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By S. F. Reiter

The paper presents isothermal recrystallization curves for 0.08 and 0.15 pct C steel at subcritical temperatures following small amounts of plastic deformation. The effects of deformation, temperature, and aging on nucleation and growth rates ore described. The free energy of activation for grain boundary migration in steel is given. SEVERAL excellent reviews of the literature have appeared concerning the recrystallization of metals.'-' The present investigation follows the approach advanced by Mehl, Stanley, and Anderson,6-7 in which the rate of recrystallization was analyzed in terms of N, the rate of nucleation, and G, the rate of growth of recrystallization nuclei. Two lots of low carbon, capped steel of the analysis given in Table I were studied. Each lot consisted of a 150 lb coil which had been hot rolled to 0.083 in. and then cold rolled to 0.042 in. at the mill. Strips 0.930 in. wide were sheared perpendicular to the rolling direction. Both steels were normalized before studying their recrystallization characteristics. The strips were cleaned, painted with a magnesia-acetone paste, and made into packs of equal weight, wrapped in 0.002 in. copper foil. The packs were placed in a salt bath at 900°C for 30 min and air cooled. A relief anneal followed in a second salt bath for 15 min at 650°C. The relief anneal was found necessary from early tests in which a longer incubation period and slower rate of recrystallization were observed in relief-annealed lot A steel than in similar material which was strained and recrystallized directly after being normalized. This effect, which indicates the presence of transformation and/or cooling stresses in steel air cooled from above the A, temperature, has also been observed by Samuels8 and Masing.9 Figs. 1 and 2 show the microstructure of lot A and B materials and illustrate the rather uniform No. 8 ASTM grain size produced by this heat treatment. Winlock and Leiter10 observed that strip specimens which had their sharp edges removed elongated more uniformly than those which were not polished. Similarly, when the sheared edges were removed on a belt grinder, it was found in the present investigation that such samples recrystallized more uniformly than did unpolished strips. Therefore, all strips were carefully rounded prior to their extension. The approximate strain limits for the production of large recrystallized grains are from 6 to 12 pct extension." It was found that for the purpose of this investigation, 8 and 9 pct elongation were suitable deformations. The strain rate employed was 0.01 in. per in. per min and produced a yield point elongation of 4 pct. Winlock and Leiter found that mild steel of No. 8 ASTM grain size gave the same yield point elongation when extended at 0.012 in. per in. per min. All of the lot A and B strips extended in tension developed a straight, stretcher strain line at each grip when the upper yield point was reached. The lines were parallel and made an angle of 55" with the edge of the strip. They approached each other with increasing strain and met near the center of the sample at the end of the yield point elongation. Immediately thereafter, a small drop in load was observed and then the load increased in a regular manner with increasing extension. The grips were initially 8 in. apart. After extension, the 6 in. gage length was carefully cut into 1 in. samples. The remainder of the strip was discarded. After a flash pickle in hot 50-50 hydrochloric acid, six samples, each of which had been taken from a different strip, were placed in a basket and submerged in a lead pot for isothermal recrystallization. Although no recovery effect was observed, strain aging did occur after extension. Therefore, samples were always recrystallized within 24 hr after their cold deformation. After recrystallization, the samples were etched with a solution comprised of one part by volume of nitric acid with three parts of water. Bromide printing paper was exposed directly at low magnifications and later used with a mask to measure the desired quantities. First, the average diameter of the largest grain visible in each sample was determined using dividers. Next, the number of recrystallized grains per unit area was counted and recorded as n. Then, for each sample, the combined area of the recrystallized grains was measured by transcribing the grain outlines to standard graph paper. Many determinations of the area of the recrystallized grains were repeated five times and indicated a standard error that was not greater than 25 pct. The average area for six samples was divided by the area of the mask to yield the percentage recrystallized. Recrystallization of 0.08 Pct C Steel The progress of recrystallization at 670°C after 8 pct elongation of lot A steel is shown in Fig. 3, a through f. The shapes of the growing crystals are approximately equiaxed, as is assumed in the

Jan 1, 1953

By N. K. Chen, C. H. Mathewson

Recrystallization of aluminum single crystals after plastic extension is carefully studied in relation to the structure of the deformed matrix. The shapes of the new grains are analyzed with regard to slip planes and to the presence or absence of deformation bands. A mechanism by which the orientations of the grains are related to the parent lattice is described. EXPERIMENTS previously reported&apos; have been extended to develop some of the characteristics of the new crystals which are formed on annealing axially strained crystals whose deformational characteristics had been documented with special care. Thus, the presence of deformation bands affects the growth contours of the crystals, some of the strained crystals produced single crystals anew, and some, polycrystals, on annealing, while others merely "recovered" or "polygonalized" after the 600°C annealing treatment generally adopted in these tests. In the matter of orientational relationships between new crystals and the strained matrix, the present experiments have added little to previous experience, which had demonstrated great variety in the range of orientations encountered and no simple theory or correlation. For example, there has been ample evidence for the predominance in various face-centered cubic metals of a favored orientational relationship; viz., a rotation of 30° to 40° around a <1ll> axis, between grains growing in a matrix with a strong single orientation texture and the matrix itself.&apos;-&apos; This reorientation has been interpreted by various investigators in support of both the "oriented nucleation" and the "oriented growth" hypothesis. In the case of axially extended single crystals of aluminum, no general relationship, such as the one stated above, can be used to correlate the orientations of the recrystallized grains with that of the original crystal. Thus, Carpenter and Elama and Burgers and Basart7 were content to assume that the orientational relationships so developed were random in nature. Mathewson, however, in the Campbell Lecture of 1943 "rgued on the basis of <112> slip that a complex strain, chiefly characterized by rotation around a variable axis in the slip plane combined with a principal rotation around the pole of the slip plane, could be responsible for such devious relationships. Nevertheless, owing to the limited data now available dealing with orientational relationships between new grains and the single crystals strained in tension from which they have recrystallized, no adequate examination of the above generalization could be made. Here, there is the disturbing preliminary condition that any desired orientational relationship may be expressed by means of two rotations about mutually perpendicular axes, so the process lacks a certain critical flavor and any successful choice of axes meeting certain theoretical requirements could be replaced by another differently selected pair. With this reservation clearly in mind the process of double rotations, as previously indicated, was used to relate the orientations of the single crystals which grew out of the strained single crystalline matrix and was construed as certain evidence in favor of the theory of incongruent shearing action proposed by Mathewsons as a necessary element in the (111) slip process with close-packed metals. There is here

Jan 1, 1953

By F. V. Lene, E. J. Westerman

The recrystallization behaviors of two extruded and cold-drawn experimental sintered aluminum powder alloys, containing 1.75 and 3.0 pct Al2O3 by weight, were compared with that of extruded and cold-drawn commercially pure alumirzum. The kinetics of recrystallization of the alloys are described semiquantitatively. For the alloy containing 1.75 pct A l203 the rates of nucleation and of growth were also semiquantitatively determined. THE most striking property of aluminum alloys strengthened by a dispersion of Al2O3, the so-called SAP alloys, is their stability at elevated temperatures. One of the manifestations of this stability is their resistance to recrystallization after they have been cold worked. Most of the commercial grades of either the Swiss SAP or of Alcoa&apos;s Aluminum Powder Metallurgy Products have not been recrys-tallized after cold working, even when they are heated for a long time at a temperature near the aluminum melting point. Lenel, however, observed that the dispersion strengthened aluminum alloys with a larger spacing between the oxide particles than that of most commercial grades would recrys-tallize.1 It appeared to be of interest to further investigate the mode and kinetics of recrystallization of these alloys, and to compare their recrystallization behavior with that of commercially pure aluminum. Because homogeneous deformation of these SAP alloys in tension did not provide sufficient cold work to induce recrystallization, they were cold worked by wire drawing; the nonuniformity of this deformation unavoidably complicated the interpretation of the recrystallization studies. EXPERIMENTAL DETAILS Extrusions—Two types of sintered aluminum powder extrusions were used in this study. One type, designated AT-400, was produced from Reynolds atomized aluminum powder consisting of spherical particles averaging 3µ in diam and containing 1.75 wt pct of Al2O3. This powder was very similar to the R3M powder from which extrusions were previously prepared with an average spacing of 0.9µ between oxide particles.2 The second type, designated MD 2100, was produced from Metals Disintegrating Co. flake powder containing 3.0 wt pct of Al2O3, with an average flake thickness of 0.8µ. The average spacing between oxide platelets in MD 2100 extru- sions was 0.45µ.2 Powder compacts of 3/4-in. diam were extruded at 1000°F into 0.097-in. diam (AT-400) and 0.093-in. diam (MD 2100) wires by methods previously described.3 In order to compare the recrystallization behavior of sintered aluminum powder extrusions with that of wrought commercially pure aluminum 3/4 in. rod stock of 1100 F aluminum was extruded at 1000°F into 0.102-in. diam wire. Wire Drawing—Tungsten carbide dies were used for the AT-400 and 1100 F alloys. They had an included angle of about 15 deg and reduced the wire area approximately 7 pct per pass. Steel dies with an included angle of 11 to 13 deg and an average reduction per pass of 10 pct were used for drawing the MD 2100 alloy, because drawing this alloy through the carbide dies produced overdrawing defects. Heat Treatment—The cold-drawn wires were cut into small samples, and the deformed ends were etched off. The samples were each wrapped tightly in a single layer of aluminum foil, and individually isothermally annealed in a lead bath. Metallography—The modes and kinetics of recrystallization were determined by metallography. Mounted and polished specimens were anodized in a solution of 1.8 pct HBF4;4 examination under polarized light clearly revealed their grain structures. The recrystallized grains were generally much larger than those of the unrecrystallized matrix, and could clearly be distinguished because they alternated between maximum and minimum light reflection when the microscope stage was rotated, while the unrecrystallized matrix had a comparatively homogeneous "salt and pepper" structure. The fractional recrystallized volumes of the dispersion hardened alloy wires were determined by cutting and weighing of recrystallized and total transverse areas on photomicrographs. The recrystallized grains in the 1100 F alloy were too small to be cut out individually; therefore a combination of cutting and lineal analysis was used in this case. RESULTS AND DISCUSSION Modes of Recrystallization—The modes of recrystallization of the three alloys varied widely. In the 1100 F alloy nucleation and growth started in the region midway between the center and the surface;

Jan 1, 1961

By M. S. Burton, G. V. Smith, A. Rosen

The kinetics of re crystallization and the effect of recovery on recrystallization of pure iron were investigated within the temperature range of 517" to 632 OC. Grain growth and activation energies were also studied. Two stages can be distinguished during recrystallization; the first is gvowth-controlled and the second is nucleation-controlled. The extent to which the first stage succeeds before the second stage begins depends on both temperature of recrystallization and temperature of recovery. The softening of cold-worked metals and alloys due to transformation of the deformed crystals to strain-free equiaxed grains during annealing is well-known, and early inestiators established that recrystallization kinetics is strongly influenced by minute quantities of impurities. Generally, it is believed that impurities decrease the rate of recrystallization and the rate of grain growth. To understand the basic phenomena of recrystallization, investigations should be on pure materials. Most of the research on high-purity materials has been on metals having the fee Bcc materials, and especially high-purity iron, have been studied only in recent years. It is known that recovery may influence recrystalliation;" however, no general description of the influence, applicable to all materials, has been presented. This paper presents results of a study of the recrystallization kinetics of high-purity iron, after 60 pct cold deformation by drawing, with particular reference to the influence of recovery on the rates of recrystallization and grain growth. From observations of these rates, conclusions are drawn concerning nucleation. MATERIAL AND EXPERIMENTAL PROCEDURE Preparation of Material. High-purity iron, prepared by zone refining of vacuum-melted electroiytic iron at Battelle Memorial Institute under sponsorship of the American Iron and Steel Institute, was used in this study. Table I gives the reported chemical analysis of the material, taken at a point near the last molten zone and thereby rep- resenting the maximum impurity level for the entire bar. Prismatic specimens, approximately 10 x 10 X 50 mm, were sawed from the 50-mm-diam bar, perpendicular to the zone-refining direction, and turned to cylindrical shape. These specimens were sealed in quartz capsules under vacuum, approximately 10"e mm Hg, austenitized at 930° C for 15 min, slowly cooled, removed from the capsules, and cold-worked in air by swaging to approximately 20-pct reduction of area. The encapsulating, austenitizing, and swaging operations were repeated two additional times, after which the samples were encapsulated, austenitized, and cold-drawn to 60-pct reduction of area. A further vacuum anneal at 630°C for 120 min and cold drawing to 60-pct reduction of area produced wire 2.8 mm in diameter. The drawn wire was electropolished to remove deformed material on the surface, after which it was sawed into 4-mm-long specimens for the recrystallization study. Microscopical examination before the final cold reduction revealed equiaxed grain structure with very fine grains in a thin layer near the surfaces of the specimen and nearly uniform ASTM 3-4 grain size in the center. Recrystallization Heat Treatment. a) Direct Recrystallization of Cold-Worked The 60 pct cold drawn iron specimens were recrystallized at five temperatures, 517, 556, 590°, 612, and 632C, in a lead bath covered with graphite (the temperature was controlled to 1°C). Specimens were treated for twelve different times at each temperature, and all were water-quenched after heat &eatment. b) Recrystallization Following Preliminary Recovery Heat Treatment. After cold working, specimens were sealed into quartz capsules under vacuum, 105 mm Hg, and recovery-annealed at 362", 400", and 440°C for 20 hr prior to recrystallization. No evidence of recrystallization was found

Jan 1, 1964

By F. J. Plecity, J. T. Michalak, W. C. Leslie

Isothermal recrystallization and grain growth in zone- and vacuum-melted irons and Fe-Mn alloys, up to 0.60 pct Mn, were studied in the range 480° to 650° C, after 60 pct cold reduction. In initial stages, rate of grain growth and rate of recrystallization of iron decrease with time. The recrystallization is typical of a growth-controlled process, and rate of growth is determined by the extent of recovery. Mn decreases rates of growth and of recrystallizatzon. The recrystallization process changes at about 0.30 pct Mn and nucleation may become time-depetzdet~t. In recent years, considerable effort has been expended in determining the effects of solute elements on recrystallization and boundary migration in fcc metals. The results have indicated that the effects produced by single solute additions are dependent upon both the element added and its concentration.&apos;-&apos; In contrast, there have been very few attempts to determine the characteristics of recrystallization and boundary migration in high-purity bcc metals, especially after heavy deformation, and the effects thereon of single solute elements.9-11 This study was undertaken to determine the recrystallization characteristics of various "high-purity" irons and the effects of manganese additions at two levels of base purity. It was hoped that the information obtained would improve our understanding of the recrystallization of pure metals and aid in formulating a theory for the effect of solute elements. The interest was not entirely academic, for the annealing of low-carbon steels, which is of very great commercial importance, is but poorly understood. MATERIALS The compositions of the irons and iron-manganese alloys used are listed in Table I. The zone-melted iron and Fe-Mn alloys were made by Battelle Memorial Institute. Iron S-1 was arc-melted in a water-cooled steel mold in an argon atmosphere. The ingot was forged into a bar, then given two horizontal zone-refining passes in an alumina boat. Iron V-4 was treated in a similar manner, but was not zone-refined. The iron for the zone-melted Fe-Mn alloys was induction melted in vacuum in MgO crucibles and cast into alumina molds. The ingots were forged into bars, machined to shape, and a groove milled down one side of each. The best available electrolytic Mn was placed in the grooves, and the bars were zone melted. The vacuum-melted Fe-Mn alloys were induction melted in this Laboratory in MgO crucibles and poured into cast-iron molds. Iron V-5 was purchased from National Research Corp. in the form of a small vacuum-cast ingot. The low-carbon steel was made by induction melting in air at the U.S. Steel Corp. Applied Research Laboratory. The history of the materials prior to the final cold reduction differed; these details are given in the Appendix. The penultimate grain size of the principal materials was kept in the range ASTM 2 to 4, except for the low-carbon steel. PROCEDURES The cold work prior to the final recrystallization anneal was kept constant at 60 pct. It is known that rolling procedure can influence the kinetics of recrystallization of ironI2; therefore, all specimens were rolled in one direction only, between clean,

Jan 1, 1962

By D. Harker, W. E. Seymour

CERTAIN alloys of iron and nickel, when rolled and annealed, possess a preferred crystal orientation: (001) in the rolling plane and [loo] in the rolling direction, when recrystallized at 850" to 1050°C after approximately 98 pct cold reduction. Since the preferred orientation makes a direction of easiest magnetization coincide with the rolling direction, these alloys, especially a 50 pct iron in nickel alloy, have found wide application in the electrical industry&apos; for choke coils and special types of transformers. The rate of the recrystallization reaction was studied at temperatures ranging from 500° to 600°C. The heat of activation for the reaction was calculated from the observed rates, and crystal orientation determinations were made before and after re-crystallization. A vacuum melted iron-nickel alloy* analyzing 49.6 pct nickel, 0.018 pct carbon, and 0.30 pct manganese was used for the experiments. The alloy was cold-rolled 98 pct into strips 1/2 in. wide by 0.002 in. thick. Specimens 1 in. long were sealed under a vacuum (approximately 10-8 mm Hg) in 1/2 in. ID pyrex glass tubes. For heat treatment these tubes were fastened to Nicrohm wires and submerged in a molten salt bath controlled to ±2°C. (The maximum measurement error was within 3°C.) The time at temperature was varied logarithmically from one sample to another, and runs were made at 500°, 525", 550" and 575°C. A molten lead bath was used for a run at 600°C which was controlled to the same accuracy. To determine the extent of recrystallization after a particular time at a given temperature, a method was used suggested by the work of Decker, Asp, and Harker.3,4 This method employs an X-ray spectrometer whereby X rays are diffracted from crystallites whose diffracting atom planes are parallel to the rolling plane of the specimen. The intensities of the diffracted rays are measured by a Geiger counter. The counter can be rotated through a range of angle, and can be motor driven through this range at a speed of 2" per min. The measured intensities are plotted vs. angle by a potentiometer recorder. In a 50 pct iron-nickel alloy it was found that only (200) reflections were obtained from the rolling plane with recrystallized material, and that only (220) reflections were obtained from the rolling plane with unrecrystallized material. No other reflections were obtained under these conditions over a range of Bragg angle of 0 to 45" using either type of specimen. As a consequence, the intensity of the (200) reflections from the rolling plane was taken to indicate the amount of recrystallized ma-terial present in a specimen, and the corresponding intensity of the (220) reflections was taken to indicate the amount of unrecrystallized material present. To insure flatness and proper alignment of the reflecting specimen in the spectrometer, the sample was laid in a slot 1/2 in. wide x 0.001 in. deep which was machined in a 3/4x2x1/2 in. steel carrier. The specimen then was taped down with cellophane tape. This steel cradle was mounted vertically in the specimen holder of the spectrometer so that the bottom edge of the carrier rested against a horizontal shoulder. Intensity data used in plotting the percent of recrystallized material vs. time at temperature were obtained by directly counting the diffracted beam of nickel filtered copper Ka radiation used throughout the work. The X-ray spectrometer was employed also in obtaining pole figure data to be used for orientation determinations. At the beginning of this investigation a transmission pole figure holder was used." As a thickness of 0.002 in. of this alloy was found to be opaque to the copper Ka radiation, it was necessary to reduce the thickness of the pole figure specimen. A cold-worked sample was etched in a 50 pct HCl solution for 5 min and was found to transmit a

Jan 1, 1951

By P. A. Beck, Hsun Hu

It has been known for many years that in cold drawn polycrystalline aluminum the recrystallization texture is practically identical with the deformation texture.l,2,3 V. Goeler and Sachs4 stated that in cold rolled polycrystalline aluminum, too, the deformation texture is retained upon recrystallization. This behavior was interpreted by Dehlinger9 as an indication that each recrystallized grain inherits the orientation of the matrix in which it grew. However, Burgers and Basart showed6 that in deformed aluminum single crystals the orientation of the recrystallized grains strongly deviates from that of the matrix. Barrett demonstrated8 that even in deformed polycrystalline aggregates the local orientation within each deformed grain changes on recrystallization. No explanation has as yet been offered of how the aggregate texture can be retained, while the local texture is everywhere changing. According to Burgers and Louwerse6 the orientation change on recrystallization in compressed and rolled aluminum single crystals corresponds to a rotation around [112] axes lying in the active slip planes and perpendicular to active slip directions. This orientation change was rationalized by them on the assumption that the orientation of the recrystallized grains is determined by the orientation of the available nuclei, and that these nuclei are small fragments of the deformed crystal, rotated in the deformation process. Barrett pointed out,? however, that these assumptions were by no means proven, and that the total volume of material necessary for the nuclei is so small, that it must be available in any orien- tation whatever. It is, therefore, unlikely that an "oriented nucleation" theory could satisfactorily explain the orientation changes in recrystallization of a deformed crystal. Furthermore, in contradiction to Burgers and LOU-werse&apos;s conclusions, Barrett&apos;s results for the orientation change could be best expressed in terms of rotations around. [Ill] axes. Thus agreement is lacking not only in the interpretations but apparently even in the experimental results contributed by the various investigators. The orientation relationships on coarsening* in a highly oriented polycrystalline matrix were first investigated by Burgers and Basart.5 They produced a fine grained highly oriented matrix by the recrystallization of a compressed or rolled single crystal of aluminum, and studied the orientation relationships in three successive generations of crystals: the "deformation texture" in the single crystal, the recrystallization texture, and the coarsening texture. Burgers24 showed that the preferred orientation of each successive generation was almost always widely different from that of the preceding one, but that the coarse grains often approximately reverted to the orientation of their grandparent, the deformed single crystal. This observation, and the idea that the orientation of the coarse grains is determined by that of the available "nuclei," led to the concept that the coarse grains are nucleated by the remnants of the deformation texture.12,15 On the other hand, Bowles and Boas16 found, in a carefully conducted experiment, that in recrystallized fine grained copper of cube texture coarse grains grow in orientations which can be derived from the orientation of the recrystallized matrix by rotation around a [lll].] direction: the coarsening texture here does not appear to be related in any simple manner to the original rolling texture from which the cube texture had been obtained by recrystallization. It may be assumed that in a recrystallized material, even with a strong texture, there always are present some grains of practically any orientation. These may serve as "nuclei" for the coarse grains, provided that the conditions are favorable for their growth. The existence of a coarsening texture may be considered as an indication that grains with certain relative orientations with respect to the preferred orientation of their neighbors can grow much faster than others. This "oriented growth" theory was briefly suggested by van Arkel, as early as 1936,13 and it was mentioned by Burgers." Recently, C. G. Dunn produced direct

Jan 1, 1950

By I. L. Dillamore

A purely geomentrical analysis based on oriented-growth relationships is presented to derive annealing-texture orientations in bcc metals from their- known deformation textures. The analysis takes as its starting point a description of- the bcc deformation texture and follows previous work on fcc metals in considering pvobable nurleation sites for recrystallization and the textural limitations on grains growing into a deformed matrix. The analy-sis accounts for the prominent and the minor coinponents of the annealing textures formed from two the deformation textures and can account for the ob-sem:ed temperature dependence of the annealing texture of bcc metals. THERE have been a number of investigations of annealing textures in bcc metals but few attempts to relate these textures to the deformation textures. This has been largely due to the lack of definition of both annealing and deformation textures, neither of which shows sharply defined orientations. It is, however, necessary to get a better understanding of primary recrystallization textures in bcc metals in view of increasingly exacting demands upon the quality of steel sheet for drawing purposes and as a necessary step towards the control of textures through processing. An analysis is presented here which relates annealing textures to deformation texture, by a purely geometrical method. This takes as its basis the oriented-growth theory of recrystallization and makes some reasonable assumptions regarding the make-up of bcc deformation textures and the limitations on growth relationships in bcc metals. Detailed information on this latter point is not available at the present time, and the present analysis may need to be streamlined or extended when such information is at hand. It is felt, however, that despite these limitations the analysis provides useful results and a valuable aid towards understanding the effect of processing variables. 1) BCC ROLLING TEXTURES Different workers have used a variety of descriptions for the texture developed in bcc metals by rolling. For the present purpose it will be assumed that two different deformation textures can be obtained: 1) a texture containing a major (112)[li0] component and a minor (001)[1i0] component for which increasing deformation causes the (001)[li0] component to increase at the expense of the (112)[li0] component, as suggested by Dillamore and ~oberts&apos; (this is the texture predicted to arise starting from randomly oriented material); 2) a t~xture containing the above components and (111)[110] and (ii1)[112] components. This texture could arise from a material with an initial (110)[001] or (iil)[112] texture. It is well-known that the (ll0)[001] orientation rotates to (ii1)[112]that on roll-

Jan 1, 1965

By Y. C. Liu, W. R. Hibbard

An aluminum single crystal cold-rolled from (110) [1121 essentially retains its initial orientation after 99.6 pct reduction in thickness. The orientation of the recrys-tallized grains of this material can be described in terms of crystallographic rotations about principal poles of deformation texture. DURING the study of the recrystallization of a copper single crystal cold-rolled from a (110) [112] initial orientation, the orientation of the re-crystallized grains could be derived by a 30" rotation of the orientation of the cold-rolled matrix about its <111> poles.&apos; The present investigation was undertaken to extend the work done on copper&apos; to an aluminum crystal also cold-rolled from a (110) [112] initial orientation. Experimental Procedure The procedure of this experiment was similar to that reported for copper.&apos; An aluminum (99.998 pct) single crystal rod* 1 % in. in diameter was grown in back-reflection technique.&apos; The specimen (1.20x 1.004x0.6787 in. thick) was then rolled along the [112] direction. The final thickness was 0.0028 in., giving a reduction in thickness of about 99.6 pet. Specimens were cut from the rolled strip with scissors, and approximately in. of disturbed metal was removed with Tucker&apos;s reagent. The rolling edge remained intact. The specimens were sandwiched between two graphite plates and annealed in a lead or lead alloy bath which was electrically heated. Pole figures were constructed using the techniques previously described.&apos; Specimens were electrolytically polished4 and etched with 47 pct HNO8, 50 pct HC1, and 3 pct of 48 pct HF. The electrolytic polishing method and etching reagent employed for aluminum specimens were not entirely satisfactory and the microstruc-tures could not be studied in any detail. Results and Discussion The octahedral pole figure of cold-rolled aluminum strip is plotted in Fig. 1. The <111> poles spread in the transverse direction approximately 8" for the highest intensity areas. The spread in the transverse direction can be related to a rotation about two <110> directions lying in a plane containing the rolling direction and rolling plane normal. The two <110> directions and a scale of rotation for the <111> poles are shown in Fig. 2. The amount of rotation is consistent for three of the four <111> poles, about 35" to 40". The discrepancy for the fourth pole is believed to be due to limitations of the film technique. Alternate inter-

Jan 1, 1956

By C. J. Bechtoldt, H. C. Vacher

Quenched alloys, prepared by powder metallurgical techniques, were examined by microscopic and X-ray diffraction methods. The compositions and heat treatments were chosen so that the chromium and nickel solvuses could be determined and a range of composition and temperature, in which a eutectoid had been reported, could be explored in small intervals. The results showed no evidence of eutectoid reactions having taken place. ALLOYS containing iron, chromium, molybdenum, and nickel are extensively used in high-temperature applications. In order to provide basic information on the solid-state reactions that occur in such alloys, the National Bureau of Standards is engaged in an extensive study of the equilibrium phases in the binary, ternary, and quaternary systems involving these four metals. Attention was directed to the chromium-nickel system because a review of the literature showed conflicting data. A recent compendium1 of the constitution of binary alloys gives two diagrams for the chromium-nickel system, one a simple eutectic and the second a diagram showing a eutectoid and a eutectic. The eutectoid was the result of an allotropic transformation in a high-temperature solid-solution form of a chromium-rich phase called 0. The approximate temperature and composition of the eutectoid was 1200°C and 30 at. pct Ni. In the preliminary study, at the Bureau, no transformation was indicated in the chromium-rich phase of ternary and quaternary alloys in which chromium and nickel were major components. Similar results have been reported from time to time in the literature,2-8 In consequence of this situation, a systematic study was made of the constitution of heat-treated chromium-nickel alloys using metallographic and X-ray diffraction methods. The compositions of the alloys were selected so as to determine the boundaries of the chromium-rich and the nickel-rich phases and to explore in small intervals the ranges in composition and temperature in which the eutectoid had been reported. The results of this study are reported and discussed in the present paper. EXPERIMENTAL PROCEDURES Materials, Alloys, and Heat Treatments—The alloys were prepared by a powder metallurgy technique similar to that used in earlier work.9 Analyses of the materials used are given in Table I. Powders were mixed using a vibrator in 30-g batches of predetermined composition; 2-g pellets were made from the mixture by compacting at room temperature in a 1/2-in. diam mold under 60,000 lb per sq in. pressure. The pellets were sintered in dry hydrogen for 10 days at 1300°C. At the end of the sintering treatment the specimens were quenched in water, which caused a pale green film to form on the chromium-rich alloys and thin black scale to form on the nickel-rich alloys. The pellets after sintering were approximately 1/2 in. diam by 3/32 in. thick. The purification train9 was modified by inserting a tube of titanium turnings, heated at 700°C to increase the efficiency of the removal of oxgen and nitrogen. It was found in the earlier work that the sintering treatment lowered the carbon, oxygen, and nitrogen contents of chromium-rich alloys to 0.01, 0.01, and 0.004 wt pct, respectively, and that there was a loss of chromium. In order to ascertain the extent of this loss, the chromium contents of certain alloys were determined chemically. They included those alloys used to determine the parameter-composition curves and those of critical composition, used to determine the chromium-solvus microscopically; these analyses were made on samples after the final heat treatments. The mixed powder values for the chromium content of those alloys that were not analyzed were adjusted to conform to a smooth curve based on the chemically analyzed values for

Jan 1, 1962

By A. H. Daane, W. J. Wunderlin, B. J. Beaudry

In an earlier study at this laboratory,&apos; the authors investigated the solid solubility of holmium in copper, silver, and gold, and also the melting point of the first eutectic on the noble-metal-rich side in these systems. In a more recent study of the solubility of rare-earth metals in gold at this laboratory. Rider, Gschneidner, and McMasters2 noted that the reported eutectic temperature in the Ho-Au system was lower than the corresponding eutectics in systems of dysprosium and erbium with gold. A redetermination of the eutectic temperature in the Ho-Au system with the same alloy used in the original study showed the eutectic temperature to be 810°C instead of 778°C as originally reported. (The eutectic temperatures in the Ho-Ag and Ho-Cu systems were also redetermined and were found to be 795" and 864°C compared to 787° and 868°C, respectively, which were reported originally.) Since this large change in eutectic temperature made the solubility data appear questionable, new alloys were prepared, heat-treated, and examined metallographically. The procedure of sample preparation and heat treatment used in the original work&apos; was followed except longer heat treatments were used ranging from 7 days at 600°C to 6 hr at 900°C. The results obtained are shown in Fig. 1. There is good agreement between the two studies in the maximum solubility of holmium in gold. Since the slope of the solvus is less pronounced in the present study, the extrapolation to 550°C shows a solubility of 1.6 wt pct Ho in gold compared with 1.0 wt pct in the original work. Since additional data were obtained and longer heat treatments were used in the present study, the larger value is believed to be more accurate. The authors wish to express their appreciation to P. Rider and K. A. Gschneidner. Jr., for bringing this discrepancy to their attention, and also to D. Thompson for assisting in the present study.

Jan 1, 1965

By S. J. Hruska

Rate expressions for the formation of two-and three-dimensional nuclei on foreign substrates are developed, taking into account previously neglected contributions to the standard Gibbs free energy of formation of critical nuclei. The temperature dependence of critical super saturation data predicted using these expressions is in accord with data for cadmium on copper and sodium on CsCl. EXPERIMENTAL data on the heterogeneous nuclea-tion of metal crystals from the vapor phase1&apos;2 exhibit the temperature dependence predicted by a nucleation rate equation derived by Pound et al.3 In their treatment, the critical nuclei are visualized according to the Volmer4 model as cap-shaped (three-dimensional). Accordingly, it seems desirable to compare these data with a nucleation rate equation which is derived on the assumption of disk-shaped (two dimensional) nuclei. Further, Lothe and Pound5 have recently shown that the standard Gibbs free energy of formation of these critical nuclei contains a contribution which has heretofore been neglected. Thus it is necessary to re-examine these nucleation data using a rate equation which contains this contribution. The van&apos;t Hoff isotherm relates n(i), the concentration of nuclei of critical size i (i = number of atoms), to nil), the concentration of adsorbed single atoms: where standard Gibbs free energy of formation of critical nuclei given by is temperature insensitive and is the bulk free energy change/volume of transformed material], T = substrate temperature and k = Boltzmann&apos;s constant. Previously,3 was determined by considering only the contributions of bulk and surface free energies in transforming i atoms from the population nil) to a cluster of i atoms. It has been shown5 that this procedure does not take into account the free energy contribution arising from the multiplicity of sites, q, where the clusters can be situated. If this contribution, -kT In q/n(l),is added to iG3 [Note that this increases n(i) by a factor q/n(l).] Since the above does not affect the remaining terms in the rate expression of Pound et al., the details are referred to their paper. The resulting nucleation rate is If the experimental AGV and T values at some common value of are employed, a plot of vs T(ln C3/l + In p&apos;) should yield a straight line of slope k/B<p and intercept . The corresponding plots for / = 1 nucleus per sq cm sec and C3 = 1018 are shown in Figs. 1 and 2 for cadmium on copper1 and sodium on CsCl2 and the values of obtained therefrom are entered in Table I. It is apparent that the data yield reasonable straight lines with about the same scatter as found using the equation of Pound et al. When the configuration of minimum free energy for a nucleus is a circular monatomic layer, the standard free energy of formation is

Jan 1, 1963

By A. J. Griest, A. P. Young, P. D. Frost

A study was made of the effect of ß grain size on the tensile ductility of a-ß titanium alloys haet treated to strengths in the range 165,000 to 180,000 psi. It was concluded that the primary cause of $ embrittlement is the large grain size which is obtained so rapidly in many a-ß titanium alloys when heated into the ß field. It was also found that grain-boundary a and acicular intragranular a in the microstructure are not necessarily detrimental to the tensile ductility if the prior ß grain size is sufficientlv fine. BETA embrittlement occurs in a-ß alloys when the finish hot-working or stages of the subsequent heat treatment have been done at temperatures in the ß field. In order to avoid this embrittlement, for-gings must be finished at temperatures under the ß transus. For better workability, it would be desirable to forge at temperatures in the ß field. For this reason, research has been conducted to determine the cause of ß embrittlement. Although ß grain size has been considered as a possible contributing factor to ß embrittlement, only limited research has been done to evaluate its effect. The effect of addition elements on ß grain growth in unalloyed titanium has been studied by Liu.&apos; Complete mechanical property data, however, were not obtained for correlation with grain size. Ogden and coworkers2 have investigated the effect of both a and ß grain size and grain shape in Ti-Cr-Mo alloys. Their data indicated that tensile ductility was relatively insensitive to ß grain size at annealed strength levels (140,000 psi ultimate). No study has apparently been made to determine the relationship between ß grain size and ß embrittlement in a-ß alloys heat treated to high strength (180,000 psi ultimate). The high-strength condition is that in which ß embrittlement is particularly severe. Beta grain size is not easily varied through the use of a range of annealing times and temperatures in the ß field, because of the rapidity with which ß grain growth occurs. Short-time heating techniques are needed to obtain the smallest ß grains. EXPERIMENTAL PROCEDURE In this research, the experimental procedure was as follows: 1) Tensile and microimpact specimen blanks were resistance heated to produce a range of ß grain sizes. 2) The tensile and microimpact blanks were then solution-treated in the a-ß field and aged to produce predetermined ultimate tensile strengths in the range 165,000 to 180,000 psi. Tensile and impact ductility were then correlated with a grain size for constant strength levels. Materials—The alloys Ti-6A1-4V, Ti-4A1-4Mn, and Ti-16V-2.5Al are representative of the heat-treatable a-ß types in which ß embrittlement can be severe. The compositions and ß transi of the heats studied are given in Table I. The Ti-16V-2.5Al heat was melted and fabricated to 1/4 in. round at Battelle; the other alloys were obtained as 1/4 in. round rolled from commercial heats. The micro-structures of the as-rolled alloys were fine a-ß mixtures. This structure is typical of titanium alloys hot-worked extensively in the a-ß field. Resistance-Heating Treatments to Establish ß Grain Size—For direit resistance heating, a 1/4-in.-diam s~ecimen was heated with a 3000-watt transformer rated for 1000 amp with adjustable secondary voltage. The apparatus included a spray quench fixture. Both heating and quenching periods could be automatically controlled. For temperature measurements, 28-gage Chromel-Alumel wires were tack-welded to the specimen at its midpoint. A high-speed recorder-controller was used to control the heating cycle.

Jan 1, 1960

By A. W. Dana, F. J. Shortsleeve, A. R. Troiano

The phenomenon of flake formation which may occur during cooling or room temperature aging of large steel sections is caused by a combination of hydrogen and stress. As such, the transformation characteristics of austenite in a particular section play a major role in the occurrence of flakes. Isothermal and continuous cooling studies demonstrated that flake formation is particularly sensitive to nature, distribution, and relative proportions of the microconstituents in the cooled sections. In the absence of transformation stresses, abnormally high hydrogen contents could be tolerated without flaking. Flakes were not found in the absence of transformation stresses. No correlation existed between average hydrogen content and flake formation where cooling stresses were low. Hydrogen in the steel was a necessary but not sufficient condition for flake formation. DESPITE a long history of laboratory and commercial investigations, the mechanics of hairline crack or flake formation in large steel sections remains unresolved. Recent publications1-5 emphasize that flaking is still a serious problem.* immediate cause of flaking is the pressure exerted by entrapped hydrogen gas that collects in small internal cavities or voids during cooling. When the temperature of steel is low enough to preclude extensive plastic flow, the cavity pressures cause local brittle fractures (flakes). 2—The microsegregation and transformation stress theory. According to this theory, flaking results from stresses arising from the volume changes accompanying the formation of martensite and/or low temperature bainite after a large portion of the section has transformed at elevated temperatures. The proponents of the hydrogen theory suggest that stresses from other sources may be additive to the stresses produced by hydrogen and may, in some cases, provide the increment of stress necessary to produce flakes. However, the critical aspect of this theory is that no stress, except that produced by hydrogen pressure, is believed to be sufficient in itself to produce flakes. For practical considerations, this means that the only safe thermal cycle is one that reduces the hydrogen content to some low critical level below which flaking will not occur regardless of the state of transformation. On the other hand, the transformation stress theory does not rule out the embrittling effect of hydrogen. This theory simply proposes that flaking does not occur in the absence of transformation stresses. With the transformation stress theory as a basis, commercial antiflaking cycles would be designed to complete the transformation of austenite prior to cooling to ambient temperatures. Both of these theories appear compatible with industrial experience. Antiflaking cycles, such as cooling at extremely conservative rates or soaking for periods of time in the upper subcritical temperature ranges prior to cooling to ambient temperatures, may allow the following: 1—diffusion of hydrogen out of the section and, as a consequence, reduction of the hydrogen content to some safe minimum value (hydrogen pressure theory) and 2—complete decomposition of the austenite at rela-

Jan 1, 1956

By P. Bardzil, J. Gurland

An experimental study of the variation of transverse-rupture strength with composition Anexperimentaland grain studysize has shown that the strength reaches a maximum for values of the mean free path between carbide particles of 0.3 to 0.6 microns. The fracture oforiginates in and proceeds through the carbide grains mainly. Impact strength and hardness also were recorded. MOST of the physical properties of sintered carbides vary linearly with composition. The transverse-rupture strength, however, shows a unique behavior. As the amount of binder metal is varied from 6 to 25 pct by weight, the strength at first increases; then, between 15 and 20 pct Co, it reaches a maximum of nearly 400,000 psi, and finally decreases with further additions of binder metal. This behavior of the transverse-rupture strength has been reported, among others, by Englel and Sandford and Trent.&apos; The significance of these observations has not been discussed in the literature. That it may be of more than specific importance is indicated by the very similar variation of strength with composition encountered in other systems sintered in the presence of a liquid phase, such as Tic-Ni3 and Fe-Cu.&apos; Experimental Details All compacts were prepared and sintered according to normal industrial practice. The average diameter of WC grains and the mean free path between grains were measured on metallographically prepared samples by a method of linear and planar analysis sing the relations where d is the average diameter of dispersed grains; Nl is the number of noncontiguous grains intersected on a metallographic plane by a line of unit length; N, is the number of noncontiguous grains per unit area; P is the mean free path between grains of dispersed phase; and f is the volume fraction of dispersed phase. Approximately 1000 grains were counted on each sample. For each composition d2 was plotted against P, the resulting straight lines serving as a check on the measurements. The distribution curves of the WC powders of different average diameters were homologous, and no attempt was made to influence the grain size by blending powders, adjusting the sintering conditions, or otherwise altering the particle size distribution. Densities were measured by differential weighings in air and water. The degree of densification did not vary consistently with either composition or grain size. The density is influenced by slight amounts of impurities, specifically by 0.1 to 0.2 pct Fe which enters the powders during ball milling. As an illus- -tration of the experimental variations, a number of measured densities are listed in Table I. They are expressed in percentage of theoretical density, as calculated from the published X-ray densities of WC and Co.&apos; For the purpose of determining the transverse-rupture strength, rectangular test specimens (3/16x 3/8x3/4 in.) were broken by loading at the center of a 9/16 in. span. The average strength of five or more samples is reported for each composition and grain size. The compacts were ground on two parallel surfaces only. The load was applied at an average rate of 6,800 psi per sec. Since the elongation after fracture of the alloys is very small, it was assumed that the compacts deform elastically to failure and the fracture stress was calculated by the conventional beam formula. The data for one alloy are presented in Table II as an example of the results and scattering ranges encountered. The precision of the test, as measured by the average difference between duplicates, is of the order of 15,000 psi. The results are strictly comparable only to compacts prepared and tested in the manner described and of similar chemical composition and grain size characteristics. Unnotched Charpy specimens were used for impact testing. Each point represents the average of 3 to 20 samples, the larger number being used in an attempt to determine the influence of grain size. Considerable scatter was encountered, the range from lowest to highest value often amounting to 30 pct of the impact strength. The hardness is reported as a Ra reading, using a 60 kg load with diamond brale indenter. Compositions are given in weight percent.

Jan 1, 1956

By B. N. Das, P. A. Beck

THE o phases have a complex tetragonal structure with Lo/ao = 0.52 and 30 atoms per unit cell.1 A large number of such phases are now known to occur in various binary systems of the transition elements and they exhibit the following typical features: 2,3 The composition of binary o phases is variable, ranging from approximately A4B to ABI. With only a few exceptions, in the o phases the A-ele-ment comes from the V- or Cr- group of the periodic table, while the B-elements are from the Mn-, Fe-, Co-, or Ni- group. In the first long period the corresponding o phases of the V- and Cr-series have approximately the same compositions. However, as the B-element changes from Mn to Fe to Co to Ni, the mean composition shifts monotonously toward higher A-contents.2-4 For example, if the mean compositions of the various o phases with vanadium are compared with each other, the composition shift mentioned above becomes plainly visible: V 30Mn0 80 Vo.45Feo..,, Vo .,Coo. 45 and Vo.5Nio.3. Similiar composition shifts, although not the same composition values, were observed in u phases formed by second and by third long-period transition elements.3&apos;4 This behavior, very characteristic of o phases, is in rather sharp contrast to the usually quite well-behaved stoichi-ometry of the Laves phases. In the latter, the AB2 stoichiometry predominates, with A the large atom and B the small atom.= The p phase occurs in the four binary systems of Mo or W with Fe or Co. On the basis of their crystal structure determination, Arnfelt and westgren6 ascribed to the p phase in the Co-W system the ideal composition W,Co7. Since all four binary pphases have nearly the same composition, it would seem quite plausible that some definite stoichiometry such as A6B7, might be characteristic of this phase, as AB2 is of the Laves phases. On the other hand, it has been noted,7 that the phases occur at average electron concentrations near to those at which the various cr phases are found. Also, it has been pointed out by Shoemaker and associates8 that structurally the a phases and the p phases are somewhat related to each other; both of these structures may be described in terms of suitable stackings of quasi-hexagonal layers&apos;of atoms. By studying a suitably chosen ter- nary phase diagram, one might expect to be able to find out which one of the two conditions, the analogy with the o phase or the constant ratio between the number of large atoms and the number of small atoms in effect governs the behavior of the p phase. Several isothermal sections of ternary systems containing o phases have been investigated. In all cases where two binary o phases occur, these were found to be connected b a more or less straight ternary o phase field.7&apos; &apos;10 Such elongated o phase fields were also found in ternary systems in which only one of the limiting binaries is known to contain o phase. In this manner a latent o forming tendency could be detected and the virtual composition of a "binary o phase", which does not actually occur as such was approximately determined by extrapolation. The behavior of the phases, including their composition shift, is analogous to that of the classical electron compounds, as described by Hume-Rothery.11 In order to decide whether the p phase is essentially a "size compound" like the Laves phases, where a fixed stoichiometric ratio is quite generally maintained between the "large atoms" and the "small atoms", or whether the p phase is typically an "electron compound" in the same sense as ois, it was decided to investigate an isothermal section of the Mo-Mn-Co system. The Mo-Co system12 and the Mo-Mn system13 each are known to have a binary o phase. It could be therefore expected that a ternary o phase field will connect these two binary cr-phase fields. The p phase is known to occur in the Mo-Co system. If the p phase should turn out to form an elongated phase field extending deep into the ternary system, the following considerations mighto apply. The atomic radius of manganese (1.314for C.N.12) is between the va,lues for Mo (1.40Afor C.N.12) and for Co (1.26Afor C.N.12). If it is assumed that p is a "size compound", and that Mn is substituting for the smaller Co atoms in the p-structure in the ternary system, the y-phase field might be expected to extend parallel to the Mn-Co binary line. If Mn is substituting for the large Mo atoms in the p-structure, the p-phase field may be expected to extend parallel to the Mn-Mo binary line. On the other hand, if the p-phase turns out to be an "electron compound" like o, the ternary p-phase field should extend parallel to the ternary o -phase field connecting (Mo,Mn)owith (Mo, Co) a

Jan 1, 1961

By K. T. Aust

The relative interfacial energies of symmetrical tilt boundaries in silver of greater than 99.999 pct purity were measured as a function of orientation difference 0 between 9° and 36° about <001>. The results are in good agreement with the dislocation model of the grain boundary. The energy vs H curve may be represented by the Shockley and Read equation in the form Eoe (0.55—In 8). READ&apos; has indicated that an ideal experimental method of testing the predictions of the dislocation theory of the grain boundary would be to measure the interfacial energies of symmetrical tilt boundaries between face-centered-cubic grains that have a common <001> axis, as a function of orientation difference 0. The misfit H should be defined by a rotation of each grain through an angle of H/2 away from the boundary. Such boundaries might be expected, from geometrical considerations, to be made up of a series of edge dislocations, at least for small values of 0. Energy vs H relationships for tin&apos; and lead:&apos; were previously obtained for an asymmetrical tilt boundary separating two grains in which generally only one grain was rotated about a <001> specimen axis through an angle of H away from the boundary, the other grain remaining fixed. It is possible, however, that the boundary atoms in tin and lead may have attained a symmetrical position, in relation to the orientations of the grains on either side of the boundary, during equilibrium annealing. The two sets of measurements on silicon ferrite&apos; were somewhat better suited for comparison with theory, since the boundaries were symmetrical tilt boundaries in which the axis of relative rotation was <110> in the first series and <l00> in the second; but this alloy has a body-centered-cubic structure. Although the grain boundaries in silver" were symmetrically tilted, the axis of relative rotation was not a simple crystallographic direction, and it varied from boundary to boundary. Although the above measurements were in good agreement with the Shockley and Read equation,"&apos;: it appeared desirable to carry out experiments under the ideal conditions specified by Read.&apos; Consequently, the relative energies of symmetrical tilt boundaries in silver between grains that have a common <001> axis were measured. The technique of equilibrating grain boundaries in oriented tricrystals was used rather than the less satisfactory thermal groove method previously employed for silver bicrystals." Experimental Details and Observations The solidification and seeding techniques, described previouslyh for growing tricrystals of controlled orientations, were used to prepare tricrystal specimens from silver of greater than 99.999 pct purity. The silver was obtained from American Platinum Works, Newark, N. J., in the form of poly crystalline rods 10 cm long and 7 mm in diam. These rods were then cold worked by rolling or drawing them into suitably shaped blanks. Single crystal seeds and tricrystals were grown in a high purity graphite boat by means of a movable furnace with globar heating elements. The graphite boat was enclosed in a Vycor tube, which was first evacuated to about l00/u Hg and then filled with a static argon atmosphere. The maximum temperature outside the Vycor tube was 1250°C. A typical tricrystal specimen of silver is shown in Fig. 1. Grains B and C were grown from seed crystals with a <001> specimen axis or longitudinal direction parallel to the direction of growth and with another <001> direction perpendicular to the surface. Each of the two seed crystals was rotated 18" about the <001> specimen axis but in opposite directions away from the boundary. A symmetrical tilt boundary, therefore, separated grains B and C with an orientation difference 8 of 36" about <001>. Grain A in Fig. 1 was grown from the middle seed with a <110> direction parallel to the specimen axis and with a <001> direction inclined at 45&apos; to the surface of the specimen. The interfaces sepa-

Jan 1, 1957

By H. C. Theuerer

EVEN the highest purity silicon available for semiconductor use contains significant amounts of donors and acceptors, usually aluminum, phosphorus, and boron. Aluminum and phosphorus can be removed from silicon by adaptations of the zone refining techniques&apos; widely used with germanium. Removal of boron, however, has been a difficult problem. The approximate distribution coefficient for boron in silicon is 0.8, so that while zone refining is possible, it is not very effective in any reasonable number of passes. It has been found, however, that boron can be effectively removed from silicon by treatment of a liquid zone with hydrogen and water vapor. Starting with 40 ohm-cm, n-type silicon, use of zone refining coupled with hydrogen

Jan 1, 1957

By B. D. Cullity

A distribution of residual stress after plastic elongation is proposed, in which the bulk of the material is strained in compression and a very small portion in tension, This distribution is shown to account both for the X-ray observations and for the effect of plastic straining on magnetic losses in silicon steel. The regions left in compression are tentatively identified with the interiors of the sub-grains revealed by the electron microscope. THIS paper is concerned with the general problem of the nature of the residual stress which is produced in metals by plastic elongation. A particular stress distribution will be suggested which accounts for the main X-ray diffraction observations which have been made. It will also be shown that certain magnetic measurements made on silicon steel can be understood in terms of this stress distribution. X-RAY OBSERVATIONS Uniform straining of a crystal lattice (macro-strain) causes a diffracted X-ray beam to shift its position, and nonuniform straining (microstrain) causes line broadening. If a bar of metal is plastically elongated in the longitudinal x direction and then unloaded, diffracted X-ray lines are observed to be both shifted and broadened.&apos;-= Although the observed line shift indicates the presence of macro-strain, experiments have shown that no macrostrain, in the usual engineering sense of the term, exists.5"7 For example, removal of a layer from one surface of a stretched and unloaded bar does not produce curvature in the remainder of the bar 5&apos;7 Fig. 1 shows the variation of lattice strain in the x direction, as determined from X-ray line shifts, with the applied stress in the same direction. The curve ABC is the normal stress-strain curve of the material, AB being the elastic portion and BC the plastic. In the elastic region AB, the strain measured by X-rays, called the lattice strain, and the strain measured mechanically are both proportional to the applied stress, and both return to zero when the applied stress is removed. Above the elastic limit the lattice strain would be expected to continue to increase along the line BD. Actually, it increases less rapidly with respect to stress, or even decreases, as shown by BE. If the applied stress is then decreased, the lattice strain decreases along EF, which is parallel to AB. As a result, there is a compressive residual lattice strain FA after unloading. STRESS DISTRIBUTION. Since a stretched and unloaded bar does not contain macrostress, it follows that the observed line shift must be due to a special distribution of mi-crostress. Such a distribution is shown in Fig. 2, which shows the variation of the stress u, across a stretched and unloaded bar. The material is assumed to consist of two kinds of regions: regions C, stressed more or less uniformly in compression, comprising the bulk of the volume of the material and responsible for the observed diffrac-

Jan 1, 1963

By K. R. Van Horn

RESIDUAL stresses in metals operate under a cloak of mystery, as they have neither been seen in the laboratory nor detected by means of the microscope. In spite of their phantom-like nature, they frequently exert metallurgical effects that cannot be ignored. In some cases the results have been detrimental, causing rejections or premature failures, but frequently the effects have been highly beneficial to the producer or consumer of metal products. First, however, what is a residual stress? When a metal is plastically deformed by bending, rolling, pressing, or by a phase transformation or precipitation from solid solution, or by a sharp temperature gradient resulting from nonuniform cooling, quenching, or welding, it remains in a state of strain. The strains or strain gradients produced by such operations and retained after all external forces are released are known as residual strains, and the accompanying stresses as internal or residual stresses. Many defects or failures in metal products have been ascribed to residual stresses, sometimes erroneously, because there was no other apparent explanation after the usual metallurgical tools of diagnosis had been applied. For example, during World War 11, the forged aluminum alloy aircraft cylinder head in the reciprocating engine began to replace the cast head with the familiar cooling fins. The fins were machined in the solid forged head by an ingenious milling operation. One plant reported an epidemic of excessive distortion during the delicate high-speed milling. A thorough examination revealed that the composition, heat treatment, mechanical properties, and metallurgical quality of these heads were comparable to those of forgings that machined satisfactorily. It was then claimed that the cause of the machining difficulties was connected with residual stresses resulting from the quenching during the solution heat treatment. An elaborate stress analysis actually demonstrated, however, that the magnitude of residual cooling stresses was lower in the cylinder heads which machined poorly than in those which were satisfactory in this respect. Subsequent tests proved that the machining problems in this case originated from variations in the tools and tool design. Sources of Residual Stresses in Metals Residual stresses are of two origins—mechanical and thermal. Thus, stresses may be produced in a metal by any cold-working process. The distribution and magnitude of these mechanically produced stresses can be calculated in a satisfactory, although approximate, manner for such simple cases as bending, torsion, and expanding of tubes. However, most manufacturing processes are too complex, and the original stress-strain relations in the products are not sufficiently known to permit calculation of the resulting residual stresses. Also, a specific process, such as wire drawing, may vary in complexity or uniformity of working, and large or small residual stresses may result, depending on the conformation of the dies and other features of the working process. Neither substantially unidirectional deformation, such as can be imparted by stretching a metal product having essentially the same mechanical properties throughout the cross section, nor deformation

Jan 1, 1954