Search Documents

By A. Phillips, H. J. Fisher

The influence of temperature and composition on the viscosity of high-purity liquid metals and alloys of the Pb-Sn and Sb-Cd systems was investigated by the logarithmic-decrement method. The variation of viscosity with temperature above the liquidus followed the equation: n = AeE/RT No large increase in viscosity was found just before normal freezing of any of the metals or alloys investigated. Certain alloys, supercooled below their stable liquidus, however, did show a marked increase in viscosity. Experimental activation energies for viscosity were determined for the metals investigated. Liquid-metal density values were obtained by a modified Joeger's method. IK an investigation of the properties of molten metals, the study of viscosity as a suitable means for studying the physical nature of the metallic liquid state has been utilized. Although interest in the relationship of the liquid to the solid-metal state holds promise of broadening the knowledge of metals in general, much information that is available regarding the influence of temperature and composition on viscosity, especially near the freezing point, is still controversial. The purpose of this paper is to present the results of recent work on this subject. Although interest in factors influencing the fluid behavior of metals and alloys has arisen from theoretical as well as applied studies of liquid-metal properties, the development of a comprehensive theory of the mechanism of viscosity has been handicapped because so little is known about the liquid state. Several theories of viscosity have been proposed and among the more recent are those of Andrade,1 Bernal,2 Frenkel,3 Eyring,4 and Gutmann and Simmons.5 Athough these contributions have helped to establish a basis of approach for studying the nature of viscosity, the fundamental aspects of the variation of viscosity with alloy composition have, in general, been neglected. Experimental Metals and Alloys Investigated: The Pb-Sn and Sb-Cd alloy systems were selected for investigation because they form constitutional features of theo-

Jan 1, 1955

By F. H. Buttner, E. R. Funk, H. Udin

Gold wires, 5 mil in diam, are found to creep viscously up to approximately 5.5x106 dynes per sq cm around 1300°K. Beyond this point, an additional slip mechanism appears. The average coefficient in the viscous range at these temperatures is 18.9 ± 7x10 12 poises. This observation and other visual observations made during the experiments agree with Herring's predictions. EARLY creep studies by Chalmers on single crystals of tin produced some of the first experimental evidence to suggest that metals deform viscously under very light stresses. That is to say, over a small initial stress range up to 150 g per sq mm, the single crystals of tin elongated at a rate proportional to the stress. The proportionality constant between strain rate and stress is by definition the coefficient of viscosity. Chalmers named this range of proportionality the microcreep range. One of the first theoretical attempts to explain the microcreep phenomenon was given by Kauzman,' who applied Eyring'sQ eneral statistical mechanical theory of shear rates to creep data then available. From the rate theory, he deduced the general hyperbolic sine law for shear rate on the assumption that the distortion of the reaction path due to stress is negligible and that the system is an infinite continuum. In order to fit the available data to the equation, it was necessary to assume that creep occurs by shear of rather large blocks of material, rather than by an atomistic shear process as in diffusion. The size of the shear units was shown to increase with increasing temperatures and lower stress, or lower strain rates. In applying the hyperbolic sine law equation to the microcreep data of tin, it was shown by Kauzman that the unit shear blocks became quite small, which suggested to him that microcreep might be a self-diffusion process. Making this an assumption, Kauz- man reworked the rate theory and arrived at an equation where the shear rate is proportional to the stress. In the form of viscosity coefficient, the equation is: o- _ \LkT V = 2qAlA where u is the stress; S, the shear rate; X, the distance in shear direction moved by flow units relative to one another in the unit process; L, the distance between layers of units of flow; T, the absolute temperature; k, Boltzmann's constant; qAL, a constant proportional to the size of flow units; and kT A, the diffusion coefficient = ------kTe-Q/RT = K X2 h Kauzman applied the expression to molten lead with a fair degree of success, the calculated viscosity being low by a factor of four. For solid lead the result is 5000 times too high. Taking q = 1, and X = dA = L = 21 = nearest neighbor distance, Udin, Shaler and Wulff8 found the equation low by a factor of lo7 for solid copper. On the basis of the discrepancy in lead, Kauzman indicated that microcreep is probably not a simple diffusion process of molecular shear units, but one involving preferential diffusion paths, or even that diffusion in solids does not involve shear at all. Cottrell and Jaswon4 treat the microcreep phenomenon on the basis of slow moving dislocations and apply it to Chalmers' data on tin with fair success. Nabarro Suggested a microcreep model in which mass movement in the direction of pull is effected by the diffusion of holes. The tension on the crystal effectively creates a greater hole concentration at regions near the crystal surfaces perpendicular to

Jan 1, 1953

By F. H. Buttner, E. R. Funk, H. Udin

A. P. Greenough (University College, swansea, Great Britain)—I have recently made some experiments on the deformation of silver wire at high temperature in an atmosphere of oxygen-free nitrogen. The observa-tions which 1 made confirm the main conclusion of this paper, that the most satisfactory mechanism so far suggested to explain the deformation which takes place

Jan 1, 1953

By A. L. Pranatis, G. M. Pound

Changes in length of copper foils of varying thickness and grain size were measured under such conditions of low stress and high temperature that it is believed that creep was predominately the result of interboundary diffusion of the type recently discussed by Conyers Herring. The surface tension of copper was calculated and results confirmed previous work within the limits of experimental error. Under the assumption of viscous flow, viscosities were calculated as a function of temperature and grain size. Predictions of the Nabarro Herring theory of surface grain boundary flow were borne out fully and the Herring theory of diffusional viscosity is strongly supported. ONLY a relatively few techniques for obtaining the surface tension of solids are presently available. Of these, the simplest and most straight forward is the direct measurement of surface tension by the application of a balancing counterforce. Thin wires or foils are lightly loaded and strain rates (either positive due to the downward force of the applied load or negative if the contracting tendency of surface tension is sufficiently greater than the applied stress) are observed. By plotting strain rates against stress, the load which exactly balances the upward pull is found and a simple calculation yields a value for the surface tension. The technique is of comparative antiquity, and solid surface tension values were reported by Chapman and Porter,' Schottky; and Berggren" in the early part of the century. Later, the filament technique became fairly well established as a method for determining the surface tension of viscous liquids, and Tammann and coworkers,'. " Sawai and co-worker and Mackh howed good agreement between the values of surface tension for glasses and tars obtained by the filament technique and by more conventional methods. With the increased confidence in the technique gained in these experiments, the method was applied to solid metals and the first reliable values of surface tension of solid metals were reported by Sawai and coworkers10' " and by Tammann and Boehme." More recently, Udin and coworkersu-'" have reported the results of experiments with gold, silver, and copper wires. Similar experiments with gold wires were carried out by Alexander, Dawson, and Kling.'" The excellent review articles of Fisher and Dunn" and of Udinl@ should be referred to for detailed criticism of the foregoing work and for discussion of underlying theory. In all the foregoing calculations, it is assumed implicitly that the material contracts or extends uni- formly along the length of the specimen and also that it flows in a viscous fashion, i.e., that strain rates are proportional to stress. For an amorphous material, such as glass, tar, or pitch, the assumptions are quite valid and good agreement is obtained with values of surface tension measured by other techniques. The values reported for metals, however, are occasionally regarded with misgiving, since it can be argued that, because of their crystalline nature, true solids can not deform in a viscous fashion. If this is true, then the results reported for solid metals over a long period of years are of only doubtful value. Thus it is clearly necessary that a mechanism be established that would explain both the viscous flow and the uniform deformation that has been assumed. Such a mechanism has been proposed by Herring."' Briefly, he suggests that, under the conditions of the experiment, deformation takes place by means of a flow of vacancies between grain boundaries and surfaces. This is a direct but independent extension of the theory proposed by Nabarro" in an attempt to explain the microcreep observed by Chalmer~.In a condensed form the Herring viscosity equation is TRL there 7 is the viscosity, T the absolute temperature, R and L grain dimensions, and D the self-diffusion coefficient. In its complete form, all constants are calculable and it includes such factors as grain shape, specimen shape, and degree of grain boundary flow. When applied to existing data, good agreement was obtained between predicted and observed flow rates. The theory received provisional confirmation from the work of Buttner, Funk, and Udin" who observed viscosities in 5 mil Au wire much higher than those in the 1 mil wire used by Alexander, Dawson, and Kling.'" More significant were the completely negligible strain rates found by Greenough" in silver single crystals. Opposed to these observations were those of Udin, Shaler, and Wulff'" who found indications of viscosity decreasing as grain size increased. Thus, complete confirmation of the theory was lacking in that the data to which it could be applied contained only a limited number of grain sizes. Hence, it was proposed that a series of experiments be carried out with thin foils of varying grain size up to and including single crystals, where, according to the Herring theory, deformation would occur only at almost infinitely slow rates.

Jan 1, 1956

By R. D. Fisher, A. G. Metcalfe, F. A. Crossley

AN investigation of the application of magnetic stirring to the consumable arc melting of aluminum and nickel demonstrated that grain refinement could be obtained when there was sufficient stirring force. Also, it was found that grain refinement could be obtained in aluminum by alternately reversing the polarity of the current through the magnetic stirring coil. The effect of the latter was to periodically reverse the direction of rotation of the molten metal.' Because of their promise, these findings were applied to conventionally cast aluminum. Shortly after this work was begun, Kondic2 reported experiments in which aluminum cast with 40° C (72° F) of superheat exhibited a grain size of 10 to 20 grains per cm2. When interrupted rotation was applied during solidification by mechanical means, a grain size of 800 to 1000 grains per cm2 was obtained. Magnetic Stirring Applied to Conventional Casting— The applicability of magnetic stirring to producing grain refinement in conventionally cast metal was evaluated in the following way. Three pounds of aluminum were cast into a clay-bonded graphite mold. The mold was surrounded by a magnetic stirring coil of 1000 turns. A direct current of 200 amp was passed through the casting by means of a graphite electrode which was immersed from the top. A current of 5 amp was passed through the stirring coil. The aluminum (1100 or 25) was superheated to 1600° F (871° C) and fluxed by passing chlorine gas through the melt for 2 min prior to casting. Two additional castings were made for comparison: 1) a conventional casting of metal superheated to 1600° F and 2) a similar casting through which 200-amp current was passed during solidification, but without current in the magnetic coil. Macrosections of these three ingots are shown in Fig. 1. Very remarkable grain refinement resulted in the magnetically stirred casting. It may be noted that the casting through which 200-amp current was passed has a coarser structure than the conventional casting. It would appear that this is due to the additional heat input generated by the current to the former casting. Mechanical Rotation Applied to Conventional Casting—A casting temperature of 1600° F was used throughout. Some 1 1/2 -lb castings rotated at 150 rpm were predominantly columnar with small areas of coarse, equiaxed grains close to the lower mold wall. Following these, a series of 3-lb castings was made. Macrosections of these ingots are shown in Fig. 2. The imposed rotational speed was 250 rpm. Turbulence or acceleration in the solidifying liquid was the significant factor. Fine grain size resulted in the material solidified during the period of acceleration of the liquid to the imposed rotational speed. When uniform rotational motion was achieved, the grain structure reverted to columnar. The final casting shown in the lower right-

Jan 1, 1962

By Harvey Cline, Donald P. Ferriss

THE violent outgassing of commercial tungsten and other refractory metals when melted in an electron beam zone refining apparatus1"3 is dealt with experimentally by one or both of two approaches. One is to provide a suitable emission current control1,2 the other is to purify the metal in the solid state before melting.4 The first of these is usually sufficient, but the authors chose also to investigate the source of the troublesome gases and to devise means of solid-state purification. Some further insights into the use of tungsten as a structural material at temperatures near its melting point were also revealed in the course of the work. One may speculate on the causes of gas formation in tungsten at high temperature by inferences from the literature and an examination of the impurities in commercial wire. Davenport5 observed microporosity in both tungsten and molybdenum filaments heated to several hundred degrees below their melting points. Studying the function of oxygen in molybdenum welds, Perry, Spacil, and wulff8 attributed similar porosity to the disproportionation of Moo2 to molybdenum metal and Moo3. Tungsten dioxide also disproportionates7 above 2000oC to yield WO3 vapor at considerable pressure. Commercial tungsten contains some 5 to 20 wt ppm O and a similar concentration of carbon depending on the details and precautions of processing. Therefore, evolution of CO is also a strong possibility as a source of gas at high temperatures. Furthermore, even for activities in the order of 0.01, it may be calculated that the pressure of CO at 3000°C would be over 4000 psi, which is in excess of the tensile strength of tungsten at this temperature.9,10 Powder metallurgy tungsten contains some 0.02 pet Fe and 0.002 to 0.005 pet of the elements Ni, Si, Al, Ca, Mn, Mg, and Mo; at temperatures over 2800°c, therefore, these elements will exhibit appreciable vapor pressure, though small compared to that of WO3 and CO. Some of these impurities may react to form high-pressure monoxides such as SiO and A10. Finally, dissolved and occluded nitrogen is an ever-present source of high-pressure gas. Commercial Type 218, General Electric filament wires, 0.025 in. diam, were heated by resistance in 10 -4 mm of Hg and in argon or hydrogen at pressures from 50 µ to atmospheric. For temperature determinations in vacuo, the Jones - Langmuir8 current-temperature relationship was employed. For gaseous atmospheres, the burn-out temperature was assumed to be the same as in vacuo so that a small, constant correction could be made for temperatures below burn-out conditions (i.e., local heating to failure). Several dozen experiments may be summarized by pointing out some structural observations. At 3050oC in 1 atm of A, porosity is very evident after 30 min, as shown in Fig. 1. For the section in Fig. 2, failure occurred 200°C below the melting point and many voids have grown in the grain bound-

Jan 1, 1962

By B. Ramaswami

INTERNAL oxidation occurs readily in silver due to the rapid diffusion of oxygen in silver.' It has a marked effect on creep in polycrystalline silver2 and raises the critical resolved shear stress in single crystals of silver.3 However, the effect of oxygen on the work-hardening parameters of silver is not known. It is the aim of this paper to describe the effect of internal oxidation on the work-hardening characteristics of single crystals of silver and an Ag-0.1 at. pct A1 alloy. The materials used were: 99.99 pct Ag from Handy and Harman and 99.993+ pct A1 from Alcoa. Single crystals, 6 mm by 6 mm in cross section of silver and Ag-0.1 at. pct A1 of mo.5 orientation, i.e., the orientation with the Schmidt factor m = 0.5. were grown by the Chalmers technique.4 One set of specimens, referred to herein as oxidized specimens, was annealed at 940°C for 24 hr in a muffle furnace, in air, and furnace-cooled to room temperature. Another set of specimens, referred to as nonoxidized specimens, was annealed in oxygen-free helium at 940°C for 24 hr and furnace-cooled over a period of 7 hr to room temperature. The annealed single crystals were tested at room temperature in a floor-model Instron testing machine. The results are presented in Figs. 1 and 2. A

Jan 1, 1965

By Goldye Leeds, Marian Balicki

A SURVEY of literature reveals the scarcity of experimental evidence relating to work hardening and reannealing of silver.'-'" With the exception of the well-known X-ray investigation of silver and other metals by W. A. Wood? the effect of progressive cold working has not been studied. The determination of thermal stability of silver in the work-hardened state by means of isochronal or isothermal annealing has been confined apparently to very high reductions only. In the survey made, no study was encountered which endeavored to produce a complete picture of the changes in various properties due to cold working and subsequent reannealing. To fill these gaps and to assemble data that could be used for the determination of activation energies and of frequency coefficients of primary recrystallization, a systematic experimental approach, which was developed by one of the authors, has been applied to pure silver. Material and Processing The silver used was Handy and Harman fine silver, with a spectroscopic analysis at the testing stage of Cu, 0.0001 to 0.001 pct; Te, 0.0001; Pb, Si, Ca, Mg, and Mn, traces. The material was supplied in the form of a rod 0.406 in. diam and was converted into test samples according to the procedure condensed in Table I. It should be mentioned that air annealing was adopted to simulate industrial practice, though it was realized that annealing in a neutral gas or in a vacuum would be preferred. The usual precautions have been taken to eliminate any structural changes and property changes resulting from the storage of the samples prior to annealing or testing. Thus the wires were kept at the fully annealed stage, and the final wire drawing, which produced the desired degree of work hardening, was done just prior to the final annealing or testing. During the short waiting period, the samples were kept in a thermosflask filled with ice. Even with these precautions some strain-age-hardening or self-annealing could occur. To test such a possibility, wires of different reductions were prepared in the manner adopted and portions of them were immediately tested. The remaining portions were similiarly tested after different periods of storage, both at room and melting-ice temperature. Within experimental error, all samples obtained from a wire of a given percentage of reduction yielded identical values. This result qualified the material for further tests and interpretations, because it showed that either strain-age-hardening and self-annealing were absent, or that these effects fully balanced each other. The final annealing was carried out in an electric resistance furnace automatically controlled to within a 10°F. It was realized that the temperature fluctuations were greater than desired for this type of work. TO diminish the errors due to fluctuations of temperature, the hot junction of the thermocouple was placed as close to the samples as possible; the time of soaking was reduced to 15 min; and the number of samples annealed at different temperatures was increased. It will be seen from Table I that some tests were performed on the same material at rising temperature. These will be discussed elsewhere. Room temperature testing was limited to the determination of some of the mechanical properties that are known to be additive in a degree sufficient to be used for indirect study of the kinetics of the reannealing process, Tensile tests, carried out on a manually operated J. Camillon machine, accurate to within permitted the determination of the ultimate stress (U.S.1 and of the 2 in. elongation, (A,). The proof stress (d,e) has been determined from a series of bend tests carried out on a Tinius Olsen Stiffness Tester by using the offset method. This involved accurate determination for each sample of load-angular deflection curves, finding a

Jan 1, 1952

By E. J. Dulis, A. Kasak, R. C. Westgren

The potential of uirought tungsten- and tantaluw-rich alloys of the W-Ta-Mo-Cb system was investigated for high-strength structural applications above 2500° F. Appreciable strengthening of tung-sten and tantalum—essentially attributable to solid-solzction effects—was obtained with binary, ternary, and quaternary alloys. Tensile strengths as high as 67,000 psi were achieved at 3000 OF. ThE quest for wrought structural materials which possess good strength properties at temperatures above 2000°F has led to a considerable research effort during the past decade. In addition to exploring the potential of various high-melting-point refractory metals (such as molybdenum, columbium, tantalum, and tungsten) for very high-temperature structural applications, alloy-development programs have been undertaken to achieve greater strengths than could be achieved with unalloyed refractory metals. The methods of strengthening refractory metal alloys have included both solid-solution and dispersion strengthening. General relationships among the relevant properties (melting point, recrystallization temperature, and high-temperature strength) of refractory metals indicate that the highest strengths at temperatures of 2500°F or higher would be obtained with tungsten-or tantalum-base alloys. Therefore, the present investigation was undertaken to determine the high-temperature strength potential of solid-solution strengthened alloys based on the binary system W-Ta; to effect further strengthening, minor additions of molybdenum and columbium (at the 6 and 12 pct levels) were made. The portion of the W-Ta-Mo-Cb quaternary alloy system of interest is shown schematically in Fig. 1. The component metals—W, Ta, Mo, and Cb—have a bcc structure at all temperatures, and their binary systems are mutually completely soluble.' Complete solid solubility in the W-Ta-Mo and W-Ta-Cb alloy systems has been demonstrated,' and, therefore, it was expected that the quarternary alloys of the system would also exhibit complete solid solubility at all temperatures. In the virtual absence of contamination by interstitial elements, all the alloys would be truly solid-solution strengthened. Twenty specific compositions of this investigation included binary, ternary, and quaternary alloys of the W-Ta-Mo-Cb system as well as unalloyed tungsten and tantalum. The compositions are shown in Table I. EXPERIMENTAL PROCEDURE Consumable-electrode vacuum-arc melting with ac power was used to produce small laboratory-sized, cylindrically shaped ingots (1-1/4 in. in diameter and 2 to 3-1/2 in. long) of the twenty compositions. A furnace was specially constructed to melt as many as four electrode rods simultaneously into molds lined with tungsten or tantalum sheet. High-purity rods of tungsten, tantalum, molybdenum, and columbium were used for consumable electrodes; the diameter of each rod was determined by the desired weight percentage of the component metal in a given alloy. The details of the construction and operation of the melting furnace will be discussed in another p~blication.

Jan 1, 1964

By S. Andrew Kulin, L. Kaufman

A general treatment of the broadening of X-ray double-crystal spectrometer rocking curves due to distributions of tilts and strains has been carried out. The results of this treatment have been applied to the case where dislocations in a crystal give rise to both tilts and strains. On this basis it is found that the rocking-curve halfwidth due to imperfections in the crystal, ßC , increases with increasing Bragg angle, 8. These considerations predict linear relationships between & and tan2 , and ßCand tan 8, for Gaussian and Cauchy distributions of dislocations, respectively. The zero intercept of the ßC us 8 curve, which is a measure of the degree of imperfection of the crystal, is found to depend directly on the distribution rather than the number of dislocations. In addition, the slope-intercept ratio for the ßc - ? curve has been calculated for both the Gaussian and Cauchy distributions. Experimental determination of the - 8 curves for a series of copper single crystals prepared by the Bridgeman and Czochralski methods yields results in agreement with the calculated slope-intercept ratio for a Cauchy distribution of dislocations. CERTAIN X-ray techniques have been used to study the perfection of single crystals. Gay, Hirsch, and Kelly have considered the spreading of spots into arcs on Debye-Sherrer rings due to imperfections. The Double-Crystal Spectrometer has also been applied to this problem.2 The characteristics of Double-Crystal Spectrometer Rocking Curves have been described in the literature by various workers.2-4 By assuming a random spacing of dislocations which give rise to a Gaussian distribution of misorientations relative to some mean orientation in a crystal Gay, et al.,1 arrive at the conclu- sion that the most probable misorientation is given by where h is the spacing between dislocations, and 8 and are the relative misorientations of neighboring regions. If ßC is the halfwidth of the rocking curve (the width at one-half the peak intensity) due to dislocations in the crystal then5

Jan 1, 1960

By C. M. Schwartz, J. R. Bridge, D. A. Vaughan

THERMAL expansion coefficients of a uranium were originally reported' on the basis of X-ray diffraction measurement of lattice constants at 25°, 300°, and 650°C. These data have been reproduced by Katz and Rabinowitch.' CuK radiation had been used in this work, with consequent crowding of the patterns. Considerable overlap of the back-reflection lines was observed as the temperature was raised. Subsequent reexamination of the data led to the conclusion that errors had resulted from failure to obtain unequivocal indexing of the high angle reflections at elevated temperatures. The measurements have been repeated, using FeK radiation, which provided sufficient dispersion to assure proper indexing of the reflections, at each temperature level. The unit cell dimensions were re-determined at ten temperatures, from 25" to 650°C. Schuch and Laquer easured the macroscopic contraction from room temperature down to —253°C, and reported a negative value from —210" to —253°C; they suggested the possibility of the occurrence of a phase change. In the present work, the lattice constants of uranium have been measured down to —253°C, to test this hypothesis. Filings were prepared from a single piece of pure uranium bar stock. They were carefully cleaned with a magnet and pickled in nitric acid to remove traces of iron from the file. They were then annealed at 600°C in a sealed evacuated silica tube. The annealed filings were pickled in strong nitric acid to remove any oxide layer, washed in water and alcohol, quickly dried, and sealed in evacuated thin-walled silica capillary tubes. If properly sealed, the sample could be heated to the a-ß transforination temperature without significant buildup of the diffraction pattern of oxide. The high temperature X-ray diffraction camera was modified from the design of Hume-Rothery and Reynolds.' The thermocouple used to record the specimen temperature was calibrated from lattice-constant measurements of a standard silver specimen, using the Hume-Rothery and Reynolds values for silver over the temperature range from 25" to 700°C. Temperatures were reproducible to 210°C. Temperatures to —210°C were attained by passing precooled gas over the sample. The gas from the cooling train was directed over the sample capillary tube and thermocouple by means of a chimney of 1-mil polystyrene. The 36-gage Cu-constantan thermocouple had been calibrated by

Jan 1, 1957

By Robert E. Green, Kenneth Reifsnider

A microscopic X-ray diffraction technique was employed for the simultaneous study of the behavior of several families of lattice planes, whose local orientatiotz changes are manufestations of internal distortions resulting from specimen deformation. Photographs taken using aluminum were single crystals 1/64 in. In diam are presented which illustrate the appearance of various types of deformation- or growth- induced structural variations. Slip and lattice bending were detected in tensile tests for strains as small as 0.1 pct. Evidence of deformation bands, lineage structure, and void formation wns also shown. AmONG the most important methods of studying internal stresses in metals is the utilization of various X-ray techniques. The general subject of X-ray metallography has been treated in a most excellent manner by Taylor,1 and the use of X-rays for the direct observation of imperfections in crystals has recently been reviewed in an article by Newkirk2 and in the book edited by Newkirk and Wernick.3 Since the inception of metallographic X-ray analysis, there have been numerous technological developments and refinements, each with its particular advantages and disadvantages and, acrording to these, its particular applications. X-ray diffraction techniques can be divided into two general categories, that of X-ray diffraction microscopy and that of X-ray diffraction macroscopy. In the former are included such methods as those of Berg-Barrett, Lang, and Schultz2,3 which are concerned with microscopic imperfections such as dislocations. The second category includes all work concerned with the study of the condition of a crystal lattice structure as indicated by the marroscopic detail in its diffraction patterns. An example of this is the study of the diffraction manifestations of inhomogeneous plastic deformation as manifested by formation of deformation bands and inhomogeneous lattice rotations. The method used in the present investigation was an X-ray diffraction macroscopy technique. The geometry and analytical aspects of the method were similar to those of Julien and Cullity.4,5 The source was collimated with a single slit in a manner simi- lar to the "parallel beam'' method of Barth and Hosemann6 except that a continuous spectrum of radiation was employed. The apparatus produced large-beam transmission Laue patterns of thin cylindrical aluminum-wire crystals, which were deformed either in tension or torsion. Although the conventional X-ray target and interposed slit were not capable of the high resolution obtainable with a fine-focus X-ray source as employed in a microfocus apparatus, resolution was a secondary consideration in our technique, and was sacrificed to obtain sufficient intensity along a sizable length of the specimen. By using a grid indexing technique similar to that of Barth,7 we were able to study several diffraction lines from various planes simultaneously. The results of these tests give additional information with regard to the inhomogeneous deformation of single crystals, and the indexing procedure used provides a correlation between portions of the test specimen and portions of a diffracted beam. EXPERIMENTAL TECHNIQUE The experimental arrangement used is shown schematically in Fig. 1. A source of continuous X radiation from a vertically mounted Machlett X-ray tube possessing a copper target and operated at 20 kv and 10 ma was passed down a horizontal lead tube 80 cm long which terminated in an adjustable vertical brass slit. The slit opening was adjusted to correspond with the diameter of the test specimen. In front of the brass slit it was possible to place a screen wire mesh, one horizontal strand of which was a lead wire which served as a fiduciary mark, the screen itself serving as an indexing system as will be described later. Behind the screen was the test specimen which consisted of an aluminum single crystal wire 1/64 in. in diameter and 3 in. long. These 3-in.-long crystals were cut from

Jan 1, 1965

By A. J. Jacobs, G. Katz

MANY of the studies of intermetallic compounds containing uranium were performed during the early 1940's under the aegis of the Manhattan Project. Subsequently, much of this work was declassified and published after 1949. In some instances this early work, completed with relatively impure materials, represents the only source of X-ray diffraction powder data available in the literature. In the case of the intermetallic compound U,Fe some discrepancies in the powder pattern exist in the literature. Since this compound has been prepared in this laboratory, it is believed that the publication of the indexed powder pattern would help clarify the conflict in the literature. In studies of the U-Fe system, Gordon and Kauf-mannl and Grogan and Clews2 independently reported the intermetallic compound U,Fe in 1950. The crystal structure was described by Baenziger, Rundle, Snow, and Wilson3 in 1950. It is isostructural with U,Mn, U,Ni, and U,Co and crystallizes in a body-centered tetragonal lattice. The lattice constants determined by Baenziger et al. are: giving an X-ray density = 17.7 g cm-3 for 4 mol per unit cell. The compound used in this study was prepared by melting a stoichiometric mixture of the constituent metals in an argon-arc furnace using a nonconsum-mable tungsten electrode. Before the argon of 99.98 pct purity was introduced into the furnace, it was passed through CaC1, to remove water vapor and afterwards through a stainless steel tube containing calcium turnings heated at 600°C for the removal of nitrogen and oxygen. The purity of the uranium used was better than 99.9 pct and that of the iron was 99.97 pct. Before and during melting a zirconium getter was used to further purify the argon atmos-

Jan 1, 1962

By C. Altstetter

THE work herein reported is restricted to the carbides which occur in quenched and tempered AISI 43XX steels with carbon contents up to 0.40 pct and silicon additions of up to 3 pct. In view of the instability and extremely small size of the carbides formed at low tempering temperatures, the technique for successfully preparing specimens for X-ray diffraction will be outlined. The alloys listed in Table I were obtained through the courtesy of the United States Steel Corp. in the form of 1/2-in. rounds forged from 100 lb. induction furnace heats (except for 4337 which was a commercial heat). The stock was normalized and then swaged and drawn to 15 mil wire with anneals at 1200F between passes. The wire was austenitized for 45 min in evacuated vycor capsules and quenched into iced brine with simultaneous smashing of the capsule. Tempering was done in air with a water quench after tempering. The carbides were extracted in a simple cell using a solution of 1M KC1 and 0.5 pct citric acid with an initial current density of 0.1 amp per sq cm. One end of a short length of wire was immersed in the solution, and the current at constant voltage was noted as a function of time. After about an hour the current dropped sharply because of the decrease in specimen cross-section. At this point it was found that the dissolution could be stopped and that the very fine wire which then resulted was just large enough to permit handling of the extracted precipitate still clinging to it, yet so small that it diffracted and absorbed only a negligible amount of the X-radiation. This rod of residue with a convenient handle of undissolved wire was rinsed in distilled water. alcohol, and acetone. Then it was dipped in a thin solution of cellulose-acetate cement and dried in vacuum. The resulting specimen was straight, uniform in density, easily handled, but most important, was completely sealed and never exposed to air. Furthermore, the residue had never been subjected to strong acids or rough handling such as in the extraction-replica technique or in the complete extraction to a powdered residue. It was found that improperly coated specimens were pyrophoric, turning to oxide with a dull red glow as they were exposed to air and yielding patterns of Fe2O3 and Fe3O4. The steels containing 3 pct Si were especially difficult to prepare for this reason. The specimens were put in a 57 mm Straumanis camera with double pinholes or slits and irradiated with filtered-chromium radiation. Readable patterns were obtained in less than an hour. A preliminary finding of some note was that for both tempered and as-quenched specimens of steels 4337 and 4337 (1.5 Si). M23C6 patterns were found along with the patterns of other constituents of the residues. This result was somewhat surprising in that previous investigators had reported that this carbide did not appear in a 0.38 pct C, 0.48 pct Mo steel1 or in chromium steels of less than about 10 pct Cr.2 Although the total amount of carbide-forming alloying elements is less than 2 pct, due to their mutual interaction and the action of the plastic deformation in promoting equilibrium, this carbide was able to form even in the steel containing 1.5 pct Si. M23C6 was not detected in the 4337 (3.0 Si) steel and the lower-carbon steels were not investigated in this condition. It is very likely then that the steels studied herein underwent a fourth stage of tempering during the anneals at 1200°F. This result has significance in that even a small amount of undissolved M23C6 in a low-carbon, low-alloy steel would exert a large effect on its hardenability. Its presence would also influence the mechanical properties by decreasing the carbon content of the matrix. Annealing in vacuum for 1 to 4 hr in the austenite field removed all traces of MZ3C+ The results on carbide precipitation during tempering, summarized in Table I, are in agreement with those of Klingler et al.3 for the higher carbon steels. For the AISI 4337 steels it is noteworthy that in the steels with added silicon the E carbide persists to longer times and higher temperatures and that silicon delays the formation of cementite. The results for the lowzr-carbon steels parallel those of the higher-carbon grade. The appearance of E carbide in the AISI 4315 is significant. There is considerable disagreem-nt in the literature as to whether this carbide forms in the tempering of steels containing less than about 0.2 pct C. Following the detection of E carbide in a 0.18 pct C plain-carbon steel,4 its occurrence in a steel containing chromium and molybdenum should be expected. The fact that the low-carbon steels have the same carbide-precipitation sequence as the high-carbon steels has bearing on the larger problem of the exact tempering reactions in all steels. Following the suggestion of Roberts et al.,' the first stage has been generally assumed to result in a metastable equilibrium of c carbide and martensite of about 0.25 pct C. From this it was concluded that a steel having less than 0.25 pct C should then be under-saturated with respect to c carbide and should not precipitate this carbide upon tempering. In view of the experimental findings of c carbide in steels hav-

Jan 1, 1962

By J. P. Boisseau, C. N. J. Wagner, E. N. Aqua

An analysis ulas made of powder-paltern peaks from cold-rolled polycrystalline copper and from copper powders, compacted into briquets (1 in. diameter) with pressures up to about 106 psi. Powder-pattern peaks from both contact faces were measured with a diffractometer and CuKa radiation. Laltice-parameter measurements indicate the presence of residual stresses in the bulk specimen of the order of a - -10 kg per sq mm after 93 pct reduction in thickness, and give some evidence for the occurrence of deformation stacking faults (probability a - 0.003) in both bulk and powder samples. Fourier analyses of the line profiles were carried out on the (111) - (222) and (200) - (400) Pairs of reflections. The particle sizes decrease rapidly with increasing deformation and reach asymptotic values of De (111) = 550A and D, (200) = 350A at about 25 pct reduction in thickness or 80,000 psi pressure for compaction. The anisotropy of the particle sizes indicates the presence of microtwins and stacking faults on (111) planes. The rms strains increase also with deformation and reach limiting values of 2 x 10-3 in the [100] direction and 1 x 10-3 in the [Ill] direction at a distance L = 100A normal to the reflecting planes. THE diffraction of X-rays in cold-worked, polycrystalline, fcc metals and alloys yields Debye-Scherrer patterns in which the individual (hkl) lines may show a broadening, a shift, and an asymmetric shape.' These effects can be explained by the fragmentation of the small, coherently diffracting domains, the presence of residual elastic strains in the lattice, and the formation of stacking faults. X-ray studies of stacking faults in fcc metals and alloys have been methodically performed during the last few years, but so far most of the investigators dealt with cold-worked powder specimens obtained by filing.2-8,10-19 In such specimens, the crystals are randomly oriented and the average elastic strains are assumed to be zero, so that the observed peak shifts are due to stacking faults only. The agreement between X-ray diffraction theory1,20 and experiment is generally good. On the contrary, cold-worked, polycrystalline bulk specimens (after wire drawing, rolling, plastic deformation by tension or compression, etc.) contain residual elastic strains, which may not average to zero in the surface of the specimen and show very strong preferred orientation of certain lattice planes (texture) parallel to the specimen surface. Nonzero elastic strains also produce peak shifts, the magnitudes of which depend upon the crystallographic orientation of the reflecting lattice planes in elastically anisotropic materials as well as on the type of plastic deformation and which have to be taken into account when measuring stacking-fault probabilities in deformed bulk specimens.21-23 The purpose of the present investigations was to perform a detailed X-ray analysis on a bulk specimen of a fcc metal deformed by rolling at room temperature and on powder of the same material deformed by compaction, and to compare these results with those previously obtained on cold-worked filings.18 Pure copper was chosen for this study since it is known to produce only a small quantity of stacking faults by filing at room temperature.3,16,17,19 The residual elastic strain in the surface of the bulk copper should be the predominant factor determining

Jan 1, 1965

By F. von Gemmingen, E. J. Fasiska, L. Zwell

EARLIER studies of the dependence of creep on structure1 and of the dependence of creep rupture on creep behavior2 did not include detailed discussion of the phases present in the specimens under examination. It is of interest to determine the nature and amounts of such phases present since it is well known that these are dependent on composition, heat treatment and creep conditions.3 This investigation has therefore been undertaken to identify these constituents and to determine their relative amounts. This report presents the results of this investigation and describes an improved "extraction replica" technique developed in the course of the work. The composition of the Type 316 austenitic stainless steels studied in this investigation is given in Table I. The specimens were solution treated at 2000°F for 1/2 hr and water quenched. Those specimens subjected to prestrain at room temperature Methods for extracting precipitate particles from materials for electron and X-ray diffraction analysis have been described by Fisher,4 Smith and Nutting: and Booker and coworkers.6'7 Electrolytic extraction methods have been described by Andrews and Hughes.8 The first two methods have been used at this Laboratory, but have not proved satisfactory for many problems requiring X-ray diffraction analysis. It has been difficult to remove the replicas or to avoid tearing them during removal. These difficulties are overcome by backing the replica with a water-soluble plastic such as Dupont 51-05 Elvanol (polyvinyl alcohol). The backing increases the thickness of the replica so that it can be mechanically stripped from unloosened particles without folding or tearing. This procedure eliminates the stripping of wet replicas, which usually have a low tear strength. By stripping replicas after drying, it is possible to extract partially loosened particles which otherwise would remain imbedded in the metal. The modified method is as follows: after the specimen is polished, it is etched for 60 min in modified glyceregia consisting of 30 ml glycerol, 7 ml nitric acid, and 4 ml of hydrochloric acid. The sample is then washed, air dried, and coated with a 20 pct Baker and Adamson 1611 collodion (85 pct amyl acetate by volume) film. After the collodion film is dry (about 15 min), the sample is again etched in the modified glyceregia for 50 min, washed with isopropyl alcohol (to prevent dissolving the collodion) and air dried. A very thick coat of polyvinyl alcohol (about 50 pct solution "Elvanol Dupont 51-05" in water) is poured over the sample and is permitted to dry for about 24 hr. The composite film containing the precipitates is then stripped from the specimen and floated, polyvinyl alcohol side down, in water (at about 50°C) until the polyvinyl alcohol dissolves. This usually takes about 15 min. Should any of the polyvinyl alcohol remain on the replica, it does not give a crystalline diffraction pattern and therefore does not hinder identification of the precipitates. The extraction replica, floating in water, is picked up on a glass fiber and mounted in the Debye-Scherrer camera for X-ray diffraction analysis. Concentration of the etchant, and also etching time, had to be increased for several of the samples. Fig. 1 shows two extraction replicas taken from different areas of spec. M74-37; X-ray analysis showed a strong diffraction pattern of M23C6 and a medium one of u phase. A

Jan 1, 1962

By J. B. Cohen

In an investigation of the microstructure of shock-loaded metal specimens1 C. S. Smith found that there was little distortion of grain boundaries or change in external dimensions, although the hardness corresponded to that produced by severe rolling. Furthermore, the hardness of individual grains was independent of the deformation structures present; grains with no markings were as hard as those heavily populated with markings. These markings which resemble twins do not appear in copper until high shock-loads of the order of 200 kb are applied. It appears that due to the high velocity of a shock wave and its sharp front, heavy deformation takes place on a submicroscopic scale. In this work an attempt was made to examine this deformation, particularly at a load below which macroecopic markings appear. The broadening of 200 and 400 diffraction peaks was examined from the face of a poly crystalline sample normal to the direction of the shock wave. These peaks were chosen because the elastic constants in copper are such that residual strains would be greatest in the <100> directions; hence, the strain-broadening contribution to these peaks would be large in comparison to other sets. Also the broadening due to stacking faults and microtwins would be greatest with this set.2 A complete Fourier analysis of these peaks was made, as described by warren,&apos; using the Stokes correction with peaks from an annealed sample.3 With the aid of the U. S. Army Ordnance Corps EDVAC computer and a curve matching program, sixty sine and sixty cosine coefficients were obtained for each peak. The last of these was about 1.5 pct or less of the largest coefficient, indicating good representation. Transverse sections from a 1.5 in. rod of as-drawn electrolytic tough-pitch copper were reduced in cross-sectional area about 50 pct by cross rolling. Disks 1.5 in. in diam were recrystallized at 275 °C for 30 min and then at 300°C for the same time. The faces were polished and deeply etched in nitric acid to remove 25 mils. The grain size was 0.02 mm. Laue back-reflection patterns indicated the sample was well recrystallized. The two diffraction peaks from this sample were recorded on a Norelco diffractometer using filtered copper radiation. Peak intensities were kept less than 600 cps to assure linearity of the counter and circuitry. This sample was then placed between two rods of the same material and diameter. The top rod was 2.25 in. long and the bottom rod 1 in. long. (In

Jan 1, 1961

By W. P. Evans, R. W. Buenneke

Warren and Averbach&apos;s multiple order, Fourier method was applied to solid specimens of SAE 1045 steel. The material was hardened to three hardness levels and specimens of each hardness were shot peened to three intensities. Particle size, root-mem-square strain, mean strain, md macro residual stress were determined for each. Microstrains caused by either hardening or peening varied markedly over microregions. In general, increasing the hardness or peening intensity increased the rms strain and decreased the particle size. Similar effects were observed by varying hardness and peening intensity independently. At a Rockwell hardness of C 50, peening had little effect on line broadening, but both mean strain and macro residual stress increased. Mean strain was independent of column length. Induced macro residual stress by peening was affected most by initial hardness, but not by specific peening intensity. The purpose of this work is to establish the state of residual strain and particle size by X-ray diffraction in hardened and cold-worked plain carbon steel and attempt to relate these X-ray measured parameters to fatigue performance. X-ray line broadening (and its micro implications), along with X-ray residual stress (and its macro implications), may be basic indicators of the inherent fatigue resistance of the material. X-ray line broadening is caused by variable lattice strains and small particle size. Both are a result of plastic deformation which accompanies hardening or cold working processes. Therefore, X-ray line broadening is a good measure of both. warren1 has recently reviewed the Warren and Averbach2,3 Fourier analysis of line broadening. Strain and particle size effects can be separated because broadening due to particle size is independent of order of the diffraction peaks, while broadening due to strain is not. Microstrain is obtained as a root-mean-square strain averaged over discrete distances within the crystals causing diffraction. These distances are quite small, varying from 10 to 10081, and may be interpreted as the gage length over which the strains are averaged. Because of their variable nature, the X-ray line is broadened. The plot of rms strain vs distance (or column length) within the specimen gives a measure of their variability. Small particles also cause X-ray line broadening as already mentioned. A particle is interpreted as a region within a crystal or grain which diffracts X-rays coherently. This region is one of given orientation and may be bounded by a small angle grain boundary, dislocations, a twin boundary, or a stacking fault. The present work covers measurement of X-ray line broadening and macro residual stress on an SAE 1045 steel, quenched and tempered to various hardnesses. Various amounts of cold working were produced by shot peening the surfaces to various Almen intensities. Particle size, root-mean-square strain, and mean strain were calculated from the Fourier coefficients of the X-ray diffraction profiles in a direction normal to the peened surface. No effort was made to separate the various causes of particle size broadening. Macro residual stresses were reported in directions parallel to the peened surface. I) X-RAY METHOD The Fourier coefficients were determined for the 110 and 220 X-ray profiles. They were corrected for instrumental broadening by the method of Stokes,4 using an annealed reference specimen of similar geometry presumed to be free from broadening due to small particles and distortions. The nth Fourier cosine coefficient, A,, is related to a particle size coefficient, Ap, and a distortional coefficient, ADn, by the equation:

Jan 1, 1963

By R. E. Ogilvie, E. T. Peters

The X-ray Kossel-line method has been used preaioz~sly for measuring lattice parameters to accuracies of 1 part in 100,000.5 A second application of this method is described for determining the crystallographic orientation of a randomly positioned single-crysta1 spherical volume that can he as small as 50 µ in diameter, within accuracy limits of ±1/2 deg. The theory, experimental procedure, and interpretation of Kossel-line patterns and an experimenta1 verification of the predicted orientation relationship of the cph k and fee a Cu-Si phases are presented. This orientation relationship can be described as (111)a, (00.1)k; [110]a [11.0]k. In addition, the lattice parameter of the a phase was found to he a. = 3.62154 ± 0.00014Å. The Kossel-line method when used in conjunction with electron microanalysis is shown to he capable of providing a complete chemical and structural analysis of a given crystal. THE most easily accomplished methods for determining the orientation of a single crystal are variations of the Laue X-ray diffraction method. Although certain materials can be oriented to within ± 1 deg accuracy by observation of exterior macroscopic features, such as etch pits, cleavage faces, or growth features, the Laue method is generally preferred for routine laboratory application. Both back-reflection and transmission patterns are coordinated by appropriate reference charts and are plotted in terms of reflection plane poles (normals) on a stereographic projection. Orientation is deduced by relating the pole distribution (which is fixed by the crystallographic symmetry of the specimen) to two specified external reference directions. The Laue method has several limitations. 1) Orientation can rarely be determined to better than ±l deg accuracy. Principal errors involve inaccuracy in specimen-to-film distance, measurement confidence of individual Laue spots, and stereographic plotting. 2) Because of the indeterminacy of the X-ray wave length diffracted to a given spot, it is not possible to determine supplementary crystallographic data, such as interplanar spacings and lattice parameters. 3) The method is generally limited to specimens of cubic symmetry or to specimens of high symmetry and known structure. 4) The relatively large cross-sectional area of the incident X-ray beam generally precludes the measurement of relative grain orientation in a polycrystalline material.* _____ Several of these limitations can be overcome by application of the Kossel-line method, which has been previously employed for precision lattice-parameter determinations.&apos;-= For this method, a point source of divergent monochromatic X-rays is generated within the crystal by means of an incident electron beam. The divergent X-rays which fulfill the Bragg law are diffracted by the specimen and are recorded on a film placed either in transmission or back reflection. Analysis of the film yields a direct measurement of orientation and lattice-spacing values to an accuracy of ±1/2 pct. As analyses can be obtained from spherical specimen volumes as small as 50 µ in diameter, the method provides a means for structural analysis of second-phase or impurity precipitates within a given matrix. The primary limitation of the Kossel-line method is the requirement for an electron microanalyzer or similar apparatus capable of producing a finely focused electron beam. This paper is designed to present the theory, experimental procedure, and geometrical interpretation of Kossel patterns. The experimentally determined orientation relationship between the k and a phases occurring in the Cu-Si system and a precision measurement of the a lattice parameter are presented as a practical application of the method. THEORY OF KOSSEL LINES Divergent X-ray beam photography utilizes an effective point source of characteristic X-rays which, when diffracted from a single crystal, form numerous diffraction and absorption cones that are recorded on film.7 The cones generated from a source lying within the crystal are called Kossel lines.&apos; Although the X-ray scattering from a divergent point source contained within a crystal is described in terms of Laue dynamical theory,9 the directions of the diffracted spectra can be ade-

Jan 1, 1965

By J. A. Berger, R. J. Towner

The pjPocesses of polygonization and subgrain growth were followed in slightly stretched 99.99 pct A1 single crystals heated for cumulative times at 400°, 500°, and 600°C. Changes in sub-grain size and boundary angle were determined from measurements on X-ray micrographs. CAHN1, 2 studied polygonization in stretched and heated aluminum single crystals of 99.99 pct A1 using various techniques, including etch pits, Laue patterns, and a slight restretching of heated specimens to reveal small changes in lattice orientation by the direction of new slip lines. He found that kink bands, which had well-defined boundaries lying in a plane perpendicular to the slip direction (at least in the early stages of deformation), formed during stretching. Also, he noted that bending occurred about the <211> axis lying in the (111) slip plane perpendicular to the <110> slip direction. His studies of polygonization were largely confined to the kink bands rather than to the weakly bent matrix regions between bands. The minimum temperature required to bring about polygonization was established at about 450 "C. Guinier and Tenevin used a focusing Laue X-ray diffraction technique to study polygonization in aluminum single-crystal specimens of 99.99 pct purity. Stretching the crystals 5 pct in tension caused a widening of the focused Laue spots. After heating for 4 hr at 450°C, their method revealed no change in the specimen. Above 450°C polygonization was detected and further annealing near 600°C led to subgrain growth. They concluded that the orientation of the crystal relative to the axis of deformation had no marked effect on polygonization. Gay and Honey-combe4 using an X-ray microbeam technique found that polygonization did not occur in a stretched aluminum crystal heated at 250oC, although some decrease in the yield strength occurred. When the temperature was raised to 475oC, the asterism became broken up as a result of polygonization. Honeycombe5 noted that reflections on X-ray mi-

Jan 1, 1961