Search Documents

By G. W. Toop

In a recent publication,31 Darken has derived an equation to describe thermodynamic behavior in ternary metallic solutions with compositions near pure component 1: Eq. [I] is understood to be a general equation, consistent with the ternary Gibbs-Duhem equation, which is proposed as a logical formalism in view of observed behavior in some binary metallic solutions31'32 rich In Eq. and am are constants obtainable from the 1-2 and 1-3 binaries. The parameter 023 may be determined from measurements on the ternary The purpose of this discussion is to compare Eq. [I) or [3] with other ternary formulations involving binary terms, within the regions of validity of Eqs. [I], [2], and [3]. First, the ternary point is considered to be at the intersection of two composition paths, one with constant N1 and another with constant N2/N3 as shown in Fig. 10. The terms in Eq. [3] may be related to the binary points shown by multiplying the first term on the right-hand side of Eq. [3] by N2 (1) /l -N1, the second term by the third term by and the fourth term by each multiplier being unity: It should be noted here that no suggestion has been made that either the binary or the ternary systems form regular solutions. However, Eq. [5] and hence Eq. [3] shows that the contribution made to the ternary excess free energy from the 1-2 and 1-3 binaries has the same form as for a regular ternary system.1 Before considering the term a23 for the above case, a second geometrical relationship is examined with the ternary point at the intersect ion of three composition paths with constant N1/N2, N2/N3, and Nl/N3, respectively, as shown in Fig. 11. For this geometry, ternary values of NZ and N3 in terms of the binary values shown may be substituted into Eq. [I]. Then by making use of identities of the form Eq. [6] contains terms that are similar to those in a ternary regular solution formulation34 based on the geometry shown in Fig. 11. Although at finite concentrations, unless the 1-2 and 1-3 binaries form

Jan 1, 1968

By Akio Suzuki, P. G. Wahlbeck

AS a part of a study of the vaporization of transition metal-chalcogen systems, the vaporization reactions for the Ti-Se system have been studied. In order to establish vaporization reactions it is important to determine the identity of vapor species in equilibrium with the condensed phases. In some cases, it is possible to deduce the identity of vapor species through observations of composition change of the condensed phase with which the vapor is in equilibrium. Determination of vapor species in equilibrium with condensed phases should precede vapor-pressure measurements and is necessary for proper thermodynamic analysis of vapor-pressure data. Bear and McTag-gart' reported that vacuum heating ot TiSea at 950°C produced a residue with a composition of 1.7 Se/Ti atomic ratio units. Analyses of condensed phases existing for the Ti-Se system have been performed by Bernusset,2"4 Gron-vold and Langmyhr,5 Hahn and Ness,' and Ehrlich.~ Results and conclusions of two types of experiments are described herein: 1) experiments where samples of known composition were vaporized followed by chemical analysis of residues and 2) experiments where the vapor species were identified by means of a mass spectrometer. Experimental Section. Sarnple Preparation. Samples of TiSe2 were prepared in a sealed, evacuated quartz ampule by heating to 1000°C stoichiometric amounts of selenium of 99.999+ pct purity obtained from the American Smelting and Refining Co. and titanium of 99.2 pct purity obtained from A. D. Mackay, Inc. After heating, the sample was ground and reheated to insure homogeneity. Samples containing less selenium than TiSez were prepared by mixing amounts of titanium powder and TiSez appropriate for the desired composition; the titanium and TiSez mixture was heated in the same manner as described for TiSe2. Analyses of titanium selenide samples contained in quartz crucibles were performed by gravimetric oxidation in oxygen at 800°C; the products of the oxidation were solid TiOz and gaseous Se02. The mass of the original sample and the mass of TiOn determined the Se/Ti atomic ratio. The sample of TiSen used in these experiments had a composition of 2.04 Se/Ti atomic ratio units. The compositions for all samples reported were analyzed by this method. Va/!orization Experiments. Samples of titanium selenides were vaporized in tungsten Knudsen crucibles. Some vaporization experiments were carried out in glass vacuum lines followed by chemical analyses of residues, and some vaporization experiments were performed with a Bendjx mass spectrometer as described previously.8

Jan 1, 1967

By T. E. Scott, O. G. Koepke

DURING research currently in progress the need arose for interplanar angles and planar spacings to analyze crystallographic data obtained from hcp yttrium. In the absence of such existing information, a program was written in Fortran-11 language and processed on an IBM 7074 computer. The program and results have been assembled in report form to make them generally available.' Of the possible combinations of, only those most frequently encountered were employed. The ranges of h, k, and 1 involved were: However, not all combinations and permutations of the above appear in the tabulation because redundancies occur in several cases. Nevertheless, fifteen types of planes and all their equivalent planes have been included, giving a total of 109 sets of Miller-Bravais indices.

Jan 1, 1967

By P. Niessen, W. C. Winegard, C. J. Beingessner

DURING the last 10 years, several grain-growth studies have been made using zone-refined metals with controlled amounts of solute to elucidate the interaction of solute with moving boundaries. In all these studies, it was more or less implicitly assumed that the alloys used were, after recrystallization and grain growth, homogeneous within the grains with respect to solute and lattice defects. This note deals with observations made on microstructures originating from solidification of dilute alloys and from grain growth. Briefly, the experimental procedure used in these studies was the following: zone-refined cadmium and master alloys were melted and cast in Pyrex under vacuum to produce bars 14 mm in diam and about 150 mm long. These bars were cut into 8-mm-thick slices which were mechanically and chemically polished. The specimens were then deformed 30 pct in compression and given a 1-week anneal at 260°C in argon. After this anneal, a second deformation produced completely recrystallized samples 4 mm thick. The time-temperature controlled anneals were carried out in a bath of silicone oil. After the grain-growth anneal, the specimens were polished in Gil-man's' solution (33 g CrOs, 6 g NazSO, in 100 ml of water). Several etches were used depending on the alloy investigated, but mostly a mixture of concentrated HC1 and HNOj (98:2 vol) was employed. In all the alloys examined, the ease with which substructures could be revealed depended strongly on the crystallographic orientation of the surfaces of the grains. However, very frequently the microstructures to be discussed here etched up over broad areas comprising several grains. Fig. 1 is a micrograph of a Cd-0.05 at. pct Mg alloy annealed for 100 sec at 270°C. Different substructures are seen in this photograph. A denotes the now existing grain boundaries. The well-defined lines and points marked B are the remains of a solidification substructure. The lines are boundaries between cell colonies, and the points are nodes located on regular two-dimensional cells. This cellular structure has the same appearance as that found by weinberg2 for rapidly quenched Zn-Au alloys. The "ghost boundaries", marked C, are very similar in appearance to a grain boundary array in a polycrystalline sample. Repeated polishing and etching showed that all the substructures observed were three-dimensional. To date, the ghost boundaries have been clearly observed in all samples containing 0.005, 0.01, 0.05, and 1 at. pct Mg, and in samples containing 0.01 at. pct Zn. Attempts to outline these ghost boundaries in cadmium alloys containing 0.01 at. pct Ag and Au were only partially successful. In these alloys, parallel lines, having a resemblance to the ghost boundaries in the Cd-Mg and Cd-Zn alloys, were observed, but it was not possible to obtain complete arrays of ghost boundaries which extended over several grains. It is possible that a different etch than that presently employed would reveal the ghost boundaries in the Cd-Au and Cd-Ag alloys as clearly as in the Cd-Zn and Cd-Mg alloys. A close examination of the ghost structure showed that it consisted of linear etch-pit arrays, Fig. 2. The ghost boundaries were resolvable even in grains which showed over-all faceting due to the etching, as seen in the corner of Fig. 2. The general appearance of the ghost structure suggests that it originated during grain growth. This is supported by the observation that the mesh width in the ghost-boundary array generally increased with increasing final grain size. To test whether the ghost structure was formed during the long homogenizing anneal or during the grain-growth anneal, some as-cast samples were deformed and given a grain-growth anneal. This anneal was terminated by air cooling or

Jan 1, 1967

By G. R. St. Pierre, L. M. Adelsberg, R. Speiser

OXIDE platelets have been observed'-3 in oxidized tantalum adjacent to the metal-oxide interface, Fig. 1. The origin and identity of the platelets are important with respect to the proposal of an acceptable mechanism of tantalum oxidation. At reaction temperatures below 750°C, it has been established that the platelets

Jan 1, 1967

By R. A. Oriani

The partial molal volume of hydrogen is one of the parameters that describe the elastic interaction between the solute and the stress fields about inclusions, dislocations, and cracks. As such the partial molal volume is probably of importance in the elucidation of phenomena such as hydrogen embrittlement and hydrogen yield point. A knowledge of this quantity would also be helpful in thinking about the state of dissolved hydrogen in iron. However, because of the very low lattice solubility of hydrogen in iron the usual ways of determining the lattice expansion are not practicable. It is therefore of interest to apply the thermodynamics of stressed bodies to two sets of measurements of the effect of elastic stress upon the permeability of hydrogen in order to deduce a value of the partial molal volume, VH, of hydrogen dissolved in a iron. Beck ..' and previously de Kazinczy, observed that a uniaxial tensile stress increases the permeability of hydrogen in iron and in various steels. Beck et 01. employed Armco iron and A.I.S.I. 4340 steel, whereas de Kazinczy used a steel the composition of which was 0.13 C, 0.23 Si, 0.46 Mn, 0.006 P, and 0.038 S. Upon releasing the stress the permeability increment disappeared if the stress was below the elastic limit. Both investigators employed cathodic charging to introduce the hydrogen. de Kazinczy measured the permeation through a thin-walled tube by collecting the gas, whereas Beck et al. measured the permeation through sheets of various thicknesses by a very sensitive electrochemical technique. Both investigators measured the steady-state permeation at constant rate of hydrogen ion discharge, and Beck measured in addition the hydrogen diffusivity by a time-lag technique which is independent of the boundary conditions. Beck et al. and de Kazinczy found a linear relationship between log (J,/Jo) and the stress, where Ju/Jo is the ratio of the flux of hydrogen when the metal is under uniaxial tensile stress, a, to the flux under zero stress, for the same temperature and charging current. Beck et al. found in addition that the diffusivity of hydrogen is not changed by stress. Both investigators concluded that the observed change in permeability is due to an increase in hydrogen concentration, and furthermore that the increase in concentration is due directly to the thermodynamic effect of stress upon concentration. Accepting this assessment of the situation for reasons given below, one may use the equation3j4 in order to evaluate I/H, the partial molal volume of hydrogen. This equation is valid for the domain of a/E «¦ 1 (where E is the Young's modulus) and under the assumption that hydrogen expands the lattice isotrop-ically. From the data of Beck el al, one calculates V7H - 2.0 cu cm per g-atom, and from those of de Kazinczy one obtains 1.8 cu cm per g-atom. That the increase of concentration with stress is indeed of thermodynamic origin is attested to by the facts that the experimental results conform to the thermodynamic relation, Eq. [I], and that the results are the same whether a pure iron1 or each of two different steels172 is used. Neither of these facts wou1.d necessarily be expected if the effect of stress were, rather, to increase the ratio kn/k, of the kinetic factors of the following competing reactions: H(ads) — H (dissolved) Such a change of kinetics at the surface could be an alternative explanation of the effect of stress on the permeability. Although this writer does not deem this explanation to be the correct one for the reasons given above, it must be admitted that unambiguous proof that the phenomenon has a thermodynamic origin does not yet exist. Two kinds of experiments may be suggested. One is to plate a variety of metals on the input surface of the steel and repeat the stress experiment at a variety of hydrogen charging currents. The other is to employ somewhat thicker specimens in order to be able to apply uniaxial compressive stress. Eq. [I] shows that ln(c,/c,) depends on the sign of the stress, but it is difficult to see a physical basis for which k2/kl would depend on the sign of a. The present value of V^ in a iron agrees with phragmen's5 estimate, which he based on comparisons with the lattice expansion by hydrogen of titanium, zir-

Jan 1, 1967

By M. Garfinkle

LITERATURE data1'3 have suggested that the resolved shear stress necessary to initiate slip in a particular slip system in tungsten single crystals is strongly dependent on the tensile orientation of the crystals. This orientation dependence is contrary to the critical resolved shear stress criterion. Because the Schmid factors for slip on particular {110}( I l l), {112}(Ill), or {123}(111) slip systems in a (100) oriented tungsten crystal are virtually identical to the respective Schmid factors for a (110) oriented crystal, slip should initiate on the same system in both orientations, independent of the values of the critical resolved shear stresses. Thus, it would be expected that, for a critical resolved shear stress model to hold, the proportional-limit stress for these two orientations must be similar. The expectation of similar proportional -limit stresses has not been borne out by reported experimental observations. Rose et nl.' reported that the proportional-limit stress for crystals near the (110) orientation was 92,000 psi, approximately three times that of (100) oriented crystals (31,000 psi). Garlick and probst2 reported greater than a fourfold difference. Most recently, Beardmore and ~ull~ examined tungsten crystals with orientations along the edge of the standard stereographic triangle and showed a gradual increase in proportional-limit stress from 28,000 psi for the (100) orientation to 93,000 psi for the (110) orientation. Again, the difference was more than threefold. As has been emphasized by these investigators, the apparent gross variation of proportional-limit stress with orientation precludes any meaningful analysis of slip mechanics using a simple critical resolved shear stress relation. The purpose of the present communication is to report that, by use of refined strain-measuring techniques, the proportional-limit stresses for the (100) and (110) orientations are quite similar. Obviously, to determine accurately the value of the proportional-limit stress, which is by definition the stress at which nonlinear stress-strain behavior first occurs, the method of measuring strain must be capable of high accuracy. The investigators cited used as the measured elongation the crosshead displacement of the tensile machine. This method, however, introduces extraneous strain contributions from the load train. Because these extraneous contributions are considerable in the initial portions of loading (as has been well-documented in the literature) the proportional-limit stress measurement, dependent on the deviation of a line from linearity, can be significantly affected. During the course of a recent study, room-temperature strain was measured directly on several (100)-and (110)-oriented tensile specimens axially oriented within 5 deg of the desired direction. Each specimen was fitted with two foil strain gages mounted on opposite sides of the 0.08-in.-diam reduced section. The tensile specimens were loaded at a crosshead speed of 0.01 in. per min on an Instron Universal Testing Machine. Strain was monitored through an external bridge circuit in which the specimen strain gages comprised two arms. The bridge output was recorded against the applied load. A strain of 2 x 10"" could be readily detected by this method. Some specimens were subjected to conventional loading while the load for others was cycled between zero and continually increasing values until the first deviation from linearity was observed. The results of these methods were similar, and the stress at which nonlinear behavior occurred was considered the proportional-limit stress. The proportional-limit stresses measured in this study are approximately 5000 and 6500 psi for the ( 100) - and ( 110) -oriented crystals, respectively, a range of values almost a magnitude less than those reported previously. Representative curves are presented in Fig. 1. Because of the nature of the measurements made, the point of departure of a line from linearity is often debatable. While the load-strain curve for the (100) -oriented crystals made a relatively abrupt deviation from linearity, the curve for the (110) -oriented crystal was more gradual, so that the actual point of tangency may be at a lower load than reported. Thus, the difference in values for the proportional-

Jan 1, 1967

By S. Shapiro, G. Krauss

RECENT investigations1 3 of the products of marten-sitic transformation in Fe-Ni and Fe-Ni-C alloys have made use of light microscopy to describe mar-tensitic fine structure. The application of conventional metallographic techniques to this problem was possible because of the similarity of distributions of parallel striations developed by etching polished surfaces to distributions of transformation twins which are positively identified in thin films by transmission electron microscopy. The surface striations frequently are not well-defined, and could also be due to, for example, rows of etch pits which are not resolved by the light microscope. This note describes the etching effects revealed by examination of surface replicas of mar-tensite in the electron microscope. The application of a replica technique both extends the observations of fine structure made with the light microscope and allows the results of conventional metallography to be used with more confidence. Samples of an Fe-33 wt pct Ni alloy were used for this study because of the detailed knowledge of the fine structure of martensite which has been developed'-4 for alloys of about this composition. Samples transformed to martensite at -120°C, and transformed samples heated to 340°C to effect a small amount of reversal of martensite to austenite, were examined. Surfaces were first prepared for replication by elec-tropolishing in a chromium oxide-acetic acid electrolyte at a current density of 0.1 amp per sq cm and a temperature of 15°C or a perchloric acid-acetic acid electrolyte at a current density of approximately 2 amps per sq cm and a temperature of 15°C. The polished surfaces were then etched for 4 to 7 sec by immersion in a solution of equal parts HC1, HNO,, and H20. Application of the etchant for this period of time produced discrete attack of certain features without loss of resolution due to overlapping of areas most susceptible to etching. The etched surfaces were replicated by 1) preshadowing with Pt-Pd alloy at an angle of 20 to 30 deg, 2) depositing a thin carbon film, and 3) stripping the film and shadowing material by immersion in a 5 pct nital solution. Two types of etching effects were observed by examination of the surface replicas in the electron microscope: l) continuous striations centered at the bottom of long grooves or the tops of pyramidal elevations on the sample surface, and 2) high densities of fine etch pits. Examples of both types of features are shown in Figs. 1 to 4. The striations are in each case continuous and have the same characteristic configurations as do transformation twins in martensite. Fig. 1 shows that the density of grooves decreases toward the edge of a martensite plate and Fig. 2 shows a region where the striations are of varying length. Similar examples of transformation twin arrangements determined by transmission electron microscopy of thinned foils of martensite have been shown in the literature,'~ and, based on these similarities, the striations and their associated grooves or mounds are considered to be evidence for the presence of transformation twins. The transf~rmation twins in martensite are on the order of l00 A thick, much too fine for resolution by the light microscope. It appears that orientation-dependent etching of the matrix martensite about the twins results in grooves or surface elevations which

Jan 1, 1967

By B. Chalmers, S. Wojciechowski

THE structure of the equiaxed zone of several A1-Cu samples mechanically stirred during unidirectional solidification was examined. The stirring was produced by rotary oscillation of the mold about its vertical axis.' It was found that in Some samples the structure is not of the same type over the whole of the equiaxed zone; it consists of regions with two different etching responses. Fig. 1 shows this structure in a Al-1 wt pct ku sample. The lighter etching regions with a coarse structure form something like a network and the darker etching regions with a finer structure can be observed as the continuation of the coarse structure inside this network. The difference in size and shape of the dendrite branches (they are rounded in the coarser structure) is similar to that found by Williamson and Chalmers in ice crystals solidified in undercooled water: when the amount of undercooling was small, the ice crystals were more rounded and coarser than these solidified with a larger amount of undercooling.' It seems justified to conclude that the observed structure resulted from solidification under different thermal conditions: the coarser structure solidified first out of the "purer" liquid and with a smaller amount of undercooling and the finer was formed later out of solute-enriched liquid under conditions of much more rapid heat extraction. A considerable change in the heat flow conditions at the later stages of solidification can be easily understood by taking into account that the coarser crystals form a continuous network and the amount of trapped liquid is relatively small; hence the contribution of latent heat is much smaller in the later stages of solidification. The difference in structure and etching characteristic reflects a difference in composition between these two regions. It was found that the darker etching re- gions are harder (30.4 to 31.3 HV5) than the lighter etching ones (25 to 26 HV5). A similar type of structure was found in a A1-4 wt pct Cu sample grown by Czochralski method. Fig. 2 shows the structure in the lower part of a sample grown slowly and then decanted by a rapid removing of the sample from the melt. In a few places trapped liquid solidified in the same manner as in the sample shown in Fig. 1.

Jan 1, 1968

By Paul J. Fopiano

SOME relationships between the flow characteristics of iron single crystals of 99.9 pct purity and the behavior of imperfections have been investigated. X-ray rocking-curve measurements and etch-pit counts were made as a function of plastic strain, and compared to the stress-strain curve obtained on a modified Polyani tensile machine. Crystals grown from rolled strips of vacuum-melted iron by the strain-anneal method1 had a high preference for a (110) longitudinal direction and a (211) face normal. The tensile specimens were prepared from 2 by i by 0.040 in. single crystals having a gage area of 3 by \ in. Rocking-curve measurements were carried out with a highly perfect germanium monochromating crystal in which the dazz spacing was matched to that of the dZl1 in the ir0n.l Well-collimated CuKal radiation was used throughout. These procedures practically eliminated errors due to geometrical and wavelength resolution. Inasmuch as the rocking-curve half breadth may vary markedly from point to point in the specimen being irradiated, the crystals were strained in place by mounting a hydraulic loading device on the double-crystal spectrometer. The rocking curves were taken after each increment of strain in the unloaded condition, since no observable difference was found in the rocking-curves between the loaded and unloaded states. The rocking-curve half breadths of the as-grown specimens were in the range 90 to 120 sec of arc when the beam irradiated an area of about -£ by -& in. on the specimen. DeMarco and weiss3 have shown that, for a well-colli- mated X-ray beam, irradiating about 10"! sq in. of the very same material, half breadths within 10 pct of the Darwin natural half breadth were observed. Since the rocking-curve specimens were stressed by the load-unload technique, the strain achieved at any given stress depended on the time of holding because of low-temperature creep. Fig. 1 shows the rocking-curve half breadth (also area/peak height) as a function of plastic strain for a relatively short holding time (2 to 5 min) at each stress level. For strains less than 0.1 pct the rocking-curve breadth is essentially constant; it is only for larger strains that there occurs a significant increase in this breadth. Where the holding times at each stress level were longer (by well over an order of magnitude) there occurs a significant increase in the rocking-curve breadth only after plastic strains of the order of 0.6 pct had been introduced into the specimen. This observation is related to the time dependence of creep phenomena and emphasizes the difficulty in comparing data obtained by two such different straining methods. Etch-pit results were obtained using a 2 pct nital etch on specimens strained in the range of 0 to 1 pct. Prior to etching, all specimens were annealed for 3 hr at 150°C, the carbon content being sufficient to decorate the dislocations for strains of at least 1 p~t.~ The data points were all taken from parts of the same single crystal which had been strained with short holding times at stress in increments of strain of the order of tenths of 1 pct. The (211) plane is particularly difficult to etch-pit in vacuum-melted iron and therefore it is felt that these values are as much as an order of magnitude low. Fig. 2 shows the etch-pit density as a function of plastic strain. The smooth curve passing through the data points is not meant to infer a quantitative correlation with the rocking-curve data. What is of interest, however, is the change in etch-pit density in the region of 0.2 pct plastic strain. The first three increments in strain (points 2,3, and 4) did not produce a measurable change in the etch-pit density while subsequent increments did produce a measurable change. While the absolute values of these results do not appear to be cor-

Jan 1, 1967

By J. G. Eberhort

ThE literature of surface phenomena shows that, except for most of the rare-earth elements, surface tensions have now been determined for almost every liquid metal. The situation for liquid metal oxides is, in contrast, characterized by a great scarcity of surface-tension data. A surface-tension correlation between these two classes of substances has been found which provides a means of estimating unknown liquid-oxide surface tensions from the corresponding known liquid-metal surface tension. Lf the surface tension of the liquid metal is a(M) and that of the liquid metal oxide is o(M,Oy), then oxides of all stoichiometries can be brought into one correlation if is plotted against with the surface tensions taken at the respective melting points. The available data is displayed in this fashion in Fig. 1 where the relationship between the surface tensions of the two classes of liquids is found to be The correlation in Fig. 1 is based on data found for nine liquid metal oxides and the corre- sponding liquid metals In cases where several sur-face-tension determinations were available on the same substance, higher values were generally favored over lower ones because they usually indicate greater Sample purity. All of the metal-metal oxide pairs are in good agreement with Eq. [I] except for B-Bz03. The reason for the departure of this pair from the correlation is not understood. To estimate the surface tension of other liquid metal oxides the corresponding liquid-metal surface tension must be found. A nearly complete bibliography of the surface tension of liauid elements is available in the 46th edition of the Handbook of Chemistry and physics. Some additional references on metals are included here for convenience Se,26Sr,'?ThanduZ5). It is also possible to estimate the surface tension of a solid metal oxide or metal from the corresponding liquid-state data. As a liquid material is cooled through its melting point the surface tension increases abruptly by an amount Ao. bondi' has estimated that the maximum value of Aa at the melting point is Ao = Ahf/A [2] where Alzf is the heat of fusion per atom and A is the area per atom in the interface. Thus with heat of fusion and crystallographic data the surface tension of a solid at the melting point can be estimated as o + Ao.

Jan 1, 1967

By A. H. Larson, L. G. Twidwell

DURING the roasting of zinc sulfide concentrates and by-product recovery from flue dusts, the zinc sul-fate phase may occur in various stages of the processes. In addition to zinc sulfide, other sulfide phases are usually present such as CdS, PbS, CuzS, and FeS. Consequently, the effect of these sulfides on the thermal decomposition of ZnS04 was investigated. Merck high-purity, anhydrous zinc sulfate was used as the starting material. The sulfate was heated under an argon atmosphere, at a rate of 10°C per min. With the first slight indication of decomposition as determined by gas analysis, the sample was removed from the furnace and allowed to cool. X-ray patterns showed no other phase present. It is estimated that less than 0.05 pct of the ZnS04 decomposed. The metal sulfides were also heated under an argon atmosphere to drive off any adsorbed water. The materials were then sized (-200 to +270 mesh), mixed in predetermined mole ratios, and pressed into pellets. The experimental measurement of the reaction rate consisted of purifying the argon carrier gas, continuous flushing of the heated reacting mixture with argon, and collection and analysis of the SOn product gas. The reaction system was heated to 600°C and al-

Jan 1, 1967

By W. A. Backofen, D. Lee, F. S. Jabara

THE empirical character of plasticity analysis insures a continuing need for measurements of the yield surfaces of anisotropic materials. Recently, Wheeler and Ireland (W-I) proposed that an octahedral yield locus could be constructed on the basis of six Knoop hardness indentations. Such simplicity would have obvious appeal, if it led to consistently dependable results. In other recent work, a much more straightforward (and more tedious) method of measurement was used to establish all quadrants of the plane-stress yield loci for two substantially anisotropic titanium alloys.2,3 The same materials have since been reex-amined by the W-I method with results being reported here. A full description of the stress state under a Knoop indentor would be complex. In principle, however, this can be avoided in relating the hardness number to a plane-stress yield locus, by the expedient of superimposing the appropriate hydrostatic component on that state of stress. Six possible orientations of in-dentor on orthogonal (symmetry) planes, along (principal) coordinate directions, are illustrated in Fig. 1(0). Pictured in Fig. l(b) are normal-stress components nominally associated with indentation n: o2(H), directly proportional to the Khn in this case, together with By overlaying a hydrostatic tension, ah, that in general is equal to the stress state around the indentation is reduced to one of plane stress in the x-y plane for which the stress ratio is a The key step in the W-I yield-locus construction is to represent the Khn for any indentor orientation as a vector quantity on the octahedral plane. In the plotting, the vector is given as deviatoric stress components along the principal axes in the ratio , where represents the direction of the minor (width) diagonal and 1 that of the major (length) diagonal. There is no attempt by W-I to justify the 7/1, although it might be supposed that the value originates in the usual ratio of major to minor diagonals in a Knoop indentation of about 7/1. If that were its origin, the link to the deviatoric stress ratio would presumably be made by first taking 7/1 and then turning to the Levy-Mises equation for isotropic material: Interpreted in this way, the W-1 approach seems arbitrary and even contradictory. Yet it would still be favored by two circumstances: the deformation under a Knoop indentor approaches plane strain: when dcw/del =a; and the shape of the locus where plane strain is represented is not overly sensitive either to the exact value of dc,/dcl or to the degree of anisotropy, within a rather wide range of both variables. The second point is illustrated below, after a few additional comments on applying hardness

Jan 1, 1968

By D. N. Seidrnan

In the present note we present thermal-analysis data for the liquidus curve from 0 to 76 at. pct Se and for the selenium-rich monotectic reaction in the Pb-Se system. We have previously reported that no expey-imental eviderzce was found for a lead-rich monotectic reaction, at -860°C with a monotectic composition of -20.5 at. pct Se, as found by Nozato and Igaki.&apos; Our additional data substantiated this earlier finding and extended the composition range studied. The alloys were prepared from semiconductor -grade lead and selenium purchased from the American Smelting and Refining Co. Both elements were 99.999+ wt pct pure as determined by the supplier. The impurities for lead were Fe (1 ppm) and Cu & ppm) while for selenium the impurities were Cu (< 1 ppm), As (< 1 ppm), Te (1 ppm), and C1 (<1 ppm). The general procedures used for thermal analysis were those specified by the National Bureau of Standards. A Pt/Pt-10 pct Rh thermocouple calibrated against the freezing points of zinc and copper purchased from the National Bureau of Standards and antimony (99.985 pct pure) purchased from A. D. Mackay, New York, was used for all the thermal analysis. The thermocouple electromotive force was measured with a Rubicon Type B potentiometer used in conjunction with a galvanometer with a sensitivity of 0.5 pV (mm) -&apos;. The absolute accuracy of this thermal-analysis system was *0.5"C. One-hundred-gram alloys of the desired composition were sealed in quartz crucibles, with a central thermocouple well, at a pressure of less than 10"1 Torr. The alloys were initially heated well above the liquidus curve and shaken vigorously to insure homogeneity. Cooling curves were then taken by the direct method at cooling rates ranging from -0.5" to 1.5"C (min)-&apos;. The phase diagram from 0 to 76 at. pct Se as determined by direct thermal analysis is shown in Fig. l.* An extrapolation of the selenium-rich portion of the liquidus curve to the monotectic reaction isotherm (678.3"C) gave a value of 76.1 at. pct Se for the monotectic composition. A tabulation of all the thermal-analysis data is given in Table I. As we previously reported no experimental evidence was found Fig. l—The partial Pb-Se phase diagram from 0 to 76 at. pct Se as determined by direct thermal analysis. For the sake of clarity the points for the 49.00 and 49.16 at. pct Se alloys were not drawn on this phase diagram, see Table I. for the lead-rich monotectic reaction found by Nozato and Igaki.&apos; This result was further substantiated by the fact that none of twelve lead-rich alloys, see Table I, examined for this monotectic reaction exhibited a thermal arrest in the temperature range (849" to 863°C) cited by Nozato and Igaki for the lead-rich monotectic reaction. Hence, our results tend to support the earlier qualitative work of ~elabon&apos; and Friedrich and ~eroux" in the 0 to 50 at. pct portion of the phase diagram, though the selenium-rich monotectic composition and reaction isotherm temperature were in agreement with the approximate values (75 at. pct Se and 672" to 680°C) given by Nozato and ~~aki. &apos;

Jan 1, 1967

By W. F. Flanagan, K. R. Evans

The strong temperature dependence of the flow stress of bcc metals has prompted considerable interest and controversy concerning the rate-controlling influence of the Peierls&apos; mechanism upon deformation in metals.18"21 Dorn and Rajnak" recently offered a criterion for Peierls&apos; deformation utilizing a line-energy model of a dislocation to estimate the saddle-point activation energy, for the nucleation of a pair of kinks as a function of applied stress and the height and shape of the peierls9- barrier. It was found that Un/2Uk, where 2Uk is the excess energy of a kink pair, was a unique function of where is the effective stress and 7p is the Peierls&apos; stress as defined in Fig. 20. The relationship found by Dorn and Rajnak between is given by the solid line of Fig. 21. may be expressed in terms of the temperature of test, T, and the athermal temperature, T,, defined in Fig. 20. Considering the strain-rate, 9, of deformation for a thermally activated process to be given by where fo is nearly a constant, it is seen that and the theoretical relationship of Fig. 21 may be examined with readily obtainable experimental parameters. Dorn and Coworkers analyzed a large amount of experimental data in this manner for materials sus-

Jan 1, 1967

By R. D. Carnahan

The authors are to be complimented on their timely study of solution-hardening effects in a bcc metal. Unfortunately there are some misleading aspects of the paper that should be discussed and clarified which is the purpose of this letter. In particular the writer is concerned about the allusions to rate theory of deformation that are inferred by the authors. This position is taken on the basis first of the "weaker" temperature dependence of the yield and flow stresses of the alloy relative to pure niobium and second of the strong temperature dependence of the Young&apos;s modulus of elasticity. It is by now well-recognized that any collection of data points used to determine a flow-stress temperature-dependence relationship must be established under isostructural conditions, i.e., similar or identical sessile and mobile dislocation densities and arrangements. Admittedly this is a formidable experimental undertaking and not what would be expected in an exploratory investigation of the present kind. As an alternative to the former one can consider, however, the temperature dependence of flow stresses at comparable strains. In the present study the authors have elected to use the lower yield stress and ultimate strengths to exhibit the temperature dependence of their alloys except for the data points taken at liquid nitrogen temperature. Here they have used the proportional limit for the yield stress and the fracture stress for the ultimate strength. This seems to be an unrealistic choice particularly in view of the fact that this temperature is below the duc tile-brittle transition region for the alloy and no supporting data points were obtained between -55" and -196°C. If the authors&apos; data in Fig. 2 are extrapolated and data points selected at a constant strain, for example a strain of 0.01, the reader can quickly verify that a temperature dependence exactly paralleling that of pure niobium is obtained.

Jan 1, 1967

By L. K. Borrett ond C. S. Yusi

The authors have made extensive use of a modern field of mathematics, topology, to give a new approach to the study of sintering. They present a topological model for the sinter body and the void space, and establish a relationship between them. However, in an interdisciplinary paper of this nature it is important that the material be presented, insofar as possible, in

Jan 1, 1967

By L. Zwell, H. A. Wriedt

In describing their procedure for measuring the lattice parameters of solid solutions, Abrahamson and Lopata report (p. 77) the final heat treatment of their alloy specimens as "700°C for 100 hr, followed by a furnace cool". The isothermal part of this treatment may be expected to precipitate solute in excess of the stable a solid-solution limit at 700°C; the subsequent slow cooling is likely to reduce the dissolved solute still further. Fig. 1 (upper) presents the data for titanium alloys so he;rt-treated and shows the lattice parameters of solid solutions containing up to 3.5 at. pct Ti; Fig. 17 (lower) shows 2 at. pct Ti as the solubility limit in a iron at 700°C. Figs. 1 and 17 are thus incompatible. The paper contains comparable incon~patibilities for zirconium alloys, for niobium alloys, and for tantalum alloys. The final heat treatment at 700°C may also be responsible for the anomalous "knee" in the lattice-parameter data for nickel alloys, Fig. 3. The "knee" composition is located near the 700°C limit of the stable a solid-solution field;37 alloys of the experimental composition range with more nickel than the "knee" composition are two-phase at 700 C and prolonged heat treatment of them at 700°C would tend to produce inhomogeneity rather than homogeneity. In Figs. 4 and 7, the composition ranges of the zirconium, hafnium, and niobium alloys examined terminate at alloy concentrations of 0.1 to 0.2 at. pct. These metals form very stable oxides and their partial removal from solid solution in iron by impurity oxygen may be expected. We believe that the authors should have reported the procedure by which they distinguished the amounts of alloying elements in solution and in oxide. The diagrams pertaining to copper in Figs. 3 and 18 (lower) are almost certainly incorrect. Three recent investigations of this system38-40 all substantially agree on the solubility of copper in a iron, finding it to be much larger than that reported by Abrahamson and Lopata. The change of the lattice parameter with composition reported by Abrahamson and Lopata is too large by a factor of three to five, as seen by comparison with the findings of other investigators.41738 Moreover, the authors violate, in Fig. 18, the accepted Fe-Cu constitution diagram37 by ignoring the eutectoid at about 850°C.

Jan 1, 1967

By Charles R. Simcoe

It was pointed out in a recent paper&apos;g that the initial flow stress of as-quenched martensite is very low even in an alloy steel with an M, well above room temperature. It was also shown that the high ultimate tensile strength resulted from a very high rate of work

Jan 1, 1967

By J. V. Gluck

In the present paper," as in earlier publications, V1&apos;2"1 the authors present experimentally obtained relations for the free energy of solution of oxygen in various metals as a function of temperature. The relations are linear and given in slope-intercept form. The authors give values for the "probable error" of the slope and intercept, citing Birge&apos;s method17 for obtaining these quantities. Birge discussed these methods as early as the period 1929-32.25726 In Ref. 25 the probable error is defined as "the numerical value which the true error is as likely to exceed as not", i.e., 50 pct probability. Ref. 26 is even more detailed and includes a lengthy discussion of the applicability of the Gaussian distribution to experimental data. However, the use of the "probable error" has come under some question. For example, Ezekiel&apos;~ states that "the use of the probable error tends to make the results appear rather more accurate than the standard error". Moroney28 stated (in 1951) that "the term &apos;probable error&apos; was used in former times to denote 0.67450 (50 pct confidence using the normal distribution)....the term, a poor one, is now very much obsolescent. It has been said that &apos;it is neither an error nor probable&apos; ". Bennett and Franklin in 1954" in discussing statistical confidence levels mentioned that "the customary use of the 5 and 1 pct levels is not completely a matter of chance; these levels probably represent a balance between the desire to be correct and the desire to be specific. Also in most people&apos;s minds the borderline between something that could possibly happen and something that is not likely to happen is somewhere in this region. Certainly 5 or 1 pct confidence limits are to be preferred to limits such as the &apos;probable error&apos; which has only a 50/50 chance of including the correct value." It may readily be seen that the 95 pct confidence level, which is given by 1.960 (assuming large sample size), thus corresponds to approximately three times the "probable error". Indeed, limits of one standard deviation correspond only to about 68 pct probability. Even if we triple the tolerances given by the authors in the equations of their Table 111, the deviations do not become excessive and would not detract from their excellent results. It could then be said with a high degree of confidence (95%) that the precision of the slope and intercept values is about *3-5 percent of their absolute levels rather than the 1-2 percent implied in Table 111. This is then compatible with an earlier suggestion of Gokcen~&apos; of a probable accuracy of 5 pct in dissolved oxygen measurements by the technique employed. Alternatively, the authors could have

Jan 1, 1967