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By Norikazu Hashimoto

SILICIDE coatings on refractory metals are often applied by transporting a silicon halide vapor to a hot metal surface . The coatings are usually grown by solid-state diffusion reaction. The diffusion is often slower than the vapor transport and hence may become rate-controlling.

Jan 1, 1968

By D. G. Westlake

THE structure observed in thin foils by transmission electron microscopy is not necessarily representative of the initial bulk material. We have shown that hydrogen, originally present in a specimen of vanadium, niobium, or tantalum, can be concentrated by the thinning operation used to prepare foils from the bulk materials.' These foils exhibited domain walls indicative of a tetragonal distortion of the bcc unit cells, probably caused by ordering of the hydrogen in preferred interstitial sites. We believe this ordering does not occur at room temperature in the bulk material which contains less than 1 at. pct H. In a continued effort to prepare metal foils whose hydrogen concentrations remain constant during preparation, we have developed some new chemical and electrothinning techniques for vanadium. Each of the procedures presented in Table I produced foils that were thin enough for transmission electron microscopy. The experiments described below were performed to test the effect of each thinning procedure on hydro-

Jan 1, 1968

By B. B. Rath, Hsun Hu, R. S. Cline

FOLLOWING the techniques used by Beck and co-worker~ "~ the characteristics of selective growth in the recrystallization of a zone-refined aluminum single crystal, rolled 80 pct at -78°C in the (110)[112] orientation, have been studied. The material was 99.999+ pct pure. The as-grown crystal had a resistance ratio, R(298°K) /R(4,2°K), of approximately 5000. The method of preparation of the single crystals and the necessary precautions in handling them during rolling in order to avoid recrystallization in locally distorted regions were described in an earlier paper.3 The rolling texture of this zone-refined aluminum crystal is practically identical with that of less pure aluminum crystals rolle! in the same orientation, i.e., a very sharp (110)[112]. Random nuclei were provided by artificial nuclea-tion by abrading one face of the rolled crystal on 600-grit emery paper in a random fashion. The thin layer of disturbed metal recrystallized at room temperature into fine grains almost immediately. An X-ray diffraction pattern was taken from the abraded surface of the crystal, and the relative intensities of the various reflection peaks were compared with those obtained from a powder specimen. As shown in Fig. 1, the relative intensities of the various peaks from the recrystallized layer varied somewhat from experiment to experiment, depending presumably on the abrading technique. However, the texture of the recrystallized layer produced by this method is nearly as random as that of a powder specimen. Fig. 2 shows the texture determined from the "growth side" (face opposite the abraded surface) of the crystal after it was kept at room temperature for 100 hr. The specimen was only partially recrystallized, as shown by the remaining deformation texture. The new orientations are derived from the recrystallized grains grown through the thickness of the crystal from the "nucleation side" (the abraded surface). Fig. 3 shows the texture after complete recrystallization produced by annealing at 60°C for 1 hr. The arrows indicate 40-deg rotation around the (111) axes of the deformation texture. The microstructure of a completely recrystallized specimen is shown in Fig. 4. As shown in Figs. 2 and 3, the texture of the re-crystallized grains grown from the nucleation side to the growth side is essentially the same as that observed in less pure aluminum' (99.994 pct) and dilute alloyz crystals rolled in the same orientation. How-

Jan 1, 1968

By D. G. Westlake, U. F. Kocks

WHILE single crystals of most materials with cph lattice structure show essentially unlimited ductility, polycrystalline specimens of the same materials exhibit the entire range of ductilities. A difference between the ductility of single crystals and polycrystals may be associated with the special stress concentrations to be expected, for example, at the intersections of slip bands or twin lamellae with grain boundaries. Whether such stress concentrations prove catastrophic depends on the cleavage strength of the material, the size of the stress concentrations, and the speed with which they are formed. Thus, the ductility may vary in degree from material to material. Another possible reason for differences in ductility between single crystals and polycrystals is that a sufficient number of independent deformation modes must be available to insure compatibility between the macroscopic strains in neighboring grains.''2 This criterion is often taken to be a necessary condition for any polycrystal ductility whatsoever, not as one that determines different degrees of ductility; thus, a material with an insufficient number of independent deformation modes would have to be brittle as a polycrystal. The "sufficient number" is five if every grain is to accommodate arbitrary shape changes ("von Mises criterion "). We should like to argue that fewer than five independent modes may be sufficient to satisfy compatibility conditions; and that the internal stresses set up when the plastic strains are not compatible reach the theoretical fracture stress only after a significant amount of macroscopic strain has taken place which may vary in magnitude from case to case, allowing an influence on the degree of ductility. Experimental evidence for these statements is taken from the following review of the number of independent deformation modes observed in the various cph

Jan 1, 1968

By Yoichi Ishida, Ching-Yao Cheng, John E. Dorn

Tile creep behavior of a iron was investigated over the range of temperatures from 375° to 1150°K. Apparent activation energies for creep, obtained by the effect of sudden changes in temperature on the creep rate, revealed the presence of- four distinguishable regions. The creep behavior of a iron in Regions II (480° to 774°K) and 111 (775° to 1045°K) was found to correlate well with a model where the creep rate is controlled by the nonconsevualive motion. of jogged screw dislocations. An anomalous increase in the apparent activation energy fur creep in Region III was found to be in harmony with the known decrease in the free activation energy for self-diffusion over the Curie transformation range. Furthermore, the creep rates in Regions II and III were found to increase with stress due not only to the effect of stress on the activation energy but also to an increase in density of mobile dislocations. The evidence suggests that pipe diffusion along moving dislocations could be a significant factor over the lower temperatures of Region II. ALTHOUGH the creep properties of iron and steel have been of interest to metallurgists for some time and an extensive literature is now available, most of the published information has not produced much toward understanding the fundamental dislocation processes controlling the creep behavior of these materials. Whereas the activation energy for high-temperature creep of metals usually agrees well with that for self-diffusion, Sherby, Orr, and Dorn1 deduced from the data of Tapsell -and c1enshaw2 that the activation energy for creep of Armco iron is about 78,000 cal per mole and more recently Lytton and sherby3 reviewed the data of Jenkins and Mellor4 and found an activation energy for creep of a iron of 80,000 cal per mole. Both values are substantially greater than the activation energy for self-diffusion in a iron. Because of the limited data suitable for purposes of identifying the controlling dislocation mechanisms of creep and the unusually high activation energies for creep quoted above, it was considered desirable to reinvestigate in detail the creep of a iron by more reliable techniques which would provide sufficient data for determination of the creep mechanisms. EXPERIMENTAL TECHNIQUE Creep specimens were prepared from 3/8 by 4 in. iron bar stock of the following composition by weight percent: 0.001 C, 0.0120 0, 0.001 N, 0.004 S, and 0.003 P. The as-received bars were cold-rolled to a thickness of 0.100 in., annealed under argon for 30 min at 1113°K, cold-rolled to a final thickness of 0.063 in., and machined into tensile specimens having gage section 0.250 in. wide and 1.70 in. long. Finally they were recrystallized under argon at 1113°K. Specimens to be crept above 1060°K were recrystallized at 1173°K. Both recrystallization treatments gave the same reproducible equiaxed ASTM No. 4 grain size. Creep testing was conducted in machines fitted with Andrade-Chalmers arms that maintained a constant stress to within ±0.2 pct of the reported values. Deformation over the specimen gage section was sensed with a linear differential transformer and recorded auto-graphically as a function of time. The strains deduced from these measurements were sensitive to ±5 x 10-5. During creep the specimens were contained in an argon-filled chamber which was immersed in a temperature-controlled molten tin bath. Creep temperatures, as measured by thermocouples attached to the specimen, were maintained to within ±10.25°K of the reported values. For activation-energy determinations rapid changes in temperature of about 12°K were obtained within 30 sec by direct resistance heating of the creep specimen, and maintained to ±1°K of the reported values. Observations of structural details of specimens before and after creep tests were made by electrolytic polishing and etching in acqueous ammonium persulfate. EXPERIMENTAL RESULTS A typical example of the determination of apparent activation energies, Q, by the effect of small changes in temperature is illustrated in Fig. 1. Q is defined by

Jan 1, 1967

By Thomas C. Wilder

The concentration and activity of oxygen in liquid copper has been measured by the reversible galvanic cell: at 1100°and 1200°C for the concentration range of oxygen of 3 to 5600 ppm Measurements for approximately thirly alloys at each temperature indicate that the activity of oxygen roughly follows Henry's law, the activity coefficients of oxygen being 0.12 and 0.205 at 1100° and 1200°C, respectively. These results compare javorably with the results of seven other electrochemical and gaseous equilibrium studies on this system, the free energy of the solution reaction 1/2 O2 = O (7 at. pct in Cu, liq) being -18.10 * 0.30 kcal per gfw at 1200°C. Estimates of the standard molar free energy of formation of CupO(S) are also made. Praclicul consideration of this cell as an oxygen sensor for liquid metals is discussed briefly. SOLID mixed-oxide electrolytes which have a defect structure in the anion sublattice have recently become a very popular means by which the chemical potential of oxygen is measured at high temperatures. Since the pioneering work of Kiukkola and Wagner1 such electrolytes have been used in numerous cell studies for determining the thermodynamic properties of metallic oxides and oxy compounds, the partial pressure of oxygen in vacuum systems and other atmospheres, and the properties of oxygen dissolved in metals and alloys. The use of a solid electrolyte in a cell for a fast reliable method of oxygen determination in liquid metals would be a very important tool to the process metallurgist. In copper, for example, the oxygen content of the molten metal in the cathode furnace is a prime factor in determining the "set" or solidification profile of cast wire bars. In this investigation the activity of oxygen in liquid copper was measured by an electrochemical cell employing the electrolyte ZrO2 + 7 1/2 wt pct CaO. The cell used at 1100° and 1200°C was

Jan 1, 1967

By N. L. Svensson

The model developed by Tuylor for the calculation of Polycrystalline yield strength has been applied to the case of an aggregate hawing a preferred orientation. In general this procedure requires the specification of texture by means of weighting factors applied to specific orientations. The problem to which the model has been applied is that of the yield-strength aniso-tropy of cold-rolled aluminum whose rolling texture was described as a combination of (110)[112] and (311) [112] In this case yield-strength anisotropy is defined by the rutio of yield strength measured at an angle 8 to the rolling direction to that measured along the rolling direction. The method of calculation of yield-strength ratio as a function of ? is described and the results show good agreement with experimental values. The orthotropic yield criterion suggested by Hill has been applied to the results and the strain ratio R also calculated as a function of ?. This has been compared with calculations using the method suggested by Elias, Heyer, and Smith which does not exhibit suck good agreement with observation. one deficietlcy of the method presented is that the strain ratios used by are those applying to iso-Irobic materials. The method should therefore be reg-clrded only as a first abbroximation to the prediction of anisotropy. THE problem of calculating the stress-strain characteristics of polycrystalline aggregates from the properties of single crystals has attracted attention for a number of years. The most important contributions to this study have been those due to: Sachs,' Cox and sopwith,2 Taylor,3 Kochendorfer,4 Batdorf and Budiansky,5 Calnan and Clews,6 Bishop and Hill,7,8 Kocks,9 Budiansky, Hashin, and sanders, 10 Kroner,11 Cyzak, Bow, and payne, 12 Budiansky and Wu,13 and Lin.14 While the earlier work has been largely superseded, recent developments tend to support Taylor's solution" within the restriction imposed by his assumptions. The essential features of Taylor's approach were: 1) the material is rigid-plastic; 2) each grain experiences the same strain components as the aggregate as a whole (the problem was that of uniaxial deformation with principal strain components in the ratio 3) all regions of each grain deform uniformly; 4) work hardening occurs equally on all slip systems. While Bishop and Hill7 have generally validated this approach, there has been some criticism offered. Kocks? as pointed out that since multiple slip must occur the single-crystal data must be determined from orientations arranged such that polyslip takes place. Boas and Hargreaves,15 and others, have shown experimentally that the strain distribution within grains is not uniform, the strains in the vicinity of grain boundaries being less than those in the center of the grains. Both of these criticisms can be largely offset by the suitable choice of single-crystal critical shear stress. However, for the problem analyzed below, the critical shear stress is not directly used and, consequently, these criticisms lose their importance. The more recent contributions have attempted to obtain a more complete analysis by considering an elas-toplastic material and considering interactions between grains of differing orientations. Lin14 has considered the early stages of yielding for a polycrystalline aggregate having specific regions of defined slip plane orientations. On the other hand, Budiansky and Wu13 have allowed for these interactions for randomly disposed grain orientations and have calculated the polycrystalline stress-strain curves for crystals exhibiting either elastic-ideally plastic or kinematic hardening characteristics. This work has shown that yielding commences when the macroscopic stress is 2.2 times the critical shear stress for slip in a single crystal (7,). The yield stress-strain curve then rises becoming asymptotic to a value of 3.072 7,. This is close to the value obtained by Bishop and Hill (3.06) in their confirmation of Taylor's method. This, of course, is to be expected since, at large strain values, the elastic strains are negligible and the rigid-plastic model is satisfactory. The results of Budiansky and Wu indicate that the result obtained by Taylor is 7.7 pct high at a plastic strain which is two times the elastic strain at the initiation of yield. By defining the anisotropy in terms of relative values, the ratio of yield strength at orientation ?, to that measured in the rolling direction, the effect of the discrepancy in Taylor's solution is considered to be of lesser consequence. Therefore, it is anticipated that an analysis based on Taylor's solution, which can be quite straightforward, should provide a reasonable estimation of the anisotropy of materials having a preferred orientation texture. OUTLINE OF TAYLOR'S METHOD In fee metals there are four possible slip planes (the octahedral planes) and in each there are three possible slip directions (the edges of the octahedron), that is a total of twelve possible slip systems. von Mises16 has shown that at least five independent slip systems must become operative in each grain of the polycrystalline aggregate in order to preserve continuity of strain. With this geometrical requirement as basis and the assumptions previously listed, Taylor determined the operative slip systems for a number of orientations of the tensile stress axis specified in the unit stereographic triangle. For the ith slip system, the critical shear stress

Jan 1, 1967

By S. H. Gelles

Samples of poly crystalline zinc of 99.999+ pct purity were observed metallographically after having been exposed to hydrostatic pressures of up to 27 kbars. The deforrnation produced by this treatment was analyzed using X-ray and metallogaphic techniques. Basal-plane slip occurred universally in all grains exumined at the lowest pressure used (8 kbars). At pressures of >23 kbars, {1012} twin nucleation and growth were noted as well as slip. Formation of bend planes, complex kink bands, and recrystallization at the gain boundaries were also observed in this pressure range. These observations are discussed in reference to the expected deformation behavior of zinc under high hydrostatic pressure. It has been shown over the past few years1'3 that anisotropic, poly crystalline metals can be made to deform plastically by the application of a hydrostatic pressure. The effect is greater 1) the larger the anisotropy of linear compressibility and 2) the smaller the stress level needed to produce plastic deformation. Zinc having both very anisotropic linear compressibilities and a very low critical resolved shear stress (CRSS) for basal-plane slip has been shown to exhibit large amounts of plastic deformation when subjected to a hydrostatic pressure.2,3 At pressures up to 15 kbars, grain boundary migration and slip on one set of glide planes have been reported.' After exposing samples to 20 kbars pressure, grain boundary migration, single slip, multiple slip, and twinning have been noted.' The identification of the deformation modes operative under these conditions has not been reported. It was the purpose of this research to identify the deformation modes induced in poly crystal line zinc by the action of a hydrostatic stress and to study the strain accommodation at grain boundaries. Hydrostatic pressure could affect the operational modes of deformation by altering the Peierls-Nabarro stress. This may be roughly approximated by the relationship4

Jan 1, 1967

By P. Marier, T. R. Ingraham

When cylindrical powder compacts of nickelous oxide (NiO) are heated in an equilibrated stream of SO3, SO,, and 02, in the temperature range 500°to 800°c, tlickelous suljate (NiSO4) is formed as an adherent layer on the oxide. The reaction is diffusion-controlled, with an activation energy of 13 ± 3 kcal per mole. When cylindrical powder compacts of NiSO4 are heated in a stream of dry nitrogen in the temperature range 1000 0to 11500C, NiO is formed at a well-defined interface between the sulfate and oxide. The interjhce migrates into the sulfate at a constant rate at a constant temperature and gas flow. The reaction rate increases with increasing gas flow and decreases with increasing partial pressure of SO3 in the gas stream. Resolution of the partial-pressure data with a Lang-itzliir Adsorption Isothern suggests that about 80 pct of the NiO interface is covered with SO3. The heat of adsovption is about 68 kcal per mole. The activation energy of the decomposition process is 61 ± 3 kcal per mole. MOST of the work reported on the formation and decomposition of nickel sulfate is related to thermodynamics.1-3 No quantitative work has been reported on the decomposition process. The only kinetic work reported on the formation is that by Fletcher and shelef.4-6 whose main purpose was to study the effects of alkali metal sulfate additions on increasing the rate of nickel sulfate formation. They found that, in the absence of an additive, only small amounts of sulfate were formed and the kinetic data were difficult to interpret. However, they suggested that the sulfa-tion of nickel oxide is a diffusion-controlled process for which the activation energy is approximately 17 kcal per mole.6 In this paper, both the formation and decomposition reactions will be examined; and based on the effects of temperature, flow rate, interfacial area, and partial-pressure of sulfur trioxide, mechanisms and activation energies will be suggested for both processes. EXPERIMENTAL Material. The nickel source material used in all experiments was Baker and Adamson Reagent Grade NiSO4. 6H2O, for which the following analysis was supplied by the manufacturer: C1, 0.001 pct; NO3, 0.005 pct; Co, 0.02 pct; Cu, 0.005 pct; Pb, 0.002 pct; Fe, 0.001 pct: insol, 0.005 pct. The anhydrous sulfate was prepared by heating the hydrate at 420°C in a muffle furnace for 5 hr. Nickel oxide was prepared by decomposing the sulfate at 950°C over a period of 10 hr. Method. The technique used for measuring the rates of formation and decomposition was developed earlier in these laboratories.7-8 The method is based on the observation that the kinetic parameters of a reaction can be established in a flow system, with specimens prepared by compacting powder to a uniform pellet shape. The results are identical with those established with solid polycrystalline specimens or single

Jan 1, 1967

By J. M. Tobin, L. H. Cadoff, L. M. Adelsberg

The reaction between liquid zirconium and graphite at temperatures above 2000 °C has been investigated. The reaction products were found to be carbon-saturated zirconium metal and ZrC which formed between the graphite and the metal. Parabolic growth behavior was observed for the ZrC Phase at all temperatures of this investigation. The parabolic growth constant at temperatures between 2000° and 2860°C was measured to be 1.83 exp 84,300/RT) sq cm per sec. The reaclion mechanism was proposed to be the rapid carbon saturation of the liquid metal and the formation of ZrC at the metal-carbide interface with diffusion of carbon through the ZrC, the "rate - determining step" of the reaction. The concentration-independent diffusion coefficient of carbon in ZrC, (DZrC), was expressed as 0.95 exp? 78,700/RT) sq cm per sec. This value mas calculated using the temperature-invariant ZrC phase fields proposed in the literature. The [ZrQiq)] — [ZYQiq) + ZrC] phase boundary over the temperature range 2000° to 2800°C was determined and the ZrC + C eutectic temperature was found to be 2890° ± 50°C. ThE Group IV and VB transition-metal refractory carbides are of interest because of their high melting points, high temperature strength properties, and relative inertness in certain corrosive environments. The present-day understanding of these materials, however, is limited by the general unavailability of accurate and reliable physical and chemical property data. This is due primarily to the difficulties associated with the preparation of suitable, high-density, high-purity carbide samples, and the achievement and control of uniform high-temperature environments. Accurate measurement of temperature is also an important factor limiting the reliability of reported data. The Zr-C reaction was selected for investigation because of the high melting point (>34000C) and favorable nuclear properties of the reaction product, ZrC. The direct reaction method afforded an opportunity to obtain kinetic data on the fully dense carbide. In this paper, layer-growth techniques were used to estimate the diffusivity of carbon in ZrC and to investigate the phase equilibria in the Zr-C system at temperatures above 2000°C. EXPERIMENTAL PROCEDURES AND DATA Crystal bar zirconium (99.9 pct Zr), purchased from the Nuclear Materials and Engineering Corp., and ZTA graphite (99.9+ pct) were used in this study. The analyses of the materials are listed in Table I. A schematic of the high-temperature carburization apparatus is shown in Fig. 1. The sample was a zirconium metal charge in a 1/2 -in.-ID graphite crucible which was capped with a tightly fitting graphite stern. The crucible and stem were designed to closely approximate black-body conditions. The graphite crucible was packed in lampblack (outgassed 1 hr at 2100°C) which provided insulation and thermal stability to the system. The inert atmosphere was maintained by a constant flow of high-purity argon or helium gas. The nozzle-diffuser section on the top flange was sufficient to prevent back-diffusion of air into the system. Chemical analysis of the carburized samples revealed oxygen and nitrogen concentrations of less than 44 and 20 ppm, respectively. The sample was heated by induction with a Westing-house 5 kw-450 kc power source. Temperature was measured with a Milletron two-color pyrometer which was sighted into the crucible by reflection from an overhead front surface mirror. Optical losses due to glass absorption and light reflection at air-glass interfaces were minimized by the employment of the dynamic-gas seal. It was found that no correction was required for the front surface reflector. The pyrometer was calibrated periodically against a U.S. Bureau of Standards tungsten ribbon secondary standard. Temperatures inside the crucible were also calibrated against the Zr-ZrC eutectic (1850°C)1 and the Nb-Nb2C eutectic (2335°C)2,3 temperatures and agreed to within ±10°C of these values. The temperature was controlled by manually adjusting the power input; variations of

Jan 1, 1967

By Charles L. Mantell, James E. Hoffmann

Mechanical inclusion, electrophoretic deposition, and adsorption were studied as mechanisms for code-position of aluminas present in copper-plating electrolytes as an insoluble disperse phase. Mechanical inclusion was not a significant factor. That codeposi-tzon of aluminas by an electrophoretic mechanism was unlikely was substantiated by measurements of the potential of the aluminas. The alumina content of the deposits was studied as a function of the pH of the bath. These tests in conjunction with sedimentation studies demonstrated the absence of an isoelectric point for the alutninas over the pH range examined. Thiourea in the electrolyte (a substance known to be adsorbed on a copper cathode during electrodeposition) affected the amount of alumina in the electrodeposit. However, no adsorption of thiourea on aluminas in aqueous dispersions was detected. If it were possible to produce a dispersion-hardened alloy of copper and alumina by electrodeposition, an alloy possessing both strength and high conductivity at elevated temperatures might be anticipated. Investigation of the mechanism of codeposition of aluminas with copper was undertaken with the hope that knowledge of the mechanism would aid in the development of such an alloy. The word "codeposit" here does not necessarily imply an electrolytic phenomenon but rather that the materials codepositing, the various aluminas, are transported to and embedded in the electrodeposited copper by some means. Mechanical inclusion in electrodeposition implies a mechanism of codeposition which is wholly mechanical in nature; the only forces acting on a particle are gravity and contact forces. Such a particle is presumed to be electrically inert and incapable of any electrical interaction with electrodes in an electrolytic plating bath. Processes for matrices containing a codeposited phase by electrodeposition from a bath containing a disperse insoluble phase frequently state that code-position is caused by mechanical inclusion.10,2,12 If settling, i.e., gravity, be the controlling mechanism for codeposition of aluminas, then assumptions may be made that 1) the content of alumina in the electrodeposit should be enhanced by increasing the particle size, 2) the geometry of the system, that is, the disposition of the cathode surfaces relative to the di- rection of the falling particles, should affect the alumina content of the electrodeposit, 3) in geometrically identical systems the chemical composition of the electrolyte employed should exercise no effect on the alumina content of the deposit, that is, the alumina content should be the same in all cathode deposits irrespective of bath composition. A bent cathode19 evaluates the clarity of filter effluent in electroplating baths by comparing the roughness of the deposit on the vertical surface with that on the horizontal surface. Two difficulties are inherent in this technique: 1) the current density on the horizontal portion of the cathode would be substantially greater than that on the vertical surface; 2) should the deposit obtained be rough, projections on the vertical face could act as horizontal planes and vitiate the relationship between the vertical and horizontal surfaces. Bath composition should have no substantial effect on the alumina content of the deposit. Two different electrolytic baths were employed. They possessed variant specific conductances and substantially different pH ranges. The experimental tanks were rectangular Pyrex battery jars 6 in. wide by 3 1/4 in. long by 9 3/4 in. deep. The cathodes were stainless steel 316 sheet of 0.030 in. thickness, cut to 7.5 by 1.75 in. and bent at right angles to form an L-shaped cathode whose horizontal surfaces measured 1.75 by 3.0 in. All edges and vertical surfaces were masked with Scotch Elec-troplaters Tape No. 470. The anodes were electrolytic cathode copper 9 in. high by 2.25 in. wide by 0.5 in. thick. To eliminate inordinately high current densities on the projecting edge of the cathode, the anode was masked 1 in. above and below the projected line of intersection of the cathode with the anode. The exposed area of the anode was equal to that of the cathode, providing both with equal average current densities. The agitator in the cell was of Pyrex glass and positioned so its center line was equidistant from cathode and anode, and a plane passed horizontally through the center of the blade would be located equidistant from the bottom of the cathode and the bottom of the deposition tank. The assembled apparatus is depicted in Fig. 1. Hatched areas on anode and cathode represent the area of the electrodes wrapped with electroplaters tape. MATERIALS The chemicals were copper sulfate—CuSO4 • 5H2O— technical powder (Fisher Scientific Co.). Spectro-graphic analysis showed substantial freedom from antimony, arsenic, and iron. Traces of nickel were present.

Jan 1, 1967

By B. W. Roberts, V. A. Phillips

A copper alloy containing- 25.5 at, pct Zn and 19.0 at. pct Ni, which was previously found to show an anoma1old.s hardening effect on quenching- from 600 "C and aging- at 400oc, has now been examined by neutron diffraction. No evidence of long-range order was found. The aged sample showed diffuse scattering- consistent with clustering. The anomalous hardening effect is now attributed to lattice strains caused by clustering rather than (long-range) order hardening. SOLID-solution Cu-Ni-Zn alloys (the commercial 'nickel silvers") have been reported to show anomalies in: change of resistivity on cold working,1-6 temperature coefficient of resistance,2-12 resistivity at low temperatures,13,14 parameter (vs temperature),2"4 calorimetric data,2,4 specific heat,15,16 dilation,2-4 and elastic modulus.17 The structure responsible for the anomalies is produced by annealing typically near 400°C and is rather loosely referred to as the ('K-Zustands" (K state), a term coined by Thomas1' who apparently meant simply that the arrangement of atoms on the sites deviated from that expected statistically. Thomas proposed that the K state occurred in a variety of (solid-solution) alloys such as Cu-Ni-Zn, Ni-Cr, Ni-A1, Ni-Cu, Fe-A1, and Fe-Si and is recognized because its formation is strongly temperature-dependent and results in an increase in electrical resistance which can then be decreased by cold working. Later workers on ('nickel silver" have interpreted the K state variously as short-range order, long-range order. or a combination. The present work was prompted by the discovery by Phillips and Jones19 of a substantial hardening effect when an 18 pct "nickel silver" alloy which is fairly close to the Cu2NiZn composition, was reheated in the range 150" to 450 C after previously quenching from 600°C or, alternatively. was slow-cooled from 600°C or above. The phenomenon was attributed to (long-range) order hardening. Due to the similarity in the atomic scattering factors of copper. nickel, and zinc atoms, the ''nickel silvers" are unfavorable for X-ray diffraction studies aimed at detecting ordering. Nevertheless Bialas et a1.,20 using a powder sample containing 47.96 wt pct Cu, 24.03 wt pct Ni, and 27.98 wt pct Zn, slow-cooled from 400" to 200°C taking 500 hr, observed weak super lattice lines. Further unpublished work" using an anomalous dispersion X-ray technique indicates that zinc atoms are regularly ordered at the corner points of the lattice cell, while the nickel and copper atoms are statistically distributed on the remaining sites. Köster 17 also observed X-ray superlattice lines, for example, in an alloy containing 43.5 wt pct Cu, 28.6 wt pct Ni, and 27.9 wt pct Zn superimposed on the basic fcc cell with a = 3.62 kX. He proposed a Cu3Au-type superlattice with the Ll2 structure in which the A sites were statistically occupied by copper and nickel atoms and the B sites by zinc. He adds that substitution must be possible so that zinc atoms partly occupy A sites. Below about 35 pct Cu, Koster had some evidence for a CuAu-type superlattice with the Llo tetragonal fcc structure with a = 3.82 kX, c/a = 0.88 which could be preserved by quenching. This is suggested17722 to correspond to CuNiZn. While the present work was in progress Hirabaya-shi et a1.23 made an independent comprehensive neutron-diffraction study of a single crystal containing 50.05 at. pct Cu, 26.57 at. pct Ni, 0.25 at. pct Mn, 0.13 at. pct Fe, balance zinc. The presence of manganese and iron is surprising since the crystal was supposedly grown from high-purity metals. The homogenized crystal showed evidence of long-range ordering after an anneal of 5 months at about 300°C. Three possible crystal models were proposed. A curious feature of their results23 is that they could not find any neutron-diffraction evidence of ordering in a powdered polycrystalline near-stoichiometric Cu2NiZn alloy. There appears to be some essential difference between a near-stoichiometric Cu2NiZn alloy and one somewhat further off stoichiometry as used by the present authors. Thus Sato14 was able to reproduce the low-temperature resistivity anomaly reported by one of the authors13 on the present alloy if he used a similar composition, but found the normal behavior of the residual resistivity in a near-stoichiometric alloy. satol2 found that the resistivity of a cold-drawn slightly off-stoichiometric alloy increased to a maximum on isothermally annealing at 300°C and then decreased ("over-aged"). Since he could not explain this on the basis of ordering phenomenon, he proposed that zinc atoms were segregating to stacking faults (Suzuki effect) and found etching bands on the surface by replication which were attributed to the widening of faults. Sato suggested14 that the hardening effect observed by Phillips and Jones19 is partly due to the Suzuki effect. EXPERIMENTAL The starting material was 1/4-in.-diam hard-drawn rod of a commercial 18 pct "nickel silver" alloy identical with that used in a previous study by Phillips

Jan 1, 1967

By Paul A. Farrar, Sanford Adler

The Tz-Zr system was reinvestigated using both metallographic and X-ray diffraction techniques. It mas found that titanium and zirconium are soluble in all proportions in both the a and 0 phases. The minimum in the transformation was found at 50 at. pct and 535°C. THE Ti-Zr system has previously been the subject of several investigations.1-6 A study by Hayes et al.5 using magnesium-reduced titanium and zirconium melted in graphite crucibles indicated that the system was a continuous series of solid solutions in both a and 0 phases with a minimum at approximately 545°C and 65 pct* Zr. These conclusions were substantiated by the work of Duwez4 as well as by the limited data of Craighead et al.,3 Fast,2 and deBoer.1 However, a more recent investigation of the titanium-rich region by Ence and Margolin6 indicated that the solubility of zirconium in a, titanium at 500°C is approximately 22 pct with the a + 0 field extending to approximately 47 pct Zr. Therefore in order to resolve this discrepancy the following investigation was initiated. EXPERIMENTAL PROCEDURES The alloys used in this investigation were prepared as 20- to 30-g buttons by nonconsumable electrode melting in a helium atmosphere. The starting materials were Bureau of Mines titanium BHN 71 and Foot Mineral iodide crystal bar zirconium. The titanium was premelted before the alloys were prepared to avoid excessive weight losses in the final melting. The compositions of the alloys prepared were as follows: Ti-12.0, 22.2, 29.0, 39.6, 50.0, 58.0, 72.4, 83.5. and 90.8 pct Zr. Prior to heat treatment the alloys were cold-worked 10 to 20 pct, stopping at the first signs of cracking. Specimens for heat treatment were wrapped in molybdenum sheet and annealed in argon-filled quartz capsules for the following times and temperatures: 750°C-40 days, 675°C-61 days, 600°C—109 days, 575°C-112 days, 550°C-112 days, 525°C—127 days, and 450°C —153 days. Quenching was accomplished by breaking the capsules in an iced-brine solution. The standard techniques used for polishing the specimens involved belt grinding, grinding on emery paper, polishing electrolytically, and etching with Remington "A" etch7 or "R" etch 8 Debye-Scherrer X-ray powder photograms were obtained for a number of samples using a 114.6-mm camera and CuK, radiation. Exposure times were from 19 to 23 hr. The powder samples were obtained by filing to 270 mesh size. After filing the samples were wrapped in molybdenum foil capsuled in quartz and reannealed at the temperature of original heat treatments; following the heat treatment the samples were quenched into iced brine without breaking the capsules. RESULTS AND CONCLUSIONS On the basis of the microstructural examinations of the heat-treated samples and of the X-ray diffraction data, the Ti-Zr system shown in Fig. 1 was constructed. The data indicate that a, and 0 titanium form a complete series of solid solutions with a, and ß zirconium. The minimum was found to occur at 65 pct (50 at. pct) Zr and 535°C, in excellent agreement with the earlier investigations,1-5 see Fig. 2. Typical microstructures are shown in Figs. 3 to 7. Figs. 3, 4, and 5 show the 22.2, 39.6, and 50.0 pct Zr alloys after heat treatment at 675°C for 61 days with the 22.2 pct Zr showing equiaxed a, and the 39.6 pct Zr alloy a + transformed ß, while the 50 pct Zr alloy shows only transformed B. Figs. 6 and 7 show the 29.0 and 39.6 pct Zr alloys after heat treatment for 109 days at 600°C. The 29 pct Zr alloy has an equiaxed a structure while the 39.6 pct alloy has a partially recrystallized a+ß structure. X-ray diffraction data obtained from the 50 pct Zr alloys after heat treatment at 525° and 450°C as well as from the as-cold-rolled material showed only those lineos which couid be indexed a: a titanium, good agreement with the previously published values. 2,4,5,9 Chemical analysis* of the 50 pct Zr alloy

Jan 1, 1967

By B. H. Kear, S. M. Copley

A dynamic theory of precipitation hardening in alloys containing cohevenl, stvess-.free, ordered particles is developed. The yield stvess is predicted from the stress dependence of the plastic strain vale, which is related to a derived dislocation velocity-stress function. The theory is shown to predict the magnilude and temperature dependence of the yield stress of a commercial nickel-base superalloy as well as many details of its slip structure. GLEITER and Hornbogen have developed a theory of the yield stress in alloys hardened by coherent, stress-free ordered ptrticles based on the observation that dislocations (b = a/2 (110)) glide in pairs.' When a dislocation pair shears through an ordered particle, the glide motion of the leading dislocation is impeded since it must create antiphase boundary (APB), whereas the motion of the trailing dislocation is assisted because it annihilates APB produced by the first one. Taking into account the APB energy, the size, and spacing of the particles, G-H predict the observed yielding behavior in Ni/18.8 Cr/6.2 A1 alloys composed of a matrix phase y '(nickel-solid solution) and particles of y' (basically Ni3A1). The G-H theory, as well as all previous theories of hardening by coherent ordered particles, do not include the details of dislocation motion; the present dynamic theory is an attempt to overcome this limitation. In the dynamic theory, the yield stress is predicted from the stress dependence of the plastic strain rate, which is related to a derived dislocation velocity-stress function. This function can be evaluated if the structure of the alloy, the APB energy of the ordered phase, and the characteristic drag or frictional stresses of the matrix and precipitate phases are known. The theory is shown to account for the observed temperature dependence of the yield stress in a commercial nickel-base superalloy. 1) NICKEL-BASE SUPERALLOYS Although their compositions are complex, the nickel-base superalloys have remarkably simple structures. A detailed examination of the commercial superalloy

Jan 1, 1968

By Ravindra M. Nadkarni, Milton E. Wadsworth

The kinetics of cetnentation of copper with iron were observed to follow first-order kinetics and increase with speed of agitation to a limiting value. Maximum rates agree closely with theoretical values based upon a model of aqueous solution diffusion through a litniting boundary film. Back reaction kinetics are shown both theoretically and experimentally to be independent of ferrous iron concentration in solution. The inlportance of attnospheres of air, oxygen, nitrogen, and hydrogen was studied and the results have been correlated with several impovtant oxidation processes involving metallic iron and copper. The kinetics of the reaction of ferric ion with metallic iron were found to be slow in the absence of metallic copper and essentially proportional to the surface area of metallic copper present in the system. THE precipitation of copper on iron is classic as an example of a relatively ancient art applied successfully for centuries with little fundamental understanding of the important parameters involved. There is some indication that the process has been a commercial means to produce copper since the sixteenth century.' The amount of fundamental work on the cementation of copper with iron is not great. Wartman and Roberson2 carried out a series of detailed copper cementation experiments using natural and synthetic mine water. The following were presented as the three principal reactions: Reaction [I] is the desired cementation reaction and accordingly 0.88 lb of iron would produce 1 lb of copper. In actual practice iron consumption would more normally fall in the range of 1.5 to 2.5 lb per lb of copper. Wartman and Roberson attributed the excess consumption of iron to Reactions [2] and [3]. They found that Reactions [I] and [2] proceeded at approximately the same velocity while Reaction [3] was much slower and would be diminished by controlling the contact time. It was also pointed out that increased agitation is beneficial in removing hydrogen bubbles and barren layers of solution at the iron surface as well as removing contaminants resulting from the hydrolysis of iron. Episkoposyan3 and Episkoposyan and Kakovskii4 studied copper and silver cementation on rotating iron disks in chloride solutions. The kinetics based upon a diffusion model were first order and varied linearly with surface area and with angular velocity raised to the one-half power according to the Levich equation. The experimental activation energy for both copper and silver was approximately 3 kcal per per mole. Excess iron consumption was found to increase with temperature. The rate of cementation first increased with increasing acidity and then diminished at high acid concentrations. sutolov5 has presented an excellent review of the Leach-Precipitation-Flotation (LPF) process including a discussion of copper cementation from an electrochemical point of view although few experimental results were presented. From voltage considerations he predicted that cementation should not be influenced by the concentration of ferrous iron in solution. He considered several secondary reactions including Reactions [2] and [3] and pointed out the importance of oxidation of ferrous iron to ferric with oxygen. In addition it was suggested that Reaction [2] was enhanced by the dissolution of metallic copper by ferric iron which in turn consumed excess iron by the cementation reaction, Eq.[1]. Cementation of copper on metals other than iron has been studied by several investigators but, as in the case of iron, the amount of fundamental work is not extensive. Bashkova and kovalenko6 and Bashkova7 studied the cementation of copper on indium from copper and indium sulfate solutions. The rate was found to be first order and to increase with acidity. This was associated with a decrease in potential (EIn — ECu) and the simultaneous reduction of hydrogen ions at low pH. The rate of cementation also decreased with increasing indium concentrations which was postulated to be due to the decrease in the rate of diffusion of the ions in solution. Below 97°C the experimental activation energy was found to have the unusually low value of 2 kcal per mole and was attributed to diffusional control. Above 97°C the rate increased suddenly and was explained as a change in the rate-controlling step to a chemical reaction. In Part I of this study Nadkarni et a1 .1 have reported on preliminary results obtained in a laboratory study of the kinetics of the cementation process. The rate was found to be first order, proportional to the surface area of the iron, and to increase with speed of stirring until a maximum rate was observed. At low stirring speeds the deposit was spongy and adherent. At medium speeds the copper peeled off in bright strips and at high speeds finely divided copper was produced and continually removed from the surface. The amount of excess iron consumed increased with speed of stirring and with temperature. The average experimental activation energy combining results from several types of iron was 5.8 + 1.6 kcal per mole suggesting diffusional control through a limiting boundary film. Traditionally copper cementation has been carried out over the centuries in gravity-fed launders of various design containing scrap iron. More recently rotating drum precipitators and activated launders8'10 have been used. In the latter, copper-bearing solutions are

Jan 1, 1968

By Henry M. Otte, Ralph P. I. Adler

The changes of line position and integral line breadth in the X-ray diffraction pattern of a polycvys-talline Cu-30Zn tensile test piece, incrementally loaded (and unloaded) up to fracture, have been an-alyzed in detail. The stacking-fault probahility, cv, increased linearly with increasing strain, E, wheveas the effective domain size, De(hkl), decreased with decreasing E-1 Over the greater part of the stress-strain curve the rate of work hardening was essentially constant (about 86 kg per sq mwz), and could be correlated with the slope of stage II of the single-crystal stress-strain curve. Consequently the theories of work hal-dening (particularly those parts relating to stage 11) as developed by Mott and Hivsch and others could be applied to the observations made on the polycrystalline brass. A relationship of the form Aa = Aao - MhklEhkl between the change, Aa, in the extrapolated lattice pararneter and the rvns strain, Ehkl, was derived and found to fit the results acceptably well. From this and other relationships developed in the papev it was estimated that the equilibrium stacking-fault energy of Cu-30Zn was between 8.4 and 12.5 ergs per sq cm, in fuirly close agreement with the (corvected) value obtained by Howie and Swann (1961)43 using transmission electron microscopy. The theory of work hardening in the jorm developed and recently presented by Hirsch (1964)3 successfully described all the pvesent observations. In order to test certain aspects of the theories of work hardening, as developed by Mott,1 Hirsch,2,3 Seeger et el,4-7 and others (for review see Nabarro, Basinski, and Holt8), several recent investigations have been concerned with relating the dislocation density, p, with the shear stress, 7 (and strain, y), applied to the specimen. The results of these investigations have shown that the square root of the dislocation density appears to be linearly related to the applied shear (or flow) stress for fcc as well as bcc metals and alloys. Furthermore, the relationship appeared to apply not only to the deformation of poly-crystalline specimens, but also to stages I and I1 of the deformation of single crystals. An expression of the form has thus come into wide use. Here b is the Burgers vector for a total dislocation, G is the shear modulus, and 70 and q are constants. A review9 of available values of q shows it to have values (at room temperature) in general between 0.3 and 0.6. Forms of Eq. [1] can be deduced from, or predicted by, the current theories, and the various constants adjusted so that they are compatible with the experimentally found value of q . No unique relationship has yet been found between the dislocation density and the applied shear strain. There are several serious objections to the use of Eq. 11]. In the first place, it relates the shear stress to the density of the dislocations without regard to their arrangement, type, or distribution; the significance of the relation may therefore be justly questioned.5 In the second place, the values of the experimental quantities usually substituted into Eq. [11 are those of the applied shear stress and the total dislocation density measured after unloaditzg. The dislocation density value that should in fact be used is that for the mobile dislocations present in the specimen when under the applied load.* Finally, in cases where the values used for p, the dislocation density, are those obtained by electron microscopy, p is subject to considerable error,' both systematic and random. The corrections to be applied are still controversial. Dislocation densities can also be measured by etch-pit and other techniques,'' each having their specific limitations. An objective of the present investigation has been to obtain information about the dislocation configyration and distribution by analyzing the changes in the position and shape of X-ray diffraction profiles as a function of deformation. The X-ray techniques employed, also open to criticism, have certain advantages, however. Thus, although the X-rays diffract only from the surface layers to an effective depth of about 20 p, the measurements can be made while the specimen is under load. The value of the dislocation density obtained by the X-ray method is also subject to errors, which are different from those of the electron microscope. Though a considerably larger volume of material is sampled by the X-rays, thereby reducing some of the statistical errors inherent in the electron microscope data, the information obtained is less detailed and is dependent on the method of analysis used to obtain a value for the dislocation density. Nevertheless, important observations can be made because the aforementioned advantages outweigh some of the limitations. In the present paper the X-ray method is briefly described and applied to a brass specimens deformed in tension. The results are then discussed in terms of some of the current concepts of work hardening. 1) EXPERIMENTAL PROCEDURE Details have already been extensively published elsewhere11-14 and therefore will only be dealt with briefly here. 1.1) Materials and Specimen Preparation. Commer-

Jan 1, 1968

By S. Nakajima, H. Okazaki

Quantitatiue studies of the deformation texture in drawn tungsten wives were made by the X-vay dif-fractottletetr. Experimental results show that the diffraction Intensities are equal to tilose pvedicted from the (1 10). fiber lexlure but the angxla), spreads of. diffraction peaks in the pole distribution curres are different for different diffraction planes and directions. For this reason a modified (110) fiber lextuve model, in which a kind of anisotropy is assumed, is proposed to explain the results. According to this model the poles lying on a line directing front the (110) to the (110) poles in the (1 10) standard stereograpllic projection should show spreads which are different from those lyitlg on a line directing from the (001) to the (001) poles, which is confirmed by the experiments. The anisolvopy and the spveads of the pole positions are large at the outer part of the wires and decrease gradually lowards the inside of the wire. The possibilily of occurrence of such anisolropy in irrelals with fcc stvuctures is discltssed. THE deformation texture of drawn tungsten wires has been assumed by different investigators to be the simple ( 110) fiber texture.' Recently, however, Leber2,3 has shown that a swaged tungsten rod has a cylindrical texture. It changes gradually to the (110) fiber texture by drawing through dies. However, even after drawing to 0.25 mm in diam, the cylindrical texture can still be found in wires together with the (110) fiber texture. This was deduced from the pole figures obtained from the longitudinal section of these wires. Use was made also of quantitative measurements of the pole distribution curves. Leber stated that the angular spread of the pole distribution curves (henceforward called dispersions) are quite different for (400) 45 deg and (400) 90 deg: the former is always larger than the latter. This inequality is accompanied by deviations of the diffraction intensities from the theoretical values for the ( 110) fiber texture. Bhandary and cullity4 have reported similar results on iron wire and explained them by assuming a cylindrical texture. Both Leber3 and Bhandary4 used only the results of the (400) reflection for the determination of the dispersion. The pole figures found by Leber3 and by Rieck5 are largely different. The model given by Leber to explain the effects is in the authors' opinion in some respects unsatisfactory, especially if one looks at other than the (400) reflections. Intensities and dispersions of diffraction peaks are conclusive factors for the determination of the fine structure in wire textures. For this reason we studied them extensively to come to a model which is more suitable to fit the facts. In the following, after giving the experimental set-up, we report about measurements of X-ray diffraction on drawn tungsten wires. Different models to describe the experimental results will be discussed. EXPERIMENTAL GO-SiO2-A12O3 doped tungsten wires drawn to 0.18 mm in diam were used for the measurements. The wires were chemically etched to various diameters down to 0.03 mm. Measurements were carried out for the different wires in order to determine the dependence of the texture on the radius. The wires were cut to pieces of 10 mm length and fixed with paste closely against each other on a flat, polished glass plate. Parallelism of the wires with the surface of the glass plate should be adequate. For the diffraction studies three different X-ray sources were applied, respectively, giving the CuK,, FeK,, and FeKp emission. The measurements were carried out with a diffrac-tometer with a GM counter. The latter was fixed to a certain diffraction angle 20hkl and the diffraction intensity was recorded as a function of the angle of rotation of the specimen around the axis, lying in the specimen surface and perpendicular to the wire axis, as shown in Fig. 1. Measurements were also done with the detector at angles slightly deviating from the diffraction maxima The measured intensities in this case were taken to be equal to the background level. The deviations were chosen as small as possible but large enough to eliminate the influence of the diffraction maxima. The useful range of the rotation angle x of the specimen is generally limited by the wavelength of the X-rays. We have: where and cp is the angle between the wire axis and the normal of the diffraction plane. Intensity measurements were made to find the necessary corrections for counting loss of the GM counter and for distortion resulting from such effects as absorption of X-rays and from inclination of the reflection plane under study with respect to the surface of the specimen. The counting loss was esti-

Jan 1, 1968

By C. Norman Cochran

The pllnse diagvam for the NaF-AlF3 system was used to calcutate an ionic model for the NaF-AlF3 system. Assuming an ideal solution,a series of simultaneous equations expressing equilibria be-tween solid and liquid phases at the euleclic, perilec-tic, and melting points were solved for the activities of the ionic species, the dissociation constants, and the entropies and heats of fusion. The calculations suggest the existence of A13F1415 ions in addition to the F-1+AlF6-3 , and AlF4-4 ions previously proposed by others. The calculaled valnes give better agreement with vapor pressures than the previous model without Al3Fl14-5. Additional possible vefinements of the model are proposed. CRYOSCOPIC1 investigations and density data2 for the NaF-A1F3 system have previously been used to study the dissociation mechanism of Na3A1F6 and to derive equilibrium constants for its dissociation to NaF and NaAlF,. Depending primarily on the heat of fusion assumed for cryolite, the dissociation constants ranged between 0.02 and 0.18 from cryoscopic studies, and from 0.09 at 1273°K to 0.16 at 1363°K from density data. In most cases the values were unable to reproduce satisfactorily the experimental liquidus lines very far on the A1F3 side of the Na3A1Fe composition. This suggested the existence of at least one other ionized compound in the melt besides NaA1F4 in the Na3A1F6-A1F3 side of the system. This is assumed to be liquid Na&13F14 (chiolite), which is already established as a stable solid in phase studies of this system. MODEL FOR THE MELT The melt is assumed to be an ideal solution with ion activities equal to anion fractions. The only cation in the model is sodium so that Temkin and simple anionic activities are identical. Although the compounds are completely ionized to Na' and the respective anion in the melt, molecular rather than ionic notation is used throughout this work. The Na3A1Fe is assumed to dissociate to NaA1F4 and NaF as in the former model, and Na&13F14 to dissociate to Na3A1Fe and NaA1F4. Other valid dissociation equilibria can be written involving these four compounds, but all of these can be obtained by combinations of the two described dissociation reactions and, thus, are automatically considered in these calculations. The model allows for no free AlF3 so that compositions for NAIF3 > 0.5 (mole fraction A1F3 on the NaF-A1F3 basis) cannot be treated. The question of the existence of free AlF3 in the melt will be discussed again later. The constants in the model were evaluated from points along the entire known liquidus line of the NaF-A1F3 system. Previous work employed only the liquidus line or densi- ties near the Na3A1F, composition. The liquidus line compositions used in the solution of the model are from unpublished work by Mr. P. A. Foster, Jr., for compositions between the Na3A1F6 melting point and the Na&13F14-A1F3 eutectic, and from the published works of Grjotheim,1 Phillips,3 and Foster4 for the remainder of the system. The relationships used in solving for the desired dissociation constants and heats and entropies of fusion are listed in Table I, and the points along the liquidus line at which each apply are indicated to the right of the relationships. The mole fractions of each of the separate species in the melt are symbolized by N. Relationships [I] and [2] are the respective dissocia-ation constants, Kl and K2, of Na3AIF6 and Na5A13F14 for this model. For simplicity, these constants will be assumed to be independent of temperature. Relationship [3] follows from the assumption of the ideal solution. The expression relating the values of N to the experimental values of NAIf3, is given in Relationship (41. Relationships [5], [6], and [7] each state the equilibrium between a compound in the melt and its pure solid phase for the portion of the liquidus lines where it precipitates. The heats of melting, AH,, and entropies of melting, AS,, used in [5], [6], and [7] are assumed to be independent of temperature. The compositions and temperatures of all five invariant points (two melting points, two eutectics, and one peritectic) along the liquidus lines from NAIF3 = 0 to NAIF3 = 0.5 were employed in the solution. The eutectic and peritectic compositions were particularly useful because each of these is involved in one more equation than other points along the liquidus lines and thus reduces the number of points required to solve for the constants. Also, their use assures that the inflection points in the derived liquidus line will correspond exactly with those on the experimental liquidus line. The total number of equations is 5k1 — 1, where n is the number of experimental composition points used. The number of unknowns is 4n + 5 (4n- 3 values of N, 3 values each of AH, and AS,, and 2 values of K). Thus, six points must be used in the solution to obtain an equal number of equations and unknowns. The one additional required experimental composition was taken on the liquidus line between the Na3A1Fe melting point and the Na3A1F6-Na5A13F14 peritectic. Previous work indicated this was a difficult portion of the curve to fit. The temperature used for the point was 1161°K, the same as for the NaF-Na3A1Fe eutectic. This choice of temperature gave two points with identical NNa3AIF6 values which simplifies the algebraic solution. The second point at this temperature is denoted 1161°'K. PROCEDURE FOR SOLUTION OF EQUATIONS Values were assumed for NNa,AIF and NNaF at the NaF-Na3A1F6 eutectic at 1161°k. By an iterative procedure, the corresponding values for NNa5A13F14 and NNaAlF4 at 1161°K were determined from 131 and 141. A value was assumed for NNaAlF4 at 1161°'K and

Jan 1, 1968

By Y. H. Liu, G. W. Powell

Thin foils made from the gold-rich region of- short (0.15 mm)Au-Ag diffusion couples annealed at 880°C for 1 hr were examined in ax electron microscope and the structures were compared with that of pure gold subjected to identical heat treatments. The couples underwent Plastic deformation (bending) during the diffusional anneal. The foils prepared from the diffusion zone have a higher dislocation density and incidence of subboundaries than pure gold. The plastic bending of the couple can be interpreted in terms of the climb of edge dislocations, which are pavallel to the bend axis, along the direction of diffusion. THE interaction of lattice defects during interdiffu-sion between two metals has been considered by several investigators. In particular, da Silva and Mehl,1 Barnes,' and Bardeen and Herring3 have proposed models based on interactions between point and line defects to account for the Kirkendall effect (marker movement). Each of these models is based on dislocation climb, which can either add or remove lattice planes, induced by an under- or supersaturation of vacancies. A theoretical treatment of the nucleation and growth of voids by the condensation of vacancies has been presented by Seitz.4 Stresses can arise in a binary diffusion couple as a result of the vacancy flux and the gradient in the lattice parameter. rinkmman' has investigated the effects of diffusion-induced stresses on void formation; the results of his analysis suggest that voids can form and grow under the influence of these stresses in the absence of an excess vacancy concentration. The relationships between vacancy supersaturation and diffusion-induced stresses and void formation have been elucidated also by Balluffi and seigle6 who concluded that the stress generated by a vacancy supersaturation aids the growth of voids. Experimental evidence which indirectly shows that stresses are produced by chemical diffusion has been obtained by several researchers.2,7-9 This evidence consists in part of the observation by light microscopy of the formation of subgrains, a process characteristic of the high-temperature deformation of some metals during creep.'0 More striking, however, is the plastic bending of short (0.2 mm) Cu-Ni couples observed by Barnes2 and of boron-doped silicon crystals reported by Queisser.9 Diffusion-induced dislocations in iron and silicon have been investigated by Ainslie et a1.11and Schwutte and Queisser,12 respectively, the former using transmission electron microscopy and the latter an X-ray transmission technique. Matthews and Crawford13 observed the formation of boundaries by the climb of interfacial misfit dislocations in thin, vapor-deposited Au-Pd couples diffused in situ in an electron microscope. In order to obtain additional information on the phenomena associated with defect interaction and diffusion-induced stresses in binary couples, an electron transmission study of foils prepared from the diffusion zone of short Au-Ag couples was undertaken. The initial objective was to investigate the processes occurring at various points of the diffusion zone. Subsequent research demonstrated that foils could be prepared only from the gold-rich region of the diffusion zone using the technique described herein. EXPERIMENTAL PROCEDURE Preparation and Annealing of the Diffusion Couples. The couples were made from annealed, high-purity (99.999 pct). polycrvstalline gold and silver sheets (0.075 mm thick). Shall (0.075 by 5 by 17 mm) elec-tropolished coupons of gold and silver were pressure-bonded by heating the two metals in a graphite device to 770°C and holding at this temperature for approximately 30 min. The quality of the bond was ascertained by metallographic examination at 150 times. Each couple subsequently was annealed at 880°C for 1hr; under these conditions, the extreme portions of the

Jan 1, 1968

By W. L. Phillips

Stress-train curves were obtained for single crystals of silver, Ag-5 pct Zn, Ag-10 pct Zn, and Ag-20 pct Zn tested in tension and shear at 78°, 195°, and 297°K. At room temperature the critical resolced shear stress gC increased, the length of' the easy-glide region increased, and the rate of' work hardening dwving easy glide decreased with increasixg zinc concentration. The change in the ratio of uc at room temperature to that at lower temperatures was significantly greater for the alloys than for pure silver. It was found that an increment in stress was necessary to continue slip when the slip direction was rotated 60 deg. The magnitude of this increment increased with strain for all alloys, increased with zinc concentration for a given strain, and for a given strain increased with decreasing -temperature. DESPITE its practical importance in improving the mechanical properties, alloying is not fully understood. Except for copper alloys few sets of systematic data are available. Von Goler and Sachs' studied the deformation of Cu-Zn alloys of increasing zinc content and found that, for dilute alloys, the critical resolved shear stress increases linearly with concentration. The range of easy glide was found to increase with increasing zinc content. Schmid and seliger,2 Sachs and Weerts,3 and Osswald4 have shown that with Mg-A1, Au-Ag, and Cu-Ni crystals, respectively, the critical resolved shear stress also varies linearly with concentration. More recently, Linde and his coworkers have investigated the variation of the critical shear stress of copper alloyed with tin , antimony, indium, germanium, silicon, nickel, and gold. They found that the slope of the critical resolved shear stress is related to the change of lattice parameter with composition, and also to the difference in Goldschmidt's atomic diameter between solvent and solute atoms. Garstone, Honey-combe, and creetham6 have shown that similar relationships can be found for small additions of silver, gold, and germanium to pure copper. They found that, with increasing silver or gold concentration, the critical shear stress for glide is increased by alloying, and so is the range of easy glide, which reaches as much as 60 pct for 0.50 pct Ag alloy and 0.62 pct Au alloy, as compared to 6 pct for pure copper of similar initial orientation. They also found that the alloying additions had little effect on the rate of hardening during easy glide, the slope scarcely changing with increasing alloy content. General secondary slip was detected only when the crystals began to harden rapidly. Although the slip appeared to be very fine in the early stages of deformation, coarser slip bands were formed towards the end of the extensive easy-glide range. The present investigation describes the deformation characteristics of single crystals of Ag-Zn containing different concentrations of zinc. Tension and shear testing were used for this study. EXPERIMENTAL PROCEDURE The method of growing the single crystals, sample preparation, and method of testing have been described in detail previously.' EXPERIMENTAL RESULTS A) Tension-Room Temperature. The initial orientations and stress-strain curves of single crystals of silver, Ag-10.0 pct Zn, and Ag-20.0 pct Zn are shown in Fig. 1. It is evident that there is considerable change in the stress-strain characteristics as a function of zinc concentration. The effects of zinc concentration on the critical resolved shear stress for both CU-zn8 and Ag-Zn alloys are summarized in Fig. 2. At all concentrations the resolved shear stress of the Cu-Zn alloys is higher than that of the Ag-Zn alloys. The resolved shear stress increases parabolically as a function of composition for both alloy systems. The length of easy-glide region increased with increasing zinc concentration, Fig. 3b). As the length increased the slope (do/de) decreased slightly, Fig. 3(b). Metallographic investigations demonstrated two significant effects of increasing zinc concentration. First, the amount of clustering increased, compare Figs. 4(a) and (b). The slip lines changed from uniform in pure silver to clustered in the Ag-20 pct Zn and Ag-30 pct Zn alloys. Second, the amount of cross slip decreased as the amount of clustering decreased.

Jan 1, 1968