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By B. Chalmers, Stefan Wojciechowski

Rotary oscillation of the mold has been used to produce mechanical stirring of the melt during unidirectional solidification. Al-Cu alloys (1 to 4 wt pct Cu) were solidified to study the influence of alloy composition, temperature at which intensive cooling was initiated, and intensity of stirring on the temperature distribution in the sample, the resulting structure, and the copper microsegregation at the columnar to equiaxed transition. The Proposed explanation for the equiaxed solidification in stirred castings consists of the melting off of dendrite fragments, their partial remelting in hotter liquid, and the subsequent growth of the surviving part when the temperature of the melt is lowered. This may result in the formation of a crystal network, which can stop the growth of the columnar crystals and produce the equiaxed zone. It has long been known and many times affirmed that ultrasonic vibrations or relative motion of liquid and solid can significantly reduce the length of the columnar zone and refine the grains in the equiaxed zone in ingots and castings. Because of the technological importance of these phenomena many investigations have been conducted in which ultrasonic energy or mechanical vibration,1-6 electromagnetic stirring,7"10'17 magnetic stirring,"'12 or mechanical stirring13'14 were used to produce the relative liquid-solid motion. More recently, the question of the importance of natural (or thermal) convection has been raised.15-l7 Several possible mechanisms have been suggested.l,8,18-20 They can be divided into two main groups. The first group includes such nucleation hypotheses as nucleation frequency enhancement due to cavitation at the mold wall or other surfaces; cavita-tion in the body of the liquid resulting from the pressure wave, or an agglomeration mechanism, which involves the formation of nuclei by the accretion of subcritical nuclei. The second group considers the grain-refining action to be due to crystal multiplication phenomena such as the removal of the dendrite fragments by viscous forces or by a high-pressure cycle following cavitation or by a melting-off process. Sbme recent investigations give good experimental support to the melting-off proposa1.21-23 The purpose of the present study was to examine the effect of mechanical stirring during the unidirectional solidification on the structure of alloy samples and on the solidification variables. The motion of the liquid was produced by rotary oscillation of the mold around its vertical axis.

Jan 1, 1969

By H. I. Aaronson, C. Laird

Cold rolling by 50 pct a A1-4 pct Cu alloy containing many 0' plates has been found to accelerate markedly the transformation of 8' to 0 upon further aging. Although the basic mechanism of this transformation remains unchanged by plastic deformation, the nuclea-tion kinetics of 8 become appreciably more rapid and also less dependent upon temperature. Particularly at lower aging temperatures, rounded idiomorphs replace several faceted rnorphologfes. The rates of growth of 9 idiomorphs in deformed specimens aged at 300°C are appreciably more rapid than simple volume diffusion control allows. This observation is shown to be explained by an excess vacancy, rather than by a dislocation Piping mechanism of growth. ThE rather complex phenomenology of the 8' —8 transformation in Al-Cu alloys has been recently elucidated in considerable detail by means of transmission electron microscopy.'-4 This technique was also employed in the present investigation in order to examine the effects of plastic deformation upon the transformation of 8' to 8. The mechanism of the transformation in undeformed Al-Cu alloys has been established as the following sequence of events.1"4 The first step is the nucleation of 9 at (Y:8' boundaries. Nucleation of a 0 crystal takes place, however, at only a very small proportion of the 8' plates present. Each 0 crystal simultaneously consumes the host 8' plate and the a! in the immediate vicinity, with growth into a being the rate-controlling process. The remaining 8' plates are then dissolved as they fall under the concentration shadow of the growing 8 crystals. The evidence on the effects of plastic deformation upon these processes is intriguing, but much less detailed. The careful X-ray studies of Graf and Guinier have shown that the aging times required to form detectable amounts of 8' and 8 are reduced by prior cold working. Thomas and Nutting confirmed these results by replication electron microscopy. Nile-shwar,* on the other hand, reported that creep deformation decreases the rate of formation of 0. While this difference may have been caused by the use of concurrent rather than successive deformation and ag- ing, the X-ray technique which he used was able to monitor only the 0 phase. It is thus possible that the times needed to form 8' were increased moreg than the kinetics of 8' — 8 transformation were accelerated. At 90 pct deformation by cold rolling, Graf and Guinier found that the usual 0' —0 8 sequence is reversed: 0 forms first. von Heimendahl 10 confirmed this result with transmission electron microscopy. Pollard and Nutting, 11 and more recently Driver and Barrand, 9 having used the same technique, report that 9 also forms first during creep deformation. In the present study, the maximum amount of deformation was limited to 50 pct reduction by cold rolling in order to insure that 8 formed principally by the decomposition of . I) EXPERIMENTAL PROCEDURES This investigation was conducted on an Al- 3.93 pct Cu alloy, prepared as previously described. 4 Morphological and crystallographic effects of plastic deformation were studied in specimens annealed 6 hr at 548°C, quenched, and then aged for either 3 or 8 hr at 250°C to form large numbers of 0' plates. After cold rolling to a 50 pct reduction in thickness, the

Jan 1, 1969

By J. P. Neumann, Y. A. Chang

Lattice parameter measurements of the hcp phase in the system Ag-A1 near the stoichiometric composition Ag2Al were carried out for specimens quenched from 825°K, annealed for 10 days at 453°K, and annealed for 100 days at 413°K. The three heat treatments resulted in the same lattice parameters at room temperature. None of the specimens showed any superlattice lines. The lattice parameters of this alloy were also measured at temperature from 77° to 750°K. An anomaly in the temperature variation of the lattice paramete.rs occurs in the region near 400°k, which may be associated with local ordering. FROM measurements of the diffuse scattering of X-rays, it is known that the [ phase in the system Ag-A1 near the stoichiometric composition Ag2A1 ex- hibits a considerable degree of short-range order at room temperature.' Moreover, based on the position of the short-range order peaks a superlattice model had been proposed in the same study and it was suggested that lowering the annealing temperature to 420°K might result in long-range order. In the present study, the diffraction patterns and the lattice parameters of three differently heat-treated specimens, i.e., quenched from 825°K, annealed for 10 days at 453°K, and annealed for 100 days at 413°K, were determined from 77" to 750°K. The purpose of these measurements was to investigate 1) whether long-range order could be established by prolonged annealing and 2) whether the lattice parameters at room temperature depended on the heat treatment, since it had been proposed earlier2 that the lattice parameters in this phase are related to the atomic arrangement. 1) EXPERIMENTAL TECHNIQUES Silver and aluminum, both 99.99 pct purity, were melted in a zirconium oxide crucible under helium in

Jan 1, 1969

By John C. Bilello

The brittle fracture behavior of cold-worked sintered tungsten was studied over the temperature range 4.2° to 298°K using a high-sensitivity strain measuring system and electronfractography. Similar observations were made on a swaged electron beam zone-refined monocrystal. In sintered tungsten irreversible plastic deformation was observed during cyclic load-unload tests at stress levels well below the fracture stress for all temperatures, but general microyielding could be detected only down to 202°K. For the zone-refined samples macroyielding occurred at all test temperatures with evidence for twinning below -202°K. The fracture stress of the sintered tmgsten was virtually independent of temperature, while the zone-refined crystal showed a 2.3 times increase over the same temperature range. Electronfractography confirmed the presence of numerous rod-shaped and spherical submicroscopic voids which ranged in diameter from 1400 to 4300A in the sintered tungsten; no voids could be found in the zone-refined tungsten. Contrast effects observed on the replicas in the vicinity of certain voids indicated that plastic deformation could be induced by the local stress concentration. It has been suggested that the presence of these voids may be responsible for the low-temperature brittle failure of sintered tungsten. Based m this suggestim und on the evidence obtained here, a dislocatim model is presented to account for the brittle behavior of sintered tungsten. In this model slip, which is induced by the local high stress concentration in the region at the edge of a favorably oriented void, could cause the void to grow to a microcrack of critical size. STUDIES of brittle fracture in bcc metals have led to the well-known experimental relationships between grain size, yield stress, fracture stress, and temperature which have formed the basis for the various dislocation pile-up1-3 or interaction4'= models for slip-induced microcrack nucleation. While microcracks can be nucleated by deformation twins,6,7 there has been no direct evidence furnished by transmission electron microscopy to support conclusively either the Zener pile-up or Cottrell dislocation reaction models for producing micro-cracks in all "brittle" materials. In addition to the "inverse" grain size relationship for yield and fracture stresses the cottrel14 theory predicts that the fracture stress below the transition temperature should behave in a fashion similar to that of the yield stress above this temperature. Such behavior has been verified for several bcc metals.8-10 With reference to both grain size effects and the tem- perature dependence of the fracture stress below the transition temperature, the behavior of sintered tungsten appears anomalous. Early work by Bechtold and Shewrnon 11 showed no apparent temperature dependence of the fracture stress below the ductile-brittle transition temperature (DBTT). They attributed this result to the intergranular nature of the fractures observed. More recent work by Wronski and Four-deux12'13 on considerably purer material did not show any systematic relationship between the fracture stress and temperature below DBTT. The dependence of flow and fracture stresses on grain size is also not clearly established for sintered tungsten. Koo, for example, has shown that the DBTT for sintered tungsten depended chiefly on the annealing temperature and was relatively insensitive to the actual grain size achieved. Using electrofractography and transmission electron microscopy, Wronski and Fourdeuxl3 showed that numerous spherical and rod-shaped submicroscopic voids could be found in sintered tungsten but not in melted tungsten of nominally the same purity. They suggested that these voids could be responsible for the temperature insensitivity of the fracture stress below the DBTT. In the present work the temperature dependence of the fracture stress for high-purity commercially sintered tungsten has been determined. The presence of submicroscopic voids in sintered materials was confirmed, and these were studied in detail to examine the role they could play in nucleating brittle fracture. A dislocation model is suggested which could cause an inherent spherical void to lengthen into a Griffith crack of critical size. EXPERIMENTAL PROCEDURE Commercially sintered tungsten rod was obtained in the as-swaged condition from Sylvania. A zone-refined crystal was obtained from the same source. This crystal was grown by giving three zone passes (at 25.4 cm per hr) to a sintered rod of high-purity tungsten. The rod axis prior to cold working was -15 deg from the [110] direction. Originally the zone-refined rod was -6 mm in diam; it was reduced to -3 mm by eight swaging passes, at high temperatures, with each step having about the same reduction of area. The final swaging step gave a 7.5 pct reduction of area at 1050°C. All swaging operations were performed in a hydrogen atmosphere. For the sintered rod a similar working schedule was employed. Metal-lographic examination of the sintered material revealed that the cold-worked structure had an apparent grain diameter of -25 u transverse to the swaging direction (obtained by the intercept method). In the longitudinal direction cold-worked grains were approximately 1.5 to 2 times their diameter. No distinct fiber structure could be observed optically for the zone-refined rod. The cold-worked structure in the

Jan 1, 1969

By Z. Moser, W. Ptak

The experiments were carried out by the method of measuring the electromotive force of concentration cells having zinc as a reference electrode, the second electrode being the liquid alloy Zn-Sn-Cd-Pb. The electrolyte consisted of liquid chlorides and had zinc ions. The measurements were made for seventy -five alloys of different mole fractions within the temperature range of 714° to 877°K. The experimental results enabled the calculation of the activity of zinc in tested solutions. The activities of zinc were calculated by means of Krupkowski's formulas.3 In addition, the formulas for coefficients of activity of zinc, tin, cadmium. and lead as the function of composition and temperature were given. Activity of zinc was compared with the values obtained from experimental results, and good agreement has been observed. On this basis it can be stated that the theoretical formulas are suitable for determining the thermodynamic properties of liquid quaternary metal solutions. IN the metallurgical processes being carried out at present multicomponent liquid metal solutions take part. For the thermodynamic analysis of these processes it is necessary to know the thermodynamic properties of these solutions. Therefore, many experimental and theoretical papers deal with this problem. The theoretical papers are generally based on the assumption that the structure of liquid metals is similar to their structure in the solid state. In this manner the model of liquid solution, consequently described by means of statistical thermodynamics, has been accepted. This method is being lately developed, especially for solid solutions. Statistical thermodynamics was applied among others by Guggenheim 1 for describing the thermodynamic properties. Unfortunately, the formulas of statistical thermodynamics are often not suitable for the interpretation of experimental results. Attention should be drawn to the relations obtained by means of formulas of phenomenological thermodynamics which always have constants derived with the aid of experimental methods. In the case of the multi-component solutions which contain some additions of impurities besides the basic metal, wagner2 introduced interaction parameters. Equations for the relationship between the activity coefficients and composition were also given by Krupkowski." he application of these formulas requires a good knowledge of the thermodynamic properties of the corresponding binary systems. In these formulas, as in Wagner's, there appear constants which should be determined from ex- perimental data. Nowadays, different experimental methods are applied for evaluating the thermodynamic functions of solutions, for instance: vapor pressure measurements, calorimetric methods, and the measurements of electromotive force of concentration cells. In the present paper this last method for evaluating the thermodynamic properties of four-component systems, Zn-Sn-Cd-Pb, was applied. For instance in the case of Zn-Sn solutions Alabyshev and Landratov, 4 Fiorani and Valenti, 5 and ptak6 performed the investigations. The Zn-Pb system was worked out by Kleppa 7 and Cd-Pb and Cd-Sn by Elliot and chipman.' This method was also applied for determining the activity of zinc in ternary solutions. 1) EXPERIMENTAL METHOD The experimental arrangement with detailed description is given in Fig. 1. It consists of resistance furnaces, one serving for melting samples and the other containing the flat-bottomed, measuring quartz tube with the liquid electrolyte. Liquid metals and alloys are in glass supremax tubes, which have an opening in their lower part above the metal level. This opening allows the filling of the tubes by the electrolyte. In these tubes tungsten wires are placed which by means of suitable conductors are connected with a potentiometer. It is assumed that tungsten dissolves Fig. 1—Schematic diagram of the experimental arrangement for the investigation of the thermodynamic properties of liquid metal solutions: 1, resistance furnaces; 2, autotransfor-mers; 3, galvanometers; 4, regulator of temperature; 5, gas purifier with concentrated H2SOP; 6, U-tube with P2O5; 7, thermostats; 8, steel block for thermostating; 9, supremax tubes for alloys; 10, tungsten electrodes; 11, inlet and outlet of argon; 12, measuring quartz tube; 13, tube for melting samples; 14, tube for thermocouple; 15, cover of quartz tube; 16, rubber seal; 17, bottom cover; 18, outlet of electrodes to potentiometer; 19, outlet of thermocouples to potentiometer; 20, upper view of the quartz tube cover; 21, orifices for cover screws; 22, orifice for argon inlet; 23, orifice for thermocouple; 24, orifices for tubes containing liquid metals; 25, inlet for water-cooling system.

Jan 1, 1969

By J. Szekely, Robert J. Fisher

A formulation is Presented and solutions are given for the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its environment. The solutions were obtained by the numerical integration of the appropriate Partial differential equation and are Presented in a graphical form by Plotting a dimensionless average temperature against the Fourier number with the radiation number as a paranreter, for various initial sphere and environment temperatures. In addition to these numerical results asymptotic analytical solutions are also given. PROBLEMS involving the transient heating or cooling of droplets and particles frequently arise and are of importance in metallurgical operations. Spray refining, vacuum degassing, high-temperature gas-solid reaction systems, and pebble heaters are but few of the numerous examples that may be quoted. The practical interest in these problems from a design or operational point of view is to evaluate the change in the particle temperature with the time given its physical properties, initial temperature, and that of the environment. At the high temperatures encountered the principal mode of heat transfer between the particles and their environment is by thermal radiation; in case of vacuum degassing due to the very low thermal conductivity of the gas space the convec-tive components are negligible and radiation is the only heat transfer mechanism. Although much work has been done on transient heat conduction problems, the special class mentioned here, in which thermal radiation is specified at the bounding surface, received little attention to date. One contributory factor to this situation may be the nonlinearity of the radiation term in temperature, which in general precludes the use of analytical techniques and requires numerical or analog solution of the appropriate differential equations. In fact the only solutions of general nature that are available at present pertain to semi-infinite media and slabs.'-3 The work on which the paper reports forms part of a program aimed at the theoretical and experimental study of transient radiative heat exchange between particles and their environment. The purpose of the present paper is to develop a formulation and solutions to the problem of transient heat conduction in a sphere that undergoes a spatially uniform radiative heat exchange with its surroundings. The solutions, obtained by the numerical integration of the appropriate differential equations, will be presented graphically, by plotting dimensionless parame- ters covering the range of variables relevant to metallurgical interests, thus affording a ready reference for design calculations. In addition to these results, approximate analytical solutions are also given which represent asymptotes, corresponding to extreme values of the variables mentioned. FORMULATION Consider a spherical particle of radius, a, initially at uniform temperature, Ti (T measured on the absolute scale), having a thermal conductivity, k, density, , specific heat, C, and thermal diffusivity, a. At time = 0 let this particle be exposed to an environment which is at a temperature T, and subsequently let there be a purely radiative heat exchange between the particle and the environment resulting in a spatially uniform heat flux at the surface. If in addition to the above we make the assumptions that the sphere is a gray body radiator, homogeneous, isotropic, and opaque, and that the physical properties are independent of temperature, conservation of heat in the sphere may be written as follows: The boundary condition contained in Eq. [3] states that the initial temperature of the sphere is considered uniform, equalling Ti, whereas Eq. [4] is readily obtained from symmetry considerations. Eq. [5] expresses the continuity of the heat flux at the surface of the sphere, or in other words the condition that the rate of heat exchange between the sur-

Jan 1, 1969

By I. S. Servi, N. W. Marr

TIN markedly increases the softening temperature of pure copper with only a moderate effect on conductivity. Smart and smith' indicated a substantial increase in softening temperature upon addition of different levels of tin up to 0.05 pct in oxygen-free copper. However, after finding no effect of tin in copper containing about 0.025 pct O, they concluded that "the presence of oxygen completely nullifies these changes in properties by precipitation of SnO2.'' Since preliminary tests on Cu-Sn-0 alloys indicated that this conclusion is not valid outside the extremely limited tin range investigated by Smart and Smith, research was primarily directed toward the partition of tin between the copper-base matrix and the oxide phases. Experimental. Material was prepared by sealing an 80 to 100-g charge consisting of oxygen-free copper, tin, and copper oxide into a y-in.-ID quartz capsule which was evacuated and back-filled with tank-grade argon to 3 atm. The sealed vials were heated to 1125ºC, kept at temperature for 30 min, occasionally agitated, and then allowed to air-cool outside the furnace ("as-cast"). The castings were cold-swaged to 0.370 in., annealed 1 hr at 600°C ("as-annealed"), and cold-swaged 16.5 pct ("as-swaged"). Cross sectional wafers were annealed for 1 hr at various temperatures and Rockwell F hardness measured. The "softening temperature" was defined as the interpolated temperature at which the hardness was 50 Rockwell F. Electrical resistance was measured by an ac poten-tiometric method on 0.040-in.-diam wires after a 1 hr anneal at 600°C. Relative accuracy was of the order of 1 pct. Chemical analyses for tin were performed by two methods, identified as "Acid flux" and "HN03 dissolution". The first consisted of fusing the sample with potassium pyrosulfate and leaching the resulting melt with 10 pct sulfuric acid. The spectrophotometric procedure which followed is described in Ref. 2. Oxygen analyses were performed by the vacuum-fusion method with a bath temperature of 1650°C. Tin content of oxides and copper phases was measured with the X-ray microprobe, using a calibration curve based on a series of oxygen-free Cu-Sn alloys. Results. In Fig. 1, the nominal tin composition for alloys containing nominally 400 ppm O was plotted vs the analyzed or the computed tin content—the latter derived from one of the following: 1) "acid flux" chemical analysis; 2) "HN03 dissolution" chemical analysis; 3) X-ray microprobe analysis of the copper matrix; 4) equivalent tin content, based on the measured increase in electrical resistivity (an increase in resistivity of 1.6 microhm-cm is approximately equivalent to 1 wt pct of sn1,3). It is evident from Fig. 1 that the results of the acid flux analysis are consistent with the nominal composition while the HNO3 dissolution method generally yields lower values, consistent with those obtained from electrical resistivity measurements and somewhat higher than those obtained by microprobe analysis. Microprobe and resistivity values are affected only by the tin in solid solution; hence the HN03 method

Jan 1, 1970

By P. T. Gallagher, W. A. Oates, J. A. Lambert

FAIRLY extensive equilibrium data exists for carbon dissolved in r iron.1-8 However the temperature coefficients of the carbon activity, ac , are insufficierltly preciseto reveal whether the heat of solution of carbon, ?HC , varies with composition. It is doubtful

Jan 1, 1970

By S. Zelouf, G. Simkovich

THE role that impurities play as dopants in the movement of species in ionic and semiconductor crystals was first conclusively demonstrated by Koch and Wagner.' At a later date Wagner demonstrated the effect of small amounts of alloying additions upon oxidation rates of pure metals, i.e., the effect of impurities as dopants in the scale being formed.'

Jan 1, 1970

By A. P. Coldren, V. Biss

SINCE the r ? a transformation rates of many carbon-free ferrous alloys and low-carbon alloy steels are relatively fast, conventional equipment is not suitable for the dilatometric determination of continuous cooling transformation diagrams. On the other hand, a method based on metallographic analysis of quenched specimens would not be practicable because the various products of shear-dominated transformation are essentially indistinguishable in low-carbon iron-base alloys. Both problems may be avoided by a thermal analysis method employing gas quenching of small specimens austenitized in vacuo. The laboratory equipment employed in the present study consisted of a Tektronix Type 564 Storage Screen Oscilloscope and a Kinney high-vacuum evaporator, modified as shown in Fig. 1, to permit heating a small specimen and cooling it slowly by programmed cooling or rapidly (up to about 8000°F per sec) by a controlled quench with helium gas. The oscilloscope records the electromotive force of a 40-gage (0.003-in.-diam) Chromel-Alumel thermocouple in the specimen during cooling. The temperature at which the cooling curve begins to show the influence of the heat produced by the phase change in the specimen was arbitrarily taken as the transformation-start temperature.*

Jan 1, 1970

By Peter L. Raffo, Walter R. Witzke

RHENIUM has a melting point of 5750°F, the second highest value among the metals.1 Its refractory nature should thus make it a useful material at high temperatures. The only available data on the high-temperature properties of bulk rhenium are from the work of Flagella and Tarr.2 These authors have shown that, over a wide range of temperatures and stresses, no appreciable linearity exists in a log-log plot of the minimum creep rate or rupture life vs stress. The purpose of the present letter is to describe some exploratory experiments designed to study the creep rate-stress-temperature relation and other facets of the creep of rhenium. The tests were carried out in vacuum in the temperature range 2200" to 4000°F (0.43 to 0.72 Tm,) at stresses ranging from 4 to 20 ksi. The powder metallurgy rhenium was purchased as 0.04-in.-thick sheet. The sheet is nominally 99.97 pct pure with the major impurities being iron (70 ppm) and molybdenum (25 ppm). The sheet was machined into specimens having a 1-in. gage length and a 0.25-in. gage width. The specimens were preannealed in hydrogen at 3000°F for 1 hr. This treatment produced

Jan 1, 1970

By B. C. Wonsiewicz, G. Y. Chin

THE presence of deformation bands in cold-worked metals is known to influence the development of deformation textures1 but has not been considered in any theoretical treatments. At the present time the most rigorous theory of deformation textures appears to be based on Taylor's concept of homogeneous deformation of a crystal within a polycrystalline aggregate.' For each crystal the Taylor theory allows the operation of several equivalent combinations of five or more slip systems. Hence deformation bands can arise from the operation of a separate combination of slips in each of several portions within a crystal. On the other hand, a second type of band may occur as a consequence of slip on systems other than those selected on the basis on homogeneous deformation. This type appears to be associated with crystals of symmetrical orientations, such as the [loo] and [lll.] axial orientations in drawn wires of fcc single crystals studied by Ahlborn.3 In this note we propose a simple mechanism of deformation banding of the second type, and compare the theoretical results for wire drawing of [loo] and [Ill] with Ahlborn's observations. In outlini the model requires that the work to accomplish a given overall shape change by banding be less than or equal to the work to accomplish the same change by homogeneous deformation. While the work by homogeneous deformation, WH = ?T ;dri, can be calculated exactly by the equivalent methods of Taylor2 or of Bishop and Hill,4 the work by banding, WB, is less certain. The latter consists of 1) Wi, work by slip within a band, 2) Wb, work associated with formation of a boundary between bands, and 3) Wc, work to correct the difference in shape change arising from banding and homogeneous deformation. The Wi term can be evaluated explicitly for a band with an assumed set of slip systems, but a satisfactory analysis of Wb and Wc has not been obtained. Since WB = Wi + Wb + Wc WH, for banding to occur, however, a necessary condition is Wi = WH . Hence it seems reasonable to choose a band with the lowest value of Wi among competing bands consistent with Wi = WH, and then minimize Wb and Wc by arranging the physical configuration of the selected band. Wc is minimized by combining neighboring bands such that their net strain matches the macroscopic strain as closely as possible, and Wb is minimized by enforcing strain compatibility across the boundary between two neighboring bands, similar to the case of a grain boundary.5 It is realized that this procedure is not completely satisfactory, but it does seem to explain Ahlborn's observations reasonably well. The procedure is now outlined for the two corner orientations. a) [l00]. Fig. 1 shows a (100) stereographic projection. The results of the Taylor analysis for axi-symmetric flow by homogeneous deformation6 show that, while [loo] itself is unstable, the rotation of the tensile axis will nevertheless be confined to within about 15 deg from [loo]. Alternatively, less work may be expended by banding with slip on a pair of systems with primary-conjugate relationship, e.g., (ll1)[10l.I + (li1.)[110]. The latter represents minimum Wi for all possible bands.* Since there are four symmetrically

Jan 1, 1970

By P. Ramachandraraa, T. R. Anantharaman

THE technique developed by Duwez, Willens and Kle-ment' for rapid solidification of molten alloys in small quantities by ejecting them on to a highly conducting substrate with the aid of a shock wave has come to be known as "liquid quenching" or "splat cooling" in literature and has already been applied to alloys of many binary systems.' The very high cooling rates of the order of l060 to 1080 per sec obtained in this technique and the consequent drastic undercooling of the melt have led to such striking results as formation of new amorphous and crystalline metastable phases and extension of solid-solubility limits in many alloy systems. The cooling rates in these experiments can, however, be neither accurately measured nor effectively controlled and hence the occurrence of either more than one metastable phase or appreciable differences in constitution in splat-cooled alloys of the same composition cannot be ruled out.3 In fact, workers in two laboratories have reported formation of two different cubic metastable phases in liquid-quenched Au-Si alloys containing 17 to 20 at. pct si.4,5 The present note deals with some new and interesting results obtained in a Ag-21 at. pct Ge alloy and a Au-27 at. pct Ge alloy subjected to the liquid-quenching treatment at different cooling rates. Two alloys of nearly the same composition had earlier been rapidly solidified by the standard "gun technique" in the same laboratory and shown to solidify in nonequilibrium structures, viz., an hcp phase (a = 2.987Å;c =4.718Å) in the Ag-Ge system6,7 and both hcp (a = 2.885Å; c = 4.754Å) and tetragonal (a = 11.627A; c = 22.491Å) phases in the Au-Ge system.3 Apart from different substrates (copper and stainless steel), different melt temperatures (50º to 500°C above the liquidus), and different capillary sizes (0.4 to 1.5 mm diam) in the "gun technique", slower cooling rates of the order of l050C per sec were also obtained in the present work by replacing the substrate by water at room temperature in a modification of the technique due to Olsen and Hultgren.8 No attempt was made to measure the cooling rate in any experiment. The products varied from fine powder (>40 pct by wt—200 mesh) obtained by quenching in water to thin flakes and foils (11.0 sq mm to 4.0 sq cm) produced by splat cooling. They were subjected to the Debye-Scherrer method of X-ray examination in each case. In case of the Ag-Ge alloy, in addition to the expected metastable hcp phase,6 a coexistent tetragonal phase (a = 5.093,Å; c = 7.009Å) was detected in some experiments. Eight weak X-ray reflections from this phase could be identified, two of them being the same as reported earlier.7 With increase in the cooling rate, the dominant hcp phase seems to be first accompanied by traces of silver or germanium and then either homogeneous or mixed with traces of this new tetragonal phase. The splat-cooled Au-Ge alloy showed generally the expected hcp and tetragonal phases,3 but sometimes traces of germanium were also present. Further, two new tetragonal phases with the following lattice param ters could be clearly identified in samples quenched

Jan 1, 1970

By M. N. Shetty

LARGE copper whiskers were grown from cuprous iodide by reduction with hydrogen at about 500°C. Carefully selected single-crystal whiskers of [loo], [110], and [Ill] orientations were used and the whisker shapes and cross sections are shown in Fig. 1. Spec-trographic analysis of a typical batch of whiskers showed that the composition was better than 99.9 pct with iron and silicon as the major impurities. The test specimens varied from about 70 to 400 u in diam and they did not show a conspicuous yield drop as observed in very fine whiskers (diam <25 u), tested by Brenner.1 The characteristics of the stress-strain curves were similar to those of bulk single crystals, even though the maximum flow stresses reached in some orientations were comparable to the yield stresses observed in fine whiskers. Mechanical properties of whiskers of different materials and copper whiskers up to about 100 u in diam have been reviewed,&apos; and a mechanism of slip band propagation in fine whiskers has been recently suggested.3 Whiskers in this work were tested in a floor-model Instron testing machine using low strain rates. (Details of the testing procedure, diameter dependence of the yield stress, and the characteristics of the load elongation and stress-strain curves have appeared esewhere.4) Due to the extensive deformation, >50

Jan 1, 1970

By P. Ramachandrarao, T. R. Anantharaman

CONSIDERABLE interest has lately been evinced as regards the nature of chill zones in solidified metals and alloys. Biloni and Chalmersl were the first to show through their study of segregation substructures in some nonferrous alloys that the formation of the dendritic region may be preceded by a diffusionless solidification process, viz., predendritic solidification. Subsequently Bower and Flemings2 tried a special solidification technique wherein the liquid was drawn into a narrow copper mold with polished surfaces and concluded that convection might trigger some multiplication mechanism leading to grain refinement. Using uncoated and partially coated surfaces for molds in the Bower-Flemings technique as well as in conventional molds, Biloni and Morando3 have very recently brought out the importance of the rate of heat extraction on the mechanism of solidification. We report here on the surface structures and substructures observed in a Sn-1 wt pct Pb alloy solidified at even higher cooling rates (riz., l05 to l07 ºc per sec) than those employed by earlier workers. The alloy was made by melting tin (99.99+ pct) and lead (99.9+ pct) in a silica tube under vacuum. Small quantities of the homogenized alloy (0.5 to 1.0 g) were then quenched (or splat-cooled) from the melt by the "gun technique" developed by Duwez et al.4 The thickness of the resultant foils varied from specimen to

Jan 1, 1970

By G. Y. Chin, W. F. Hosford

It has long been recognized that, for a crystal to undergo an arbitrary shape change by crystallographic shear, at least five independent shear systems must be activated. Taylor1 analyzed the deformation of fcc crystals by {111}<110> slip and showed that the principle of minimum work could be used to determine which combination of slip systems might act to produce a given shape change. Later Bishop and Hi112 attacked the same problem by first identifying the state of stress which could physically activate five or more {111)(110) systems simultaneously and then invoking the principle of maximum virtual work to determine which combination would act for a given shape change. Taylor&apos;s general approach has been used to calculate the active slip systems and the relative strengths during axisymmetric flow of cubic crystals with other deformation modes, including {112}<111> slip3 and {111}<112> twinning.&apos; It is the purpose of this note to identify the stress states capable of activating simultaneously five or more of these systems. {111}<112> Twinning. The {111}<112> systems are defined in Table I and illustrated in Fig. 1. The sense of the shears are those for twinning in fcc crystals. The shear stress on any system may be written in terms of the stress components expressed relative to the 1,2,3 cube axes. For example, the stress For five or more of the systems ij to be activated simultaneously, it is necessary that Tij/T be equal to unity in at least five of the expressions [3], while Tij < T for the remainder. (These restrictions assume that the same shear stress T is required to activate each system and that the shear stress on any system cannot exceed that for its activation.) The discrete values of the stress components A through H which can satisfy these restrictions are listed in Table II together with the values of Tij/T for all systems. It may be noted that Tij/ T is not necessarily zero on all nonactive systems as found by Bishop and Hill for <110> {111} slip. In fact, for the case of twinning Tij/T may reach negative values as large as -2 for shear stress in the reverse direction, Table 11. This means that, if those stress states are to be valid, the shear stress to activate reverse twinning must be greater than twice that for forward twinning. Such stress states are probably valid in view of the directionality of the twinning process. There has been no documentation of reverse twinning thus far. It may be noted that the stress states fall into four classes, which may simultaneously activate eight, six, six, and five twin systems respectively. These solutions may be applied to the {112}(111)

Jan 1, 1970

By P. Ramachandrarao, T. R. Anantharaman

EVER since the technique of quenching metals and alloys from the melt (splat cooling) was perfected a decade ago, it has been recognized that the grain size of products solidified by this technique may be extremely small.&apos; The further observation that fcc metals quenched from the liquid state contain very few dislocations has led to the inference2 that metals are subjected to negligible or no stresses during the rapid solidification characteristic of the "gun" or "piston-and-anvil" technique. Evidence for the incidence of appreciable densities of stacking faults has, however, been obtained in case of some splat-cooled fcc and hcp alloys,3 although not for pure metals. In the light of these earlier observations it was considered desirable to study X-ray line-broadening effects, if any, in fcc metals rapidly cooled from the melt. In the present work pure silver (>99.99 pct), aluminum (>99.99 pct) and lead (>99.9 pct) were quenched from the liquid state from temperatures about 50°C above the melting point by the "gun technique" and the resulting foils were subjected to X-ray examination in a Philips Diffractometer. The quenched foils (up to -10 u thick) did not generally stick to the substrate surface and could be easily transferred to the Diffractometer without introducing any plastic deformation. The profiles of the first five reflections from the foils were recorded in each case with Cu Ka, radiation at the slowest available scanning speed of 1/8 deg per min. To correct for instrumental broadening, profiles were also recorded from the metals annealed in vacuo at suitable temperatures. The integral breadths of the X-ray reflections were arrived at by a procedure described earlier.&apos; There was a distinct suggestion of preferred orientation in the recorded intensities of reflections from aluminum and lead foils. Such an effect was not observed in case of silver. In addition, the integral breadths of X-ray reflections from splat-cooled aluminum and lead were not significantly different from those recorded for the annealed metals. The analysis was therefore continued only for silver where the X-ray line broadening was appreciable. The pure diffraction broadening, B, was evaluated for each X-ray reflection (hkl) from silver from the observed, B, and instrumental, b, breadths with the aid of each of the three equations due to Scherrer,5 Anantharaman and Christian,6 and Warren and Biscoe,7 respectively: Bs= B-b BAC=B- b2/B Table I gives the values of particle size, 71, the lattice strain, E, arrived at by the use of the following well-known relations and on the assumption that all observed diffraction broadening could be attributed to lattice strain or particle size, respectively: E = 1/4 cos ? n= B cos ? where A is the wavelength of X-radiation and 0 is the Bragg angle. As no significant peak shifts or asymmetry could be detected in the profiles from the foils, the possibility of any significant contribution due to twins or stacking faults was ruled out. The absence of faults is by no means surprising since pure silver is known to develop stacking faults only on severe deformation and the stacking fault densities recorded so far for even silver filings have been extremely low.&apos; The very low values for percentage mean deviation from the mean value for the particle size in Table I strongly suggest that all observed broadening in splat-cooled silver can be attributed only to small particle size. This conclusion receives further support from the lowest mean deviation recorded for data computed from the Scherrer equation based on Cauchy profiles that are considered characteristic of particle size broadening. Further analysis for separation of particle size and lattice strain effects was considered unnecessary in view of the very large mean deviations obtained for strain values and also the earlier results suggesting absence of even detectable strain in metals and alloys quenched from the melt. It is to be stressed in this connection that the particles are actually grains and not cells formed by walls of high dislocation density usually encountered in deformed samples. As such, the absence of strains is not surprising. The present results are probably the first to record X-ray line broadening due only to small particle

Jan 1, 1970

By J. Lindbo, B. Vigeholm

IN transmission electron microscopy, specimen thicknesses quoted are frequently based upon either traditionally familiar values or a few evaluations representing the whole material. Taking aluminum in 100 kv TEM as an example, average and maximum values are widely accepted as being 2000 to 2500 and 6000 to 7OOOÅ, respectively. It is the purpose of this note to revise these figures and to point out the importance of evaluating individual specimens carefully. All evaluations have been based upon slip trace widths and lattice orientations as determined from diffraction patterns. In many cases where two or more slip systems have been operating the geometrical method described by Crocker and Bevis1 has been applied as a check. The foils were usually oriented to within 2 deg from the exact Bragg angle. Kikuchi patterns were used as indications of correct orientations but not applied in the evaluations. The tilt of the foil surface relative to the beam normal may with certain geometrical relations between the tilt axis and the operating slip plane lead to substantial errors.2&apos;3 Where these geometries were inevitable the samples were omitted in the investigations. Various measures were taken in order to overcome ambiguities, e.g., comparison with neighboring grains, tilts, evaluations based upon two or three slip systems,&apos; and comparison with extinction contour evaluations where s = 0 conditions were obtained. Errors caused by misinterpretation of the slip traces on a micrograph are easily avoided by considering the bright-dark sequence on opposite surfaces and by taking into account the tapering of the foil usually leading to a distinguishable divergence of the pair of traces. In the investigations described here the interpretation was further facilitated as the slip trace formation was observed on the microscope screen and sketches taken down. In a few observations slipping was so violent that the distinction of pairs was considered dubious and consequently given up. To assess average values, thickness evaluations carried out in two independent investigations were analyzed: I) 99.998 pct A1 extruded, cold-drawn, and recrys-tallized to grain sizes between 35 and 500 um were deformed in tension at room temperature. In order to determine the dislocation densities as a function of strain,4 specimens prepared by spark machining and electropolishing in a PTFE holder were analyzed in the electron microscope at 100 kv. Thicknesses were evaluated for 569 selected areas. Histogram I in Fig. 1 shows the results, the average thickness being 4900Å. II) Electropolished specimens prepared from 99.9999 pct A1 with magnesium contents from 0.005 to 0.5 pct rolled to foil and annealed were subjected to fission fragment irradiationa2 For volumetric dose and defect concentration determinations thickness evaluations were performed on 123 areas. Histogram II in Fig. 1 shows the thicknesses of these areas averaging 4250Å. Whereas in investigation I no selection related to thickness has been made, some thin as well as thick areas have been omitted from I1 for experimental reasons. This and the application of two different microscopes although of the same type may account for the difference in average thickness. Assuming a mean error of 10 pct for a single evaluation, the error of the average should be negligible. In order to investigate the maximum transmissible foil thickness in aluminum, specimens were prepared from single crystals with (111) and (110) orientations parallel to the beam, and from polycrystalline material. Maximum values of thickness that could be measured were given by the stopping of the dislocations. The visibility often extended far beyond the end of the slip trace, but with no means of knowing the

Jan 1, 1970

By C. Atkinson

A method is described for the numerical solution of the diffusion equation with a composition-dependent diffusion coefficient and applied to the radial growth of a cylinder; the radial growth of a sphere, and the symmetric growth of an ellipsoid. Sample applications of the method are made to the growth of particles of proeutectoid ferrite into austenite. RECENTLY&apos; we described a method for numerical solution of the diffusion equation with a composition-dependent diffusion coefficient for the case of the growth of a planar interface. In this paper we extend this method to describe the radial growth of a cylinder, the radial growth of a sphere, and the symmetric growth of an ellipsoid. In the latter case, limiting values of the axial ratios of the ellipsoid reduces the problem to one of a cylinder, a sphere, or a plane depending on the axial ratio. A check on these limiting values is made in the results section. In all of these cases we consider growth from zero size. A natural consequence of this assumption as applied to the sphere, for example, is that the radius of the sphere is proportional to the square root of the time. This is consistent with the condition that the radius is zero initially, i.e., grows from zero size. It may be argued that it is more realistic to consider particles which grow from a nucleus of finite initial size; even in this case the analysis of this paper is likely to be applicable. This can be seen if a comparison is made of the work of Cable and Evans,2 who consider a sphere of initially finite size growing by diffusion in a matrix with a constant diffusion coefficient, with the results of Scriven3 for growth from zero size. This comparison shows that the rates of growth in each case differ trivially by the time the particle has grown to about five times its initial size." This investigation is a generalization of those of Zener,4 Ham,5 and Horvay and cahn6 to the situation often encountered experimentally, in which the diffusion coefficient varies with concentration. First let us consider each of the cases separately. I) GROWTH OF SPHERICAL PARTICLES FROM ZERO SIZE In this case the differential equation in the matrix depends only on R, the radius in spherical coordinates, and can be written: ? 1 <^\ ^13D . , dt U\dRz + R 3Rj + dR dR [ J where C is the composition, t is the time, and D is the diffusion coefficient which depends on c. The boundary conditions will be: c = c, at the moving interface in the matrix, c = c, at infinity in the matrix (and at t = 0, everywhere in the matrix), c = X, is the composition in the spherical particle. Each of the above compositions is assumed constant. In addition there is the flu condition at the moving interface which can be written: , dR0 ~/3c dt \dR/H =Ra where R,, which is a function of t, is the position of the moving interface. We make the substitution q = RI~ in [I] reducing this equation to: & - m - *ws) »i where we have written D = D,F(c) or simply D,F, and Do = D(c,). Thus F[c(q0)] = 1 where q, = ~,/a is the value of the dimensionless parameter q evaluated at the interface. Multiplying Eq. [2] by dq/dc and integrating, we find: where the lower limit of the integral has been chosen so that dc/dq — 0 as c — c,, thereby satisfying the boundary condition at infinity. We require, then, to solve Eq. [3] subject to the condition c = c, when q = q, (this follows from putting R = R, at the interface) together with the flux condition which can be rewritten in terms of q as: Eqs. [3] and [4] together with the condition c = c, at q = q0 enable us to find 77, and the concentration profile c = c(q). Numerical Method. We treat Eq. [3] in the same way as we did the corresponding equation for the planar interface problem&apos; i.e., by dividing the interval c, to c, into n equal steps so that: cr = ca -rbc [5] where r takes the values 0, 1, ... n and we call no,, q1, ... nn the values of n corresponding to the compositions c,, c,, ... c,.

Jan 1, 1970

By S. A. Levy, J. D. Wood, J. F. Libsch

A study of the preparation and characteristics of a sevies of Fe-C-N alloys has been conducted. X-ray, microhardness, and metallographic data from a series of single-phase alloys produced by controlled nitriding of carburized foils are reported. The existence of a, y&apos;, and E carbonitride has been confirmed and it has been found that y&apos; is the hardest of these three phases. These results have been used to interpret the structures observed in nitrided steels. ThIS paper represents the second phase of a three-part study concerning combined nitriding and induction hardening. The first part&apos; reports the engineering properties (depth hardness, fatigue, corrosion, and tempering resistance) obtained when seven different steels were subjected to the combined surface hardening treatment. The present paper concerns the nature of a series of single-phase alloys prepared by controlled nitriding of carburized foils. The objective was to simulate the various layers present in the as-nitrided steels. A third paper will report data concerning induction hardening of the foils and will attempt to set forth a mechanism for the high hardness obtained with the combined treatment. Studies of nitriding generally fall into three categories. The first were performed with bars using conventional nitriding procedures, thus yielding a nitrogen gradient and a series of phase layers near the surface.2-6 Such studies were complicated by the presence of the nitrogen gradient, for it was difficult to correlate microhardness and X-ray data with chemical composition. There were always complications due to penetration of the X-ray beam which yielded data influenced by underlying layers. Similar difficulty was experienced in taking hardness readings on a tapered specimen or in isolating various layers by machining. A second group of investigations was primarily concerned with establishment of regions in the Fe-N7,9,10 or the Fe-C-N phase diagram.8 These were performed with powder specimens which were nitrided in am-monia-hydrogen mixtures to produce a series of single-phase specimens. Unfortunately, the powder specimens were not amenable to either microstruc-ture or microhardness study. The third was essentially a compromise of the first two. Bose and Hawkes," using 0.005-in.-thick iron foils, were able to obtain microhardness, microstruc-ture, composition, and X-ray data on Fe-N alloys of eutectoid composition by equilibration in ammonia-hydrogen mixtures at 1290°F. To obtain a better understanding of the nitriding process and the characteristics of the phases in ni-trided plain carbon steels, the present investigation was undertaken. The investigation was patterned after that of Bose and Hawkes with the exception that nitriding was performed at 930°F (below the eutectoid temperature), as in the case of conventional nitriding. In addition to gaining some understanding of the source of high hardness of nitrided and induction-hardened steels, found in a previous study,&apos; this investigation was concerned with the possibility of controlling the phases present in a nitrided case through the use of ammonia-hydrogen mixtures. Knowledge of the properties of each phase and the conditions necessary for its production could make it possible to avoid undesirable surface layers in nitriding. EXPERIMENTAL PROCEDURE Specimen Preparation. A specimen thickness of 0.005 in. was selected to insure that a uniform nitrogen concentration could be obtained in a reasonable length of time by equilibration in an ammonia-hydro-gen atmosphere. The starting material was a vacuum-cast ingot of pure iron, the major impurities of which were: C, 0.003 pct; 0, 0.014 pct; S, 0.004 pct; N, 0.003 pct.* &apos;Compositions are quoted as weight percent except as noted. The ingot was heated to 1500°F in a nitrogen atmosphere and forged to a slab 0.25 in. thick. The material was then reduced to 0.005 in. by alternately cold rolling and annealing in a nitrogen atmosphere at 1600°F. This material was divided into five groups of specimens which, after carburizing, yielded the following carbon contents: 0.003, 0.28, 0.36, 0.46, and 0.74 pct C. The carburizing was performed by the Leeds and Northrup Research Laboratories, using a controlled "carburizing potential" which yielded a uniform carbon concentration throughout the cross section.

Jan 1, 1970