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By M. J. Mullikin, J. B. Conway

for use in describing combined first- and second-stage creep data. In the above ?o represents the instantaneous strain on loading, ?t the limit of transient creep, ?S the steady-state creep rate, t the time, and ? a constant leading to the exhaustion rate of transient creep. It was noted that this equation was similar in form to that proposed originally2 by McVetty. This type of equation was also suggested by Andrade and Aboav3 in studies of the shear strain of cadmium. Calculation of the constants ?o, ?t, ?, and ?s, in Eq. [ l] is somewhat involved due to the slight complexity of this relationship. In the paper by Garofalo a computer approach based on a least-squares analysis was recommended. Such an approach involves a trial and error solution but when a computer facility is available the difficulties in this calculation are of little consequence. It does mean however that the evaluation of this type of equation would become quite tedious if computer facilities were not available. Some recent studies have identified a fairly straightforward method for calculating the constants in the Garofalo equation. While not leading to a least-squares evaluation the approach is accurate and is recom-

Jan 1, 1967

By V. Leroy, A. G. Guy

Serious disagreements are often found between experimentally determined intrinsic diffusion coefficients and those calculated employing the usual form of the vacancy theory. In the new theory it is proposed that the total intrinsic flux, Ji, of component i, is the sum of a part, f, due to the usual random exclzanges of component i with the vacancies, and a second part, Ji, due to exchanges with the uacancies composing the net vacancy flux. The present treatment, while less powerful than that of Manning, has the advantage of easy uisualization and of facilitating the application of the vacancy-flux effect to complex systems. IT is becoming increasingly evident that there are serious deficiencies in the version of the vacancy theory of diffusion that has been widely used for the past 20 years. One type of evidence is the frequent lack of agreement between intrinsic diffusion coefficients and tracer diffusion coefficients, even taking account of the thermodynamic factor. A second kind of evidence is the observation of a Kirkendall shift larger than theoretically possible, that is, larger than can be accounted for without assigning a negative value to one of the two intrinsic diffusion coefficient.'- The thermodynamic factor could conceivably make both coefficients negative, but not just one. It is clear that a cause of these anomalies, apart from any inadequacy of the usual vacancy theory, might lie in an oversimplified treatment of the data. Adequate experimental techniques, including the use of moderate pressure during the diffusion anneal, are now available to insure that porosity, lateral expansion, and so forth, can be kept negligibly small in most cases. The effect of differences in atomic volume can be of major importance, and it is essential that one of the available methods4 be used to account for this factor. In the present treatment this is accomplished by the consistent use of moles per cubic centimeter as the unit of concentration. Of the various possible inadequacies of the vacancy theory, attention will be given here only to effects of the net vacancy flux. annin' has previously considered this question, beginning with an analysis of atomic jumping of tracer atoms. When he added the effect of a concentration gradient, new terms arose that could be associated with the flow of vacancies. The present treatment uses quite a different approach. The usual vacancy flux, J,, is introduced explicitly, and a simple analysis predicts major changes in the intrinsic diffusion coefficients from this cause. The usual assumptions are made that only a vacancy mechanism is operative, that the formation of voids can be neglected, and that changes in the partial molal volumes, vl and v2, are negligible. The significant diffusion coefficients for the present topic are Dl and D,, the intrinsic coefficients, which enter in the equations, where the flux Ji, moles per sq cm per sec, is that crossing the Kirkendall interface. The concentration, ci, is in units of moles per cu cm, and the concentration gradient, aci/ax, is evaluated at the Kirkendall interface. It will be recalled' that the calculation of Dl and D2 involves the measurement of areas on the diffusion curve with respect to the positions of the Kirkendall and Matano interfaces. In the case of the anomalies mentioned earlier, the Kirkendall shift is too large to be accounted for by the diiferetzce in fluxes (J2 -J1), given by Eqs. [I] and [2]. The logical inference is that the flux of the solvent atoms, J1, is actually in the same direction as the flux of the solute atoms, Jz. In terms of Eq. [I] this requires that Dl have a negative value. However, it would be somewhat misleading to state that the solvent atoms are diffusing up their own concentration gradient. The explanation that will be advanced here pictures competing processes producing the net flux of solvent atoms: 1) diffusion of the solvent atoms down their own gradient by random exchanges with vacancies; and 2) diffusion of solvent atoms in the opposite direction by exchanges with the net vacancy flux. ACTION OF THE NET VACANCY FLUX Theories of vacancy diffusion can be formulated with varying degrees of refinement, and the present theory has purposely been kept as simple as appeared adequate to explain the phenomenon in question. In particular the following aspects have been neglected: 1) the gradient of vacancy concentration in comparison to the gradient of the atomic species; 2) departure of vacancy concentration from the local equilibrium value; 3) variation of the jump frequency, LO, with the specific surroundings of the atom-vacancy pair being considered; 4) correlation effects. These and other refinements can be considered once the essential mechanism has been established. The essential idea of the present analysis is to calculate the total intrinsic flux, Ji, of component i as the sum, JlJ?±j{ [3] where J; is attributable to the usual random atomic jumping, and J{ is a contribution arising from the net vacancy flux, J,. The latter quantity, of course,

Jan 1, 1967

By K. A. Jackson, J. D. Hunt

A new classification of eutectics is proposed, based on tlze entvopies of wzelting of the tuio eutectic phases. The clnssification was used to predict suitable tvansparent analogs of the metallic systems. Experimental confir?nation loas obtained for the theovetical shape of the lamellar solid-liquid interface, fov the fault mechanisms of lanzellar spacing changes, and for the development of low-energy solid-solid boundaries between the lamellae. An explanation is presented to account jov the irvegular and coinplex regular structures zrhich are found in some eritectic systems. FrOM experimental observations, single-phase materials can be divided into two groups according to their solidification characteristics, those that grow as faceted crystals and those that do not. acksonl' showed from thermodynamic reasoning that the type of growth depended on a factor a which was almost thg entropy of melting. Most nonmetals have high entropies of melting (a greater than 2) and grow with crystalline facets. Most metals have low entropies of melting (CY less than 2) and grow almost isotropically with no facets. The authors propose that eutectics may be classified in a similar manner. There are three groups of eutectics, those in which both phases have low entropies of melting, those in which one phase has a high and the other phase has a low entropy of melting, and those in which both phases have high entropies of melting. Lamellar or rodlike structures are formed in systems in which both phases have low entropies of melting. In these alloys dendrites of either phase may be formed, when the alloy is rich in the relevant component. Examples are Pb-Sn, Sn-Cd, Pb-Cd, Sn-Zn, Al-Zn. Irregular, Fig. 14((), or complex regular, Fig. 14(b), structures are formed in alloys in which one phase has a high entropy of melting and the other has a low entropy of melting. Examples are A1-Si, Zn-MgzZnll, Pb-Bi, Sn-Bi. When the alloys are rich in the low entropy of melting phase, dendrites are formed; when the alloys are rich in the high entropy of melting phase, faceted primary crystals are produced. These crystals are sometimes called hoppers or pseudodendrites. In this work the term dendrite will only be used to describe nonfaceted primary crystals. Dendrites are not formed during solidification in high entropy of melting single-phase materials. The third group of eutectics includes alloys in which both phases have high entropies of melting. Each phase grows with a faceted solid-liquid interface. Since most metals do not have high entropies of melting, metallic examples in this eutectic group are rare. However they may occur between some intermetallics and semiconductors or semimetals such as silicon, germanium, and bismuth. Attempts have been made to study eutectic solidification visually by watching the growth process.374 Since metals are not transparent, the observations had to be made on external surfaces. This difficulty can be overcome by using transparent analogs of the metallic systems. As was mentioned earlier, most single-phase compounds have entropies of melting greater than 2 and so grow as faceted crystals. Recently organic materials with entropies of melting less than 2 were investigated.' These materials grow in exactly the same way as the low entropy of melting metals. When the materials are pure, they grow with a solid-liquid interface parallel to an isotherm; when they are impure, cells or dendrites are formed. Since these materials are transparent, have low melting points, and even have cubic structures, they should be ideal for making up transparent analogs of the metallic eutectics. The purpose of the present work was to investigate these organic eutectics and to see whether this quite different series of eutectics could be classified in the same way as the metallic systems. The observations made on the organic alloys are also discussed with reference to the current theories of lamellar growth. Explanations are proposed to account for the structures formed in the other eutectic groups. EXPERIMENTAL Thin cells containing the organic alloys were uni-direction ally solidified on a specially constructed microscope stage.' Uniform growth rates were obtained by moving the cells, with a motor drive, through a fixed temperature gradient, so that the solid-liquid interface remained stationary with respect to the microscope objective lens. The cells were made by fusing two microscope cover slides 7/8 by 7/8 by 1/100 in. together on three sides, leaving a gap of 1 to 3 mils between the slides, and these were filled by surface tension. A preliminary investigation of the phase diagram between two components could be made very rapidly. One side of the cell was filled with component A and the other side with component B. Since only a small amount of mixing could occur every composition from pure A to pure B was present in the cell. When the cell was placed in the temperature gradient a pictorial representation of the phase diagram was obtained. Eutectics, peritectics, "interorganics", and solid -solid transformations could be readily detected. Fig. 1 shows part of a eutectic phase diagram. The Sample was first grown slowly then stopped. The two

Jan 1, 1967

By A. Gittens

In two recent papers stevens13,14 has compared the methods used by various investigators to calculate the contribution of grain boundary sliding to the total creep strain. In previous work Gittins15 has shown that the strain due to grain boundary sliding Egb may be estimated from the lateral, d, and vertical, v, displacements of a longitudinal marker line as it crosses a grain boundary. He obtained the formula, where nL is the number of grains per unit length measured on the specimens before creep, and \p and ?2 are, respectively, the angle between the grain boundary and the stress axis in the plane of the surface and normal to the surface (see Ref. 13, Fig. 1). The subscript L indicates that observations are made in a longitudinal direction parallel to the stress axis. It was generally found more convenient to measure the grain size of a specimen before creep; this was necessary to characterize the specimen. Stevens13,14 however prefers to define Egb in terms of NL, the number of grains per unit length after creep. Since nL - NL(l + €1) where cr is the total strain, Eq. 1 11 becomes The quantities d and ?, can be determined directly from the marker lines, while v and ?2 are found by sectioning normal to the surface. In the interior when symmetry considerations suggest that v = d and ?1 - ?2 the strain due to grain boundary sliding may be estimated from a suitable internal longitudinal marker line by the equation To determine cgb at the surface using either Eqs. |1| or [2] requires a large number of observations, particularly if many estimates of cgb are required, and also it is impossible to determine the variation of cgh with creep strain on the same specimen because the specimen must be sectioned to determine ?2. Gittins15 found that for a number of materials the sliding vectors d and v were related to each other so that provided one was measured the other could be estimated. Also during creep, grain boundaries tend to migrate to meet the surface at angles close to 90 deg,16 so that the term nL(v/tan?2)L was comparatively small when 4,- 90 deg. By determining the frequency distributions of ?2 on control specimens this term can be estimated without sectioning the creep specimen. In this way an empirical equation based on Eqs. |1| and |2| enables cgb to be determined with reasonable accuracy with fewer observations of the angles and sliding components. For B brass, the relationship between the sliding vectors indicated that ceb = 0.85nLVL . In Table I of Stevens paper this equation is stated to be incorrectly derived. However it should be pointed out that this is an empirical equation derived from Eq. |1|, based on a knowledge of the relationship between d and v and on the frequency distributions of ?1 and ?2 for a particular material under given experimental conditions. It was used only when these relationships were known, to reduce the number of observations required to estimate cb. Therefore the comment "derivation incorrect does not apply. Gittins did in fact make use of Eqs. |1| and 131. Author's Reply I must apologize to Dr. Gittins for the inadvertent misrepresentation of his work. Other slight errors in Table I have been pointed out to me. Langdon (No. 12 Table I), Gifkins (No. 7, Table I), and possibly other workers did not measure the number of boundaries per unit length after creep (A') but the corresponding quantity bejove creep (n). As Dr. Gittins points out, a completely analogous set of equations to those given in the paper can be derived by the same method: using the number of boundaries per unit length before instead of after creep. The basic equations corresponding to Eqs. [2] and 171 of the paper, from which all the others can be derived, are

Jan 1, 1968

By J. C. Scully

In June, 1965, Sanderson and scully5 reported at the Conference on Environment Sensitive Mechanical Properties of Materials at the Research Institute for Advanced Studies at Baltimore that thin foils of titanium could be prepared by chemical polishing in a mixture of 44 pct HF and 73 pct HNO3 in the volumetric ratio 2:3. The technique is simpler than that since reported by Rice and Orava. As-received annealed titanium (containing 0.8 pct Fe and 30 ppm H) in the form of sheet 0.05 cm thick is placed in the solution and moved up and down. The reaction is violent but suitable foils are obtained very easily and consistently. A typical micrograph is shown in Fig. 3. The small precipitates were not identified. Yamane and ueda6 observed many spotlike features which they referred to as small dislocation loops. While their spots may be due to the reaction of the warm foil with the air as suggested by Rice and Orava, the precipitates in Fig. 3 are also found when foils of titanium are prepared by electro-polishing at low temperatures and subsequently examined in the electron microscope without any inter- mediate warming. Furthermore, they are not a surface effect. It is necessary to add that alloys of titanium cannot be so easily thinned by the chemical polishing solution described above since it contaminates the a, phase with hydrogen and produces y hydride. These matters are described at length in a paper7 and their relevance to stress corrosion is considered elsewhere.'-* Author's Reply The authors are grateful to Dr. Scully for bringing to our attention his hitherto unpublished technique for thinning unalloyed titanium, and deeply regret the unintended apparent duplication. The chemical thinning solution (7 parts HNO3 and 3 parts HF, by volume) reported by us is the same as that with which, for some period in the past, we had experienced success in the preparation of foils from single and polycrystalline niobium. Its subsequent effective application to titanium was a logical step, which, clearly independently of Scully, was conceived by Mr. Rice, to whom full credit is due. A few comments are warranted concerning some of the details of the preceding Discussion. It is evident to the discerning reader that the two thinning techniques under consideration are chemically almost identical, and in that sense are equally "simple". The chemical aspect is, of course, the one of primary importance in both communications. Thereafter, the relative simplicity is dictated by the mechanics of the actual thinning operation selected by the individual investigator. Our standard dimpling, or dishing, procedure was chosen with a view toward providing, for the electron transparent areas of the sample, the maximum protection from extraneous deformation during handling. That the long, straight dislocations visible in Scully's electron micrograph of a seemingly recovered structure closely resemble handling dislocations would tend to indicate the merit of our adopted technique. Features similar to those which Scully has attributed to precipitates, without any apparent diffraction contrast confirmation, were not observed in any of our clean foils taken from annealed or deformed specimens. This was admittedly somewhat surprising since the 3700 ppm (nominal) Fe in the A-70 commercial-grade titanium examined should have given rise to TiFe precipitates. Presumably these existed but were un-resolvable. Curiously, Scully's "precipitate1' density is fairly high although the iron content quoted was less than one-fourth of that in our material. One is forced to conclude from the evidence that prior thermal and mechanical treatments are responsible for the two different types of structure observed.

Jan 1, 1968

By R. Kossowsky

USING etch-pit techniques, Johnston and Gilman' have shown that the stress dependence of dislocation velocity can be represented by the expression where r, is the dislocation velocity, a is the applied stress, and oa, is the stress to produce a unit velocity. Noble and Hul12 showed that the exponent m is strain-dependent and increases rapidly in the work-hardening region. This was explained by arguing that in the work-hardened material the applied stress required for any given velocity will be greater than in the annealed material by an amount equal to a back stress due to work hardening. schadler3 has stressed the importance of substructure as a possible source of error in dislocation velocity measurements, and took care to make velocity measurements in which dislocations moved such short distances that interactions with boundaries were avoided. schadler3 also pointed out that, if standard testing equipment is used, measurements of m from flow stress data could be seriously in error in materials with a high initial work-hardening rate. Noble and Hu112 have further argued that, due to the strain dependence of m , the extrapolation to zero strain4 to obtain the true value of m can be justified only in the preyield region. Microstrain experiments in high-purity iron5,6 have led to the conclusion that aiA (Ref. 5) (defined as the stress to first produce a permanent set of 10-6 in. per in.) and oflow are not controlled by the same deformation mechanism. It has been proposed5,6 that aA is governed by the lattice resistance to the motion of screw dislocations in a given slip plane and that oflow is controlled by the lattice resistance to a full-scale cross slip. The purpose of this note is to extend Noble and Hull's argument further and to show that measurements of m from flow stress data can be in error due to the rapid increase in stress in the microstrain region6 when stress is increased beyond aA. Double z-one-refined single crystals of molybdenum (with the (101)[ 111] slip system operating and a Schmidt factor of 0.475) were used in an experimen-

Jan 1, 1968

By W. C. Ellis

Growth directions of tin, zinc, and cadmiun whisker crystals grown spontaneously fi-om the solid are summarized. In tin the edge and diagonal directions of the unit cell are jound with the exception oj- the [110] diagonal. In cadmiurn and zinc the usual dip-ections are a or a + c. The c direction has not been ohserwed. The gvouth directions from the solid are for the most part the same as those found for vapor-grozun crystals and are the ohserz:ed glide directions in plastic j-lou. Whisker crystals of these elements grown from the solid are not twinned. Specular lateral reflections are associated with planes of snall crystallographic indices. WHISKER crystals of tin, zinc, or cadmium grow spontaneously at room temperature in periods from months to years from thin electroplates and other prepared films of the respective metals.''2 It has been established that these crystals are single, but the question of twinning, such as occurs in whisker crystals of silicon,3'4 has not been resolved. Studies of morphology have been restricted to determinations of growth directions.5-' Whisker crystals are both straight and kinked. A few studies have been made on kinked whiskers including measurements of kink anglesa and determinations of growth directions,' but unfortunately not both on the same crystals. The kink angles, for the most part, for each species are grouped closely about a few unique values, but these values are not always those between observed growth directions in a single crystal. To supplement existing data, the growth directions, identification of lateral features, and presence or absence of twinning were determined with a Weissenberg goniometer by a method described elsewhereg on eight whisker crystals of tin, five of zinc, and five of cadmium. One kinked cadmium whisker was examined in detail. The specimens were needlelike, a few microns in cross section, and of the order of a millimeter in length. They were removed from electroplated substrates on laboratory specimens and commercial equipment after several years of growth as described in Table I. Since the specimens were less than 10 p in cross section they were ideally strong with no attendant risk of plastic deformation or damage in handling. Only deformation twinning has been reported for these elements. Therefore, twinning probably should not be expected in whisker crystals of these metals, particularly a twin plane containing the growth direction. A twin plane oriented in this direction was the one sought in this study. No examination was made for twinning at the boundary between kink segments except for one cadmium crystal. Well-defined reflections occur as a whisker crystal of tin, zinc, or cadmium is rotated about its growth direction when illuminated by a beam of light Although these reflections had been noted in earlier investigations, no study of them was made, probably because the earlier studies had disclosed also that

Jan 1, 1967

By A. E. Jenkins, L. A. Baker, N. A. Warner

Rates oj decarburization of levilated Fe-C droplets conlaining 5.5 to 0 pct C have been measured at 1660°C. Gas mixtures of 1, 10, and 100 pct 0, with helium diluenl were used at velocities of 12.5 and 62.5 cm per sec. Rates were independent of carbon concentration in the mell and in good agreement with the calculated rule of oxygen diffusion through the gas boundary layer. The effects of flow rale and total pressure are as predicled and the rates are approxitnalely 2.5 times those with CO2 as oxidant. The mass-transfer correlation used incorporaled the efject of natural convection as well as forced conrection. Graphile spheres are shown to oxidize at the same rate as Fe-C droplets under the same experimental codlions. It is concluded that, for high carbon concentrations in the melt, the rate of- decarburizalion is controlled wholly by the rate of gaseous diffusion. Rate measurements with pure CO, are reported for low carbon concentrations where CO bubbles nucleate within the droplet. Under these circumstances the decarburi-zation decreased with carbon concentration and it is proposed that carbon diffusion is significant in conlrolling the decnvburization rate. In an earlier paper1 decarburization rate measurements were reported for levitated Fe-C alloys at 1660°C but with CO2 as the oxidant. The decarburization rate was found to be independent of carbon concentration in the melt but slightly affected by total pressure. The authors were unable to explain the slight pressure effect but in all other respects the results were consistent with control by diffusion in the gas boundary layer. Subsequent work has been directed at finding the reason for the slight pressure effect and whether the kinetics with oxygen as oxidant parallel those with CO2. Recently Ito and Sano2 have shown that with water vapor-argon atmospheres the decarburization rate is gaseous diffusion controlled until an oxide film appears on the surface. In this work the melts were contained in crucibles. MASS TRANSFER IN THE GAS PHASE In the earlier analysis1 only forced-convection mass transfer was considered. Subsequent recognition of the existence of some free-convection mass transfer explained the observed small effect of total pressure on the decarburization rate. Steinberger and Treybal3 and Kinard, Manning, and Manning4 have developed correlations involving the linear addition of the contribution of radial diffusion, free and forced convection. Steinberger and Treybal&apos;s correlation was chosen as the most applicable to the present work since it correlated most of the data available in the literature and handled the low Reynolds number region exceptionally well. The correlation for (Gr&apos;Sc) < 108 is where Nu&apos; is the Nusselt number for mass transfer based upon the total surface of a sphere in an infinite medium, G&apos; is the mean Grashof number for mass transfer defined by Eq. [2], Sc is the Schmidt number (µ/pDAB)f, Re is the sphere Reynolds number (dpu,pf/µf), p is the viscosity of the gas (poise), p is the density of the gas (g cm-3), Dab is the binary diffusivity for the system A-B (sq cm sec-&apos;), dp is the sphere diameter (cm), u is the approach velocity of the gas (cm sec-I), and subscript f denotes the property value is computed at the film temperature Tf defined by Tf = +1/2(To + Tr) where To is the specimen temperature and T, is the approach gas temperature (oK). Natural convection occurs when inhomogeneities exist in gas density. These may be caused by concentration gradients, temperature gradients, or both. In the present work the temperature gradient between the sphere and the bulk gas was very large and in some cases, for example the runs with pure oxygen, the concentration gradient was also appreciable. The Grashof number defined by Mathers, Madden, and piret5 was used since it took account of both temperature and concentration gradients: where Gr&apos; is the Grashof number for mass transfer (p2fgd3|-yA-yA|/µ2f), Gr is the Grashof number for heat transfer (p2f gd3p|To - T,]/µ2fTf), Pr is the Prandtl number (cpµ/k)f, g is the acceleration due to gravity (cm sec-&apos;f, a is the concentration densification coefficient (1/p)(ap/ayA)T, yA is the mole fraction of component A at the gas-metal interface, yA is the mole fraction of component A in the bulk gas stream, cp is the heat capacity of the gas per unit mass at constant pressure (cal g-I OK-&apos;), and k is the thermal conductivity of the gas (cal cm-&apos; sec-1 OK-1). Mathers et al. tested this combined Grashof number

Jan 1, 1968

By G. A. Beske, P. Hilsch, J. Wulff

The effects of the growth precipitates on the su-perconduching properties of an Al- 15 al. pel Zu alloy have been studied using magneization, transition lem-perature, and residual resistivity measurements. Aging at 230C for 1/2 to 11 he produces an increase in Hfp, Ike field of first penetration, and tut increase in trapped flux. The upper critical field, Hc2 remains constant for such aging tunes. Aging at 200°C produces a decrease in Hfp and an increase in trapped flux. The transition temperature remains constant at Tc - 1.227° ± 0.02°K for aging at 220°C for tims of from 1/2 to 10 hr, and for aging at 200°C it remains constant at Tc. = 1.18° i 0.02°K for times from 1/2 hv to 26 hr. The observed behavior indicates that the superconducting matrix when aged at 220°C behaves tike a type U su-perconducior, but when aged at 200°C behares like a type I superconductor. The magnetization changes after aging can be attributed to the growth and clutnge in distribution of the precipitate in a matrix of fixed composition. IT has been realized for some time that the superconducting properties of alloys are highly structure-sensitive. This is evident in the work of Mould and Mapother1 who examined the properties of an aluminum alloy. Precipitation effects have also been briefly mentioned in other studies.2-4 Bonnin and coworkers5 have observed a sharp inc rease in trapped flux in an A1-Mg alloy when the residual resistivity reaches a value that indicates it is a type II superconductor. Recently Blanc, Goodman, and Nemoz5p have reported on precipitation effects in A1-Ag alloys. Detailed studies of precipitation in Pb-Sn and Pb-Cd alloys made by Livingston6 serve to show that the upper critical fields are enhanced by quenched-in solute. Furthermore. at various stages in the precipitation process? the upper critical field is determined largely by the remanent solute. The observed magnetic hysteresis and trapped flux in such alloys result from the interaction between precipitate and the flux filaments in the mixed state. The flux trapping appears to depend largely on the precipitate distribution and is greater if the superconductor is type II than if it is type I. To examine the effect of precipitation in another alloy system, particularly one in which the composition of the superconducting phase does not change significantly during the course of precipitation, the Al-Zn system seems interesting, especially in view of the transition temperature and resistivity studies of Chiou and seraphim.&apos; Furthermore, the recent detailed electron-microscope studies of an Al-Zn alloy by Richards and Garwood8 provide a guide for relating superconducting properties to changes in structure. For these reasons, magnetization, transition temperature, and residual resistivity measurements for varying times of heat treatment at two temperatures were made with a -15 at. pct Al-Zn alloy. The results are reported in this paper. I) EXPERIMENTAL The alloy used was prepared by Cominco Products Inc. from 99.9999 A1 and 99.999 Zn. It was chill-cast, swaged, and drawn to 0.125-in.-diam rod. The analyzed composition was 15.6 at. pct Zn (31.1 wt pct). A jeweler&apos;s saw was used to cut the 0.125-in.-diam rod into the 0.875-in. lengths needed for magnetization measurements. The ends of the cylinders were slightly beveled to remove the sharp edges. A portion of the original 0.125-in.-diam rod was drawn into 0.010-in.-diam wire and used for transition temperature measurements. Specimens were suspended from wires within a vertical furnace during heat treatment. All were homogenized at 500°C for a minimum of 3 days and subsequently solutionized for times in excess of 6 hr. The solutionizing temperature was held constant to +3°C. Individual specimens were homogenized, quenched, and aged several times and no effects indicating loss of zinc were noted. The suspended specimens were quenched by cutting the wires and allowing the specimens to fall into a silicone oil bath held at the aging temperature. They were then isothermally transforked by aging in the same bath used for quenching. After aging for the required time (approximately 10 min aging was necessary before the upper critical field reached a fixed value), they were briefly (1 to 2 sec) dipped into an acetone bath at room temperature to remove adherent oil and then immediately transferred to liquid nitrogen where they remained until inserted into the helium bath (usually within an hour). The temperature of the aging bath was held constant to +3°C for longer aging times. The cryostat used for the measurement of superconducting properties consisted of outer and inner dewars for liquid nitrogen and liquid helium, Stokes 6-in. booster diffusion pump and Stokes Model 212 mechanical pump, temperature controller to measure and control the temperature of the helium bath, and a superconducting solenoid with inserted search coils to provide the magnetic field and measure the magnetic moment of the specimens. A schematic diagram of the cryostat is shown in Fig. 1. An ultimate temperature of 0.85°K was reached with this apparatus. The temperature controller used is similar to the one described by Blake and chase.&apos; A 0.5 pct Allen-Bradley carbon resistor and a nichronle heater (200

Jan 1, 1968

By Joseph M. Jacisin

Fatigue tests were conducted on 2017-T4 alumium in alloy in an u1lrcthig.h vacuum of 2 x 10-lo Torr and in air. The vatio of vacuum-to-air faligue life for this ~malerial varied Jrom 3.5:1 at a strain of 2.5 X 1O-3 ill. pegr in. to 8:l at a strum of 3.3 x X ill. per 171. Sotlze pvelivtlinary data were also obtained on the faligue life of the alumirnum alloy in a dvy-nitrogen atmosphere. A dark deposit observed on the fracture surfaces of the aiv-tested specimens was identified as oxides of tr~angarzese and magnesium This observalion, and the close correlalion betaveen results obtained in vaCuum and dry-nitrogen environtments, tend to confirm that air stvongly influences the fatigue mechanism by a covrosion process. THE fatigue life of certain metals is known to increase when the atmospheric pressure is reduced. Gough and Sopwith1-2 postulated that this is due to a joint chemical and mechanical process operating in air at the surface of the metal with oxygen and water vapor playing significant roles. Wadsworth and Hutchings3 observed that aluminum is mainly affected by the presence of water vapor. Very little information is available on the fatigue properties of structural aluminum alloys in a vacuum environment. This report describes work performed on 2017-T4 aluminum alloy in an ultrahigh vacuum (2 x 10-loTorr) and in air. Some preliminary data are also presented on the fatigue life of the alloy in a dry-nitrogen environment. 1) EXPERIMENT 1.1) Test Material. The material tested was commerciaT 2017-T4 aluminum alloy which, in addition to aluminum, has an approximate composition of 4 pct Cu, 1 pct Fe, 0.8 pct Si, 0.5 pct Mg, 0.5 pct Mn, plus smaller amounts of other elements.* Some typical naturally age to a substantially stable condition. Specimens were then machined from these rods and ground to a No. 8 microfinish. In order to minimize variation in material characteristics, specimens were made from rods procured from the same lot. 1.2) Apparatus. The apparatus and test specimen used in the fatigue tests are shown in Fig. 1. The device utilized a single-cantilever beam with rotating-bending loading. Bending stress was applied to the fatigue test specimen by placing a spacer beneath the bearing support, thereby providing a constant deflec-

Jan 1, 1968

By Pradeep K. Rohatgi, Clyde M. Adams

An analysis of heal conduction in the freezing of a solution has been performed. The case considered is the semi-infinite mass of solution, bounded by a con-stant-temperature plane with one-dimensional heat flow, Numerical cooling rate and freezing rate distributions hare been calcutated for the particular case of unidirectional freezing of aqueous solutions against. a cold copper chill. The solution at each level parallel to the chill surface is subjected to a spectra of frcezing rates; the freezing rate is inilially lour., passes through a maximum, and then decreases until solidification is camplete. Arange and maximum freeeing rates are inversely proportional to the square of distance from the chill surface. The temperature of the chill surface in contact with the solution remains constant during solidification. Experimentally, it is observed that deudrite sparing increases linearly with distance from the chill surface; in the light of heat -flow analysis this means that the dendrile spacing is imersely proportional to the square root of the maximum freezing rate. SOLIDIFICATION of liquids is accompanied by rejection of latent heat at the solid-liquid interface. The over-all rate of liquid to solid transformation is governed by the rate of heat extraction. Analysis of the heat transfer in the liquid during freezing is important since it determines the freezing rate and resulting structure. A considerable amount of work has been done on metallic systems since solidification is frequently a major step in processing metals. Unidirectional freezing from heat sinks has been treated by several investigators.1-4 Much of the work has been limited to the simpler case of substances such as pure metals which freeze isothermally at a unique transformation temperature. In this case the thickness of the solid zone y, next to a chill surface. is a parabolic function of the time. 8. where a and b are constants. Eq. |1| is a close approximation giving the progress of solidification for the case in which there is a small but finite thermal contact resistance at the interface between the freezing liquid and the chill.&apos; It has been used with some success in connection with large steel ingots4 when the therma1 contact resistance is negligibly small (as is the case when water is brought into contact with the metal chill). The constant, b. becomes zero and Eq. [l] is then exact. even when the thermal properties of the chill and the freezing liquid depend on temperature. Analysis of unidirectional solidification of solutions is more complicated since the latent heat is evolved over a range of temperatures. Next to the all-solid zone in contact with the chill surface there is a solid plus liquid zone in which solidification takes place. Although the equations presented are considered quite general the numerical and experimental results are for freezing of aqueous solutions from a copper chill. I) EXPERIMENTAL PROCEDURE Solutions of potassium chloride, sodium chloride. and lithium chloride have been used. These solutions form a eutectic: a typical phase diagram is shown in Fig. 1. A solution at its liquid us temperature is poured into a tygon tube mounted on a relatively large copper chill. The chill is immersed in a freezing mixture of dry ice and acetone at -70°C. A thermocouple connected to a high-speed recorder was mounted near the top of the chill to measure the fluctuation in the temperature of chill surface in contact with the solution. In this system the progress of solidification can be visually observed through the tygon tube. After the specimens freeze to a desired height they are removed from the copper chill and stripped from the tygon tube. Longitudinal and transverse sections are cut from the specimen for micrographic examination. Specimens in the form of a thin slice are mounted on a transparent glass slide by freezing small drops of water around the periphery. They are then polished on a series of emery papers; the final finishing is done on a soft tissue paper. A Leitz Biological microscope was used for structural observations; photography was

Jan 1, 1968

By T. G. Nilan

Steels containing 0.4 and 0.8 pet C have been transformed isothermally at pressures up to 34 kbuv. Decomposilion mechanisms are so intimately related to phase equilibvia that, as the equilibria shift under high pressure, the microstruclures of the decomposition producls change, maintaining at pressure the same correspondence between a given phase equilibrium and a given microstructure as a1 1 atm. A bainitic unicvo-structure occurs in these steels at high pressure that IS observed only at 1 aim abole 1.4 pct C. This strrrcl111,e 1s ruliorzalized in terms of the effect of pressure on the transformation to lower bainite. The pressuve depetlderlce of the kinetics of pearlile formation is descrihed by an absolute rule theory amalysis. The activation volume for the transformation is 7 cu cm per mlole, which is indicative of a phase-interface transformation-rate cotntrol mechanism. This fortmulation, when expressed in terms of known solule effects on the energelics of tvansformation, gives promise of explaining the effects of alloying elemenls on hnrden-abilily, particularly that of &apos;coball. KINETIC processes in solids are functions of the primary thermodynamic variables of state: composition, temperature, and pressure. Until the development of high-pressure techniques&apos; that permitted the generation of sustained high pressure at high temperatures, metallurgical studies of such reactions were largely limited to isobaric conditions at atmospheric pressure. The data so obtained, and theoretical deductions based on these data, were necessarily incomplete For the particular case of austenite decomposition, a knowledge of the phenomenology of the reaction in terms of all the state variables should lead to a clarification of the process. This deeper understanding should facilitate a decision between conflicting theories that have been proposed to rationalize these phe- nomena. An analysis, derived from an understanding of the transformation mechanisms, may aid in the optimization of alloy steel development. The first studies of the effect of pressure on transformations in steel were made by Kulin et al. in 1952.&apos; In a study of the influence of applied stress on mar-tensite formation in a 30 pct Ni steel, they found that the martensite start (M,) was depressed 8°C per kbar* by hydrostatic pressure. Jellinghaus and Friedewold3 were apparently the first to investigate the effect of pressure on isothermal transformations above the Ms. They found that the bainite transformation rate in a 1.2 pct C, 3.8 pct Mn steel was reduced by a factor of 3 by a hydrostatic pressure of 4 kbar. In both of these investigations,2,3 the M, of the steels studied was below room temperature. Austenitizing and quenching were done at atmospheric pressure, followed by the decomposition of the metastable austenite under pressure. The maximum temperature at pressure in the bainite study3 was 350°C. Until the advent of the present high-pressure devices, it was not possible to conduct isobaric high-pressure heat treatments from austenitizing through isothermal decomposition and quenching. The exploitation of high pressure as a variable in metallurgical studies was greatly advanced by the apparatus and techniques developed by Hall4 and co-workers. Utilizing these techniques, Radcliffe et a1.5 and Hilliard6 etermined the pressure dependence of phase equilibria in the Fe-C system. Hilliard and cahn7 examined the pearlite transformation rate in an AISI 1080 steel and also in a high-purity 0.92 C Fe-C alloy at 1 atm and at 34 kbar and found a 700-fold reduction in rate at pressure in the 1080 steel but only a fivefold reduction in the high-purity alloy. In agreement with the shift of phase equilibria under pressure, the microstructures were hypereutectoid at 34 kbar pressure, whereas they are eutectoid at 1 atm. Determination of the effect of pressure on carbon diffu-

Jan 1, 1968

By N. A. Gjostein

The real and apparent dependence of the surface self-diffusion coefficient, Ds, of gold on crystallo-graphic orientation has been investigated by isolated scratch smoothing and grain boundary grooving experiments. No systematic variation of Ds with orientation was found along the [100] zone. In view of the experimental scatter in these results, however, only aniso-tropy ratios, p, greater than -1.3 would be detectable. Anomalously low values of Ds were found on the [0ll] and [110] zones when the diffusion direction lies along (the scratch or grain boundary groove is perpendicular to) these zones. By comparing these results with a previous y plot study of gold, it is hypothesized that this is not an intrinsic diffusivity effect, but rather it results from a decreased driving force for mass transfer at orientations where the y-plot curvature is negative and appreciable in magnitude relative to y. The characteristics of this type of anisotropy do not appear sEVERAL investigations1-7 have dealt with the anisotropy of the surface self-diffusion coefficient, Ds, of metals as measured by the decay of single or multiple to be in agreement with the hypothesis of fast diffusion along ledges in the surface structure. In certain cases the Fourier method of determining Ds, described in Paper I of this series9 was compared with the second moment analysis in order to determine whether or not the method of analysis affects the anisotropy ratio. While the type of analysis does influence the magnitude of the anisotropy ratio, this effect is not associated with the shape of the profile, but rather is connected with the iterative volume diffusion correction used in conjunction with the second moment analysis. It is further demonstrated that the volume diffusion correction can be too large by either method when the y-plot curvature effect is large. Certain orientations exhibit an unusual temperature dependence of Ds ; this is discussed in terms of the y-plot curvature effect and/or the influence of impurities on Ds . scratches in the surface. Depending on the system investigated, both large1"3&apos;6&apos;7 and small4&apos;5 anisotropies in Ds have been found. Although adsorbed impurities undoubtedly play an important role in determining the magnitude of the anisotropy,8 there are other factors that can give rise to an apparent anisotropy in Ds, thus obscuring the true nature of an intrinsic anisotropy in

Jan 1, 1968

By J. J. Demo

The effect of aluminum additions on the coating vale and corrosion resistance of Cr-Fe diffusiou coalings on a mild steel substvate has been studied. Aluminum additions up to 2 wt pct increase the chromium penetration rate while further additions retard it. The apparent cor$lict between these data and metallogyapkic ineasurements, which show a continuially increasing coaling thickness with aluminum addition, is discrissed. Compavisorz of corrosion resistance on the basis of equal thickness of tlre entire coating measured mnetal- ALTHOUGH ferrous metal articles are cheap and widely used, they are often quickly degraded by corrosion. To prevent or slow down the corrosion process, lographically is misleading; equal thickness of the cor-rosion-resistant portion of the coating is a bette.v basis of conzpavison. Inter difision coefFicients for Cr-Al-Fe coatings of different aluminum content have been detevmined and found to dary logarithmically when plotted againnst chromium concentvation. A general method of calculating diffusion profiles for different lrealment limes and surfuce coucentralions IS described. many types of coating are applied to steel.&apos; Among these are diffusion coatings, formed by high-temperature diffusion of selected elements into the surface, which then becomes the coating Diffusion coatings are metallurgically bonded to the substrate and show a continuously varying concentration gradient from surface to substrate. Generally, these coatings have the advantage of adhering to the substrate upon deformation of the composite. Moreover, when chromium is one of the diffusion elements, a mild steel substrate

Jan 1, 1968

By David J. Mack, Dennis R. O’Boyle

The mechanical properties of three polycrystalline intermediale Phases that have the y bvass structure were measured in compression between 400° and 900°K. At the lower testing temperatures— termed Region I— no plaslic deformalion occurred prior to brittle fracture. A1 higher temperatuves— lermed Region III—the three phases deformted plaslically for all strain rules from 1.5 to 36.0 x 10-4 sec-1. The homologous temperature for the inilialion of plaslic flow increased in the same order as tile atomic size difference between atoms in each plmse (0.50Tmp for y AgZn, 0.62Tmp for y CuZn, and 0.76 Tmp for y CuCd). The increased flow resistance oj. y CuCd above 0.50Tmp is explaitzed in terms of the more random arrangement of copper and cadmiwn atoms on the laltice sites of&apos; the y bvass slrilctlire. Plaslic deformation of the three intevmiediate phases in the smooth plaslic flow region appears to be controlled by oacancy-induced dislocation climb. RESULTS are reported in this paper on the mechanical properties of three binary intermediate phases having the complex cubic y brass structure (D82, 143m) containing fifty-two atoms in the unit cell. The structure of the prototype y brass phase, y CuZn, was first analyzed by Bradley and Thewlis&apos; based on the X-ray work of Westgren and Phragmen.2 The y brass structure can be visualized as an arrangement of twenty-seven body centered cubes (3 by 3 by 3) into a unit cell containing fifty-four atoms. From this cell the center atom and the four corner atoms are removed and the remaining fifty-two atoms are slightly displaced, resulting in the y brass structure. Approximately thirty-five binary intermediate phases that have an electron to atom ratio of 21:13 have been reported to form the y brass structure. The three y brass intermediate phases selected for this study are formed from elements in groups IB and IIB of the first and second long period. Each compound exists over a composition range that includes the stoi-chiometric composition A5BB (Cu5Zn8, Ag5Zn8, Cu5Cd8). y CuZn (a0 = 9.944A) has solubility limits extending from 57 to 67 at. pct Zn at 500°C apd melts peritecti-cally at 834°C; y AgZn (a0 = 9.326A) has a solubility range from 58 to 63 at. pct Za and melts peritectically at 661°C. y CuCd (a, = 9.596A) melts congruently at 563°C and has a maximum range of solubility extending from 58 to 64 at. pct Cd. In order to minimize coring and microporosity during solidification, the composi- tion of the compounds that form peritectically (y CuZn and y AgZn) was chosen so that the temperature difference between the liquidus and the solidus is only a few degrees centigrade. In selecting y brass compounds for this study, phases were avoided that contained a transition element or that had an electron to atom ratio greater than 1.70. Hume-Rothery et a1.3 has observed that, when the electron to atom ratio of y brass intermediate phases exceeds 1.70, atoms begin to drop out of the unit cell to maintain a constant electron to unit cell ratio. EXPERIMENTAL PROCEDURE Each of the three intermediate phases was prepared from elements having a purity >99.999 pct. Only trace quantities of impurities (<0.0001 pct) were detected by spectrographic analysis of the four elements. A master alloy of each compound weighing approximately 130 g was prepared by melting the elements in evacuated sealed quartz tubes heated in an electric furnace. Specimens having the desired diameter for the mechanical property measurements were obtained by remelting the master alloy in a Vycor tube under argon and drawing specimens from the melt into 4-mm-diam quartz tubes. To obtain a smooth surface on specimens drawn from the melt, the inside of the quartz tube was coated with a thin layer of graphite formed by thermally decompositing acetone. All specimens were imbedded in sealing wax and cut to the proper length with a diamond-impregnated cut-off wheel. The individual specimens (4 mm diam by 8 mm long) were then sealed in evacuated Pyrex tubes and homogenized at 500°C for 72 hr. Chemical composition, variations over the length of the rod (10 cm long) were generally less than 0.2 pct and the analyzed composition differed from the desired composition by less than 0.5 pct.4 Metallographic evaluation of the specimens after homogenization showed no evidence of a second phase in any of the compounds. The average grain size of the specimens after homogenization was 1 to 2 mm. All mechanical property measurements were carried out in an argon atmosphere using a compression apparatus described previously.5 Prior to applying the load to the specimen, the test apparatus was evacuated, back-filled with argon, and heated to the test temperature for 20 min to establish thermal equilibrium. EXPERIMENTAL RESULTS Mechanical properties measured as a function of temperature and strain rate for each of the three y brass phases were similar. From room temperature to the ductile-to-brittle transition temperature, only elastic deformation was observed prior to fracture.

Jan 1, 1968

By R. C. Gifkins, K. U. Snowden

The value of the index n in power ktivs for the stress sensitivity of minimum creep rale at lead is derived front results drawn from lite literature and from previously unpublished nork on commercial (99.99 pel) and high-purity (99.999 pel) lead polycryslalline and hi crystal specimens. In tests al 0.5Tm (22 to 50&apos;C) for slvesses below 250 psi, n fulls to mily for poly-cr,yslullirle specimens, single crystals, and bicrystals, and toy grain boundary sliding in bicrystals. Between 250 and 500 psi there is a tyansilion range and, for the polycrystalline specimens al least, u high-stress regime for 500 to 1500 psi where n is 5 or 6. These results are such that none of the suggested stress taws can he used to extrapolate to very loir stresses. Meclianisms for deformation in Ike grains and toy grain boundary sliding in the low-strcss regime are outlined. In particular, the mechanism for grain boundary sliding involves sliding controlled by diffusion from tensile to compressire Ledges. predictions based on this model give promising numerical agree-nicul with experiment. II is suggested that the mechanism for grain boundary sliding may he important in other circumstances, e.g., in creep of ceramic materials or superplaslicity, because it can operate with lille or no dislocation aclirity. WhEN the stress dependence of secondary creep rate is represented by a power law the values taken by the stress exponent n are found to vary between 1 and 7, see, c.g., Garofalo.&apos; In Eq. 1 11 u is the applied stress and A a constant. The case for accepting values of v = 1 rests principally upon tests at high temperatures (>0.9Tm) and there have only been isolated tests at lower temperatures (rather than plots of creep rate against stress) for which the creep rates are such that some form of Nabarro-Herring creep with n = 1 is applicable. Hanson5 and Greenwood and cole6 plotted creep rate against stress for tests made in the vicinity of 0.5Tw, and found a "creep yield", so that below a certain low stress the creep rate was linearly related to stress: these observations appear to have been subsequently ignored. Various models have been proposed which agree with a large body of experimental results in which n equals -5 at high stresses (e.g., weertman7 and McLean8). Various alternatives to Eq. [1] have been proposed principally as a means of unifying creep data, but sometimes, it seems, in order to obviate the necessity for assuming a series of regimes of deformation associated with the various values of n; further refer- ence to these will be made in the section on stress laws. This paper calls attention to extensive results which show n = 1 for the creep of lead at room temperature (0.5 T,). RESULTS Fig. 1 is a composite diagram based on figures in the literature6,9,10 with additional results obtained by the present authors and their colleagues11,12 in the course of a number of investigations not directly concerned with stress sensitivity. In Fig. 1 In creep rate is plotted against In stress. The curves show results for two kinds of material. Lead I is of commercial purity (99.99 pct Pb) and lead IT a specially refined material, hydrogen-purified to remove oxygen; it contains 99.999 pct Pb. Curve A is for lead I in polycrystalline form (grain diameter 0.02 to 0.05 cm) at room temperature (22&apos; to 26°C). Curve B1 is for lead I, polycrystalline, tested at 50C. Curve B2 is for lead 11, polycrystalline (grain diameter 0.02 cm), tested at room temperature (22 O- Curves C to F relate to tests made of bicrystals of lead 11: all of the same nominal orientation ("Y" in Ref. 12). Curves C and V are for creep within the component crystals of the bi crystals at 22°C (AB and CD in Fig. 2). Curve E is for creep measured in a gage straddling the boundary, approximately 0.15 mm either side (BC in Fig. 2). Curve F shows rates of grain boundary sliding (as distinct from strain rates in the other curves), obtained by averaging the offsets of six marker lines on the bi-crystal boundaries. The principal feature of the results is that the stress sensitivity falls into two distinct regimes, according to whether the stress is below approximately 250 or above 500 psi (there is a transitional range between 250 and 500 psi). The new result is that below -250 psi two of the curves (A and BI) give a value of n 1, and the other curves also drop below n - 2 to -1.5 but do not extend to low enough stresses to show clear evidence of n 1. At very high stresses the curves tend to give values of n - 6, as previously determined in other investigations. Curve R2 for the high-purity lead in polycrystalline form at room tenlperature almost merges with B, and thus gives new significance to the values for stresses of 150 and 200 psi; previously&apos;3 these points had seemed to fall away from the curve of slope -3, but they now can be seen as almost completing a transition to n = 1. It should be noted that there was originally considerable apparent scatter in the results for the high-purity lead. However, this was found to be associated with annealing conditions or variations in residual content of oxygen and curve B2 was constructed using the highest rate (i .e., the rate for the purest lead) determined for each stress during the course of various investigations over the years: altogether, some forty tests were used in constructing curve R2.

Jan 1, 1968

By J. F. Smith, J. R. Ogren, N. J. Magnani

The uapor pressrcres of magnesium over binary alloys of magnesium with twelve of the yare-earth eletnetzts have been measured by the Knudsen effuion method in the temperature range 675° to 910°K. These vapor-pressure measurments were combined with data concerning the tevtrlitzul magnesium solubility and the vapor pressure of pure magnesinm to evaluale the standuvd free energies of pluase jormation. These free-etzergy values indicate that the CsCl structures of the heacy rave earths tend to be somewhat less stable than those of the light rare earths. This dif-]eying- behaviov covrelates with differences which have been obsevz~ed in other alloy systetns wherein a phuse appeurs, disappeavs, or changes crystal stvucture as the atomic number of the rare-earth com-ponent is changed. This behauior also appears to correlate with the struclurul rariations within the rare-earth elements themselves, and it is speculated that cariations in the spatial extent of the 4f orbitals are responsihle. STUDIES of the phase relationships and crystal structures in the binary systems between rare-earth metals (lanthanons) and magnesium are extensive but far from complete. However, the currently available information1-10 does produce a rather interesting pattern. This is illustrated in Table I. If one excludes europium and ytterbium from consideration because of their generally atypical behavior, it can be seen from the table that the phase relationships in the magnesium-rich regions show a distinctly different pattern for the lighter lanthanons as compared to the heavier lanthanons. For the lighter lanthanons, LnMg2 phases occur from lanthanum to gadolinium with the cubic MgCu2 structure, LnMg3 phases occur from lanthanum to terbium with the BiLi3 structure, and magnesium-rich phases occur from lanthanum to gadolinium with stoi-chiometries between Ln5Mg42 and LnMg12. In contrast, for the heavier lanthanons, those LnMg2 structures which have been examined have the hexagonal MgZn2 structure, LnMg3 phases have not been observed beyond terbium, and the magnesium-rich phases occur with the a manganese structure near a stoichiometry of Ln5MgZ4. The heavy lanthanon-magnesium systems thus appear to be analogous to the Y-Mg system""2 wherein YMg has the CsCl structure, YMg2 has the MgZn2 structure, and the region Y4Mgz5-Y5Mg24 has the a manganese structure, and no other intermediate phases are observed. Similarity in alloying behavior between yttrium and the heavy lanthanons occurs commonly, and on this basis it seems likely that LnMg2 phases will be found with the MgZn2 structure in the binary systems of dysprosium, thulium, and lutetium with magnesium when the appropriate investigations are made. In the case of the magnesium-rich phases of the lighter lanthanons, only the Ce-Mg phase relationships have been investigated thoroughly and in detail, and until similar investigations are made for the other systems there will remain questions as to which magnesium-rich stoichiometries represent equilibrium phases and what systematic variations occur in the sequence from lanthanum to gadolinium. Thus the data in Table I show that only the LnMg phases occur with the same crystallographic structure throughout the sequence from lanthanum to lutetium. It was speculated that the relative stability of these LnMg phases might vary from one lanthanon to the next in such a way as to presage the differences which occur among the more magnesium-rich lanthanon-magnesium phases. On this basis the present investigation of the thermodynamics of phase formation was Gndertaken for the LnMg phases. PROCEDURE AND RESULTS A generalized phase diagram for the lanthanon-rich portion of a lanthanon-magnesium alloy system is shown in Fig. 1 where ß represents a high-temperature bcc

Jan 1, 1968

By E. H. Rennhack

When cast hypoeutectic Zn-Ti alloys are rolled, the TiZn15 compound particles arising from eutectic decomposition form a network of fibers promoting improved creep resistance.&apos; The effect is magnified with increasing titanium content and extends to hy-pereutectic concentrations. Strip produced from the latter-type alloys, however, also contains large, primary crystals of the compound that tend to initiate cracking during subsequent fabrication operations. In a study of the influence of various casting modifications on the size and distribution of these crystals, the phase relationships existing between the eutectic and the TiZnIs intermetallic compound in the Zn-Ti system were of major interest. Although several in- vestigators1 4 have explored the equilibria within this compositional range, their results show considerable lack of agreement. Consequently, with the exception of the solvus boundary, the constitution of this system containing up to approximately 1.0 wt pct Ti was . The findings are reported in the present note.

Jan 1, 1967

By E. Miller, K. L. Komarek

Equatiorzs have been derived which related maximum solid solubilities in semicondcting compounds having retvograde solidus curves with 1iqllidus data. Liquidus curves in Lke Pb-Te, Pb-Se, ard PB-S systetris have been defermined by thertrzal aralyses. Fvotrz expevimental maximum solibilities ia CdTe, PbTe, uxd PbS vetvograde tetrperatures hale beep1 calculated. TIze resllts support the concept that under certaiz conditiots pronounced itjlections in the liquidis curves arc indzcatiz:e of retropade solidus curves and that the tenlperatltre of the lmaximum solid solubility will be close to the temperature of the point of inflection in the liquidus curve. The maximum solid solihility within a gvoup of homologous cottrpoods SeetlLs to increase with increasing flatness ol the liquidus curvres. The phenomenon of retrograde solubility in metals, i.e., maximum solubility in a solid terminal phase in equilibrium with a liquid phase, has been theoretically predicted by Van aar&apos; in his calculations of hypothetical binary phase diagrams. It was not until 1926, however, that retrograde solubility was experimentally verified in the Zn-Cd system.&apos; Since then many sys- tems with retrograde solubility have been found, so that at present approximately fifty binary diagrams with a retrograde solidus curve are known.3 Meijering4 has critically appraised the accumulated data and has presented calculations which alloy predictions as to whether or not a solidus line will be retrograde. Interest in retrograde solubility increased when it was found that the solidus curves of germanium and silicon alloyed with a great many doping elements are retrrade. The problem was treated thermody-namically by odkinson,% d all available data on solid solutions in germanium and silicon were summarized by Trumbore.7 Although it is to be expected that intermetallic compounds will also exhibit retrograde solubility, experimental evidence is much more limited. Until now retrograde solidus curves have been reported for the compounds de,&apos; be, Ps:" ne," SnSe," and SnS.13 All these compounds are semiconductors, and the solidus curves were usually obtained by determining the carrier concentration at room temperature of samples equilibrated at elevated temperatures and then quenched. It has been hown,&apos;&apos; however, that it is not always possible to quench in the equilibrium compositions from above a certain temperature. Theoretical discussions have either explicitly excluded intermetallic compounds4 or not treated them with respect to retrograde slubilit.j In the following a thermodynamic treatment of retrograde solu-

Jan 1, 1967

By P. M. Robinson, J. S. LI. Leach

The heats of solution oj&apos; indiurrr, tin, lend, nrzd tellurium have been calculated from the measured heat effects when mechanical mixtres of indium and telLuium tin and tellurium, and lead and tellurium were added to liquid bismuth. The results are in good agreement xith publislzed values.s for the separate sollction of each eleltzent in bismuth. The heats oj solution of cadmium and tellurium calculated from the rneasuved heat effects on adding trechanical mixtures of these elements do not ugree zc,itl the published values jbv the separate solution of each element. It is shown that at 623°K Ile interaction between cadmium and tellurium dissolved in liquid bismuth is strong enough to led lo preciPitation of solid CdTc. The heats oj- jor-mation of CdTe at 273" nd 623°K (1)-c crilculated fi-or the measured heat ejlfecls. The calcnlaled az&apos;erage deviation from the Kopp-l\&apos;ez?,zunrz rule fov solid CdTe is less than 0.06 cat per g-atom- C over this lertzperalure range. Tlze importance 0.f these oDserl.ations to the determination of heals of formation hy metal solution calorimetry is considered. LIQUID metal solution calorimetry is a convenient method for determining the heats of formation of solid compounds. In this technique the heat of formation is the difference between the measured heat effects on dissolution of the compounds and of mechanical mixtures of the components in the liquid metal.&apos; The heat of solution of the mechanical mixture may be calculated from the measured heat effect. At infinite dilution of the solutes, this heat of solution is equal to the sum of the heats of solution of the separate components. If the heat of solution of one of the components is known, the value for the other can be derived; if both are known, they may be used to check the accuracy of the calorimetric technique. The heats of formation of the tellurides of cadmium, indium, tin, and lead have recently been measured by metal solution alorimetr. The heats of solution of indium, tin, lead, and tellurium at infinite dilution in liquid bismuth at 623"K, calculated from the measured heat effects on solution of the mechanical mixtures, are in good agreement with the published values. The heats of solution of cadmium and of tellurium calculated from the measured heat effect on solution in bismuth at 623&apos;K of mechanical mixtures of cadmium and tellurium, however, do not agree with values estimated from the literature. 1) EXPERIMENTAL PROCEDURE AND RESULTS The Heats of Solution of Indium, Tin, Lead, and Tellurium in Bismuth. The heat effects were measured when mechanical mixtures corresponding to the compounds In,Te, InTe, In2Te3, In2Te5, SnTe, and PbTe were dissolved in bismuth. The calorimetric procedure and the method of calculation have been described elsewhere.&apos; The heats of solution of the mechanical mixtures were obtained by subtracting the change in heat content per gram-atom of the sample between the addition temperature (273°K) and the bath temperature (623"K), (H623°K - H273°K)S, from the measured heat effects. The calorimeter was calibrated with pure bismuth. The reported values of the measured heat effects are based on (HGoK - ^273oK)Bi = 4.96 kcal per g-atom.3 The measured heat effects are found to be linear functions of the solute concentrations of the bath in the dilute solution range. The values, extrapolated to infinite dilution, are listed in Table I, together with the heats of solution of the mechanical mixtures calculated using the published values of (H 623°K - H273°k)s for indium, tin, lead,3 and tellrium. All the error limits quoted in this work represent the spread of values obtained. The heats of solution in liquid bismuth at 623°K of mechanical mixtures of indium and tellurium in four different proportions were determined. Values of the heats of solution of the two components were then calculated from the resulting four simultaneous equations: The heats of solution at infinite dilution of tin and lead in liquid bismuth at 623°K were calculated from the heats of solution of the mechanical mixtures of tin and tellurium and of lead and tellurium using the heat of solution of tellurium calculated above. These values of the heats of solution are listed in Table I1 together with some published values for comparison.

Jan 1, 1967