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By R. N. Orava, L. A. Rice

One of the difficulties encountered in the preparation of titanium specimens for transmission electron microscopy is the formation of a surface hydride phase during the thinning operation at ambient temperatures. This necessarily destroys contrast, obscures features of interest, and often leads to misleading results. By cooling the polishing solution to temperatures below 0°C this problem has been overcome in the past.' However, since the cooling procedure is somewhat inconvenient, a technique was developed at this laboratory for thinning titanium at room temperature. The material examined was A-70 grade commercial-purity titanium purchased from the Crucible Steel Co. of America. The mechanical and thermal treatments, described elsewhere,* yielded a recrystallized grain size of 4 to 5 p. A slice, 0.5 mm thick and 1.5 mm wide, was cut from a bulk specimen2 using a diamond cut-off wheel. The sample was then coated with paraffin wax. Two concentric holes, about 0.03 in. in diam, one at each broad face, were scribed through the wax to the surface of the metal. Subsequent polishing for several minutes resulted in a preferentially thinned or "dimpled" region. Thereafter, the wax was removed and the entire specimen polished to the point of breakthrough at the base of the dimple. Polishing was effected chemically in a solution comprised of 30 pct HF and 70 pct HN03 by volume, kept at room temperature (20" to 25OC). The specimens were mounted in a stereo holder and examined at 100 kv in a Philips l00 B Electron Microscope. A micrograph from a foil prepared in this way is shown in Fig. 1. Several points are noteworthy. This electron micrograph shows neither evidence for the formation of a hydride phase due to specimen preparation nor, moreover, any obvious surface contamination in electron-transparent areas of a freshly prepared foil. Localized variations in foil thickness observed in some specimens seem to be a characteristic of this chemical polish but do not seriously detract from foil quality. With care, the lifetime of a good specimen exceeded 2 hr in the beam. On the other hand, the exposure of a sample to air at atmospheric pressure, when still warm from the beam, clearly resulted in the deterioration of a formerly clean area just previously in the field of view. An example in Fig. 2 of a contaminated region reveals features, and "spots", not unlike those observed in much purer material by Yamane and Ueda. Consequently, one can conclude that: 1) titanium can be thinned satisfactorily in a solution at room temperature for transmission electron microscopy; 2) large-scale precipitates, >50A in diam, are absent in commercial-purity, recrystallized, furnace-cooled, A-70 titanium containing about 3800 wt ppm interstitials and the same amount of iron; 3) care must be taken not to attribute surface contaminants to precipitates. The authors are grateful to the Franklin Institute for financial support and permission to publish.

Jan 1, 1967

By P. Wynblatt, J. E. Dorn

The effect of strain rate, temperature, and interstitial impurity concentration on the flow stress was investigated in a poly crystalline Fe-2 pct Mn alloy. The temperature dependence of the flow stress was found to be independent of the interstitial impurity concentration, removal of interstitials merely decreasing the atherma1 stress level. Below 160%, the large temperature dependence of the flow stress was interpreted in terms of the Dorn-Rajnak theory of the Peierls mechanism of plastic deformation. Above 160"K, some other thermally activated intrinsic meckanisln seems to be operating. The strong temperature dependence of the flow stress of bcc iron at low temperatures has been studied by numerous investigators and interpreted in terms of several different thermally activated dislocation mechanisms. The following mechanisms have been proposed: a) interaction of dislocations with interstitial impurity atoms1 or with solute atoms in general; b) interaction of dislocations with clusters of impurity atoms;3 c) resistance to the motion of dislocations due to jogs on screw dislocations;* d) resistance to the motion of dislocations due to the Snoeck effect;' and e) interaction of dislocations with the intrinsic resistance of the bcc lattice or Peierls "hills". In previous work: it was found that the plastic behavior of polycrystalline iron containing 2 wt pct Mn (and 100 ppm C + N) is in good agreement with predictions based on the Peierls mechanismlo from 77" to 160°K whereas from 160" to about 370°K another as yet unidentified thermally activated mechanism is operative. The purpose of the present investigation was to determine the effect of interstitial impurities on the temperature dependence of the flow stress, by purifying the previously investigated alloy with respect to interstitial impurities. The investigation revealed that removal of the interstitial impurities to a level that eliminated Cottrell locking and the Portevin-LeChatelier effect (i.e., serrations in the stress-strain curve due to dynamic strain aging) affects neither the strong temperature dependence of the flow stress at low temperatures nor the general characteristics of the higher-temperature behavior. Such purification, however, lowered the athermal yield stress. I) EXPERIMENTAL PROCEDURE AND RESULTS The material used in this investigation consisted of an Fe-2 wt pct Mn alloy having the following additional elements present: 0.004 pct C, 0.006 pct N, 0.05 pct 0, 0.004 pct S, 0.003 pct P, and 0.001 pct Si. This was the same material as that studied in the previous investigation and will henceforth be referred to as the "impure material". The as received -jr by 2 in. hot-rolled bars were cold-rolled to 0.08-in. thickness, recrys-tallized under argon for 30 min at 80O0C, and further cold-rolled to 0.053-in. thickness. Flat tensile specimens 3 in. wide having a 1.625-in.-long gage section were machined from the sheet and then purified. The first stage of purification consisted of holding the specimens at 850°C for 24 hr in a stream of hydrogen saturated with water vapor at room temperature. Material prepared in this fashion will subsequently be referred to as "wet hydrogen purified material". It has been estimated that this type of treatment reduces the carbon content of iron to less than 5 ppm.' The second stage of purification consisted of holding the specimens in a closed system through which hydrogen was circulated past the heated specimens as well as a zirconium hydride getter. The specimens were held at 850°C and the getter at 800°C. The process was continued for 212 hr. The starting material for this process was wet hydrogen purified material. Material prepared in this manner will be referred to as "ZrHz purified material". The technique used was substantially the same as that described by Stein et al.' who have shown that the carbon level at the end of the process is reduced to about 5 parts per billion. The mean grain size of the three materials was found to be -60 C( for the impure material and -160p for the wet hydrogen and ZrHz purified materials. All tensile testing was carried out on an Instron Testing Machine either in controlled-temperature baths or at fixed-point baths such as boiling liquid nitrogen, and so forth. When fixed points were used the temperature was kept constant to better than *1°C whereas in all other tests the temperature variation was less than *2°C. Test of Purity. It was not possible to determine the purity achieved at each stage of the purification because the resulting level of interstitial impurities was near or below the limit of sensitivity of standard analytical techniques. It was possible, however, to obtain a qualitative measure of the extent of purification from the appearance of the stress-strain curves for the three materials. Fig. 1 shows the stress-strain curves for the three different materials tested at 300°K. It can be seen that the effect of wet hydrogen

Jan 1, 1967

By George A. Colligan, John M. Lo

Electrical resistivity as a function of temperature was investigated in undercooled gallium and under-cooled Ga-In alloy of eutectic compositian to examine structural changes in undercooled melts. A continuous linear extension of the resistivity was determined for 99.999 pct pure gallium when undercooled below the stable Ga(l)-liquid, and the metastable Gafl)-liquid equilibria. In icndercooled Ga-In, a significant continuous negative departure from linear resistivity behavior was observed below the eutectic temperature. All resistivity measurements were made by the four-point probe technique. ThE temperature range for investigations into the physical properties of liquids before freezing has been greatly extended with the undercooling of massive melts of pure metals and alloys. Experimental determinations of thermal and transport properties and diffraction patterns in undercooled systems should throw further light on the structural behavior of liquids. Many measurements showing prefreezing anomalies in viscosity1'5 have been regarded677 as evidence for structural groupings in the liquid state. However, the majority of viscosity results,~)~-~~ conforming to the law 17 =A exp(~/RT), do not support theories of atomic aggregation. For the system Cd-Sb, which exhibits a metastable solid phase, Fisher and Phillipsg reported that, in undercooled alloys, the activation energies for viscous flow below the stable liquidus are much higher than those above it. Similarly, Miller et a1." observed a doubling of the activation energies for electrical conductivity in undercooled Cd-ib alloys. These effects were suggested as indicative of atomic association and clustering in the liquids at lower temperatures. With the recent establishment of metastable phases in pure gallium22 and its alloys,23 attempts were made during this investigation to undercool bulk samples and to determine the temperature dependence of electrical resistivitv. Pure gallium, when undercooled below -17°C at atmospheric pressure, can crystallize to either a stable Ga(1) phase (mp, 29.78"C) or a metastable phase identi-

Jan 1, 1967

By A. W. H. Morris, G. H. Laurie, J. N. Pratt

Using- galvanic cells of the form Sn(liq)/Sn" (LiCl-KC1-SnCl,)/Sn-Ag (alloy), measurements have been made of relative thermodynamic properties of the a, C, E, and liquid phases of the Ag-Sn alloy system. Partial heats of solution of the components in the liquid alloys lzave also been observed by direct cal-orimetric measurement in an isoperibol calorimeter. The thermodynanzic quantities are disczlssed in relation to structural and other properties and the existence of anomalous minor fluctuations in the partial heats and entropies of solution in liquid alloys is tentatively suggested. In the course of a recent electro motive-force study of the thermodynamic properties of Sn-Ag-Pd liquids,' some measurements were also performed on the Ag-Sn binary system. Most previous thermodynamic studies of this system have been concerned with the liquid state. Measurements confined to the limiting heat of solution of silver in liquid tin have been made by many calorimetric workers2 while high-temperature calorimetric measurements of the heats of formation of the full range of liquid alloys are reported in the early work of Kawakami~ (1323°K) and more recently by Wittig and Gehrin~(1248°K). Electromotive-force studies on liquid alloys have been made by Yanko, Drake, and Hovorka' (606" to 686°K; 86 to 99.4 at. pct Sn) and by Frantik and Mc Donald' (900°K; 30 to 90 at. pct Sn). The only known measurements on the solid state are of heats of formation of the a, £, and c phases; these values were obtained using tin-solution calorimetry, at 723"K, by Kleppa,~ whose investigation also yielded heats of formation of liquid alloys containing more than 64 at. pct Sn. The present experiments on the Ag-Sn alloys include a re-examination of the liquid phase and, because of the dearth of free-energy data for the solid state, attempted measurements on the a, c, and E phases. The principal new feature of electromotive-force results obtained for the liquid phase was an indication of anomalous fluctuations in the partial heats and entropies of solution of tin at certain compositions. However, since the values for these thermodynamic quantities were determined from the temperature coefficients of cell potentials, which are commonly subject to considerable error, confirmation by calorimetric measurements was considered desirable. A detailed investigation of the partial heats of solution of the components in the binary liquids was made using a liquid metal solution calorimeter. I) GALVANIC CELL STUDIES a) Experimental Details. Measurements were made, as a function of alloy composition and temperature, of the potentials of reversible galvanic cells of the form: ~n(liq)/~n++/~n-Ag (solid or liquid alloy) Details of the apparatus and experimental techniques have been given elsewhere.' so that a brief account will suffice here. Molten salt, 58 mole pct LiC1-42 mole pct KC1, containing small amounts (1 to 2 mole pct) of stannous chloride was used as the electrolyte. The salts were dehydrated by pre-electrolysis and vacuum -drying techniques. Cells were established under an argon atmosphere by immersing tin and alloy electrodes in the molten salt contained in a large silica tube, heated in a vertical resistance furnace. The tube was sealed at the top by a head plate provided with openings permitting the simultaneous insertion of six electrodes, a central thermocouple sheath, and connections to vacuum and argon lines. Temperatures were controlled to *0.2"C over prolonged periods, with maximum variation over the electrodes at any time of 0.l°C. Temperatures were measured with a standardized Pt/13 pct Rh-Pt couple. The electromotive force of this and the cell potentials were measured on a Cambridge Vernier potentiometer and short-period galvanometer. Alloys were prepared from Pass "S" tin (99.999 pct) and Johnson-Matthey high-purity silver (99.999 pct) by melting in evacuated silica capsules and quenching in cold water. For liquid phase experiments, pieces of the resulting alloys were remelted into prepared silica electrode units, while solid electrodes were prepared by remelting into 3-mm bore tubing, inserting a cleaned molybdenum lead wire, and quenching to produce uniform rods about 3 cm in length, with soundly attached leads. In all cases remelting was done under an argon atmosphere. The solid electrodes were subsequently annealed in evacu ated silica tubes for 14 days at about 20°C below the solidus and quenched. Analyses showed that these techniques produced uniform electrodes with no significant change from weighed out compositions. b) Results and Discussion. Measurements were made on about forty alloys in the solid and liquid states, over varying ranges of temperature between 550" and 1050°K. Stable, mutually consistent, and reproducible electromotive-force data were obtained with most liquid alloys and these are shown in Fig. 1. Investigations were extended below the liquidus tem-

Jan 1, 1967

By R. E. Mussler, F. E. Block, T. T. Campbell

An exploratovy study was made to deternzine the feasibility of preparing beryllium by the metallother-. mic reduction of beryllium oxide. The procedure involved heating a relatively nonvolatile metal reductant in contact with beryllium oxide in a vacuum. Beryllium vapors formed in the reaction were condensed as a coherent deposit on a heated surface. Reductants tested included tanthanun, yttrium, thorium, Th-Mg, and Zr- Ti alloys, and the hydrides of lanthaniir~z, yttriunz, and zirconiur?7,. Test ten7pevatures ranged from 1350'to 175O' C, and reaction times ranged frot 30 to 100 lzr. In most cases metal recoveries were lola, although yields close to 90 pct of theoretical were obtained with latzthanum, yttrium, and zirconium reductants. In most cases metal deposits were contanzinated by beryllides, /ls/cally of the Beln M or Bel3 M type. BERYLLIUM has a variety of unique properties including light weight (sp gr 1.85), low thermal neutron absorption cross section, high scattering cross section, excellent dimensional stability, high strength to weight ratio, high melting point (1285"C), high specific heat, and high thermal conductivity. Interest in beryllium as a structural material in aerospace and nuclear-reactor applications is based on these properties. In general, the potential of beryllium has been only partially realized, largely because of the brittleness of poly crystalline forms of beryllium, difficulties associated in its fabrication, and joining problems encountered in its use in structural applications. Several excellent books and monographs are available to those interested in the occurrence, extractive metallurgy, and utilization of beryllium.1"* Although an extensive amount of research on beryllium has been in progress during the past 10 years, much of the work has been concerned either with the so-called "ductility problem" or with the development of methods of fabrication and evaluation of properties of various commercial or purified grades of metal. A recent survey of the literature indicates that only limited efforts are presently being directed toward developing new methods for reducing beryllium compounds to metal. Two major commercial methods now used to produce beryllium are the magnesium reduction of beryllium fluoride and e lec trow inn ing of beryllium from fused sodium chloride-beryllium chloride salt baths. Only a limited amount of work has been done on the direct reduction of beryllium oxide. Major factors which complicate this method are the great stability of beryllium oxide and the reactive nature of beryllium metal. The stability of the oxide necessitates extremely high reduction temperatures and vacuum operation to liberate beryllium metal vapor and cause reactions of the following type to proceed: XBeO(s) +YM(s)-MYOX(s) + XBe(& As early as 1939, roll' used this reaction for the direct reduction of beryllia by zirconium and titanium, and later in 1952 ~a~el~ studied the reduction of beryl-

Jan 1, 1967

By S. A. Mersol, C. T. Lynch, F. W. Vahldiek

The room-temperature microhardness of as-grown and annealed MoaC single crystals was measured on the (0001), {2110), and1012) planes using Knoop and Vickevs indenters at loads ranging front 25 to 1000 g. The orientatimz dependence of hardness with respect to crystal axes was also studied. The average random hardness of as-grown crystals was determined to be 1520 kg per sq nm. Annealing to 2000°C decreased. the average hardness by 150 units. An increase in hardness after annealing at 2200 ;C was noted. Optical and electron microscopy revealed slip and twin traces on all planes studied, as produced by mi-cvohavdness indentations. Basal (0001)(2i10) slip was determined to be the primary slip system and was substantiated by electron transmission microscopy. A secondary {1010)(2110) slip was produced by mi-crohardness indentations. The lattev also produced twinning- of the {10i2)[0001] type, as proven by electron diffraction. Electrical resistivity and elastic-modulus anisotropy were found and correlated with hardness anisotropy and Mo2C crystal structure. Elastic-modulus values were obtained by microhard-uess and ullrasonic methods. Bonding mechanism of Mo2C is discussed. ROOM-TEMPERATURE microhardness indentations are useful for studying hardness anisotropy, slip, and twinning in brittle materials. Slip has previously been produced in this manner in and WS~~.~ Recently, the authors5 reported slip of the {10i0)(11~0) type produced by high pressure and microhardness indentations on hexagonal TiBz (c/a = 1.066) single and polycrystals. This slip system was also reported by French and ~homas' and Taka-hashi and ~reise~ for hexagonal WC (c/a = 0.976) crystals. These results suggest that prismatic rather than basal slip is favored in hexagonal nonmetallic materials having a c/a ratio considerably less than the ideal (1.633). Buerger precession and cylindrical X-ray rotation patterns were previously' taken on cleaved sections of the Mo2C single crystals studied in this work. Th~y were found to be hexagonal MoaC with a. = 3.0233A, co = 4.7344A, and C/O = 1.5660. The latter ratio is close to that of the beryllium metal (c/a = 1.57), which slips primarily on the (0001) plane: but also slips on the (1010) planes.'0 ~irconium" (c/u = 1.59) and titanium12 (c/o = 1.59) deform mainly by slip on nonbasal planes which contain a close-packed direction. This is due to the fact that for these two metals the initial resolved shear stress for slip on the (10i0) prismatic planes is lower than that on the (0001) plane. The prominence of basal rather than prismatic slip in metals of high c/o ratios is shown by cadmium (c/a = 1.89), zinc (c/a = 1.86), and magnesium (c/a = 1.62) which deform mainly by basal slip. However, in case of the latter, by stressing magnesium crystals in tension or compression parallel to the basal plane, slip on (10i0) planes can also be produced.13 Several hardness values for polycrystalline Mo2C are reported in the literature: Biickle ' and Samsonov'~ give a value of 1800 and 1479 kg per sq mm, respectively, at a 100-g load; and Kieffer and Benesovsk~'~ report a value of 1950 kg per sq mm at a 50-g load. ~ott'~ reports a Vickers hardness value of 2000 kg per sq mm, with the load unspecified. A Rockwell A hardness value of RA = 88 has also been reported.'' In the present work, for comparison with single-crystal Mo2C hardness values, a Khnloo value of 1600 It 150 kg per sq mm was found on 99.6 pct pure and 99 pct dense hot-pressed Mo2C. This work was undertaken partly to explain the considerable differences in hardness values reported for polycrystalline Mo2C. EXPERIMENTAL The Mo2C single crystals investigated were prepared by a Verneuil-type process using an electric arc by the Linde Co. of the Union Carbide Corp.lg The largest specimens grown were boules 7 mm in diam by 40 mm in length. The crystals had an average density of 9.04 g per cu cm, with a Mo + C content of 99.8 wt pct. The major impurities were: 100 ppm each Na, Zr, and Ca; 85 ppm 0, 55 ppm Fe, and 10 ppm each Cr and Ta. The crystals were found to be carbon-poor, the average carbon content being 5.73 wt pct (stoichiometric value is 5.89 pct). The molybdenum content was found to be 94.08 pct, which is nearly stoichiometric. Electron-microprobe traverses of selected specimens were done with a Phillips-AMR microanalyzer. Thin-film and carbon replicas were used to prepare electron micrographs. This work was done with a JEM-6A electron microscope. Prior to optical and electron-optical studies, specimens were mounted in Lucite and polished on a vibratory polisher using diamond-paste grades ranging from 9-1 p and Linde A powder for up to 48 hr. Dilute nitric acid was used for thin-section polishing and chemical etching for 1-15 min. Electrical-resistivity measurements at room temperature were taken with a Rubicon bridge, using gold contacts. For hardness measurements, a Tukon Microhardness Tester Type FB with Knoop and Vickers indenters was used. Measurements were taken at loads ranging from 25 to 1000 g; however, the 100-g load was chosen as the standard load. All measurements were taken at room temperature. Indentations of cracking classes 1 and 2 only were considered for hardness determinations.20)21 (There are six cracking classes, ranging from "class 1" for a perfect inden-

Jan 1, 1967

By R. Ebeling, M. F. Ashby

The paper is in two parts. The first develops the formulae and method needed to calculate the size, nu)nber, spacing, and volume fraction of hard or inert particles in the interior of a specimen from measurernents made on an extraction replica; throughout, the spread of- particle sizes in a single specimen is taken into account, and the extraction efficiency of the replica is considered. A method for testing whether the particles are randotnly distributed in space is described, and the spacing of randomly distributed particles is discussed. The second Part describes the application of the method to copper containing spherical particles of silica; the description includes an estimate of the errors involved, and a comparison of this with alternative methods. All parameters except uolume fraction can be determined satisfactorily, and the method offers advantages over other electron-,rzicroscopic techniques when dealing with hard particles in a softer matrix, or inert particles in a chem-ically less inert matrix. 1 HE experimental measurement of sizes and numbers of discrete particles of a second phase embedded in a matrix material from opaque, plane sections has been considered by many authors, notably by Fullman.' It is assumed that, when the specimen is sectioned, the particles are also sectioned, so that the diameters of the circles of intersection of particles with the plane of the cross section ("surface diameters") are measured. It is difficult to derive the distribution of true particle diameters ("volume diameters") from measurements of the distribution of "surface diameters" on a plane section. The measurement of size and numbers of small second-phase particles by transmission electron microscopy through thin foils of matrix containing the particles has been described by Cahn and ~uttin~' and by ~illiard.~ Because of overlap and the fact that particles which intersect the foil surface may be sectioned whereas those in the bulk of the foil are not, it is again difficult to measure the true distribution of particle sizes. The use of replicas for this sort of measurement has not been analyzed in detail. A replica made from an opaque cross section, thus replicating the circles of intersection of particles with the plane of section, is analyzed by Fullman's method and suffers from the same difficulties. Under certain circumstances, however, extraction replicas can be used, and offer a special advantage in that they make the determination of the true distribution of particle diameters particularly simple. It is the purpose of this paper to describe this extraction replica method. Consider the example of an alloy consisting of SiOz particles, whose mean diameter is about 1000A, dispersed in a copper matrix. When the alloy is sectioned and mechanically polished, the particles are not sectioned, because they are much harder than the matrix, and so will be either left in the surface or pulled out whole, and because the particle size is smaller than the abrasive size of even the finest abrasive. The particles are chemically inert in solutions which chemically etch or electropolish the matrix, so that chemical treatments do not section the particles either. (Experimental measurements of particle shape in this alloy confirm this—truncated particles are never seen.) Small, hard or inert, particles are therefore not sectioned when the specimen is sectioned and polished. An extraction replica taken from this polished surface shows the true "volume" diameter of each extracted particle; the distribution of diameters seen on the replica is the surface distribution of true "volume" diameters, and the volume distribution of true "volume" diameters is easily derived from it. The extraction replica method is not subject to the difficulties associated with sectioning of particles, and avoids the problem of overlap from which the transmission method suffers. The method is well-suited for studying hard particles in a soft matrix. Examples are provided by internally oxidized alloys, oxide-dispersion strengthened metals like T.D. Nickel, and carbides, nitrides, and strong intermetallic compounds in metals. It should be possible to adapt polishing techniques in alloys containing softer but inert particles to avoid sectioning the particles (say by electropolishing or etching). The method is tested and illustrated in Sections 8 and 9 by applying it to a dispersion of spherical SiO2 particles in a copper matrix. I) SYMBOLS Symbols are defined where they first appear in the text. Volume fractions of particles are denoted by the symbol f, particle diameters by x, center-to-center particle spacings by D, and numbers of particles by N. Mean particle diameters and standard deviations about these means are denoted by x and a. Both arithmetic (subscript A) and geometric (subscript G) means are employed. In this paper we measure the distribution of true diameters of particles which touch or pass through a random-plane section of the specimen. We may want to know the distribution of particle diameters in the

Jan 1, 1967

By W. M. Robertson

The rate of crack Propagation thvough a solid meta1 in the presence of a liquid metal has been calculated. The crack is assumed to propagate by solution of the solid in the liquid under the influence of an applied stress, with volume diffusion of the dissolved solute through the liquid controlling the propagation. The calculated velocities can be tens of centimeters per second or higher. THE embrittlement of normally ductile solid metals by liquid metals has been the subject of extensive study, as summarized in the book by Rostoker, McCaughey, and arkuus.' In experimental studies of liquid-metal embrittlement it is usually concluded that the observed crack-propagation rates are too high to be accounted for by diffusion processes. Diffusion is considered to be an unimportant factor and various other mechanisms are invoked to account for the experimental observations. The similarities of liquid-metal embrittlement to stress-corrosion cracking, to hydrogen embrittlement of steel, and to low-temperature embrittlement of bcc metals are frequently used as analogies for these mechanisms.1"3 The present paper assesses how rapidly a crack could propagate by a mechanism of volume diffusion through the liquid metal. We assume that the crack propagates by solution of the solid in the liquid at the crack tip under the influence of the applied stress and diffusion of the dissolved solute away from the crack tip. The model uses only macroscopic thermodynamic, kinetic, and elastic concepts. The calculations indicate that this dissolution-diffusion mechanism can give high crack velocities. In some previous treatments4'' of crack propagation in a liquid-metal environment the fundamental step has been the breaking of atomic bonds at the crack tip. The liquid greatly decreases the energy necessary to break these bonds. The present model assumes the crack is filled with liquid metal; the presence of the liquid is essential because diffusion through the liquid is assumed to control the rate of propagation. With proper modification this model could also apply to stress corrosion in a liquid environment. THEORY Consider a crack in a homogeneous elastic continuum, ignoring all the structural details of the solid. This neglects a host of metallurgical details which can be significant in the problem of liquid-metal embrittlement;' but this simple assumption is a useful approach in evaluating the role of diffusion through the liquid. The stress distribution around the crack tip establishes a gradient in the chemical potential at the tip, which causes a diffusion flux through the liquid away from the tip. The solid-liquid interfacial tension works against crack propagation, since propagation requires creation of interfacial area. From these two considerations we derive the diffusion flux, which then yields an expression for the velocity of the crack tip. The concentration of the solute in the liquid, C, is equal to the equilibrium concentration in the presence of an unstressed, flat surface, Co, plus the excess concentration due to the stress, AC(a), plus the excess concentration due to capillarity, AC(y): We calculate AC(o) and AC(y) and then obtain the diffusion flux. Consider (Fig. 1) a long flat crack of length 2L, thickness 2r, and tip radius r, where r remains constant as the crack propagates in the positive x direction. There is no stress ay in the y direction across the flat surfaces of the crack. The magnitude of the stress at the crack tip due to the applied stress, a,, is given by the relation6 ^=^[l-2^] 12] which, for long narrow cracks, becomes The stress increases the chemical potential in proportion to the strain energy.? The excess chemical potential due to the stress, Ap(a), is given by where 52 is the atomic volume of the solid and E the Young's modulus. Inserting Eq. [3] gives Now consider the crack to be filled with a liquid metal. The excess solubility due to stress, hC(a), is given by the excess chemical potential due to capillarity, Ap(y), is given by8 where y is the solid-liquid interfacial energy, and v1 and YZ are the two principal radii of curvature of any surface point. At the crack tip, r1 = -r and vz = m, so TRANSACTIONS OF THE METALLURGICAL SOCIETY OF AIME

Jan 1, 1967

By J. B. Conway

Stress-vuptuve data for several of- the refractory metals are frequently found to yield a linear relationship between the Larson-Miller parameter and the logarithm of the applied stress. In such cases linear stress-rupture isotherms result with slopes bearing a definite relationship to the temperature. It also follows that the stress to produce rupture in a certain period of time will be linear in temperature. Data for several refractory metals have been reviewed and excellent linearity is shown in this type of isochronal plot. In addition, the af ore - mentioned lineavity leads to a linear relation between the log of the stress to produce rupture in a certain time and the homologous temperature. This has been illustrated for the Group VI-A metals, tungsten and molybdenum. EXTENSIVE use has been made of the Larson-Miller' parameter in the interpolation and extrapolation of stress-rupture and creep data. In those cases where this particular parametric approach is applicable a convenient and fairly straightforward procedure is made available for the correlation of experimental stress-rupture data. It is quite common to employ this parameter in the form of a master rupture plot in which the parameter, T(C + log tr), is expressed as a function of log stress. In many cases this functional relationship in log stress is linear within acceptable accuracy and hence the following relation results: where P is the parameter, C is the Larson-Miller constant, T is the absolute temperature, t~ is the rupture time, a is the stress, and a and b are constants. Examples of such a relationship are contained in the work of Green, Smith, and 01son2 dealing with high-temperature rupture behavior of molybdenum and in the work of Green' dealing with the high-temperature behavior of tungsten. In addition, pugh4 has shown a similar linearity for some fairly low-temperature data for molybdenum. It can be shown that when the relationship in Eq. [I] is exhibited certain generalizations can be made concerning the form of the stress-rupture isotherms. For example, rearranging yields: For a given material (constant C) at a given temperature the first term on the right-hand side of Eq. [2] is a constant and hence this equation defines a straight line when log stress is plotted as a function of log-rupture time. This is recognized as the standard form usually employed in this type of data presentation. Such linearity then suggests the linear form of the Larson-Miller parameter. Or, in other words, the linear parametric relationship in Eq. [2] results only when the stress-rupture data are linear on a log-log plot of stress vs rupture time. Another interesting observation can be made in regard to Eq. [2]. It can be noted that the slope of the stress-rupture isotherms is given by - T/b and hence a direct calculation of the constant b is available. It also follows that since the value of b is the same for all temperatures the slopes of the various isotherms on the log-log stress-rupture plot cannot be the same. Indeed, the existence of the relationship in Eq. [2] precludes a system of parallel lines on this common stress-rupture plot. As a matter of fact it further specifies that in addition to being nonparallel the slope of these isotherms must decrease (i.e., become more negative) with increasing temperature. Such a condition is indeed found to exist in the case of the stress-rupture data reported for molybdenum.' As a corollary to the above, it may be stated that stress-rupture data which do not lead to a linear log-log stress-rupture plot or whose isotherms do not exhibit a decrease in slope as the temperature increases will not yield the linear relationship of Eq. [I]. Applying Eq. [2] to two different temperatures and solving for C yields: Eq. [3] affords a simple and rapid method for calculating the Larson-Miller constant from the log-log stress-rupture plot. The slope of a given linear isotherm is measured and the value of "b" calculated based on Eq. [2] as: slope = - -Tb Then at an abscissa value of 1.0 hr (making log tr in Eq. [3] equal to zero) read the stress corresponding to rupture for two different temperatures. Substitution in [3] yields: A value of the Larson-Miller constant can thus be calculated from a few simple mathematical procedures employing data read directly from the log-log plot of the stress-rupture data. Of course, it is not to be overlooked that the above reasoning has been based on the linear relationship of Eq. [I] being applicable. However, if as mentioned above the log-log plot is

Jan 1, 1967

Jan 1, 1967

Jan 1, 1968

By T. F. Kassner

The dissolution kinetics of type 304 stainless steel in the Bi-Sn eutectic alloy have been investigated under the well-defined hydrodynamic conditions produced by the rotating-disc sample geometry. In addition, the mutual solubilities of iron, chromium, nickel, and manganese from 304 stainless steel in the eutectic alloy were determined over the temperature range 450" to 985°C. The convective -diffusion model for mass transport from a rotating disc was used to interpret the experinlental dissolution data. The dissolution process was found to be liquid-diffusion-controlled under specific conditions of temperature and Reynolds number. Liquid penetration into the 304 stainless steel resulted in a reduction of the di,ffusion-controlled mass flux and thus precluded the calculation of the diffusion coeficients of the four components from 304 stainless steel in the Bi-Sn eutectic alloy. The convective-diffusion model for diffusional limitations of electrode reactions and mass transport at the tationssurface of a rotating disc set forth by Levich 1,2 has found wide applicability in the investigation of electrochemical and dissolution phenomena in aqueous systems. Riddiford 3 and Rosner have reviewed the model and also include numerous references on work of this nature. More recently the rotating-disc system has been applied to the investigation of hetereogeneous reactions in liquid-metal systems. Shurygin and Kryuk 5 have measured the dissolution rates of carbon discs in molten Fe-C, Fe-Si, Fe-P, and Fe-Ni alloys. Shurygin and shantarin6 also studied the dissolution kinetics of iron, molybdenum, chromium, and tungsten, and the carbides of chromium and tungsten in Fe-C solutions with a rotating-disc sample geometry. In these systems it was possible to distinguish between diffusion and reaction control mainly through experimental confirmation of the velocity dependence of the dissolution rate predicted by the model. However in the absence of dependable solubility data and the virtual lack of diffusion data in these systems, a quantitative check of the magnitude and the temperature dependence of the rate was not possible. In many instances, estimates of the activation energy for solute diffusion and the diffusion coefficient based upon the experimental dissolution data are not credible. A recent study by this author7 has resulted in a critical test of the model in a liquid-metal system. The solution rates of tantalum discs in liquid tin were measured over a wide range of temperature and velocity conditions. In addition, the solubility and diffusion coefficient of tantalum in liquid tin were determined as a function of temperature. The latter data were used with the model to predict both the magnitude and the temperature dependence of the dissolution flux. In that work it was also deemed necessary to reevaluate the solution to the convective diffusion equation to incorporate the effect of the lower range of Schmidt numbers encountered in liquid-metal systems. Good agreement between the model and the experimental dissolution data in the region of diffusion control was obtained in the Ta-Sn system. The Bi-Sn eutectic alloy is used as a seal between the reactor head and the reactor vessel in the Experimental Breeder Reactor-11. The alloy is fused periodically prior to fuel-handling operations. In that connection, it was necessary to investigate the compatibility of the liquid alloy with the type 304 stainless-steel containment material. The results of a rotating-disc study in this multicomponent system are presented. EXPERIMENTAL METHOD The 5.08-cm-diam discs were machined from 0.317-cm-thick plate. Chemical analysis information for the type 304 SS material is given in Table I. The discs were ground flat on metallographic paper and given a final polish on Linde B abrasive. A thin support rod was threaded into the disc and the region around the threads was fused under an inert gas. The support rod was fitted with a quartz protection tube and then was attached to a supporting shaft which passed through a rotary push-pull vacuum seal. The disc and supporting shafts were dynamically balanced prior to insertion into the furnace tube. The apparatus is shown schematically in Fig. 1. The 58 pct Bi-42 pct Sn eutectic alloy melts were prepared from 99.995 pct pure Bi and Sn by fusing the components in a 7-cm-ID Pyrex crucible. The system in which the melts were made was evacuated to a pressure of 1 x 10-6 Torr and back-filled with purified argon several times before melting the charge. The ingot was reweighed and placed in a slightly larger-diameter Vycor crucible used in the dissolution runs. A run was started by lowering the disc into the liquid

Jan 1, 1968

By M. C. Flemings, P. J. Ahearn

Dendvite morphology of unidirectionally solidified Sn-12 pct Bi alloy was determined with the aid of X-ray and macroetch techniques. Columnar growth direction (growth direction of primary arms) in this alloy is [110]; secondary arms grow in the [lii], [111), and [112] directions. Interstices between [112] dendrite arms fill in during early stages of solidification so that well-defined (110) planes are seen in the final structure (parallel to the heat-flozo direction). Similarly, interslices betweex the [111] secondary arrlls fill in to form (112) planes, and interstices between [1111 ] arms fill in to form (112) planes. DENDRITE morphology in alloys is conveniently studied in unidirectionally solidified castings. In this type of solidification, heat is extracted from a single chill surface of the casting while other surfaces are insulated. Solidification progresses from the chill and results in cast grains that are columnar with the long axis of the grain perpendicular to the chill. Dendrite morphology is conveniently studied by examination of etched surfaces parallel and perpendicular to the chill, as previously described.'" Experimental studies on the growth direction for tin are in general agreement. The major growth direction is [110]:-' although this is altered somewhat by supercooling. In one study, tin dendrites pulled from a supercooled melt had a growth orientation 12 deg away from the [110] direction toward the [002] direction.' This orientation could be changed back to the [110] or close to the [110] direction by changing the tempera- ture gradient in the melt. In a study using autoradio-graphic techniques, (111) directions were shown to be directions of preferred growth in addition to the [110) direction.7 PROCEDURE The samples employed in this study were cut from 12 pct Bi-88 pct Sn castings, 1.5 in. in diam and 3.5 in. tall. The casting procedure consisted of heating the charge to 390°C and then pouring the molten alloy directly into a gypsum sleeve mounted on a massive copper chill. Specimens were cut from the ingot, mounted, polished, and etched with Taffs reagent [FeC13 .6H2O, 2 g; HC1, 5 cu cm;H20, 30 cu cm; CzHaOH (95 pct), 60 cu cm].' The dendritic pattern was clearly visible after etching. Photomicrographs at about 8 and 35 times were taken on surfaces parallel and perpendicular to the chill. Laue back-reflection patterns were obtained from three different columnar grains in a singIe polished face 2 in. from the chill. The cut face was polished and positioned in the beam of a Laue camera, so that diffraction occurred from a single dendritic grain. The resulting diffraction pattern was interpreted to determine crystal log raphic orientation in relation to the heat-flow direction and in relation to microstruc-ture of the given grain. RESULTS Fig. 1 shows a horizontal and vertical section of the columnar structure, at low magnification. Light regions are rich in tin, and darker regions tin-poor; the primary phase is tin-rich a phase. The two sections shown were taken orthogonally from the same metallographic specimen. It is readily seen from Fig. 1 that the dendrites have

Jan 1, 1968

By Charles C. Fatino, Joel S. Hirschhorn

Loose compacts of strained and annealed stainless-steel powders were sintered at various temperatures and times to determine the effect of residual strains on the sintering behavior. The atomized powders were prepared by annealing, ball milling, and rean-nealing. The residual strains and domain size were determined by a Fourier analysis of X-ray diffvaction dala. The specimens were prepared by siwzultaneously sintering cylinders of both strained and unstrained powder. The evaluation of the sintered compacts included density measurements, metallographic examinations, and analyses of X- ray diffraction data. The results of these studies reveal a definite increase in sintered density and sintering rate for the strained powders. THE pressure compacting of metal powders causes deformation of the particles, mechanical interlocking, and increased contact area. After the deformation, severe residual strains remain in these particles. The subsequent contributions of these strains to the sintering process have been considered to be negligible, since the recovery and recrystallization temperatures usually occur prior to the temperature required for the sintering process. Sintering is con-sidered to be the process by which the powders are transformed into solid compacts at temperatures below their melting points. The sintering operation for stainless steel usually takes place in the range of 2050" to 2400°F (0.84 to 0.95 T,, where T, is the absolute melting point or liquidus temperature) while the temperature required for recovery is approximately 1800°F (0.75 T,). However, it has been shown for several metal powders that densification becomes significant in the range of 0.35 to 0.45 T,.' It is the purpose of this study to determine what effect residual strains have upon the sintering behavior of stainless-steel compacts. Loose compacts were selected for study in order to isolate the strain contributions and eliminate the variables inherent in sintering of pressure-formed compacts. Additional variables were minimized by using only one mesh size, one composition, one particle shape, and also by simultaneously sintering both types of powder. Very little work has been carried out previous to the present study to delineate the effect of strains on sintering behavior. Lenel et 01.2 observed that residual stresses in copper compacts caused shrinkage at comparatively low temperatures. Delisle3 loose-sintered ball-milled electrolytic iron and observed that bonding among particles began at a lower temperature as compared to the behavior of annealed powder. Increased densification of ball-milled oxide powders has also been noted.4'5 EXPERIMENTAL PROCEDURES Powder Preparation. The powder used for this study was a commercial-type 316L stainless steel made by the atomization process. A typical chemical analysis is: C- 0.025 pct Mo- 2.2 pct Cr-18.6 pct Ni-12.5 pct Fe—Balance The atomizing process is essentially the rapid freezing of liquid droplets. This nonequilibrium cooling causes coring to occur and two distinct phases are present within the solid particle, the austenitic phase and the ferritic phase. Due to the presence of this ferritic phase, the particles tended to fracture as well as become cold-worked during the subsequent ball-milling operation. (It was also found that this type of cooling produced a broadened and shifted

Jan 1, 1968

By M. C. Flemings, F. R. Mollard

Conditions necessary for plane front growth of two-piwse solids from a single-phase melt are discussed. Alloys consideved are those from a simple binary system containing a eutectic, but are not, in general, of eutectic cornposition. It is concluded that: 1) plane front solzdification is favored by low growth rate, steep thermal gradient, and essential absence of convection; and 2) for steady-state solidification, the structure should resemble that of directionally solidified eutectics (lamellar, rodlike). Factors affecting THERE are many materials, including metals, available today with strengths in excess of 10' psi when in whisker or fiber form. The challenge facing those interested in practical application of such materials has been, and remains, the economic production and incorporation of the whiskers or fibers into useful engineering composites. solute redistribution along the growth direction are described quantitatively, by numerical solution of the diffusion equation. Effects of variations in growtlz rate on average composition of the solidifying composite are significant. For alloys not too close to a single-phase region, the initial transient at constant gvowth velocity is the order of D/R where D is diffusion coefficient in the liquid and R is interface velocity. Composites consisting of the reinforcing phase within a metallic matrix have excited particular interest in recent years because of their potential for high strength at elevated temperature and for resistance to brittle fracture. Techniques employed to incorporate the whiskers or fibers in the metallic phase have included 1) liquid metal infiltration, 2) solid or liquid phase sintering, and 3) direct growth of composites from the melt, of rodlike or lamellar morphology, by directional solidification of eutectic alloys. Two recent books"2 have reviewed the status of this growing field. Concerning the last method, growth of eutectics, it has been shown that the reinforcing phase (e.g., rods)

Jan 1, 1968

By M. C. Flemings, F. R. Mollard

Two-phase Pb-Sn alloys, ranging in compositiotz from 12 to 26 at. pct Pb, were unidirectionally solidified in a convection-fvee system, with thermal gradients in the liquid of up to 480°C per cm. Plane front solidification Loas achieved in all alloys at sufficiently steep gradient and slow growth rate. Conditions causing breakdown of the interface to a cellular or dendritic structure were roughly as predicted by a sinlple constitutional supercooling criterion. Structures of alloys of near-eutectic composition, solidified with plane front, exhibited a lamellar structure; the alloys furthest from the eutectic exhibited a rod-like morphology. Assumptions used in a previous paper for calculations of solute redistribution in two-phase plane front growth are shown to be reasonable for Pb-Sn alloys. Results of calculations are in good agveement with experiment. These show that variations in growth rate during solidification of the composite produce marked changes in average composition of the solid. IN a previous paper, Part I,' conditions necessary for plane front solidification of two-phase alloys were discussed and calculations given on solute redistribution in this type of solidification. This paper, Part 11, describes experiments on Pb-Sn alloys, designed to check the assumptions of the analyses presented, and to demonstrate their applicability to a given alloy system (Pb-Sn). APPARATUS AND PROCEDURE General. A vertical crystal growing unit was built for the study as described below, and "normal solidification" employed throughout (i.e., the ingot was completely melted except for a portion near the bottom end and then solidification initiated). The furnace was designed to permit achieving very low interface velocities, and steep gradients, in essential absence of convection; it is sketched in Figs. 1 and 2. Simple heat flow considerations indicated choice of a small-diameter specimen (ingot) to achieve high thermal gradients; ingot size chosen was 0.3 cm in diam. The ingots were held inside silica tubes 0.06 cm wall thickness. The requirement for an essentially convection-free system was met by use of the vertical furnace with the heat source over the heat sink, as well as by use of the small diameter ingots. In addition, by selection of tin-rich Pb-Sn alloys, the diffusion boundary layer (lead-rich) was denser than the bulk liquid and would not cause convection. The only apparent driving force for convection in this system was the small transverse temperature gradient resulting from heat flow into the samples from the furnace. Such convection must have been small, however, since 1) no temperature fluctuations in the melt were noted in the recordings, which would have indicated turbulent convection, and 2) experimental results obtained and described below could not have been achieved in presence of significant convection. Ingot Preparation. Pb-Sn alloys ranging from 12 to 26 at. pct Pb were prepared from high-purity lead and tin (99.9999 pct pure metal). Each alloy was prepared by first melting the pure metals in the proper ratio in air, in a Pyrex container. The melt was then stirred thoroughly with a graphite rod and cast into a preheated graphite mold. Ingots were then prepared from these castings for use in the actual experiments; each ingot consisted of a rod of alloy, 15 cm long in a 25-cm-long transparent fused-silica tube, 0.3 cm ID and 0.06 cm wall thickness. One chromel-alumel thermocouple, made with 0.004-in.-diam wire and protected by a two-hole alumina tube, was inserted into each ingot. The 1.5 cm of the thermocouple nearest the bead were protruding from the alumina tube and were coated with a very thin layer of boron nitride paste which provided electrical insulation while allowing good heat conduction. The electrically welded junction size was about that of each wire and the cross section of the two wires represented about 0.3 pct of the sample cross section. Including the coating, the thermocouple cross section still represented less than 0.5 pct of the ingot cross

Jan 1, 1968

By J. C. Coughlin, M. C. Flemings, T. Z. Kattamis

Experiments on Al-4.5 pct Cu alloy shou the dendrite arnz spacing increases with time during isothermal holding in the liquid-solid region. This coarsening of the dendrite structure is then shown to occur at roughly the same rate during solidification as during isothermal holding. Final dendrite arm spacing in both types of experiments depends primarily on coarsening kinetics. It is concluded that driving force for the coarsening is reduction of liquid-solid sur/ace area. Calculations based on two simple models show qualitative apreement with experinzent. 1 HERE has been considerable interest in recent years in determining effects of solidification variables on dendrite arm spacing in cast alloys. The interest has resulted primarily from the clear evidence that 1) the degree of homogeneity which can be obtained in a cast alloy with commercially practical homogeni- zation treatments depends on dendrite arm spacing, and 2) mechanical properties of the heat-treated casting depend on the homogeneity obtained.'-' In wrought alloys, microsegregation from the original ingot is carried to some extent into the final wrought product, and affects mechanical properties in similar fashion Experimental evidence available indicates that dendrite arm spacing in cast aluminum alloys is influenced only by cooling rate (or "local solidification timev*) and alloy content.Fig. 1, for example,

Jan 1, 1968

By F. E. Pawlek, J. K. Gerlach

The chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. In the first part of the investigations the reaction rate of the chlorides of sodium or calcium with gas mixtures of SO,-0, or SO ,-O2 ,-SO , was measured. The rate for reactions with gas mixtures SO2-O2 is ThE chloridizing roasting of ores is applied when metal sulfides and oxides are to be converted into soluble or volatile compounds. At present the process is mainly applied to produce nonferrous metals which occur in pyrite cinders in small concentrations. Thereby the nonferrous metals are converted into water-soluble, acid-soluble, or volatile compounds whereas all the iron remains as insoluble oxide. The chlorine required is either obtained from the admixed chlorides of sodium or calcium or added in the gaseous state. The reactions occurring during the roasting process can be divided into two groups: solid-solid reaction and gas-solid reaction. The reactions between solids proceed by means of solid-state diffusion and are therefore of low velocity. The heterogeneous reactions between solids and gases of the roasting atmosphere5 are high-velocity processes and determine the velocity of the chloridizing roasting. These gas-solid reactions shall be the subject of the paper presented. In order to investigate the still little-known processes which occur during the chloridizing roasting 6-' the complex reaction is split into several partial steps. First the reactions of NaCl and CaCl, with gas mixtures of SO2 and 0, have been investigated at temperatures between 500" and 600°C by measuring the weight increase of the samples. The gas mixtures used in this series of experiments had first variable compositions, then the amount of SO 2 had been increased. Furthermore the influence of Fe 2 O3 admixtures upon these reactions, the behavior of pure Fe 2 O3 with the gaseous reactants, and the chlorination of the sulfides of lead, copper, nickel, and zinc have been investigated. FORMATION OF GASEOUS CHLORINE Pyrite cinders are never completely roasted and therefore contain still a small amount of sulfide sulfur. When heated again in air, this sulfur is converted into SO,. Accordingly the formation of chlorine can first be described by the reactions: dependent on the composition of the gas phase. If more than 1 pct SO 3 is added to the roasting gas, the reaction rate is determined only by the concentrations of the SO,. In the second part the reactions between chlorine and metal sulfides are discussed. The rate of formation of gaseous chlorine is higher by me order of magnitude than is the reaction rate between ZnS and chlorine. The reaction rate of NiS and PbS lies considerably below that of ZnS. The conversion rate of both pure Fe 2 O 3 and Fe 2 O 3 containing NaCl or CaCl2 when reacting with SO2-O2, mixtures with and without SO3 portions was measured at temperatures of 500", 550°, and 600°C. The weight increase of pressings was determined by means of a spiral balanceg and the reaction rate calculated therefrom according to Eqs. [ll to [31 and [5] to [7]. The prepared samples were suspended on a platinum filament in a vertically mounted tube of mullite (ID 4 cm, length 110 cm) which could be heated by a resistance tube furnace. The platinum filament was tied to the lower end of the spiral balance. A supremax glass tube (length 70 cm) was mounted gas-tight on top of the reaction tube. The unit was sealed up at its top by a ground-in stopper which was holding the spiral balance with the sample. The spiral balance therefore hung outside the high-temperature region of the furnace. Fig. 2 shows the experimental arrangement schematically. While lowering the sample into the reaction tube pure nitrogen was flowing through the reaction zone providing a protective atmosphere. After the sample had reached the reaction temperature within approximately 1 min, the protective gas was replaced by the sulfur dioxide-oxygen reaction mixture. It took about 30 sec until the mixture filled the tube homogeneously. A Ni/NiCr thermocouple placed in the center of the furnace where the sample hung during the measure-

Jan 1, 1968

By Peter R. Morris

The effecl of preferred orienlation on X-vay dzffvaction measurements of retained austenzte was investigated for four precipitation-hardening staznless steels in sheet form. A method is preserzted for estimating the ervor in measurement associated with a given samplirig direction. The method was used to select an "optimum" sampling direclion in order to minimize errors in measurement due to preferred orientation. hleasuremenls of retained austenite content employing lhe proposed sampling direction are conzpaved to measuretnents enzploying the more commonly used normal direclion for a series of sawzples. THE first application of X-ray diffraction to the measurement of retained austenite in steels is due to Sekito, 1 who employed a photographic technique in which the (111) reflection from a thin strip of gold affixed to a cylindrical sample was employed as a standard. Averbach 2 introduced the "direct comparison" method in which the ratios of observed to calculated random intensity are assumed proportional to the austenite and/or martensite contents. Averbach's work forms the basis of most subsequent X-ray diffraction methods for the determination of retained austenite. Subsequent improvements are due to: Averbach and Cohen,3 who employed a sodium chloride crystal to monochromate cobalt radiation; Averbach et a1.,4 who introduced a bent sodium chloride monochromator; Mager,' who used a bent quartz crystal to monochromate chromium radiation ; Littmam, who first used a geiger counter diffractometer for this purpose; Beu and Beu and Koistinen, 11,12 who studied effects of absorption factor, surface preparation, sample geometry, integrated intensity vs peak height, choice of radiation, monochromator, and filter. The possibility of errors in measured values due to orientation effects was noted by Miller,13 who suggested examination of a surface other than the plane of rolling. Lopata and Kula 14 have developed an experimental technique in which the preferred orientation is measured in each sample. They illustrated the method for a sample containing 42 pct retained austenite. Application of their technique to the 1 to 15 pct range typical for the precipitation-hardening stainless steels does not appear feasible. EXPERIMENTAL PROCEDURE The nominal compositions of the precipitation-hardening stainless steels investigated are listed in Table I. Ingots were solution-treated, hot-rolled to approximately 0.2 in., and reduced to 0.050 in. by a suc- cession of cold rolling and annealing operations. After this treatment the 17-4PH sample was in the marten-sitic condition, while the 17-7PH, PH 14-8Mo, and PH 15-7Mo samples were in the austenitic condition. Samples of 17-7PH and PH 15-7Mo steels in the mar-tensitic condition were obtained by heating to 1750'F for 10 min and holding at -100°F for 8 hr. A sample of PH 14-8Mo steel in the martensitic condition was obtained by heating to 1700°F for 1 hr and holding at -100°F for 8 hr, followed by aging at 950" for 1 hr. POLE FIGURE DETERMINATIONS Samples were thinned to 0.003 to 0.005 in. by etching in a solution containing 250 ml reagent-grade phosphoric acid (85 to 87 pct H3PO4), 250 ml technical-grade hydrogen peroxide (30 to 35 pct H 2 O 2), and 50 to 100 ml reagent-grade hydrochloric acid (37 to 38 pct HCl). The specimens were placed in an "integrating" sample holder which provided a 1-in. oscillation in the plane of the sample. The diffractometer was aligned to measure the intensity diffracted by planes of the particular {hkl} type being studied. The sample was Set for a given latitude angle, a, measured from the plane of the sheet, and diffracted intensity recorded as the longitude angle, 0, measured in the plane of the sheet from the rolling direction, was increased from 0 to 360 deg. After a 360-deg scan of B, a was incremented by 5 deg, and the process repeated. Random standards obtained by spraying suspensions of powdered iron (bcc structure) and nickel (fcc structure) in lacquer were used to correct observed intensities for absorption and geometrical effects. Zirconium-filtered molybdenum radiation was used to determine the transmission regions of the (111) (0to 45 deg), (200) (0 to 60 deg), and (220) (0 to 45 deg) austenite and (110) (0 to 45 deg), (200) (0 to 50 deg), and (211) (0 to 35 deg) martensite pole figures. Vanadium-filtered chromium radiation was used to

Jan 1, 1968

By David Kramer, Cecil G. Rhodes

Critical transport currents were measured as a function of perpendicular external magnetic field in Ti-22 at. pct Nb wire samples. These samples were heat-treated to yield w Phase precipitates at denslties ranging from 10 to 10 17cm-3. The Precipitates are ellipsoids of revolution with major axes of 50 to 1300A. Flux-Pinning by w precipitates is responsible for the high critical transport currents that were ob- ThE ability of a type II superconductor to sustain a zero-resistance transport current (Jc) in an external magnetic field (H) is due to the presence of micro-structural features which can impede the motion of magnetic flux penetrating the superconductor under the influence of a Lorentz force. Such features are referred to as pinning sites. The pinning strength is tained. A sample cooled from 800°C and annealed 1 hr at 450°C carried a critical tramport current of 10 amp per sq cm at 30 kG. Variations in the current-carrying ability of this alloy are due to changes in its pinning strength which is a function of precipitate density and composition and of the composition of the matrix. the reaction of the bulk superconductor to the Lorentz force and depends on the efficiency of the individual pinning sites and on their volume density. The super -current density increases with pinning strength, other things being equal. The above concepts are discussed in detail in a comprehensive review by Livingston and Schadler.' In Ti-Nb alloys, as in other binary titanium alloys, the metastable hexagonal w phase usually forms below the p/a + p phase boundary near the titanium side of the phase diagram. Stiegler et a1.' have summarized much of what is known about w phase in titanium and zirconium binary alloys. The present work deals with

Jan 1, 1968