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By N. N. Breyer, W. R. Warke, S. Dinda

A model for the low-temperature peak, LTP, in fcc metals is presented. In high stacking fault energy metals, e.g., aluminum and nickel, it is proposed that a reversible dislocation glide and climb process might give rise to the observed high relaxation strengths and activation energies equivalent to volume self-diffusion values. In low stacking fault energy metals such as copper, gold, and silver, dislocation climb is energetically unfavorable at T < 0.5 Tm and the relaxation process is therefore mainly one of reversible glide. This model is used to explain the effect of a change in grain size and impurities on the LTP. THE low-temperature grain boundary damping peak, LTP, in spectroscopically pure aluminum,&apos; copper,17&apos; gold,2 nickel,3 and silver4 has recently been the subject of a detailed investigation by our laboratory. The main results are summarized in Table I. An empirical relationship was found between the peak relaxation strength, AE, and the width of the dissociated dislocation, do,* given by: do = µa2/24p? (Ref. 5) [I] where p is the shear modulus, y is the stacking fault energy,6-8 and a is the lattice parameter, Table 11. 4E is plotted against do in Fig. 1. Two regions are apparent: region (a)! which contains all but one of the metals, where AE decreases linearly with increasing do, i.e,, AE 1/do; and region (b), where ?E is approximately independent of do. A similar trend is observed when the ratio Qp/QL is plotted as a function of do, Fig. 2. (Qp and Ql are the activation energies for the peak and for lattice diffusion, respectively). In the past, when Qp and QL were found to be comparable, the relaxation peak was explained in terms of grain boundary sliding.10 The equivalence of Q, and Qb. the activation energy for grain boundary diffusion, prompted the suggestion that it was a consequence of reversible grain boundary migration on an atomic scale." A new model for the LTP, which is based on the experimental relationships in Figs. 1 and 2, is presented. In region (a) it is suggested that stress relaxation occurs through the reversible glide and climb of grain boundary dislocations; in region (b) only reversible glide can take place. The resultant effect on the grain boundary might be sliding or "a bowing out", but, since the total distance moved will be 50A, the atomic movements are considered of primary im- portance. It must be emphasized that this is only a qualitative model, but at the moment it appears the most likely way to explain the widely varying, but re-

Jan 1, 1969

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

Treatment of the finite, diffusion-controlled, two-phase, moving-interface homogenization problem has been carried out by numerical methods for a wide range of input parameters. Solutions have been obtained for planar, cylindrical, and spherical diffusion geometries. The effects of parameters such as the interdiffusion coefficients (concentration-independent) of- both phases, the concentrations (time-independent) of each phase at the interlace, mean composition, initial size of the dissolving- phase, and initial composition of- the two phases are considered. The results are displayed to show both the position of the interjace and the degree of homogenization (expressed in terms of concentration at the matrix phase symmetry boundary) as a function of diffusion time. Typical exaw~ples to which the results may be applied are discussed. A limited number of exact, closed-form solutions to the multiphase, diffusion-controlled, moving-interface problem exists in the literature, e.g., Refs. 1 to 7. The exact, closed-form solutions generally consider the outermost phases to be infinite in extent and also assume an interfacial velocity function. It is through use of such boundary conditions that closed-form solutions are readily obtained. An extensive literature also exists on numerical solutions to the mathematically analogous solidification problem, e.g., Refs. 8 to 12. In addition, a numerical solution involving mass transfer with spherical interfaces and infinite boundaries has recently been carried out.13 A practically important class of diffusion problems exists, however, in which the boundaries of each phase away from the interface are finite. For example the finite boundary condition arises when one sets up a model for analyzing the homogenization behavior of two-component powder compacts in two-phase systems or for studying the solution behavior of precipitates. Although exact, closed-form solutions have as yet not been found to this class of problems, solutions are possible using numerical methods. The purpose of this paper is twofold: 1) to describe a numerical method for treating the two-phase, diffusion-controlled, moving-interface problem involving finite boundaries with planar, cylindrical, and spherical interfaces; 2) to present the results of a parametric study which identifies the role played by each variable appearing in the analytical model. R. A. TANZlLLI,Student MemberAIME,onleaveofabsence from the General Electric Co., Re-entry Systems Department and A. W. HECKEL, Member AIME, are Graduate Student in Materials Engineering, and Professor, Department of Metallurgical Engineering, respectively, Drexel Institute of Technology, Philadelphia, Pa. Manuscript submitted May 6. 1968. IMD MATHEMATICAL MODEL The three geometries analyzed are shown in Fig. 1. For each configuration a symmetry element is shown, across whose boundaries the mass transfer is zero. Mean composition, C, and the characteristic solute-rich phase half-thickness (or radius), 1/2, are the independent variables while the characteristic symmetry element half-thickness, L/2 (measured from solute-rich phase center to the matrix phase plane of zero mass transfer), is a dependent variable. The symmetry element for a planar interface accurately represents a real diffusion situation involving the stacking of symmetry elements of constant size. Because cylindrical and spherical symmetry elements of constant size cannot be stacked to fill space, the meaning of the dimension, L/2, for these situations may be considered in terms of the following approximations: and where NA is the number of parallel cylindrical elements per unit area on a surface normal to the cylinder axes and Nv is the number of spherical elements per unit volume. The model consists of a solute-rich phase matrix phase composite of limited mutual solubility. The concentrations at the interface are assumed constant with time; no assumption of local equilibrium at the interface is necessary except for the case where the

Jan 1, 1969

By E. J. Nielsen, P. R. Strutt

A study has been made of the progressive changes in the distribution of etch-pit structures occurring during high-temperature creep in copper + 7 wt pct Al single crystals oriented with a [113] tensile axis. The two equally stressed glide systems with the highest Schmid factor would be expected to form subboundaries of the type predicted by Kear.2 The alignments of etch-pits on sections parallel to different (111} planes consistent with these types of boundaries were not observed. However, they were consistent with planar subboundaries (on a macroscopic scale). From an analysis of Amelinckx1 it may be shown that stable cross-grid dislocation boundaries may form in the primary slip planes. These boundaries form when dislocations with a Burgers vector not in the slip plane move into the plane by combination of climb and glide. THE geometry of subboundaries formed by the interaction of dislocations of two glide systems has been analyzed by Amelinckx,1 and the particular types produced by deforming fee crystals are predicted by ear.&apos; In this paper types of boundaries which may be formed when climb as well as glide occur are discussed as this is relevant in high-temperature creep. It is assumed in the present investigation that the etch-pits observed in Cu + 7 wt pct A1 on surfaces parallel to {111} planes delineate the sites of dislocations. Although there is no direct evidence for this previous work on a-Cu/Al single crystals by Mitchell, Chevrier, Hockey, and Mon-aghan,3 would show this assumption to be reasonable. The alignments of etch-pits which form during creep are studied on sections parallel to each {111) plane. It is then deduced that these alignments are consistent with a specific type of planar subboundary. The Cu + 7 wt pct A1 single crystals had a [113] tensile axis and Fig. 1(a) shows schematically the relation of the slip planes and slip directions (as represented by tetrahedron ABCD) with reference to the tensile axis. The two equally stressed glide systems with the maximum Schmid factor namely ß-AD and (a-BD, from the analysis of Kear,2 would be expected to form the boundaries shown in Fig. l(a) and (b), also Fig. 5(a) and (b). EXPERIMENTAL PROCEDURE The a-Cu/Al single crystals were grown and annealed in a "gettered" argon atmosphere. Chemical analysis showed the aluminum content to be uniform in each crystal and the difference between crystals was maintained to an accuracy of ± 0.25 wt pct. The initial dislocation density and mean subgrain diameter after annealing was -106 cm-2 and 250 µ, respectively. Surfaces parallel to (111) planes were produced by specially developed electrolytic machining processes. The {111} faces were next electropolished for 5 min in a solution consisting of 25 g chromium trioxide, 113 ml glacial acetic acid and 40 ml water; the applied potential was 8 v. Dislocation etch-pits were revealed using l an etchant described by 1 ml bromine, 45 ml HCl, and - 250 ml water. RESULTS In crystals strained into secondary creep at higher stresses (443 and 750 g - mm-2 at 650° C aligned rows of etch-pits parallel to slip plane traces were evident in sections parallel to the (1111, (ill), and (111) planes, see Fig. 3. As well as the longitudinal alignments in Fig. 3, well formed randomly oriented arrays indicative of an equiaxed subgrain structure are evident. At the lower stresses (100 to 230 g . mm-2) only an equiaxed structure formed during creep. The sections in Fig. 3 are from a crystal crept for 70 hr at 650°C with a CRSS of 443 g.mm-2. Two identically oriented crystals were also deformed at the same temperature and stress for 5 min and 4 hr. In the crystal crept for 5 min, the etch-pits were randomly distributed with no tendency for directional alignment, see Fig. 2(a). As shown in Fig. 2(b) aligned arrays were evident after 4 hr creep but they were not nearly so well defined as in Fig. 3. The alignments (parallel to the arrows) in Fig. 3 are consistent with the existence of boundaries in the two main slip planes a and ß. The way in which this is deduced is seen by reference to Fig. l(c), where the existence of boundaries in the a and ß planes is verified by sectioning parallel to a,ß, and d. The (111) and ß(111) planes intersect the d(111) plane along BC [101 ] and AT [011] and alignments parallel to [101] and [011] are clearly evident in Fig. 3(c) in a section parallel to the d(111) plane. Similarly the a, and ß planes in Fig. l(a) intersect each other along DC [110] and hence there will be an alignment parallel to [110 ] in sections parallel to the a-plane and the ß-plane; this is evident in Fig. 3(a) and Fig. 3(b). It is interesting to note that alignments of etch-pits consistent with the boundaries predicted by Kear2 were not observed; see Figs. l(a) and l(b). The geometry of boundaries in {111} planes as shown in Fig. l(c) is discussed later. In Fig. 4(a) the individual etch-pits are resolved and the alignments are exactly parallel to the slip trace direction [101]. However, in some areas alignments deviate away from the slip trace direction by as much as 10 to 15 deg, this is evident in Fig. 4(b), and in Fig.

Jan 1, 1969

By A. R. Krause, C. Laird

In order to establish whether or not there is a real temperature effect in fatigue (independent of environment) , poly crystalline copper and Cu- 7.9 A1 alloy have been cycled at 298° and 7° K in vacuo and the fatigue lives compared with those in air and in liquid nitrogen. The lives of both copper and the alloy were found to be highly temperature-dependent in the absence of environment. This result casts serious doubt on the validity of the cell structure hypothesis for stage I crack propagation as presently formulated, because it predicts that there should be no such tempevnture dependence. On the other hand, the plastic blunling process is consistent with the result. Effects of environment aside, the homogenization of slip which accompanies testing at low temperature, and at low strains, seems to be the main cause for increased fatigue life. At high strain amplitudes, the fatigue lives of wavy slip materials, typically copper, are independent of temperature.&apos; It is well-known, however, that low-strain lives greatly as as the temperature of testing is decreased. By contrast, the lives of planar slip materials, such as Cu-7.9 pct A1 alloy, increase to an even greater extent with decreasing temperature throughout both the high and low strain ranges.1&apos;2&apos;5 The mechanism of this temperature effect is associated with the earliest stages of fatigue failure,&apos;" crack nucleation, and stage I growth,"&apos; which is slow propagation along slip bands to the depth of a few grain diameters. Such life behavior has been interpreted on at least two different bases. On the one hand, those interested in the temperature effect at high strain amplitudes1 believe that stage I growth occurs by the plastic blunting process of crack propagation.7&apos;9 They explain the effect in planar slip materials by the homogenization of slip* which accompanies fatigue testing at low temper- atures and serves both to delay crack nucleation and to decrease the rate of stage I propagation. On the other hand, Holt and Backofen,2 who have studied the effect in low strain fatigue, believe that stage I growth can be interpreted by a cell structure hypothesis.10-12 They have challenged2 the conclusion that there is a real temperature effect in this regime of fatigue testing and have interpreted the increased fatigue lives almost entirely in terms of the "environmental-protective&apos;&apos; effect of the liquid nitrogen and helium baths used to obtain low temperatures. This interpretation by Holt and Backofen2 may offer a means of discriminating between these two mechanisms as currently formulated and used to explain stage I growth. On the basis of the plastic blunting process applied to stage I crack propagation,7* the low strain fatigue lives of both wavy and planar slip materials should be increased with decreasing temperature. This follows because both materials show increased slip homogenization in this strain regime."13 Consequently, crack nucleation in intensified bands will be delayed and the linking of such small cracks into larger stage I cracks will be difficult. In addition, the blunting process required to lengthen a stage I crack from the order of 2 to 10 (where the strain concentration of the crack begins to overcome the slip homogenization property of the material) will also be retarded. These delays will give rise to longer lives in both kinds of material. In contrast to the blunting hypothesis, no temperature dependence has been predicted on the basis of the cell structure hypothesis, because it is well-known that materials cycled at low temperature show no differences in type of dislocation structure for a given strain amplitude.18"20 If the lives of wavy and planar slip materials do show a temperature dependence when the environment is eliminated as a variable, then it is questionable whether cell structures per se have a fundamental role in fatigue fracture. Accordingly, specimens of copper and Cu-7.9 wt pct A1 have been cycled at 298° and 77°K in vacuo and the fatigue lives compared with those in air and in liquid nitrogen, in order to establish whether or not there is a real temperature effect in low strain fatigue. Since it is difficult to measure the strains in specimens when cycled in vacuo, S-N curves have been used as the basis of comparison. In studying the influence of temperature on fatigue life in ordinary environment, Holt and Backofen2 used the superior basis of E-N curves. However, they also published S-N curves and thus established the relationship between E-N and S-N curves. This relationship is used to support the S-N comparison reported in the present investigation. EXPERIMENTAL Materials. The copper employed in this investigation was of 99.99 pct purity and the cu-7.9 pct A1 was prepared from metals of the same purity. The stock, of 3 in. initial diam, was reduced in size by rolling

Jan 1, 1969

By S. Dinda

A series of as -quenched 4340 bars were drawn through a carbide die to various reductions. The X-ray diffraction technique of Lopata and Kula was employed to detect preferred orientation in drawn martensitic steel bars with low amounts of deformation, as lord as 0.8 pct The specimen face of each bar examined was cut at a 45-deg angle to the bar axis. The reflecting planes in the 45-deg face were varied by appropriate rotation of the sample using a spectrogonionzeter. TIE X-ray bean of a diffractometer was reflected from the center of the bar and the diffracted intensity was delected with a proportional counter and recorded. Intensity peaks were developed by cold working for 110 planes oriented at 0 and 60 deg to the bar axis. The intensity peaks increased with increasing defortnalion us a preferred orientation with a 110 texture developed parallel to the drawing direction. The intensity peaks for deformed as-quenched specimens remain unchanged after tempering at temperatures as high as 1000°F. The same amount of preferred orienlalion was observed both inferritic (hot-rolled) and martensitic (as-quenched) structures after an equivalent amount of deformation. THE deformation of martensite with medium carbon content. less than 0.5 pct, has been studied by Breyer et a1.1,2 It was reported that changes in properties such as resistivity, carbide precipitation, and the introduction of a yield point phenomenon were produced after cold reduction of as-quenched AISI 4340 steel bars. Later, Breyer and Nachtman3 studied the effect of cold reduction upon X-ray line intensity. They showed that the integrated 110 line intensity increased with increasing deformation when the planes examined were perpendicular to the die drawing direction. The integrated 110 line intensity for planes oriented at 45 deg to the die drawing direction, in contrast, were found to slightly decrease. These changes were proposed to be consistent with the previously proposed model of a stress-induced ordering of carbon atoms in the vicinity of dislocations.1,2 Objections can be raised to the above interpretation of the X-ray results on two grounds: a) Rough structure factor calculations indicate that the intensity changes are too large (50 pct observed vs 2 pct calculated4,5) to be the result of changes in the location of iron atoms produced by the stress-induced ordering of the carbon atoms. b) The results might be explained in terms of preferred orientations, although X-ray evidence of the development of texture has not been reported in the literature for deformations as slight as 1 or 2 pct. The aim of the present work was to determine if preferred orientation was present in such cold-drawn martensitic steel bars. In drawn rod or wire there is generally a certain crystallographic direction which is aligned in the direction of the wire axis, and the crystallographic planes are distributed symmetrically around this "fiber axis".6-8 This type of cylindrical specimen, with the fiber axis located at the center, will show rotational symmetry. Lopata and Kula9 proposed an experimental method utilizing a specimen cut at 45 deg, see Fig. 1. The X-ray beam is diffracted from the center of this bar cross section. The specimen is rotated around an axis perpendicular to the bar axis and lying in the 45-deg cut face. This permits the angle between the normals to the reflecting planes and the bar axis to be varied from 0 to 90 deg.9 With this arrangement the errors due to absorption and irradiated volume compensate each other.&apos; This greatly simplifies analysis of the data and is of considerable advantage for quantitative measurements. If there is preferred orientation in the specimen, more planes are oriented in a particular direction in the bar. When the bar is rotated to the favorable Bragg condition for that particular orientation, the intensity will be higher than that for some other angle. This technique was adopted for the present investigation.

Jan 1, 1969

By A. F. Crawley

The density and viscosity of 1iquid thallium have been measured by absolute methods to temperatures of about 200° and 150°C, respectively, above the melting point. These new data reported, especially density data, do not closely confirm previous work. Density p, in g per cu Cm, is shown to vary linearly with temperaluve t, in °C, according to the equation p = 11.658 - 1.439 X l0-3t. The viscosity data obey the well-known Andrade equation nv1/3 = A exp C/vT , the constants A and C for thallium having values of 2.19 x A and 79.648, respectively. This paper reports some new data for the density and viscosity .of liquid thallium. Measurements of these fundamental physical properties were undertaken as part of a continuing research program at the Mines Branch, Department of Energy, Mines and Resources, Ottawa. Canada. A literature search has revealed that data are so scarce that there could not be a consensus on the true values of the density and viscosity of liquid thallium. To be more specific, there exists only one set of viscosity data&apos; and only two acceptable sets of density data,273 one of which is limited in scope.3 In Liquid Metals Handbook,3 another density study is reported but indications of impurities in the thallium render the results suspect. In this situation, further careful experimentation was required to realize the true density and viscosity of thallium. EXPERIMENTAL METHODS Density. Densities were determined using a graphite pycnometer. The technique and its accuracy have been discussed in earlier papers.4&apos;5 It is considered that experimental data can be obtained which are accurate within +0.05 pct, all sources of random and systematic errors having been evaluated. Density results for thallium were identical whether measured under an atmosphere of argon or a vacuum of 5 x 10-6 torr and, for the most part, the argon atmosphere was used. Viscosity. Viscosity measurements were made in an oscillational viscosimeter by an absolute method—the liquid metal being held in a closed graphite cylinder. Design and operation of the apparatus, constructed in this laboratory, have previously been discussed.6 For thallium, runs were made under a vacuum of about 2 x 10-6 torr. To evaluate viscosity coefficients from the various experimental parameters, the mathematical analysis of Roscoe7 was used. Measurements of the necessary parameters and the accuracy of these measurements have also been discussed.6 The cylinder dimensions were corrected for the anisotropic expansion of graphite, as discussed for density measurements.4,5 It is well-known that thallium oxidizes rapidly and hence a newly machined surface quickly tarnishes in air. The oxide film, however. is nonadherent and is easily removed by rubbing or by solution in water. Hence, immediately before use, both density and viscosity charges were immersed in water, wiped dry, and quickly transferred to the apparatus which was then rapidly evacuated. Specimens removed after determinations were only slightly tarnished and there was no other evidence that tarnishing affected the results. For example, the sharpness of the specimen edges from the containing vessels indicated complete filling by the liquid metal. Thallium of 99.999 pct purity was used in this investigation. Because of its high toxicity care was exercised in handling this material. For example, the melting procedure to prepare machinable ingots was carried out in an open, well-ventilated area, while protective gloves were always worn when handling the solid metal. RESULTS AND DISCUSSION Density. Measurements were made over a tempera-ture range of about 200°C above the melting point. The results are listed in Table I and plotted in Fig. 1. From the graph it is evident that the relation between density and temperature is linear. Such a relation has been observed before in this program for other metals and alloys475 and elsewhere by other workers. A least-squares analysis of experimental data gives the equation: pT1 = 11.658 - 1.439 x 10-3t where p = density in g per cu cm and t = temperature in "C. In Fig. 1, together with the present results, the data of Schneider and Heymer2 in the corresponding temperature range have also been plotted. Evidently, the two sets of data do not agree well, the results of Schneider and Heymer being about 0.6 pct higher. Viscosity. Viscosity data were obtained from the melting point, 303.5°C, up to 457.5"C. The data are listed in Table I and in Fig. 2 the plot of these results demonstrates a smooth curvilinear relation between

Jan 1, 1969

By Gordon H. Geiger, John M. Svoboda

One mechanism of metal penetration into mold aggregates by cast steels is vapor state mass transport. In order to further understand and quantify this mechanism, the steady-state diffusion of metallic vapors was studied at 1250" to 1600°C in controlled oxygen pressure atmospheres by measuring the weight loss from a metal bath whose vapors were allowed to diffuse through a porous aggregate compact held at constant temperature. Mass transport rates substantially greater than those predicted from the assumption that the vaporizing species was the elemental metal vapor were observed. Vaporization rates were found to increase with an increase in the oxygen partial pressure in the gas atmosphere with maximum vaporization occurring at oxygen partial pressures just below those in equilibrium with a liquid oxide layer at the given temperature. When the liquid oxide layer was present, no vaporization was observed. Metal carbonyls were ruled out as the vapor species involved because of their thermodynamic properties. The species with the enhanced volatility were deduced to be gaseous metal-oxygen molecules, probably the polynuclear oxides (FeO)2 and (Mn0)2. Diffusion followed the ordinary diffusion mode, and Knudsen diffusion is not important in normal foundry molds. The interdiffusivities of the metallic vapors and the mold atmosphere, through the porous aggregates, were measured. The effective interdif-fusivity of the vapor species and mold atmosphere through the aggregate may be expressed as follows: Deff,12 - — where E is the void fraction of the aggregate and 7 is the "tortuosity factor". Aggregate material had no effect on diffusion rates, and the only relevant parameter was the void fraction. Values for 7 ranged from 3 to 6 for normal foundry aggregates with 4 being considered a good representative value. An area of interest in high-temperature metallurgical processes which has received little attention in the past is the diffusion of metal vapor species in porous aggregates. Research into the metal penetration phenomenon&apos; in foundry molds has shown that a major penetration mechanism is the vapor transport of metallic species into the porous foundry sand molds, followed by condensation of metallic films on the sand grains. Considerable study of the vaporization of metallic species has been reported in the literature, and the vapor transport properties of many metallic species have been determined.2&apos;3 Many instances have been observed where the vaporization behavior could only be explained by the existence of a metallic species with a vapor pressure greater than the elemental metallic species. These species were identified or, in some cases, presumed to be carbonyls,4,5 hydroxides,6-9 or vaporous oxides.10-16 The diffusion of gases through porous aggregates has received considerable attention in the literature pertaining to catalysis, although primarily at low temperature, and more recently in the literature concerned with ore reduction.17-22 The following experiments were devised and carried out in order to determine the nature of the metallic species involved in the metal penetration phenomenon, and the effective diffusivities involved. EXPERIMENTAL APPROACH Steady-state diffusion was selected for experimental convenience. The experimental systems used, shown in Figs. 1 and 2, consisted of a porous aggregate specimen contained in an impermeable alumina tube held above, and just separate from a metal bath. The entire system was held at constant temperature and pressure in a furnace with a controlled oxygen partial pressure atmosphere. After a brief period of nonsteady state behavior, a steady flux of metal vapor through the porous aggregate will develop due to the concentration gradient of metallic vapor in the gas phase. The flux of metallic vapor from pressure may be neglected because there is no pressure gradient. There is no flux from convection because there is no net flow of gas within the metal-aggregate system, and thermal diffusion is negligible compared to the flux from ordinary diffusion. If the material being studied is allowed to vaporize until steady-state behavior is attained, the experimental results may be analyzed using Fick&apos;s First Law.

Jan 1, 1970

By David L. Holt, Walter A. Backofen, Anwar-uI Karim

Specimens of a hydrided Mg-0.5 Zr alloy were strained in tension at 500°C and constant rates of 2 x10-3 5 x 10-3, and 2 X 10" min-1. Hydride-denuded zones formed at grain boundaries normal to the tensile-stress direction as a result of magnesium transport during difusional flow. The width of the zones could be measured and the measurement used for calculating the diffusional component of the imposed tensile strain. The strain from diffusional flow was found to increase with imposed strain at a diminishing rate, tending to saturate at approximately 12 pct. Strain rate sensitivity of flow stress was low. The apparent non Newtonian character of the diffusional flow is attributed to a non Newtonian process acting in parallel with it which could be boundary shear. Fracture grows out of voids that form in the denuded zones. DEFORMATION of a grain by diffusion of atoms from boundaries stressed in compression to boundaries stressed in tension is Newtonian viscous,1-3 and evidence has accumulated in recent years that such a process may be responsible for the high strain-rate sensitivity of the flow stress of super-plastic alloys.4"7 One piece of evidence is that experimental stress: strain-rate relationships can be quantitatively explained.5-7 There is also metallo-graphic evidence of diffusional flow in superplas-ticity, but in a limited amount. The formation of striated bands on the surface of superplastically deformed specimens has been attributed to diffusional flow.5"7 The basis of that attribution came from experiments on a coarse-grained, nonsuperplastic and hydrided Mg-½ wt pct Zr alloy which formed hydride-denuded, light etching zones at tension-stressed boundaries when strained in tension at 270?C.6 The origin of these zones had already been traced to the diffusional flow of magnesium atoms to the boundaries.&apos; The particular observations in the more recent work were of striated-band formation on the surface and denuded-zone formation internally, with both the bands and zones having the same width and appearing at tension-stressed boundaries. It was argued that the bands were a surface manifestation of the zones and hence of diffusional flow. Of course in superplastic alloys which do not contain internal metallographic "markers", the surface bands can be the only metallographic indication. In the present work, denuded-zone formation was utilized, as it has been by others,9-11 to extend the observations of diffusional flow and to measure the strain, ed, resulting from it. Grain size had to be large to measure ed with accuracy. The grain size chosen for this study was -30 , and with that a strain of 10 pct from diffusional flow produces a denuded zone only 3 µ in width. The large grain size naturally precludes superplasticity. The observations of diffusional flow were complemented by determining the strain from the other operative deformation modes: slip, e,, and grain boundary shear, egb. An incremental specimen extension is the sum of increments from slip, and grain boundary shear as well as diffusional flow. Division by a common length is required to convert to strain. If this length is taken as the initial specimen length, then imposed engineering strain, e, is given in terms of the component engineering strains by e = ed + es + egb [1] Stress:strain-rate relationships are determined by the way in which this "strain balance" is made up. EXPERIMENTAL Material. Zirconium hydride markers were introduced into the Mg-0.5Zr alloy by annealing in hydrogen at 450°C for 30 min. The hydride concentration was particularly high at zirconium rich stringers, which was fortunate in that the transverse boundaries at which denuded zones form lie perpendicular to the stringers. Grain size after annealing was 30 µ. Photomicrographs of unstrained and strained material are shown in Fig. 1. Procedure. Specimens were strained in tension with an Instron machine at crosshead velocities of either 2 x 10"3, 5 x X or 1 x 10-2 in. min-&apos;. Specimen length and diameter were 1.0 and 0.2 in., respectively, so that initial strain rates in tests at constant crosshead speed were 2 x 10"3, 5 x X and 1 X l0-2 min-1. Tests were made at 500°C which is a compromise temperature at which diffusional flow is still measurable but grain growth is not active enough to interfere with metallographic measurements. The tests were made in a hydrogen atmosphere. Strain Balance. An equation additional to [I] is eg = ed + es [2] where eg is strain measured from grain elongation. Measurement was made of ed, eg, and, of course, e, which enabled all the strains in Eq. [I] to be determined. For this purpose, strained specimens were sectioned longitudinally, polished, and etched. The strain from diffusional flow, ed, was computed by measuring on photomicrographs the width in the tensile direction of denuded zones at either end of a grain XI, X2, adding them, and dividing by twice the initial longitudinal grain dimension L0, Fig. 2. Reported values are the results of measurements on seventy randomly selected grains; 95 pct confidence limits on ed were +1.5 pct strain. To measure eg, the maximum length, L, and the maximum width, W,

Jan 1, 1970

By J. J. Frawley, W. J. Childs

Experiments were carried out to induce grain refinement during solidification by applying vibrational energy (freq 20 kc) to small specimens of bismuth, tin, and bismuth-tin alloys. The results show that if the intensity of the applied sound -field is not great enough to fragment the growing dendrites of a pure metal, no grain refinement is observed and the pain size of the dynamically nucleated specimens is the same as the grain size of a specimen statically supercooled the same amount. Bismuth specimens did not show any grain refinement; whereas, the tin specimens did show grain refinement. This phenomenon is the result of the difference in growth habit between the bismuth and tin dendrites. The bismuth-tin alloys showed grain refinement and, in addition, the segregation pattern was changed. THE solidification process is a change in phase requiring the nucleation of the solid phase from the liquid and the growth of this solid phase at the expense of the liquid phase. Since many physical properties and also the integrity of a casting are dependent on the solidification process, understanding and controlling this process are very important.&apos; A good example in the controlling of a cast structure using heterogeneous nucleation theory is the reduction of grain size in aluminum castings by nucleation catalysis.2 This mechanism of nucleation catalysis has been explained by Turnbull.3 Another technique for grain refinement, which has received much attention but the mechanism has not been fully understood, is to vibrate the solidifying melt. Vibrations can be applied to the melt either by vibrating the mold directly or by introducing a vibrating rod into the melt.4-13 Three mechanisms have been proposed to explain this phenomenon: 1) The mechanical fragmentation of the original dendrites that grew into the melt. These crystals or fragmented dendrites act as new growth sites. 2) The nucleation of new grains in the liquid by the generation of very high pressure pulses caused by cavitation in the liquid. 3) The remelting of the dendrite arms during the solidification process. This mechanism is operative only in alloy systems and would be enhanced by stirring or mechanical vibration. The purpose of this investigation was to determine the mechanism that will increase the number of grains when mechanical energy is introduced into a solidifying melt. APPARATUS The unit used to generate the ultrasonic vibrations was manufactured by the Redford Co., and is similar to the one used in ultrasonic soldering. Fig. 1 is a sketch of the major components used for generating ultrasonic vibrations. The crystal transducer assembly consisted of four lead zirconate ti-tanate piezoelectric crystals in an aluminum holder. An acoustical horn, which was fabricated from stainless steel, was attached to the holder by a set screw. The resonant frequency of this unit was 20,000 cycles per sec. A Pyrex crucible, 4 in. in diam and 4 in. high, was contained in a hole in the top of the horn. The piezoelectric crystals changed volume when excited by an electric signal, thereby generating a sound signal which passed through the horn. The crucible was coupled to the horn by a liquid silicone oil. The purpose of the couplant was to transmit the soundwaves from the horn to the crucible. Without the couplant, much of the sound energy would be lost. The energy transmitted was sufficient at the resonant frequency used, so that acoustical cavitation always occurred in the molten metal. The presence of acoustical cavitation was detected by the characteristic hissing sound emitted from the liquid. EXPERIMENTAL PROCEDURE The influence of ultrasonic vibration on the grain refinement of bismuth, tin, and bismuth-tin alloys was studied. These metals were chosen because of their low melting temperature and the relative ease with which they can be thermally supercooled. The following procedure was used for obtaining large amounts of supercooling. Pure bismuth (99.999+), which was received in bar form, was mechanically broken into pieces small enough to be accommodated in a 50 ml beaker. About 200 to 300 g of bismuth and a few grams of SnCl2 as a flux were placed in the 50 ml beaker and melted by induction heating. The melt was held for 20 min at

Jan 1, 1970

By E. T. Turkdogan, Klaus Schwerdtfeger, P. Grieveson

The rate of growth of "Fe4N" on a iron was measured by nitriding purified iron strips in flowing am -monia -hydrogen gas mixtures at 504" and 554°C. It is shown that a dense nitride layer is formed when a zone -refined iron is used in the experiments. With less pure iron, the nitride layer is found to be porous. Through theoretical treatment, the self-diffusivity of nitrogen is evaluated porn the parabolic rate constant, and found to be essentially independent of nitrogen actirlity, e.g., D* = 3.2 x l0-12 and 7.9x l0-12 sq cm per sec at 504" and 554?C. Some consideration is given to the mechanism of diffusion in the nitride phase. THERE is a great deal of background knowledge on the solubility and diffusivity of nitrogen in iron, and on the thermodynamics and crystallography of several phases in the Fe-N system. Although case-nitrided steels have many applications in practice, no work seems to have been done on the diffusivity of nitrogen in the iron nitride, ?&apos;, phase. The only work reported on the related subject of which the authors are aware is an investigation by Prenosil,1 who measured the growth rate of the e phase on iron by nitriding in ammonia-hydrogen gas mixtures. EXPERIMENTS Purified iron plates of approximate dimensions 1 by 0.5 by 0.03 cm were nitrided in flowing mixtures of ammonia and hydrogen, in a vertical furnace fitted with a gas-tight recrystallized alumina tube. After a specified time of reaction, the sample was cooled to room temperature by withdrawal to the water cooled top of the reaction tube. The furnace temperature was controlled electronically in the usual manner within *l°C; the temperature was measured using a calibrated Pt/Pt-10 pct Rh thermocouple. For each experiment the iron strip sample was cleaned with fine emery cloth and degreased with tri-chloroethylene prior to the experiment. The ammonia-hydrogen gas mixtures were prepared from anhydrous ammonia and purified hydrogen using constant pressure-head capillary flowmeters. The gas mixture flowed upward in the furnace with flow rate of 400 cc per min at stp. The composition of the gas mixture was checked by chemical analysis at regular intervals. In most cases, the compositions of the exit gas and metered input gas agreed within about 0.3 pct, indicating that cracking of ammonia did not pose a problem at the temperatures employed. Two series of experiments were carried out using two different types of purified iron samples. In the first series of experiments at 550°C, vacuum carbon deoxidized "Plastiron" was used. The main impurities present in this iron were, in ppm: 4043, 50-Cr, 20-Zr, 40-Mn, 20-P, 20-S, 20-C, 50-0, and 10-N. In these experiments the rate data were obtained by measuring the change in weight of the iron specimen suspended in the hot zone of the furnace by a platinum wire from a silica spring balance. The nitride layer formed in these experiments was found to be porous, particularly near the outer surface. In other experiments, high purity zone-refined iron (prepared in this laboratory) was used. The total impurity content of this iron was 30 ppm of which 20 ppm was Co + Ni, 4 ppm 0, other metallic impurities were less than 1 ppm. The zone-refined iron bar, -2.5 cm diam, was cold rolled to a thickness of about 0.03 cm and the specimens were prepared for the experiment as described earlier. After the nitriding experiment, the sample was copper plated electro-lytically and mounted in plastic for metallographic polishing. After polishing, the thickness of the ?&apos; layer was measured using a metallographic microscope. The nitride layer formed on the zone-refined iron was essentially free of pores. RESULTS The different morphology of the nitride layers grown on "Plastiron" and zone-refined iron is shown in Fig. 1. Both samples were nitrided side by side for 55 hr. The holes in the less pure iron, Fig. l(a), are confined to a region about one half thickness from the outer surface. The dense layer grown on zone-refined iron, Fig. l(b), is thinner than the porous layer on the "Plastiron". The impurities in the iron are believed to be responsible for the formation of a porous nitride layer. The pore formation may be due to the high nitrogen pressures existing within the nitride layer, e.g., the equilibrium nitrogen pressure is 1.2 x l05 atm in the 38.6 pct NH3-61.4 pct H2 and 6.6 x l03 atm at the Fe-Fe4N interface at 554°C and 0.96 atm. It is possible that the oxide inclusions present in the electrolytic iron may facilitate the nuclea-tion of nitrogen gas bubbles within the nitride layer. Support for this reasoning is the fact that pores are only encountered in the outer range of the layer where nitrogen pressures are largest. The photomicrographs in Fig. 2 show the effect of reaction time on the thickness of the dense nitride layer formed on zone-refined iron. These sections are from samples nitrided in a stream of 29 pct NH3-71 pct H2 mixture at 554°C for 22, 70, and 255 hr. In all the sections examined the nitride-iron interface was noted to be rugged. These irregularities are be-

Jan 1, 1970

By C. R. Barrett, N. N. Singh Deo

The high-temperature steady-state creep behavior of a series of dilute copper-silicon alloys was studied to determine the effect of stacking fault energy on the creep-rate. The steady-state creep rate is, when taken at equivalent diffusivities decreases with decreasing stacking fault energy. The stress and temperature dependencies of is suggest that creep is a difusion controlled dislocation climb process. Electron microscopy studies of the creep substructure revealed: 1) the subgrain size is not a function of the stacking fault energy in these alloys, 2) the dislocation density not attributed to the subgrain walls seems to be higher during primary creep and decreases to a lower steady value during steady-state creep, and 3) the dislocation density during steady-state creep decreases with decreasing stacking fault energy. In the past few years numerous investigators have studied the influence of stacking fault energy on high-temperature creep strength. Most of these investigators have confined their attentions to studying the relationship between steady-state creep rate, is, and stacking fault energy, ?, when samples are tested under conditions of comparable stress and temperature. For the case of fcc metals, it was initially shown by Barrett and Sherbyl and since confirmed by many others2"4 that is decreases with decreasing ?, often following an empirical relation of the form i ?m where m is a constant about equal to 3. The application of theory to explain this observation has not been entirely successful. One of the main difficulties has been the almost complete lack of structural information (dislocation density, subgrain size, and so forth) for samples with different stacking fault energies, tested under high-temperature creep conditions. weertman5 has attempted to explain the stacking fault energy dependence of is on the basis of a dislocation climb mechanism. Assuming that both the rate of dislocation core diffusion and the ease of athermal jog formation decreases as ? decreases Weertman has argued that the rate of dislocation climb and hence the creep rate should also decrease as ? decreases. One questionable aspect of Weertman&apos;s analysis is the assumption that core diffusion down extended dislocations is slower than core diffusion down unextended dislocations. The only experimental work done in this area, by Birnbaum et al.6 on nickel and Ni-60 Co, has shown the core diffusivity to increase with decreasing ?. Theories of steady-state creep based on the diffusive motion of jogged screw dislocations often seem unable to predict even the qualitative nature of the es- relationship. Assuming that Weertman is correct in his assumption that the dislocation jog density decreases with decreasing ? then the jogged screw theories predict an increasing dislocation velocity with lower ?. It is usually assumed that the increase in dislocation velocity implies a corresponding increase in creep rate. However, two other factors must be considered before such a statement can be made. That is, we must know how both the mobile dislocation density and the effective stress (the difference between applied stress and internal stress) vary with ?. Significant changes in either one of these factors could outweigh any change in dislocation velocity accompanying a change in ?. And with the slower rates of recovery expected in low stacking fault energy materials it seems likely to expect both mobile dislocation density and effective stress to be dependent on ?. Sherby and Burke7 have suggested that stacking fault energy influences the creep rate in an indirect way. These authors cite evidence that the steady-state subgrain size generated during high-temperature creep is a function of ? decreasing with decreasing ?. Assuming the creep rate to be proportional to the area swept out by each expanding dislocation loop and that subgrain boundaries are good barriers to dislocations, then the creep rate should be proportional to subgrain area, hence increasing as ? increases. A critical evaluation of any of the above theories requires more quantitative information concerning the dislocation substructure generated during high-temperature creep. Accordingly this investigation was undertaken with an aim of studying the influence of stacking fault energy on tbe steady-state creep characteristics of a series of dilute copper-silicon alloys. Special emphasis was placed on studying the strain dependence of both the dislocation configuration and density. MATERIALS AND PROCEDURE Dilute copper-silicon alloys of the compositions shown in Table I were tested in tension at constant stress. The relative stacking fault energy of these alloys has been determined and is shown in Table 11. An Andrade-Chalmers lever arm was used to maintain constant stress and testing was carried out in a water

Jan 1, 1970

By George S. Ansell, Thomas E. Davidson

It has been known for a considerable period of time that the ductility of even quite brittle materials can be enhanced if they are deformed under a superposed hydrostatic pressure of sufficient magnitude. The response of ductility to pressure, however, has been shown to vary considerably between materials. Prior work has shown that the effects of pressure upon the tensile ductility of Fe-C materials depend upon the amount, shape and distribution of the brittle cementite phase. In this current investigation, the effects of pressure upon the fracture mechanisms in a series of annealed and spheroidized Fe-C materials were examined. It was observed that the principal effect of pressure is to suppress void growth and coalescence, retard cleavage fracture and to enhance the ductility of cementite platelets in pearlite. Based upon the observed effects of pressure upon the fracture mechanisms, a proposed explanation for the enhancement in ductility by pressure and for the structure sensitivity of the phenomena is presented and discussed. THE effect of superposed pressure upon the tensile ductility of a variety of metals has been well documented.&apos;-&apos;&apos; Some of the results from several investigators are summarized in Fig. 1 where tensile ductility in terms of true strain to fracture (ef) is plotted as a function of the superposed pressure. As can be seen, a pressure of sufficient magnitude can significantly enhance the ductility of metals. However, Fig. 1 also demonstrates that the response of ductility to pressure and the form of the ductility-pressure relationship varies considerably between materials. Several explanations have been offered for the observed enhancement in ductility by a superposed pressure. Although no experimental evidence was provided, Bridgman13 and Bobrowsky10 proposed that the observed effect was due to the prevention or healing of microcracks or holes. Bulychev et a1.14 observed that cracks and voids in initially prestrained copper were healed in the necked region of a tensile specimen upon further straining while under a superposed pressure. Also, pugh5 observed that large cavities were suppressed in copper fractured in tension while under pressure. A second proposal has been forwarded by Beresnev et at al.6 This proposal is based upon the hypothesis that a material fails in a brittle manner because the normal tensile stress reaches a critical value before the shear stress is of sufficient magnitude to cause plastic flow. Since a superposed hydrostatic pressure will increase the ratio of shear to normal tensile stress, a sufficiently high hydrostatic pressure should favor plastic flow while retarding brittle fracture. Galli15 reported that a superposed pressure shifts the ductile-brittle transition temperature of molybdenum. This was explained based upon the reduction of the normal tensile stress by the superposed pressure. Pugh5 explained the occurrence of the observed pressure induced brittle-to-ductile transition in zinc in the same manner. Davidson et al.12 proposed an explanation for the enhancement of ductility by pressure based upon the effects of pressure upon the stress-state-sensitive stages of various fracture propagation mechanisms. Basically, they proposed that pressure will retard cleavage and intergranular fracture by counteracting the required normal tensile stress or will suppress void growth. They observed suppression of intergranular fracture and void growth in magnesium by pressure. Davidson and .Ansell16 reported ductility as a function of pressure for a series of annealed and spheroidized Fe-C alloys. Fig. 2, from this prior work, demonstrates that the effect of pressure upon ductility is structure sensitive in terms of the amount, shape and distribution of the brittle cementite phase. As shown in Fig. 2, in the absence of cementite or when the cementite is in isolated particle form (spheroidized), the ductility-pressure relationship is linear and the slope decreases with increasing carbon content. In the annealed carbon-bearing alloys wherein the cementite is in the form of closely spaced platelets (pearlite) or in the form of a continuous network along prior aus-tenite boundaries (1.1 pct C material), ductility as a function of pressure is nonlinear (polynomial relationship) in which the slope increases with increasing pressure. At the highest pressures studied (22.8 kbars), the slope of the curves for these materials tends to approach those for the spheroidized material of the same carbon content. In this current investigation the change in fracture mechanisms as a function of pressure for the materials shown in Fig. 2 has been examined. The possible connection between the observed effects of pressure upon the fracture mechanisms and the effect of pressure upon ductility is discussed.

Jan 1, 1970

By G. A. Chadwick, D. Jaffrey

The morpho1ogies and orientation relationships of the phases in the Sn-Zn and A1-A13Ni eutectic systems were examined by electron microscopy and X-ray diffraction techniques. In each alloy the "transition" from the lamellar to the fibrous morphology was found to be one of scale, not of type. The minor phase in both systems exhibited certain well developed facets which were not affected by changes in the ingot solidification rate. The crystallographic relationships displayed by the pairs of phases in both systems were also insensitive to the growth rate. In the Sn-Zn alloy, the unique relationship of: growth direction - II [1201 Sn - II [01101 Zn and ribbon interface plane 11 (101) Sn 11 (7012) Zn was determined. The Al-Al3Ni alloy phases did not possess any particular orientation relationship, though the Al3Ni phase invariably grew in the [010] direction and exhibited the same set of facet planes. These results are discussed in relation to current eutectic growth theories and explanations of the "lamellar to fibrous transition". THE lamellar to fibrous transition that occurs in many eutectic alloys has been the subject of considerable speculation and experimental study. In some alloys it can be induced solely by an increase in the solidification rate,&apos;-3 whereas in others the transition supposedly occurs only if the lamellae are forced to grow out of the overall ingot growth direction.4-6 he cause of this latter type of transition has been attributed to deviations of the lamellae from their low energy habit planes;4&apos;5&apos;7 fibers are produced because the sustaining force for lamellar growth (a low energy boundary) is destroyed. Implicit in these explanations is the assumption that fibers are circular in cross-section and completely lacking in low energy inter-phase interfaces. The "natural" growth rate dependent transition has been studied less thoroughly although Tiller8 has attempted a theoretical explanation of it. Tiller&apos;s arguments are not completely satisfactory9 but his suggestion that the relative undercoolings of the solid/liquid interface for lamellar and fibrous morphologies are growth rate dependent cannot be totally discounted; it is possible, for instance, that the relative interfacial undercoolings could alter and produce the observed morphology change if the orientation relationships between the phases and the associated interphase bound- ary energies were sensitive to growth rate. Salkind et al." have reported finding a change in the orientation relationships in the A1-A13Ni system accompanying the lamellar to fibrous transition, but contradictory evidence has also been reported for this3&apos;" and another system,12 so the position remains unclear. In an attempt to clarify matters a study was made of the "lamellar to fibrous" transition in the Sn-Zn and A1-A13Ni eutectic systems; the morphologies of these two selected systems are quite similar when viewed by optical microscopy. In the present research the morphologies and morphology changes were investigated by electron microscopy. The orientation relationships existing between the eutectic phases were also determined for both morphologies in both eutectic systems. EXPERIMENTAL PROCEDURE The materials and method of alloy preparation and ingot solidification for the Sn-Zn system have been reported previously.2 In this investigation nine horizontally grown ingots of the highest purity (99.9997 pct) were used. The temperature gradient in the melt was not intentionally varied and was approximately 10°C per cm. Seven growth rates between 1.3 cm per hr and 20 cm per hr were imposed. The A1-A13Ni alloys were prepared from "Spec. Pure" nickel and 99.995 pct aluminum by melting the components in an open alumina crucible and casting the melt into the cold graphite mold. Six ingots of the Al-Al3Ni alloy were unidirectionally solidified at growth rates from 1 cm per hr to 12 cm per hr under high purity argon. A typical ingot was 20 cm long, 1 cm wide, and 0.75 cm to 1.5 cm thick. Samples taken from the bars at positions 12 cm from the nucleation end were examined by conventional orthogonal-section metallo-graphic techniques. When required, samples were mounted for X-ray diffraction analysis using the Laue back-reflection technique with a finely focussed X-ray source. The surfaces of the A1-A13Ni specimens were prepared by mechanically polishing them down to the 1 µ diamond pad stage followed by an electropolish in 80/20 methanol/perchloric acid solution at 0°C and 20 to 30 v. The Sn-Zn specimens were repeatedly polished on an alumina pad and etched in hot dilute (2 pct) nitric acid until the diffraction spots were found to be sharp. Thin films of the alloys were prepared for observation in an electron microscope by spark machining thin discs (0.03 to 0.04 in. thick) from longitudinal and lateral sections of the bars and elec-trolytically thinning them via a jet polishing technique. For the A1-A13Ni eutectic alloy, an 80/20 mixture of ethanol/perchloric acid at 40 v and 20°C was found to be satisfactory. A solution of 70/20/10 methanol/perchloric acid/butylcellosolve at 25 v and 20°C was used on the Sn-Zn alloy. For the former alloy the jet nozzles (cathodes) and the disc clamps were of aluminum;

Jan 1, 1970

By J. L. Kenty, J. P. Hirth

The concept of a critical super saturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, is discussed with reference to vapor-solid nucleation. The necessary and sufficient conditions deduced for observations of this type of behavior are: 1) the nucleation rate must exhibit a sharp dependence on super saturation, 2) the growth rate must be sufficiently large that nuclei become observable in the time period of the experiment, and 3) the number of highly preferred nucleation sites must be small. Experiments reveal that the nucleation of silver on sodium chloride is visually detectable at all experimentally accessible super saturations and does not exhibit critical nucleation behavior. Failure to observe a critical super saturation is attributed to the insensitivity of nucleation rate to supersaturation as a consequence of the particular values of the contact angle and the surface free energy for this system. THE concept of a critical supersaturation, below which the nucleation rate is essentially zero and above which it is essentially infinite, arises naturally in homogeneous nucleation theory. Experimentally this type of behavior has been found by Volmer1 and others for water and other low surface tension liquids, as reviewed by several authors.2&apos;3 The same type of behavior has been predicted and observed for heterogeneous nucleation of solids by Yang et al.4 and others,596 as also recently reviewed.2,7,8 In the work reported here on the heterogeneous nucleation of silver on NaC1, however, no critical super-saturation was found. Similar observations have been made recently for other systems.9-11 These results led to a reexamination of nucleation theory which revealed that there are conditions for which critical behavior is not predicted, either for homogeneous or heterogeneous nucleation. Although heterogeneous nucleation is of primary importance in this paper, some insight into critical behavior for such a case can be gained by considering homogeneous nucleation. Accordingly both types of nucleation theory are reviewed briefly. The requisite conditions for critical supersaturation behavior are then considered. The experimental results for the nucleation of silver on NaCl are presented and interpreted in terms of the theoretical presentation. REVIEW OF NUCLEATION THEORY There are essentially two approaches to nucleation theory, the so-called classical theory involving the concepts of bulk thermodynamics, and the statistical mechanical theory in which nuclei are regarded as macromolecules. The classical theory is based on the work of Volmer and Weber12,13 and Becker and. Doring14 and has been extended by Pound et al.15 The crucial assumption in the classical theory is that the small clusters or nuclei can be characterized by the same thermodynamic properties as those of the stable bulk phase. Thus, the nuclei are assumed to have a surface free energy, y, and a volume free energy of formation (relative to the vapor phase), ,, identical to that of the bulk. For deposition under low super-saturation conditions, the nuclei are large and this assumption is satisfactory. However, in many cases of interest, the nuclei contain only a few atoms and this assumption is highly questionable. The statistical mechanical models originated, for the specific case of a dimer as the critical nucleus, with the work of Frenkel16 and were extended later to larger sizes by Walton,17,18 Hirth19 and, more recently, Ht Zinsmeister. These models describe the nucleus in terms of a partition function, the estimation of which is tractable for clusters of 2 to 10 atoms, but extremely difficult for clusters larger than 10 atoms. Although the classical and statistical mechanical models are expected to apply for the limiting cases of large and small nuclei, both are uncertain for intermediate sizes. In this paper we shall treat only the classical model, recognizing that it is exact only for large nucleus sizes and regarding it as a phenom-enological description for small nucleus sizes. When analyses of experimental data using bulk properties show the nucleus size to be small, the resulting parameters should be regarded as largely empirical parameters describing the relative nucleation potency of the system. Considerable justification for the continued use of classical theory is provided by its general success in predicting nucleation behavior as a function of supersaturation and temperature. We emphasize that the qualitative features of the statistical mechanical models, particularly the critical super-saturation behavior that is central to the present work, are the same as those of the classical model. Of course, potential energy terms and surface partition functions replace the volume and surface energy terms of the latter model. The most recent versions of classical nucleation theory have been extensively reviewed.2,3,7 so that only the results are presented here. For homogeneous nucleation of a condensed phase from the vapor phase, the volume free energy change is ?Gv=vrT = =^ln£ [1] where v is the molecular volume of the condensing species. The supersaturation ratio,

Jan 1, 1970

By G. L. Fisher, R. H. Geils

The effect of small amounts of columbium (<0.01 to 0.10 pct) on the ?-a transformation occurring during the continuous cooling of a low carbon Ni-Cu steel was investigated. Dilatometer specimens were aus-tenitized at 950" and 1068?C and cooled at 17? and 375 C° per min. Columbium caused a marked depression in the ?-a transformation temperature except when cooling at the slower rate from 950°C. The effec of columbium on the transformation temperature was greater the higher the austenitizing temperature and rate of cooling. A maximum depression of 92 C" was observed. Metallographic examination of specimens of <0.01 and 0.07pct Cb steels heated at 1200°C for 1 hr and cooled at various rates showed that columbium had a major effect on the ferrite morphology. The fer rite in the columbium -free steel remained equiaxed at cooling rates as high as 440 C? per min while the columbium-bearing steel exhibited mixed structures o equiaxed and bainitic ferrite at cooling rates as low as 130 C° per min. The ? grain boundaries in the columbium -free steel provided the ferrite nucleation sites in rapidly cooled specimens. There was a complete absence of nucleation at these sites in the colum bium-bearing steel. It is concluded that columbium depresses the transformation temperature by suppressing ferrite nucleation at the austenite grain bound-aries. In this respect the effects of columbium are analogous to those of boron in low C-Mo steels. It is well known that small columbium additions can substantially strengthen plain carbon steels. As little as 0.02 pct Cb can increase the yield strength of mild steels by 10,000 psi.1 A fine precipitate of CbC has been observed in columbium-bearing steels2 and is generally thought to be responsible for the strengthening. Little attention has been devoted to the effect of columbium on the ?-a transformation. Webster and woodhead3 have studied the effect of columbium on the isothermal proeutectoid ferrite reaction in mild steels. They found similar transformation behavior in steels both with and without columbium additions. However, as the austenitizing temperature increased, the incubation time for the start of the ferrite transformation became longer in the columbium-containing steel. Morrison1 found that the addition of 0.03 pct Cb to a C-Mn steel lowered the transformation temperature by 50 C° during cooling from 1200°C at a rate of 80 C" per min. The strengthening effect of columbium has recently been utilized in an age-hardenable, low-alloy steel containing copper and nickel.4 A small amount of columbium has a substantial effect on the as-rolled strength of this steel. By increasing the columbium level from <0.01 to 0.13 pct the as-rolled yield strength is increased by 15,000 psi. Columbium also significantly lowers the ?-to-a transformation temperature of this steel during continuous cooling from the austenitizing temperature. Because of the low carbon level in this steel (0.05 pct max), it is almost entirely ferritic. Thus, it offers the opportunity of studying the effect of small columbium additions on the proeutectoid ferrite reaction. Of particular interest in this study was the reason for the marked lowering of the transformation temperature by columbium during continuous cooling. EXPERIMENTAL PROCEDURE Materials. The compositions of the steels used in this investigation are shown in Table I. The steels were 30-lb air induction melts. They were forged to 4 by 8 by 1 in. plate at 1230°C, air cooled, and then reheated to 1230°C and cross-rolled in two passes to in. plates. Dilatometry. A Leitz Bollenrath dilatometer was used to record the transformation during continuous cooling from two different austenitizing temperatures. The dilatometer specimens were + in. in diam and 2 in. long. Oxidation and decarburization of the specimens was prevented by maintaining a small positive pressure of dry argon in the dilatometer furnace and by plating the specimens with 1 mil of Cu. For the lowest cooling rate, 17 C" per min, the temperature of the specimen was measured with a Pt-Pt 10 pct Rh thermocouple placed in a & in. diam well in the center of the specimen. During air cooling, 375 C° per min, this method of measuring the temperature interfered with the operation of the dilatometer. However, it was found that the temperature of the specimen could be measured accurately by placing a thermocouple in an identical specimen in a holder adjacent to the one being used to operate the dilatometer mechanism. The dilation-temperature curves were recorded on photographic film and then converted to volume percent ferrite-vs-temper-ature curves. The cooling rates obtained with the dilatometer are shown in Table 11. Cooling rates of

Jan 1, 1970

By R. A. Graham, R. W. Rohde

The effect of hydrostatic pressure upon the austenite start temperature of a commercial Fe-28.4 at. pct Ni-0.5 at. pct C alloy has been determined. For pressures to 20 kbar, the austenite start temperature decreased from its atmospheric pressure value of 380°C at the rate of about 4°C per kbar. These data are analyzed by two different thermodynamic approaches; first, considering the transformation as an isothermal process, and second, considering the transformation as an isentropic process. It was found that both these approaches fit the experimental data equally well. The effect of hydrostatic pressure upon the austenite start temperature is best described by considering the mechanical work done during the transformation as that work obtained by multiplying the applied pressure with the gross volume change of the transformation. It is widely recognized1 that strain has an important effect on the initiation of martensitic transformations.* For example, the martensite start tempera- *In this paper, use of the term martensitic transformation implies the reversal of martensite to austenite as wen as the formation of martensite from austenite. ture, M,, may be increased by plastic deformation. Similarly, plastic deformation is observed to lower the austenite start temperature, A,. The effect of uniaxial stress on the M, of iron-nickel alloys has been studied by Kulin, Cohen, and Averbach.2 They found that the martensite start temperature was significantly changed by stresses well within the elastic region. Moreover, the effect of tensile and compres-sive stresses differed. These effects were explained in terms of the interaction of the applied stress with both the dilational and shear components of the transformation strain. The magnitudes of the influence of uniaxial tension, compression and hydrostatic pressure on Ms were measured in 30 pct Ni 70 pct Fe by Pate1 and Cohen.3 Their thermodynamic calculations and similar calculations by Fisher and Turnbull4 predicted the experimental results when the transformation was assumed to occur isothermally at some fixed driving force. This driving force was assumed to be supplied by a combination of the chemical free energy difference between the austenitic and martensitic phases and the work performed during transformation by the applied stress. More recently, Russell and winchel15 reported the effect of rapidly applied shear stress on the reversal of martensite to austenite in iron-nickel-carbon alloys. They performed a thermodynamic analysis of this transformation based upon the assumption that the re- versal occurred adiabatically. They concluded that the applied shear stress did not significantly interact with the transformation strain and thus did not assist in inducing the reversal. Rather they concluded that the reversal was effected by localized strain heating which resulted from the gross local shear deformation of the experiment. In either the adiabatic or isothermal analysis it is necessary to compute the work performed by the interaction of the applied stress and the transformation strains. In the case of hydrostatic pressure this interaction has been treated by two different methods. In either case the applied pressure is assumed to remain constant during the transformation. In one treatment the applied pressure is assumed to interact directly with the dilatational strain associated with the formation of an individual martensite plate.3&apos;4 This local strain has been measured at atmospheric pressure in iron-nickel alloys by Machlin and Cohen.6 In the above treatment this local strain is assumed invariant with temperature and pressure changes. In the other treatment the applied pressure is assumed to interact with the gross volume change of the transformation.7,8 The usefulness of this latter treatment has been demonstrated by Kaufman, Leyenaar, and Harvey7 who calculated the effects of pressure upon the martensite and austenite start temperatures of Fe-10 at. pct Ni and Fe-25 at. pct Ni alloys. Excellent agreement was obtained between their calculations and their experimental data on an Fe-9.5 at. pct Ni alloy. However, this treatment suffers from the fact that the data required to calculate the volume change of the transformation (i.e., the initial specific volumes, the thermal expansion and compressibility data for both the austenitic and martensitic phases) is, in general, not available for any material except pure iron. Thus the calculations of Kaufman et al.7 were necessarily performed by assuming that the volume change of the martensitic transformation in the iron-nickel alloys was that same volume change occurring during the a-? transformation in pure iron. While this approximation may suffice for very dilute alloys it is likely to be inaccurate in high nickel alloys. We have performed measurements of the effect of hydrostatic pressure to 20 kbar on the A, temperature of an Fe-28.4 at. pct Ni-0.5 at. pct C alloy. The composition is similar to the alloy used by Pate1 and Cohen3 to determine the effect of pressure upon the M, temperature. The present measurements permit calculation of the interaction between the applied pressure and the transformation strain. Additionally, measurements have been made which allow precise determination of the gross volume change of the transformation. The data allow direct comparison between the alternate hypotheses of the interaction between the applied pressure and a dilatational transformation strain characterized by either the formation

Jan 1, 1970

By M. W. Dumais, E. P. Abrahamson

In a paper by Abrahamson and Alexander concerning a series of correlations between electronic structure and property changes, it was hypothesized that each solute atom in a dilute solution had a characteristic volume of solvent atoms over which some form of electronic interaction occurred. From this description it is possible to picture the solute atoms as occurring in an ordered array for the most efficient arrangement. A recent review article2 has shown that some form of anomaly exists for a whole series of properties when dilute additions of tungsten are made to iron, of. Fig. 1. Any mechanism to fit one property must also be amenable to mechanisms for the other properties. The possibility of some structural change in this region appears to offer the best hope. The system chosen for investigation was the iron tungsten system. Zone-refined iron with zone-leveled tungsten additions were supplied by Materials Research Corp. as 3/8-in.-diam bars. Transmission electron microscopy was used to study the structure. One-quarter inch specimens of each alloy were cold-rolled to 10-mil sheets, cleaned, punched to electron-microscope specimen-holder size, and annealed in vacuum for 2 hr at 800°C and 2 hr at 700°C followed by a furnace cool. The specimens were attached to a platinum wire and the specimen edge and wire were painted prior to thinning in a solution of 10 pct perchloric acid in glacial acetic acid. It was believed that if ordering were present due to electronic interactions the polishing procedure chosen would provide a simultaneous combination of chemical attack and electropolishing to exhibit the ordered structure. The chemical attack would be expected to penetrate those areas equidistant from the tungsten atoms, while the electropolishing would serve to "plane off" the volumes where the chemical attack had taken place. If one of the ordered tungsten planes were parallel to the specimen face at the edge of the thinned hole, a plate or micalike structure would be expected. A typical result of this polishing is shown in Fig. 2. Here a series of plates can be seen lying one upon the other. In several other specimens the plates parallel to the electron beam have been observed, behaving like slices of bread in a loaf. These edge views coupled with moire patterns indicate that the minimum plate thickness is 37 to 42A. This is equivalent to a concentration of 455 at. ppm of W if a simple cubic superlat-tice exists, or one tungsten atom every twelve iron atoms on the ordered plane. It was further noted that the base iron exhibited no signs of platelike structure. As the concentrations increased above 100 at. ppm W the amount of plate material increased. Among the specimens investigated was that shown

Jan 1, 1967

By D. T. Camp, J. A. Clum

WITH experience, the indexing of back-reflection Laue patterns for cubic crystals is usually a straightforward matter. However, for noncubic systems where in general tables of interplanar angles are not available or when inexperienced personnel are involved, properly indexing a crystal is normally a tedious, time-consuming affair. The authors have written a digital-computer program which calculates and prints out a table of interplanar angles for an arbitrary crystal structure and then systematically searches through this table attempting to obtain a consistent fit to back-reflection Laue data supplied by the user. Of course it is possible simply to calculate a desired set of interplanar angles should this be the only requirement. The program was originally written in ALGOL for use on a Control Data G-21 computer and a preliminary version is described elsewhere.&apos; A version in FORTRAN TV which has been run on an IBM 7040 and one in FORTRAN II run on an IBM 1620 are also available. While it is not the purpose of this communication to describe the program in detail, an indication of how the program operates may help one to decide whether the program would be useful under particular circumstances. The hypothetical example chosen involves the indexing of the zinc crystal which has a hexagonal structure and a c/a ratio of 1.856. Input data for this example consists of only nine cards: The first card controls the list of families of planes to be considered. If the Miller indices of a prospective family are (h k 1), the first digit places a limit, in this case 3, on the absolute values of any individual index. The second digit limits the sum (h +k + l + 1), in this case to 5. Therefore the families (013) and (112) are considered but the family (122) is not. All systems, including the hexagonal, are treated using three-digit Miller indices. The second card contains the crystallographic parameters required to define the system. The first digit is 0 if the system is rectangular, that is all angles are 90 deg. If the system is nonrectangular, as in this example, the digit 1 so indicates. The next three values are the lengths of the sides of the reference cell, a, b, c. The final three entries on the card are the angles, a, 8, y between the sides. The digit 0 on the third card indicates that more data follows, the digit 6 shows that a set of six planes is to be indexed, and the value 2.0 indicates that agreement between a tabulated angle and an input angle is considered adequate if their absolute difference is less than 2 deg. The fourth card lists the measured input angles. a12 = 38 deg, a13 = 24 deg, and so forth. More input angles are listed on cards five to eight with the latter giving the input angle 058 = 40 deg. The final card in this series indicates by the digit 1 that no more data is to be processed. The program operates in the following manner: 1) The input data from cards 1 and 2 is read, thereby indicating the crystal system to be examined and the crystallographic parameters of the particular crystal to be indexed. 2) A table of interplanar angles is generated. 3) The input angles contained on cards 4 to 8 are read. 4) The measured input data is systematically compared with the generated table of standard angles. All combinations of poles whose interplanar angles compare with the requisite, specified accuracy are printed out. If no adequate fit is found an indication of this is printed. A typical line from the generated table of interplanar angles is: (001) - (111) 74.92 64.99 It can be shown that in the Miller-Bravais system the first value corresponds to the angles between (0001)-(1121) and the second to that between (0001)-(1011). This particular set of data gave the following result for the planes 1 to 6: (011) (110) (121) (111) (112) (010) The ALGOL version also has the option of simply providing the Greninger-chart coordinates ? and 6

Jan 1, 1967

By Donald L. Johnson

REVIEWS on the applications of optical ellipsometry to the study of polycrystalline metal surfaces and oxidation-corrosion processes have been presented by Kruger and Hayfield, and white.&apos; In view of the ability of this method to measure differences in film thicknesses to below 10A, ellipsometry was used to study nitrogen chromium surface reactions during the early stages of growth. Chromium specimens in the form of a vapor-deposited film on glass substrate were exposed to purified nitrogen for selected time increments at 700°F. This temperature was selected because it gave the best combination of exposure time and thickness change. Ellipsometer readings were taken immediately after exposure to determine polarizer and analyzer angles using monochromatic light at 5000A.2 After each set of readings was obtained, the specimens were exposed for an additional increment of time in nitrogen and a new set of readings taken. Film thickness was computed from LUCy&apos;s3 equation for nonabsorbing thin films. In Lucy&apos;s derivation, two equations for computing thickness were obtained. Peterson and Bashara4 have discussed the validity for using one of these equations when an independent value of the refractive index is used. The film was assumed to be Cr2N (Ref. 5) and was determined to be optically isotropic. Optical isotropy was determined by rotating the films about the surface normal and noting that the azimuth and phase difference did not change. Since Cr2N is reported to be hexagonal, it is assumed that optical isotropy results from randomly oriented grains of very small size. The thickness was computed using refractive indexes varying from 1.6 to 2.0. The maximum variation in computed thickness over this range for a given exposure was 20 pct. The data reported are based on a refractive index of 1.8. Reference readings on the metal surface were taken just prior to nitrogen exposure. No attempt was made to deoxidize or denitride the metal surface after vapor deposition, although specimens were observed to gain approximately 2A per day in air at room temperature. Twelve experimental exposures were made on a single sample over a total accumulative time of 132 min. Additional experiments over longer time intervals were made to determine the effect of heat up and cool down during and after exposure. As a result of these experiments, the thickness computed for each exposure was increased by 4A. Time profiles based on the linear law are similar to the oxidation profiles for many metals.&apos; The rate of accumulation of the nitride film is rapid at first and slows down as the film thickness increases. The parabolic law x2 =k1t +k2 [11 gives a straight line in Fig. 1; therefore, it is concluded that the kinetic behavior is parabolic. Sey-bolt and Haman5 reported similar results for CrlN on chromium at 1000°C although the order of the thickness was much greater (10-3 cm). Analysis of thickness data based on other values of refractive index shows that the curves are shifted vertically but retain the same shape. According to Mott,7 it is expected that for thin films k2 is zero in Eq. [I]. Since the plot in Fig. 1 is linear through the origin, k2 is zero and the parabolic nature of the film growth is further indicated. The parabolic rate constant, calculated from the slope in Fig. 1, is 4.4 x 10-16 sq cm per sec. The corresponding work (+) required to bring an electron from the metal into the oxide is estimated to be 1.5 ev.7 The author thanks professor N. M. Bashara and D. W. Peterson, Electrical Materials Laboratory, University of Nebraska, for making the ellipsometer available and providing technical assistance. The Electrical Materials Laboratory is supported by the office of Naval Research, NONR 3718 (01). This work was partially supported by the Engineering Experiment Station and the Mechanical Engineering Department, University of Nebraska.

Jan 1, 1967

By Robert M. Asimow, Bisuddhi Riddhagni

THE use of back-reflection Laue photographs for crystal orientation is standard in many research projects. The time required for the orientation of any given crystal depends largely on luck and the skill of the investigator. In any case, where large numbers of crystals are used, this time can be quite considerable when the standard methods involving a Greninger chart and Wulff net are employed. For this reason the technique described below was developed. This new procedure applicable for cubic crystals (without preparation of new charts) largely eliminates the skill and luck factors and makes possible the determination of orientation in minutes. The procedure works in the following way: the Laue photograph is examined and arbitrarily an important hyperbola is picked out. An important hyperbola is defined as one which contains some spots through which several hyperbolas pass. Such a hyperbola inevitably corresponds to a low-index zone axis. The angles between the reflection planes causing all the spots on this hyperbola can be read directly from a Greninger chart in the usual manner. If the hyperbola contains more than five spots, these interplanar angles will positively identify the zone axis and the indices of each of the reflecting planes. However, initially since neither the zone axis nor the Miller indices of a diffraction spot are known, there are a very large number of possibilities that must be considered. Using tables of interplanar angles to check out every possibility would be quite tedious, so that this approach is not generally used. Instead, various poles are plotted on a stereographic projection. In the cubic system, however, it is possible to plot out once and for all the angles between all planes of a particular zone axis up to some upper limit of Miller indices. This has been done for all low-index zone axes in Fig. 1. Given these charts, it is quite a simple matter to identify the spots of the unknown hyperbola. All that is necessary is to plot the angles read off the Greninger chart to the same scale as Fig. l(b) on a strip of paper. Then this strip can be slid along each zone axis of Fig. l(a) until a good fit is obtained. Once this is accomplished, the Miller indices of each spot are given and thus the orientation problem is solved. To check, it is possible to pick a second hyperbola and see whether a compatible solution is obtained. This is most conveniently done by picking for the second hyperbola one that contains a spot common with the first. If the specimen axis is chosen parallel to the incident X-ray beam, then usually the [ loo] hyperbola will appear on the film as one of the more important hyperbolas and consequently will be either chosen initially or as a check. Using the [100] hyperbola, after the (001) or (011) spots have been identified, the latitude and longitude of the specimen axis can be read directly from the Greninger chart so that it is unnecessary to use a Wulff net for the entire orientation procedure. This makes the operation not only quicker but more accurate. Of course, if neither the first nor second hyperbolas correspond to [loo] then a third hyperbola can be chosen.

Jan 1, 1967