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By W. H. Class

The embrittling effects of oxygen, ozone, nitrogen, air, and surface residues, on NaCl has been investigated. The embrittlement by ozone and oxygen was found to be associated with the formation of a NaClO3 surface compound. In these cases the initial crack that was responsible for fracture (in a bend test) always nucleated at the corners between the tension and side faces. The behavior of air was very erratic and on certain days did not produce enzbrittlement. During these periods, crystals that had become embrittled by the ozone treatment completely recovered their ductility after a short exposure to the ambient atmosphere, It was established many years ago1 that considerable ductility could be obtained in NaCl single-crystal specimens if the crystal surfaces were dissolved in water either during or immediately prior to the test. The original interpretation of this effect by Joffe attributed the enhanced ductility to the removal of surface microcracks by dissolution. Later investigations2'3 have suggested that the exclusion of air from the specimen surface is the criterion for extensive plastic flow prior to fracture. The air em-brittlement in this later work was attributed to the diffusion of gaseous atoms into the surface layers of the crystal, thereby impeding the movement of dislocations. This model satisfactorily accounts for the reembrittlement observed after further air exposure subsequent to the water dissolution treatment. However, the situation has recently become more complex by the observations in several laboratories4-t that under certain conditions air exposure does not impair the ductility of NaC1. It has also been recognized5 that improper drying operations after water dissolution can leave surface precipitates that lead to embrittlement. Cleavage defects on as-cleaved crystals can often be another source of embrittlement. In the present work the effect of the gaseous atmospheres nitrogen, argon, air, oxygen, and ozone, on the ductility of rock salt was studied extensively. The embrittlement resulting from oxygen and ozone exposures was found to be associated with the formation of a NaC1O3 surface film. It is suggested that certain atmospheres, one of which often can be ambient air, which inhibit the formation or favor the decomposition of this compound, can promote ductility. Thus one aspect of the Joffe effect is certainly related to the removal of surface compounds or complexes by water dissolution. The effect of surface precipitates that remain after drying operations and of cleavage defects were also studied. In neither of the latter cases was the embrittlement as severe as that found with a NaClO3 surface layer. PROCEDURE AND SPECIMEN PREPARATION The nature of the embrittlement produced by the agents mentioned above was studied by means of microscopy, mechanical testing, and X-ray diffraction. Specimens were cleaved from large crystals of optical quality sodium chloride obtained from the Harshaw Chemical Co., and, except for those tested in the as-cleaved condition, were given a 15- to 20-sec immersion in distilled water followed by a rinse in absolute methyl alcohol. The specimens were then blotted on a soft, absorbent paper, and dried by a few seconds exposure to a stream of warm, dry air. Such a procedure was found to give a control surface which was microscopically free of residues. (A few crystals were intentionally painted with a concentrated NaCl solution in order to investigate the effect of surface residues). All specimens were of 0.140 sq in. cross-section. Crystals prepared in the above manner were immediately placed in a gas train where they could be exposed to the desired gases for preselected periods of time. For the oxygen and nitrogen exposures, pure reagent-grade gases were employed. The ozone was provided in the form of an ozone-oxygen mixture (approximately 10 pct ozone) prepared by passing commercial grade oxygen over a strong ultraviolet light source. All gases were dried prior to their introduction into the train. Since argon was found to be completely inert in its behavior (i.e., residue-free specimens that were exposed to argon were not embrittled), it was periodically utilized to check the control specimen surfaces as well as the condition of the gas train used for aging the specimens. After exposure to the gaseous media in question, the crystals to be used for the measurement of the strain to fracture were transferred from the gas train to a protective oil bath (without further exposure to the atmosphere) where the tests were conducted in three-point bending. The apparatus was so adjusted that the load could be applied at a constant, continuous rate. Other Snecimens from the gas train were deformed

Jan 1, 1962

By W. M. Merritts

A joint investigation by the Bureau of Mines and the Christopher Coal Co. at the Humphrey No. 7 mine, operating in the Pittsburgh coalbed in northern West Virginia, was undertaken to gain more insight concerning the hazardous emission of methane gas in mining, This report describes the equipment, procedure, and results. Horizontal bleeder holes drilled in the faces drained large quantities of methane, eliminating downtime of mining equipment. Also, larger quantities of methane were removed by forcing 14 to 25 g.p.m. water at 25 to 200 p.s.i. 5 pressure into the bleeder holes, In one infusion test a fluorescein dye was added to the infusion water; in later mining operations, the infusion water was traced for a distance of 1,500 feet. With vacuum pump applied to the horizontal hole the gas-flow rate increased, and the methane content decreased.

Jan 1, 1962

By Lindsay D. Norman

Eleven major pyrometallurgical processes and operations suggested for recovering manganese from domestic resources are described. These include seven pyrometallurgical processes that usually yield a ferroalloy or a product from which ferromanganese can be produced in one operation. The remaining four involve pyrometallurgical operations whose products require either an additional two-stage process to produce ferromanganese or chemical processing to recover a high-quality manganese oxide product.

Jan 1, 1962

By Michael G. Zabetakis

Vaporization of a solvent into an airstream at temperatures above the flash point of the solvent is hazardous if vapor is liberated at a rate that is sufficient to produce a flammable mixture. In may operations, the formation of such a mixture is prevented by rapid diluton of the vapors with air. The minimum air requirements for the dilution process are determined by the composition of the lower limit mixture at the temperature and pressure of interest. Because limits of flammability cannot always be calculated with sufficient accuracy for a proposed operation, they .rust often be determined experimentally. The present Bureau of Mines investigation was prompted by an application in which the lower limits of flammability of a number of solvent mixtures were required over a range of temperatures at atmospheric pressure. These limits were to be used along with available solvent-vaporization-rate data to establish minimum airflow rates needed to prevent the formation of flammable mixtures in an industrial process. Lower limits of flammability were determined for a number of mixtures containing methyl ethyl ketone, tetrahydrofuran, toluene, ethyl alcohol, and ethyl acetate in dry air-at atmospheric pressure and temperatures between 16° and 200° C. The experimental values were found to be in good agreement at with those predicted by Le Chatelier's law; variations with temperature were in fair agreement with those predicted by a modified Burgess-Wheeler law.

Jan 1, 1962

By James R. Kerr

Although metallurgical benefits of processing metals in a vacuum or reduced atmosphere have been realized for a hundred years, the problem of creating a vacuum in the range from 10-0 to 10-4 mm. of mercury in a moderately sized furnace chamber has been difficult to solve. The demand for these and lower pressures, with the advent of World War II, for separating the fission-able uranium isotope from its stable twin by the electromagnetic process, gave impetus to developing pumps capable of delivering extremely low pressures. With the release of data by the Atomic Energy Commission on methods of securing high vacuum in large equipment, steel companies took the initiative, and the growth of the vacuum-melting industry was assured. Vacuum-induction melting of steel in the United States began on a small scale in early 1945 and in 10 years grew to 60,000 pounds per month or 720,000 pounds per year. The years following 1954 showed tremendous expansion, culminating in 1958 in a capacity of more than 36 million pounds.

Jan 1, 1962

By R. W. Kraft

A back- reflection precession-type X-yay camera for determining the crystallographic orientation of the crystallites of both phases in small areas of thick specimens of polyphase alloys is described ad the geometry, advantages, and limitations of the apparatus are discussed. Metallographic obseg-vations of interfacial angles (or habit planes or growth direction are made on the same specimen so that the crystallographic and metallographzc orientation data call be directly correlated. An example of the application of tile technique to a unidi-~~ectionally solidified CuA12-A1 eutectic specimen is presented. The interfacial planes ad growth directions of each phase were established, and the orientation relationship between the phases was observed and found to be approximately intermediate between two previously reported relationships. The crystallographic interfacial relationship between two solid phases is an important parameter in a variety of metallurgical phenomena because of the energy associated with the interface and because this energy is at least partly associated with the way in which the two space lattices are in contact along the interface. In order to describe the interfacial planes in the crystallites of both phases it is necessary to determine the crystallographic orientation of each phase in a specimen relative to each other, and to directly correlate these data with met-allographic measurements from which the interfacial planes can be determined on the same specimen. The back-reflection Laue technique is the easiest way to determine the orientation of thick single crystals or large grains and the method can be combined with metallographic techniques to provide the necessary data, provided the reflections from each phase can be distinguished from one another. However, if the crystallites are small or of varying orientation or if one or both phases has a unit cell with less than the maximum symmetry, many overlapping and complex Laue patterns are recorded simultaneously and it becomes impractical if not impossible to interpret the photographs. All of these complexities were present in a unidirectionally so- lidified A1-CuA12 eutectic alloy1 for which a crystallographic analysis was desired. Consequently the method described here was developed since no known X-ray or electron diffraction technique had all of the following attributes which were required. 1) Method should yield data from which the crys-tallographic orientation of every crystallite or diffracting unit in the irradiated area can be determined. 2) Method should be adaptable to the study of small areas. Depending upon the degree of preferred orientation in the specimens, it should be possible to obtain reliable data in a reasonable length of time on irradiated areas as small as 1.0 or even 0.1 mm in diam. 3) Method should permit direct correlation of crystallographic data with microscopic orientation data pertaining to crystallite axes, habit, morphology, and growth directions as determined by optical microscopy. 4) method should be such that selected areas of large specimens can be easily studied. Trepanning of a small specimen (such as an electron microscope specimen) from larger specimens was undesirable since it would greatly increase the problem of correlating the crystallographic and microscopic directional data. Requirements 3 and 4 dictated that an X-ray back-reflection pinhole technique should be used on large samples, such as metallographic specimens which had previously been examined and analyzed for their microscopic characteristics. Similarly, requirement 2 could be satisfied by choosing a collimator of appropriately small diameter. Exposure times would not be excessive provided the detector were close enough to the specimen. Because of space limitations film was chosen in preference to a Geiger counter. Requirement 1 was fulfilled by using monochromatic radiation and providing enough additional degrees of freedom in specimen rotation to compensate for Bragg law restrictions on diffracted beams. DESCRIPTION OF APPARATUS The apparatus shown in Fig. 1 consists of a pin-hole collimator, (a), projecting through a rotatable circular film in a holder, (b), which records X-ray reflections in the back-reflection region. The specimen, (c), is mounted on the end of a shaft, (d), which is provided with an adjustment, (e), so that the specimen surface can be placed accurately on

Jan 1, 1962

By William J. Campbell

Expansion measurements of platinum, added as an internal standard, are used for thermal calibration of X-ray cameras and diffractometers. Accuracy of the temperatures derived by this technique depends on the precision of expansion measurements and the reliability of reference expansion data. Temperature measurements to ± 1° C. require ?d or ?a to be determined within ± 0.001 percent. Selected expansion data are concluded to be reliable to 2° C., 5° C., and 25° C., over the temperature ranges 0° C. to 700° C., 700° C. to 1,000° C., and 1,000° C. to 1,700° C., respectively. Tabular expansion values from 25° C. to 1,700° C. in 2° C. intervals were calculated from the following equation; Expansion, percent = [8.91 + 1.28 x 10-3(t-25) + 0.04 x 10-6(t-25) ] [t-25.104 ] These tabular values facilitate future corrections of published temperatures as more reliable expansion-temperature data become available.

Jan 1, 1962

By Michael G. Zabetakis

The spillage of liquid diethyl ether in rooms at floor level and 3 feet above the floor resulted in flammable vapor-air mixtures in the immediate vicinity of the exposed liquido The liquid temperature was found to decrease by as much as 35° C., with a resultant decrease in vaporization rate. A search of the literature yielded numerous references to unstable peroxide (residue) formed by the autoxidation of ether. Such residues appear to constitute an explosion hazard in the condensed state.

Jan 1, 1962

By Walter C. Lorenz

In connection with its renewed study seeking solutions to problems created by release of acid water from bituminous coal mines, the Bureau of Mines recently surveyed reports already written on the subject. This publication is based on that search. The Problem Poor distribution of water is evident on an ordinary geographic map of the United States. The more abundant supplies of surface water appear to be centered in the northeast, the southeast, and the central humid areas of the country. It is in the midst of this abundant surface water, in the Ohio River Valley, that most of the bituminous coal is mined. Varied industry has located in the valley to use the coal and the river. The coal is a source of power and o raw material. The river provides transportation for raw and finished materials; equally important, it provides the water that is used for cooling and processing in manufacturing. It also serves as a vehicle for the disposal of waste.

Jan 1, 1962

By R. Barany

In this paper, closed expressions have been obtained for the frequency spectrum of a Born-Karman square lattice in terms of elliptic and hyperelliptic integrals. This work is part of continuing research by the Bureau of Mines with the thermodynamic properties of metals and minerals. Although other workers have obtained various types of approximations for the general case of the frequency spectrum of a square lattice, no one previously has obtained closed analytic expressions for this spectrum. To understand the optical and thermodynamic properties of crystals, several investigators have studied the distribution of frequencies of normal modes of vibration of the crystal lattice. Born and Karman3 laid the foundation for the theory of lattice dynamics and obtained detailed results for the case of a one-dimensional lattice. Blackman4 used numerical techniques to estimate the frequency distribution of a two-dimensional square lattice. Mbntroll5 analytically determined the frequency distribution of a square lattice for a particular value of the force constants. He also studied the more general problem and obtained some analytic approximations, using the method of moments. However, the calculations by this method were so difficult that it was not always practicable to carry them out. Van Hove6 and Montroll7 studied the nature of the singularities in the frequency spectrum of both a two and

Jan 1, 1962

By R. L. Lincoln

The effects of adding from 1 to 50 atomic percent (a/o) to vanadium were investigated by the Bureau of Mines. Properties studied included as-cast and annealed hardness, microstructure, fabricability at room temperature and elevated temperature, tensile strength, electrical resistivity, and oxidation resistance at 625° and 800° 2. Additions of small amounts of hafnium resulted in lessened as-cast hardness, decreased electrical resistivity, impaired roll- ability, increased oxidation resistance, and greater tensile strength. Larger amount of hafnium caused greater as-cast hardness, increased electrical resistivity, further impaired rollability, continued increase in oxidation resistance, and lessened tensile strength. INTRODUCTION The purpose of this study was to determine the effect of hafnium additions on the properties of vanadium and to learn if this binary alloy had any special or unusual properties. This investigation is a part of a larger research project in which new and expanded uses of vanadium are being sought. Domes tic vanadium is found frequently in combination with uranium, and because of the demand for uranium as a nuclear fuel, there now exists a surplus of vanadium-bearing minerals and vanadium pentoxide as a byproduct of uranium production. Primary principles of conservation demand that greater use be made of this readily available surplus; finding suitable metals to alloy with vanadium to enhance its properties is one way to increase its utilization. This report is the result of an investigation of the effects on the properties of vanadium when hafnium is added in amounts from 1 to 50 a/o.

Jan 1, 1962

By Alla D. Mah

The need for more and better basic thermodynamic data for the oxides of many of the rare metals is evident to anyone who attempts thermodynamic calculations involving these substances. In continuation of a Bureau of Mines program to meet this need, this paper reports new experimental values of the heats of formation at 298.15° K. of the hexagonal crystalline variety of germanium dioxide and germanium dioxide glass. The values were obtained by means of combustion calorimetry and sodium hydroxide-solution calorimetry. The calorimetric results also made possible the derivation of values for the heat and entropy of fusion of hexagonal germanium dioxide at its melting point. The newly measured data were combined with previously known entropy and high-temperature heat content values to obtain heats and free energies of formation of germanium dioxide (in the hexagonal crystalline, glassy, and liquid states) over the temperature range from 298.15° to 2,000° K.

Jan 1, 1962

By R. M. Waterstrat

X-ray diffraction and metallographic examination of binary Mn-rich alloys with Ti revealed the presence of intermediate phases in this system. A binary R phase has been identified and also a phase having an a-Mn type structure. The X-ray pattern of the phase TiMn3 is presented and a tentative phase diagram for the Mn-rich portion of this binary system has been constndcted. MANGANESE-rich alloys with titanium have been subjected to thermal analysis at temperatures down to 1100°C by Hellawell and Hume-Rothery.1 Their results indicate the existence of an intermediate phase TiMn3 in this binary system. This phase appears to coexist with the Laves phase TiMn2, and with terminal solid solutions based on the allotropes of manganese, at least down to 1100°C. The above investigators did not attempt to determine the crystal structure of this phase, however. Since, by analogy to the binary systems Mn-V and Mn-Cr3 one might expect to find a phase in this region of the diagram, it seemed desirable to obtain X-ray diffraction patterns of alloys in the concentration range in question, in order to ascertain whether the sigma phase or related structures occur. EXPERIMENTAL PROCEDURES Alloys were prepared by arc-melting electrolytic manganese and iodide titanium in a water-cooled copper crucible under a helium atmosphere. Excess manganese was added to each melt in order to allow for losses incurred during melting. The alloys were then wrapped in molybdenum foil and sealed in evacuated quartz tubes for annealing at various temperatures, as shown in Table I, followed by quenching in cold water. Although the inside of the tubes showed evidence for some loss of manganese from the specimen during annealing, there was no evidence of any reaction between the specimen and either the molybdenum foil or the quartz tube at these temperatures. It was later found that the manganese loss was considerably reduced by annealing these alloys in sealed quartz tubes containing one atmosphere of purified argon. As an added precaution the surface of each specimen was ground off before crushing the alloys to -270 mesh powder, using a hardened steel mortar and pestle. X-ray powder patterns were obtained using either FeKa or CrKa radiation in an asymmetrical focusing camera, which gave excellent dispersion of the closely spaced lines. Pictures were also obtained using a Debye camera of 5-cm radius which provided data in the angular region not covered by the focusing camera. The alloy specimens were polished and examined metallographically, using an etchant consisting of 60 pct glycerine, 20 pct nitric acid, and 20 pct hydrofluoric acid. The 10-g buttons were in each case broken in half and found to be well-melted and free of any gross segregation. One half of certain alloy buttons was submitted to chemical analysis in the "as-cast" condition. No appreciable change in composition seemed to occur during annealing . RESULTS The X-ray pattern of alloy Ti1.17Mn0.83 was found to agree well with that of the ternary R phase which was first found in the Mo-Cr-Co system,' and re-

Jan 1, 1962

By R. C. Bates

Uranium mine workers? daily exposure to radon daughters was estimated by two methods of sampling, detailed and spot-check. Both methods involve time- weighting measured exposure levels to arrive at an average exposure figure. Random sampling, or sampling without regard for the duration of exposure, has proved inadequate for estimating average exposure levels. During the first phase of the study, the breathing zones of eight workmen in three underground uranium mines were sampled for an entire shift; 20 to 36 radon-daughter samples were collected per man-shift, Analysis of these data indicated that a suitably accurate estimate of the full-shift exposure could be made by time weighting a considerable lesser number of representative radon-daughter samples. This analysis led to the spot-check method of estimating full-shift exposures to radon daughters. Additional detailed studies were made in seven mines to Learn more about the full-shift radon-daughter exposures and to test the spot-check method, In all, 617 radon-daughter samples were taken in 10 underground uranium mines during 26 man-shifts, and the spot-check method was tested 35 times.

Jan 1, 1962

By C. J. Chindgren

Upgrading of commercial red cake and recovery of vanadium oxide from uranium-vanadium mill solutions were investigated by the Bureau of Mines. Alternative procedures potentially useful for manufacture of high-quality vanadium oxide at the mill site were explored and developed. The simplest and best procedure for converting commercial red cake containing about 10 percent combined sodium and potassium oxides (Na20) (K20) into a 98- to 99-percent vanadium pentoxide (V205 product appeared to be a metathesis in an ammoniacal solution of ammonium sulfate. Molybdenum, as well as the alkali metal oxides, was removed from the red cake by this procedure at a modest expenditure of labor and reagents. When preparing vanadium oxide of higher grade, it was necessary to dissolve the red cake and reprecipitate the vanadium as ammonium metavanadate. Calcination at 450° C, decomposed the metavanadate and yielded oxide of about 99.5 percent V205. By recyrstallizing the metavanadate before decomposition, an oxide product approaching 99.9-percent purity was obtained.

Jan 1, 1962

resident Schloss called the meeting to order at 9:30 a.m. Bob Dean, manager of the Hotel Colorado, gave a brief explanation of hotel policies governing the swimming pool, and also extended an invitation to the Institute to return in 1963, and stated that the dates June 30 through July 3 were available for next year. He also stated that June 28 through July 1 were available for 1964. He felt that holding the convention during the 4th was not good policy, and that dates prior to or following the 4th would make for better attendance. John A. Reeves, chairman of the Resolutions Committee presented the following resolutions: RESOLVED: That the members of the Rocky Mountain Coal Mining Institute in convention assembled, hereby ratify and confirm all official actions of the officers, the Executive Committee and other committees of the Institute between June 28, 1961, and the present time.

Jan 1, 1962

By Robert K. Koch

Laboratory-scale studies on defluorination of natural and synthetic fluorspars by pyrohydrolysis at 1,500° C. were made to determine the feasibility of developing a process for producing hydrogen fluoride from siliceous fluorspars. It was found that the reaction (at 1,500° C.) is not promising for process development, even though a silica-free offgas can be generated. The primary difficulty is the low hydrogen fluoride content of the offgases; an HF content of 6 percent was the best achieved. Previous research by the Bureau of Mines has demonstrated that offgases averaging 27 percent hydrogen fluoride can be produced under carefully controlled conditions at 1,280° C. The lower temperature process is a better method for production of HF. However, charges in which the CaF to Si02 mole ratio varied from 0.4 to 2 could be processed with similar results. Also, combined alumina and ferric oxide contents up to 25 mole-percent did not noticeably alter the rate of defluorination. Therefore, virtually any natural siliceous fluorspar would respond in essentially the same manner when exposed to water vapor at 1,500° C.

Jan 1, 1962

By S. J. Aresco

The Bureau of Mines has been active in promoting the purchase of coal for Government use under specifications that define the requirements in terms of heating value of the coal, expressed in British thermal units, and the composition as shown by proximate analyses. To these, when required, are added the ash-softening temperature, the free-swelling index, and the Hardgrove grindability index. Under most of these specification contracts the bidders guarantee the quality of the coal, and that guaranteed by the successful bidder becomes the standard of his contract. The deliveries are sampled in accordance with instructions 5/ issued by the Bureau of Mines; the samples are analyzed in the Bureau laboratory to determine whether the coal is of the quality guaranteed by the contractor and, if it is not, a price adjustment is made. Analyses of the delivered coal and tipple samples (samples collected at mine tipples as coal is being loaded into railroad cars or trucks) provide valuable data for use in evaluating future bids. In addition, the continuous sampling of coal as delivered is a check on the practical results obtained in burning the coal.

Jan 1, 1962

By Clark F. Grain

These investigations were undertaken as part of the Bureau of Mines program for the development and evaluation of high temperature nonmetallic materials. This report consists of thermal expansion and phase inversion measurements by high-temperature X-ray diffractometry on the principal oxides of beryllium (BeO), calcium (CaO), titanium (TiO2 ), zirconium (ZrO2 ), hafnium (HfO2), and thorium (ThO2); all were high-purity commercially available oxides. Thermal expansion values were calculated from unit cell dimensions measured at selected temperatures. Expansion was determined parallel to each major crystallographic axis for the anisotropic oxides: BeO, TOi2, ZrC2, and HfO2. Combined random and systematic errors in the thermal expansion values are considered to be less than 3 percent of the total expansion at 500° C. and approximately 2 percent at 1,000° C. No hysteresis in the expansion curves was noted between heating and cooling cycles. The Bureau's values were compared with published expansion measurements obtained by X-ray diffraction, dilatometric, interferometric, and telemicroscopic techniques. For anisotropic oxides, average linear expansion values were calculated from the volume expansion.

Jan 1, 1962

By J. E. Dorn, S. K. Mitra

The low -temperature tensile and creep behaviors of single crystals of copper were evaluated and analyzed in such a manner as to provide an estimate of the separate contributions of short-and long-range stress fields to strain-hardening. Furthermore, the average force-displacement diagram for thermally activated intep-section of two dislocations was estublished. This diagram plus a knowledge of the variation of dislocation spacing and the long-range back stresses with strain permits on accurate prediction of creep rates. The calculated activation energy for intersection under conditions of a constant strain rate increases linearly with the absolute tempevatus-e as required by theory. AN understanding of the detailed mechanisms for strain hardening constitutes one of the principal unsolved problems in dislocation theory. Two major models for strain hardening have been advanced in the past. The one that has received greatest attention assumes that strain hardening arises exclusively from long range interaction stresses between moving dislocations and piled-up arrays of blocked dislocations on the slip planes. This type of interaction was first announced by Taylor' who revealed that the back stress fields due to a simple uniform array of positive and negative dislocations entrapped in the deformed crystal would result in parabolic hardening. Shortly thereafter Andrade and Henderson" demonstrated that the strain hardening of fcc single crystals was not parabolic, as previously thought, and finally it was recognized that a typical stress-strain curve consisted of three successive stages of deformation, niz., the easy glide, Stage I, linear hardening, Stage 11, and the parabolic hardening, Stage 111, ranges. The objections to Taylor's somewhat na'ive model, which were presented so forcefully by cottrell; were largely removed by the more realistic details incorporated in Mott's analysis.5 But because Mott's theory for hardening via long range stress fields gave somewhat analogous results to that of Taylor's (inasmuch as it also predicted a parabolic rate of strain hardening whereas the observed rate of strain hardening in Stages I and I1 were linear), it was not widely accepted. Major consideration was therefore given to models, such as those which were advanced by Friedel and seegere that were formulated for the ad hoc purpose of yielding linear rates of strain hardening. The second major thought regarding strain hardening is based on the concept that it arises principally from short-range stress fields due to the interactions between intersecting dislocations. Cottrell and stokes7 showed, several years ago, that the constancy of the flow stress ratio at two temperatures regardless of the strain was inconsistent with the concept that strain hardening arose exclusively from long-range back stresses. The argument that strain hardening was primarily due to local interactions of intersecting dislocations was presented in considerable detail by asinski.' Extending Basinski's method of analysis of the intersection process, Mitra, Os-borne, and dorn recently demonstrated that indeed the strain hardening in aluminum single crystals arises principally from local effects coincident with intersection; however, these conclusions, too, must be modified, as will be shown later in this report. The present investigation, devoted principally to the low-temperature deformation of copper single crystals, was initiated in an attempt to ascertain whether or not the same conclusions arrived at for aluminum also apply to metals, such as copper, which have much wider stacking faults. It was soon observed that the strain hardening in copper could not be attributed exclusively to local effects between intersecting dislocations. Previously no analytical method for arriving at the possible simultaneous contributions of long-range stress fields and localized forces on intersecting dislocations was available; consequently, the separation of these two factors could not be readily accomplished. In the present report a method of estimating the separate contributions of each of these two factors to strain-hardening will be presented. The authors will show that both long-range stress fields of the type contemplated by Seeger and Friedel as well as short-range forces of the type considered by Basinski are responsible for strain hardening in fcc metals at low temperatures. This method of analysis also accounts for, in a satisfactory way, the effect of stress, temperature, and strain on the creep rate under constant stress. Furthermore, in the course of presenting their methods of analysis the authors will also reveal the rather complete agreement of their experimental data with the concepts of the theory for thermally activated intersection of dislocations. INTERSECTION MODEL As shown by seegerl0 the strain rate arising from thermally activated intersection of dislocations is given by

Jan 1, 1962