Search Documents

By R. F. Hehemann, S. T. Zegler

The w phase in zirconium alloys containing more than G pct Nb can form in a difjUsionless manner during quenching or with composition change during aging at temperatures below 550°C. The latter treatment establishes a metastable equilibrium between an w phase containing 5 pct Nb and a ß phase containing 45 pct Nb. The superconducting transition temperat~ire of quenched Z?-10 pct Nb and Zr-15 pct Nb alloys is increased by aging at 375°C and both alloys exhibit the same Tc after prolonged aging. The superconducting transition both in the quenched and in the aged alloys is relatively sharp (occurring ovev a temperature range of <0.5°K), and is interpreted in terms of the microstructure that characterizes the ß-w) mixture and proximity effects postulated for thin-film superconductors. At elevated temperatures alloys of the transition elements from groups 4 to 6 in the periodic table exhibit wide ranges of mutual solubility in the bcc structure. Except for compositions that are high in a group 4 element? the bcc structure can be retained at room temperature by quenching and several systematic studies of the influence of composition on superconductivity in bcc alloys have been reported.&apos;&apos;2 The high-temperature bcc form (ß) of the group 4 elements—titanium, zirconium, hafnium—is not retained upon quenching but instead transforms marten-sitically to the hcp structure (a). The Ms temperature can be lowered by alloying the group 4 metals with a solute from a higher group and with a critical amount of solute the martensitic transformation can be suppressed. The 3 phase, however, is not retained without modification. Rather, a metastable phase, w (in particular in titanium- and zirconium-base alloys), occurs over a fairly wide range of compositions above that required for suppression of the martensitic transformation.3,4 As in the formation of a, the transformation of ß to w occurs in a diffusionless manner during quenching and the temperature for its initiation (ws) is lowered by increasing solute content. The ws temperature can be well below room temperature and reversibility of the transformation allows w that forms on cooling to low temperatures to disappear again when the sample is returned to room temperature.5 In Zr-Nb alloys the w phase can also be formed during aging at temperatures below 550°c.5 In this treatment, a metastable equilibrium is established between a niobium-rich ß phase and a zirconium-rich w phase. The present study of Zr-Nb alloys was undertaken to examine the influence of microstructure: as controlled by composition and heat treatment, on the superconducting transition temperature, Tc. MATERIALS AND PROCEDURE The alloys were prepared from zirconium crystal bar that was spectrochemically pure except for 30 ppm of Al, 40 ppm of Cu, 100 ppm of Fe, and 1 ppm of each B and Pb. The niobium used was 99.5+ pct pure containing according to the suppliers&apos; (Stauffer Chemical Co.) analysis a maximum of 50 ppmO, 60 ppm of N, 30 ppm of C, 5 ppm of H, 200 ppm of Ta, 50 ppm of Mo, and 15 ppm each of Fe, Co, and Ni. The alloys were prepared in the form of buttons weighing approximately 4 g by arc melting on a water-cooled copper hearth in an inert-gas atmosphere. All alloys were heat-treated in the ß-phase region for 3 days at 1000°C and water-quenched. For heat treatment, the specimens, 0.5 cm in diam by 1.0 cm long, were wrapped in zirconium foil and sealed in an inert-gas atmosphere inside quartz capsules. Quenching was done by breaking the capsules under water. Subsequent aging treatments of Zr-10 pct Nb and Zr-15 pct Nb alloys were done by placing the specimens in a lead bath at 375°C and quenching in chilled brine. The phases present in the quenched and aged alloys were identified by optical and X-ray metallography. X-ray powder patterns were taken at room temperature with a 114.6-mm-diam Debye-Scherrer camera and CuK-a radiation. Superconducting transition temperatures were determined from magnetic-permeability measurements6 in a 10 oe field. The superconducting transition temperature was determined from a plot of galvanometric deflection as a function of temperature by extrapolation of the linear portion of the curve to zero deflection. In Figs. 1 and 3 the arrows indicate the temperature range of the transitions. RESULTS AND DISCUSSION Superconductivity in Quenched Alloys. In Fig. 1 Tc for alloys quenched from 1000°C is plotted against nominal composition. Indicated also in Fig. 1 are results of metallographic studies. Alloys containing less than 5 pct Nb transform martensitically to a during quenching from 1000°C and Fig. 1 demonstrates that Tc increases significantly as the niobium concentration in a is increased. On the basis of the Bardeen-Cooper-Schreiffer theory of superconductivity7 it seems most likely that this increase in Tc results from an increase in the density of electronic states as zirconium is alloyed with niobium. This increased density of states has been revealed clearly in low-temperature specific-heat measurements.8 The martensitic transformation to a is suppressed when the alloy content exceeds 5 pct Nb. In the range from approximately 6 to 30 pct Nb, quenched alloys consist of a mixture of B and w phases and the amount

Jan 1, 1967

By J. N. Maycock, P. W. M. Jacobs

Previous measurements of the thermoelectric power of ionic crystals are reviewed briefly. It is concluded that, while extensive measurerements are available on systems in which the electrode M has a cation in cornon with the sall MX, there is as yet little modern work on systems in which the metal electrode M&apos; does not haue a calion in common with the salt. We haue now measured the thermoelectric power of- single cryslals of KC1 and of KC1 + SrCl2 between plati.nu?n electrodes over a much wider range of temperature than before. individual ionic heats of transport, which, while probably not very accurate, are of a reasonable order of magnitude, are obtained from this data on the basis of an assumption that charge carriers do not cross the electrode/salt interface. RELATIVELY little work has been done on thermal diffusion in ionic crystals. Reinhold and coworkers1-I measured the thermoelectric power and Soret effect in silver and cuprous salts and their mixed crystals. One electrode was kept at constant temperature and electromotive force was measured as a function of the temperature gradient. This is not a satisfactory technique if the results are to be compared with theory; rather should the electromotive force be measured for small temperature differences as a function of the mean temperature of the two electrodes. They used electrodes having the same cation as the salt. Patrick and Lawsons measured the thermoelectric power of AgBr and of AgBr containing 0.25 mole pct CdBr2 using silver electrodes and temperature gradients of 10°C in the temperature range 100° to 400°C. The results were analyzed using the Teltow9 values of the ratio of the mobility of the two types of charge carrier (cation vacancies and interstitials) found from conductance measurements and the wagnerlo estimate of the heterogeneous contribution to the thermopower, Ohet They obtained values of qi = 0.017 ev and q$ = -0.385 ev for the heats of transport of interstitial Ag ions and cation vacancies, respectively. Their data has been reanalyzed by Haga using the corrections to the Wagner formula for ehet given by Howard andLidiard; Haga found ev. Christy et a1.14 have measured the thermopower of AgBr containing 0.01 to 1.0 mole pct CdBr,. They analyzed their results in terms of the theory of Howard and Lidiard and found that excellent agreement with the theory was obtained if q5 + : + hF was set equal to 0.70 ev at 175°C and equal to 0.58 ev at 250°C. Since Teltow&apos;s value for hF, the enthalpy of formation of a Frenkel defect pair, is 1.27 ev, this means that qt + q: increases in magnitude from -0.57 ev at 175°C to -0.69 ev at 250°C. This result is in poor agreement with Patrick and Lawson&apos;s value of -0.37 ev for pure AgBr (for which the corrections to the Wagner estimate for ehet are very small). christy1&apos; has also reported thermopower measurements for pure silver halides and for the systems he finds that qr + qt for AgBr increases in magnitude from about -0.55 ev at 150°C to about -1.1 ev at 400°C. The temperature dependence of the sum of the heats of transport in AgCl is very similar in magnitude. The sum qi + q cannot be decomposed into the individual interstitial and vacancy heats of transport without a knowledge of the entropy contribution from the change in the lattice vibrational frequencies around the interstitial and vacancy. Despite this it seems an inescapable conclusion from Christy&apos;s analysis that and -6 = Q Ag are quite strongly temperature-de pendent and that -q: is much greater in magnitude than the corresponding activation energy for vacancy migration, +0.37 ev. It remains a mystery as to why the data for pure AgBr are fitted so well by the assumption of temperature-independent heats of transport if association of impurity ions and vacancies is neglected.l The values for q$ and q: so obtained are also much more in line with those expected from a simple kinetic interpretation of the heats of transport due to wirtz.17 Christy and Hsueh have also measured the thermopower of CuCl between copper electrodes; 0 for pure CuCl is comparable with that for the silver halides but, owing to the limited solubility of divalent cation impurities it was not found possible to deduce values for the heats of transport. In contrast to these extensive measurements on cells of the type M MX 1 M, there have been relatively few attempts to measure the thermoelectric power of cells of the form M&apos; 1 MX I M&apos;. (We specifically exclude from discussion cells of this type in which the metal electrodes M&apos; are in contact with gas containing a controlled partial pressure of either M or X,, since in these cells the electrochemical reactions are analogous to those of the first type.) The thermoelectric power of Pb12, PbC12, TlC1, TlBr, TlI, NaNO3, and KNO 3 between platinum electrodes was measured by Thie1e.l3 In discussing these measurements Holtan20 asserts that the thermopotential initially fluctuated wildly and even changed sign before approaching a steady value. A high degree of irreproducibility is also evident in the work of Nikitinskaya and Murin21 who first studied the thermopower of NaCl and KC1 between platinum electrodes. Much better reproduci-bility was achieved in our earlier measurements on KC1;22 these were, however, confined to a relatively narrow temperature range and one of the objects of the work reported in this paper was to extend the temperature range of the measurements of the thermoelectric power 8 of KC1. The only other published

Jan 1, 1967

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

By Earl G. Alexander, W. R. Runyan

The nature of silicon growths which form on amorphous silicon dioxide during epitaxial deposition in unmasked areas was investigated. Octahedral silicon crystals nucleate and grow on the oxide at pinholes, adjacent to foreign matter, and probably at oxygen-deficient sites. Generation of these oxygen-deficient sites on the oxide surface is shown to be thermody-namically favorable under usual deposition conditions. The conditions which affect saturation (SiCl4 concentration, flow rate, temperature) determine the number of sites on which silicon will nucleate and grow. Reaction product HCl is likely responsible for suppressing silicon growths on the oxide near exposed areas of silicon. Evidence is given that the oxide-silicon interaction occurs in hydrogen only and involves water as a transport agent. SINCE shortly after the first epitaxial layers of silicon and germanium were grown over large areas, efforts have been underway to grow selectively on specified portions of the surface. Such selective growth should be particularly applicable to monolithic integrated circuits. Usually the approach has been to use a mask to delineate the desired area,&apos;-7 but the VLS methoda can also be used, and direct programmed atomic beam deposition has been suggested.9 The masking techniques may embody two forms: in one the mask is a material which can later be removed along with any growths attached to it; in the other, attempts are made to prevent growth on the mask, so that over a whole slice the only deposition that will occur is in the unmasked regions. The present work is concerned with only the latter case, and specifically with silicon. Joyce and Baldrey1 suggested the use of thermally grown silicon dioxide as a mask material and showed that for the proper choice of operating conditions (total flow, SiCl4 concentration, total deposition time, and temperature) spurious growth could be minimized and that if the deposition times were not too large, and the criteria not too stringent, a usable process occurred. Later Schnable et al 4 observed that after extended deposition times, during which most of the silicon dioxide became covered with growth, there was always a band of oxide around the exposed silicon area that was quite free of spurious silicon crystallites. This latter observation is particularly intriguing since it extends the hope that with proper precautions masking can be much more versatile than it presently is. EXPERIMENTAL PROCEDURE Silicon substrates oriented to within 1.5 deg of a (111) plane were prepared by etch polishing lapped

Jan 1, 1967

By Victor A. Phillips

A series of specimens of a Cu- 3.23 pct Co alloy were prepared with particle diameters from zero to 590A. The samples were then cold-rolled 95 pct and the effects of the particle size on the behavior on annealing for hr at temperatures between 100" and 900°C were studied (by hardness, light, and electron metallography). Particles, particularly for d r 105 to 590A, greatly impeded softening and vecvystallizn-tion, and tended to give elongated grains. Particles deformed fairly homogeneously with the ,matrix, be- IN a previous study by the author,&apos; the growth of cobalt-rich precipitates was followed electron microscopically in Cu-3.12 Co alloy as a function of aging, typically at 650°C. The coherent spherical precipitates grew to 520 + lOOA average diam before spontaneously losing coherency and developing (111) facets. Stretching a few percent after precipitation 2aused loss of coherency to occur sooner at about 220A average particle diam. The particles apparently retained their fcc structure after loss of coherency. coming lau2ellae. For d = 55 to 180A, these lamellae gave streak-contrast effects apparently due to coherency strains , and spheroidized on annealing at 600" to 650°C, forming coherent particles. Particles of d = 250 ov 320A lost coherency during t-olling, giving incoherent lamellae. Recrystallization apparently occured by growth of new grains into unrecrystallized (recovered) material at temperatures below that at which cobalt atoms had much mobility. The present study was undertaken to explore the effect of cobalt-rjch particles of various average sizes from 50 to 600A diam on the isochronal annealing behavior of copper after heavy cold rolling. The previous work&apos; was used as a guide in preparing the two-phase series of prerolling structures. The solution-treated alloy was also rolled for comparison. A further question of interest in the present study was whether dislocation and particle hardening were additive, since the prerolling structures covered the full range unaged - peak aged — overaged, and further precipitation might occur on annealing after cold rolling. Although there have been exhaustive studies of the isothermal2"6 and is~chronal annealing behavior of

Jan 1, 1967

By O. Hoover, M. Herman, V. V. Damiano

The Jetter and borie&apos; teclznique of determining textures using a spherical specimen has been applied to tlze study of compression-rolled beryllium sheet. Snzall spheres the order of 1 mm in diam cut from the beryllium sheet were autotnatically rotated about tz41o axes using the G.E. single-crystal goniometer. Quantitative pole figures were obtained without tke need to apply absorption corrections. Compression-rolled beryllium exhibited peak intensities ,for (0002) planes of positions tilted 10 deg to the rolling plane and a near random distribution of (1010) planes about the nornal to the rolling plane. TECHNIQUES for determining textures of rolled sheet material are amply described in the literature. The techniques are found to be variations of two basic methods. One due to Decker, Asp, and arker, referred to as the transmission method, utilizes a thin-sheet specimen in which the X-ray beam enters the specimen from one side and the intensity of the beam which emerges from the opposite side is measured. The second method due to chulz,3 referred to as the reflection method, utilizes a thick specimen and the intensity of the beam emerging from the same side is measured. The two rotations of the specimen in the beam are designated a and 8. In order to completely determine the texture of sheet material, it is generally necessary to use a combination of the two methods. The calculations involved in correcting the raw X-ray data for absorption effects and the combining of the data obtained by the two methods are very laborious and time consuming. To avoid the intensity corrections which arise as a result of the changing diffraction volume and path length within the sample other methods have been proposed. The Norton method utilizes a cylindrically shaped specimen cut from the sheet material. Since the rods have rotational symmetry, the absorption correction is constant for rotations about the sheet texture. Jetter and Borie&apos; employed a spherical specimen to analyze the fiber texture of extruded aluminum rods. The spheres were rotated rapidly about the fiber axis to include a large number of grains in the X-ray beam and changes in intensity with respect to tilts of the fiber axis were measured. The absorption correction was constant for all angles and was neglected. The Jetter and Borie&apos; technique finds excellent ap- plication to very fine-grained low-absorbing metals in which the entire sphere volume can contribute to the diffraction volume. In the case of low-absorbing metals, however, serious limitations on specimen thickness occur as demonstrated by Braggs due to de-focussing effects. Peak shifts may occur which negate the assumption that integrated intensities are proportional to peak intensities. These limitations in sphere size to the order of 0.5 to 1 mm for beryllium require that the grain size be sufficiently small to include a large enough statistical sample. The present paper describes the application of spherical specimens less than 1 mm in diam to the quantitative determination of pole figures for compression-rolled beryllium sheet having a grain size the order of 10 p. EXPERIMENTAL 1) Specimen Preparation. Two techniques for spark-machining beryllium spheres were tried. One involved the use of a hollow cylinder as a cutting tool. The tool was fed into the rotating cylindrical specimen as shown in Fig. l(a). The hollow cylinder was carefully aligned such that the axis of the cylinder and the axis of the specimen lay in the same plane and were 90 deg to each other. As the hollow cylinder was fed into the rotating cylindrical specimen, a spherical shape was formed as shown in Fig. 1. Alignment was very critical. Slight misalignment resulted in the formation of a barrel-shaped specimen instead of a sphere. A second technique involved the use of a cutting wheel shaped as shown in Fig. 2 with a groove of the desired radius. A section of the sheet specimen was first turned into a cylinder on the left part of the cutting wheel. It was then shifted to the right and a spherical specimen was turned as shown in Fig. 2. The axis of the cylinder lay in the plane of the sheet. Flats corresponding to the rolling plane of the sheet were used to grip the specimen during the machining operation and these served to identify the rolling plane of the sphere. 2) Rotation of Spec=. The spherical specimen is shown mounted on the G.E. single-crystal goniometer in Fig. 3. The knob A of the goniometer shown in Fig. 3 rotates the specimen about the pedestal axis. These angles have been designated as @ angles. The knob B rotates the specimen about an axis perpendicular to the pedestal axis. These angles have been designated as p angles. A device was made to automatically drive the single-crystal goniometer by means of two flexible shafts connected to the A and B knobs as shown in Fig. 3. The motor system was designed to rotate the knob A, thus rotating the specimen through angles of $I while the B knob remained stationary. After one complete

Jan 1, 1967

By T. G. R. Rawlins, L. E. Brosselard

Direct platinum carbon replicas have been used to study substrates prior to growth and after initial nu-cleation of the layer. Replicas have been directly stripped and correlations have been made with other replica techniques. Mechanically polished substrates are very flat with occasional areas of "dirt", which is apparently silicon. When such substrates are etched in hydrochloric acid gas, scratches and hexagonal defects (thought to be polishing compound) are revealed, together with areas of apparent redeposition. Chemically polished substrates are much less flat although much more homogeneous in appearance. Heat treat)nents have no effect. Nuclei deposited on these surfaces, using a normal silicon tetrachloride system, have been examined. Nuclei on mechanically polished subsrates occur in random areas only, whereas on chemically polished surfaces they are more uniformly distributed. THE interest in the study of thin films and now their rapidly expanding use in many fields has increased over a period of years. Much of this current interest, particularly in the field of single-crystal or epitaxial thin films, has derived its stimulus not only from possibilities for application but also from fundamental electron-microscope studies which have indicated the manner of growth of such layers from the initial nuclei.1-5 Previous work involving study of growth processes may be divided into three categories. First, vacuum deposition, primarily of metals, on a variety of substrates has been studied by electron microscopy and electron-diffraction techniques. These have shown the three-dimensional aspect of nucleation and the remarkable liquidlike behavior of the growing nuclei which coalesce to form a complete layer. More recently this work has been expanded in two ways: by growth inside the electron microscope this has obvious advantages for kinetic studies; and by growth in ultrahigh vacuum—much of this work has been done on semiconductors.8-11 It is of interest to note that metals, specifically gold deposited on rock salt, will form only polycrystalline layers in ultrahigh vacuum unless the substrate surface is contaminated.12 In general the mode of growth for vacuum-deposited semiconductor films is the same as that for metal films. The second method of growth that has been studied is that of electrodeposition.13,14 The little that has been published suggests that the mode of growth is similar to the vacuum case, except that irregularities may perturb the electric field and disturb the growth process. The third and last primary method of growing epitaxial layers is by use of chemical methods. These techniques have generated much interest and much has been published on them. Considerable electron-microscope work has been done on the defects in the layers; however comparatively little work has been undertaken on the initial nucleation and early stages of growth. Confining ourselves now exclusively to the case of silicon, Charig et a1.15 have considered the growth of silicon on silicon substrates by hydrogen reduction of trichlorosilane, and studied the films by means of replica and transmission techniques. Subsequently they have studied the same system for growth on quartz,16 and with the addition of pyrolysis of silane on quartz and alumina.17 Also Manasevit el al. have studied deposits using silane and silicon tetrachloride on sapphire.18-14 Finally, in this volume studies of deposition on beryllia and sapphire are reported. Although Revesz and Evans20 have examined complete layers, grown by means of the widely used silicon tetrachloride reaction, no detailed examination similar to that published by Charig and Joyce21 for the trichlorosilane system has been given. Therefore this investigation has examined substrate surfaces prior to growth and then nucleation on these surfaces for the silicon tetrachloride system. EXPERIMENTAL In this work the surfaces have been studied by means of standard replica techniques. Because of the very real problems associated with artifacts introduced,22 different replicas and different cleaning

Jan 1, 1967

By John J. Reed

This paper was prepared as a supplement to the general review by Dr. N. G. W. Cook. His analysis of the problem in terms of the strain energy involved in making the excavation is excellent. It will contribute much towards a clearer understanding of rock behavior and control. Several of the practical applications described herein can be directly related to Dr. Cook&apos;s theories and conclusions, and are based on the very same principles. CONTROLLED BLASTING IN ROCK EXCAVATION Generally speaking, the natural rock is a relatively strong and competent structural material, if we conserve its inherent good properties and perhaps reinforce its weak spots. The difficulty often lies in blasting out the tunnel or chamber without damaging the walls and roof we wish to have remain afterwards. Much progress has been made in the last five years in better understanding the controlled excavation of rock. The specialized techniques known as smooth wall blasting and presplit blasting have now developed from the status of curiosities of rock excavation to the point where these techniques are specified in contracts drawn up for such rock excavation projects as tunnels, underground pourer houses, etc. These techniques have been well described and discussed in previous publications; there is no need to reiterate here. It might be well to point out that recent research has demonstrated the effect that inherent rock stress may have on presplitting in certain directions. Material can be presplit most readily parallel to the direction of maximum compressive stress, and this may not always be in the direction desired. Inherent rock stress measurements by stress relief over coring, etc., may have important value in deciding how to best presplit proposed excavations. In addition, recent work at the Colorado School of Mines has demonstrated the feasibility of con-

Jan 1, 1967

By Charles E. Lundin, Albert S. Yamamoto

The phase eqrtilibria of the binavy system, Nb-Al, weye established by metallographic, X-ray diffraction, hardness, and thermal-analysis techniques. Three intermediate phases were identijied, Nb3.41, Nb2Al, and NbAl,. The N6,Al and NbAl phases have extensiue ranges of solubility. The maximum solubility of aluminum in niobiuitz is 23.0 i0.5 at. pct (8.0 wt pct) A1 clt 1960" i 10°C. The maximumt solinbility oj niobiunz in alunzinutz is less than 0.3 i0.1 at. pct (1.0 tut pct) fib. The A&apos;h,Al and Nbgl interinediate phases forr peritectically at 1960° 1UcC and 1870" i 1U9C, respectively, zuhereas the NbAl, phase fornts congvuently fio11t the melt at 1605" 10°C. A eutectic reaction oc- The intent of an over-all research program was to develop niobium-aluminide-base coatings for refractory metals since these coatings exhibit useful high- curs at 57.8 i 0.5 at. pct (28.5 wt pet) A1 and 1500" 10°C between NbAl and NbAl3. The aluminum-rich region of the system has a peritectic reaction where liquid reacts with NbAL, to form aluminum solid solution. Structural and lattice -pavarneter data /or the intermediate phases were determined by X-ray diffraction analyses. An unusual transfov?nation having charactevistics of nucleation-growth and martensitic nleclanisils occurs on cooling the niobium solid solution in the region from 18 at. pct (6 wt pct) Al to 23 at. pct (8 wt pct) Al. The transfornzed product on rapid quenchirzg is an acicular NhAl. temperature resistance to oxidation. As a prerequisite, the phase equilibria of the system, Nb-A1, were necessary. A literature survey revealed that the phase-equilibria data reported by various investigators were rather incomplete and conflicting. Therefore a complete determination of the system was undertaken by the authors from 0 to 100 pct of solute addition.&apos; In 1959 Savitskiyz presented a tentative diagram which

Jan 1, 1967

By G. W. Thomas

Jan 1, 1967

By R. W. Vieth, S. A. Bradford

THE orientations of tetragonal tin crystals are commonly examined by either the transmission Laue method or the back-reflection Laue method. The predominant planes and zone axes of the pattern are plotted on a Wulff net and indexed by measuring the angles between planes and directions. The problem of identifying the Laue spots has been approached in several different ways. Nicholas 1 tabulated interplanar angles for ten planes but did not relate the angles to permutation of indices or sign. A table of angles between adjacent planes and of angles between adjacent zones was published by Chandrasekhar and veal.&apos; These tables are very helpful, provided the film shows all the low-order zones that occur within about 20 deg of each other. Frounfelker and Hirthe&apos;s compilation3 of angles between the (001) plane and twenty-nine other planes is useful for the indexing, only if the (001) spot can be found on the film. For all but the simplest orientations, however, more information is needed to index the diffraction spots. Standard stereographic projections, such as those published by Bicelli, 4 provide part of the information required. By their nature, these projections show the positions of only a few zone axes. In the tetragonal system many low-order zone axes are not normal to the planes having the same indices. Consequently, planes and directions can have entirely different positions on a stereographic projection. For example, the [011] zone axis is 33 deg from the normal to the (011) plane. The crystallographic orientation usually has to be deduced from a combination of the predominant zone axes and a few low-order planes that appear on the film. In addition to a standard stereographic projection of the planes, a stereographic projection of the directions is needed. Such a projection can be constructed from the angles given in Table I. To provide more information about angles between planes and directions, we have calculated interplanar angles up to (332) and angles between planes and directions up to [332] on an IBM 1620 computer. The angles are differentiated according to permutations of sign and indices. Those doing research on tin single crystals are welcome to request a copy of these tables from the authors.

Jan 1, 1967

By I. H. Silberberg, R. L. Reed, O. K. Kimbler

interfacial films have frequently been observed at interfaces between certain crude oils and water. Several investigators have postulated that the presence of these films should influence the efficiency of oil recovery in water drive or waterflood operations. They may also influence the stability of emulsions which are sometimes a problem in petroleum production, and may be a factor in the fonation of paraffin deposits in oil well tubing and flow lines. This paper presents a technique with which a modified Langmuir film balance may be used to study the compressibility and collapse pressure of these natural interfacial films. Experimental data are presented for several nude oil-water systems. Data developed are used to infer the phase state of the film as a function of such variables as rate of reduction of interfacial area, ionic composition of the subtrate and pH of the subtrate. A film of known physical characteristics is shown to have a sinnificant effect on oil recovery from an unconsolidated sand pack. Possible applications of these results to petroleum production are discussed. INTRODUCTION The use of water to displace petroleum from reservoir rocks is of major importance both as a primary and a secondary recovery process. As water invades the rock, oil is completely displaced from some pores and left as a discontinuous phase in other pores. The manner in which water moves from pore to pore is strongly influenced by capillary forces. In view of the complexity of reservoir fluid systems, there can be little doubt that complicated interactions take place at both the liquid-solid and oil-water interfaces. One of the more interesting, and least understood, of the phenomena which take place at the oil-water interface is the formation of interfacial films. These films are believed to result from the adsorption of high molecular weight polar molecules at the interface.l.2 Presence of such molecules may cause a striking alteration in interfacial tension. When the oil-water interfacial area of certain crudes is rapidly reduced, a thin region (film) about the interface assumes the appearance of a solid membrane, and striations, wrinkles and gross distortions may occur. If such a film is solid, it should greatly alter the interfacial tension normally assumed to exist between the oil and water phases. If the membrane is continuous, a solid phase would separate the oil and water. Interfacial films between crude oil and water were observed in 1949 by Bartell and Niederhausers who commented upon the apparent rigidity of the films and their possible importance in the petroleum industry. Morrell and Egloff4 had earlier attributed the extreme stability of emulsions of sea water in fuel oil to very stable asphaltic films. Numerous investigators have observed rigid films in the course of crude oil-water interfacial tension determinations by the pendent drop method. Several investigators5,6,2 have separated inter-facially active materials from crudes and attempted to characterize them chemically. Reisberg and Doscher,2 using Ventura crude, showed the interfacial tension against water (as measured by the pendent drop method) to be affected by aging, contraction and expansion of the interface, and the pH of the water. These investigators attributed the adhesion of oil to a water-wetted surface and the distortions of flow paths in glass capillaries to the presence of rigid films. Dodd7 has studied the interfacial viscosity of adsorbed films and found them to be non-Newtonian in behavior. Craighead and Harvey8 reported a series of displacements in tubes packed with 60 mesh glass beads. They interpreted the results as indicating an effect of stearic acid films on waterflood recovery and imply that natural films may produce similar results.

Jan 1, 1967

By J. Grosso, D. J. Nagel

In many metallurgical studies, it is necessary to reveal the composition and structural properties of materials. Usually this is done by etching, but some substances do not etch well or easily. Anodizing is known to provide an alternate treatment in many cases. In general, this technique is simple, often more sensitive to composition differences than etching, has excellent resolution, and provides variable contrast in those elements and alloys which anodize. Here we report the use of anodizing in diffusion studies in the TiCb system. Fig. 1 shows a cross section of the diffusion zone in a TiCb couple. The anodizing has clearly revealed both composition and crystallographic features. The maximum bulk penetration of the titanium into the columbium is marked by a sharp line because of the steep concentration gradient. The titanium grain size and orientation differences are also evident. Variation in the grain size reflects the gradually decreasing columbium concentration.

Jan 1, 1967

By D. L. Kelley

High-viscosity water injection has been proposed for use in reservoirs containing high-viscosity crude oils. Previous publications have largely ignored the possible effects of the connate water on the proposed process. This paper describes experimental work which indicates that the connate water will be forced ahead of the injected water to form a bank of low-viscosity water. This decreases the oil recovery which would be expected if such a bank were not formed. These effects are shown for a range of fluid mobilities and connate-water saturations for a five-spot injection system. In general, oil recoveries using viscous water are significantly greater than for untreated water even though they are less than would be expected if no connate water bank were formed. INTRODUCTION The effect of mobility ratio on the oil recovery of wa-terfloods has been known for many years. Muskat first pointed out that the fluid mobilities (k/µ) in the oil and water regions would affect the performance of the water-flood, and he estimated the general effect of these variables.&apos; Since this early work, studies of the effect of mobility ratio on secondary recovery have been reported where mathematical,&apos; potentiometric3 and scaled flow models&apos; were used. These studies have shown that a reduction in the mobility ratio between the oil and the displacing fluid would cause additional oil recovery when water-flooding reservoirs containing viscous crude oils. Studies reported by Pye- nd Sandiford 8 have indicated that chemicals to increase injection water viscosity are now available and can be used to reduce the over-all mobility ratio of a waterflood. Where mobility ratios are controlled by the injection of viscous fluids, the connate water of the reservoir can play an important part in the displacement of the reservoir oil. The purpose of this study was to determine the effect of the connate-water saturation in waterfloods where viscous waters are used for injection. DISPLACEMENT OF THE CONNATE WATER Russell, Morgan and Muskat7 were the first to recognize the mobility of connate waters in waterflooding. They conducted waterfloods on oil-saturated cores containing 20 and 35 per cent irreducible water saturations, and found that from 80 to 90 per cent of the "irreducible" water was produced after only one pore volume of water was injected. However, their experiments were conducted at rates of flow significantly higher than those ordinarily occurring in waterfloods. Also, the cores were only from 4.0 to 8.5 cm long. Brown 4 studied a 100-cm linear sand pack which had been prepared to contain connate water and oil. He used 140- and 1.8-cp oils with injection water of essentially the same viscosity as the connate water. He found that all of the connate water was displaced by the injection water in both cases. However, the injection volumes required for complete displacement of the connate water were considerably higher in the case of the more viscous oil. To verify the results of the foregoing experiment, a 10-ft-long linear model was constructed by packing 250-300 mesh sand in a 1/2-in. diameter nylon tube. The model was evacuated, saturated with a brine of 1-cp viscosity, and flooded with a 41-cp mineral oil to the irreducible water saturation of 10.9 per cent. The model was then waterflooded by the injection of a water solution which had an apparent viscosity of 42.6 cp. The solution consisted of 0.5 per cent methylcellulose in distilled water. The viscosities of the oil and connate water were measured with an Ostwald viscosimeter. The viscosity of the polymer solution was calculated by Darcy&apos;s law using pressures measured during actual flow conditions. The ratio of the mobility in the oil region to the mobility in the inject ion-water region was approximately 0.32. The mobility ratio of the oil region to the connate-water bank was approximately 14. The mobility ratio between the connate-water bank and the injection water region was 0.024. Approximately 84.5 per cent of the recoverable oil was produced before water breakthrough. Immediately following breakthrough, oil and connate water were produced at an increasing water-oil ratio until the viscous injection water broke through. At viscous-water breakthrough, 96 per cent of the original connate water had been produced. After breakthrough of the viscous water, there was no additional production of connate water or oil. The near-

Jan 1, 1967

By H. I. Aaronson, H. A. Domian, G. M. Pound

Zener&apos;s two-parameter theory of the y a reaction in Fe-X alloys is extended to encornpass austenite-stabilizing as well as fewite-stabilizing elements, and is then cottzbitzed with statistical thermodynamic theories of Fe-C alloys to permit development of a ther-modynamic description of the proeutectoid fewite reaction in Fe-C-X alloys. Equilibrium tielines are calculated for tile a + y rep&apos;on from experimental data and frort extrapolations of the y/y +a equilibrium surface. Sectzovs of the y/y + 0 surface are calculaled for the tzetastable sstuation LYL u-kich alloyrtg eleitzents do not partition betzseen azrstenite andfer-rite. The finding that the metastable y/a + y curves Lie close to their equilibriuwz counterparts when X = Si, .Vo, Co, Al, and Cu but well below them when X = A/ln or Ari pr-elides a thermodunamic explanation for the expcri1?7e?ztally obserted absence of partition during the proeutec toid ferrite reartlon in the fortner alloys and for the occurrence of partition at hzgher ternperatures in the latter alloys. Cotarison ofno- patitzoa free-energy changes and y/y i a curr,es in Fe-C-X alloys with the equilibrium 11al1es of these quantities in Fe-C alloys furnishes additional qualitative insight into the irqluence of allojling elements upon the kinetics of the proeutectoicl ferrite reaction. THE introduction of a substitutional alloying element, X, appreciably complicates calculation of the thermodynamics of the formation of proeutectoid ferrite from austenite. As noted in the preceding paper,&apos; the positional entropy of the interstitial species is the principal component of the free energy of an interstitial solid solution with which theory has so far been able to deal. One would expect, however, that other components of the free energy of this type of solid solution may be significantly altered by the addition of a substitutional alloying element. Even if the assumptions are made, by analogy to the case of Fe-C alloys,&apos; that changes in the positional entropy of carbon represent a significant part of the thermodynamic effects of an alloying element, and that the remaining effects can be taken into account by fitting the equations developed on this basis to experimental data on Fe-C-X phase diagrams or on the activities of carbon in alloyed austenite and ferrite, the experimental information available on either of these quantities is not yet sufficiently accurate or extensive, respectively, to make such an approach useful. An attempt made by Zener on the former basis to explain the effects of alloying elements on the thermodynamics of Fe-C alloys in terms of a temperature-independent "free-energy change" (actually enthalpy hane&apos;) required to transfer 1 mole of an alloying element from austenite to ferrite, in which the "free-energy change" was determined by fitting the theoretical relationships developed to Fe-C-X phase diagrams, thus proved inadequate in part because of deficiencies in the available ternary-phase-diagram data.= Other difficulties of a more fundamental nature, however, also indicated the desirability of a different approach to the problem.3y4y6 zener6 subsequently proposed that the free-energy change associated with y — a transformation in pure iron can be decomposed into magnetic and nonmagnetic components. Alloying elements were assumed to affect those components separately. One parameter was used to describe the quantitative effect exerted on each component. These parameters were evaluated from Ms (martensite-start) temperature data and from other experimental information usually either readily available or measurable with acceptable accuracy. Zener applied this treatment only to the calculation of Fe-X phase diagrams in which X is a ferrite-stabilizing element. In the present study, this treatment is extended to include austenite-stabilizing elements, and then combined with treatments previously considered for Fe-C alloys1 to permit calculation of the thermodynamic quantities of interest in the austenite - proeutectoid ferrite transformation in Fe-C-X alloys, where a number of representative, and commonly used alloying elements are chosen for X, including Si, Mn, Co, Mo, Al, Cr, and Cu. The results are used to explain important features of the partition of alloying elements between austenite and proeutectoid ferrite, as reported in a companion paper7 on the basis of electron-probe analysis, and to provide some additional understanding of the influence of alloying elements upon the kinetics of nucleation and growth of proeutectoid ferrite. Portions of this treatment6 have been clarified in the course of a review by Kaufman and Cohen.3 The consolidated summary of these developments with which this section is begun provides a basis for further clarification of the treatment, from which extension to include austenite- as well as ferrite-stabilizing elements is a natural consequence. The division of the free-energy change associated with the 7 - a transformation in pure iron, into two independent components is formally stated as:

Jan 1, 1967

By R. C. Ku, R. G. Davies

The stress-strain behavior of Fe-C and Fe-Ni solid-solution alloys has been investigated at 25°C. It is found that the rate of solid-solution strengthening is dependent upon the strain at which the yield stress is measured, the macroyield stress being much more concentration-dependent than the microyield stress. In fact the addition of nickel does not lead to any increase in the microyield stress of iron. The primary effect of increasing the carbon or nickel content is to increase the slope of the stress-strain curve in the microyield region; this effect has been correlated, by means of transmission electron microscopy, with a decreased ability of the dislocations to cross-slip. It is concluded that the Mott-Nabarro theory is a good description of true solid-solution hardening in these and other iron-base alloys. A.LL theories of the solid-solution strengthening1-4 indicate that the flow stress of an alloy increases both with solute concentration and "misfit" between the solvent and solute atoms. The functional relationship between strength, solute concentration, C, and misfit depends upon the particular theory. Mott and Nabarro1,2 and Schoeck and Seeger3 both predict a linear increase in strength with concentration, while Fleischer4 indicates that the strength should be proportional to C1/2; there are in the literature experimental observations to support both these compositional dependencies.1&apos;8 The experimental evidence used to support the theories is the change in macroscopic yield stress (strain, e, = 10-3) with composition. However, recent investigations have revealed that solid-solution strengthening in a Cu-Al single crystals7 and in Fe-V polycrystal-line" alloys depends upon the strain at which the flow stress is measured; a flow stress in the microplastic range (e = 10-6 to 10-5) is much less concentration-dependent than the macroyield stress. Since the theories of solid-solution strengthening are concerned in particular with the stress to move a dislocation in a dislocation-free matrix, they should only be compared with microyield-stress data; it will be shown that in a material deforming homogeneously the microyield stress (e = 10-6) is approximately the stress to move through the matrix those dislocations which have been nucleated by stress concentrations such as particles or grain boundary ledges.9-11 In contrast, the macro-yield stress is more complex in that it is affected by several phenomena: dislocation multiplication, dislocation interactions, and the ease of propagating slip across grain boundaries. For example, it is experimentally observed that when long-range order12&apos;13 or solute effects10 restrict cross alip the grain boundary

Jan 1, 1967

By D. A. Munro, G. P. Contractor

Fourteen 50-lb laboratory melts were investigated to determine the effect of uranium on the tenpering characteristics of loo-carbon (0.06 to 0.1 pct C) steels. It was found that uranium additions, particularly in the range 0.30 to 0.45 pct, enhanced the hardness and both ultimate and yield strength of the experivzental steels in the quenched and tempered condition. The structural and morphological chazges indicated that uranium retarded tempering of the tnartensite, thereby hindering the normal formation of polygonal ferrite formed in the late stages of tempering. The effect of this was to make possible the re-tension of the acicilar ferritic structure in the uranium-bearing&apos; steels. The iraniuin-bearing steels also showed IVidnzanstatten-type growth of ferrite plates and had large prior austenite grains containing assenzblies of fine ferrite grains, mainly acicular in geometry. The fine-grained ferrite structure and the presence of more numerous and apparently smaller precipitates in the uranium-bearing steels are thought to he principally responsible for the itnproved tensile strength and hardness of the experinzental uranium-bearing steels. At ternperirzg temperatures above 455% (850&apos;F) the ferrite in the higher-uraniun steels nzaintained acicularity and, hence, its strength and resistance to tempering. Uranium did not produce a secondary hardening peak. However, it retarded softening during the third stage of tempering because of its effect of inhibiting the grouth of cementite particles and of retaining the acicularity of ferrite plates. The resistance to coalescence accounted for the slow grocth of the ferrite grains in the uranium-modified steels and, hence, fov the persistence of the acicular ferrite structure. IT had been found previously1 that uranium additions up to about 0.45 pct had no significant effect on the tensile properties of low-carbon steel (0.06 to 0.10 pct C) in the as-rolled and normalized conditions, Fig. 1. On the other hand, it was observed that uranium in excess of about 0.30 pct had an embrittling effect as revealed by Charpy V-notch impact results. It was also noted that, as the uranium content increased, the morphology of pearlite changed from lamellar to feathery and the ferrite grains showed an etching effect resembling striated or dashed markings, suggestive of precipitation. The sharp drop in the impact properties shown in Fig. 2 warranted an assumption that the uranium content of about 0.30 to 0.45 pct may produce some secondary hardening reaction on tempering, analogous to that associated with a Cr-Mo-V steel, which shows very poor CVN toughness at the secondary hardness peak in the tempering curve.1&apos; With this background and the reported findings of Hasegawa and noda that low-carbon uranium-treated steel showed signs of secondary hardening, the present investigation was undertaken to determine the effect of uranium additions on the mechanical properties of 0.10 pct C steels. No attempts were made to investigate in detail the mechanisms of hardening, although some suggestions based on the experiments are made. MATERIALS AND PROCEDURES A series of 50-lb induction-furnace melts was made using AISI 1008 rimming steel billets as the melting stock. The melting, forging, and rolling techniques proven satisfactory in previous projects&apos;-3 were employed as a guide for this investigation. The steel was deoxidized with aluminum (2 lb per ton) prior to the addition of high-purity uranium. The analysis of each melt is given in Table I. Properties were evaluated as a function of heat treatment and are presented in terms of hardness and tensile strength vs tempering temperatures. The variation of hardness with the tempering temperature was studied on the quenched and tempered specimens, some of which measured 0.50 by 0.25 in. diam and the others 0.40-in. cubes. Before quenching, the specimens were vacuum-sealed in glass tubes and normalized at 900°C (1650°F) for 20 min. Following this treatment, the sealed specimens were hardened by austenitizing at 955°C (1750°F) for 20 min and water quenching, and then tempered for 1 hr in the range 150 to 730°C

Jan 1, 1967

By J. M. McCormack, R. K. Saxer, J. R. Myers

ThE Knudsen effusion technique was used to determine the chemical activities of copper and platinum in binary Cu-Pt alloys in the temperature range 1542" to 1673°K. Wiebke and Matthes1 previously obtained chemical activities of copper and platinum in this system at 673° and 923°K by the electromotive-force measurement method. They reported that the copper activities exhibited negative deviation from Raoult&apos;s law at all compositions. The chemical activities of platinum were found to change from a positive to a negative deviation at 923°K. Myles2 recently studied this system in the temperature range 1265° to 1356°K by means of the torsional-effusion technique. His results indicated that both copper and platinum exhibited negative deviation from ideality at all compositions. The use of the Knudsen effusion technique to obtain the vapor pressure of metals and alloys is well-known.3 In this work, Knudsen cells were fabricated from seamless tantalum tubing of 1-in. OD and 0.020-in. wall thickness; cell bases and covers were cut from 0.010-in.-thick tantalum sheet and welded to the cells in an argon atmosphere. Orifices were drilled and reamed to approximate a knife-edge of 30-deg included angle. Calculation based on Balson&apos;s4 derivation showed the orifice to be nearly ideal. All temperature measurements were made with a Leeds and Northrup disappearing-filament-type optical pyrometer at the orifice of the cell, which closely approximated black-body conditions and eliminated the need for emissivity corrections. Details of the experimental techniques used, and the necessary correction factors required during this investigation are essentially those previously described.5,6 Before investigating the Cu-Pt alloys, vapor-pressure measurements were obtained over specimens of pure (OFHC) copper. The pure-copper data5 served to assure the accuracy of the experimental apparatus and technique.

Jan 1, 1967

By W. F. Flanagan, D. H. Polonis, S. D. Dahlgren

Rotation diffraction patterns of Cu-4.84 wt pct Si polymystalline samples were taken during the course of isothel-ma1 affing of the suPersaturated a phase, a diffraction spots were obserzled to streak during the initial stages of aging, and this streaking was similar to the streaking of a spots observed earlier by Barvett with deformed super saturated samples of the same composition. Although it was suggested that stacking faults were the sole cause of styeaking in the deformed samples, the present study has shown that plates with one small crystallite dimension can also contribute to the streaking when there is lattice coherency across close-packed planes. THE decomposition of the supersaturated a phase in Cu-Si alloys has been reported to occur by means of both thermal and stress activation.1-4 According to the Cu-Si phase diagram,3 Fig. 1, the supersaturated a phase (fcc) is expected to transform during aging by the precipitation of the y phase. The results of earlier studies2,4 have indicated that metastable k phase (hcp with nearly ideal close packing) forms initially at temperatures below the eutectoid temperature, after which the k transforms to the a and y phases. Hof-mann et al.4 have proposed a metastable version of the phase diagram, showing the approximate boundaries for k formation below the eutectoid temperature. In view of the close-packed nature of both the a and k phases, it is essential to consider the role assumed by stacking faults in the transformation. Streaking effects have been reported by Barrett 1 in the rotating crystal X-ray patterns of strained Cu-Si alloys and were attributed to stacking faults rather than particle size effects. This deduction was based on the observation that streaks in the diffraction patterns did not occur tangent to the 220fee Debye ring. It is known that the atom movements involved in faulting leave some X-ray reflections unaffected while others are broadened,&apos; and, in particular, it has been shown that faulting will not cause streaking of 220fee reflections tangent to the 220fee Debye ring as would be expected if all the reflections were broadened.&apos; The formation

Jan 1, 1967

By E. M. Tory, P. T. Shannon

An analysis of batch and continuous thickening in terms of the movement of planes of constant concentration (i.e. continuity waves) is presented. Use of solids flux as a primary variable greatly facilitates the analysis and clarifies the relationship between batch and continuous thickening. An "ideal" slurry is defined as one whose settling rate is a function only of the local solids concentration. An analysis of continuous thickening of this ideal slurry in an ideal thickener explains many aspects of the steady — and unsteady — state behavior of real slurries, such as the main features of a thickener&apos;s "solids profile" (including the break attributed to rake action), the sudden appearance at abnormally high feed rates of a zone of constant concentration and the velocity with which it rises, and the effect of detention time at constant weight of sludge per unit area. Where deviations exist, they are explained in terms of the batch settling behavior of real slurries. The purpose of this paper is to interpret continuous thickening phenomena in terms of batch settling behavior. Both types of thickening may be considered as the process of propagating concentration changes, due to the downward movement of the solids, from the bottom of the settling vessel upward through the slurry.&apos; These concentration changes may be either finite or infinitesimal as in the case of the propagation of a continuous concentration gradient. The slurry itself may be moving downward as in the case of continuous thickening. The downward velocity of the slurry may be such that the concentration changes being propagated up from below remain stationary relative to the thickener walls. This is the case for steady-state thickening. It seems appropriate to analyze continuous thickening in terms of the movement of planes of constant concentration. This has already been done for batch settling."3 Although our main interest is in real slurries, there are certain aspects of both types of settling which can be deduced from a theoretical analysis of highly idealized systems. To this end, an "ideal slurry" is defined as one for which the dimensionless settling rate at any point is a function only of the local solids concentration.1,2 An "ideal thickener" is one in which there is no radial variation in either the solids concentration or in the downward component of slurry velocity. The underflow outlet is a point sink. It is to be expected that the behavior of non-ideal systems will deviate in some measure from theoretical results. However, the same characteristics which cause deviations in continuous thickening should be evident in batch settling, permitting a rational explanation of the former in terms of the latter. PREDICTED RESULTS FOR AN IDEAL SLURRY IN AN IDEAL CONTINUOUS THICKENER General Theory: In continuous thickening, the downward solids flux (mass/area-time) relative to the thickener, G, results from two different

Jan 1, 1967