or more. On the contrary the internal fissures observed, as a result of fatigue cycling, occurred for a total extension of some 5 pct and furthermore followed the directions of the slip zones. Finally, it is not our contention, as implied in Dr. Alden&apos;s last paragraph, that the tensile stress is an important factor in crack propagation. Indeed, in connection with the reference to the companion report, special note is made of the fact that "Deformation was apparently concentrated in grains which have a slip plane nearly perpendicular to the specimen axis and thus near the plane of maximum applied shear." This dependence of the growth of fissures on the orientation of the slip planes with respect to the direction of maximum applied shear is clearly shown in work on the torsional cycling of single crystals which has been submitted for publication. method was by heating and cooling curves with W/W-26 pct Re thermocouple. Counting the original resistometric method, four different methods have yielded 1750" 20°C as the transformation temperature of hafnium. All our work on determination of the hafnium transformation temperature has shown that the specimen under test must be quickly heated to and through the transformation temperature if the lowest possible transformation value is to be determined; otherwise a higher value not representative of pure hafnium will result. Speed was emphasized in all methods. In our resistometric work the corresponding voltage, amperage, and temperature readings were taken quickly and the transformation temperature was usually reached within 5 min total heating time. In the thermal analysis work involving Hf/W or W/W-26 pct Re thermocouples the transformation temperature was attained within three minutes total heating time, this time being less because the two variables were

Jan 1, 1963

By R. E. Smallman

R. E. Smallman (University of Birmingham, England)—Recently, Tedmon and Ferriss11 have determined the yield stress parameters oi and ky for tantalum by measuring the lower yield stress as a function of grain size 2d and fitting the results to a relationship of the form They report that although ky , which is taken to be a measure of the dislocation locking strength, is small (- 2 to 4 x 106 cgs units) a substantial yield drop is nevertheless observed in a normal tensile test. Niobium gives a similar result,12-14 as pointed out in the original work by Adams et a1.,12 and in order to check this apparent anomaly the yield-stress parameters of electron beam-melted niobium have recently been reanalyzed15 by the Luders strain technique. In this method the strain hardening part of the stress-strain curve is extrapolated to zero plastic strain; the intercept on the preyield portion of the curve is taken to give oi, whilst the difference between oi and the lower yield stress gives kyd-1/2. The results indicate that ky increases with increasing grain size and hence, a plot of vs d-112 yields an apparent ky, which is lower than the true value. A similar effect could account for the small ky found in the relatively pure tantalum used by Tedmon and Ferriss. The variation of ky with grain size shows that dislocations are more strongly locked in coarse-grained specimens than in fine-grained samples. In niobium, this may be attributed to the fact that the dislocation density in the fine-grained material is higher than that found in the coarse-grained samples which are given a sufficiently prolonged anneal to remove any residual substructure and, since the metal contains only a small amount of interstitual impurity, a variation in locking occurs. By contrast, application of both the grain size analysis and the Luders strain method to yield-stress data from commercially pure vanadium containing a large amount of interstitial impurity gives consistent values of oi and ky, with ky independent of grain size and temperature. Electron microscope observations show minor variations in dislocation density from grain size to grain size, but in any case in this material the dislocations are heavily locked with precipitate. On yielding new dislocations are generated and, as a consequence, the importance of any differences in dislocation density between the various specimens of different grain size is considerably reduced. It is perhaps significant that Adams and lannucci,16 working with a grade of tantalum containing a higher interstitial content than that used by Tedmon and Ferriss, prepared the specimens of different grain size by annealing in the temperature range 1500" to 2000° C to minimize any differences in dislocation structure, and found that ky had a value of 1.04 x 107 cgs units, independent of testing temperature. Such behavior is consistent with the dislocations being locked by carbide precipitates so that the generation of free dislocations is an athermal process. The recent work of Gilbert et al.17 also shows that in tantalum there is no significant variation of ky with grain size provided it contains 150 ppm of oxygen. In this case, however, the dislocations are not locked by precipitate and ky is temperature dependent. C. S. Tedmon and D. P. Ferriss (authors&apos; reply)— We would like to thank Dr. Smallman for his interesting comments and discussion to our paper, "The Dependence of Yield Stress on Grain Size for Tantalum and a 10 pct W-90 pct Ta Alloy".18 It was suggested that perhaps the relatively small values obtained by us for ky of tantalum could be attributed to the same cause that accounts for the apparently small values of ky that result when it is determined by the Luders Strain technique. Since our values were obtained by plotting the lower yield stress vs the reciprocal of the square root of the grain size, it is not clear how this could be the case. The values of ky in this experiment have been calculated, using the Luders strain technique. With this method, values for ky on the order of 2 x 105 to 5 x lo6 cgs units were obtained. In spite of this rather large variation, the magnitudes are still small, and there appeared to be no good correlation between ky and the grain size or the yield stress, probably because of the difficulty in accurately extrapolating the work-hardening portion of the curve back to zero plastic strain. As was shown in the original data,18 there was little work hardening in any of the curves, at any temperature. In his discussion, Dr. Smallman also points out how ky has been observed to increase with increasing grain size, when determined by the Luders strain technique. There are at least two possible explanations for this. In the first case, if it is assumed that the bulk of the interstitial impurities are concentrated at the grain boundaries, then, of course, the available grain boundary area would decrease with increasing grain size, thus presenting less area for the interstitials, which would then presumably increase the concentration within the grains, thereby increasing the locking of the dislocations. In the second case, the increase in ky with increasing grain size would be attributed to the nature of the grain boundary itself. One of the several ways of deriving the Hall-Petch equation19 is based on the stress concentration arising from a pile-up of dislocations at the boundary. The ability of the stress concentration to unlock a source in a neighboring grain would depend on the strength of the grain boundary. As is well-known, the nature and struc-

Jan 1, 1963

By W. C. Leslie

W. C. Leslie (Edgar C. Bain Laboratory for Funda mental Research)—This investigation, with its com bination of high-purity metal, calorimetry, and metallography, will serve as a model for annealing studies for a long time to come. The evidence for a competition between recovery and recrystalliza-tion is particularly convincing. The demonstration of edge-nucleated recrystallization was so clear that it may obscure the necessity for other types of "nucleation" sites; otherwise, single crystals of aluminum could not be recrystallized after cold work. At least three types of sites have been found to operate in iron: 1) high-angle boundaries, probably in the same manner as in aluminum, 2) matrix sites, 3) inclusions or second-phase particles. In each instance, the cells developed during cold work and perfected during recovery are the "nucle for recrystallization. Observations by ourselves and others of the dislocation structure of cold-worked metals and of the structural changes that occur during annealing have led us to doubt the validity of the basic assumption of the Lucke-Detert theory, and of the modification developed by Gordon and Vandermeer, that during recrystallization of a metal containing foreign elements in solid solution a high-angle boundary is ad vancing into a cold-worked matrix having a random distribution of solute atoms. We contend that an es sential part of the cold-working and annealing of solid solution alloys is the trapping of solute atoms by the low-energy "wells" afforded by individual dislocations and by dislocation arrays. If cells are formed during cold work, the cell walls are stabilized by this concentration of solute atoms. Thus, solutes inhibit recrystallization not only by decreas-ing the rate of high-angle boundary migration, but also by preventing the formation of high-angle boundaries by subgrain growth or coalescence, i.e., solutes can inhibit both "nucleation" and growth. In addition to stabilizing the dislocation Structure, the solute-dislocation interactions may produce clusters of solute atoms which are not as readily assimilated into the recrystallized grains as are individual solute atoms. There is an additional complication. The dislocation structure formed upon cold working a dilute solid solution may not be the same as that formed during cold working of the pure solvent metal. The solute can either enhance or minimize the formation of cells during cold working. Both effects have been observed in binary alloys of iron. The annealing process is inextricably connected with the mechanisms of strain hardening and solid solution hardening. Although the correlation between experimental boundary migration rates and the predictions made from the theoretical equations are impressive, it should be mentioned that in at least four other instances (Pb-Ag and pb-Au,15, Fe-Mn,16, Fe-Mo)17 the agreement was rather poor. In brief, while it is probable that the migration of high-angle boundaries is held back by solutes in the manner described, this is only a partial explanation of the total effect of solutes upon recrystallization of cold-worked alloys. Paul Gordon and R. A. Vandermeer (author&apos;s reply)— The authors first wish to thank Dr. Leslie for his compliments of this work. It is perhaps worth pointing out that some of Dr. Leslie&apos;s remarks are directed toward subject matter covered in two earlier papers in our work.18,19 We agree with Dr. Leslie&apos;s main contention that the exact nature of the metal structure in the vicinity of a boundary should have an effect on the boundary migration. The theory of Lucke and Detert does not take such detail into account, nor does it account for orientation effects on the migration rates. We assume that since our data checks the theory so well, the effects of detailed structure are statistically averaged out by the polycrystalline techniques used just as are the effects of orientation factors.

Jan 1, 1963

By E. A. Steigerwald

E. A. Steigerwald (Thompson Ramo Wooldridge, Inc.1— he authors&apos; results clearly indicate that cracking can be produced by the hydrogen pressure developed during a charging operation. This type of cracking or blistering has also been observed in polycrystalline materials24"28 when the charging conditions are sufficiently severe and is often referred to as irreversible embrittlement since it cannot be removed by a baking treatment. There are additional data, however, which must be considered before a pressure theory can be generally employed to account for all failures which occur as a result of hydrogen. In many cases, hydrogen embrittlement in a tensile test or in delayed failures under static loads is a reversible phenomena which cannot be simply explained on the basis of preexisting cracks generated by the charging operation. It is this aspect of the problem which has prompted many investigators to seek mechanisms other than hydrogen pressure to explain their results.24&apos;n728 Fig. 15 indicates an example where, under specific experimental circumstances, hydrogen embrittlement can occur at liquid nitrogen temperatures. In this case, which has been previously decribed,&apos;&apos; specimens were charged with varying quantities of hydrogen, immediately quenched, and tested in liquid nitrogen (-320°F). A companion set of identical specimens were charged, aged at 300°F to remove the hydrogen, and also tested at -320°F. When the current density was greater than lo-&apos; amp per sq in., embrittlekent occurred in both sets of specimens, indicating that cracking had occurred during charging and the embrittlement, as in the case of Fe-Si single crystals, was irreversible. At current densities between approximately 103 and lo-&apos; amp per sq in, the embrittlement was present only for those specimens which contained hydrogen during the testing sequence. The embrittlement was therefore reversible with respect to the aging and charging operations. Since extensive hydrogen movement would not be expected at -320°F, it is difficult to reconcile these data with a mechanism which requires pressure and pressure dependent growth of preexisting cracks. There are other features of hydrogen embrittlement such as the reversibility of the incubation time for delayed failure with respect to applied stressg0 and the influence of prestraining31 which are also difficult to explain using a pressure model. Any general mechanism of hydrogen embrittlement will have to consider the reversible aspects of the embrittlement data as well as the irreversible portion which has been clearly presented for the Fe-Si crystals and which is consistent with a pressure model. A. S. Tetelman and W. D. Robertson (authors&apos; reply)—he authors agree with Dr. Steigerwald that a general mechanism of hydrogen embrittlement must be applicable in all cases where embrittlement occurs. Dr. Steigerwald&apos;s experiments were performed on an iron alloy which has an extremely complex microstructure, and therefore does not lend itself to the direct and detailed observations that can be made in Fe-Si. The change in the characteristics of cracks as a consequence of annealing at 300°F is not really known in detail but it is probable that stress-relaxation (blunting) occurs, dislocations produced near the crack tips will be pinned by carbon atoms, and hydrogen will be lost to the atmosphere. Any, or all of these effects of annealing will alter the ease with which a crack subsequently propagates under applied stress. A quantitative treatment of the problem must take these effects into account. Since diffusional processes are presumably eliminated at -320°F, the general mechanism proposed by Dr. Steigerwald&apos;s colleagues cannot be operative at this temperature. A detailed discussion of the general&apos; inapplicability of this mechanism has been presented elsewhere. However, the data presented by Dr. Steigerwald in his discussion can be explained in terms of a pressure model. Crack propagation under internal pressure P and applied stress occurs when where is the total energy expended in creating new surface area and by plastic work at the crack tip. The total crack length increases with increasing current density, since we have shown that it systematically increases with hydrogen concentration and Dr. Steigerwald has shown that hydrogen concentration increases with current density. For large L (high current density) Eq. [I] can be satisfied even if P = 0 and the embrittlement process does not require the presence of hydrogen. Specimens charged at a lower current density will con-

Jan 1, 1963

By J. D. Meakin

J. D. Meakin (The Franklin Institute Laboratories)— In a recent paper Garofalo12 has shown that a number of experimental creep results can be represented by the empirical relation In this expression ? is the steady creep rate, s is the applied stress, and A is a constant at a given temperature; a and n are adjustable parameters. Garofalo has shown that Expression [6] approximates to a power function at low stresses and a simple exponential function at high stresses. Among the data used by Garofalo are the results we published for creep of copper." For these results we found that the best correlation was an exponential law with different parameters in the low-and high-stress region, respectively. That is, i = A exp qs where A and q have different values above and below a critical stress a,. In Ref. 13 are listed a variety of observations which support the proposal that different mechanisms are operative at stresses above and below a,, and it is not felt appropriate to repeat those observations here. The purpose of this note is to demonstrate that, although the representation used by Garofalo does fit the experimental data very well, this fit cannot be used to conclude that only one mechanism is rate-controlling. The argument is best made graphically and is illustrated in Fig. 9. The continuous curves 2 and 3 represent pairs of simple exponential functions which intersect at i = 10-5. The curve 2 closely resembles the copper results in that a change of slope of 2:1 occurs at i = 10-5; the two functions shown are in fact: e = 10-7 exp (1.150) and ? = 10-6&apos; exp (0.576s) For purposes of comparison, curve 3 represents two exponential functions with a change of exponent of 3:1 and curve 1 has the exponent 1.150 throughout. It is quite clear that a satisfactory straight-line fit is obtained on a Garofalo plot for all three curves. The curves represent processes which have either a single stress exponent or two ex- ponents in a ratio as high as 3:l. It must, therefore, be concluded that the ability to obtain a linear dependence between log i and log (sinh cyo) cannot be taken as evidence for a single activated process. In fact, to some extent the way the experimental points quoted by Garofalo lie about a best fit straight line on the log (sinh as) plot indicates that two processes are indeed occurring. This is seen in Figs. 7(c) and 8(c) of Ref. 12 where it is particularly evident that the experimental points deviate from the straight line in a manner similar to curves 2 and 3 of Fig. 9. It is, of course, recognized that the generally used exponential form is an approximation to the hyperbolic sine function which is not valid for exponents of less than 1.2, e.g., qs < 1.2. The only curve in Ref. 12 which is affected by this restriction is Fig. 6(b) where the deviation from a In ? vs s

Jan 1, 1964

By T. S. Lundy, J. Askill

J. Askill and T. S. Lundy (Oak Ridge National Laboratory)—Moore has proposed a simple correlation between the activation energy for solute diffusion in fee metals and the atomic volume of the diffusing species using both tracer and chemical-diffusion data. The first point we wish to make is that it is wrong to attempt such correlations without separating the two types of data. Activation energies obtained using tracer techniques cannot, in general, be directly compared with those obtained from chemical-diffusion experiments. A knowledge of the variations of chemical potentials with composition is necessary and chemical-diffusion data must be corrected for such variations, even for dilute alloys, before a comparison is possible. Secondly, for nickel, iron, aluminum, and lead, Moore neglected a number of recently published works, e.g., Al26 and Mn54 in aluminum,46 cr51 in nickel,47 and Fe55 in iron.48 These and others should have been used. If one considers only the tracer diffusion data, there is left no simple correlation of the type proposed by Moore. For example, in the case of solute diffusion in aluminum the only reliable tracer data listed by Moore are for zinc and aluminum. The nickel, cobalt, and iron data of Agarwala49 are representative of near-surface diffusion-not bulk diffusion. In conclusion we suggest that for tracer diffusion data in these fee metals there is no justification for proposing any simple correlation of activation energy with atomic volume using the limited data that are presently available. R. H. Moore (author&apos;s reply)—The writer has proposed a simple correlation which is useful in estimating the internal consistency of diffusion data. The accuracy of the correlation is, of course, a function of the number of data available. Lundy and Askill take issue with the writer&apos;s decision to include data for the systems: nickel, iron, aluminum, and lead, taking the view that the data are insufficient to establish the correlation. The writer agrees that the data are insufficient and has cau- tioned the reader that the correlation is tentative in these instances. Inclusion of these systems is justified by the interesting trends the correlation reveals. For example, the distinction between interstitial and substitutional diffusion may be clearly established, Figs. 4 and 6, and the behavior of transition elements and nontransition elements is indicated to parallel the behavior illustrated by the silver and copper systems. Lundy and Askill have singled out the aluminum system for special criticism. The writer chose to discuss the data for diffusion of iron, nickel, and cobalt in aluminum in the terms used by the original authors9 and has included the comments of Balluffi.l0 The writer did not intend the reader to conclude that data for these elements should correlate with data for the nontransition elements as Lundy and Askill have evidently assumed. Iron, nickel, and cobalt form intermetallic compounds with aluminum, so the activity coefficients of these elements may be expected to deviate markedly from unity. This may account for the low frequency factors observed by Hirano.9 The nontransition elements, on the other hand, yield relatively simple phase diagrams with no evidence for intermetallic compound formation as in the case of iron, nickel, and cobalt. In dilute solution, Henry&apos;s law should be closely obeyed, the activity coefficients should not deviate markedly from unity, and the effect on the activation energy should not be large. The accuracy of the correlation applied to these systems will improve as the data is extended. It does not seem unreasonable to conclude that its extension should be encouraged.

Jan 1, 1965