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By C. G. Dunn, P. K. Koh

Microstructure, magnetic torque, and texture data before and after grain growth were obtained on two 3.25 pet Si-Fe specimens having initially the same cold-rolled textures and the same primary recrystallization textures. The latter textures consisted of four components, two only of which were strong; the strong components were near (120) [001] and (320) [001]. The textures of the two specimens obtained by grain growth were different. In one specimen the two weak components were converted into strong components by a secondary recrystallization process; in the other specimen the primary recrystallization texture was retained by a normal grain-growth process. The difference in behavior of the two specimens was interpreted in terms of a difference in the relative grain sizes between weak and strong components; i.e., in terms of a geometrical factor that would alter the early growth rates of grains belonging to the two weak components of the texture. Specifically the growth rate was considered as the product of two terms: a driving force and a boundary mobility. The texture changes observed are considered to favor the oriented-nucleation growth-selectivity theory more than the oriented-growth theory. WHEN primary recrystallization and grain-growth textures form as a result of annealing deformed metals or alloys, the fundamental processes involved are nucleation and growth. Knowledge, therefore, about nuclei and the factors influencing their growth is required not only for the understanding of texture development but also for its control. In the oriented-growth theory of texture formation1, 2, 3 the problem of nuclei is generally disposed of by the assumption that nuclei are available in all orientations; the theory then has to explain the final texture from the initial texture and the way boundary mobility depends on orientation. In the oriented nucleation theory of texture formation"' nuclei are considered to be present only in certain orientations but the importance of growth selectivity is still recognized. For example, the mobility of boundaries of approximately the same orientation and of the coherent type in twins is believed to be low while that of high-angle boundaries, in general, is high. Because of this the theory may be described as an oriented-nucleation growth-selectivity theory. The main feature of the oriented-nucleation theory, however, is the importance given to nuclei; i.e., how they form in specific orientations and how they grow. In the present investigation two cold-rolled single crystals were used to study the effects of growth after primary recrystallization. The cold-rolled textures and the primary recrystallization textures were determined from portions of these specimens and reported earlier.",' The two cold-rolled crystals were in the (111) [112] stable end orientation, the recrystallization textures were nearly identical and consisted of two strong components, designated M and M', which were near (120) [00l] and (320) [00l], respectively, and also some specific weak components near (111) [110] and (111) [110]. It is well recognized that a single strong component in the primary recrystallization texture may be needed for secondary recrystallization3, 5, 8 but unfortunately when this is the case the amount of material left in deviating orientation may be too small either for growth or for positive identification. The present samples proved to be almost ideal for the study of minor components and their influence on texture changes produced by growth after primary recrystallization. The results obtained are interpreted in terms of present knowledge of grain-growth processes. Experimental Procedure Two lots of silicon-iron alloy of essentially the same composition, namely, 3.25 pet Si, 0.004 C, 0.009 P, 0.010 S, 0.035 Mn, 0.070 Ni, 0.090 Cu, 0.009 Sn, with traces of A1 and Cr and the balance Fe, were converted into single crystals 0.025 in. thick and 1.25 in. wide. The orientations were predetermined by the method of reorienting a seed crystal as described elsewhere.3 pecimen 1 from one lot had the (335) [556] orientation while specimen 2 from the second lot had the (111) [112] orientation.* Both crystals were cold rolled to a reduction in thickness of 70 pet while widening approximately 20 pet. Samples of each were selected for determining 1) the cold-rolled texture, 2) the time required at

Jan 1, 1959

By R. T. Hukki

THE accepted basis of comparisons between mills of different diameter is the percentage critical speed. If n = actual mill speed, rpm, nc = calculated critical speed, rpm, np = calculated percentage critical speed, and D == inside diameter of the mill in feet, then n, In the following analysis capacity, T, is expressed in short tons per hour, tph, and power consumption, P, in kilowatts, kw. Accordingly power consumption per unit of capacity, P will be expressed in kilowatt hours per short ton, or kw-hr per ton. In all equations D refers to the inside diameter of the mill in feet and v to the peripheral speed of the mill in feet per minute inside the liners. ' Comparison between separate mills must be based on equivalent grinding conditions, i.e., same feed, same size distribution of feed, same size distribution of product, and same percentage of solids. In addition, comparisons between separate rod mills must be based on the same rods, same type of liners, and same percentage rod load. Comparisons between separate ball mills presuppose the same balls, similar liners, and same relative ball load. The practical np-range through which the equations apply varies, being narrower for fine grinding in ball mills and wider for coarse crushing in rod mills. The Relationship between Capacity and Speed It is the general belief that the capacity, T, of a tumbling mill is directly proportional to the speed of the mill, other things remaining constant.' Mathematically this is represented by the equation T - c¹ n tph [4] where c, is a factor related with the grinding characteristics of the ore, method of reduction, and the units chosen. It is proposed here that the general equation relating mill capacity and speed should be of the form T = c¹ nm tph [5] In other words, the capacity should be proportional to the mill speed raised to power m, the numerical value of the exponent being 1 5 m 5 1.5, depending on the circumstances. Eq. 5 can also be written in the following forms: T = c, (np)m tph, and [6] T=Ca vm tph, [71 where v = peripheral speed of the mill in feet per minute. If the observed capacity of a mill at speed n¹ is = T¹ tph, the capacity T² of the same mill at speed n² should be T² = T¹ (n²/n¹)tph [8] The Relationship between Power Consumption, Mill Diameter, and Speed The only well known theoretical deduction relating power consumption, P, and mill diameter appears to be the formula of duPont introduced by Gow, Guggenheim, Campbell, and Coghill.' According to duPont, the power required to operate a mill is a function of the mass of the balls, of the lever arm of the ball mass, and of the speed of the mill. The ball mass per unit of mill length is proportional to the square of the diameter, the lever arm is directly proportional to the diameter, and the critical mill speed or any percentage thereof is inversely proportional to the square root of the mill diameter. Following this reasoning, the original duPont formula is of the form P = c4D² c D • c6D-0.5 = c7D2.5 [9] If the mill speed in the above equation is expressed in terms of Eq. 3, the duPont formula may be written as follows: P=f1(D2) f2(D) f³(—np) or [10] vD P = c np D2.5 kw [11] Eq. 11 may also be derived from the mechanical principle of force, which is equal to mass x acceleration. Power necessary to operate a mill may be considered to be an homogeneous linear function of the force developed. Ball or rod mass per unit of mill length is a function of D2. The acceleration factor of the ball or rod mass is a function of the peripheral speed of the mill. Thus P = f4(F) = /x(D2) f5(v) Indicating that v = nDn, and n = c9 np /vD, the above equation becomes P = f2 (D2) -fa (D ca np/vD

Jan 1, 1955

By L. R. Plitt, E. O. Lilge

Tests carried out with both kaolin and silica slurries show that flocculants of the polyacrylamide type can be used to improve the thickening performance of hydrocyclones. This thickening improvement demonstrates that contrary to previously held theories, flocs can be formed which are capable of resisting the shear forces in a hydrocyclone. For the 1.25-in.-diam cyclone used, optimum thickening occurs when the flocculant solution is injected into the slurry stream at or near the feed inlet. Hydrocyclones offer many distinct advantages over gravity thickeners. These advantages include simplicity, low initial and operating costs, small space requirements, and flexibility of operation. In spite of these advantages hydrocyclones have not been widely used as thickeners. The main reason for their lack of application is that hydrocyclones are unable to efficiently remove semicolloidal particles (less than 5 microns) from the suspending solution. In gravity thickeners, the fine particles can be induced to form particle aggregates, or flocs, which have the settling characteristics of large particles. In the hydrocyclone, however, it was always assumed that the existence of shear would prevent the formation of flocs.1-3 Thus, if no floc structure is retained, the thickening hydrocyclone must be designed so that its separation size is below the size of the smallest particle to be recovered. To obtain a very small separation size requires the formation of very high centrifugal forces, which necessitates the use of small-diameter cyclones. Small hydrocyclones have, in turn, very low throughput capacities which render them impractical for many industrial thickening applications. Thus, if the effects of flocculation cannot be utilized, the usefulness of hydrocyclones as thickeners remains limited to pulps which contain no very fine particles. It is well established that most substances acquire a surface electric charge when brought into contact with an aqueous medium. The repulsive interactions between similarly charged particles act to prevent flocculation. One method of flocculating a dispersion is to neutralize the repulsive surface charges by the addition of an electrolyte. The reduction of the electrostatic surface charge (Zeta potential) then permits the universal van der Waals attractive forces to operate between the atoms of the various particles and form particle aggregates. The lime additions used by thickener operators promotes flocculation by this mechanism. A second method of flocculating a dispersion is by the addition of long-chain macromolecules. In this case flocculation is brought about by a bridging mechanism in which the molecules are adsorbed with part of their length on two or more particles, thus forming a molecular bridge between the particles.4,5 The molecules also form bridges between themselves when a single particle is bonded to several polymer molecules. The type of bonding between the flocculant molecule and the particle may be hydrogen bonding, chemical bonding, or electrolytic attraction.6 The flour and glue which are used as thickener additives are believed to promote flocculation in this manner. In the past decade synthetic long-chain polymers with extremely high flocculating capabilities have been developed. The flocs formed by these new polymeric flocculants are larger and more shear-resistant than those formed by the presence of electrolytes.7 The advent of these flocculants raises the question: Are the flocs formed by these synthetic polymers stable enough to resist the liquid shearing forces in a hydrocyclone? The investigations reported in this paper were carried out in order to provide some answers to this question. EXPERIMENTAL WORK For the bulk of the test work a 5% slurry of commercially available kaolin with an average particle size of 5 microns was used. An initial evaluation of the available flocculants was carried out to determine which flocculant formed the most shear-resistant flocs. A combination of the techniques used by Healy7 and Booth8 was used for this purpose. This initial study revealed that the neutral high-molecular weight polyacrylamides produced the most shear-resistant flocs. One of these flocculants, Separan MGL*, was selected and then used for all the hydrocyclone tests. The flocculant was dissolved in water and added to the hydrocyclone as a dilute solution.

Jan 1, 1968

By Michael Hoch, Walter C. Wyder

The isothermul section of the Nb-Ti-Zr-O system at 1500°C was investigated using X-ray dzffraction and metallographic techniques. UP to 66.7 at. pct 0, the system contains nine four-phase regions. Tsopleths at 10, 20, 30, 40, 50, and 55 at. pct 0 weye constructed. The purpose of this investigation was to determine the general shape of the quaternary equilibrium phase diagram of niobium, titanium, zirconium, and oxygen at 1500°C. The system was truncated at 66.7 at. pct. O., PREVIOUS INVESTIGATIONS The Ti-Zr-O system was investigated in this laboratory.' The binary systems of interest have been compiled and discussed by anssen2 and Levin, McMurdie, and Ha11. Elliott4 has determined the Nb-O system by metallographic and X-ray diffraction techniques. He shows the existence of three oxides, namely NbO, NbO2, and Nb2O5. At 1500°C the solubility of oxygen in niobium is about 4 at. pct. No solid solubility region is shown for either NbO or NbO2. EQUIPMENT The same equipment as that for the study of the Ti-Zr-O system was used. The X-ray diffraction patterns were analyzed with the help of the ASTM card set5 and NBS circulars.6 MATERIALS The niobium powder (99 pct pure), the titanium powder (99.6 pct pure), the niobium pentoxide, and the zirconium dioxide used in this study were purchased from the Fairmount Chemical Co., Newark, N.J. The zirconium powder (99.4 pct pure) was obtained from the Charles Hardy Co., Inc., N.Y. Reagent-grade titanium dioxide was purchased from the Matheson Co., Inc., Norwood, Ohio. The oxides were dried in air at 700°C for 24 hr before use. Though the materials used were not "hyper-pure," the impurities present do not affect the results (lattice parameters, phase boundaries), within the experimental accuracy. PROCEDURE Samples of the desired compositions were made up, in mole pct, from the materials listed above. In some cases the intermediate binary compounds, such as NbO and TiZrO4 were prepared beforehand and used in the preparation of the samples. This technique enabled equilibrium to be reached from two sides. The components of each sample were mechanically mixed in a mortar and pestle and pressed into 3/16-in. diam pellets. The pressures used in compacting were of the order of 50 to 100 x 103 psi. Sintering was accomplished by heating the samples in a tungsten crucible (3/4-in. high, %-in. diam, 1/8-in. wall, lid with XB-in. hole). The pellets were separated from each other and from the crucible by means of small spiral coils of tungsten wire placed between the stacked pellets and on the bottom of the crucible. The sintering time was from 4 to 12 hr at 1500°C under a vacuum of 6 x 101-5 to 1 x 10-6 mm of Hg. All samples were reground after the first or second heating repressed, and reheated. In most cases: equilibrium was obtained after the first heating, as the X-ray diffraction pictures after each heating remained unchanged. Quenching of the samples from 1500°C was at first only possible by allowing the crucible and its contents to lose heat by radiation. The temperature dropped from 1500° to 900°c in approximately 1 1/2 min, which was considered adequate when compared to the times used by other investigators to reach equilibrium in the temperature range of 1000°c and lower. Later, a new technique for faster quenching of the samples was cleveloped. This technique involved the removal of the samples from the crucible, whereupon they were quenched by coming in contact with the water-cooled copper base of the furnace. This manipulation was performed without breaking the vacuum. The sample pellets were placed on a tungsten wire rack inside the crucible. The wire rack passed through the hole in the crucible lid, where it was connected to a small nonmagnetic chain. The chain was fed to the side of the furnace by means of a brass rack which fitted between the body and lid of the furnace. Suspended at the end of the chain, near the furnace wall, were three magnetic washers. With the use of a strong

Jan 1, 1962

By O. N. Carlson, H. A. Wilhelm, J. M. Dickinson

On the basis of microscopic studies, melting-point observations, and X-ray analyses, a phase diagram is proposed for the Cb-V system. A complete series of solid solutions is formed with a minimum in the solidus at 1810°C near 35 wt pct Cb. No compounds or intermediate phases were found in the system above 650°C. THERE is an ever increasing need for better structural metals and alloys for use in nuclear reactors. In addition to the normal properties of engineering structural materials, such as high temperature strength, resistance to corrosion, and fabric-abil~ty, the nuclear properties of the material must be considered. In a nuclear reactor it is important to conserve neutrons, so a material which removes these neutrons from the reaction excessively is considered to have unfavorable nuclear properties. In nuclear-reactor design the engineer must have nuclear as well as other data available on alloys in order to make a wise selection of materials. Due to the fact that many of the common structural materials have undesirable nuclear properties, it is vital that new alloys of metals having more favorable nuclear properties be investigated. Columbium and vanadium are both high melting metals, both exhibit resistance to chemical attack, and no great difficulty is encountered in fabricating them into desired shapes. With proper treatment both metals can be cold rolled extensively without failure. In addition they have desirable nuclear properties for certain types of reactors. Therefore, the alloys of columbium and vanadium should be of interest in the atomic energy program. Since an alloy-development program is enhanced by a knowledge of the phase equilibria of the components, this investigation was undertaken to establish the phase diagram for the Cb-V system. According to the Hume-Rothery rules for alloying,' the chemical similarity, crystal structure, and atomic-size factor are favorable for a complete series of solid solutions for this system. Both elements are in the same family of group V of the periodic table and thus are quite similar chemically. The crystal structures of columbium and vanadium are compatible for extensive solid solubility, since both have body-centered-cubic structures. The atomic diameters of columbium and vanadium are 2.85 and 2.62Å, respectively. This difference of slightly more than 8 pct is well within the 15 pct maximum difference allowed for extensive solid solubility. Experimental Procedures Source of Materials: Columbium powder and sheet trimmings were obtained from the Fansteel Metallurgical Corp. According to the manufacturer the metal contains less than 1 pct impurity. An analysis of the metal showed approximately 1800 ppm C in the powder while the sheet trimmings contained less than 500 ppm C. Spectrographic analysis showed minor amounts of Ca, Cr, Fe, Mn, Si, Ti, V, and Zr in both forms of the columbium. No commercial source of vanadium having the ductility and purity desired was available to the authors at the beginning of this investigation. As a result, all of the vanadium used in this study was prepared by the bomb reduction of vanadium pen-toxide with calcium employing the method reported by Long.' Yields of massive vanadium normally were about 80 pct. Chemical analysis of the vanadium prepared in this manner showed the presence of 200 to 500 ppm N and 800 to 1000 ppm C. Minor amounts of Ca, Fe, Mn, Si, Zr, Cr, and Cb were detected by spectrographic analysis. This vanadium metal was ductile and was cold rolled into 5 mil sheet. Annealing was not necessary during this rolling and the metal retained its cold-rolling characteristic after are-melting. Preparation of Alloys: The Cb-V alloys were prepared by melting pieces of vanadium sheet togethel-with columbium in the form of sheet or pellets of powder. The melting was carried out under argon in conventional arc-melting equipment employing a tungsten electrode and a water-cooled copper crucible. Each alloy was remelted three or four times, inverting the alloy after each melting in order to assure complete mixing. Alloys normally were obtained as round flat disks, weighed approximately 70 grams, and had roughly the shape of a disk 1 1/2 in. in diameter and 1/4 in. thick. Half of each alloy

Jan 1, 1955

By R. E. Miner, J. K. Jackson, T. L. Wilson

A study has been made of the transformation kintetics and morphology in gas-quenched Fe-5 pct Ni alloys. Massive ferrite or nlurtensite was found to form at temperatures in agreement with earlier results. Surface Preparation appeared to have the greatest effect in determining the type of transformation Product formed. Grain size change, subgrain morphology, and dislocation densities of massive ferrite were essen-tinlly invariant functions of cooling rate. The mar-tens~tic structures were typical of transformation in austenite grains of the order of the sample thickness. BY introducing the idea of a massive transformation in dilute iron-base alloys, Gilbert and Owen in 1962 served to stimulate a closer inspection of phase transformations in ferrous systems.' A wealth of literature has followed concerned with the morphology,2-5 transformation mode,2'3'6-8 and thermodynamics of transformations.2,5,9 interesting controversies have resulted from the experimental observations; closer attention has been paid to the definition of massive transformations and still to be resolved is the Ms temperature of pure iron. The purpose of this note is to report some observations made in a detailed kinetic and metallographic examination of the transformations that occur in gas quenched Fe-5 pct Ni. The results are pertinent to the Ms extrapolations that have been made for pure iron and the observed substructure of massively transformed alloys. PROCEDURE The material used in this investigation was cast as a 5 lb vacuum induction melted, carbon deoxidized heat. The ingot was hot worked to a strip 0.10 in. thick, decarburized, and cold rolled to final thickness. Specimens were punched to sample shape and decarburized in wet hydrogen at 600°C. The chemistry of test specimens is indicated in Table I. Samples 1 by $ in., by thickness were resistance heated and rapidly cooled in an apparatus as illustrated in Fig. 1. Similar helium quenching apparatuses have been described previously;2,6'10 the distinguishing feature of this apparatus is the nozzle geometry. Twin nozzles with three convergent-divergent, sonic ports were mounted perpendicular to the specimen for quenching purposes. The specimen temperature was monitored with an intrinsic 3 mil chromel-alumel thermocouple spot welded to the specimen and con- nected to an oscilloscope. A single switch stopped the current flow through the specimen, opened a gas flow solenoid valve, and initiated an oscilloscope sweep. Cooling rates were read directly from a photograph of the oscilloscope trace and the quenching rates quoted later were made at a point immediately prior to transformation on the trace. All quenching studies were conducted either under a vacuum of 10"-5 torr or a helium atmosphere. The sample geometry was chosen large enough to permit optical and electron microscopy to be performed on samples. The samples were electropolished for both types of examination in a perchloric-acetic solution. Electron microscopy was conducted on a HU 11A microscope operated at 100 kv. Dislocation densities were determined at the same general operating reflection (110) on foils thick enough to produce Kikuchi patterns. RESULTS AND DISCUSSION Transformation Temperature Observations and OD-tical Microscopy. The quenching results of this study are illustrated in Fig. -2(a). Samples which were treated in the as-decarburized condition transformed in a manner similar to that reported previously—a decrease in transformation temperature occurred as the quenching rate increased until a plateau region was reached. Within the scatter of the results obtained here, there was no break in the transformation temperature-quenching rate plot. This suggests no change in transformation mode. Further metallographic examination confirmed this observation. A martensitic transformation was obtained for similarly treated samples except that the surface was first electropolished. The Ms temperature was approximately 85°C below the plateau determined for the unpolished samples and cooling rates as slow as 2000°C per sec were adequate for producing marten-site. The transformation temperatures are in gen- / STRIP SAMPLE / COPPER I SAX/-/}' / CONNECTOR-----A f, SON|C poRTS AC LEADS 3j ]j"I rofe[ \ Mf/yinK/iKj''^ THERMOCOUPLE X-(^—iie"s*c? ' LEADS 1 INCH Fig. 1-—Schematic scction of gas quenching apparatus

Jan 1, 1970

By P. Bardzil, J. Gurland

An experimental study of the variation of transverse-rupture strength with composition Anexperimentaland grain studysize has shown that the strength reaches a maximum for values of the mean free path between carbide particles of 0.3 to 0.6 microns. The fracture oforiginates in and proceeds through the carbide grains mainly. Impact strength and hardness also were recorded. MOST of the physical properties of sintered carbides vary linearly with composition. The transverse-rupture strength, however, shows a unique behavior. As the amount of binder metal is varied from 6 to 25 pct by weight, the strength at first increases; then, between 15 and 20 pct Co, it reaches a maximum of nearly 400,000 psi, and finally decreases with further additions of binder metal. This behavior of the transverse-rupture strength has been reported, among others, by Englel and Sandford and Trent.' The significance of these observations has not been discussed in the literature. That it may be of more than specific importance is indicated by the very similar variation of strength with composition encountered in other systems sintered in the presence of a liquid phase, such as Tic-Ni3 and Fe-Cu.' Experimental Details All compacts were prepared and sintered according to normal industrial practice. The average diameter of WC grains and the mean free path between grains were measured on metallographically prepared samples by a method of linear and planar analysis sing the relations where d is the average diameter of dispersed grains; Nl is the number of noncontiguous grains intersected on a metallographic plane by a line of unit length; N, is the number of noncontiguous grains per unit area; P is the mean free path between grains of dispersed phase; and f is the volume fraction of dispersed phase. Approximately 1000 grains were counted on each sample. For each composition d2 was plotted against P, the resulting straight lines serving as a check on the measurements. The distribution curves of the WC powders of different average diameters were homologous, and no attempt was made to influence the grain size by blending powders, adjusting the sintering conditions, or otherwise altering the particle size distribution. Densities were measured by differential weighings in air and water. The degree of densification did not vary consistently with either composition or grain size. The density is influenced by slight amounts of impurities, specifically by 0.1 to 0.2 pct Fe which enters the powders during ball milling. As an illus- -tration of the experimental variations, a number of measured densities are listed in Table I. They are expressed in percentage of theoretical density, as calculated from the published X-ray densities of WC and Co.' For the purpose of determining the transverse-rupture strength, rectangular test specimens (3/16x 3/8x3/4 in.) were broken by loading at the center of a 9/16 in. span. The average strength of five or more samples is reported for each composition and grain size. The compacts were ground on two parallel surfaces only. The load was applied at an average rate of 6,800 psi per sec. Since the elongation after fracture of the alloys is very small, it was assumed that the compacts deform elastically to failure and the fracture stress was calculated by the conventional beam formula. The data for one alloy are presented in Table II as an example of the results and scattering ranges encountered. The precision of the test, as measured by the average difference between duplicates, is of the order of 15,000 psi. The results are strictly comparable only to compacts prepared and tested in the manner described and of similar chemical composition and grain size characteristics. Unnotched Charpy specimens were used for impact testing. Each point represents the average of 3 to 20 samples, the larger number being used in an attempt to determine the influence of grain size. Considerable scatter was encountered, the range from lowest to highest value often amounting to 30 pct of the impact strength. The hardness is reported as a Ra reading, using a 60 kg load with diamond brale indenter. Compositions are given in weight percent.

Jan 1, 1956

By M. J. Marcinkowski, E. N. Hopkins

An investigation has been made of the ß(fcc) — a(hexagonal) transformation which occurs in lanthanum using both electrical resistivity and transmission electron microscopy techniques. It has been shown that the ß phase can be retained below the transformation temperature by rapid quenching but that the sample immediately begins to transform to the a phase. The transformation is observed to nucleate in the vicinity of inclusions. Based on the above observations, a detailed model of the transformation has been advanced which involves the nucleation of an extrinsic stacking fault bounded by a pair of Shockley partial dislocations in the vicinity of some heterogeneity, i.e., an inclusion. The stress field of the resultant dislocation pair acts to nucleate extrinsic faults in adjacent planes and leads quite naturally to the B-a conversion with a minimum of strain energy induced in the crystal. LANTHANUM possesses an fcc structure ß) (8) upon cooling transforms to a hexagonal modification (a) in much the same way as cobalt. The one exception, however, is that the stacking sequence of the closest packed planes in a La is ABAC ABAC, and so forth,1 whereas in cobalt it is ABAB, and so forth, i.e., hep. Mainly on the basis of transmission electron microscopy techniques, there seems to be little doubt that the 0 — a transformation in cobalt involves a dislocation mechanism2 although its exact nature still remains obscure. Although the ß - a transformation in lanthanum is somewhat more complex than that occurring in cobalt, it was thought that its very uniqueness would be helpful in understanding fcc — hexagonal transformations in general. Such a general understanding of these transformations is important since they represent what are perhaps the simplest of the martensitic class of transformations. The experimental techniques used were those of electrical resistivity and transmission electron microscopy. EXPERIMENTAL PROCEDURE The lanthanum used in this investigation was prepared by the calcium reduction of lanthanum fluoride in a tantalum crucible under an argon atmosphere as described by Spedding et al. The residual calcium was removed by vacuum remelting in a tantalum container. Portions of the metal were then analyzed by emission spectroscopy as well as vacuum fusion. The amounts of the various impurities that were found are listed in Table I. A portion of the lanthanum ingot was swaged at room temperature into 0.030-in.-diam rod for the resistivity samples while the remainder was rolled into 0.010-in.-thick sheet for the transmission electron microscopy phase of this investigation. In order to eliminate the plastic deformation induced in the samples during fabrication, they were sealed in evacuated tantalum lined quartz capsules and annealed for 1 hr at 700° C. Specimen resistances were measured using the conventional "four-wire" technique described by MacDonald, 4 employing a type K-3 Universal Potentiometer and a standard 0.001-ohm resistor, both manufactured by Leeds and Northrup Co. By taking into account all of the possible errors in the apparatus, it was felt that the absolute resistivities of the approximately 0.87-in.-long specimens measured are reliable to 3 pct. Resistances from room temperature to 700°C were measured using a vacuum furnace. In order to avoid sample contamination by the thermocouple, chromel-alumel leads were spot-welded into a tantalum shield which in turn was welded to the lanthanum specimen. Resistances below room temperature were obtained by transferring the sample to a helium gas-filled quench tube and slowly dripping liquid nitrogen into a surrounding dewar flask. A steady reduction of temperature to about —190°C was completed in about 23 hr, and the resistances were measured at various temperature intervals. As will be shown shortly, rapid quenching from above about 350°C was sufficient to suppress the B -a transformation initially but subsequent annealing at lower temperatures leads to a partial ß --a conversion. To investigate this aspect of the transformation, the samples were suspended in the hot zone of a helium-filled furnace from which they could be rapidly dropped into the quench tube mentioned previously which was now

Jan 1, 1969

By E. S. Machlin

An extension of the thermodynamic theory has been made for the case of irreversible growth processes occurring by the motion of an interface. The theory is applicable to such diverse phenomena as diffusion, growth in recrystallization, continuous grain growth, growth of carbides, etc., growth of eutectoid products, growth in solidification, recovery, "slipless" flow, etc. THE publication of a recent book1 has served to focus attention on a very powerful means of treating certain irreversible processes. This method which has been formally described as the thermodynamic theory of irreversible processes is applicable to processes which involve an approach to equilibrium and for which the deviations from equilibrium are small. The irreversible processes can be classified into three groups: chemical reactions, transport processes (diffusion, heat and electrical flows), and relaxation phenomena involving a degradation of internal energy to more stable states. The limits of applicability of the theory can be precisely defined1,2 for each type of irreversible process. For example, in a chemical reaction at constant temperature and pressure, the Gibbs free energy released per mol in the process should be less than the thermal energy, RT. Another type of irreversible process, which sometimes involves a combination of the first two of the above-mentioned groups, is treated in this paper. This process is one characterized by the motion of an interface separating two regions having different values of free energy and may be briefly described as a growth process. Prigogine2 and Herring3 have treated special cases of this type of process. Previous conscious applications of the theory in metallurgy have been limited to the field of diffusion, one of the transport processes. Darken,4 Bardeen,5 Prigogine2 and others have made significant contributions in this respect. Some other applications of the theory are described in this paper. The Theory The thermodynamic theory of irreversible processes is based on the work of Onsager,6 DeDonder,7 Prigogine2 and others. A resume of the theory has been given by Prigogine2 and DeGroot.1 A brief description of the theory follows, although for a complete understanding the reader is urged to read the references. It is first assumed that the change in entropy, even for a system removed from equilibrium, is given by dS = [dU + pdV - Si µi, dn, - Sk Pk dxk]T-1 Using this expression, the irreversible entropy production in the system is calculated by subtracting the contribution to the change in entropy of the system by transfer of heat, work, or matter from the surroundings. Thus, for example, the irreversible entropy production of a system at constant temperature and pressure is given by dtS = — — dG (DeDonder7) Now it has been shown by Prigogine,2 DeDonder,7 and DeGroot1 that the rate of irreversible entropy production diS/dt, when calculated in the manner suggested, can be written as a sum of products of conjugate forces XK and fluxes Jk, i.e., d,s/ = Sk Jk Xk [I-1] dt The assumption is next made that a linear relation exists between a given flux and the forces, obtained from Eq. I-1, i.e., Ji = Sk Lik Xk (i = 1, 2, . . . n) [I-2] Generally, there is a degree of freedom in choice of the fluxes and forces. However, for all the choices consistent with Eq. I-1 the Onsager8 relations, based on the principle of microscopic reversibility, namely, Lik = Lki, are valid. The coefficients Lik, depending upon the choice of the conjugate fluxes and forces, may be more or less dependent upon the parameters defining the state of the system. In general, the proper choice of fluxes and forces utilizing Eq. I-1, makes the coefficients Lik independent of time. Also, because many of the three classes of irreversible phenomena have already been treated,1,2 a proper choice can be made by analogy. In any case, the validity of Eq. 1-2, from whatever choice made using Eq. I-1, must be tested by experimentation. The theory, thus, comprises the following steps: 1—The irreversible entropy production is calculated to yield Eq. I-1. 2—The terms in Eq. I-1 are grouped

Jan 1, 1954

By W. S. Row

This mine is operated at 4000 to 4500 tons daily through a single shaft, with one rock hoist and one senice hoist. Latest shaft construction is concrete with wooden dividers. Economics of drifters and air-leg drills are compared, as well as costs of shrinkage and sub-level stoping. Economy of large haulage equipment and underground crushing is shown. THE property of Kerr-Addison Gold Mines is located in the Larder Lake district of Ontario about 3 miles from the Quebec boundary on the highway between Kirkland Lake and Noranda. It is roughly 320 miles due north of Toronto and 365 miles north of Buffalo, N. Y. The property was staked in 1906 and after several development efforts finally came into continuous production at 500 tons per day in 1937. In 1939 the daily tonnage -was increased to 1200 and in 1941 to 2100 tons. At the end of the war, because of the shortage of labor, tonnage was down to 1100 tons per day, rising to 2200 in February 1947. A further plant expansion inaugurated in 1946 was completed by December 1948, bringing the capacity of the mine and mill to a production rate of 4000 tons per day. Current production, with 880 men employed, is 4400 tons per day. Changes in mining methods and equipment, required by the recently completed expansion program, have yielded interesting comparative results, some of which are described in this paper. Hoisting of ore and waste from the mine, as well as all service facilities for handling men and supplies underground, are provided for in a single vertical five-compartment shaft. Ore and waste are hoisted in 12½-ton skips in balance by a 14-ft diam hoist with drums 115 in. wide, grooved for 2?-in. wire ropes. This hoist, with a total rope pull of 85,000 lb, was designed to operate at a speed of 2600 ft per min to a depth of 4000 ft, hoisting 15 tons of ore in each skip. It is amplidyne-controlled and powered with dual drive dc motors of 2250-hp each, through flexible couplings to two pinion shafts, one on each side of the main gear. Each motor has a peak load rating of 4500-hp at point of greatest duty. Direct current power to the hoist motors is supplied from a motor generator set consisting of a 5000-hp synchronous motor driving two 1750-kw dc generators. The loading pockets used so far are at depths of 1500 and 2725 ft respectively. Consequently the present hoisting speed is 2000 ft per min and the skips capacity only 12½ tons. Now that the shaft has been deepened the new pockets at 3934 ft will be increasingly used so that the speed and the skip size will be increased up to original specifications as required. Some difficulty in meeting the required hoisting cycle is expected because of the shape of the skips. As now in use the cross-sectional dimensions of the inside of the skip are 4 ft 6 in. x 3 ft 8 in. To hold 121/2 tons, therefore, they are 14 ft 10 in. deep. Since the skips are the conventional overturning or Kim-berley type, considerable hoisting time is lost in retardation in entering the headframe dump and in acceleration when leaving. It is expected that to obtain the specified tonnage from this hoist when the skip size is increased to 15 tons it may be necessary to resort to bottom dump skips. This type of skip could reduce considerably the present excessive acceleration and retardation times. Analyses of the skip-hoisting operation are made monthly, and every effort is made to reduce controllable delays. For a nine-month period in 1951 such an analysis shows that the hoist was in operation 92.5 pct of the available time, which was allotted as shown in Table I. Overall hoisting costs, cage and skip, for the year 1951, averaged $0.168 per ton of ore milled. The mine is serviced entirely by means of a single cage, capacity 35 men or 15,700 lb, operating in con-

Jan 1, 1954

By J. L. Taylor, Pol Duwez

THE present knowledge of the Ti-Al system is limited to the portion of the diagram extending from pure aluminum to the intermetallic compound TiAl3' A preliminary investigation of the titanium-rich Ti-A1 alloys revealed that the solubility of aluminum in titanium is quite extensive and that the transformation temperature of titanium is raised by alloying with aluminum. From an X-ray diffraction study of alloys containing up to 75 atomic pct Al (TiAl3), the phase boundaries at 750°C were located as follows: the a titanium solid solution extends from 0 to about 36 atomic pct Al, a two-phase region exists from 36 to 46 atomic pct Al, and an intermediate phase of varying concentration extends from 46 to 62 atomic pct Al. The purpose of the present paper is to describe the crystal structure of this new phase. The alloys were prepared by melting in a helium arc furnace on a water-cooled copper plate, using a furnace essentially the same as that described in ref. 2. The titanium metal was of the iodide type furnished by the New Jersey Zinc Co., and a piece of pure aluminum (99.99 pct) was obtained through the courtesy of the Aluminum Co. of America. After melting, the samples, weighing approximately 5 g, were sealed in evacuated fused silica tubes and homogenized for 4 hr at 1000°C. The specimens were then held for 10 days at 750°C and rapidly cooled to room temperature. Filings were then taken from each sample, sealed in evacuated vials, annealed at 750°C for 4 hr, and rapidly cooled to room temperature by quenching the vials in water. Powder diffraction patterns were obtained with a 14.32 cm diam camera, using K copper radiation filtered through a nickel foil. Structure Determination The X-ray diffraction patterns of the alloys containing 46, 50, 55. 60, and 62 atomic pct Al were identical, except for a slight shift in the positions of the reflections. The alloy containing 55 atomic pct Al was chosen far structure determination. The powder pattern contained 37 reflections and the a, doublets were well resolved in the back-reflection range. The relatively small number of reflections and the sharpness of the pattern were considered as an indication of a simple atomic arrangement in a relatively small unit cell of high symmetry, and an attempt was therefore made to solve the structure without single crystal work. A satisfactory fit was found on a large scale Hull-Davey tetragonal chart for an axial ratio of approximately 1.45. All the reflections were readily indexed and the tentative unit cell dimensions were computed to be a - 2.81 kX, c - 4.07 kX, and c/a = 1.448. The indices (hkl) and the values of d and sin2 A are given in Table I. The agreement between observed and computed sin2 is quite satisfactory. Once the unit cell was known, the details of the structure were readily found. First, it is obvious that the number of atoms per unit cell cannot exceed two, since more than two atoms would lead to a density greater than that of pure titanium. The next logical step is to assume that the two atoms occupy the corner and center of the cell. If this assumption is correct, the structure may be described as follows: space group D1, - P 4/mmm; one titanium atom in a: 000; one aluminum atom in d: 1/2 1/2 1/2: and no extinctions. Assuming this structure to be the correct one. intensities were computed by means of the usual equation: sin2 0 cos 0 where F is the structure factor; 8, the Bragg angle. and p, the multiplicity factor. The calculated values of intensities are compared in Table I with the visually estimated intensities. The agreement is quite satisfactory and the structure is therefore confirmed. The crystal structure of TiAl just described is the same as that of AuCu ordered. The AuCu ordered

Jan 1, 1953

By Jean-Jacques Prompsy, J. S. Rinehart

Some time ago a study was initiated at the Colorado School of Mines in an effort to arrive at a better understanding of the stress fields developed within drill bits under dynamic loading and the influence that these stress fields could have on the failure of the bits. Particular emphasis has been given to the influence that bit shape has on the establishment of highly localized, potentially destructive stress inhomogeneities within the bit. The study has been divided into three phases involving three velocity regimes: impacts at very low velocities, 0 to 20 ft/sec, a velocity range in which dynamic effects are just beginning to be found; impacts at velocities ranging from 20 to several hundred ft/sec, a range commonly encountered in practical drilling operations; and impulsive loading through the detonation of explosives, a region in which the dynamic effects are greatly exaggerated and made more identifiable. The ultimate objective is to provide basic data which will enable the mitigation through judicious design of the frequency and severity of these transient concentrations of intense stress, thereby prolonging and increasing drill efficiency. This paper presents results of the third phase of this study — the development of a better understanding of the dynamics and mechanics of failures caused by transient stress-wave interactions. The impulsive loading or transient waves in these experiments were generated by detonating small explosive charges placed on the ends of Plexiglas cylindrical rods terminating in truncated cones. Under such intense loading, dynamic effects are greatly exaggerated and, hence, made more identifiable. The explosion generates a high-intensity transient stress disturbance which moves through the rod, reflects from surfaces which lie in its path, and establishes momentarily narrow regions of high concentrations of stress where failure of fracture may occur. The peregrinations of these waves, their interactions and their effects have already been described in the literature (see, for example, Refs. 1 and 2). The locations and extent of the regions quite apparently are strongly dependent on specimen shape, making it possible through judicious shaping of specimens to relocate the highly stressed regions, minimize their extent, or eliminate them entirely. These experiments were designed, first, to identify more clearly the vulnerable regions in geometries relevant to drill-bit design and, then, to modify these regions in a predictable way by changing specimen shape. Through this latter process, it is anticipated that better bit design might evolve. The specimens used in the experiments were cylindrical rods, 1 1/2 and 1 1/8 in. in diameter, ended by a truncated cone, with the cone angles ranging from 45° to 130°. Upper cone face diameters were 1/2, 3/4, or 1 in. A small plastic-covered electric blasting cap detonated on the axis of the specimen produced the spherical shock wave. The detonators used were Olin Mathieson No. 6, which induced into the rod a transient saw-toothed stress disturbance of about 3-microseconds duration, corresponding to a wave length of 0.3 in. in the Plexiglas. Five distinct systems of fracture were observed: (1) along the axis of the rod, a lower system of fractures, the cracks focusing around one point for specimens having cone angles of 80° and 90° and, as the cone angle was increased, spreading downward; (2) just above these fractures, an upper system of fractures composed of horizontal cracks observable in some specimens but not of any appreciable extent; (3) a third system of axial cracks still above the latter, observable in the small cone-angle specimens; (4) in the upper part of the specimen, a system of radial fractures extending from the blasting point; and (5) circular spalling due to reflection of the wave on the boundary of the cylinder. Only the first three systems, the axial fractures, are examined here. LOWER TENSILE FRACTURE SYSTEM The first, lower system of tensile fractures, shown in the photograph of Fig. 1, was observed in almost all of the specimens. It was due to the reflected tensile wave coming in from the boundary of the cylinder as shown in Fig. 2. The reflected wave was cylindrically convergent and focused

By R. Stickler, A. Vinckier

An optical and electron microscope study was made on a commercial 302 stainless steel heat treated for massive carbide precipitation. Convincirg evidence was obtained that the grain boundary precipitate does not grow away from the grain boundary into the matrix, but grows as a network of large thin dendrites in between the grains. IN austenitic stainless steels the carbon in supersaturated solution precipitates when the steel is heated in the temperature range 450" to 1000°C. During such heat treatments the chromium-rich carbide occurs primarily at the grain boundaries and has adverse effects on the corrosion resistance and low-temperature ductility of the material. It has been shown that the morphology of the precipitated particles differs widely depending on the time and temperature of the heat treatment, the nature of the boundary, the misfit between the grains, and so forth.1"5 It was assumed by Mahla et al.,' Streicher,' and Mc Nutt' that the carbide particles which nucleate in the grain boundary grow in various geometric or dendritic forms away from the boundary into the matrix. However, Kinzel,' Hatwell et a, and Plateau et aL4 found that the particles nucleate in the grain boundary and grow as a network of thin dendrites in the grain boundary interface. We have made a comprehensive studyg of the precipitation occurring in a commercial 302 austenitic stainless steel heat treated for times ranging from 0.15 to 1500 hr at various temperatures from 480" to 1065"~. This study was made to elucidate the influence of heat treatments on both the mechanical and the corrosion properties of this steel. Part of this investigation which is pertinent to the morphology of the grain boundary carbides referred to above is separately reported here. We found that the particles which nucleated in the boundaries grew in the interface of these boundaries, thus supporting the viewpoints of Kinzel,' Hatwell et al.,3 and Plateau et al.4 Furthermore, when carbide particles nucleated in the matrix very close to the boundaries, they possessed a morphology distinctively different from the particles growing in the grain boundaries. MATERIAL A study of metallographic samples and of fracture surfaces of a 302 stainless steel is reported in this paper. The composition and heat treatments are listed in Table I. Polished and etched samples were examined und813r the optical microscope, and carbon extraction replicas of etched micrographic samples and various fracture surfaces3'8'9 were examined under the electron microscope. RESULTS AND DISCUSSION A representative optical micrograph of the 302 steel, condition A, is shown in Fig. l(a). Particles can be seen on the grain boundaries but no traces can be found of particles which grow from the grain boundaries into the matrix. A carbon extraction replica of this sample shows numerous large thin dendrites, Fig. l(b). The lateral dimension of such carbide particles vary up to 100 p, and their thickness estimated from the amoun! of electron penetration i:; between 500 and 1000A. Such large dendrites are extracted from almost all grain boundaries and, if they had grown into the grains, they would definitely be revealed by etching traces in the matrix, Fig. l(a). The reason why these large dendrites on the extraction replica appear to be grown into the grain is due to the mechanism of the extraction replica process. Thus, these dendrites are supported by the carbon replica film only at the edges originally along the grain boundary trace A-A, Fig. l(b), in the polished metal section and have subsequently fallen over onto the carbon replica film during handling. Although such dendrites generally fall only to one particular side of the grain boundary trace, one finds occasionally that parts of a dendrite have fallen to both sides, as shown in Fig. l(b). Further evidence for the growth of carbide in the grain boundary can be obtained from the appearance of fracture surfaces. A small impact specimen of the 302 steel, condition A, was broken at liquid nitrogen temperature. The fracture path follows the

Jan 1, 1962

By B. L. Averbach

Recovery and primary recrystalliza-tion in cold worked metals are usually considered as two competing processes. Some of the effects which usually accompany recovery are: alleviation of stress corrosion tendencies, changes in thermal emf,1 damping capacity,2 electrical resistivity,2 and magnetic properties,3 and only minor changes in hardness or the related strength properties. During primary recrystalliza-tion new unstrained grains are formed at the expense of the strained matrix. These new grains eventually become visible metallographically, and nucle-ation and growth kinetics have been indicated for this process.4,5 Frequent attempts have been made to study the cold-working phenomenon by observations on the line broadening by X ray diffraction patterns. Relatively few measurements of line intensities have been made, although Brind-ley and his collaborators, 6,7,8 by means of film techniques, compared the intensities of cold worked Cu, Ni, and Rh patterns with those from chemically precipitated powders. These precipitated powders were presumed to be strain free, and it was found that the intensities for the cold-worked materials progressively decreased as the Bragg angle increased except for the first line, where there was an increase due to reduction in extinction. This was interpreted as a randomness in atomic position induced by cold work. Such randomness is similar to that caused by thermal agitation and has been described as "frozen heat" displacement of 0.08-0.10 A from the mean atomic position. In a recent study9 on the effect of cold work in metals on their powder pattern intensities, the changes in integrated intensity for heavily cold worked alpha brass were observed as a function of the annealing temperature. These measurements were made with a manually operated Geiger-counter spectrometer using CuKa radiation monochromated with a rock salt crystal. Intensity measurements were made with a scaling meter over small intervals of angle, and the equipment was so arranged that the diffracted and incident beams made equal angles with the specimen. Intensities could be compared directly by simply interchanging specimens, and comparisons from day to day were made with a standard whose line intensities did not change on aging. It was shown that a cold worked alpha brass standard was stable for at least a year. Table 1 indicates the results of the integrated intensity measurements on a 70 Cu-30 Zn brass. In the sample preparation, a brass plate was first cold rolled 50 pct and then filed, screened to —325 mesh, compacted into briquettes at a pressure of 60,000 psi and finally annealed for one hour at various temperatures up to 400°C. The briquetting pressure did not seem to influence the integrated intensities, and most of the cold work was introduced by the filing. Although this method of cold work is not quantitative, it was used to obtain random orientation (and thus uniform diffraction lines) in order to make accurate measurements of integrated intensity. Back reflection patterns were taken in each case to check the uniformity of the lines, and from the observed line broadening it was apparent that this type of plastic deformation was quite severe. Care was taken to traverse the entire background of the pattern and to assign to each peak the total intensity above this background. The bases of the diffraction lines were quite broad and spread out over several degrees, even for the narrow peaks. The theoretical intensities were calculated to include a temperature correction, a dispersion correction, and a Lorenz- polarization factor corrected for the crystal monochromated beam. In Table 1 it was necessary to match the calculated and observed values at only one point, and the rest of the experimental values were converted directly to this arbitrary scale. The integrated intensities in Table 1 are listed in arbitrary units, and the accuracy was sufficient to reproduce any of the measured line intensities to within + 1.5 units. It is evident that the percentage error on the strongest line (111) was quite low. The calculated values and the observed intensities for the cold worked material matched reasonably well. As the annealing temperature was raised, however, the intensity of the strongest reflections, particularly the (lll), decreased measurably. Since the background intensities of all of these patterns were identical, such behavior could be interpreted as a primary

Jan 1, 1950

By AIME AIME

MANY of the important papers to be presented at the World Congress of Engineering at Tokyo, in November, 1929, are being furnished by members of A.I.M.E. and a list of them is given below: "Fifty Years of Physical Metallurgy,,-by H. M. Boylston, Case School of Applied Science, Cleveland, Ohio.

Jan 1, 1929

Olof Venstrom (communication to the Secretary*):—In order to do justice to a property, once the largest producer of copper in the world, which is now being reopened, with a fair promise of again becoming important, I beg to add a few words in connection with Mr. Souder's remarks on the El Cobre copper-mines. The El Cobre copper-mines were worked by the old English

Jan 1, 1905

By R. S. Busk

TWO groups of binary alloys were prepared. The first group consisted of those elements relatively soluble in magnesium: Li, Al, Zn, Ga, Ag, Cd, In, Sn, Hg, T1, Pb, and Bi. These are predominately Group B elements. The second group consisted of most of the remaining metallic elements, all of which are relatively insoluble in magnesium: As, Au, Ba, Ca, Ce, Cu, Ir, La, Mn, Ni, Pd, Pt, Rh, Sb, Si, Te, Ti, W, and Zr. These are all Group A, transition, or rare earth elements. Alloys of the first group were prepared by melting sublimed magnesium and elements as pure as obtainable in a graphite crucible, using a standard flux1 for protection. The melts were poured into a small graphite mold to produce 3xY4 in. diam slugs. Spectroscopic analyses were made of each slug. In all cases, the total impurity content was less than 0.05 pct. The slugs were then heat treated 5°C below the eutectic temperature until complete solution, as judged metallographically, was obtained. Filings from the center of the slugs were compacted at room temperature into 1/2 in. long x 1/4 in. diam cylinders, sealed in pyrex under 1/2 atm of purified argon, annealed at the heat-treating temperature for 1 hr, and quenched in water. After the X-ray diffraction patterns were made, each compact was analyzed chemically for the solute. It was found that the Mg-Li alloys reacted during filing to reduce the Li in solid solution. For this series of alloys, the slug was cold worked, annealed in purified argon, the surface dissolved in dilute HC1 to a depth of about 0.005 in., and the X-ray exposure made on the fresh surface. This procedure resulted in sharp, continuous lines and in true values for the lattice parameters. The alloys in the second group were prepared in the same way except that about 1 wt pct of each solute was added. Since the solubility limit was exceeded, not all the solute dissolved. These alloys were analyzed spectroscopically only to confirm the presence of the solute. The diffraction patterns were of the back-reflec-tion type using the characteristic copper radiation* and a flat cassette. Both the film and the specimen were rotated. The specimen temperature was maintained at 25" ± 1°C. The films had sharp lines; their diameters were measured directly to 0.01 cm. The parameters were calculated from the line diameters using a modified version of Cohen's extrapolation method.2 his method effectively eliminates systematic errors such as film shrinkage, inaccurate alignment, and non-precise film-to-speci-men distance. The random errors were minimized

Jan 1, 1951

By H. L. Teichman, E. M. Sipprelle

ENACTMENT' of Public Law 290 by the 78th Congress authorized the U. S. Department of the Interior, Bureau of Mines, to conduct an experimental program to develop the technology for obtaining oil from oil shale. In adopting and later extending this legislation, the Congress recognized the impending necessity of supplementing ground petroleum reserves with synthetic fuels. Under the provisions of this legislation, the Bureau of Mines, among other things, was charged with the responsibility of developing mining techniques, methods, and equipment for mining the oil shales of the Green River formation of Colorado, Utah, and Wyoming. The oil shales of western Colorado are apparently richer, more accessible, and more amenable to exploitation than elsewhere in the Rocky Mountain region. The site chosen for the Bureau's Experimental mine is about 10 miles west of Rifle in northwestern Colorado. It is within a 1000-sq-mile area from which, it has been estimated, 300 billion barrels of shale oil could be produced from a 500-ft measure near the top of the formation. One hundred billion barrels of this amount could be produced from the Mahogany ledge, a 60 to 100-ft section near the bottom of the 500-ft measure. This ledge is considered to have economic importance at present. The Green River formation was laid down as sediment in the bottom of vast, shallow inland lakes during Eocene time. The deposit is flat-lying, and there are no faults, fissures, or local rolls. Oil shale is actually a strong, tough magnesium marlstone, which will stand unsupported over relatively wide spans. These and other natural physical characteristics favor mechanized, low-cost mining, which is essential for establishment of an oil-shale industry. It was realized from the outset that an extensive research program would be necessary to develop mining methods, equipment, and techniques for a mechanized, low-cost operation. The program was designed to include research. into all the productive phases of mining, such as drilling, blasting, loading, transportation, and maintenance of the mine structure. The methods, equipment, and techniques developed as a result of this research have established a production of 116 tons per man-shift total labor at a direct cost of $0,292 per ton. Another important phase of the research program that has received little publicity because of its theoretical nature is study of the roofstone behavior and determination of mine structure stresses. This paper purposes to discuss this phase of the research program. Preliminary studies of the physical properties of the Green River oil-shale formation were made in the Barodyramics Laboratory at Columbia University during the latter part of 1945 and the early part of 1946.* The purpose of these studies was to determine the maximum size of unsupported underground openings that would be commensurate with safety and still permit the use of large, efficient mining equipment. Also to be determined were the pillar support to extraction ratio and the shape, size, and spacing of supporting pillars. Selected samples of possible roofstones near the top of the Mahogany ledge, as well as representative samples of different rock types found within the ledge, were obtained from the Bureau's oil-shale mine for these studies. The maximum safe unsupported roof span calculated from this work was 200 ft. Using a safety factor of four, it was theoretically determined that openings 60 ft wide could be advanced under a roofstone at the top of the Mahogany ledge. To support the overburden, 60-ft-sq pillars would be left in a checkerboard pattern. From visual observations made of core samples through the selected roofstone at the oil-shale mine, it was determined that the roofstone was actually a plate 6 to 8 ft thick. Because the calculations were theoretical and allowance had to be made for unknown cracks and fractures in the formation, openings 50 ft wide and pillars 60 ft sq were originally contemplated in the Bureau's Experimental mine. This would be the minimum allowable width that would permit use of large underground mining equipment. For lower mining costs and greater efficiency larger openings were desirable. Different but analogous approaches were made to the problem at the Bureau of Mines Applied Physics

Jan 1, 1951

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949

By Walter Rose

In a recent technical note, Owen Thornton&apos; suggests that wetting liquid relative permeability may be derived from the relationship: where Pd/Pc is the ratio of displacement pressure to capillary pressure at the wetting liquid satdration Sw, and I is the resistivity index at this saturation. Thornton shows that this expression gives values for relative permeability in good agreement with those experimentally determined by Leverett. We have recently developed another expression for krw which seems preferable to Equation 1 since it requires fewer experimental data for its verification. This equation may be derived in the following manner. Making use of the analogy between mass transfer of fluid in a porous medium and electrical conductivity through the fluid in the same medium, we can postulate a hydraulic formation resistivity factor analogous to an electrical formation resistivity factor. From Poiseuille&apos;s Law the resistivity to flow in a tube of radius R is of the form 8u/R², where is the viscosity of the fluid. Similarly7 the resistivity to flow in a porous medium of the same dimensions as the tube is given by D&apos;Arcy&apos;s Law as where k is the permeability of the medium. The hydraulic formation resistivity factor, Ff, is thus the quotient of these two resistivities, or: But permeability is defined by the KO-zeny equation as: where: r is the average pore radius of the porous medium, L. is the average tortuous length of the average pore, + is the porosity, and L is the bed length. This gives Fr as a function of the (La/L) .-.-.tortuosity ratio and porosity, or in explicit form: where: T = (La/L)&apos;, and N is the number of pores of radius, r, which will be found in any cross sectional area, x R&apos;. That is, N = R²/r². It will be clear from the foregoing considerations that the hydraulic formation fat. tor should be dependent on the value of R which in every case must be arbitrarily selected. By analogy, the hydrauiic formation factor, Fcf, characterizing the porous medium at Sw<1,will be given by: R² NT. where ke is the effective wetting liquid permeability obtaining at Sw<l, and Te is the square of the (Las/L) ratio defined by Thornton. Therefore, the hydraulic resistivity index, If, is: However, Thrnton gives I as: and it follows that: Equation 2, when checked against the data of wyckoff and Botset² and some of the Morse et al data³, gives comparisons as shown at the bottom of this page. Computations based on Leverett&apos;s data, quoted by Thorntaon, gives computed krw values somewhat lower than the experimental values. Moreover, other instances can be cited where we find that neither Equation 1 nor Equa tion 2 is checked by experimental data. The work of Botset&apos; on the Nichols Buff sandstone and Morse et a1 on oil wetted Bradford sandstone are such instances. A reason for these discrepancies may lie in the fact that if both Equations 1 and 2 are presumed always to give accurate values for krw, it follows that PC = Pd/Sw". Such an expression, it is well known, is too simple to describe accurately the capillary pressure behavior of all porous media. However, it is believed that a particular advantage resides on the use of Equation 2, since it is not dependent for its utility on a knowledge of the capillary pressures obtaining in dynamic flow svsterns. No practical technique for measuring the capillary pressures characterizing the fluid distributions in dynamic flow systems has yet been proposed. Acknowledgment is given to Dr. Paul D. Foote, executive vice-president of the Gulf Research and Development Company, for permission to publish this note. 1. Owen F. Thornton, "A Note on the Valuation of Relative Permeability," J. Pet. Tech., 1:7, Section 1, July, 1949. 2. R. D. Wyckoff arid H. G. Botset, "The Flow of Gas-Liquid Mixtures through Porous Media," Physics, 7:325-345, 1936. 3. R. A. Morse, P: L. Terwilliger, .and S. T. Yuster, "Relative Permeability Measurements of Small Core Samples," Oil and Gas J., 46:109-125, Aug. 23, 1947. 4. H. G. Botset, "Flow of Gas-Liquid Mixtures Through Consolidated Sand," Trans. AIME, 136:91, 1940.

Jan 1, 1949