Search Documents

By R. S. Wagner, W. C. Ellis

A new mechanism of crystal growth involving oapor, liquid, crnd solid phases explains many observations of the effect of implurities in crystal growth from the vapor. The role of the impuuitq is to form a liquid Solution with the crystalline tnalerial to be grown from the vapor. Since the solution is n prefevred site for deposition firorti the uapor, the liquid becorrles supersaturated. Crystal growth occurs by precipitatzon from the supersaturated liquid crt tlie solid-liquid zntevfnce. A crystalline defect, such as a screw dislocation, is not essetztial for VLS (vapor -liquid-solid) growth. The concept of the VLS mechanism is discussed in detail with reference to tire controlled growth of silicon crystals using gold, platinum, palladium, nickel, silver, or copper as an implurity agent. RECENTLY a short communication' described a new concept of crystal growth from the vapor, the VLS mechanism. In this paper we present a detailed description of the process and its application to the growth of silicon crystals and we discuss its relevance to existing concepts of .'whisker" crystal growth. Crystal growth from the vapor is usually explained by a theory proposed by Frank2 and developed in detail by Burton, Cabrera, and Frank.3 In this theory a screw dislocation terminating at the growth surface provides a self-perpetuating step. Accommodation of atoms at the step is energetically favorable, and is possible of much lower supersatu-ration than required for two-dimensional nucleation. Crystals of a unique form resulting from aniso-tropic growth from the vapor are "whisker" or filamentary ones. Such crystals have a lengthwise dimension orders of magnitude larger than those of the cross section. For most filamentary crystals both the fast-growth direction and directions of lateral growth have small Miller indices. The special growth form for a whisker crystal implies that the tip surface of the crystal must be a preferred growth site. sears4 proposed that, according to the Frank theory. a whisker contains a screw dislocation emergent at the growing tip. Such an axial defect provides a preferred growth site and accounts for unidirectional growth. The hypothesis was extended by Price. Vermilyea. and Webb," still implying the presence of a dislocation at the whisker tip. They postulated that impurities arriving at the fast-growing tip face become buried while those arriving on the surface of slow-growing lateral faces accumulate and thereby hinder growth. These considerations led to a whisker morphology. There is increasing evidence that most whisker crystals grown from the vapor are dislocation-free. Webb and his coworkers6 searched for an Eshelby twist7 in zinc? cadmium, iron. copper, silver, and palladium whisker crystals. They found unequivocal evidence for an axial screw dislocation in only one element, palladium. However, not every palladium crystal examined contained a dislocation. Observations with the electron microscope have failed to show dislocations in whisker crystals of zinc, silicon.9 and one morphology of AlN.10 Since many whiskers are completely free of dislocations, an axial dislocation does not appear to be required for whisker growth of many substances. A significant advance in understanding whisker growth has been a recognition of the need for impurities. This requirement has been clearly demonstrated for copper,11 iron,13 and silicon9-1 whiskers. For silicon, detailed studies proved conclusively that certain impurities, for example, nickel or gold, are essential. Another pertinent phenomenon which has received little attention is the presence of a liquid layer or droplets on the surface of some crystals growing from the vapor. Crystals in which this has been observed include p-toluidine,14 MoO3,15 ferrites,16 and silicon carbide.'" The liquid layers or globules were considered to be metastable phases, molecular complexes, or intermediate polymers originating from condensation of the vapor phase. The possibility has been suggested that the halide being reduced is condensed at the tip18 or adsorbed on the surface11 of a growing metal whisker, for example copper. The literature on whiskers discloses illustrations of rounded terminations at the tips. These appear. for example, on crystals of A12O3,19,20 sic,21 and BeO.22 For BeO, Edwards and Happel suggested that during growth of the whisker the rounded termination consisted of molten beryllium enclosed in a solid shell of BeO. A recent paper9 on the growth of silicon whiskers contains many observations pertinent to an understanding of the mechanisnl of whisker growth. These observations are summarized as follows. 1) Silicon whiskers are dislocation-free. 2) Certain impurities are essential for whisker growth. Without such impurities the silicon deposit is in the form of a film or consists of discrete polyhedral crystals.

Jan 1, 1965

By N. P. Pinto

Compacting below the recrystallization temperature was studied. Ideal density was attained at 550° to 600°C using 25 tsi. Compacts have strength and hardness higher than cold worked beryllium. The recrystallization temperature of this highly stressed metal is that of cast, cold worked beryllium and appears independent of pressing temperature. THE process metallurgy of beryllium is beset by many difficulties that hinder the production of sound beryllium shapes of controlled properties. Most of these obstacles are traceable directly to the low density, low ductility, and high affinity for oxygen of the metal. Castings are susceptible to cracking and porosity, and controlled grain size is not easily attained, yet is critical to further working. Any process must carefully avoid oxygen pickup. Conventional metallurgical processes, including melting, casting, forging, rolling, and extruding have been treated previously,'" as have the conventional powder metallurgical methods.' More recently, a method has been advanced for producing powder compacts of high density by hot pressing at 1000" to 1100°C, using pressures of 0.25 to 0.5 tons per sq in. (tsi).3 Here, Seybolt and coworkers attained theoretical density of 1.85 grams per cc using pres-sure-temperature combinations of 500 psi-1100°C, 750 psi-1075"C, and higher. The warm pressing of beryllium is a practical method for producing bars of controlled properties and appears to have certain advantages, particularly when high strength and hardness are required. Other investigators have studied the hot pressing of various pure metals, such as copper,"-" gold," iron,10-11 and aluminum." Their results indicate that ideal densities may be attained by compacting at temperatures less than 50 pct of the absolute melt-

Jan 1, 1955

By N. F. Mott

Jan 1, 1961

By H. Schwartzbart, J. R. Low

Annealed, .Poly crystalline, low carbon steel exhibits a phenomenon known as the "yield point." If such a steel is loaded in tension, the load increases steadily with elastic strain, drops suddenly, fluctuates about some constant load value for a time and then rises with further strain. The load at which the sudden drop occurs is called the "upper yield point"; the load at which deformation proceeds at constant load is known as the "lower yield point"; the amount of elongation at constant load is termed the "yield point elongation." Deformation which occurs during the yield point elongation is heterogeneous in nature, deformed metal existing next to undeformed metal. The drop in load from the upper yield point is concurrent with the formation of a band of deformed metal which usually appears at a stress concentration such as a fillet and at an angle of approximately 45" with the direction of pull. As deformation proceeds during the yield point elongation, the deformed region grows until the entire specimen has been strained an amount equal to the strain in the first band. A phenomenon very often associated with the yield point is that of strain aging. Aging in steels may be of two types: quench aging, or precipitation hardening, and strain-aging. Strain aging differs from precipitation hardening in that if the metal is merely strained instead of given a solution anneal and quenched, it then undergoes changes in properties similar to those observed in quench aging. The yield point effect and strain aging are most markedly exhibited by low carbon steel, but have been observed in other alloys. Numerous explanations for the mechanisms of both phenomena have been advanced, but the evidence for the acceptance of any of the hypotheses is incomplete. One of the explanations of the yield point phenomenon frequently proposed is that there exists a honeycomb of grain boundary material that supports the load above the yield strength of the ferrite and that when this network ruptures, the ferrite flows with no increase in load. This notion was first advanced by Dalbyl in 1913 and has been since put forward in more concrete form by many investigators. The testing of this hypothesis was, in part, the object of the present investigation. Similarly, the mechanism by which strain aging occurs remains to be explained. Presumably, it is a precipitation hardening phenomenon similar to quench aging, the precipitation being initiated by strain. However, it is not known whether the process is a solution and precipitation effect or a change in solubility due to strain. One obvious method of determining whether or not the yield point is a grain boundary phenomenon is to determine if single crystals exhibit a yield point. Low and Gensamer2 have shown that carbon and nitrogen are responsible for the yield point and aging in steel and that these effects can be eliminated by the removal of these elements through wet hydrogen purification. Single crystals that have been grown in wet hydrogen treated material must then be recarburized or re-nitrided in order to evaluate the effect of grain boundaries. In the present investigation, single crystals of iron which had been annealed in wet hydrogen to remove the carbon and nitrogen were cut into two specimens having the same orientation with respect to the tension axis. Of these, one specimen was pulled in tension in the wet hydrogen treated state and the other was carburized or nitrided and tested similarly. All the crystals were examined for a yield-point and strain aging. The grain boundary hypothesis for the explanation of the yield point in steel has been tested only indirectly previously. Arrowsmith,3 Andrew and Lee,4 Edwards and Pfeil,5 Fell,6 Ludwik and Scheu,7 Winlock and Leiter8 and others found a decrease in proportional limit and yield point effect with an in-

Jan 1, 1950

By W. F. Chiao, R. B. Gordon

Tile sharp-yield point found in magnesium crystals in the solulion-treated and aged condition is studied by dislocation internal-friction experiments. The results show that the sharp yield is not file to the sudden release of pinned dislocations hut is movc likely due to the rapid multiplication of an initially small number of dislocations. Recovery or the dislocation internal friction after deformation is also studied. This yecovery results from the re-pinning of dislocations by a solute, presumably nitrogen, which moves with a relatively small activation energy. SHARP-yield points, when they occur, are a striking feature of the stress-strain curve generated during a tensile test. Although commonly associated with steel, sharp yielding has been found in a variety of metallic and nonmetallic crystalline materials. In particular, sharp-yield points have been found in zinc"' and cadmium3 containing nitrogen. With this background, Geiselman and Guy4 investigated the tensile properties of magnesium single crystals containing nitrogen to see if sharp yielding also occurs in this system. They found that sharp yields did indeed occur in solution-treated and aged specimens tested at elevated temperature but were not able to give conclusive proof that the sharp yield was caused by nitrogen, a yield drop being observed even in their purest crystals. Sharp-yield points have also been found in various polycrystalline magnesium alloys.7'8 In the study of the sharp-yield phenomenon it is desired to observe the behavior of dislocations in the earliest stages of the deformation process. Internal-friction experiments are useful for this purpose because dislocation damping is sensitive to the mobility of free-dislocation segments. At low strain amplitudes the damping, A, due to the the forced vibration of dislocation segments of average length L is ? =KAL4 [1] where A is the dislocation density and K, if the applied frequency is well below the resonant frequency of the dislocation segments? is a constant for the sample under observation.5 Dislocation damping, because of the fourth-power dependence on L, is particularly sensitive to the creation of free-dislocation segments during deformation. Since sharp yielding is associated with the sudden release of pinned-dislocation segments, marked changes in the dislocation damping are expected at the yield point.6 The use of the dislocation-damping observations to help elucidate the incompletely understood mechanism of yielding in magnesium is the primary objective of the experiments reported here. PROCEDURE Many investigations have shown that very marked and rapid changes occur in the dislocation damping of of a deformed material as soon as the straining is stopped.5 It was quite essential, then, for the purpose of this investigation, to make the damping measurements during the deformation of the samples. This can only be accomplished through the use of the ultrasonic-pulse method. In this method traveling sound-wave pulses are used and, in contrast to resonating-bar methods, only the sample ends are set in vibration. Thus, the sample can be gripped along its sides in the tensile-test machine without disturbing the damping measurements. In the pulse method, the decrease in the amplitude of a sound pulse is measured as it travels back and forth through the sample. If A is the amplitude after traversing a distance x and A. is the initial amplitude, A=Aoe-ax [2] and a is called the attenuation. It is commonly measured either in units of cm-I or as db per µ sec. The observed attenuation in a metal sample is due to a number of causes. These include scattering by grain boundaries and impurity particles, thermo-elastic damping, diffraction effects, stress-induced ordering of solute atoms, and dislocation damping. The total observed attenuation in a given sample usually cannot be resolved into these various components, but changes in a due solely to changes in dislocation damping can be accurately determined, provided the experiment is arranged so that all other sources of damping are held constant. It is desired to reduce the extraneous sources of attenuation to a minimum and for this reason the experiments are done on single crystals of high purity. Magnesium crystals offer the further advantage that, when properly oriented, only a single set of slip planes is active during deformation. Crystal Preparation. The method of sample preparation is similar to that of Geiselman and Guy.4 The starting material was high-purity, sublimed magnesium rod supplied by the Dow Chemical Co. Melting under Dow 310 flux was used to reduce the nitrogen content of the starting material: the fluxing was done under an argon atmosphere and the

Jan 1, 1965

By A. H. Daane, R. L. Myklebust

The yttrium-manganese system has been investigated by thermal, metallographic, and X-ray diffraction methods. There are three intermetallic compounds present: YMn2 which melts congruently, YMn4, which undergoes syntectic decomposition, and YMn,, which undergoes peritectic decomposition. The compound YMn4 is ferromagnetic at room temperature with a Curie temperature of 214°C. There are eutectics at 25.2, 60.9, and 82.0 wt pct Mn which melt at 878°, 1100°, and 1075°C, respectively. Crys-tallographic data are given for YMn4, and YMn12 . The terminal solid solubilities are low. In a general program of study of yttrium metal in this laboratory some alloy systems of this metal with elements of the first transition period have been examined. This work was originally instigated by experiences in cladding yttrium with jackets of some protective metals such as Inconel for high-temperature service in air.' In some cases a low-melting phase was observed to form between the Inconel and the yttrium resulting in failure of the samples. In characterizing this reaction, a survey was made of the systems of yttrium with chromium, manganese, iron and nickel,, and it was found that a eutectic was formed between these metals and yttrium on the yttrium-rich side of the system. This present study of the Y-Mn system was carried out to examine in more detail the alloying nature of yttrium, and to correlate trends that have been observed in previous related studies. It was observed by Voge13 that in the systems of lanthanum, cerium, and praseodymium with each of the metals in the first transition series, the tendency to form compounds diminished in the order nickel, cobalt, and iron while no compounds were formed with manganese, chromium, or titanium. Beaudry and Daane4 observed a similar behavior in the systems of yttrium with some members of the first transition series except that the tendency for compound formation was greater. Both the Y-Ti5 and Y-Cra systems consist of simple eutectics, while in the Y-Fe,7 Y-CO, and Y-Ni4 systems, there are four, eight, and nine compounds, respectively. In addition to the above trends, the similar atomic radii and electronegativities of yttrium and thorium invite a comparison between their alloying behaviors with a common element such as manganese. In crys- tallographic studies, Florio et al.' have identified three intermediate phases in this system which are ThMn2, Th6Mn23, and ThMn,,. Gschneidner and Waber10 have examined published information on alloy systems of the rare-earth metals and have correlated this information with current alloying theory. From their study, they predicted that the Y-Mn system would contain one intermetallic compound. On the basis of this prediction, the trend in the alloying behavior of yttrium with the elements of the first transition series and the alloying behavior of thorium with manganese, one might expect from one to three intermetallic compounds to form in the Y-Mn system. A consideration of Hume-Rothery's rules of alloying based on size-factor, electronegativity, and valency suggested a small terminal solubility and possible compound formation. The present study was undertaken to confirm these predictions of low terminal solid solubility and compound formation and to establish the general alloying behavior of yttrium with manganese. EXPERIMENTAL Materials. The manganese used in this investigation was obtained from the Foote Mineral Co. as electrolytic plates of 99.9 pct stated purity; the yttrium metal was prepared in this laboratory. Table I gives the analyses of these materials. For the solubility studies at the yttrium-rich end of the alloy system, distilled yttrium, whose major impurity was 200 ppm Ti, was used. Preparation of Alloys. The alloys were formed by comelting the two metals in an are-melting furnace under an atmosphere of argon. The buttons thus formed were inverted and remelted three to five times to promote homogeneity. Due to the high vapor pressure of manganese, it was assumed that the weight lost during are-melting was all manganese. This assumption was based on the very good agreement observed between calculated compositions and chemical analyses of several alloys. The compositions of the dilute alloys used for solid solu-

Jan 1, 1962

By P. D. Hunt, B. Tani, M. G. Chasanov, R. Schablaske

The Zn-Vphase diagram was studied by thermal. metallographic, X-ray, and sampling techniques. Three ternary phase equilibria were observed: Mutual solid solubilities in vanadium and zinc appear to be negligible. The liquidus line is retrograde from 670° to 756°C. 1 HE only information in the literature relating to the Zn-V system was a study of corrosion of vanadium by liquid zinc' and an examination of the effectiveness of zinc coatings in protecting vanadium-base alloys from oxidation at high temperatures.2 Establishment of the Zn-V phase diagram was undertaken as part of a study of transition metal solubilities in liquid metal solvents. Chemical, metallographic, thermal, and X-ray diffraction analyses were used to determine the diagram. MATERIALS AND EXPERIMENTAL PROCEDURES Vanadium (99.86 pct) in the form of powder and small chips was employed. Stick zinc (99.99 pct; major impurities: 10 to 15 ppm Pb and 20 ppm Cu) was used in the liquidus determinations and thermal analyses; zinc powder (98.80 pct) was used to prepare intermediate compositions. The liquidus lines were determined by chemical analysis of filtered samples of the saturated melts. The apparatus and sampling techniques were similar to those described by Martin, et al.3 The entire metal sample was dissolved to preclude analytical errors due to segregation on cooling. Vanadium was determined amperometrically, using iron (11) as the titrant,4 to an estimated accuracy of 1 pct. Standard techniques of thermal analysis were employed to examine alloy specimens contained in alumina crucibles under helium. Heating and cooling rates were about 1°C per min. At least five heating and cooling cycles over the range 420° to 700°C were performed for each of two Zn-15 pct V alloys. A Zn-0.2 pct V alloy was used in the determination of the eutectic temperature. The separation of intermediate phases from zinc-rich alloys was carried out by selective leaching with ammonium nitrate solutions. For further investigation of intermediate phases 1/4 in. diam powder compacts were prepared by pressing at 80,000 psi and were annealed in argon at 415" to 450°C for 10 days. Larger quantities of intermediate phases were prepared in sealed tantalum capsules heated in a rocking furnace. Temperatures were determined to an estimated accuracy of 0.5°C with a Pt/Pt-10 pct Rh thermo-

Jan 1, 1963

By J. Alfred Berger, O. M. Katz

The Zv-Hf-H ternary system was studied between 500° and 900°C at pressures less than 1 atm of hydrogen gas between 1 and 60 at. pct H. A new and unique microgravimentric apparatus was used. Cizanges of slope on pressure-hydrogen composition isothernis delineated phase boundaries. These boundaries separatecl the three regions, a, 0, and y—so designated to correspond to the regions of the Zr-H binary system—from the multiphased areas between them. A eutectoidal decomposition was found with the ß region phase or phases decornposing into a lamellar product on quenching to rool ter,zperatuve. Reproducible decomposition-pressure hysteresis occilrved lnainly at lower hydrogen cornpositions and at lower temperatures across multiplzase vegions between a and 0 and a and y. Tire effects of hqfniur7z on the hydriding charactevistics of zirconiurrz weYe as follows: 1) stabilization of the a and y vegions while destabilizing the 0 region; 2) a/?preciable elevation of the decomposition pressrkres in the multiphase region between the a and /3 field; 3) ~nouenzent of the eutectoid reaction to high te~nperatures; 4) reduction in the total qiiantity of hydrogen absorbed under one atmospheve of Hz p7-essure; and 5) introduction of a split deconzposilion at the eiitectoiclal poinl in pa?? of the ternavy. Assuru~ptions based on an ir-2terstitial vandonl-solulion rtioclel 0.f hydrogen in metals slzowed that the bindit~g energy between solute sites prednnzinatecl at low /i?!dvogen concentrations. However, at high hydrogen contents the entropy was the predorninatlt factor in determining the stability of the Zr-Hf-H al1o.s. This was interpreted to mean a scarcity of filrtlzer itltevslilinl solute sites caused by hydrogen-hydvogen intet-actions in the metal lattice. INTEREST in the reaction of hydrogen with metals has increased in the past few years for the following reasons: 1) the formation or use of high hydrogen potential environments in nuclear reactors; 2) the reaction of hydrogen with alloys in nuclear reactors with the accompanying deleterious effects on the mechanical and corrosion properties; 3) the theoretical implications of thermodynamic data on the theory and rules of alloy formation in the metal-hydrogen systems; 4) the use of hydrogen-containing fuels in rocket engines; 5) the need for a process of making fine metal powders of high-melting reactive metals; and 6) the beneficial impregnation of superconducting alloys with hydrogen. In nuclear pressurized-water reactors, the problem exists of limiting the hydrogen pickup of zirconium alloys which are utilized as fuel cladding, heat shields, and support members. In general, zirconium alloys have good mechanical and corrosion-resistant properties in high-temperature water. However, hydrogen is absorbed from the corrosion reaction between metal and water, greatly accelerating the formation of the corrosion product ZrOz as well as mechanically embrittling the underlying metal. In addition, recent observations1 at zirconium to hafnium welds showed that secondary elements in zirconium can have an appreciable, and somewhat unexpected, effect on hydrogen absorption. This paper lists the thermochemical data in the range 500" to 900°C for the equilibrium reaction of four high-purity Zr-Hf alloys with hydrogen. Phase boundaries and thermodynamic functions are determined while the structural data will be presented in a future paper. In general, the Zr-Hf-H system approximates the well-known, eutectoidal, Zr-H diagram2,3 with modifications introduced through the behavior of hafnium.4,5 The Hf-H system,' published while this work was in progress, provided a consistent trend with the Zr-Hf-H data. PREPARATION OF Zr-Hf ALLOYS Table I presents a complete flow chart of the preparation procedure. The zirconium and hafnium crystal bars were completely immersed in high-purity kerosene and slowly cut into thin wafers. Wafers were then cold-sheared into approximately 1-g pieces, thoroughly cleaned, weighed, and inserted into the furnace. The alloys, B-2, B-4, B-6, and B-8, were then nonconsumable arc-melted under 500 mm of purified argon. Additional purification of the argon was accomplished by melting a large titanium button each time an alloy was re-melted or a different alloy melted. Each alloy button, which weighed 25 g, was remelted four times in an approach to complete homogeneity. Material losses were less than 0.02 wt pct. Alloy buttons were alternately cold-rolled and vacuum-annealed into 10- and 20-mil sheets. Table I1 gives the composition of the four alloys used. Very little elemental segregation existed be-

Jan 1, 1965

By J. Alfred Berger, O. M. Katz

Selected samples of hydrided Zr-Hf alloys were rapidly quenched to voom temperature and exrtrnined metallographically, by X-ray diffraction, and through micro hardness studies to confirm high-temperutuve data Confirming experiments sllowed that there were five phases in this Lernary system: 1) hextrgonal with lattice parameters similar to that of the initia1 Zr-Hf alloy but slightly enlarged due to dissolved hydrogen; 2) fee with properties of a brittle, intermediate, hydride compound; 3) fct with c/a crvoltnd 1.07 and which appeared as a neetilelike precipitale; 4) hexagonal, designated ?, with c/a ratio of 2.37; and 5) orthorhombic, designated X, with a = 4.67, b = 4.49, and c = 5.093 and whose tnicro-st?ruct~ival nppetrl-nnce depcncled o/i, heat lvecrt~r~ent. The tetragonrrl phase never crppeal-erl witkorct the cubic hydricle. Abpecrrtrnce of 0 and A also tlependet on the hafnium content of the zirconium. A previous paper' on the Zr-Hf-H system described the thermochemical data obtained with a high-vacuum, high-sensitivity mirrogravimetric apparatus. This data presented a fairly complete picture of the phase relationships at elevated temperatures. However, it could not establish the actual crystal structures, lattice parameters, or metallographic disposition of the hydride phases. The present complementary study utilizes X-ray powder patterns along with light and electron microscopy to characterize completely the five hydrided phases found in Zr-Hf-H alloys quenched to room temperature. Crystallographic features of the zr-Hf,2,4 zr-H,5-7 and Hf-H8 systems have been summarized in Table I. Designations of a, ß, and ? were retained in the Zr-Hf-H system for the phase regions through which the pressure-composition isotherms always sloped. However, it was not firmly agreed that these were single-phase regions.' In fact, the region designated y always contained a cubic as well as a tetragonal phase after quenching to -196°C. MATERIALS Preparation of the high-purity Zr-Hf alloys has been described.' The four zirconium alloys which were hydrided contained 37 wt pct Hf (23 at. pct), 51 wt pct Hf (37 at. pct), 73 wt pct Hf (58 at. pct), and 91 wt pct Hf (82 at. pct), respectively. These were designated B-2, B-4, B-6, and B-8. Photomicrographs of the initial alloys showed the material to be quite clean as would be expected from the precautions exercised in producing them. However, there were a number of annealing twins but no other subgrain structure. In addition to the four original alloys, fifteen hydrided samples were observed at room temperature. Hydrogen compositions are given at the top of Tables I1 to V. APPARATUS The phases present at elevated temperatures were studied by quenching hydrided samples to room temperature by two different methods, both under vacuum: 1) fast cooling of the sample tubes of the microgravimetric apparatus1'9 with flowing air and 2) rapid quenching into liquid nitrogen. The cooling rate for 1) was 750° to 250°C in 30 sec. Since the microbalance chamber was not designed to permit very rapid cooling of a hydride sample, all liquid-nitrogen quenching was done in an auxiliary experiment. The auxiliary quenching apparatus consisted of a small-bore, high-temperature furnace, a sealed SiO2 tube containing the sample, and a dewar quenching flask filled with liquid nitrogen. The hydrided sample, previously quenched in the microgravimetric reaction chamber, was placed in a platinum boat in a vacuum-degassed SiO2 tube. A zirconium wire getter and degassed SiO2 rod, to reduce the internal volume, were also in the tube. After sealing the tube under vacuum the zirconium getter was heated to absorb the last traces of gas. Only the sample was heated at the reaction temperature for the desired length of time, and then the tube dropped through the opposite end of the furnace into the dewar. A quenching rate of 200" to 400° C per sec was estimated. Analyses of samples after the auxiliary experiment also showed practically no increase in oxygen or nitrogen content from heating in the SiO2 tube. All of the samples were examined at room temperature by the X-ray powder method. The majority of the powder patterns were obtained with double nickel-filtered CuKa radiation after 8- and 16-hr exposures in an 11.48-cm-diam camera. Cobalt and chromium radiation were also used to spread out the high d value end of the Pattern. Such patterns readily identified the minor phases. NO oxide or nitride lines were found. Where sharp back-reflection lines existed it was possible to reduce the

Jan 1, 1965

By C. Hays, R. E. Swift, E. G. Kendall

Investigations of the Zr-Pt system, by metallography, incipient melting, and X-ray diffraction, determined the phase relationshifis from 0 to 50 at. pct Pt. Phase fields in the Pt-~ich region were outlined, and three intermetallics (ZrPt, Zr2Pt, and ZrPtd were located. A eutectic between Zr and Zr2Pt, and a eutectoid veaction between Zr and a Zr + Zr2Pt, were established. The maximum solubility of Pt in P Zr was approximately 13.5 wt pct, as opposed to less than 1 wt pct solubility in a Zr. EARLIER work on the Zr-Pt system was limited to an X-ray study on the intermetallic compound, ZrPt3, by H. J. Wallbaum,1 It was reported that ZrPt3 existed at 86.52 wt pct Pt, and had a hexagonal structure, isomorphous with TiNi3. Wallbaum's data revealed the following structural particulars: a = 5.633A, c = 9.21A, and c/a = 1.635A. Other studies allied to Zr-Pt alloys concerned only 1) Pt-rich alloys (0.05 to 5.0 pct Zr) for corrosion resistance,2 2) a Zr-base alloy with 5 pct Pt and 0.124 pct C for oxidation resistance,3 and 3) electroclad-ding of Zr with Pt for in-pile corrosion resistance of Zr to uranyl sulphate. 4 Metallographic, incipient melting, and X-ray diffraction techniques were applied to accurately resolve the phase relationships in the 0 to 50 at. pct (68.2 wt pct) Pt region, and to outline the phase fields in the Pt-rich area. Three intermediate phases: Zr2Pt, ZrPt, and ZrPt3, were also established by the same methods. PROCEDURE Melting stock for this program was of the highest purity obtainable. The Zr was iodide crystal bar with a low hafnium content of about 0.05 wt pct (Westinghouse "Grade 3"). The as-received Zr was treated to remove the surface film of corrosion product that resulted from a standard autoclave grade designation test. Next, the bars were processed to yield material suitable for arc melting and free of contaminants. Sheet platinum metal (Baker and Co. "Grade 2") was used for alloying additions. This material con-

Jan 1, 1962

By J. W. Downey, M. V. Nevitt

The phase boundaries for the 950" isothermal sections in the ternary systems Zr-Co-0 and `Zr-Ni-0 have been determined for the composition range from 50 to 100 at. pct Zr. The two systems show very similar phase relations, having no extensive solid solution phase fields. Each contains a ternary phase. These phases are apparently isostructural, but their structure has not been determined. Some aspects of the phase relations are discussed in terms of the alloying behavior of transition metals. THE work described in this paper is the outgrowth of a recent study of the occurrence of phases having the Ti2Ni-type structure (structure-type E9,) in certain ternary systems involving Ti, Zr, or Hf with another transition metal and O.", In the Zr-CO-0 and Zr-Ni-0 systems no Ti2Ni-type phases were found to occur. However, there are several interesting aspects of the phase relations in the two systems which have significance from the point of view of the alloying behavior of transition metals. The results of this investigation may also have some importance in studies of the oxidation of Zr-Co and Zr-Ni alloys. In both the Zr-Co-0 and Zr-Ni-0 systems only the 950" isothermal sections were investigated and, as a further restriction, the study was limited to the composition range from 50 to 100 at. pct Zr. A tentative Zr-Co binary diagram has been published by Larsen, Williams, and Pehin. In the composition range pertinent to the present work they report a eutectic at 980°C and 75.9 at. pct Zr, the products of which are the terminal solid solution based on /3 Zr and the compound Zr2Co, and a eutectic at 1080" and 64.8 at. pct Zr whose products are Zr,Co and ZrCo. The solid solution based on /3 Zr is shown to decompose eutectoidally at 826°C into a Zr and Zr2Co. The limits of solubility of Co in a and /3 Zr have not been established. The structure of Zr2Co is not identified in the publication just cited. Dwight has reported that ZrCo has the CsC1-type strcture. The Zr-rich portion of the Zr-Ni diagram has been determined by Hayes, Roberson, and Paasche." The phase relations are very similar to those of the ZrCo system. A eutectic reaction whose products are /3 Zr containing 2.9 at. pct Ni and Zr,Ni occurs at 961°c, and a eutectic between Zr,Ni and ZrNi is found at 985". The solid solution based on /3 Zr decomposes eutectoidally at 808°C. The solubility of Ni in a Zr is not known accurately but is believed to be very small. Smith, Kirkpatrick, Bailey, and Williams7 have found that Zr2Ni has a tetragonal structure of the A1,Cu-type and that ZrNi is orthorhombic. Domagala and McPherson8 have published a constitution diagram for the system Zr-ZrO,. At 950" their diagram indicates that the solid solution of 0 in 0 Zr is stable from 0 to 0.5 at. pct while the phase field of 0 in a Zr extends from 6 to 29 at. pct. These solubility limits were adopted in the present study and no binary Zr-0 alloys were made. No previous data on the phase diagrams of the ternary systems are known to exist. EXPERIMENTAL PROCEDURE The experimental details involved in the preparation of alloys in this laboratory by arc melting have been described in several previous papers"3 and they will not be repeated here. Information concerning the purity of the metals used is given in Table I. Oxygen was added in the form of reagent grade ZrO,. All of the cast specimens in both alloy systems were annealed in air-atmosphere tube furnaces at 950 3' for 72 hr and water quenched. The specimens were protected from oxidation by wrapping them in Mo foil and sealing them in quartz tubes that had been evacuated at room temperature to a pressure of 1 x 10B mm of Hg. The phase boundaries were determined by metallography, and identification of the phases was accomplished primarily by X-ray diffraction methods which employed a powder camera having a diameter of 114.6 mm. The diffraction techniques which are in use in this laboratory have been previously described.' An etchant that proved satisfactory for most of the alloys consisted of 5 pct by vol of AgNO

Jan 1, 1962

By C. Wagner

When an alloy solidifies and the composition of the solid differs from the composition of the liquid, atoms of the alloying elements rejected at the solid-liquid interface have to diffuse toward the bulk liquid. Diffusion may be supported by convection. Theoretical calculations have been made for a liquid without convection, for a liquid involving natural convection, and for solidification of a liquid alloy at the surface of a rotating disk as an example of forced convection. WHEN an alloy solidifies, the equilibrium composition of the originating solid phase differs in general from the composition of the liquid phase. Thus, segregation may take place, i.e., the composition of the solid phase formed at different times differs from the bulk composition. The degree of segregation depends on several factors such as the partition ratio of the alloying elements between the liquid and the solid phase, the rate of solidification, and convection. To clarify, a theoretical analysis has been worked out. The following presuppositions are made: 1—Calculations are confined to the solidification of binary alloys in which the concentration of component A (solvent) is much greater than that of component B (solute). 2—The equilibrium concentration of the alloying element B is assumed to be lower in the solid phase than in the coexisting liquid phase. 3—At the solid-liquid interface, partition equilibrium is assumed. 4—The dependence of the partition ratio of the solute between the liquid and the solid phase on concentration and temperature is disregarded since only small concentrations of the solute are considered. 5—The concentration of the alloying element B in the solid phase is supposed to be lower than the saturation concentration for the formation of a second solid phase. 6—diffusion in the solid phase is disregarded, since diffusion rates in the solid state are comparatively low. When the partition ratio of the solute between the liquid and the solid phase is greater than unity, a part of the solute is rejected at the solid-liquid inter- face and has to diffuse toward the bulk liquid. Thus there is necessarily a concentration difference in the liquid between the solid-liquid interface and the bulk liquid as has been pointed out by Hayes and Chipman,' Rutter and Chalmers,' Tiller, Jackson, Rutter, and Chalmers, and others (see Fig. 1). In view of the concentration gradient in the liquid phase, the ratio of the concentration of the solute in the solid phase to that in the bulk liquid differs from the equilibrium ratio, although at the solid-liquid interface, partition equilibrium is assumed. Under certain limiting conditions, the solid may even have virtually the composition of the bulk liquid as is shown below. General Equations Let u be the linear crystallization velocity in cm per sec, D the diffusion coefficient of component B in the liquid phase in cm2 sec-', c',, and c", the concentrations of component B in the liquid and the solid phase, respectively, in mol per cm", and s the distance from the solid-liquid interface toward the bulk liquid at a given time t. The partition ratio is assumed to be equal to a partition constant K. Thus. The difference in the specific volume between the liquid and the solid phase may be disregarded. In view of the discontinuity of the concentration of the solute at the interface according to Eq. 1, u(c', — c",), , , = tic', (S = 0)(1 — K) gram-atoms B per unit area per unit time are rejected at the interface and have to diffuse toward the bulk liquid. From Fick's first law it follows that uc',,(s = 0) (1 ~K) == - D(dc',,/?>s). _-„. [2] The concentration profile in the liquid near the interface depends on the interplay of diffusion and convection as is discussed in the following sections. A schematic concentration profile is shown in Fig. 1. The "effective thickness of the diffusion boundary

Jan 1, 1955

By D. R. de Fontaine

By computing the values of the resolved shear stress for a great many orientations of the tensile axis on all 12 (111) <110> slip systems, Taylor and Elam&apos; were able to map out a stereogram of slip systems, given here, Fig. 1, in Diehl&apos;s notation (see, for example Hauser and Jackson&apos;). The purpose of the present note is to derive such a stereogram by mathematical reasoning and to give a simple method of defining the system with highest resolved shear stress for any direction of the tensile axis, thereby eliminating tedious computation of the Schmid factor. Let the tensile axis, of direction cosines [xyz], make the angles 0 and relative to the slip plane normal [HKL] and the slip direction [hkl] respectively. Fig. 2 shows a simple cubic cell whose edges define a Cartesian coordinate system. Let A be a unit vector of origin 0 supported by the tensile axis. Its end point [xyz] then lies on a sphere of unit radius, on the positive hemisphere of which the planes z = 0, x = y, y = z limit the so called primitive triangle of a standard [loo] stereographic projection. For any point of this triangle, the following hold: 0«2 «y *sx « 1 [l] Now, for given [xpz], the most highly stressed system will be the one for which the following expression of the Schmid factor has the largest possible value: (HKL) belonging to the form (111) and [hkl] to the form <110>, the denominator on the right hand side of Eq. [2] is equal to 1.fi.a. The unknowns H, ... h, . . . can now be determined by correctly distributing +1 and -1 to H, K, L, and +1, -1,O to h,k, 1 giving the numerator of Eq. [2] its greatest positive value (the angles 0 and cpare chosen acute) subject to the condition: Hh+Kk+Ll = 0 [3] since the slip direction must lie in the slip plane. Condition [3] can be satisfied only by having one of its terms vanish and the other two equal to +1 and -1. Taking the case of the tensile axis lying in the primitive triangle, x2y, z and therefore Hh will be chosen equal to +1 with H = h = +1 in order to retain a maximum of + signs. There remain two alternatives: either 1 = 0 or k = 0. 1) take 2 = 0 Then Kk = -1 and the numerator of [2] becomes: Retaining a maximum of + signs gives L = k = +1 and becomes: 2) take k = 0 Then L1 = -1and, likewise, the numerator of [2] becomes: xz - z2 + xy + yz [5] But the difference [5] - [4] can be written: (y - z)(x+y +z) [6] positive or zero by virtue of [I]. If [6] is positive (y > z), then the largest possible value for the numerator of [2] for any xyz inside the primitive triangle is given by [5], i.e., for: That is to say, the active slip system corresponding to an orientat:~on of the tensile axis inside the primitive triangle is:

Jan 1, 1962

By P. A. Flinn

ALTHOUGH many physical properties of superlat-tices have been studied intensively, relatively little attention has been paid to their mechanical properties until recently. Even for the well-known transformation in 0 brass, the effect of the transformation on plastic behavior has only lately been extensively investigated.&apos;&apos;&apos; A partial analysis of dislocation structure in superlattices has been given by cottrel13 and his theory agrees well with the experimental results on CU3AU.4,5 His analysis, however, is implicitly limited to low-temperature effects, since it does not include the behavior of dislocations at temperatures high enough for diffusion, and hence climb, to occur. The work of Herman and Brown2 on the creep of 0 brass indicates that important effects occur under such conditions, and consequently, the theory should be extended to include them. Such high-temperature effects cannot be observed in Cu3Au, since it disorders below the temperature at which diffusion occurs at a reasonable rate. There are materials of the same structure, however, such as Ni3A1, which retain their order up to, or close to, the melting point. GEOMETRY OF THE COMMON SUPERLATTICES The two best-known ordered structures are the 0 brass type, B2, shown in Fig. 1, and the Cu3Au type, Ll2, shown in Fig. 2. In the B2 structure the (000) and (1/2, 1/2, 1/2) sites are different in that they are occupied by different types of atoms. The symmetry of the structure is then lowered from a body-centered cubic, A2, in which the sites are equivalent, with atoms located randomly in the sites, to simple cubic. This lowering of symmetry has the consequence that two types of regions may occur within a crystal: regions where A atoms are in the (0, 0, 0) sites, and regions where they are in (1/2, 1/2, 1/2) sites. The boundary between two such regions will contain bonds between like atoms, and be a surface of higher energy. These regions are known as antiphase domains and the boundary as antiphase boundary. In the B2 structure, boundary formed during the ordering process should disappear as a result of domain growth, since any domain growing to the boundary of two others will join one and engulf the other.&apos; In any well annealed crystal, only a single domain should exist, with antiphase boundary present only in connection with dislocations, as discussed below. The L1, structure is related to the A1 (face-centered cubic) in much the same way as the B2 is to the A2. The face-center sites are occupied by A atoms, and the corner sites by B atoms. The symmetry is again lowered to simple cubic, and antiphase domains can exist. In this case, however, there are four initially equivalent sites in the unit cell: (0,0,0), (0, 1/2, 1/2), (1/2,0, 1/2) and (1/2, 1/2, 0). In the ordered structure any one may be occupied by a B atom and the other three by A atoms. Thus four types of antiphase domains can occur in this structure. This is sufficient to permit a metastable "foam structure" to exist within a crystal.&apos;&apos;7 Antiphase boundaries along three different planes are shown in Figs. 3, 4, and 5.* *The presence of a layer of disordered material between antiphase domains, as suggested by Jones and Sykes8 does not seem likely. Such a layer would be a region of unnecessarily high energy which could readily be reduced by the formation of the type of boundary discussed here.__________________________________________________________ The notation (111) [110] means a boundary lying along a (111) plane between antiphase regions related by a 1/2 [I10] translation. It may be seen in Figs. 3 and 4 that an antiphase boundary usually results in incorrect nearest neighbors (shown connected by braces). However, as pointed out by Wilson, a boundary of the (001) [I101 type can exist

Jan 1, 1961

By David Turnbull

IN isothermal recrystallization processes, new crystals generally grow into the matrix until they impinge upon other new crystals or an external surface, at constant linear rates G. Before impingement the perceptible course of growth can be described by the equation: 1 = G(t-7) C1I where, G = dl/dt, 1 is a crystal dimension measured in a constant direction, t is the time, and 7, the nucleation period, is a positive intercept on the time axis. Fig. 1 is a schematic representation of I as a function of time for a recrystallizing grain. G is dependent upon temperature, driving energy (strain or surface energy), relative grain and boundary orientations, but is generally independent of time. The frequency of nucleation, fi, (time" volume") can be defined by the equation: N = 1/fV [2] where ? is the mean nucleation period and V is the volume of the specimen that has not recrystallized. The kinetics of primary and secondary recrystallization generally can be described satisfactorily in terms of the parameters N and G only.&apos;-" After recrystallization is complete the average grain size 7 increases with time by "normal grain growth;" didt, the average rate of grain growth, is strongly time dependent and has not yet been precisely related to G for the motion of the individual grain boundaries constituting the system. It has been suggested4* " that the elementary act in grain boundary migration is closely related to the elementary act in grain boundary self-diffusion. Although the distance of atom movement in the two processes may be somewhat different, there is reason to expect that the activated states may be very similar, so that the free energy of activation for grain boundary migration should be of the same order of magnitude as for grain boundary self-diffusion. Therefore, it is desirable to develop a satisfactory basis for comparing data on self-diffusion and grain boundary migration and to make such comparisons where possible. Theory The formal theory of grain boundary migration rates is analogous to the theory for the rate of growth of crystals into supercooled liquids reviewed elsewhere 6-8. Boreliuss has shown that the latter theory describes, within the theoretical uncertainty, the growth of selenium crystals into supercooled liquid selenium. Motto and more recently Smolu-chowski" have derived expressions for the rate of boundary migration in recrystallization. The treatment to be presented is similar to Mott&apos;s excepting that the formalism of the absolute reaction rate theory will be used. The atomic mobility, M, in grain boundary migration is defined by: G = -M6p/6x where p is the chemical potential per atom and x is the coordinate measured in the direction of grain boundary movement. Let AF be the free energy difference per gram atom on the two sides of the boundary and k the thickness of the boundary. For RT>>AF the potential gradient across the boundary (6p/6x) is essentially linear and it follows that: SF/8x = - aF/N\ [4] where N is Avogadro&apos;s number. According to the Nernst-Einstein equation, M is related to a diffusion coefficient, Do, for matter transport in grain boundary migration by the equation: M = Da/kT [5] Substituting eqs 4 and 5 into eq 3 gives the basic relation between Do and G: G = DoaF/\RT [6] Do values may be calculated from experimental values of G from eq 6 and directly compared with the coefficient of self-diffusion within the crystal, DL, or the grain boundary self-diffusion coefficient D,. However, a more convenient, though equivalent, basis for comparing atomic mobility in grain boundary migration and self-diffusion is through the constants of the absolute reaction rate theory. According to this theory diffusion coefficients may be written:" D = k2(kT/h) exp [-AF,/RT] 171 aFa, the free energy of activation, is related to the measured energy of activation, Q, by the equation: AFA = Q - T aSx - RT [8] where aSa is the entropy of activation. Substituting eqs 8 and 7 into eq 6 gives: G = ek(kT/h) (aF/RT) exp [(AS,,)C/R] exp C-Qc/RTI C91 where the subscript G refers to boundary migration. The relationship between the driving free energy and the free energy of activation in boundary migration is indicated schematically in Fig. 2. Experience indicates that the variation of G with temperature can be described by: G= Go exp [- Qc/RT] [10] where Go and Qc are generally temperature independent over wide ranges of temperature. Comparison of eq 9 with eq 10 gives:

Jan 1, 1952

By E. S. Machlin

The alternate processes by which solute atoms can limit the migration of grain boundaries have been considered. At the lowest solute concentrations the controlling process is "mechanical breakaway" in which the solute atoms affect the driving force and not the mobility. In the next higher range of solute concentration, solute atoms are bound to the boundary and diffuse by boundary diffusion along cusps in the boundary developed at the solute atoms. In this region the boundary velocity is controlled by the component in the direction of boundary migration of the rate at which the bound solute atoms can diffuse along the boundary. At still higher concentrations, it is predicted that boundaries break away from the binding solute atoms by thermal activation. The specific behavior Predicted is consistent with the observations of Aust and Rutter. The most striking agreement between prediction and experiment is that obtained for a range of solute concentration in which the boundary velocity is inversely proportional to the cube power of the solute concentration. MaNY models have been devised for the atomic steps in the motion of a grain boundary. McLean1 has listed some of these models and Aust and utter&apos; have evaluated these and other models. If there are

Jan 1, 1962

By J. Weertman

An explanation is advanced for the recent results of Barrett and Sherby on the high-temperature creep of fee metals. Their measurements indicate that metals with a low stacking fault energy creep at a much slower rate than metals with a high stacking fault energy. The explanation is based on the assumption that the rate of core diffusion is much smaller in partial dislocations than in perfect dislocations. An experiment is suggested to test this assumption. The explanation also requires that the jog density is small on widely split dislocations. SHERBY and Barrett1,2 recently established an important result in the field of high-temperature steady-state creep. They have shown that fee metals whose dislocations split into partial dislocations separated by a wide stacking-fault ribbon creep at a much slower rate than fee metals whose dislocations are not split appreciably. The creep rates in the two cases may differ by a factor as high as 6000. (For the purpose of comparison, the test temperature of each metal was chosen so that its rate of self-diffusion was equal to a standard value. Similarly the stress levels were such that the ratio of the stress to an appropriate elastic modulus was the same for each metal. In all cases the stresses were sufficiently low that the steady-state creep rate was proportional to the stress raised to a power.) It is the purpose of the present paper to attempt an explanation of this interesting and significant result of Sherby and Barrett. The activation energies of high-temperature creep of the metals tested by Sherby and Barrett (aluminum, nickel, copper, and silver) were equal to their self-diffusion activation energies. Hence it appears reasonable to assume that this type of creep is controlled by a dislocation-climb process, which in turn is controlled by the diffusion of vacancies to or from dislocation lines. (It will be assumed that the diffusion of interstitial atoms is unimportant in the climb process. The analysis could be repeated for the case in which interstitial atoms are important.) In prior papers374 I have treated dislocation climb by using the assumptions that core diffusion is extremely fast down a dislocation and that a dislocation always maintains an appropriate vacancy concentration in its immediate vicinity. In this

Jan 1, 1965

By A. G. Metcalfe

Observations at temperature are used to investigate the phase changes in alloys containing more than 50 pct Co and above 1000°C. The nonsuppressible transformations in cobalt above 1120°C and in the intermetallic compound Co2Cr3 are studied. The liquidus and solidus surfaces are determined. Insufficient data is obtained to complete the constitution diagram. A REVIEW of some of the earlier work on cobalt&apos; and on the binary systems with chromium2-4 and with molybdenum,5 showed that one likely source of differences might be attributed to the presence of phases at high temperatures which could not be retained by quenching. Consequently, the decision was made that only methods of examination at temperature should be used in this work. The correctness of this decision was confirmed during the course of the work by the investigation of the martensitic nature of the transformation in cobalt- and by the decomposition of the high temperature form of the phase Co2Cr3 on quenching.&apos; The use of high temperature methods, including dilatometry and thermal etching led to the postula-tion of the existence of a high temperature form of cobalt with a probable hexagonal close-packed structure, transforming from cubic cobalt over a range of temperature from 1119° to 1145°C.8 One of the important pieces of evidence for this transformation was that it was observed in alloys with chromium and molybdenum which were nonmagnetic at this temperature so that confusion with magnetostriction effects was impossible. These results were not reported in this earlier paper, so that the data given here supply further evidence for the existence of a second allotropic transformation in cobalt. High temperature observations are necessarily much slower in producing results than the examination of quenched specimens at room temperature by conventional means such as X-ray diffraction or microexamination. The investigation has only covered a limited part of the field, as a result, extending from the liquidus down to about 1050°C and from the cobalt corner up to 50 pct alloying elements. The differences between the various reported diagrams for the constitution of the Co-Mo and Co-Cr systems have already been mentioned. The best available diagram in the first system is due to Sykes and Graff&apos; which is shown in Fig. 1. Fig. 2 shows the latest Co-Cr diagram due to Elsea, Westerman, and Manning.&apos; A comparison reveals that these are incompatible because of the disagreement with regard to the number of allotropes of cobalt. Elsea, Westerman and Manning took their liquidus and solidus curves from Wever and Haschimoto.2 The temperature horizontal in the two-phase field beneath the eutectic was placed 35" to 39°C higher than in earlier work2,4 with a new interpretation of the nature of this transformation. This interpretation also required a peritectic horizontal at about 1470°C, which has been confirmed here for an alloy with 53 pct Cr. No investigation had been made of the ternary system until after this work had been terminated, when a section at 1200°C was published." In this work a ternary compound was found by the X-ray diffraction examination of quenched alloys. This compound contained less than 50 pct Co, and was thus outside the field investigated here. However, some reactions were found dilatometrically which could not be fitted on the diagram and are now believed

Jan 1, 1954

By Atmaram H. Soni

A statistical study of machinability led the writer to examine existing data in regard to a thermal conductivity-mechanical properties relationship. Various functional relationships were proposed and the multiple correlation determined by statistical methods discussed in detail in the 1iterature.4 The relationship having the greatest engineering and statistical significance is discussed below. The data for cast and wrought aluminum alloys&apos;&apos;2 have been compiled and analyzed separately. The results of these analyses are presented in Table I. The empirical equations for estimating the thermal conductivity (cal sec-&apos; cm-I °C) are: for cast aluminum alloys K = 0.584 -0.00984/ -0.00263 Hb [1] and for wrought aluminum alloys K = 0.604 -0.00424l- 0.00170 Hb [2] where 1 and Hb are the percentage elongation and Brinell hardness number. Results of a similar analysis pertaining to stainless steel3 are also given in Table I. This empirical equation for estimating thermal conductivity (Btu per sq ft per hr per °F per in.) is K = 216.19- 1.716l - 0.0997 Hb [3] The relationship between electrical resistivity and mechanical properties was also examined for aluminum alloys using the same statistical method. These results are listed in Table II. While the situation of exact multiple correlation

Jan 1, 1965

By O. D. Gonzalez, R. A. Oriani

A thermo-osmosis technique has been used to measure the heat of transport, Q* , of hydrogen and of deuterium dissolved in a iron and in nickel, and of hydrogen in Feo.6Nio.4 in the tempevature range 400° to 600°C. For all these systems, Q* is negative and has a large temperature coefficient; an isotope effect can be established for the solutes only in nickel. The magnitude of Q* is considerably larger than the activation energy, E , for migration in the case of these isotopes in a iron, so that all variants of the Wirtz model must be rejected. The phenomenological definition of Q* is developed to show that Q* is related to the mechanisms by which the activation energy is dissipated back into the lattice, and that Q*/E is a function of the ratios of the mean free paths of electrons and of phonons to the distance of jump of the diffusing atom. A correlation is shown to exist between the sign of Q* in thermal diffusion and that of the effective charge in electro migration, and may be understood as due to the large ratio of the mean free path of electrons to that of phonons. THE study of nonisothermal diffusion in the solid state is of interest because certain aspects of the mechanism of diffusion are made manifest which remain concealed though still present in the isothermal case. The thermodynamics of irreversible processes characterizes nonisothermal diffusion, known as thermal diffusion or as the Ludwig-Soret effect, by a quantity, Q*, called the heat of transport, which essentially measures the sign and the magnitude of the steady-state concentration gradient produced by the imposed temperature gradient. The problem then is to understand the quantity Q* at the atomistic level. There does not exist a theory for the atomistic interpretation of the heat of transport. There are, however, two classes of simple models which seem to afford some physical insight into Q*. Wirtz&apos;s model1, z and its subsequent generalizations partition the activation energy, E, for the migration of the atom spatially about the region of the migrating atom, so that Q* is the difference between the portion of the activation energy centered about the original site of the jumping atom and that portion about the arrival site. Clearly, the magnitude of Q* cannot on this model be larger than the activation energy for migration. The model of Oriani3 also considers the spatial distribution of E not only before but also after the atomic jump, and Q* is related to the variation of the spatial distribution of E that is produced by the jump. The simplest kind of system with which to compare the consequences of these ideas is the interstitial solid solution, since one may easily choose a temperature at which only the interstitial component moves, the solvent lattice serving as a completely satisfactory frame of reference. Thus, one avoids complications arising when both species in a binary system move. In addition, one avoids the necessity of knowing the energy for the formation of a vacancy, something which is needed for the analysis of thermal-diffusion data on metals which diffuse by the vacancy-exchange mechanism. However, the number of well-measured interstitial systems is extremely small, and, in particular, there are almost no data in the published literature for the temperature dependence of the heat of transport. If one works with solutes which are gases in the pure state at ordinary temperatures, one may use the technique of thermo-osmosis4 which permits thermal diffusion to be measured over a small temperature difference so that the temperature dependence of Q* can be more easily determined. The choice of dissolved hydrogen in iron and nickel was based on these considerations as well as on the desire to look for an isotope effect associated with localized

Jan 1, 1965