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By J. D. Wood, J. T. Smith

ALLOYS with a dispersed second phase in a metallic matrix are generally much stronger than the matrix itself. Plastic deformation in dispersion-strengthened alloys is usually confined to the matrix phase when recovery processes are active, while in the absence of recovery both phases may yield.' The alloy system studied in the present research was WC-12 wt pct Co and consisted of noncoherent WC particles dispersed in the cobalt matrix. Some particle-to-particle contact existed but not enough to produce a continuous WC skeleton. The microstruc-ture of the WC particles was characterized by very straight edges, forming a trapezoidal shape in any plane of polish. Previous investigations with WC-Co alloys at room temperature have shown that fracture of the WC particles occurs in transverse rupture testing.' Room-temperature slip was reported for WC particles after indentation for hardness measurements.3 Elevated-temperature deformation of WC particles in a WC-12 pct Co alloy was suggested by recent electron microscope studies of specimens deformed at 900' to 1000°C.4 In highly deformed alloys, the WC edges were serrated in contrast to the usual straight or smooth appearance. WC-12 pct Co and WC-15 pct Co alloys have been previously studied under elevated-temperature com-pressive-creep conditions by the present authors. Electron microscope studies of two-stage replicas from deformed specimens showed no evidence of slip or fracture of the WC particles. These specimens were brought to temperature and allowed to equilibrate prior to the application of the creep load. It was believed that the load-application rate, a crosshead speed of 0.005 in. per min on an Instron universal testing machine, was sufficiently low that recovery within the cobalt matrix was sufficient to limit the deformation to this matrix. A series of experiments was performed to evaluate the influence of loading rate on the deformation of WC-Co alloys. A WC-12 pct Co alloy was selected for these determinations. The average WC particle size was 4.45 p with an average linear separation between particles of 0.59 p. The selected temperature was 800°C and was monitored with a Chromel-Alumel thermocouple attached to the specimen. Testing was conducted in an argon-atmosphere chamber to prevent oxidation of the WC-Co specimens. This chamber was mounted on an Instron universal testing machine equipped to apply the load at a fixed rate. Each specimen was loaded to 110,000 psi compression stress at 0.05 and 0.5 in. per min. The loading rate was monitored prior to insertion of the test chamber and was found to be almost precisely the nominal rate selected. The specimens were raised to temperature and held to equilibrate with the surroundings, and then the load was applied and held for 4 hr to duplicate the exposure time utilized for the creep specimens. The time to reach full load at a crosshead speed of 0.005 in. per min was some 500 sec and was reduced to 50 and 5 sec as the loading rate was increased to 0.05 and 0.5 in, per min, respectively. The model developed by Ansell,' when recovery processes do not occur, considers that fracture or deformation of the dispersed particles is necessary to relieve back stresses on dislocation sources and allow dislocations piled up against particles to sweep out in the matrix to cause plastic deformation; he further states that, even at elevated temperatures, the dispersed-particle deformation is necessary for yielding in the absence of recovery. For the case of straight dislocation segments piled up against a straight barrier, such as the straight-sided WC particles, the shear stress, 7 exerted on a particle is: where h is the spacing between particles (0.59 p), a is the applied stress (110,000 psi), p, is the shear modulus of the matrix (6.7 X lo6 psi at 80O°C), and b is the Burgers vector of the matrix dislocation. From Eq. [I], the shear stress, 7, exerted on the WC particles when no recovery occurs is of the order of 6 X lo6 psi at 800°C. The limiting stress, F, that will

Jan 1, 1969

By Jaakko Kajamaa

Neutron diffraction was applied to determine sheet textures by the transmission method. Cold-rolled and recrystallized copper sheets were investigated. The amount of cube texture was determined for three compositions, in which the phosphorus content was, respectively, 0, 0.005, and 0.03 wt pct. The heat treatment was in every case 8 sec at 650°C. In the two latter cases the cube texture was prevented. In addition a comparison with the X-ray diffraction transmission method was made with the 96 pct cold-rolled copper sheet. Outer parts of both (111) pole figures can be considered to be rather identical. This is seen from the fact that the intensity ratio ITD/120" was 0.45 for neutron diffraction and 0.40 for X-ray diffraction. Differences between the methods were discussed in detail. Features peculiar to neutron and X-ray diffraction in texture studies were listed and compared. In this work neutron diffraction was applied to determine sheet textures. Specifically, it was desired to ascertain whether this method can be used to reveal differences when compared to other methods. In addition, the amount of the cube texture in copper sheets was determined as a function of phosphorus content. Previous applications of neutron diffraction to texture problems include the following: nickel wires,' wire of some bcc metals,' and uranium bars.3 In the neutron diffraction technique the greatest difference is in the sample—its method of production and its volume. A sample needs no treatment and its volume is roughly 105 times larger than the volume of an X-ray diffraction sample. The cold-rolled sheet was investigated both by neutron diffraction and by X-ray diffraction, because it is expected that, due to large number of defects, possible differences in the results of the two methods would be revealed. It is a well-known fact that X-ray lines show broadening when cold-worked. Analysis has shown that this is based chiefly on small crystalline size, micro-stresses, and/or faults.4'5 Neutrons are sensitive to the above-mentioned disturbing factors as well, but circumstances in diffraction are different from the X-ray case. Because the sample represents a larger volume, the result is an average over that volume. In addition, it can be assumed that the sample has preserved its original structure, because it needs no special preparation. The particular limitation of neutrons is the relatively low neutron intensity available from nuclear reactors. This decreases the resolution as compared to the X-ray diffraction methods. Furthermore, absorption mainly reduces diffracted X-ray intensity, while multiple scattering effects, i.e., secondary extinction, disturb neutron diffraction. SO neutrons and X-rays behave in a different way when interacting with matter. As in other structural investigations, one can utilize this difference in texture studies as well. One cold-rolled and three recrystallization textures in copper sheets were investigated by neutron diffraction. The samples were produced at the Outokumpu copper factory to the specifications shown in Table I. The paper is divided into five parts. The first deals with the theory of the measurement. In the second, experimental procedures are described. Results are presented in the third part. Both cold-rolled and re-crystallized samples are studied. Discussion is in the fourth part, and finally in the fifth part some conclusions are drawn. 1) THEORETICAL CONSIDERATIONS Properties peculiar to neutron diffraction are the following: a) the scattering length varies greatly between one element and another; b) many of the elements do not absorb neutrons appreciably. In this connection it is of primary interest to know the interaction of neutrons with lattice imperfections. As with X-rays this problem leads to diffraction analysis of deformed and recrystallized metals. From the physical point of view the main difference is that neutrons are scattered by nuclei (magnetic scattering is not considered here), whereas X-rays are scattered by electrons. The features peculiar to neutron and X-ray diffraction methods in texture studies are listed in Table 11. Pole figures are an important tool in performing structural analysis of deformed or recrystallized metal. Present texture research technology requires pole figures which are as precise as possible. The choice between these two methods depends on the technical information which is required. The X-ray diffraction transmission technique may give results which are not necessarily representative of the average physical state of the sample. Although foil samples normally contain enough crystallites for diffraction, they may not necessarily represent the whole structure. An example of this problem is the frequently observed difference between the "surface" and the "inside" texture of a sample. The production of foil samples may disturb the original structure of the parent material. The selection and orientation of the foil from the sample is quite arbitrary. Normally, a highly deformed piece of metal has several texture components. Different components are deformed in a slightly different manner. This is a re-

Jan 1, 1969

By Craig S. Hartley

Expressions are obtained for the energy changes associated with the reaction of (a& (111) slip dislocations on intersecting (110)planes in anisotropic bcc metals. An energy criterion for assessing the likelihood of dissociation of the products of such reactions is also presented. It is found that the "burrier reactions" which form a(100) dislocations at the intersection of two active {110) slip planes are more energetically favorable in metals which exhibit a high value of Zener's anisotropy factor, A, than those which have a low value. The results are presented in a form which permits the stacking fault energy to be obtained from a measurement of the separation between par-tials in a dissociated configuration. However, until accurate calculations or measurements of the stacking fault energies involved are available, it is not possible to assess the physical importance of dissociated dislocations. In a recent paper,' the energy changes associated with several types of reactions between two slip dislocations, (a/2)(111){110), in bcc structures were calculated.* Isotropic elasticity and the approxima- tion v = -3- were employed. The purpose of this work is to present calculations of the energy changes for many of the same reactions using anisotropic elasticity. The problem of dissociation of a(100) and a(110) dislocations is also considered, and maximum fault energies for which dissociation will be energetically favorable are calculated for several bcc metals. Two general types of reactions are considered; those for which the reactant (a/2)(111) dislocations have long-range attractive forces and those for which the reverse is true. An example of the former is: (a/2)[lll] + (a/2)[lll]-a[l00] while the latter are typified by: (a/2)[lll] + (a/2)[111] -a[011] Only reactants lying in different slip planes are considered; therefore, the products must lie along (111) or (100) directions, which are the intersection of two {llO} planes. It will be assumed that the reactants and products are infinitely long parallel dislocations, since in this case the energy change associated with the reactions is a maximum.' THEORY The self-energy per unit length of a straight mixed dislocation in an anisotropic medium can be written? where b is the Burgers vector, K is an appropriate combination of the single-crystal elastic constants, and R and ro are, respectively, outer and inner cut-off radii of the elastic solution. The energy given by Eq. [I] does not account for any variation of the core energy with orientation. This could be manifested by an orientation dependence of the core radius or, equivalently, the Peierls width, of the dislocation. However, the energy contribution due to this source is expected to be small, and current models of the dislocation core are not sufficiently accurate to justify such a refinement. It has already been shown that for the isotropic case the energy contributions due to nonzero tractions across the cores of the reactants and products exactly cancel one another in the reaction.' Accordingly, it will be assumed that this contribution to the total energy change in the anisotropic case is small. In the subsequent discussion it is also assumed that the core radii of the reactant and product dislocation are the same and that, where stacking faults are formed, the faulted region is bounded by the centers of the partials. Consequently only changes in elastic energy due to the reactions will be considered. When the dislocation is parallel to either the (111) or the (100) directions, K may be written:375 K = (Ke sin2 a + Ks cos2 a) [2] where K, and Ks are the combination of elastic constants corresponding to an edge and screw dislocation lying along the same direction as the mixed dislocation, and a is the angle between the direction tangent to the dislocation line and the Burgers vector. Eq. [2] should not be confused with the isotropic approximation to the variation in energy with line Orientation.6 It should be noted that the essentially isotropic expression for K is a result of the characteristic symmetry of the (111) and (100) directions and is not, in general, valid for other dislocation directions in anisotropic cubic metals. The energy* change for a reaction in which the re- actant and product dislocations are parallel perfect dislocations can be written: where Ep and E, refer to the self-energies of the products and reactants, respectively. For dislocations parallel to (100) and (111) directions, Eq. [3] becomes:

Jan 1, 1969

By O. P. Quist, S. H. Carpenter

The internal friction of single-crystal LiF has been investigated as a function of crystal orientation, while simultaneously applying a static compressive load. Three different crystal orientations were used, these being samples with the (100), (110), and (111) directions along the sample length. Results show the internal friction measured to be similar in appearance but different in magnitude for the (100) and (110) samples. With both orientations, application of a static stress caused an increase in the amplitude-independent damping, which recovered with time. The amplitude-dependent damping was found to first decrease with load up to the yield stress and then increase rapidly. Samples of the (111) orientation were found to have no measurable internal friction even when loaded up to 3.0 kg per sq mm. These results are discussed in terms of current theories of internal friction in ionic crystals. This paper presents the results of an investigation of the dislocation mobility and dislocation motion in high-purity single-crystal LiF at applied stress levels up to the yield stress. Internal friction measurements of the dislocation damping while simultaneously applying a static compressive load was the experimental technique used. LiF crystals much prefer to slip on the (110) set of slip planes. However, with a suitable stress distribution they can be forced to slip on the {100} set of slip planes.' For both sets of slip planes the slip direction is the same, namely (110). The object of this investigation was to try and learn more about the dynamical properties of dislocations on the different slip systems in LiF crystals. EXPERIMENTAL PROCEDURE Dislocation damping was measured, in terms of the log decrement, using a five-component marx2 composite piezoelectric oscillator. The apparatus used allows one to measure the dislocation damping while simultaneously applying a static compressive load on the sample. A schematic of the apparatus used is shown in Fig. 1 and a complete discussion of its construction and operation is given elsewhere.3 All measurements were made at room temperature with a longitudinal resonant frequency of approximately 50 kc per sec. Damping measurements were made using longitudinal vibrations with strain amplitudes from up to 10. Static loads up to 3.0 kg per sq mm were applied to the sample while the damping was being measured. Samples used in this investigation were high-purity single crystals of LiF purchased from the Harshaw Chemical Co. All samples were approximately of an in. square and were hand-ground in length to one-half wavelength to match the resonant frequency of the driver and gage quartz crystals. Samples of three different crystallographic orientations were used, namely, crystals with the (loo), (110), and (111) direction parallel to their length. The magnitude of the damping is a direct measure of the area on the slip planes swept out by dislocations during a complete oscillatory cycle. With a sample of the (100) orientation the maximum applied shear stress, due to longitudinal vibrations, is on the (110) slip planes with zero shear stress on the (100) slip planes. Thus, damping measured from a (100) sample is due entirely to dislocation motion taking place on the (110) set of slip planes. Similarly, for a sample of the (111) orientation there is zero shear stress on the (110) set of slip planes and the damping measured from a sample of this orientation is due entirely to dislocation motion on the (100) set of slip planes. Samples of the (110) orientation will have a component of shear stress on both sets of slip planes and

Jan 1, 1969

By K. E. Manchester, A. H. Clark

Hall measurements have been made on three groups of silicon samples, which were implanted with boron, aluininunz, and phosphorus ions. Boron and phosphorus implants show essentially bulk properties when annealed under previously determined conditions, i.e., 15 min at 80O°C for boron and 10 mirz at 600°C for phosphorus. Bulk properties were also observed in alu?rrilzum-implanted samples when ion concentrations were below 1015 cm-'; however, strange low- terrzperalure behavior and a falloff in cavrier concenlralion was observed for sarnples with ion concenlration abozle loL5 ern-'. This can be attributed to solid-solubility effects since the average bulk concentration f0.r the sample exhibiting bulk properties was below the reported solubility limit for aluminum, while the other samples were above the limit. A detailed study of the annealirzg process indicates that mobilities reach bulk c~alues in phosphorus implants at 250DC, in alutninurn ivnplanls a1 500°C, and in boron implants at 700°C. A simple rnodel has been proposed to fit the annealing data. THE technique of semiconductor doping by direct injection of energetic ions is being actively investigated at this Center. Previously published results from this laboratory have been concerned with the investigation of implanted profiles in silicon and the electrical properties of the resultant p-n structures.1'2 Diode properties have been reported for junctions produced by implantation of boron ions and aluminum ions in n-type silicon and phosphorus ions in p-type silicon. Reverse current characteristics, as well as electron diffraction data, have indicated that the damage to the structure produced by the energetic ions during the stopping process can be minimized by a gentle anneal. The time-temperature conditions for this process have been determined by sheet resistivity studies.3 Electrical profiles of implanted phosphorus ions which have been determined by a differential sheet conductivity technique are based on the assumption that the carrier mobilities and activation energies for ionization are the same as in bulk silicon. These assumptions have been substantiated experimentally by measurement of Hall constants and resistivities of these implanted structures and the results are presented herein. After establishing the bulk property equivalence of the annealed layers, a more detailed examination of the annealing process was undertaken. The sheet resistivity technique initially used to determine anneal conditions has been broadened to include Hall constants and mobility behavior with anneal conditions. PROCEDURE The three groups of samples prepared for Hall measurements were implanted with mass-separated beams of boron, aluminum, and phosphorus ions. Ion concentrations are equivalent surface concentration and they have been determined from beam current measurements during implantation. Implant conditions for the samples are shown in Table I. In all cases, the samples had previously been angle-lapped on one edge and the junction delineated with an HF-copper sulfate solution. The surfaces of the implanted regions of the samples were exposed to the delineating solution and in the case of the "n"-type phosphorus-implanted areas it was later discovered that a finite amount of surface could be etched by this solution. This is discussed in the section on results. The implanted samples were ultrasonically cut into the conventional six-probe configuration shown in Fig. l.* In the annealing studies, for which the meas- urements were taken at room temperature, the sample holder was a Bakelite jig incorporating tungsten mechanical probes. The other measurements were taken using a conventional liquid-nitrogen cryostat, in which the temperature could be varied from 77" to about 400°K. For these measurements, 10-mil aluminum dots were evaporated onto the samples and alloyed with the silicon at 530°C for 15 min. The samples were then mounted in flat-packs, and gold wires were bonded to the aluminum dots. The electrical measurements were made with either a Leeds & Northrup K-5 Potentiometer, a Keithley 147 Nanovolt Null Detector, or a Keithley 601 Electrometer. No external bias was applied to the substrate. There is an inherent self-biasing arrangement at one or the other of the current contacts (depending upon the polarity), and this suffices to limit the current flow to the implanted layer. The magnetic field was generated by an A. D. Little electromagnet. Except for occasional checks of linearity of the Hall voltage with

Jan 1, 1969

By J. H. Swisher

When an Fe-Mn alloy is internally oxidized, the inclusions formed are MnO which contains some dissolzled FeO. In the internal oxidation reaction, not all of the manganese is oxidized; some remains in solid solution as a result of the high Mn-0 solubility product in iron. Taking these factors into consideration, the rate of internal oxidation of an Fe-1.0 pct Mn alloy is computed as a function of temperature, using available thermodynanzic data and recently published data for the solubility and diffusivity of oxygen in iron. The predicted and experimentally determined rates for the temperature range from 950 to 1350°C are in good agreement. ThE rates of internal oxidation of austenitic Fe-A1 and Fe-Si alloys have been studied extensively.1"4 Schenck et al. report the results of a few experiments with Fe-Mn alloys at 854" and 956C, and Bradford5 has studied the rate of internal oxidation of commercial alloys containing manganese in the temperature range from 677" to 899°C. When Fe-Mn alloys are internally oxidized, the inclusions formed are solutions of FeO in MnO, the composition depending on the experimental conditions. Since the thermodynamics of the Fe-Mn and FeO-MnO systems have been investigated,6"9 and since the solubility and diffusion coefficient of oxygen in y iron have been determined recently,' it is possible to predict the rate of internal oxidation from known data. The calculations used in predicting the rate of internal oxidation will first be outlined, then the results of the prediction will be compared with the experimental results of this investigation. PREDICTION OF PERMEABILITY FROM THERMODYNAMIC AND DIFFUSIVITY DATA Oxygen is provided for internal oxidation in these experiments by the dissociation of water vapor on the surface of the alloy. The dissociation reaction is: + H2(g) + [O] [1] where [0] denotes oxygen in solution. The equilibrium constant for this reaction is known as a function of temperature:' log As oxygen diffuses into the alloy, oxide inclusions are formed which are MnO with some FeO in solid solution. The reactions occurring are: [Mn] + [0] = (MnO) [31 and [Fe] + [0] = (FeO) [41 where [ Mn] is manganese dissolved in iron and (FeO) is iron oxide dissolved in MnO. The overall reactions may be written as follows: [Mn] + HOte) = (MnO) + H2(£) [5] and [Fe] + H20(g) = (FeO) + Hz(R) [61 The standard free-energy changes and equilibrium constants for Reactions [5] and [6] are known.6 Therefore the equilibrium constants for Reactions [3] and [4] may be obtained by combining known thermodynamic data for Reactions [I], [5], and [6]. For Reactions [3] and [4]: K = and For the present purpose, both the Fe-Mn7,8 and FeO-~n0' systems can be considered to be ideal, i.e., [amn] = [NM~] and (aFeO) = (NM~~) = 1 - (NFeO) where the Ns are mole fractions. These relations, together with Eqs. [I] and [8], permit us to compute both the oxide and metal compositions as a function of temperature and oxygen potential at any point in the specimen. For cases where the oxygen concentration gradient between the surface and the subscale-base metal interface is linear, the kinetics of internal oxidation is an application of Fick's first law: where dn/dt is the instantaneous flux of oxygen into the specimen, g-atom per sq cm sec; 6 is the instantaneous thickness of the subscale, cm; Do is the diffusion coefficient of oxygen in iron, sq cm per sec; p is density of iron, g per cu cm; h[%O] is the oxygen concentration difference between the surface and sub-scale-base metal interface, wt pct. B6hm and ~ahlweit" derived an exact solution to the diffusion equation for systems in which there is a stoichiometric oxide formed. They showed that the oxygen concentration gradient is given by a rather complex error function relation. For the Fe-Mn-0 system and for most other systems that have been studied, however, variations in oxide compositions are small and rates of internal oxidation are sufficiently slow that the deviation from linearity in the concentration gradient of oxygen is negligible. The mass of oxygen transported across a unit area of the specimen for the total time of the experiment is given by the mass balance equation:

Jan 1, 1969

By R. V. Mrazek, F. E. Block, S. B. Knapp

The mixed homogeneous and heterogeneous kinetics of the thermal decomposition of tungsten hexacarbonyl were studied by employing a batch reactor. The system was such that a sample of tungsten hexacarbonyl could be injected into the preheated reactor, and the progress of the reaction followed by a simple pressure measurement. Both the homogeneous and heterogeneous reactions were found to be first order, and approximate activation energies were determined for each reaction. It is shown that the dis-proportionation of carbon monoxide to give carbon and carbon dioxide cannot be the source of carbon in tungsten deposits prepared by this reaction. The kinetics of the thermal decomposition of tungsten hexacarbonyl have been investigated as part of a continuing study by the U.S. Bureau of Mines on the decomposition of organometallic compounds. Reactions involving the thermal decomposition of metal carbonyls have a potential application in the preparation of pure metals and fine metal powders. Indeed, it was these applications which provided the impetus for much of the early work involving the carbonyls of nickel1 and iron.' The relative lack of study of other metal carbonyls can be traced to the comparative difficulty in synthesizing these compounds. The most common use for tungsten hexacarbonyl has been as an intermediate in vapor-phase plating.7'8 However, attempts to obtain a carbon-free deposit of tungsten by this method have not been successful, and some investigators have taken advantage of the carbon contamination and used this process to form tungsten carbide deposits.lo Other investigators have studied the thermodynamic properties11"14 and molecular structure of tungsten hexacarbonyl. However, very little is known about the kinetics of this thermal decomposition, the mechanisms involved," or the source of carbon in the resulting plate. In contrast, studies have been made of the kinetics of the thermal decomposition of nickel tetracarbonyl, iron pentacarbonyl, and molybdenum hexacarbonyl.'l It has been found that these thermal decompositions occur by a mechanism which is partially heterogeneous in nature. Information available on the equilibrium constants for the decomposition of tungsten hexacarbonyl was used to determine a temperature range, 500" to 560°K, in which the reaction could be expected to be essentially complete. APPARATUS The apparatus used allowed the injection of a sample of tungsten hexacarbonyl into a preheated batch reactor and the use of a simple pressure measurement to follow the progress of the reaction in the sealed reactor. The pressure was sensed by means of a pressure transducer (Consolidated Electrodynamics Corp., 0.3 pct)* capable of operating at the *Reference to specific products is made to facilitate understanding and does not imply endorsement of such brands by the Bureau of Mines._______ reaction temperature. This type of sensing element was chosen to avoid the problem of condensation of the sublimed carbonyl in the capillary tubing leading to any type of remote pressure-sensing device. stirring was provided by rotating the entire apparatus. Glass beads placed in the reactor provided a pulsating agitation. To minimize thermal gradients in the reactor walls, the reactor was constructed of aluminum. The support tube which held the reactor in the furnace was thin-walled stainless steel to minimize heat conduction out of the reactor. As a result of these measures, a nearly uniform temperature (°C) was maintained throughout the reactor. Fig. 1 is a schematic diagram of the apparatus. The small gear motor rotated the entire apparatus at about 200 rpm. The bearings shown at the ends of the air cylinder were perforated to allow air to be fed to the charging piston and to allow inert gas to be fed to the reactor during the preheating period. The sample was simultaneously injected and sealed inside the reactor by operation of the air piston. Fig. 2 shows a cross section of the air cylinder and the adjoining portion of the support tube leading to the reactor. The sample carrier is shown in place at the right-hand end of the injection rod extending from the air piston. The piston is shown in the retracted position, as it would be prior to the start of an experiment. The small Teflon gasket which encircled the sample carrier at the end of the injection rod sealed the reactor when the sample was injected. This seal was maintained throughout the test by maintaining air pressure on the piston. The sample carrier was a 2-in. section of thin-walled, -in.-diam nickel tubing with an internal blank about 1 in. from the base and with the base end sealed.

Jan 1, 1969

By H. Biloni, R. Morando

The surface structure and substructure of Al-Cu alloys solidified as conventional ingots and under particular conditions such as those used by Bower and Flemings are studied. The influence of lampblack coating on the mold walls is especially considered and the results compared with those obtained in copper and graphite molds where no coatings exist. When high heat extraction conditions exist the observations show that mechanism of copious nucleation is responsible for most of the chill zone. When the heat extraction through the mold walls is low, a coarse grain structure with dendritic morphology arises, with a size that depends on the degree of convection present, analogous to that analyzed by Bower and Flemings. In both cases the effect of the convection on the macroscopic and microscopic appearance is discussed. The ingot macrostructure consists of one or more of three zones: "chill zone", "columnar zone", and central "equiaxed zone". The mechanism of the columnar-equiaxed transition has been subject of considerable interest and at present at least three theories exist about the formation of the equiaxed region: 1) the constitutional supercooling theory1 maintains that the equiaxed crystals nucleate after the columnar zone has formed, as a result of the constitutional supercooling of the remaining liquid; 2) chalmers2 pointed out, however, that there were several objections to this proposal, and that consideration should be given to the possibility that all the crystals, equiaxed as well as columnar, originated during the initial chilling of the liquid layer in contact with the mold; 3) Jackson et aL3 and O'Hara and ~iller~ suggested that a remelting mechanism of the dendrite arms is responsible for the formation of the equiaxed region. After the work of Cole and Bolling and other authors6 it became evident that convection (natural, reduced, or forced) plays a very important role in the transition from columnar to equiaxed and on the size of the resultant equiaxed structure. Until recently the accepted explanation of the chill zone was that it occurs as a result of copious nucleation in the liquid layer in contact with the mold walls.798 The columnar region is a subsequent result of the growth of favorably oriented grains and, as a result of a selection mechanism studied by Walton and Chalmers,9 elongated grains with marked texture are formed. Recently, however, Bower and Flemings" using an ingenious laboratory experiment introduced the idea that the "copious nucleation" mechanism is not responsible for the formation of the chill zone and that the presence of convection, introducing some form of "crystal multiplication", plays a decisive role in the formation of the chill zone. Unfortunately, it is important to consider that for their conclusions Bower and Flemings extrapolated the results obtained in their special experiments to the case of conventional ingots, and that these authors only analyzed the macrostructures of the specimens. Let us consider the work by Biloni and chalmers" concerning predendritic solidification. These authors were able to show that a study of the segregation substructure of A1-Cu gives information about the nucleation and growth of crystals formed in contact with a cold surface. A spherical predendritic region characterizes the first part of every grain nucleated in contact with the surface as a result of the chill effect. The aim of this paper is to elucidate through the observation of the segregation substructure the conditions under which (in the Bower and Flemings type of experiments and in conventional ingots) either the nucleation or the multiplication mechanism gives rise to the structure in contact with the mold walls. I) EXPERIMENTAL TECHNIQUES The experiments were performed on two alloys: Al-1 wt pct Cu and A1-5 wt pct Cu. The purity of the aluminum was 99.99 pct and the copper 99.999 pct. The results obtained with both alloys were similar. In the Bower and Flemings type of experiments the apparatus employed to obtain rapid solidification against a surface was similar to that used by those authors. The liquid was drawn by partial vacuum into the thin section mold cavity. Plate casts were 5 cm wide and usually 7.5 cm high. The thicknesses of the cast were 0.1 and 0.3 cm. Two different materials were used for the mold, copper and nuclear-grade graphite. The internal mold surfaces were polished and left uncoated for some experiments. In other experiments, the copper or graphite surface was coated with a thin film of lampblack material. In some of these particular experiments one of the mold walls was left with an uncoated region (usually in the form of a cross). The conventional ingots were cast in graphite or copper molds. In different experiments the mold walls were sometimes uncoated or coated with lampblack material. The results obtained in conventional and Bower and Flemings copper molds were compared with those obtained with copper molds coated with a very thin film of graphite; the results obtained were essentially similar. The size of the conventional ingots was 5 cm diam and 7 cm high in all cases. The cast surfaces produced by the Bower and Flemings type of experiments and conventional methods were observed macroscopically and microscopically without any metallographic preparation. As Biloni and Chalmers showed," the observation of the chill surface can give considerable information about the structure and segregation substructure.

Jan 1, 1969

By L. F. Bryant, J. P. Hirth, R. Speiser

The surface, gain boundary, and twin boundary energies, as well as the surface diffusion coefficient, of cobalt were determined from tests at 1354°C in pure hydrogen. A value of 1970 ergs per sq cm was calculated for the surface energy, using the zero creep method. It was possible to measure the creep strains at room temperature because the phase transformation was accompanied by negligible irreversible strain and no kinking. Established techniques based on interference microscopy were used to obtain values for the other three properties. The gain boundary and twin boundary energies were 650 ad 12.7 ergs per sq cm, respectively, while a value of 2.75 x l0 sq cm per sec was determined for the surface dufusion coefficient. In the course of a general study of cobalt and cobalt-base alloys, information was required about the surface energy of cobalt. Hence, the present program was undertaken to measure the interfacial free energy, or, briefly, the surface energy, of the solid-vapor interface of cobalt. The microcreep method was selected for this measurement because other surface properties could also be determined from the accompanying thermal grooving at grain boundaries and twin boundaries. A brief summary of the methods for determining the various surface properties follows. At very high temperatures and under applied stresses too small to initiate slip, small-diameter wires will change in length by the process of diffu-sional creep described by Herring.1 The wires acquire the familiar bamboo structure and increase or decrease in length in direct proportion to the net force on the specimen. For a specimen experiencing a zero creep rate, the applied load, wo, necessary to offset the effects of the surface energy, y,, and grain boundary energy, y b, is given by the relation: where r is the wire radius and n is the number of grains per unit length of wire. The first results obtained from wire specimens were reported by Udin, Shaler, and Wulff.' udin3 later corrected these results for the effect of grain boundary energy. The grain boundary energy is determined from measurements of the dihedral angle 8 of the groove which develops by thermal etching at the grain boundary-free surface junction. For an equilibrium configuration: Measurements of the angle 8 can be made on the creep specimens4'5 or on sheet material, as was done in this investigation by a method employing interference microscopy.= If the vapor pressure is low, the rate at which grain boundary grooves widen is determined primarily by surface diffusion and, to a lesser extent, by bulk diffusion. The surface diffusion coefficient, D,, is obtained from interferometric measurements of the groove width as a function of the annealing time, t. As predicted by Mullins~ and verified by experiment, the distance, w,, between the maxima of the humps formed on either side of the grain boundary increases in proportion to if grooving proceeds by surface diffusion alone. For this case: where fl is the atomic volume and n is the number of atoms per square centimeter of surface. When volume diffusion also contributes to the widening, the surface diffusion contribution can be extracted from the data by the method described by Mullins and shewmon.8 Where a pair of twin boundaries intersects a free surface, a groove with an included angle of A + B (using the groove figure and notations of Robertson and shewmong) forms by thermal etching at one twin boundary-free surface junction. If the "torque terms", i.e., the terms in the Herring10 equations describing the orientation dependence of the surface energy, are sufficiently large, an "inverted groove" with an included angle of 360 deg-A'-B' develops at the other intersection. The angles A + B and A' + B' are measured interferometrically. When the angle, , between the twinning plane and the macroscopic surface plane is near 90 deg, the twin boundary energy is calculated from the relation: 1) EXPERIMENTAL TECHNIQUES Five-mil-diam wire containing 56 parts per million impurities was used for making ten creep specimens. These specimens had about 15 mm gage lengths with appended loops of wire and carried loads (the specimen weight below the midpoint of the gage length) ranging from 3.7 to 149.8 mg. The wires were hung inside a can made from 99.6 pct pure cobalt sheet. Beneath the wires were placed small specimens of 20-mil-thick, 99.9982 pct pure cobalt sheet from which the relative twin boundary and grain boundary energies and the surface diffusion coefficient were measured. All the specimens were annealed at a temperature of 1354" i 3°C which is 92 pct of the absolute melting point of cobalt. The furnace atmosphere was 99.9 pct pure hydrogen that was purified further by a Deoxo catalytic unit, magnesium perchlorate, and a liquid-nitrogen cold trap. As a precautionary measure the gas was then passed through titanium alloy turnings which were heated to 280" to 420°C and replaced after every test period. The hydrogen was maintained at a

Jan 1, 1969

By D. O. Hobson

Zirconium single crystals of various specific orientations were fabricated by rolling or drawing. The resulting textures were determined and are discussed with respect to the deformation modes that produced them. The crystals deformed in a predictable manner by combinations of up to third-order twinning with three twinning modes and by slip. Twinning was found to play a major role in initial texture formation. Texture changes produced by slip occurred only at the higher reductions. The twinning sequences that produced each intensity peak during the initial reductions could be identified. Schmid factor criteria were found useful in predicting which deformation modes to expect for each crystal orientation and fabrication procedure. The possible application of these data to poly-crystalline material is discussed. PREFERRED orientation or texture has a significant effect on the properties of most materials, causing anisotropy in fabricated cubic metals and enhancing the natural anisotropy of noncubic metals. This study evaluates the effects of several fabrication methods on the textures formed from specific starting orientations of zirconium single crystals and, it is hoped, gives an insight into the effects of the same operations on poly-crystalline material. BACKGROUND In fcc and bcc metals, texture changes take place by gradual lattice rotations caused by the operation of one or more slip systems. Deformation twinning plays an insignificant role in the deformation of such metals. In zirconium and its alloys, however, and in many other hep metals the ability to twin allows very rapid texture changes to be made with very small amounts of deformation. The deformation systems found in zirconium and its alloys are prism slip and three twinning modes.1 Slip occurs on the {1010}< 1120) system. There is little or no appreciable basal slip in zirconium. The twinning planes, illustrated in Fig. 1, are {1012}, {ll2l}, and {1122}. Two twinning modes, the {1012} and the {ll2l} operate for a tensile stress along the basal pole. A compressive stress parallel to the basal pole is required for {ll22} twinning. These twinning operations cause a 35- to 85-deg reorientation of the basal pole. The {1012} twin is the predominant tensile twin at room temperature. The twinning shears, S, are shown in the figure. A criterion for predicting which deformation system will operate when a grain is subjected to a known stress state is the Schmid (orientation) factor. This factor gives the fraction of the applied stress that computer program was written2 to calculate the Schmid factors for the four deformation modes in zirconium. It assumed three orthogonal stress axes and considered ninety-one different orientations of the basal pole in one octant of this stress space. At each basal pole position the Schmid factors were calculated for seven positions of rotation at 10-deg increments of the unit cell about the basal pole. Schmid factors were determined for a total of 637 orientations and for twenty-four deformation systems in each orientation. The program listed the Schmid factors for uniaxial stress parallel to each axis and, to approximate rolling, or-thonormal biaxial stress was also considered. Fig. 2 shows the range of orientations over which the various types of deformation would tend to predominate in biaxial plane strain with the stresses, equal magnitude. The exact boundary position between regions of different deformation modes depends, however, on the relative values of the critical shear stress for each deformation mode. Fig. 2 is drawn on the assumption that they are equal and it therefore may be only approximately correct. It is also recognized that the biaxial stress analysis may not be applicable in certain crystal orientations. EXPERIMENTAL PROCEDURE Single crystals of zone-refined zirconium, produced by Wilson of this Laboratory,3 were electrical-discharge-machined to form specimens for rolling, tube-drawing, and rod-drawing studies. Specimens were rolled at room temperature on 2-|--in.-diam hand-powered rolls from three different starting orientations: 1) the basal plane parallel to the rolling plane and the [1120] in the rolling direction, (0001)[ll20]; 2) the (1120) plane parallel to the rolling plane and the basal pole in the rolling direction, (1120)[0001]; and 3)_the (1120) plane parallel to the rolling plane and the [1100] in the rolling direction, (1120)[ll00]. Drawing specimens were cut with the [0001] direction as the drawing direction in the tube blank and [1120] as the drawing direction in the rod specimen. The drawing

Jan 1, 1969

By J. Szekely, Robert G. Lee

Calculations are presented for the prediction of the combined radiative-convective heat loss from molten steel held in a ladle, covered by initially molten slag. A mathematical formulation is given and numerical solutions are presented of the resultant partial differential equation. It is shown that a slag layer of about 2 to 3 in. thick would prevent any significant heat loss from the top metal surface for Periods of up to 1 hr. For thinner slag layers (or in the absence of the protective slag) appreciable heat losses would occur; plots given in the paper allow the quantitative evaluation of the fall in the metal temperature due to this heat loss. The ironmaking-steel processing operation involves several intermediate steps where the molten metal is held or transfered in ladles. The quantitative assessment of the heat losses occurring under these conditions is of considerable importance in process design considerations since the temperature of the metal may have to meet rigid specifications in any given part of the processing sequence. While the metal is held in a ladle, heat is lost by two mechanisms: i) by conduction into the ladle walls; ii) by radiation and convection from the top surface. Calculations relating to the conductive heat loss, are readily made and information may be found in the literature both on data pertaining to metallurgical situations and on the techniques that are available for performing additional computations.&apos;-3 The evaluation of the combined convective-radiative heat loss is less straightforward, especially when there exists a protective slag layer covering the metal. In this latter case, as the top slag surface loses heat partial solidification may occur and the latent heat thus given up by the slag may represent an effective barrier to the heat loss from the metal. A semiquantitative assessment of the role played by the slag in preventing heat loss from the metal has been made in a previous paper,4 where it was shown that a slag layer 6 in. thick would act as a near-perfect insulator for periods of up to 2 hr. However, this first paper reported on an essentially preliminary investigation that considered only one slag layer thickness; furthermore, the boundary conditions used for the calculations were somewhat restrictive since no allowance was made for changes in the metal temperature. The purpose of this second paper is to extend the scope of the preliminary investigation previously reported by: i) considering several slag layer thicknesses; ii) allowing for variations in the metal temperature; and finally iii) by performing calculations on the net loss from the metal rather than from the slag surface. FORMULATION Consider a slag phase extending from y = 0 to y = L1, covering a metal phase that occupies the region extending from y = Ll to y = L, as illustrated in Fig. 1. Denote the slag and metal temperatures by TS and Tm and assume that initially both slag and metal are molten, having a uniform temperature Ti. At time = zero the surface represented by the y = 0 plane (top slag surface) is brought into contact with cold air, the temperature of which is given as T Thus for time > zero, heat will be transfered from the slag to the air by natural convection and thermal radiation; as a result of this heat loss the slag temperature will fall and after some time a solid phase is formed and a solidification boundary (more realistically described as a zone) will move progressively from y = 0 toward y = L1. Once the region of temperature gradients, moving ahead of the solidification zone, reach the slag-metal interface (y = L1) there will be a net transfer of heat from the metal through the slag to the cold air, across the y = 0 plane. In the formulation of moving boundary problems, involving phase changes that require computer solution, it is convenient to represent both phases by a single equation, making allowance for the latent heat of solidification by assigning an appropriate temperature dependence to the specific heat content. Thus the energy equation for the whole of the slag may be written as follows:

Jan 1, 1969

By J. D. Hunt, D. T. J. Hurle

A uariety of eutectic structures are formed in faceted/nonfaceted eutectics. The various structures are explained in terms of the absence or presence of small facets in the liquid groove. Regular structures are produced when, for purely geometric reasons facels cannot form. The presence of a facet in the liquid groove leads to the formation of an irregular or a cell-like complex regular structure, due to the relative immobility of the groove. A classification of eutectics was proposed by Hunt and jackson, based on the presence or absence of facets on the primary phases (the absence of facets may be predicted from the dimensionless entropy of melting2). Eutectics were divided into three groups: 1) eutectics in which both phases grow in a nonfaceted manner; 2) eutectics in which one phase grows faceted, the other nonfaceted; 3) eutectics in which both phases grow faceted. It was suggested that regular1 rodlike or lamellar structures1 should be formed in the first group, that irregular or complex regular structures1 should be formed in the&apos; second, and that irregular structures1 should be formed in the third. Recently it has been shown that the structural classification is incomplete. Regular rodlike structures (InSb-NiSb eutectic3), or broken lamellar structure (Bi-Zn eutectic, Fig. 8), are formed in alloys of the second group when the faceted phase has a large volume fraction. Hunt and jackson&apos; argued that regular structures could form in faceted/nonfaceted systems, but that such structures would be unstable in the presence of microfacets on the lamella of the faceting phase, because the growth rate at a point on such a facet would depend on the kinetic undercooling at the point of nu-cleation on the facet, and not on the local kinetic undercooling. In these circumstances it would not be possible to consistently balance the compositional and kinetic undercooling over a lamellar structure and thus obtain a stable isothermal interface. In this paper we discuss in detail the origin of the various structures formed in faceted/nonfaceted systems, pointing out that the most important factor promoting the formation of a regular structure is the absence of a facet in the liquid groove. 1) FACET FORMATION IN SINGLE-PHASE MATERIALS Facets form when there is an energy barrier for the addition of a new solid layer on an existing solid. When a barrier is present,2 growth proceeds by the lateral movement of steps across a crystallographic plane. The rate-controlling stage of the process occurs when the step is first formed. Hulme and Mullin6 have shown that faceting in single-phase materials can only occur when both interface curvatures are convex with respect to the solid and when the surface is tangential to the facet plane. When even one of the curvatures is concave a facet does not form because new layers of solid from adjacent regions can always feed the facet plane, Fig. 1. Growth under these conditions is then as easy as elsewhere. Similar considerations will apply to eutectic growth; consequently the shape of the faceted phase is extremely important. 2) LAMELLAR SPACING CHANGES IN EUTECTICS Jackson and Hunt7 have shown that the interface undercooling AT of a growing lamellar interface (neglecting kinetic undercooling) is related to the lamellar spacing, A, and growth velocity, v, by an expression of the form: where m, Ql, and nL are constants of the system given in Ref. 7. Eq. [I] is plotted for fixed v in Fig. 2. Jackson and Hunt postulate that a regular eutectic grows near, but to the right of the minimum in the AT vs A curve. They argue that the spacing cannot be to the left of the minimum because the interface is then unstable to fluctuations in A. It cannot grow too far to the right, because when the spacing becomes too wide an isothermal interface can no longer be maintained over the large-volume-fraction phase.7 It is argued that during any change in growth rate the lamellar spacing remains in the permitted range by the movement of lamellar faults. When the spacing is too wide, the fault, shown in Fig. 3, moves to the left; when the spacing is too narrow it moves to the right. The faults, however, have to be formed. heir formation has been shown to occur when local regions deviate considerably from the spacing defined by the lamellar When the spacing is locally too narrow (it passes to the left of the minimum, Fig. 2), pinching off of the narrow phase occurs. When the spacing is locally too wide, the interface on the large volume-fraction phase can no longer be maintained as an iso-

Jan 1, 1969

By M. G. Benz

The superconducting performmce of diffusion-processed Nb3Sn is influenced by its micro structure. High isotropic transverse current density may be achieved in this material by a process which forms a precipitate of ZrO, within the Nb3Sn. FOR an ideal type-I1 superconductor, little or no transport current can be carried in the mixed state; i.e., little or no transport current can be carried above the lower critical field H,,, where the field penetrates abruptly in the form of current vortices or fluxoids, even though full transition to the normal state does not occur until the upper critical field H,,.&apos; Fortunately, nonideal type-I1 superconductors can be readily obtained and these carry large transport currents up to the upper critical field H. Both theoretical and experimental investigations have attributed this current-carrying capability for nonideal type-I1 superconductors to pinning of the fluxoid lattice by heterogeneities in the microstructure of the superconducting material. These heterogeneities may take the form of dislocations or dislocation clusters,2"5 grain boundaries: structural imperfections introduced by phase transformations; radiation damage,8"10 or precipitates.11"15 Nb3Sn formed by diffusion processing is a type-I1 superconductor. Heterogeneities are needed for high superconducting critical currents above H,,. This paper will cover: a) what the microstructure of diffusion-processed NbSn looks like; b) what changes in the microstructure take place when the system is doped with precipitates, and c) how these changes in microstructure influence the superconducting critical currents. EXPERIMENTAL Preparation of Samples. Diffusion processing was used to form the Nb3Sn. The procedure used was as follows: a) coat the surface of a niobium tape with tin; b) heat-treat this tape at a temperature above 930°C to form a layer of Nb3Sn at the Sn-Nb interface. Such a layer of NbsSn is shown in Fig. 1 The thickness of the NbsSn layer formed was controlled by the time and temperature of the heat treatment. The same general procedure was used for preparation of both undoped samples and samples doped with a precipitate. An additional step was included in the preparation of the doped samples which consisted of internal oxidation of zirconium to form ZrOn. The details of the doping process will be reported in a later paper. Sample Testing. The Nb3Sn tape samples were soldered to a copper or brass shunt. Current and voltage leads were then attached to the sample in the usual four-probe resistance measurement configuration. The sample was cooled to 42°K. In some cases it was cooled in the presence of a high magnetic field and in other cases with the field turned off. The results were the same for both cases. The samples were oriented in a configuration with field transverse to current but could be rotated such that the angle between the field vector and the wide side of the tape sample could be changed. Measurements up to 100 kG were done in a superconducting solenoid and measurements above 100 kG in a water-cooled copper magnet at the MIT National Magnet Laboratory. Once the test field was reached, the current in the sample was increased until voltage was detected across the sample. The critical current was taken as the current at which voltage was first detected in excess of background noise. In most cases this was 1 to 2 x 10~6 v for a— in.-wide sample carrying several hundred amperes with a in. separation between voltage leads and with a 10 "-ohm shunt resistance. RESULTS AND DISCUSSION Microstructure. Examination of the microstructure of the undoped Nb3Sn shows rather large-diameter (1 to 2 columnar grains growing outward from the niobium surface toward the tin surface. As the layer is made thicker by longer diffusion times, these grains grow longer. Few new grains are started. Transmission electron microscopy shows little or no second-phase material within the bulk of the Nb3Sn layer. The microstructure of a diffusion-processed NbsSn layer changes quite drastically when the system is doped so as to form a precipitate within the NbsSn layer. Instead of large-diameter columnar grains of NbaSn forming, smaller-diameter (0.5 to 1 ) equiaxed grains of Nb3Sn decorated with the precipitate form. Fig. 2 shows a transmission electron micrograph of a Nb3Sn layer doped with zirconium oxide. This layer has been etched so that one may look between the grains

Jan 1, 1969

By P. Chiotti, J. T. Mason

Thermal, X-ray, metallographic, and resistivity data were obtained to establish the phase diagram for the Yb-Zn system. Six intermetallic compounds and five eutectics have been identified. The compounds position at 695°C. No evidence for the compound YbZn,, was observed. Whether this compound is stabilized or inhibited by small amounts of impurities is uncertain. SEVERAL aspects of the Yb-Zn system have been reported in the literature. Much of this work deals with the crystallographic identification of some of the compounds. The YbZn compound has been reported by Iandelli and palenzonal and the YbZn, structure and thermal data for the composition range between YbZn and Yb3Znll have been reported by Michel et al. A compound of uncertain stoichiometry in the range 60 to 68 wt pct Zn with a cubic structure has been reported by Kuz&apos;ma et aL4 The YbzZn17, YbZn,,, and YbZn13 compounds have been reported by both Kuz&apos;ma et a1 and Iandelli and Palenzona.&apos; YbnZn17 has also been identified by Laube. This investigation was undertaken to establish the phase diagram of this system. Ytterbium in many respects behaves as an alkaline earth rather than a rare earth metal6 and it is of interest to note the resemblance between the Yb-Zn system, the Ca-Zn,&apos; and typical rare earth-zinc systems.g&apos;10 MATERIALS AND EXPERIMENTAL PROCEDURES The materials used in this investigation were Ames Laboratory ytterbium and Bunker-Hill slab zinc, 99.99 pct pure. Analyses of the ytterbium showed 38 ppm Ta, 82 ppm 0, and 15 ppm N with Ca, Cu, C, Mg, Al, Si, Cr, Fe, Ni, Sc, Y, Er, Tm, and Lu all less than 50 ppm. The ytterbium was dehydrogenated by heating in tantalum under vacuum for 8 hr at 900°C. The metal was kept under argon except when being cut with shears and when being weighed. Tantalum was found to be a suitable container for alloys in the composition range between ytterbium and Yb2Zn17. With higher zinc concentrations the tantalum was penetrated by the alloy and failed after several days at temperatures of 600" to 700°C. Approximately 20 g of zinc and ytterbium metal were sealed under argon in *-in.-diam tantalum cruci- bles equipped with thermocouple wells. The crucibles were in turn sealed in stainless-steel jackets. The alloys were equilibrated in an oscillating furnace and given various heat treatments in a soaking furnace. The steel jackets were removed and differential thermal analysis data were obtained under an atmosphere of argon. The thermal analysis apparatus was calibrated against the melting points of pure zinc, aluminum, silver, and copper and found to give thermal arrests within 1°C of the accepted melting temperatures for these elements. The thermal analysis apparatus has been described in an earlier paper.g Alloys were further heat-treated as necessary and subjected to metallographic examination and X-ray diffraction analysis. Most alloys were etched with Nital (0.5 to 10 pct nitric acid in alcohol). EXPERIMENTAL RESULTS The results of the thermal analysis are summarized by the points on the phase diagram, Fig. 1. Six compounds and five eutectics were observed. The eutectic temperature and compositions in weight percent zinc are 491°C and 12 pct, 645°C and 32 pct, 687°C and 54 pct, 742°C and 67 pct, and 750°C and 77 pct. The compounds YbZn, YbZn2, Yb2Zng, Yb2Zn17, and YbZnll melt congruently at 650°, 751°, 75Z°, 754", and 755"C, respectively. The compound Yb3Znll undergoes a peritectic decomposition at 695°C. The transformation and melting temperatures for the ytterbium were observed to be 797" and 817°C. re-

Jan 1, 1969

By R. M. Waterstrat

The phase VPt has been reported to have a crystal structure of the B19 (AuCd) type at low temperatures.&apos;&apos;&apos; A recent investigation3 has indicated that this phase forms by an ordering reaction from the disordered fcc Pt(V) solid solution which is stable at high temperatures. olander4 has shown that there exists a close structural relationship between the orthorhombic B19 structure and a fcc structure possessing the L1 , (CuAu) type of atomic ordering. One may derive the B19 structure by a shear-like displacement of the atoms in the (002) plane of the ordered fcc lattice along the (010) direction through a distance equal to one eighth of the unit cell dimension, see Fig. 1, followed by an orthorhombic distor; tion of the cube axes such that a = 2.693A. h = 4.413A. and c =4.767A (estimated uncertainty 0.005A). Filings of this phase were produced by grinding a VPt alloy having the B19 structure with a diamond dental grinding disc. When these filings were subjected to X-ray diffraction examination, a pattern of a severely cold-worked fcc structure was obtained. higher solution temperature used (1200 C) or to a much lower oxygen pressure than he reported, due to transfer through many bends and tubes in his complicated apparatus. An interesting observation was made when an oxygen addition was attempted in a cylindrical sample of columbium in the cold worked condition rather than in the annealed condition. The interior of the sample re-crystallized during the oxygen addition at 900°C. The periphery, however. (1 mm) did not recrystallize. A similar sample without oxygen recrystallized throughout the entire cross section. It appears that the re-crystallization is hindered by interstitial oxygen. Presumably, the interior recrystallized before appreciable oxygen could diffuse into the core. This work was supported by the United States Atomic Energy Commission. When the filings were annealed in a high vacuum furnace for 15 min at 110O0C, however. they returned to the B19 structure perhaps as a result of reordering. Subsequent less-severe cold-working of these filings by grinding in a hardened steel mortar and pestle at room temperature produced a transformation into a cold-worked L1, structure which was slightly tetragonal. Thus it appears that the degree of deformation may influence the final structure. Considerable line-broadening was observed in X-ray diffraction patterns obtained from the cold-worked filings and therefore no attempt was made to obtain accurate lattice parameters. Vacuum annealing treatments at 1100&apos;C intended

Jan 1, 1970

By H. Biloni, H. R. Bertorello

GruZLESKI and winegard1 have recently reported on the origin and development of the cellular substructure in Sn-Cd eutectic unidirectionally grown with different amounts of constitutional supercooling (CS). This communication deals with the results obtained in a parallel study on the instability of a plane interface in Al-Cu eutectic unidirectionally grown. Similarities as well as differences with the results of these authors1 will be presented. A1-Cu eutectic alloy ingots of 99.999 pct purity were grown unidirectionally under different G/R ratios where G = thermal gradient in the liquid, R = solidification rate. The ingots were cut in slices perpendicular to the solidification axes and the substructure studied on parallel sections following the sense of growth. It was generally found that the last part of the ingot to solidify presented a well developed colony substructure as a result of impurity build up and constitutional supercooling. The results obtained were: 1) When the structure was observed with low niagnification (of the order of 150 to 300 times) the first instabilities were observed at the grain boundaries and node-like structures formed at the junctions of the growth-induced boundaries, as reported by Gruz-leski and Winegard.1 Inside the grains the first signs of instability appear later and correspond to the type shown in Fig. 1; this is a two dimensional cell substructure. &apos; 2) Figs. 2 and 3 correspond to the evolution from a two dimensional substructure to a cellular type. In the A1-Cu eutectic the boundaries of the two dimensional cell are always perpendicular to the laniellaes instead of parallel as in the Sn-Cd eutectic. 1

Jan 1, 1970

By P. O. Metz, E. L. Wiehe, J. S. Foster

BASED on their analyses of growth kinetics, ibbs&apos; and Harris et al.&apos; have recently proposed that the rate of subcritical graphitization of steel is controlled by the rate of diffusion of carbon in ferrite. illert has concluded that this is the rate controlling growth mechanism when the growing graphite particles are relatively large. Harris et al.&apos; also propose that the matrix surrounding a growing graphite particle is plastically deformed to make room for the growing particle. If this plastic deformation does occur, then preferred recrystallization may be observed around the larger particles. If diffusion of carbon in ferrite is rate controlling, then a graphite particle growing in a matrix of, say, tempered martensite or pearlite, should be surrounded by a carbide depleted zone. Thus, the simple metallographic experiments reported here are sufficient to determine whether or not diffusion of carbon in ferrite is the dominant mechanism for the growth of graphite in steel. The present investigation considers graphitization in five alloys. The compositions are given in Table I. Graphitization was carried out at three temperatures: 900°K (627"C), 950°K (677"C), and 990°K (&apos;717°C). Samples were reacted in both the martensitic and the pearlitic initial conditions. In the hypoeutectoid steels, Sets 7 and 8, .and in the hypereutectoid Fe-C binary, Set 6, graphitization was very limited after 1000 hr at temperature. In these samples graphite particles observed were less than 10 p in diam. In the hypereutectoid commercial steels, Sets 1 and 3, large graphite particles (100 p) did not appear until after 250 hr at temperature. The limited number of graphite particles observed and the range of sizes obtained prohibited measurement of growth rates in this investigation. However, in all samples showing graphitization, neithe a carbide depleted zone nor recrystallization was observed. illert&apos;s model predicts that diffusion of carbon in ferrite should become dominant for graphite particles larger than about 300 p in diam. The largest graphite particle observed in this investigation was approximately 450 p in diam. No evidence of carbide depletion was noted. Fig. 1 shows a typical graphite particle. This nodule is from an initially pearlitic sample from Set 3 after

Jan 1, 1970

By Neils Hansen

The microstructure of dispersion-strengthened aluminum aluminum-oxide products containing from 0.2 to 4.7 wt pct of aluminum oxide has been examined by optical and transmission electron microscopy, and the flow stress has been determined at room temperature and at 400C by tensile testing. Products were examined as recrystallized and as high-temperature extruded, and the microstructures consisted of a fine dispersion of oxide particles in a matrix divided by respectively recrystallized grain boundaries and subgrain boundaries. The flow stress (0.2 pct offset) at room temperature of recrystallized dispersion strengthened aluminum aluminum-oxide products is the superposition of dispersion strengthening and grain boundary strengthening. This superposition has been found to be linear. The flow stress (a) can be related to the grain size (t) by the Petch equation: ing content of oxide and k is a constant independent of the oxide content. For extruded products a similar relation has been found by replacing the grain size by the subgrain size. The k-value is of the same order for the two types of structure, which shows that the subgrain boundaries are as effective slip barriers as grain boundaries. Tensile testing at 400C of re-crystallized and extruded products shows that oxide dispersion strengthening is very effective, whereas the strengthening effect of grain boundaries and subgrain boundaries is small. THE microstructure of dispersion-strengthened products consists of hard particles finely distributed in a metal matrix. The strengthening effect of the dispersed phase has been fairly well established,1 and it has been found that the size and volume fractions of the dispersed particles are important structural parameters. However, in many dispersion-strengthened products which have been worked and heat-treated during manufacture the matrix is divided into well-defined grains or sub-grains, which may also have a strengthening effect. A model of the matrix strengthening in dispersed products worked during manufacture has been proposed,2 introducing the energy of the structure as a strengthening factor, especially at low temperatures. A difficulty in this model is, however, to relate this (stored) energy to the structural parameters directly observable as for instance grain size. The strengthening effect of the matrix grain size after recrystallization has been in- vestigated for nickel-thoria (TD-Nickel) products3 and for copper aluminum-oxide products. Conclusive results were, however, not obtained as the grain size of TD-nickel was constant. 5 to II , after recrystallization at temperatures from 700 to 1200°C and as the copper products containing 5 to 1 wt pct of aluminum oxide could not be recrystallized even after severe cold reduction and heat treatment at 1050C. For aluminum aluminum-oxide products containing from 1 to 5 wt pct of aluminum oxide it has been shown that the tensile strength at room temperature decreases when an extruded product is cold-worked and recrystallized. The matrix in the extruded products is divided into well-defined subgrains of micron size, and as the grain size of the recrystallized products is about two orders of magnitude higher, it is obvious that grain boundary strengthening occurs. Preliminary results8 have indicated that the flow stress containing no grain boundaries, A is a constant and t is the subgrain size. At elevated temperatures the effect of boundaries is more complex; it has been shown11 that recrystallized products having an oxide content of about 3 wt pct are more creep resistant than extruded material in the temperature range 400° to 600°C, whereas on application of a higher strain rate the tensile flow stress (0.2 pct offset) is higher in extruded than in recrystallized aluminum—5 wt pct aluminum oxide products at temperatures from room temperature to 427°C (800), Finally it has been shown12 that the Brinell hardness at 350°C of extruded products having about the same content of aluminum oxide increases with decreasing grain size, determined by X-ray line-width measurements. The present study was undertaken to obtain a quantitative relationship between the tensile strength and the grain size of aluminum aluminum-oxide products in the recrystallized as well as in the extruded state. The tensile testing was performed at room temperature and at 400uC. The grain size of the recrystallized products was varied by changing the degree of cold-work preceding the recrystallization heat treatment. In extruded products grain (or subgrain) size variations were obtained by high-temperature heat treatment after extrusion. EXPERIMENTAL a) Materials. Aluminum aluminum-oxide products have been manufactured by consolidation of aluminum powder covered with a layer of aluminum oxide formed during powder manufacturing. The products examined were manufactured from atomized powder containing

Jan 1, 1970

By W. L. Mamme, G. Y. Chin

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain was analyzed by Taylor and by Bishop and Hill in terms of a minimum (internal) and a maximum (external) work criterion, respectively. These two criteria have now been generalized to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (noncrystallographic) pencil glide. The generalized treatment also takes into account the possibility of a Bauschinger effect and of unequal hardening among the shear systems, which were considered in the Bishop and Hill work. Optimization techniques of linear and nonlinear programming are shown to be applicable for the numerical calculation of the minimum or maximum work. In the case of crystallographic shear, the constraint functions are linear and hence the optimal work is obtained as the saddle value of the lagrangian function Wi(y) e minimum and W,(u) + (a) for the maximum, where Wi is the (internal) work, We is the (external) work, Y is the crystallographic shear strain, u is the applied stress, and and are constraints. It is shown that the Lagrangians are functionally the same and the saddle value of one problem is identical to the saddle value of the other, proving that the two analyses are completely equivalent. In the case of pencil glide, although the constraint functions are nonlinear and neither convex nor concave, the equivalence of the optimal values to the saddle value of the Lagrangian (which is again identical for both problems) is still valid. WHEN a crystal deforms plastically by crystallographic shear, five independent shears are generally required to accommodate five independent strain components specifying the deformation. Assuming slip as the only shear mechanism, Taylor1 in 1938 analyzed the deformation in terms of a minimum work criterion. He hypothesized that of all combinations of five slip systems which are capable of accommodating the deformation, the active combination is that one for which the internal work C is a minimum, where 1 TI is the critical resolved shear stress for slip on the 1-th slip system and is the corresponding simple shear. By further assuming equal 72 for all equivalent slip systems and no Bauschinger effect, Taylor re- duced the minimum work problem to one of minimum and applied the analysis to the case of axisym- Metric flow by {111}(110) slip in fcc crystals. However, he did not consider the question of whether the resolved shear stress has in fact attained the critical value for slip on the newly found active systems without exceeding it on the inactive systems. In 1951 Bishop and ill&apos; put forth the maximum work analysis in which slip is again assumed as the only deformation mechanism. In this analysis, the work o1 done in a given strain ij by a stress ujj not violating the yield condition is maximized. In addition, the analysis takes into account the possibility that the critical resolved shear stress for slip may not be equal among the slip systems and that the slip behavior may exhibit the Bauschinger effect. As with Taylor, a single set of slip systems—{111)(110) — was analyzed numerically. It thus appears that the Bishop and Hill treatment is on a more sound physical basis than the Taylor treatment. However, Bishop and Hill showed that where there is equal hardening among all slip systems and when there is no Bauschinger effect, Eq. [11 ] of Ref. 2, as assumed by Taylor, the results of their maximum work analysis are the same as those of Taylor&apos;s minimum work analysis. Hence at least under those conditions there is an implication that the Taylor analysis does lead to a critical resolved shear stress for slip on the predicted active systems without violating the yield condition on the inactive systems. Recently, the Taylor analysis was applied for numerical solutions of the axisymmetric flow problem, for slip on {110}(111), {112}(111). {123)(111) systems as well as a mixture of all three sets of svstems."1 Computational techniques based on the optimization theories of linear and nonlinear programming4 were employed in these solutions. The same techniques were employed in the solutions of an axisymmetric flow problem of deformation by slip on (111) (110) systems and twinning on (111)(112) systems5 which had been considered theoretically from a modified Taylor approach. The utilization of these techniques has led to the realization that the solutions of Taylor&apos;s minimum work problem imply the solutions of Bishop and Hill&apos;s maximum work problem. The two problems turn out to be dual problems in the well known sense of mathematical programming. It is thus the purpose of this paper to first generalize the minimum and maximum work analyses to include crystallographic slip on several sets of slip systems, twinning mixed with slip, and slip by (non-crystallographic) pencil glide, as well as the possibility of a Bauschinger effect and of unequal hardening

Jan 1, 1970

By J. Szekely, V. Stanek

Steady state heat transfer and fluid flow rates are predicted for the counter-current contacting of gas and solid streams. For a .fixed pressure drop across the bed the convective heat transfer rate is affected by the gas flow rate, which in turn is affected by the temperature distribution in the system. Variations in bed voidage and in particle size were found to change the predicted temperature profiles quite markedly, in particular when the thermal capacities of the gas and solid streams were equal. IN Part I we examined the effect of step and pulse changes in the inlet gas temperature on transients in the flow of gases through fixed packed beds. Here we shall discuss heat flow and fluid flow interactions in the counter-current heat exchange between packed solids and a gas stream. Counter-current heat exchange in packed beds has been extensively studied. In his now classical paper, Furnas&apos; assumed constant property values and developed a simple analytical. expression for the temperature profiles in the gas and in the solid stream. A highly sophisticated analysis of counterflow systems, allowing for transients and interparticle conduction was developed by Amundsen. In preparing a very readable review of this topic Elliott&apos; also presented a number of elegant solutions, including the case involving heat generation. A great deal of work has been done on the application of these concepts to the modelling of the blast furnace. However, in all this previous work the mass flow of the gas was regarded as a quantity independent of the gas-solid heat exchange process. In the following we shall consider counter-current heat exchange between a gas stream and a packed bed of solids, under conditions where the pressure drop across the bed is specified, rather than the mass flow of the gas. FORMULATION Consider a packed bed, extending from y&apos; = 0 to y&apos; = L, in which moving solids and a moving gas are contacted in a counterflow arrangement. Let cold solids, with an initial temperature Tsi and mass flow GA, enter at y&apos; = L, and hot gas with an initial temperature of Tgi and mass flow Gg enter at y&apos; = 0. In contrast to the problems considered in Part I this system has a nontrivial steady state and we shall restrict our attention to the study of the pressure drop flow relationships and the resultant temperature distributions for steady state conditions. Under these conditions the formulation of the problem requires the statement of the following: 1) heat balance on the gas 2) heat balance on the solids 3) the mechanical energy balance equation and in addition the knowledge of the equation of state, and a functional relationship between viscosity and temperature and an expression for the heat transfer coefficient in terms of the other parameters. On neglecting temperature gradients within the solids and for a constant mass flow of the gas, the solution to this problem is well known.&apos;" The expressions for the temperature profiles of the gas and solid streams may be put in the following form: where Tg and T, denote the dimensionless gas and solid temperatures respectively, y is a dimensionless distance, and R is the ratio of the thermal masses. These quantities are defined as follows: For the particular case of equal thermal mass capacities by the gas and the solid, that is R = 1, the Eqs. [1]and[2] simplify to Eqs. (71 and[8], respectively: i.e., the resultant profiles are linear. As for most practical cases , solutions given by Eqs. [7] and [8] will contain only the inlet temperatures as parameters. For a fixed, predetermined value of C;b the above

Jan 1, 1970