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By John C. Sawyer

The mechanism of catastrophic oxidation of chromium and 446 stainless steel is examined. Data are presented to show that accelerated oxidation of these two materials, as caused by lead oxide, can occur in the absence of a liquid layer contrary to presently accepted theory. An alternate theory is proposed in which the rate of accelerated oxidation is a function of the rate at which lead oxide destroys the protective oxide formed on the base metal. An example of the application of the theory is given for the catastrophic oxidation of chromium in the presence of lead oxide. WHEN stainless iron-, nickel-, or cobalt-base alloys are heated in air to moderate temperatures in the presence of certain metallic oxides, oxidation will proceed at an accelerated rate. This phenomenon, often called "catastrophic oxidation", is most pronounced for the stainless steels. With these alloys the condition is so severe that large masses of oxide will form on the surface of the alloy in 1 hr or less at temperatures of 1200o to 1700oF. While a number of oxides are known to cause this effect, PbO, V2O5, and Moo3 are the most familiar, having been the subject of one or more investigations which have appeared in the literature.1-7 In presenting the results of these investigations, many of the authors have offered possible explanations to account for the more rapid rate of oxidation observed; however, the liquid layer theory as proposed by Rathenau and Meijering 2 has been the most commonly accepted mechanism. The liquid layer theory proposes that a low-melting oxide layer is formed on the surface of the alloy as the result of the interaction of the alloy oxide and the contaminating oxide. When the temperature of oxidation is above the melting point of the oxide on the surface, a liquid layer will form and oxidation will proceed at an accelerated rate. At temperatures below the melting point of the surface oxide, oxidation will proceed more slowly in the normal manner. It is argued that the rates of diffusion of oxygen and metal ions through the liquid layer are extremely rapid thereby accounting for the high rate of oxidation. Various experimental data have been presented to show that the temperature at which accelerated oxidation first becomes apparent coincides with the melting point of the eutectic oxide which would be present on the surface. Some exceptions have been observed, e.g., silver will oxidize in the presence of Moo3 at temperatures below the lowest melting eutectic; on the other hand, stainless steel will not be catastrophically oxidized at 1500oF in a molten bath of PbO and SiO2. In reviewing the various theories which have been used to explain catastrophic oxidation, Kubaschewski and Hopkins 8 favor the liquid layer theory, but note that, ".. .as experimental observations are not altogether in agreement with this theory (liquid layer theory), one should consider it a necessary but not a sufficient condition." In contemplating the liquid layer theory, it appears that sufficient evidence has not been presented to establish the theory beyond question. As a means of further clarification, a program of research was undertaken to determine in greater detail the mechanism of accelerated oxidation as caused by lead oxide. The first part of the program deals with a comparison of the oxidation of both AISI 446 stainless steel and chromium metal in the presence of lead oxide, vs the oxidation of these two materials in air alone. These comparisons are made at a number of different temperatures, most of which are below the melting point of the surface oxides. The second part of the program is concerned with a presentation of an alternate theory of accelerated oxidation exemplified by the system Cr-PbO-Air. PROCEDURE AND RESULTS Several experimental methods are commonly used to follow the progress of oxidation. One of these, the weight-gain method, was chosen for this work. This procedure requires that a specimen of the alloy be weighed, oxidized for a given period of time at an elevated temperature, and reweighed—the difference between the two weights being noted. The weight gain of the specimen represents the amount of oxygen acquired from the atmosphere to transform a portion of the specimen to oxide. In those cases where there is a tendency for the specimen or oxide to volatilize at the testing temperature, additional data must be collected so that a correction factor can be determined. This factor must be applied to the weight change in order to ascertain the actual amount of oxidation which has taken place. The specimens used for this work were 1 1/2 in.

Jan 1, 1963

By Michael Epstein, Daniel E. Rosner

Fume nucleation sufficiently close to vaporizing suvfaces can augment net vaporization rates into cooler environments. Environmental conditions favoring large vaporization rate enhancements are briefly discussed and a previous theoretical treatment of this nucleation phenomenon is generalized to account for the self-regulating effect of condensalion-heat release within the boundary layer. Despite kinetic limitations on homogeneous nucleation, and latent heat release, non-diffusive condensate removal processes appear to make possible large enhancements in steady-state vaporization rates, provided surface temperatures are well below the boiling point. When condensed phases vaporize (or dissolve) into cooler media, the diffusion-limited mass loss rate can be strongly influenced by the process of nucleation/con-densation (or precipitation) within the thermal boundary layer. This condensation process (which typically leads to mists or fumes in the case of evaporation into cooler gases) has the effect of steepening the vapor pressure profiles near the evaporating surface, since the condensation zone acts as a vapor sink. However. the resulting enhancement in the diffusion-limited evaporation rate can be estimated (as first done by Turkdogan1 for the case of molten iron/nickel alloys evaporating into helium) only if one has independent knowledge of the critical supersaturation, sCrit(T), required to homogeneously nucleate the vapor.* In a recent reformulation and generalization of the theoretical model of Ref. 1 it has been shown that, when log sCrit is approximately linear in reciprocal temperature, rather simple expressions can be derived4 for the ratio of the actual rate of vaporization j" to either the minimum (no condensation) rate j"min, or the maximum (equilibrium condensation) rate j"max In the present communication we wish to briefly report on further developments and implications of the formulation of Ref. 4, with emphasis on i) environmental conditions favoring large enhancements in vaporization rate, and ii) the self-regulatory influence of condensation heat release (neglected in Refs. 1 to 4) on predicted vaporization rates. Additionally, we take this opportunity to correct several misprints appear- ing in Ref. 4, and comment on Elenbaas's recent criticism5 of Ref. 1. MAXIMUM POSSIBLE VAPORIZATION RATE IN PRESENCE OF CONDENSATION A nonequilibrium theory is of interest because of the very large difference between the minimum (no condensation) and maximum (equilibrium condensation) vaporization rate. The magnitude of this maximum possible enhancement can be shown quite clearly by combining a result of Refs. 3 and 4 with the fact that for most liquids there is a simple relationship between the molar heat of evaporation, A, and its boiling point, i.e., A/(RTBp) = C, where the constant C, often called the Trouton ratio, takes on values not very different from 11.* More generally, for any substance (including The Trouton ratio (which for water is 13, for methane, 10, and so forth) will be recognized as the ratio of the molar entropy change upon vaporization (at TBP or Ttransf) to the unlversal gas constant R. Its near constancy reflects the fact that the change in atomic order upon vaporization depends only weakly on the kinds of molecules involved. those that sublime under ordinary conditions) we can define a characteristic transformation temperature. Ttransf, by a relation of the form Ttransf =A/(CR), and then examine the maximum possible evaporation rates as a function of how far removed from Ttransf are the surface temperature, Tw, and ambient temperature, T. Subject to the assumptions: 1) equilibrium vapor pressure, pv,eq, everywhere small compared to prevailing total pressure, p, and 2) negligible effect of condensation heat on temperature profile, the maximum enhancement ratio was found (Eq. [17], Ref. 4) to be: where, for most vapors, Nu/NuD (the ratio of heat transfer coefficient to mass transfer coefficient for the same configuration) is a number near unity.* Ex- *An alternative derivation of the Nu = NuD special case of this equation. revealing its validity for arbitrary velocity/temperature profiles in a laminar boundary layer, is given in Ref. 3. amining this result for a "Trouton substance", one obtains the results shown in Fig. 1, constructed for C = 11. Since we are concerned with vaporization enhancements (j'max/J"min > 1) at surface temperatures below Ttransf, this area of interest is shown unshaded. One notes that at a fixed ambient temperature (hence, T/TtranSf) there is a unique surface temperature, 2T , at which j"max/j"min attains its peak value; moreover, the peak enhancement ratio, see dashed locus. Fig. 1, is: (NuA/NuD)(C/4)(Ttransf/T,). Hence, if Nu = NuD, when the ambient temperature is less than 1/4 of TtranSf the peak enhancement exceeds the Trouton

Jan 1, 1969

By D. M. Waldorf

Steam permeability measurements have been made in the laboratory on several samples of natural reservoir materials. The steam temperatures and pressures were selected to simulate conditions which might exist in a reservoir during the injection of steam. For each sample tested, the experimental permeability to superheated steam was comparable to that measured with air and no evidence of plugging was detected. Some samples were exposed to water at various temperatures and plugging was found to occur in materials which contained significant quantities of monmorillonite clay. Temperature had little effect on the degree of plug-ning between 75 and 325 F. The measured pemeabilities tended to increase slightly with temperature, but the changes were small compared with the initial loss of per~neability on wetting. Sequential pemzeability measurements were made on two samples using air, water, steam, water and air, in that order. Both samples were water-sensitive and plugged extensively after the initial injection of water. Upon exposure to superheated steatm the samples dehydrated and their permenbilities to superheated steam were comparable to those initially measured with air. The remaining measuretnetzts with water and air confirmed that the water plugging was reversible and that the samples were not seriorrsly damaged during the tests. INTRODUCTION The swelling of water-sensitive clays during water floods has long been recognized as a potential source of reservoir damage. The recent extensive application of steam injection and stimulation has compounded this problem since both hot water and steam (as well as fresh water at reservoir temperatures) are, at sume time, in contact with the producing zone adjacent to the bore of a steam injection well. The purpose of this paper is to present data which compare the sensitivity of some natural sedimentary rock samples to water at various temperatures, and to super-heated steam. Some properties of montmorillonite clay are briefly reviewed, and comparisons are drawn between empirical data and the predicted behavior of the montmorillonite known to be present in the samples. PROPERTIES OF MONTMORILLONIT E CLAY Water initially adsorbs on dry N a -montmorillonite clay in discrete layers in the interlaminar space between clal platelets. The platelet spacing, which is 9.6 A (angstroms) for a dehydrated clay, has been observed to expand in discrete steps to 12.4, 15.5, 18.4 and 21.4 A spacings, indicating the formation of four discrete layers of regularly oriented water molecules.' The first two layers are easily formed by hydrating a dry sample to equilibrium in an atmosphere with carefully controlled humidity. The formation of the higher layers is more difficult. The usual X-ray diffraction patterns of the more highly hydrated samples indicate a gradual increase in the average spacing betwcen 15.5 and 19.2 A, followed by a discontinuous expansion to 31 A when the weight ratio of water to dry clay is between 0.5 and 1.2.' Platelet expansion above 31 A proceeds monotonically as the moisture is increased and no regular arrangement of the platelets ib observed. Water-sensitivity in sedimentary rocks is usually associated with Na-montmorillonite clay when it is in the noncrystal-line state. Mering3 found that the average lattice spacing of sodium montmorillonite hydrated at 68 F and 70 per cent relative humidity was 15.5 A, and that the spacing, at 92 per cent humidity was 16.5 A. The water adsorbed at the higher humidity has the same free energy as liquid water at 65.6 F. Kolaian and Low' used a tensiometer to measure the thermodynamic properties of water in diffuse suspensions of montmorillonite clays relative to pure water. They observed that water in suspensions as dilute as 6 per cent clay became partially oriented when left undisturbed. The bonding associated with this orientation was not extensive because the free energy difference between the water in suspension and pure water was only a few millicalories per mole. They also found that the measured free energy difference decreased rapidly with temperature and became negligible above 100 F. This evidence indicates that montmorillonites contained in sedimentary rocks would dehydrate to a crystalline structure when exposed to superheated steam, and that the rock permeability measured with steam would be equivalent to that measured with air. The effect of elevated temperatures on the swelline of montmorillonite clays in aqueous suspensions has not been investigated. The Gouy-Chapman diffuse-ion-layer theory has been used to predict the swelling pressure of clay suspensions in dilute salt solutions at room temperature with reasonable success. theory also correctly predicts the direction of the thermal response of Na-mont-morillonite swelling pressures in dilute salt suspensions, 9 Over the temperature range of 33 to 68 F, an increase in

Jan 1, 1966

By B. D. Cullity, K. S. Sree Harsha

When a copper or aluminum single crystal is swaged into wire, the resulting deformation texture depends on the original orientation of the crystal. The<100> and <111>orientations me essentially stable, while <110> is unstable. The greater the <100> content of the deformation texture, the stronger the wire is in torsion. the greater the<111>content, the stvonger it is in tenszotz. The preferred orientation (texture) of fcc wires, either after deformation or recrystallization, is usually a double fiber texture in which some grains have <100> parallel to the wire axis and others have <111>. The relative amounts of these two texture components, as reported by different investigators for the same metal, vary considerably. Previous work in this laboratory&apos; has shown that the starting texture of a wire, i.e., the texture which it has before deformation, can have a decided influence on the texture produced by deformation. In particular, it was found that the deformation texture of copper wire is essentially a single <100> texture, if the wire before deformation contains only a <100> component. This is true even when the deformation is carried to more than 98 pct reduction in area. This paper reports on further studies of the role played by the starting texture. Copper and aluminum single crystals of various orientations have been cold swaged into wire, and quantitative measurements of the resulting deformation textures have been made. The tensile and torsional properties of the deformed wires have also been measured, and the relation between these properties has been correlated with the texture of the wire. These measurements were made in order to demonstrate that a cold-worked wire can be made relatively strong in torsion and weak in tension, or vice versa, by proper selection of the texture before deformation. MATERIALS The copper was of the tough-pitch variety, containing, by weight, 99.962 pct Cu, 0.003 pct Fe, 0.025 pct 0, and 0.0021 pct Si. The aluminum contained more than 99.99 pct .&apos;41; the only reported impurities were 0.001 pct Fe, 0.001 pct Si, and 0.003 pct Zn, by weight. Large single crystals of these metals were grown by the Bridgman method in graphite crucibles and a helium atmospliere. Cylindrical specimens of predetermined orientation, about 1.5 in. long and 0.36 in. in diameter, were machined from the as-grown crystals and then etched to 0.25 in. to remove the effects of machining. Their orientations were checked by back-reflection Laue photographs, and they were then swaged to a diameter of 0.050 in. (96 pct reduction in area). 111 order to study the "inside texture" of the deformed wires, they were etched, after swaging, to a diameter of 0.040 in. before the texture measurements were made. TEXTURE MEASUREMENTS The fiber texture which exists in wire or rod can be represented by a curve showing the relation between the pole density I, for some selected crystal-lographic plane, and the angle $ between the pole of that plane and the wire axis (fiber axis). Such a curve will show maxima at particular values of , and these values disclose the texture components which are present. The relative amounts of these components can be determined2&apos;3 from the areas under the maxima on a curve of I sin F vs F. It is seldom necesszlry to measure I over the whole range of F from 0 to 90 deg, since the existence of maxima in the low-F relgion can be inferred from measurements confined to the high-F region. The X-ray measurements were made with a General Electric XRD-5 diffractometer and filtered copper radiation, according to one or the other of the following procedures: 1) A method developed in this laboratory,4 involving diffraction from a single piece of wire. 2) A modification of the Field and Merchant method.5 This method was originally devised for the examination of sheet specimens, but it can easily be adapted to the measurement of fiber texture. Three or four short lengths of wire are held in grooves machined in the flat face of a special lucite specimen holder. The axes of the wires are parallel to the plane defined by the incident and diffracted X-ray beams, and the holder to which the wires are attached can be rotated step-wise about the diffractometer axis for measurements at various angles 9.

Jan 1, 1962

By Elwood G. Haney, R. N. Parkins

Stress corrosion cracking of two heats of 18 pct Ni maraging steel in rod form immersed in an aqueous solution of 0.6N NaCl at pH 2.2 has been studied on un-notched specimens stressed in a hard tensilf machite. Austenitizing temperature in the range 1830 to 1400 F has been shown to have a marked influence on the propensity to crack, the loulest austenitizing- temperature producing the greatest resistance to failure. In the nzosl susceptible conditions, the cracks followed the original austenile grain boundaries; but when tlze steels zcere heal treated to inproze their resistance to stress corrosion, the cracks becatne appreciably less branched and slzouqed significant tendencies to become trans granular. Electron metallography of the steels indicated the presence of snzall particles, possibly of titanium carbide, along- the prior austenite grain boundaries and these particles u:ere more readily detectable in the structures that were most susceptible to cracking. Crack propagation rates, which appeared to be dependent upon applied stress and structure, were usually in tlze reg-ion of 0.5 mm per hr and may, therefore, be e.xplained on tlze basis of a purely electrochetnical ,nechanism. However, there is some ezliderzce from fractography that crack extension may be assisted by ttlechanical processes. Anodic stit)zulation reduced the tiwe to fracture, although cathodic currents of small magnitudes delayed cracking-; further increase in cathodic current resulted in a sharp drop i,n fracture litne, possibly due to the onset of hydrogen ewbrittlement. THE use of the high strength maraging steels, with their attractive fracture toughness characteristics, is restricted because of their susceptibility to stress corrosion cracking in chloride solutions. Although this limitation has resulted in investigations of the stress corrosion susceptibilities of these steels, there have been few systematic studies aimed at defining the various parameters that determine the level of susceptibility. It is the case that the usual tests have been performed with the object of defining some stress or time limit, on unnotched or precracked specimens, within which failure was not observed,&apos; but while such results may be of some use in design considerations, they are necessarily concerned only with the steels as they currently exist and not with their improvement to render them more resistant to stress corrosion failure. This omission may be considered unfortunate because the indications are that stress corrosion in maraging steels shows dependence on structure in following an intergranular path, and since experience with other systems of intergranular stress corrosion crack- ing is that susceptibility may be varied by modifying heat treatments, a similar effect may be expected with maraging steels. It is sometimes from such observations that a fuller understanding of the mechanism of stress corrosion crack propagation begins to emerge, leading in time to the development of more resistant grades of material. The present work was undertaken to study only one aspect of the influence of heat treatment upon the cracking propensities of the 18 pct Ni maraging steel, namely the effect of austenitizing temperature, although certain ancillary measurements and experiments have been undertaken. EXPERIMENTAL TECHNIQUES Most of the measurements were made on a steel, A, having the analysis shown below, although a few results were obtained on a steel, B, having a slightly different composition. Both steels were supplied in the austenitized condition, A as 3/8-in-diam rod and B as 1/2-in.-diam rod. Cylindrical tensile test pieces were machined from the rods: the overal length was 2 1/2 in., the gage length 1 in. and the diameter 0.128 to 0.136 in. The stress corrosion tests were carried out with the specimens strained in tension in a hard beam testing machine, the necessary total strain being applied to the specimen over a period of about 30 sec, after which the moving crosshead was locked in position and the load allowed to relax as crack propagation proceeded; the load relaxation was recorded. The load was applied after the specimen had been brought into contact with the corrosive solution, the latter being contained in a polyethylene dish having a central hole through which the specimen passed, leakage being prevented by the application of a film of rubber cement. The specimen was in contact with the solution for over half of its gage length and the solution was exposed to the air during testing. The solution was prepared from distilled and deionized water to which NaCl was added, 0.6N, and the pH adjusted to 2.2 by HCl additions. The composition of the solution

Jan 1, 1969

By L. F. Mondolfo, W. T. Collins

A study of the relationship between undercooling for nucleation and structure in Sn-Cu alloys with 0.1 to 5 pct Cu has shown that in hypereutectic allojls the halo of tin that surrounds the primary crystals of Cu3Sn5 is larger, the larger the undercooling for nucleation o,f the tin. This increase of halo size results in a decrease of coupled eutectic, and, in alloys far from the eulectic composition, may produce its complete disappeavance, with the formation of a divorced eutectic structure. This was confirnred by the excrrnination of other alloys in which divorced eutectic slructuves are formed, and leads to the conclusion that they ave only an extrenle case of halo forrtzalion , which results when the two phases freeze one at a time and solidification of the first is completed Defove the second starts. It was also found that under proper conditions of nucleation all types of eutectic structures can be formed in the sartte system , and therefore divorced eutectics, like normal and anomalous, are not characteristic of the syslett~, but are mainly controlled by nucleatiorz. Dizlovced eutectics are formed when the phase that tutcleates the eulectic vequires a large undevcooling for ils nucleation and when the cotnpositiorz of the alloy is far from the eutectic., on the side of the primary phase that does not nucleate the other phase. It is recommended that the tevm "divorced" be used in preference to degenerate because it is more desct-iptice of the morphology and mode of forinalion of the structures. ThE variety of structures found in eutectic alloys has been extensively investigated and classified. The most accepted classification is the one by ~cheil,&apos; in which three different types of eutectic were distinguished: 1) normal, 2) anomalous, 3) degenerate (divorced). ATornlal eutectics are typified by the simultaneous growth of the two phases ("coupling") by which the two phases appear as interpenetrating crystals. The presence of a crystallization front, in which the two phases grow side by side, creates the eutectic grains, with the boundaries where the fronts meet. The presence of eutectic grains is the .distinguishing feature of a normal eutectic, according to Scheil. Straumanis and Brakss2 examined the Cd-Zn system and showed that there was a crystallographic relationship between the phases. Later, others4 also investigated additional systems and found definite crystallographic relationships in the coupled eutectics. The anornalous eutectic shows much less coupling than the normal; the two phases are intimately mixed but &apos;grow without a uniform crystallization front—a consistent crystallographic relationship— and the eutectic grain is conspicuously absent. As in the normal eutectics faster rates of growth result in a finer structure, but there is not the typical uniform spacing of normal eutectics. The degenerate eutectic shows no coupling; in fact the two phases attempt to minimize their area of contact and to form separate crystals. It has been suggested5" that slow cooling may favor this type of structure. Scheil believes that normal eutectics are formed when the two solid phases are present in more or less equal proportions, whereas both anomalous and degenerate eutectics form when one of the phases is present only in small amounts. spengler7 extended much farther this qualitative relationship between the eutectic type and the ratio of the two phases, and added a relationship to the melting point of the constituents. On this basis he proposed two equations for determining into which of Scheil&apos;s classifications an alloy belongs. The first equation is: where TI is the melting temperature of the lower-melting component, Tp of the higher-melting component, and Te the eutectic temperature. The second equations is: where is the volume percent of the lower-melting phase and $2 of the higher-melting phase at the eutectic composition. If 0 and/or 4 are in the range 0.1 to 1, a normal eutectic is formed; if in the range 0.01 to 0.1, anomalous; if less than 0.01, degenerate. Although the examples given by Spengler show a good agreement with the formulas, chadwick found that the Zn-Sn eutectic is normal to all growth rates, even though the volume ratio is 12/1, and Davies9 reports that the A1-AlgCo2 eutectic is normal, with a volume ratio of more than 30/1. Many more discrepancies of this type can also be found. Neither Scheil nor most of the other investigators have considered nucleation as a factor in the formation of divorced eutectics. Daviesg states that divorced eutectics form when neither phase acts as

Jan 1, 1965

By J. Philibert, A. G. Guy

Diffusion in the presence of deformation was studied by the method of vacuum dezincification of copper-rich and silver-rich solid solutions containing 7 to 30 pct Zn. The specimens were designed to permit the study of diffusion in separate portions of a given specimen characterized by strain rates ranging from essentially zero to approximately 10 sec-. No effect of deformation on diffusion was observed. BEGINNING with the work of Buffington and Cohen: interest in the question of the effect of stress or strain on diffusion has largely been concentrated on the enhancement of diffusion in specimens subjected to Continuous plastic deformation. The present research is a contribution to this limited area. However, as a preliminary to focusing attention on this special topic, it will be desirable to make a broad survey of the larger question, especially since there has been considerable foreign work in areas outside those of current interest in the United States. Since most of the topics referred to in the following section are both complex and imperfectly understood at present, it has been expedient in most instances to offer only a guide to the general nature of the work rather than a critical evaluation. PREVIOUS WORK The effect of elastic stress on diffusion has received considerable attention, especially with regard to the thermodynamic driving force for diffusion. The thermodynamic treatments have been based on the work of Gibb, Voigt, Planck, and Leontovich.&apos; Konobeevskii and Selisski6 made a first attempt at treating the problem in 1933, and Gorskii7 a few years later gave a solution applicable to single crystals as well as to polycrystalline specimens. In 1943 Konobeevski8 published treatments that have been the basis of much Russian work up to the present. For example, Aleksandrov and Lyubov used his work in explaining the velocity of lateral growth of pearlite. Early work in the United States was that of Mooradian and Norton, which showed that lattice distortion tends to be relieved before it can significantly affect the diffusion process. Druyvesteyn and Berghoutl1 observed a slight effect of elastic strain on self-diffusion in copper, while de Kazinczy12 found that both elastic and plastic deformation increased the rate of diffusion of hydrogen in steel. On the other hand, Grimes58 observed no effect of either elastic or plastic straining on the diffusion of hydrogen in nickel. High-frequency alternating stresses have been reported by various investigator s13-l5 to increase the rate of diffusion. A special form of elastic stressing is the imposition of hydrostatic pressure, a condition that is amenable to Conventional thermodvnamic analysis. Most of the experimental results in this area are consistent in showing a slight decrease in diffusion rates at high pressures.16-l8 Although Geguzinl reported a pronounced effect of relatively small pressures, Barnes and Mazey20 failed to Corroborate this finding, while Guy and Spinelli21 advanced an explanation of the phenomenon observed by Geguzin. It has been recognized that the thermodynamic treatment of diffusion phenomena in an arbitrarily stressed body is complicated by the fact that the desired state of quasi-equilibrium of the shear stresses cannot be maintained during a general diffusion process. However, attempts have been made by Meix-ner22-24 and Fasto to treat certain restricted cases, such as relaxation. FastovZ7 has also incorporated the general stress tensor into the thermodynamics of irreversible processes. The lattice strain that accompanies the formation of a solid solution has been the subject of much study,28-s0 and indirectly it has entered into many recent theories of diffusion. However, some Russian investigators31&apos;32 have taken other views of this matter and have predicted large effects on diffusion rates because of concentration stresses.o In completing this brief resume of previous work involving elastic strains and before proceeding to a consideration of the effect of continuous plastic deformation, it should be pointed out that deformation of various additional types may also influence diffusion. The effect of cold-working on subsequent diffusion has been studied directly by AndreevaS and by Schumann and Erdmann-Jesnitzer, while indirect evidence has been obtained by Miller and Guarnieri and by Vitman.38 Thermal stresses may also influence diffusion, contributions to this subject having been made by Fastovs7 and by Aleksandrov and Lyubv. The work of Johnson and Martin,o Dienes and Damask,3Band DamaskS considered the question of radiation-enhanced diffusion. In considering previous work on the subject of plastic deformation and diffusion, attention will be directed to those studies concerned primarily with diffusion rather than with its relation to Creep, e.g., the work of Dorn, or to the acceleration of diffusion -controlled reactions. Observations of the effect of

Jan 1, 1962

By G. H. F. Gardner

The velocity and attenuation of elastic waves in sandstones were measured as a function of both pressure and fluid saturation. A large change occurs in these quantities if water is added and the rock is not compressed, but the change is small if the rock is subjected to a large overburden pressure. Measurements were made by vibrating cylindrical samples in both the extensional and torsional modes at frequencies up to 30,000 cycles/sec. Formulas were derived which enable the attenuation of dilatational waves in dry rocks to be deduced from the data. Similar experimental methods were used to investigate the properties of unconsolidated sands. Velocities were found to vary with the 1/4 power of the overburden pressure and attenuations to decrease with the 1/6 power. The effects of grain size, amplitude and fluid saturation were studied. Formulas by which the effects produced by a jacket around the sample may be calculated were derived. The practical application of these results to formation valuation is discussed. INTRODUCTION The attenuation of elastic waves in the earth has been of interest to the seismologist and geophysicist for many years, but only recently to the petroleum engineer. Engineering interest has been brought about by the success of velocity logging devices, for it is possible by modification of these instruments to measure the attenuation of sound waves in addition to their velocity and, hence, deduce the mobility of formation fluids as well as the porosities of the rocks which contain them. The main problem is to decide whether field measurements can be made with sufficient accuracy to be of practical use. This problem can only be solved after we know the magnitude of the attenuations which are typical of the earth at various depths. The logarithmic decrement of a fluid-saturated rock is the sum of a "sloshing" decrement and a "jostling" decrement, the former caused by the mobility of the fluid contained within the rock and the latter by the granular framework of the rock. Sloshing decrements can be calculated&apos; using Biot&apos;s theory, but the jostling losses are less well understood. The present paper reports an experimental investigation of jostling losses in consolidated and uncon- solidated sands, particularly with respect to the effect of overburden pressure and fluid saturation. Born&apos; showed that the decrement of a sandstone may increase dramatically when only a few per cent by weight of distilled water is added, and that the additional loss is proportional to the frequency of vibration. His measurements were made with no compressive stress on the framework of the rock. M. Gondouin3 investigated similar phenomena for fluid-saturated plasters but also did not compress the samples. In the present paper it is shown that compression of the framework reduces this effect, so that at depth the jostling decrement of a sandstone may be expected to be almost independent of fluid saturation and frequency. Decrements for many sedimentary rocks have been given by Volarovich,4 but all for the state of zero overburden pressure. Anomalously low velocities have been logged in shallow unconsolidated gas sands. Results of the present investigation confirm that these velocities are not caused by correspondingly high attenuations, because the jostling decrement in a packing of sand grains is small and much less than in a consolidated sandstone at the same depth. Velocities in sands have been measured by Tsareva5 and by Hardin6 as a function of pressure, but the corresponding decrements do not appear to have been measured previously. The widely used "resonant bar method" of measuring velocities and decrements was employed. Comments on variations of this technique have recently been published by McSkimmin.7 The main novelty of the present technique was the application of pressure to the samples. It was found possible to do this by placing the apparatus inside a pressure vessel, provided the conditions leading to large additional losses were avoided. These conditions are discussed below. EXPERIMENTAL TECHNIQUE Cylindrical samples were caused to vibrate in both the extensional and torsional mode of vibration and the amplitude of vibration was measured as a function of frequency in the neighborhood of a resonant frequency. The resonant frequency, fr, is related to the corresponding elastic modulus by the formulas where E and N are Young&apos;s modulus and the modulus of rigidity, p is the density of the sample, and A the wavelength of the vibration.

Jan 1, 1965

By N. J. Olson, G. W. Toop

A series of equations previously derived for calculating ternary thermodynamic properties using binary data has been applied to the problem of predicting ternary phase diagrams and quaternary excess free energy. The methods are considered to be rigorous for regular ternary and quaternary systerns and empirical for nonregular systems. The equations have been used to predict ternary phase boundaries in the Pb-Sn-Zn system at 926°K and the Ag-Pd-Cu system at 1000ºK. Calculated quaternary excess free-energy values are presented for the Pb-Sn-Cd-Bi system at 773°K. A method for predicting the location of ternary phase boundaries would be a useful supplement to experimental measurements in ternary systems. This has been recognized with the considerable work that has been done to find models to predict or extend thermodynamic properties and phase diagrams in binary and ternary systems1-18 for which direct experimental measurements are limited. With the access to highspeed digital computers and mechanical plotting devices, it is currently rather easy to compare mathematical models with experimental data. The regular-solution model is consistent with systems which exhibit negative heats of mixing, positive heats of mixing, and miscibility gaps, and therefore it is applicable to simple phase diagrams. The purpose of this paper is to illustrate the use of regular-solution equations to predict, empirically, phase equilibria in some types of nonregular ternary systems. Corresponding equations for regular quaternary systems are given and used to calculate empirical quaternary excess free-energy data. METHOD FOR PREDICTING THE LOCATION OF TERNARY PHASE BOUNDARIES USING BINARY DATA Meijerin1,6 has used the regular-solution model to calculate common tangent points to ternary free energy of mixing surfaces and hence to determine phase boundaries in ternary systems involving miscibility gaps. He used the following equation to calculate ternary excess free energy of mixing values: stants characteristic of the binary solutions, and Ni is the mole fraction of component i. An alternate expression which gives for regular solutions as a function of binary values of along composition paths with constant N1/N2, N2lN3, and N1/N3 may also be derived:15 ternary r xs 1 ?c-*n.Ti*.U*. This expression for is more useful for the empirical calculation of ternary excess free-energy values for nonregular systems because actual binary AFXS data may be used in the expression rather than attempting to find suitable constants for Eq. [I]. The results of this feature of Eq. [2] are illustrated in Table I where calculated excess free-energy values for the Ni-Mn-Fe system at 1232°K are compared with experimental data of Smith, Paxton, and McCabe.19 Although regular-solution equations have been shown to give calculated thermodynamic quantities which agree quite well with experiment for single-phase nonregular ternary systems,14,15 care should be exercised in the use of the equations to predict thermo-dynamic properties of multiphase ternary systems in which strong compound formation is suspected. This precaution is consistent with the simple regular-solution model which for negative values of ai_j will indicate a tendency toward compound formation but even for very large negative values of ai-jwill not give multiphase binary or ternary systems involving a distinct stable compound. Hence, calculated ternary free-energy data using Eq. [2] might be expected to vary between being rigorous and poor, in the following order, for ternary systems which are: a) regular solutions, b) nonregular single-phase liquids in which random mixing is nearly realized, c) nonregular single-phase solids, d) nonregular multiphase systems exhibiting miscibility gaps, e) nonregular multiphase systems with binary compounds but no ternary compounds, f) nonregular multiphase systems with highly stable binary and ternary compounds. The calculated data will be expected to be least accurate for the last two cases. The general method adopted in this paper involves two-dimensional plots of ternary activity curves. The principle used is that tie lines indicating two-phase equilibria join conjugate phases a and B for example, for which a1(a) = a1(B), a2(a) = a2(B), and a3(a) = a3(B). Tie lines may be determined by plotting the ternary activities of two components along an isoactivity line for the third component and the unique points where the above equalities hold may be found graphically.

Jan 1, 1970

By F. C. Bond

SIZE of grinding media is one of the principal factors affecting efficiency and capacity of tumbling-type grinding mills. It is best determined for any particular installation by lengthy plant tests with carefully kept records. However, a method of calculating the proper sizes, based on correct theoretical principles and tested by experience, can be very helpful, both for new installations and for guiding existing operations. As a general principle, the proper size of the make-up grinding balls added to an operating mill is the size that will just break the largest feed particles. If the balls are too large the number of breaking contacts will be reduced and grinding capacity will suffer. Moreover, the amount of extreme fines produced by each contact will be increased, and size distribution of the ground product may be adversely affected. If the balls added are too small, grinding efficiency is decreased by wasted contacts that are too weak to break the particles nipped; these largest particles are gradually worn down in the mill by the progressive breakage of corners and edges. Ball rationing is the regular addition of make-up balls of more than one size. The largest balls added are aimed at the largest and hardest particles. However, the contacts are governed entirely by chance, and the probability of inefficient contacts of large balls with small particles, and of small balls with large particles, is as great as the desired contact of large balls with large particles. Ball rationing should be considered an adjunct or secondary modification of the principle of selecting the make-up ball size to break the largest particle present. Empirical Equation In 19521,2 the author presented the following emerical equation for the make-up ball size: B - ball, rod, or pebble diameter in inches. F = size in microns 80 pct of new feed passes. Wi - work index at the feed size F. Cs - percentage of mill critical speed. S — specific gravity of material being ground. D == mill diameter in feet inside liners. K - 200 for balls, 300 for rods, 100 for silica pebbles. Eq. 1 was derived by selecting the factors that apparently should influence make-up ball size selection and by considering plant experience with each factor. Even though Eq. 1 is completely empirical, it has been generally successful in selecting the proper size of make-up balls for specific operations. But an equation based on theoretical considerations should be used with more confidence and have wider application. The theoretical influence of each of the governing factors listed under Eq. 1 was accordingly considered in detail, as described below, and a theoretical equation for make-up ball sizes was derived. Derivation of Theoretical Equation Ball Size and Feed Size: The basis of this analysis is that the largest ball in a mill should be just sufficient to break the largest feed particle into several pieces, excluding occasional pieces of tramp oversize. In this article the size F which 80 pct passes is considered the criterion of the effective maximum particle feed size. The smallest dimension of the largest particles present controls their breaking strength. This dimension is approximately equal to F. As a starting point for the analysis it is assumed that a 1-in. steel ball will effectively grind material with 80 pct passing 1 mm, or with F- 1000µ or about 16 mesh. The breaking force exerted by a ball varies with its weight, or as the cube of its diameter R. The force in pounds per square inch required to break a particle varies as its cross-sectional area, or as its diameter squared. It follows that when a 1-in. ball breaks a 1-mm particle, a 2-in. ball will break a 4-mm particle, and a 3-in. ball a 9-mm particle. This is in accordance with practical experience, as well as being theoretically correct. Confirmation of this reasoning is supplied by the Third Theory of Comminution," which states that the work necessary to break a particle of diameter F varies as F. Since work equals force times distance, and the distance of deformation before breaka4e varies as F it follolvs that the breaking force should vary as F½ These relationships are expressed in Table I, with a 1-in. ball representing one unit of force and breaking a 1-mm particle. This establishes theoretically the general rule used in Eq. 1 that the ball size should vary as the square root of the particle size to be broken. Ball Size and Work Index: The work input W required per ton" varies as the work index Wi, and the

Jan 1, 1959

By W. L. Martin, J. N. Dew, H. B. Steves, M. L. Powers

This paper presents and discusses the results obtained during a pilot test in the Loco field in southern Okla homa. The test was conducted in a 2%-acre pattern that was part of a 20-acre conventional waterflood pilot area. The conventional flood was well past its economic limit when the hot waterflood was initiated to obtain technical information and operating experience. Temperature data from nine observation wells showed that about 75 percent of the pattern was affected by heat, and that heat losses were severe in the pilot pattern. About 60 percent of the injected heat was lost to overburden and underburden zones during hot-water injection. Wellbore heat losses were held at tolerable levels at the shallow depth of the test by providing a low-pressure air annulus between the injection tubing and well casing. Hot water provided water injectivity increases of 200 to 400 percent. The hot water channeled across the lower portion of the oil sand in three directions through zones of relatively high water saturation. There was no conclusive evidence that natural fractures or pressure partings aflected the flow of fluids in the pilot pattern; however response undoubtedly was aflected by localized pressure gradients and by injection-production rate ratios. The results showed that hot waterflooding increased oil recovery in a reservoir containing 600 cp oil. The total tertiary oil production from the pilot pattern area was 3,896 bbl or about 156 bbl/acre-ft swept by heat. The corre.sponding WOR was about 34:I. Description of the Hot Waterflood Process To hot waterflood an oil reservoir, water is injected that has been heated to a temperature substantially higher than the original reservoir temperature, but lower than the vaporization temperature of water at the prevailing pressures. In the reservoir the hot water flows continuously into cooler sand and rapidly loses heat to the sand until it has been cooled to the original reservoir temperature. Thus, a heated zone and a region or "bank" of cooled water begins to accumulate immediately after hot water injection is started. This bank of cooled water continues to grow ahead of the heated zone, which also grows, but at a slower rate. This occurs because heat transfer is almost instantaneous, and the ratio of heat capacities of water to rock is such that two or three unit PV of hot water must be injected to heat a given unit bulk volume of the reservoir. The primary displacement mechanism is the same for both hot and conventional cold waterfloods; i.e., "piston" displacement occurs at the original reservoir temperature. The incremental benefits of hot waterflooding usually occur long after the breakthrough of cold water at producing wells, and the increased oil recovery necessarily is accomplished with high WOR&apos;s (water-oil ratios). Heat decreases the viscosity and density of oil and water. These effects result in more rapid and increased recovery of secondary or tertiary oil. If the cost of the required heat is low enough, the ultimate oil recovery of a hot waterflood should be increased substantially over what would be expected at the economic limit of a conventional cold waterflood. The economic benefits of any hot-fluid injection project depend primarily upon the cost of the heat required to produce more oil at an increased rate. This cost depends in part upon the amount of heat lost to surrounding formations. Heat loss depends upon reservoir thickness, water injection rate and temperature, the depth of the formation, well spacing, and the characteristics of the reservoir rock and surrounding formations. In general, percentage heat losses decrease as injection rate and reservoir thickness increase. Although it is an old idea, hot-water injection has not received widespread field application in the oil industry as a drive process. Much of the original field work with hot water was done in Pennsylvania fields where water permeabilities and injection rates are low. In these cases, hot-water injection was used primarily as a means of increasing in-jectivities — not as a recovery process. Ramey&apos; recently has published an excellent review of the development of hot fluid injection processes. Recent publications"&apos; and our own experiences now indicate that hot water or steam injection also can effectively increase the oil recovery from reservoirs containing viscous crudes. However, the economics of these methods as displacement processes have not been established. Several theoretical predictive techniques have been published (for a review see Ramey&apos;), but simplifying assumptions make

Jan 1, 1969

By R. E. Schilson, F. H. Poettmann

The direct determination of the stabilized performance behavior of low capacity, slowly stabilizing gas wells is extremely time-consuming and wasteful of gas. From both field experience and theoretical considerations, a test procedure has been evolved by which the stabilized hack pressure behavior of such gas wells can he predicted without having to revert to long time flow tests. The method consists of using the isochrona1 test procedure to establish the slope of the back pressure curve, "n", and the short time variation of the performance coeficient, "C", with time. From this short time transient flow data and theoretical considerations, the value of C at large times can he established. By assuming the radius of drainage of a well to be half the distance between wells, one can calculate the stabilization time for various well spacing patterns. Once the stabilization time for a given .spacing has been determined, the value of C can be calculated and the stabilized back-pressure curve can he. establbrhed. The calculated perfortnance coefficient as a function of tinze was cotnpared to the experintentally measured values for a number of gas wel1.e. The deviation of the calc~*lated from the cxperimental res1tlt.s vary depending on the set of short time experimental points used to evabrate the parcrttzeters of the equation. The longer the tirne far the flow test data user1 in the calculations, the better was the agreement with the experimental results. The time necessary to obtain this data from well tests varies consitlerably, depending on the physical natrcre oj the rt3scrvoir under consideratiot~. INTRODUCTION For many years, the U. S. Bureau of Mines Monograph 7&apos; has served as a guide for testing and evaluating the performance of gas wells by means of the back-pressure method. The back-pressure performance of a gas well is expressed by the following equation: Q~ CW-W.........(I) where the characteristics of the back-pressure equation are determined by C, the performance coefficient, and n, the exponent which corresponds to the slope of the straight line when Q and {P* - PN2) are plotted on logarithmic paper. Q is gas flow rate at standard conditions, and P, and P, are equalized and flowing bottom-hole pressures, respectively. Prior to the development of the back-pressure tcst, the "open flow" capacity method of testing a well was common. By this method, the wells were flowed wide open to the air and the flow rate measured. Such procedure was wasteful of gas and did not provide information on the deliverability of the gas to the pipe line. Monograph 7 Procedure The back-pressure method of testing wells was developed to overcome these shortcomings. Although much has been learned regarding the laws of the flow of gas through porous formations, the original development of the back-pressure relationship was based entirely on empirical methods. The back-pressure behavior provides the engineer with information essential in predicting the future development of a field. It permits him to calculate the deliverability of gas into a pipe line at predetermined line pressures, to design and analyze gas gathering lines, to determine the spacing and number of wells to he drilled during the development of a field to meet gas purchasers&apos; requirements, and to solve many other technical and economic problems. As described in Monograph 7, the flow-after-flow method of back-pressure testing, when applied to fast stabilizing and usually high capacity wells, correctly characterized the behavior of the well. However, as the value of the gas at the wellhead increased, small capacity gas wells having slow rates of stabilization became economically operable. The flow-after-flow method of testing could not be used to describe the behavior of these slowly stabilizing wells. The procedure of Rawlins and Shellhardtl for establishing the back-pressure behavior of a gas well was based on the rcquirement that the data be obtained under stabilized flow conditions; that is, that C is constant and does not vary with time. C depends on the physical properties of the reservoir, the location, extent and geometry of the drainage radius, and the properties of the flowing fluid. In a highly permeable formation, only a very short period of time is required for the well to reach a stabilized condition, and, consequently, the requirements for the test procedure described in Monograph 7 are met. For a given well, n is also constant

By G. H. Bishop

The kinetics of the inter granular penetration and embrittlement of [100] tilt boundaries in 99.998 pct pure nickel upon exposure to bismuth-rich Ni-Bi liquids have been determined in the temperature range from 700° to 900°C. The kinetics of penetration are parabolic in time at constant temperature over most of the temperature range. In a series of 43-deg bicrystals the rate of penetration is anisotropic with respect to the direction of penetration into the grain boundaries. In lower-angle bicrystals the penetration rate is isotropic. The rate of penetration decreases with tilt angle at 700°C. The activation energy for penetration in the 43-deg bicrystals is 42 kcal per g-atom independent of direction. It is concluded that the intergranular penetration and embrittlement in the presence of the liquid proceeds by a grain boundary diffusion process and not by the intrusion of a liquid film. This was confirmed by a determination that the kinetics of penetration and embrittlement were the same in the 43-deg bicrystals upon exposure to bismuth vapor under conditions such that no bulk liquid phase would be thermodynamically stable. WhEN solid metals are exposed to a corrosive liquid-metal environment, the grain boundaries are sites of preferential attack. Depending on the temperature, the composition of the liquid, and the composition, structure, and state of stress of the solid, a number of modes of attack are possible. This paper reports a study of the kinetics of intergranular penetration and embrittlement of high-purity nickel bicrystals upon exposure to bismuth which, together with an earlier study by Cheney, Hochgraf, and Spencer,&apos; demonstrates that there are at least two modes of intergranular attack possible in the Ni-Bi system. In the study by Cheney et al., columnar-grain specimens of 99.5 pct pure nickel were exposed to liquid bismuth presaturated with nickel in the temperature range 670" to 1050°C. They found that the majority of the boundaries, which were predominantely high-angle boundaries, were penetrated by capillary liquid films, the attack proceeding by a process which will be termed grain boundary wetting. This process occurs in a stress-free solid when twice the liquid-solid surface tension is less than the surface tension of the grain boundary,* i.e., when 2yLs < YGB In this case the penetration of the grain boundary by the liquid occurs at a relatively rapid rate, resulting in the severe embrittlement of a polycrystalline solid. Grain boundary wetting is a common mode of intergranular attack in systems in which the lower melting component is relatively insoluble in the solid, but the solid has an appreciable solubility in the liquid, for example, the Ni-Bi system, Fig. 1. In systems of this type at temperatures above the range of stability of any intermetallic phases, once the liquid is saturated with respect to the solid so that no gross solution occurs, chemical gradients are small, and surface tensions become major driving forces for attack, provided the solid is stress-free. The results of Cheney et al. appear to be typical of those encountered when grain boundary wetting occurs.&apos; Capillary films were observed in the boundaries after quenching from the exposure temperature. The mean depth of penetration increased linearly with time, and the activation energy for the process was found to be 22 kcal per g-atom. In a study of the Cu-Bi system Yukawa and sinott4 found that the depth of penetration of bismuth into high-purity copper bicrystals of orientations from 22 to 63 deg of tilt about (100) at 649°C ranged from 0.05 to 0.25 in. after a 12-hr anneal. This corresponds to a linear rate of 6 to 15 X 10~6 cm per sec. At the same reduced temperature of 0.68 the rate for the Ni-Bi system&apos; was 7 x lo-&apos; cm per sec. In another study of the Cu-Bi system, Scheil and schess15 determined the kinetics of grain boundary wetting in hot-worked commercial rod. While there were several complicating factors present in this study, there is general agreement with the above results. The kinetics of penetration were linear, the activation energy was 20 kcal per g-atom, and at 650°C the rate of wetting was 2 to 5 x 10-6 cm per sec. The rate of wetting in the A1-Ga system6 is somewhat

Jan 1, 1969

By L. H. Van Vlack, T. Y. Tien, R. J. Martin

The phase relationships of the MnTe-MnS system were studied by DTA procedures. There is an eutectic at 810°C with about 10 mole pct MnS-90 mole pct MnTe. An eutectoid occurs at about 710°C with approximately 7 mole pct MnS where the MnTe(NaCl) solid solution dissociates on cooling to MnTe(NiAs) and MnS. There is very little solid solubility of MnTe in MnS. ALTHOUGH MnS may exist in three different crystal forms,&apos; only the NaC1-type phase is stable.2 Above 1040°C, MnTe also has the cubic NaC1-type structure. Below that temperature, MnTe changes to the NiAs-type structure.3 This phase transition is rapid for both heating and cooling. As a result the high-temperature crystal form of MnTe cannot be retained at room temperature. Because MnO, MnS, and MnSe are all stable with the NaC1-type structure, and MnTe has this structure at high temperatures,4 solid solution formation could be expected among these compounds. It is interesting to note, however, that a complete series of solid solutions exist only in the MnS-MnSe system,&apos; and that the solid solution is quite limited in the MnO-MnS system.&apos; The MnSe-MnTe system possesses a complete series of solid solutions at high temperatures with separation at lower temperatures.7 Although ion size may be critical in the miscibility of MnO-MnS, it is quite possible that the bond type plays a more important role with the miscibility of MnSe-MnTe. This would permit us to speculate that the miscibility gap would be extensive in the MnTe-MnS system. EXPERIMENTAL Preparation. The samples were prepared by mixing and compacting MnTe and MnS powders. The MnS was previously prepared through the sulfur reduction of Mnso4.8 The MnTe had been prepared by mixing and compacting double vacuum distilled metallic manganese and high-purity tellurium in stoichiometric ratio modified with 1 wt pct excess tellurium. The compacted powders were put in a graphite crucible which was sealed in an evacuated vycor tube. The free space in the vycor tube was made minimal to reduce the loss of tellurium. The sealed assembly was then heated slowly to about 500° C where the free manganese and tellurium reacted vigorously, melting the MnTe which formed. Only one phase, MnTe, was detected by X-ray powder patterns and metallographic techniques. Each compact of MnTe-MnS was placed in a graphite crucible and then sealed in an evacuated vycor tube. The samples were heated at 1250°C for 4 hr and furnace-cooled. Microscopic examination revealed no third phase beyond MnS and MnTe. A typical microstructure is presented in Fig. 1. Identification. X-ray powder patterns were obtained using 114.6 mm Debye-Scherrer camera and Fe-Ka radiation. Mixtures of cubic MnS and hexagonal MnTe were observed in all of the compositions prepared. No lattice parameter change was noticed among different compositions, indicating no solid solution could be retained at room temperatures between these two end-members. A lattice parameter of 5.244Å for MnS was obtained by the Nelson and Riley9 extrapolation method using the diffraction lines of (h2 + k2 + 12) equal 12, 16, 20, and 24. The values, a = 4.145Å and c = 6.708Å, for hexagonal MnTe were obtained from the (006) and (220) lines in the back-reflection region. These values agree well with the values reported by Taylor and Kag1e.10 Differential Thermal Analysis. A differential thermal analysis procedure was used to determine phase relationships since the high-temperature equilibrium conditions could not be retained for examination at room temperature, even when the sealed samples (~0.5 g) were quenched in water. The samples were sealed in an evacuated 4 mm vycor tube with a recess in the bottom to accept a thermocouple. An Al2O3 reference was similarly prepared and the two placed within a piece of insulating fire brick to dampen spurious temperature changes within the furnace. The furnace was controlled by a mechanically driven rheostat which increased the temperature at a rate of about 15°C per min. Known phase changes in the Pb-Sn system1&apos; and the a-to-ß quartz inversion12 were used for calibration

Jan 1, 1969

By Willard C. Lacy

Rather than attempting to present a summary of the many and highly varied papers that have been presented at this symposium on sampling and grade control, I will attempt to extract the general philosophy of analysis and approach, and attempt to identify the trend of future developments. First, the term "sampling" is used with its broadest connotations. A sample consists of a representative portion of a larger mass, and must represent the mass not only in the grade of contained metals or minerals, but also in all other respects in terms of mineralogy and mineral quality (1, 5), deleterious materials, recoverability of economic components, physical behavior, geophysical response (I), and even archaeological and environmental aspects (7, 11). The sample must be taken from a locality and in such a manner and quantity that it is representative of the larger rock mass. This calls for complete and accurate geological control and an understanding of the nature and distribution of the contained chemical and physical elements and a record of the effectiveness of the different sampling methods. Second, value of a given mass of ore material is based upon its profitability - the difference between recoverable value and costs to achieve recovery, beneficiation and sale. There is a strong movement in mining geology control toward more complete analysis in determining cutoff grades and in grade control, as illustrated by the kriging of metallurgical recovery factors as well as grade at the Mercur Mine (8). To achieve a "profit- ability factor" as a guide for economic mining practice requires further integration of: 1) the value of contained metal or mineral, 2) percentage recovery of values, 3) dilution of ore with waste rock, 4) addition to, or loss of value as a consequence of by-product materials or deleterious components, 5) cost of producing a saleable product plus mini- mum profit to justify the effort (cutoff), and 6) cost of land restoration (7, 11). All these parameters vary with the rock type, rock structure, mineralogy, depth, geometry, mining and metallurgical methods, but they must be sampled and analyzed if sampling and grade control are to reflect profitability. A wide variety of deposits has been presented at this symposium; each deposit with its own problems and special solutions. Deposits containing high unit-value components, e.g. precious metals and diamonds, present special problems in the obtaining of accurate samples and generally require statistical analysis control methods or may disregard or modify occasional high or occasional low values, based upon experience (12 ) Grade control may be accurate for the long term but may vary for the short term. Bulk sampling is always essential. Deposits containing metals or minerals with low unit value are very sensitive to transport costs, and they are often very sensitive to small amounts of deleterious components or differences in physical or chemical behavior. Problems of sampling and grade control change with the genetic type of deposit, with the stage of deposit development and with the size of the information base. Precious metal epithermal deposits (2, 6, 8), because of rapid vertical zonation and erratic lateral distribution of values, have always been difficult to evaluate and maintain grade control and ore reserves. On the other hand, evaluation and grade control are relatively easy in bulk-low- grade deposits (4, 13). However, these deposits generally have a low margin of profit and are sensitive to mining and beneficiaton costs, price fluctuations and political costs. Industrial mineral deposits (5) often must be evaluated on the basis of their behavior, rather than by chemical analysis. Environmental impact generally increases with the scale of the operation, but certain elements or minerals have especially high impact effects (7, 11). In the exploration phase there is no production control of sampling procedures and careful geological observations are particularly essential. The greatest number of problems is related to the oxidized outcrop where the chemical environment of the ore body has changed and the contained values may have been enriched, depleted or values left unchanged (2, 6). Present evidence suggests that gold values may be very mobile under certain conditions (2, 6) and stable under others. Everything must be sampled in detail. Principal values and by-product or deleterious elements may vary dependent upon their position within the soil profile. Such factors as geomorphic position, erosion rate, vegetation, climate, etc., may affect the interpretation (1, 3). During the development phase it is equally easy to overtest, to have "paralysis by analysis," as to undertest (3, 6). Bulk samplng and testing are

Jan 1, 1985

By J. B. Clark, A. J. McEvily, R. L. Snyder

The nonuniform distribution of precipitate particles has been recognized as a leading factor contributing to the relatively low fatigue resistance of aluminum alloys. The structure of many of these alloys is characterized by narrow precipitate-free zones adjacent to the grain boundaries. Alloys with such zones exhibit a tendency for brittle inter crystalline fracture. The interrelation between this type of structure and mechanical properties was investigated in an Al-10 wt pct Mg alloy. It was found that deformation during fatigue occurs preferentially along these zones and cracks initiate there. In Al-10wt pct Mg, the zones were found to be supersaturated even after extensive general precipitation and are due to the absence of proper precipitate nuclei in the region near the grain boundaries. Cold working the alloy prior to aging improves the mechanical properties by inducing precipitation within the zones and also by jogging of grain boundaries. The mode of fracture is changed from brittle inter crystalline to more ductile trans granular fracture. THE process of fatigue is highly structure sensitive, with the strength of the whole often dependent upon some localized discontinuity, either geometrical or metallurgical in nature. Much has been learned about the role of geometrical discontinuities, e.g., notches, in fatigue, but with the exception of the effects of inclusions or the shapes of carbides, relatively little is known about the specific effects of discontinuities in metallurgical structure such as nonuniform precipitation. In most age-hardening aluminum alloys, metallo-graphic studies have shown that the extent of precipitation adjacent to grain boundaries is much less than that which occurs in the interior of the grains. The width of these almost precipitate-free regions, which are sometimes called denuded zones, and the extent of solute depletion within them, are dependent upon the particular alloy and its aging treatment. It has been observed1 that these zones are relatively soft with the result that plastic deformation takes place preferentially within them. It has also been shown 2-4 that there exists a tendency for intercrys- talline cracking in fatigue when such zones are present. It is of interest to note that Broom et al.2,3 were able to reduce the incidence of this type of failure in an A1-4 wt pct Cu alloy by stretching the material 10 pct prior to aging. In the present study, the effects of precipitate-free regions on the fatigue properties of an A1-10 wt pct Mg alloy were studied in detail, and the effects of deformation prior to aging on the nature of the precipitation process as well as on fatigue properties were also investigated. MATERIAL AND PROCESSING An A1-10 wt pct Mg alloy was selected for this study, because it was known that well-defined precipitate-free regions along the grain boundaries are readily obtained in this alloy after aging at 200oC.5 The starting materials were 99.998 pct A1 and singly sublimed magnesium of about 99.9 pct purity. The aluminum was induction melted in a graphite crucible, and then the magnesium addition was immersed until dissolved. Chlorine gas was then bubbled through the molten alloy for 4 min to degas the melt, after which the melt was cast at a pouring temperature of 730" to 760°C into a cold, graphite-coated, tapered steel mold. Since A1-Mg alloys are difficult to homogenize,5 special care was taken to obtain a uniform composition. Two-in. cubes were cut from the ingot and heated at 446°C for 30 min. These cubes were then hot forged approximately 35 pct in each of the three cube directions and homogenized for 16 hr at 446°C. Sheet specimens were then obtained by pressing 40 pct and rolling 35 pct per pass with reheating between reduction steps to a final thickness of approximately 0.10 in. The sheet was then solution treated for 16 hr at 446°C and water quenched. The age hardening behavior of this material at 200°C was then determined, and the results are shown in Fig. 1. The age hardening of this alloy when subjected to cold work prior to aging is also shown in this figure. Preliminary work indicated that extensive deformation after quenching was required to affect drastically the precipitate-free regions in this alloy, and a rolling reduction of 50 pct was chosen. For purposes of comparison the following three conditions were studied: a) Solution treated, quenched, and aged 20 hr at 200°C

Jan 1, 1963

By S. N. Singh, M. C. Flemings

Results are presented of a study on the combined influences of ingot dendrite am spacing and thermo-mechanical treatments on the fracture behavior and mechanical properties of high purity 7075 aluminum alloy. The most important single variable influencing mechanical properties was found to be undissolved alloy second Phase (microsegregation inherited from the original ingot). Ultimate and yield strengths were found to increase linearly with decreasing amount of alloy second phase while ductility increased markedly. At low amounts of second phase, transverse properties were approximately equal to longitudinal properties. In tensile testing, microcracks and holes were invariably found to originate in or around second phase particles. Fracture occurred both by propagation of cracks and coalescence of holes, depending on the distribution and amount of second phase. IN most commercial wrought alloys, second phase particles are present that are inherited from the original cast ingot. These include, for example, non-equilibrium alloy second phases such as CuAl2 and impurity second phases such as FeA13 and Cr2A1, in aluminum alloys. A previous paper1 has dealt with the morphology of these second phases in cast and wrought aluminum 7075 alloy, and with their behavior during various thermomechanical treatments. In this paper we discuss the influence of the particles on mechanical properties and fracture behavior of the alloy. Previous experimental work indicating a direct and major effect of second phase particles on mechanical properties (especially on ductility) includes the work of Edelson and Baldwin on pure copper.&apos; Also relevant are the many studies demonstrating the important effect of nonmetallic inclusions on the fracture of. steel.3&apos;4 Work on aluminum includes that of Antes, Lipson, and Rosenthal5 who showed that a dramatic improvement in ductility of wrought aluminum alloys of the 7000 series is achieved by eliminating second phases. It now seems well established that included second phases play a dominant role in controlling ductility (as measured, for example, by reduction in area in a tensile test) of a variety of materials. There is, therefore, considerable current interest in the mechanisms by which second phase particles affect ductile fracture. Experiments done by various workers have shown that second phase particles or discontinuities in the microstructure are potential sites for nuclea-tion of microcracks and of holes,6-l3 which then grow and cause premature fracture and the loss of ductility. Theoretical attempts have been made to explain the observed phenomena; most are able to explain observations qualitatively, but lack quantitative agreement. Much experimental work needs to be done to aid extension of theoretical models. A recent review article by Rosenfield summarizes work in this general area.14 PROCEDURE Material used in the previously described study on solution kinetics of cast and wrought 7075 alloy1 was also used in this study. Procedures for ingot casting, solution treating, and working were described in detail in that paper. Test bars were obtained for material of 76 initial dendrite arm spacing (11/2 in. from the ingot base) and 95 µ initial dendrite arm spacing (51/2 in. from the ingot base) for the following thermomechanical treatments (solution temperature 860°F; reduction by cold rolling). a) Solution treated 12 hr, reduced 2/1, 4/1, and 16/1. b) Solution treated 12 hr, reduced 16/1, solution treated approximately 5 hr after reduction. c) Same as a) except solution treated 24 hr prior to reduction. d) Same as b) except solution treated 24 hr prior to reduction. e) Same as d) except solution treated 20 hr after reduction. Test bars were taken both longitudinally and transverse to the rolling direction. Transverse properties are in the long transverse direction; since the final product was sheet (0.030 in. thick), properties in the short transverse direction could not be obtained. Test bars were flat specimens, of gage cross section1/-| in. by 0.030 in. and 1/2 in. gage length. After machining the test bars, they were given an additional 1/2 hr solution treatment of 860°F and aged 24 hr at 250°F. Three bars were tested for each location and thermomechanical treatment, after rejection of mechanically flawed bars. The average results of these three bars are reported. Elongation was measured using a $ in. extensometer and reduction in area was determined using a profilometer to measure the area after fracture. INFLUENCE OF THERMOMECHANICAL TREATMENTS AND SECOND PHASE ON MECHANICAL PROPERTIES Results of mechanical testing are presented in Figs. 1 to 4 and in tabular form in the Appendix. A general conclusion from results obtained is that details of the thermomechanical treatments studied were important only insofar as they influenced the amount of residual second phase. Figs. 1 and 4 show the longitudinal properties obtained (regardless of thermomechanical

Jan 1, 1970

By L. T. Lloyd, H. H. Chiswik

The operative deformation elements in a-uranium single crystals under compression at room temperature have been determined as a function of the compression directions. The deformation mechanisms noted may be arranged with respect to their frequency of occurrence and ease of operation in the following order: 1 — (010)-[I001 slip, 2—{130} twinning, 3—{~172} twinning, and 4bunder special conditions of stress application, kinking, cross-slip, {.-176) twinning, and (011) slip. The composition planes of the (172) and (176) systems were found to be irrational. Cross-slip was shown to be associated with the major (010) slip system, coupled with localized interaction of slip on the (001) planes. The mechanism of kinking was found to be similar to that observed in other metals in that it occurred chiefly when the compression direction was, nearly parallel to the principal slip direction [loo] and was associated with a lattice rotation about an axis contained in the slip plane and normal to the slip direction: the [001] in the uranium lattice. The resolved critical shear stress for slip on the (010)-[100] system was found to be 0.34 kg per mm2 In a single test it was shown that under compression in suitable directions twinning on the (130) also occurs at 600°C. DEFORMATION mechanisms of large grained polycrystalline orthorhombic a-uranium have been studied by Cahn.1 A major slip system identified as the (010) with a probable [loo] slip direction and a minor slip system on the (110) planes were reported; the slip direction of the minor system was not determined. The twinning systems that were identified experimentally included the (130) and the irrational (172) composition planes; observations of other traces which were not as frequent and which did not lend themselves to positive experimental identification led Cahn to postulate on the basis of indirect evidence that twinning also occurred on (112) and (121) planes. In addition to the foregoing slip and twinning mechanisms, Cahn also observed kinking and cross-slip in conjunction with the major (010) system; the cooperative cross-slip plane was not identified. The availability of single crystals to the present authors has enabled them to check these results, particularly with reference to the doubtful mechanisms and the preference of operation of any one mechanism in relation to the direction of stress application. The tests were confined to compression only, primarily because of experimental limitations imposed by the size and shape of the available crystals. The tests were performed at room temperature except for one crystal compressed at 600°C. The compression directions were chosen to obtain a representative coverage of one quadrant of the stereo-graphic projection. To test the existence of some of the deformation elements that were reported by Cahn, but were not found in the present study, several additional crystals were compressed in specifically chosen directions considered most ideal for their operation. Experimental Techniques The single crystals were obtained by the grain coarsening technique described by Fisher? They grinding and polishing on rotating laps, with final surface preparation performed in a H3PO4-HNO3 electropolishing bath. A typical crystal readied for compression is shown in Fig. 1; their dimensions were rather small and depended upon the testing direction. Crystals isolated for compression in a direction close to the [010] axis, which lay roughly parallel to the longitudinal axis of the polycrystalline rod, were about 3 to 4 mm long and 5 mm2 in cross-section, while those prepared for compression in other directions were smaller. Most of the crystals were free from twin markings and showed no evidence of Laue asterism. Several crystals, however, contained twin traces prior to compression; these were identified prior to compression so as to clearly distinguish them from those initiated during deformation. The origin of the twin markings prior to deformation may be ascribed to two sources: thermal stresses and specimen handling during isolation and preparation. Two other types of imperfections in the crystals should be mentioned: inclusions, which were probably oxides or carbides. and three of the crystals contained a small number of spherical included grains (<0.01 mm diam), which were remnants of unabsorbed grains from the coarsening treatment. The volume represented by these imperfections was small, and their presence presented no difficulties in the interpretation of the macrodeformation processes during subsequent compression. Two compression fixtures were employed: crystals A, B, C, E, and G were compressed in a hand-operated screw-driven jig whose compression platens were designed to minimize axial rotation;

Jan 1, 1956

By C. G. Dunn, J. L. Walter

Secondary recrystallization to the (110) [001] texture in high-purity silicon iron occurs if low-oxygen material is annealed in a nonoxidizing atmosphere. Any departure from these conditions results in a growth of (100) oriented grains. The nature of the matrix and secondary recrystallization structures and textures and the nature of grain boundary interactions during growth show that the low gas-metal interfacial energy of the (110) surfaces provides the driving force for growth of these grains. A type of grain growth, characterized by a driving force which derives from energy differences of {hkl} surfaces at the gas-metal interface, has been treated in recent papers.&apos;-7 Secondary recrystallization to the cube text!:: in high-purity silicon iron provides one example. The present paper also deals with a surface energy driving force but the texture that results by secondary recrystallization is not the cube texture; it is a texture in which the (110) plane is in the plane of rolling and the [001] direction is in the direction of rolling. The phenomenon described in this paper is different from the impurity (dispersed phase)-controlled secondary recrystallization process in which the (110) [001] oriented grains grow under the action of grain boundary driving forces.8-12 It is also different from tertiary recrystallization,2 which also produces the (110) [001] texture in high-purity silicon iron, since the matrix textures and grain sizes are different. Finally, it is unlike any other form of secondary recrystallization reported in the literature. The possibility of obtaining the (110) [001] texture in high-purity silicon iron became clear in a study of the effect of impurity atoms on the energy relationships of (100) and (110) surfaces. In this study Walter and Dunn6 observed the migration of (100)/(110) boundaries, i.e., boundaries between two grains, one of which has a (100) plane and the other a (110) plane, respectively, parallel to the plane of the sheet specimen. At 1200°C the (100)/(110) boundaries advanced into (100) grains in a vacuum anneal, then reversed their direction and migrated into (110) grains in a subsequent anneal in impure argon. Finally, the direction of migration reversed once again with (110) grains growing into (100) grains in a second vacuum anneal. These results were explained in terms of a change in concentration of oxygen atoms at the gas-metal interface during the anneals. Thus, oxygen atoms were added to the surface during the anneals in impure argon to the point where ?100, the specific surface energy of the (100) oriented grains, was lower than ?110, the surface energy of (110) oriented grains. In vacuum, however, the oxygen concentration at the surface was lowered to the point where ?110 < ?100. Concerning the possibility of secondary recrystallization in high-purity silicon iron with a low initial oxygen concentration, the observed effect of adsorbed oxygen atoms has indicated6 that a good vacuum anneal would favor the rapid growth of matrix grains with the (110) plane in the plane of the sheet much more than grains in the (100) orientation. The growth of only (110) oriented grains of course would depend upon y110 being less than ?hkl, where hkl refers to any plane different from (110). The present paper is concerned with the application of the above ideas to secondary recrystallization to the (110) [001] texture in high-purity silicon iron. The matrix and secondary recrystallization textures and structures are defined and discussed. Observations of growth of nuclei for secondary recrystallization and of boundary interactions are included to provide direct information on the surface energy relationships between (110) and other (hkl) surfaces. EXPERIMENTAL PROCEDURE As before, 2,4-6 high-purity iron and silicon were melted and cast in vacuum to provide an alloy containing 3 pct Si with less than 0.005 wt pct impurities. The oxygen content of the ingot was lower than in previous ingots, being approximately 3 ppm (by weight). The carbon content of this ingot may have been slightly higher than was found for previous ingots. The same rolling and annealing schedule used previously2 was followed in this study to obtain samples 0.012 in. (0.3 mm) thick. These samples were electropolished prior to annealing. After rolling and polishing, the oxygen content of the material was approximately 6 ppm; material used in the previous studies contained about twice this amount of oxygen.

Jan 1, 1961

By J. W. Spretnak, G. W. Powell, J. H. Bucher

Tlze room-temperature tensile fracture oj smooth, round specitnens of three ultrnhigh- strength steels tempered to a wide range of strength levels was studied by means by light and electron-microscopic examination of the fracture surfaces. The fracture of AISI 4340 and 300 M at all the strength levels studied, and H-11, except after tempering at 1200° and 1300°F, occurs in three stages. The initiation of fracture is internal (except in some lightly tcmpeved specimers in which fracture is initiated at surface flaws), and is nucleated largely by separation at metal-second phase intevjaces. TIze voids grow and, coalesce to form a crack. When the crack has reached a sufficienl size, rapid propngutio~z ensues. Failure in this stage of fracture usually occurs by dimpled rupture of inicroshear stefis. In the case of H-11 tempered in the 1125° to 1300°F range, fracture in the shear steps is predominantly by concentrated deformation without void formation. The termination of fracture is usually occomplished by the formation of a shear lib in which fracture occurs by shear dimpled rupture. In the case of H-11 tempered at 1200° and 1300°F, no shear lip was obserued, and the radial elelments extend to the surface—a true termination slage does not exist. ThE tensile fracture of several metals and alloys has been investigated.2-4 In the case of polycrystal-line materials, cup-cone fracture usually results. The mechanism of cup-cone fracture may be summarized as follows.5 Cavities are formed in the necked region of the specimen. They usually are initiated by inclusions or second-phase particles. The cavities extend outwards by means of internal necking, and a crack lying about perpendicular to the length of the specimen is formed in the necked region. Subsequent crack growth occurs by the spread of bands of concentrated plastic deformation inclined at an angle of 30 to 40 deg to the tensile axis. Cavities are formed in the bands of concentrated deformation. The deformation bands zigzag across the bar with the net result that mac-roscopically the crack extends about perpendicular to the specimen axis. The final separation, or cone formation, appears to occur by continued crack propagation along one of the deformation bands out to the surface of the specimen. The micromechanics of the tensile fracture of ultrahigh-strength steels have not been thoroughly investigated. Larson and carr6,7 studied the tensile-fracture surfaces of AISI 4340 with a low-power microscope and reported that three stages of fracture could be observed in general. A centrally located region characterized by circumferential ridges, an annular region characterized by radial surface striations, and a peripheral shear lip were found. It was first pointed out by 1rwin8 that the central region is very probably one of fracture initiation and slow growth, and that the annular, radially striated region is one of rapid crack growth. Presumably the crack grows slowly, assuming roughly a lenticular shape, until it is large enough for the initiation of rapid propagation. In this investigation, it was attempted to determine the fine-scale aspects of the room-temperature tensile fracture of some ultrahigh-strength steels, and to relate the variation in fracture mode with microstructure. The steels studied were AISI 4340, 300M, and H-11 tempered to a wide range of strength levels. I) EXPERIMENTAL PROCEDURE The compositions of the steels studied are given in Table I. The steel was received in the form of hot-rolled bar stock 5/8 to 1 in. in diameter from which oversized specimens were machined and heat-treated. The heat treatments employed are given in Table 11. Subsequent to heat treatment, the specimens were ground to the final dimensions and stress-relieved by heating for 1 hr at 350°F (with the exception of the as-quenched steel). Standard smooth round specimens of 0.252-in. diameter and 1-in. gage length were tested in a Tinius Olsen Universal Testing Machine using a cross-head speed of 0.025 in. per min. The relatively coarse aspects of the fracture topography were determined by light-microscopic examination of sections through the fracture surface of nickel-plated specimens. A direct carbon-replication technique9 was used in the electron-microscopic study of the fracture surfaces. The replicas were examined in the electron microscope, and stereo pairs of electron micrographs were taken. The stereo pairs were then examined using a Wild ST4 Mirror Stereoscope. Carbide and inclusion particles extracted in the replicas were analyzed by selected-area electron diffraction. II) EXPERIMENTAL RESULTS The mechanical testing data are summarized in Table 111. The values reported are the average of

Jan 1, 1965