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By M. Garfinkle

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

Jan 1, 1967

By S. Shapiro, G. Krauss

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

Jan 1, 1967

By B. Chalmers, S. Wojciechowski

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

Jan 1, 1968

By J. G. Eberhort

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

Jan 1, 1967

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

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

Jan 1, 1967

By D. N. Seidrnan

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

Jan 1, 1967

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

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

Jan 1, 1967

By R. D. Carnahan

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

Jan 1, 1967

By L. Zwell, H. A. Wriedt

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

Jan 1, 1967

By J. V. Gluck

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

Jan 1, 1967

By W. C. Winegard, J. R. Carruthers, A. Plumtree, L. R. Morris

The unidirectional solidification of dendrites containing central twin planes was studied in A1-Ti alloys. Once nucleated, the twinned dendrites are a Twore ejficient form for solute redistribution and therefore grow in preference to the normal columnar dendvites. Comparison of these twinned dendrites to adjacent colunmar dendrites by means of decanting experinzents and electron-probe rnicvoarmlysis indicates that these special dendrites grow with less undercooling than normal dendrites. These findings are further supported by the effect of forced convection on the dendrite morphologies. COMMERCIAL semicontinuous cast ingots of most aluminum alloys frequently exhibit large grains which appear to be composed of hundreds of parallel, continuous, thin lamellae. This structure has been termed "basaltic",&apos; "fiederkristall", or, commonly, "feathery grain". The lamellae are &apos;about 100 p thick, several inches long, and each lamella contains a central (111) coherent twin boundary. The feathery grain has been reported to have a (112) direction2 and a (110) direction4 in the twin plane parallel to the casting direction, in contrast with the usual columnar structure where a (100) direction predominates. Aust et uZ.~ proposed that the twin boundaries were growth twins nucleated by stacking faults on the octahedral planes. chalmers6 has suggested that feathery grain may grow by a re-entrant edge mechanism, as proposed by wagner7 for twinned dendritic growth in germanium. Cahn et ~1.~ have concluded that the occurrence of feathery grain is evidence of some form of lateral layer growth rather than the atomically continuous growth normally observed in metals. The postulates by Chalmers and Cahn would seem to be contradicted by the work of Nakao~"&apos; who showed that feathery grain only occurs when growth rates are high and the aluminum contains some solute. Specifically, Nakao found that in order to obtain feathery grain, in small castings solidified unidirec-tionally upward, the rate of growth must be above 2.4 cm per min and a critical solute concentration must be present. Below this solute concentration the grain structure was totally columnar. The critical solute concentration was found to be approximately: 0.04 wt pct Ti, 2 wt pct Cu or Mg, and 8 wt pct Zn. As pointed out by Chalmers it is not obvious why a twin-plane re-entrant edge mechanism would occur in aluminum which is thought to have a diffuse solid-liquid interface. The present experiments were undertaken to determine the growth mechanisms in- volved and to study the solute segregation in more detail. EXPERIMENTAL PROCEDURES Alloys ranging in composition from 0.05 to 0.23 wt pct Ti* were prepared from 99.9 pct pure Ti and 99.993 pct pure Al. Two-hundred-gram samples of A1-Ti binary alloys were solidified unidirectionally and vertically upward from a water-cooled copper base, in a heated insulated mold. The 1-in.-diam, 6-in.-length mold was made of Marinite (manufactured by Johns-Manville Co.). The mold was attached to a 24-in. pivoted arm such that by dropping a weight the mold was rotated 180 deg, throwing the liquid metal from the solid. In this way, the solid-liquid interface was revealed by decanting. A sketch of the decanting mold is shown in Fig. 1. The alloy was poured into the mold at temperatures ranging from 680" to 750°C, partially solidified by water cooling from the base, and decanted after a measured time interval. Growth rates for each metal-pouring temperature were calculated from solidification-time vs length solidified curves. Temperature gradients in the melt were measured using four No. 34 gage thermocouples which protruded into the mold cavity. Grain orientations were determined by X-ray diffraction using Laue back-reflection techniques. Grain substructures were examined metallographically, using polarized light, by applying a thin epitaxial anodic film to polished sections after the method of Hone and pearson." Titanium micro segregation was measured by electron-probe microanalysis using a NORELCO AMR/~ with a mica crystal and proportional-flow counter. Several of the cast samples exhibited feathery and columnar dendrites growing in the same direction and

Jan 1, 1967

By H. H. Kellogg

A model of the slag-fuming process for recovery of zinc oxide fume from lead blast furnace slags, adapted to solution by a digital computer, is presented. The model incorporates the variaticm with time of the following: the fuming of zinc and lead, the change in the ferrous-ferric ratio in the slag, the transfer of sulfur to and from the slag, the temperature of the liquid slag, the temperature of the gases and fume which exit to the flue, the heat losses to the water jackets, and the amount of frozen slag on the water jackets. The assumptions which underlie the model-some of which are but crude approximations—are discussed. Despite some obvious shortcomings, the model simulates faithfully many of the important features of practical slag-fuming operations. The behavior of the model is compared with the operation of the American Smelting and Refining Co. fumzace at El Paso, Tex. The model is used to predict the effects on performance of changes in the coal rate, the temperature of the secondary air, and the composition of the coal. THE fuming of lead blast furnace slag for recovery of zinc oxide is standard practice today, and it has been the subject of several previous attempts at mathematical process analysis.&apos;-&apos; The mathematical process model described in this paper incorporates many of the features from the earlier studies, but it is a far more complete and realistic representation of the commercial process in that the following additional features have been included: the fuming of lead as well as zinc; the transfer of sulfur between slag and gas; the addition of slag feed in batches, over a period of time; tapping of the final slag over a period of time; the change of slag temperature with time. The additional features of the present model add greatly to the mathematical complexity, but this difficulty has been obviated by programming the model for solution by a digital computer. The IBM 7094 computer solves the model for one operating cycle of the fuming furnace in less than 1 min. It is doubtful if the same calculations could be completed with the aid of a desk calculator in less than a month. The computer program, written in the Fortran IV language, is too lengthy for presentation here.* Instead, this paper As shown in the sections which follow, it does simulate with remarkable faithfulness most of the known behavior of the industrial process. On the other hand, the model contains several gross simplifications of both the chemistry and heat balance, necessitated by the lack of more exact knowledge. In addition to these known weaknesses, it is not unlikely that those more intimately acquainted with industrial practice than the author will find other additions to or modifications of the model which will improve its utility and reliability. CHEMISTRY In brief outline, the present model treats the fuming furnace as two units, A and B, in series. In A the batch of slag reacts with the continuous stream of air (primary and secondary) and fuel injected at the tuyeres, to produce a stream of hot, reduced gases containing zinc vapor. The zinc content of both the slag and the product gas changes with time because of the batch nature of the process. Unit A is called the "lower furnace" in this paper; physically, it is considered to be that part of the fuming furnace which lies below the charge port. In B, the "upper furnace", the product gas from A is burned with the stream of "tertiary" air, to produce zinc oxide fume. The performance of B also depends on time because of the time dependence inherited from the product gas of A. The rate behavior in the lower furnace determines the important features of the process—the rate of elimination of zinc and lead from the slag, and the amount of fuel required for this purpose. Bell, Turner, and peters&apos; published the first useful model of the lower furnace. They employed the assumption that, at any instant of time, the slag and reduced gas reach a state of equilibrium, according to the reactions: They cited only indirect evidence in support of their assumption of slag-gas equilibrium, yet several more recent laboratory studies of the activity of zinc oxide in slags4-8 have produced evidence which supports their view. On first acquaintance it seems unlikely that a high-output "rate" process like slag fuming would even approach an equilibrium state. The author, in an earlier study,&apos; established, however, that the gas-slag interface in a fuming furnace was capable of such high mass-transfer rates that a close approach to equilibrium between gas and slag was quite probable. In devising the present model it was decided to assume a state of equilibrium between slag and gas at the outset, and then to modify this assumption as necessary in order to make the model agree with the be -havior of the actual process. Up to this time the assumption remains a part of the model, since no behavior

Jan 1, 1968

By J. Clair, H. Mirabel

The determination of the temperature and electrical potential distributicms in the cathodes of aluminum electrolytic cells is difficult. The reascms come from the various nature and the intricate three-dimensional geometry of the materials; besides thermal and electrical phenomena react upon each other. A method of calculation using a computer program applied to a mathematical model, figuring the cathode, is developed. Both of the thermal and electrical phenomena are simultaneously considered. Temperature and electrical potential distributions are finally obtained by successive iterations. Results are compared with measurements on industrial cells. Theoretical and practical applications of these studies are given. Up to the present time the study of the distribution of the temperatures and electric potentials in the electrodes, anode and cathode, of the electrolytic cells used for the production of aluminum was limited to one of the two aspects of the phenomena because of lack of a simultaneous method of calculation. For example, the anode or cathode drop was studied assuming that the temperatures in the iron and carbon are known, a method that obviously is very approximate since iron resistivity, in particular, greatly varies with temperature, which in turn depends on current density. Consequently we tried to find a method of calculation simultaneously taking into account both thermal and electrical phenomena. We proceeded to the study of the cathodes as an initial approach to the problem. Although the cathode and surrounding materials may have varied forms and particularly very heterogeneous characteristics, their structures are simpler than that of the Sijderberg anode and boundary conditions are more easily represented than in the case of anodes even though they are prebaked. The study was in two parts: a) development of a model schematizing the true geometry of a cathode and defining the thermal and electrical boundary conditions, and b) working out a method of calculation of the temperatures and potentials by means of an electronic computer. To facilitate solution of the problem, a model was used initially much simplified in comparison with an actual cathode. This model permitted development of the method of calculation. In a second phase, this model was adjusted to the study of actual cathodes and applied to different types of cells: low- or high-intensity cells, cells set up at ground level or above ground level, cells with cathodes more or less heat-insulated. Simultaneously measurements were made with cells equipped with cathodes of the types studied to compare the values resulting from calculation. The initial model was also used for general studies, in particular for studying the effects of current density in the carbon and iron. The results were confirmed or made precise by the model of the true cathodes. This report successively describes: a) the manner in which the model representing a cathode was worked out, with the simplifications and/or the hypotheses used, b) the method of solution of the problem by means of the electronic computer, and c) an example, stating the extent to which the results obtained may be realistic. Further the possibilities offered by such a study are examined. 1) CATHODE REPRESENTATION The purpose of this phase is to represent the cathode in the form of a so-called "mathematical model", that is with a simplified geometrical configuration, in order to meet the subsequent calculation requirements, while keeping to the true facts as closely as possible. This model further includes the thermal and electric conductivities with regard to temperature for the varied materials composing the cathode, as well as the thermal and electrical conditions at the model boundaries. 1.1) Guiding Principles. For calculating the temperatures and potentials the model is divided by trior-thogonal planes into a network of small elementary parallelepipeds. At the summit of these parallelepipeds&apos; so-called mesh points, the temperatures and potentials are computed. The number of mesh points is of course limited by the capabilities of the computer, since 1) the number of equations to be solved depends on the number of mesh points selected, and 2) the amount of time spent by the computer considerably increases with increasing this number. These conditions call for the following requirements as concerns the model: a) Dimensional requirements: the calculation will be all the more accurate as the network is more closely meshed. Since the number of mesh points is limited in practice, it is necessary to restrict the dimensions of the model. b) Geometrical requirements: so as to make things easier in working out the network, the model must be given a simple geometry. In particular, it will be convenient to have the cathode so constituted that the surfaces limiting the cathode and the surfaces within the cathodes separating the different materials consist of triorthogonal planes. 1.2) Schematization of the Cathodes. After the tech-

Jan 1, 1968

By G. Y. Chin, W. L. Mammel

The problem of selection of the active slip systems for a crystal undergoing an arbitrary strain has been analyzed by Taylor and by Bishop and Hill. The Taylor analysis is based on a principle of&apos; virtual work, and involves finding, among numerous cotnbinalions of slip systems that satisfy the imposed strain, the combination in which the sum of the glide shears is a minimum. Previously, Taylor has treated the case of axisymmetric flow when slip occurs on (111)(110) (or {110)(111)) systems only. His analysis has now been extended by computer methods to the cases of slip on {112}(111) and {123)(111) systerns and of mixed slip on {110), {1 12), and (123) planes with a common (111) slip direction, all of which are important in the deformation of bcc crystals. The results are computer-plotted as contours of the ratio of the floe strength to the critical resolved slzea-r stress for slip, for axial orientations distributed throughout the standard stereographic triangle. Implications of the computer results to texture develop,merit, texture hardening, and dislocation theories oj work hardening are discussed. WhEN a single crystal is extended in the usual tension test, the lateral dimensions can change relatively freely. In this case, the glide shear produced by slip on a single slip system is sufficient to accommodate the (tensile) deformation. Since slip is governed by a critical resolved shear stress law (the Schmid law&apos;), the single active slip system is one for which the stress, resolved on the slip plane and in the slip direction, is the highest among the several equivalent slip systems. This amounts to saying that a value M = U/t = y/~ is a minimum among the equivalent systems, where M is the inverse of the familiar Schmid factor (a and E refer to tensile stress and strain, and T and y refer to resolved shear stress and shear strain). A grain embedded in a polycrystalline aggregate, on the other hand, cannot freely change its shape due to constraint from its neighbors. In this case, slip from five independent slip systems (to accommodate five independent strains) is generally required.&apos; Based on the principle of virtual work and assuming that the critical resolved shear stress for slip is the same for all systems, Taylor hypothesized that, among all combinations of (five) slip systems which are capable of accommodating the imposed strain, the active combination is that one for which the sum of the absolute values of the glide shears is a minimum. Again, this is equivalent to saying that the value of M = CjlyjI/ is a minimum, in analogy to the single slip case. Taylor aminimum,analyzed the case of {111)(110) slip for fcc metals, and applied the analysis to crystals undergoing axisymmetric flow, that is, the same macroscopic shape change as the poly crystalline aggregate under uniaxial tension (or compression). For the twelve equivalent {111}( 110) slip systems, there are 384 independent combinations of selecting five systems to satisfy the five independent linear equations of imposed strain.4 Taylor calculated the value of M for each combination* and obtained the active com- *A number of the independent combinations were omitted from consideration in Taylor&apos;s original work (see Ref. 5). bination (minimum M) for a number of axial orientations distributed throughout the standard stereographic triangle. Later work by Bishop and Hill*&apos;8 showed that Taylor&apos;s least-shear hypothesis was equivalent to a maximum work principle which they advanced. Using the simplified Bishop and Hill method for {111)(110) slip, Hosford and Backofen&apos; obtained detailed contours of constant minimum M for the same axisymmetric flow case. In contrast to {111}(110) slip in fcc metals, slip in bcc metals is generally described as occurring on {ll~)(lll), {112)(111), {123) (111) systems as well as mixed slip composed of all three. Since the direction cosines of the slip plane normal and the slip direction enter as a product in the Taylor analysis, the Taylor solutions of ,M for {110)(111) slip are identical to those for { 111} 110) slip. The other three cases of slip, however, have not been solved. In view of the numerous combinations of slip systems involved in the calculations, the Taylor analysis is clearly oriented toward computerized solutions. THE TAYLOR ANALYSIS In order to obtain the active combination of (five) slip systems by solving for the minimum value of M = we first express the (small) strain components E,, with respect to the cubic axes 1, 2, 3 ([loo], [010], [001], respectively) of the crystal, in terms of the sum of the glide shears yj from slip systems j: where n, and n,j refer to direction cosines of the slip plane normal, and dri and dsi to direction cosines of the slip direction, of slip system j, all referred to the cubic axes. In practice, the strain components are given with respect to the specimen axes X, y, 2. These components are readily converted to ers through the tensor transformation where irk and 1,~ are the direction cosines between the two sets of coordinate axes.

Jan 1, 1968

By E. L. Raymond

The effect of heat treatment on the microstructure and resultant notch-bar rupture life of ZNCONEL alloys X- 750 and 718 was studied. It was found that the primary effect of heat treatment in rendering these alloys notch-ductile is the elimination of any y&apos; denuded zone adjacent to the pain boundaries. The mechanisms by which such a denuded zone can arise and be eliminated by heat treatment are discussed. InCONEL Ni-Cr alloy X-750 and INCONEL Ni-Cr alloy 718 are age-hardenable austenitic materials. Alloy X-750 is used for its corrosion and oxidation resistance and high creep-rupture strength up to 1500°F. Alloy 718 is used most effectively up to 1300°F. One of the most important areas in their development has been establishment of consistently good rupture properties, especially in the presence of a stress concentration, such as imposed by a notch. A desire to improve these properties has led to extensive studies of the effect of heat treatment on the micro structure of these alloys and their performance in stress-rupture tests. In earlier investigations"~ of INCONEL* alloy X-750, *INCONEL i s a Registered Trademark of The International Nickel Co., Inc. grain boundary carbide morphology was linked with stress-rupture properties. If, during heat treatment, the carbide MZSC was precipitated in the grain bound-ary in a cellular form, poor rupture properties re-

Jan 1, 1968

By J. E. Hanlon, S. R. Butler, R. J. Wasilewski

It is known that stoichiometric NiTi transforms to a structure of lower symmetry near room temperature. The present investigation deals primarily with the changes in the electrical and magnetic properties which occur at the transformation. The effects of composition and various heat treatments on electrical properties are also discussed. In recent investigations by Purdy and Parr,&apos; Wang et a1.,2 Dautovich and Purdy,~ Dautovich et a1.,4 and the authors, ~,&apos; NiTi has been observed to undergo a martensitic phase transformation from the ordered CsCl (B2) structure to one of lower symmetry. The crystal structure of the low-temperature modification is still not completely worked out. This transformation occurs near room temperature for the stoichiometric composition. The thermodynamic, elastic, crystallographic, and microstructural characteristics of this transformation for some compositions have been previously reported.&apos;-= In the present investigation, the changes in the electrical transport properties and magnetic susceptibility of NiTi when it undergoes the martensitic phase transformation have been measured. The approximate composition range covered is 48 to 52 pct Ti.* *All compositions are given in atomic percent._____________________ EXPERIMENTAL PROCEDURES AND RESULTS 1) Sample Preparation. The NiTi alloys were prepared from iodide titanium (>99.92 pct Ti) and vacuum-premelted carbonyl nickel (>99.95 pct Ni) by repeated arc melting under gettered argon and casting in a water-cooled copper mold. After the cast buttons were hot-forged at 800" to 950°C, the oxidized surface was removed by grinding and etching. Samples were cut from the worked polycrystalline buttons. After fabrication, the samples were annealed 1 hr at 900°C and water-quenched. The composition of the alloys was assumed to be the same as in the initial feed. This assumption was supported by material balance checks on 100-g arc-melted buttons which demonstrated quantitative recovery to within k0.02 pct. The oxygen content of the alloys was &apos;150 ppma (weight) and the carbon content was 30 to 50 ppm. 2) Electrical Resistivity and Hall Effect. The electrical resistivity was measured over the composition range 48 to 52 pct Ti for temperatures varying from 4.2"K to 900°C. The high-temperature and many of the low-temperature experiments were carried out using conventional 4-probe dc techniques.7 The Hall coefficient and ac resistivity were measured at 20 cps using the apparatus shown schematically in Fig. 1. The equipment is basically an ac potentiometer: The resistive or Hall voltage of the sample is balanced by a comparison voltage provided by a dividing network across a standard series resistance. The off-balance signal is amplified by a Tektronix 122 amplifier and detected by a Princeton Applied Research (PAR) phase-sensitive detector. The precision of the resistivity and Hall coefficient measurements is i0.1 and i3 pct, respectively. The uncertainty in the data is increased by i2 pct from the precision limits because of uncertainty in dimensions and possible end effects. The temperature dependence of the electrical resistivity and Hall effect for a stoichiometric (50.0 pct Ti) NiTi sample are illustrated in Fig. 2. Above 75"C, this sample has essentially the B2 structure, while below about 0°C it is completely in the low-tempera-

Jan 1, 1968

By A. E. Jenkins, A. Jostsons

Isothermal sections of the Ti-0-H phase diagvam at 600°, 700°, and 800°C have been constructed from equilibrium hydrogen pressure measurements over a range of Ti-0-H alloys containing up to 34 at. pct 0. Oxygen reduces the hydrogen solubility at fixed hydrogen pressure but increases the terminal solubility in the a solid solutions at the a/(a + P) phase boundary. Metal-lographic studies of alloys annealed below the eutectoid temperature show that oxygen also increases the ter-ninal solubility of hydrogen in the a solid solution in equilibrium with the hydride phase. The effect of oxygen on hydrogen solubility is discussed in terms of the electronic and geometric structure of interstitial solid solutions. THE isothermal solubility of hydrogen in a Ti-0 alloys at 800°C has been measured by Hepworth and ~chuhmann&apos; who subsequently used ternary Gibbs-Duhem integrations to calculate oxygen activities in binary Ti-0 alloys. The present study aims to extend Hepworth and Schuhmann&apos;s measurements to alloys richer in oxygen and to a range of temperatures. This paper presents the results of hydrogen equilibrium pressure/concentration measurements in Ti-0 alloys as well as observations on the effect of oxygen on the terminal solubility of hydrogen in a titanium. The thermodynamic properties of binary Ti-0 alloys, derived from these measurements, will be published separately.&apos; EXPERIMENTAL METHODS Specimen Preparation. Ti-0 alloys were prepared from iodide-refined titanium and titanium dioxide obtained by hydrolysis of redistilled titanium tetrachlo- ride. Specimens containing up to 16 at. pct 0 were prepared by electromagnetic levitation3 whereas a conventional tungsten arc furnace with a water-cooled copper hearth was used to melt oxygen-rich alloys. The specimen homogeneity was indicated by the constancy of lattice parameters of samples from various parts of the ingot as well as by the sharpness of the reflections on X-ray powder patterns. Oxygen-rich specimens in the composition range (20 to 34 at. pct), where ordering has been ~bserved,~ were annealed for 300 hr at 600°C prior to use in hydrogen solubility measurements. Apparatus. The hydrogen pressure/concentration measurements were made with a modified Sieverts apparatus shown diagrammatically in Fig. 1. Specimens were placed in a clear silica tube and impurity pickup by direct reaction with silica was prevented by lining the heated end of the silica tube with thin molybdenum sheet. A double silica tube was required to eliminate loss of hydrogen by diffusion through silica at high temperatures and high hydrogen pressures, the space between the tubes being maintained at a hydrogen pressure equal to that above the specimen. Hydrogen was purified by diffusion through a Ag-Pd tube.= Hydrogen pressures were measured with a mercury McLeod gage in the range 0.001 to 4 Torr

Jan 1, 1968

By M. C. Flemings, G. E. Nereo

General expressions are given to describe macro-segregation in castings and ingots which results from mass flow of solute-rich liquid to feed solidification and thermal contractions. Analytical solutions are given for solidification with planar isotherms (unidirectional and bidirectional heat flow). These solutions describe inverse segregation and centerline segregation. Numerical examples are given for A1-4.5 pct Cu alloy. In 1540, Vannoccio Biringuccio published one of the first references to macrosegregation, describing the problem of exudation and inverse segregation in the manufacture of bronze gun barrels.&apos; Since then, a great many studies of macrosegregation have been reported. Recent work of particular engineering interest includes that of Marburg 2 and others:" on centerline segregation and other types of segregation in large steel ingots, and work of Adams,5 Scheil, 6 and Kirkaldy and youdelis7 on inverse segregation in nonferrous ingots. In most studies on this subject, the various types of macrosegregation have been treated as separate phenomena. For example, quite different mechanisms have been proposed for formation of centerline segregation, negative cone of segregation, inverse segregation, banding, and so forth. In this, and in several papers to follow, it is proposed that these as well as other types of macrosegregation result from the same basic mechanism and can be quantitatively described by the same basic equation. It has often been suggested that some types of segregation (such as centerline segregation and banding) occur as a result of buildup of solute at the tips of growing dendrites.2-4 ,8-10 As example, banding can be induced in centrifugal castings by mechanical vibration, and Northcott 10 suggests this might be due to the influence of the vibration on the boundary layer at the dendrite tips of the growing dendrites. However, in view of the extremely small boundary layer known to exist at the tips of the dendrites,11,12 any interpretation of macrosegregation based on this boundary layer is clearly incorrect. Note that experiment has shown that significant buildup of solute does not occur at dendrite tips in ingot solidification, but even if such buildup occurred the thickness of the enriched zone would only be the order of D/U where D is liquid diffusion coefficient and U is dendrite tip velocity. For usual casting or ingot solidification this solute-enriched layer is 10"3 cm, far too small to account, for example, for centerline segregation.11&apos;12 It has also been suggested that convection in the bulk liquid (ahead of the advancing dendrites) might cause segregation by sweeping away the solute-rich boundary layer in front of the dendrites.3 However, since there is no significant boundary layer, this explanation must be incorrect. The convection might directly cause segregation by penetrating between the dendrite arms, and presumably in a rimming steel ingot it is sufficiently vigorous to cause some segregation in this way. Centerline segregation, however, cannot be interpreted as resulting from this convection since a sharply segregated zone is usually found near the centerline, with the bulk of the ingot being nearly of nominal composition. If convection in the bulk liquid were the direct cause, a gradual change in ingot composition over the entire cross section would be expected. It is known that sudden changes in convection of the bulk liquid during solidification can result in banding,14 but it is not clear that the banding results directly from the effect of convection on solute distribution. Changes in convection also affect thermal conditions in the liquid-solid region of a solidifying ingot. It will be seen later in this paper, and in a paper to follow, that macrosegregation is strongly influenced by these thermal changes. Recognizing that in some cases of ingot solidification (as in solidification of rimming steels) convection in the bulk liquid may have a direct effect on solute distribution, we neglect it in this paper and in the several to follow. We then derive general expressions describing macrosegregation which results from the mechanism of interdendritic flow of solute-rich liquid

Jan 1, 1968

By Klaus Schwerdtfeger

In order to test the performance of ZrO, (CaO) and Tho,(Yz03) electrolytes in the electrochemical determination of oxygen activities in liquid metals at steel-rrzakitng temperatures , electromotive force measurements have been made with the following cells: The oxygen-- activities are calculated from the electmrnotive forces for the investigated systems. The standard free energy of- formation of MnO and the activity of manganese in Fe-Mn melts are derived. Indications are that the Zr 0z(Ca0) electrolyte exhibits little electronic conductivity at oxygen pressures as low as 10&apos;a atnz at 1600°C; however, the partial electronic conductivity may become noticeable at lower oxygen activities. The Tho,(Yz03) electrolyte is found to be an ionic conductor at the oxygen pressure as low as that for the Mn + MnO equilibrium, but exhibits partial electronic conductivity at oxygen pressures higher than 10"1 atm (1500°C). fi. better control of oxidation and deoxidation reactions in steelmaking may be facilitated if the oxygen activity in the steel is known during various stages of the process. In the present work oxygen activities have been measured in liquid iron, manganese, and iron alloys with galvanic cells using ZrOz(CaO) and s solid electrolytes with the object of establishing the range of oxygen pressure in which these materials can be used as electrolytes at steelmaking temperatures. Calcia-stabilized zirconia and Tho2-Y203 solid solutions are oxygen ion conductors. Such electrolytes were first used by Kiukkola and Wagner1 and Peters and ~ann&apos; in galvanic cells for the determination of thermodynamicquantities of oxide systems in the temperature range 700" to 1200°C. At these moderate temperatures calcia-stabilized zirconia has been found to exhibit predominantly ionic conductivity at oxygen pressures as low as those for the Cr + Crz03 equilibrium,394 but at lower oxygen pressures elec- tronic contribution to conductivity becomes significants4 The Th02-Y203 solid solutions are ionic conductors at oxygen pressures lower than those applicable to zirconia base electrolytes.5&apos;6 At high oxygen pressures Thoz base electrolytes exhibit significant p-type semiconduction. At the time the present experiments were carried out several papers1&apos;-* were published on the electrochemical determination of oxygen activities in liquid iron using the ZrOz(CaO) electrolyte. The results of different authors do not agree well. For instance, according to Fischer and ~ckermann" stabilized zirconia can be used to measure oxygen contents in liquid iron larger than 0.02 wt pct, but according to Baker and west1&apos; ZrOz(CaO) cannot be used for the determination of oxygen content in liquid iron because of high electronic contribution to the conductivity. Fig. 1 is a schematic diagram of the apparatus used. About 500 g of liquid metal is contained in a crucible into which a stabilized zirconia or Th02(Y203) tube is immersed. A platinum contact wire is pressed (with a spring mechanism) against the inside bottom wall of the electrolyte tube. The tube is flushed continuously with a stream of air, CO-CO, (or Hz-C02) (at 0.96 atm and at a rate of about 300 cu cm per min), via an alumina tube inserted inside the electrolyte tube. This alumina tube also contains the Pt-Pt/10 pct Rh thermocouple. A capillary alumina tube shielding the other contact wire is immersed in the melt. The molybdenum contact wires were used mostly; in some cases platinum wire was employed. Molybdenum has the advantage that it dissolves more slowly in the melt than platinum. The whole cell was contained in the alumina reaction tube of a resistance furnace with molybdenum winding. The reaction tube was closed gas tight at both ends and flushed continuously with argon. Because of the poor thermal shock resistance of the electrolyte tubes the cell had to be assembled in the cold furnace. The electrolyte tube and alumina sheath

Jan 1, 1968

By Fred H. Perfect

The thermite process, now approximately 80 years old, has heretofore been practiced in ceramic vessels. This paper outlines the successful production of several million pounds of alloy produced in zuater-cooled copper vessels. THE high temperatures necessary to produce fluid high-alumina slags have probably discouraged earlier workers from attempting to utilize water-cooled vessels. The following is a report of the successful application of this method, together with a report of the physical and chemical problems which had to be solved to make the process practical. About 1955, when Reading Alloys was more concerned with the production of ferrotungsten than with most other types of alloys, it was found to be exceedingly difficult to predict the reaction rate that one would experience from one tungsten ore to another . This difficulty was increased for two reasons: the physical state of the ore as received was seldom uniform, and the size of the mass to be reduced is a very important factor in developing the proper mix for the final reaction rate and temperature. For example, the reduction of ferric oxide with aluminum would theoretically produce temperatures of about 2600°C, and, in spite of the losses due to radiation, the energy is quite sufficient to produce a very fluid slag and iron effecting a very clean separation. On the other hand, the reduction of ferrous oxide with aluminum, while it is not as energetic as the first reaction, nevertheless should give temperatures above 2000"C, which should cause separation of alumina and iron, but, in practice, this is not the case and good fluid slag is not obtained. The heat of reaction, calculated from the thermo-dynamic heats of formation of the constituents of the reaction, offers a convenient guide to the feasibility of a thermite reaction. Thus, the values listed in Table I can be used as an approximate guide for estimating the results which may be expected in the reduction of various oxides and combinations of oxides using aluminum as the reducing agent. As a generalization, those reactions releasing approximately 600 cal per g of total mass represent the lower limit at which to expect separation of slag and metal. On the other hand, those reactions which release 1100 to 1200 cal per g are too violent to be used successfully without the addition of considerable inert material, such as lime, fluorspar, and so forth. Reaction rate is also a very important factor. This, of course, is governed very largely by the sizing and intermingling of the oxidant and reductant and by the starting temperature of the reactants. This is why those figures shown in Table I can only be a general guide. Further, it must be understood, that by adding powerful oxidizing agents, such as nitrates, chlorates or metallic oxides, such as molybdenum trioxide or chromium trioxide, certain problems respecting low temperatures are not necessarily solved. This is true in the addition of oxidants, such as sodium chlorate. By adding too high a concentration of sodium chlorate as a booster for a particular reduction, explosions are generated. Generally, they are of an intermittent type so as to give a Roman Candle effect to the reduction itself; with each surge resulting from a minor explosion more and more material is thrown

Jan 1, 1968