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By S. F. Reiter, You-Chao Liu, W. R. Hibbard

Cyril Stanley Smith in his classic 1948 Institute of Metals Lecture&apos; noted in the case of annealing twins that: "It is well known that approximately the same number of twins per grain and the same general geometry are maintained in large grains as in small ones, a fact that certainly suggests a mechanism such as the above where boundaries and twins grow proportionately together. If this view is correct, a spherical grain should have no mechanism for keeping its twins." Such a constancy of twins per grain would be of particular interest as a tool for the study of the origin of annealing twins. It has been proposed by Mathewson2 and later by Barrett3 that in face-centered cubic metals slip occurs in the {111} Plane by <112> shears which combine in pairs to produce the macroscopically observed <110> movement. This proposal is schematically inviting since <112> slip permits the atoms of one plane to move along the interatomic valleys of its neighbor rather than up the hills across the atom sites. There is strong experimental evidence? that annealing twins result from the growth of nuclei in the form of "twin faults" produced by single <112> shears. It is possible that more twin faults would form at low deformation temperatures than at high ones, because the more rigid lattice may increase the tendency to "freeze" the twin faults and prevent their dissipation in slip. This is suggested by (1) the greater resistance to slip at low temperatures and (2) greater tendency toward mechanical type twinning at low temperatures (a summary of these factors is presented by Seigle and Brick5). These considerations would suggest the following: a. Constant twin/grain ratio for specimens deformed constant amounts at a constant temperature, but annealed at various temperatures above the recrystalliza-tion temperature. b. Larger twin/grain ratios for re-crystallized specimens previously deformed constant amounts at lower temperatures. The purpose of this investigation is to test these considerations. One half in. rods of phosphorous deoxidized electrolytic copper and 70-30 alpha brass (68.36 pct Cu, 0.005 pct Pb, 0.01 pct Fe, 31.62 pct Zn remainder) were rolled to a thickness of 0.350 in., milled to specimens 0.350 X 0.437 X 2 in., and annealed at 700°C to an average grain size of 0.065 and 0.090 mm, respectively. These specimens of each metal were then rolled 50 pct reduction in thickness and annealed one hour under conditions which were all combinations of the following: Rolling Annealing Temperatures. Temperatures. °C °C -70 400 25 500 200 600 Standard metallographic techniques&apos; were used to prepare specimens. By the method of lineal analysis7 using a minimum of ten samples of fifty grains each for each specimen, the ratios of twins* per total grains, twins per twinned grain, twin families* per total grains and twins per twin family were determined. Recrystallized grain size was determined by A.S.T.M. comparison methods.8 All observations were made on the rolling plane. The results are tabulated in Table 1.

Jan 1, 1950

By K. S. Krishnam, A. G. Guy

VOLUME 6 of the Transactions of the Baikov Institute of Metallurgy, Moscow, is devoted to the subject of "the experimental and theoretical study of the physical characteristics of dilute solid solutions,11 and summarizes work that has been done largely in the years 1958-9. In view of the attention that Soviet investigators have given to this subject, it seemed useful to carry out an independent experimental investigation in an effort to judge the scientific basis and practical significance of this field of study. The present note is a preliminary report of this investigation. The first property studied by the Soviet group was X-ray spectra of solid-solution alloys.&apos; An anomaly observed at low concentrations (--0.05 at. pct) of the alloying element led to the theory that each impurity atom in a transition-metal base alloy is the center of a "block" of affected atoms with a radius of about 10"7 cm. This theory was further developed in a later paper.2 By this time similar anomalies had been found in diffusion coefficients3 and in thermal expansion.4 The entire development up to 1959 was reviewed in a comprehensive paper, and further theoretical ideas were also published at this time. Finally, the volume mentioned above was published in 19607 giving new experimental data on anomalies in optical properties and Hall constant, and a new theoretical treatment also appeared.&apos; Although western scientists have done both theoretical work, summarized recently by Friedel,9 and considerable experimental work on dilute solid solutions, there is little support for the marked anomalies reported in the Soviet papers. Of the physical properties studied by the Soviet investigators, thermal expansion was chosen for the present investigation because of the relative ease of obtaining the necessary precision of measurement. A Leitz dilatometer was used for this purpose, and a special technique involving interchanging of the two specimens being compared permitted a precision of 0.05 x X in average thermal expansion over the range 27° to 600°C. The specimens were heated and cooled in vacuum or in a protective atmosphere at a rate of 50 °C per hr. Ferrovac E iron was used as the comparison specimen and in every case had a coefficient of expansion higher than (or equal to) that of the alloy. Since unintentional impurities are an important factor in studies of dilute alloys, special attention was given to the purity of the iron and the alloys used. The alloys were the same of those used by Abrahamson10 and by Michalak," and their preparation is described in these references. Chemical analyses of the Ferrovac E iron and of typical Fe-W and Fe-Mo alloys are given in Table I. The purity of the iron and alloys is undoubtedly higher than in the

Jan 1, 1962

By M. F. Smith

BELOW the nose of the bainitic C curves in isothermal transformation diagrams, the rate of the austenite-to-bainite transformation usually decreases with decreasing temperature. However, in some steels and iron-carbon alloys, there is a noticeable acceleration in the initial reaction rate at temperatures just above Ms. Such speeding-up of the bainitic transformation would be understandable at temperatures just below Ms because of the catalytic effect of the martensite formed,&apos; but the reversal in isothermal kinetics just above Ms seems quite anomalous. This behavior was observed by Howard and Cohen&apos; in a 1.35 pct C steel and, on the basis of metallo-graphic examination, it was attributed to the formation of a thin plate-like product not belonging in the bainitic sequence. More recently, schaaber2 found two-stage reactions occurring in the vicinity of Ms in a number of steels, and suggested that the first stage might be the isothermal formation of marten-site, preceding the isothermal formation of bainite in the second stage. A decrease in the bainitic incu-

Jan 1, 1960

By D. L. Albright, R. W. Kraft, J. A. Ford

HE unidirectional solidification of A1-CuAl, eutec-tic specimens to produce an essentially parallel lamellar structure has been described previously.&apos; Ingots solidified in this manner ordinarily exhibit three macroscopic zones. In Zone I, at the head end of the ingot, a large number of slightly elongated grains occur in which the lamellae are highly distorted and twisted. After a few centimeters of growth, this distribution gradually changes to a small number of coarse grains elongated in the growth direction and in which the lamellae are quite regular, Zone 11. Zone 111, at the tail end of the ingot,

Jan 1, 1963

By G. M. Ault, G. C. Deutsch

The paper reviews the efforts made to utilize powder metallurgy to solve problems encountered when using alloys at high temperatures. The following subjects are discussed: comparison of wrought and sintered super alloys, sintered aluminum powder, porous materials for transpiration cooling, molybdenum, and cermets. TODAY, powder-metallurgy techniques are be-JL coming increasingly important, producing materials which at the present time cannot be made by any other method. Among these materials are high melting-point metals such as tantalum and tungsten, porous metals for filters and lubricant-containing bearings, electrical contacts and electrodes (i.e., tungsten-copper), cutting tools of the cemented carbides, and magnet alloys. In addition, the powder-metallurgy industry has grown because, through the application of its methods, shaped parts, such as gears, can be produced at tremendous rates with a low scrap loss in comparison with manufacture by casting or forging and machining. In the past few years, by utilizing powder metallurgy, several approaches to the problem of high temperature materials have been investigated. In this paper the authors will review some of the studies on application of materials having properties above 1350°F. Since their experience lies in the aeronautical field, possible uses of powder-metallurgy techniques in the production of aircraft en- gines will be emphasized. A large portion of the work is classified, but such a restriction has not eliminated any field from discussion, although limiting the amount of detail it is possible to present. The development of high temperature alloys from powders and porous metals for cooling will be discussed as well as research done on molybdenum and molybdenum alloys, cermets, and intermetallics. Some studies on the utilization of cermets will be considered along with special problems that have been revealed through these investigations. Special interest in certain factors of sintered aluminum powder (SAP) makes it desirable to discuss this material although its use temperature is below the 1350°F limitation set for this paper. High Temperature Alloys from Powders In general, components made from powders for room-temperature application have been investigated with the primary purpose of taking advantage of the high production rates and economies made possible by powder metallurgy. From the standpoint of properties, the ojective of the powder metallurgist has been to obtain a product comparable to the cast or wrought product that is to be replaced. Comparisons of the properties of alloys made by powder-metallurgy methods with those of similar compositions made by casting and forging are reported in the literature.12 In many cases equivalent

Jan 1, 1955

By A. G. Guy

IN the course of a research on steady-state diffusion it became necessary to make diffusion calculations for a finite solid. This problem was found to be sufficiently different from the corresponding problem for the semi-infinite solid for an entirely new approach to be necessary in obtaining a useful solution. The assumption of an exponential variation of the diffusion coefficient with concentration&apos; was no longer a practical necessity, so that the new solution offered the possibility of handling diffusion in semi-infinite solids for arbitrary variations of the diffusion coefficient with concentration. In discussing the principle on which this method of calculation is based, it is convenient to consider the relatively simple problem of one dimensional diffusion into a matrix that initially contains none of the diffusing substance. The solution of the set- ond Fick Law,?C/?t=D0?2C/?x2, for diffusion into a semi-infinite solid is3 C/C=1-F(x/2vD0t [1] where C is the concentration of the diffusing substance at a depth x cm below the surface after dif- A. G. GUY, Member AIME, and M. GOLOMB are Professor of Metollurgicol Engineering and Professor of Mathematics, respectively, Purdue University, Lafayette, Ind., A. S. YUE, formerly with Purdue University, is now with the Research Laboratory, Dow Chemical Co., Midland, Mich. TP 4505E. Manuscript, July 18,1956. fusion has occurred for t seconds; C, is the concentration of the diffusing substance at the surface of the matrix; Do is the diffusion constant, expressed in sq cm per sec; and + represents the Gauss error function. The corresponding solution for diffusion into a finite solid of thickness, 1, is conveniently written for the change in concentration, C+, at a point midway through the matrix and for times, t, great enough for the following equation to be used4 c1/2/C1=(1/2-2/?e-?2D0t/l2) [2] In Eqs. 1 and 2 the diffusion coefficient is represented by the symbol Do (rather than by D) to emphasize that these equations are valid only for constant values of D. To understand how these equations can be modified to take account of actual variations of D, such as that shown in Fig. 1, first consider the fact that for a given time of diffusion theconcentration at a given point is determined, not by the D value alone, but by the ratio x/vD0 in Eq. 1 and by a similar ratio, l2/D0 in Eq. 2. Even though in fact D varies, it is possible to keep this ratio constant by using a special coordinate system, x,, that varies with D in the appropriate manner. The necessary character of this special coordinate system can be easily visualized by imagining that

Jan 1, 1958

By A. E. Bibb, J. R. Fascia

Single-crystal wafers of zirconium have been exposed to 680°F neutral water. The single crystals were of known orientation and weight-gain data as a function of crystal orientation were obtained. These data show that all the crystal faces studied obeyed a cubic rate law out to the time of transition whereupon the crystals corroded at an approximately linear rate. The time to transition varied from 114 days for (1074) crystals to about 325 days for the (2130) faces. The epitaxial relationship be-tween metal and monoclinic oxide was found to be (0001) H (111) and [1120] 11 [101]. A black tight adherent oxide layer was formed on the crystals in the pretransition range. This black oxide was found to be monocrystalline. The white corrosion product produced after transition was found to be polycrys-talline but highly oriented. X-ray line-broadening studies found that the black oxide was a highly strained structure whereas the white oxide was relatively strain-free. These results indicate a strain-induced re crystallization or fragmentation accompanies the change from protective black oxide to nonprotective white oxide. ZIRCONIUM alloys have been used quite extensively in high-temperature aqueous environments. Alloy additions can be made to commercial sponge zirconium which enhance the corrosion resistance of the zirconium in both water and steam media, which raise the tolerance limit for certain impurities detrimental to corrosion resistance, and which reduce the amount of free hydrogen pickup during corrosion. The development of the corrosion-resistant zirconium alloys has been a long and tedious job involving trial and error methods. This technique has been necessary because of a lack of fundamental data and hence understanding of the corrosion mechanisms. The objective of the work described herein was to provide some fundamental data with respect to the aqueous corrosion of zirconium crystals as a function of the orientation of the exposed surfaces. Hg. The zirconium chunk was then cooled to below the transformation temperature (862°C) and reheated to 1200°C for 8 hr. The ultimate size of the zirconium grains increased with the number of cycles. Rapid or even furnace cooling through the transformation temperature produces a considerable amount of substructure which was intolerable in corrosion experiments as it would be in the study of any crystallographically dependent property. It was found that a high-temperature a-phase anneal for approximately 4 days reduced the substructure below the limits detectable by visual or X-ray means. Crystals so produced were carefully cut from the massive zirconium chunk and oriented by standard back-reflection Laue techniques. The crystals were then mounted in a goniometer head and, by using the three degrees of freedom available, slices on the order of 0.015 to 0.020 in. were cut parallel to any desired crystal plane. These slices were then carefully polished on both sides to produce smooth flat faces, pickled to remove about 0.002 in. per face, annealed for 1/2 hr at &apos;750°C in a vacuum of approximately 10"5 mm Hg, flash pickled, and checked for orientation. The pickling solution was 45-45-10 vol pct HN0,-H20-HF and continuous agitation was provided to eliminate pitting of the slices. Any slice that was not within 2 deg of the desired orientation was discarded, and any evidence of substructure as indicated by the Laue spots was also grounds for discarding the sample. Thin slices were used for the corrosion tests because weight gain per area data could be obtained with only a minimum area exposed to the corrosive media that was not of the desired orientation. The thin single-crystal slices were of irregular shape and as a result the areas were determined by placing a crystal inside an inscribed square of known area, enlarging a picture of this assembly about X5, and tracing both the enlarged square and crystal with a planimeter. The zirconium used to produce these single crystals was crystal-bar grade, a typical analysis of which is given in Table I. An oxygen analysis on prepared crystals gave a concentration of 205 ppm. The hydrogen concentrations are believed to be less than 15 ppm due to the dynamic vacuum anneal given each crystal. Typical nitrogen values for zirconium treated in this manner are about 10 to 20 ppm. RESULTS AND DISCUSSION Single-crystal wafers have been exposed to de-oxygenated, deionized water in static autoclaves.

Jan 1, 1964

By F. W. Aul, R. C. Glenn

EXTRACTION techniques are of particular importance in determining size, shape an: crystal structure of particles smaller than l000Å in steels and other alloys. However, artifacts that can arise during the preparation of extraction replicas may lead to erroneous conclusions. The purpose of this note is to illustrate some of these artifacts and the misinformation that can result from their presence. An alloy of iron with 0.8 pct Cu was investigated in the following conditions: 1) Solution treated 3 days at 925°C in dry hydrogen and quenched in water. Aged in steps to precipitate copper, as follows: heated to 700°C, held 1 day; then furnace cooled to 50O°C, held 3 days; then furnace cooled to room temperature. 2) Solution treated 3 days at 925OC in dry hydrogen and furnace cooled to room temperature. 3) Solution treated 3 days at 925OC or 17 hr at 1100°C in dry hydrogen to dissolve all copper, then quenched in water. A normal parlodion dry-extraction technique was employed after etching the specimens with super picralP or with 2 pct nital. A wet-extraction method

Jan 1, 1962

By J. G. Faller, L. P. Skolnick

The distribution of cobalt and vanadium over non-equivalent crystallographic sites in C14-type Zr(VCo), alloys has been investigated. An anomalous X-ray scattering technique developed by Skolnick, Kondo. and lavine7 by which the separation in the scattering factors of two similar atoms can be enhanced was employed. Six alloys spanning the pseudobinary section ZrV1.6Co0.4-ZrVO.6CO1.4 at 10pct steps showed a nonrandom compositionally dependent distribution. Specifically, at high vanadium content cobalt preferentially occupied sites of type (6h) and vanadium, sites of type (2a; at low vanadium content the reverse was observed. In addition to the distribution fraction the structural parameters x and z were obtained. There was no significant deviation of these parameters from those obtained in the ideal C14 structure. Certain suggestions are made to account for the observed nonrandomness in the distribution of atoms on the two types of sites. INTERMETALLIC compounds of formula AB2 iso-morphous with MgCu2, MgZn2, and MgNi2 are known as Laves phases. Because Laves phases exhibit high symmetry and coordination numbers, the highest possible for an AB2-type compound,1 they are among the most frequently observed compounds in nature. In recent years interest has centered about the purely transition metal Laves phases2-&apos; in efforts to understand the function of atomic size and electronic structure in the formation of these compounds. It has been observed that pseudobinary Laves phase systems often show a variation of structure across the phase diagram. Such a system is the ZrV2-ZrCo2 in which the structure varies from cubic MgCu2 to hexagonal MgZn2 to cubic MgCu2.4 Some understanding about the conditions under which the second modification is stable can perhaps be gained by studying the distribution of cobalt and vanadium atoms on lattice sites in the MgZn2 modification of the system ZrV2-ZrCo2. In both the MgZn2 and MgNi2-types there exist nonequivalent positions open to occupancy by the B element, whereas in the MgCu2 prototype all sites are equivalent. Skolnick, Kondo, and La-vine7 have developed an anomalous scattering technique suitable for this type of investigation. Whereas the influence of size on the formation of a Laves phase is well recognized, no substantial evidence has been put forth in support of the size ratio dependence of a particular prototype. Berry and Raynor8 suggested that RA /RB ratio does indeed affect the type of structure that is chosen, MgZn2 compounds tending to cluster about 1.225 while MgCu2 compounds were found at larger deviations from this ratio. Dwight,3 however, from a study of 164 Laves phases does not believe this generalization to be justified. Electronic effects are certain to play a part in the stability of Laves phases in general and in the choice of a structure type in particular. For example, size along would favor the formation of Laves compounds of Ti, Zr, Hf, Ta, or Nb as the A element with nickel or copper as the B element. The absence of such is attributed to an unfavorable electron : atom ratio by Elliott and rostoker.4 Early experiments of Laves and witte9 with pseudobinary and pseudoternary systems of the three prototypes established the dependence of crystal structure upon electron: atom ratios. They observed that the MgCu2 structure dissolved elements of higher valency until the electron: atom ratio of =1.8 was reached; the MgZn2 likewise dissolved elements of lower valency replacing zinc. witte,6 from calculations of the electron : atom volumes of Brillouin Zones, obtained limits of stability for the prototypes MgCu2 and MgZn2. Elliott and Rostoker4 used these limits with considerable success in the all-transition element Laves phases they investigated. According to witte,6 compounds between the electron :atom ratios of 1.80 and 2.32 were of the MgZn2 type; those above and below exhibited the MgCu2-type structure. On the basis of these limits and an assumed valency of zirconium based upon the near tetra-valence of titanium, Elliott and Rostoker obtained valencies for the first transition series elements. For the Laves phases with which this investigation is concerned, ZrV2 and ZrCo2, the authors calculated electron :atom ratios of 2.54 and 1.56, respectively. These ratios are for the MgCu2-type structure and straddle the stability band of the MgZn2 modification. One could, therefore, predict that a pseudobinary system ZrV2-ZrCo2 should pass through the MgZn2 modification in traversing the composition diagram from one end to the other. Implicit in this assumption is a smooth change of the electron: atom ratio from 2&apos;54 to 1.56. MOSS10 states that his finding the low temperature structure of ZrCr2 to be C15 instead of C14 alters greatly Elliott&apos;s valency of zirconium and hence the assumed valencies of the other metals. Such a quantitative correlation of structure with electron : atom

Jan 1, 1963

By M. J. Marcinkowski, R. M. Fisher

The flow stress-grain size relationship has been determined at room temperature in both a disordered and a fully ordered FeCo for plastic strains up to 30 pct. The results are in agreement with a Hall-Petch relation of the type given by Of =a,+kd-1/2 where of is the flour stress and a, increases mono-tonically with increasing strain to a maximum value which is much higher for the ordered than for the disordered alloy. The slope, k, is found to increase FOLLOWING the original work of Halll and petch relating the effect of grain size to the lower yield stress of iron and steel, it has been generally found that the yield stress oy.s. of polycrystalline metals with strain to a maximum and then decrease for both ordered and disordered alloys. However, k for the ordered alloy is in general higher than that for the disordered alloy and the critical strain for k max somewhat larger. All of these observations can be satisfactorily accounted for quantitatively and in some cases semiquantitatively by using a slip band-grain boundary intersection model, and by taking note of the fact that, in general, moss slip, while quite common in the disordered alloy, is extremely difficult in the ordered alloy. obeys a relation of the form oy.s.=a0+kd-1/2 [1] where a, and k are constants and d is the mean grain diameter. For convenience, and in accord with prevailing custom, Eq. [I] will be referred to simply as the Petch relation. Tjerkstra3 and Armstrong, Codd, Douthwaite, and petch4 showed that the flow stress af of iron or steel measured at strains of up to at least 20 pct also obeyed a relationship of the type given by Eq. (11. The latter investigators have also shown that Eq. [I] applies to fcc and hcp metals and alloys.

Jan 1, 1965

By R. G. Treuting, W. C. Ellis

The twinned state is characterized by a lattice of coincidence sites. Imperfections are required at stable lateral twin interfaces. Twinned regions can occur with relative ease in the diamond cubic IN recent contributions1,2 on the origin and growth of cubic annealing twins, attention has been directed to the orientation relations between such twinned components and their parent matrix. There are some aspects of twinning which may be illuminated by a more detailed consideration of the twinned state" alone. As an extreme example, the dense twinning in cast ingots of germanium,&apos; as contrasted with the rarity of twins in cast face-centered cubic metals, is yet to be accounted for. It has been this that has led us to the present work, which, it will be noted, uses methods and constructions in many respects similar to those of Kronberg and Wilson.&apos; In the cubic systems, a 70" 32&apos; rotation about a <110> axis is angularly equivalent, as to twinning, to the more usually considered 180" rotation about a <111> axis. Figs. 1 and 2 show a (110) projection of a twinned face-centered cubic lattice and a twinned diamond cubic lattice. In both figures, the two adjacent planes A and B, shown by the larger and smaller circles, are sufficient to represent the entire array. In each case a section of lattice, the original atom sites of which are shown by open circles, has been rotated as indicated through 70" 32&apos; to bring an original. [112] direction into coincidence with the [112] diiection. The latter is the intercept on the (110) projection of the (ill) plane normal thereto, the twinning plane. In the face-centered cubic case the rotation can be performed about an axis passing through an atom-site; the mirror plane then is also a composition plane containing atoms common to both twinned and untwinned lattices. The diamond cubic lattice may be construed as two interpenetrated face-centered lattices. Its (111) planes recur in a sequence of alternately short and long interspacings. Consequently a mirror plane for twinning cannot be a composition plane, but must be the bisector of one of the spacings. When the longer spacing is selected, the closest distance of approach across the mirror plane in the [ill] direc- tion is identical with that in the untwinned structure. In each case periodically recurring (ill) planes (parallel with the twinning plane) are found, on which there is coincidence of atom sites of the pre-twinned and twinned orientations; these are indicated by the cross-hatched circles. In the face-centered lattice there is such coincidence every third (ill) plane; in the diamond cubic lattice, on two adjacent planes in every six. At the twinning interface in the latter, there is on each side of the mirror plane a (ill) plane of atoms common to both twin components. Conceivably, there is little influence on a plane of atoms about to be adhered to such a pair of coincidence planes, whether it be laid down in a normal or in a twinned position with respect to the previously formed structure. Slawson% as attributed the high incidence of twinning in diamond to this boundary state. Further examination shows that the motion of intermediate planes can consist of various pairs of equal and opposite translations, for example of (ill) planes in the [l&apos;;i2) direction, the familiar twinning shear, indicated in the small schematics in the figures. Since the translations form a system of shears of alternating sign between coincidence planes, twinning could take place by such a mechanism over an extended region without extensive shear; in fact, in this case any atom moves but the distance in the [1i2] direction. One alternative construction for the face-centered cubic lattice leading to the same end result is illustrated in Fig. 3. The plane (711) with respect to the pretwinning orientation (the twinning plane of Fig. 1) is given, the twinned region arbitrarily bounded by <110> and <112> directions. The coupled shear is identical to that of Fig. 1. The "rotational" movement about coincidence sites generating the same twinned position could consist as shown of the translation a,/d% for each atom of a group of three in the B layer in a different one of the three <112> directions, and a similar translation of the underlying three atoms in the C layer in either the same or the opposite sense. This is not dissimilar to Kronberg and Wilson&apos;s construction for their 22" rotation of three adjacent (111) planes.

Jan 1, 1952

By R. G. Treuting, W. C. Ellis

D. Whitwham, M. Mouflard, and P. Lacombe (British Council Research Fellow, Labratoire du Professor Chaudron, Vitry-sur-Seine; Inqenieur de Recherches, Labratoire de Vitry; and Maitre de Recherches, Labratoire de Vitry, Professeur Adjoint de Metallurgie, Ecole des Mines, Paris)—The authors&apos; work is of great interest in bringing out the geometrical relations existing between twinned lattices, and for the notion of a coincidence super lattice developed from this. We should like to point out that a similar idea was put forward by Friedel8 in his book on the subject of lattice merohedrism "merihedrie réticulaire:"—When two crystals A and B are twinned with respect to a mirror plane, there exists a common superlattice, "réseau periode," which is independent of the contact surface between the two crystals. The volume V of this superlattice is a simple multiple of the volume v of the lattice of crystals A, or B, (Fig. 5). This "multiple cell" is defined by the twin plane (p q r) and a row of atoms [h k l] normal to this plane, the base being taken as the smallest unit (two-dimensional) of this plane. Two cases must be considered. First when the multiple cell, as defined, has no atom site at its center nor at the center of its faces other than (p q r), v the twinning index is defined by —. In the second v case, when one of the two above conditions does not v apply, then the twinning index is V 2v A more intuitive definition of the twinning index would be the proportion of atoms of C, which would coincide with those of C1 when the C, lattice is imagined to extend on the other side of the contact surface. In the case of cubic crystals, the twinning index

Jan 1, 1952

By P. S. Rudman

Laves phases, AB2, are considered as Izerrzisub-stitutional solutions m1hich are defined by a one-for-truo replacement scheme. Atomic-size tnisfit is considered in terms of deviations of the ratio 2V°b/V°A from unity, where v° = atomic volume. A simple elastic model has been used to calculated deviations from "Vegard&apos;s law of atomic vol-umes". Comparison has been made between calculated and observed atomic-volume deviations fov 222 Laves phases. Agreement is generally very good although there ave some few exceptions which appear to be excusable in terms of electronic changes that ore beyond the scope of the present model. We can consider the formation of a binary sub-stitutional solution A-B from an A solvent as one-for-one replacements of A atoms by B atoms. As the atomic-size ratio deviates from unity, the solution becomes thermodynamically less stable and hence more restricted because of atomic-misfit strain energy. In accordance with our previously presented conclusion1 that the atomic volume, v, is in general the most appropriate measure of atomic size, the ideal size ratio for a binary sub-stitutional solution is vg/vA = 1. The Laves phases have been described by Berry and Raynor2 in terms of various stacking sequences of hexagonal layers of B atoms for the three structures MgZn2(C14), MgCu2(C15), and MgNi2(C36). To form the Laves phase of ideal composition AB, we start with complete hexagonal layers of B atoms in the appropriate stacking sequence and we remove, according to an appropriate scheme for each structure, two out of every four B atoms and replace the two removed atoms by one A atom. We thus might expect to find that the ideal size ratio for the Laves phases is 2v/B/ VA= 1. From this point of view, then, we call Laves phases hemi-substitutional solutions since we employ one-for-two replacements. By analogy with substitutional solutions we can expect for Laves phases that as the ratio 2VB/Va deviates from unity the phase occurrence will be more restricted. Laves3 has plotted the distribution of Laves phases as a function of the radius ratio, ?A/rB, and found that, while the distribution extended from 1.05 < rA/B < 1.50, the

Jan 1, 1965

By E. F. Bailey, W. J. Harris

THE temperature of the ferrite to austenite re-action is established frequently by continuous heating experiments. However, equilibrium studies of this reaction have demonstrated that austenite may form at temperatures considerably below those at which the reaction is first observed during continuous heating. Because of this discrepancy, tempering is sometimes performed above the true critical temperature and in these cases austenite forms during tempering. The lowest temperature at which austenite forms and the kinetics of the reaction have been studied by Bain,&apos; Bleakney and Gros-venor,2 and Dube and Cunningham. This austenite can affect the properties either as austenite per se, if it is retained at room temperature, or as a decomposition product if it transforms. The effect of austenite formation during tempering on low temperature impact properties of an 8 1/2 pct nickel steel was reported by Brophy and Miller4 in work published after the present investigation was initiated. They concluded that the improvement in low-temperature notch toughness which followed tempering at certain temperatures could be attributed to the austenite formed during tempering. Kramer et al.5 found anomalous hardness increases and embrittlement after tempering of a low-carbon manganese-nickel steel. They concluded that austenite formed during tempering, and that the decomposition products were responsible for the increase in hardness and the embrittlement. Quan-titative correlations of the microconstituents and mechanical properties were not made by these investigators. The present study was undertaken in order to establish the kinetics of formation of austenite at various temperatures, the characteristics of the decomposition of this austenite, and the relationship between mechanical properties and the phases present. Experimental Procedure A low-carbon manganese-nickel steel was selected because of the sluggishness of its austenite decom-position reactions. The composition of this steel in percent was: C, 0.10; Mn, 3.52; Ni, 2.34; Mo, 0.52; Cr, 0.17; Si, 0.19; V, 0.15; P, 0.019; and S, 0.020. Samples were prepared by forging sections from a large ingot to 3/4 in. bars. Formation and decomposition of austenite were investigated by dilatometric techniques which were checked by X-ray measurements. Dilatometer specimens were hollow cylinders 1 in. long, 1/2 in. diam, with a 1/8 in. central hole. All specimens were aus-tenitized for 1 hr at 1650°F and quenched in water prior to insertion in the dilatometer. Oxidation was prevented by using an inert atmosphere of purified nitrogen. Dilation was measured with a dial gauge which could be read by interpolation to 0.00005 in. Temperature was maintained within ± 3°F by a Brown Electronik Controller. Chromel-alumel thermocouple leads were welded to opposite ends of the specimen with the specimen serving as the hot junction. As a check on temperature uniformity comparison was made of the specimen temperature as measured with the chromel-alumel leads and the temperature of the center of the specimen as measured with a calibrated platinum—platinum-rhodium thermocouple embedded in asbestos in the central hole of the specimen. During heating a 5°F temperature difference was noted below 1000°F, but none above, while in cooling, a 5°F difference was observed from 1300" to 735°F, but none below. Heating rates of 35°F per min and cooling rates of 60°F per min were employed for all dilatometric studies. For transformation studies below room temperature, the dilatometer was allowed to cool to 150°F and then was quenched into liquid nitrogen.

Jan 1, 1951

By O. P. Arora, M. Metzger

Single-phase aluminum containing 1 to 600ppm copper was studied in 7 to 26 pct HCl. The corrosion rate in the autocatalytic stage was resolved into a constant intrinsic component and an acdelerating autocatalytic component, and attention was focused on the part of this stage where the corrosion rate could be described by a simple empirical relation. Autocatalytic corrosion in this period was localized and its rate increased rapidly with copper content and with the strength and chlaride content of the acid. The effects of adding cupric ion to 16 pct HCI were functionally and quantitatively inconsistent with the autocatalytic rates observed. A theory of these rates was given based on the deposition in nzetallic contact with the aluminum of part of the copper introduced by corrosion. It has long been known in a general way that aluminum containing sufficient copper suffers in hydrochloric acid an autocatalytic acceleration of corrosion resulting from the introduction into the acid of copper ions and their reduction on the specimen as elemental copper, which provides cathodes of low hydrogen overvoltage.&apos;-3 In a previous paper, this phenomenon was identified in single-phase high-purity material at copper levels as low as 20 ppm and an empirical equation describing autocatalytic corrosion rates in 16 and 20 pct HC1 was presented. In the present work the range of acid strength and chemistry studied was extended, a more accurate empirical equation for the autocatalytic rate was determined, and a theory of this rate was formulated. A major source of interest in this system is the intergranular corrosion, which is also strongly influenced by copper content,= and an objective of the present work on general corrosion was to provide a basis for studying the role of copper content in intergranular corrosion, which is experimentally much less accessible.

Jan 1, 1963

By R. J. Wasilewski

THERMAL expansion of rhenium data have been reported by Agte et al.,&apos; and Medoff and cadoff,&apos; respectively, while the linear expansion coefficient was determined by Sims et Al.3 Denoting expansion coefficients parallel and at right angle to c axis by all and Al respectively, their weighted mean should be equal to dilatometric linear coefficient of a random polycrystalline specimen. The values reported for these coefficients are tabulated below: Since these values are in poor agreement, and because of anomalous expansion behavior observed in titanium 4 and chromium, a rede termination of the axial expansion was carried out. A Unicam 19-cm-diam high-temperature camera was used, with unfiltered CuK radiation. Camera calibration was carried out using at Pt wire standarde at temperatures up to 1100oC, the variation between indicated and true temperature being within the experimental error (estimated at <3oC) above 750o C. Rhenium Johnson Matthey spectrographic standard) was vacuum annealed at 1000 oC prior to X-ray diffraction experiments. Lattice parameters were obtained by least-squares solution using the reflec- tions (1232), (1015), (2024), and (3030) for all the patterns, and the additional reflection (2133) for higher temperature (400°C and above) patterns. The relative expansion data obtained are shown in Fig. 1, lengths of the vertical bars indicating the spread in the parameter values obtained by using various combinations of three spacings from the four or five measured. The data calculated from the equation of Ref. 2 are included for comparison purposes. Several specimens were used to obtain the above data, neither of them showing a significant parameter change after completion of the high temperature runs. Some parameter data and the corresponding expansion coefficients between 25 oC and the measurement temperature are tabulated below. The comparison of the present data with those previously reported shows reasonable agreement with the results of Medoff and cadoff2 within the temperature range covered by them (up to 1000 oC). The a values are appreciably higher throughout most of the investigated temperature range. The basal expansion is—in agreement with their findings—appreciably higher than that in the direction of hexagonal axis. The expansion coefficient, al, however, decreases rather more slowly with temperature than previously reported. The expansion along the c axis up to nearly 1000°C appears in excellent agreement. However, at higher temperatures there is a marked deviation towards higher expansion, reproducible between different specimens. Furthermore, there seems to be some irregularity in the variation of all with temperature, the apparent local minimum and maximum values at 510o and 1024o C, Table II, being well outside the experimental error limits. It must be stressed that the apparent discontinuity in the c parameter expansion is still insufficient to account for the expansion value reported by Agte et al.&apos; since a total expansion of close to 2 pct would

Jan 1, 1962

By W. F. Hosford

A series of aluminum single crystals was subjected to axially symmetric flow by drawing through dies. The orientation dependence of the drawing stress, which indicates the resistance to this type of flow, compares reasonably with predictions of Taylor and of Bishop and Hill. Measured lattice rotations likewise are generally consistent with theory. The most successful analyses of the plastic behavior of polycrystalline metal and its relationship to single crystal behavior are those of Taylor1-3 and of Bishop and Hill.4-6 The purpose of this paper is to provide a critical test of some of the basic assumptions involved in these theories. Both treatments apply to fcc metals and assume the shape change of each grain in a polycrystal to be the same as that of the polycrystal as a whole. Thus for a randomly oriented polycrystal extended under uni-axial tension each grain is assumed to undergo axially symmetric flow. dey = dez = -1/2dex, deyZ = dezx = dexy = 0 [l] where x, y, and z are a set of orthogonal axes, x being the tensile axis. Although [011.] oriented grains in bcc and fcc metals may depart markedly from this ideal behavior,7,8 the assumption is probably quite reasonable for most grains. Under a uniaxial tensile stress, ox, the work dW per unit volume expended in producing an increment of axial strain dex is, dW=oxdex [21 Since this work is expended in slip, dw =STi dyi 131 where Ti and yi are the shear stress and shear strain on the active slip systems. In both analyses Ti is taken to be the same on all slip systems, and dependent only on the total prior shear strain on all systems, so dw = Tdy [41 where t is the shear stress required for slip and y is the sum of the shear strain yi on all slip systems. Combining 121 and [4] and defining M = oX/T The ratio M is a generalized Schmid factor. It relates the tensile stress required for axially symmetric flow, ox, to the basic shear stress, 7, and it also expresses the ratio of crystallographic strain, y, to the tensile strain, Ex It depends only on the orientation of the crystal. Taylor evaluated M for various orientations by finding the least value of dy/dEx which could satisfy the shape change. Bishop and Hill, on the other hand, found M by considering the relative work (1/T)dW/dEx expended by stress states which could activate enough slip systems to produce the shape changes. The results of both methods appear to be equivalent, although certain omissions were made in Taylor&apos;s original work. The orientation dependence of M, calculated by the second method,9 is shown in Fig. 1. Taylor used the average 2= 3.06 for all possible orientations to predict the tensile stress-strain curve (oxvs Ex) for a random polycrystal from the shear stress-strain curve (t vs y) of a single crystal. Changes in M from lattice rotation were neglected so points on the ox vs ex curve were simply taken at ox = 3.06t and e = y/3.06 from corresponding points on the t vs y curve. Recent extension of the analyses of Taylor and of Bishop and Hill to crystallographically textured metals has been used to relate plastic anisotropy to textures, and to predict the potential texture hardening that could result from texture control.9 Unfortunately there have been relatively few experimental tests of the underlying theory. Taylor found that the tensile stress-strain curve of polycrystalline aluminum did agree reasonably well with that predicted from a single-crystal T-y curve. Had the single crystal undergone easy glide, how-

Jan 1, 1965

By J. D. Lubahn

The Bauschinger effect, or rounding of the corner of the stress-strain curve upon reloading, represents a temporary apparent softness that is more pronounced at large strains than small and for complete unloading than for partial unloading. Interrupted creep tests on copper exhibit a similar temporary softness (high creep rate) upon reloading. The fact that the strainwise dying-out time of these effects is the same in both tensile and creep tests shows that they are related. Thus, the term Bauschinger effect appears to embrace behavior following partial or complete unloading and reloading in addition to behavior following reversed loading. It is suggested that the term may properly apply also to certain creep behaviors following a small load decrement. INTERRUPTED tensile tests at low temperatures show1 a rounding of the corner of the stress-strain curve for reloading, which indicates a temporarily low deformation resistance. In the absence of recovery, the curve soon rises to the value that would have prevailed if the test had not been interrupted. The rounding of the reloading tensile curve has sometimes been referred to1 as the Bauschinger effect, although the term is more commonly applied to low deformation resistance in compression following tensile prestrain. The unusually broad usage of the term Bauschinger eflect in ref. 1 seems justified by the obvious interconnection of the various behaviors to which it has been applied.&apos; In fact, the following discussion will indicate that still broader usage might be desirable. The Bauschinger effect is common at room temperature but apparently disappears at higher temperatures.2 Interrupted creep tests and tensile tests were made on certified OFHC copper (nongaseous impurities exclusive of silver were 0.004 pct), cold drawn 84 pct to ½ in. diam, and annealed at 600" (about 0.025 mm grains) or 850°C (about 0.2 mm grains). The tests were made in standard creep or tensile machines, using an O.S. Peters microformer-type extensometer or, for the small plastic strains, a special arrangement employing General Electric magnetic gage heads.&apos; Interrupted creep tests at room temperature show3,4 an initial softness after reloading, manifested by an initial creep rate that is higher than that which would have prevailed if the test had not been interrupted. Fig. 1 shows some typical examples. This effect is apparently temporary (as is that in tensile tests): in four of the five tests shown, the log rate vs strain curve becomes parallel to an

Jan 1, 1956

By F. N. Rhines

STUDIES upon the sintering of metal powders, in the solid state, have led to the proposal that the surface energy of the powder particles provides the driving force that causes points of contact between pairs of particles to grow into broad welds which isolate the residual vacant space into pores that tend to spheroidize and gradually to diminish in total volume.&apos; Investigators differ with regard to the mechanism of the movement of the metal, under the influence of surface energy, to accomplish these changes. One school asserts that there is a mass movement of the metal, referred to as a "viscous flow," while the other school prefers to view the movement as a self diffusion process, wherein individual atoms are, transferred without disturbance of the basic pattern of the crystal lattice. Extensive experimental studies upon the sintering of copper, conducted recently by A. J. Shaler,2 have been in- terpreted by their author as support for the viscous flow mechanism of transport, the theory of which was developed originally by J. Frenkel.3 Duplicating a portion of this work with minor changes, G. C. Kuczynski4 is led to the alternate view, namely, that the initial stages of sintering, at least, proceed as a self-diffusion process. Both of these investigations were designed to deal with an isolated unit of sintering, i.e., with the shrinkage of a single pore, or with the growth of a single point weld. It remains to ascertain the behavior of a typical metal powder compact composed of a large number of particles of varying size and sintering to a body with a multiplicity of pores. The observation of density changes alone during sintering is not sufficient in such a case; it is essential to know how the internal geometry of the compact changes. This has been the object of the present investigation, the results of which are used to support the self-diffusion mechanism of sintering. The present studies consist in the measurement of the number of pores as a function of size and time at temperature during the sintering of a copper compact made from a commercial copper powder lightly pressed and sintered in several different atmospheres. A brief survey was made also of the change in shape of the pores, under the influence of the same variables. All of this was done by direct observation with the microscope. Densities were measured on the same sample. It is found that, while the compact is exhibiting an overall shrink-

Jan 1, 1951

By C. E. Birchenall, F. N. Rhines, L. A. Hughes

A. J. Shaler—I should like to congratulate the authors on the presentation of this paper, which we have been awaiting a long time. The view they have taken of the sintering process, namely that voids are comparable to particles of a second phase capable of dissolving to a slight extent in the metal phase, is an interesting but dangerous one. Pines has given a first-order solution of the problem and Has predicted a decrease in the concentration of pores near the surface. The authors of the present paper have experimentally demonstrated the second-order effects, that is, the diffusion of the space phase between voids of different sizes, and also the movement of atoms from highly curved parts of a void to less curved regions of the same void. I have recently calculated the rate of vapor-phase transport within odd-shaped pores in copper at 850 °C and found that probably at that temperature volume flow is the more rapid shape-changing mechanism. The authors of the present paper have found that at 1000°C, vapor-phase transport is dominant. There is no disagreement here, I think. The dominant phenomenon can easily be different&apos; in different temperature ranges and with different pore shapes: I used a cylinder going to a sphere, not a tricuspid going to a "triple cuspidor." But there is some danger in the other art of the explanation, that is, in the study of the diffusion of vacancies from a pore to its neighbors and to the outside. A vacancy is very different in dimension from an atom. When it moves, it carries a field of elastic strain. This has to be taken into account. A concentration gradient of vacancies can cause them to diffuse. But in the absence of such a gradient, they can be made to diffuse by a field of stress. What happens in some of our experiments, and it is most noticeable in the shrinkage of synthetic cylindrical pores, like the tubes we have been working with, may be broken down into the following steps. (1) The presence of a surface establishes a vacancy concentration gradient, as Dr. Kuczynski and the present authors have shown. (2) Vacancies then diffuse in order to decrease this gradient. (3) In so doing, they cause an elastic field to be built up in such a direction as to oppose the diffusion, so that it slows down until it reaches a steady-state rate. (4) The steady-state flow is due to the fact that the surface tension acting on curved surfaces applies a stress to the system which itself mechanically causes vacancy diffusion. What I have said is that the diffusive types of flow of the authors and of Dr. Kuczynski are transient phenomena which soon stop if the pores are large. We are then left with a mechanical problem only, and our researches have not yet disclosed just what the mechanism of flow is; it may be a slip process, or it may take place by a vacancy diffusion of the type Nabarro has de-

Jan 1, 1951