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By S. G. Proctor, D. L. Baaso, W. V. Conner

A double crucible system was developed for I-g scale plutonium reductions. The equipment consists of an inner MgO crucible, an outer MgO crucible, and a stainless steel pressure vessel. The reduction charge is PIaced in the inner crucible and the annulus between the inner and outer crucibles is filled with a mixture of calcium and iodine. The exothermic reaction between the calcium and iodine in the annulus supplies the heat required for complete reaction of the reduction charge ana' good metal coalescence. Metal yields of 80 to 85 ,pct were obtained from I-g scale reductions and yields as high as 97.5 pct were obtained from 0.5-g scale reductions. The system was used to reduce charges containing as little as 0.1 g of Pu resulting in metal yields up to 90 Pct. THIN metal foils of highly enriched plutonium isotopes are used as targets for cross section and other measurements. The isotopes are separated in the calutrons at Oak Ridge and are very expensive to prepare. Often, only 1 or 2 g of material are available thereby emphasizing the need for a method of preparing these small quantities of metal. Procedures for 1-g scale plutonium reductions have been described, but these procedures require elaborate or expensive equipment. For example, the procedure described by Anselin et al.1 requires an inert atmosphere glovebox and induction heating equipment. The procedure described by Baker2 also uses induction heating equipment to obtain the recommended heating rates and liner temperatures. Baker's procedure also requires high purity PuF4 with very little PuO2 present. The procedure described in this paper resulted from a search for a simple and inexpensive method for making 1-g scale plutonium reductions. EXPERIMENTAL Equipment. The equipment required for the double crucible system consists of a pressure vessel, two MgO crucibles, a MgO crucible lid, and a resistance-heated, vertical crucible furnace. The crucibles were slip cast from high purity MgO and were supplied by the Coors Porcelain Co. and the Norton Co. The pressure vessel and lid were fabricated from 316 stainless steel. Materials. The PuF4 used for this study was obtained from the P1utoniu:m Metal Production Department at Rocky Flats. The PuF4 was prepared in a con- tinuous hydrofluorinator by reacting Pu02 with HF at 650°C. The isotopic composition of the plutonium was approximately 93 pct 239PU, 6 pct 240PU, and 0.5 pct 241PU. Some of this PuF, contained less than 1 pct Pu02 (Batch No. 6 and 7), while other batches contained up to 15 pct Pu02 (Batch No. 3). The chemical analyses of all the PuF4 used for this study is given in Table I. The calcium was 99 pct pure, AEC grade, and only that fraction which would pass through a 20 mesh screen was used. The I2 was USP grade re-sublimed I2 which was ground before being used. Procedure. Various charge compositions and methods for loading the double crucible system were tested. The optimum conditions for 1-g scale reductions are described below. The double crucible system was loaded as shown in Fig. 1. The outer crucible was placed in the pressure vessel and the annulus between them was filled with MgO sand. The inner crucible was placed in the outer crucible, supported by a layer of MgO sand in the bottom of the outer crucible. A mixture of 5.2 g of Ca and 25 g of I2 was placed in the annulas between the two crucibles. The upper portion of the annulas was filled with MgO sand. Next, a layer of a mixture of calcium and I, equal to 20 wt pct of the calcium and I2 used in the main charge was placed in the bottom of the inner crucible. The PuF, to be reduced was mixed with a 30 pct excess of calcium and 1 mole of I2 per mole of Pu and this mixture was placed in the inner crucible. The charge was topped with a layer of a mixture of calcium and I2 equal to 20 wt pct of the calcium and I2 used in the main charge. The pressure vessel was sealed with a flat copper gasket and was purged by alternately evacuating and filling with argon. The purge valve was closed and the vessel was placed in a vertical crucible furnace which was preheated to 950°C. The furnace was turned off after 20 min of heating and the vessel allowed to cool. Experience has shown that. this amount of heating is sufficient to assure complete reaction of the charge. RESULTS AND DISCUSSION The double crucible system has been used to produce plutonium metal on a 0.1- to 1-g scale. Reduction

Jan 1, 1970

By D. R. Pratt, R. W. Hanks

The method of Caldwell and Babbitt for detennining Bingham plastic rheological constants from engineering pipe flow data has been erroneously used in many previous applications. A reanalysis of extensive pipe flow data from the literature is performed. Critical Reynolds numbers corresponding to the laminar-turbulent transition calculated from these data are found to agree with theoretically calculated values for the entire flow range studied. Similar agreement is found for the authors&apos; own data&apos; for flow of 10 slurries between parallel plates. The Bingham plastic model is shown to be a reliable representation of the flow of non-Newtonian slurries provided it is properly applied. If the Hedstrom number He = pD2 t0/?2 > 104, then the linear approximation method of Caldwell and Babbitt is invalid for pipe flow data obtained in systems of ordinary engineering interest, and the complete nonlinear form of the pipe flow Bingham plastic equation must be used in determining rheological parameters. INTRODUCTION Many materials of engineering interest must be handled and transported as slurries or suspensions of insoluble particulate matter in a Newtonian liquid. These suspensions frequently exhibit non-Newtonian rheological behavior which is reasonably well described by the simple Bingham plastic rheological equation1 Using this particular equation to describe the laminar flow characteristics of slurries was discussed at length by Caldwell and Babbitt2-4 who considered the flow of various clay slurries and sewage sludges. The model has since been used by many others.5-7 More recently the problem of predicting the laminar turbulent transition Reynolds number for Bingham plastic fluids has been treated8 for the case of flow in pipes. This paper points out errors which have existed in the analysis of Bingham plastic flow since the work of Caldwell and Babbitt2-4 and presents a reanalysis of the laminar turbulent transition calculatiod for Bingham plastic flow in pipes. In addition, new data obtained for flow of Bingham plastic slurries between parallel plates, both in laminar flow and in the laminar turbulent transition region, will be presented and compared with the theoretical analysis of laminar turbulent transition for flow between parallel plates. THEORETICAL ANALYSIS PIPE FLOW The mathematical analysisl-4 of laminar flow of a Bingham plastic fluid leads to the following equation. where q = <v>/R is a pseudoshear rate, rw is the wall shear stress Eo = r0/rw, r0 is the yield stress and 1 is the coefficient of rigidity or plastic viscosity from Eq. 1. Caldwell and Babbitt2-4 recognized that the quartic term in Eq. 2 was small compared to the other terms whenever 5, « 1, and that for large values of 7, a plot of Eq. 2 becomes linear. The slope of such a plot with rw as ordinate is 4? and the intercept is (4/3) ro. This approximation is illustrated schematically in Fig. 1. The shaded region between the true curve and the straight-line approximation near the origin represents the contribution of the quartic term. In principle, therefore,

By Renato G. Bautista, KNona C. Liddell

A model of the reaction of chalcopyrite, CuFeS2, with Fe3+ and with 02 is considered. Homogeneous solution phase reactions are assumed to be always at equilibrium throughout the dissolution of the mineral. The dissociation of USOb- and several complexation reactions involving cu2+, Fez+ and Fe3+ are incorporated in the model equations. The relative importance of Fe3+, 02, and H+ as oxidants and the role of solution equilibria are assessed and the implications for leaching practice discussed.

Jan 1, 1981

By J. Nutting, D. H. Kirkwood

IT is clearly of great metallurgical interest to know the conditions of temperature and gas composition under which different products will form in sulphide roasting. A method of graphically presenting the relevant thermodynamic data will be demonstrated, such that these conditions are readily obtainable. The products of sulphide roasting may be oxide, sulphate, or oxysulphates, and the equilibria between these may be represented in the following way: 2 MSO4 = MOMSO4 + SO3 MO-MSO4 = 2 MO + SO3

Jan 1, 1961

[Officers and Committees of the Society of Petroleum Engineers 1 Officers and Staff of the AIME 2 Officers of AIME Sections Predominantly Petroleum in Membership 3 Society of Petroleum Engineers By-Laws 5 Alphabetical List of Members 9 Geographical List of Members 110 List of Members by Companies 127 Advertisers&apos; Index 137]

Jan 1, 1961

By R. B. Gavert, David J. Mack

ROOM- and elevated-temperature compression tests were made on the binary 3/2 electron compounds AuZn, CuAu, AgZn, AgMg, AuCd, and NiA1. These compounds possess either the B2 CsC1-type ordered structure or the A2 bee disordered structure represented commonly as ß and ß on equilibrium phase diagrams. In testing at room temperature, cylindrical specimens 0.508 cm by 0.330 cm diam were seated directly on an instron compression load cell (CF 0 to 10,000 lb). At elevated temperatures, testing included a special apparatus with a furnace heat source and a protective atmosphere.&apos; The specimens were strained at a rate of 1 pet per min. The compounds were prepared from 99.99 pet or better high-purity elements. Vacuum and/or argon cover gas was used throughout the mixing, melting, and specimen drawing processes. The generally equi-axed specimen grains varied in size from 0.5 to 1.5 mm for the five different compounds. The stress-strain curves in compression showed

Jan 1, 1968

By C. E. Brukl, E. Rudy, St. Windisch

The ternary-alloy system Nb-Mo-C was investigated by means of X-ray, melting point, DTA, and metallo-graphic techniques; a complete phase diagram for temperatures above 1500°C was established. Above 1960°C, niobium monocarbide and the cubic (Bl) high-tenzperature phase in the Mo-C system form an uninterrupted series of solid solutions. The ternary range of the pseudocubic q MoCl-, is very restricted. Dimolyb-denum carbide dissolves up to 44 mol pct Nb2C (2240°C), whereas the maximum solid solubility of MO2C in Nb2C does not exceed 5 mol pct. The order-disorder transformation temperatures in Mo2C and Nb2C are lowered by the mutual metal exchanges. Six invariant (p = const) reactzons occur in the ternary system; three correspond to class 11-type four-phase reactions involving a liquid phase, one to a class I (eutectoid)-type, and two further isotherms are associated with limiting tie lines. The results of the Phase diagram investigation are discussed, and the thermodynamic interpretation identifies the low relative stability of the binary sub-carbides in conjunction with the large stability diflerences between niobium and molybdenum carbides as the cause for the formation of a stable equilibrium between the monocarbide and the metal phase in the ternary reson. Due to their refractoriness, the carbides of the high-melting transition metals have received increased interest in recent years as base materials in composite structures for aerospace applications at high temperatures and for the development of self-bonded cutting tool materials; other novel fields of application include power reactors, where operation at high temperatures becomes essential for attaining high power efficiencies. In these applications, the increased reaction rates at high temperatures require a close consideration of the chemical interactions between the alloy constituents. As a consequence, a detailed knowledge of the phase relationships in the alloy systems is required in order to provide a sound basis for developmental -type work. Partly as a result of the considerable experimental difficulties associated with the investigation of this high-melting alloy class, no complete studies of ternary metal-carbon systems have been performed until recently. Even the high-temperature phase relationships in the binary transition metal-carbon systems have been delineated only during the past few years to a degree of accuracy required for a more detailed study of ternary or higher-order alloys. In recent investigations of binary and ternary systems of refractory transition metals with carbon, boron, and silicon,&apos; alloys from the ternary systems Nb-Mo-C became of interest because of the demonstrated possibility2,3 of obtaining compatible composites based on metal + monocarbide combinations. In the meantime, however, studies in other, but related, ternary metal-carbon systems, such as Ta-W-C, have shown that the solid-state equilibria may change significantly toward higher temperatures (>2000°C), and that extrapolations based on low-temperature equilibrium data are, in general, not very reliable. Although the lower-temperature (<2000°C) phase relationships in the Nb-Mo-C system are similar to those found in Ta-W-C, a cursory thermodynamic analysis of the equilibria indicated4 that complete solid-solution formation between Mo2C and Nb2C should not occur at higher temperatures. The present work was conducted in order to experimentally verify these expectations and, in addition, to provide phase equilibrium data in the melting range of the alloys. In the boundary systems, niobium and molybdenum are known to form a continuous series of solid solutions.576 The continuous solubility was also confirmed by Kornilov and Polyakova,7,8 who also observed a minimum melting point at 22 at. pct Mo and 2345°C. The phase diagram investigations of the Nb-C system by Storms and Krikorian9 and Kimura and Sasaki10 were recently supplemented by Rudy et al.11,12 The system contains a high-melting monocarbide with the B1 structure, Table I, and a subcarbide, Nb2C, which exists in at least two different states of sublattice order at low temperatures47"-&apos;3 and a disordered state above approximately 2500°C.11,12 The melting-point measurements by Rudy et al .11,14 are in close confirmation of the data by Kimura and Sasaki.10 The rather complex phase relationships in the Mo-C system were only recently Clarified.15,18 The system is characterized by three congruently melting, intermediate phases, MozC, ? MoC1-x and a Mol-,, Table I, of which only Mo2C is stable at temperatures below 1650°C. Substoichiometric MozC exists in several states of sublattice order which interconvert in homogeneous phase transitions. Hyperstoichiometric compositions cannot exist in the ordered state. Upon cooling through a critical temperature range, the

Jan 1, 1968

By Craig S. Hartley

Expressions are obtained for the energy changes associated with the reaction of (a& (111) slip dislocations on intersecting (110)planes in anisotropic bcc metals. An energy criterion for assessing the likelihood of dissociation of the products of such reactions is also presented. It is found that the "burrier reactions" which form a(100) dislocations at the intersection of two active {110) slip planes are more energetically favorable in metals which exhibit a high value of Zener&apos;s anisotropy factor, A, than those which have a low value. The results are presented in a form which permits the stacking fault energy to be obtained from a measurement of the separation between par-tials in a dissociated configuration. However, until accurate calculations or measurements of the stacking fault energies involved are available, it is not possible to assess the physical importance of dissociated dislocations. In a recent paper,&apos; the energy changes associated with several types of reactions between two slip dislocations, (a/2)(111){110), in bcc structures were calculated.* Isotropic elasticity and the approxima- tion v = -3- were employed. The purpose of this work is to present calculations of the energy changes for many of the same reactions using anisotropic elasticity. The problem of dissociation of a(100) and a(110) dislocations is also considered, and maximum fault energies for which dissociation will be energetically favorable are calculated for several bcc metals. Two general types of reactions are considered; those for which the reactant (a/2)(111) dislocations have long-range attractive forces and those for which the reverse is true. An example of the former is: (a/2)[lll] + (a/2)[lll]-a[l00] while the latter are typified by: (a/2)[lll] + (a/2)[111] -a[011] Only reactants lying in different slip planes are considered; therefore, the products must lie along (111) or (100) directions, which are the intersection of two {llO} planes. It will be assumed that the reactants and products are infinitely long parallel dislocations, since in this case the energy change associated with the reactions is a maximum.&apos; THEORY The self-energy per unit length of a straight mixed dislocation in an anisotropic medium can be written? where b is the Burgers vector, K is an appropriate combination of the single-crystal elastic constants, and R and ro are, respectively, outer and inner cut-off radii of the elastic solution. The energy given by Eq. [I] does not account for any variation of the core energy with orientation. This could be manifested by an orientation dependence of the core radius or, equivalently, the Peierls width, of the dislocation. However, the energy contribution due to this source is expected to be small, and current models of the dislocation core are not sufficiently accurate to justify such a refinement. It has already been shown that for the isotropic case the energy contributions due to nonzero tractions across the cores of the reactants and products exactly cancel one another in the reaction.&apos; Accordingly, it will be assumed that this contribution to the total energy change in the anisotropic case is small. In the subsequent discussion it is also assumed that the core radii of the reactant and product dislocation are the same and that, where stacking faults are formed, the faulted region is bounded by the centers of the partials. Consequently only changes in elastic energy due to the reactions will be considered. When the dislocation is parallel to either the (111) or the (100) directions, K may be written:375 K = (Ke sin2 a + Ks cos2 a) [2] where K, and Ks are the combination of elastic constants corresponding to an edge and screw dislocation lying along the same direction as the mixed dislocation, and a is the angle between the direction tangent to the dislocation line and the Burgers vector. Eq. [2] should not be confused with the isotropic approximation to the variation in energy with line Orientation.6 It should be noted that the essentially isotropic expression for K is a result of the characteristic symmetry of the (111) and (100) directions and is not, in general, valid for other dislocation directions in anisotropic cubic metals. The energy* change for a reaction in which the re- actant and product dislocations are parallel perfect dislocations can be written: where Ep and E, refer to the self-energies of the products and reactants, respectively. For dislocations parallel to (100) and (111) directions, Eq. [3] becomes:

Jan 1, 1969

By A. H. Geisler, R. F. Mehl, C. S. Barrett

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1&apos;2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y&apos; are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y&apos; and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y&apos; is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By R. F. Mehl, C. S. Barrett, A. H. Geisler

The mechanism by which the supersaturated solid solution of 20 per cent silver in aluminum decomposes has been reported in two previous publications.1&apos;2 The analysis of streaks in Laue photograms showed that thin platelike particles (the so-called Guinier-Preston aggregates) form upon matrix planes in the early state of decomposition.1 The size of these particles is larger, the higher the temperature at which they form in accordance with nucleation theory;³ at all temperatures they increase in size with aging.2 When they have grown thick enough to afford three-dimensional diffraction, powder X-ray photograms show that the structure is not that of the equilibrium precipitate but that of a transition lattice . Sincc this is also platelike in shape and also lies upon the (III) matrix planes with the [IIO] direction in the matrix parallel to the [II.O] direction in it seems likely that the original platelet particles are merely in an early stage of formation, and thus finely dispersed. The atomic spacing and pattern on the (00.1) plane in y&apos; are identical with those on the (111) matrix plane to which it lies parallel, and since comparable directions in the two planes are parallel, the lattices are thus coherent at the interface; an analogous coherence has been found in aluminum-copper alloys.3 The structures y&apos; and y are both close-packed hexagonal and are oriented alike; they differ only in interatomic distances. Consequently, y&apos; is regarded as y strained from its ordinary dimensions by the lattice coherency between it and the matrix.2 The lattice movements that transform the matrix to the equilibrium precipitate appear to be very simple.2 The mechanism of precipitation in this system is simpler and is more precisely known than that in any other system hence the system should be a profitable one for the difficult task of correlating property changes with structural alterations. The present report provides additional studies on powder X-ray diffraction from alloys of 10 per cent, 20 per cent and 30 per cent Ag, and presents the correlation of crystallographic changes with changes in microstructurc, Brinell hardness and electrical resistivity of the three alloys. Preparation of Samples and Experimental Procedure The preparation of the 20.2 per cent Ag alloy has been described2 Alloys containing 9.9 and 29.7 per cent Ag were prepared from 99.97 per cent A1 and 99.99+ per cent Ag using a similar procedure. Rolled

Jan 1, 1943

By Robert A. Colten, Frederick C. Hull, Robert F. Mehl

It is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth.l,2 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in I939.3 Two types of process were described: (I) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemispheres and then after impingement as roughly radial-columnar structures; and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth. Both cases are met in the formation of pearlite from austenite (Fig. I);2,4 the former, occurring near the knee of the S-curve, has been named "grain-boundary transformation," and the latter, occurring at temperatures near Ael, has been named "group-nodule transformation." In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important1,2 to obtain data on the rate of nucleation and the rate of growth of pearlite. Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the factors that affect hardenabil-ity; when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite.2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature, and the degree of homogeneity of the parent austenite. The studies are restricted chiefly to plain carbon commercial steels." Previous Data on Rate of nucleation and rate of Growth Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Meh1,l and by Dorn, De Garmo and Flanigan.2, It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc.), austenite grain size, and mode of formation of pearlite at the temperatures given. Except for the approximations of Mehl and the work of Dorn, austenite grain size was disregarded, though it is well known

Jan 1, 1942

By Robert A. Colten, Frederick C. Hull, Robert F. Mehl

It is known that pearlite forms from austenite by a process of nucleation and growth, and that the rate of formation of pearlite may be described by a rate of nucleation and a rate of growth.l,2 The manner in which these two quantities operate to produce the observed isothermal reaction curve has been analyzed in a paper published in I939.3 Two types of process were described: (I) that in which nucleation occurs at the grain boundaries of the parent phase, with the nodules growing toward the centers of the grains, initially as hemispheres and then after impingement as roughly radial-columnar structures; and (2) that in which nucleation occurs generally, with the nodules growing to full spheres until impingement with other growing nodules restricts growth. Both cases are met in the formation of pearlite from austenite (Fig. I);2,4 the former, occurring near the knee of the S-curve, has been named "grain-boundary transformation," and the latter, occurring at temperatures near Ael, has been named "group-nodule transformation." In developing our knowledge of the factors that determine the rate of formation of pearlite from austenite, it is important1,2 to obtain data on the rate of nucleation and the rate of growth of pearlite. Such data, when obtained near the knee of the S-curve, will furnish information of use in understanding the factors that affect hardenabil-ity; when obtained at higher temperatures, such data will be useful in understanding the behavior of steels that during heat-treatment react to pearlite.2 It is the purpose of this paper to present data on the rate of nucleation and the rate of growth of pearlite in dependence upon composition, grain size, temperature, and the degree of homogeneity of the parent austenite. The studies are restricted chiefly to plain carbon commercial steels." Previous Data on Rate of nucleation and rate of Growth Data on the rate of nucleation and the rate of growth of pearlite have been published by Scheil and Lange-Weise,5 by Mirkin and Blanter,6,7 by Meh1,l and by Dorn, De Garmo and Flanigan.2, It is difficult to interpret the data, for in most cases too little information is given on austenitizing temperatures and times, the state of homogeneity of the austenite (presence or absence of carbide, etc.), austenite grain size, and mode of formation of pearlite at the temperatures given. Except for the approximations of Mehl and the work of Dorn, austenite grain size was disregarded, though it is well known

Jan 1, 1942

By J. P. Hirth, C. S. Hartley

A simple graphical technique is presented for rapidly determining the ratio of resolved shear stress on slip systems in single crystals to the applied stress (Schmid factor) for various simple states of stress. Master plots are presented which, when used in conjunction with an appropriate stereo-graphic projection, allow one to determine the Schmid factor for all slip systems in a crystal of given orientation. It is shown that one such plot suffices for simple tension or compression, flex-ural bending, and biaxial compression, while a combination of two different plots must be used for torsion and simple shear. STUDIES of the deformation behavior of single crystals are most valuable when the applied stresses are resolved onto the various slip systems of the crystal. A careful study of the available slip systems and proper selection of the state of stress used and the specimen orientation can then yield quantitative information about the probability of specific dislocation reactions, the strength of barriers to plastic flow, and the mechanisms of yielding and flow in general. It is the purpose of this work to analyze some common states of stress used in deformation studies and to present a simplified way of determining for these cases the ratio of the resolved shear stress on the slip systems to the applied stress (Schmid factor). I) CALCULATIONS We first define two orthogonal coordinate systems: one based on the specimen geometry (a right circular cylinder of radius, R, is considered here) and one based on the particular slip system of interest. The unit vectors and angles specifying the two coordinate systems and the relationship between them are listed in Table I. The relationships among the various angles and unit vectors are shown on a stereographic projection in Fig. 1. The transformation matrix between the (XI X2 X3) and (x&apos;1 x&apos;2 x&apos;3) system is x1 x2 x3 X&apos;1 a11 al2 a13 x&apos;2 a21 a22 a23 x&apos;9 a31 a32 a33 where in this case the direction cosines aij are given by a11 a12 a13 aij = a21 a22 a23 a31 a32 a33 sin 0 cos F cos 0 sin F cos 9 = -cos 0 cos F sin 0 sin F sin 6 [1] 0 -sin F cos (p In terms of Eq. [I.], the stresses sij, referred to the slip system, are determined from oij, referred to the specimen axes, by1,2

Jan 1, 1965

By John B. Mertie

More than 200 minerals are known that contain the rare-earths and thorium. Monazite and bastnaesite, however, are the principal commercial sources of the rare-earths, and monazite is the principal source of thorium. Monazite was in demand in earlier years mainly for its content of thorium, which was used in the manufacture of Welsbach gas mantles; but beginning in the latter part of the nineteenth century, the rare-earths became progressively more important than thorium. Recently, however, the tenor of thorium in monazite has again become a matter of commercial interest. Rare-Earths and Thorium The rare-earths proper are defined by spectroscopists as the oxides of 14 elements with atomic numbers ranging from 58 to 71; but more commonly lanthanum, with an atomic number of 57, is also included, in which case these 15 elements are often designated as the lanthanides. Chemists also include scandium and yttrium as elements of the rare-earths. A second group of elements, beginning with actinium and including thorium, protactinium, uranium, and all the transuranium elements so far produced, with atomic numbers ranging from 89 upward, are chemically and structurally related to the lanthanides, and are known as the higher rare-earths or actinides. Berzelius discovered that the lanthanides could be separated roughly into three groups, based upon the solubility of their double salts, R2(SO4)3-K2SO4-2H2O, in excess of K2SO4. This separation, with the substitution of sodium for potassium, is still used commercially. The double salts of the cerium earths were found to be almost insoluble; the terbium earths, partly soluble; and the yttrium earths, completely soluble. Based upon the degree of solubility, scandium belongs with the cerium earths; and yttrium belongs with, and gives its name to, the yttrium earths. These three groups with their atomic numbers are shown below. [ ] The prevailing state of oxidation for the rare-earths is R2O3, but cerium may readily be oxidized to the tetravalent state, in which condition it may be separated chemically from the other cerium earths. Praseodymium and terbium may also exist with the valence IV, and samarium, europium, and ytterbium may have the valence II. Most of the elements of the rare-earths, however, are very difficult to separate, and their initial isolation required the work of many chemists over a period of 150 years.20 Fractional crystallization, fractional precipitation, and ion exchange are the principal methods so far used, and fractional precipitation is now employed commercially on a large scale. Ion exchange columns are

Jan 1, 1960

By Akio Suzuki, P. G. Wahlbeck

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

Jan 1, 1967

By R. A. Bergman, C. J. B. Fincham

THERMODYNAMIC properties of many high-temperature systems containing sulfur, such as slags, metal sulfides, and solutions of sulfur in liquid metals, have been studied by means of equilibration with known gas mixtures.&apos;" This method presupposes a complete and accurate knowledge of the thermodynamic data for all possible components of the gas phase at high temperatures. However, a survey of the data available up to 1952 on the thermodynamics of gaseous sulfur species and compounds, by Richardson and Jeffes,&apos; showed that there was considerable uncertainty in the values of the free energies of formation of S, SO, HS, and CS. In many cases, this uncertainty made it impossible to decide whether or not these species would form a significant proportion of the sulfur present in the gas phase in any given system. After the review by Richardson and Jeffes had been published, St. Pierre and Chipman6 measured, by an indirect method, the free energy of formation of SO. This also enabled a clear choice to be made among the three possible spectroscopic values for the dissociation energy of S2 into atoms10 thereby determining the free energy of formation of S from S2, and fixing the free energy of formation of HS more accurately" The main purpose of the present investigation was to measure the free energy of formation of CS, which was still in considerable doubt. For example, at 1600°C, it could be estimated to be +6 +25 kcal per mole,* most of the uncertainty being in the * Based on the dissociation energles of CS6 and S2,5 the heat of sublimation of graphite, and, the assumption that the entropy of formation of CS is the same as that of CO. value of the dissociation energy." A secondary purpose of the investigation was to determine more accurately the equilibrium sulfur pressures over dilute solutions of sulfur in carbon-saturated liquid iron. General Method Dilute solutions of sulfur in liquid iron, saturated with carbon, were brought to equilibrium at 1600" and 1800°C, with known gas mixtures consisting, initially, of A and CS2. After equilibrium had been reached, the melts were quenched and analyzed for sulfur. In the high temperature region of the furnace, an equilibrium was set up between the various possible sulfur species and compounds in the gas phase; namely, CS2, CS, S2, and S. (It can be calculated that the amounts of S6 and S, are negligible at these temperatures:) Morris and Bueh17 and Kitchener, Bockris, and Libermana had previously studied the corresponding

Jan 1, 1958

By H. A. Hancock, L. M. Pidgeon

Equilibrium carbon monoxide pressures were measured over the reaction between chromium oxide and a number of solid ferrochromium alloys in the composition range 0.4 to 4.8 pct C and 0 to 49 pct Fe. Measurements were also made for the carbides Cr23C6 and Cr7C3 which agreed well with previous investigations. Between 1050°and 1400°C the pvessures varied from 0.1 to 56 mm and increased markedly with the iron and carbon contents of the alloys. The data were used to estimate the activity of carbon in the alloys and to calculate the equilibrium conditions for the decarburization of a useful range of ferrochromium alloys. WHEN ferrochromium is produced by the reduction of chromite with carbon in an electric arc furnace it invariably contains up to 10 wt pct C. For many purposes such as the production of stainless steel, it is necessary that the carbon content be as low as from 0.02 to 0.05 pct. Thus an important part of the ferrochromium industry consists of the production of low carbon ferrochromium. The classical Bessemer steelmaking technique cannot be used to oxidize low carbon contents in chromium and ferrochromium alloys without also oxidizing the chromium. Recently a new commercial process2-4 has been introduced for oxidizing carbon from high chromium content alloys which consists of heating the solid alloy with such oxidizing agents as Cr2O3, Fe2O3, or SiO2 in a retort at reduced pressures. By maintaining the carbon monoxide pressure below the equilibrium value for the system, the carbon can be removed as carbon monoxide without oxidizing the chromium. The equilibrium conditions for the decarburization of solid chromium carbon alloys have been determined by Boericke5 who measured the carbon monoxide pressure over the reaction between the various chromium carbides and chromium oxide. A typical reaction is shown below. Cr23C6 + 2Cr2O3 =u 27Cr + 6CO [1] These values are not applicable to the decarburization of commercial ferrochromium alloys which invariably contain major amounts of iron. The present investigation was therefore undertaken to measure the change in the equilibrium carbon monoxide pressure brought about by additions of iron to the Cr-C-0 system, thus extending the work of Boericke into the region of the production of low carbon ferrochromium. MATERIALS AND METHOD Materials. Measurements were made on two carbides of chromium, Cr233C6 and Cr7C3, and fifteen Fe-Cr-C alloys. The chromium carbides were made

Jan 1, 1963

By W. O. Philbrook, K. M. Goldman, G. Derge

T. Rosenqvist—The most interesting point in this paper is the observed transfer of iron into the slag in the initial stage of the desulphurization process, after which the iron again is reduced to the metallic state. The authors interpret this observation as showing that the sulphur enters the slag as an iron-sulphur compound which subsequently is decomposed by the slag. The present writer has previously suggested the following equation for the desulphurization process: S + O2- ? S2- + O For equilibrium in the blast furnace the oxygen potential is defined by equilibrium with graphite and CO of 1 atm pressure: C + O ? CO [2] During the desulphurization process the reactions proceed in the direction of the arrows. If one assumes eq 2 to be significantly slower than eq 1, the transfer of sulphur into the slag, in accordance with eq 1, will build up a local oxygen potential at the metal-slag interface very much higher than that corresponding to the value defined by eq 2. This is possible because the equilibrium oxygen potential in eq 1 is high as long as the sulphur content in the slag is low. This oxygen potential will again be able to oxidize some iron: Fe + O ? Fe2+ + O2- and an increase in the iron content of the slag will be observed. Adding up eqs 1 and 3 one obtains: S + Fe ? S2- + Fe2+ The net effect is thus in harmony with the experimental observation but is obtained without assuming any close ties between the sulphur and iron atoms during the process. Furthermore, it follows from eqs 1 and 2 that when the sulphur content in the slag increases, and equilibrium with C and CO is finally approached, the local oxygen potential at the metal-slag interface will decrease, and the iron in the slag will be reduced back into its metallic state. C. E. Sims-—The data and conclusions presented in this paper are thoroughly convincing in establishing the mechanism of sulphur transfer from iron to slag as in a blast furnace. The evolution of gaseous CO in step 3 of the reactions given on p. 1112 makes the process virtually irreversible. Assuming that the process is similar in slag-metal systems other than in the blast furnace, it is readily seen why free CaO and re-ducing conditions so greatly favor desulphurization. On the other hand, the very effective desulphurization obtained in oxidizing slags when strongly basic, must be attributed to the relatively high stability of CaS as compared to FeS. The ease and simplicity with which the reactions of classic chemistry agree with the experimental data and explain the mechanism is noteworthy. The concept of molecules of FeS, soluble in both phases (metallic iron is not soluble in the slag), migrating from the iron to the slag and there reacting with CaO, which is soluble only in the slag phase, is clear and uncomplicated. This is likewise true for step 3. Those who would deny the existence of molecules or molecular-type combinations in liquid iron, must strain to provide a mechanism so lucid. In the absence of molecules, the Fe and S exhibit a remarkable collusion. L. S. Darken—The investigation and interpretation of rate phenomena in the range of steelmaking temperatures is a difficult task. Most of the laboratory investigations of steelmaking reactions have been concerned with equilibrium. Having determined the equilibrium, our attention naturally focuses next on the mechanism and rate of approach to equilibrium. The authors seem to have contributed substantially to our understanding of these factors for the case of sulphur transfer. I should like to ask the authors whether they consider that the sulphur transfer reaction is diffusion controlled as many high-temperature reactions seem to be. If so, it would seem reasonable to suppose that the slow diffusion step of the process is the transfer across a pseudo-static layer or film similar to that considered in heat flow problems. As the diffusivity and fluidity are smaller for the slag than for the metal, it may tentatively be assumed that the sulphur gradient exists in a thin layer in the slag adjacent to the slag-metal interface and that the metal and the main mass of slag are each maintained uniform by convection. On this basis the amount of sulphur transferred across unit area per unit time is D p (?S%)/100 ?1, where D is the diffusivity, p the density, (?S%) the difference in percent sulphur on the two sides of the layer, and ?l is the layer thickness. At the beginning of the experiment the main body of the slag and hence one side of the layer contains no sulphur; therefore (?S%) may be replaced by (S%), the sulphur content of the slag at the slag-metal interface, which in turn is equal to L[S%] where [S%] is the sulphur content of the metal and L is the distribution coefficient. The rate of transfer thus becomes DpL[S%]/100 ?l, which the authors designate K[S%]. Equating these two quantities and setting D = 10-6 cm2 per sec, p = 3 g per cm3, L = 40, and K = lo-+ g cm-2 sec-1, it is found that ?l, the film thickness, is about 0.01 cm—a value of the order of magnitude of that found in heat transfer problems in liquids. The uncertainty of the numerical values used leaves much to be desired, but at least it can be said that this calculation tends to support the proposed model involving diffusion through a film. Although this does not seem to affect the general argument, I should like to call attention to the fact that the diffusivity3 of sulphur in hot metal is found (on conversion of units) to be about 10-4 cm2 per sec rather than 104 cm2 per sec as stated by the authors. The three equations written by the authors to express the steps in the overall process of sulphur transfer may alternatively be written ionically as only two Fe + S = Fe++ + S-- Fe++ + O-- + C (graphite or metal) = CO (gas) + Fe where the underscore is used to designate the metallic phase; ionic species are slag constituents. After the authors have so neatly demonstrated that iron and sulphur transfer together (at least initially), this fact seems almost self evident; from eq 4 it is seen that if sulphur acquires a negative charge during transfer

Jan 1, 1951

By Will Mitchell, T. G. Kirkland, C. L. Sollenberger

BENEFICIATION of a Korean scheelite ore has been studied during the past year in the Basic Industries Laboratory at Allis-Chalmers Manufacturing Co. A flowsheet has been recommended including flotation, gravity separation, and a final cleaning by a magnetic separator. The investigation was continued in the field of flotation in order to establish the effect of certain variables on recovery and grade of rougher concentrates. The results of this investigation are recorded here. Mineralogy The scheelite ore was obtained from Korea and was mined from the Sang Dong deposit. This deposit is described as lying in gently dipping metamorphosed sedimentary beds of Cambrian age.&apos; The metamorphism was probably either metasomatic replacement or recrystallization, or both, with subsequent hydrothermal deposition. Igneous bodies in the form of granite porphyry have been found within 7 km of the main shaft and are considered to be a possible source of the mineralizing solutions. The Myobong formation, the host for the Sang Dong deposit, was laid down in middle Cambrian times and consists of series of mudstone, siltstone, shale, and marl, with local stratification of mica schists, hornfels, and tactites. The scheelite is found in quartz bands in the tactites. Although there are six of these bands, only one, the "main bed" averaging 1.75 pct WOs, has been mined to any extent. The ore sample as received in the laboratory was the product of a cone crusher and was all —2 in. The rock appeared to be even textured, medium to fine grained, and gray green in color. No scheelite could be recognized by the unaided eye. However, under ultraviolet light of 2537 A, the scheelite fluoresced and could be distinguished from the gangue. Under the black light, the scheelite showed no definite vein structure but was disseminated throughout the specimen. The raw ore had a specific gravity of 2.96 and weighed about 125 lb per cu ft at —20-mesh Tyler. The —2-in. material was stage crushed through 20-mesh, and samples were cut for mineralogical, chemical, and spectrochemical analyses. Several polished sections were cut from hand specimens. Figs. 1 and 2 show quartz to be the matrix for scheelite. It was reported by Kim2 that the greatest scheelite concentration in the mine is found with a high concentration of quartz and a decrease in the abundance of garnet. Diameters of scheelite particles ranged from 1.2 mm down to less than 50 microns. Spectrochemical analysis showed the ore to be high in aluminum, bismuth, calcium, iron, magnesium, manganese, silicon, tungsten, and with lesser amounts of beryllium, chromium, lithium, sodium, and titanium. Chemical assays showed the —20-

Jan 1, 1952

By Stephen Krickovic

AS it is commonly understood in the bituminous coal mining industry, pillaring means removal, as completely as is practical, of all pillars formed in the development of headings and rooms on first mining. The degree to which this can be accomplished, termed percent of recovery, is of course dependent generally upon the physical conditions of the bottom and the overburden, the system of min-

Jan 1, 1956