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By Walter Crafts, D. C. Hilty

The liquidus diagram for the iron field of the Fe-S-O system has been derived experimentally. The solubility of oxygen in molten Fe-S alloys has been measured at several temperatures and found first to decrease slightly and then increase rapidly with increasing sulphur content. IT is well-known that the types, distribution, and amount of inclusions in any given steel are closely allied with the oxygen and sulphur contents of the metal, so that the term "deoxidation" as conventionally applied in steelmaking refers not only to the control of oxygen and oxide inclusions but to collateral modification of sulphide inclusions as well. Inclusions commonly occur in steel as mixtures of oxides and sulphides, sometimes closely associated and sometimes apparently completely divorced. Their effects on the properties of the metal may vary widely depending on their types and distribution as well as on their quantity. The mechanism by which inclusions form, however, and the means for controlling it are exceedingly complex and not well understood. Nevertheless, as described by Benedicts and Lofquist' and by Wentrup' all oxide and sulphide inclusions, excluding mechanically entrained matter, must result from specific modifications of the basic equilibria of the Fe-S-O system. In an investigation of the mechanism of deoxidation and inclusion formation being carried out at the Union Carbide and Carbon Research Laboratories, it became evident that quantitative data for the fundamental Fe-S-O system were essential to a better understanding of the problem. Consequently, the liquidus surface of the portion of the Fe-S-O diagram of interest in steelmaking has been determined, and the solubility of oxygen in liquid iron containing sulphur has been measured. Fe-S-O Diagram The portion of the Fe-S-O diagram of specific interest in steelmaking is the Fe-FeS-FeO corner. Of the contiguous binary diagrams for this partial system, only those for Fe-FeO and Fe-FeS are known with reasonable certainty.3 Several attempts to derive the FeO-FeS diagram have been made, chief among them being the work of Giani as reported by Oberhoffer,4 and, more recently, that of Vogel and Fulling." Although both Giani and Vogel and Fulling published diagrams for the FeO-FeS system, their observations indicated that the oxide component approximated Fe3O4 rather than FeO, so that there is doubt whether the system is truly binary. Benedicts and Lofquist and also Wentrup published qualitative sketches of the ternary diagram based on the assumption that it was of the type described by Marsh for a ternary system in which two of the contiguous binary systems are simple eutectic systems and the third exhibits a solubility gap in the liquid. Apparently, however, the only previous effort to establish the diagram experimentally was that of Vogel and Fülling whose results are reproduced in Fig. 1. Although defining approximately the limits of the miscibility gap and the location of the ternary eutectic, point E in Fig. I, Vogel and Fülling's diagram must be considered only semiquantitative. It was derived from a limited number of observations mainly along two quasi-binary sections, and the directions of the tie-lines and the location of the critical point, K in Fig. 1, were estimated by computation. Experimental Procedure The experimental technique employed for the present investigation involved melting mixtures of ferrous sulphide and ferric oxide in contact with iron. Since it was considered that in this part of the system the vapor pressures of sulphur and SO, are so low that they would not affect the results significantly, the melting was carried out in a current of argon to sweep out products of any initial re-

Jan 1, 1953

By G. R. Purdy, J. A. Malcolm

The isothermal dendritic precipitation of y in p CuZnSn is compared with the isothermal formation of Widmanstatten a plates in p CuZn. Although both precipitates are evidently bounded by semicoherent interfaces, the dendritic shape of y evolves through smooth "sinuoidal" shape perturbations, while a-p interfaces tend to be strictly planar, or rnicroscopically faceted. An estimate of the average inter-facial free energy of cube-oriented y in p through the Mullins-Sekerka analysis indicates that it is low (of the order of 50 ergs per sq cm). Interface mication is apparently controlled by volunle dij'usion, and the observed anisotropy in growth probably results from anisotropy of inter facial free energy. Studies of the grain boundary precipitation of y in p indicate that the precipitate can grow in both $ grains, but becomes unstable with respect to the grain with which it shares a mobile semicoherent interface. Facets observed at the tips of Kurdjumov-Sacks-oriented Wid-manstatten a plates correspond to variants of an irrational hahit, near (231)0. Comparison with Hu and Smith's determination of relative interfacial free energies of a-(3 boundaries suggests that this system possesses an extremely deep o cup, which results in an ej'ective low-o zone. The possible effects of such a cup on the stability of a-p interfaces are discussed, a needles, grown during rapid continuous cooling, possess microscopically smooth interfaces, and are characterized by a high degree of' damage in the region of the boundaries. These boundaries, induced to move on tempering at 200"C, become faceted as equilibrium is approached, which seems to indicate that boundary structure and mobility in this system are dependent on the local degvee of departure from equilibrium MULLINS and sekerkal have elucidated the phase boundary stabilizing effect of surface tension. a factor not taken into account in previous treatments of morphological development. Their analysis applies to the isothermal growth of a pure spherical precipitate (planar in the limit of infinite radius) in a slightly supersaturated solution, under conditions of inter-facial local equilibrium and isotropy of interfacial free energy. More recently, several other factors which might tend to stabilize planar interfaces have received attention. These are: i) interface diffusion;4"8 and ii) slow interfacial reaction. cahn7 included a slight anisotropy in interfacial free energy, and showed that it has no stabilizing effect, but forces shape perturbations to reflect the anisotropy. shewmon4 noted that dendritic morphologies are rarely observed in solid-solid systems, and, in particular, postulated that slow interfacial reaction occurs at all boundaries between proeutectoid ferrite and austenite, except those which propagate parallel to {11 l)y planes (for Kurdjumov-Sachs [K-S] related phases). Previously, Aaronson~ had proposed interfacial reaction at the broad faces of Widmanstatten plates, and expected that the lateral motion of high-mobility incoherent ledge edges would produce planar precipitates bounded by law-mobility semi-coherent interfaces. The problem of interfacial reaction during the dif-fusional formation of precipitates has often been ignored, although it is apparent that a small component of chemical reaction must exist at any moving interface." Further, all solutions of the diffusion equations for boundary conditions corresponding to isothermal growth predict infinite growth rate at time zero, so that elements of interfacial reaction would be most easily detected at early times. However, reported deviations from diffusion control are comparatively rare," and the local-equilibrium diffusion-control model appears adequate for the description of many isothermal growth systems.'2"9 Cahn14 has treated the problem of migration of an interface which is able to reach positional energy minima, and concluded that such an interface, if subjected to a high local ther-modynamic "driving force", may migrate normal to itself without the benefit of ledges. As local equi-

Jan 1, 1968

By C. van der Poel, R. L. Chuoke P. van Meurs

When an initially planar interface between two im-ttitcihle liquids is displaced at constant rate, U, nor-mat to the front, instability will occur for all rates greater than a critical rate. U, given by provided the Fourier decomposition of the spatial pertmrbcrtiott or deformation of the moving displacetment front contains modes with wavelengths. A, greater than a critical wavelength, given by tit there expressions, p, p and k, with the subscripts I and 2 distinguishing the two 1iquids under consideration, are density, viscosity and effective pemeability coefficients respectively; g is the absolute value of the acceleration due to gravity; and cos (zz') is the direction cosit7e between the vertical carlesian coordinate z' (positive upward) and the z coordinate norma1 to the initially plane macroscopic interface taken positive in the direction from Liquid I to Liquid 2. U is the average volumetric velocity (injected volume of liquid pet. unit time per unit of area normal to Z) and is positive for Liquid I displacing Liquid 2, negative for the reversc displacement and r2 is an effective inter-fucial tension (for displacements between parrallel plates, t0= s the ordinary bulk interfacial tension). further, there is a wavelength of maximum instability given by For natural perturbations, this wavelength will preclotninate and characterize the form of the instability as a quasi-sinusoidal deformation, i.e., viscous fitzgers of peak-to-peak separatiotr, A,,. Comparison of experitient with theory rei'eals tltat these considerations are recsonably valid for displacements in hoth parallel plate chantzels and nnconsoli-clutt'd glass ptnvder packs. These results are. tij particular interest for interpretation of data from laboratory experiments with regard to fielil applica/iotz.s. It is quite possible for A,, although st7zall relative to the large lateral dimension of the reservoir, to rxceed the greatr.st lateral extent of the lahoratory sample or model. If it does, frontal displace- ment occurs in the laboratory experiments, and oil INTRODUCTION Thc puposes of this paper are to present theoretical and experimental evidence for occurrence of macroscopic instabilities in displacement of one viscous fluid by another immiscible with it through a uniform porous medium and to compare available experimental data with some predictions of a theory of instability developed by the first author. The instabilities are referred to as macroscopic in the sense that spatially quasi-sinusoidal, growing fingers of the displacing liquid are formed, the width and peak-to-peak separation (wavelength) of which is large relative to a characteristic length of the particular permeable medium such as grain size. Visual models of two kinds have been used to obtain observations: displacement of oil by water-glycerine solutions through the flow channel formed by closely spaced parallel plates and displacement of oil by water with and without initial interstitial water through unconsolidated glass powder packs, employing the technique of matching indices of refraction. In all cases we have observed macroscopic instabilities or fingers under conditions predicted by the theory to be favorable for their occurrence. The phenomenon discussed here is not the production of streamers due to gross inhomogeneities such as permeability stratification of the porous medium. It is our object to show, on the contrary, that a quantitative prediction of finger spacing is possible in a porous medium known to be macroscopically homogeneous and isotropic throughout. The importance of the phenomenon in its influence on the configuration of oil and water with respect to oil production behavior was noted earlier by Engel-berts and Klinkenberg' who coined the term "viscous fingering". THEORY Necessary and Sufficient Conditions ior Instability anc Initial Kinematics There are several levels of increasing complexity in the theoretical description of instabiIity of fluid displacements in permeable media. Of these, the simplest description, ;tdapted to low permeability systems, is selected for presentation.' More inclusivc tlescriptions are reserved for separate publication.

By V. Kondic, W. M. Rumball

HUNT and Jackson' have recently suggested that binary eutectics might be classified according to the entropy of fusion of the component phases. Such a classification was in fact proposed2 some time ago by the authors and the purpose of this communication is to present some supporting evidence. As pointed out by Hunt and Jackson' typical metals of low entropy of fusion, ?S, tend to form normal eutectics (using Scheil's terminology3). Where one phase is metallic (low ?S) and the other nonmetallic (high AS) then anomalous structures are formed. These anomalous structures may either be regular (e.g., Bi-Sn)or irregular (e.g., A1-Si). Finally Hunt and Jackson suggest that where both phases are of high ?S regular faceted structures are formed. In the proposed classification2 the ratio of the entropies of fusion is taken as the quantitative parameter, i.e., ?Sa/?SB = E, where e > 1.0. An extensive literature survey has been carried out2,4 for reliable photomicrographs of eutectic structures. The structures, numbering 151, have been classified into two classes, viz., normal (i.e., lamellar and rodlike) and anomalous. The latter group has been arbitrarily subdivided into regular and irregular anomalous eutectics. Details and sources of the structures are given elsewhere.2,4 In the absence of better thermodynamic data the value of E has been determined for each of the systems making the following assumptions and approximations: l) The entropy of fusion of solid solutions may be calculated additively;5 ii) Inter metallic compounds are treated similarly but with the addition of the following term for fully ordered structures.5 -4.573(Ni lOg10 Nl + N2 log10 N2) where Nl and N2 are the atomic fractions. It might be argued that the entropies of fusion are meaningless as the eutectic phases form at some temperature (T,°K) below their true melting point (Ta or Tb). As AS, = Lo/To if La the latent heat of fusion of a, is assumed independent of temperature, the actual entropy change AS& is given by La/Te. The ratio of entropies of fusion then becomes Fig. 1 shows E' plotted against cumulative totals for normal and anomalous systems from which it is seen that normal eutectics predominate at low values of E'; e.g., some 90 pct of normal systems lie below E' = 1.5 with 65 pct of anomalous systems above this value. Fig. 1 also shows that the regular anomalous structures occur mostly at low values of c' possibly suggesting growth more akin to normal than anomalous growth. The choice of c as a classification parameter was based on nucleation concepts, it being observed that metals widely separated in Sundquist and Mondolfo's8 nucleation series were anomalous and those close together normal. The basis of these classification views is really outside the intended scope of this communication but it is hoped to explain them fully in the near future.7 Having arrived at this entropy of fusion classification by nucleation considerations it is interesting to note that Hunt and Jackson's ideas are based on growth considerations. Elsewhere one of the authors4 has shown that an even better classification of the metallographic structures reviewed is obtained from purely conventional heterogeneous nucleation concepts. It has been found that systems having a value of the parameter +b less than 0.28 are almost certainly normal and above this anomalous: V, is the gram atomic volume. This parameter is nevertheless closely related to c and c', these being an approximation of p. The parameter is also related to the other classification3,8,9 which have met with any success in the past. All these classifications are to be reviewed shortly by the authorsU7 A significant thing about the classifications based on

Jan 1, 1968

By E. Miller, N. Chou, K. Komarek

The solid solubilities of the compounds PbS, PbSe, and PbTe have been determined by equilibrating single crystals with two phase alloys. The solubilities were determined by measuring the Hall coefficient of the equilibrated samples. The observed maximum deviations from stoichiometry on the lead rich and the chalcogen-rich side of the phase fields were: at. pct excess Pb at pct excess S at 850°C; PbSe--4 x 10'" at. pct excess Pb at at. pct excess at 800°C; and PbTe-2.8 x 10 4 at. pct excess Pb at 780°C, 10"1 at. pct excess Te at 720°C. The previously developed theory of retrograde solubility has been expanded to include intrinsic disorder in the compounds, and the experimental results are in agreement with the theory. THE solid solubility limits of intermetallic semiconducting compounds are of considerable interest, since many of these compounds have potential use as thermoelements in thermoelectric devices, as infrared detectors, or in semiconductor devices. The solidus curves of a significant number of these compounds have been reported to be retrograde with the maximum solid solubility occurring between the eu-tectic and the maximum melting temperatures. In a previous paper,' equations were derived which permit calculation of the maximum solid solubility of an AB compound exhibiting retrograde solubility. Derivation of these equations was based on the assumption that the compound is a nondegenerate semiconductor at the temperature under consideration, that the defects were unassociated, and that the vibrational contribution to the entropy of the compound could be evaluated by the Einstein approximation. It was shown that at the temperature of the maximum solid solubility The entropy term ASS is composed of the entropy of formation of the solid stoichiometric compound (AS$)*, and the entropy due to deviations from stoichiometric composition which is the sum of a con-figurational term (aS*), a vibrational term (AS,), and an electronic term (AS,). In the previous paper the positional entropy was evaluated considering the con- N. CHOU, Member AIME, formerly Graduate Student, New York University, N. Y., is with IBM, Yorktown Heights, N. Y. K. L. KOMAREK, Member AIME, formerly with New York University, is Professor, Department of Inorganic Chemistry, University of Vienna, Vienna, Austria. E. MI LLER, Member AIME, formerly with New York University, is Associate Professor of Mechanical Engineering, California State College at Long Beach, Calif. The paper is based on a thesis submitted by N. CHOU to the Graduate Division, School of Engineering and Science, New York University, in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Materials Science. tributions from defects arising from deviations from stoichiometric composition. The derivation is generalized in the appendix to include intrinsic disorder. The electronic entropy term is also recalculated in the appendix. Of the various semiconducting compounds, the solidus curves of Pbs,' and ~b~e,~ have been most extensively studied. The solidus of PbSe has also been determined, but the temperature of maximum solubility has not been accurately established.5129 The present investigation was undertaken to compare the experimental solid solubility data for these systems with the values predicted theoretically. Since the temperature and composition of the maximum solubility of PbSe has not been accurately determined, experimental emphasis was placed on determining the solidus curves for PbSe in the region of maximum solubility, although experiments were also performed on PbS and PbTe at several temperatures. X-ray diffraction studies were also made on carefully prepared powder samples of PbSe to determine the variation of lattice parameter with composition. EXPERIMENTAL PROCEDURE The procedure of Brebrick and Allgaier was employed for determining the solidus data. Monocrystal-

Jan 1, 1970

By V. P. Petrov, V. S. Znamensky

There are a great number of asbestos deposits in the USSR, and some are quite large. The main deposits of chrysotile asbestos are shown in Fig. 1. The Bazhenovo deposit, which is located in the Sverdlovsk region, is the largest and has been mined since 1889. Systematic studies of asbestos deposits were begun from the very be- ginning of Soviet government and are most often connected with the names K.E. Tarasov, P.M. Tatarinov, B.J. Merenkov, N.D. Sobolev, F.V. Syromjatnikov, V.N. Lodochnikov, V.P. Petrov, V.P. Eremeev, L.A. Sokolova, V.R. Artemov, and V.F. Dybkov. Investigations by these people and others helped the USSR be one of the most important producers of asbestos in the world. In this chapter, the main asbestos deposits of the USSR are explained in a general outline from the point of view of their genesis, common features, and differences that must be taken into account for forecasting, exploration, and the mining of asbestos. All chrysotile asbestos deposits of the USSR were formed from magnesium rock as a result of comparatively low grade temperature, hydrothermal alteration, and free crystallization of fibrous chrysotile in open cavities that served as catalysts. Chrysotile, a widely distributed rock-forming mineral, is not in general an important mineral for industry as it is a long fibrous and main vein variety. However, it must serve for geologists as an important prospecting criteria. And, the geologist should search for the mineral not only in places of possible chrysotile generation, but in places where asbestos may be crystallized in its long fibers. The Soviet geologists distinguish chrysotile asbestos deposits in two groups: (1) ultrabasic rocks and (2) sedimentary dolomite terranes, taking into account how the maternal rock was affected by hydrothermal solutions. The largest deposits are related to ultrabasite. In dolomite, the largest deposits are small and their asbestos contains almost no iron, which makes it a better filler for insulating plastics. There are a few types of asbestos deposits within the limits of the ultrabasic group, the largest being a Bazhenovo type to which the deposits of the Urals are attributed. This Bazhenovo asbestos is characterized by the most complete zonality of disposition for various kinds of asbestization. These types of deposits are, for the most part, the only ones presently working in the USSR. The Bazhenovo deposit is connected to the gabbro-peridotite intrusive belt that is about 180 km long and is broken into a number of fault blocks as shown in Fig. 2. Granitoid veins of intruded rocks are found along the deepest faults, and were sources of hydrothermal solutions that affected the maternal rock. The nearest granitoid vein, ultrabasite, is substituted by listwanite that consists of quartz, talc, carbonate, and some other essentially talcous rock. The next zone of hydrothermal alteration is composed of serpentine. The boundry between serpentinite and unaltered ultrabasite is as irregular, diffuse, and rough as the boundaries between all other zones. Nearer the vein of granitic rock, ultrabasite is entirely serpentinized into massif serpentinization that penetrates through cracks and fissures. There is an unaltered ultrabasite space between fissures, and the biggest block is preserved unaltered in the central part of the massif. The Soviet geologists call this ultrabasic sopka. Preservation of the unchanged blocks is of great importance for deposit formation as volume changes are impossible during the process of asbestization and serpentinization. It may be confidently said that asbestization in Bazhenovo type deposits is possible only when alteration of ultrabasite has not completely occurred. Under conditions of massif volume, a very big mass of substance must be carried out of the ultrabasite for the progressive stage of serpentinization. However, in the regressive stage,

Jan 1, 1986

By F. R. Scauzillo

Equilibrium data which should be useful in the design and/or evaluation of glycol dehydration units were prepared from an analysis of various published data and the correlation of these data by the use of the thermo-dynamic equilibrium ratio. The equilibrium ratios of water are used to solve the glycol absorber problem; such solutions are necessary to define the number of trays and the glycol circulation rate needed to meet drying requirements. Activity coefficients were obtained which relate directly to the equilibrium ratios of water in the water-TEG-natural gas system. These activity coefficients have been used to calculate the equilibrium dew points for aqueous TEG concentrations of 60 to 99.9 weight per cent for the temperature range of 40° to 120° F. They also provide a means of calculating equilibrium ratios for water in the water-TEG-natural gas system; this applies to any desired TEG concentration and to the temperature range from 40° to 120°F. INTRODUCTION During the last several years, the drying of natural gas with aqueous triethylene-glycol (TEG) solutions has become very prominent. Most users of TEG as a drying agent have been satisfied with the performance of TEG solutions at the conditions used; however, there always has been some discussion of the drying ability of TEG solutions at conditions not commonly encountered such as temperatures below 50° or 60°F, but more particularly temperatures above 100°F, and pressures above 1,000 psia. Today, when higher wellhead temperatures such as 120°F are more commonly encountered many are skeptical of TEG's ability to dry sufficiently well to provide dew points around 32°F, which is generally the maximum tolerable when attempting to dry a gas to contract specifications of 7 Ib/MMscf. These views probably have evolved to some extent from the days when suppliers would not guarantee dew-point depressions in excess of 65° to 75 °OF. Also, the feelings about TEG drying may have arisen from the lack of information about the equilibrium relation of water in the drying operations. Porter and Reid' have reported equilibrium data for a 95 per cent TEG solution, while Townsend2 reported equilibrium data for 95, 98 and 100 per cent TEG solutions. Townsend also presented a calculational method which obtains activity coefficients in the liquid phase and, subsequently, the equilibrium water content of a saturated gas over glycol from published3 atmospheric dew points. Wise, Puck and Failey' presented activity data for the water-TEG system at atmospheric pressure. In the past, the equilibrium ratios published for water in a 95 per cent by weight aqueous TEG solution have been used indiscriminately by many for all concentrations of TEG encountered in gas drying operations. Since essentially all such gas operations require the use of more concentrated TEG solutions, a study was undertaken to correlate the existing equilibrium data for aqueous TEG and gas systems and to provide some means of calculating the equilibrium ratio of water in the natural gas-water-TEG system where TEG concentrations were other than 95 per cent. The data presented herein consider only the equilibrium drying ability of the TEG solutions and do not consider the effect of temperature and pressure on the tray eficiency of contactors. In other words, this paper is concerned primarily with the development of the equilibrium relationship between water in the dried natural gas and the water in the lean TEG entering the top tray of the absorber. BASIC EQUILIBRIUM RELATIONS A relationship which relates the K value of water in the natural gas-water-TEG system to the vapor pressure of water at the system temperature, the total pressure of the system and the activities of the liquid and gas phases has been evaluated. It is well known that, for any component of a mixture at equilibrium between a gas phase and a liquid phase,

By P. R. Sahm, T. V. Pruss, D. A. Gandolfo

Cb 3 Sn powders were hot-pressed to estahlish densi-fication conditions and assess the possible use of such compacts in multiphase structures with ceramic or magnetic inclusions. Superconducting transition temperatures, Tc, were measured as a function of powder particle size, pressing temperature, and second-phase admixtures. The highest transition temperatures were found in coarse powder (5 to 500 u) compacts and were only weakly depended on pressing temperatures up to 1200°C. Fine powders (below 5 p), however, both single-phase CbsSn and Cb3 Sn-composites, showed a stronger dependence on hot-pressing temperatures. While Al2 O3 phase admixtures did not affect T, much more, a Pronounced T, degradation was observed upon the addition of ferrimagnetic Fe2 Mno. 5 Zno.5 O4 powders. Likewise, critical current densities, Jc, at 4.2° K were lowered appreciably in the ferrite doped samples, whereas the neutral A1203 inclusiow gave slightly improved Jc values. MULTIPHASE structures in electronically active materials have recently gained in interest as pointed out by Galasso in a review article.' In superconductors the most widely reported group are eutectic alloys which have been mostly investigated with respect to the proximity effect.2"4 In addition, "artificial eu-tectics", for example in the form of mercury-vycor glass sponge5 or fine niobium wires imbedded in a copper matrix,= have been prepared to attain higher critical fields and critical current densities. The idea was to enhance flux pinning phenomena by second-phase inclusions or ho1es. 7 Flux pinning should also be possible by the introduction of insulator inclusions into a superconducting matrix. Ceramic-metal combinations are most easily produced by hot pressing (= pressure sintering), as it permits an almost unlimited selection of material combinations. Cb 3 Sn has been prepared by vapor phase growths or in the form of thin films. Large compacts must be sintered,1° however, and normally present difficulties. At temperatures below 1350°C insufficient densities are obtained and at higher temperatures the loss of tin due to dissociation upsets the stoichiometry. Hot pressing is a natural approach to circumvent the problems, since one can obtain satisfactory densities despite low sintering temperatures. This work was mostly concerned with establishing conditions to hot press Cb3 Sn and Cb3 Sn multiphase structures (= composites), because no data are presently available, and to evaluate these with respect to their transition temperatures. However, a few measurements on critical current densities were also carried out, in particular to assess the value of ferrimagnetic inclusions. I) EXPERIMENTAL PROCEDURE The experimental procedure involved the preparation of feed material and powders, hot pressing, and evaluation of the resulting ingots. As no attempts were made to synthesize Cb3Sn from the elements during hot pressing, feed material had to be produced. For this purpose, a stoichiometric Cb-Sn powder mixture was compacted into a 3-cm-diam ingot (80,000 psi) and then inserted into a quartz tube and evacuated. Rf heating was employed. Above the tin melting point (230°C) liquid tin was forced out of the ingot, but was pulled back by capillary action after approximately 0.5 hr of continuous pumping at 700°C. Thus, it appears that evacuation at this temperature caused desorption of impurity gas creating wetting surfaces which, later on, favored alloying at relatively low temperatures. After a presintering period of 17 hr at 800°C, the quartz tube was tipped off and sealed into another such larger-diameter tube which, in turn, was connected to a pump system. This configuration permitted a temperature treatment at 1400°C, carried out for 65 hr, without collapsing of the glass walls or unfavorable chemical interaction of Cb3Sn with the quartz. The resulting material was

Jan 1, 1969

By John P. Hager, Igor A. Wilkomirsky

The thermodynamic properties of the Pb-Ag system have been determined between 775° and 950°C by the cell: Electrotransport measurements on silica-saturated PbO-SiO2 melts established that the conduction was entirely ionic and that lead is present only in the divalent state. The activities of lead and silver exhibit Positive deviations from ideal behavior. In dilute solutions the activities of lead and silver follow Henry's law. The values obtained for yhb and yig at 1200°K are 1.49 and 1.69, respectively. Determination of a portion of the liquidus curve agrees well with the established phase diagram. provides an accurate means for the thermodynamic study of liquid alloy systems. However, Wagner and wernerl have shown that cells of type I are limited to alloy systems for which the reaction at the alloy-electrolyte interface will be extremely small. The traditional electrolyte for cells of type I has been a low melting point mixture of group IA chlorides, to which a small amount of the compound ACIZa has been added. However, the choice of a chloride electrolyte may not always be practical, in that the Gibbs free energies of formation of the compounds ACIZ, and BCIZb may not be sufficiently different to minimize Reaction [I]. On the other hand, the Gibbs free energies of formation of the oxides of metals A and B may be sufficiently different to minimize Reaction [I]. In this case, the use of molten oxide electrolyte would be clearly advantageous. In the present study, the thermodynamic properties of the Pb-Ag system have been investigated using the cell: Previous galvanic cell studies on the Pb-Ag system2'= are not reliable due to the displacement reaction between the alloys and the chloride electrolyte. Wagner and ~erner,' using Laitinen and Liu's' value at 450°C for the standard electrode potential of Reaction 111, have estimated the percent error in the activity of lead bPb) when using a chloride electrolyte. At 1000°C the error for xpb = 0.10 is 12 pct. Taking the Gibbs free energies of formation for PbClz and Ag cI,' and the equations of Wagner and Werner,' the error in apb at 1000°C and Xpb =0.10 was calculated to be 140 pct. However, using the Gibbs free energies of formation for Pb O' and an estimated value for Ag 20, the error in apb when using a molten oxide electrolyte at 1000°C was estimated to be less than 1 pct for The virtual reaction of cell I1 for the passage of n Faradays of positive electricity from left to right in the cell is: where 5 is the Faraday equivalent (23,063 cal per v equivalent), E is the electromotive force of the cell in volts, and n is the number of Faradays of electricity required for the transfer of 1 g-atom of lead through the cell. The value of n should be equal to 2 since lead is generally divalent in oxide melts. However, the presence of either tetravalent lead ions or electronic conductivity through the molten oxide electrolyte will result in a value of n greater than 2. Bockris, Kitchener, and Davies' have determined the amount of ionic conductance in a liquid PbO-SiO2 mixture (xPbO= 0.50) at 920°C by measurement of the volumes of CO and C& evolved at a carbon anode during electrolysis. From their data a value of 2.13 * 0.16 was calculated for n. Although their measurements indicate the possible presence of multivalent lead ions and/or electronic conductivity, their measurements were not at silica saturation and no definite conclusions can be drawn. However, as a result of the electrotransport measurements described in the next section the ;due of n can be taken as equal to 2.

Jan 1, 1969

By C. S. Smith, Chih-Chung Wang

TURNBULL and his collaborators1,2 have developed the theory of homogeneous nucleation as applied, inter alia, to solidification of liquid metals. Vonnegut³ and Turnbull4 have shown that if a liquid metal is subdivided into small droplets a vast majority of them will undercool very considerably before solidification, generally to as low as about 0.8 of the freezing temperature on the absolute scale. The nuclei effective at small degrees of supercooling in bulk metal seem to be internal or surface heterogeneities, relatively small in number. If the metal is subdivided, those droplets that happen to contain such nuclei will solidify at a temperature not greatly below the true freezing point, but only a small part of the whole volume will be affected and the majority of the drops will under-cool to the much lower temperature at which homo- geneous nucleation occurs as a result of fluctuations. It occurred to one of the authors that an appropriate subdivision to give effective freedom from random nuclei is produced during the solidification of many alloys that contain a minor amount of a phase of low melting point, and that one might then expect marked undercooling of the distributed phase. Experimental: The alloys selected for initial study were copper with minor amounts of lead and bismuth, and aluminum with tin. In all these alloys, the major component freezes at a temperature not much below that of the pure metal, and there is little further change in constitution on cooling until the lower melting point constituent freezes in an almost pure state. Cooling curves were taken using the controlled heat flow method permitting approximate specific heats to be obtained. Chromel-alumel thermocouples were used, with the standard emf tables, since extreme precision was not needed. The crucible (3/4 in. id, 5/16 in. wall) was made of B & W K-20 insulating brick. It held about 10 cc of the alloy being investigated. The cooling rate was 2.5" to 2.9°C per min under a controlled temperature difference of 20°. Approximate specific heats were computed from the inverse rate curves together with data from a blank run and from a standard run with a copper cylinder of known heat capacity. The alloys for investigation were made from high-purity metals (99.99+pct) and cast into graphite molds. The castings were machined to fit the crucible and to provide a hole for the inner thermocouple. Cooling curves were taken after heating to a temperature about 50" above the melting point of the minor, lower melting-point, constituent. Results The lead phase in an alloy of copper with 5 pct lead did not undercool more than 3" below the melting point of lead (327°C) either as cast or after annealing to produce a new dispersion of the liquid phase. A copper-zinc-lead alloy with 23.75 pct zinc and 5 pct lead undercooled more but showed no thermal effect below 319°C. A cast alloy of copper with 5 pct bismuth undercooled to 249°C (M.P. bismuth 27l °C), but once solidification started it was completed at the same temperature. This was anticipated, since the bismuth forms a nearly continuous phase between the grains of copper, and a solid crystal nucleated anywhere would rapidly* con- sume the entire network of liquid, unless the physical continuity of the liquid were broken through volume changes, inadequate fluidity, or gas evolution. Similar arguments apply in the case of copper-lead alloys, where the lead-rich liquid forms a network along grain edges, though not grain faces. In both cases there would be a few isolated particles

Jan 1, 1951

By N. J. Grant, B. C. Giessen, U. Wolff

With the aid of the splat-cooling technique of rapid quenching, metastable alloy phases based on antimony ad bismuth have been prepared. At room temperature, simple cubic phases were found in the Sb + Au, 56 + Yd, and Sb + Ni systems. Another phase was retained in the Au-Bi system at -190°C; in this systent, a microcrystalline phase and a rhombohedrally distorted phase were also observed. The crystal chemistry of these phases is discussed in terms of their valence electron concentration range. A remarkable five-step Phase sequence was found upon heating and equilibration of certain metastable Au-Bi alloys. USING the splat- cooling technique of rapid quenching from the liquid,' a large number of metastable intermediate alloy phases have been prepared in recent years. Thus, Hume-Rothery phases of the hexagonal type based on the valence electron concentration have been produced in systems where they are missing in equilibrium, e.g., Ag-Ge 1 or AU-Sb. 3 In a comprehensive study of metastable alloys based on tin, simple hexagonal metastable y phases were found, raising the total of stable and metastable y phases from 3 to 13. 4 In the In-Bi system, five new metastable intermediate phases were retained.' In most cases, the new metastable phases have some crystal chemical characteristics in common: a) They have rather simple, elementlike structures with few atoms per unit cell, e.g., y phase,4'5 or the metastable primitive cubic phases in the Ag-Te and and Au-Te systems.= b) Their structures are often related to those of the terminal phases, or to elements that are straddled in their position in the periodic table by the constituent elements; this is the case for metastable ß (In-Bi) with the structure of white ß Sn,' or metastable a (Cd-sn). 4 c) They seem to represent the crystal structures appropriate to certain average group number (AGN) ranges in which no or few single-phase structures exist in equilibrium. These average group number ranges can probably be equated in the case of many elements of the Ba(Zn)-Bs(As) groups with the averaged valence electron concentration. In the present work, the splat-cooling technique has been applied to the alloys of antimony and bismuth. In equilibrium, neither element forms intermediate alloy phases with other B elements from groups Bl(Cu) to B4(Si) that contain more than 66.7 at. pct of Sb or Bi, respectively, e.g., AUSb 2. 7 Thus, antimony- or bismuth-rich phases, which might be closely related to antimony or bismuth, and which would reflect struc- tural changes occurring on alloying with small amounts of addition elements, do not exist. Also, the terminal solubility of antimony and bismuth for all B metals is very small. It was therefore of interest to investigate the influence of enforced, nonequilibrium solid solution of addition elements in antimony and bismuth on their crystal structures. It was found that additions of group B 2-B4 metals act distinctly differently than additions of group T 10 and B1 metals. The latter set of additives will be treated here. EXPERIMENTAL TECHNIQUES Alloy preparation and splat-quenching followed closely the procedures described in Refs. 1, 4, and 5; they consisted of the preparation of master alloys from high-purity starting materials (99.99+ pct) and blast-atomizing of 20-mg quantities onto copper sheets. The resulting approximately 1 to 5 u thick foils were investigated by X-ray diffraction. The cooling rates obtained are of the order of 107 to 10 8 C per set,'" causing solidification to proceed at a rat; of approximately 100 cm per sec.' Powder patterns of the resulting fine-crystalline materials were taken with filtered CuK, radiation. For antimony alloys the substrates were held at room temperature and for bismuth alloys at -190°C both during splat foil deposition and X-ray investigation. Annealing treatments at several

Jan 1, 1969

By W. G. Pfann

Under certain conditions, a molten zone can be made to move through a solid by impressing a stationary temperature gradient across the solid. This phenomenon can be utilized in fabricating semiconductive devices, growing single crystals, joining, boring fine holes in solids, measuring diffusivities in liquids, small scale alloying, and purification. Fundamentals and exemplary applications are outlined. ANEW aspect of the travel of a molten zone through a solid is considered in this paper. Whereas, in previously described zone melting techniques,'-' zones were usually caused to move by changing the position or temperature of a heat source, in the present technique a zone is made to move by impressing a temperature gradient across it. For example, a thin layer of molten A1-Si alloy, sandwiched between two silicon slabs having a temperature gradient normal to the layer, will travel through the hotter slab. One feature of temperature gradient zone melting, as this technique will be called here, is that zones of unusually small dimensions can be maintained. This leads to such diverse uses as have been listed in the abstract. In this paper fundamentals of the movement of a molten zone in a temperature gradient, and some practical applications thereof, are outlined. Assumptions The movement of a molten zone through a solid body of solvent substance in which a temperature gradient exists will be discussed. The length of the zone will be its dimension in the direction of motion. The direction of the temperature gradient will be toward the region of higher temperature. To be considered is a binary or higher order solute-solvent system in which the concentration of solute in the molten zone is sufficient to produce a lowering of the freezing temperature of the solvent which is at least of the order of the temperature range impressed on the charge. While we discuss primarily molten zones in a solid matrix, the principles are applicable to solid or vaporous zones in a solid matrix, a requirement being that the diffusivity in the zone be substantially greater than in the matrix. Diffusion of solute into the surrounding solid will be assumed negligible. In general, its presence will not basically alter the conclusions to be drawn. For illustration, a system represented by the partial constitutional diagram of Fig. la will be discussed, in which k, the distribution coefficient defined in the figure, is constant and less than unity. However, the technique is applicable to any solute- solvent system in which one component lowers the melting point of another component. Movement of a Molten Zone in a Temperature Gradient Consider, in the system AB of Fig. 1, where B is designated the solute and A the solvent, the effect of sandwiching a thin layer of solid B between blocks of solid A and placing the whole in a temperature gradient such that the temperature of the layer is above the lowest melting temperature of the system. Surrounded by an excess of A, the layer will dissolve A, becoming molten, and expand in length." As so- lution of A continues, at both interfaces, the mean solute concentration in the zone will move to the right in Fig. la, until at temperature T, the liquid at the cooler interface reaches the liquidus concentration C,. Solution of A thereupon ceases because the liquid T1 is saturated with A. The liquid at the hotter end of the zone, being at temperature T2, is not saturated with A at concentration C1. Hence solution of A continues there and concentration C2 is approached. A concentration gradient therefore is set up in the zone, causing A to diffuse toward the cool end and B toward the hot end. As a result, the liquid at the cool interface becomes supersaturated and a layer of crystalline A containing concentration kc, of B in solid solution freezes. Since a source of A

Jan 1, 1956

By P. E. Arnold, G. S. Ansell

RELAXATION in metals has been studied in detail by many workers in recent years.1-5 These studies have shown that there is an energy-loss peak observed in a metal placed in mechanical resonance at low frequencies which may be correlated with various metallurgical processes. These experiments have been largely used to study single-phase materials. In order to study the effect of a finely dispersed second phase in a metal matrix upon this phenomenon, the relaxation behavior of an aluminum-aluminum oxide SAP-Type alloy in both the fine-grained as-extruded and coarse-grained recrystallized conditions was investigated by the use of internal-friction measurements. The alloys studied, designated MD 2100, consist of a matrix of commercial-purity aluminum containing a finely dispersed second phase of aluminum oxide. The aluminum oxide is present in this alloy in the form of fine platelets approximately 130A units thick and several microns on edge. The mean free path betwen dispersed platelets is approximately 0.5 p. The grain size of this alloy is extremely stable at temperatures as high as the melting temperature of the aluminum matrix. In the as-extruded condition the grain diameter is several microns, while in the recrystallized condition it is several millimeters in diameter. The damping characteristics of the alloy samples were determined using a torsional-pendulum device. The internal-friction constant was determined for this alloy in both the fine-grained as-extruded and coarse-grained recrystallized conditions over the temperature range from 343" to 923°K at frequencies of 0.9, 1.3, and 1.8 cycles per sec. An internal-friction peak was observed in testing the fine-grained alloys which was not observed for the coarse-grained alloys. This peak, which might be associated with a type of grain-boundary relaxation, was observed at each of the three different test frequencies for the fine-grained sample. The temperature at which the relaxation peak occurred for each of the three different frequencies is shown in Table I. From these data an activation energy of relaxation for each pair of frequencies was determined by comparing the temperature shift of the relaxation peak with frequency between each of the test frequencies, assuming that an Arrhenius-type rate equation is applicable. The activation energy of relaxation determined from these data is also shown in Table I. The mean value of the activation energy was about 6 kcal per mole. The activation energy for the relaxation process determined in this investigation indicates that the relaxation associated with the grain boundaries in this aluminum-aluminum oxide SAP-Type alloy is quite a different process than grain boundary relaxation in single-phase aluminum alloys. In these latter alloys, the activation energy for relaxation has been found to be the activation energy for self-diffusion, approximately 36 kcal per mole1,2 Where the activation energy is the same as the activation energy for self diffusion, it has been proposed that the relaxation phenomena is dependent upon vacancy formation and motion. It is apparent therefore, that, in this aluminum-aluminum oxide SAP-Type alloy, the relaxation must be due to another type of atom transport. It has been shown previously in studies of the high-temperature, low-stress, steady-state creep behavior of as-extruded aluminum SAP-Type alloys, that the activation energy for steady-state creep is one that may be characterized by the nucleation of dislocations from the grain boundaries. It is proposed that the relaxation behavior observed here is due to a similar effect. In this case, the internal-friction peak is a resonance behavior due to the time-dependent nucleation of dislocations from grain boundaries in the sample. A process of this type would have an activation energy which is undoubtedly stress-dependent and of the form Q = Q, + (dQ/du)u

Jan 1, 1962

By Leonard R. Weisberg

The general properties of diffusion in GaAs are reviewed. A total of .fourteen atoms have been studied to date, and activation energies for eleven reported are (in ev): Ga (5.6), As (lo), Zn (2.49), Cd (2.43), Sn (2.5). Mn (2.75). S (4.0). Se (4.2). Ag (0.33), Cu (0.52). and Li (1.0). The dijfusion of the first eight atoms, as measured by Goldstein using radiotracer techniques, established the principle of sub lattice diffusion for both host and impurity atoms, since atoms substituting for gallium have lower activation energies than those substituting for arsenic. The diffusion constant of interstitial copper has been determined for the first time by Hall and Racette using heavily doped p-type samples in which interstitial copper predominates. The anomalous behavior of zinc, which has an abrupt diffusion front and a strong dependence on zinc concentration, has recently been quantitatively explained in terms of an interstitial-substi-tutional equilibrium-diffusion mechanism. Lithium and silver diffuse mainly interstitially, while the diffusion of phosphorus is complicated by the continual formation ofGap. Junction-migration measurements indicate diiferent results than radiotracer techniques, and this is one problem that still remains, together with discrepancies in cadmium-diffusion results, and an unexplained dependence of impurity diffusion on arsenic pressure. BESIDES the usual insights into the behavior of atoms in solids, studies of diffusion in semiconductors have additional importance for device applications. In fact, the amount of diffusion studies performed on a semiconductor might serve as a simple barometer of its technological importance. Thus, the information accumulated for GaAs is not yet quite comparable to that for germanium or silicon, but considerable knowledge is available. The diffusion of at least fourteen atoms has been investigated for GaAs, and the diffusion constants have been determined for eleven of these. Interesting results were found for GaAs that elucidated problems not previously solved for germanium or silicon. For example, the interstitial-diffusion constant for the very fast diffusant, copper, was first measured in GaAs. Also, solutions for interstitial-substitu-tional equilibrium diffusion in extrinsic material were provided first for GaAs, although they are ap- plicable to germanium, silicon, and other semiconductors. Studies in GaAs firmly established the concept of sublattice diffusion, which should have application in many different compound systems. The purpose of this paper is to review briefly the general state of knowledge concerning diffusion in GaAs. First some general aspects of diffusion will be covered, and next attention will be given to the results mentioned above. Diffusion in GaAs has been measured both by radiotracer and junction-penetration techniques, and some discussion will be given of differences in the two sets of results. The comprehensive work of oldsteinl-' has served as the primary reference for the diffusion of well-behaved substitutional atoms in GaAs. Since a review has recently been presented of many of these reults, details of the diffusion data will not be repeated. Neither will any discussion be given of the experimental techniques of diffusion measurements, except to note here, in passing, the simplicity and effectiveness of the precision lapping device employed by Goldstein.' I) EXPERIMENTAL RESULTS AND DISCUSSION A) Summary of Experimental Results. Diffusion constants D = Do exp(E/kT) have been determined for eleven atoms in GaAs: a,' AS,' n,'" Cd,'" n,' n,8 s, e,' Ag,O CU," and i." These results are summarized in Table I. In addition, diffusion was investigated for phosphorus,4'12 germanium,I3 and ilicon,' but Do and E were not determined. Radiotracer techniques were used for most of the studies except for lithium, where a combination of chemical and electrical techniques was employed, and germanium and silicon, where junction-migration techniques were applied. The diffusion of zinc, manganese, sulfur, and tin was also measured using junction migration.13'14 Goldstein demon-

Jan 1, 1964

By C. S. Matthews, P. Hazebroek, F. Brons

A method has been developed for calculating the average pressure in a bounded reservoir. The reservoir is first divided into the individual drainage volumes of each well, by using the criterion that at steady state each individual drainage volume is proportional to a well's production rate. The average pressure in each drainage volume is then calculated by a method developed in the report. By volumetrically averaging these individual drainage volume pressures, the average pressure in the entire reservoir is obtained. To calculate the average pressure in each drainage volume, a correction is applied to the ordinary extrapolated pressure, i.e., the pressure obtained by extrapolating to infinite time the linear portion of the graph of closed-in pressure versus log[?t/(t + ?t)], where At is the closed-in time and t the production time. The correction, which is a function of the production time, is presented in graphical form for different shapes of the drainage area (horizontal cross section of the drainage volume). INTRODUCTION It is important to be able to find the volumetric average pressure in a reservoir so that the size of the reservoir may be determined from material balance calculations. It is also desirable to be able to find the approximate distribution of pressure within a reservoir for detection of fluid movement. 'The purpose of this paper is to present a method for calculating both the average reservoir pressure and the approximate distribution of pressure within a bounded reservoir — that is, a reservoir with no water drive. In reservoirs where the pressure builds up rapidly after wells are shut in, the determination of average pressure generally poses little problem, for one often need only average the final buildup pressures. It is when pressure buildup is slow that difficulties arise. For practical and economical reasons, the time allowable for closing in wells is limited. If at the maximum allowable closed-in time the pressure has not reached a con- stant value (and this is more often the case than is generally realized), calculation of average pressure presents difficulties. One method which has been used in the past for obtaining an "average" pressure involves the extrapolation to infinite closed-in time of curves of pressure as a function of closed-in time. Contour maps of these extrapolated pressures are used in arriving at an average pressure. In some cases wells are shut in for arbitrary Lengths of time, and contours of these arbitrary shut-in pressures are used for calculation. All these methods are somewhat arbitrary and suffer from lack of fundamental theoretical basis. For example, no precise meaning can be given either to the extrapolated or to the arbitrary shut-in pressure. Furthermore, there seems to be no reason why either set of pressures should be contourable. It was because of the vagueness of these old methods and their lack of a sound theoretical basis that, the present method for determining average reservoir pressure was developed. SYMBOLS A = drainage area of a well, cm' A, = drainage area of well j, cm2 A , = total drainage area of all wells in a reservoir, cm2 c = coefficient of compressibility of fluid at reservoir temperature, atm-1 f = hydrocarbin-filled porosity, fraction h = net thickness of formation, cm k = permeability of formation, darcy p = pressure at a well, atm p0 = initial reservoir pressure, atm p* = pressure obtained by straight-line extrapolation of linear portion of plot of p versus log [At/(t+ At)] p = volumetric average pressure inside drainage volume of a well q = volume flow rate at a well, cc/sec a: prevailing reservoir conditions q, = total volumetric flow rate from a reservoir, cc/sec at prevailing reservoir conditions rw = radius of well bore, cm T = kt/fµcA t = corrected time of production of a well, seconds, defined by

Jan 1, 1955

By J. N. Ong

The oxidation of tantalum is assumed to occur by four simultaneous first-order chain reactions; solution of oxygen in the metal, nucleation and growth of a suboxide phase at the metal surface and two phase boundary processes which give rise to two different modifications of Ta2O5. A rate equation is then formulated which accounts for all principal details of oxidation behavior, unifies and correlatss the results of the principal investigations, and expresses the rate as a function of pressure, temperature, and time. For purposes of practical application, the expressions: may be used below and above 700T respectively to determine the regression rate of tantalum in cm per hr, where T is to be expressed in "K and P in atmospheres pressure of oxygm. The equations will reproduce within a factor of two all reported experimental rates in the temperature range 475" to 1400°C and pressure range 0.000026 to 40.8 atm 0. 1 HE oxidation kinetics of tantalum have been investigated thoroughly in the temperature range 50" to 1400 and pressure range 1.32 x l0-' to 40.8 atm pressure of 0,and as a result, the principal features of the oxidation of tantalum are known and have been described in considerable detail. The exposition of the characteristics of the behavior of tantalum in oxygen has been largely descriptive, with considerable attention being devoted to elucidating the structure, composition, and morphology of the resulting oxide products. The weight change vs time results have usually been reported graphically. With the exception of the linear rate below 700 C and the process of diffusion of interstitial oxygen into the metal,6'9 no effort has been made to characterize the reaction rates in functional form. It is the purpose of this paper to demonstrate that when the fundamental principles of chemical kinetics are rigorously followed, the results of the principal investigations will be correlated and unified and the oxidation rale may be expressed as an analytic function of pressure, temperature, and time. In addition to accounting for the temperature and pressure dependency of the oxidation rate, the following minor features will be accounted for as a result of the basic analysis: the initial period of nonline-arity in rate at low temperatures, which decreases with increasing temperature;3'5'7 the rate vs temperature cusps obtained at constant pressure"5 the concentration gradient of oxygen interstitially dissolved in the metal.5'7 The analysis will also be consistent with the overall chemistry of reaction and with all visual, microscopic, and X-ray observations. DEVELOPMENT OF RATE EQUATION As a fundamental basis for the treatment of metal-oxygen reaction kinetics, it will be regarded that the rate of reaction is determined by the concentration and not the activity or chemical potential. It is further assumed that all metal-oxygen reactions are first order complex chain reactions" whose rate is dependent on the concentration of an intermediate species which is a complex function of the oxygen concentration, or oxygen pressure, only. The basic rate equation is therefore: is the weight of oxygen consumed by the reaction, A is that portion of the area of the metal over which the reaction is occurring (cm2), t the time (sec), kf the rate constant for forward reaction, C the intermediate species concentration and f '([Oz]) and f (Po,) are complex functions of oxygen concentration and Oxygen pressure respectively. Reverse reactions may usually be neglected in metal-oxygen systems since a large negative free energy generally accompanies these reactions. Eq. [I] takes different forms when the rate of reaction is controlled by diffusion into or through a phase or at a phase boundary. For diffusion into the metal phase, the rate is given by1' Di is the diffusion coefficient of species diffusing into the metal phase (cm2/sec), and Q is the corre-

Jan 1, 1962

By W. E. Heinrichs, R. W. Davis

Introduction Cross borehole seismic tomography (CBST) is a geophysical technique that allows definition of the distribution of some physical rock property between two boreholes. The method is similar to the computer-assisted tomography (CAT) scans used by the medical industry. This paper describes the method, its applications and the developing trends in its use that interest the mining industry. The idea of using tomography in connection with geophysical methods for measuring rock properties between boreholes has been around for three or four decades. Until the advent of high-speed, large-capacity computers, the necessary calculations were too formidable for production use. Another factor in the development of the technique has been the refinement of a mathematical base to meet the needs of the medical industry. The geophysical applications have benefited from this refinement. An extensive discussion of the basic theory is given in Kak and Slaney (1988). CBST, although widely researched and written about, is still not extensively put to use in mining and engineering projects. Most real world examples in the literature have come from research carried out by government laboratories or by large companies. An exception is the regular use by Prospection Geophysique Francaise (Cottin et al., 1986) in damsite investigations. The Japanese appear to be doing extensive research and testing of CBST's uses in civil engineering projects (Saito et al., 1988). Canada is researching the use of the method in connection with nuclear waste site investigations (Wong et al., 1987). Finland has tested the method in connection with a foundation investigation for a nuclear power plant (Cosma et al., 1984). In the US, the US Bureau of Mines has taken an interest in using CBST as a means to enhance in situ mining operations (Tweeton, 1988). Major oil companies are examining the method as a tool in oil field development (Justice et al., 1989). Description of the method CBST involves placing a series of receivers down one borehole and recording transmissions from an energy source placed successively at a series of positions in another hole. The objective is to generate a dense network of seismic raypaths between the holes. The denser the network of raypaths, the better the features between the boreholes are resolved. Either seismic travel times or sine wave amplitudes are measured by the receivers. Analysis of travel times between boreholes develops a picture of rock velocities between the holes. Analysis of seismic wave amplitudes develops a picture of the distribution of energy transmission characteristics between the holes. These seismic properties can be used to define occurrences of fracture zones, lenticular sequences or other important geologic data not apparent from examination of the borehole logs. When longitudinal (compressional) and transverse (shear) waves are analyzed, the physical properties, such as elastic moduli, can also be mapped. When wave amplitudes are measured, rather extensive corrections to the data are necessary. There is some disagreement among researchers as to the feasibility of making some of the corrections. For this reason, this paper will concentrate primarily on travel time analysis. Wave amplitude analysis will be mentioned occasionally only in passing. This does not mean that amplitude analysis does not provide important data on rock parameters, only that for the present there are limitations on its uses. Vertical seismic profiling (VSP), extensively used in recent years in oil exploration, is similar to CBST. Instead of using two boreholes, however, the VSP method uses an array of seismic sources or detectors down one hole and an array of detectors or sources along the surface radiating outward from the hole. While adequate for determining vertical velocity distributions, the VSP method is not, by itself, suitable for most engineering or mining projects. Computer programs used to analyze the field data make use of the fact that the total travel time or change in signal amplitude between boreholes is described by Dines and Lytle (1979) as: [9k = f Rk f( x,Y) ds (1)] where gk = the total time or attenuation along the kth ray path,

Jan 1, 1992

By J. C. Fisher

Nucleation theory is applied to martensite nucleation in substitutional iron alloys. Composition fluctuations are neglected, and a steady rate of nucleation is predicted for any composition and temperature. The maximum rate of nucleation (as a function of temperature) is shown to be measurable only for on extremely narrow composition range, being too great or too small outside this range. A number of experimental observations, including completely isothermal transformation in some alloys and composition-dependence of M. temperature in others, are compared with the calculated behavior. IN a previous report,¹ nucleation theory was applied to the formation of isothermal martensite in an Fe-Ni-Mn alloy. The experimental observations of Cech and Hollomon² were accounted for quantitatively. It now is of interest to examine the predictions of nucleation theory with respect to martensite transformation in substitutional iron alloys of other compositions. Since Fe-Ni alloys have received considerable attention, both as to their transformation kinetics and their free energies, they will be treated in detail, although the results apply with equal validity to other substitutional alloys. In substitutional alloys, where composition fluctuations can be neglected in volumes of critical nuclear size, the rate of nucleation of martensite in subcooled austenite is¹ n - Nv exp (—W*/kT) [I] where the free energy of formation of the critical size nucleus is W* = 8192 p (?² s³) [2] In the expressions for n and W*, the symbols have the following meanings: N is the number of atoms per unit volume; v, the atomic vibration frequency; 8, a function of the elastic constants of austenite and the shear angle of martensite; , the austenite/mar-tensite inter facial free energy; and ?fc is the free energy change per unit volume accompanying the transformation. Jones and Pumphrey² have determined the austenite to martensite free energy change as a function of nickel content and temperature for Fe-Ni alloys. Their expression is ?F = 2500 C + 1.25 (1 —C)?FFc cal per mol [3] where C is the atom fraction of nickel, and ?Ffe is the free energy change per unit volume for pure iron as tabulated by Zener4 (or, equivalently, Fisher"). From Eqs. 1 to 3, it is possible to calculate isothermal nucleation rates as a function of temperature and composition for Fe-Ni alloys. The only unknown parameter is (?² s³). The best value of this parameter for Fe-Ni alloys, determined from M. temperatures in a manner to be described shortly, is (?² s³)= 9.92 (10)21 cgs units [4] Taking this value of (?² s³), C-curves for isothermal nucleation were calculated for Fe-Ni alloys of several compositions, and are plotted in Fig. 1. It is evident from Fig. 1 that completely isothermal nucleation of martensite in Fe-Ni alloys can be observed experimentally for only a very narrow range of compositions. Cech and Hollomon find that a nucleation rate of about 10' nuclei per cc per sec is as fast as they can follow dilatometrically, and a rate of about 10-1 nucleus per cc per sec is about the slowest that can be measured conveniently. If the nucleation rate is to lie between the limits 10-1 10 the nickel content of an Fe-Ni alloy must fall in the atomic fraction range 0.299 5 C 5 0.302. Nickel contents lower than 0.299 correspond to nucleation rates too great to follow, and those higher than 0.302 to nucleation rates too slow to measure in a reasonable time.* In view of the narrow corn- position range in which successful isothermal measurements can be made, it is not surprising that only one substitutional alloy has been described' that comes close to being in the proper range.

Jan 1, 1954

By B. H. Bergstrom, J. J. Gilvarry

Previously the authors showed that the Gilvarry equation correctly describes the distribution of fragment size in single fracture, provided the exoclastic particles showing original surface of the specimen are removed from the distribution. In the present work this conclusion has been strengthened in two respects. First, it has been shown that the existence of two peaks in the differential distribution for the endoclastic particles, corresponding to the effect of surface and volume flaws in the interior of the specimen, can be demonstrated from the average of data for a large number of specimens. Second, it has been shown by means of a Coulter counter that data obtained from specimens fractured in gelatin display the behavior at fragment sizes approaching 1 p which is demanded by the limiting form of the Gilvarry equation in this case. In previous work, a rigorous derivation of the proper distribution function for fragment size in single fracture of a brittle solid has been given by Gilvarry,' based on a closely defined physical model and deduced strictly by the laws of probability. Experimental work has been reported by Gilvarry and Berg-str~m,~ confirming the theory in its broad outlines. Subsequently, Gilvarry and Bergstrom extended the theoretical discussion to include comminution and presented experimental data bearing on this point. They have described further experimental results for the case of single fracture recently. The experimental evidence regarding single fracture was rather convincing. However, it was based on only five specimens for which fragment sizes were determined by sieve analyses and three for which measurements in the finer sizes were made on a Coulter counter. The purpose of the present paper is to extend the experimental results as obtained by means of both sieve analyses and the Coulter technique. In the former case, sufficient specimens are included so that the average data should vield ac- curately the detailed behavior of the distribution function for the coarser fragment sizes. In the latter case, measurements for the finer sizes are reported which correspond to single fracture more closely than prior results and fill a lacuna left in the experimental verification. In addition, an extension of the theory given recently bGilvarry for the case of fracture of a two-dimensional solid will be outlined, and experimental results obtained by him will be discussed.6 THREE-DIMENSIONAL CASE Gilvarry' has shown that the Schuhmann size modulus is a measure, in a sense specified later, of the number of activated edge flaws in a specimen undergoing single fracture. Single fracture is defined as that resulting from a single instantaneous application of energy, such as the blow of a hammer whose motion is halted when fracture begins. Plural fracture consists of a short sequence of single fractures, as in a jaw or gyratory crusher; multiple fracture obtains when many applications of energy are made, as in a ball mill. The Griffith flaws associated with fracture of a specimen are flaws occurring within the volume of the body, on the new surfaces created within its interior and on the new edges (intersections of two surfaces) within the body. Fracture proceeds by activation of flaws in the volume of the specimen, in the fracture surfaces throughout its interior, and in the edges produced by intersection of fracture surfaces. If all the flaws and all groups of flaws are distributed at random, independently of other flaws or groups thereof, it has been shown by Gilvarry that the distribution function for fragment size has the form of a Poisson distribution. The fraction y, by weight or volume, passing a sieve of mesh size x is given by where k is an average spacing of activated edge flaws, j2 is an average amount of surface containing one activated surface flaw and i3 is an average volume corresponding to an activated volume flaw. The averages in question are referred to the mean dimension x of a fragment. On the basis of the theoretical

Jan 1, 1962

By P. G. Carpenter, R. G. Nisle, F. W. Bubb

It is the purpose of this paper to describe an electrical computer which has been constructed to solve the equations for vapor-liquid equilibrium in multi-component systems. The instrument consists of seven component-computing units each with proper indicating means and power supplies. Each unit is a resistance network with a voltage matching servomechanism, and each provides an output voltage proportional to the mol-fractions for vapor and liquid phases. These voltages are summed and matched with a reference voltage to provide the solutions. Any reasonable number of such units may be put together to make a computer. The theory and operation of the computer is discussed. A number of applications and examples of computer results are given. The computer yields the over-all vapor or liquid fraction to a probable error of 0.002. An interpolation method is described which reduces the probable error to 0.0002. INTRODUCTION The process known as Flash Vaporization may be described as follows: A mixture of known composition of relatively volatile components is allowed to come to thermodynamic equilibrium at some given temperature and pressure by any path whatsoever. In general, a vapor and a liquid phase will be present at equilbrium. The problem is to determine the fractions of the mixture in the vapor and liquid phases, and to determine the mol fractions of the various components in each phase. The relations that exist between these various quantities at equilibrium are well known and will be given later. These equations are difficult to solve, yielding only to trial-and-error methods. The virtues of the analog computer are its speed and the automatic character of its calculations. The device is operated by turning a crank which varies the value of v, the total vapor fraction. This actuates a number of servomechanisms which perform automatically all computations. This computer facilitates the solution of such problems as (to mention a few] : Analysis of separator operation, studies of changes in composition of reservoir fluids with pressure decline, and analysis of natural gasoline plant operation. Examples of some of these problems are given in detail later. STATEMENT OF THE PROBLEM The essential equations are xm = 1+(km-l)v . . (1) Kmzm ym =------------------------. . (2) 1 + (Km-l)v ; n n S S xm= --------------------=1 1 + (Km-l)v m = 1 m=1 ......(3) n n S = S Km Zm =1 S ym 1 + (Km-1)v m=1 m = l ......(4) where ym = Vm/V = Mol fraction of m-th component in vapor phase. xm = Lm/L = Mol fraction of m-th component in liquid phase. Zm = Fm/F = Mol fraction of m-th component in mixture. KM = ym/xm = Equilibrium constant for m-th component at the given temperature and pressure. v = V/F = Mol fraction of vapor in the mixture. F = Total mols of a mixture of n components. V - Total mols of vapor in the mixture. L = Total mols of liquid in the mixture. Fm = Total mols of m-th component. Lm = Mols of m-th component in liquid phase. Vm = Mols of m-th component in vapor phase. Assuming the total mols of the mixture F and its composition (all the Fm) to be known — either from a quantitative analysis or from the amounts put together to make the mixture — the zm = Fm/F may be regarded as known quantities. From the given temperature and pressure of the mixture the K., are known (principally from experimental data). The primary problem is then: having given all the zm and Km to calculate v and all the fractions xm and ym. Having calculated these ratios, it is a simple matter to calculate V. L. Vm, Lm from their defining equations. SOLUTION OF THE PROBLEM Basic Computer Unit The computer consists of n units, each of which provides voltages xEo and YE, proportional to x and y as in

Jan 1, 1950