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By M. B. Kasen

eralized strain equation appear quite different they are really identical. This identity can be shown in a simple mathematical rearrangement. Referring to Eq. [I], the substitution of ln(1 +?E) for ? (where ?E is the engineering strain) yields: a =s8- (s8?so)e?1/?c) ln(1 +s8??E) [4] or s =s8?(s8?so)(l +?E)-1 [5] Replacing (1 + cE) with its equivalent, (l/lo): s=s8?(s8?so)l/€c [6] Adding and subtracting the quantity (s8 - so) yields: s=s8?(s8?so)+ (s8-so) l-(^)l/£c [7] = s0+(s8?so)ri-(^0)1/^l [8] Letting n = 1/?c it follows that: This equation will be seen to be identical to the generalized strain expression in Eq. [3], the coefficients a and b being equal to so and (s8?so)/?c or n(s8?so), respectively. Confirmation of the relationship noted above was provided by fitting experimental stress-strain data5 for 304 stainless steel (total strain from 0.072 to 1.15) at room temperature at a true total strain rate of 4 x 10-3 sec-1 to Eqs. [I] and [3]. In this study nonlinear regression analyses were used to evaluate the equation constants. The results of this evaluation are presented in Table I. When these constants are used in Eqs. [I] and [3] the curves obtained are coincident. It will also be noted that the value of n is equal to YE,, the value of a is equal to so, and the value of b is equal to (s8 - so)/Ec. These equalities are illustrated in Table I where the Voce constants in parentheses were calculated from a, b, and n values. Excellent agreement is seen to exist. It is concluded, therefore, that the Voce equation is, indeed, identical to the linear expression involving generalized strain. In applying the generalized strain concept to stress-strain data, it has been noted3 that data within what was termed the transition region (first few points in the plastic flow region) must be excluded from the analysis in order to obtain the linearity in Eq. [3]. A similar exclusion applies in the use of the Voce equation since an expression which would describe the strain-hardening region would usually be found to be not too effective in the elastic-plastic fillet2 which connects the elastic line to the strain-hardening region. These considerations further substantiate that Eqs. [I] and [3] do indeed describe identical behavior. Note added in proof. Since this manuscript was submitted for publication, correspondence with Professor S. R. Davies, University of Edinburgh, (of Ref. 3) indicated that his associates have also confirmed the identity between the Voce equation and the generalized strain concept. It is sometimes desirable to obtain a small grain size in super-purity metals. Unfortunately, the absence of impurities, the low recrystallization temperatures, and the low activation energies for boundary motion result in rapid growth of relatively few grains when conventional recrystallization practices are used. For example, Arajs et al.1 were unable to obtain a mean grain diameter less than about 0.4 mm in iron containing 38 at. ppm of impurity. The <1 at. ppm purity range in many modern superpurity metals results in yet larger limiting grain sizes. It is the purpose of this communication to describe a technique by which mean grain diameters as small as 30 µ have been produced in aluminum having an impurity content < 0.5 at. ppm. The technique should be applicable to superpurity metals other than aluminum and has potential applications to grain refinement of commercial alloys. The necessary and sufficient requirements for production of a small grain size are as follows: a) a large number of potential nucleating sites must be created randomly within the cold worked material, b) sufficient thermal energy must be provided at a rate that will simultaneously activate a large fraction of the potential nuclei, and c) the grain growth must be stopped shortly after grain impingement.&apos; A high density of potential grain nuclei may be cre-

Jan 1, 1970

By T. T. Field, M. Gell

MUCH has been learned about plastic deformation behavior in crystals through the use of dislocation and slip band etchants. Slip in nickel and nickel-base alloys has previously been revealed by various etching techniques.l-5 The techniques for nickel-base super-alloys4,5 were successful only in the Udimet 700 composition in specific heat-treated conditions. The objective of this work was to develop a more generally applicable slip-band etching procedure. The nominal compositions of the alloys used in this study are listed in Table I. The low carbon Mar-M2OO alloy referred to in the text is the same as listed in Table I with the exception that the carbon content is less than 100 ppm. Mar-M200 and Udimet 700 were solutionized at 2250" and 2150°F, respectively. The aging treatment for both cast alloys was 32 hr at 1600°F and for wrought Udimet 700 was 4 hr at 1975"F, 24 hr at 1550°F, and 16 hr at 1400°F. The new slip-band etching technique consists of a chemical etch followed by a short electropolish, Table 11. Fig. l(a) shows the best result obtained on an internal section of a plastically deformed single crystal of Mar-M2OO when using a conventional slip-band etching procedure which consists of electropolishing followed by etching. Ghostlike traces corresponding to planar slip bands are observed, but the contrast between the bands and the background is weak. Fig. l(b) shows the same field using the new slip-band etching technique. After the etching step of this technique, the same ghostlike traces of Fig. l(a) are observed, but the subsequent electropolishing accentuates the slip bands and the subgrain boundaries while the rest of the matrix is being polished. Longer electropolishing obliterates the slip bands. The new slip-band etching technique makes use of the etchants and electrolytes that are normally used for a given material. Because of this, it should be possible to slip-band etch other nickel-base superal-loys by using existing etchants and electrolytes for a material and following the procedures outlined in the "Comments" section of Table 11. All the illustrative examples given below show internal plastic deformation in single crystals of regular and low carbon Mar-M200 in the solutionized and

Jan 1, 1970

By G. P. Tiwari

Recrystallization and grain growth in thoria dispersed nickel and nichrome were recently studied by Webster as a function of temperature and deformation. The unexpected part of these results was that specimens which had received heavier deformation developed greater resistance to recrystallization. Retardation of recrystallization was accompanied by the formation of voids around thoria dispersion. To explain these results, Webster suggested that the formation of void around the particles increased the effective size of thoria particles. This resulted in greater impediment to the grain-boundary migration and as a consequence the recrystallization of the matrix is retarded. In the present note an alternative and more probable explanation for the effect of voids on recrystallization is presented. The exact mechanism of void formation in thoria dispersed nickel or nichrome is not known. However, it is reasonably certain that it must be preceded by the stress concentration in the matrix around thoria dispersion during the deformation.&apos;&apos; The resulting stress concentration must be sufficient enough to supply the surface energy for the new surfaces created. Further, the decrease in the strain energy of the matrix surrounding the potential void nucleus must be larger than the surface energy of the newly created surface. The release of strain energy due to formation of crack results in a strain free cylinder of the material around the voids.13 If the void formation is not localized, at few points only (as is the case here), this process may lead to considerable amount of release of strain energy of the matrix. The pattern of recrystallization behavior of single phase homogeneous matrix as well as the matrix having a second phase dispersion is same except for the fact recovery and recrystallization are more clearly delineated.14 In general, the recrystallization temperature is lowered (i.e., recrystallization is easier) with increase in the amount of cold work. This is due to the increase in stored energy in the matrix with increasing amount of deformation. If somehow there is a relaxation of strain energy in the matrix, the recrystallization should become difficult because of the decrease in the amount of stored energy available for recrystallization. Since the formation of voids leads to a decrease in the strain energy of matrix, the recrystallization of the matrix would be inhibited due to the formation of voids during deformation prior to recrystallization. It has been observed by earlier workers15&apos;16 that the presence of preexisting voids in a matrix retards the recrystallization. The essential issue here is how do the voids act to produce this effect. If the voids influence recrystallization only by blocking the grain boundary migration, then the effect should be maximum when they are present almost exclusively along grain boundary. These conditions are obtained during high temperature deformation. However, the voids produced due to creep along grain boundary are not able to prevent recrystallization17 suggesting that they are not effective in blocking grain boundary movement. Recently it was shown by Davies and Williams that the voids can act as sinks for vacancies." As a result the processes dependent on vacancy diffusion like recovery, recrystallization, dislocation climb, and so forth, will be hindered. This fact may be responsible for inhibition of recrystallization during subsequent deformation and annealing cycles. It is to be noted here that there is a large difference between the density of voids in creep experiments and the other experiments where retarding effect of voids on recrystallization is seen. The voids in former may number up to l04 to l05 per sq cm whereas in latter cases the voids density is typically around 1010 to 1013 per sq cm. It appears that the decrease in supply of vacancies in creep is insufficient to adversely affect the recrystallization due to low void population. The author is grateful to P. Das Gupta and S. P. Ray for helpful discussions. Author&apos;s Reply D. Webster Tiwari appears to have misunderstood the nature of grain boundary-particle interactions. Tiwari (quoting Cahn) states that second phase particles become more effective as they become smaller, therefore as the voids in TDNiC make the thoria particles effectively bigger their ability to resist grain boundary movement is impaired. This particle size argument was originally proposed in the form of an equation by Zener 20 years agol9 and is not necessarily valid as is discussed below. However, assuming it is valid, it predicts a greater boundary restraining effect by smaller particles simply because their combined cross sectional area is greater at a constant volume. If the number of particles remains the same and their effective size increases, as in the present case, Zener&apos;s equation predicts a greatly reduced grain size. This is because the effect

Jan 1, 1970

By R. D. Nelson, F. E. Bowman

Assumptions are made of ideal mixing and that the density of silver can be obtained by extrapolating reported liquid density-temperature data through the freezing point back to the temperature range of interest. The results of this procedure using liquid silver density data of Kirshenbaum et al.5 are presented in Table I1 where it is observed that agreement is everywhere within <0.1 pct and generally is within 0.05 pct. Because the Sn-Ag alloys are dilute, the assumption of ideal behavior is, therefore, probably justified. In conclusion, the densities of dilute liquid solutions of silver in tin have been determined. Even for concentrations as low as 0.1 pct, the effect of silver on the density of liquid tin is clearly measurable. This work also suggests that for dilute alloys at temperatures far below the freezing point of the solute metal, densities may be accurately calculated by extrapolation of the pure metal data without having recourse to physical measurement on the alloy itself. plutonium having a grain size of about 100 µ. This paper presents data showing that large elongations of fine-grained a Pu can be obtained by using slow deformation rates. Large plasticity, however, of a Pu in compression has been observed.4 Reductions in thickness of 90 pct have been observed with no edge cracking. These large reductions are accompanied by concurrent re-crystallization. The deformation modes, which are quite complex, have been studied extensively by observing the deformation microstructures of polished surfaces that had been deformed in compression.5-7 Although slip apparently is a predominant mode of deformation at room temperature, grain boundary sliding and concurrent recrystallization become more predominant at high a temperatures.4&apos;7 Although recovery occurs,8,9 no grain growth has been reported in a Pu even at temperatures near the a =ß equilibrium temperature (-115oC), which is 0.7 of the calculated melting temperature of a Pu.10 From studies on other materials, it appears that high elongations can be obtained in alloys when the THE purpose of this technical note is to present briefly some data revealing high ductility of a Pu, which is normally considered brittle. The very low ductility of a Pu in tension has been reported by many investigators.&apos;-3 Gardner,1 for example, reported that the total elongation of a Pu at a testing speed of 0.015 ipm is less than 0.1 pct at room temperature and only about 1 pct at 100°C. The only tensile creep studies that have been reported&apos; indicate no large ductility, but they were performed on relatively low purity

Jan 1, 1970

By J. W. Edington

THE Hopkinson bar has become a popular technique for the measurement of the mechanical properties of materials deformed at high strain rate. Maximum use of the equipment is made in the arrangement first used by Kolskyl in which a short compression specimen is sandwiched between two pressure bars and is loaded by a single pulse travelling through the system. The pressure bars are used both to apply the load to the specimen and as transducers to obtain continuous strain-time histories of three pulses, incident on, reflected, and transmitted by the specimen. The data measured by the pressure bars can be analyzed in terms of the stress/strain behavior of the specimen.2&apos;3 However, one of the assumptions of the analysis of the observed pulses is that the total stress and total strain do not vary significantly from point to point within the specimen at any given instant during the deformation process. Although this assumption is generally justified for very short disc-like specimens2 the situation is uncertain for larger specimens. For example, at small plastic strains (-0.01) Hauser et al.2 have some evidence of small flucations in the total stress within the crystal during deformation, even in relatively short aluminum specimens. In addition, Karnes4 has shown that the plastic strain, and by inference strain rate, is different at each end of a compression specimen tested in a Hopkinson bar, although the length of the specimen was not specified. Recently, the mechanical properties and the dislocation substructure have been investigated in single crystals of columbium5 (length 0.25 in., diam 0.19 in.), and copper6 (length 0.5 in., diam 0.5 in.) deformed at high strain rates. As part of this research program the assumption that the plastic strain is constant throughout the specimen has been checked by measuring the total dislocation density as a function of position in the specimen. Compression specimens of the same orientations and dimensions were tested as described previously5,6 sing a split Hopkinson bar. Since any discontinuity in strain distribution is most likely to arise during the initial stages of deformation the investigation was performed on specimens deformed to plastic shear strains of 0.054 (copper) at a strain rate 1.2 x l03 sec-1, and 0.06 (columbium) at a strain rate 1.5 X l03 sec-1. The orientation of the single crystals is shown in Figs. 1 and 3. Thin foils were taken parallel to the most highly stressed slip plane, i.e., (111) in copper and (011) in columbium, using conventional disc techniques. The dislocation densities were measured using first order reflections with compensation for invisible dislocations.5&apos;6 In the copper single crystals the discs were randomly distributed throughout the cross section of the specimen. However, the dislocation density obtained from each disc was plotted vs the disc positions relative to the ends of the specimen. The results for the copper specimens are shown in Fig. 1. Clearly the dislocation density is constant throughout the main portion of specimen within the experimental error. The error bars on the dislocation densities correspond to a shear strain variation of 0.015 on the basis of previous measurements% ± of the rate of increase of dislocation density with strain in copper single crystals of the same geometry. Thus within this experimental error the plastic strain can be concluded to be constant within the specimen and the assumptions used in the analysis of the stress/time curves are therefore reasonably valid. The higher measured dslocation density near the impact end and the lower dislocation density at the bar end of the copper specimen is in agreement with the results of Karnes4 who showed that this strain/time curve rose to a maximum more rapidly at the impact end compared with the bar end. Hauser et al.2 have also pointed out that at small plastic strains (-0.01) the strain at the impact end of the specimen may be greater than that at the bar end. Thin foils taken from different points within the columbium single crystals demonstrated that the dislocation density could vary significantly within the specimen, see Fig. 2. Large areas of some thin foils up to 30 µ sq contained very few dislocations, see Fig. 2(a). However, in other parts of the compression specimen dislocation configurations like those shown in Fig. 2(b) existed over large areas (-30 µ sq). As a result, when the average dislocation density in a thin foil is plotted as a function of the position of the thin foil relative to the ends of the specimen, considerable scatter is observed, see Fig. 3. In this material then, the local dislocation density, and consequently the

Jan 1, 1970

By L. H. Sjodahl, J. B. Conway

of each particle on grain boundary movement is proportional to the area it occupies on the grain boundary and this increases with the square of the particle radius. In contrast to the impression gained by Tiwari the effectiveness of a particle, as a grain boundary obstacle, increases rapidly as the particle size increases. The counterbalancing factor in a dispersion of constant volume (e.g., those considered by Zener) is of course the rapidly diminishing number of particles, a situation which does not exist in thoria dispersed materials where the volume fraction of thoria remains constant. Although it has been assumed that the Zener approach is valid for the sake of the above argument, it is open to the following objections: 1) It assumes that the effect of many small particles along a grain boundary is cumulative and does not take into account the possibility of each small particle being overcome separately. In this case the boundary will not be able to move forward until the largest particle on the boundary has been overcome. This means that the rate controlling factor will be the rate at which a few relatively large particles are overcome with the remaining small particles playing a negligible role. 2) When the dispersion consists of very small particles the interparticle spacing is usually small compared to the grain size and most particles are located away from grain boundaries where they can play no part. The most efficient dispersion, from a purely geometrical viewpoint, is one where the particle spacing is equal to the grain size so that all the particles are on grain boundaries. Tiwari&apos;s second point that voids cannot prevent re-crystallization seems to be unfounded as several workes20-23 have shown that voids alone can retard grain boundary movement and recrystallization. To further convince Tiwari, Fig. 17 shows a void in deformed TD Nichrome holding back a recrystallization interface. Tiwari&apos;s explanation for the effect of voids on recrystallization, i.e., they reduce local strain energy and hence lower the driving force for recrystallization may be valid in itself but is irrelevant to the present case where even complete recrystallization after ONE of the more recently proposed expressions for describing stress-strain behavior is that due to Voce.1,2 This equation is usually written: s =s8 ?(s8?so)e??/?c [l] where s is the true stress, ? is true strain, cC is a constant called the characteristic strain, s8 is the asymptotic stress approached at high strain values, and so is the threshold stress at which the plastic deformation begins. While this expression has not been universally accepted as yet it does contain certain features which are consistent with experimental stress-strain behavior. In a more recent publication Hsu, Davies, and Royles3 employed the concept of generalized strain proposed by seth4 and identified a method for linearizing the stress-strain plot. In this approach the generalized strain was given by: where 7 is the generalized strain, 1 is the instantaneous length, 1, the datum length, and n is a constant called the "coefficient of strain measure". A value of n was said to exist which would yield the linearity: s —s+ S[.-(tf] [3] In recent studies of both these approaches, it has been found that while the Voce equation and the gen-

Jan 1, 1970

By Robert E. Green, Kenneth Reifsnider

Several experiments have been performed in order to illustrate the application of a recently developed X-ray image intensifier system to metallurgical investigations. In the present work the system has been used to study the instantaneous alterations in Laue transmission X-ray diffraction patterns during tensile deformation of aluminum single crystals. Expem&apos;mental results are presented which demonstrate the capability of the system for crystal orientation, for following orientation changes due to lattice rotation during tensile deformation, and for showing changes in the homogeneity of the lattice planes along the specimen length as a function of strain rate. RECENTLY, a new X-ray system has been developed which incorporates a cascaded image intensifier and permits direct viewing and recording of X-ray diffraction patterns produced on a fluorescent screen.1"3 In the present work the results of several experiments are presented which demonstrate the usefulness of this system for metallurgical applications. EXPERIMENTAL PROCEDURE A schematic diagram of the experimental arrangement is shown in Fig. 1. In this system a Machlett AEG-50-S tungsten target X-ray tube, normally operated at 50 kv and 40 ma, serves as the X-ray source. The X-ray tube is placed in direct contact with a 10-in.-long collimator, which transforms the X-ray beam from one with a circular cross section to one with a rectangular cross section 3 in. high and 1/6in. wide. By blocking off all but a small portion of the rectangular slit, it is possible to work with the more conventional "pinhole" collimated X-ray beam commonly used for obtaining Laue diffraction patterns. In the present work the test specimens were 99.99+ pct aluminum single crystal wires & in. in diam and 3 in. long. For the deformation tests the wire crystals were mounted in a special set of grips in a table model Instron machine so that diffraction patterns could be recorded during specimen deformation. For the orientation tests the wire crystals were mounted in a rotating goniometer so that diffraction patterns could be recorded during specimen rotation. At a distance of 3 cm from the specimen axis, a 6 in. diam DuPont CB-2 fluorescent screen is positioned to transform the X-ray image to a visible one. A Super Farron f/0.87 72 mm coupling lens, corrected for 4 to 1 demagnification, transmits the visible image to the image tube. The image intensifier used is a three-stage magnetically focused RCA type C70021A with an S-20 input photocathode and a P-20 output phosphor. The tube has unity magnification and useful input and output screen diameters of 1.5 in. The image on the output phosphor is of sufficient intensity to be viewed directly, to be recorded cine-matographically, or to be displayed by vidicon pick-up on a television monitor. The recording device most commonly used is a 16 mm Bolex motion picture camera fitted with a Canon f/0.95, 50 mm lens. The overall gain of the system is 16,000 for direct viewing and 2240 for recording on 16 mm movie film. The resolution of the system is limited to 1 line pair per mm which is approximately that of the fluorescent screen. This system has been used for cine recording of transmission Laue X-ray diffraction patterns with exposure times as short as 1/220 sec and for vidicon television pick-up and display at a scan time of 1/30 sec. Quantitative information may be obtained from each frame of the movie film, by either stopping the vertical slit down to a point source in order to obtain a conventional Laue photograph or else by retaining the linear beam and introducing fiducial marks as described in a previous paper.4 In either case, each frame may be enlarged to appropriate size for analysis by either using a photographic enlarger and making prints of the desired frames, or, more conveniently, by using a microfilm reader. EXPERIMENTAL RESULTS The first series of photographs which are presented in Fig. 2 serves to demonstrate the usefulness of the system for crystallographic orientation determination. This series of prints, made from enlargements of a 16 mm movie film, shows the dynamic Laue transmission patterns produced by an aluminum single crystal wire which was rotating about the wire axis when the patterns were recorded. The movie films were taken at 16 frames per sec and the crystal was rotated at a rate of 15 rpm.

Jan 1, 1970

By B. C. Allen

Grain boundary grooving has been studied in chromium, molybdenum, and tungsten under a variety of conditions using high vacuum techniques and tantalum -gettered argon. The average surface free energy of solid chromium, and the chromium-liquid silver interface free energy were respectively found to be 2200 ± 250 and 500 i 130 ergs per sq cm from groove formation kinetics and estimates of pertinent volume difffusion coefficients. The results for chromium were unffected by variations in interstitial content ranging from 0.003 to 0.09 pct C, or 0.003 to 0.03 pct O. Surface diffusion is the primary mechanism of groove formation in chromium under 1 atm argon at 1200" to 140O°C, and is essentially unaffected by 0.003 to 0.09 pct C, 0.003 to 0.03 pct O , metastable nitrogen contents up to -0.01 pct, and up to 2 torr Ag vapor. At higher temperatures, the major mechanism is volume diffusion in argon or evaporation-condensation in stutic vacuum. Surface diffusion occurs in molybdenum at 0.5 to 0.96 and in tungsten at 0.5 to 0.9 of the absolute melting tempera -ture by a single mechanism, possibly by the migration of single adatoms or vacancies. Results were slightly affected by up to 23 tory Sn vapor, and in molybdenum were essentially unaffected by 0.5 Ti or carbon in the range 0.002 to 0.02 pct. Volume difffusion through the liquid is the mechanism of groove formation in chromium-liquid silver at 1200" to 1400°C and in molybdenum-, Mo-0.5Ti-, and tungsten-liquid tin at 1200" to 2000°C. The solid-liquid interface free energies involved were estimated from grooving kanetics. WHEN a grain boundary intersects a solid surface, a groove tends to form along the line of intersection at temperatures above about half the absolute melting point (0.5 TM). The groove progressively grows by preferential atomic migration either by diffusion or evaporation. Establishment of a groove angle occurs in accordance with the grain boundary and surface free energies involved. The motivation for groove formation is a reduction in the total surface free energy of the system. This study is a continuation of previous work on thermal grooving of chromium, molybdenum, and tungsten.&apos; The temperature ranges were extended, and the effect of metallic and interstitial impurities was evaluated. The results were such that certain interface free energies and surface self-diffusion coefficients were deduced from the grooving kinetics. EXPERIMENTAL WORK Materials and Preparation. As indicated in Table I, the 0.05-0.08-cm-thick chromium, molybdenum, and tungsten sheet used was nominally 99.99 pct after recrystallization. Two lots of molybdenum with about the same analysis, Mo-0.5Ti,* and tungsten were ob- *Alloy compsitions are expressed in weight percent . tained commercially. Extruded chromium rod,&apos; prepared from iodide process crystals, was warm rolled to sheet at 700°C. Sheet of three Cr-0 impurity alloys containing up to 0.03 pct 0 was prepared by warm rolling arc melted, extruded, and swaged rod. Two Cr-C impurity alloys containing up to 0.09 pct C were made by equilibrating unalloyed chromium with a known amount of CH4 for 24 hr at 1150°C in previously evacuated quartz capsules. Chromium containing nominally 0.015 and 0.06 pct N was similarly prepared by equilibration with NH3. The sheet was recrystallized to give a stable grain size about equal to the sheet thickness. Molybdenum and Mo-O.5Ti were recrystallized in a tantalum resistance furnace 1 hr at 1 x lo-5 torr at 2300" and 220O°C, respectively. Tungsten was similarly annealed for 1 hr at 2500°C. Chromium and its impurity alloys were outgassed at 1100°C and recrystallized 1 hr at 1700°C under 1 atm Ar. Except for nitrogen, the impurity content stayed roughly constant. Nitrogen in both alloys was reduced to <0.001 pct. In fact, over 80 pct of the added nitrogen was lost after outgassing at llOO°C and annealing sheet 1 hr at 1300°C in argon in the presence of tantalum. Such a rapid loss can be rationalized since -2 torr N are required for equilibrium with 0.04 pct N in solution,3 while the equilibrium pressure is ~10-5 torr over tantalum at 1300°C.4 The recrystallized sheet was cut into small coupons which were metallographically ground and polished on one side with a minimum of grain boundary relief. The surface roughness was on the order of 0.01 µ. The tin and silver used were nominally 99.999 spec-trographically pure. After being outgassed at 1100°C and equilibrated in a molybdenum crucible for 0.5 hr at 1800°C in argon, the tin contained 3 ppm 0, <0.3 ppm N, and 0.1 ppm H. Following outgassing at 900°C and equilibration in a chromium crucible 1 hr at 1400°C in argon, the gas content of the silver was 1 ppm O, <0.5 ppm N, and 0.3 ppm H. Grooving Under Argon or Vacuum. All specimens were placed in unsealed containers made from rod or sheet of the same alloy, thereby enabling the polished surface to achieve gas-solid equilibrium. The annealing fixtures are shown in Fig. 1. The specimen was placed in a resistance furnace with a tantalum or Ta-10W heating element plus tantalum fixtures or radiation shields. Chromium was outgassed at 1100°C, and molybdenum and tungsten were outgassed at 1900°C to 1 x l0-5 torr or at the grooving temperature, whichever was lower. In vacuum anneals, the specimen was then heated directly to the intended grooving temperature. In argon anneals, 99.996 Ar was admitted

Jan 1, 1970

By H. H. Podgurski, J. C. M. Li, Y. T. Chou, F. N. Davis, R. A. Oriani

When an Fe-2 pct A1 alloy is nitrogemted at 500ºC with a gus tnixture (NH3-H2) in which the nitrogen activity has been kept Lou] enough to avoid the formation of iron nitride, a two-phase alloy is generuled which consists of AlN particles and a ferrite phase cotaining a heavy network of dislocations. The amount of nitrogen contained in such an alloy, when equilibrated with the nitrogenating atmosphere, far exceeds both that needed to satisfy the normal solution requirements of a Fe and that needed to convert all of the aluninuwi to AlN. This excess nitrogen is accounted for as being trapped on dislocations, adsorbed at the ferrite -AlN interface, and as an en-Iuznced lattice solubility in strained ferrite. This excessive uptake of nitrogen had previously been attribuled by other investigators to the formation of a nonstoichiornetric aluminum nitride. Isotope exchange experiments revealed various amomts of exchargeable N14 present in the originally nitrided samples that could not be removed by reduction with HS at 500ºC. This exchangeable nitrogen has been identified us that bound to the AlN -ferrite interface. Estimates of inter facial areas in alloys containing -3 pct by weight of A1N are as high as 10 sq m per g of alloy. ThE first1 of this series of papers described the experiments forming the basis for the elucidation of the mechanism of the formation of aluminum nitride particles within an Fe-A1 alloy. It was found that not only are dislocations necessary for the nucleation of the AlN particles but also the nitriding reaction in turn produces a dense network of dislocations in the ferrite matrix. It was also observed that nitrogen in excess of that needed for the formation of stoichiometric AIN is taken up by the alloy without the formation of an iron nitride. The present paper is an analysis of the excess nitrogen sorbed by the nitrided Fe-A1 alloy which considers the structure generated by the formation of the aluminum nitride particles. Because of the high density of dislocations, this system has proved to be quite useful in studying nitrogen-dislocation interactions. Wriedt and Darken2 have already reported such studies in a cold-worked ferritic steel. EXPERIMENTAL Nitrogen Sorption. The specimens of this alloy were cold worked (50 pct reduction) to 0.011 in. thickness and chemically cleaned in a 2:1 concentrated phosphoric acid-50 pct hydrogen peroxide solution before nitrogenation. The flowing nitrogenating atmosphere (11 pct NH3-89 pct H2) was established before the ni- trogenating temperature was reached. The same gravimetric and gas-flow equipment described in an earlier paper1 was also used in this investigation. Changes in nitrogen concentration were followed gravimetrically when establishing the isotherms. In the isotope exchange experiments, concentration changes were followed volumetrically. In some instances chemical analyses (Kjeldahl method) were used to check for material balances in both the gravimetric and volumetric procedures. Our objective was to obtain reversible nitrogen sorption isotherms for alloys equilibrated with NH3-H2 gas mixtures over a large range of nitrogen activity* and temperature. The *Defined as equal to PN H /P3/2 ,where P corresponds to partial pressure in atmospheres. Actually the nitrogen activity, aN, in the alloy equals K PNH3 /p3/2H2, where K is the equilibrium constant for the reaction NH3 = N + 3/2H2. upper limit for nitrogen activity was below that which would produce iron nitride; for reasons which will become apparent later, most of the sorption studies were made in the temperature range between 400" and 500&apos;C. The alloy sample studied most extensively in this investigation was given a series of successive reductions (100 pct H2) and nitrogenating treatments at 500°C to attain a stabilized structure. Presumably some dislocations were lost during these treatments. Throughout most of the sorption studies, temperature was held at ± 1°C and the gas-phase composition was held to k0.2 pet NH3. Based upon the results of numerous diffusion experiments with this alloy* the &apos;Results to be published in a third paper of this series. times chosen for equilibration were considered more than adequate, Nitrogen Isotope Exchange. The first exchange experiments were carried out by circulating a measured quantity of H2 and NH3* (with a predetermined isotopic *The NH3 was synthesized over a synthetic ammonia iron catalyst using H2, and N2, enriched with N15. AS the NH3 was formed it was removed continuously from the gas phase by circulating the mixture through a refrigerated (78ºK) trap. When most of the nitrogen had been converted to NH3, it was distilled from the trap into a glass storage vessel. composition, N15/N14) over a nitrided specimen at 450°C in a closed glass system. Attempts to reach the exchange limit isothermally, i.e., an isotopic ratio (N15/N14) in the gas phase identical with the extractable nitrogen in the nitrided alloy, were futile. The exchange rate between the gas phase and the alloy was too slow, involving many days. To circumvent the slow exchange with the gas phase, measured amounts of N15 and N14 were introduced into the alloy by nitrogenating with an NH3-H2, mixture at 500°C containing an N15/N14 ratio of 7.76; the charged specimens were then sealed by allowing an oxide film to form over them in air, and in this final condition the specimens were subjected to 500°C in vacuum for various times during which isotope exchange was allowed to proceed within the specimen. It was estab-

Jan 1, 1970

By B. B. Rath, Hsun Hu

Rates of migration of large-angle boundaries have been studied in zone-refined aluminum crystals, defonned 80 pct by rolling in the (110)[112] orientation at -78°C followed by a recovery anneal at 80°C. Artificially nucleated grains show a marked variation. by an order of magnitude, in their growth rates in different directions. The average activation energy for the migration of all boundaries was found to be about 16,000 cal per mole. The anisotropy of the boundary migration is rationalized on the basis of the boundary structure. It has been observed by Beck and HU,1 Kohara el al,2,3 and Czjzek and Haessner4 that recrystallized grains formed upon annealing Of deformed sing1e crystals of aluminum show anisotropic growth characteristics. Kohara et al. found that single crystals rolled in the (110)[112] orientation, when random nuclei were provided on one side of the crystal by rubbing with emery paper and annealing, developed a sharp recrys-tallization texture on the other side of the crystal upon further annealing. This sharp recrystallization texture consisted of four components, which were related to the deformation texture of the crystal, i.e. (110)[112], by rotations of ±40 deg around each of the two common [ 111] axes&apos; They also noted that recrystallized grains were elongated in directions perpendicular to either of these two common [1111 axes. They attributed this anisotropic growth to the difference in the rate of self-diffusion or diffusion of impurity atoms along the tilt and the twist boundaries. A somewhat similar investigation was conducted by Czjzek and Haessner4 On strained single-crystal sheets Of alum- inum. These authors claimed that the matrix structure of the deformed crystal had a greater effect on the growth anisotropy of the recrystallized grains than did the boundary orientation itself. In the present investigation quantitative measurements of the rate of grain boundary migration in anisotropic growth have been made in zone-refined aluminum (99.9999+pct pure) crystals deformed 80 pct by rolling in the (110) 112] orientation. Crystals of this particular orientation were chosen because of the following desirable features: 1) the crystal does not change its orientation during rolling; 2) the rolling plane contains all the significant crystallographic directions; and 3) when annealed, following deformation, the crystal does not re-crystallize spontaneously but polygonizes to a stable and homogeneous structure. Hence, the initial orientation of the crystal and a constant strain energy in the matrix can be maintained during subsequent grain boundary migration studies. It is essential to keep the driving force constant for the study of boundary mobility.5 EXPERIMENTAL PROCEDURE A cylindrical single crystal of 1 in. diam was grown by the Bridgman method in a high-purity graphite mold. The resistance ratio, R(4.2°K) /R(298°K) , of the grown crystal was approximately 2.0 x 10-4. A number of slices, 1/4 in. thick, were cut from the crystal along the (110) plane and were mechanically and electrolyti-cally polished to remove the strained surface layer. The crystals were then rolled along the [112] direction to 80 pct reduction in thickness at -78°C. To minimize surface friction, the crystals were rolled between two layers of 0.005-in. teflon sheet. Rolling was interrupted, prior to completion, to remove the surface layers and the edges by electropolishing. These and similar precautions in handling the rolled crystals

Jan 1, 1967

By R. W. Bartlett

DISILICIDE coatings, MeSi2, on refractory metals are usually grown by a solid-state diffusion reaction similar to the parabolic oxidation of metals. Two or more silicide compounds occur in each of the binary silicon-refractory metal systems. When an adequate source of silicon is available during the coating process, the lower silicide compounds are usually not formed.1 However, during service application of the coated refractory metal, continued heating causes further diffusion and growth of the lower silicides. A study of the growth kinetics of the lower silicides in the molybdenum and tungsten binary systems with silicon was previously reported.2 The present study is concerned with the growth kinetics of Ta5Si3 and Cb5Si3, formed as conjugate layers between TaSi2/Ta and CbSi2/Cb diffusion couples, respectively. Diffusion couples consisting of disilicide-coated tantalum and columbium sheet coupons were subjected to diffusion heat treatments, cross-sectioned, and scanned by an electron-microprobe analyzer to determine the relative X-ray intensity profiles. These profiles correspond closely to concentration profiles for the constituents, and were used to identify phases and locate phase boundaries. The analysis of a single specimen after a diffusion-anneal provides only one value for the Me5Si3 phase thickness, corresponding to the time and temperature of the diffusion treatment. Consequently, each isothermal curve showing the rate of accumulation or depletion of silicide phases required several samples with identical diffusion temperatures but different diffusion times. The disilicide coatings were prepared by pyrolizing commercially pure silane in a hydrogen carrier gas. The hydrogen was purified by passage through a palladium membrane. Commercially pure tantalum and columbium sheet metal coupons, 0.005 by $ by 2 in., were used. All of the coated specimens for each system were prepared together in a single group in order to minimize coating variations among individual specimens. During pyrolysis, the brightness temperature was maintained at 1200°C. With suitable flow rates at this temperature, only the disilicides of tantalum and columbium were formed in detectable amounts. Coated specimens were subjected to diffusion an-neals in a tube furnace with automatic proportional control within ±10°C. A H2-Ar mixture, deoxidized and dried over anhydrous magnesium perchlorate, was used to prevent oxidation during the diffusion anneal. Diffusion couples were cross-sectioned, polished and examined with an A.R.L. electron-microprobe X-ray analyzer. Both metal constituents in each specimen were simultaneously scanned using a 1-p beam spot size and either 1- or 2-µ steps. Analyses were performed using the Ka radiation of columbium and silicon, and the La, radiation of tantalum. For all specimens, an acceleration voltage of 30 kv was used, and integration was made against the specimen current. LiF and A DP monochrometers were used to isolate characteristic radiations. Three or more traverses were made on each specimen. The intensity scales were adjusted using the constituent metals and standard samples of the silicide compounds which had been verified by X-ray diffraction. The relative intensity profiles were used directly, in conjunction with the standard samples, to identify compounds and phase boundaries. The stoichiometries differ considerably between the silicide compounds in both systems, and the homogeneity range for these silicide compounds is narrow. These characteristics result in marked differences in relative intensities of the fluorescing elements—differences which permit ready identification of phases and phase boundaries. Projections of both electron back-scattered images and characteristic

Jan 1, 1967

By Harry A. Lipsitt, Attwell M. Adair

A number of papers have appeared in the past several years concerning the nature of the fatigue limit. The hypotheses presented in those papers fall into three groups. Some authors attribute the fatigue limit to the distribution of interstitials prior to testing (static group). Others consider the fatigue limit to be due to dislocation-interstitial reactions during testing (dynamic group). Still other propose that the fatigue limit results from a characteristic peculiar to the iron (bee) lattice (inherent group). This communication is an attempt to digest the salient features of each of the hypotheses, discuss them, and present some constructive criticism. It is shown that each of the extant ideas has some merit, and that each of the mechanisms thus far proposed is necessary, but individually insufficient, to provide the desired level of understanding of the fatigue-limit behavior of metals. Static Group. The data of Oates and wilson1 on finegrained (=0.022 mm diam) low-carbon steel indicate that the fatigue limit exists in the absence of sufficient plastic deformation for any dynamic strain-aging mechanism to be operative. Specimens tested just below the fatigue limit showed yield-point behavior typical for unstrained material when removed from the fatigue machine and tested in tension. These results led them to the conclusion that initial dislocation locking controls the fatigue limit in this material, which has a yield stress higher than the fatigue-limit stress. Prestraining this material just prior to fatigue testing would be expected to lower the fatigue-limit stress; this they observed experimentally. Yoshikawa and sugeno2 are of the opinion that the sharp fatigue limit in fine-grained iron is caused by

Jan 1, 1967

By L. T. Larson, M. L. Picklesimer

The relationship between the apparent angle of rotation of monochromatic plane polarized light and the tilt of the basal pole from the surface normal has been experimentally determined for zirconium over the wavelength range of 500 to 655 mp. This relationship allows the determination of the spatial orientation of the basal pole of an individual grain in a polycvystal-ling zivrconium specimen to within ±3 deg by three simple tneasurements with a polarized-light metallurgical microscope. The method of measurement is discussed in detail. THE optical anisotropy of materials having noncubic crystal structures has long been used to reveal features by polarized-light microscopy. Petrographers have used measurements of certain optical properties to identify and classify transparent or translucent minerals. More recent work (i.e., Cameron1) has extended such measurements to opaque minerals in reflected light. Few attempts have been made to make similar measurements on noncubic metals. Couling and pearsall2 have reported that a sensitive tint plate can be used in a polarized-light metallurgical microscope to determine the position of the basal-plane trace in a grain of polycrystalline magnesium. Reed-Hill3 has reported that the same technique can be used for zirconium. We have found that the precision of measurement can be increased to about ±0.5 deg by using a Nakamura plate4,5 to determine the exact extinction position after the sensitive tint plate has been used to locate approximately the basal-plane trace. This report describes a method for measurement of another optical property, the apparent angle of rotation. This measurement permits determination of the angle between the basal pole of a grain of a hcp metal and the normal to the surface of the specimen. When the two measurements are combined, the orientation of the basal pole in space can be determined from three simple measurements on a single surface. One to two hundred such determinations will permit plotting of a basal-pole figure for the polycrystalline material with reasonable accuracy. When normally incident, monochromatic, plane-polarized light is reflected from the surface of an optically anisotropic material, the light may be converted to elliptically polarized light, the plane of vibration may be rotated, or both may occur. The el- lipticity, the angle of rotation, and the reflectivity can be related to the indices of refraction and the absorption coefficients of the material.6,7 Ellipticity values can be determined with an elliptical compensator, but not with the ease and precision desirable for the present purposes. Measurement of the angle of rotation requires only the determination of the angle from the crossed position (90 deg to the polarizer) that the analyzer must be rotated to obtain extinction when the trace of the optical axis in the surface is at 45 deg to the vibration direction of the polarizer. The angle of rotation of the analyzer is approximately 6/5 that of the true angle of rotation of the light as reflected from the specimen because there is a small amount of additional rotation produced during the passage of the reflected light through the mirror of the microscope. Since we are presently interested only in determining the tilt of the basal pole, the angle of rotation of the analyzer (the apparent angle of rotation of the light, i.e., uncorrected) can be used. Precision of the measurement can be increased substantially by the use of a Nakamura plate4,5 in determining the extinction position. In an optically uniaxial material (hcp or tetragonal crystal structure) the angle of rotation depends only on the optical properties of the material and the orientation of the optical axis of the grain relative to the plane of incidence of the plane-polarized light.7,8 Thus, in a metal such as zirconium, the apparent angle of rotation at the 45-deg position in any given wavelength of light is a direct measure of the tilt of the basal pole from the normal to the surface. If the optical properties vary with wavelength, the apparent angle of rotation for any given tilt of the basal pole will vary. None of the required information exists in the literature for zirconium nor for any other non-cubic metal. MEASUREMENTS ON SINGLE-CRYSTAL ZIRCONIUM A single-crystal sphere of zirconium 9/16 in. in diam was spark-cut from a single-crystal rod grown from iodide bar by an electron-beam zone-melting process.9 The damaged surface was removed by chemical polishing in a 45/45/10 mixture (by vol) of water, concentrated HNO3, and HF (48 pct) and then electropolishing at 50 v in a bath1&apos; of methyl alcohol and perchloric acid (95/5 by vol) at -70-C. The single-crystal sphere was mounted in a five-axis goniometer stage having a removable eucentric X-ray diffraction goniometer head for the two inner orientation axes. The basal pole of the single-crysta sphere was aligned parallel to a third axis of the goniometer stage by using the sensitive tint method to determine the basal-plane trace at several rotational positions of the sphere. The alignment was then checked by removing the sphere and eucentric gonio-

Jan 1, 1967

By N. O. Gray, John Henderson

Hydrogen-reduction data for naturally occurring single crystals and Prepared polycrystals of dense hematite have been presented. Results cover the temperature range 400o to 1000oC, for particles from ten sources, ranging in size from 0.07 to 10 mm and in shape from spheres to cylinders, cubes, and thin slabs. A consistent pattern of behavior has been demonstrated for single crystals and the reduction mechanism shown to be temperature-dependent. Below 579oC reduction is a simple topochemical process but at higher temperatuves it is complex and occurs in two distinct stages. Prepared particles from these laboratories behave in a similar manner to the single crystals. Data from two investigators showing topochernical reduction of Prepared particles above 575°C are inconsistent with that for other dense hematites. It is concluded that topochenzical reaction should not be used as a model for generalized rate expressions for dense hematites. SINCE 1958, McKewan1-6 has brought to prominence a simple concept of dense hematite reduction. This model is that oxygen is lost from a hematite particle undergoing reduction only from an oxide-iron interface that recedes in such a way that the oxide remaining retains the original shape of the particle, i.e., reduction occurs topochemically. An adjunct to this concept is that any intermediate oxides in the transition from hematite to iron only form thin layers so that oxygen cannot be lost from the particle without movement of the oxide-iron interface. Further, the rate of oxygen loss from the particle is said to be proportional to the area of the receding interface so that the iron layer grows linearly with time and the over-all reduction process can be described by the equation where ro and do are the initial particle radius and density, respectively, R is the fraction of the original oxygen lost, i.e., the fractional reduction, at time t, and K is the rate constant. The idea of an underlying simplicity in hematite reduction is attractive because it gives a tractable basis from which general theories of hematite reduction can be developed and it has received wide support,7-14 based mainly on the large amount of data13 that can be fitted to Eq. [I]. However, despite the fact that this equation has been derived for dense materials, the bulk of the data that have been used to test it13 have been for materials of only about 90 pct of theoretical density (5.26 g cm-3) or less, so that its generality for dense hematites has not been demonstrated. In any case, as will be seen, adherence of reduction data to Eq. [1] does not necessarily imply that reaction occurs topochemically. In this work only data for hematites approaching theoretical density are considered and it will be shown that in only one study besides McKewan&apos;s is topochemical behavior observed over the whole range of temperature investigated. For the majority of materials a linear rate of interface advance is observed to complete reduction only when wustite is not a stable intermediate phase in the transition of hematite to iron, i.e., at temperatures below about 575°C. Above this temperature, reduction is an exceedingly complex series of reactions that takes place in two distinct stages and it is only in the first stage that reaction in any way resembles a topochemical process. This means then that, far from representing general behavior as has commonly been supposed, topochemical reaction for dense hematites is only a particular behavior that may be observed under some circumstances. EXPERIMENTAL Hydrogen-reduction data have been collected and cross-checked in these laboratories by three techniques, weight loss, collection of water evolved in the reduction reactions, and direct metallographic examination. Details of these techniques are discussed elsewhere," where it is shown that results obtained by the three methods are in close agreement. The weight-loss method, by which most of the results were obtained, consisted of hanging the sample in a platinum mesh basket from an Ainsworth Model AV-AU-1 vacuum recording balance inside a vertical l 1/4-in.-ID alumina tube furnace. Dry deoxidized hydrogen was flowed downwards through the tube at 2 to 4 liters min-1 (stp). Single crystals from two sources and artificial oxides from three sources have been examined. The single crystals were from hematite deposits at Yampi Sound, Western Australia, and Brazil, the latter being obtained from Gregory, Bottley and Co., London, U.K. The "Yampi Blue" crystals were hand-picked from washed, magnetically concentrated, sized fractions, -200 mesh BSS (mean diameter ca 0.07 mm) and —36 + 44 mesh BSS (mean diameter ca 0.4 mm) while 10-mm cubes were cut from the Brazilian crystals with a diamond saw. The starting materials for the prepared particles were hematites designated, respectively, "Specpure Iron Oxide", Laboratory No. S639 from Johnson Matthey & Co. Ltd., London, U.K., "Calcined Ferric Oxide" from B.D.H. Laboratory Chemicals Division, Poole, U.K., and "Pigment Grade Oxide", EPR-50, from C. K. Williams & Co., Easton, Pa., U.S.A. Approximately spherical particles were prepared from the artificial oxides by rolling the material, moistened if necessary, in a glass jar, and cylindrical compacts approximately 10 mm in diam and of approximately equal height were pressed in a steel die at 200 psi. These spheres and cylinders were subsequently fired in oxygen for 20 to 100 hr at 1370°C. The

Jan 1, 1967

By A. P. Woods, J. A. Elias, A. J. Heckler

A method is described by whichX-ray pole figures and axis density figures may be plotted automatically. The X-ray data are obtained using a Siemens texture gonionleter and the Schulz reflection method. Composite sampling methods are used to obtain a full quadrant of the pole figure. The contour lines of the pole figure and axis density figures are drawn using a computer-controlled x-y plotter. The computer program used to draw the contours was obtained from ZBM. POLE figures used to describe crystallographic orientations of poly crystalline sheet materials are usually plotted manually from X-ray diffraction output in the form of a strip chart recording of the intensity distribution of a given crystallographic pole in physical space. Today&apos;s computers and associated plotting equipment now make it possible to plot pole figures and axis density figures automatically. Inverse pole figures have been determined by mathematically "inverting" X-ray pole figure data.&apos;-&apos; In general, these methods require complicated, time-consuming numerical calculations. A more economical but less accurate method is to determine the axis densities of low-index crystallographic poles using an X-ray diffractometer. When these axis densities are plotted in a unit stereographic triangle contour lines can be drawn to represent the axis density distribution. This can now be done automatically. Computers were used to plot pole figures by a method developed by Holland, Engler, and powers.&apos; In their method intensity ratios based on a random standard sample were obtained from a strip chart recording, and the stereographic (x, y) coordinates of these ratios were determined by a computer. Symbols characteristic of different intensity ratio levels were then plotted using an automatic x, y plotter and intensity contours were drawn manually. The present paper describes a method by which pole figures and axis density figures have been automatically plotted from digital data obtained from a Siemens X-ray unit. Plotting was accomplished using an IBM 1620 computer and a Calcomp 563 digital plotter. COMPUTER PROGRAM The computer program was obtained from IBM Systems Reference Library, No. 1620-CS-05X, and was designed to plot contour maps from randomly distributed data. It consists of a set of twelve separate subprograms, four of which were used in this work. The program takes a given distribution of data points and by a numerical method determines the values at mesh points of a square grid system superimposed over the input data. The output data from this program is in a form suitable for input to the contour plotting program. A smoothing program is also available which calculates new mesh point values from a continuous function fitted to neighboring mesh points. The degree of smoothing depends on the number of points around a given grid point which are used to adjust or smooth the grid value. The contour plotting program is designed to allow the user to specify the interval, scale, and annotation of the contours to be plotted. EXPERIMENTAL PROCEDURE Pole Figure Data Points. Diffracted X-ray intensities were determined using a Siemens texture goniometer and the schulzs reflection method. Due to geometric

Jan 1, 1968

By C. S. Sivaramakrishnan, Manjit Singh, Rajendra Kumar

Regarding liquid nzetals structurally as a suspm-sion of clusters , having derivated solid-state coordination, in truly liquid atoms, the recently developed Kuvlar-Samarin technique of centrifuging- in liquid state enabled the determination of the cluster sizes inAl-Cu mid Pb-Sn systems. It is shown that the colutne fraction of the clusters does not exceed 9 pct and the energy of their formation in Al-Cu is about 5.5 kcal per g-atom and in Pb-Sn eutectic alloys about 25 kcal per y-atoni. STRUCTURAL investigations of liquid state have principally followed the following three courses: i) studies with X-ray, electron, or neutron diffraction; these investigations have shown that there is a certain amount of regularity in the structure of liquid metals which can be defined by a coordination number and that the structure is a derived function of that in the solid state; ii) thermodynamical investigations which are based on the concept of ideal behavior; these describe the liquid state in terms of free-energy values and other thermodynamic functions; although these investigations are of help in the study of the general effects of alloying, they do not provide any structural insight into the precise atomic distribution in liquid state; iii) measurements of surface tension and viscosity; although it is natural to expect that the viscosity is related to the structure in liquid state, these investigations have so far only provided information which can be used by the foundry technologists and has been little utilized in formulating models of the structure of liquid state. As it happens, investigators in the three groups have worked almost independently of each other and there is practically no structural correlation between the results of one group with those of another. The purpose of the present paper is to indicate that the experimentally measured parameters of these three groups of research are closely related to the structure in the liquid state. STRUCTURE OF LIQUID METALS Although atomic distribution in solid and gaseous states is rigorously known, that of the liquid state is only appreciated on the fringes. There is no universal model of atomic distribution in liquid state, but two diverse models are at present hotly contested. The first, largely expounded by ~ildebrand,&apos; regards the liquids as condensed gas since many of their properties and much of their behavior can be adequately described by regarding them as fluids. The second mode12j3 considers that some form of near-solid as- sociation of large number of atoms exists in the liquid state. On the other hand, ~ernal&apos; was able to predict rather precisely the radial distribution functions in liquids on the basis of statistical geometric approach which considered that liquids are "homogeneous, coherent, and essentially irregular assemblage of molecules containing no crystalline regions or holes large enough to admit another molecule". He introduced the concept of pseudonuclei in the otherwise random structure as aggregates of closely packed tetrahedra which gradually merge into irregularity and continually replace each other. To what extent the pseudonuclei can be regarded as regions of near-solid association is indefinite but Bernal suggested that the concept of pseudonuclei can be compromised with the latter model if the near-solid associations are regarded as extremely dense and not necessarily crystalline. The difficulty in projecting the structure of liquid metals arises because they exhibit duplicity of character as some of their properties are closer to those of crystalline solids and others to fluids. There is an increasing tendency to discuss the structure of liquid metals in terms of the second concept according to which the structure of liquid metals may be conceived as consisting of i) clusters of atoms where the aggregation is a close derivative of that in the crystalline state, ii) individual atoms which behave like true liquids in respect to degrees of freedom and iii) excess number of vacancies. It is noteworthy that the introduction of only 5 pct vacancies is sufficient to transform crystalline matter into the liquid state. At any instant of time thermodynamic equilibrium exists between i, ii, and iii, but the relative proportion of the clusters and random atoms is not known. That this is so can be appreciated by the fact that, when liquid metal is rapidly cooled, liquid state vacancies may condense in the form of dislocation loops and vacancies in excess of their equilibrium number in solid state. These dislocation loops have been observed in thin foils of aluminum prepared from rapid cooled aluminum. As temperature increases above melting point the number and volume fraction of clusters decrease but those of vacancies and random atoms increase. Clusters are transient in nature. In pure metals the cluster is an aggregation of the metal itself. In alloys, however, the nature of the cluster largely depends on the interaction between solvent and solute atoms. If the interaction between unlike atoms is greater than between like atoms: the clusters are then aggregates of unlike atoms. Examples of this kind of system are A1-Cu, Mg-Pb, and so forth, i.e., systems which exhibit negative departures from the Raoult&apos;s law. In systems where the interaction between unlike atoms is smaller than be-

Jan 1, 1968

By R. D. Carnahan, G. A. Stone, R. J. Arsenault

An experimental technique has been developed for carrying out a dynamic tensile stress-strain test in which plastic strain is measured continuously throughout the microstrain region extending through the macroflow region to total deformations of 5 pet. The tests were carried out on niobium, samples having interstitial impurity levels of 160 and -800 ppm at temperatures ranging from room temperature down to 100°K. A band spectrum of activation energies was obtained from calculations based on the measured activation volumes and temperature dependence of flow stress. The inability of a single rate-controlling process to predict such a phenomenon has led to the proposal that several sequential rate-controlling dislocation mechanisms are operative in the preyield micro-strain region. These are thought to be: the motion of geometrical kinks, the formation of double kinks in edges, and finally in the macrostrain region the formation of double kinks in screws. In less pure niobium the effect of interstitial impurities is shown to be dominant in the microstrain region, suggesting that a fourth probable mechanism is overcoming interstitial barriers instead of geometrical kink motion and the formation of double kinks in edge dislocations. THE principal fundamental aim of most mechanical properties studies of crystalline solids is to determine the dislocation mechanisms responsible for the plastic behavior. The extension of such studies to the region of preyield microstrain behavior has received renewed attention in the past few years as the details of macroscopic flow behavior have become better understood. For the most part, microstrain studies have been carried out using one of two variations of a single experimental technique.1 The first method involves loading the sample at a constant extension rate to a predetermined stress level (less than the macroscopic yield stress), instantaneously unloading, and then determining the extent of plastic deformation to a sensitivity of 10"6. The microscopic stress-strain curve is then constructed from the results of a repeated series of such individual measurements, each of which involves loading to an incrementally higher stress level, by relating the accumulated plastic microstrain for each step to the maximum applied stress in that step. The second variation, also carried out by step-wise increases in stress, measures the total strain to a sensitivity of ~10"6 and relates the maximum stress to the area of closed hysteresis loops that are generated under certain conditions (namely, prestrained samples). The foregoing methods have yielded interesting information about the nature of preyield deformation and plastic response to stresses below the yield stress, but they offer certain disadvantages for studying the dynamic behavior of dislocations. In the first method it is physically impossible to specify a plastic strain rate inasmuch as the test sample is reexposed, as it is loaded to its maximum stress in a particular step, to lower stresses at which flow will take place. The strain corresponding to a given stress level on the stress-microstrain curve thus generated will then always be greater than that at the corresponding stress level of a truly dynamic test carried out at the same extension rate. The second method has been used to obtain correlations with dynamic macroscopic flow parameters by applying dislocation damping theory to the hysteresis loop areas.2 The approach has had some success but suffers in that only samples that have been prestrained a few percent can be studied. Although the stresses

Jan 1, 1968

By G. L. F. Powell

Bulk samples of silver have beat undercooled lo a large degree in contact with crystalline siliceous and ceramic oxide materials, indicating lhat stable oxides and oxide compounds are not the heterogeneous nucleants which normally catalyze cryslallization within a feu degrees of the equilibrium freezing point. Since 400-g samples were undercooled 250°C in contact with cristobalite, it is concluded that the undercooling required for homogeneous nucleation of sil11er is greater than 250°C. Undercooling was Jacilitated by precleaning the crucibles with a high-fires -sure blast of gas. IN numerous experiments on the undercooling of metal melts it has been assumed that a solid glassy surface, being non crystal line, will have no effect in catalyzing crystal nucleation from the melt. Conversely, it is usually accepted that any crystalline surface, in contact with a metal melt, will catalyze nucleation of metal crystals from the melt at degrees of undercooling less than that at which homogeneous nucleation will occur. Both these assumptions were implicit in the claim that homogeneous nucleation was observed in experiments1&apos;2 on the undercooling of small metal droplets (10 to 100 mp diam). The droplets were thought to be freed of suspended crystalline particles which would otherwise catalyze heterogeneous nucleation. They were supported on flakes of silica glass which were assumed to be amorphous, and therefore incapable of acting as substrates for heterogeneous nucleation. In later experiments, large samples of molten metal were undercooled to temperatures similar to those achieved by the droplet technique by melting in a fused-silica crucible3 or a boro-silicate glass slag.4 Since these samples were usually fully enclosed in glass at the moment of freezing, it seemed possible that nucleation was homogeneous when maximum degrees of undercooling were achieved, despite the large size of the samples (up to 500 g). In experiments on the undercooling of silver5 the metal was contained in vitreous silica crucibles, the

Jan 1, 1968

By S. Jana, C. M. Wayman

The reverse transformation of bcc martensite to the fcc phase was studied in an Fe-33.95 wl pct Ni alloy by nzeans oj dilatometry, melallography, and electron microscopy. Upon "slozc" heating (-1°C per min) length cJmnge us temperature plots showed u gradual contracLion over the temperature range 200" to 280"C ,followed by a more abrupt contraction beginning a1 -280°C. Howet,ev, zchen the heating rate was increased -4°C per tnin, no gradual contraction was observed and only the abrupt contraction starting at -2BO"C was found. Thus on slower heating- the AS "temperature" for the subject alloy, unlike the MS temperature, is better defined as a range of temperatures. Both optical and transmissiorl electron microscope observations showed that some of the martensite plates exizibited a partial loss of transformation twins during reversal. The midvib region of the martensite plates disappeaved relatively early duirng the reversal. Metallographic observations slowed that the earliest detectable stage of the rezlerse tvansforrvration begins (axd Moues inulardly) at The Martensens i te - parent interface. At higher temperatirres, the. formation of martensitically reversed jcc plates within the bcc martensite plales was observed. It is concluded that the reverse transformation consists of a diffusion less process (martensitic); but this is ps-obably aided by a prior or simultaneous dijjusiorz-comltvolled process, at leasl in the case of slower heat-ing&apos; experiments. ALTHOUGH numerous investigations have dealt with the parent-to-martensite ("forward") transformation (fcc — bcc) in Fe-Ni alloys, comparatively little is reported on the ("reverse7&apos;) martensite-to-parent transformation.&apos;-4 Even though such reverse transformations have been studied in detail in some nonferrous systems, one of the difficulties of studying the reverse transformation in most ferrous mar-tensites is that the martensite decomposes by tempering during heating. However, carbonless Fe-Ni alloys do not exhibit this difficulty since the transformation in these alloys is completely reversible. The present investigation represents an attempt to shed more light on the nature and mechanism of the martensite-to-parent transformation. 1) EXPERIMENTAL PROCEDURE 1.1) Alloy Prepatation. Fe-Ni alloys of compositions near 34 wt pct Ni were prepared from zone-refined iron (99.994 wt pct Fe) and high-purity nickel (99.999 wt pct Ni) by induction melting in recrystallized alumina crucibles in an argon atmosphere, with prior vacuum evacuation to 10"3 mm Hg. The alloys were homogenized by induction stirring in the molten state for 5 min. After solidification, the alloys were further homogenized in evacuated quartz capsules for 96 hr at 1230°C. 1.2) Dilatometry. Slices of the ingot were hot-forged (750°C in air) into approximate rod form and these specimens were then hot-swaged (750°C in air) into long cylindrical rods 0.55 mm diam. From the rods, specimens about 1 in. long were cut. These were then vacuum-annealed for 24 hr at 1200°C, cooled to room temperature, and subsequently transformed to martensite in liquid nitrogen (whereby about 40 pct transformation was obtained). Dilatation measurements were made by observing length changes in a vacuum dilatometer with an externally mounted LVDT sensing element. 1. 3) Preparation of Electron Microscope Specimens. Slices of the ingots were cold-rolled (with intermediate vacuum anneals) to -0.020 in. Out of these rolled sheets, specimens (about 1 by 1 in.) were cut. These were then vacuum-annealed, transformed to martensite by cooling in liquid nitrogen, and subsequently heated from room temperature to various temperatures to effect either partial or complete reverse transformation. These specimens were then chemically polished to 0.002 in. in l:l HsOz (30 pct) and &PO4 (85 pct) solution, and thinned to electron transparency in an electrolyte consisting of 150 g CraOs, 750 ml glacial acetic acid, and 30 ml ~~0.~ Observations were made with a 100-kv Hitachi HU-11 electron microscope equipped with an HK-2A tilting device. 1.4) Optical Microscopy. Metallographic observations were made with a Leitz MM5 metallograph on the same 0.020-in. sheet specimens as were used for electron microscopy and on bulk specimens which were 0.2 in. or more on a side. The chemical thinning solution when cooled below 20°C also served as an etchant for this alloy. Observations of surface relief were made with a Zeiss interference microscope employing a Thallium light source of wavelength 0.54 p. Specimens for interference studies were prepared by two-stage polishing on Buehler vibromet polishers using 0.3 and 0.05 p alumina abrasives. 2) EXPERIMENTAL RESULTS 2.1) Comparison of the MS,AS, and Af Tempera-tures wTth Previous Re sults. The AS aLd Af tempera -tures of several Fe-Ni alloys were determined dila-tometrically. The MS temperatures of the same alloys were determined by continuously lowering the temperature using a mixture of isopentane and liquid nitrogen and observing the highest temperature at which a prepolished specimen showed surface upheavals. For the present the As temperature is defined as the temperature at which an abrupt decrease in length occurs in the dilatation plot. The Ms,As7 and A determinations in the present investigation and those of Kaufman

Jan 1, 1968

By J. B. Wagner, B. Swaroop

The atomic ratios of oxygen to iron in zlarious corn-posilions of wustite in the vicinity oj the reported p to n transformation were determined in the temperalure range between 950" and 1250°C. For these conditions, equilibrium vacancy concenrations have also been determined at vatious mixtures of C0,-CO. The data show a continuos introduction of iron vacancies as oxygen is introduced into wuistite. No phase change is observed with in the wuustite field. However, the value of n in the isothermal oxygen pressure dependence, the weight change shifts to 1ower values as the concentration of oxygen increases. WUSTITE is a metal deficit semiconductor with the majority lattice disorder being cation vacancies. Using the notation similar to that of Kroger and ink,&apos; the dissolution of oxygen into wiistite using C02-CO mixtures is represented by, WHere v+! denotes a cation vacancy with k effective negative charges and kh • denotes k electron holes, h -. Applying the law of mass action and assuming a dilute solution of defects in the wiistite yields Where the square brackets denote concentrations. Furthermore, when k = 2 the cation vacancies are completely ionized, and both the concentration of cation vacancies and the concentration of electron holes are proportional to the third root of the ratio, PC /PCo. This analysis is valid for one particular mael based on an ideal solution at elevated temperatures (in this case t > 1000°C). At lower temperatures, it has been shown2 that the pressure dependence of the electronic conductivity changes in a manner which suggests that vacancies interact with or "trap" electron holes. At the very high concentrations of defects, 10&apos;&apos; to 10" per cu cm, these simple models no longer hold. Recently Tannhauser,3 Geiger et a1.&apos; Bransky and Tannhauser; and Hillegas&apos; have found an apparent p to n transformation in wiistite in the temperature range of 950" to 1300°C. This junction was found by thermoelectric and electronic conductivity measurements. Geiger eta1.&apos; found that the electronic conductivity became almost independent of the oxygen pressure at high temperatures and oxygen concentrations within the experimental error. In addition, Vallet, Raccah, and coworkers6&apos;7 have reported the existence of several "varieties" of wiistite which were reported to exist within what was heretofor presumed to be a

Jan 1, 1968