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By J. Paces, E. Miller, K. L. Komarek

The resistivity was determined as a function of temperature over the composition range from pure cadmium to 40 at. pct Cd. Melts with cadmium contents less than 85 at. pct had negative temperature coefficients of resistinity. On cooling below a transition temperature close to the liquidus temperature, the slope of the resistivity-temperature curve changed sharply. The activation energy calculated from the slope was 0.07 ev above the transition temperature and 0.14 ev below. The resistivity vs composition curve shows two maxima corresponding in composition approximately to CdSb and Cd3Sb2. THE relationship between the structure of a liquid and that of the crystal formed on solidification is at present not well-under stood. Various experimental determinations of the properties of liquids indicate that deviations from random atomic arrangements in liquids occur and that the properties of a solid and of its melt are closely related. Thermody-namic activities of liquids usually show negative deviations in systems where compound formation occurs in the solid,' and X-ray data indicate that close-packed solids and their melts frequently have nearly the same coordination number. Electrical resistivities and viscosities of liquids frequently exhibit maxima at compositions corresponding to compounds in the solid state. It should be of interest to study systems which have both stable and metastable compounds in the solid, and to determine if the short-range order in the liquid is affected by the existence of the metastable solid phase. The Cd-Sb system exhibits such a metastable phase. The phase diagram is shown in Fig. 1.3 The stable system has one intermetallic compound, CdSb, crystallizing in the orthorhombic crystal structure, with a melting point of 456°C. The metastable system also has one compound, Cd3Sb2, melting at 420°C and crystallizing in the monoclinic structure. Metastable alloys transform to the stable crystal structure in the temperature range from 250o to 350°C. Several distinct indications of very strong short-range order in the liquid phase have been reported in this system, with a close relation between the ordering in the liquid and the existence of both the stable and metastable solid phases. Scheil and Baach4 have observed distinctly different vapor pressures for liquid Cd-Sb alloys depending on whether the liquid solidified to the metastable- or stable-phase configuration. They observed an unusually sharp increase of the activity in a limited temperature interval immediately above the liquidus temperature of stable alloys, followed by a sudden decrease in slope to what they considered normal values. On cooling, the activity data reproduced the values in the normal range but then deviated from the values obtained on heating. They also observed that specimens of the stable phase upon melting and resolidifying always crystallized in the stable crystal structure as long as the melt was not heated to more than 485° to 525°C; otherwise solidification to the metastable phase occurred. However, in a later investigation, these results were not reproduced (13). The resistivity of liquid Cd-Sb alloys has been investigated by Matuyama 5, Oleari and Fioram, 8 and Belaschenko (141, but only above 500°C, the temperature region where Scheil and Baach observed no vapor-pressure anomalies. The data of Matuyama and of Oleari and Fiorani are reproduced in Fig. 5 and show a maximum in resistivity at 50 at. pct Cd. The data of Oleari and Fiorani, however, show the maximum as being rounded, and their values in general are slightly higher than those of Matuyama.

Jan 1, 1964

By O. C. Holbrook, George G. Bernard

A new theoretical treatment has been obtained for the behavior of pattern waterflood injection wells when closed in. Two cases are treated: Case I where oil and water are assumed to have the same properties, and Case 2 where they arc different. In applying the method, one plots log (p — p,) vs closed-in time, where p is well-bore pressure at any tims and p, is static pressure. The value of p. is determined by trial and error as that value which makes the plot linear at large time. A value for the permeability-thickness product can be determined from the intercept of this linear part, and a value of the skin factor from the injection pressure at time of closing in. Application of the method to data from water floods at three fields seems to give reasonable results. For the case of unit mobility ratio, it is proved that this new method should give the same value for permeability-thickness product as the conventional pressure build-up method. In addition, the new method gives correct values for static pressure, whereas the conventional method does not, often indicating negative static pressures. The new method may be used in cases where the surface pressure persists after closing in as well as in cases where it does not. INTRODUCTION It is of considerable interest and importance to be able to determine the characteristics of the reservoir in an area surrounding a water injection well. Thus, if we can determine early in the life of an injection well that there is a considerable "skin effect", remedial measures can be started before a full-scale pattern flood begins. Similarly, if it can be shown that a gradual buildup of skin effect is occurring with time, measures to free the water of plugging material can be taken. Determination of static pressure in the water-injection well may show that the water is entering a thief zone and not the desired reservoir. Finally, determination of the permeability of the sand around the injection well will allow estimation of the future relation between injection pressure and rate. It should be possible to determine average reservoir permeability, skin effect and static pressure from pressure fall-off data. However, at the time we began work on this subject, it was thought that no adequate theory on which to base such determinations' was available. According to the conventional method which considers the reservoir to be filled with one fluid of small compressibility (see Van Everdingen, Joers2, and Nowak2), shut-in pressure is plotted vs log where is injection time, and At is closed-in time. The physical significance of injection time, may well be questioned in this case, since in a reservoir completely filled with a single fluid (as required by this theory) and with input and output rates equal, the pressure behavior after an initial transient is independent of t,. Attempts by our Tulsa area to use this theory led to negative values of static pressure in most cases. Because of these limitations of the method discussed above, it was decided to attempt to develop a new theory of pressure behavior in water injection wells, one which would apply when there is a gas saturation, as is so often the case in water floods. In the following treatment the assumptions and basic equations are given first, then the method of application of the equations. A complete example is given to clarify details of application. All difficult mathematics has been placed in the appendices so that the reader can follow the text without difficulty. However, if he wishes only to apply the results without knowing the basis for them, he can learn how to do this from reading only the sections entitled "Plotting of Experimental Results" and "Example." ASSUMPTIONS AND BASIC EQUATIONS Statement of Problem It will be assumed that a horizontal layer of constant thickness contains in its pore system a mixture of oil, gas and water. While water is being injected into this pore- system through a well at constant rate, an oil bank is built up, gas being expelled from the space taken by the oil as shown in Fig. 1. The saturations within each

By E. A. Gulbransen, A. Pebler

Pressure-composition isotherms have been determinedfor the systems ZrMo2 -H2 between 0" and 900°C at hydrogen pressures between 10-4 and 760 Torr. Tkese studies plus X-ray diffraction analyses of selected compositions show that these intermetallic compounds form a complete series of hydrogen solid solutions within this temperature and pressure range. The partial molar enthalpies and entropies of solution of hydrogen in the three intermetallic compounds were calculated. The solubility of hydrogen in these Laves phases can be related to their free electron concentration. ThE reaction of hydrogen with inter metallic compounds of zirconium with Laves phase-type structure has both theoretical and practical interest. The in-termetallic compounds have structures different from any of the pure metals. In addition the electron to atom ratio of the intermetallics varies appreciably. In the nuclear materials field, these materials are of interest since intermetallic compounds may exist as precipitates in commercial zirconium alloys with transition metals. From studies on the hydrogen reaction, one can establish the stability of the intermetallic compounds relative to the hydrides of the component metals. The intermetallic compounds may also be used as getters for hydrogen and as materials for hydrogen storage. This paper will present the results of equilibrium and structural investigations of the ZrCr2-H2, the ZrV2-H2, and the ZrMo2-H2 systems for the temperature range of 0" to 900°C and the pressure range of Torr to 1 atm. A complete thermochemical analysis will be made of the measurements. Some of the results have been referred to in a survey paper' covering the types of hydrogen behavior observed in zirconium alloys. LITERATURE ZrCr2 is the only intermetallic phase in the Zr-Cr system.' It exists in two allotropic modifications. Between 900" and 1000°C the hexagonal MgZa (C14) structure transforms into the cubic MgCu2 (C15) structure. Beck4 has previously shown that the intermetallic ZrCrz takes up hydrogen into solid solution up to a composition H/ZrCr2 = 1.14 at room temperature and 1 atm hydrogen. A ZrCr2 hydride was stated to have a fcc structure. The binary Zr-V system has been investigated by williams5 although Rostoker and Yamamoto 6 had given earlier a partial phase diagram. ZrV2 was the only intermediate phase found in the system. wallbaum7 reported earlier that the compound ZrV2 hp the MgZm (CJ4) type structure with a = 5.288A and c = 8.664A. This was not comfirmed by Elliot8 nor by Matthias, Compton, and corenzwit9 who reported that ZrV2 has a cubic MgCua LC15) type structure. The latter authors gave a = 7.429A. Also, several authors do not agree on the temperature of the peri-tectic horizontal. It appears that ZrV2 may exist in several modifications. A high capacity for occluding hydrogen was reported by Beck4 who found H/ZrV2 = 1.38 at room temperature and 1 atm of hydrogen. ZrMoz is the only intermetallic phase in the Zr-Mo system.10 ZrMoa is formed by a peritectic reaction of the melt with a molybdenum-rich solid solution. ZrMo2 has the C15-type structure with a = 7.59A. MATERIALS High-purity chromium, vanadium, and molybdenum were used together with grade 1 crystal bar zirconium to prepare the alloys. Table I lists the chemical analysis and the sources for the metals. Ten-gram alloy compacts were levitated and melted in an inert argon

Jan 1, 1968

By Rees D. Rawlings, C. W. A. Newey

The aging characteristics of an Fe-11 at. pct Mo alloy have been studied by means of light metallography together with density, Young&apos;s modulus, and hardness measurements. The results were consistent with the precipitation of a single intermetallic compound during aging; overaging was slow relative to that in other iron-based binary alloys. The solution treatment temperature had a small effect on the rate of hardening whereas deformation prior to aging had a marked effect on both the rate of hardening and the peak hardness. The density data indicate that the compound precipitated is Fe3MO2 and not the Laves phase Fe2Mo. Analysis of the modulus and density results gave values for the time exponent for precipitate growth of approximately 1.0 and 1.5 for the alloy aged with and without prior deformation, respectively. DETAILED studies of precipitation hardening in bcc matrices have been confined largely to the effects of carbides and nitrides. In view of this and the growing technological interest in intermetallic compound strengthening, e.g., in maraging steels, a study of precipitation in iron-based alloys with a low interstitial content has been undertaken. This paper is concerned with the aging behavior of an Fe-11 at. pct Mo alloy; the mechanical behavior of the alloy will be reported later. The early work of sykes on Fe-Mo alloys showed that precipitation of the intermetallic compound was accompanied by an increase in hardness and a decrease in volume of the material. More recent surveys of the strengthening associated with precipitation have been made3-5 and, in particular, Elsen and wassermann4 showed that deformation prior to aging increased the rate of hardening. These latter workers also followed the precipitation process by means of dilatometry, electrical resistivity, and lattice parameter measurements. Their results confirmed that there is a decrease in volume on aging. Except for the work of Hornbogen on an Fe-20 at. pct Mo alloy, neither clustering nor the precipitation of a nonequilibrium phase has been observed in Fe-Mo alloys. Studies of alloys of lower molybdenum content475 indicate that the equilibrium intermetallic compound is precipitated during aging. However, there is some doubt concerning the nature of the equilibrium precipitate phase. According to the phase diagram constructed by Hansen,8 the phase should be precipitated. This phase has a rhombohedra1 crystal structure which is characterized by the formula Fe706,&apos; although the composition of the molybdenum-rich boundary corresponds approximately to Fe3Mo2. The version of the diagram proposed by Sinha, Buckley, and Hume-Rother indicates that the A phase, a Laves phase Fe2Mo, should be precipitated. Their observation of a Laves phase supports the earlier findings of Bechtoldt and Vacher,13 although, in a recent study of the system by means of diffusion couples, Rawlings and Newey did not detect the phase. The work presented here describes the effect of solution-treatment temperature, aging temperature, and prior deformation on the aging characteristics of the alloy as revealed by light metallography together with hardness, density, and Young&apos;s modulus measurements. In addition the density data are used in an attempt to determine the compound precipitated during aging. EXPERIMENTAL PROCEDURE A 29-kg ingot of the alloy was cast at R.A.R.D.E., Fort Halstead, from deoxidized, Japanese electrolytic iron and sintered molybdenum. The ingot was homogenized for 6 hr at 1473°K and then worked, with intermediate anneals, into 6- and 16-mm-diam rods and 6-mm plate. Chemical analysis of the alloy gave, wt pct: Mo, 17.5 (11 at. pct); C, 0.003; Si, 0.002; S, 0.005; P, <0.002; and02, 0.0098. Solution treatments were carried out under a dynamic argon atmosphere in a vertical, "crusilite" element, furnace which had a facility for rapid quenching into iced water. Except for the study of the effect of solution treatment temperature, all specimens were solution-treated at 1573" * 2°K for 1 hr. Salt baths were used for the aging treatments. Specimens for hardness, density, and Young&apos;s modulus measurements were produced, after heat treatment, from the stock rod or bar using a precision silicon carbide slitting wheel. As described later, the quenching treatment produced local plastic strain in the stock material; consequently, care was taken to ensure that the specimens were not prepared from these regions. Those specimens used in the studies of the effects of prior deformation on the aging behavior were strained in compression in a Denison universal testing machine. Specimens for light metallographic observations were mechanically polished on successively finer grades of diamond paste down to and then etched in either alcoholic ferric chloride or in a 2 pct nital solution. Vickers diamond pyramid hardness data were obtained using a 30-kg load. At least five impressions were averaged for each determination. Density measurements were made using a displacement technique in which each specimen was weighed in air and in dibromoethane at 296°K. The specimens were cylindrical and weighed 3 to 4 g; all weighings were made on a balance reading to 1 x 10"5 g. For each specimen the mean value of five weighings was used to calculate the density. The density of the dibromoethane was determined using the displacement procedure and a standard nickel specimen. The error in an absolute density value was estimated to be HI.01 pct. To obtain the density as a function of aging time a single specimen was used and the density meas-

Jan 1, 1969

By J. P. Boisseau, C. N. J. Wagner, E. N. Aqua

An analysis ulas made of powder-paltern peaks from cold-rolled polycrystalline copper and from copper powders, compacted into briquets (1 in. diameter) with pressures up to about 106 psi. Powder-pattern peaks from both contact faces were measured with a diffractometer and CuKa radiation. Laltice-parameter measurements indicate the presence of residual stresses in the bulk specimen of the order of a - -10 kg per sq mm after 93 pct reduction in thickness, and give some evidence for the occurrence of deformation stacking faults (probability a - 0.003) in both bulk and powder samples. Fourier analyses of the line profiles were carried out on the (111) - (222) and (200) - (400) Pairs of reflections. The particle sizes decrease rapidly with increasing deformation and reach asymptotic values of De (111) = 550A and D, (200) = 350A at about 25 pct reduction in thickness or 80,000 psi pressure for compaction. The anisotropy of the particle sizes indicates the presence of microtwins and stacking faults on (111) planes. The rms strains increase also with deformation and reach limiting values of 2 x 10-3 in the [100] direction and 1 x 10-3 in the [Ill] direction at a distance L = 100A normal to the reflecting planes. THE diffraction of X-rays in cold-worked, polycrystalline, fcc metals and alloys yields Debye-Scherrer patterns in which the individual (hkl) lines may show a broadening, a shift, and an asymmetric shape.&apos; These effects can be explained by the fragmentation of the small, coherently diffracting domains, the presence of residual elastic strains in the lattice, and the formation of stacking faults. X-ray studies of stacking faults in fcc metals and alloys have been methodically performed during the last few years, but so far most of the investigators dealt with cold-worked powder specimens obtained by filing.2-8,10-19 In such specimens, the crystals are randomly oriented and the average elastic strains are assumed to be zero, so that the observed peak shifts are due to stacking faults only. The agreement between X-ray diffraction theory1,20 and experiment is generally good. On the contrary, cold-worked, polycrystalline bulk specimens (after wire drawing, rolling, plastic deformation by tension or compression, etc.) contain residual elastic strains, which may not average to zero in the surface of the specimen and show very strong preferred orientation of certain lattice planes (texture) parallel to the specimen surface. Nonzero elastic strains also produce peak shifts, the magnitudes of which depend upon the crystallographic orientation of the reflecting lattice planes in elastically anisotropic materials as well as on the type of plastic deformation and which have to be taken into account when measuring stacking-fault probabilities in deformed bulk specimens.21-23 The purpose of the present investigations was to perform a detailed X-ray analysis on a bulk specimen of a fcc metal deformed by rolling at room temperature and on powder of the same material deformed by compaction, and to compare these results with those previously obtained on cold-worked filings.18 Pure copper was chosen for this study since it is known to produce only a small quantity of stacking faults by filing at room temperature.3,16,17,19 The residual elastic strain in the surface of the bulk copper should be the predominant factor determining

Jan 1, 1965

By G. J. W. Kor, F. D. Richardson

The sulfide capacities a1 1500°C of slags in the systern CaO + CaF, +Al2O3 have been measured by bringing samples into equilibrium with gas mixtures made from CO + CO2 + SO, + N2. The capacities are negligzble both JOY CaF, and CaF, + Al2O3 melts but when lime is present even at 20 wt pct capacilies as high as 30 x lom3 can be obtained. The results have yielded information concerning the liquidus at 1500°C and fluoride-oxide melts in general. The slags used in electroslag refining contain substantial amounts of calcium fluoride. Robinson and Grainger&apos; report that good results can be obtained by using slags of the approximate composition 70 wt pct CaF2 + 30 pct Al2O3. It has also been reported2 that a mixture of 50 pct CaF2 + 30 pct A12O3 + 20 pct CaO makes a good slag for general use. In view of the fact that very low sulfur contents are claimed for ingots produced by the electroslag process. studies have been made of the sulfide capacities [c, = wt pct S (PO2/Ps2)1/2 at 1500°C. of slags consisting of pure calcium fluoride, and of its mixtures with lime and/or alumina. These studies have also provided information on the phase diagrams. The slags were brought into equilibrium with gas mixtures prepared from NZ + CO + CO2 + SO2. Because CaFz is volatile and also easily hydrolyzed. measurements were made of its loss in weight in various flowing gas mixtures. EXPERIMENTAL Procedure. The apparatus and procedure were the same as described previously. Both platinum and iridium crucibles were used (height and inner diameter about 1 cm), but those made from iridium were stronger and able to withstand a greater number of experiments. In each experiment two crucibles were set in an alumina support and 1 g of slag mixture was divided between them. The materials from each crucible were analyzed separately after being brought to equilibrium with the gas, and then quenched in the water-cooled end of the reaction tube. Materials. Alumina and lime were prepared as de-scribed previously.4 Calcium fluoride was obtained by igniting Analar calcium fluoride in a platinum boat at about 800°C in a stream of pure dry nitrogen: the product was cooled in a desiccator. The slags were produced from mixtures of the powdered constituents, these being melted together in the course of each equilibrium experiment. The sulfur analyses and the X-ray diffraction meas- urements on the solidified slags were made as described previously.4 From the latter it appears that the CaF2 contained less than 0.5 mol pct CaO. RESULTS Values of (ps2/po2) for the Gas Mixtures. The re-sults have been represented in terms of (ps, /Po,)"? for the various gas mixtures used. The va1;es of this function at 1500°C are listed in Table I: they were calculated from the data cited previously for calculations at 1350°C 4 Weight Losses with CaF, and CaF, + CaO. The re-sults of the weight loss measurements* at 1500°C for

Jan 1, 1970

By R. T. DeHoff, F. N. Rhines

The problem of determining the number of particles of a phase distributed randomly in unit volume c an opaque matrix from measurements made on random plane sections is closely investigated. A formalized derivation for the general case is presented. Applications of this formal result are made to specific types of aggregates dispersed in a matrix; circles, particles with flat circular ends, cylinders, and constant shape aggregates of ellipsoids of revolution. Quantitative measurements of the average geometric properties of these aggregates are developed. In 1953 R L. ullman&apos; developed a technique for determining, from measurements made on random plane sections, the number per unit volume, Nv, of particles imbedded in an opaque matrix. Using meas urements previously developed for volume fraction, vV,&apos; and surface area per unit volume, .SV,= he was able to determine average volume, average surface area, and average dimensions of particles, independent of size distribution, for spheres and circular disks,&apos; as well as for uniformly sized cylinders of any axial ratio.4 The technique is mathematically rigorous for the cases studied. Recent studies of this problem have yielded rigorous solutions for the general case of cylinders, permitting evaluation of NV independent of size distribution and with all axial ratios intermixed. Generalization to shapes having flat, circular ends has been deduced. A solution has also been obtained for the ellipsoid of revolution, independent of size distribution, but requiring a constant axial ratio in the generating ellipses. In the following derivations, as in Fullman&apos;s work, it is assumed that the problem is purely a combination of geometry and probability theory,that is,eithe the particles to be measured are imbedded randomly in the matrix, or a sufficient number of random plane sections are taken to make the sample representative. A relationship exists between the number of par- ticles of a given size and shape that may be situated in unit volume (Ny) and the number of intersections a random plane can be expected to make with these particles (Na). It is the purpose of the following section to derive this relationship. The probability of Intersecting Convex Bodies. Consider a convex, closed surface, that is, one for which no two surface normals point in the same direction, situated at some arbitrary position and orientation in a cube of material that is one unit long at each edge. It is not necessary to assume that this surface is symmetrical. Let planes be constructed in the cube parallel to the top face and at random distances from it. Those planes which lie between the two planes which are just tangent to the top and bottom of the surface will intersect it. The probability that a plane will intersect the body may be defined as the limit of the fraction of planes that lie between the two tangent planes as the total number of planes constructed becomes infinite. This fraction, in the limit, is equal to the distance between the two tangent planes, DV, divided by the total length over which planes are constructed, which has been taken as unity. If the body is now rotated to a new orientation, applying the same argument, the probability of intersection is again numerically equal to the distance between tangent planes. Let DV ($, 0) be defined as the distance between tangent planes of a convex body as a function of orientation, Fig. 1. The probability, Pr, of intersecting the body with a randomly oriented and randomly positioned plane, is then equal to the average value of DV (0, $) over all possible orientations. It may be easily shown that for a system of spherical coordinates the probability of finding an orientation between Q and Q + de, $ and $ + d$ is (1/4n) sin $ dB d$, so that This relationship may be applied to each body in an aggregate of convex bodies. In particular, if the bodies in an aggregate are classified according to size and shape, and the ithsuch class is considered, Eq. 111 may be applied to this entire class, the probability of intersecting any body in this class being

Jan 1, 1962

By A. Hultgren, B. Herrlander

The original aim of the present investigation was to study the mechanism of cracking on hot-deforming red-short steels. During the microscopical examination of hot-deformed soft steels attention was directed to various patterns of so-called veining in the ferrite, as related to variations in the deformation procedure and the heat-treatment of the steels. Later, a hot-short steel of higher carbon content was also studied. Historical Storey1 suggested in 1914 that veining developed during the gamma-alpha transformation from the growing together of several alpha nuclei within the same gamma grain. Rawdon and Berglund2 found that in soft steel, forged somewhat below A3, the ferrite showed profuse veining, while usually there was very little veining after forging at very high temperatures. They emphasized the similarity between the pattern of veining formed by deformation about 600°C and that of slip lines formed by deformation at room temperature. They also suggested a relation between the gamma-alpha transformation and veining. They became convinced from etching and from the slip-line pattern in cold-deformed material, that the orientation within any ferrite grain showing veining was uniform. In recrystallized alpha grains veining was absent. Veining did not appear materially to affect the properties of ferrite. Independent of veining, continuous networks, attributed to preexisting delta and gamma grain boundaries were sometimes found, the former only in cast steel. Those networks were usually connected with small inclusions. Ammermann and Kornfeld3 confirmed that recrystallized ferrite grains showed no veining. In soft steel annealed between A1 and A3 there was veining only in the ferrite grains formed during cooling. Electrolytic iron deformed at 880&apos; was free from veining. Bannister and Jones&apos; considered veining in ferrite to be a manifestation of microscopical and sub-microscopica~ inclusions. NorthCOtt,5,6 in studies on veining in steel and other metals and alloys, attributed veining to oxide inclusions. It could generally be removed by annealing in hydrogen, a suggestion earlier made by Rawdon and Berg1und. TrittOn (discussion in ref. 5) emphasized the importance of perfect polishing for bringing out veining by etching, and thought the veins or subboundaries were produced during the gamma-alpha transformation, when it was rapid, as a result of the volume change and contraction during cooling. Slight distortion would not allow projecting parts of a growing crystal to join up with atomic symmetry. Hanemann and co-workers showed that veining in ferrite consisted of ridges

Jan 1, 1948

By Pradeep K. Rohatgi, David N. French, Surendar M. Jain, Clyde M. Adams

The effect of solute concentration and diffussivity on dendritic solidification of dilute binary aqueous solutions has been investigated; chlorides of sodium, potassium, lithiurn, and hydrogen were used as solutes. Dendrite spacings were measured in spherical droplets and in unidirectionally solidified specimens. In the droplets, the freezing rate is uniform over the entire specimen and remains constant from the beginning to the end of solidification. In the unidirec-tionally frozen specimens the freezing rate varies within a given volume of liquid during the solidification cycle; in addition, it varies with location uithin the specimen. Mass transport analysis has been used to calculate the supersaturation, AC, supercooling, AT, and transcerse growth velocity, V , of ice dendrites during solidijication from the dendrite spacings measured in the droplels. The ice dendrite spacing in a given solute increases lineary with the solule concentralion at a fixed freezing rate. The ualues of AC, AT, and V increase with an increase in solule concentration. The value of AT in the aqueous solution is of the same order of magnitude as in Al-Cu alloys of the same concentration; the dendrite spacings in Al-Cu alloys also increase with an increase in solute concentralion. For the jamily of aqueozrs solulions incestigaled, the dendrite spacing increases linearly with solute diffusivity at fixed values of concertralion and freezing ,rate. The values of ?C and ?T decrease, whereas the value of V increases with an increase in solule diffusicity. The measured dendrite spacings , L, can be expressed by the relatiun: L = K;(dfa/db) 4 K2C +K3D - K4 where dfs/d? is-change in fraction solid with time (freezing rate), C is solute concentration, D is solute diffusivit K1 = (14 * 4)pmin1&apos;2, K2 = (70 ± 10) pl (moles)- K3 = (24 r 3) . l05 psec (cm)-~. K. = -132 ± 10) 1. FREEZING of solutions is almost always an ehunmix-ing" process because the composition of crystallizing solid generally differs from that of the parent liquid. " Solute concentration and transport are therefore in]portant considerations in solidification of solutions. The influence of these factors on the dendritic solutions produced from metallic solutions is of practical significance since the properties of the solid aggre-gate are often strongly influenced by dendrite spacing.&apos;&apos;&apos; Alexander and Fthines3 found that dendrite spac- ings generally increase with solute concentration in several metallic systems. Michael and Bever1 have observed an increase in a aluminum dendrite spacings in dilute A1-Cu alloys. Rohatgi and AdamsJ have reported a linear increase in a aluminum dendrite spacings with increasing copper contents up to 28 pct in A1-Cu alloys. Bolling and Tiller"&apos; have theoretically examined the effects of solute concentration and diffusivity on the growth of cells and dendrites. Their analysis of dendritic growth assumes a steady-state growth and the maximum possible velocity for dendrite propagation. In addition, the quantitative analysis is restricted to dendrites of rotational symmetry and is therefore not directly applicable to the plate-shaped dendrites of ice obtained in the present study. There are practically no experimental observations of the effect of solute diffusivity on dendrite spacings in metallic systems. The reason appears to be the lack of experimental data on solute diffusion coefficients in liquid metallic solutions. The present work is concerned with the effect of solute concentration and diffusivity on dendritic solidification of dilute aqueous solutions: the solutes examined are potassium chloride. sodium chloride, lithium chloride. and hydrogen chloride. There were several reasons for selecting these solutes. The variation of dendrite spacing with freezing rate in these solutiolls is similar to that observed in A1-Cu alloys.8 These aqueous solutions have almost identical phase diagrams at dilute concentrations. Fig. 1. and the diffusion coefficients show very little variation with solute Concentration.9,10 Dendrite spacings were measured as a function of freezing rate. solute concentration. and solute diffusivity. Dendrite spacings were measured in two different types of freezing systems. droplet and unidirectional, respectively. In the droplet freezing system

Jan 1, 1970

By F. I. Grace, L. E. Murr

The mechanical responses and residual defect structures in 70/30 brass and type 304 stainless steel following explosive shock loading and cold reduction by rolling have been studied. A distinct relationship was observed to exist between the residual mechanical properties and micro structures observed by transmission electron microscopy. Shock-loaded brass deformed primarily by the formation of coplanar arrays of dislocations and stacking faults at lower pressures, and twin-faults (deformation twins and €-martensite bundles) at higher pressures (> 200 kbar). The micro -structures of cold-rolled brass were characterized by dense dislocation fields elongated in the rolling direction. Stainless steel was observed to deform by the formation of dense arrays of stacking faults at lower shock pressures and twin-faults at high shock pressures (>200 kbar). Lightly cold-rolled stainless steel deformed similar to low Pressure shock-loaded stainless steel, but transformed to a&apos; martensite in heavily cold-rolled stainless steel. Discontinuous yielding was observed for the heavily cold-rolled stainless steel, and stress reluxution in the weyield region for cold-rolled and shock -loaded stainless steel was interpreted as an indication of the ability of twin-faults and stacking faults to act as effective barriers to dislocation motion. A simple model for the formation of the planar defects and a&apos; martetnsite is presented based on the propagating of Shochley partial and half-partial dislocations. A considerable effort has been expended over the past decade in an attempt to elucidate the response of metallic-crystalline solids to the passage of a high velocity shock wave (e.g., smith,&apos; Dieter,2 and zukas3). While it has been possible to obtain relevant information pertaining to the residual defect structures and mechanical properties, there have been few rigorous attempts to draw a direct comparison between these structures and properties. In addition, numerous investigators have recently observed the occurrence of deformation twinning in shock deformed fcc metals (e.g., Nolder and Thomas,4 and Johari and Thomas5), but little attempt has been made to elucidate the mechanisms of formation of these defects. Comparative data for metals deformed by shock-loading and the same metals deformed by more conventional modes of deformation such as cold-reduction by rolling is also generally lacking. The present investigation therefore has the following objectives: 1) to examine the mechanical properties of some explosively shock loaded and cold-rolled fcc metals of low stacking-fault energy as a function of their residual substructures; 2) to present a simple model for the formation twin-faults and related defect structures in the low stack-ing-fault energy materials of interest (70/30 brass, ySFg= 14 ergs per sq cm; and 304 stainless steel, ySF = 21 ergs per sq cm); 3) to make some deductions with regard to the residual characteristics of dislocation and planar defect substructures in cold rolled and shock loaded 70/30 brass and type 304 stainless steel. In particular, it was desirable to characterize the residual hardening effects of particular deformation substructures. I) EXPERIMENTAL PROCEDURE Sheet samples of 70/30 brass (0.005 and 0.15 in. thick; annealed at 659°C for 2 hr) and type 304 stainless steel (0.007 in. thick; annealed 0.25 hr at 1060°C) of nominal compositions shown in Table I were cold-rolled in one direction only to produce reductions in thickness of 15, 30, 45, 60, and 75 pct in the brass; and 5, 15, 25, 35, and 45 pct in the stainless steel. Identical sheet samples in the annealed (unrolled) state were subjected to plane compressive shock waves to various peak pressures ranging from 0 to 400 kbar in the brass and 0 to 425 kbar in the stainless steel; and with a constant peak pressure duration of approximately 2 microseconds. A detailed description of the shock loading technique has been given previously.6 Tensile specimens 1.0 in. in length and 0.125 in. in width were cut from the cold-rolled sheets (tensile axis parallel to the rolling direction), and the shock-loaded sheet specimens. Stress (load)-strain (elongation) measurements on the tensile specimens were made on a Tinius-Olsen load-compensating tensile tester using a strain rate of 2.7 x 10-3 sec-1. Tensile tests were repeated at least twice, giving essentially the same results. Stress relaxation measurements in the preyield region were also made using an initial strain rate of 5.4 x 10-4 sec-1. In addition to tensile and stress relaxation measurements, Vickers microhardness measurements were made on all samples. A total of 100 microhard-ness readings were obtained for each specimen following a light electropolish to ensure uniform surface conditions for all tests. The hardness averages ob-

Jan 1, 1970

By W. M. Robertson

The kinetics of grain boundary groove formation on copper surfaces immersed in liquid lead have been studied over the temperature range of 400° to 900°C. The groove widths were Proportional to the cube root of the annealing time, indicating that the diffusion of copper through the saturated liquid-lead solution is the mechanism by which grooves form. The rate constant for the process can be calculated by a theory due to Mullins. Using published data for the solubility of copper in liquid lead, for the interfacial energy of the solid copper-liquid lead interface, and for the diffusion coefficient of copper in liquid lead, the calculated rate constants almost exactly reproduce the measured values over the entire temperature range. The decay of scratches placed on copper surfaces has also been studied. The rate constant for scratch decay agrees with that for grain boundary groove growth, though scratch decay is sensitive to convection currents in the liquid. The interaction of solid and liquid metals has been studied extensively and has been found to be rather complex. Many of the studies have been complicated by a host of competing effects, including temperature gradients, concentration gradients, the formation of one or more intermetallic phases, natural or forced convection, and the presence in both the solid and liquid of considerable amounts of impurities and alloying elements. Recently theories have been developed of changes in surface profiles driven by capillary forces,&apos; which allow the interaction of the solid and liquid to be analyzed quite directly. The present paper reports a study of the formation of grain boundary grooves on pure copper immersed in liquid lead, which allows the theory to be checked quantitatively. The Cu-Pb equilibrium diagram is quite simple: there are no intermetallic compounds, copper is just slightly soluble in liquid lead, and lead is almost completely insoluble in solid copper.2 The Cu-Pb system has been studied extensively,3-9 and all of the quantities—interfacial energy, diffusion coefficients, and equilibrium solubilities-necessary to calculate the rate of groove growth by a volume-diffusion mechanism are known. The kinetics of grain boundary grooving and scratch smoothing have been studied on the noble metals and the iron group metals in a reducing atmosphere or in vacuum.10 The main interest of these studies has been the determination of surface-diffusion coefficients at metal-gas interfaces using the theories developed by Mullins.1 The present paper uses similar methods for the study of diffusion processes at the interface between two condensed phases. There has been one previous study" of the kinetics of groove growth in a solid-liquid system, which, however, was troubled by the fact that neither interface energies nor diffusion coefficients were known in the Ni-S system studied. THEORY The theory of grain boundary groove growth has been developed by Mullins for the cases of volume diffusion," surface diffusion," and a combination of the two processes.14 He has also analyzed the kinetics of the flattening of a scratched surface by these processes.l5,l6 Several assumptions and approximations were used in the derivations of the surface profile shapes. The applicability of these assumptions and approximations to the present system will be considered in the discussion. At the intersection of a grain boundary with an initially flat interface the equilibrium between the interfacial energy and the grain boundary energy establishes an equilibrium groove angle. This induces curvatures in the interface. The chemical potential of material at a curved interface is higher than at a flat interface, so that material moves away from the region of the grain boundary. Mullins&apos; calculations indicated that the groove profile would be similar to that shown schematically in Fig. 1. Small humps form above the level of the original flat surface. For a volume-diffusion mechanism the separation, w, of these humps at a time, t, is given by and where co is the equilibrium concentration of the solid in the liquid, y, the solid-liquid interfacial free energy, O the volume occupied by a solute atom in the liquid, D the diffusion coefficient of the solid in the liquid, and kT has its usual meaning. For a surface-diffusion mechanism the groove width is proportional to the fourth root of the time. For grooves forming by a combined surface and volume-diffusion mechanism the exponent of the

Jan 1, 1965

By R. H. Kolb

A long term project at Shell Development Co.&apos;s Exploration and Production Research Laboratory has been the improvement of the accuracy and the ease of BHP measurements. As a result of these efforts, two complete and separate systems have now been built for the automatic logging of BHP variations. The first of these is a small-diameter instrument suitable for running through production tubing on a single-conductor well cable. During the development of this instrument, as much emphasis was placed on providing a high degree of usable sensitivity and repeatable accuracy as on obtaining the advantages of surface recording. The second system combines the benefits of automatic, unattended recording with the convenience of a permanently installed Maihak BHP transmitter.&apos; THE CABLE INSTRUMENT For many years the standard instrument for BHP determination has been the wireline-operated Amerada recording pressure gauge or one of several other similar devices. This gauge records on a small clock-driven chart carried within the instrument, and although relatively precise readings from the chart are possible, they are difficult to ob-tain. a Both the maximum recording time and the resolution of the time measurements are limited by chart size, and when a slow clock is required for long tests, the precision of the time measurement is often inadequate. Since it is impossible to determine the data being recorded until the gauge has been returned to the surface, wasted time often results when a test is protracted beyond the necessary time or when it is terminated too soon and must be re-run. Clock stoppage or other malfunctions which would be immediately apparent with surface recording remains undetected with down-hole recording; the test is continued for its full term with a consequent loss in production time. As new uses for subsurface pressure data evolved, the shortcomings of the wireline instrument became increasingly apparent, and the concurrent development of a surface-recording pressure gauge and the associated high-pressure well cable service unit&apos; was undertaken. Description of the Instrument Because of its ready availability and advanced degree of development, the Amerada bourdon-tube element was chosen as the basic pressure-sensing device. This element converts a given pressure into a proportional angular displacement of its output shaft, and a suitable telemetering system was designed to measure accurately the extent of this displacement and to transmit the measurement to the surface and record it. The telemetering system furnishes a digital record printed on paper tape by an adding machine-type printer. The present arrangement provides a resolution of one part in 42,000 over the angular equivalent of full-scale deflection, giving a usable sensitivity of better than 0.0025 per cent of full scale. An additional refinement simultaneously records on the tape the time or the depth of the measurement, also in digital form. When the instrument is placed in operation, an adjustable programer can be set to initiate a read-out cycle automatically at selected time intervals. When subsurface pressures are changing rapidly, readings may be recorded as frequently as once every 10 seconds; when pressures are more nearly stabilized, the period between readings may be extended to as much as 30 minutes. Because the instrument is surface-powered as well as surface-recording, the maximum period of continuous logging is (for all prac. tical purposes) unlimited. The subsurface instrument is a tubular tool, 1 1/4-in. in diameter and 6.5 ft in length, operating on 12,000 ft of conventional 3/16-in. IHO logging cable. The transmitting section, mounted above the bourdon-tube element in place of the regular recording mechanism, contains no fragile vacuum tubes or temperature-sensitive transistors. This unit has been laboratory-tested to 1 0,000 psi and 300°F and has performed dependably during a number of field operations. The down-hole transmitting arrangement can be fitted to any standard Amerada pressure element, regardless of range and with no modification of the element itself. Calibration To obtain a repeatability commensurate with the sensitivity and resolution of the instrument, it was necessary to develop a special calibrating technique. The manufacturers of the Amerada recording pressure gauge claim an accuracy of only 0.25 per cent of full scale, which is a realistic figure for normal calibrating and operating procedures. An exhaustive investigation was made of the errors inherent in the bourdon-tube element, itself, independent

By A. R. Marder

Fe-C alloys have been investigated at temperatures below the eutectoid transformation to determine whether the superplasticity phenomenon exists for these materials. As a result of void formation at the carbide-ferrite interfaces that led to void coalescence and premature failure, the large elongations characteristic of superplustic matem&apos;als did not develop. It had generally been assumed that the conditions for obtaining superplasticity include: a) T/Tm =0.5, b) a strain rate sensitivity of the flow stress that results in m s 0.3, and c) fine-grain structure. Although superphsticity was not observed in the alloys studied, stress-strain rate measurements indicated that an additional condition for the existence of superplasticitv in Fe-C allovs is that the fine-wain structure be equiaxed in agveement with previous results on Zn-Al al1oys. MANY investigations have been made on the hot deformation of iron-base alloys in order to obtain an understanding of the variables that may affect high-temperature strength and ductility.&apos;-6 However, only a few papers have studied the effect of carbon content on the high-temperature properties of iron-base alloys. Peretayat&apos;ko and Zaikov and Wallquist and carlen4 studied the effect of carbon on strength in the y temperature range, and recently Robbins, Shepard, and sherby6 studied the influence of carbon on the torsional behavior of iron in the a and cu-plus-cemen-tite temperature ranges. In addition to studying hot deformation behavior, current investigations have also been concerned with the phenomenon of superplasticity in nonferrous materials, and, in particular, ferrous alloys. Superplasticity is identified by the increased resistance to necking that results from a high strain rate sensitivity of the flow tress. ackofenr proposed the strain rate hardening coefficient m = d log a/d log e as a measure of strain rate sensitivity and showed that m must be "-0.3 for superplasticity to exist. In addition, a fine-grained microstrcture,- a eutectic or eutectoid ornosition,- and a test temperature in the creep range (TITm > 0.5)" have also been advanced as necessary conditions for superplasticity. Although many workers""23 investigated superplasticity associated with the allotropic transformation in iron and the eutectoid transformation in steel, and recently chadler " and orrison have studied superplasticity in the a - y phase region, no one has measured the superplastic effect in the a + cementite temperature region. Therefore, the purpose of this investiga- tion was to determine the effect of carbon content, microstructure, and test temperature on the strain rate sensitivity of Fe-C alloys at temperatures below the eulectoid transformation. EXPERIMENTAL PROCEDURE Fe-C alloys with carbon contents of 0.2, 0.4, 0.6, 0.8, and 1.0 wt pct were prepared as 100 lb 54 in. ingots by vacuum-induction melting. The compositions are listed in Table I. All the ingots were soaked at 2100°F for 2 hr prior to rolling to 4 in. plate. The minimum finishing temperature for rolling was 1800°F. The plate was sheared in 10-in. lengths and tensile bars were rough-machined prior to heat treatment. The samples were heat-treated according to the schedule in Table I1 in order to obtain a fine-grained microstructure consisting of finely dispersed carbides in a matrix of small ferrite grains. All the tensile specimens were heat-treated prior to finish machining, and tensile testing was accomplished on an Instron machine in conjunction with a clamshell furnace. The buttonhead specimen configuration is shown in Fig. 1. An inert atmosphere, helium, was maintained during testing with a steel tube shroud in a bell jar arrangement. Predried helium was continually purged over the buttonhead specimens and exhausted through ceramic fiber at the bottom of the tube to keep oxidation at a minimum and to prevent

Jan 1, 1970

By V. B. Kurfman

The temperature, strain rate, and orientation deDendence of defbrnzation of single-crystal MgAg has been examined. The crystals exhibit a tendency to single glide and little or no hardening at 25°C for many orientations. A much higher hardening rate is observed when multiple glide occurs, such as can be initiated by surface defects. The tendency for easy glide becomes less dependent on surface preparation and orientation as T — 100°C and bars so tested often fail after one-dimensional necking-. At T > 200°C (transition temperature for single-crystal notch sensitivity and poly crystalline ductility) single glide diminishes and two-dirnensionul necking begins. The crystals do not strictly obey a critical resolved shear stress law, but show the influence of {loo) cracks in determining the slip mode. The results are correlated with the difficulty of sciperdzslocation intersection and semibrittle behavior of this compound in single-crystal and poly crystalline form. Comparisons are made with the slip selection mode observed in tungsten, with the reported observations of easy glide in bee metals. and with the mechanical behavior of poly crystalline MgAg. PREVIOUS work on tensile deformation of polycrys-talline MgAgl and bending deformation of single-crystal MgAg2 has shown that the compound is semi-brittle (i.e., notch and grain boundary brittle). If this semibrittleness is supposed to result from the difficulty of multiple glide (associated with the problems of superdislocation intersection) one might expect single crystals deformed in tension to show pronounced single glide and strong orientation dependence of hardening rate. These experiments were done to examine this supposition and to study the tensile deformation of a highly ordered system which may be considered bcc if the difference between the two kinds of atoms is ignored (actual structure: CsC1). EXPERIMENTAL Single-crystal ingots were grown by directional freezing as previously described.&apos; These ingots were sliced into a by a by 2 in, rectangular bars by electric discharge machining, then round tensile bars were conventionally machined to 1/8-in.-diam by 1-in.-long reduced section. The bars were typically tested without an anneal because of the problem of magnesium vapor loss and they were typically tested as mechanically polished. The analyses are within the same limits as those reported earlier; i.e., the average composition for each specimen is within 0.5 at. pct of stoichiometry, while the total range from end to end in a given specimen varies from 0.7 to 1.4 at, pct. There has been no indication in the results of any variation in slip or fracture mode attributable to the composition fluctuations. The slip systems were determined by two-surface analysis of the bars after testing to failure at room temperature. Single glide was so dominant that there was little difficulty in identification of the dominant slip system even though the tensile elongation to failure often approached 7 to 8 pct in room-tempera- ture tests. Elevated-temperature testing was done in a silicone oil bath and low-temperature testing was done in liquid Np or a dry-ice bath. All stress measurements are reported as engineering stress unless otherwise specified, and crosshead travel is used as the strain measurement. RESULTS The tendency toward single glide is best seen in the pictures, Figs. 1, 2, and 3, which depict deformation at fracture as a function of test temperature. While it is possible to find regions of secondary slip by careful microscopy, such regions are very small. The development of a ribbon-shaped configuration from an initially round section bar pulled at 100°C is typical, occurred by single glide, and illustrates the degree to which such glide continues. At temperatures =100°C the bars typically show elongation of 20 to 50 pct by predominently single glide. Despite the large elongation, fracture even at 150°C occurs in a brittle mode, Fig. 2, in the sense that it is an abrupt failure which shows no discernible necking in the second dimension of the bar&apos;s cross section (i.e., there is no appreciable action of any slip modes which would decrease the broad dimension of the cross section). Near 200°C the fracture mode changes slightly. Although most of the sample extension is by single glide, after the bar develops the characteristic ribbon shape it begins to neck in the second (i.e., broad) cross-sectional dimension. The bar becomes very thin in the "necked down" region, Fig. 3, and the reduction in area approaches 100 pct. Often there oc-

Jan 1, 1967

By Linda Lee, R. E. Reed-Hill, C. R. Smeal

Four fcc metal surfaces, etched to make them responsive to polarized light, have been studied with an electron microscope. Jones&apos;prediction that these surfaces are grooved has been verified. Optical-goniometer measurements made on commercially pure nickel indicate that the groove walls are poorly defined (100) facets. Surface mientations close to either 4001 or {ill).- show no extinctions on the polam&apos;zid-light microscope. An explanation is offered for this orientation dependence. It has also been deduced that polarized-light extinctions on a grooved cubic-metal surface should not be used directly in crystallographic-orientation determinations. The nature of the etching solutions that produce these surfaces is considered. A cubic-metal surface may be made responsive to polarized light in two basic ways."&apos; In one, an anodic film, believed anisotropic, is formed on the surface. A plane-polarized-light beam, at normal incidence, should be reflected from this type of film with an ellipticity that varies with grain orientation. Under crossed polarizers of a polarized-light microscope, each grain may be distinguished from its neighbors by a difference in reflected-light intensity. An alternate treatment,&apos; more generally applicable to cubic metals and of principal concern here, involves etching of grain surfaces. The characteristic features of this surface were first deduced by Jones3 from light-microscope observations. She concluded that, in general, grain surfaces were furrowed so that light was reflected from two parallel sets of etched facets. A grooved surface produces elliptical polarization of a plane-polarized beam because the beam does not strike groove walls at normal incidence. Jones also observed that the furrows must have faces inclined to each other by approximately 90 deg, since the light returns along the incident path, and that a grooved surface should show four maxima and minima of reflected-light intensity during a 360-deg stage rotation of the polarizing microscope. Positions of maximum extinction were predicted to occur when groove axes were parallel to either polarizer or analyzer vibration directions. Because of the limited resolving power of Jones&apos; optical microscope, her deductions were primarily indirect. Proof of the correctness of her conclu-sions, as demonstrated by the electron microscope, will be given as well as evidence concerning the crystallographic nature of the etch furrows and the types of etching solutions that produce them. EXPERIMENTAL PROCEDURE During a comprehensive study of hot plastic deformation in nickel and nickel alloys, an etch was evolved that produced a surface with an excellent polarized-light response on Nickel 200 ("A" Nickel). The etching solution and associated metal-lographic procedures are given in Table I. In evaluating this etch, a study was made of the topological features of the etched surface and their relation to the underlying crystalline structure. As part of this investigation, large crystals (2 mm average diameter) were grown in a 1-cm-sq Nickel 200 specimen. After the surface was etched, the crystallographic orientations of ten grains were determined by the standard back-reflection Laue technique of Gren-inger.4 Maximum extinction positions during a microscope stage rotation were also measured for the ten grains. Groove-wall positions on the surfaces of the ten grains were measured with a two-circle optical goniometer. The technique was essentially that of Barrett and Levenson.5 Several grain surfaces were photographed with a Philips Model 100A electron microscope. All specimens were replicated with collodion, or collodion backed with formvar and chromium shadowed at 18 to 20 deg. The basic material was Nickel 200. However, an electron-micrographic study was also made of surfaces developed by polarized-light etches on other fcc metals (90-10 a brass, Monel 400, and lead). All etching procedures are given in Tables I and 11. EXPERIMENTAL RESULTS Fig. 1 shows typical electron micrographs of three different fcc metal specimens and an optical micrograph of a fourth. All photographs show a grooved structure corresponding closely to Jones&apos;3 predictions. Also, as noted by Jones, extinctions were always observed when groove axes were either parallel or perpendicular to the microscopes&apos; vertical cross hair. The symmetry of the grooves, with respect to the twin boundaries in Fig. 1, implies that furrows have a crystallographic basis. The coarse-grained Nickel 200 specimen was used to study this basis. Facet Orientation. The poles of the ten Nickel 200

Jan 1, 1964

By M. Mills, M. W. Clegg

This Paper Presents an approximate analytical solution to the problem of the pressure distributions arising from the production of a compressible liquid in a partially penetrating well. The limits of validity of the approximation are discussed and it is shown that the basic approximation is the same as that used in previous numerical of the problem. The variation in pressure at the production well with time for different penetration ratios is investigated and is shown to agree with previous work. The solutiOns are used to assess the effects of partial penetration at large distances from the well and at the wellbore itself. In the latter case the effects of anisotropy are also studied for constant, but unequal, horizontal and vertical permeabilities. It is &apos;uggested that measurements of the Pressure drawdown below the producing interval in a well should give some indication of a thickness-vertical permeability product for the formation; this would chmacterize the effectiveness of the formation below the producing interval. INTRODUCTION In many oil and gas reservoirs the producing wells are completed as partially penetrating wells; that is, only a portion of the pay zone is perforated. This may be done for a variety of reasons, but the most common one is to prevent or delay the intrusion of unwanted fluids into the wellbore. This paper studies the effects of partial penetration on the pressure distribution resulting from the production of a compressible liquid at a constant rate. To simplify the mathematical analysis the case of a single well located in an infinite reservoir of constant thickness is considered, and it is assumed that this well is perforated over an interval adjacent to the upper (or lower) impermeable boundary of the formation. A well producing from an arbitrary interval within the bulk of the formation could be treated in a similar way, but this action would merely add to the complexities of the solution and contribute little to the appreciation of the over-all effects of partial penetration. In a recently published paper by Odeh,10 the more general problem of producing from an arbitrary interval within the pay zone was studied for the quasi-steady state flow of a compressible liquid, This is the case in which there is a a potential at the outer boundary and a constant flux across the same boundary. This contrasts with the problem studied here, which is concerned with the nonsteady-state behavior in an infinite reservoir. The exact solution of the partial penetration problem presents great analytical problems because the boundary conditions that solutions of the partial differential equations must satisfy are mixed; i.e., on one of the boundaries the pressure is specified on one portion and the flux on the other. This difficulty occurs at the wellbore, for the flux over the nonproductive section of the well is zero, and the potential over the perforated interval must be constant. In the case of constant rate production from the well, this uniform potential is time dependent and unknown, and the additional condition that where hl is the thickness of the perforated interval, must also b&apos;e satisfied. This problem may be overcome in the case of constant rate production by making the assumption that the flux into the well is uniform over the entire perforated interval, so that on the wellbore the flux is specified over the total formation thickness. This approximation naturally leads to an error in the solution since the potential (pressure) will not

Jan 1, 1970

By J. C. Swartz

New measurements of graphite and cementite solubilities in ferrite have been obtained to resolve disagreements among previous data. To measure graphite solubility, specimens of iron were equilibrated with rarious carburizing atmospheres at temperatures be-twee~z 480" and 1435°C. The carbon activity of each atmosphere relative to graphite was taken from published data. After quenching from each equilibration treatment the concentration of carbon (typically 10 pprn by wt) was determined from the height of the Snoek peak in the internal friction spectrum. A few inclividual analyses by combustion support the reszdts of Smith on the solubility of graphite near the eutectoid temperature. Combination of these combustion and internal friction analyses determines In a, (at 0.01 wt pct) = 24,000/RT - 12.72, where a, is the activtity relative to graphite in ferrite at fixed cornposition. The same specimens were used to determine the solubility of self-stressed cementite precipitates. The results indicate solubilities of 6.3, 23.2, and 68 pprn carbon by wt at respectively 400°, 500". and 600°C. The once large discrepancy between the cementite solubility determined by internal frictiori and that calculated from flee energy data has been almost completely resolved. A recent study1 (hereafter designated I) on the solubility of cementite in a iron did not fully resolve the disagreement among previous data. The remaining disagreement is illustrated by the phase diagram in Fig. L The data of I are represented by the line labeled "stress-free" cementite. They determine a heat of solution of cementite of (14.8 * 0.2) kcal per mole which contrasts with the (20 * 1) kcal per mole derived from Smith&apos;s graphite solubility2 and the formation energy of cementite.3 Toward resolving this disagreement we have obtained new data on the solubilities of graphite and cementite. METHODS As in I the Snoek peak in the internal friction spectrum was used to measure the concentration of carbon dissolved in ferrite. This method relies on the relation C=kQ-1 [1] in which C is the concentration of dissolved carbon, Q-I is the Snoek peak height, and k is a proportionality factor which is a function of the peak temperature, polycrystalline texture, and other parameters characteristic of the ferrite lattice. To determine true heats of solution via Eq. [1], it is necessary to establish that k is independent of the temperature from which the specimen is quenched. Some evidence on this point is contained in a separate report.* Additional evidence is shown by the data points in Fig. 1. These represent the Snoek peaks of two specimens carburized to about 10 ppm C, copper plated, and quenched first from 888º then from 588°C. The copper plate was removed before each Snoek peak measurement. These data show that there is no detectable dependence of k on quenching temperature. The solubility of graphite was determined by repeatedly carburizing various specimens of iron wire with gas mixtures of known carbon activity relative to graphite. To cover a wide temperature range within the a phase boundaries it is desirable to use as low a carbon concentration as is compatible with reasonable precision. With the present internal friction apparatus the best compromise of these desires is a concentration near 10 wt ppm. The dashed line in Fig. 1 was used to approximate the activity of carbon* for

Jan 1, 1970

By Lawrence A. Shepard, Richard H. Krock

A series of ductile, two phase W-Ni-Fe composites, sintered in the presence of a liquid phase, were tested in tension. Identical room temperature stress-strain curves were obtained for specimens containing from 80 to 92 wt pct W (58 to 75 vol pct W particles). The composites exhibited a maximum elongation of 29pct at room temperature, and 10.7 pct at 77 °K. The tungsten particles in the composite elongated by the same amount at these temperatures. Single-phase alloy specimens matching the composition of the composite matrix showed about one half the flow stress of the composites. The test results demonstrated that the mechanical properties of W-Ni-Fe composites are determined by the tungsten particles alone and are independent of matrix volume fraction or mean free path over the composition range studied. A general prediction of the plastic behavior of two-phase alloys or composites from a knowledge of the properties, size, shape, and dispersion of the individual components is not, at present, possible. The excellent theoretical and experimental exposition of the dispersion-strengthening problem applies only to cases where the stronger phase is present as fine particles and in volume fractions of a few percent. Materials in which the stronger phase constitutes a significant fraction of the volume, although of broad engineering interest, have received comparatively little analytical attention. This important group of materials is the concern of the present study. The degree of deformation of each phase during the plastic working of a ductile two-phase alloy has been established by Boas and Honeycombe,1 Clare-brough,2 and Clarebrough and berger.3 These workers empirically correlated the recrystallization temperature of the individual phases with the degree of cold work sustained by each. It was shown that the deformations of both phases are equal and therefore the same as that sustained by the composite whole when the volume fraction of the stronger phase exceeds 35 pct. At yielding, however, deformation begins in the weaker phase. A direct correlation of composite strength, as a function of deformation, with the strength of the individual components cannot be made. In the presence of stronger phase particles, the flow stress of the weaker matrix phase is enhanced by an additional hydrostatic component. The development and potential magnitude of matrix strength promotion upon straining has not even been experimentally established. Quantitative work in this field has been confined to ceramic-metal composites. These materials fracture at strains considerably below 1 pct by cracking of the ceramic particles.4-6 An indication of the potential constrained matrix strength capacity is given by the observation by Nishimatsu and Gur-land4 that the maximum tensile strength of a WC-Co composite is almost double the bulk strength of the cobalt matrix. The relationship between composite strength and geometry is ordinarily expressed in terms of the mean-free matrix path (referred to subsequently as MFP) between the stronger particles.* This factor takes into account both the volume fraction of matrix phase and the average size of the particles. unke17 concluded that composite strength varied directly with the decreasing log MFP, following the Gen-samer8 relationship. However, Gurland and ~radzil~ reported a strength maximum at an MFP of the order of 1 p in WC-Co composites. A ductile two phase metallic composite was chosen for the present investigation of composite mechanical properties with the view of avoiding the difficulties and ambiguities noted above. The W-Ni-Fe heavy alloy of Green, Jones, and pitkin9 contains 80 to 94 wt pct W, and nickel and iron in a weight ratio

Jan 1, 1963

By T. R. A. Davey

IN 1947 the author became interested in the fundamental aspects of the desilverizing of lead by zinc, conducted some experimental work, and searched the technical literature for all available fundamental data. Since then a revival of interest in the subject in Europe resulted in the appearance of quite a number of papers. It became evident that it would be more profitable to collect together and examine thoroughly the results of various workers, than to attempt to duplicate the experimental determinations. There are many inconsistencies in the various publications, and it is opportune to review at this time the present status of knowledge on the Ag-Pb-Zn system. There is also a need for a clear description, in fundamental terms, of the various desilverizing procedures. This paper is presented in four sections: 1—There is an historical review of the origins of the Parkes process, of the results of many attempts to find a satisfactory fundamental explanation for the phenomena, and of the modifications proposed to date. 2—A diagram of the Ag-Pb-Zn system is presented. This is believed to be free of obvious inconsistencies or theoretical impossibilities, although thermodynamic analysis subsequently may reveal errors. 3—The fundamental bases of the various desilverizing procedures, which have been used up to the present day, are described; and a new method is suggested for desilverizing a continuous flow of softened bullion in which the bullion is stirred at a low temperature in two stages producing desilverized lead at least as low in silver as that from the Williams continuous process and a crust which, on liquation, yields a very high-silver Ag-Zn alloy. 4—A suggestion is made for the revival of de-golding practice, following a recently published account which does not seem to have attracted the attention it deserves. The terms "eutectic trough" and "peritectic fold" as used in this paper are synonymous with "line of binary eutectic crystallization" and "line of binary peritectic crystallization" as used by Masing.&apos; The German literature on ternary and higher systems is rather extensive and a fairly general system of nomenclature has arisen, whereas in English usage the corresponding terms are not as well established. For this reason the meanings of terms used in this paper, together with the equivalent German terms, are given as follows: 1—Eutectic trough—eutektische rinne: line at which a liquid precipitates two solids S1 and S2 simultaneously. If the composition of a liquid which is cooling reaches this line, it then follows the course of this line until a eutectic point is reached, or until all the liquid is exhausted. The tangent to the eutec-tic trough cuts the line joining S1S2. 2—Peritectic fold—peritektische rinne: line at which a solid S1 and a liquid L transform into another solid S2. If the composition of a liquid which is precipitating S1 reaches the line, on further cooling only S2 is precipitated. The liquid composition moves from one phase region (L + S1) into the other (L + S2), and does not follow the course of the boundary. The tangent to the peritectic fold cuts the line S1S2 produced nearer S,. 3—Liquid miscibility gap, or conjugate solution region—mischungslucke: the region within which two liquid phases coexist in equilibrium over a certain range of temperature. A system whose composition is represented by a point in this region comprises one liquid at high temperature; then as the temperature is progressively reduced, two liquids, one liquid and one solid, one liquid and two solids, and finally three solids. 4—Liquid miscibility gap boundary—begrenzung der flussigen mischungsliicke: the line along which the surface of the miscibility gap dome, considered as a solid model, intersects the surrounding liquidus surfaces. 5—Tie lines—konoden: lines joining points representing the compositions of two liquids, a liquid and a solid, or two solids, in equilibrium. In binary systems the only tie lines customarily drawn are those through invariant points, e.g., through the eutectics of the Pb-Zn and Ag-Pb systems, or the various peritectics of the Ag-Zn system, as in Figs. 1 to 3. In ternary systems it is desirable to draw sufficient tie lines to indicate the slopes of all possible tie lines. 6—Ternary eutectic point—ternares eutektikum: point at which liquid transforms isothermally to three solids, S1, S2, and S Such a point can lie only within the triangle 7—Invariant peritectic (transformation) point— nonvariante peritektische umsetzungspunkt: (a) — On the miscibility gap boundary, the point at which two liquids and two solids react isothermally so that L, + S, + L, + S2. (b)—On the eutectic trough, the point at which a liquid and three solids react iso-thermally so that L + S, + S2 + S3. Such a point must lie on that side of the line joining S,S which is further from S,. (c)—A further possibility, not found in this ternary system, is that the point is at the intersection of two peritectic folds when the reaction concerned is L + S, + S, + S Historical Introduction Karsten discovered in 1842 that silver and gold may be separated from lead by the addition of zinc.2 Ten years later Parkes used this fact to develop the well known desilverizing process which bears his

Jan 1, 1955

By Seymour G. Epstein

Using a modified capillary-reservoir technique, electromigration of dilute solutions of silver in liquid bismuth has been measured with relatively good precision. The effects of experiment duration, temperature. current density, and silver concentration have been investigated. Chemical diffusion coefficients of silver in liquid bismuth were also measured at temperatures ranging from 300°to 600°C. The effective valence of silver in bismuth was calculated as a function of temperature from a comparison of electric mobilities and diffusion coefficients. In an alloy containing 1 wt pct Ag, the electric mobility of silver increased from 1.65 x X sq cm per v-sec at 300°C to 2.38 x 10-4at 600°C; the diffusion coefficient in-creased from 3.0 to 17.5 x 10-5 sq cm per sec over the same temperature range. Calculated values of effective valence decreased from 0.28 at 300°C to 0.10 at 600°c. ALTHOUGH there has been considerable progress in the theoretical treatment of electron-transport properties in liquid metals, the mechanisms of mass-transport phenomena in liquid metals are still not clearly understood. This is especially true for the case of electro migration, alternatively termed elec-trotransport or electrodiffusion, which is mass transport induced by an applied electric field. A thorough knowledge of the mechanisms governing electromigration will considerably aid in understanding the electronic state of an impurity atom in a liquid metal. Electromigration has been long observed and studied in liquid metals and alloys. However, no satisfactory theory to explain the observed effects has been developed. The disparity in the present theoretical treatments, summarized by Verhoeven,1 has been attributed to the difficulty in describing the momentum transfer between electrons and ions and to the lack of precise measurements in liquid metals, especially at elevated temperatures. Prior to the last decade most of the electromigration studies were qualitative, in that only the direction of migration of alloy constituents was determined with any degree of reliability. These results have been summarized by schwarz,2 who was able to measure the electric mobility of several elements in mercury. More recently electromigration in liquid metals has been measured by a variety of techniques, with a varying degree of success. Mangelsdorf3,4 made precise measurements on dilute amalgams at room temperature, using a technique relating changes in composition to changes in alloy resistivity, but was unable to make measurements at elevated temperatures. Using a modification of this technique, Verhoeven and Hucke5 measured electromigration and resistivities in liquid Bi-Sn alloys. However, the resistivity technique is not sensitive to small composition changes and is impractical for very dilute alloys. Verhoeven and Hucke6 also measured electromigration of several solutes in liquid bismuth by adapting the capillary-reservoir method for determining diffusion coefficients in liquids. The reported precision of these measurements was poor, however, primarily due to the large uncertainties in the chemical analyses to determine concentration changes. Belashchenko7 has summarized the recent Russian investigations of electromigration, many of which, however, are of questionable accuracy. The present study was initiated to develop an experimental technique which would be both versatile and sufficiently sensitive to yield precise measurements of electromigration of solutes in dilute metal alloys at elevated temperatures. Using this technique, a comprehensive study of silver in liquid bismuth was made to determine the effects of experimental variables on the apparent electric mobilities. Chemical diffusion coefficients of silver in liquid bismuth were also measured over the same temperature range for comparison with the electromigration data. EXPERIMENTAL TECHNIQUE Electromigration Measurements. Electromigration of silver in liquid bismuth was measured by the capillary-reservoir technique, similar to that used by Verhoeven and Hucke,6 but modified to yield more

Jan 1, 1967