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By B. G. Zambre, G. A. Parks, J. N. Roco

Automatic controls have long been a fact of technological life. Some understanding of control systems is rapidly becoming essential to the competence of mineral engineers. Students in undergraduate mineral engineering curricula, however, should not be expected to develop proficiency in the design and interpretation of control systems. They should be provided the opportunity to absorb some of the fundamental concepts and cant of such highly specialized peripheral fields as automatic controls. The present paper describes the components of a simple, flexible and relatively inexpensive control system designed primarily for the use of students in independent study projects. The control system is based on a continuous on-stream optical analyzer analogous to commercially available systems using X-Ray fluorescence analysis. The components can be easily adapted to control other separators and separations. As described here, they have been arranged to control the magnetic separation of a magnetite bearing specular hematite from quartz to produce a quartz product of fixed hematite content using a minimum of power. The control system consists of the magnetic separator* with a vibrating feeder, † a sampler, an optical scanner, a differential amplifier, a millivolt recorder ‡ and a motor driven, metered variable DC power supply for the separator electromagnet. An optional magnet current recorder is useful. The system as arranged for closed loop control is illustrated in Fig. 1. The elements of the loop are identified in automatic control jargon in Table I. The same components can be easily adapted for use in other control modes.§.1 * A Carpco Induced Roll High Intensity Magnetic Separator (Carpco Manufacturing, Inc., Jacksonville, Fla.); modified for external magnet power supply. A Jeffrey-Traylor Vibrating Feeder Type 1B (Jeffrey Manufacturing Co., Columbus, 0.). A Beckman Laboratory Potentiometric Recorder (Beckman Instruments, Inc., 619-A) fitted with adjustable limit switches for external circuit control (Beckman Instruments, Inc.. 71980). Terminology is taken from ref. 1. CLOSED LOOP OPERATION The separation is monitored through the optical reflectivity of the tailings stream which is proportional to the hematite content, THA. The difference, A, between the measured analysis (actually a proportional voltage) and a reference analysis (also a proportional voltage) is continuously recorded. The separation is controlled through changes in the electromagnet current, I, supplied from a motor driven variable source. The two primary variables, ? and I, are linked through adjustable limit switches on the

Jan 1, 1965

By R. W. Heckel

The growth and shrinkage rates of second-phase particles of various size distributions are analyzed in terms of five mathematical models. These models apply to various forms of diffusion-controlled growth (one model) and interjace-controlled growth (four models). The expression for diffusion-controlled growth assumes local equilibrium at the interface between the second Phase and the matrix and through the choice of the proper flux area perrnits the definition of minimum diffusion-controlled growth kinetics. The interface-controlled kinetics models consider the situations where the rate-controlling step occurs at either the interlace undergoing solution or the interface undergoing deposition. In addition, each of these interface-controlled kinetics models is analyzed for interface reaction rates which are independent of the thermodynamic activity gradient across the interface or proportional to the gradient. THE variation of the size distribution of second-phase particles in a solute-saturated matrix has been a stimulating topic for many years. Research has been carried out in this area for situations where the matrix was either liquid or solid. It is well-understood that the over-all process results in an increase in the average particle size, a decrease in the total number of particles per unit volume, and a net decrease in surface area. Greenwood1 has presented a mathematical model based upon the mass balance existing between growing and shrinking particles. His analysis is stated in terms of Fick's First Law using concentration gradients set up between particles of different size as a result of the effect of surface curvature on solubility. Greenwood's analysis indicates that the mean particle size should increase approximately as the cube root of time. Asimow2 has shown that several of the simplifying assumptions employed by Greenwood may be eliminated from this diffusion-controlled model with little increase in complexity. Lifshits and Slyozov3-5 have also considered the growth-shrinkage problem involving diffusion-controlled kinetics. Their analysis was extended to include the effects of interacting particles ("kinetic approximation"), particle shape, and elastic strains. These authors also show that the mean particle size varies as the cube root of the reaction time. wagner6 has formulated expressions for both diffusion-controlled kinetics and interface-controlled kinetics in the growth-shrinkage problem. Wagner's diffusion-controlled kinetics is based upon the same form of mass balance using Fick's First Law as used by others and is shown to be applicable to situations where kr >> D (k is the interface reaction constant, r is the particle radius, and D is the diffusion coefficient). This analysis also yields a mean particle size which varies as the cube root of time, in agreement with other workers. Wagner also developed interface-controlled kinetics to handle kr « D. This model was based upon the fact that the interface reaction rate is proportional to the interface area. Wagner assumed that the rate was also proportional to the thermodynamic activity difference, ?a, existing across the interface. Thus, the specific reaction rate at the surface of radius r was defined as k • 4nr2 . ?a. It is the purpose of the present paper to reconsider the processes of diffusion-controlled growth and interface-controlled growth in the variation of particle-size distributions as a function of time at constant second-phase volume. The analyses are formulated in a manner which permits data obtained

Jan 1, 1965

By F. V. Lenel, G. S. Ansell, M. J. Salkind

An experiment is described in which the growth of interparticle necks in an array of loose spherical silver powder at temperatures near 300°C was determined by measuring changes in the electrical resistance of the array. The activation energy for neck growth of contacts was derived by abruptly changing temperature and noting the change in the rate of neck growth. Since the experiments were run under an external load, the changes in activation energy with stress could he determined. The activation energy was found to decrease rapidly with increasing stress. It is concluded that the material transport in the experiments is one of plastic flow by dislocation motion. The variation of activation energy with stress is typical for cross slip of dislocations, an important material transport mechanism in the temperature range investigated. THE process in which powder compacts or aggregates of loose powder are held at an elevated temperature under an external load is called hot pressing or sintering under pressure by powder metallurgists. In this investigation the early stages of this process as applied to loose spherical silver- powder aggregates were studied. The powder particles were approximately 100µ in diameter and the temperature was near 300°C, i.e., below one half of the melting point of silver in degrees Kelvin, where volume diffusion is not expected to contribute to sintering. In the process, the contact or neck areas between powder particles grow. Since this involves plastic deformation of the particles under a constant external load (even though not under constant stress) it would be termed creep by mechanical metallurgists. On the other hand, the growth in neck area observed in compacts or loose-powder aggregates held at elevated temperature without the application of an external load is termed sintering by powder metallurgists. During sintering the major driving force is the stress due to surface tension. However, even when no load is placed on the compact or powder aggregate, an external stress, i.e., gravity, plays an important role in sintering in addition to those stresses arising from surface tension, as was shown in two previous investigations.'" It is therefore postulated that no sharp dividing line can be drawn between the phenomena of "creep" and "sintering". Different material transport mechanisms may be involved in either of these phenomena, but they will depend upon the temperature and the level of stress, but not necessarily upon the nature of the driving force: surface tension or external load. At the low temperatures of this investigation, an external stress much higher than the stress due to surface tension is necessary to obtain measurable rates of neck growth. In order to avoid misunderstanding this phenomenon will be called "creep". The rate of growth in contact area in the loose silver-powder aggregates was determined by meas-

Jan 1, 1965

By R. S. Wagner, W. C. Ellis

A new mechanism of crystal growth involving oapor, liquid, crnd solid phases explains many observations of the effect of implurities in crystal growth from the vapor. The role of the impuuitq is to form a liquid Solution with the crystalline tnalerial to be grown from the vapor. Since the solution is n prefevred site for deposition firorti the uapor, the liquid becorrles supersaturated. Crystal growth occurs by precipitatzon from the supersaturated liquid crt tlie solid-liquid zntevfnce. A crystalline defect, such as a screw dislocation, is not essetztial for VLS (vapor -liquid-solid) growth. The concept of the VLS mechanism is discussed in detail with reference to tire controlled growth of silicon crystals using gold, platinum, palladium, nickel, silver, or copper as an implurity agent. RECENTLY a short communication' described a new concept of crystal growth from the vapor, the VLS mechanism. In this paper we present a detailed description of the process and its application to the growth of silicon crystals and we discuss its relevance to existing concepts of .'whisker" crystal growth. Crystal growth from the vapor is usually explained by a theory proposed by Frank2 and developed in detail by Burton, Cabrera, and Frank.3 In this theory a screw dislocation terminating at the growth surface provides a self-perpetuating step. Accommodation of atoms at the step is energetically favorable, and is possible of much lower supersatu-ration than required for two-dimensional nucleation. Crystals of a unique form resulting from aniso-tropic growth from the vapor are "whisker" or filamentary ones. Such crystals have a lengthwise dimension orders of magnitude larger than those of the cross section. For most filamentary crystals both the fast-growth direction and directions of lateral growth have small Miller indices. The special growth form for a whisker crystal implies that the tip surface of the crystal must be a preferred growth site. sears4 proposed that, according to the Frank theory. a whisker contains a screw dislocation emergent at the growing tip. Such an axial defect provides a preferred growth site and accounts for unidirectional growth. The hypothesis was extended by Price. Vermilyea. and Webb," still implying the presence of a dislocation at the whisker tip. They postulated that impurities arriving at the fast-growing tip face become buried while those arriving on the surface of slow-growing lateral faces accumulate and thereby hinder growth. These considerations led to a whisker morphology. There is increasing evidence that most whisker crystals grown from the vapor are dislocation-free. Webb and his coworkers6 searched for an Eshelby twist7 in zinc? cadmium, iron. copper, silver, and palladium whisker crystals. They found unequivocal evidence for an axial screw dislocation in only one element, palladium. However, not every palladium crystal examined contained a dislocation. Observations with the electron microscope have failed to show dislocations in whisker crystals of zinc, silicon.9 and one morphology of AlN.10 Since many whiskers are completely free of dislocations, an axial dislocation does not appear to be required for whisker growth of many substances. A significant advance in understanding whisker growth has been a recognition of the need for impurities. This requirement has been clearly demonstrated for copper,11 iron,13 and silicon9-1 whiskers. For silicon, detailed studies proved conclusively that certain impurities, for example, nickel or gold, are essential. Another pertinent phenomenon which has received little attention is the presence of a liquid layer or droplets on the surface of some crystals growing from the vapor. Crystals in which this has been observed include p-toluidine,14 MoO3,15 ferrites,16 and silicon carbide.'" The liquid layers or globules were considered to be metastable phases, molecular complexes, or intermediate polymers originating from condensation of the vapor phase. The possibility has been suggested that the halide being reduced is condensed at the tip18 or adsorbed on the surface11 of a growing metal whisker, for example copper. The literature on whiskers discloses illustrations of rounded terminations at the tips. These appear. for example, on crystals of A12O3,19,20 sic,21 and BeO.22 For BeO, Edwards and Happel suggested that during growth of the whisker the rounded termination consisted of molten beryllium enclosed in a solid shell of BeO. A recent paper9 on the growth of silicon whiskers contains many observations pertinent to an understanding of the mechanisnl of whisker growth. These observations are summarized as follows. 1) Silicon whiskers are dislocation-free. 2) Certain impurities are essential for whisker growth. Without such impurities the silicon deposit is in the form of a film or consists of discrete polyhedral crystals.

Jan 1, 1965

By William Klement

THIS note reports the results of some attempts to metastably extend the primary solid solubilities of tin, antimony, and silicon in silver by rapidly quenching these binary alloys from the melt. The procedures employed for alloy preparation, quenching, and Debye-Scherrer X-ray diffraction measurements have been described elsewhere. The lattice parameters obtained for the fcc structures in Ag-Sn and Ag-Sb alloys are presented in Fig. 1, together with the results of Owen and Roberts.4 Alloy compositions are believed to be within ± 0.2 at. pct on the basis of negligible weight losses during preparation and reproducibility of the lattice spacings. Diffraction lines from hcp phases were also detected: the relative visual intensities of the fcc (200) and hcp (10.2) lines were estimated as shown in Table I. The intensities were m for the (200) and w for the (10.2) in a quenched 13.6 at. pct Sn alloy: a lattice spacing for the fcc structure could not be reliably obtained, however. As seen from Fig. 1, the lattice parameters vary linearly with composition up to 8., at. pct Sb and 13." at. pct Sn, respectively, which may be compared with the maximum equilibrium solid solubilities5 of 7.2 at. pct Sb and 11.5 at. pct Sn, respectively. The presence of the hcp phases, which were found together with the fcc phases, is a consequence of the competition1,3 in the nucleation and growth processes during solidification. Both the fcc and hcp phases must be of the same composition for those alloys in the range where lattice parameters increase linearly with solute concentration. Despite much effort with quenched alloys of several silicon concentrations, it has not been possible to obtain lattice spacings of sufficient precision to establish the variation of lattice parameter with composition or the maximum metastable solid solubility: the equilibrium data5 suggest little primary solid solubility of silicon in silver. For alloys containing less than 16 at. pct Si, the Si (111) diffraction line was not observed. For alloys containing 10 to 25 at. pct Si, faint low-angle lines were detected and these could be indexed as the (10.0), (00.2). and (10.1) reflections of an hcp structure with a = 2.87 + 3A. c = 4.52 ± 3A, and c/a = 1.57 ± 2. The 16 at. pct Si alloy was quenched to, and examined at. liquid nitrogen temperatures without any change observed in the proportion of the hcp phase. These experiments were jointly supported by the Atomic Energy Commission and Office of Naval Research under a program directed by Professor P. Duwez. The assistance of H.-L. Luo and A. Abu-Shumays is acknowledged. as is the support afforded

Jan 1, 1965

By John Brownson

Ge-Si N-N heterodiodes hare been built recently which show promise as high-speed logic devices. Low-resistivity germanium is deposited on silicon substrates held at temperatures above the germanium melting point and an alloyed heterojunction formed. The diodes are fabricated from this material using conventional mesa techniques. Over-all device qualify has been greatly improved by the use of epitaxial silicon substrates, that is, a subsirale consisting of a film of thin, high -resistivity silicon on a thicker Piece of low-resistirily silicon crystal. A semimpirical device design equation has been devised which predicts switching performance fairly well within the range of resistivitics and geometries employed. Switching times 01 0.9 ns and PIV 's of —20 v are typical of the better 10-ma diodes. Switching times as low as 0.5 ns have been observed for 10-ma diodes and as low as 2.8 ns for 200-ma diodes. With further development it should be possible to improve switching speed by a factor of four. IN our laboratory, Ge-Si heterodiodes have been built recently which show promise as high-speed logic devices. The diodes have been built using a process reported in some detail in an earlier publication.' The process in short involves alloying a thin film of low-resistivity germanium into a silicon substrate. the germanium having been transported and deposited by the well-known Theuerer halide reduction process.2 This process contrasts with that reported earlier by Oldham who used an essentially conventional direct epitaxial deposition technique.3 Oldham's process, unlike ours, requires cleavage of the silicon sample inside the reactor furnace the instant prior to deposition. Our process has the advantage of yielding large-area macro-scopically plane heterojunctions. Heterodiodes in general have several interesting properties. Without attempting to summarize the theory of heterojunctions.4 two of these properties which have direct relevance should be mentioned. First, N-.V and P-P heterojunction diodes rectify alternating current. Provided that either the band gap or the electron affinity of the two materials is different (which in general is the case), electronic barriers will exist in the junction band structure. When the device is sufficiently forward-biased, the barriers shift so as to permit current flow, and when it is reverse-biased. the barriers block current flow. Second, for N-N and P-P heterodiodes. the foward-conduction process involves majority carriers only. Consequently. when such a device is turned off. there is no minority-carrier storage and hence the diodes switch on and off quite rapidly. As we have reported earlier. N-P and N-N Ge-Si heterodiodes have been built in this laboratory. As one would predict from theory, the N-P heterodiodes were rather slow in turning off while the N-N's were quite fast. Similarly, the turn-off time of the N-P's increased rapidly with forward current while that of the N-N's was independent of forward current. Both N-N's and N-P's were moderately photosensitive. Photocurrents resulting from normal room illumination were as high as 1 µa at 1 v for small-area devices. The most disappointing parameter of the early N-N devices was reverse leakage.' The reverse characteristic was invariably "soft" and leakage at only several volts reverse bias was intolerable. The reverse characteristic was greatly improved by using higher-resistivity silicon substrates. Leakage becomes large at voltages about one third of the avalanche voltage one would expect of a P-N homo-junction formed on silicon of the same resistivity. Thus leakage could be reduced to reasonable limits by using unconventionally high-resistivity silicon. Medium-power diodes formed on 30 ohm-cm substrates leaked typically 15 to 50 µa at 100 v reverse bias. The use of high-resistivity silicon substrate material, however, created a new problem. In order to have an acceptable forward-conductance characteristic. the area of the diodes had to be increased. With this increase in area, the capacitance increased. Switching time for N-N heterodiodes is essentially a linear function of capacitance. Thus when the resistivity was raised. so was the switching time. A SEMIEMPIRICAL HETERODIODE DESIGN EQUATION As a result of our experiments with a limited range of diode geometries and resistivities. a semi-

Jan 1, 1965

By W. C. Hauber

Techniques previously published to predict the production performance of a water flood when the mobility ratio is not unity have been primarily restricted to a five-spot well pattern. When other types of well patterns are considered, the prediction of performance has required either a model study or a complex numerical solution of a multiple-fluid system with a high-speed digital computer. Simple methods are developed in this report for predicting the areal sweep efficiency and injectivity history of a water flood for arbitrary well patterns and mobility ratios. The effect of an initial gas saturation can be incorporated into this method of prediction. With the layer superposition concepts published by Prats, et al.,1 these methods can be used to predict the production performance of a water flood in a reservoir having a wide range in permeability. A reasonably good agreement is shown by comparisons of the results calculated by this method with those obtained either by model studies or by complex numerical solution of multiple-fluid systems. Therefore, it has been concluded that a reasonably accurate method has been developed for predicting the production performance of a water flood employing an arbitrary type of well pattern for any given mobility ratio. A medium-speed digital computer can be used in applying this method. INTRODUCTION Production performance of multi-fluid five-spot water floods can be predicted by the techniques published by Prats, et al.1 This technique takes into account the effects of initial gas saturation, mobility ratio and vertical variations in horizontal permeability. A basic assumption in applying this technique is that unit displacement efficiency does not vary with time after the passage of the flood front. Prats, et al. demonstrated that this assumption is valid for normal waterflood applications with small mobility ratios. To extend Prats' technique to other types of well patterns has required either an experimental model study or a numerical solution of a multiple-fluid system to describe the performance of an individual homogeneous layer. Sheldon and Dougherty2 presented an exact numerical solution employing any arbitrary well pattern. This technique is complex to apply, requiring (1) numerical solution of the single-fluid system, (2) conformal mapping of the streamlines and iso-potential lines to form a new grid network, and (3) a numerical solution of the multi-fluid system on the new grid network. A method was developed in this paper to approximate areal sweep efficiency and injectivity as functions of time for an individual homogeneous layer for arbitrary well patterns and mobility ratios. Analytic expressions were derived to directly apply this method to five-spot and direct line drive well patterns. For other types of well patterns, this method is similar to the approach of Higgids and Leighton,6 in that it utilizes the stream tubes and iso-potential lines obtained by the solution of differential equations when the mobility ratio is unity. However, this method is easier to apply than the Higgins-Leighton method since it does not require knowledge of the variation between oil and water relative permeabilities and saturation. Using the relationship between areal sweep efficiency, injectivity and the volume of water injected into an individual homogeneous layer as obtained by the method presented in this paper, and Prats' technique for the superposition of individual layers, one can predict the production performance of any water flood. ASSUMPTIONS GENERAL Basic assumptions made in this report are that fluids are incompressible and the layers are horizontal, homogeneous and uniformly thick. It is assumed that as water is injected into the layer, three distinct regions are formed —a water bank, an oil bank, and an unflooded region. Each region is assumed to displace other regions in a pis-tonlike manner, with only one fluid flowing in each region, so that there is no change in unit displacement efficiency with time after the flood front has passed in the reservoir. Therefore, the residual oil saturation in the water bank and the oil saturations in the unflooded region are constant throughout the layer. The ratio (F) of the bulk volume of a layer occupied by the oil and water banks at any time before oil breakthrough, to the corresponding bulk volume of a layer occupied by the water bank, is given' by the equation BREAKTHROUGH AREAL SWEEP EFFICIENCY To predict the behavior of any type of waterflood pattern, one must know the breakthrough areal sweep efficiency Eb(Mc,o, F) for the pattern for any water:oil mo-

Jan 1, 1965

By Harmon D. Nine

DISCONTINUITIES in the strain vs cycles to failure (S-N) fatigue curves have been reported for polycrystalline materials by Porter and Levy for copper,&apos; by Benham and Ford for mild steel,&apos; and by Williams and Stevens for 18/5 stainless steel.3 However, the considerable scatter of the points for polycrystalline materials have made a statistical analysis of the data necessary to confirm the discontinuities. By using oriented single crystals of high-purity material and low grown-in dislocation content, the reproducibility has been improved to a degree which makes statistical analysis unnecessary and clearly shows discontinuities in the S-N curves. A recent publication4 reports an abrupt change of slope in the S-N curve for ( 100) axially oriented copper single crystals fatigued in torsion. The reported discontinuities in the S-N curve, along with a different mode of failure in the two branches of the curve, have been interpreted as being due to two different amplitude-dependent mechanisms. Further work on copper single crystals of (111) axial orientation has now been completed which supports the existence of an amplitude-dependent change in the mechanism of fatigue. In the present study torsional-fatigue experiments were performed at room temperature in air on (111) axially oriented single crystals. The crystals were grown and prepared as reported in Ref. 4. Two different methods of growing the crystals also discussed in Ref. 4 produced crystals of two different perfections: Type I with dislocation density of >l06 per sq cm and Type I1 with dislocation density of <l05 per sq cm. In accordance with the accepted hypothesis that crystal flaws are primarily responsible for the scatter of fatigue lifetimes, particularly at low amplitudes, the values for the three lowest amplitudes for Type I crystal are believed to be uncertain. They are marked in braces in Fig. 1. On the other hand, at amplitudes above a surface shear strain (SSS) of *0.003, the data for both types of crystals are in agreement. Most remarkably the S-N curve for torsional fatigue of (111)-oriented single crystals is composed of three segments separated by rather large discontinuities, Fig. 1. Metallographic and X-ray measurements indicate that the lower branch corresponds to the low-amplitude (F) region of the (100) copper single-crystal results as discussed in Ref. 4, and the two upper branches correspond to the high-amplitude (H) region. The lower discontinuity in the (111) S-N curve and metallographic evidence give further support to the hypothesis that different mechanisms of failure operate for high and low strain amplitudes. Reference to the resolved shear stress diagram, Fig. 2, shows that the highest stressed systems in

Jan 1, 1965

By R. W. Parsons

This discussion concerns fitting an ellipse to angle, where the permeability k is measured for a series of plugs cut from varying angles in the horizontal plane. The conclusions and procedures given by Greenkorn, et al. are in no way affected by these comments, since the degree of anisotropy (ratio of maximum to minimum permeabilities) they found is generally quite close to one (see their Table A-1). However, since large anisotropies may arise, I feel that the comments should be made. Both Marcusl and Scheidegger2 have shown that there are two limiting expressions for the permeability of an unbounded anisotropic media. If the permeability is measured in the direction of the pressure gradient, the result is equivalent to the author&apos;s Eq. 11. This is the equation used to find kl1 and k22 from the experimental data. If, however, the permeability is measured in the direction of flow, then the resulting equation for the measured permeability is From these equations it follows that plots on angle will be ellipses. The principal axes will correspond with the major and minor permeability axes. The question arises as to what permeability is actually being measured on an anisotropic sample in the laboratory. An overall pressure gradient and a gross flow rate are determined and a permeability calculated by Darcy&apos;s law. The details of the macroscopic flow within the sample will be determined by the boundary conditions of the sample and the orientation and magnitude of the major and minor permeability axes. The situation is shown in Fig. 1 for the two-dimensional case. Using the method of conformal mapping, Marcusl has solved the problem of determining the overall apparent (or measured) permeability for this experiment for any condition of W-L ratios and orientation and magnitude of the principle permeability axes. For W-L ratios approaching zero, the streamlines are all forced by the boundary conditions to be in the direction of the measured permeability which is equal to kg. For W-L ratios approaching infinity, the effects of the no-flow bounds are negligible, and the pressure gradient and measured permeatility direction are parall;l. The streamlines are

Jan 1, 1965

By B. C. H. Steele, C. B. Alcock

In choosing solid oxide electrolytes for use in the measurement of thermodynamic quantities at high temperatures, the two most important criteria are the values of the partial ionic and electronic conduc tizities. Measurements of these conducticities have been made for some Group IVA oxides and solid solutions of these oxides with CaO, Y2O3, and La2O3. The total conductivities as a function of temperature. oxygen partial pressure, and composition were determined, as well as the electromotive forces of cells in which the oxygen partial Pressures of the electrodes were between 10-7 and 10-29 atm at 1000°C. Additional factors that influence the experimental arrangements, such as the operating temperature, the appropviate cell atmosphere, and electrode kinetics, are also discussed. IT has long been recognized that galvanic cells incorporating solid electrolytes can possess many advantages for the measurement of high-temperature thermodynamic data. Unfortunately, the electrical-transport properties have only been established for a few solid electrolytes, although attempts have been made, and are still being made, to use such materials as porcelain&apos; and magnesia.&apos; Kuikkola and Wagner have discussed3 and demonstrated4 various applications of solid electrolytes, and, in particular, their work stimulated the electrochemical measurement of oxygen activities using cells incorporating the solid oxide electrolyte, Zr0.85Ca0.15O1.85 The excellent characteristics of this oxide electrolyte have been confirmed by the investigations of Kingery et al.5 (oxygen ion diffusion), Carter and Rhodes6 (zirconium and calcium ion diffusion), and Weissbart and Ruka7 (electronic transference number). However the observations of Peters and Mobius,8 later confirmed by Schmalzried,9 indicated that the electronic component of zirconia-based electrolytes could become significant at low oxygen chemical potentials. Under these conditions, thoria-based electrolytes have obvious advantages arising from their superior thermodynamic stability. It was known that certain thoria solid solutions possessed defect fluorite structures containing anionic vacancies (cf. Zro.85Cao.l50O1. 85), although data on their electrical properties were conflicting. Kiukkola and wagner4 concluded that thoria-based electrolytes exhibited appreciable electronic conductivity, whereas Peters and Mobius8 mentioned that the electronic conductivity only became important at high oxygen partial pressures, but gave no further details. In addition, both Kiukkola and wagner4 and Peters and Mann&apos;" had determined the oxygen chemical potentials associated with the Fe-FeO, Co-COO, Ni-NiO, and Cu-Cu2O equilibria, and it was not known whether discrepancies in their results could be attributed to the different cell design, or the thoria-based electrolyte used by Peters and Mann. These uncertainties have been resolved during the present investigation into the measurement of low oxygen chemical potentials, and transport properties of the relevant oxide electrolytes are presented and discussed. Other experimental difficulties associated with low oxygen chemical potential measurements are also described, with particular reference to the Nb-O system. 1. THEORETICAL CONSIDERATIONS Oxide systems of potential use as solid electrolytes possess a large energy gap between the valence and conduction bands. Little is known about the defects present in these wide-gap metal oxides as a function of impurity content and deviations from stoichiom-etry, or the mechanisms by which electronic charges move in these solids. For these materials it is convenient to represent the measured conductivity as the the sum of three terms: where a, is the conductivity due to positive hole conduction (p type), and oe is the electronic conductivity due to electron conduction (n type). U there is a large concentration of ionic vacancies fixed by composition then the ionic contribution will not be a function of oxygen pressure. Although the possibility of a pressure-independent electronic component also cannot be ignored, it is likely that such a term would only become significant at very high temperatures, and in general the positive hole conduction will increase with increasing oxygen pressure, and the electron conduction will increase with decreasing oxygen pressure. It follows that the total conductivity is related to oxygen partial pressure as follows:

Jan 1, 1965

By D. B. Hunter, H. W. Rosenberg

The titanium-rich portion of the Ti-Pd system was investigated from 0 to 75 wt pct Pd by metallo-graphic and X-ray techniques. A 0 eutectoid occurs at 24 wt pct Pd and 1190°F. Two compoutzds are indicated in the region below 75 wt pct Pd, Ti,Pd and Ti2Pd3. The solubility of palladium its a titanium is low, probably less than 1 pct. In 1960 Rudnitskii and Birunl published a complete version of the Ti-Pd phase diagram. However, their work was in disagreement with the earlier literature in that they reported only one inter metallic compound, whereas three had been reported earlier. In view of these discrepancies, it was therefore necessary to redetermine those portions of the diagram of immediate interest. The following account describes our work on the system over the range of 0 to 75 wt pct Pd. MATERIALS AND METHODS Distilled titanium sponge and elemental palladium were used in the formulation of the alloys; the chemistry of these materials is detailed in Table I. The alloys were prepared as 10 to 50 g blended compacts that were melted into buttons by arc melting under gettered argon on a water-cooled copper hearth. Weighing of the ingredients before and after melting showed that negligible weight changes occurred. Therefore, no analyses were undertaken and the compositions of all alloys are nominal. All alloys were fabricated by hot rolling at 1700°F to 0.070-in.-thick sheet. Scale was removed by sandblasting and pickling in a 5 pct HF-35 pct HNO,, balance H20 solution. For metallographic examination, specimens were mounted after heat treatment transverse to the rolling direction, ground on silicon carbide papers of increasing fineness to 600 grit, and then electro-polished using a solution containing 600 ml me-thanol, 60 ml perchloric acid, 360 ml butyl cello-solve, and 2 ml "Solvent X". Unless otherwise specified, etching of alloys containing up to 42 pct Pd was carried out by swabbing with a 12 pct HN03-1 pct HF aqueous etch where a bright etch was required, or by a 1 pct hydrofluoric in saturated oxalic acid solution where contrast between phases was required. The Ti-52.8 Pd alloy was etched with a solution of 25 ml HF, 40 ml glycerine, 35 ml methanol, and 18 g benzalkonium chloride. For X-ray examination, 1/2-in.-square speci- mens of sheet were mounted flat in a standard 1-in. metallographic mount and ground and polished as above. X-ray diffraction was performed using a Norelco type 12045 Diffractometer, employing CuKa radiation with a nickel filter at 40 kv and 20 ma. Specimens were rotated about the sheet normal during exposure. Although this procedure did not remove the effects of sheet texture from the relative intensities, it had the advantage that oxidation or contaminants entering during preparation of powder samples could not confuse the patterns obtained. RESULTS AND DISCUSSION Fig. 1 illustrates the Ti-Pd phase diagram according to Rudnitskii and Birunl with the work of the present authors superimposed. Both interpretations agree that the system is of the 0 -eutectoid type with an extensive 0-phase field, and that the eutectoid temperature is just below 1200°F. There is also agreement that the solubility of palladium in a titanium is restricted. Our work would indicate that the a solubility of palladium is low, probably less than 1 pct. However, whereas Rudnitskii and Birunl place the eutectoid composition at 41 wt pct Pd, this investigation shows it to be at about 24 wt pct Pd. Moreover, this investigation confirms the existence of compounds at Ti2Pd and Ti2Pd3, whereas Rudnitskii and Birun report only a single Berthol-lide phase covering the TiPd to TiPd, range. Laves et a1.&apos; and Wallbaum, whose work was summarized by Maykuth , reported the existence of Ti2Pd3 and TiPd, in addition to Ti2Pd. More recently, Nevitt and Downe~&apos; have reported the structure of

Jan 1, 1965

By S. R. Goodman, Hsun Hu

A study has hem made of the formation of annealing textures in an 18-8 austenitic stainless steel (Type 304L) from various deformation textures obtained by rolling at different temperatures. When the deformation texture is a mixture of the ferritic type and the brass type owing to the pres -ence of both martensitic ferrite and retained aus-tenite in the specimen, recrystallization takes place by the growth of the existing austenite phase. In a previous report,&apos; it was shown that the rolling texture of austenitic stainless steel (Type 304L) changed gradually from the brass type to the copper type with increasing temperature of deformation above 200°C. These changes are similar to those in high-purity silver2,3 and electrolytic copper;4 a brass-type texture is favored at low rolling temperatures, whereas a copper-type texture is favored During the course of rolling -texture transition from the brass type to the copper type, the subsequent recrystallization textures change accordingly. The orientation relationship between the annealing textures and the various rolling textures, being consistent with previous observations on various fcc metals, can be described as [Ill] rotations of approximately 25 to 40 deg. Carhide precipitation may influence the annealing textures. at high rolling temperatures. Furthermore, the annealing textures in high-purity silver5 and electrolytic copper4 were found to depend entirely on the prior deformation texture. From a copper-type rolling texture a strong cube texture will form upon recrystallization, whereas from a brass-type rolling texture the annealing texture will be quite different from the cube orientation. In an earlier comm~nication,6 the formation of a strong cube texture in 18-8 austenite stainless steels (Types 304 and 304L) was reported briefly by the authors. The present paper constitutes the results of a complete study of the annealing textures obtained from a

Jan 1, 1965

By R. D. Pehlke, P. D. Goodell, R. W. Dunlap

The rate of dissolution of steel bars in molten pig iron has been measured experimentally in the temperature range 2300° to 2650° F. The rate of solution is shown to be a .function of bath composition, temperature, and stirring. A kinetic model based on carbon diffusion in the liquid phase has been derived to fit the experimental results. THE rate of scrap melting has long been an important variable in steelmaking operations. With the advent of the oxygen steelmaking process and the accompanying shorter heat times, the rate of scrap melting has now become one of the rate-limiting factors in steel production. As observed in commercial practice, the solution rate is influenced by the compositions of liquid and solid, the temperature, agitation, and time. However, no definitive work has been done on the Fe-C system, and there is very little information in the literature regarding the relative effects of these variables in steelmaking systems. A number of questions have been raised in regard to scrap utilization in basic oxygen steelmaking operations. Consideration has been given to the optimum size and shape of scrap, and to the use of preheated scrap as a means for decreasing the pig-iron requirement in oxygen blowing. The determination of an optimum scrap practice for a specific installation depends to a large extent upon the economics of the scrap market and also upon the behavior of scrap in the vessel. The present research was undertaken as a preliminary study in evaluating the behavior of steel in a pig-iron bath under various conditions of temperature, composition, and agitation, as might be encountered in oxygen converter operations or in any steelmaking operation where scrap behavior is an important process variable. Related studies have been carried out on non-ferrous systems. The solution rate of solid aluminum in a molten A1-Si alloy has been studied.&apos; Furthermore, the increasing use of liquid metals has created considerable interest in studies related to dissolution of a solid in a liquid, or mass transfer taking place between a solid interface and a liquid metallic phase.2-10 In an effort to clarify the relative importance of factors influencing the dissolution of scrap in Fe-C alloys, this paper presents the results of a study of the rate of dissolution of a low-carbon steel cylinder in a molten Fe-C bath at various bath compositions, temperatures, and conditions of agitation. An attempt has been made to determine the mechanism of solution, and a model has been derived to fit the experimental results. The rate of heat transfer between the molten pig-iron bath and the solid-steel cylinder has also been studied. EXPERIMENTAL PROCEDURE A molten bath of pig iron (nominal composition 4.2 pct C, 0.5 pct Mn, 0.8 pct Si)* was held in a 200- *In view of the fact that the composition of the pig-iron bath was slowly changing with time because of steel dissolution and reaction with the surrounding atmosphere, intermittent samples of the liquid bath were taken throughout each experiment, Table 1. lb induction melting unit. The internal diameter of the furnace was 8-1/2 in. and the bath depth approximately 14 in. Cold-finished 1020 steel cylinders of 1/2-, 3/4-, 1-, 1-1/2-, and 2-in. diameters were cut into 1 -ft lengths for use as test specimens. One end of each bar was machined to fit a hand-driven, mechanical stirring device which rested on top of the furnace. This fixture permitted 7 to 8 in. of the bar to be immersed in the melt. The steel cylinders were cleaned to free the surface of grease and oxide. The rods, at ambient temperature, were immersed into the molten pig-iron bath. The melt temperatures studied in this investigation were 2300°, 2500°, and 2650°F. Different agitation conditions were achieved by operating with a) the power to the furnace, giving induction stirring; b) induction stirring plus mechanical stirring, using hand rotation with a chain and sprocket assembly at approximately 200 rpm; c) mechanical stirring alone with the power off; and d) the power off and no mechanical stirring resulting in minimum agitation, i.e., only that caused by natural convection currents in the bath. The samples were immersed in the melt for prescribed times ranging from 30 sec up to 6 min. Immersion times were measured with a stopwatch and temperature control of the melt was achieved by power adjustment following temperature measurement with an optical pyrometer. The measurements with the calibrated pyrometer were checked out to within less than 10°F with simultaneous thermocouple measurements. Following immersion, the bars were water-quenched and the diameters were measured with a micrometer at several positions on the reduced area, and by volumetric displacement. The dissolution rates calculated from the

Jan 1, 1965

By S. F. Ramseyer, E. A. Steigerwald

INFILTRATED structures represent composite materials which are capable of combining high-temperature strength with adequate low-temperature toughness and thermal shock resistance. Although copper- and silver-infiltrated tungsten structures are actually being used in rocket nozzle hardware, adequate understanding of the fracture mechanics of these composite systems is not available. Specifically the relative importance of the strength, ductility, and modulus of the infiltrant in determining composite properties is not known to the extent that optimum composites can be selected. The major portion of experimental effort in the area of composite strength has been devoted to fiber-reinforced systems1 or to systems where a discontinuous phase is imbedded in a relatively ductile matrix.2&apos;3 In the case of high-temperature systems, which are composed of a relatively brittle matrix, such as tungsten or an oxide, a continuous phase exists for the propagation of a crack. The method by which the presence of a conjugate ductile continuous phase influences the gross properties of the composite represents an area which requires further investigation. This technical note presents results which evaluate the effect of infiltrant strength on the strength of the tungsten-base composite. A tungsten matrix and copper-base infiltrant were selected for the initial studies because of the ease of fabrication. Tungsten structures with nominally 20 and 30 pct porosity were evaluated. The porosity was controlled by varying the initial powder size and a ratio of open-to-total porosity greater than 95 pct was obtained by selective sintering cycles. The processing sequence involved hydrostatic pressing followed by a 72-hr presinter in hydrogen at 2000° F and a final sinter at 4000°F for 4 hr in vacuum. The 20 pct porous structure was obtained

Jan 1, 1965

By P. R. Gage, R. W. Bartlett

SILICIDE coatings on refractory metals are often applied by transporting a silicon halide vapor to a hot metal surface where dissociation or hydrogen reduction occurs. The subsequent chemical reaction to produce the coating requires diffusion of silicon or the refractory metal through the in situ silicide layer. This solid-state diffusion process step is often slower than the vapor-transport step and, therefore, rate controlling. This situation is analogous to the parabolic oxidation of metals in which the oxidation rate is controlled by diffusion through the oxide layer. The purposes of this study were to 1) measure the rate of formation of MoSiz and MoSi2 coatings under conditions such that the silicide diffusion process is rate controlling and lower silicide compounds are not formed and 2) determine by a marker experiment whether silicon or the respective refractory metals are the principal diffusing species in the disilicides.

Jan 1, 1965

By K. M. Busen, J. Lindmayer

A heterojunction model is suggested for descrihzng the electronic conditions at oxide -semiconductor interfaces. Detailed study of the silicon oxide-silicon interface shows that the heterojunction model explains many experimental facts; however, it is necessary to assume that a transition layer exists at the interface. It will he demonstrated that ionic contrbution way also he present. Extended low-temperature heating stabilizes the oxide to a charge carrier density in the order of 10&apos; cln-: determined by the heterojuncton model. OXIDIZED semiconductor surfaces are widely used, since they offer technological advantages and "passivate" the surfaces of semiconductor devices. However, it has been recognized that there are always n-type inversion layers formed in the silicon oxide-silicon system, which must be regarded as a definite disadvantage. An added complication is the "instability" of these inversion layers;&apos; the inversion layer appears to vary with the processing and they change at temperatures as low as 100" to 200°C This paper will point out that the inversion layer is a result of the dissimilarity of the contacting materials and therefore must always be present. The dissimilarity is the essence of the heterojunction or electronic model and involves directly the structure of the materials involved. In addition, one finds the contribution from ions; this disturbance, however. can be eliminated for the case of silicon oxide-silicon interface. The strength of the inversion layer or channel will be expressed in terms of the density of elementary charges per square centimeter, N*, maintaining the channel. The next section contains the formulation of the heterojunction model by assuming a contact between two homogeneous materials. This calculation should not imply that silicon oxide is homogeneous; it serves only to point out the general properties of the electronic model. Following the electronic model, the practical case of the silicon oxide-silicon interface will be discussed. I) THE HETEROJUNCTION MODEL Contacting an oxide with a semiconductor, a work-function difference must be accommodated. Fig. 1 represents the oxide and the semiconductor before and after contact. When the contact has been made, one finds that qVi + qV, = A@; i.e., the work-function difference is distributed between the oxide and the semiconductor. Normally, the work-function difference appears on the wide-bandgap material, but in the present case the oxide is thin and far from being a single crystal. Accordingly, a significant fraction of the work-function difference must appear on the semiconductor. The work function of silicon2 is about 4.8 ev, but we shall not assign any particular work function for the oxide as it may vary. However, oxides usually have lower work functions and therefore the potentials must build up in the manner shown in Fig. 1. Such an argument predicts that the inversion layer must be n type, as opposed to the clean surface which is p type. Another important factor to be considered is that the oxide is disorderly and therefore contains many trapping levels. As a result, the charges in the oxide arise primarily from the change in trap occupation, while on the semiconductor side the space charge is composed of mobile free electrons. The consequence of this fact is that a change to another thermal equilibrium will require some time, dictated by the traps in the oxide. The conditions can easily be calculated on the semiconductor side. Assuming an intrinsic semiconductor, Poisson&apos;s equation is

Jan 1, 1965

By D. C. Shelton

Eq. 4 and 5 on page 5 of the March 1965 issue of Transactions, and Eq. 12 on page 8 of the same issue should read respectively:

Jan 1, 1965

By Gareth Thomas

The analysis of Kikuchi pattersns of exct ovientalions from single cryslals and paired Kikuchi lines from single and overlapping crystals is shown to be useful and quanlitalve and is applied to Phase transfovnzcitions including ordering, spinodals, mavten-silic, and nuclealion and growth pyocesses. 112 pinciple, the analysis of exacl orientations enables the crystal system and the Bravais lattice of a crystal to he determined. The advantages of the davk-field imaging technigure for detecting vevy small precipitates are also described. ALTHOUGH Kikuchi electron-diffraction patterns were first observed nearly 40 years ago,&apos; little systematic application seems to have been made of them, until fairly recently during electron microscopy, when their usefulness in contrast experimen and for determining exact orientations8&apos;9 has been pointed out. With the availability of gonio-metric specimen tilting stages it has now become possible to make much wider use of diffraction patterns, particularly the Kikuchi pattern, which is the main subject of this paper. The treatment presented here is not exhaustive but it is hoped that it will stimulate more use of Kikuchi patterns during electron-microscopy investigations. The Kikuchi pattern is formed as a result of Bragg diffraction of the inelastically scattered electrons produced during the interaction of the beam and thick specimens, The important feature of these patterns is that they give an accurate representation of the symmetry of the crystal being investigated, so that it is possible to identify crystal systems and even the Bravais lattice. This means that new structures, e.g., formed in phase transformations, may be identified during normal electron microscopy, so that Kikuchi-pattern analyses considerably extend the uses of the electron microscope. Recent work has also shown that dark-field images are more informative than bright-field images, particularly, for observing small precipitates. The second part of this paper discusses some applications and advantages of dark-field imaging in studies of two-phase systems. 1) DIFFRACTION PATTERNS 1.1) Spot Patterns. Electron-diffraction spot patterns have their limitations because of the importance of the form factor on the intensities and shape of the reciprocal lattice points. Because of the extension of these points into relrods, reflections are possible over a large angular range (+5 deg) and the patterns from thin regions can be complicated because second-layer relrods intersect the reflecting sphere. Spot patterns can thus give only an approximate idea of the crystallography unless the foil is tilted into exact orientation. In this case the spot pattern is symmetrical, with equal numbers of spots on the positive and negative zone directions about the origin. Such cases are necessary for structural analyses and have been used recently to determine the crystal structure of the ordered Ta64C phase." Exact orientation means that the plane of the reciprocal lattice lies exactly normal to the incident beam as shown in Fig. 1(b). It should be noted that in exact orientations the angle of reflection is less than the exact Bragg angle 9 so that the reciprocal lattice points lie to the outside of the sphere, Fig. 1(b). This deviation is denoted by the parameter s and in the usual convention4 s is negative for exact orientations and, of course, zero at the exact reflecting position shown in Fig. l(a). In order to avoid secondary reflections from thickness relrods it is advantageous to work in thicker regions of foils. Diffraction from thick regions may also produce Kikuchi patterns and as dis-

Jan 1, 1965

By L. A. Dale, D. A. Dahlstrom

Closed-water circuits are justified today from two standpoints: economical operation and prevention of stream pollution. In today&apos;s modern preparation plant, it has been found very desirable to have the plant circulating water maintained at a relatively low solids concentration of around 3%. In so doing, bene-ficiation equipment can operate at a much higher efficiency. However, makeup water requirements would become excessive if the fines were to be removed from the preparation plant by bleeding a 3% solids concentration to a tailings pond. With the ever increasing percentage of —200 mesh coal, clay and slimes in the raw coal, coupled with the creation of these fines within the preparation plant, the need for water conservation for economy reasons becomes even more important. Because of stream pollution laws, tailings ponds have become very costly to operate and maintain, resulting in the necessity of employing an in-plant method of water recovery. Accordingly, the primary system employed in water recovery in the coal preparation plant today consists of a solids concentration device to thicken refuse solids while at the same time producing a sufficiently clarified effluent that can go back to the preparation plant for water reuse. The thickened product is then normally passed to a dewatering device that will produce a handleable solid that can be disposed of

Jan 1, 1965

By R. H. Schnitzel

Internal-friction peaks have been observed in tungsten single crystals at about 300° and 400°C. The characteristics of these peaks are similar to interstitial peaks observed in other bee metals; therefore, the origin of these peaks appears to he the Snoek mechanism. The interstitial responsible for the peak at about 300°C has not been identified. Carburizing increases the magnitude of the peak at about 400°C; consequently, it appears reasonable to suppose that the specific interstitial associated with this peak is carbon. The activation energies associated with the 300° and 400°Cpeaks are about 35,000 and 45,000 cal per mole, respectively. INTERNAL - friction peaks resulting from the stress-induced diffusion of interstitials (Snoek relaxation peaks) have been frequently observed in bee metals.1-5 Attempts to detect Snoek relaxation peaks in tungsten have, however, not been fruitful.&apos; Failure to find Snoek peaks in sintered tungsten can perhaps be attributed to one or more of the following difficulties: a) the relatively low purity of the sintered tungsten; b) the lack of extensive metallurgical knowledge about tungsten-interstitial alloys, such as suitable interstitial dosing and quenching procedures; and c) the inconsistency of some of the interstitial analyses of tungsten, which reflects itself in one&apos;s inability to be sure of the nature of the specimens. This present investigation did not overcome all of these difficulties for successful tungsten internal-friction measurements. Some of these difficulties still persist and new difficulties were encountered during the course of this investigation. Nevertheless, the use of electron-beam tungsten single crystals having somewhat greater purity levels than sintered tungsten combined with appropriate carburizing and quenching procedures permitted a reasonable attempt to be made. As a consequence, internal-friction peaks were observed in these tungsten single crystals at about 300° and 400°C. These peaks were found to be unstable, since they annealed rapidly away during a sequence of internal-friction measurements. Hence, it was necessary to construct an apparatus having a faster heating rate to study some of the details of these peaks. From the behavior of these peaks as well as our knowledge of similar peaks in other bee metals, one can reasonably conclude that these peaks are caused by residual interstitial impurities within these crystals. Further investigation of these peaks after the application of various metallurgical treatments lent credence to this supposition. EXPERIMENTAL TECHNIQUE The internal friction of tungsten single crystals was measured using two different pieces of apparatus both of which are of essentially the same conventional design, namely the KE type of torsion pendulum. The important difference between these two types of apparatus was in the attainable heating rate and method of protection of the specimen from atmospheric contamination. The apparatus designated "number 1" was enclosed in a vacuum chamber which was heated by an externally mounted furnace. It had a slow rate of heating which was estimated to be about 4°C per min from room temperature to about 350°C and then about 1°C per min to 600°C. The internal friction of tantalum was measured with this apparatus and the established Snoek peaks were found.&apos; These tantalum peaks in the temperature range from room temperature to 400° C served as a check for the apparatus. The apparatus designated "number 2" having a faster heating rate than number 1 was not elaborate. It consisted of a mounted nickel tube to which split heating elements were attached. Argon was used as the protective atmosphere. The measured heating rate was about 12° to 15°C per min whereas the cooling rate was somewhat slower at about 10° C per min because of the increased difficulty encountered in stabilizing the temperature. No surface oxidation of the specimen was noted after any test. This apparatus was also checked with the known peaks of tantalum.1 The preparation of the single-crystal specimens for internal-friction measurements consisted of centerless grinding the crystals from an approximate 0.200 in. diameter to 0.030 to 0.040 in. in diameter, and then electropolishing them to about 0.020 in. in diameter. Single crystals processed in this manner are designated as being in the virgin condition. Since the length of crystal varied from 3 to 9 in., the test frequency varied from about 1 to 2 cps. The frequencies of measurement, axial orientations, and chemical analyses for the various crystals are listed in Table I. The controlled addition of carbon into tungsten is a difficult problem. Attempts to find the critical conditions necessary for an equilibrium treatment were not fruitful. Therefore, a simple nonequi-librium method was used. The addition of carbon to these crystals consisted of appropriately combining three treatments—carburizing to achieve a case, annealing to partially dissolve the carbon into the

Jan 1, 1965