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By J. E. Hilliard

Various methods are given for estimating the number per unit volume and average size of convex particles from measurements on a projection through a slice of the structure. The determination of the size distribution is considered specifically for spherical particles. The results are applicable to any type of transmission microscopy and also to the correction of measurements made by reflected light on semitransparent materials. WITH the advent of electron transmission microscopy, the metallurgist is confronted with the problem of relating a projected image to the three-dimensional properties of the structure. This paper deals with the estimation of the number per unit volume and size of particles dispersed in a matrix. The case of convex particles will first be treated (the results will be applicable as approximations to particles of more general shape) and then spherical particles will be considered specifically. The latter represent a special case frequently encountered in practice and one which is also amenable to a calculation of the effect of overlap on the observed particle-size distribution. Although the present treatment was prompted by the needs of the electron microscopist, the results are applicable to transmission studies with any type of radiation. In addition, they can be used in the analysis of semitransparent materials by reflected light, the depth of light penetration corresponding to the thickness of the slice or section used in the transmission studies. 1) CONVEX PARTICLES 1.1) General Expression for N,. We will suppose that a "center" (such as the center of mass) is assigned to each particle. The convention used for defining the center is immaterial providing it does not depend on the orientation or location of the particle. Consider a slice through the structure having a pair of parallel faces a distance t apart. It will be assumed that the slice is randomly located with respect to its perpendicular distance from some fixed point, but it is not necessary to assume that its orientation is random. Our problem is to deduce the relationship between the number of par- ticle images seen on an orthogonal projection through the slice with the number, Nv, of particles per unit volume in the original structure.* *Symbols are listed in the Table. The expected number of particles with centers lying within the slice is Nvt per unit area. In addition, there will be elements in the slice contributed by particles whose centers lie without. The number of such elements will be the same as the number of intersections occurring on a two-dimensional plane through the structure; namely N~K, where K is the mean distance, Fig. 1, between tangent planes to a particle averaged over all particles, i.e., Where Ni is the number of particles of class i having the same shape and size, and pi (4, 8) is the probability that an i particle will have a given orientation with respect to the slice. If the particles are randomly oriented, then K is independent of the orientation of the slice and equal to the mean cali-per diameter. The total number of particle elements in the slice is therefore Nv(t + K) per unit area, but fewer will be seen as separate images on the projection plane because of overlap. If MA is the number of elements "lost" by overlap, the number of images per unit area will be NA = Nv(t + K) -MA 121 MA is a function of the slice thickness and must vanish at t = 0. As t increases, NA at first increases, reaches a maximum, and thereafter decreases as the overlap term MA becomes predomi-

Jan 1, 1962

By P. Greenfield, C. C. Smith, A. M. Taylor

J. E. Harris (Berkeley Nucclear Laboratories, England)—Greenfield et al.11 attribute abrupt changes in slope of their log o/log i curves for heat-treated Mg/0.5 pet Zr alloy (zA) to &apos;atmosphere&apos; locking. It is proposed here that a more reasonable explanation of the apparent strengthening at low rates of strain can be based on precipitation either during the preanneal or during the creep tests. All the tests were carried out above 0.5 Tm where solute atmospheres are likely to be largely evaporated2 and can migrate sufficiently rapidly so as not to impose any &apos;drag&apos; on the moving dislocations. McLean3 has derived an expression for determining the temperature Tc above which, due to the high-migration rate of the atmospheres, Cottrell or Suzuki locking can play no part in determining creep strength. This expression, which holds for an applied shear stress of not greater than 5 X 107 dynes per sq cm is: Tc/Tm= 7/6.8 - log10? where i = secondary creep rate The values for T, corresponding to the maximum and minimum reported creep rates at each temperature have been calculated from the data of Greenfield et al. These are given in Table VII. All the test temperatures were above T,, the margin being greater for the higher temperatures and for the lower strain rates where the breaks in the log s/log ? curves occurred. Dorn and his collaborators14, 17 have studied systematically the effect of solute hardening on the creep properties of an A1/3.2 at. pet Mg alloy. In the temperature range where strain aging occurred in tensile tests, abnormally high-activation energies for secondary creep were obtained but at temperatures above 0.43 Tm, solute alloying did not have any effect on the creep parameters. Moreover, there have been no reports of any strain aging phenomenon during elevated temperature tensile tests with ZA material.18 Instead of the observed strengthening being due to atmosphere locking, it is now proposed that precipitates play an important role in enhancing the creep strength of the material. There are two possibilities—precipitation of zirconium hydride during the high-temperature preanneal and/or precipitation of the hydride or a-zirconium during creep. On the basis of the former the results can be interpreted in terms of a critical stress being necessary to force the dislocations through or over preexisting precipitates. From the latter, if the strengthening is due to pre- cipitation during the test then hardening should be associated with a critical strain rate. At low rates of strain, time is available during the tests for precipitation to occur either directly onto dislocations (thus pinning them) or generally throughout the matrix (which would impede dislocation movements). Examination of the data of Greenfield et al. suggests that both mechanisms may be operative since they observed precipitation during creep and also found that their alloys exhibited high-creep strength in the early stages of the low-stress tests, i.e., before creep-induced precipitation had time to occur. It is not easy to understand why they considered that precipitation of zirconium hydride is unlikely to occur at 600°C while it can take place in tests in air at as low a temperature as 200°C. Precipitation of the hydride during the preanneal cannot be ruled out merely on the basis of metallographic examination. Hydride precipitates in ZA type alloys are very small and can only be accurately resolved in the electron microscope.9 For example, in this laboratory20 hydride platelets with major dimensions <(1/10) µ have been observed by electron transmission through thin film specimens of hy-drogenated ZA material. Complex interactions between dislocations and such particles are illustrated in Fig. 12. Additional evidence for precipitation during pre-annealing is provided by the data presented in Greenfield&apos;s Fig. 1 and Table IT. These show that the creep strength at 200o and 400°C increases with the time of preanneal at 600°C. Such increases cannot be explained on the basis of increases in grain size alone for further improvements in strength were observed when the material was annealed for longer times than that required to stabilize the grains. Although the main discussion is confined to ZA material, similar arguments can be used against the strain aging hypothesis proposed to explain the binary Mg/Mn alloy data. In this case no precipitation is possible during the preanneal, but precipitation-hardening during creep can occur.

Jan 1, 1962

By S. Saito, P. A. Beck

The crystal structure of MoNi3 was determined by means of X-ray diffraction. This structure is isotype with that of ovgered TiCu3. The lattice parameters are: a. = 5.064A, bo = 4.224A, co = 4.448A, and zf 0.157. If the orthorhombic distortion (slight relative to the corresponding orthohexagonal unit cell) is disregarded, the structure may be described in terms of a close-packed ordered atomic layer, stacked in the sequence: abab. The structztres of ordered TiCu3 and TiAl3 are homotectic. The three types of ordered hexagonal phases, iso-structural with TiNi3, MgCd3, and VCo3, are known to occur in AB3 alloys of transition elements of the first, second, ad third long periods. It was noted1 that phases with the TiNi3 structure occur selectively in alloys of Ti-group elements with Ni-group elements. In AB3 alloys of Ti-group and V-group elements with Co-group elements the AuCu3-type structure predominates.&apos; The vCO3 structure, which was determined very recently,&apos; has hexagonal symmetry, but the actual atomic arrangement here, too, is rather closely related to the ordered cubic structure of AuCu3-type. However, an ordered hexagonal close-packed structure of the MgCd3-type occurs in MOCO33 and WCO3.4 Consequently, the question arises as to whether or not the crystal structure of MoNi3 is also of the MgCd3-type. Grube and winkler5 found that MoNi3 has a hexagonal close-packed structure with a = 2.54A and c/a = 1.65. They pointed out that some additional weak diffraction lines could be observed in the powder pattern, which may have been due to an ordered atomic arrangement in this phase. However, no detailed information was obtained by them and the structure was apparently not further investigated by others. The present work was, therefore, undertaken in an attempt to determine in detail the structure of MoNi3, and to investigate the possibility of ordering. EXPERIMENTAL METHODS Alloys used in the present work were arc-melted in a water-cooled copper crucible under helium atmosphere. Electrolytic nickel and molybdenum, both 99.9 pct pure, were used. Chemical analyses were not made, but the melting loss was not higher than 2 pct for any alloy. Ingots were first homogenized at 1200°C for 48hr, quenched, heavily cold worked, and then annealed at 820" or 860°C for 1 week, followed by quenching in cold water. Powder specimens for X-ray work were prepared by crushing the heat-treated solid specimens. In order to remove strains, the powders were reannealed in evacuated scaled fused silica capsules for 6 hr at the same temperature at which the corresponding solid specimens were annealed. X-ray photographs were taken with an asymmetric focussing camera, using unfiltered CrK or CuK radiation. EXPERIMENTAL RESULTS The X-ray diffraction patterns of alloys containing 20.8, 25, and 26.4 at. pct Mo, homogenized at 1200°C, showed the face-centered-cubic structure of the Ni-base a-solid solution. It was revealed, however, by micrographic examination that the 26.4 at. pct Mo alloy contained in addition very small amounts of a second phase, in accordance with the phase diagram.6 On the other hand, the 20.8 at. pct Mo alloy after annealing at 820°C gave the X-ray diffraction pattern of the ordered face-centered-tetragonal MONi4.7 In this pattern several additional weak diffraction lines were also observed, corresponding to the strongest diffraction lines of MoNi3. The alloys containing 25 and 26.4 at. pct Mo after annealing at 820" or 860°C gave X-ray diffraction patterns, as shown in Tables I and 11, corresponding to MoNi3. Each one of the reflections which could be tentatively indexed on the hexagonal close-packed cell of Grube and Winkler,5 with the exception of the basal plane reflections, was split into a doublet, as seen in Table I. Since microscopically the alloy consisted of a single phase, it seemed probable that the lattice of MoNi3 is actually slightly deformed, as compared with the tentative hexagonal unit cell. In addition to these diffraction lines, several weak lines were also present, as shown in Table 11, which could not be indexed at all on the hexagonal close-packed cell considered. Satisfactory indexing of all diffraction lines observed was found to be possible by using an orthorhombic unit cell with ao = 5.064A, ft = 4.224A, and c = 4.448A. These values, whose accuracy is estimated to approximately ± 0.008A, correspond to 95.14A3 for the volume of the unit cell, and to an X-ray density of 9.50 g per cm3. If no attention were paid to the weak reflections listed in Table II, a reduced -unit cell of half the volume (a = 2.532A, b = 4.448A, and c = 4.224A), closely related to the orthohexagonal cell, might be used. The dimensions of the orthohexagonal cell of the same volume as the reduced cell are: a = 2.562A, b = 4.437 A, and c = 4.183A. It may be seen that in the reduced cell the a axis is slightly shorter, while the b and c axes are slightly longer than those corresponding to the orthohexagonal cell of the same volume. This slight orthorhombic distortion is re-

Jan 1, 1960

By D. Harker, E. Epremian

The constitution of the nickel-tungsten system has been studied by a number of investigators, the most recent of which are Ellinger and Sykes.1 On the basis of metallography, electrical resistivity and hardness measurements and some X ray diffraction work, they constructed a consitution diagram (Fig 1). Ellinger and Sykes report a0 for the alpha face-centered cubic phase (nickel saturated with tungsten) as 3.66?.‡ The gamma phase (tungsten saturated with nickel) is given as body-centered cubic, but no value of a. is recorded. At 43 pct tungsten by weight (approximately 20 at. pct) a beta phase is reported, but structure and lattice parameter are not known. Primarily on the basis of metallographic evidence, they conclude that beta is a new phase and rule out the possibility of formation of a superlattice since they- observe a new phase in the microstructure. Grube and Schlecht2 report an ordering reaction in a system similar to the Ni-W (Ni-Mo) and Harker3 has shown that NirMo forms a superlattice upon the pre-existing face-centered cubic lattice of the alpha phase. Elliniger arid Sykes observed a change in the diffraction pattern of a 4.3 pct W alloy upon aging and attributed it to the formation of a new phase. Thus, there appears to be some question as to the character of the beta phase reported by Ellinger and Sykes. The purpose of the present work is to determine precisely the structure and nature of the beta phase in the Ni-w system of X ray diffraction methods. Experimental Procedure One inch diameter ingots of 43.66 pct, 40.15 pct and 34.06 pct .tungsten by weight (19.8, 17.6 and 14.1 at. pct respectively) were melted and cast under vacuum from electrolytic nickel and pure wire filament grade tungsten. The ingots were soaked for 16 hr at 1300°C in a hydrogen atmosphere furnace, then swaged at this temperature and finally drawn to 0.020 in. diam wire. Some of the bar stock was retained in 1/2 in. diam rod for hardness and metallographic studies. Wire samples for diffraction work were sealed in evacuated quartz tubes and subjected to the various solution and aging heat treatments in a hydrogen furnace. X ray photograms were taken in a Debeye-Slierrer camera using copper K radiation filtered by nickel foil. Results X RAY DIFFRACTION The lattice parameters of the alpha and gamma phases at saturation were determined by an X ray photogram of the 19.8 at. pct W alloy after solution heat treatment at a temperature well within the alpha-gamma range above the peritectoid temperature (17 hr at 1150°C—oil quenched). The alpha phase was found to be face-centeted cubic with a. of 3.594 ± 0.001?, while the gamma phase was determined as body-centered cubic with a. of 3.158 ± 0.001?. Exactly the same phases and parameters were ohtained with the 17.6 at. pct W alloy for the same solution heat treatment. Thorough analysis was made of an X ray photogram of a 19.8 at. pct alloy sample in the quenched and aged condition (solution treated 1T hr at

Jan 1, 1950

By J. F. Tavernelli, L. F. Coffin

The deformation and fracture characteristics of eight metals subjected to fully reversed cyclic strain ranging from 0.2 to 50 pct were investigated at room temperature. Strain-hardening characteristics unique to the interna1 structure of a particular metal were found. Complete removal of the strain-hardening effects resulting from prior deformation was brought about by subsequent cyclic strain. Further support for the validity of the inverse relationship between the plastic strain range and the square root of the number of cycles for failure is given. THE resistance of materials to cyclic plastic strain is of interest both from a fundamental and practical point of view. It is now a well-accepted fact that fatigue failure in metals is a consequence of the localized slip deformation which occurs within the individual crystals of metal.&apos;-&apos; Hence the failure process should be strongly dependent upon the magnitude of the gross cyclic plastic deformation of the metal under conditions where this is a measurable quantity. Therefore, an experimental investigation of metals in which the cyclic plastic strain is the independent variable should shed new light on some of the basic aspects of the problem. From the practical point of view, there are many uses for information relating to the cyclic strain resistance of metals. One is the case of thermal stress fatigue where fatigue failure can occur as a consequence of a com- paratively few cycles of thermally induced mechanical deformation. Another is the mechanical working of metals where large cyclic strains are employed. In recent years several publications have appeared relating to the cyclic-strain resistance of metals,8-11 dealing mostly with the fracture aspects where the temperature is cycled simultaneously with the mechanical strain. Some work has been reported on the cyclic-strain resistance of metals at constant temperature, again oriented more toward the fracture aspects of the problem than the deformation aspects. 12-16 The present research investigation was undertaken to obtain information regarding the deformation characteristics of several metals whose structure-property relationships were simple and straightforward under conditions of both cyclic and monotonic strain. It has been shown for example that under cyclic-strain conditions some materials will strain harden, while other materials, particularly cold-worked structures, strain soften and these effects required further clarification.8,17-19 It was also de-

Jan 1, 1960

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 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 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 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. 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 John D. Verhoeven

A technique has been developed for carrying out normal freezing experiments with a current density of 2000 amp per sq cut passing through the solid-liquid interface. The equation relating the effective distribution coefficient to the equilibrium distribution coefficient in electric field-aided solidification, originally developed by Huckc et al.,1 has been modified for the case of concentrated solutions. Preliminary experiments on the Sn-Bi system give qualitative agreement with the equation. The data are analyzed by a slightly novel use of the normal freeze equation which allows one to determine the effective distribution coefficient more easily. Very extensive mixing in the liquid was found at these high current densities and it is postulated that the mixing results from a vertical component of the magnetic Lorentz force generated by the electric current. In the search for techniques of obtaining ultrahigh-purity metals the inefficient but very effective technique of electrotransport has received little attention. Electrotransport is most effective in the liquid state and a natural application, therefore, is to apply an electric field across the liquid zone of a zone-melting experiment. The present investigation was undertaken to study the effect of an electric field upon solidification of metals, so that the usefulness of electrotransport in such solidification experiments as zone melting could be determined. In zone-melting and normal-freezing experiments it is difficult to achieve complete mixing in the liquid in the immediate vicinity of the solidifying interface. Consequently a solute build-up will occur at the interface in the portion of the liquid where complete mixing does not occur (an equilibrium distribution coefficient, ko, less than one, and unidirectional atom motion will be implied throughout). This local solute build-up produces a corresponding rise in the solute concentration in the solid so that the ratio of the solute concentration between the solid and the bulk liquid is larger than the equilibrium distribution coefficient. This ratio is defined as the effective distribution coefficient, k,. The differential equation describing the solidification process may be derived by applying the continuity equation to an expression for the net solute flux at the interface. The solution to this differential equation then allows one to determine the solute distribution in the liquid and the relationship between k0 and ke. One of the most useful solutions to this equation was first derived by Burton, Prim, and Slichter,&apos; in which they assumed that a) the equilibrium distribution of solute was maintained on the plane of the interface, 11) the solute build-up ahead of the interface in the liquid disappeared at a distance 6 from the interface, and c) the solute distribution in the liquid was invariant with time. The following well-known relation between ko and ke was then obtained, where R is the rate of solidification and D the diffusion coefficient of the solute in the liquid. This equation appears to correlate the data from a number of different types of solidification experiments very well. Application of an electric field across the solid-liquid interface can produce an additional flow of solute atoms as a result of the electrotransport. When the polarity of the field is such as to direct the electrotransport flux away from the interface the solute build-up may be diminished, even to the point of producing a solute depletion and a consequent ke smaller than ko. The quantitative description of this process and the resulting form of Eq. [I] was first given by Hucke et al.1* and then inde- where E is the electric-field intensity and U is the differential mobility, i.e., the velocity of the solute atoms with respect to the solvent atoms per unit electric field. Both authors follow the method of Burton, Prim, and Slichter in their derivation, the only difference being the additional electrotransport term in the flux equation. It has been pointed out1,3 that Eq. [2] predicts the possibility of a noticeable increase in the purification of materials by solidification in an electric field. The validity of Eq. 121 has not been checked experimentally and it is possible that other factors&apos; arising from the presence of an electric field across

Jan 1, 1965

By E. G. Schempp, W. A. Morgan

The influence of modifications in the molybdenum, vanadium and, to a limited degree, carbon and boron content to a basic composition of 5 pct Cr, 0.75 pct Mo, 1 pct V hot-work tool steel composition, was studied in respect to hardenability, grpain- coarsening temperature, and tempering charactevistics. Tensile, impact, and fatigue pvoperties were studied for the most promising compositions. An alloy with a typical composition of 0.43 pct C, 4.97 pct CI-, 0.33 pct Si, 2.25 pct Mo, and 1.00 pct V uas found to offer the most favorable combination of properties in respect to high-strength applicntions when tempered at 1100°F. MANY 5 pct Cr high-strength steels are at present being manufactured in North America which fit well into the classification of the AISI-SAE system. Much interest has been shown in these materials as ultra-high-strength steels for use at elevated temperatures. The limiting temperature of use lies at the point where the steels begin to soften rapidly. Although a great deal of information has been made available in the past two years on the properties of selected alloys in this series, little information exists on the effect of systematically varying the ccntent of one or more elements in the 5 pct Cr-base alloy. This paper presents the results of an investigation of the effect of variations of the carbon, molybdenum, vanadium, and, to a limited extent, the silicon, manganese, boron, and niobium content of a 5 pct Cr steel to the AISI H-13 base analysis. EXPERIMENTAL PROCEDURE All experimental heats were melted in a 50-lb. induction furnace. The melting stock consisted of

Jan 1, 1962

By F. M. Yans, A. D. Donaldson, A. R. Kaufmann

Beryllium was mixed by powder. metallurgical techniques with copper, nickel, iron, and chromium, respectively, to form beryllium -rich binary alloys which Mere then extyuded and rolled transtverse to the extrusion direction. The effect of each alloying element was determined by tensile testing. In solid solution, small amounts of iron and nickel had an embrittling effect, while copper in solution increased the strength but had no effect on ductility. The effect of chromium was complicated and not readily explainable. Observations concerning the planes and modes of fracture were made. BERYLLIUM possesses some very attractive properties for general design applications, especially its strength to weight ratio which is approximately twice that of aluminum and three times that of stainless steel. Equally significant, however, is its combination of high moduli , high strength (approximately 70,000 psi tension and 40,000 psi shear), and low density (0.0658 Ib per in.3), which has made it a potentially important structural material for use in high-speed aircraft and missiles. The main attractions of beryllium are most marked when compared to other constructional alloys now in use. For example, while its density is approximateiy that of magnesium, its modulus of elasticity is approximately seven times that of magnesium, three times that of titanium, four times that of aluminum, and 1 1/3 times that of steel. Furthermore, its relatively high strength and high melting temperature permit design for service temperatures to about 1100°F. It is felt by the aircraft industry in general,&apos; that the high cost of beryllium can easily be amortized by the savings in fuel costs, and increases in aircraft payload and range. The only factor which has prevented the use of the metal in structural applications is its lack of sufficient ductility. It is this property that has retarded the development and utilization of beryllium. Beryllium&apos;s modes of deformation, Fig. 1 indicate that the main fracture planes at room temperature in a randomly oriented sample are the (0001) basal planes; the (1150) prism planes are the planes of secondary fracture.&apos; Klein, Macres, Woodard, and Greenspan3 obtained elongations of up to 40 pct in beryllium sheet rolled above 700°C when the (0001) basal planes were oriented parallel to the plane of the sheet (see Fig. 2).

Jan 1, 1962

By J. T. McGrath, R. C. A. Thurston

Poly crystalline specimens of copper, and copper with various additions of zinc, were tested in plane-bending fatigue. In tests performed at a constant stress, the fatigue life of copper increased slightly with the addition of up to fifteen per cent zinc. There was a sharp increase in fatigue life as further additions of zinc of up to 35 pct were made. Surface observations showed that the coarse slip bands that are characteristic of fatigue became narrower as the concentration of zinc increased. The rate of crack propagation also decreased with increasing zinc content. It is suggested that the fatigue behavior is controlled by cross slip processes. CROSS slip occurs when dislocations move from one primary slip plane to another along a connecting or cross slip plane. The primary and cross slip planes have a common slip direction. Wide stacking faults, having low energy, tend to make cross slip more difficult. According to recent theories, the ability of a material to cross slip is important to the formation and propagation of fatigue cracks. McEvily and Machlin2 have examined this concept experimentally by fatiguing single crys tals of lithium fluoride, sodium chloride, silver chloride, and KRS-5.* The latter two materials ex- hibit easy cross slip, while the former two do not. Normal rapid fatigue failure was obtained in the silver chloride and KRS-5 specimens, whereas it was much more difficult to achieve in sodium chloride and lithium fluoride crystals. Furthermore, numerous slip band extrusions and intrusions were found in silver chloride and KRS-5 crystals, whereas only one isolated extrusion was found in lithium fluoride and none was found in sodium chloride. McEvily and Machlin also consider that there is no clear-cut demarcation between crack initiation and propagation. The intrusion-extrusion process, which initiates crack formation, continues ahead of the cracks to allow propagation of these cracks along slip bands. The process of cross slip is therefore important not only to crack initiation, but also to crack propagation. Holden4 postulates that fatigue crack growth is dependent upon cross slip and thus upon stacking-fault energy. Using an X-ray microbeam technique, he found a cyclic subgrain structure in fatigued aluminum and a-iron. Holden suggests that micro-cracks develop in the densely-packed sub-boundaries ahead of the main crack front, and when sufficiently numerous join up to promote crack growth. The ease with which a subgrain structure could form would depend upon the ability of the dislocations to cross slip, and thus upon the stacking-fault energy. Hence in aluminum, which has a high stack-ing-fault energy and in which cross slip is easy, Holden found that the relative rate of fatigue crack propagation was considerably greater than in stainless steel, a low stacking-fault energy material. It has been shown by a number of investigators that the probability of forming deformation stacking faults in copper increases as zinc is added.5-7 Cross slip should, therefore, become more difficult as the zinc concentration is increased. In order to check the validity of the foregoing theories, it was decided to test copper and copper with various additions of zinc in plane bending fatigue, and determine to what extent their fatigue properties are dependent upon their ability to cross slip. EXPERIMENTAL PROCEDURE Fatigue tests were carried out on polycrystalline OFHC copper and various copper-zinc alloys with 5, 15, 20, 30, and 35 wt pct Zn. The Cu-Zn alloys were obtained commercially in sheet form. Test specimens, as shown in Fig. 1, were machined from sheet that had been reduced to an approximate grain size of 0.040 mm, the heat-treatment procedure being similar to that of Feltham anc copley.8

Jan 1, 1963

By H. E. Biber

DURING the production of tin plate a thin layer of FeSn2, is formed at the interface between the steel sheet and the protective tin coating. Because excessive amounts of this alloy layer are undesirable, the kinetics of its formation is a subject of interest in the tin-plate industry. A recent study of this subject at our laboratory uncovered a relationship which should be of general interest to anyone studying kinetics of reactions in metallic systems. It had been previously concluded that, at any given temperature in the range 175" to 330°C, the Fe-Sn alloy layer would have a parabolic growth rate.1,2 However, our studies showed that this rule apparently holds only when the tin plate is heated very slowly to the "reaction" temperature; when the tin plate is rapidly heated, considerably different growth rates occur. An example of this effect of heating rate on growth behavior is contained in the accompanying results of alloy-layer growth measurements at 240°C in oil baths stirred at 10,500, 1800, and 0 rpm. The heating curves for these three conditions are given in Fig. 1, and the growth data are presented in Fig. 2. With the rapid heating rate, provided by the stirring at 10,500 rpm, the alloy layer had three distinct stages of growth. In the initial stage, which persisted well beyond the time required to heat the tin plate to bath temperature, the alloy layer formed very rapidly. The growth followed a rate law of the form w = ktn where n > 1. This initial stage was followed by a growth-retardation stage of about 50-sec duration in which little additional alloy was formed. In the third stage the growth again followed a rate law of the form w = ktn, but here « =0.3. With the intermediate heating rate provided by stirring at 1800 rpm, the three-stage nature was less pronounced and the slope of the third stage increased (i.e., n > 0.3). With the slow heating rate provided by the unstirred oil bath, the alloy layer grew in two stages. The initial rapid-growth stage persisted only until the specimen was heated to bath temperature, no growth retardation was observed, and the slope of the main portion of the plotted data was greater than in the stirred baths, having a value of almost 0.5. Similar results were obtained for other bath temperatures in the range 200" to 300°C. This effect of heating rate on growth behavior may be due to changes in the rate of nucleation of FeSn, crystallites. The iron and tin are in contact from the onset of heating. Thus the initial formation of FeSn, occurs not at the "reaction" temperature but rather while the tin plate is being heated to that temperature. Because nucleation is in general temperature-dependent, different heating rates could cause different over-all nucleation rates, which in turn could cause different growth behaviors. A more detailed discussion of the growth of Fe-Sn alloy layer and the effect of heating rate will be published shortly.

Jan 1, 1965

By B. C. Allen, R. I. Jaffee, D. J. Maykuth

Wrought unalloyed iodide chromium, containing 39 to 95 ppm total interstitials, has a tensile transition temperature of —15°C. Re crystallizing at 1100°C causes the transition to rise to 90° to 390°C, depending on the purity, grain size, and cooling rate after annealing. At about the 100 ppm level, individual additions of carbon or nitrogen raise the transition of both wrought and recrystallized chromium by as much as 210°C, while oxygen has a lesser effect, and sulfur essentially no effect. High transitzon temperatures are exhibited by recrystallized and quenched chromium, and appear to be associated with the amount and distribution of inter-stitials. The latter cm be either in solid solution or in the form of precipitates within the grains or at the grain boundaries. Quench hardening in chromium is primarily caused by nitrogen. The hardness, re crystallization, and grain growth behavior of chromium with and without impurity additions were also investigated. BECAUSE of low density and good oxidation resistance, chromium-base alloys are potentially useful for elevated-temperature applications. The main deterrent to the use of chromium in structural applications is its lack of low-temperature ductility, especially in the recrystallized condition. Accumulated evidence has shown that the ductility of chromium is sensitive to purity. The objective of the current study was to determine the effect of common nonmetallic impurities on the tensile properties of high purity chromium. The separate effects of carbon, oxygen, nitrogen, and sulfur additions on the ductile-to-brittle transition were evaluated for wrought and recrystallized material after various cooling rates. EXPERIMENTAL WORK Unalloyed iodide chromium and seven impurity alloys containing individual carbon, oxygen, nitrogen, or sulfur additions were prepared in rod form. Nominal additions were 100 ppm C, N, and S, and 100 to 500 ppm O. The additions were about a factor of ten greater than the residual amounts in the unalloyed material. The seven alloys and two unalloyed compositions were consolidated into four-pound ingots by conventional consumable arc melting of pressed and welded electrodes under 0.5 atm of helium. Impurity additions were made to the electrode in the form of crushed master alloys. The impurity alloys were double melted to improve homogeneity. The ingots were broken down by extrusion at 1200°C in evacuated steel cans at a reduction ratio of 18 :1, using a molten borosilicate glass lubricant and a ram speed of 80 in. per min. The cans were removed by acid pickling, and the chromium core ground free of surface undulations. Cut lengths were sheathed in mild steel and swaged at 900°C until the core was about 1/4 in. in diam. Two additional 15-lb ingots of unalloyed chromium (ICr-3, ICr-4) were prepared by arc melting and broken down by 26:1 extrusion at 1250°C without a steel can. The billet was lubricated and protected from contamination by a coating of molten glass. The resulting extrusion was then sheath swaged as described previously. Representative chemical analyses of each of the materials, after removal of a 10-mil surface layer

Jan 1, 1963

By N. A. D. Parlee, I. D. Shah, W. C. Phelps

THIS note reports on a continuation of a program on the thermodynamics of Fe-S-X systems in the "steel-burning" temperature range begun by Bock, Barloga, and parlee.&apos; Small coils of 0.039-in.-diameter pure iron (Ferrovac-E) wire were equilibrated with Fe-S-0 melts in ingot iron crucibles under argon at 1324°C in the assembly shown in Fig. 1, the lower part of which was heated in a large Globar furnace. Fig. 1 shows (R) the coiled iron wire sample, (M) the Fe-S-0 melt prepared from desired proportions of ferrous sulfide and ferric oxide, (K) the iron crucible, (I) a mullite guide tube, (J) an alumina crucible, (L) alundum sand, (N) crushed mullite, (Q) hollow cylinders of K30 brick, (C) a steel rod, (B), (El, (F), (G), (P), and (O), details of brass water-cooled head, and (H) a mullite tube 2-3/4 in. ID and 26 in. long. The rod (C) bearing the sample could be removed at will and be replaced by a tube for sampling the melt, or by a thermocouple for comparing the melt temperature with a control thermocouple not far from the 2-3/4-in. mullite tube. After equilibration the iron coils were treated with acid to remove the outer layer of metal and then they were analyzed for sulfur by a standard combustion method. The melt samples were analyzed for oxygen by a variation of Lander&apos;s2 hydrogen-reduction method for mattes, and for sulfur by the ASTM combustion-iodometric method NO. E 30-47. When the results of some forty-two runs were examined it was found that the sulfur and oxygen contents of the equilibrated melts showed good consistency, in that the plotted compositions fell along the smooth curve shown in Fig. 2. The points on this curve represent the experimental compositions of melts in equilibrium with ?-iron (Fe-S-0) solid solutions. These solid solutions are saturated with sulfur and oxygen with respect to the melt and therefore have the same sulfur and oxygen activities as the melt. The curve drawn through the points therefore delineates the ? liquidus. It falls in such a position as to roughly confirm the liquidus curves of Hilty and crafts3 at 1200" and 1300°C which are

Jan 1, 1965

By Nicholas J. Grant, W. Michael Yim

The creep-rupture properties of nickel, in as-prestrained or prestrain-polygonized condition, were studied at 1300°F and 4000 psi, and also at 700°F and 26,000 psi. An improvement of strength was noted in both the as -prestrained and the prestrain-polygonized tests at each temperature. The as-prestrained tests, however, showed superior creep resistance to the prestrain-polygonized ones. From the results of X-ray and etch-pit studies, the strengthc gain was interpreted in terms of dislocation density and the stability of preformed substructures. COLD work is known to improve the strength properties of metals at low temperatures. At high temperatures, however, the strength improvement is often lost if gross structural changes, such as re-crystallization, take place prior to or during the test. Even in the absence of recrystallization, a prestrained metal may undergo structural changes— polygonization and the formation of well-defined subgrains—which importantly effect the resultant properties. The relationship between substructure and creep properties has received considerable attention in recent years. The work of wood1 indicated that the creep strength of aluminum and its alloys was closely related to the subgrain size. Hazlett and Hansen,2 and Ancker, Hazlett, and parker,3 working with nickel and nickel alloys, had shown that small amounts of prestrain at room temperature followed by a recovery anneal at 800°C (1470°F) improved the strength at both low and high temperatures. The strength gain was attributed to an increase in the number of subgrain boundaries as a result of the prestrain-polygonization treatment. More recently Coldren and Freeman4 studied the effect of substructures on the creep rate of nickel at 1550°F. Their conclusions indicated that the substructure size as measured by the number of boundaries was the factor that controlled the creep rate. In addition, the perfection of the subgrain boundary has been indicated to have an important role on the strength.&apos; On the other hand, there are data which disagree with the above observations. Grant, Chaudhuri, Silver, and Ganow6 found no creep strength improvement by a prestraining treatment. In reviewing the role of subgrains on high-temperature creep, Shepard and Dorn7 concluded that the contribution of the subgrains to high-temperature creep strength was a minor one. Guard,8 in a recent study on poly-gonized nickel, has cast doubt on the validity of the postulate that subgrain size controls the creep rate. In the majority of the previous studies, the subgrain boundaries have been singled out as the most important factor in determining creep strength; however, there is no firm theoretical ground for the postulate that the subgrain boundaries act as effective barriers to dislocation motion.B910 Little effort has been directed toward the study of the relationship between creep strength and other structural variables, such as dislocation density, lattice strain,

Jan 1, 1963

By John W. Cahn, John E. Hilliard

Single crystals of copper and silicon-iron were cold rolled in orientations chosen to produce individually the major components of the poly crystalline deformation texture. The orientation dependence of the recrystallization kinetics was studied relative to the primary recrystallization textures of these specimens. It is not possible to rationalize the poly crystalline re crystallized textures on this basis. The results suggest an important role of the interaction of adjacent crystals during the deformation of aggregates. BRICK and Williamson1 first noted evidence that the recrystallization temperature was different for straight-rolled and cross-rolled copper given comparable reductions. Michalak and Hibbard2 investigated quantitatively the effect of rolling procedure on the kinetics of recrystallization of cold-rolled copper and found that material cold-rolled the same amount by straight-pass, cross-pass, and compression-pass techniques developed different deformation and recrystallization textures, different 1-hr recrystallization temperatures, and different recrystallization kinetics. However, the temperature dependence of the rate of recrystallization was essentially the same for all techniques. Similar results were obtained on iron. Dunn and Koh3 in studying the recrystallization textures of cold-rolled silicon-iron single crystals reported large differences in the annealing temperatures and times required to recrystallize specimens of different orientations cold-rolled the same amount. Liu4 and Liu and Hibbard5 utilized the concept of different recrystallization temperatures for different orientations of cold-rolled crystals to rationalize the difference in recrystallization textures found in various face-centered-cubic metals. Their explanation predicted a significant difference in the recrystallization kinetics of deformed (110) [112] crystals as compared to (358) [352] crystals, and, in fact, Liu4 reported evidence that this difference existed at least qualitatively. Verbraak6 who rolled and recrystallized a series of copper single crystals found that the double (112) [111] rolled orientation is related to recrystallized cube texture formation. The effect of rolling intensity on the relative amount of cube component suggests an important role of recrystallization kinetics. Walter and Hibbard7 while trying to relate the behavior of rolled and recrystallized single crystals of silicon-iron to the behavior of polycrystal-line silicon-iron again noted that differences in recrystallization kinetics were necessary to rationalize their results. The purpose of the present investigation was to obtain quantitative kinetic data on the recrystallization of single crystals of both copper and silicon-iron rolled to initial isolated individual orientations corresponding to those found in the polycrystalline deformation textures. These data might indicate the importance of the deformation orientation, i.e. the range of available nuclei, the deformed matrix orientation into which these nuclei grow, and the orientation dependence of their growth rate during primary recrystallization on this texture. I. COPPER Experimental Procedure—A single crystal of 99.98 pet purity copper, grown by the Bridgman technique, was purchased in the form of a bar 1 1/2

Jan 1, 1962

By N. S. Kenny, A. A. Burr

THE purpose of this note is to present evidence that vacancies, which have been produced by quenching from a high temperature, alter the rate of strain-hardening of an hep single crystal. The majority of investigations of the effects of quenched-in vacancies on the yield stress of metals have been made using fee samples in the form of thin wires. However, there is an inherent disadvantage in using such wires to study the effects of vacancies on the rate of strain-hardening of metals because fee wires begin stage II slip either immediately upon yielding or very shortly thereafter. When stage II slip occurs, very rapid strain hardening also occurs, masking the effects of vacancies on the rate of hardening. In this investigation single crystals of magnesium hep were studied since magnesium has only one slip plane at low temperatures and has, therefore, an extensive easy glide region. In addition, the effect of both static and dynamic recovery on the rate of hardening were eliminated by testing in liquid nitrogen. Both forms of recovery occur in hep metals by dislocation climb, which is a diffusion controlled mechanism and is negligible at liquid nitrogen temperatures. Finally, the dependence of the strain-hardening rate on the crystal orientation was eliminated by using the equations of Schmid and Boas.&apos; Variations in the strain-hardening rate could, therefore, be attributed to the presence of vacancies. Single crystals in the form of rods approximately 5 mm in diam and 6 cm long were grown by a modified Bridgman technique from commercial high-purity magnesium (99.97 pet) supplied by the Dow Chemical

Jan 1, 1962