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By R. Ruka, E. A. Gulbransen

ONE of the interesting questions in the understanding of the reaction of iron with oxygen is the kinetics and the mechanism of the crystal structure changes occurring in the formation and breakdown of the oxide film. In a recent work' the electron diffraction method was applied to the study of the solid phase reactions occurring internally in the oxide film on iron above 570°C and under vacuum conditions. The higher oxides which form under oxidizing conditions are reduced internally by the diffusion of iron into the oxide leaving the bulk of the oxide FeO (wüstite). This paper will ask and consider three questions. These are: (1) What is the nature of the depressed transformation temperature for the Fe3O4 + Fe ? 4Fe0 reaction in very thin oxide films?; (2) What is the mechanism of the forward transformation of Fe3O4 to FeO at or near 570°C?; and (3) What is the nature and mechanism of the slow reverse transformation of FeO to Fe3O4 and Fe below 570°C?. The composition of the oxide as well as its electrical, magnetic, mechanical, and chemical properties depends upon the kinetics of these reactions. Literature Survey The composition of the oxide film on pure iron at temperatures up to 570°C has been studied extensively by the electron diffraction method. Nelson,' Jackson and Quarrell,3 and Gulbransen and Hick-man4 have shown that Fe3O4 and a-Fe2O8 are formed in the temperature range of 225" to 570°C, while y-Fe,O, is most likely formed below 225°C for long oxidation times. In very thin films FeO (wüstite) is found to form at temperatures as low as 400°C, and its existence depends essentially upon the extent of initial oxidation. FeO is not found in the formation of thick films below 570°C. On the other hand X-ray5 and micrographic8 studies show that Fe3O4 may exist as the main com-ponent in thick films up to 650°C, well above the equilibrium temperature for the reaction Fe3O4 + Fe ? 4FeO. The kinetics of the forward and reverse trans-formations of the reaction Fe3O4 + Fe ? 4FeO have not been studied in oxide films. However, analysis of the data of Gulbransen and Hickman4 on the heat-ing and cooling of iron oxide films of known thick-nesses in high vacua shows that the forward reac-tion proceeds rapidly even for a 4000 A film at temperatures of 575" to 600°C. The reverse reaction or decomposition of wüstite (FeO) occurs at tem-peratures below 450°C. Thus, there appears to be a slow process in the decomposition which is in marked contrast to the rapid forward reaction. The decomposition of a bulk sample of FeO free from the metal has been studied extensively by Chaudron, Benard and coworkers using the micro-graphic, X-ray diffraction, and thermomagnetic methods. Chaudron7,8 first observed that the de-composition of FeO (wüstite) below 570°C occurs by the reaction 4FeO ? Fe3O4 + Fe. Later work by Chaudron and Forestier5 showed that the rate of de-

Jan 1, 1951

By D. Turnbull, J. H. Hollomon, J. C. Fisher

Application of the concepts of nu-cleation and growth to the analysis of experimental transformation data has led to valuable descriptions of phase transformations, an outstanding example being the transformation austenite —* pearlite which has been examined with particular care by Mehl and co-workers.&apos;-5 In addition to the pearlite transformation, the proeutectoid fer-rite and proeutectoid carbide transformations are known to proceed by nucleation and growth. Martensite, on the contrary, until recently was thought to form by a mechanism involving neither nucleation nor growth; however, extension of standard nucleation theory6 suggests that martensite, bain-ite, and the other products of austenite decomposition all grow from nuclei in the parent phase. The theory that martensite forms by nucleation and growth is strongly supported by recent experimental work of Kurdjumov and Maksimova.7 The concepts of nucleatioli and growth have been fruitful also in providing a sound basis for quantitative theoretical treatments of the kinetics of phase transformations. For example, Volmer and Weber8 and Becker and Döring9 developed the theory of nucleation from fundamental considerations to a point where excellent agreement was obtained with the results of experiments on the condensation of supercooled vapors. As a result of their analysis, the kinetics of vapor-liquid transformations now can be predicted. It seems probable that application of the theories of nucleation and growth to a quantitative study of austenite decomposition similarly will clarify the nature of the individual transfor: mations involved, and will enable the calculation of austenite transformation kinetics. In the present paper, the theories of nucleation and growth are applied to the austenite ? martensite transformation in steels. The analysis begins with a discussion of nucleation in single component systems. Martensite appears to be coherent with the parent austenite, hence the nucleation theory is modified to include the effects of elastic distortion. Nucleation in the two component iron-carbon system then is discussed, for most steels are primarily alloys of these two elements. Finally, M. temperatures and martensite transformation curves are calculated for each of several alloy steels of varying carbon and chromium content, and are compared with those determined experimentally by Lyman and Troiano10 and Harris and Cohen.11 Nucleation Theory NUCLEATION IN SINGLE COMPONENT SYSTEMS6,12-14 The work required for reversible formation of a region of phase within the parent a phase is expressed conveniently as the sum of two terms: W1 = Aa, the product of the area of the interface and the interfacial free energy, and W2 = VAf, the product of the volume of the region and the free energy increase per unit volume associated with the transformation. The total work is therefore W = Aa + VAf. When a is more stable than ß, Af is positive and W increases without limit as the volume increases. The transformation a ?ß does not occur. It is nevertheless true that small regions of phase ß enjoy temporary existence here and there in the a. The equilibrium number of ß regions of given size is proportional to exp(— W/kT) per unit volume of a, assuring that larger (ß regions occur with diminishing probability. When a is less stable than ß, Af is negative and W passes through a maximum as V increases. Assuming for simplicity that regions of ß are spherical, as is true when the interfacial tension is isotropic and there are no elastic strains, W = 4r2a + (4/3)*r3Af The maximum value of W is W* = 16iro3/3Af2 [1] for regions with radius r* = -2o/Af. [2] For single component condensed systems it has been shown14 that the steady rate of nucleation of 0 per unit volume of untransformed a is nearly proportional to exp[- (W* + Q)/kT] where Q is the activation energy for the unit processes of adding or removing one atom from an embryo or nucleus. If To is the temperature at which a and ß are in equilibrium, the rate of nucleation is a maximum at a temperature 0 < T < To where (W* + Q)/kT is a minimum. P regions smaller than critical size are called embryos; they tend to grow smaller and disappear, only exceptionally growing larger. Regions equal to or larger than critical size are called nuclei. A critical size nucleus may grow indefinitely large or may shrink back to a, either process decreasing the free energy of the region.

Jan 1, 1950

By B. N. Bose, M. F. Hawk

SINCE Davenport and Bain&apos; introduced the isothermal transformation technique for the study of austenite decomposition in steels, a new field of investigation has opened up. Extensive research has been carried out on many different steels, but relatively little work has been done on eutectoid transformations in analogous alloy systems. The researches of Smith and Lindlief,² Mack,³ and Klier and Grymko²0 on the beta-phase transformation in copper-aluminum alloys, of Hibbard, Eichelrnan, and Saunders4 and Smith5 on the kappa-phase transformation in copper-silicon alloys, of Chaudron and Forester6 on the decomposition of "FeO," and of Wasserman7 on similarities between the iron-carbon, copper-aluminum, copper-tin, and copper-beryllium systems essentially comprise the field. The iron-nitrogen system, in view of its remarkable similarity to the iron-carbon system, is particularly attractive for the study of eutectoid decomposition. The present investigation is concerned with the study of isothermal transformation, proceeding by the familiar nucleation and growth processes, and of martensitic transformation characteristics of pure iron-nitrogen alloys. The kinetics of transformation and the morphology of the transformation products have been investigated, for these must be the factors determining the properties and behavior of the final product. The Iron-Nitrogen System he binary iron-nitrogen phase diagram has been a matter of considerable disagreement among vari01.1s investigators. However, the phase diagram according to Eisenhut and Kaupp8 and Lehrer10 is now considered essentially correct as reproduced in fig. 1. The important values, 2.35 pct nitrogen and 591°C, for the co-ordinates of the eutectoid point (obtained from this diagram and used in the re- search to be described) were confirmed in a concurrent study of Paranjpe, Cohen, Bever and Floe." The eutectoid decomposition involves the transformation of the ? face-centered cubic interstitial solid solution of nitrogen in iron to the a body-centered cubic interstitial solid solution of nitrogen in iron and the ?&apos; nitride of iron. This nitride is essentially the compound Fe,N; it also possesses a face-centered cubic lattice but a considerably larger one than the ?; the nitrogen atoms in ?&apos; are arranged in an ordered way in the centers of the unit cubes.8,10,11 A martensitic structure has also been reported8,12 in iron-nitrogen alloys and was studied in the research to be described here. Materials and Methods The specimens used in this investigation were prepared by nitriding "pure" iron. This iron was supplied by the Westinghouse Research Laboratories and is the product bearing their trade name "Puron"; it contains about 0.04 wt pct total impurities, the major portion of which is oxygen. Specimens were ribbons several inches long, a tenth of an inch wide, and 0.125 mm thick; this was the

Jan 1, 1951

By C. Alstetter, V. Kerlins

By using alloys with subzero Ms temperatures, this investigation demonstrates that the amount of decomposition of martensite during the quench from austenite may be considerable and especially so in specimens of large cross -sections and high Ms temperatures. The activation energy for decomposition as measured dilutometrically is PREVTOUS investigations of the initial decomposition of Fe-C system martensite have invariably been limited to alloys having M, temperatures above a function of the amount of transformation which has taken place. The amount of transformation is a linear finction of log time. A correction term to the activation energy is derived for dilatometric measurements in which no end-point of the transformation is detected. room temperature. In such alloys the martensite is tempered during the quench to an extent dictated by the quench rate and temperature of formation. This tempering, called quench-tempering, Q-tempering, self-tempering, or auto-tempering, although frequently acknowledged, has not been studied or treated quantitatively. To do so one should obtain absolutely untempered martensite and study its decomposition. This as-formed martensite could be obtained either by extremely rapid quenching, requiring very thin specimens, or by lowering the martensite formation temperature range. The second alternative is more effective, because

Jan 1, 1963

By J. S. Kirkaldy, G. R. Purdy

THE formation of ferrite in supersaturated aus-tenite has been the subject of considerable speculation and investigation. Aaronson has recently reviewed the data pertinent to this reaction.&apos; Since these data in all cases refer to ternary or high-order alloys it is not possible to put them to the test of simple binary diffusion formalism. It has not, therefore, been possible to make a certain statement as to the controlling mechanisms in the process. An assessment of the difficulties inherent in the conventional statistical metallographic approach suggested that a study of the problem by means of a macroscopic two-phase diffusion couple might contribute useful information. Accordingly, such a couple was synthesized, and the rate of motion of a ferrite-austenite phase boundary (the growth of an austenite layer at the expense of a ferrite layer) was determined. Wagner originally produced a diffusion solution applicable to the motion of a planar phase interface in a binary diffusion couple, assuming local equilibrium throughout the diffusion zone. This solution, which is stated free of typographical error* in Ref. where a is the position of the interface in A space (A = x/fi), C; and CL1 are the equilibrium inter-facial concentrations in phases I and 11, C: and C*1 are the initial bulk concentrations in phases I and 11, and & and are diffusion coefficients (assumed constant). If a diffusion couple consisting of homogeneous layers of ferrite and austenite in equilibrium is raised to a higher temperature, the austenite layer will grow at the expense of the ferrite. Provided that the thickness of the ferrite layer is much less than the diffusion length of carbon in ferrite, we can set , so that Wagner&apos;s solution reduces to

Jan 1, 1963

By E. A. Gulbransen, K. F. Andrew

THIS paper. will present the results of our studies on the kinetics of the gas phase reactions of co-lumbium and tantalum with O2, N2 and H2. Studies on zirconium and titanium have been previously reported.9,11 Due to their high melting points and their many excellent physical and chemical properties, colurn-bium and tantalum have been finding their places as useful metals in science and industry. Chemically the metals are very inert to gas and liquid phase corrosion at room temperature. However, at moderate temperatures of 250°C and higher the metals react readily with oxygen and hydrogen. It is of interest to study the gas phase reactions of these metals for the following reasons: (1) to compare the rates of the several reactions with those of other metals and to correlate the rate data with theory and structure predictions, (2) to add basic information on the practical difficulties of the reduction, refining and working of columbium and tantalum, (3) to anticipate new uses for the metals and (4) to understand the role that the metals play as components in high temperature alloys. Literature Survey A number of papers exist in the literature on the gas phase reactions of columbium and tantalum with O2, N2 and H2; however, only fragmentary data have been reported on the kinetics of these reactions. Although the free energy of formation of the oxide Ta2O520at 25°C has been determined and some thermodynamic work has been reported on columbium and its oxides, the data are not sufficient to make equilibria calculations at elevated temperatures. Oxidation: 1. Kinetics: The rate of oxidation of columbium and tantalum has been studied by McAdam and Geil23 using the interference color method. Tantalum is reported to oxidize more slowly than columbium, zirconium and iron. The amounts of oxidation of columbium after 20 hr in air for several temperatures are reported by the Fansteel Metallurgical Corporation.36 Columbium starts to oxidize in air at about 200°C. The oxide is said to be adherent and prevents further oxidation until the temperature is raised. Columbium is reported not to become brittle on heating in air for short periods like tantalum because the oxide film prevents further reaction. The columbium oxides dissolve into the metal when heated in a vacuum at temperatures between red heat and 1200°C. Above 1200°C the oxides are reported to evaporate. Columbium, in the oxide free state, is an active getter in vacuum tubes. 2. Preparation and Structure: G. Grube, O. Kuba-schewski and K. Zwiauer15 have studied the decomposition of Cb2O5 in argon. They find that CbO2 is formed slowly at 1150° and rapidly at 1300°C. Cb2O5 can be reduced to CbO2 by moist H2. The reduction of this dioxide to the lower oxides is rapid. By varying conditions CbO2, Cb2O3, CbO and Cb2O can be formed. CbO2, CbO and Cb2O have independent lattices while Cb2O3 is a stoichiometric mixture of CbO and CbO2. In a later paper O. Kuba-schewski" has shown that CbO is cubic and that CbO2 has a rutile type of lattice. The most exhaustive work on the oxides of columbium is that of G. Brauer.8 The number and constitution of the solid phases in the binary system Cb-O were investigated by the preparative, analytical and X ray methods. He indicates that only the oxides Cb2O5, CbO2 and CbO exist with limited regions of homogeneity. The solid oxide Cb,O, exists

Jan 1, 1951

By E. A. Gulbransen, K. F. Andrew

The gas-metal reactions of zirconium are very interesting. The metal is extremely stable at room temperature to reactions with the several gases present in air and the metal will stay bright indefinitely. However, at temperatures of several hundred degrees higher the metal reacts readily with oxygen, nitrogen and hydrogen. This behavior, in addition to the fact that zirconium is one of the higher melting point metals which might have high temperature applications under the proper conditions, resulted in the work reported in this communication. There are several factors which indicate that zirconium might have good oxidation resistance at elevated temperatures. These are: (1) the high melting point of approximately 1860°C, (2) the high melting point of the oxide of approximately 2675°C, (3) the high degree of thermodynamic stability of the oxide to chemical reaction and the low decomposition pressure of the oxide and (4) the possible formation of a continuous oxide film since the volume ratio of oxide to metal is greater than unity. The unfavorable factors are: (1) the metal reacts to form nitrides, hydrides and carbides, (2) the oxide is soluble at elevated temperatures in the metal and (3) the oxide ZrO2 undergoes crystal structure transformations at high temperature. The oxidation resistance of this metal is not only a question of the rate of film formation but is complicated by the fact that the oxide and other reaction products dissolve in the metal which in turn will affect the physical and mechanical properties of the metal. The protection of the metal to nitride formation must be considered separately from the oxide problem. One unfavorable factor is that the volume ratio of the nitride to the metal is about unity. This indicates that a discontinuous film might be formed. This paper will present measurements on the rates of reaction of the metal with O2, H2 and N2 over a wide temperature and pressure range. The reaction in high vacuum and the stability of the several compounds formed will be presented. The results are correlated with fundamental rate theory and with the physical and chemical structure of the metal and film. Literature Although many papers have been published on the chemical reactions of zirconium with various gases, comparatively few are concerned with the protective nature of the metal and its reactions at normal pressures. The studies in the pressure range below 0.01 mm of Hg gas pressure are largely of interest in the nature of the adsorption of gases by hot filaments in high vacuum apparatus. The reactions of zirconium in this pressure range have been reviewed by Fast8 and by RaynOr.27 In spite of certain differences of opinion as to the maximum adsorption temperatures for various gases, the low pressure range is qualitatively understood. Some of these papers will be mentioned briefly here. 1. LOW PRESSURE Ehrke and Slack&apos; find that oxygen reacts above 885°C and hydrogen above 760°C. Nitrogen does not react up to a temperature of 1527°C. Fast9 on the other hand observes that oxygen is absorbed above 700°C and nitrogen at temperatures exceeding 1000°C. Hydrogen is absorbed from 300" to 400°C and liberated between 500" and 800°C. It is readsorbed at 862°C and released above 862°C. Hukagawa and Nambo22 find a rather complicated picture for the absorption of oxygen. A rapid initial absorption is found between 180" to 230°C. Further oxygen is not taken up until a temperature of 450°C is reached. The optimum temperature for complete absorption is 650" to 700°C. Nitrogen is found to be completely adsorbed at 600°C. However some of the gas is evolved at higher temperatures. Their data on the absorption of hydrogen indicate some of the gas is removed at 550°C. Guldner and Wooten17 in a study of the low pressure reactions of zirconium with various gases observed that the reaction with oxygen occurs at temperatures above 400°C and that the oxide is formed. The reactions with carbon monoxide and carbon dioxide occur rapidly at temperatures of about 800°C with the oxide and carbide being formed. Zirconium reacts at temperatures of 400°C slowly and at 800°C rapidly to form the nitride and with hydrogen and water at 300°C to form the hydride and a mixture of the oxide and hydride respectively. 2. NORMAL PRESSURE DeBoer and Fast3 in a study of the electrolysis of oxygen in zirconium find that the metal absorbs up to 40 at. pct of oxygen without forming a new phase. The solubility of nitrogen in the lattice has been studied by de Boer and Fast4 and Fast10 and is found to be considerable. At higher temperatures the oxide dissolves in the lattice at an appreciable rate according to Fast10 and the zirconium surface becomes active. De Boer and Fast4 and Hägg18 have studied the solubility of hydrogen and find that at room temperature the solubility corresponds to ZrH1.95 Desorption occurs on lowering the pressure. Hydrogen is stated to be more soluble in the ß-form and the

Jan 1, 1950

By R. K. McGeary, B. Lustman

Orientation relationships and rates of annealing of 97 pct cold rolled zirconium have been studied by X-ray techniques, metallography, and by hardness measurements. The process of annealing occurring by the formation of domains, and their subsequent growth without recrystallization, is demonstrated. NUMEROUS investigators1-&apos; have revealed sub-grain formation after annealing cold worked metal single crystals and have generally described the results in terms of a dislocation mechanism of polygonization.5,6 in heavily cold rolled polycrystal-line aluminum the first stages of heating cause an apparently spontaneous subdivision of regions of the deformed matrix into a great number of slightly disoriented domains followed or accompanied by rapid growth of certain domains to form a recrystallization texture.7,8 In the present investigation the isothermal rate of annealing of cold worked polycrystalline zirconium has been studied by X-ray techniques, metallography, and by hardness measurement. It will be shown that, rather than by the usual nucleation and growth mechanism,"12 the process of annealing can best be explained by the formation of domains early in the annealing treatment and the subsequent growth of these domains without recrystallization. Experimental Procedure All the experimental work was performed on an arc-melted ingot of high purity zirconium crystal bar made by Westinghouse in a production scale deBoer unit. The weight percentage of impurities in the zirconium were as follows: C, 0.04; Fe, 0.05; Hf, 0.014; W, 0.01; Ti, Ni, and Al, 0.003; Si and N, 0.002; Cr and Cu, 0.001. Metallographically the zirconium showed only a single phase. The 4 in. diarn ingot was forged at 760°C to a 1 1/2x3 in. plate and was then rolled at 760°C to 0.150 in. thickness and annealed at this temperature for 20 min to produce an equiaxed grain structure of about 0.1 mm average grain diameter. The hot rolled plate was roller-leveled, surface ground to 0.135 in., cold rolled 83 pct reduction in thickness on a two-high mill, and then to a total reduction of 97 pct on a Sendzimir mill. The 0.004 in. strip material so produced received no subsequent mechanical treatment. Specimens % in. square were sheared from the rolled strip and isothermally annealed at 104 mm Hg in an all glass vacuum system equipped with a Vycor furnace tube. The temperature data presented are the average temperatures during the runs and did not vary more than about k3"C. X-ray Diffraction Methods: When zirconium is drastically cold rolled, a high degree of preferred orientation results in which prism poles, {1010}, are perpendicular to the rolling direction. After fully annealing this material an entirely new texture develops which corresponds to a 20" or 40" rotation of the deformation texture about hexagonal axes of

Jan 1, 1954

By J. T. Norton, N. J. Grant, A. M. Gervais

An investigation of the creep deformation of coarse grained specimens of high purity aluminum in the temperature range 800&apos; to 1150°F, permitted the formulation of a theory explaining the formation of kink bands. The X-ray Laue back-reflection technique was used in conjunction with metallographic studies to determine the crystallographic elements involved in kinking and to measure the rotations of the bands. THAT metals deform by the formation of kink bands was first shown by Orowan1 in 1942. He manually compressed cadmium single-crystal wires, the basal planes of which were parallel to the wire axis and to the direction of compression. He found that kink bands formed quite suddenly. Similar experiments were performed by Hess and Barrett2 on zinc with a hydraulic testing machine to permit slower more careful compression. They observed that kink bands formed progressively with increasing compression. Recently Washburn and Parker3 observed the formation of kink bands in zinc single-crystal specimens during tension creep experiments. Each of these authors observed the formation of kink bands but did not make a complete analyses of the crystallographic relationships. In addition to these studies on hexagonal metals, extensive investigations of kink bands formed during deformation of aluminum in tension at room temperature have been reported. Two types of deformation bands have been observed during the deformation of aluminum at room temperature. These are: 1—kink bands: these exhibit a sharp curvature of the lattice along certain surfaces, and 2—bands formed by secondary slip along certain regions. As has already been shown by Honeycombe,4 it is important to point out the difference characterizing the two types of deformation bands. In the first case. for moderate deformation, only one system of slip planes normally is active; in the second case, however, two slip systems are active in the deformation bands. The latter have a rumpled surface because of the action of the two slip systems. In the present work only the first type of band was studied and to avoid any confusion the term kink band will be used exclusively in the discussion which follows. Honeycombe&apos; observed that very narrow kink bands (width, 0.01 mm) formed along the (110) planes during the deformation of high purity aluminum at room temperature. He observed narrower ones in commercially pure aluminum and found also that their width decreased with decreasing temperatures. Chen and Mathewson5 reported the formation of kink bands during tensile testing of single crystals of high purity aluminum at room temperature and pointed out that some rotation occurred about a [211] direction. The influence of the bending moment on the formation of kink bands was illustrated by the experiments of Rohm and Kochendorferl0 who used a Polanyi apparatus to obtain pure shear during tensile testing of high purity aluminum single crystals. Under such conditions only one slip system was active and no kink bands were observed; consequently, no noticeable asterism was detected after deformation. The influence of the bending moment will be discussed later. Calnan8 gave a detailed account of the work performed on kink bands obtained during deformation of aluminum at room temperature. Because no explanation of the process of kink band formation in creep was given in the previous investigations and because some of the above observations are vital to the following discussion the brief review of the literature has been given. It is proposed in the present work to provide an explanation of kink band formation during creep deformation at elevated temperatures. Results and Discussion Kink bands were observed to form during tensile creep testing of high purity (99.995 pct) aluminum specimens, having a very large grain size, in the temperature range 800" to 1150°F. These observations were made in grains which occupied the whole cross section of the specimen. The specimens were originally round (diameter, 0.187 in.; gage length, 1 in.) and had parallel flats milled to permit easier metallographic and X-ray observations. The final

Jan 1, 1954

By K. A. Jackson, G. A. Chadwick, A. Klugert

The diffusion field ahead of a lamellar interfnce is analyzed using an electrical analog. A self-consistent solution is obtained for the shape of the interfnce and the diffusion field by an iterative process. The solutions presented here are for a 50-50 eutectoid or eutectic, The shape of the interface is found to he independent of growth velocity and lamellar spacing, and to depend on the relative values of interfacial free energies at the phase houndaries . The mode of growth of lamellar eutectics and eutectoids has been a subject of much interest for many years.1-4 Mehl and Hagel 1 have shown photomicrographs taken by Tardif when he attempted to determine experimentally the shape of an advancing pearlite interface; the results are completely ambiguous. Brandt&apos; and schei13 have made approximate calculations of the composition ahead of a lamellar growth front. The shape of the advancing front and the composition distribution ahead of the front are difficult to calculate because one depends on the other. It is the purpose of the present paper to describe a method by which this calculation has been done. Lamellar-eutectic growth usually occurs under conditions where the growth is fairly rapid, and the interface temperature is close to the eutectic temperature. The growth rate is usually determined by heat flow. Eutectoid growth, on the other hand, can best be studied by quenching to some temperature, and allowing growth to proceed isother-mally. In both cases the growth is believed to be controlled by diffusion* rather than by the atomic kinetics of the transformation. This being the case, a single treatment of the diffusion equation will apply to both cases, provided the region of the interface in a eutectic may be considered to be isothermal. If a part of the interface could appreciably change its thermodynamic driving force by advancing ahead of or lagging behind the mean interface, then the two cases would not be similar. Eutectics normally grow in temperature gradients of the or-der of a few degrees per centimeter. The normal eutectic spacing is the order of a few microns. Part of the interface would have to extend many lamellar spacings ahead of the mean interface before it experienced sensibly different conditions. The interface temperature is usually a few tenths of a degree below the eutectic temperature so that temperature differences of the order of one-thousandths of a degree (a displacement of one lamellar spacing) would be unimportant. Protrusions large compared to the mean spacing do occur when one phase only grows into a eutectic liquid. This is usually a dendritic type of growth, and easily distinguishable from the lamellar mode of growth. A single treatment of lamellar growth will apply equally well to both eutectic and eutectoid decomposition. At the interface, which as shown above is essentially isothermal, the difference between the equilibrium eutectic temperature Teu and the actual interface temperature Ti, can be divided into two parts: 1) the composition varies across the interface, so that the local equilibrium temperature is not Teu; and 2) the interface is curved, so that the local equilibrium temperature is depressed according to the Gibbs-Thompson relationship. This undercooling can be written as Teu-Ti =?T = mAC(x) + a/r(x) [1] where ?C(X) is the departure of the composition at a point x on the interface from the eutectic composition, see Fig. 1, r(x) is the local radius of curvature at a point x on the interface, m is the slope of the liquidus line on the phase diagram, and a is a constant given by where s is the interfacial free energy, TE is the equilibrium temperature, and L is the latent heat of fusion. The calculations in this paper will be made only for the case where the phase diagram is symmetric, that is, the eutectic occurs at 50 pct, the liquidi have the same magnitude slope m at the eutectic temperature, and C,, the amount of B rejected when unit volume of a freezes, see Fig. 2(a), is the same for both phases. As shown in Fig. 2(b), the composition ahead of the a phase will be rich in B, the composition ahead of the ß phase will be rich in A. The composition at the phase boundary is the eutectic composition. The difference between the local liquidus temperature and the actual tempera-

Jan 1, 1964

By A. S. Yue

Small-angle tilt boundaries have been observed in a lamellar eutectic structure. These boundaries are morphologically similar to a theoretical till boundary originally proposed by Burgers. The production of a small-angle tilt boundary in the lamellar eutectic structure is attributed to the formation of an indentation on a planar solid-liquid interface during growth. Constitutional supercooling due to the accumulation of impurity atoms ahead of the interface is primarily responsible for the generation of an indentation. The distance between two faults of like sign, designated as lamellar fault distance, is calculated by the Burgers equation for small-angle boundaries. It was found that the lamellar fault distance decreases exponentially and the tilt angle increases exponentially with freezing rate. SMALL-ANGLE tilt boundaries have been observed in many crystals in the as-grown states by etching techniques. However, a detailed substantial proof for revealing the presence of dislocations in the form of etch-pits was recently accomplished by Vogel. These boundaries are described as an array of dislocations of like sign. The angle of tilt associated with a boundary is treated theoretically by Burgers3 and is given by 0 = b/D for small tilt-angle where b is the Burgers vector of the dislocations and D is their average spacing. During the course of experimentation on the solidi fication of the lamellar Mg-32 wt pct Al eutectic a microstructure which was strikingly similar to a dislocation tilt boundary was observed. An example of the type of microstructure is given in Fig. 1, which shows a combination of transverse and top sections of the lamellar eutectic structure. The lamellae of the top section on one side of the apparent tilt angle are not parallel with those on the other side. Consequently, some lamellae must be terminated somewhere. Fig. 1 shows that the termination of lamellae is analogous to a dislocation tilt boundary in a crystal lattice originally proposed by Burgers. This work represents a closer look at such structures. The factors governing the production of the small-angle tilt boundary are discussed in terms of the freezing condition and impurity distribution in the melt. The effect of freezing rate on the distance between two faults, designated as lamellar fault distance, and the tilt angle is also described. In addition, the lamellar fault distance is determined by means of the Burgers equation for small-angle tilt boundary. EXPERIMENTAL PROCEDURE The slightly impure Mg-32 wt pct Al eutectic rods, 5/8 in. in diam and 12 in. long, were made from 99.99 wt pct Al and 99.98 wt pct Mg and were cast in a high-purity graphite mold. Some of these rods were purified by zone-refining the eutectic using direct-radiation helical-coil furnaces5 A molten zone about 2 in. long was passed through the cast rods at a speed of 5.3 x 104 cm per sec for ten passes of the molten zone. Before the freezing experiment was begun, 2-1/2 in. of the material from the head and tail ends of the zone-refined eutectic were removed from the rod to eliminate any impurity. The freezing experiments were carried out under controlled conditions,8 using a protective atmosphere of purified argon. At the end of each run, observation of the tilt boundary was made throughout the entire length of the rod with a light microscope on the top, longitudinal, and transverse sections (three mutually perpendicular sections) of the lamellar eutectic solid. The experimental data used for the determination of interlamellar spacing and tilt angle were taken from the middle portion of

Jan 1, 1964

By U. F. Kocks

The flow stress in some latent slip systems of aluminum and silver crystals after various deformations in single slip was investigated by transverse compression and supplemented by experiments on overshoot of the compression axis and the stability of corner orientations. Work hardening was found to be remarkably isotropic, the ratio of the flow stress in the latent system to that in the primary system being between 1.0 and 1.3. The strain-rate dependence was not significantly larger in the latent system. This low anisotropy suggests that specific dislocation interactions are not the direct cause of work hardening. Either the obstacles are essentially impenetrable so that only their distance enters, or a fairly random distribution of dislocations of all systems is. in fact. formed during single slip. The latter seems to he excluded by the observations on the strain-mte dependence and on the amount of secondary strain. The amount of seconzdary strains occurring in single slip was determined by shape-change mensurements and by a new method connected with the latent-hardening experiments. It is definitely less than 1/300 times the strain in the primary svstem. WORK hardening is due to dislocation interactions; this is a hypothesis, and possibly the only one, on which all present work-harden ing theories agree. About a dozen specific interactions have been considered, and it is unlikely that any essential one has been missed. Different work-hardening theories differ to a large extent in the specific interactions which are deemed most important. The presence or absence of any particular interaction, and its degree, depend on the geometrical relationships between the two dislocations interacting. Let us enumerate some examples. Two dislocations may react, with a varying reaction energy, to form a third dislocation, and this reaction product may be sessile or glissile. Two dislocations may intersect and a jog may be formed on both, on one of them, or on neither; this jog may be sessile17Z or glissile and it may, if moved nonconservatively, lead to the production of vacancies or interstitials. Finally, a dislocation may bypass another one and thus interact only with its stress field. All these interactions depend on the specific relation between the Burgers vectors and line directions of the two dislocations. Any dislocation generated during plastic deformation of fcc crystals belongs to one of twelve slip systems. Taking any one dislocation, its relationship to each of the other eleven can fall, by symmetry, into one of only five classes. These relationships are enumerated in Fig. 1 and Table I. Each slip system is represented in the stereo-graphic projection by two triangles, namely those in one of which the specimen axis would have to lie if the specimen were to deform in single slip on this slip system in a given sense, in a tension test. Let us represent the primary slip system by the shaded triangles. The other slip systems are classified only with respect to their relationship to this primary system. The code letters (initials of established names* in German) are explained in Table I. Three specific interactions are also listed in cases where they may be strong: the product of a reaction, the formation of jogs in either system, and the elastic bypass stress. The last column relates to the types of experiments reported in this paper and summarizes their results. To decide experimentally between the relative importance of the various interactions one would like to produce a group of dislocations in one slip system and then measure the stress necessary to force another group of dislocations of a specific second system through them. Hopefully, one can produce the first set of dislocations by plastically deforming the specimen in single slip. Then one can try to achieve single slip in a specific, previously latent system and measure its flow stress. If it is different from the virgin flow stress, there has been "latent hardening". Some types of latent-hardening experiments will be discussed in the next section. The strain-rate and temperature dependence of the flow stress is an indication of the importance of dislocation intersections. By extending an investigation of this dependence to the latent systems, one can determine how much more important forest contributions are here. seeger3 has used the as-

Jan 1, 1964

By T. H. Alden

A correlation has been found in rock-salt structure single crystals between the latent hardening, measured by the direct stress activation of oblique slip systems, and the stress-strain behavior in simple compression. Materials with high latent hardening, like LiF, strain-harden at a low rate (Stage I) even when severely constrained. KCl, in contrast, shows low latent hardening and a tendency to strain-harden at a high rate (Stage 11). This correlation suggests that oblique slip is essential for Stage II hardening of these materials. THE role of secondary slip in the strain hardening of metal single crystals is a topic of lively controversy. On the one hand are theories in which secondary dislocations participate directly in Stage II hardening in the fcc metals, for example through the production of sessile dislocations,1 forest intersections, or jog formation. Much of the experimental evidence on which these theories are based has been reviewed by Clarebrough and Hargreaves.~ On the other hand, a recent theory5 denies that secondary slip has an essential role in Stage II hardening or in the transition from Stage I to Stage 11. In the latter view, Stage I is not terminated by an increase in the activity of secondary systems but by the exhaustion of undeformed material.6 The experiments reported in this paper will not resolve this controversy since the materials being studied are cubic ionic crystals rather than metals. However, the results do show in an unusual way a direct connection between "secondary" (nonortho-gonal or oblique) slip and strain hardening in these materials. Specifically, a correlation has been found between two independently measured properties, first the latent hardening of oblique (110)(1i0) slip systems as measured by direct stress activation of these systems, and second the stress-strain behavior at small strains. From prior work, it was known that in most cubi-cally oriented rock-salt structure crystals, two orthogonal slip systems operate and exclude the other equally stressed pair, oblique to the first pair.7&apos;8 This observation apparently indicates that a significant interference exists between slip on oblique (110) planes and a relatively small interference between orthogonal (110) planes. The present experiments were begun with the intent of obtaining a quantitative measure of this difference by means of a study of latent hardening in these crystals. I) EXPERIMENTAL METHODS The experiments were basically of two types, first the determination of stress-strain curves by compression along a single (100) axis, and second the measurement of latent hardening by compressive prestrain along one cube axis followed by the determination of the yield stress in a second (latent) cube direction. All tests were done at room temperature in an Instron machine by compression between lapped, parallel steel faces. Three specimen shapes were used. For long crystals (nominal dimensions, 1/8 in. square by 1/2 in. long) the ends were lubricated with an oil-graphite mixture. Superior results with short crystals (about 1/8 in. cube) were obtained using 0.003-in. teflon film.&apos; Thin crystals (1/4 in. square by 3/32 in.) were used for latent-hardening measurements and similar results were obtained with either lubricant. Test specimens were cleaved from Harshaw single crystals which had been irradiated to a dose of lo8 roentgen using a cobalt-60 source. The irradiation raises the yield stress and tends to prevent plastic deformation during sample preparation.10 Prior to testing, the irradiation hardening was removed by an anneal at 400°C. Ideal compression specimens have flat, parallel faces. In short specimens particularly, satisfactory results demand a close approximation to this ideal. In the present work, cleaved surfaces were often used directly as compression faces. The degree of success using this method depends on two factors: 1) the smoothness of cleavage faces, and 2) the extent to which the crystal is deformed or crushed by the chisel during the cutting of a long crystal into short pieces. Unfortunately, only one material of those studied, LiF, was completely satisfactory. NaF, NaC1, KC1, and KBr behaved less well so that

Jan 1, 1964

By B. Ramaswami, U. F. Kocks, B. Chalmers

The latent hardening of silver and an Ag-Au alloy was investigated by lateral compression, overshoot in tension and cormpression, and the stability of multiple-slib orientations. The latent hardening of a secondary slip systenz depends on its relation to the primary slip system. For most secondary slip systems the latent hardening is larger for Ag-10 at. pct Au than for pure silver. The maximum increase in. flow stress on a secondary slip system over that of the primary slip system was 40 pct. The work hardening during the lateral-compression test on the latent system after prestress on the primary system is iuterbreted in terms of the preferential distribution of barriers to dislocation movement with respect to the active slip system in work-lzardened fcc crystals. The work-hardening in fcc crystals is mainly due to the dislocation interactions and the barriers to dislocation movement formed as a result of reactions between dislocations of different slip systems. The operation of sources on the latent system depends on the flow stress of those systems; hence, the increase in flow stress of a latent system due to glide on an active system, which is called latent hardening, is an important element in understanding the phenomenon of work hardening. The problem of latent hardening has attracted the attention of many investigators in the past. For example, a theoretical study of the elastic latent hardening of the latent systems due to glide on an operative system has been made by Haasen&apos; and ~troh. These calculations, however, neglect the stress required for the intersection of forest dislocations by the glide dislocations, a factor which would be important for producing macroscopic strains on the secondary slip systems. The importance of this factor will become evident from the results presented here. Attempts have also been made to determine the latent hardening of different slip systems by experimental means by the methods summarized in Table I.3-9 The experimental methods used have been subject to certain limitations. For instance, in the method used by Hauser,9 frictional constraints between the specimen and the compression platen were not eliminated by proper lubrication (see Hos- ford10). Secondly, with the exception of Kocks,6 Hauser,9 and Rohm and Kochendorfer,11 latent-hardening studies have been made on only one of the slip systems, i.e., on either the conjugate or the coplanar slip system; hence, extensive results are not available on the latent hardening of different slip systems in the same materials, with the exception of aluminum.6 It was therefore decided to study the latent hardening of the conjugate, critical and half-related slip systems in silver. Similar experiments were done in Ag-10 at. pct Au to study the effect of solute (gold) on the latent hardening of silver. Lastly, indirect evidence can be obtained by a study of the orientation stability of crystals of multiple-slip orientations in tension and compression. This method has been used by Kocks6 to supplement his studies of latent hardening in aluminum. Similar studies were made at room temperature in single crystals of silver. EXPERIMENTAL PROCEDURE The single crystals of the desired orientations were grown and the tensile test specimens were prepared as described in Ref. 12. The compression tests were made on 1/4-in.-cube specimens. The specimens were cut from single crystals, in the Servomet spark-erosion machine.13 The two cut surfaces were planed using the lowest available planing rate in the machine to minimize the deformation layer. A brass strip was used as the planing tool. This method of preparation ensured plane parallel faces for the compression tests. The deformed material was removed by prolonged etching in a weak etching solution. A weak etching solution was used to prevent pitting of the surfaces and to ensure uniform etching. About 25 to 50 µ of material were removed from all faces by the etching treatment. The specimens were then annealed for 24 hr at 940°C in oxygen-free helium and cooled in the furnace to room temperature over a period of 7 hr. After annealing, the orientation of the specimens was determined by Laue back-reflection technique to make sure that no recrystallization had occurred on annealing. The compression-test technique and setup are described in Ref. 14. The Laue back-reflection technique was used to study the overshoot in tension, the overshoot in compression, and the stability of the axial orientation in tension and compression. The tests were interrupted after every few percent strain to determine the axial orientation. In investigating the overshoot in compression, the operative system was determined by studying the asterism of the Laue spots.

Jan 1, 1965

By L. S. Darken, H. A. Wriedt

An investigation has been made of nitrogen absorption by the lattice defects in a low-carbon steel afte~ Plastic deformation. Specimens in which defects were distributed by various combinations of cold rolling and vacuum heat treatment were equilibrated with controlled ammonia + hydrogen mixtures at 300° to 450°C to study the relation between the solubility and the thermodynamic activity of nitrogen. The results are interpreted in terms of nitrogen being absorbed upon two different types of defect sites, called A sites and B sites. The concentrations of these sites are calculated for specimens with various histories of straining and annealing; and the thermodynamic relations descrihing the equilibrium distribution of nitrogen among the A, B, and ordinary interstitial sites in ferrite are evaluated as follows: THE generalization that the solute atoms in a solid solution interact with imperfections in the solvent lattice is now universally recognized and the subject of an extensive literature. All types of imperfections—point, line, or surface—exhibit these interactions, but the relative importance of each type depends upon its concentration, the strength of its interaction with the particular solute atom, and whether the interaction is attractive or repulsive. The strength and sign of the interaction vary with the vectorial displacement of the solute atom from the imperfection in the crystal. The concentration of lattice defects increases during plastic deformation and the effect of the imperfections upon the solute atoms is usually perceived only after cold work or irradiation. Two experimental methods have previously been used to observe the effects of interaction between nitrogen atoms and lattice imperfections in a iron. Internal friction, which was first used for this purpose by Dijkstra,1 has been applied more often than the electrical-resistivity method of Cottrell and Churchman.2 The method of the present investigation has not been used before.* Uniform specimens of steel with a metastable defect structure are produced by cold rolling and subsequent heat treatment below the recrystallization temperature. Variations in the defect structure are obtained by varying the amount of strain and the heat-treatment conditions. The specimens are then saturated with nitrogen at moderately elevated temperatures in ammonia + hydrogen mixtures having various thermodynamic activities of nitrogen below saturation with Fe4N. From the nitrogen contents of analyzed samples, the metastable equilibria of interactions between the defects and nitrogen can be established and the concentration of sites for nitrogen atoms in the lattice defects calculated. A steel was used in the present experiments instead of purified iron or iron alloys because the amount of nitrogen absorbed at defects is larger in the steel over a much wider range of experimental conditions and could therefore be measured more accurately. The effect of alloy composition is discussed in Part II of this paper; it is sufficient to say here that impurities and phase heterogeneity in ferritic alloys favor the generation and/or retention of larger defect concentrations during plastic deformation and annealing at 300° to 500°C. MATERIALS AND EXPERIMENTAL PROCEDURE The experimental specimens were prepared from stock of a low-carbon steel, which will be called "X steel" here, with the composition: C, 0.12 pct; Mn, 0.43 pct; P, 0.010 pct; S, 0.034 pct; Si, 0.007 pct; As, 0.086 pct; Cu, 0.022 pct; Ni, 0.009 pct; Cr, 0.003 pct. The stock was all from a single ingot made by the basic open-hearth process, which was hot-rolled to strip 0.080 in. thick.. This hot-rolled strip, given the code designation "XH", was the starting material for preparing a series of cold-rolled sheets. The latter are designated "XC27",

Jan 1, 1965

By L. S. Darken, H. A. Wriedt

In a previous paper,1 an experimental study of nitrogen dissolved in a cold-rolled ad heat-treated, low-carbon steel at 300° to 450°C yielded the equilibrium solubility relations and the concentrations of the two types of deject sites involved. In this paper, the probable identities of the defects that absorb nitrogen are restricted from the available evidence to screw dislocatioms for B sites, and to either micro crack surfaces or edge In a previous paper.&apos; we reported an experimental study of the excess nitrogen solubility in a low-carbon steel produced by a combination of plastic deformation and nonrecrystallizing heat treatment. The concentrations of the defect sites that absorb the excess nitrogen were measured in terms of their capacities for nitrogen. Also measured were the equilibria of nitrogen distribution among the sites. Several problems and questions arise from these measurements. We should like a physical identifi- dislocations for A sites. The concentrations of these defects in experimental steel specimens are estimated from the concentrations of defect sites. finally, the influence of chemical composition upon the nitrogen-trapping defects—the relative numbers generated in deformation, the relative numbers surviving as temperature is raised, the apparent numbers observed, and the distribution equilibria-is discussed. cation of the defects involved and of the two kinds of nitrogen-absorbing sites, called A and B types, upon those defects; the concentrations of the defects themselves could then be computed. We should also like to know how exclusively the findings apply to the "X steel" used in the experiments and to what extent they apply to cold-rolled steel given no subsequent treatment. By considering the data already given, together with results from a few specific tests which will be reported as they are invoked, we are able to eliminate some interpretations altogether and to secure an acceptable though limited interpretation from among the remaining possibilities.

Jan 1, 1965

By L. Zwell, H. A. Wriedt

X-ray Lattice parameter and bulk density measurements were made at room temperature on solid solutions of nitrogen in purified a, iron, containing from 0 to 0.053 wt pct N. When nitrogen is dissolved in a, iron, the fractional increase in unit cell volume (X-ray diffraction) and the fractional increase in volume per gram of iron (bulk density measurement) are the same within experimental error. The two sets of results when averaged show that the unit cell edge of a, iron increases linearly by 3.2 X 10-2 A per wt pct N dissolved and that the partial gram-atomic volume of nitrogen at infinite dilution in a, iron is the same as it is in nitrogen-martensite, that is, 5.90 cm3. RECENT reviews17&apos; of literature dealing with the lattice parameter of ferritic iron-nitrogen alloys indicate that the dilating effect of dissolved nitrogen on the bcc unit cell of a iron is not known with confidence. Five investigations3-7 either revealed no effect of nitrogen or were inconclusive. Among other investigations, where quantitative data were obtained, the results of Osawa and Iwaizumi8 indicate too large an effect, and those of Eisenhut and Kaupp9 show the lattice parameter of ferrite varying with the nitrogen content at concentrations far beyond the known solubility limit. It is not clear in Burns&apos;10 data what value should be used for the lattice parameter of nitrogen-free ferrite in calculating the dilation. Burdese11 shares with Burns the shortcoming that the iron-nitrogen alloys were solution-treated and quenched with undissolved nitride present. The consequence is that the un- certainties in the solubility limit1 are added to those in the lattice parameter measurements when the variation of lattice parameter with nitrogen content is computed. For a system of such widespread interest, we felt that a new investigation was merited. Both X-ray diffraction and bulk density measurements were used to determine the dilation of the , a iron lattice by dissolved nitrogen. EXPERIMENTAL PROCEDURE Material. The bulk density and X-ray diffraction experiments were both made with specimens of a purified iron (denoted as "B iron")- from Battelle Memorial Institute. The impurity contents were as follows: As, C, Cu and Pb—50 ppm; Ag, Al, Co, Ga, 0, Ti-11 to 50 ppm; B, Be, Ca, Cd, Cr, Mg, Mn, Mo, N, Ni, S, Sb, Si, Sn, V, W-10 ppm or less. The vacuum-cast ingot was hot-forged and annealed. Pieces of the forged stock were machined and cold-rolled to give strip stock 0.08 and 0.002 in. thick for density and for X-ray measurements, respectively. Preparation of Specimens. Starting with a piece of the cold-rolled iron stock, the general sequence of operations, after an initial recrystallizing anneal, was to measure the density or lattice parameter, nitrogenize, remeasure the property, age or denitrogenize, and again measure the property. Duplicate analyses for nitrogen were made by a modified Kjeldahl method on portions of the actual density specimens and on pieces nitrogenized to equilibrium alongside the X-ray specimens. Annealing of the density specimens was performed by sealing the pieces with the as-rolled surfaces removed by filing into evacuated "Vycor" capsules and treating for 1 hr at 750°C followed by furnace cooling. (TO check the effect, if any, of annealing procedure, a specimen also was

Jan 1, 1962

By R. S. Busk

TWO groups of binary alloys were prepared. The first group consisted of those elements relatively soluble in magnesium: Li, Al, Zn, Ga, Ag, Cd, In, Sn, Hg, T1, Pb, and Bi. These are predominately Group B elements. The second group consisted of most of the remaining metallic elements, all of which are relatively insoluble in magnesium: As, Au, Ba, Ca, Ce, Cu, Ir, La, Mn, Ni, Pd, Pt, Rh, Sb, Si, Te, Ti, W, and Zr. These are all Group A, transition, or rare earth elements. Alloys of the first group were prepared by melting sublimed magnesium and elements as pure as obtainable in a graphite crucible, using a standard flux1 for protection. The melts were poured into a small graphite mold to produce 3xY4 in. diam slugs. Spectroscopic analyses were made of each slug. In all cases, the total impurity content was less than 0.05 pct. The slugs were then heat treated 5°C below the eutectic temperature until complete solution, as judged metallographically, was obtained. Filings from the center of the slugs were compacted at room temperature into 1/2 in. long x 1/4 in. diam cylinders, sealed in pyrex under 1/2 atm of purified argon, annealed at the heat-treating temperature for 1 hr, and quenched in water. After the X-ray diffraction patterns were made, each compact was analyzed chemically for the solute. It was found that the Mg-Li alloys reacted during filing to reduce the Li in solid solution. For this series of alloys, the slug was cold worked, annealed in purified argon, the surface dissolved in dilute HC1 to a depth of about 0.005 in., and the X-ray exposure made on the fresh surface. This procedure resulted in sharp, continuous lines and in true values for the lattice parameters. The alloys in the second group were prepared in the same way except that about 1 wt pct of each solute was added. Since the solubility limit was exceeded, not all the solute dissolved. These alloys were analyzed spectroscopically only to confirm the presence of the solute. The diffraction patterns were of the back-reflec-tion type using the characteristic copper radiation* and a flat cassette. Both the film and the specimen were rotated. The specimen temperature was maintained at 25" ± 1°C. The films had sharp lines; their diameters were measured directly to 0.01 cm. The parameters were calculated from the line diameters using a modified version of Cohen&apos;s extrapolation method.2 his method effectively eliminates systematic errors such as film shrinkage, inaccurate alignment, and non-precise film-to-speci-men distance. The random errors were minimized

Jan 1, 1951

By John T. Norton, Matthew J. Donachie

Residual lattice strai?zs were produced in 2024 aluminum and ingot iron by uniaxial tensile deformation. These strains were rneasured on the original surface and ulith depth below the surface. The strains conformed approximately to those from a macroscopic stress distribution but they were not truly macroscopic in nature. The exact mechanism which apparently causes the coherently difi9,acting region of each grain to behave as if macroscopically stressed was not determined. MACROSCOPIC stresses in metals produce strains in the lattice which result in X-ray line broadening and line displacements. The latter effect can be utilized in a technique for determining stresses in metals as first shown by Lester and born.&apos; Subsequent advances in technique have enabled the X-ray method of stress measurement to be satisfactorily applied to many problems involving residual stresses of a macroscopic nature, such as those due to welding, grinding, shot-peening, and so forth. In the case of stresses such as those described above, the correlation of X-ray- and mechanically determined data has been generally good. However, plastically extended polycrystalline metals have sometimes been reported2 to show line displacements upon release of the applied tensile load, yet the nature or origin of the residual lattice strains, rls, producing these displacements has never been clear. As will be pointed out, this lack of clarity regarding the macroscopic or microscopic nature and origin of these stresses casts doubt on the validity of results achieved by the commonly accepted techniques of X-ray stress measurement. This anomalous behavior requires clarification to remove the doubts concerning X-ray stress measurement. The present paper is the result of an investigation of the interesting behavior of such plastically extended polycrystalline metal bodies. The studies were originated to carry out the following tasks: 1) Observe whether a residual lattice strain is produced as a result of plastic extension and show whether any residual lattice strains produced can be related to the usual concept of a macrostress. 2) Examine the origin of any residual lattice strains observed. 3) Consider the implications or consequences of the existence of such residual lattice strains on the problem of X-ray stress measurement. THEORY 1) Lattice Strains. The theoretical developments necessary for the treatment of lattice strains and their relation to stresses follow from the classical theory of elasticity and have been adequately covered by arrett. For an isotropic solid under homogeneous deformation, it can be shown that, for uniaxial stresses where Dl is the macrostress acting in the longitudinal direction; E$L is the lattice strain in the plane defined by the surface normal and the longitudinal direction at an angle, , from the surface normal; ET is the similar strain in the transverse plane; E is Young&apos;s modulus; and v is Poisson&apos;s ratio. Eq. [2] is independent of angle + and Eq. [I] is a linear function of sin2, see Fig. 1, and can be solved analytically for DL if E and u are known and EL is measured. Thus, a uniaxial macrostress will be indicated by a linear E,L vs sinZ plot and a

Jan 1, 1962

By R. E. Hanneman, A. N. Mariano

In conjunction with the need for accurate volumetric data in the Fe-V system for subsequent use in calculating the high-pressure diagrams, room- and high-temperature X-ray diffraction measurements have been carried out. No previous measurements have been published on lattice parameters or volume changes associated with the a transformation for Fe-V alloys. The existing literature on lattice-parameter data for the a and s phases has been reviewed by pearson1 with considerable uncertainty indicated in the data. In order to obtain a good estimate of ?Va-? for thermodynamic calculations of the a D ?(bee D fee) phase stability, high-temperature vacuum X-ray diffraction measurements were made on an Fe-V alloy of 0.92 wt pet V. The term ?Va-? is the difference of molar volumes of the limiting solubilities of the a and y phases at any given temperature; these values can be calculated readily from the appropriate lattice-parameter data. The equipment used was a commercially available MRC (Materials Research Corp.) high-temperature X-ray camera which was fitted to a Norelco diffractometer

Jan 1, 1964