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By W. L. Phillips

Stress-strain curves were obtained for single crystals of 70 pct Ag-30 pct Zn tested in tension and shear. Samples tested in tension and shear had comparable resolved shear stresses and stress-strain curves. The {111} <110> slip system was observed. It zoas found that the9.e is a barrier to slip in both latent close -packed directions and that the magnitude of these barriers is proportional to prior strain during easy glide. It was observed that cross-slip in tension and shear was most frequent in crystals with an initial orientation near <100> "Oershoot" zoas observed in tension. The amount of this "overshoot" was independent of initial orientation. AN idealized concept of plastic deformation indicates that a single crystal should yield at some stress that is dependent on crystal perfection and it should then continue to deform plastically by the process of easy glide which is characterized by a linear stress-strain curve and a low coefficient, d/dy, of work hardening. Hexagonal metal crystals generally conform to this ideal concept of laminar flow. In fcc metals the range of easy glide is always restricted in magnitude and it is strongly dependent on orientation, composition, crystal size, shape, surface preparation, and temperature. Since one of the principal differences between the two crystal systems, both of which deform by slip on close packed planes, is the existence of latent slip planes in the fcc crystals, it has been proposed that the transition from easy glide to turbulent flow, characterized by rapid linear hardening, is due to slip on secondary planes intersecting the primary plane.ls Several theories have been proposed to explain the linear hardening and parabolic stages of the stress -strain curve.6"10 The easy-glide region is the least understood of the three stages. The stress-strain characteristics of Cu-Zn, which shows a long easy-glide region, have been extensively investigated."-" In light of recent ideas on dislocations, cross-slip, effect of solute atoms, and stacking fault energy, it was felt that the certain features of this earlier work might be compared with another alloy, Ag-30 pct Zn, which also exhibits a long easy-glide region. Tension and shear stress at room temperatures were employed. The results obtained, together with some interpretation of the observations, are described below. EXPERIMENTAL PROCEDURE The silver and zinc used for mixing the alloys were 99.99 pct pure. The two components were weighed to within 0.1 pct of the weights required fo the alloy composition. They were then placed in a closed graphite mold and the mold and contents were heated in 100°C stages from 500&apos; to 900°C with sufficient time and vigorous agitation at each stage provided to dissolve the silver. The crucible was then heated to 1150°C and agitated violently before being quenched in oil. The resulting alloy rod was machined free of sur face defects and then placed in a graphite mold designed for growing single crystals. The graphite mold was closed with a graphite plug and was encased in a pyrex glass tube which was connected to a vacuum system. The tube and mold assembly were placed in a furnace; the tube was evacuated and the furnace was rapidly heated to a temperature sufficient for fusing and sealing the glass. The glass-encased evacuated mold and contents were then lowered through a vertical furnace. The top section of the furnace was held at 100 °C above the melting point of the alloy. The lowering rate was 1.5 in. per hr. The tension specimens were 1/4 in. diam; the shear specimens were 1/2 in. diam. These specimens were then removed from the mold, etched, and chemically polished with hot (60°C) Chase etch reagent (Crz03-4.0 g, NH4C1-7.5 g, NHOs-150 cc, HzS04-52 cc, and Hz0 to make 1 liter). In preparation for tensile testing, the specimens were carefully machined to a diameter of about 0.200 in. to permit a gage length of 6 in., annealed for 16 hr at 800&apos; to reduce coring, and then cleaned and polished. A modified Bausch-type shear apparatus which has been described previously18 were employed. The gage length was 1/8 in. This shear apparatus was placed in an Instron tensile testing machine. EXPERIMENTAL RESULTS A) Tension. Several specimens were extended at room temperature to determine the effect of initial orientation on the stress-strain curves of Ag-30 pct Zn. The initial orientation and the resolved shear stress supported by the active slip system at various total strains are plotted in Fig. 1. The critical resolved shear stress, t,, initial rate of work hardening, d/dy, and length of the easy-glide region are independent of orientation. The arrival at the symmetry line is shown by an arrow in Fig. 1. During the easy-glide region of the stress-strain

Jan 1, 1963

By C. P. Gazzara and

The modulus of elasticity and yield strength of commercially pure, annealed titanium sheet was investigated at room temperature as a function of strain rate and direction of loading. The value of E varied with direction of measuremeni in the sheet but was unaffected by strain rate in the range 0.04 x 10-to 10-2min-1. The yield strength increased with increase it2 strain rate and varied with specimen orientation. VALUES of the modulus of elasticity, E, in tension for commercially pure titanium have been reported at from 14 to 20Xl06 psi.&apos; Reasons suggested for this variation have been a) composition, b) strain rate, c) texturing, and d) creep. For example, alloys of titanium with aluminum, manganese, and nitrogen have yielded modulus values of from 12.5 to 16.8 x lo6 psi at room temperature.&apos; It was shown by Klier that the modulus in titanium plate was sensi-tive to strain rate. while Dotson and kattus meas- ured variations in E as the strain rate was increased from 3X to 60 min-l. For RC-7OA, 0.040-in. titanium sheet at room temperature Dotson and Kattus found that the average values of E, for specimens in the rolling direction, increased from 14.7 to 16.0 X lo6 psi as the strain rate increased. Simultaneously, the 0.2 pct yield strength increased from 74,700 to 95,700 psi for the same specimens. Differences in yield strength and E have been reported as a function of directionality in titanium sheet.= Dotson and Kattus report such an effect, and Feola6 found in annealed titanium sheet marked anisotropy in tensile strength, yield strength, reduction in area and elongation at room temperature, with

Jan 1, 1961

By P. Duwez, C. B. Jordan

The phenomenon of the change of volume of pressed powder compacts upon sintering is well known in the field of powder metallurgy. Depending upon the metal or metals involved and the pressure used in forming, a compact may, in the course of time of sintering at a given temperature, expand mono-tonically, contract monotonically, or first show a volume change of one sign followed by a change of the opposite sign. It is clearly desirable to have accurate knowledge of the magnitude and sign of the change in dimensions to be expected in any given case, both from the point of view of direct usefulness in the fabrication of parts by powder metallurgy, and from the longer range viewpoint of elucidating the fundamental mechanism of metallic sintering. The present study was therefore undertaken as a first step in acquiring systematic and reasonably quantitative knowledge of the change in density of metal powder compacts during sintering. For practical reasons, copper was selected as the material to be studied first, and its densification followed as a function of temperature and time of sintering in hydrogen and in vacuum. Experimental Procedure The copper powder used was that designated by the manufacturer (Metals Disintegrating Co., Elizabeth, N. J.) as MD-151. This powder was sifted through Tyler standard screens to separate the fraction having particle size range between 200 mesh and 325 mesh, and this fraction was used in all the subsequent work. Compacts weighing about 10 g were then pressed in a 1 in. diam round die, using a pressure of 20,000 psi throughout. Sintering was carried out in commercially built electric furnaces in which the resistance windings are so disposed as to produce a nearly uniform temperature along the axis of the furnace for a length of about 18 in. centrally located. In order to be able to sinter in a controlled atmosphere, a 2 in. stainless steel tubing was inserted in the furnace. Each end of the tube was cooled by a water jacket about 7 in. long, and closed with a rubber stopper. The hydrogen used for one series of specimens was purified as described in Ref. 1. For the other set, a pressure of about 0.5 mm Hg was maintained during sintering by a Welch Duo-Seal Pump. The specimens were heated on square trays made of stainless steel. In placing specimens in the trays, a thin even layer of powdered aluminum oxide was first sprinkled on the bottom of the tray. A copper guard disk about half the thickness of the specimen was then placed in the tray and covered with a second layer of alumina. The actual specimen was then set on the guard disk, and a final coat of alumina sprinkled over the specimen. This technique was evolved for sintering the specimens in such a way as to reduce the influence of unknown extraneous factors to a minimum. If the specimen is placed directly on the tray and sintered, it is found that the resulting shape is that of a frustum of a cone, rather than a section of a right circular cylinder, since friction with the tray prevents the bottom of the specimen from contracting at the same rate as the top. In the arrangement used in these experiments, the guard disk provided a support which shrank at the same rate as the specimen, and the alumina powder reduced to a minimum friction between guard disk and tray, and between specimen and guard disk. The procedure followed in sintering consisted of bringing the furnace to the required temperature, and then inserting the specimen into the central heated portion of the furnace tube in one of the two atmospheres used. At the end of the heating period, the specimen was cooled by bringing it into a portion of the furnace surrounded by a water jacket. These manipulations were carried out without opening the furnace, by means of rods which were attached to the trays and operated through a sliding seal in the rubber stopper. The progress of densification of the copper compacts was studied at 1300, 1400, 1500, 1600, 1700, and 1800°F. At each of these temperatures, a specimen was allowed to sinter for each of the following time intervals: M, 1, 2, 4, 8, 16, 32, and 64 hr. The thickness and diameter of each specimen were measured with micrometers before and after sintering, and each was weighed on an analytical balance after sintering. Results The techniques described in the preceding section were found to give satisfactory results. The specimens were not detectibly warped after sintering, and were usually of uniform diameter (that is, truly round) to within 0.001 in., a very few showing a variation in diameter of ±0.002 in. All specimens were found to have the same diameter

Jan 1, 1950

By P. Duwez, C. B. Jordan

A. J. SHALER*—I should like to congratulate the authors for having carried out such a precise set of experiments. It has been found useful, in sintering experimental compacts in vacuo, to make certain that the residual gas is not one which reacts with the metal. Since traces of oxygen can be kept away only with great difficulty, the technique is often adopted of using a "getter " of powder in the vicinity of the compacts, and, in addition, of permitting a small hydrogen leak to flow into the vacuum chamber. Did the authors use similar devices? This paper brings up a question concerning the definition of the word &apos; sintering.&apos; The authors restrict its use to the adhesion between particles. Kuczynski, in a paper presented at this meeting, applies the word to the growth of areas of contact between particles. I have used it to mean both these phenomena and also the dimensional changes which continue to take place after the first two have run their course. May I suggest that we should come to an agreement on the use of these words ? Fig 1 and 2 show an interesting feature: extrapolation of the curves to zero time does not give a densification parameter of zero. The higher the temperature, the higher is the intercept on that axis. These observations agree with the concept of a practically instantaneous densification taking place while the compact is being brought to heat. Such a change may be brought about by plastic deformation and primary creep. The stress pattern causing this first rapid flow is, to my mind, due to the force of attraction between the surfaces of opposite particles in the regions immediately flanking their common areas of contact. The stress is not temperature-sensitive, but at room temperature plastic deformation only proceeds until the metal in the area of contact can support it elastically. As the metal is heated, the elastic limit falls, and further plastic flow occurs. At the higher temperatures, this is followed by primary creep, and finally by the steady-state rate-reaction which the authors are seeking. If they were to recalculate their densification-parameter values, using, not the initial density of the cold compact, but the density after the compacts have been brought to temperature, the systematic deviations from linearity in Fig 3 and 4 might be eliminated. Such initial densities might be obtained by extrapolating the curves of Fig 1 and 2 to zero time. I am naturally pleased to see that such a very well done series of experiments leads to a heat of activation (for the densification process in hydrogen) that is much higher than that for self-diffusion, in confirmation of the less elaborate results reported by Wulff and myself (Ind. and Eng. Chem., (1948) 40, 838). J. T. KEMP*—I would like to comment on Dr. Shaler&apos;s remarks. There are apparently different interpretations of the word "sintering." It seems to me that an accurate definition of our word is essential in all metallurgy. May I point out, in this connection, that in practical metallurgy the word "sintering" has been applied to a bonding process in the preparation of ores and flue dust for fur-nacing. It would be unfortunate if in the area of powdered metallurgy we should establish a definition that is essentially different in meaning. F. N. RHINES*—I think that I can answer the question by saying that I see no essential difference between the use of the term "sintering" in extractive metallurgy and in powder metallurgy; physically the same things are going on. I admit sintering is used for different end purposes in the two cases. When we resort to the sintering of lead ore mixture we are doing so to obtain a chemically reactive, loose texture of some rigidity. This is only a difference in use. After all, in powder metallurgy we sometimes deliberately produce a very porous material which has just a little strength, just as in the case of sinter cake. P. DUWEZ (authors&apos; reply)—We agree that it would be helpful to have well-established definitions of such terms as "sintering." Since the question has now been raised, the time might be appropriate for its consideration by some suitable committee of one or more of the metallurgical societies. In answer to Dr. Shaler&apos;s first question, no getter nor hydrogen leak was used in our vacuum experiments, except insofar as the guard disks (used to reduce friction between specimens and trays) may have acted as getters. Dr. Shaler&apos;s statement that extrapolation of the curves of Fig 1 and 2 does not lead to zero densification at zero time apparently overlooks the logarithmic

Jan 1, 1950

By Norman Brown

It is suggested that the difference in ease of cross-slip among the fcc metals determines the relative amounts of [111] and [100] wire texture which occur in each metal. Since the ease of cross-slip is controlled by the stacking fault energy, it turns out that the amount of [111] texture should increase as the stacking fault energy increases. Arguments and existing data are presented to support the above suggestion. THE fcc metals generally have a dual texture, [11 and [loo], after wire drawing. As yet no fundament explanation exists concerning the variation of the amounts of each texture among the metals. Barrett&apos; has compiled data which show how the relative amounts of each texture vary from 100 pct [Ill] in the case of aluminum to 25 pct [l1] for silver. In this paper it is suggested that the value of stacking fault energy plays a major part in determining the amount of each type of texture. The double texture has its origin in the classical rotation of a single crystal under tension. An equilibrium position of the crystal is one in which three or more equivalent slip systems are operating simu taneously. Most crystals, initially, tend to rotate toward the [1ll] or the [l00] pole depending upon its initial orientation. This single-crystal behavior is essentially the same as the rotational behavior of the polycrystalline metal as worked out by Taylor.2 The next point to consider is whether the [Ill] or [100] orientation is more stable. There have been many discussions of this question3&apos;" which, in general, have lead to the conclusion that 11111 is most stable. For example, Pickus and Mathewson 4 suggested that a [Ill] texture produces more effective flow becake the [ 110] slip direction makes a smaller angle with the [111] than with the [loo]. A crude statistical argument will be presented which again favors the (1111 orientation. In order to maintain a pure [loo] wire texure, slip must occur in equal proportions in four of the six possible <110>slip directions. In order to maintain a pure [Ill] texture, slip must occur in equal proportions in only three of the six <110>directions. Since the <110> directions are the only slip directions in a fcc metal and if it is assumed that each of these six directions is equally probable, then the relative probability of a [1ll] texture vs a [l00] texture may be calculated. The statistical weight of a particular texture is the multiplicity of a texture times the probability of obtaining any one. The statistical weight for [Ill] is

Jan 1, 1962

By C. D. Tedmon, D. P. Ferriss

THE yield stress, o of low-carbon steel has been shown to vary with the average grain diameter, d, according to the relation1-3 where o is taken to be the lower yield-point stress Of is the friction stress on an unlocked dislocation, and ky is a constant. The interpretation2,4 of ky in terms of dislocation theory relates this constant to the stress to unlock a source across a grain boundary. cottrel14 predicted that ky would increase with decreasing temperature. This was observed to be the case by Adams and coworkers5 in their investigation of niobium (columbium). However, petch6 and Backofen: both working with low-carbon steel, found ky insensitive to temperature. In his work with high-purity niobium, Johnson&apos; found ky equal to zero. Evansg showed that k, was essentially zero for niobium containing nitrogen in an appreciable concentration range. The present experiments were designed to check this apparent anomaly in the value of ky in another Group V metal. Yield points were determined as a function of grain size at several temperatures for tantalum and a tantalum-tungsten alloy. The material used was double are-melted tantalum and a double are-melted alloy of 90 pct Ta and 10 pct tungsten (by weight), both obtained as unannealed, swaged rod. The impurity content of the materials is given in Table I. The tantalum was annealed at 1325"C. in a vacuum resistance furnace using a tantalum boat. The alloy was similarly annealed at 1660°C. Annealing times varied from 15 min to 2 hr, depending on the desired grain size. Nominal pressure in the furnace was 3 X 10~4 mm of Kg. Metallographic examination showed that the annealing treatment produced grain sizes ranging frorn 0.021 to 0.200 mm in the tantalum, and 0.060 to 0.160 mm in the alloy. Tensile bars were made by centerless grinding the annealed specimen;, and then electropolishing to remove all grinding marks. The specimens were than pulled :it 2 1/2 pct per rnin in an Instron testing machine. The tantalum specimens were tested at 77", 195", and 300°K. The alloy was tested at 300°K only. All specimens exhibited a yield-point phenomenon at all temperatures. Typical load-elongation curves at the three test temperatures are shown in Fig. 1. The lower yield stress is plotted as a function of (grain size) in Figs. 2 and 3 for tantalum and the 90 pct Ta-10 pct W alloy, respectfully. The position and slope of the curves was determined by least-

Jan 1, 1962

By R. E. Caffrey, S. K. Tung

This paper reports some of tile results obtained from the vapor-phase reaction of a volatile metal halide with a hydrogen and carbon dioxide mixture in an epitaxial-deposition chamber. Tile oxides deposited were silicon di oxide, aluminum oxide, mix-12tves of silicon di oxide and aluminum oxide, and titanium oxide. Tile deposited silicon di oxide was transparent and amorphous and had a density and index of refraction similar to that of thermally grown silica. The vote of etching was determined. The thickness uniformily of the oxide was found to he related to the aerodynamics of the system employed for deposition. A clear silicon di oxide layer was found to be dependent upon the quality of the surface prior- to aside deposition. The process parameters affecting the vale 0f deposition were studied. The deposited aluminum oxide was transparent, holy-cl-ysttrlliile, and possessed remarkable resistance to hydrofluoric acids. By measurements it has been shown that the deposited aluminum oxide is both insulating and continuous. ThE cleanness of an epitaxial silicon surface both immediately after growth and during device processing is thought to be one of the major factors contributing to the electrical properties of a final device. The advantage of protecting an epitaxial silicon wafer surface with an oxide grown immediately following epitaxial deposition is obvious. The successive growth of silicon and silicon diox- ide in epitaxial apparatus was studied by Steinmaier and loem.&apos; They formed silicon dioxide films on a silicon substrate by adding water vapor to the silicon tetrachloride-hydrogen mixture in an epitaxial system. They also showed that, when a gaseous mixture of carbon dioxide and hydrogen is injected, water is formed only at elevated temperatures. Thus the reaction of water vapor and silicon tetra-: chloride will be limited to a relatively small reaction zone near the substrate. This paper reports some results of oxide films obtained from a vapor-phase reaction of a volatile metal halide with a hydrogen and carbon dioxide mixture in an epitaxial-deposition chamber. EXPERIMENTAL APPARATUS The system employed for the oxide deposition is a modification of a vertical system used to produce high-resistivity silicon layers by the hydrogen reduction of silicon tetrachloride.&apos; The modification shown schematically in Fig. 1 consisted of an additional carbon dioxide gas stream which entered the reaction chamber with a hydrogen stream saturated with metal halide vapor and a diluting hydrogen stream. Silicon dioxide layers made from a mixture of silicon tetrachloride, hydrogen, and carbon dioxide gases will be discussed first. EXPERIMENTAL RESULTS 1) Factors Affecting the Rate of Oxidation. An epitaxial silicon layer was deposited by the hydrogen reduction of silicon tetrachloride on an n-type,

Jan 1, 1965

By H. D. Williams, R. A. Scriven

The distribution of elevation angle of finite plane facets distributed symmetrically about a given axis is derived in terms of the angular distribution of lines which these facets produce in a plane section parallel to the axis. It is assumed that the facets are not markedly elongated in preferential directions. The theory is intended for application to the angular distribution in polycrystalline metals of slip planes and of particular grain boundaries on which certain phenomena such as cavitation can occuv. Illustrative examples are given in closed form and simple numerical techniques are de-ueloped for practical application. The results are applied to the distribution of cavitated boundaries in a copper specimen after fatigue at 400°C and it is found that voids form on the boundaries that exper~enced maximum shear stress. When investigating the distribution of elevation angle between a given axis and planes symmetrically distributed about this axis the angular distribution observed in a plane section parallel to the axis is not necessarily the same as the required distribution. Consequently a technique for processing the results obtained by sectioning methods is required. An example where such a technique would find application is in the problem of intercrystalline void formation during uniaxial tensile creep. Two theories have been proposed to explain this cavitation in terms of the normal and the shear components of stress, respectively. Hull and Rimmer (1959) postulate that the growth of intercrystalline voids is controlled by the rate of supply of vacancies from the grain boundary, the local vacancy concentration being proportional to the normal stress on the boundary. Gifkins (1956) considers that slip arising within a grain causes a ledge to be formed at the grain boundary which is subsequently opened up into a cavity by grain boundary sliding. It might be possible to differentiate between these mechanisms by determining the angular distribution of grain boundaries containing cavities since the former theory predicts a predominance of cavitated facets normal to the stress direction whereas the latter should favor an angle of 45 deg to this direction. In a similar manner an indication may be obtained of the type of mechanism responsible for intercrystalline cavitation during high-temperature fatigue. Davies and Wilshire (1962) have analyzed the slip-plane distribution in a nickel specimen but the problem was not treated in any detail nor was any account taken of the finite extent of the planes being sectioned. Hilliard (1962) has given a very general account of how anisotropy in the microstruciure can be related to measurements taken in one or more plane sections by expressing both the measured and the true angular distributions as expansions in spherical harmonics.* The present analysis is con-

Jan 1, 1965

By T. H. Alden

In several recent studies of fatigue fracture in single-phase metals, tests have been made using the condition of essentially constant plastic strain amplitude.1-4 This procedure departs from the more common practice of holding the amplitude of stress constant. From these studies have emerged two important generalizations about the behavior of metals during cyclic straining. First, measurements of the stress amplitude, required to impose the fixed plastic strain amplitude, have shown that the rate of cyclic strain hardening in annealed metals is rapid in the early cycles but decays quickly to a very low value.1"5 This behavior is displayed particularly for a range of strain amplitudes below about 2 pct and at low and high temperature. Frequently, the hardening rate becomes so low that one can determine a "saturation" stress. This stress increases with strain amplitude. In addition, an experimental relation between fracture life and plastic strain amplitude was obtained by Coffin and Taternelli,&apos; namely N 1/2 ep = constant. For several metal:;, this equation has been shown to hold down to a strain amplitude of 0.1 pct. Whether it also holds in the "low amplitude" range (lives of more than about 105 cycles) has not been established. The importance of the saturation stress level (a value derived from strain hardening measurements) to the question of fracture life (the usual quantity of interest of fatigue testing) lies in the observation that cracks start to form when the cyclic hardening rate is essentially zero, and not before.4"5 This point suggests immediately a means of relating tests at constant stress and constant strain amplitudes. When making comparison, the stress in a constant stress test is to be identified with the saturation stress in a constant strain test. If these ideas are correct, then it should be possible, using the relation between fracture life and strain amplitude and experimental curves of saturation stress versus strain amplitude, to predict the fracture life as a function of stress, i.e. predict the S -N curve, for low stress fatigue. Saturation stress amplitude-plastic strain amplitude data, obtained in tension-compression, exist only for a few metals and for relatively high amplitudes of strain. Comparable S -N curves (push-pull loading) were known by the author only for OFHC copper. Values for this metal taken from Ref. 2 are shown in Fig. 1. The strain amplitudes, the lowest

Jan 1, 1962

By R. E. Morgan, D. L. Douglass

The determination of phase relationships and solid-solubility limits can be performed by quantitative metallography in addition to the usual X-ray and metallographic techniques. For example, Beck and smith1 redetermined the ß/ß + ?, ß + ?/?, a/a + ß and a + ß/ß boundaries in the Cu-Zn system by measuring the volume fraction of second phase of several alloys and extrapolating the volume fraction-composition curves to 0 and 100 pct. A modification of this technique is suggested for certain alloy systems, in which it is not necessary to use several alloy compositions but merely one. A single two-phase alloy may be used to determine terminal solubilities in the following manner. The method consists of equilibrating samples of the alloy in a two-phase region adjacent to the desired solid solution, at three or more temperatures, quenching, measuring the volume fraction of second phase present, and applying an analytical treatment to calculate the unknown solid solution. However, two restrictions are inherent in this technique. They are: 1) only certain types of alloy systems are amenable to it, and 2) the general features of the system must be known. The first drawback to the new technique, i.e., that only certain types of systems may be studied, necessitates that the composition at one end of the tieline must either be constant with temperature or well established as a function of temperature. Either a pure metal or some intermetallic compounds fulfill the former. If it is assumed that the volume per gram-atom of a dilute solution is unchanged by the addition of element B to element A, the composition of the solid solution in equilibrium with the second phase may be determined by a material balance and is given by where X, = volume fraction of B in a solid solution Xc = volume fraction of B in compound c X = volume fraction of B in alloy f = volume fraction of second phase The composition by weight may then be determined by the use of tables in the Metals Handbook2 when the density ratio of the solid solution constituents is known. A possible alternative treatment involving the use of the lever rule is less precise than the above tech- nique. This may be used when the density of the solid solution is either known or may be calculated from X-ray data for several compositions. The following analysis is then made. The ratio of compound to solid solution (by weight) may be expressed as follows: x0 - x wc = xr-x = x0 - x r2i Xc -X where Wc = weight of compound w = weight of solid solution x, - alloy composition, weight percent x = unknown composition Xe = compound composition but where V, = volume of compound VA = volume of solid solution pc = density of compound p, = density of solid solution fc = volume fraction of compound fB = volume fraction of solid solution and fs = l -fc then If pc and xc are known, and f, is measured, then pB is the only unknown on the right side of Eq. [4]. The known densities of the solid solution can be plotted for various compositions and can then be expressed mathematically as a function of composition. The use of an expression of pB = f(x)reduces the equation to one unknown—the desired solubility. In the event that the densities are unknown, they may be calculated for various compositions from Vegard&apos;s law. The calculated values are then plotted and expressed analytically. The most accurate results are obtained for Eq. [4] when fc<< 1, i.c., when (x, -x,) - 0, &/l-f, - m; but as fc/l -fc - 0, (xl-x,)- (x, - x), and x - x,,. However, the accuracy with which fc can be measured decreases as f, decreases.3 Alloys for investigation must be selected by a compromise, which is based upon an error analysis of Eq. [4] and knowledge of the accuracy of volume fraction measurements. An examination of phase diagrams in the literature showed many which were amenable to the technique described here. The zirconium-copper system was selected in order to determine the solubility of copper in beta zirconium. Pieces of an alloy which was arc-melted three times were wrapped in tantalum foil and sealed under an argon atmosphere in Vycor tubes. The sealed samples were equilibrated at temperatures from 850" to 960°C for 3 weeks and quenched to room temperature by smashing the capsule in water. Several planes of polish were examined, and

Jan 1, 1960

By J. B. Clark, A. S. Yue

The zone-melting technique can be adapted for the de-termination of the eutectic composition in complex metal systerrzs. The application of this method is demonstrated in a simple eutectic system, Mg-AE, in which the eutectic composition is known and in a complex ternary system, Mg-Al-Zn, in which the literature is uncertain as to the composition of the ternary eutectic. The advantages and limitations of this unique approach for the determirution of the eutectic composition are discussed. ThE eutectic composition in phase diagrams is usually determined by thermal analysis of a series of arbitarily selected alloy compositions. The temperatures of the liquidus and eutectic arrests for each alloy are plotted and the eutectic composition is estimated by extrapolation to the entectic temperature of the curve formed by the liquidus arrest temperatures for the series of alloys. Although this approach readily yields the eutectic temperatures, several dekrminations are needed to estimate the eutectic composition, even in a simple system. In a complex ternary system, a great many determinations are often necessary to estimate, even approximately, the ternary eutectic composition. Thus, the conventional method is inherently tedious and time consuming. The application of zone melting provides a relatively efficient method of determining the eutectic composition.&apos; As an illustration, consider the zone melting of an alloy composition C, in the simple eutectic system A-B, shown in Fig. 1, under the ideal conditions of infinitely rapid diffusion in the liquid, no diffusion in the solid, and ease of nucleation of both phases. As the zone moves along the bar, the composition of the zone is enriched by solute rejected during the freezing of the a phase and the zone composition approaches the eutectic composition CE.Once the zone composition attains the lowest melting composition, i.e., the eutectic composition, it remains at this composition as the zone moves along the bar and finally freezes as such at the end of the bar. Chemical analysis of the end of such a zone-melted bar then should yield the eutectic composition CE of the system A-B. A corresponding analysis can be made for a ternary eutectic system. Under the ideal conditions noted above, only one pass of the molten zone is required to yield the eutectic composition. Experimentally, however, a solute-rich layer forms at the solid-liquid interface2 and the composition of the zone does not attain the eutectic composition as rapidly or as uniformly as in the ideal case outlined above. But with agitation of the melt, the ideal conditions can be approximated experimentally. Also, as shown below, zone melting permits a cumulative build-up of the solute at the end of the bar to the eutectic composition. The purpose of this paper is to demonstrate this unique method for determining the eutectic composition. The method is here applied to two systems: first, to the binary Mg-A1 system, in which the composition is well established, and second, to the complex Mg-Al-Zn system in which there is doubt concerning the composition of the ternary eutectic. EXPERIMENTAL PROCEDURE The zone-melting apparatus used in this study is described in detail elsewhere.3 Briefly, the binary alloy rods (5/8 in. in diam and 9 in. long) and the ternary alloy rods (5/8 in. in diam and 6 in. long), with the compositions given in Table I, were zone

Jan 1, 1962

By R. T. DeHoff

A general method for determining the geometric properties of structures composed of particles which are all the same shape and size is presented. The application of the method requires a knowledge of&apos; the qualitative shape of the particles in the structure, ad a maximum of three simple counting measurenzents, which are made on a representative plane section taken through the structure. It is also shown that the number of different kinds of measurements necessary JOY the complete description of the structure can be decreased if some independent information about individual particles is available. The geometric properties that can be determined quantitatiz~ely from counting measurements for susch structures are size, shape, number, surface area, vlolume, ad such extensive properties as volume Mction and surface area per unit volume. THE simplest kinds of measurements that may be made on a metallographic section are counting measurements. There are three such simple counting measurements, which are determined by sampling the microstructure with a point, a line, and an area. The first of these, the point count, is probably the most familiar among metallographers. The second count, the number of intersections a test line makes with particle outline, is somewhat more recent in its origin and application. The third counting measurement, the number of particle sections observed in unit area of the plane of polish, has long been used in the estimation of grain sizes. The real utility of these three counting measurements lies in the fact that they are rigorously and unambiguously related to certain extensive geometric properties of the three-dimensional structure of which the metallographic section is a sample. These relationships will be reviewed briefly below. Of somewhat secondary importance to the fundamental relationships is the observation that, if some simplifying assumptions about the geometry of the three-dimensional structure are introduced, manipulation of the counting measurements gives a more complete description of the structure. Specifically, in addition to the extensive properties which these measurements rigorously estimate, the number of particles, their size, and their shape may be determined. The purpose of the present paper is to explore the consequences of introducing the assumption of constant size and shape. A later paper will deal with the estimation of geometric properties of structures which may be characterized by a two-parameter size distribution. It should be mentioned that the introduction of this simplest of assumptions, while clearly not generally justified in metallurgical structures, is not without precedent. For example, many estimates of the number of particles per unit volume of structure, based upon a single counting measurement, are scattered throughout the literature.13 Virtually all of these developments assume a constant particle shape, e.g., spherical or polyhydral, and constant size. That such an assumption is necessary is evident from the fact that, for more general structures, more than a single parameter is required to describe the three-dimensional structure, so that the determination of a single parameter on a section would be insufficient to specify the structure. Similar developments for the estimation of particle size from a single counting measurement, e.g., routine grain-size determinations, make the same very limiting assumption,435 but have nonetheless proven of practical value. The present paper embodies a generalized approach to the development of relationships among the two-dimensional counting measurements and the three-dimensional geometry of the structure, subject to the assumption of constant particle size and shape. It is the hope of the author that by presenting the relationships and the assumptions involved in dealing with this approximation, in a single, unified treatment, the reader may be impressed with the usefulness of the counting measurements, may be guided in their application to the estimation of details of the geometry in specific structures in which he may be interested, and may be moved to apply the results, with understanding, to new structural problems. Several authors6, 7 have demonstrated independently that it is possible to obtain unbiased estimates

Jan 1, 1964

By R. T. DeHoff

Saltykov&apos;s meihod for the determination of the size distribution of spherical particles from measurements made on random plane sections is extended to particle shapes which are not equiaxed. The analysis permits the deterrrzination of the size distribution of aggregates of ellipsoidol particles provided all particles have tlze same shape. V ARIOUS solutions to the problem of the determination of the size distribution of spherical particles from measurements made on random plane sections have appeared in the literature since the original solution was first published by Scheill in 1934. Solutions have been offered utilizing measurements of the diameter1y2 or area3&apos;4 of circular sections that result when a test plane is passed through an aggregate of spherical particles, and the length of intercept5y6 that results when a test line is passed through the aggregate. To the best of the knowledge of the author, no method has been proposed which permits the determination of the size distribution of particles that are not equiaxed. The purpose of this paper is to develop a method which permits the determination of the size distribution for a specific class of particle shapes which cover awide range of axial ratios; namely, ellipsoids of revolution. In the interests of simplicity, it is necessary to limit consideration to aggregates of particles which are all similar in shape; that is, the ellipses which, by rotation about one of their axes, generate the particles, all have the same axial ratio. The size distribution, which is to be determined by the analysis, is arbitrary. It is also assumed that the section, or sections, upon which the measurements are made represent the average of all possible sections through the structure. This ideal condition can be approached as nearly as may be desired by observing a sufficient area of sections taken at random positions in a randomly oriented aggregate, and in random positions and orientations in an aggregate that has one or more axes of orientation. SIZE DISTRIBUTION FOR PROLATE ELLIPSOIDS Consider an aggregate of cigar shaped, geometrically similar particles (prolate ellipsoids), dispersed in an opaque matrix. Let the size of each particle be specified by the length of its minor axis, By Fig. 1, and the shape, q, be defined by the ratio of its minor to its major axis, B/A. Let the index, j, refer to dimensions of ellipsoids in a particular size class, and the index, i, to dimensions of an ellipse resulting from the intersection of a test plane and a particle. The size of such a section is specified by the length of its minor axis, b. Let the particles be arbitrarily divided into k size classes, and let the increment of size between each class be A, where A = &,$, B,,,being the minor axis of the ellipsoids in the largest size class. Since all sections are represented on the test plane, the minor axis of the largest of the sections observed, results from the intersection of the test plane with an ellipsoid in the largest size class at its center, and is therefore equal to Bmax Thus the increment, A = The final result will consist of the k numbers which represent the number of particles in each size class per unit volume of aggregate:

Jan 1, 1962

By R. A. Wood, R. I. Jaffee, H. R. Ogden, D. N. Williams

The tensile properties, creep resistance. and thermal stability of highly alloyed Ti-Al-Zr alloys were examined. On the basis of these studies, the Ti-7Al-1ZZr composition was selected for more complete evaluation. The alloy was found to be weldable and free from excessive directionality. In addition, it developed maximum properties without requiring heat treatment other than an annealing operation in the alpha field. The alloy was recommended for scale up and is presently being investigated on a production-level basis. One of the more attractive properties of titanium alloys is their ability to withstand stress at moderately high temperatures, and a considerable amount of effort has been devoted to increasing the maximum service temperature of titanium alloys. This work has suggested that the optimum alloys for high-temperature service will be single-phase a (close-packed hexagonal) alloys containing significant amounts of aluminum. However, the maximum amount of aluminum which can be alloyed with titanium is between 6 and 8 pct,l since at high-aluminum contents an embrittlement reaction occurs in the anticipated service temperature range, 800" to 1100°F. It has been shown that the embrittlement reaction involves decomposition of the high-aluminum a phase to one or more new phases.&apos; Since this reaction does not occur at intermediate or low-aluminum contents, it was felt that intermediate Ti-A1 alloys might be strengthened by a-soluble ternary additions without inducing the embrittlement reaction. The first alloying addition considered was tin, which shows extensive solubility in a titanium and has moderate strengthening tendencies. Unfortunately, it was soon apparent that tin also promoted the embrittlement reaction, and that to obtain a stable alloy, the aluminum content had to be reduced as the tin content was increased. The second alloying addition considered was zirconium, which is similar to tin in its effects on titanium. This element did not contribute to the embrittlement reaction and, in fact, appeared to increase the maximum amount of aluminum which could be alloyed with titanium without inducing instability. This paper describes an investigation of the Ti-A1-Zr a alloy region. Alloys containing from 4 to 12 pct A1 and from 6 to 15 pct Zr were examined. The properties of these alloys are described and the bases for selecting an optimum composition is outlined. This composition, Ti-7A1-12Zr, is presently being scaled up in tonnage quantities, and is being evaluated extensively throughout the industry. In addition to presenting the basis for its selection, this paper presents a description of the properties developed in laboratory material as determined during the alloy investigation. These properties suggest that this alloy can fill an important position in applications requiring light weight, fabrica-bility, weldability, and strength to 1000oF or higher. EXPERIMENTAL PROCEDURES Titanium alloy ingots were prepared by inert electrode arc melting under an argon atmosphere. Alloying elements used were 110 Bhn titanium sponge, high-purity aluminum, and reactor-grade zirconium. Pancake-shaped ingots were prepared weighing approximately 300 g. The composition of the ingots was checked by weight measurements before and after melting. The pancake ingots were forged at 2000°F to approximately half their original thickness to give a flat plate roughly 1/2 in. thick. This plate was then rolled at 1800&apos; to 1600°F to 0.250 in. thick. All of the alloys examined fabricated well. However, alloys containing 15 pct Zr tended to overheat due to exothermic oxidation, and scaling was excessive. As might be anticipated from its effect in decreasing the ß transus, increased zirconium appeared to improve fabricability somewhat, especially during rolling at lower temperatures. Except for a limited study of heat-treatment response, all alloys were examined in the a-annealed condition. Prior to heat treatment the a and ß tran-sus temperatures were determined by metallo-graphic examination of samples quenched after annealing at 50-deg intervals in the transformation region. These data are shown in Fig. 1. Recrystal-lization appeared to occur in about 1 hr in the range 1300º to 1500ºF. Therefore, alloys were annealed for 1 hr at 1550ºF (4 and 5 pct Al), 1600ºF (6 through 7-1/2 pct Al), or 1650°F (8 or more pct Al). This produced an equiaxed a grain structure. In most alloys, a "ghost" structure was visible after the a-annealing treatment, as shown in Fig. 2. This structure apparently resulted from the acicular

Jan 1, 1963

By J. K. Stanley

Knowledge of the diffusivity of carbon in the low temperature form of iron (alpha iron existing below 910°C) is at the moment of considerable interest in the study of the decomposition of austenite and martensite, the elastic after-effect,123 the magnetic after-effect4 and the decarburization of steel below 910°C. Information on the solubility of carbon in iron, and to a lesser extent its diffusion, is also important in consideration of such phenomena as blue-brittleness, temper-brittleness, "magnetic" aging, quench-aging, strain-aging, and possibly the yield point. In order to obtain more information on these subjects more fundamental knowledge is necessary. It is the purpose of this work to present data on the diffusion and solubility of carbon in the alpha iron. The high temperature form of iron (gamma; face-centered cubic) existing above 910°C is capable of dissolving relatively large amounts of carbon, up to 1.7 pet at 1130°C, while the low temperature form (alpha, body-centered cubic) existing below 910° dissolves only a limited maximum amount of less than 0.02 pet carbon at 725°C, according to data obtained here. Since the solubility of carbon in the face-centered or gamma iron is large, relatively speaking, no great analytical difficulties have been encountered in the determination of the solubility lines5 or of the diffusion of carbon.0 The limited solubility of carbon in alpha iron offers difficulties because experimental procedures and analytical methods for low carbon contents below say 0.01 pet have to be more refined than techniques used for work with gamma iron. Because of the difficulties of applying conventional methods to the determination of the diffusion of carbon in alpha iron, virtually no work has been done on this subject. However, by proper refinement of the analytical method for small amounts of carbon, the determination of the diffusion coefficient can be made readily using modified procedures. The solubility of carbon in alpha iron has been determined over a temperature range by various investigators, but the agreement among them is poor. The present investigation establishes the limits quite accurately. Information of this kind is useful in establishing the correctness of equilibrium diagrams but, more significantly, such information on maximum solubilities, especially when extended to alloyed ferrites, should be extremely important in the study of aging and related phenomena. Literature The literature existing on the diffusion, in particular, and on the solubility of carbon in alpha iron is not extensive. The data which exist are not of a high order of accuracy, much of them being in the realm of conjecture. THE DIFFUSION OF CARBON IN ALPHA IRON Whiteley7 made the qualitative ob- servation, using metallographic techniques, that the rate of diffusion of carbon at the A1 (725°C) point was very rapid and that its diffusion was still rapid at 550°C. Snoek,4 studying the magnetic aftereffect in high purity iron, arrived at the conclusion that the after-effect could be explained by the presence of small amounts of carbon diffusing under the influence of magnetostrictive strain (lattice distortion due to magnetic interaction). In later work, Snoek8 made an estimate of the ratio of carbon diffusion in alpha to its diffusion in gamma iron, and concluded that for a temperature of 910°C the ratio of Da/D? was 2600. Polder,9 basing his calculations of D on relaxation phenomena in the elastic after-effect, estimated that Da is about 1/3 of D? at 910°C (1183°K) and is about 1/12 of Dy at 727°C (1000°K). Polder&apos;s equation for the diffusion of carbon in alpha iron was calculated to be 18000 D = 5.2 X 10-4 e-RT cm2 per sec Ham10 obtained data for the diffusion and solid solubility of carbon in alpha iron at two temperatures by using one technique similar to that employed in this study. He found a D of 8.0 X 10-7 cm2 per sec at 702°C and of 2.7 X 10-7 at 648°C. THE SOLUBILITY OF CARBON IN ALPHA IRON Although pearlite is absent in steels containing 0.06 pet,11 0.05 pet,12 or 0.045 pet C,13 it appears that the carbon in these steels cannot be in solution in ferrite. The solubility of carbon at the A1 (725°C) point was first determined by Scott14 on the basis of cooling curves, and was found to be between 0.03 and 0.04 pet C. Tamura15 by interpolating between the solubility of carbon in delta iron at 1400°C and in alpha at room temperature (assuming zero solubility) ar-

Jan 1, 1950

By A. S. Appleton

The diffusion of carbon in Fe-Co-C austenites was studied as a function of cobalt concentration up to 12 at. pet, using an autoradiographic technique. The diffusion coefficient was found to initially decrease and then increase with increasing cobalt concentration, the trends being more marked the higher the temperature of diffusion. These effects were paralleled by variations in the activation energy and the constant for diffusion which, however, were found to be dependent also on the carbon content. The results are compared with the previously available data and their significance is discussed in terms of the kinetics of solid-state reactions in this systern. THE influence of cobalt on the diffusivity of carbon in austenite was first studied by Smoluchowski,&apos; his data being that most commonly cited in works

Jan 1, 1964

By H. Becke, D. Stolnitz, D. Flatley, W. Kern

Zinc difhsions in gallium arsenide having surface concentrations as low as 5 x 10&apos;&apos; atoms per cu cm have been attained. A multiple-difhsion sequence is employed during which zinc enters the gallium arsenide from a silicon dioxide film in a solid-to-solid diffusion step. The technique is illustrated for the case of a zinc surface concentration of -1 x 1017 atoms per cu cm and a junction depth of 1.2 p. Radiotracer measurements of -0.1-p layers of gallium arsenide are used to delineate the resulting profile. A diffusion coefficient for zinc in pyrolytically deposited silicon dioxide is reported. ZINC is frequently used as an acceptor impurity in gallium arsenide. As examples, p-n junctions are formed using zinc-diffused layers in solar cells, lasers, and varactor diodes. For these purposes surface concentrations of 10&apos;&apos; to over loz0 zinc atoms per cu cm are desired and readily obtained from a vapor source. Diffusion of zinc into gallium arsenide to yield surface concentrations of about 1017 atoms per cu cm, however, is more difficult. For instance, oldstein&apos; reports that large changes in the vapor density of zinc produce only small changes in surface concentration. Such low surface concentrations are necessary in forming the diffused base of a gallium arsenide double-diffused n-p-n transistor in order to obtain an adequate emitter efficiency. An alternative approach to zinc diffusion which can provide reduction in surface concentration of several orders of magnitude is the introduction of the diffusant from a solid source. This can be conveniently accomplished by using oxide films of the type generally employed for selective diffusion masking. Such oxides also serve to prevent the dissociation of the gallium arsenide surface at the high temperatures of diffusion. DIFFUSION PROCEDURE Fig. 1 illustrates the diffusion sequence which is employed for obtaining zinc surface concentrations in the range from 5 x lom to 1 X 10" atoms per cu cm. The description of technique will be given for the instance of -1 x 1017, which is typically utilized in double-diffused gallium arsenide transistor investigations at this laboratory. Tin- or germanium-doped gallium arsenide wafers drawn from crystals grown by horizontal Bridgman or Czochralski techniques are used, with bulk concentrations ranging from 1 to 3 X 10" carrier atoms per cu cm. Each wafer is chemically polished on the (iii) arsenic face using a mixture of five parts concentrated sul-furic acid, one part water, and one part 30 pct hydrogen peroxide at room temperature, followed by rinsing in deionized and quartz-distilled water. Pyrolytic silicon dioxide was chosen as the oxide coating because of the high quality of the films obtainable, the ease of their preparation, and the excellent control over film thickness and uniformity.

Jan 1, 1964

By Rodney P. Smith

The rate of motion of the boundary between a single-phase a-iron region and a two phase a-iron plus ?-iron, or a-iron plus cementite region has been measured on decarburization at several temperatures between 500" and 865°C. These data, together with data for the carbon content of a-iron at the boundary, yield the diffusivity of carbon in a-iron. The activation energy for carbon diffusion is 19.8 kcal per mole for the temperature range —50° to 150°C and increases to an average value of 23.0 kcaL per mole for the temperature range 727" to 865°C. AS part of an investigation of the diffusivity of carbon in iron using a steady-state method,&apos; the diffusivity of carbon in a-iron was determined at the temperatures 802" and 851°C. The diffusion constant thus obtained was larger, by nearly a factor of two, than that predicted from the combined results of stanley2 and of Wert.3 It seemed desirable, therefore, to continue the investigation. Since the temperature range in which the steady-state method can be conveniently used is limited, we have chosen a decarburization method, based on the laws of diffusion in metal accompanied by a phase change.4,5 If the initial carbon content of the Fe-C alloy is such that two phases coexist at the decar-burizing temperature* and decarburization is car- ried out such that the surface is maintained at substantially zero wt pct. C, the carbon distribution after a time, t, will be as shown in Fig. 1. The boundary between the single-phase and two-phase regions moves from y = 0 to y = x in the time, t, where x is proportional4 to tl". If the initial carbon (content of the sample is Ci, and CB is

Jan 1, 1962

By R. P. Smith

The diffusivity of carbon in iron, cobalt, and alloys of 89.7 and 79.3 wt pct Co has been determined by a decarburization method for the temperature range 850° to 1100°C. The Plots of log D us 1/T for the two Fe-Co alloys are linear through the region of the Curie temperature, showing that, unlike some cases of substitutional diffusion, carbon diffusion in these alloys is not affected by electron spin order. RECENT investigations1-&apos; have shown that for substitutional diffusion in iron the change in diffusivity with temperature does not follow an Arrhenius equation, at temperatures near the Curie temperature. Data on the diffusivity of carbon in a iron5"9 indicate that this anomaly does not exist for interstitial diffusion; however, this has not been definitely established. Since cobalt and Fe-Co alloys, 80 to 100 pct Co, have Curie temperatures in a temperature range convenient for carbon-diffusion measurements they are suitable systems for studying the relation of interstitial diffusion and the Curie temperature. EXPERIMENTAL The carbon diffusivity, D, was determined by a decarburization method. The diffusion cylinders, made from small vacuum melts of electrolytic cobalt and plastiron, were about 0.76 cm diam and 6.3 cm long. A small amount of carbon was added to each melt to keep the oxygen content as low as possible. The cylinders were first treated with a hydrogen-3 pct water vapor mixture at 1100°C to constant weight, then carburized to the desired initial carbon content with a suitable CO-C02 gas mix-

Jan 1, 1964

By E. W. Johnson, M. L. Hill

The dijfusiuity D was determined at 25° to 780°C- from hyd?-ogen evolution rates. Anomalous evolution from air-melted iron was att~zbztted to residual hydrogen, which is interpreted as a hydrogen compound that decomposes at a strongly temperature-(Ieperzdent rate above 500°C. Above 200°C, D = 0.0014 cm2sec-1 exp (-3200 cal per g atom/RT). Below, 200°C the diffusivity is anomalously low and represented by D = 0.12 cm2sec-l exp (-7820 cal per g atom/RT). It is postulated that at low temperatures the hydrogen in the metal is "trapped" with an energy 4.8 kcaL per g atom below- that of the interstitial hydrogen. 1 HE purpose of the present experimental study was to determine the diffusivity of hydrogen in a-Fe over an extended temperature range. As certain anomalies were encountered, attempts were made to understand the anomalies themselves. This research was in progress both before and after a determination of the diffusivity of hydrogen in nicke1.l The latter system was found to exhibit none of the anomalies of hydrogen in iron, and its description was far simpler. The experiments on nickel also

Jan 1, 1961