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By R. I. Jaffee, H. R. Ogden, D. J. Maykuth

IN THE past year, Jaffee and Campbell&apos; and Finlay and Snyder2 reported on the mechanical properties of titanium-base alloys, some of which were in the same ranges of composition as are covered in this paper. In this paper, evidence confirming that given by Finlay and Snyder on the effects of carbon, oxygen, and nitrogen on titanium will be presented; and, in addition, new data will be given on the effects of these elements on the flow properties and phase transformation of titanium. Materials and Preparation of Alloys The preparation and general properties of iodide titanium have been adequately described elsewhere.&apos; , As-deposited iodide titanium rod, prepared at Battelle, of Vickers hardness less than 90 was employed as the base metal in the present work. This was the same material as that used by Finlay and Snyder.2 The probable analysis reported by them for standard quality metal holds here also: N 0.005 pct, 0 0.01 pct, C 0.03 pct, Fe <0.04 pct, A1 <0.05 pct, Si <0.03 pct, and Ti 99.85 pct. Carbon was added in the form of flake graphite supplied by the Joseph Dixon Crucible Co. Oxygen was added in the form of c.p. grade TiO, powder, produced by J. T. Baker Chemical Co. Nitrogen was added in Ti3N4 powder, supplied by the Remington Arms Co. Individual ingots weighed 7 or 8 g. Carbon, oxygen, or nitrogen was added by placing the corresponding powder in a capsule made from as-deposited iodide titanium rods and melting the capsule with the balance of the charge. The charge was are-melted with a tungsten electrode on a water-cooled copper hearth under a partial vacuum of very pure argon (99.92 pct minimum). Melting was practically contamination free. Vick-ers hardness increases of less than 10 points were normal for unalloyed iodide titanium control melts. Nitrogen analyses of are-melted iodide titanium showed a nitrogen content of 0.005 pct, about the same as is present in the as-deposited rod. No tungsten pickup was found in a melt of iodide titanium analyzed for tungsten. Weight losses in melting nitrogen-free alloys were very small and varied consistently from nil to 0.015 g (0 to 0.2 pct). This permitted the use of nominal composition for these alloys. Chemical analyses made for carbon, which can be analyzed conveniently by combustion methods, justified this procedure. Where nitrogen was added, considerable splattering took place. Here it was necessary to analyze for nitrogen by the Kjeldahl method. The ingots were hot rolled at 850°C to about 0.045 in. thick. After hot rolling, the strips were descaled by mechanical grinding, and then given a cold reduction of 5 to 10 pct to insure a uniform thickness throughout the length of the specimen. The edge strips and the tensile strips were annealed in a vacuum of 1x10-4 mm Hg pressure for 3 1/2 hr at 850°C and furnace cooled. Methods of Investigation Hardness Measurements: At least five Vickers hardness measurements were taken using a 10-kg load on each sample in the following conditions: (1) top and bottom of each ingot, (2) top and bottom surface of as-rolled and annealed sheet, and (3) on cross-section of annealed sheet and all quenched specimens. Tensile Tests: Tensile tests were conducted on Baldwin-Southwark testing machines having load ranges of 600 or 2000 lb. Tests were made on 1-in. gauge-length specimens, 3 1/4-in. overall length, 1/2 in. wide, 0.040 in. thick, with a reduced section 1 1/4 in. long and 0.250 in. wide. Two SR-4, A-7 strain gauges, one mounted on each side of the specimen, were used to measure the strain over a limited range to determine the modulus of elasticity. After the modulus of elasticity readings had been taken, load vs. strain readings were taken, using only one strain gauge, at increments of 0.0001 in. until the yield points were passed and then at 0.001-in. increments to the limit of the strain-gauge indicator (0.02 in.). Strain readings above 0.02 in. per in. were taken every 0.01 in., using dividers to measure the strain between the 1-in. gauge marks until the maximum load had been reached. Crosshead speed, when using the SR-4 gauges, was 0.005 in. per min, and, when using dividers, 0.01 in. per min. Flow Curves: Flow curves were determined using the true stress-true strain data obtained during the tension test. The usefulness of this type of information has been dealt with very adequately elsewhere by L. R. Jackson,&apos; J. H. Hollomon,6 and many others. Flow curves of true stress vs. true strain could be converted to the more conventional cold-work curve of 0.2 pct offset yield strength vs. percentage of cold reduction by means of the transformation, 1/1 = 1/1-R, where R is the fraction reduction in cold working. Thus, the true strains corresponding to percentage reduction can be calculated, and the 0.2 pct offset yield strengths scaled off the — 6 curve by taking the true stresses corresponding to the values of 6 + 0.002 strain. Heat Treatment: For the transformation studies, the alloys were heat treated in a horizontal-tube furnace using a dried 99.92 pct argon atmosphere, and quenched into water. Essentially no contamination was found after several hours of heat treatment at temperatures up to 1050°C. Metallography: Specimens were prepared in the

Jan 1, 1951

By J. A. Rowland, C. W. Funk

THIS investigation is a part of the United States Bureau of Mines work in conserving the Nation&apos;s resources. The isothermal sections presented were developed as a guide to a comprehensive investigation of the properties and fabricating characteristics of copper-base alloys containing manganese and tin. These alloys are being investigated as possible replacements for the commercial bronzes containing substantial quantities of tin. Development of the isothermal sections has, therefore, been limited to the area between 0 to 20 pct Mn and 0 to 25 pct Sn. Since Heusler1 reported the ferromagnetic properties of the Cu-Mn-Sn alloys in 1903, the system has been the subject of several investigations. These studies were largely concerned with correlation of magnetic properties and crystal structure.2-6 Vero,&apos; however, established the solidus surface of the system, between 20 pct Mn and 40 pct Sn, by thermal and microscopic methods. The a, ß, and y solid solutions were also observed by Vero and reported to extend into the interior of the ternary system. For the present study, the annotated diagram of the Cu-Sn system prepared by Raynor&apos; and the Cu-Mn diagram by Dean and coworkers9 were used as the binary borders of the ternary system. Procedure The metals used in this investigation were electrolytic manganese, washed cathode copper, and three-star tin. The manganese, produced at the Boulder City pilot plant of the Bureau of Mines, had a purity of 99.9 pct; the copper contained less than 0.004 pct Bi and 0.001 pct S; the tin contained 0.070 pct Pb, 0.070 pct Sb, 0.050 pct Fe, and 0.065 pct Si. Heats of 1 lb were melted in alundum crucibles with a 3-kw induction furnace. The heats were chill-cast in iron or copper molds to form 6-in. ingots 3/4 in. in diameter. Molds were washed with graphite or zirconia, depending on the manganese content, and preheated to 150°C. The maximum impurity content of any alloy was 0.03 pct Fe, 0.02 pct Si, and 0.02 pct Al; in most cases, they contained less than half this quantity of any of these impurities. Composition of the alloys and their treatment prior to homogenizing are shown in Fig. 1. Designations adjacent to each composition refer to the heat numbers. With a few exceptions, ingots containing 20 pct Sn or less were hot-swaged. These ingots were swaged, after a 24-hr preheat at 650°C, to obtain a total reduction of 70 pct in cross section. Intermittent reheating was necessary, and reductions were limited to either 0.025 or 0.050 in. in diameter per pass. Selection of a 200-hr homogenizing treatment was based on extensive experiments which indicated that virtual equilibrium was reached after 150 hr. Structures were retained by quenching in water. Grain sizes in the specimens homogenized at 350" and 450°C were generally small. These homogenizing treatments were preceded by a 50-hr anneal at 650°C to facilitate phase identification by increasing the grain size in these specimens. The specimens were furnace-cooled from this temperature to the homogenizing temperature, and the heat treatment was continued for the standard 200-hr period. The homogenized samples were bisected to provide an internal section for metallographic examination. Optimum definition of the microstructure was obtained by successive polishing and etching. Quarter-strength ASTM copper reagent No. 13 gave the most satisfactory results.10 Filings from interior sections of the samples were used for diffraction studies. These filings were annealed in evacuated glass tubes at homogenizing temperatures for periods exceeding 50 hr and quenched in water. During this treatment the manganese content was reduced by significant amounts, probably by vaporization. This change in composition was considered in applying the diffraction data, which were used only as a means of identifying phases where the data were consistent with the metallographic evidence. Phase Identification The a solid solution is readily distinguished by the copper-colored, twinned, polyhedral grains, as shown in Fig. 2, and a face-centered cubic X-ray pattern. Tukon indentations, using a 25-g load, indicate a Knoop hardness of 155 for a quenched from 650°C. Using white light developed by a Wratten 78 A filter, the ß grains in etched specimens have a dark brown tint in contrast to the lighter copper-colored grains of the a phase. Knoop hardness values of 284 were obtained for the ß structure in specimens quenched from 650°C. The ß structure was also distinguished from the a phase by its body-centered cubic lattice. The acicular structure appearing in Fig. 3 was evident in several alloys of higher tin content after quenching from either 750&apos; or 650°C. Since a trans-

Jan 1, 1954

By Nicholas J. Grant, Michio Yamazaki

Cast copper alloys containing 10, 20, and 30 pct Ni and 0.75 to 0.80 pct Al were machine-milled into chips, then comminuted in a rod mill to fine flake powder utilizing a number of processing variables. The powders here internally oxidized, mostly at 800°C, in a low-pressure oxygen atmosphere. The consolidated powders were hot-extruded into bar stock. Room-tenmperature tension tests, stress-rupture tests mostly at 650°C, but also at 450° and 850°C, and hardness measurements after various annealing temperature treatments to study alloy stability were perfomted. Excellent room-temperature strength, high rupture strength at 650°C, and resistance to recrystallization at 1050°C were obtained. Problems in optimizing conditions for internal oxidation of Cu-Ni base alloys are discussed. THE interesting high-temperature properties of SAP&apos; have stimulated considerable effort in the study of more refractory alloy systems where the potential for high-strength alloys at high temperature is great.2-13 A number of methods have been utilized to produce the desired fine, hard particle dispersions, of which internal oxidation2,9,7 of dilute solid-solution systems offers considerable promise by virtue of the potential for producing ultrafine, well-dispersed oxides. While most of the published works are concerned with pure metal matrices, a number of investigators have studied the effects of solid-solution strengthening.10,19 Use of more complex alloy matrices (for example, aging systems) has been unsuccessful because overaging still occurs at high temperatures in the oxide-containing alloys.14.15 Solid-solution strengthening is, however, effective at very high temperatures9,10 and might be expected to contribute importantly to the strength of oxide-dispersion strengthened alloys. For this study, internal oxidation of solid-solution alloys of copper and nickel, containing small amounts of aluminum, was chosen as the method of alloy preparation. PREPARATION OF ALLOYS Three copper alloys containing about 10, 20, and 30 pct Ni and each containing 0.75 to 0.80 pct A1 (enough to yield about 3.5 vol pct alumina) were prepared as air-cast ingots measuring 2.5 in. diameter by 6 in. high (see Table I for the analyses). Processing steps for all the alloys were as follows (also see Table 11): 1) Homogenization of the ingot at 982°C (1800°F) for 45 hr in an argon atmosphere. 2) Machine milling of ingots into fine chips. Average thickness was about 0.1 to 0.2 mm. 3) Hydrogen reduction of chips at 593°C (1100° F) for 1 hr to reduce copper and nickel oxides. 4) Rod milling of chips to finer powders. 5) Hydrogen treatment of powders as in step 3. 6) Internal oxidation of the powders. 7) Hydrogen treatment of oxidized powders as in step 3. 8) Hydrostatic compression of evacuated powders. 9) Sintering of compacts in hydrogen. 10) Hot extrusion. Variations in processing among the alloys were made in steps 4, 5, and 10 (see Table 11). In the past, two methods were utilized to internally oxidize alloy powders. Preston and Grant3 surface-oxidized dilute Cu-Al powders to obtain the necessary amount of oxygen to oxidize the solute metal (aluminum and silicon), and then permitted the formed copper oxide to diffuse and react with the solute in an argon atmosphere. Bonis and Grant4 exposed Ni-A1 and other nickel alloys to an oxygen pressure derived from the decomposition of nickel oxide at a preselected temperature, in an argon atmosphere. Both methods are applicable and can be modified to generate a range of oxygen pressures for oxidation of the solute but not the solvent metals. Procedure I: Surface Oxidation of Alloy A3, Cu-10Ni-0.76A1. Powders of -20 to +28 mesh were surface-oxidized at 500°C (932°F) to obtain the desired amount of oxygen for oxidation of the aluminum to alumina; the powder was then sealed in Vycor and heated at 900°C (1652°F) for various times up to

Jan 1, 1965

By W. L. Phillips

Aluminum and copper single crystals were strained in shear, unloaded and rotated 60, 120, and 180 deg. The magnitude of the Bauschinger strain increased rapidly during the easy glide region and became constant as the easy glide limit was reached. An increment in stress was not required to continue slip in any close-packed plane or in the reverse direction during easy glide. A qualitative theory is proposed to explain the present results. FOLLOWING the initial work on tin by Bausch,&apos; there have been several investigatorsB7 who have employed the shear test to study the deformation of aluminum. In all cases the shear technique was employed in an attempt to obtain a more homogeneous shear than in the conventional tension test The direct shear technique has the obvious advantage, relative to the tension test, that a crystal may be stressed in any predetermined plane and direction, including the reversal of strain sense. In the present investigation the shear technique was employed with aluminum and copper single crystals and their behavior was studied with respect to deformation in all close-packed directions in the octahedral plane. In contrast to previous investigations, the shear technique was used in an attempt to obtain a stress-strain curve in shear which is identical with the corresponding tension curve and then to use the additional degree of freedom of the shear test to study the mechanical behavior of crystals in all close-packed directions in the octahedral plane. PREPARATION OF CRYSTALS Single crystals 1/2 in. in diam and 6 to 7 in. long, were prepared from aluminum containing 0.001 pct Si, 0.001 pct Fe, and 0.001 pct Zn, by spectro-graphic ana1ysis and from OFHC copper. Crystals were grown from the melt in graphite at a rate of 1 5 in. per hr. The copper crystals were grown under an argon atmosphere. No lineage structure was observed in Laue patterns, though small angle boundaries were present in the crystals. The aluminum and copper crystals were annealed at 640" and 900°C, respectively, for 24 hr and furnace-

Jan 1, 1962

By C. Elbaum

If a thin layer of liquid gallium is spread on a surface of solid aluminum, the gallium penetrates high-angle grain boundaries at a very rapid rate and separation along these boundaries follows. An experiment was carried out to investigate this phenomenon. A well-annealed specimen of aluminum 99.994 pct pure, consisting of several large grains was used, Fig. 1. The dimensions of the sample were 25 mm wide by 2.5 mm thick and all the grain boundaries extended through the entire thickness of the plate. This sample was prepared by strain-annealing and, as can be seen in Fig. 1, contained one long, straight boundary. An examination of the crystal orientations showed this boundary to be a coherent twin boundary. The angular misorientations between the grains forming the other boundaries were all in excess of 20 deg. A thin layer of liquid gallium was spread on one side of the specimen at about 30°C (the melting point of gallium is 29.7"C). After the application of the liquid the temperature was lowered to about 27°C. The gallium remained liquid at this temperature and it can be seen from the A1-Ga phase diagram1 that the liquid was probably saturated with aluminum.

Jan 1, 1960

By S. Weissmann, P. R. Swann, D. F. Wriedt

The sizes and density of precipitates in an intemally oxidized 0.19 wt pct Al-Ag single crystal have been determined by low-angle X-ray scattering and by transmission electron microscopy . The correlation in particle sizes measured by the two techniques is reasonably good. For an oxidizing temperature of 800°C the particles were found to INTERNAL oxidation of dilute alloys of aluminum in silver produces an oxide which has an excess of oxygen compared to Al2O3.&apos; It is believed that the excess oxygen is an indication of the small sizes of the oxide particles. Depending upon the particular model chosen for the oxide structure, the size of the o-A1 particles can be calculated as a function of the oxygen-to-aluminum ratio. These calculations pre- have diameters in the range 30 to 140A, with a mean size of about 50.4 as observed by electron microscopy. At lower oxidizing temperatures, less than 600°C, no clearly resolved particles are formed, and it is suspected that if A1-0 clusters exist they must be exceedingly small, i.e., 10A or less in diameter. dicto that the particles would vary in size from 15 to 100A. This range of sizes is amenable to detection by both small-angle X-ray scattering and transmission electron microscopy. This paper compares the cluster sizes in such internally oxidized A1-Ag alloys determined by transmission electron microscopy and small-angle X-ray scattering. SPECIMEN PREPARATION Single crystals were prepared from 99.9999 pct Ag, obtained from Cominco Products, and 99.99 pct Al, obtained from Aluminum Co. of America. All melting operations were carried out in graphite molds under flowing purified hydrogen in a horizontal zone refiner. The silver was first degassed,

Jan 1, 1964

By Herbert Herman, M. E. Fine

THE first decomposition product of a supersaturated aluminum-rich A1-Ag alloy at low tempera- tures is Guinier-Preston zones.&apos;-, The zones are ideal and each consists of a spherical shaped silver-rich cluster about 16 A in diam syrounded by a silver-poor shell approximately 72A in diam.&apos; The composition of the two regions is not known with certainty., After quenching from the solution anneal, these zones form rapidly on aging at temperatures as low as -30°C.5 The rate of zone formation increases with aging temperature; the activation

Jan 1, 1961

By Colman Goldberg

IT is customary to plot crystallographic planes or axes on a Wulff stereographic net which is ruled with parallels of latitude and meridians of longitude. If a single crystal is placed at the center of a sphere, the coordinates of a crystallographic plane or axis are the coordinates of the point where the axis intersects the sphere. The standard (HKL) projection is the projection for which the sphere is rotated so that the (HKL) pole is at the center of the projection. Schiebold and Sachs&apos; and many others have published standard projections for the more important planes of a cubic crystal. With Tables I and 11, it is possible to plot any plane (HKL) of a cubic crystal on a standard (001) projection if the absolute values of the individual H, K, and L are nine or less, which is almost always the case. Using the methods outlined by Barrett,&apos; the standard (001) projection can be rotated so that any arbitrary plane is at the center of the projection. The tables are believed to be important for two reasons: 1—The heretofore published standard projections usually are not of the proper size to fit the stereographic nets available. With these tables a standard projection can be made which will be of exactly the proper size for the available stereographic net. 2—With the tables, planes that do not appear on the previously published standard projections can be easily plotted. For these reasons, the tables are especially useful in the study of optical reflections from etched surfaces and can also be used to make a standard projection for the axis which is normal to the macroscopic surface. (This axis can be found by X-ray or optical methods.) Then if the crystal is etched, the effect of the etchant can readily be determined by comparing the latitude and longitude of the reflecting planes (as determined with an optical goniometer) with the standard projection that has been prepared. Use of the Tables Fig. 1 shows the meridians and parallel which have been designated as zero longitude and latitude. The tables themselves are self-explanatory. The

Jan 1, 1953

By R. W. Heckel

The conzpaction of metal powders is analyzed through density-pressure curves as a three-stage process — die filling, individual particle motion, gross compact deformatim. The densification occurring during each of these stages is evaluated quantitatively. The amount of densification in the first and second stages is primarily a function of particle geometry. The densification taking place in the third stage is dependent mainly upon the material. AT the present time the densification of powders during compaction is usually described by terms such as "compactibility," "compressibility," and "compression ratio." Schwarzkopfl has proposedthat compactibility be defined as the minimum pressure needed to produce a given green strength, while compressibility be used to indicate the extent towhichthe density of a powder is increased by a given pressure. Compression ratio is generally defined as the ratio of the compact density obtained at a given pressure to the apparent density of the loose powder. 13alshina found that the pressure imposed on a compact affects the relative volume of the compact according to the following relation: hP= - LV + C [ll where: P is the applied pressure, V is the relative volume of the compact, Ratio of the specific volume of the compact to that of the material without porosity. Lisa constant described as the modulus of pressing and is determined by the slope of a plot of h P vs V, and C is a constant which is determined by the intercept of a plot of InP vs V. Several drawbacks of the Balshin analysis may be noted from Fig. 1, which is a plot of pressure (loga-

Jan 1, 1962

By M. H. Richman, E. S. Meieran

An analytical method is presented which enables the electron diffraction patterns from a twinned region to be indexed. The method has only been applied to (112) twins in bcc lattices, but can easily be adapted to other types of twinned lattices. Calculations of all twin spots, including those superimposed on matrix spots, is made possible by this method. SINCE the advent of transmission electron microscopy, the analysis of selected-area electron diffraction patterns has become very important in the interpretation of electron micrographs. Frequently, as in the case of some martensites, twinned areas are observed and give rise to complex diffraction patterns, which so far can be analyzed only for the simplest orientations of the thin foil specimen with respect to the electron beam. In order to simplify the analysis of twin patterns of more complex orientations, an analytical method was devised which is capable of predicting the positions of all reflections from both matrix and twin regions for all possible foil orientations. Although the method has only been applied to the case of bcc metals twinned about a (112) plane, it is equally applicable to other Bravais lattices. This method has been successfully applied to selected-area electron diffraction patterns of Fe-Ni and Fe-Ni-C martensites and drawn tungsten wire. PROCEDURE Imagine the reciprocal lattice corresponding to a bcc material, with each point hkl representing the crystallographic plane (hkl). Since the extinction conditions require that for this lattice, only reflections where h + k + 1 = even integer are allowed, the three dimensional reciprocal lattice is actually fcc. Since in real space twinned regions and matrix regions are mirrored across a (112) plane, the twinned reciprocal lattice is derived from the matrix reciprocal lattice by a rotation of 180 deg about a (112) direction. While it is possible to calculate how a point hkl will shift under a twinning transformation to a new point htktlt using only the reciprocal lattice based on the orthonormal vectors [100], [010], and [001], the calculations are greatly simplified if a new orthonormal coordinate system containing the twin axis is introduced. The twinning operation then becomes a simple rotation of 180 deg about a principal coordinate axis (in this case the twinning axis), and a retransformation back to the original reciprocal space will give the position htktIt of the twinned reflection.

Jan 1, 1963

By W. L. Phillips

Single crystals of aluminum, brass, and copper oriented for (100) and (110) slip were extended at 25°, 400°, and 600°C in simple shear. Aluminum specimens oriented for nonoctahedral slip began to shear at a higher critical resolved shear stress than specimens oriented for octahedral slip. Parabolic stress-strain curves were obtained from zero strain. The initial rate of parabolic hardening was lower for specimens sheared on the (100) plane in a close-packed direction <110>, than for specimens sheared in a nonclose-packed direction <100>. metallographic evidence, however, showed that all slip traces could be explained in terms of (111) <100> slip. All attempts to cause nonoctahedral slip in copper and 70-30 a-brass single crystals were unsuccessful. Instead of shearing, the crystals bent, allowing {111} type planes to come into action. NONOCTAHEDRAL slip in aluminum has been reported under three different conditions: first, as the main mode of slip in tension experiments at elevated temperatures;&apos;-&apos; second, as the main mode of slip in direct shear experiments at room temperat~re; and third, as a minor mode of deformation, i.e., as cross-slip, in tension, shear, and bicrystal experiments at room and elevated temperatures."-l2 However, as far as the author knows, nonoctahedral slip has not been reported in either copper or 70-30 a-brass. The present study was undertaken to determine whether nonoctahedral slip could be obtained in aluminum, brass, or copper at room or elevated temperatures when the shear stress was approximately constant over the cross-section, a maximum at the center, or a maximum at the surface. EXPERIMENTAL PROCEDURE A detailed description of the crystal preparation and shearing apparatus has been given previo~sly. Cylindrical crystals 1/2 in. in diam and 8 in. long were grown from the melt in a temperature-gradient furnace. The aluminum contained 0.001 pct Zn, 0.001 pct S, and 0.001 pct Fe; the 70-30 brass contained 0.015 pct Pb, 0.001 pct Fe, 0.01 pct Ni, 0.02 pct Sn, and 0.005 pct Se; the copper was certified OFHC of 99.98 pct purity. All samples were electropolished prior to testing. The shear apparatus was a modified Bausch type. The strain sensitivity was 4 x lob4 Load was applied by clamping the rods attached to the shear plates in an Instron tensile machine. The rate of loading was 0.02 in. per min. In all cases a 1/8-in. gage length was used. For the tests performed at 400° and 600°C the shear plates, collars, and rods were made of stainless steel. These elevated-temperature tests were performed in an argon atmosphere. A) Aluminum at Room Temperature. Values of a and ß for the various slip planes and slip directions investigated are shown in Table I where a is the complement of the angle between the specimen axis and the slip direction, and ß is the angle between the specimen axis and the normal to the shear plane. The shear stress is a function of a (assuming ß - 0);10 when a is less than 27 deg, the shear stress on the slip plane for which the specimen is oriented has a maximum at the center of the crystal; at a = 27 deg the shear stress is constant across the slip plane; for a greater than 27 deg the shear stress is a minimum at the center. Fig. 1 shows the stress-strain curves for specimens cut from crystals 1, 2, and 5, which were sheared on the (010) plane in the [loll direction at room temperature. These three crystals have shear-stress distributions corresponding to the three dif-

Jan 1, 1962

By G. F. Bolling

HE high mobility of grain boundaries in zone-refined metals has been particularly demonstrated for lead above 150°C in grain growth studies1 and in the extensive work by Aust and Rutter.1 In these investigations, no elaborate precautions were taken to eliminate oxygen from the zone-refined lead; however the alteration of creep characteristics by oxygen concentrations of less than 5 x 10 -5 wt pet

Jan 1, 1962

By A. S. Keh, H. A. Wriedt

The Precipitation of nitrides in quenched Fe-N alloys, aged between 25° and 200°C, was studied by transmission electron microscopy. Different dislocation substructures were introduced into the materials by recrystallization, cold working, and by Phase transformation prior to the introduction of nitrogen. It was found that the precipitated nitrides, tentatively identified as Fe16N2, have (100) habit planes. Nucleation takes place Preferentially at dislocations and at subboundaries. It sometimes occurs in the matrix, probably on vacancy clusters, but rarely on high-angle boundaries. The process of nucleation on dislocations and subboundaries is very temperature dependent. At room temperature there is no particular orientation relationship between the dislocations involved and the (100) planes on which the nitride Particles formed. With increasing temperature, the nucleation sites tend to become restricted to those dislocation segments lying in (100) planes. The change of yield stress of the 0.022 and 0.043 pet N alloys during quench aging can be correlated semiquantitatively with the change in particle distribution. Strain aging in quenched alloys can be separated into two stages. The early stage is attributed to nitrogen segregation to dislocations and the later stage is associated with precipitation. When previously quench-aged specimens were strained and aged, no additional Precipitates could be seen, although a considerable amount of strain aging occurred. DURING the past two decades, the precipitation of nitrides from a iron has been extensively studied by various techniques. It has been established that two types of nitride exist. The stable nitride, Fe4N, forms at temperatures above 250oC and Fe16N2, the

Jan 1, 1962

By Hsun Hu

The microstructural changes during rolling and at various stages of recrystallization in (111)[112] oriented single crystals of Si-Fe have been studied by transmission electron microscopy. At very low deformation, the dislocation structure consists of jogged dislocation lines, edge dislocation dipoles, and numerous dislocation loops, which may be interpreted by the jog-formation mechanism in moving screw dislocations. Up to 70 pct rolling reduction, no sharply defined cells are formed. Subgrain forma- tion takes place somewhat earlier in the annealing process than in a similarly processed (110)[001] crystal. This may be partly responsible for the reported difference in the rate of recrystallization between (111)[112] and (110)[001] crystals. Evidence indicates that the formation of recrystallization nuclei occurs largely by the coalescence of sub -grains. This is consistent with previous observations on other Si-Fe crystals. AVAILABLE data in the literature indicate that the main features of rolling and annealing textures in (111)[112] and (110)[001] crystals are essentially similar. A (111)[112] or (111)[112] crystal can be rolled 70 pct without changing its initial orienta-

Jan 1, 1964

By F. Garofalo

It has been shown by various investigators that during constant stress creep the dependence of minimum creep rate, 6,, on stress, o, is given by em = A onat low stress levels, md by 6, = A&apos; exp [ß s] at high stress levels. In these relations A, n, A&apos;, and ß are constant at constant temperature. A single relation has been found which satisfies conditions for both high and low stresses and agrees well with experimental results. This relation is 2, = AN (sinh a s)n, where A" is a constant at constunt temperature and a = p/n. This relation also satisfies the linear relation, 6, = k s, found at temperatures near the melting point at low stresses. EXPERIMENTAL creep results have led to a number of empirical relationships between minimum creep rate, 6,, and the applied stress, s. Under conditions of constant stress it is generally found that at low-stress levels,&apos;-&apos; the dependence of minimum creep rate is given by 6, = Asn. At high-stress levels&apos;74 the experimental results fit the relation, 6, = A&apos; exp [po l. In these relations A, n, A&apos; and ß are constant at constant temperature. A model based on climb-of-edge dislocations from a pile-up array leads to a relation similar to that found experimentally at low stresses.&apos; On the other hand. theories based on chemical-reaction rate,5 nonconservatively moving dislocation jogs, and jog migration and climb-of-edge dislocations4 lead to a relation similar to that found experimentally at high stresses. No difference in mechanism between low and high stress levels has been clearly defined; it is questionable whether such a difference really exists. In any event, the major argument usually given in substantiation of a change in mechanism from low to high stresses is that no single relation exists for defining the stress dependence of the creep rate over wide ranges in stress. However, such a relation has been found and is of the form, dm = A" (sinh a s)n, where A" is a constant at con- stant temperature and a = ß/n. This relation agrees well with experimental results over wide ranges in stress and temperature for copper, aluminum, an A1-3.1 pct Mg alloy, and an austenitic stainless steel. STRESS DEPENDENCE OF MINIMUM CREEP RATE At low stress levels the minimum creep rate, gm, depends on the stress, 0, under conditions of constant stress creep through the relation em=Aon [1] The quantities A and n have been defined previously. In the range in which this relation applies, a linear dependence is found in a log em,-log o plot. Above the stress range of application of relation [I], the minimum creep rate increases much mar; rapidly than predicted by relation [I]. This behavior is shown in Fig. 1 for a series of creep tests on copper4 at various temperatures ranging from 673 o to 973°K. Relation [I] is satisfied at the lower stresses, although the results at 973°K are quite limited. In all cases the transition beyond the applicable range of relation [I] is a gradual one indicating no abrupt change in mechanism. For all test temperatures, values of n have been determined from the results in Fig. 1. These are reported in Table I under Alog tm/hlog o. At high stress levels the stress dependence of minimum creep rate under conditions of constant stress is given by im = A&apos; exp [ß a] 2] All factors have been defined previously. In a log em-0 plot, relation [2] predicts a linear function. Experimentally, a pronounced deviation from the prediction of relation [2] is found at lower stresses. As the stress is lowered, the minimum creep rate decreases more rapidly than predicted by relation [2]. This shown for copper in Fig. 2. Again it is found that the transition from high to low stresses is gradual and no really sharp change is found. Values of p determined from the high stress results are given in Table I. The dependence of minimum creep rate on stress at constant temperature for all ranges in stress

Jan 1, 1963

By R. W. Guard

ALTHOUGH etching techniques have been developed for revealing dislocation sites in several metals and ionic crystals,h t is valuable to extend the technique to new metals. An etch pit method for nickel has been developed on the basis some suggestions of Dr. John R. Cuthill of the National Bureau of Standards who had observed etch pits in creep specimens of nickel. The etchant used was proposed first by wensch2 for revealing grain size in nickel. The present paper describes the evidence that the technique can be used to reveal dislocations and gives the conditions under which etching can be carried out. The specimens examined were vacuum melted high-purity Ni (99.985 pct Ni) and commercial "A" nickel (99.8 pct Ni). Both materials contained greater than 0.008 pet C and had been annealed in nitrogen or dry hydrogen at 1100o to 1200°C. This gave a grain size of 1.5 mm in the high-purity nickel and 0.050 mm in "A" nickel. Tensile specimens (0.254 in. diam) were deformed from 0.25 to 10 pct at room temperature and then heated for 1/2 hr at different temperatures from 400" to 900°C. The specimens were sectioned longitudinally then polished electrolytically in 60 pct H2SO4 and etched in 35 pct H3PO4 solution at 0.2 to 0.4 v for 30 sec to 3 min. The best method for setting the proper voltage for etching is to increase the voltage until gas bubbles are evolved vigorously from the specimen and then cut it back by 10 pct. It is necessary to heat the specimen above 500°C after deformation in order that etch pits will be formed. This "decoration" treatment permits carbon to segregate to the dislocation rendering them sensitive to etching. It was demonstrated that carbon was the decorating impurity by decarburizing some specimens in wet H2 at 1200°C. The susceptibility to etch pitting was lost following this treatment but could be restored by carburizing in contact with graphite. Some rearrangement of the dislocations in the as-deformed structure occurs on heating at 500oC and above so that the technique can not be used to study the nature of dislocation patterns in deformed specimens. Extended etching does not change the number of pits although the background becomes rough and the pits quite large. The polycrystalline specimens with various strains were examined after annealing at different temperatures. Typical patterns are shown in Figs. 1 and 2. In the unstrained specimen, Fig. 1, the density of pits is 2.5 X 10&apos; per sq cm. All grains show pits regardless of their orientation although there is a

Jan 1, 1961

By E. N. Mazza, H. S. Kalish

The effect of sintering types 302, 3028, and 430 stainless steel powder compacts in hydrogen and dissociated ammonia was investigated. It was found that sintering in dissociated ammonia resulted in as much as 0.5 wt pct increase in the nitrogen content of stainless steel even though the dissociation of the gas was complete. Sintering in hydrogen, on the other hand, reduced the nitrogen content of the stainless steel to less than 0.01 wt pct. In the case of the 302-type stainless steel, the low nitrogen content resulted in a material that was largely ferritic, whereas the high nitrogen content rendered the material fully austenitic. Sintering in dissociated ammonia resulted in lower density, generally lower tensile strength, less ductility, and higher hardness than sintering under equivalent conditions in hydrogen. The reduction of oxides on both stainless steel and iron particles was found to be effected by hydrogen partial pressure in the sintering atmosphere. Compacting pressure was found also to effect oxide reduction during sintering. DISSOCIATED ammonia often is used as a substitute&apos;.&apos; for hydrogen in sintering and in annealing, since economic advantages sometimes can be obtained by such a substitution. In addition, anhydrous ammonia contains very little impurity. Thus, dissociated ammonia gas is very dry whereas tank hydrogen often must be freed of oxygen and water vapor prior to use in many applications. The sintering of stainless steel powder compacts as well as bright annealing is well recognized as requiring a hydrogen atmosphere and for the foregoing reasons dissociated ammonia is frequently substituted. It has generally been overlooked, however, that the nitrogen in dissociated ammonia might have an important effect on the sintering process and on the properties of stainless steel compacts. Considered an inert gas in many applications, nitrogen, on the other hand, is very reactive with cer- tain metals. Dissociated ammonia could not be used for hydriding zirconium or titanium. Nitrogen reacts with columbium, tantalum, chromium, uranium, thorium, and many other active metals. Iron and iron-base alloys are, for the most part, inert in nitrogen but there are many borderline cases. It has been reported that stainless steel stabilized with columbium or titanium should not be sintered in dissociated ammonia.3 olybdenum has been reported as reacting with dissociated ammonia to a minor extent.&apos; Although most of the reactions with iron-base alloys are attributed to the action of un-dissociated ammonia and the action of nascent nitrogen, Uhlig4 showed how readily pure molecular nitrogen reacts with and diffuses into 18-8 stainless steel at 1150°C. He also pointed out how readily nitrogen diffuses out of 18-8 stainless steel when heated in pure dry hydrogen, and these thorough investigations on the subject show that commercial stainless steels are nitrogen-bearing, since they are melted in air. The effects of nitrogen in stainless steel, particularly the 18-8 Cr-Ni type, previously have received considerable attention." In 1926, it was pointed out

Jan 1, 1956

By J. E. Hilliard, J. W. Cahn

calculation has been made of the standard deviations to be expected in the measurement of volume fractions by areal analysis, lineal analysis and four point-counting Procedures. The effect of experimetztal errors is not included. Our conclusion is that a point count using a two-dimensional grid will be the most efficient method of volume fraction analvsis providing the grid spacing IS coarse enough. The predicted standard deviation for such an analysis is shown to he in good agreement with that determined experimentally. A metallurgist wishing to estimate a structural property by means of quantitative metallography is often faced with a choice between several different procedures. In such a case, he will naturally wish to know: a) Which procedure is the most efficient in the sense of requiring the least effort for a given precision? b) For a given procedure, what are the conditions for maximum efficiency? c) Under these conditions, how many measurements are required to attain a given precision? It is our aim in this paper to provide at least partial answers to these queries as they relate to the estimation of volume fractions from measurements on a random two-dimensional section of an opaque specimen. The commonly used techniques1,2 for volume-fraction analyses are based on one or more of the following principles: i) For an areal or Delesse3 analysis: That the areal fraction of a three-dimensional feature intercepted by a random plane provides an unbiased estimate of the volume fraction of that feature. ii) For a lineal or Rosiwal4 analysis: That the fractional intercept on a line passing at random through a two-or three-dimensional feature provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. iii) For a point-count analysis: That the fractional number of randomly or regularly dispersed points falling within the boundaries of a two-dimensional feature on a plane, or within the boundaries of a three-dimensional feature in a volume, provides an unbiased estimate of, respectively, the areal or volume fraction of that feature. The absence of bias referred to in these principles does not, of course, imply that the results of an analysis will be free of error, but only that the expected result is equal to the true one. Application of the foregoing principles provide the following six possible experimental procedures: a) An Areal Analysis—This involves the measurement with a planimeter (or other means) of the area of a constitutent intercepted by the plane of polish b) A Two-Dimensional Random Point Count—Apos-sible experimental procedure for this analysis is to superimpose a sheet of transparent graph paper on a micrograph, and then use a table of random numbers to select coordinates for the points. c) A Two-Dimensiotuzl Systematic Point Count-Similar to b) except that the points are distributed in a prescribed manner, usually at the corners of a lattice superimposed on a micrograph or the screen of a projection microscope. d)A Lineal Analysis—A measurement of the fractional line length intercepted. It is usually performed by traversing the specimen under the cross hairs of a microscope and recording the distance travelled in each constituent. e) 4 One-Dimensional Random-Point Count— This could be performed by traversing the specimen with stops at random intervals to identify the constituent then present under the cross hairs. f) A One-Dimensionul Systematic Point Count— Similar to e) except that the traverse is stopped at prescribed (usually equal) intervals. It will be noted that the point-counting procedures b) and c) can be regarded as methods of estimating the areal fraction. Similarly, e) and f) are indirect methods of making a lineal analysis. All of the six procedures described above involve at least one stage of sampling. Thus, quite apart from any experimental errors, there will always be a statistical uncertainty associated with the final results. It is with the calculation of this uncertainty that we will be concerned. To avoid unnecessary repetition, the statistical relationships that will be used in the calculations are collected together in the appendix. For a fuller discussion reference should be made to one of the many textbooks5,6 on statistics. For symbols relating to the specimen structure we will follow as far as possible the terminology used by Smith and Guttman.7

Jan 1, 1962

By H. M. Otte, A. L. Esquivel

A new leasl-squares method is Presented for determining lattice parameters of hexagonal or tetragonul structures. The method is adapted for use on electronic computers and involves a reiterative procedure. The correction factor employed raries linearly with the lattice parameter, a (determined from the Brag, angle). In contrast, Cohen&apos;s method and recent modifications of it use a correction factor that varies incersely as the squure of the lattice paramneter, a. While the recent modifications attempt to improve the precision of the extrapolated lattice parameter, a, (or-cu). by stressing the importance of the weighting factor. the present approach emphasizes the need for choosing the correct extrapolation function. A comparison between the present method (the Linear method) and Cohen&apos;s method indicates that the Linear method may be more appropriale in certain cases. through a priori no critertion appears to he available for making a chorce between the methods. The size of hexagonal and tetragonal crystal lattices is determined by two parameters, a, and c,. Although in principle the two lattice parameters can be determined independently from reflections for which h - k = 0 and 1 = 0, respectively, in practice this may be inconvenient (because of the angular positions at which these reflections may occur) or not easily possible (because of low intensity). Furthermore, if a high precision or accuracy is required, the limited number of reflections of this type available, particularly in the high-angle region, is not sufficient for the necessary corrections (mainly due to absorption) to be determined with accuracy. Several methods1-7,11-13 have been proposed employing all reflections, to obtain the optimum values, a. and co, either by a trial and error procedure or a least-squares fit. Of the latter method, cohen&apos;s5 is the best known one since it provides explicit expressions for the optimum a. and c,. However, Cohen&apos;s method is only strictly valid if an extrapolation function is used that varies linearly with l/a2 or lie2 (see Section 3), a requirement that does not appear to be generally appreciated. On the other hand, all the better known and more widely used A recent trial and error method was proposed by Massalski and King8,7 who computed extensive auxiliary tables of axial ratios vs the functions A = [(4/3)(h2 + hk +k2) + l2+(a/c)2] and C = A(c/a)2 used in computing a and c values from the observed Bragg angles. These values of a and c were then plotted against a function which permitted linear extrapolation. As a criteria; for the "optimum" values, Massalski and King rely upon a visual fitting of the line through points representing reflections of low 1-index points to compute the extrapolated value of ao and high 1-index reflections to obtain CO. The successive computations and graphical plotting required to reach the "optimum" value are quite lengthy and tedious even on a desk calculator and no quantitative assurance is obtained of having in fact selected the optimum value.* If the method of Massalski and King is used on an electronic computer, then their published tables become redundant and a least-squares fit becomes a natural selection for the choice of optimum values. Such an approach will be called the Linear method. For work now in progress on the effect of certain physical variables on the lattice parameters of hexagonal crystals, it has become essential to determine the confidence limits of small changes in the lattice parameters. Since extrapolation functions that varied linearly with a and c actually also appeared to vary linearly with l/a2 or l/c2 when tested against published as well as our data, a comparison of Cohen&apos;s method and the Linear method was considered desirable (Sections 3 and 4). For the latter method an electronic computer was required since a reiterative procedure to obtain the optimum ao and co values had to be employed. The purpose of this paper is to describe the principles of the Linear method, illustrate its application, and compare it with Cohen&apos;s method. 1) THE LINEAR METHOD The standard practice in obtaining the lattice parameters in the Debye-Scherrer method is to

Jan 1, 1965

By R. E. Carter, F. D. Richardson

Self-diffusion coefficients have been measured for iron in wustite (700° to 1000°C) and for cobalt in cobaltous oxide (800&apos; to 1350°C) by means of radio-isotopes. Both sectioning and decrease of surface-activity methods have been used and a particular shortcoming of the latter method has been disclosed for wustite. The effects of oxygen pressure on the composition of cobaltous oxide and on the diffusion coefficient of cobalt in the oxide have been established. The effect of the preparation conditions of the cobalt-oxide specimens on the diffusion measurements has been determined. It has been concluded that diffusion of cobalt occurs via vacant cation sites and that a cobaltous-oxide disk reaches equilibrium with its environment in a time which is very short compared with that needed for diffusion of the radio-isotope. THE availability of radioactive isotopes in recent years has permitted the measurement of many self-diffusion coefficients which were hitherto impossible to determine. With the advent of radioactivity, the method of measuring diffusion coefficients has also changed. The earlier sectioning method by which the concentration profile of the diffusing species was determined in the diffusion specimen has often been rejected in favor of the decrease of surface-activity method first developed by Von Hevesy,&apos; and extended by Steigman, Shockley, and Nix,&apos; and Raynor, Thomassen, and Rouse." With the experimental arrangement where an infinitely thin deposit of tracer is diffused into a semi-infinite cylinder, the decrease in activity of the active face due to diffusion of the tracer into the specimen is measured by counting the active face before and after diffusion. Under these conditions, the appropriate solution of the diffusion equation is R = e*(l-<K/Z) [1] where R is the ratio of the counting rates after-to-before diffusion, $& is the Gaussian error integral of \/Z, and Z is defined as Z = p2Dt, p being the linear-absorption coefficient of the detected radiation in the diffusion specimen, D the self-diffusion coefficient, and t the diffusion time. In the older sectioning method the concentration distribution of the tracer is found after diffusion by analysing thin parallel sections cut from the active face of the diffusion specimen. As seen from the solution of Fick&apos;s second law for the distribution of an infinitely thin source after diffusion into a semi-infinite cylinder the log of the concentration plotted against x&apos; will be a straight line of slope log e/4 Dt. The diffusion coefficient thus can be calculated directly. The units of the tracer concentration are completely arbitrary, since any change in units does not change the slope of the log c vs x2 lot. Although both of the above methods have been widely used, a thorough experimental comparison does not appear to have been made. Birchenall and Mehl,&apos; during an investigation of the self-diffusion rate of a and r iron by the surface method using Fe" tracer, diffused and sectioned one welded couple. The diffusion coefficient from this run agreed with those by the surface method. Buffington, Bakalar, and Cohen," during an investigation on a and y iron

Jan 1, 1955